Finite Group Databasebeta

← #49135480

Subgroups — #49135480

Order 36224.

1134 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827212C211yesmaximal, characteristic, complemented
2#31827211C211yesmaximal, characteristic, complemented
3#31827210C211yesmaximal, characteristic, complemented
4#31827171C211yesmaximal, characteristic, complemented
5#31827169C211yesmaximal, characteristic, complemented
6#31827125C211yesmaximal, characteristic, complemented
7#31827123C211yesmaximal, characteristic, complemented
8#31827117C211yesmaximal, characteristic, complemented
9#31827113C211yesmaximal, characteristic, complemented
10#31827112C211yesmaximal, characteristic, complemented
11#31827108C211yesmaximal, characteristic, complemented
12#31827107C211yesmaximal, characteristic, complemented
13#31827107C211yesmaximal, characteristic, complemented
14#31827104C211yesmaximal, characteristic, complemented
15#31827104C211yesmaximal, characteristic, complemented
16#31827090C211yesmaximal, characteristic, complemented
17#31827090C211yesmaximal, characteristic, complemented
18#31827083C211yesmaximal, characteristic, complemented
19#31827079C211yesmaximal, characteristic, complemented
20#31827063C211yesmaximal, characteristic, complemented
21#31827058C211yesmaximal, characteristic, complemented
22#31827051C211yesmaximal, characteristic, complemented
23#31827049C211yesmaximal, characteristic, complemented
24#31827045C211yesmaximal, characteristic, complemented
25#31827044C211yesmaximal, characteristic, complemented
26#31827044C211yesmaximal, characteristic, complemented
27#31827042C211yesmaximal, characteristic, complemented
28#31826973C211yesmaximal, characteristic, complemented
29C22⋊Q8×D283C211yesmaximal, characteristic, complemented
30#121×D283C211yesmaximal, characteristic, complemented
31#562×C283C211yesmaximal, characteristic, complemented
32C2×#17985393C2211yescharacteristic, complemented
33C2×#17985392C2211yescharacteristic, complemented
34C2×#17985392C2211yescharacteristic, complemented
35C2×#17985392C2211yescharacteristic, complemented
36C2×#17985391C2211yescharacteristic, complemented
37C2×#17985391C2211yescharacteristic, complemented
38C2×#17985391C2211yescharacteristic, complemented
39C2×Q8×D283C2211yescharacteristic, complemented
40C2×D4×D283C2211yescharacteristic
41C2×D4×D283C2211yescharacteristic
42C2×D4×D283C2211yescharacteristic
43C22×C4×D283C2211yescharacteristic
44#22583609C2211yescharacteristic, complemented
45#22583608C2211yescharacteristic, complemented
46#22583605C2211yescharacteristic, complemented
47#22583604C2211yescharacteristic, complemented
48#22583603C2211yescharacteristic, complemented
49#22583603C2211yescharacteristic, complemented
50#22583601C2211yescharacteristic, complemented
51#22583600C2211yescharacteristic, complemented
52#22583600C2211yescharacteristic, complemented
53#22583599C2211yescharacteristic, complemented
54#22583597C2211yescharacteristic, complemented
55#22583596C2211yescharacteristic, complemented
56#22583596C2211yescharacteristic, complemented
57#22583596C2211yescharacteristic, complemented
58#22583596C2211yescharacteristic, complemented
59#22583596C2211yescharacteristic, complemented
60#22583596C2211yescharacteristic, complemented
61#22583595C2211yescharacteristic, complemented
62#22583595C2211yescharacteristic, complemented
63#22583595C2211yescharacteristic, complemented
64#22583595C2211yescharacteristic, complemented
65#22583595C2211yescharacteristic, complemented
66#22583594C2211yescharacteristic, complemented
