Finite Group Databasebeta

← #44564584

Subgroups — #44564584

Order 32128.

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#30632434C211yesmaximal, characteristic, complemented
2#30632433C211yesmaximal, characteristic, complemented
3#30632432C211yesmaximal, characteristic, complemented
4#30632393C211yesmaximal, characteristic, complemented
5#30632391C211yesmaximal, characteristic, complemented
6#30632347C211yesmaximal, characteristic, complemented
7#30632345C211yesmaximal, characteristic, complemented
8#30632339C211yesmaximal, characteristic, complemented
9#30632335C211yesmaximal, characteristic, complemented
10#30632334C211yesmaximal, characteristic, complemented
11#30632330C211yesmaximal, characteristic, complemented
12#30632329C211yesmaximal, characteristic, complemented
13#30632329C211yesmaximal, characteristic, complemented
14#30632326C211yesmaximal, characteristic, complemented
15#30632326C211yesmaximal, characteristic, complemented
16#30632312C211yesmaximal, characteristic, complemented
17#30632312C211yesmaximal, characteristic, complemented
18#30632305C211yesmaximal, characteristic, complemented
19#30632301C211yesmaximal, characteristic, complemented
20#30632285C211yesmaximal, characteristic, complemented
21#30632280C211yesmaximal, characteristic, complemented
22#30632273C211yesmaximal, characteristic, complemented
23#30632271C211yesmaximal, characteristic, complemented
24#30632267C211yesmaximal, characteristic, complemented
25#30632266C211yesmaximal, characteristic, complemented
26#30632266C211yesmaximal, characteristic, complemented
27#30632264C211yesmaximal, characteristic, complemented
28#30632195C211yesmaximal, characteristic, complemented
29C22⋊Q8×D251C211yesmaximal, characteristic, complemented
30#121×D251C211yesmaximal, characteristic, complemented
31#562×C251C211yesmaximal, characteristic, complemented
32C2×#16860811C2211yescharacteristic, complemented
33C2×#16860810C2211yescharacteristic, complemented
34C2×#16860810C2211yescharacteristic, complemented
35C2×#16860810C2211yescharacteristic, complemented
36C2×#16860809C2211yescharacteristic, complemented
37C2×#16860809C2211yescharacteristic, complemented
38C2×#16860809C2211yescharacteristic, complemented
39C2×Q8×D251C2211yescharacteristic, complemented
40C2×D4×D251C2211yescharacteristic
41C2×D4×D251C2211yescharacteristic
42C2×D4×D251C2211yescharacteristic
43C22×C4×D251C2211yescharacteristic
44#22548714C2211yescharacteristic, complemented
45#22548713C2211yescharacteristic, complemented
46#22548710C2211yescharacteristic, complemented
47#22548709C2211yescharacteristic, complemented
48#22548708C2211yescharacteristic, complemented
49#22548708C2211yescharacteristic, complemented
50#22548706C2211yescharacteristic, complemented
51#22548705C2211yescharacteristic, complemented
52#22548705C2211yescharacteristic, complemented
53#22548704C2211yescharacteristic, complemented
54#22548702C2211yescharacteristic, complemented
55#22548701C2211yescharacteristic, complemented
56#22548701C2211yescharacteristic, complemented
57#22548701C2211yescharacteristic, complemented
58#22548701C2211yescharacteristic, complemented
59#22548701C2211yescharacteristic, complemented
60#22548701C2211yescharacteristic, complemented
61#22548700C2211yescharacteristic, complemented
62#22548700C2211yescharacteristic, complemented
63#22548700C2211yescharacteristic, complemented
64#22548700C2211yescharacteristic, complemented
65#22548700C2211yescharacteristic, complemented
66#22548699C2211yescharacteristic, complemented
67#22548698C2211yescharacteristic, complemented
68#22548697C2211yescharacteristic, complemented
69#22548697C2211yescharacteristic, complemented
70#22548697C2211yescharacteristic, complemented
71#22548697C2211yescharacteristic, complemented
72#22548697C2211yescharacteristic, complemented
73#22548696C2211yescharacteristic, complemented
74#22548696C2211yescharacteristic, complemented
75#22548695C2211yescharacteristic
76#22548695C2211yescharacteristic
