Finite Group Databasebeta

← #49135453

Subgroups — #49135453

Order 36224.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827211C211yesmaximal, characteristic, complemented
2#31827205C211yesmaximal, characteristic, complemented
3#31827203C211yesmaximal, characteristic, complemented
4#31827168C211yesmaximal, characteristic, complemented
5#31827160C211yesmaximal, characteristic, complemented
6#31827143C211yesmaximal, characteristic, complemented
7#31827142C211yesmaximal, characteristic, complemented
8#31827112C211yesmaximal, characteristic, complemented
9#31827108C211yesmaximal, characteristic, complemented
10#31827108C211yesmaximal, characteristic, complemented
11#31827107C211yesmaximal, characteristic, complemented
12#31827106C211yesmaximal, characteristic, complemented
13#31827106C211yesmaximal, characteristic, complemented
14#31827099C211yesmaximal, characteristic, complemented
15#31827099C211yesmaximal, characteristic, complemented
16#31827067C211yesmaximal, characteristic, complemented
17#31827065C211yesmaximal, characteristic, complemented
18#31827063C211yesmaximal, characteristic, complemented
19#31827061C211yesmaximal, characteristic, complemented
20#31827061C211yesmaximal, characteristic, complemented
21#31827049C211yesmaximal, characteristic, complemented
22#31827049C211yesmaximal, characteristic, complemented
23#31827047C211yesmaximal, characteristic, complemented
24#31827045C211yesmaximal, characteristic, complemented
25#31827026C211yesmaximal, characteristic, complemented
26#31827026C211yesmaximal, characteristic, complemented
27#31827023C211yesmaximal, characteristic, complemented
28#31826978C211yesmaximal, characteristic, complemented
29#123×D283C211yesmaximal, characteristic, complemented
30#121×D283C211yesmaximal, characteristic, complemented
31#562×C283C211yesmaximal, characteristic, complemented
32C2×#17985393C2211yescharacteristic, complemented
33C2×#17985393C2211yescharacteristic, complemented
34C2×#17985392C2211yescharacteristic, complemented
35C22×D1132C2211yescharacteristic, complemented
36C22×D1132C2211yescharacteristic, complemented
37C2×D4×D283C2211yescharacteristic
38C2×D4×D283C2211yescharacteristic, complemented
39C2×D4×D283C2211yescharacteristic, complemented
40C2×D4×D283C2211yescharacteristic, complemented
41C2×D4×D283C2211yescharacteristic, complemented
42C2×D4×D283C2211yescharacteristic, complemented
43C22×C4×D283C2211yescharacteristic, complemented
44#22583606C2211yescharacteristic, complemented
45#22583606C2211yescharacteristic, complemented
46#22583605C2211yescharacteristic, complemented
47#22583605C2211yescharacteristic, complemented
48#22583605C2211yescharacteristic, complemented
49#22583605C2211yescharacteristic, complemented
50#22583604C2211yescharacteristic, complemented
51#22583603C2211yescharacteristic, complemented
52#22583603C2211yescharacteristic, complemented
53#22583603C2211yescharacteristic, complemented
54#22583600C2211yescharacteristic, complemented
55#22583600C2211yescharacteristic, complemented
56#22583600C2211yescharacteristic, complemented
57#22583599C2211yescharacteristic, complemented
58#22583599C2211yescharacteristic, complemented
59#22583597C2211yescharacteristic, complemented
60#22583596C2211yescharacteristic, complemented
61#22583595C2211yescharacteristic, complemented
62#22583595C2211yescharacteristic, complemented
63#22583595C2211yescharacteristic, complemented
64#22583595C2211yescharacteristic, complemented
65#22583595C2211yescharacteristic, complemented
66#22583595C2211yescharacteristic, complemented
67#22583595C2211yescharacteristic, complemented
68#22583595C2211yescharacteristic, complemented
69#22583595C2211yescharacteristic, complemented
70#22583595C2211yescharacteristic, complemented
71#22583594C2211yescharacteristic, complemented
72#22583594C2211yescharacteristic, complemented
73#22583593C2211yescharacteristic, complemented
74#22583593C2211yescharacteristic, complemented
75#22583593C2211yescharacteristic, complemented
76#22583592C2211yescharacteristic, complemented
77#22583592C2211yescharacteristic, complemented
78#22583592C2211yescharacteristic, complemented
79#22583592C2211yescharacteristic, complemented
80#22583592C2211yescharacteristic, complemented
81#22583592C2211yescharacteristic, complemented
82#22583592C2211yescharacteristic, complemented
83#22583592C2211yescharacteristic, complemented
84#22583591C2211yescharacteristic, complemented