67#22583593C2211yescharacteristic, complemented
68#22583592C2211yescharacteristic, complemented
69#22583592C2211yescharacteristic, complemented
70#22583592C2211yescharacteristic, complemented
71#22583592C2211yescharacteristic, complemented
72#22583592C2211yescharacteristic, complemented
73#22583591C2211yescharacteristic, complemented
74#22583591C2211yescharacteristic, complemented
75#22583590C2211yescharacteristic
76#22583590C2211yescharacteristic
77#22583590C2211yescharacteristic, complemented
78#22583590C2211yescharacteristic, complemented
79#22583590C2211yescharacteristic, complemented
80#22583589C2211yescharacteristic, complemented
81#22583589C2211yescharacteristic, complemented
82#22583589C2211yescharacteristic, complemented
83#22583588C2211yescharacteristic
84#22583588C2211yescharacteristic
85#22583588C2211yescharacteristic
86#22583588C2211yescharacteristic
87#22583588C2211yescharacteristic
88#22583588C2211yescharacteristic, complemented
89#22583588C2211yescharacteristic, complemented
90#22583588C2211yescharacteristic, complemented
91#22583588C2211yescharacteristic, complemented
92#22583588C2211yescharacteristic, complemented
93#22583588C2211yescharacteristic, complemented
94#22583588C2211yescharacteristic, complemented
95#22583587C2211yescharacteristic, complemented
96#22583587C2211yescharacteristic, complemented
97#22583587C2211yescharacteristic, complemented
98#22583587C2211yescharacteristic, complemented
99#22583587C2211yescharacteristic, complemented
100#22583587C2211yescharacteristic, complemented
101#22583587C2211yescharacteristic, complemented
102#22583587C2211yescharacteristic, complemented
103#22583586C2211yescharacteristic
104#22583586C2211yescharacteristic
105#22583586C2211yescharacteristic, complemented
106#22583586C2211yescharacteristic, complemented
107#22583585C2211yescharacteristic
108#22583585C2211yescharacteristic, complemented
109#22583585C2211yescharacteristic, complemented
110#22583584C2211yescharacteristic
111#22583584C2211yescharacteristic, complemented
112#22583583C2211yescharacteristic
113#22583583C2211yescharacteristic
114#22583583C2211yescharacteristic
115#22583583C2211yescharacteristic, complemented
116#22583583C2211yescharacteristic, complemented
117#22583583C2211yescharacteristic, complemented
118#22583583C2211yescharacteristic, complemented
119#22583583C2211yescharacteristic, complemented
120#22583583C2211yescharacteristic, complemented
121#22583583C2211yescharacteristic, complemented
122#22583583C2211yescharacteristic, complemented
123#22583582C2211yescharacteristic
124#22583582C2211yescharacteristic
125#22583582C2211yescharacteristic, complemented
126#22583582C2211yescharacteristic, complemented
127#22583582C2211yescharacteristic, complemented
128#22583582C2211yescharacteristic, complemented
129#22583582C2211yescharacteristic, complemented
130#22583581C2211yescharacteristic
131#22583581C2211yescharacteristic, complemented
132#22583581C2211yescharacteristic, complemented
133#22583581C2211yescharacteristic, complemented
134#22583581C2211yescharacteristic, complemented
135#22583580C2211yescharacteristic
136#22583580C2211yescharacteristic
137#22583580C2211yescharacteristic
138#22583578C2211yescharacteristic
139#22583578C2211yescharacteristic
140#22583578C2211yescharacteristic
141C4×Dic566C2211yescharacteristic, complemented
142#22583575C2211yescharacteristic, complemented
143C4×D1132C2211yescharacteristic
144C4×D1132C2211yescharacteristic, complemented
145#22583572C2211yescharacteristic
146#22583572C2211yescharacteristic