77#22548695C2211yescharacteristic, complemented
78#22548695C2211yescharacteristic, complemented
79#22548695C2211yescharacteristic, complemented
80#22548694C2211yescharacteristic, complemented
81#22548694C2211yescharacteristic, complemented
82#22548694C2211yescharacteristic, complemented
83#22548693C2211yescharacteristic
84#22548693C2211yescharacteristic
85#22548693C2211yescharacteristic
86#22548693C2211yescharacteristic
87#22548693C2211yescharacteristic
88#22548693C2211yescharacteristic, complemented
89#22548693C2211yescharacteristic, complemented
90#22548693C2211yescharacteristic, complemented
91#22548693C2211yescharacteristic, complemented
92#22548693C2211yescharacteristic, complemented
93#22548693C2211yescharacteristic, complemented
94#22548693C2211yescharacteristic, complemented
95#22548692C2211yescharacteristic, complemented
96#22548692C2211yescharacteristic, complemented
97#22548692C2211yescharacteristic, complemented
98#22548692C2211yescharacteristic, complemented
99#22548692C2211yescharacteristic, complemented
100#22548692C2211yescharacteristic, complemented
101#22548692C2211yescharacteristic, complemented
102#22548692C2211yescharacteristic, complemented
103#22548691C2211yescharacteristic
104#22548691C2211yescharacteristic
105#22548691C2211yescharacteristic, complemented
106#22548691C2211yescharacteristic, complemented
107#22548690C2211yescharacteristic
108#22548690C2211yescharacteristic, complemented
109#22548690C2211yescharacteristic, complemented
110#22548689C2211yescharacteristic
111#22548689C2211yescharacteristic, complemented
112#22548688C2211yescharacteristic
113#22548688C2211yescharacteristic
114#22548688C2211yescharacteristic
115#22548688C2211yescharacteristic, complemented
116#22548688C2211yescharacteristic, complemented
117#22548688C2211yescharacteristic, complemented
118#22548688C2211yescharacteristic, complemented
119#22548688C2211yescharacteristic, complemented
120#22548688C2211yescharacteristic, complemented
121#22548688C2211yescharacteristic, complemented
122#22548688C2211yescharacteristic, complemented
123#22548687C2211yescharacteristic
124#22548687C2211yescharacteristic
125#22548687C2211yescharacteristic, complemented
126#22548687C2211yescharacteristic, complemented
127#22548687C2211yescharacteristic, complemented
128#22548687C2211yescharacteristic, complemented
129#22548687C2211yescharacteristic, complemented
130#22548686C2211yescharacteristic
131#22548686C2211yescharacteristic, complemented
132#22548686C2211yescharacteristic, complemented
133#22548686C2211yescharacteristic, complemented
134#22548686C2211yescharacteristic, complemented
135#22548685C2211yescharacteristic
136#22548685C2211yescharacteristic
137#22548685C2211yescharacteristic
138#22548683C2211yescharacteristic
139#22548683C2211yescharacteristic
140#22548683C2211yescharacteristic
141C4×Dic502C2211yescharacteristic, complemented
142#22548680C2211yescharacteristic, complemented
143C4×D1004C2211yescharacteristic
144C4×D1004C2211yescharacteristic, complemented
145#22548677C2211yescharacteristic
146#22548677C2211yescharacteristic
147#22548677C2211yescharacteristic, complemented
148#22548677C2211yescharacteristic, complemented
149C4×C22⋊D251C2211yescharacteristic
150C4×C22⋊D251C2211yescharacteristic, complemented
151C4×C22⋊D251C2211yescharacteristic, complemented
152(C22⋊D251)⋊C4C2211yescharacteristic
153(C22⋊D251)⋊C4C2211yescharacteristic
154(C22⋊D251)⋊C4C2211yescharacteristic, complemented
155(C22⋊D251)⋊C4C2211yescharacteristic, complemented
156(C22⋊D251)⋊C4C2211yescharacteristic, complemented
157#22548671C2211yescharacteristic, complemented
158C2×Dic251⋊C4C2211yescharacteristic, complemented
159C4⋊C4×D251C2211yescharacteristic
160C4⋊C4×D251C2211yescharacteristic, complemented
161C4⋊C4×D251C2211yescharacteristic, complemented
162C4⋊C4×D251C2211yescharacteristic, complemented
163C4⋊C4×D251C2211yescharacteristic, complemented
164C2×(C2×D251)⋊C4C2211yescharacteristic
165C2×(C2×D251)⋊C4C2211yescharacteristic
166C22⋊C4×D251C2211yescharacteristic