85#22583590C2211yescharacteristic, complemented
86#22583588C2211yescharacteristic, complemented
87#22583588C2211yescharacteristic, complemented
88#22583588C2211yescharacteristic, complemented
89#22583586C2211yescharacteristic, complemented
90#22583586C2211yescharacteristic, complemented
91#22583586C2211yescharacteristic, complemented
92#22583586C2211yescharacteristic, complemented
93#22583585C2211yescharacteristic
94#22583585C2211yescharacteristic, complemented
95#22583585C2211yescharacteristic, complemented
96#22583585C2211yescharacteristic, complemented
97#22583585C2211yescharacteristic, complemented
98#22583585C2211yescharacteristic, complemented
99#22583585C2211yescharacteristic, complemented
100#22583585C2211yescharacteristic, complemented
101#22583585C2211yescharacteristic, complemented
102#22583584C2211yescharacteristic, complemented
103#22583584C2211yescharacteristic, complemented
104#22583584C2211yescharacteristic, complemented
105#22583583C2211yescharacteristic
106#22583583C2211yescharacteristic
107#22583583C2211yescharacteristic, complemented
108#22583583C2211yescharacteristic, complemented
109#22583583C2211yescharacteristic, complemented
110#22583583C2211yescharacteristic, complemented
111#22583583C2211yescharacteristic, complemented
112#22583583C2211yescharacteristic, complemented
113#22583583C2211yescharacteristic, complemented
114#22583583C2211yescharacteristic, complemented
115#22583583C2211yescharacteristic, complemented
116#22583583C2211yescharacteristic, complemented
117#22583582C2211yescharacteristic, complemented
118#22583582C2211yescharacteristic, complemented
119#22583582C2211yescharacteristic, complemented
120#22583582C2211yescharacteristic, complemented
121#22583582C2211yescharacteristic, complemented
122#22583581C2211yescharacteristic, complemented
123#22583581C2211yescharacteristic, complemented
124#22583581C2211yescharacteristic, complemented
125#22583580C2211yescharacteristic
126#22583580C2211yescharacteristic, complemented
127#22583580C2211yescharacteristic, complemented
128#22583580C2211yescharacteristic, complemented
129#22583580C2211yescharacteristic, complemented
130#22583580C2211yescharacteristic, complemented
131#22583580C2211yescharacteristic, complemented
132#22583580C2211yescharacteristic, complemented
133#22583580C2211yescharacteristic, complemented
134#22583580C2211yescharacteristic, complemented
135#22583578C2211yescharacteristic
136#22583578C2211yescharacteristic, complemented
137#22583578C2211yescharacteristic, complemented
138#22583578C2211yescharacteristic, complemented
139#22583578C2211yescharacteristic, complemented
140#22583578C2211yescharacteristic, complemented
141C4×D1132C2211yescharacteristic, complemented
142C4×D1132C2211yescharacteristic, complemented
143C4×D1132C2211yescharacteristic, complemented
144#22583572C2211yescharacteristic, complemented
145#22583572C2211yescharacteristic, complemented
146#22583572C2211yescharacteristic, complemented
147#22583572C2211yescharacteristic, complemented
148#22583572C2211yescharacteristic, complemented
149C4×C22⋊D283C2211yescharacteristic, complemented
150C4×C22⋊D283C2211yescharacteristic, complemented
151C4×C22⋊D283C2211yescharacteristic, complemented
152C4×C22⋊D283C2211yescharacteristic, complemented
153C4×C22⋊D283C2211yescharacteristic, complemented
154(C22⋊D283)⋊C4C2211yescharacteristic, complemented
155(C22⋊D283)⋊C4C2211yescharacteristic, complemented
156(C22⋊D283)⋊C4C2211yescharacteristic, complemented
157#22583568C2211yescharacteristic, complemented
158#22583568C2211yescharacteristic, complemented
159#22583566C2211yescharacteristic, complemented
160C4⋊C4×D283C2211yescharacteristic, complemented
161C4⋊C4×D283C2211yescharacteristic, complemented
162C4⋊C4×D283C2211yescharacteristic, complemented
163C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
164C22⋊C4×D283C2211yescharacteristic, complemented
165C22⋊C4×D283C2211yescharacteristic, complemented
166C22⋊C4×D283C2211yescharacteristic, complemented
167C22⋊C4×D283C2211yescharacteristic, complemented
168C22⋊C4×D283C2211yescharacteristic, complemented
169C22⋊C4×D283C2211yescharacteristic, complemented
170C22⋊C4×D283C2211yescharacteristic, complemented
171C22⋊C4×D283C2211yescharacteristic, complemented
172#125×C283C2211yescharacteristic, complemented
173#124×C283C2211yescharacteristic, complemented
174#124×C283C2211yescharacteristic, complemented
175#123×C283C2211yescharacteristic, complemented