147#22583572C2211yescharacteristic, complemented
148#22583572C2211yescharacteristic, complemented
149C4×C22⋊D283C2211yescharacteristic
150C4×C22⋊D283C2211yescharacteristic, complemented
151C4×C22⋊D283C2211yescharacteristic, complemented
152(C22⋊D283)⋊C4C2211yescharacteristic
153(C22⋊D283)⋊C4C2211yescharacteristic
154(C22⋊D283)⋊C4C2211yescharacteristic, complemented
155(C22⋊D283)⋊C4C2211yescharacteristic, complemented
156(C22⋊D283)⋊C4C2211yescharacteristic, complemented
157#22583566C2211yescharacteristic, complemented
158C2×Dic283⋊C4C2211yescharacteristic, complemented
159C4⋊C4×D283C2211yescharacteristic
160C4⋊C4×D283C2211yescharacteristic, complemented
161C4⋊C4×D283C2211yescharacteristic, complemented
162C4⋊C4×D283C2211yescharacteristic, complemented
163C4⋊C4×D283C2211yescharacteristic, complemented
164C2×(C2×D283)⋊C4C2211yescharacteristic
165C2×(C2×D283)⋊C4C2211yescharacteristic
166C22⋊C4×D283C2211yescharacteristic
167C22⋊C4×D283C2211yescharacteristic
168C22⋊C4×D283C2211yescharacteristic
169C22⋊C4×D283C2211yescharacteristic
170C22⋊C4×D283C2211yescharacteristic
171C22⋊C4×D283C2211yescharacteristic
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
184#121×C283C2211yescharacteristic, complemented
185#121×C283C2211yescharacteristic, complemented
186#121×C283C2211yescharacteristic, complemented
187C23×D283C2311yescharacteristic
188C23×D283C2311yescharacteristic
189C23×D283C2311yescharacteristic
190#17985393—42no—
191#17985392—42no—
192#17985392—42no—
193#17985392—42no—
194#17985391—42no—
195#17985391—42no—
196#17985391—42no—
197C2×Dic566C2311yescharacteristic
198C2×Dic566C2311yescharacteristic
199C2×Dic566C2311yescharacteristic
200C2×Dic566C2311yescharacteristic
201C2×Dic566C2311yescharacteristic
202C2×Dic566C2311yescharacteristic
203C2×Dic566C2311yescharacteristic
204Q8×D283—42no—
205C2×D1132C2311yescharacteristic
206C2×D1132C2311yescharacteristic
207C2×D1132C2311yescharacteristic
208C2×D1132C2311yescharacteristic
209C2×D1132C2311yescharacteristic
210C2×D1132C2311yescharacteristic
211C2×D1132C2311yescharacteristic
212C2×C22⋊D283C2311yescharacteristic
213C2×C22⋊D283C2311yescharacteristic
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
226D4×D283—42no—
227D4×D283—42no—
228D4×D283—42no—
229C22×Dic283C2311yescharacteristic
230C22×Dic283C2311yescharacteristic
231C22×Dic283C2311yescharacteristic
232C22×Dic283C2311yescharacteristic
233C22×Dic283C2311yescharacteristic
234C2×C4×D283—42no—
235C2×C4×D283C2311yescharacteristic
236C2×C4×D283C2311yescharacteristic
237C2×C4×D283C2311yescharacteristic
238C2×C4×D283C2311yescharacteristic
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
252C4⋊Dic283C2311yescharacteristic
253C4⋊Dic283C2311yescharacteristic
254C4⋊Dic283C2311yescharacteristic
255C4⋊Dic283C2311yescharacteristic
256C4⋊Dic283C2311yescharacteristic
257C4⋊Dic283C2311yescharacteristic
258C4⋊Dic283C2311yescharacteristic
259C4⋊Dic283C2311yescharacteristic
260Dic283⋊C4C2311yescharacteristic
261Dic283⋊C4C2311yescharacteristic
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
276Dic283⋊C4C2311yescharacteristic
277Dic283⋊C4C2311yescharacteristic
278Dic283⋊C4C2311yescharacteristic
279Dic283⋊C4C2311yescharacteristic
280C22⋊Dic283C2311yescharacteristic
281C22⋊Dic283C2311yescharacteristic
282C22⋊Dic283C2311yescharacteristic
283C22⋊Dic283C2311yescharacteristic
284C22⋊Dic283C2311yescharacteristic
285C22⋊Dic283C2311yescharacteristic
286C22⋊Dic283C2311yescharacteristic
287C22⋊Dic283C2311yescharacteristic
288C22⋊Dic283C2311yescharacteristic