167C22⋊C4×D251C2211yescharacteristic
168C22⋊C4×D251C2211yescharacteristic
169C22⋊C4×D251C2211yescharacteristic
170C22⋊C4×D251C2211yescharacteristic
171C22⋊C4×D251C2211yescharacteristic
172#125×C251C2211yescharacteristic, complemented
173#124×C251C2211yescharacteristic, complemented
174#124×C251C2211yescharacteristic, complemented
175#123×C251C2211yescharacteristic, complemented
176#123×C251C2211yescharacteristic, complemented
177#123×C251C2211yescharacteristic, complemented
178#123×C251C2211yescharacteristic, complemented
179C22⋊Q8×C251C2211yescharacteristic, complemented
180C22⋊Q8×C251C2211yescharacteristic, complemented
181C22⋊Q8×C251C2211yescharacteristic, complemented
182C22⋊Q8×C251C2211yescharacteristic, complemented
183#121×C251C2211yescharacteristic
184#121×C251C2211yescharacteristic, complemented
185#121×C251C2211yescharacteristic, complemented
186#121×C251C2211yescharacteristic, complemented
187C23×D251C2311yescharacteristic
188C23×D251C2311yescharacteristic
189C23×D251C2311yescharacteristic
190#16860811—42no—
191#16860810—42no—
192#16860810—42no—
193#16860810—42no—
194#16860809—42no—
195#16860809—42no—
196#16860809—42no—
197C2×Dic502C2311yescharacteristic
198C2×Dic502C2311yescharacteristic
199C2×Dic502C2311yescharacteristic
200C2×Dic502C2311yescharacteristic
201C2×Dic502C2311yescharacteristic
202C2×Dic502C2311yescharacteristic
203C2×Dic502C2311yescharacteristic
204Q8×D251—42no—
205C2×D1004C2311yescharacteristic
206C2×D1004C2311yescharacteristic
207C2×D1004C2311yescharacteristic
208C2×D1004C2311yescharacteristic
209C2×D1004C2311yescharacteristic
210C2×D1004C2311yescharacteristic
211C2×D1004C2311yescharacteristic
212C2×C22⋊D251C2311yescharacteristic
213C2×C22⋊D251C2311yescharacteristic
214C2×C22⋊D251C2311yescharacteristic
215C2×C22⋊D251C2311yescharacteristic
216C2×C22⋊D251C2311yescharacteristic
217C2×C22⋊D251C2311yescharacteristic
218C2×C22⋊D251C2311yescharacteristic
219C2×C22⋊D251C2311yescharacteristic
220C2×C22⋊D251C2311yescharacteristic
221C2×C22⋊D251C2311yescharacteristic
222C2×C22⋊D251C2311yescharacteristic
223C2×C22⋊D251C2311yescharacteristic
224C2×C22⋊D251C2311yescharacteristic
225C2×C22⋊D251C2311yescharacteristic
226D4×D251—42no—
227D4×D251—42no—
228D4×D251—42no—
229C22×Dic251C2311yescharacteristic
230C22×Dic251C2311yescharacteristic
231C22×Dic251C2311yescharacteristic
232C22×Dic251C2311yescharacteristic
233C22×Dic251C2311yescharacteristic
234C2×C4×D251—42no—
235C2×C4×D251C2311yescharacteristic
236C2×C4×D251C2311yescharacteristic
237C2×C4×D251C2311yescharacteristic
238C2×C4×D251C2311yescharacteristic
239C2×C4×D251C2311yescharacteristic
240C2×C4×D251C2311yescharacteristic
241C2×C4×D251C2311yescharacteristic
242C2×C4×D251C2311yescharacteristic
243C2×C4×D251C2311yescharacteristic
244C2×C4×D251C2311yescharacteristic
245C2×C4×D251C2311yescharacteristic
246C2×C4×D251C2311yescharacteristic
247C2×C4×D251C2311yescharacteristic
248C2×C4×D251C2311yescharacteristic
249C2×C4×D251C2311yescharacteristic
250C2×C4×D251C2311yescharacteristic
251C2×C4×D251C2311yescharacteristic
252C4⋊Dic251C2311yescharacteristic
253C4⋊Dic251C2311yescharacteristic
254C4⋊Dic251C2311yescharacteristic
255C4⋊Dic251C2311yescharacteristic
256C4⋊Dic251C2311yescharacteristic
257C4⋊Dic251C2311yescharacteristic
258C4⋊Dic251C2311yescharacteristic
259C4⋊Dic251C2311yescharacteristic
260Dic251⋊C4C2311yescharacteristic
261Dic251⋊C4C2311yescharacteristic
262Dic251⋊C4C2311yescharacteristic
263Dic251⋊C4C2311yescharacteristic
264Dic251⋊C4C2311yescharacteristic
265Dic251⋊C4C2311yescharacteristic
266Dic251⋊C4C2311yescharacteristic
267Dic251⋊C4C2311yescharacteristic
268Dic251⋊C4C2311yescharacteristic
269Dic251⋊C4C2311yescharacteristic
270Dic251⋊C4C2311yescharacteristic
271Dic251⋊C4C2311yescharacteristic
272Dic251⋊C4C2311yescharacteristic
273Dic251⋊C4C2311yescharacteristic
274Dic251⋊C4C2311yescharacteristic
275Dic251⋊C4C2311yescharacteristic
276Dic251⋊C4C2311yescharacteristic
277Dic251⋊C4C2311yescharacteristic
278Dic251⋊C4C2311yescharacteristic