176#123×C283C2211yescharacteristic, complemented
177#123×C283C2211yescharacteristic, complemented
178#123×C283C2211yescharacteristic, complemented
179C22⋊Q8×C283C2211yescharacteristic, complemented
180C22⋊Q8×C283C2211yescharacteristic, complemented
181C22⋊Q8×C283C2211yescharacteristic, complemented
182C22⋊Q8×C283C2211yescharacteristic, complemented
183#121×C283C2211yescharacteristic, complemented
184#121×C283C2211yescharacteristic, complemented
185#121×C283C2211yescharacteristic, complemented
186#121×C283C2211yescharacteristic, complemented
187C23×D283C2311yescharacteristic
188C23×D283C2311yescharacteristic
189C23×D283C2311yescharacteristic
190C23×D283C2311yescharacteristic
191C23×D283C2311yescharacteristic
192C23×D283C2311yescharacteristic
193#17985393—42no—
194#17985393—42no—
195#17985392—42no—
196C2×Dic566C2311yescharacteristic
197C2×D1132—42no—
198C2×D1132—42no—
199C2×D1132C2311yescharacteristic
200C2×D1132C2311yescharacteristic
201C2×D1132C2311yescharacteristic
202C2×D1132C2311yescharacteristic
203C2×D1132C2311yescharacteristic
204C2×D1132C2311yescharacteristic
205C2×D1132C2311yescharacteristic
206C2×D1132C2311yescharacteristic
207C2×D1132C2311yescharacteristic
208C2×D1132C2311yescharacteristic
209C2×D1132C2311yescharacteristic
210C2×D1132C2311yescharacteristic
211C2×D1132C2311yescharacteristic
212C2×D1132C2311yescharacteristic
213C2×D1132C2311yescharacteristic
214C2×C22⋊D283C2311yescharacteristic
215C2×C22⋊D283C2311yescharacteristic
216C2×C22⋊D283C2311yescharacteristic
217C2×C22⋊D283C2311yescharacteristic
218C2×C22⋊D283C2311yescharacteristic
219C2×C22⋊D283C2311yescharacteristic
220C2×C22⋊D283C2311yescharacteristic
221C2×C22⋊D283C2311yescharacteristic
222C2×C22⋊D283C2311yescharacteristic
223C2×C22⋊D283C2311yescharacteristic
224C2×C22⋊D283C2311yescharacteristic
225C2×C22⋊D283C2311yescharacteristic
226C2×C22⋊D283C2311yescharacteristic
227C2×C22⋊D283C2311yescharacteristic
228C2×C22⋊D283C2311yescharacteristic
229C2×C22⋊D283C2311yescharacteristic
230D4×D283—42no—
231D4×D283—42no—
232D4×D283—42no—
233D4×D283—42no—
234D4×D283—42no—
235D4×D283—42no—
236C22×Dic283C2311yescharacteristic
237C22×Dic283C2311yescharacteristic
238C2×C4×D283—42no—
239C2×C4×D283C2311yescharacteristic
240C2×C4×D283C2311yescharacteristic
241C2×C4×D283C2311yescharacteristic
242C2×C4×D283C2311yescharacteristic
243C2×C4×D283C2311yescharacteristic
244C2×C4×D283C2311yescharacteristic
245C2×C4×D283C2311yescharacteristic
246C2×C4×D283C2311yescharacteristic
247C2×C4×D283C2311yescharacteristic
248C2×C4×D283C2311yescharacteristic
249C2×C4×D283C2311yescharacteristic
250C2×C4×D283C2311yescharacteristic
251C2×C4×D283C2311yescharacteristic
252C2×C4×D283C2311yescharacteristic
253C2×C4×D283C2311yescharacteristic
254C2×C4×D283C2311yescharacteristic
255C2×C4×D283C2311yescharacteristic
256C4⋊Dic283C2311yescharacteristic
257C4⋊Dic283C2311yescharacteristic
258C4⋊Dic283C2311yescharacteristic
259C4⋊Dic283C2311yescharacteristic
260C4⋊Dic283C2311yescharacteristic
261C4⋊Dic283C2311yescharacteristic
262Dic283⋊C4C2311yescharacteristic
263Dic283⋊C4C2311yescharacteristic
264Dic283⋊C4C2311yescharacteristic
265Dic283⋊C4C2311yescharacteristic
266Dic283⋊C4C2311yescharacteristic
267Dic283⋊C4C2311yescharacteristic
268Dic283⋊C4C2311yescharacteristic
269Dic283⋊C4C2311yescharacteristic
270Dic283⋊C4C2311yescharacteristic
271Dic283⋊C4C2311yescharacteristic
272Dic283⋊C4C2311yescharacteristic
273Dic283⋊C4C2311yescharacteristic
274Dic283⋊C4C2311yescharacteristic
275Dic283⋊C4C2311yescharacteristic
276C22⋊Dic283C2311yescharacteristic
277C22⋊Dic283C2311yescharacteristic
278C22⋊Dic283C2311yescharacteristic
279C22⋊Dic283C2311yescharacteristic
280C22⋊Dic283C2311yescharacteristic
281C22⋊Dic283C2311yescharacteristic
282C22⋊Dic283C2311yescharacteristic
283C22⋊Dic283C2311yescharacteristic
284(C2×D283)⋊C4C2311yescharacteristic
285(C2×D283)⋊C4C2311yescharacteristic
286(C2×D283)⋊C4C2311yescharacteristic
287(C2×D283)⋊C4C2311yescharacteristic
288(C2×D283)⋊C4C2311yescharacteristic
289(C2×D283)⋊C4C2311yescharacteristic
290(C2×D283)⋊C4C2311yescharacteristic
291(C2×D283)⋊C4C2311yescharacteristic
292(C2×D283)⋊C4C2311yescharacteristic
293(C2×D283)⋊C4C2311yescharacteristic
294(C2×D283)⋊C4C2311yescharacteristic
295(C2×D283)⋊C4C2311yescharacteristic
296(C2×D283)⋊C4C2311yescharacteristic
297(C2×D283)⋊C4C2311yescharacteristic
298(C2×D283)⋊C4C2311yescharacteristic
299(C2×D283)⋊C4C2311yescharacteristic
300(C2×D283)⋊C4C2311yescharacteristic