289C22⋊Dic283C2311yescharacteristic
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—41no—
359C22×D283—41no—
360C22×D283—41no—
361C22×D283—41no—
362C22×D283—41no—
363C22×D283C2411yescharacteristic
364C22×D283C2411yescharacteristic
365C22×D283C2411yescharacteristic
366C22×D283C2411yescharacteristic
367C22×D283C2411yescharacteristic
368Dic566—22no—
369Dic566—22no—
370Dic566—41no—
371Dic566—41no—
372Dic566—41no—
373Dic566—41no—
374Dic566—41no—
375D1132—22no—
376D1132—22no—
377D1132—22no—
378D1132—22no—
379D1132—41no—
380D1132—41no—
381D1132—41no—
382C22⋊D283—22no—
383C22⋊D283—22no—
384C22⋊D283—22no—
385C22⋊D283—22no—
386C22⋊D283—22no—
387C22⋊D283—22no—
388C22⋊D283—41no—
389C22⋊D283—41no—
390C22⋊D283—41no—
391C22⋊D283—41no—
392C22⋊D283—41no—
393C22⋊D283—41no—
394C22⋊D283—41no—
395C22⋊D283—41no—
396C2×Dic283—22no—
397C2×Dic283—22no—
398C2×Dic283—41no—
399C2×Dic283—41no—
400C2×Dic283—41no—
401C2×Dic283C2411yescharacteristic
402C2×Dic283C2411yescharacteristic
403C2×Dic283C2411yescharacteristic
404C2×Dic283C2411yescharacteristic
405C2×Dic283C2411yescharacteristic
406C2×Dic283C2411yescharacteristic
407C2×Dic283C2411yescharacteristic
408C2×Dic283C2411yescharacteristic
409C2×Dic283C2411yescharacteristic
410C2×Dic283C2411yescharacteristic
411C2×Dic283C2411yescharacteristic
412C4×D283—22no—
413C4×D283—22no—
414C4×D283—22no—
415C4×D283—22no—
416C4×D283—22no—
417C4×D283—41no—
418C4×D283—41no—
419C4×D283—41no—
420C4×D283—41no—
421C4×D283—41no—
422C4×D283—41no—
423C4×D283—41no—
424C4×D283—41no—
425C4×D283—41no—
426C4×D283—41no—
427C4×D283—41no—
428C4×D283—41no—
429C23×C283C2411yescharacteristic
430C23×C283C2411yescharacteristic
431C23×C283C2411yescharacteristic
432C23×C283C2411yescharacteristic
433Q8×C283—41no—
434Q8×C283—41no—
435D4×C283—41no—
436D4×C283—41no—
437D4×C283—41no—
438D4×C283—41no—
439D4×C283—41no—
440D4×C283—41no—
441C2×C4×C283—41no—
442C2×C4×C283—41no—
443C2×C4×C283—41no—
444C2×C4×C283—41no—
445C2×C4×C283C2411yescharacteristic
446C2×C4×C283C2411yescharacteristic
447C2×C4×C283C2411yescharacteristic
448C2×C4×C283C2411yescharacteristic
449C2×C4×C283C2411yescharacteristic
450C2×C4×C283C2411yescharacteristic
451C2×C4×C283C2411yescharacteristic
452C2×C4×C283C2411yescharacteristic
453C2×C4×C283C2411yescharacteristic
454C2×C4×C283C2411yescharacteristic
455C2×C4×C283C2411yescharacteristic
456C22×C283—21no—
457C22×C283—21no—
458C22×C283—21no—
459C22×C283—21no—
460C22×C283—21no—
461C22×C283—21no—
462C22×C283—21no—
463C22×C283—21no—
464C22×C283—21no—
465C22×C283—21no—
466C22×C283—21no—
467C22×C283—21no—
468C22×C283C2511yescharacteristic
469C2×D283—21no—
470C2×D283—21no—
471C2×D283—21no—
472C2×D283—21no—
473C2×D283—21no—
474C2×D283—21no—
475C2×D283—21no—
476C2×D283—21no—
477C2×D283—21no—
478C2×D283—21no—
479C2×D283—21no—
480C2×D283—21no—
481C2×D283—21no—
482C2×D283—44no—
483C2×D283—82no—
484C2×D283—82no—
485C2×D283H(5,𝔽2)12yes—
486C2×D2832−1+412yes—
487C4×C283—21no—
488C4×C283—21no—
489C4×C283—21no—
490C4×C283—21no—
491C4×C283—21no—
492C4×C283—21no—
493C4×C283—21no—
494C4×C283—21no—
495C4×C283—21no—
496C4×C283—21no—
497C4×C283—21no—
498Dic283—21no—
499Dic283—21no—
500Dic283—21no—
501Dic283—21no—
502Dic283—21no—
503Dic283—21no—
504Dic283—21no—
505Dic283—21no—
506Dic283—21no—
507Dic283—21no—
508Dic283H(5,𝔽2)12yes—
509C2×C283—41no—
510C2×C283—41no—
511C2×C283—41no—
512C2×C283—41no—
513C2×C283C2×H(5,𝔽2)11yescharacteristic
514C2×C283C2×H(5,𝔽2)11yescharacteristic
515C2×C283C2×2−1+411yescharacteristic
516D283—22no—
517D283—22no—
518D283—41no—
519D283—41no—