279Dic251⋊C4C2311yescharacteristic
280C22⋊Dic251C2311yescharacteristic
281C22⋊Dic251C2311yescharacteristic
282C22⋊Dic251C2311yescharacteristic
283C22⋊Dic251C2311yescharacteristic
284C22⋊Dic251C2311yescharacteristic
285C22⋊Dic251C2311yescharacteristic
286C22⋊Dic251C2311yescharacteristic
287C22⋊Dic251C2311yescharacteristic
288C22⋊Dic251C2311yescharacteristic
289C22⋊Dic251C2311yescharacteristic
290(C2×D251)⋊C4C2311yescharacteristic
291(C2×D251)⋊C4C2311yescharacteristic
292(C2×D251)⋊C4C2311yescharacteristic
293(C2×D251)⋊C4C2311yescharacteristic
294(C2×D251)⋊C4C2311yescharacteristic
295(C2×D251)⋊C4C2311yescharacteristic
296(C2×D251)⋊C4C2311yescharacteristic
297(C2×D251)⋊C4C2311yescharacteristic
298(C2×D251)⋊C4C2311yescharacteristic
299(C2×D251)⋊C4C2311yescharacteristic
300(C2×D251)⋊C4C2311yescharacteristic
301(C2×D251)⋊C4C2311yescharacteristic
302(C2×D251)⋊C4C2311yescharacteristic
303(C2×D251)⋊C4C2311yescharacteristic
304(C2×D251)⋊C4C2311yescharacteristic
305(C2×D251)⋊C4C2311yescharacteristic
306(C2×D251)⋊C4C2311yescharacteristic
307(C2×D251)⋊C4C2311yescharacteristic
308(C2×D251)⋊C4C2311yescharacteristic
309(C2×D251)⋊C4C2311yescharacteristic
310(C2×D251)⋊C4C2311yescharacteristic
311(C2×D251)⋊C4C2311yescharacteristic
312(C2×D251)⋊C4C2311yescharacteristic
313(C2×D251)⋊C4C2311yescharacteristic
314C4×Dic251C2311yescharacteristic
315C4×Dic251C2311yescharacteristic
316C4×Dic251C2311yescharacteristic
317C4×Dic251C2311yescharacteristic
318C4×Dic251C2311yescharacteristic
319C2×Q8×C251C2311yescharacteristic
320C2×Q8×C251C2311yescharacteristic
321C2×D4×C251C2311yescharacteristic
322C2×D4×C251C2311yescharacteristic
323C2×D4×C251C2311yescharacteristic
324C2×D4×C251C2311yescharacteristic
325C2×D4×C251C2311yescharacteristic
326C2×D4×C251C2311yescharacteristic
327C22×C4×C251C2311yescharacteristic
328C22×C4×C251C2311yescharacteristic
329C22×C4×C251C2311yescharacteristic
330C22×C4×C251C2311yescharacteristic
331C4⋊C4×C251C2311yescharacteristic
332C4⋊C4×C251C2311yescharacteristic
333C4⋊C4×C251C2311yescharacteristic
334C4⋊C4×C251C2311yescharacteristic
335C4⋊C4×C251C2311yescharacteristic
336C4⋊C4×C251C2311yescharacteristic
337C4⋊C4×C251C2311yescharacteristic
338C4⋊C4×C251C2311yescharacteristic
339C4⋊C4×C251C2311yescharacteristic
340C4⋊C4×C251C2311yescharacteristic
341C22⋊C4×C251C2311yescharacteristic
342C22⋊C4×C251C2311yescharacteristic
343C22⋊C4×C251C2311yescharacteristic
344C22⋊C4×C251C2311yescharacteristic
345C22⋊C4×C251C2311yescharacteristic
346C22⋊C4×C251C2311yescharacteristic
347C22⋊C4×C251C2311yescharacteristic
348C22⋊C4×C251C2311yescharacteristic
349C22⋊C4×C251C2311yescharacteristic
350C22⋊C4×C251C2311yescharacteristic
351C22⋊C4×C251C2311yescharacteristic
352C22⋊C4×C251C2311yescharacteristic
353C42×C251C2311yescharacteristic
354C22×D251—22no—
355C22×D251—22no—
356C22×D251—22no—
357C22×D251—22no—
358C22×D251—41no—
359C22×D251—41no—
360C22×D251—41no—
361C22×D251—41no—
362C22×D251—41no—
363C22×D251C2411yescharacteristic
364C22×D251C2411yescharacteristic
365C22×D251C2411yescharacteristic
366C22×D251C2411yescharacteristic
367C22×D251C2411yescharacteristic
368Dic502—22no—
369Dic502—22no—
370Dic502—41no—
371Dic502—41no—
372Dic502—41no—
373Dic502—41no—
374Dic502—41no—
375D1004—22no—
376D1004—22no—
377D1004—22no—
378D1004—22no—
379D1004—41no—
380D1004—41no—
381D1004—41no—
382C22⋊D251—22no—
383C22⋊D251—22no—
384C22⋊D251—22no—
385C22⋊D251—22no—
386C22⋊D251—22no—
387C22⋊D251—22no—
388C22⋊D251—41no—
389C22⋊D251—41no—
390C22⋊D251—41no—
391C22⋊D251—41no—
392C22⋊D251—41no—
393C22⋊D251—41no—
394C22⋊D251—41no—
395C22⋊D251—41no—
396C2×Dic251—22no—
397C2×Dic251—22no—
398C2×Dic251—41no—
399C2×Dic251—41no—
400C2×Dic251—41no—
401C2×Dic251C2411yescharacteristic
402C2×Dic251C2411yescharacteristic
403C2×Dic251C2411yescharacteristic
404C2×Dic251C2411yescharacteristic
405C2×Dic251C2411yescharacteristic
406C2×Dic251C2411yescharacteristic
407C2×Dic251C2411yescharacteristic
408C2×Dic251C2411yescharacteristic
409C2×Dic251C2411yescharacteristic
410C2×Dic251C2411yescharacteristic