301(C2×D283)⋊C4C2311yescharacteristic
302(C2×D283)⋊C4C2311yescharacteristic
303(C2×D283)⋊C4C2311yescharacteristic
304(C2×D283)⋊C4C2311yescharacteristic
305(C2×D283)⋊C4C2311yescharacteristic
306(C2×D283)⋊C4C2311yescharacteristic
307(C2×D283)⋊C4C2311yescharacteristic
308(C2×D283)⋊C4C2311yescharacteristic
309(C2×D283)⋊C4C2311yescharacteristic
310(C2×D283)⋊C4C2311yescharacteristic
311(C2×D283)⋊C4C2311yescharacteristic
312(C2×D283)⋊C4C2311yescharacteristic
313(C2×D283)⋊C4C2311yescharacteristic
314C4×Dic283C2311yescharacteristic
315C4×Dic283C2311yescharacteristic
316C4×Dic283C2311yescharacteristic
317C4×Dic283C2311yescharacteristic
318C4×Dic283C2311yescharacteristic
319C2×Q8×C283C2311yescharacteristic
320C2×Q8×C283C2311yescharacteristic
321C2×D4×C283C2311yescharacteristic
322C2×D4×C283C2311yescharacteristic
323C2×D4×C283C2311yescharacteristic
324C2×D4×C283C2311yescharacteristic
325C2×D4×C283C2311yescharacteristic
326C2×D4×C283C2311yescharacteristic
327C22×C4×C283C2311yescharacteristic
328C22×C4×C283C2311yescharacteristic
329C22×C4×C283C2311yescharacteristic
330C22×C4×C283C2311yescharacteristic
331C4⋊C4×C283C2311yescharacteristic
332C4⋊C4×C283C2311yescharacteristic
333C4⋊C4×C283C2311yescharacteristic
334C4⋊C4×C283C2311yescharacteristic
335C4⋊C4×C283C2311yescharacteristic
336C4⋊C4×C283C2311yescharacteristic
337C4⋊C4×C283C2311yescharacteristic
338C4⋊C4×C283C2311yescharacteristic
339C4⋊C4×C283C2311yescharacteristic
340C4⋊C4×C283C2311yescharacteristic
341C22⋊C4×C283C2311yescharacteristic
342C22⋊C4×C283C2311yescharacteristic
343C22⋊C4×C283C2311yescharacteristic
344C22⋊C4×C283C2311yescharacteristic
345C22⋊C4×C283C2311yescharacteristic
346C22⋊C4×C283C2311yescharacteristic
347C22⋊C4×C283C2311yescharacteristic
348C22⋊C4×C283C2311yescharacteristic
349C22⋊C4×C283C2311yescharacteristic
350C22⋊C4×C283C2311yescharacteristic
351C22⋊C4×C283C2311yescharacteristic
352C22⋊C4×C283C2311yescharacteristic
353C42×C283C2311yescharacteristic
354C22×D283—22no—
355C22×D283—22no—
356C22×D283—22no—
357C22×D283—22no—
358C22×D283—22no—
359C22×D283—41no—
360C22×D283—41no—
361C22×D283—41no—
362C22×D283—41no—
363C22×D283—41no—
364C22×D283—41no—
365C22×D283—41no—
366C22×D283—41no—
367C22×D283—41no—
368C22×D283—41no—
369C22×D283—41no—
370C22×D283—41no—
371C22×D283—41no—
372C22×D283C2411yescharacteristic
373C22×D283C2411yescharacteristic
374C22×D283C2411yescharacteristic
375C22×D283C2411yescharacteristic
376C22×D283C2411yescharacteristic
377C22×D283C2411yescharacteristic
378C22×D283C2411yescharacteristic
379Dic566—41no—
380D1132—22no—
381D1132—22no—
382D1132—22no—
383D1132—22no—
384D1132—22no—
385D1132—22no—
386D1132—22no—
387D1132—41no—
388D1132—41no—
389D1132—41no—
390D1132—41no—
391D1132—41no—
392D1132—41no—
393D1132—41no—
394D1132—41no—
395C22⋊D283—22no—
396C22⋊D283—22no—
397C22⋊D283—22no—
398C22⋊D283—41no—
399C22⋊D283—41no—
400C22⋊D283—41no—
401C22⋊D283—41no—
402C22⋊D283—41no—
403C22⋊D283—41no—
404C22⋊D283—41no—
405C22⋊D283—41no—
406C22⋊D283—41no—
407C22⋊D283—41no—
408C22⋊D283—41no—
409C22⋊D283—41no—
410C22⋊D283—41no—
411C2×Dic283—41no—
412C2×Dic283—41no—
413C2×Dic283C2411yescharacteristic
414C2×Dic283C2411yescharacteristic
415C2×Dic283C2411yescharacteristic
416C2×Dic283C2411yescharacteristic
417C2×Dic283C2411yescharacteristic
418C2×Dic283C2411yescharacteristic
419C2×Dic283C2411yescharacteristic
420C2×Dic283C2411yescharacteristic
421C2×Dic283C2411yescharacteristic
422C4×D283—22no—
423C4×D283—22no—
424C4×D283—22no—
425C4×D283—41no—
426C4×D283—41no—
427C4×D283—41no—
428C4×D283—41no—
429C4×D283—41no—
430C4×D283—41no—
431C4×D283—41no—
432C4×D283—41no—
433C4×D283—41no—
434C4×D283—41no—
435C4×D283—41no—
436C4×D283—41no—
437C4×D283—41no—
438C4×D283—41no—
439C23×C283C2411yescharacteristic
440C23×C283C2411yescharacteristic
441C23×C283C2411yescharacteristic
442C23×C283C2411yescharacteristic
443Q8×C283—41no—
444Q8×C283—41no—
445D4×C283—41no—
446D4×C283—41no—
447D4×C283—41no—
448D4×C283—41no—
449D4×C283—41no—
450D4×C283—41no—
451C2×C4×C283—41no—
452C2×C4×C283—41no—
453C2×C4×C283—41no—
454C2×C4×C283—41no—
455C2×C4×C283C2411yescharacteristic
456C2×C4×C283C2411yescharacteristic
457C2×C4×C283C2411yescharacteristic
458C2×C4×C283C2411yescharacteristic
459C2×C4×C283C2411yescharacteristic
460C2×C4×C283C2411yescharacteristic
461C2×C4×C283C2411yescharacteristic
462C2×C4×C283C2411yescharacteristic
463C2×C4×C283C2411yescharacteristic
464C2×C4×C283C2411yescharacteristic
465C2×C4×C283C2411yescharacteristic