520D283—41no—
521C283#353611yescharacteristic, complemented, Sylow
522#3536—2831nomaximal, Sylow
523#562—2831no—
524#562—2831no—
525#562—2831no—
526#562D28311yescharacteristic, complemented
527#554—2831no—
528#554—2831no—
529#548—2831no—
530#548—2831no—
531#547—2831no—
532#547—2831no—
533#546—2831no—
534#546—2831no—
535#546—2831no—
536#546—2831no—
537#546—2831no—
538#546—2831no—
539#543—2831no—
540#543—2831no—
541#542—2831no—
542#542—2831no—
543#539—2831no—
544#539—2831no—
545#538—2831no—
546#538—2831no—
547#537—2831no—
548#537—2831no—
549#537—2831no—
550#537—2831no—
551#525—2831no—
552C2×C22⋊Q8—2831no—
553C2×#121—2831no—
554C2×#41—2831no—
555C2×#41—2831no—
556C2×#41—2831no—
557C2×#41—2831no—
558C2×#41—2831no—
559C2×#41—2831no—
560C2×#41—2831no—
561C22×Q8—2831no—
562C22×D4—2831no—
563C22×D4—2831no—
564C22×D4—2831no—
565C23×C4—2831no—
566C4⋊Q8—2831no—
567C4⋊Q8—2831no—
568#126—2831no—
569#126—2831no—
570#126—2831no—
571#126—2831no—
572#125—2831no—
573#125—2831no—
574#125—2831no—
575#125C2×D28311yescharacteristic, complemented
576#124—2831no—
577#124—2831no—
578#124—2831no—
579#124—2831no—
580#124—2831no—
581#124—2831no—
582#124—2831no—
583#124—2831no—
584#124C2×D28311yescharacteristic, complemented
585#124C2×D28311yescharacteristic, complemented
586#123—2831no—
587#123—2831no—
588#123—2831no—
589#123—2831no—
590#123—2831no—
591#123—2831no—
592#123—2831no—
593#123—2831no—
594#123—2831no—
595#123—2831no—
596#123—2831no—
597#123—2831no—
598#123—2831no—
599#123—2831no—
600#123C2×D28311yescharacteristic, complemented
601#123C2×D28311yescharacteristic, complemented
602#123C2×D28311yescharacteristic, complemented
603#123C2×D28311yescharacteristic, complemented
604C22⋊Q8—2831no—
605C22⋊Q8—2831no—
606C22⋊Q8—2831no—
607C22⋊Q8—2831no—
608C22⋊Q8—2831no—
609C22⋊Q8—2831no—
610C22⋊Q8—2831no—
611C22⋊Q8—2831no—
612C22⋊Q8—2831no—
613C22⋊Q8—2831no—
614C22⋊Q8—2831no—
615C22⋊Q8—2831no—
616C22⋊Q8—2831no—
617C22⋊Q8—2831no—
618C22⋊Q8—2831no—
619C22⋊Q8—2831no—
620C22⋊Q8—2831no—
621C22⋊Q8—2831no—
622C22⋊Q8—2831no—
623C22⋊Q8—2831no—
624C22⋊Q8—2831no—
625C22⋊Q8—2831no—
626C22⋊Q8—2831no—
627C22⋊Q8—2831no—
628C22⋊Q8—2831no—
629C22⋊Q8—2831no—
630C22⋊Q8—2831no—
631C22⋊Q8—2831no—
632C22⋊Q8—2831no—
633C22⋊Q8—2831no—
634C22⋊Q8—2831no—
635C22⋊Q8—2831no—
636C22⋊Q8C2×D28311yescharacteristic, complemented
637C22⋊Q8C2×D28311yescharacteristic, complemented
638C22⋊Q8C2×D28311yescharacteristic, complemented
639C22⋊Q8C2×D28311yescharacteristic, complemented
640#121—2831no—
641#121—2831no—
642#121—2831no—
643#121—2831no—
644#121—2831no—
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#121C2×D28311yescharacteristic
669#121C2×D28311yescharacteristic, complemented
670#121C2×D28311yescharacteristic, complemented
671#121C2×D28311yescharacteristic, complemented
672#120—2831no—
673#120—2831no—
674#120—2831no—
675#120—2831no—
676#120—2831no—
677#120—2831no—
678C4×Q8—2831no—
679C4×Q8—2831no—
680C4×D4—2831no—
681C4×D4—2831no—
682C4×D4—2831no—
683C4×D4—2831no—
684C4×D4—2831no—
685C4×D4—2831no—
686C4×D4—2831no—
687C4×D4—2831no—
688C4×D4—2831no—
689C4×D4—2831no—
690C4×D4—2831no—
691C4×D4—2831no—
692C4×D4—2831no—
693C4×D4—2831no—
694#117—2831no—
695C2×C4⋊C4—2831no—
696C2×C4⋊C4—2831no—
697C2×C4⋊C4—2831no—
698C2×C4⋊C4—2831no—
699C2×C4⋊C4—2831no—
700C2×C4⋊C4—2831no—
701C2×C22⋊C4—2831no—
702C2×C22⋊C4—2831no—
703C2×C22⋊C4—2831no—
704C2×C22⋊C4—2831no—
705C2×C22⋊C4—2831no—
706C2×C22⋊C4—2831no—
707C2×C22⋊C4—2831no—
708C2×C22⋊C4—2831no—
709C24—2831no—
710C24—2831no—
711C24—2831no—
712#41—11322no—
713#41—11322no—