411C2×Dic251C2411yescharacteristic
412C4×D251—22no—
413C4×D251—22no—
414C4×D251—22no—
415C4×D251—22no—
416C4×D251—22no—
417C4×D251—41no—
418C4×D251—41no—
419C4×D251—41no—
420C4×D251—41no—
421C4×D251—41no—
422C4×D251—41no—
423C4×D251—41no—
424C4×D251—41no—
425C4×D251—41no—
426C4×D251—41no—
427C4×D251—41no—
428C4×D251—41no—
429C23×C251C2411yescharacteristic
430C23×C251C2411yescharacteristic
431C23×C251C2411yescharacteristic
432C23×C251C2411yescharacteristic
433Q8×C251—41no—
434Q8×C251—41no—
435D4×C251—41no—
436D4×C251—41no—
437D4×C251—41no—
438D4×C251—41no—
439D4×C251—41no—
440D4×C251—41no—
441C2×C4×C251—41no—
442C2×C4×C251—41no—
443C2×C4×C251—41no—
444C2×C4×C251—41no—
445C2×C4×C251C2411yescharacteristic
446C2×C4×C251C2411yescharacteristic
447C2×C4×C251C2411yescharacteristic
448C2×C4×C251C2411yescharacteristic
449C2×C4×C251C2411yescharacteristic
450C2×C4×C251C2411yescharacteristic
451C2×C4×C251C2411yescharacteristic
452C2×C4×C251C2411yescharacteristic
453C2×C4×C251C2411yescharacteristic
454C2×C4×C251C2411yescharacteristic
455C2×C4×C251C2411yescharacteristic
456C22×C251—21no—
457C22×C251—21no—
458C22×C251—21no—
459C22×C251—21no—
460C22×C251—21no—
461C22×C251—21no—
462C22×C251—21no—
463C22×C251—21no—
464C22×C251—21no—
465C22×C251—21no—
466C22×C251—21no—
467C22×C251—21no—
468C22×C251C2511yescharacteristic
469C2×D251—21no—
470C2×D251—21no—
471C2×D251—21no—
472C2×D251—21no—
473C2×D251—21no—
474C2×D251—21no—
475C2×D251—21no—
476C2×D251—21no—
477C2×D251—21no—
478C2×D251—21no—
479C2×D251—21no—
480C2×D251—21no—
481C2×D251—21no—
482C2×D251—44no—
483C2×D251—82no—
484C2×D251—82no—
485C2×D251H(5,𝔽2)12yes—
486C2×D2512−1+412yes—
487C4×C251—21no—
488C4×C251—21no—
489C4×C251—21no—
490C4×C251—21no—
491C4×C251—21no—
492C4×C251—21no—
493C4×C251—21no—
494C4×C251—21no—
495C4×C251—21no—
496C4×C251—21no—
497C4×C251—21no—
498Dic251—21no—
499Dic251—21no—
500Dic251—21no—
501Dic251—21no—
502Dic251—21no—
503Dic251—21no—
504Dic251—21no—
505Dic251—21no—
506Dic251—21no—
507Dic251—21no—
508Dic251H(5,𝔽2)12yes—
509C2×C251—41no—
510C2×C251—41no—
511C2×C251—41no—
512C2×C251—41no—
513C2×C251C2×H(5,𝔽2)11yescharacteristic
514C2×C251C2×H(5,𝔽2)11yescharacteristic
515C2×C251C2×2−1+411yescharacteristic
516D251—22no—
517D251—22no—
518D251—41no—
519D251—41no—
520D251—41no—
521C251#353611yescharacteristic, complemented, Sylow
522#3536—2511nomaximal, Sylow
523#562—2511no—
524#562—2511no—
525#562—2511no—
526#562D25111yescharacteristic, complemented
527#554—2511no—
528#554—2511no—
529#548—2511no—
530#548—2511no—
531#547—2511no—
532#547—2511no—
533#546—2511no—
534#546—2511no—
535#546—2511no—
536#546—2511no—
537#546—2511no—
538#546—2511no—
539#543—2511no—
540#543—2511no—
541#542—2511no—
542#542—2511no—
543#539—2511no—
544#539—2511no—
545#538—2511no—
546#538—2511no—
547#537—2511no—
548#537—2511no—
549#537—2511no—
550#537—2511no—
551#525—2511no—
552C2×C22⋊Q8—2511no—
553C2×#121—2511no—
554C2×#41—2511no—
555C2×#41—2511no—
556C2×#41—2511no—
557C2×#41—2511no—
558C2×#41—2511no—
559C2×#41—2511no—
560C2×#41—2511no—
561C22×Q8—2511no—
562C22×D4—2511no—
563C22×D4—2511no—
564C22×D4—2511no—
565C23×C4—2511no—
566C4⋊Q8—2511no—
567C4⋊Q8—2511no—
568#126—2511no—
569#126—2511no—
570#126—2511no—
571#126—2511no—
572#125—2511no—
573#125—2511no—
574#125—2511no—
575#125C2×D25111yescharacteristic, complemented
576#124—2511no—
577#124—2511no—
578#124—2511no—
579#124—2511no—
580#124—2511no—
581#124—2511no—
582#124—2511no—
583#124—2511no—
584#124C2×D25111yescharacteristic, complemented
585#124C2×D25111yescharacteristic, complemented
586#123—2511no—
587#123—2511no—
588#123—2511no—
589#123—2511no—
590#123—2511no—
591#123—2511no—
592#123—2511no—
593#123—2511no—
594#123—2511no—
595#123—2511no—
596#123—2511no—
597#123—2511no—
598#123—2511no—
599#123—2511no—
600#123C2×D25111yescharacteristic, complemented
601#123C2×D25111yescharacteristic, complemented
602#123C2×D25111yescharacteristic, complemented
603#123C2×D25111yescharacteristic, complemented
604C22⋊Q8—2511no—
605C22⋊Q8—2511no—