466C22×C283—21no—
467C22×C283—21no—
468C22×C283—21no—
469C22×C283—21no—
470C22×C283—21no—
471C22×C283—21no—
472C22×C283—21no—
473C22×C283—21no—
474C22×C283—21no—
475C22×C283—21no—
476C22×C283—21no—
477C22×C283—21no—
478C22×C283C2511yescharacteristic
479C2×D283—21no—
480C2×D283—21no—
481C2×D283—21no—
482C2×D283—21no—
483C2×D283—21no—
484C2×D283—21no—
485C2×D283—21no—
486C2×D283—21no—
487C2×D283—21no—
488C2×D283—21no—
489C2×D283—21no—
490C2×D283—21no—
491C2×D283—21no—
492C2×D283—21no—
493C2×D283—21no—
494C2×D283—21no—
495C2×D283—21no—
496C2×D283—21no—
497C2×D283—21no—
498C2×D283—44no—
499C2×D283—82no—
500C2×D283—82no—
501C2×D283—82no—
502C2×D283—82no—
503C2×D283—82no—
504C2×D283H(5,𝔽2)12yes—
505C2×D283H(5,𝔽2)12yes—
506C4×C283—21no—
507C4×C283—21no—
508C4×C283—21no—
509C4×C283—21no—
510C4×C283—21no—
511C4×C283—21no—
512C4×C283—21no—
513C4×C283—21no—
514C4×C283—21no—
515C4×C283—21no—
516C4×C283—21no—
517Dic283—21no—
518Dic283—21no—
519Dic283—21no—
520Dic283—21no—
521Dic283—21no—
522Dic283—21no—
523Dic283—21no—
524Dic283—21no—
525Dic283—21no—
526C2×C283—41no—
527C2×C283—41no—
528C2×C283—41no—
529C2×C283—41no—
530C2×C283C2×H(5,𝔽2)11yescharacteristic
531C2×C283C2×H(5,𝔽2)11yescharacteristic
532C2×C283#58511yescharacteristic
533D283—22no—
534D283—22no—
535D283—41no—
536D283—41no—
537D283—41no—
538D283—41no—
539D283—41no—
540C283#353411yescharacteristic, complemented, Sylow
541#3534—2831nomaximal, Sylow
542#562—2831no—
543#562D28311yescharacteristic, complemented
544#560—2831no—
545#560—2831no—
546#553—2831no—
547#553—2831no—
548#551—2831no—
549#551—2831no—
550#546—2831no—
551#546—2831no—
552#546—2831no—
553#546—2831no—
554#546—2831no—
555#546—2831no—
556D42—2831no—
557D42—2831no—
558#540—2831no—
559#540—2831no—
560#539—2831no—
561#539—2831no—
562#539—2831no—
563#538—2831no—
564#538—2831no—
565#538—2831no—
566#537—2831no—
567#534—2831no—
568#534—2831no—
569#534—2831no—
570#525—2831no—
571C2×#123—2831no—
572C2×#121—2831no—
573C2×#41—2831no—
574C2×#41—2831no—
575C2×#41—2831no—
576C22×D4—2831no—
577C22×D4—2831no—
578C22×D4—2831no—
579C22×D4—2831no—
580C22×D4—2831no—
581C22×D4—2831no—
582C22×D4—2831no—
583C22×D4—2831no—
584C23×C4—2831no—
585#127—2831no—
586#127—2831no—
587#126—2831no—
588#126—2831no—
589#126—2831no—
590#126—2831no—
591#126—2831no—
592#126—2831no—
593#126—2831no—
594#126—2831no—
595#125—2831no—
596#125—2831no—
597#125—2831no—
598#125C2×D28311yescharacteristic, complemented
599#124—2831no—
600#124—2831no—
601#124—2831no—
602#124—2831no—
603#124C2×D28311yescharacteristic, complemented
604#124C2×D28311yescharacteristic, complemented
605#123—2831no—
606#123—2831no—
607#123—2831no—
608#123—2831no—
609#123—2831no—
610#123—2831no—
611#123—2831no—
612#123—2831no—
613#123—2831no—
614#123—2831no—
615#123—2831no—
616#123—2831no—
617#123—2831no—
618#123—2831no—
619#123—2831no—
620#123—2831no—
621#123—2831no—
622#123—2831no—
623#123—2831no—
624#123—2831no—
625#123—2831no—
626#123—2831no—
627#123—2831no—
628#123—2831no—
629#123C2×D28311yescharacteristic, complemented
630#123C2×D28311yescharacteristic, complemented
631#123C2×D28311yescharacteristic, complemented
632#123C2×D28311yescharacteristic, complemented
633C22⋊Q8—2831no—
634C22⋊Q8—2831no—
635C22⋊Q8—2831no—
636C22⋊Q8—2831no—
637C22⋊Q8—2831no—
638C22⋊Q8—2831no—
639C22⋊Q8—2831no—
640C22⋊Q8—2831no—
641C22⋊Q8C2×D28311yescharacteristic, complemented
642C22⋊Q8C2×D28311yescharacteristic, complemented
643C22⋊Q8C2×D28311yescharacteristic, complemented
644C22⋊Q8C2×D28311yescharacteristic, complemented
645#121—2831no—
646#121—2831no—
647#121—2831no—
648#121—2831no—
649#121—2831no—
650#121—2831no—
651#121—2831no—
652#121—2831no—
653#121—2831no—
654#121—2831no—
655#121—2831no—
656#121—2831no—
657#121—2831no—
658#121—2831no—
659#121—2831no—
660#121—2831no—
661#121—2831no—
662#121—2831no—
663#121—2831no—
664#121—2831no—
665#121—2831no—
666#121—2831no—
667#121—2831no—
668#121—2831no—
669#121—2831no—
670#121—2831no—
671#121—2831no—
672#121—2831no—
673#121—2831no—
674#121—2831no—
675#121—2831no—
676#121—2831no—
677#121C2×D28311yescharacteristic, complemented
678#121C2×D28311yescharacteristic, complemented
679#121C2×D28311yescharacteristic, complemented
680#121C2×D28311yescharacteristic, complemented
681#120—2831no—
682#120—2831no—
683#120—2831no—
684#120—2831no—
685#120—2831no—
686#120—2831no—
687#120—2831no—
688#120—2831no—
689#120—2831no—
690#120—2831no—
691#120—2831no—
692#120—2831no—
693#120—2831no—