714#41—11322no—
715#41—11322no—
716#41—11322no—
717#41—11322no—
718#41—11322no—
719C2×Q8—2831no—
720C2×Q8—2831no—
721C2×Q8—2831no—
722C2×Q8—2831no—
723C2×Q8—2831no—
724C2×Q8—2831no—
725C2×Q8—2831no—
726C2×Q8—11322no—
727C2×Q8C22×D28311yescharacteristic
728C2×Q8C22×D28311yescharacteristic
729C2×D4—2831no—
730C2×D4—2831no—
731C2×D4—2831no—
732C2×D4—2831no—
733C2×D4—2831no—
734C2×D4—2831no—
735C2×D4—2831no—
736C2×D4—2831no—
737C2×D4—2831no—
738C2×D4—2831no—
739C2×D4—2831no—
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—11322no—
751C2×D4—11322no—
752C2×D4—11322no—
753C2×D4C22×D28311yescharacteristic
754C2×D4C22×D28311yescharacteristic
755C2×D4C22×D28311yescharacteristic
756C2×D4C22×D28311yescharacteristic
757C2×D4C22×D28311yescharacteristic
758C2×D4C22×D28311yescharacteristic
759C22×C4—2831no—
760C22×C4—2831no—
761C22×C4—2831no—
762C22×C4—2831no—
763C22×C4—2831no—
764C22×C4—2831no—
765C22×C4—2831no—
766C22×C4—2831no—
767C22×C4—2831no—
768C22×C4—2831no—
769C22×C4—2831no—
770C22×C4—2831no—
771C22×C4—2831no—
772C22×C4—2831no—
773C22×C4—2831no—
774C22×C4—2831no—
775C22×C4—2831no—
776C22×C4—2831no—
777C22×C4—2831no—
778C22×C4—2831no—
779C22×C4—2831no—
780C22×C4—2831no—
781C22×C4—11322no—
782C22×C4C22×D28311yescharacteristic
783C22×C4C22×D28311yescharacteristic
784C22×C4C22×D28311yescharacteristic
785C22×C4C22×D28311yescharacteristic
786C4⋊C4—2831no—
787C4⋊C4—2831no—
788C4⋊C4—2831no—
789C4⋊C4—2831no—
790C4⋊C4—2831no—
791C4⋊C4—2831no—
792C4⋊C4—2831no—
793C4⋊C4—2831no—
794C4⋊C4—2831no—
795C4⋊C4—2831no—
796C4⋊C4—2831no—
797C4⋊C4—2831no—
798C4⋊C4—2831no—
799C4⋊C4—2831no—
800C4⋊C4—2831no—
801C4⋊C4—2831no—
802C4⋊C4—2831no—
803C4⋊C4—2831no—
804C4⋊C4—2831no—
805C4⋊C4—2831no—
806C4⋊C4—2831no—
807C4⋊C4—2831no—
808C4⋊C4—2831no—
809C4⋊C4—2831no—
810C4⋊C4—2831no—
811C4⋊C4—2831no—
812C4⋊C4—2831no—
813C4⋊C4—2831no—
814C4⋊C4C22×D28311yescharacteristic
815C4⋊C4C22×D28311yescharacteristic
816C4⋊C4C22×D28311yescharacteristic
817C4⋊C4C22×D28311yescharacteristic
818C4⋊C4C22×D28311yescharacteristic
819C4⋊C4C22×D28311yescharacteristic
820C4⋊C4C22×D28311yescharacteristic
821C4⋊C4C22×D28311yescharacteristic
822C4⋊C4C22×D28311yescharacteristic
823C4⋊C4C22×D28311yescharacteristic
824C22⋊C4—2831no—
825C22⋊C4—2831no—
826C22⋊C4—2831no—
827C22⋊C4—2831no—
828C22⋊C4—2831no—
829C22⋊C4—2831no—
830C22⋊C4—2831no—
831C22⋊C4—2831no—
832C22⋊C4—2831no—
833C22⋊C4—2831no—
834C22⋊C4—2831no—
835C22⋊C4—2831no—
836C22⋊C4—2831no—
837C22⋊C4—2831no—
838C22⋊C4—2831no—
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⋊C4C22×D28311yescharacteristic
859C22⋊C4C22×D28311yescharacteristic
860C22⋊C4C22×D28311yescharacteristic
861C22⋊C4C22×D28311yescharacteristic
862C22⋊C4C22×D28311yescharacteristic
863C22⋊C4C22×D28311yescharacteristic
864C22⋊C4C22×D28311yescharacteristic
865C22⋊C4C22×D28311yescharacteristic
866C22⋊C4C22×D28311yescharacteristic
867C22⋊C4C22×D28311yescharacteristic
868C22⋊C4C22×D28311yescharacteristic
869C22⋊C4C22×D28311yescharacteristic
870C42—2831no—
871C42—2831no—
872C42—2831no—
873C42—2831no—
874C42—2831no—
875C42C22×D28311yescharacteristic
876C23—2831no—
877C23—2831no—
878C23—2831no—
879C23—2831no—
880C23—2831no—
881C23—5662no—
882C23—5662no—
883C23—5662no—
884C23—5662no—
885C23—11321no—
886C23—11321no—
887C23—11321no—
888C23—11321no—
889C23—11321no—
890C23C23×D28311yescharacteristic
891C23C23×D28311yescharacteristic
892C23C23×D28311yescharacteristic
893C23C23×D28311yescharacteristic
894Q8—41no—
895Q8—41no—
896Q8—5662no—
897Q8—5662no—
898Q8—11321no—
899Q8—11321no—
900Q8—11321no—