606C22⋊Q8—2511no—
607C22⋊Q8—2511no—
608C22⋊Q8—2511no—
609C22⋊Q8—2511no—
610C22⋊Q8—2511no—
611C22⋊Q8—2511no—
612C22⋊Q8—2511no—
613C22⋊Q8—2511no—
614C22⋊Q8—2511no—
615C22⋊Q8—2511no—
616C22⋊Q8—2511no—
617C22⋊Q8—2511no—
618C22⋊Q8—2511no—
619C22⋊Q8—2511no—
620C22⋊Q8—2511no—
621C22⋊Q8—2511no—
622C22⋊Q8—2511no—
623C22⋊Q8—2511no—
624C22⋊Q8—2511no—
625C22⋊Q8—2511no—
626C22⋊Q8—2511no—
627C22⋊Q8—2511no—
628C22⋊Q8—2511no—
629C22⋊Q8—2511no—
630C22⋊Q8—2511no—
631C22⋊Q8—2511no—
632C22⋊Q8—2511no—
633C22⋊Q8—2511no—
634C22⋊Q8—2511no—
635C22⋊Q8—2511no—
636C22⋊Q8C2×D25111yescharacteristic, complemented
637C22⋊Q8C2×D25111yescharacteristic, complemented
638C22⋊Q8C2×D25111yescharacteristic, complemented
639C22⋊Q8C2×D25111yescharacteristic, complemented
640#121—2511no—
641#121—2511no—
642#121—2511no—
643#121—2511no—
644#121—2511no—
645#121—2511no—
646#121—2511no—
647#121—2511no—
648#121—2511no—
649#121—2511no—
650#121—2511no—
651#121—2511no—
652#121—2511no—
653#121—2511no—
654#121—2511no—
655#121—2511no—
656#121—2511no—
657#121—2511no—
658#121—2511no—
659#121—2511no—
660#121—2511no—
661#121—2511no—
662#121—2511no—
663#121—2511no—
664#121—2511no—
665#121—2511no—
666#121—2511no—
667#121—2511no—
668#121C2×D25111yescharacteristic
669#121C2×D25111yescharacteristic, complemented
670#121C2×D25111yescharacteristic, complemented
671#121C2×D25111yescharacteristic, complemented
672#120—2511no—
673#120—2511no—
674#120—2511no—
675#120—2511no—
676#120—2511no—
677#120—2511no—
678C4×Q8—2511no—
679C4×Q8—2511no—
680C4×D4—2511no—
681C4×D4—2511no—
682C4×D4—2511no—
683C4×D4—2511no—
684C4×D4—2511no—
685C4×D4—2511no—
686C4×D4—2511no—
687C4×D4—2511no—
688C4×D4—2511no—
689C4×D4—2511no—
690C4×D4—2511no—
691C4×D4—2511no—
692C4×D4—2511no—
693C4×D4—2511no—
694#117—2511no—
695C2×C4⋊C4—2511no—
696C2×C4⋊C4—2511no—
697C2×C4⋊C4—2511no—
698C2×C4⋊C4—2511no—
699C2×C4⋊C4—2511no—
700C2×C4⋊C4—2511no—
701C2×C22⋊C4—2511no—
702C2×C22⋊C4—2511no—
703C2×C22⋊C4—2511no—
704C2×C22⋊C4—2511no—
705C2×C22⋊C4—2511no—
706C2×C22⋊C4—2511no—
707C2×C22⋊C4—2511no—
708C2×C22⋊C4—2511no—
709C24—2511no—
710C24—2511no—
711C24—2511no—
712#41—10042no—
713#41—10042no—
714#41—10042no—
715#41—10042no—
716#41—10042no—
717#41—10042no—
718#41—10042no—
719C2×Q8—10042no—
720C2×Q8—2511no—
721C2×Q8—2511no—
722C2×Q8—2511no—
723C2×Q8—2511no—
724C2×Q8—2511no—
725C2×Q8—2511no—
726C2×Q8—2511no—
727C2×Q8C22×D25111yescharacteristic
728C2×Q8C22×D25111yescharacteristic
729C2×D4—10042no—
730C2×D4—10042no—
731C2×D4—10042no—
732C2×D4—2511no—
733C2×D4—2511no—
734C2×D4—2511no—
735C2×D4—2511no—
736C2×D4—2511no—
737C2×D4—2511no—
738C2×D4—2511no—
739C2×D4—2511no—
740C2×D4—2511no—
741C2×D4—2511no—
742C2×D4—2511no—
743C2×D4—2511no—
744C2×D4—2511no—
745C2×D4—2511no—
746C2×D4—2511no—
747C2×D4—2511no—
748C2×D4—2511no—
749C2×D4—2511no—
750C2×D4—2511no—
751C2×D4—2511no—
752C2×D4—2511no—
753C2×D4C22×D25111yescharacteristic
754C2×D4C22×D25111yescharacteristic
755C2×D4C22×D25111yescharacteristic
756C2×D4C22×D25111yescharacteristic
757C2×D4C22×D25111yescharacteristic
758C2×D4C22×D25111yescharacteristic
759C22×C4—10042no—
760C22×C4—2511no—
761C22×C4—2511no—
762C22×C4—2511no—
763C22×C4—2511no—
764C22×C4—2511no—
765C22×C4—2511no—
766C22×C4—2511no—
767C22×C4—2511no—
768C22×C4—2511no—
769C22×C4—2511no—
770C22×C4—2511no—
771C22×C4—2511no—
772C22×C4—2511no—
773C22×C4—2511no—
774C22×C4—2511no—
775C22×C4—2511no—
776C22×C4—2511no—
777C22×C4—2511no—
778C22×C4—2511no—
779C22×C4—2511no—
780C22×C4—2511no—
781C22×C4—2511no—
782C22×C4C22×D25111yescharacteristic
783C22×C4C22×D25111yescharacteristic
784C22×C4C22×D25111yescharacteristic
785C22×C4C22×D25111yescharacteristic
786C4⋊C4—2511no—
787C4⋊C4—2511no—
788C4⋊C4—2511no—
789C4⋊C4—2511no—
790C4⋊C4—2511no—
791C4⋊C4—2511no—
792C4⋊C4—2511no—
793C4⋊C4—2511no—
794C4⋊C4—2511no—
795C4⋊C4—2511no—
796C4⋊C4—2511no—
797C4⋊C4—2511no—
798C4⋊C4—2511no—
799C4⋊C4—2511no—
800C4⋊C4—2511no—
801C4⋊C4—2511no—
802C4⋊C4—2511no—
803C4⋊C4—2511no—
804C4⋊C4—2511no—
805C4⋊C4—2511no—
806C4⋊C4—2511no—
807C4⋊C4—2511no—
808C4⋊C4—2511no—