694#120—2831no—
695#120—2831no—
696#120—2831no—
697C4×D4—2831no—
698C4×D4—2831no—
699C4×D4—2831no—
700C4×D4—2831no—
701C4×D4—2831no—
702C4×D4—2831no—
703C4×D4—2831no—
704C4×D4—2831no—
705C4×D4—2831no—
706C4×D4—2831no—
707C4×D4—2831no—
708C4×D4—2831no—
709C4×D4—2831no—
710C4×D4—2831no—
711C4×D4—2831no—
712C4×D4—2831no—
713#117—2831no—
714#117—2831no—
715#117—2831no—
716C2×C4⋊C4—2831no—
717C2×C4⋊C4—2831no—
718C2×C4⋊C4—2831no—
719C2×C22⋊C4—2831no—
720C2×C22⋊C4—2831no—
721C2×C22⋊C4—2831no—
722C2×C22⋊C4—2831no—
723C2×C22⋊C4—2831no—
724C2×C22⋊C4—2831no—
725C2×C22⋊C4—2831no—
726C2×C22⋊C4—2831no—
727C2×C22⋊C4—2831no—
728C24—2831no—
729C24—2831no—
730C24—2831no—
731C24—2831no—
732C24—2831no—
733C24—2831no—
734#41—11322no—
735#41—11322no—
736#41—11322no—
737C2×Q8—2831no—
738C2×Q8C22×D28311yescharacteristic
739C2×Q8C22×D28311yescharacteristic
740C2×D4—2831no—
741C2×D4—2831no—
742C2×D4—2831no—
743C2×D4—2831no—
744C2×D4—2831no—
745C2×D4—2831no—
746C2×D4—2831no—
747C2×D4—2831no—
748C2×D4—2831no—
749C2×D4—2831no—
750C2×D4—2831no—
751C2×D4—2831no—
752C2×D4—2831no—
753C2×D4—2831no—
754C2×D4—2831no—
755C2×D4—2831no—
756C2×D4—2831no—
757C2×D4—2831no—
758C2×D4—2831no—
759C2×D4—2831no—
760C2×D4—2831no—
761C2×D4—2831no—
762C2×D4—2831no—
763C2×D4—2831no—
764C2×D4—2831no—
765C2×D4—2831no—
766C2×D4—2831no—
767C2×D4—2831no—
768C2×D4—2831no—
769C2×D4—2831no—
770C2×D4—2831no—
771C2×D4—11322no—
772C2×D4—11322no—
773C2×D4—11322no—
774C2×D4—11322no—
775C2×D4—11322no—
776C2×D4—11322no—
777C2×D4—11322no—
778C2×D4—11322no—
779C2×D4C22×D28311yescharacteristic
780C2×D4C22×D28311yescharacteristic
781C2×D4C22×D28311yescharacteristic
782C2×D4C22×D28311yescharacteristic
783C2×D4C22×D28311yescharacteristic
784C2×D4C22×D28311yescharacteristic
785C22×C4—2831no—
786C22×C4—2831no—
787C22×C4—2831no—
788C22×C4—2831no—
789C22×C4—2831no—
790C22×C4—2831no—
791C22×C4—2831no—
792C22×C4—2831no—
793C22×C4—2831no—
794C22×C4—2831no—
795C22×C4—2831no—
796C22×C4—2831no—
797C22×C4—2831no—
798C22×C4—2831no—
799C22×C4—2831no—
800C22×C4—2831no—
801C22×C4—2831no—
802C22×C4—2831no—
803C22×C4—2831no—
804C22×C4—11322no—
805C22×C4C22×D28311yescharacteristic
806C22×C4C22×D28311yescharacteristic
807C22×C4C22×D28311yescharacteristic
808C22×C4C22×D28311yescharacteristic
809C4⋊C4—2831no—
810C4⋊C4—2831no—
811C4⋊C4—2831no—
812C4⋊C4—2831no—
813C4⋊C4—2831no—
814C4⋊C4—2831no—
815C4⋊C4—2831no—
816C4⋊C4—2831no—
817C4⋊C4—2831no—
818C4⋊C4—2831no—
819C4⋊C4—2831no—
820C4⋊C4—2831no—
821C4⋊C4—2831no—
822C4⋊C4—2831no—
823C4⋊C4—2831no—
824C4⋊C4—2831no—
825C4⋊C4—2831no—
826C4⋊C4—2831no—
827C4⋊C4—2831no—
828C4⋊C4—2831no—
829C4⋊C4C22×D28311yescharacteristic
830C4⋊C4C22×D28311yescharacteristic
831C4⋊C4C22×D28311yescharacteristic
832C4⋊C4C22×D28311yescharacteristic
833C4⋊C4C22×D28311yescharacteristic
834C4⋊C4C22×D28311yescharacteristic
835C4⋊C4C22×D28311yescharacteristic
836C4⋊C4C22×D28311yescharacteristic
837C4⋊C4C22×D28311yescharacteristic
838C4⋊C4C22×D28311yescharacteristic
839C22⋊C4—2831no—
840C22⋊C4—2831no—
841C22⋊C4—2831no—
842C22⋊C4—2831no—
843C22⋊C4—2831no—
844C22⋊C4—2831no—
845C22⋊C4—2831no—
846C22⋊C4—2831no—
847C22⋊C4—2831no—
848C22⋊C4—2831no—
849C22⋊C4—2831no—
850C22⋊C4—2831no—
851C22⋊C4—2831no—
852C22⋊C4—2831no—
853C22⋊C4—2831no—
854C22⋊C4—2831no—
855C22⋊C4—2831no—
856C22⋊C4—2831no—
857C22⋊C4—2831no—
858C22⋊C4—2831no—
859C22⋊C4—2831no—
860C22⋊C4—2831no—
861C22⋊C4—2831no—
862C22⋊C4—2831no—
863C22⋊C4—2831no—
864C22⋊C4—2831no—
865C22⋊C4—2831no—
866C22⋊C4—2831no—
867C22⋊C4—2831no—
868C22⋊C4—2831no—
869C22⋊C4—2831no—
870C22⋊C4—2831no—
871C22⋊C4—2831no—
872C22⋊C4—2831no—
873C22⋊C4—2831no—
874C22⋊C4—2831no—
875C22⋊C4—2831no—
876C22⋊C4—2831no—
877C22⋊C4C22×D28311yescharacteristic
878C22⋊C4C22×D28311yescharacteristic
879C22⋊C4C22×D28311yescharacteristic
880C22⋊C4C22×D28311yescharacteristic
881C22⋊C4C22×D28311yescharacteristic
882C22⋊C4C22×D28311yescharacteristic
883C22⋊C4C22×D28311yescharacteristic
884C22⋊C4C22×D28311yescharacteristic
885C22⋊C4C22×D28311yescharacteristic
886C22⋊C4C22×D28311yescharacteristic
887C22⋊C4C22×D28311yescharacteristic
888C22⋊C4C22×D28311yescharacteristic
889C42—2831no—
890C42—2831no—
891C42—2831no—
892C42—2831no—
893C42—2831no—
894C42C22×D28311yescharacteristic
895C23—2831no—
896C23—2831no—
897C23—2831no—
898C23—2831no—
899C23—2831no—
900C23—2831no—
901C23—2831no—
902C23—5662no—
903C23—5662no—
904C23—5662no—
905C23—5662no—
906C23—5662no—
907C23—11321no—
908C23—11321no—
909C23—11321no—