901Q8—11321no—
902Q8—11321no—
903D4—41no—
904D4—41no—
905D4—41no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—5662no—
910D4—5662no—
911D4—5662no—
912D4—5662no—
913D4—5662no—
914D4—5662no—
915D4—5662no—
916D4—5662no—
917D4—5662no—
918D4—5662no—
919D4—11321no—
920D4—11321no—
921D4—11321no—
922D4—11321no—
923D4—11321no—
924D4—11321no—
925D4—11321no—
926D4—11321no—
927D4—11321no—
928D4—11321no—
929D4—11321no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—2831no—
935C2×C4—2831no—
936C2×C4—2831no—
937C2×C4—2831no—
938C2×C4—2831no—
939C2×C4—2831no—
940C2×C4—2831no—
941C2×C4—2831no—
942C2×C4—2831no—
943C2×C4—2831no—
944C2×C4—2831no—
945C2×C4—5662no—
946C2×C4—5662no—
947C2×C4—5662no—
948C2×C4—5662no—
949C2×C4—5662no—
950C2×C4—5662no—
951C2×C4—5662no—
952C2×C4—11321no—
953C2×C4—11321no—
954C2×C4—11321no—
955C2×C4—11321no—
956C2×C4—11321no—
957C2×C4—11321no—
958C2×C4—11321no—
959C2×C4—11321no—
960C2×C4—11321no—
961C2×C4—11321no—
962C2×C4—11321no—
963C2×C4—11321no—
964C2×C4—11321no—
965C2×C4—11321no—
966C2×C4—11321no—
967C2×C4C23×D28311yescharacteristic
968C2×C4C23×D28311yescharacteristic
969C2×C4C23×D28311yescharacteristic
970C2×C4C23×D28311yescharacteristic
971C2×C4C23×D28311yescharacteristic
972C2×C4C23×D28311yescharacteristic
973C2×C4C23×D28311yescharacteristic
974C2×C4C23×D28311yescharacteristic
975C2×C4C23×D28311yescharacteristic
976C2×C4C23×D28311yescharacteristic
977C2×C4C23×D28311yescharacteristic
978C22—21no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—21no—
983C22—21no—
984C22—21no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—2832no—
991C22—2832no—
992C22—5661no—
993C22—5661no—
994C22—5661no—
995C22—5661no—
996C22—5661no—
997C22—5661no—
998C22—5661no—
999C22—5661no—
1000C22—5661no—
1001C22—5661no—
1002C22—5661no—
1003C22—5661no—
1004C22—5661no—
1005C22—11324no—
1006C22—22642no—
1007C22—22642no—
1008C22C24×D28311yescharacteristic
1009C4—21no—
1010C4—21no—
1011C4—21no—
1012C4—21no—
1013C4—21no—
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—2832no—
1021C4—5661no—
1022C4—5661no—
1023C4—5661no—
1024C4—5661no—
1025C4—5661no—
1026C4—5661no—
1027C4—5661no—
1028C4—5661no—
1029C4—5661no—
1030C4—5661no—
1031C2—41no—
1032C2—41no—
1033C2—41no—
1034C2—41no—
1035C2—5662no—
1036C2—5662no—
1037C2—11321no—
1038C2—11321no—
1039C2—11321no—
1040C2H(5,𝔽2)×D28311yescharacteristic
1041C2H(5,𝔽2)×D28311yescharacteristic
1042C22−1+4×D28311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D283
commutator, socle, cosocleC22×C283C25
Fitting#562×C283C2
hypercenter#562D283
hypocenterC283#3536
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #31827212C2semidirect
2. #31827211C2semidirect
3. #31827210C2semidirect
4. #31827171C2semidirect
5. #31827169C2semidirect
6. #31827125C2semidirect
7. #31827123C2semidirect
8. #31827117C2semidirect
9. #31827113C2semidirect
10. #31827112C2semidirect
11. #31827108C2semidirect
12. #31827107C2semidirect
13. #31827107C2semidirect
14. #31827104C2semidirect
15. #31827104C2semidirect
16. #31827090C2semidirect
17. #31827090C2semidirect
18. #31827083C2semidirect
19. #31827079C2semidirect
20. #31827063C2semidirect
21. #31827058C2semidirect
22. #31827051C2semidirect
23. #31827049C2semidirect
24. #31827045C2semidirect
25. #31827044C2semidirect
26. #31827044C2semidirect
27. #31827042C2semidirect
28. #31826973C2semidirect
29. C22⋊Q8×D283C2semidirect
30. #121×D283C2semidirect
31. #562×C283C2semidirect
32. C2×#17985393C22semidirect
33. C2×#17985392C22semidirect
34. C2×#17985392C22semidirect
35. C2×#17985392C22semidirect