809C4⋊C4—2511no—
810C4⋊C4—2511no—
811C4⋊C4—2511no—
812C4⋊C4—2511no—
813C4⋊C4—2511no—
814C4⋊C4C22×D25111yescharacteristic
815C4⋊C4C22×D25111yescharacteristic
816C4⋊C4C22×D25111yescharacteristic
817C4⋊C4C22×D25111yescharacteristic
818C4⋊C4C22×D25111yescharacteristic
819C4⋊C4C22×D25111yescharacteristic
820C4⋊C4C22×D25111yescharacteristic
821C4⋊C4C22×D25111yescharacteristic
822C4⋊C4C22×D25111yescharacteristic
823C4⋊C4C22×D25111yescharacteristic
824C22⋊C4—2511no—
825C22⋊C4—2511no—
826C22⋊C4—2511no—
827C22⋊C4—2511no—
828C22⋊C4—2511no—
829C22⋊C4—2511no—
830C22⋊C4—2511no—
831C22⋊C4—2511no—
832C22⋊C4—2511no—
833C22⋊C4—2511no—
834C22⋊C4—2511no—
835C22⋊C4—2511no—
836C22⋊C4—2511no—
837C22⋊C4—2511no—
838C22⋊C4—2511no—
839C22⋊C4—2511no—
840C22⋊C4—2511no—
841C22⋊C4—2511no—
842C22⋊C4—2511no—
843C22⋊C4—2511no—
844C22⋊C4—2511no—
845C22⋊C4—2511no—
846C22⋊C4—2511no—
847C22⋊C4—2511no—
848C22⋊C4—2511no—
849C22⋊C4—2511no—
850C22⋊C4—2511no—
851C22⋊C4—2511no—
852C22⋊C4—2511no—
853C22⋊C4—2511no—
854C22⋊C4—2511no—
855C22⋊C4—2511no—
856C22⋊C4—2511no—
857C22⋊C4—2511no—
858C22⋊C4C22×D25111yescharacteristic
859C22⋊C4C22×D25111yescharacteristic
860C22⋊C4C22×D25111yescharacteristic
861C22⋊C4C22×D25111yescharacteristic
862C22⋊C4C22×D25111yescharacteristic
863C22⋊C4C22×D25111yescharacteristic
864C22⋊C4C22×D25111yescharacteristic
865C22⋊C4C22×D25111yescharacteristic
866C22⋊C4C22×D25111yescharacteristic
867C22⋊C4C22×D25111yescharacteristic
868C22⋊C4C22×D25111yescharacteristic
869C22⋊C4C22×D25111yescharacteristic
870C42—2511no—
871C42—2511no—
872C42—2511no—
873C42—2511no—
874C42—2511no—
875C42C22×D25111yescharacteristic
876C23—10041no—
877C23—10041no—
878C23—10041no—
879C23—10041no—
880C23—10041no—
881C23—5022no—
882C23—5022no—
883C23—5022no—
884C23—5022no—
885C23—2511no—
886C23—2511no—
887C23—2511no—
888C23—2511no—
889C23—2511no—
890C23C23×D25111yescharacteristic
891C23C23×D25111yescharacteristic
892C23C23×D25111yescharacteristic
893C23C23×D25111yescharacteristic
894Q8—41no—
895Q8—41no—
896Q8—10041no—
897Q8—10041no—
898Q8—10041no—
899Q8—10041no—
900Q8—10041no—
901Q8—5022no—
902Q8—5022no—
903D4—41no—
904D4—41no—
905D4—41no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—10041no—
910D4—10041no—
911D4—10041no—
912D4—10041no—
913D4—10041no—
914D4—10041no—
915D4—10041no—
916D4—10041no—
917D4—10041no—
918D4—10041no—
919D4—10041no—
920D4—5022no—
921D4—5022no—
922D4—5022no—
923D4—5022no—
924D4—5022no—
925D4—5022no—
926D4—5022no—
927D4—5022no—
928D4—5022no—
929D4—5022no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—10041no—
935C2×C4—10041no—
936C2×C4—10041no—
937C2×C4—10041no—
938C2×C4—10041no—
939C2×C4—10041no—
940C2×C4—10041no—
941C2×C4—10041no—
942C2×C4—10041no—
943C2×C4—10041no—
944C2×C4—10041no—
945C2×C4—10041no—
946C2×C4—10041no—
947C2×C4—10041no—
948C2×C4—10041no—
949C2×C4—5022no—
950C2×C4—5022no—
951C2×C4—5022no—
952C2×C4—5022no—
953C2×C4—5022no—
954C2×C4—5022no—
955C2×C4—5022no—
956C2×C4—2511no—
957C2×C4—2511no—
958C2×C4—2511no—
959C2×C4—2511no—
960C2×C4—2511no—
961C2×C4—2511no—
962C2×C4—2511no—
963C2×C4—2511no—
964C2×C4—2511no—
965C2×C4—2511no—
966C2×C4—2511no—
967C2×C4C23×D25111yescharacteristic
968C2×C4C23×D25111yescharacteristic
969C2×C4C23×D25111yescharacteristic
970C2×C4C23×D25111yescharacteristic
971C2×C4C23×D25111yescharacteristic
972C2×C4C23×D25111yescharacteristic
973C2×C4C23×D25111yescharacteristic
974C2×C4C23×D25111yescharacteristic
975C2×C4C23×D25111yescharacteristic
976C2×C4C23×D25111yescharacteristic
977C2×C4C23×D25111yescharacteristic
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—20082no—
991C22—20082no—
992C22—10044no—
993C22—5021no—
994C22—5021no—
995C22—5021no—
996C22—5021no—
997C22—5021no—
998C22—5021no—
999C22—5021no—
1000C22—5021no—
1001C22—5021no—
1002C22—5021no—
1003C22—5021no—
1004C22—5021no—
1005C22—5021no—
1006C22—2512no—
1007C22—2512no—
1008C22C24×D25111yescharacteristic
1009C4—21no—
1010C4—21no—
1011C4—21no—
1012C4—21no—
1013C4—21no—
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—5021no—