910C23—11321no—
911C23—11321no—
912C23—11321no—
913C23—11321no—
914C23—11321no—
915C23—11321no—
916C23—11321no—
917C23—11321no—
918C23—11321no—
919C23—11321no—
920C23C23×D28311yescharacteristic
921C23C23×D28311yescharacteristic
922C23C23×D28311yescharacteristic
923C23C23×D28311yescharacteristic
924Q8—41no—
925Q8—41no—
926Q8—11321no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—5662no—
934D4—5662no—
935D4—5662no—
936D4—5662no—
937D4—5662no—
938D4—5662no—
939D4—5662no—
940D4—5662no—
941D4—5662no—
942D4—5662no—
943D4—11321no—
944D4—11321no—
945D4—11321no—
946D4—11321no—
947D4—11321no—
948D4—11321no—
949D4—11321no—
950D4—11321no—
951D4—11321no—
952D4—11321no—
953D4—11321no—
954D4—11321no—
955D4—11321no—
956D4—11321no—
957D4—11321no—
958D4—11321no—
959D4—11321no—
960D4—11321no—
961D4—11321no—
962D4—11321no—
963D4—11321no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—2831no—
969C2×C4—2831no—
970C2×C4—2831no—
971C2×C4—2831no—
972C2×C4—2831no—
973C2×C4—2831no—
974C2×C4—2831no—
975C2×C4—2831no—
976C2×C4—2831no—
977C2×C4—5662no—
978C2×C4—5662no—
979C2×C4—5662no—
980C2×C4—11321no—
981C2×C4—11321no—
982C2×C4—11321no—
983C2×C4—11321no—
984C2×C4—11321no—
985C2×C4—11321no—
986C2×C4—11321no—
987C2×C4—11321no—
988C2×C4—11321no—
989C2×C4—11321no—
990C2×C4—11321no—
991C2×C4—11321no—
992C2×C4—11321no—
993C2×C4—11321no—
994C2×C4—11321no—
995C2×C4—11321no—
996C2×C4C23×D28311yescharacteristic
997C2×C4C23×D28311yescharacteristic
998C2×C4C23×D28311yescharacteristic
999C2×C4C23×D28311yescharacteristic
1000C2×C4C23×D28311yescharacteristic
1001C2×C4C23×D28311yescharacteristic
1002C2×C4C23×D28311yescharacteristic
1003C2×C4C23×D28311yescharacteristic
1004C2×C4C23×D28311yescharacteristic
1005C2×C4C23×D28311yescharacteristic
1006C2×C4C23×D28311yescharacteristic
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—21no—
1019C22—2832no—
1020C22—2832no—
1021C22—5661no—
1022C22—5661no—
1023C22—5661no—
1024C22—5661no—
1025C22—5661no—
1026C22—5661no—
1027C22—5661no—
1028C22—5661no—
1029C22—5661no—
1030C22—5661no—
1031C22—5661no—
1032C22—5661no—
1033C22—5661no—
1034C22—5661no—
1035C22—5661no—
1036C22—5661no—
1037C22—5661no—
1038C22—5661no—
1039C22—5661no—
1040C22—11324no—
1041C22—22642no—
1042C22—22642no—
1043C22—22642no—
1044C22—22642no—
1045C22—22642no—
1046C22C24×D28311yescharacteristic
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—21no—
1054C4—21no—
1055C4—21no—
1056C4—21no—
1057C4—21no—
1058C4—5661no—
1059C4—5661no—
1060C4—5661no—
1061C4—5661no—
1062C4—5661no—
1063C4—5661no—
1064C4—5661no—
1065C4—5661no—
1066C4—5661no—
1067C2—41no—
1068C2—41no—
1069C2—41no—
1070C2—41no—
1071C2—5662no—
1072C2—5662no—
1073C2—11321no—
1074C2—11321no—
1075C2—11321no—
1076C2—11321no—
1077C2—11321no—
1078C2H(5,𝔽2)×D28311yescharacteristic
1079C2H(5,𝔽2)×D28311yescharacteristic
1080C2#3182730211yescharacteristic
subgroupG/H
center, FrattiniC22C24×D283
commutator, socle, cosocleC22×C283C25
Fitting#562×C283C2
hypercenter#562D283
hypocenterC283#3534
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ #562

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #31827211C2semidirect
2. #31827205C2semidirect
3. #31827203C2semidirect
4. #31827168C2semidirect
5. #31827160C2semidirect
6. #31827143C2semidirect
7. #31827142C2semidirect
8. #31827112C2semidirect
9. #31827108C2semidirect
10. #31827108C2semidirect
11. #31827107C2semidirect
12. #31827106C2semidirect
13. #31827106C2semidirect
14. #31827099C2semidirect
15. #31827099C2semidirect
16. #31827067C2semidirect
17. #31827065C2semidirect
18. #31827063C2semidirect
19. #31827061C2semidirect
20. #31827061C2semidirect
21. #31827049C2semidirect
22. #31827049C2semidirect
23. #31827047C2semidirect
24. #31827045C2semidirect
25. #31827026C2semidirect
26. #31827026C2semidirect
27. #31827023C2semidirect
28. #31826978C2semidirect
29. #123×D283C2semidirect
30. #121×D283C2semidirect
31. #562×C283C2semidirect
32. C2×#17985393C22semidirect
33. C2×#17985393C22semidirect
34. C2×#17985392C22semidirect
35. C22×D1132C22semidirect
36. C22×D1132C22semidirect
38. C2×D4×D283C22semidirect
39. C2×D4×D283C22semidirect
40. C2×D4×D283C22semidirect
41. C2×D4×D283C22semidirect
42. C2×D4×D283C22semidirect
43. C22×C4×D283C22semidirect
44. #22583606C22semidirect
45. #22583606C22semidirect
46. #22583605C22semidirect
47. #22583605C22semidirect
48. #22583605C22semidirect
49. #22583605C22semidirect
50. #22583604C22semidirect
51. #22583603C22semidirect
52. #22583603C22semidirect