36. C2×#17985391C22semidirect
37. C2×#17985391C22semidirect
38. C2×#17985391C22semidirect
39. C2×Q8×D283C22semidirect
44. #22583609C22semidirect
45. #22583608C22semidirect
46. #22583605C22semidirect
47. #22583604C22semidirect
48. #22583603C22semidirect
49. #22583603C22semidirect
50. #22583601C22semidirect
51. #22583600C22semidirect
52. #22583600C22semidirect
53. #22583599C22semidirect
54. #22583597C22semidirect
55. #22583596C22semidirect
56. #22583596C22semidirect
57. #22583596C22semidirect
58. #22583596C22semidirect
59. #22583596C22semidirect
60. #22583596C22semidirect
61. #22583595C22semidirect
62. #22583595C22semidirect
63. #22583595C22semidirect
64. #22583595C22semidirect
65. #22583595C22semidirect
66. #22583594C22semidirect
67. #22583593C22semidirect
68. #22583592C22semidirect
69. #22583592C22semidirect
70. #22583592C22semidirect
71. #22583592C22semidirect
72. #22583592C22semidirect
73. #22583591C22semidirect
74. #22583591C22semidirect
77. #22583590C22semidirect
78. #22583590C22semidirect
79. #22583590C22semidirect
80. #22583589C22semidirect
81. #22583589C22semidirect
82. #22583589C22semidirect
88. #22583588C22semidirect
89. #22583588C22semidirect
90. #22583588C22semidirect
91. #22583588C22semidirect
92. #22583588C22semidirect
93. #22583588C22semidirect
94. #22583588C22semidirect
95. #22583587C22semidirect
96. #22583587C22semidirect
97. #22583587C22semidirect
98. #22583587C22semidirect
99. #22583587C22semidirect
100. #22583587C22semidirect
101. #22583587C22semidirect
102. #22583587C22semidirect
105. #22583586C22semidirect
106. #22583586C22semidirect
108. #22583585C22semidirect
109. #22583585C22semidirect
111. #22583584C22semidirect
115. #22583583C22semidirect
116. #22583583C22semidirect
117. #22583583C22semidirect
118. #22583583C22semidirect
119. #22583583C22semidirect
120. #22583583C22semidirect
121. #22583583C22semidirect
122. #22583583C22semidirect
125. #22583582C22semidirect
126. #22583582C22semidirect
127. #22583582C22semidirect
128. #22583582C22semidirect
129. #22583582C22semidirect
131. #22583581C22semidirect
132. #22583581C22semidirect
133. #22583581C22semidirect
134. #22583581C22semidirect
141. C4×Dic566C22semidirect
142. #22583575C22semidirect
144. C4×D1132C22semidirect
147. #22583572C22semidirect
148. #22583572C22semidirect
150. C4×C22⋊D283C22semidirect
151. C4×C22⋊D283C22semidirect
154. (C22⋊D283)⋊C4C22semidirect
155. (C22⋊D283)⋊C4C22semidirect
156. (C22⋊D283)⋊C4C22semidirect
157. #22583566C22semidirect
158. C2×Dic283⋊C4C22semidirect
160. C4⋊C4×D283C22semidirect
161. C4⋊C4×D283C22semidirect
162. C4⋊C4×D283C22semidirect
163. C4⋊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
184. #121×C283C22semidirect
185. #121×C283C22semidirect
186. #121×C283C22semidirect
521. C283#3536semidirect
526. #562D283semidirect
575. #125C2×D283semidirect
584. #124C2×D283semidirect
585. #124C2×D283semidirect
600. #123C2×D283semidirect
601. #123C2×D283semidirect
602. #123C2×D283semidirect
603. #123C2×D283semidirect
636. C22⋊Q8C2×D283semidirect
637. C22⋊Q8C2×D283semidirect
638. C22⋊Q8C2×D283semidirect
639. C22⋊Q8C2×D283semidirect
669. #121C2×D283semidirect
670. #121C2×D283semidirect
671. #121C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318272122
#318272112
#318272102
#318271712
#318271692
#318271252
#318271232
#318271172
#318271132
#318271122
#318271082
#318271072
#318271042
#318270902
#318270832
#318270792
#318270632
#318270582
#318270512
#318270492
#318270452
#318270442
#318270422
#318269732
C22⋊Q8×D2832
#121×D2832
#562×C2832
#3536283