53. #22583603C22semidirect
54. #22583600C22semidirect
55. #22583600C22semidirect
56. #22583600C22semidirect
57. #22583599C22semidirect
58. #22583599C22semidirect
59. #22583597C22semidirect
60. #22583596C22semidirect
61. #22583595C22semidirect
62. #22583595C22semidirect
63. #22583595C22semidirect
64. #22583595C22semidirect
65. #22583595C22semidirect
66. #22583595C22semidirect
67. #22583595C22semidirect
68. #22583595C22semidirect
69. #22583595C22semidirect
70. #22583595C22semidirect
71. #22583594C22semidirect
72. #22583594C22semidirect
73. #22583593C22semidirect
74. #22583593C22semidirect
75. #22583593C22semidirect
76. #22583592C22semidirect
77. #22583592C22semidirect
78. #22583592C22semidirect
79. #22583592C22semidirect
80. #22583592C22semidirect
81. #22583592C22semidirect
82. #22583592C22semidirect
83. #22583592C22semidirect
84. #22583591C22semidirect
85. #22583590C22semidirect
86. #22583588C22semidirect
87. #22583588C22semidirect
88. #22583588C22semidirect
89. #22583586C22semidirect
90. #22583586C22semidirect
91. #22583586C22semidirect
92. #22583586C22semidirect
94. #22583585C22semidirect
95. #22583585C22semidirect
96. #22583585C22semidirect
97. #22583585C22semidirect
98. #22583585C22semidirect
99. #22583585C22semidirect
100. #22583585C22semidirect
101. #22583585C22semidirect
102. #22583584C22semidirect
103. #22583584C22semidirect
104. #22583584C22semidirect
107. #22583583C22semidirect
108. #22583583C22semidirect
109. #22583583C22semidirect
110. #22583583C22semidirect
111. #22583583C22semidirect
112. #22583583C22semidirect
113. #22583583C22semidirect
114. #22583583C22semidirect
115. #22583583C22semidirect
116. #22583583C22semidirect
117. #22583582C22semidirect
118. #22583582C22semidirect
119. #22583582C22semidirect
120. #22583582C22semidirect
121. #22583582C22semidirect
122. #22583581C22semidirect
123. #22583581C22semidirect
124. #22583581C22semidirect
126. #22583580C22semidirect
127. #22583580C22semidirect
128. #22583580C22semidirect
129. #22583580C22semidirect
130. #22583580C22semidirect
131. #22583580C22semidirect
132. #22583580C22semidirect
133. #22583580C22semidirect
134. #22583580C22semidirect
136. #22583578C22semidirect
137. #22583578C22semidirect
138. #22583578C22semidirect
139. #22583578C22semidirect
140. #22583578C22semidirect
141. C4×D1132C22semidirect
142. C4×D1132C22semidirect
143. C4×D1132C22semidirect
144. #22583572C22semidirect
145. #22583572C22semidirect
146. #22583572C22semidirect
147. #22583572C22semidirect
148. #22583572C22semidirect
149. C4×C22⋊D283C22semidirect
150. C4×C22⋊D283C22semidirect
151. C4×C22⋊D283C22semidirect
152. C4×C22⋊D283C22semidirect
153. C4×C22⋊D283C22semidirect
154. (C22⋊D283)⋊C4C22semidirect
155. (C22⋊D283)⋊C4C22semidirect
156. (C22⋊D283)⋊C4C22semidirect
157. #22583568C22semidirect
158. #22583568C22semidirect
159. #22583566C22semidirect
160. C4⋊C4×D283C22semidirect
161. C4⋊C4×D283C22semidirect
162. C4⋊C4×D283C22semidirect
163. C2×(C2×D283)⋊C4C22semidirect
164. C22⋊C4×D283C22semidirect
165. C22⋊C4×D283C22semidirect
166. C22⋊C4×D283C22semidirect
167. C22⋊C4×D283C22semidirect
168. C22⋊C4×D283C22semidirect
169. C22⋊C4×D283C22semidirect
170. C22⋊C4×D283C22semidirect
171. C22⋊C4×D283C22semidirect
172. #125×C283C22semidirect
173. #124×C283C22semidirect
174. #124×C283C22semidirect
175. #123×C283C22semidirect
176. #123×C283C22semidirect
177. #123×C283C22semidirect
178. #123×C283C22semidirect
179. C22⋊Q8×C283C22semidirect
180. C22⋊Q8×C283C22semidirect
181. C22⋊Q8×C283C22semidirect
182. C22⋊Q8×C283C22semidirect
183. #121×C283C22semidirect
184. #121×C283C22semidirect
185. #121×C283C22semidirect
186. #121×C283C22semidirect
540. C283#3534semidirect
543. #562D283semidirect
598. #125C2×D283semidirect
603. #124C2×D283semidirect
604. #124C2×D283semidirect
629. #123C2×D283semidirect
630. #123C2×D283semidirect
631. #123C2×D283semidirect
632. #123C2×D283semidirect
641. C22⋊Q8C2×D283semidirect
642. C22⋊Q8C2×D283semidirect
643. C22⋊Q8C2×D283semidirect
644. C22⋊Q8C2×D283semidirect
677. #121C2×D283semidirect
678. #121C2×D283semidirect
679. #121C2×D283semidirect
680. #121C2×D283semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#318272112
#318272052
#318272032
#318271682
#318271602
#318271432
#318271422
#318271122
#318271082
#318271072
#318271062
#318270992
#318270672
#318270652
#318270632
#318270612
#318270492
#318270472
#318270452
#318270262
#318270232
#318269782
#123×D2832
#121×D2832
#562×C2832
#3534283