1021C4—5021no—
1022C4—5021no—
1023C4—5021no—
1024C4—5021no—
1025C4—5021no—
1026C4—5021no—
1027C4—5021no—
1028C4—5021no—
1029C4—5021no—
1030C4—2512no—
1031C2—41no—
1032C2—41no—
1033C2—41no—
1034C2—41no—
1035C2—10041no—
1036C2—10041no—
1037C2—10041no—
1038C2—5022no—
1039C2—5022no—
1040C2H(5,𝔽2)×D25111yescharacteristic
1041C2H(5,𝔽2)×D25111yescharacteristic
1042C22−1+4×D25111yescharacteristic
subgroupG/H
center, FrattiniC22C24×D251
commutator, socle, cosocleC22×C251C25
Fitting#562×C251C2
hypercenter#562D251
hypocenterC251#3536
LCSG ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #30632434C2semidirect
2. #30632433C2semidirect
3. #30632432C2semidirect
4. #30632393C2semidirect
5. #30632391C2semidirect
6. #30632347C2semidirect
7. #30632345C2semidirect
8. #30632339C2semidirect
9. #30632335C2semidirect
10. #30632334C2semidirect
11. #30632330C2semidirect
12. #30632329C2semidirect
13. #30632329C2semidirect
14. #30632326C2semidirect
15. #30632326C2semidirect
16. #30632312C2semidirect
17. #30632312C2semidirect
18. #30632305C2semidirect
19. #30632301C2semidirect
20. #30632285C2semidirect
21. #30632280C2semidirect
22. #30632273C2semidirect
23. #30632271C2semidirect
24. #30632267C2semidirect
25. #30632266C2semidirect
26. #30632266C2semidirect
27. #30632264C2semidirect
28. #30632195C2semidirect
29. C22⋊Q8×D251C2semidirect
30. #121×D251C2semidirect
31. #562×C251C2semidirect
32. C2×#16860811C22semidirect
33. C2×#16860810C22semidirect
34. C2×#16860810C22semidirect
35. C2×#16860810C22semidirect
36. C2×#16860809C22semidirect
37. C2×#16860809C22semidirect
38. C2×#16860809C22semidirect
39. C2×Q8×D251C22semidirect
44. #22548714C22semidirect
45. #22548713C22semidirect
46. #22548710C22semidirect
47. #22548709C22semidirect
48. #22548708C22semidirect
49. #22548708C22semidirect
50. #22548706C22semidirect
51. #22548705C22semidirect
52. #22548705C22semidirect
53. #22548704C22semidirect
54. #22548702C22semidirect
55. #22548701C22semidirect
56. #22548701C22semidirect
57. #22548701C22semidirect
58. #22548701C22semidirect
59. #22548701C22semidirect
60. #22548701C22semidirect
61. #22548700C22semidirect
62. #22548700C22semidirect
63. #22548700C22semidirect
64. #22548700C22semidirect
65. #22548700C22semidirect
66. #22548699C22semidirect
67. #22548698C22semidirect
68. #22548697C22semidirect
69. #22548697C22semidirect
70. #22548697C22semidirect
71. #22548697C22semidirect
72. #22548697C22semidirect
73. #22548696C22semidirect
74. #22548696C22semidirect
77. #22548695C22semidirect
78. #22548695C22semidirect
79. #22548695C22semidirect
80. #22548694C22semidirect
81. #22548694C22semidirect
82. #22548694C22semidirect
88. #22548693C22semidirect
89. #22548693C22semidirect
90. #22548693C22semidirect
91. #22548693C22semidirect
92. #22548693C22semidirect
93. #22548693C22semidirect
94. #22548693C22semidirect
95. #22548692C22semidirect
96. #22548692C22semidirect
97. #22548692C22semidirect
98. #22548692C22semidirect
99. #22548692C22semidirect
100. #22548692C22semidirect
101. #22548692C22semidirect
102. #22548692C22semidirect
105. #22548691C22semidirect
106. #22548691C22semidirect
108. #22548690C22semidirect
109. #22548690C22semidirect
111. #22548689C22semidirect
115. #22548688C22semidirect
116. #22548688C22semidirect
117. #22548688C22semidirect
118. #22548688C22semidirect
119. #22548688C22semidirect
120. #22548688C22semidirect
121. #22548688C22semidirect
122. #22548688C22semidirect
125. #22548687C22semidirect
126. #22548687C22semidirect
127. #22548687C22semidirect
128. #22548687C22semidirect
129. #22548687C22semidirect
131. #22548686C22semidirect
132. #22548686C22semidirect
133. #22548686C22semidirect
134. #22548686C22semidirect
141. C4×Dic502C22semidirect
142. #22548680C22semidirect
144. C4×D1004C22semidirect
147. #22548677C22semidirect
148. #22548677C22semidirect
150. C4×C22⋊D251C22semidirect
151. C4×C22⋊D251C22semidirect
154. (C22⋊D251)⋊C4C22semidirect
155. (C22⋊D251)⋊C4C22semidirect
156. (C22⋊D251)⋊C4C22semidirect
157. #22548671C22semidirect
158. C2×Dic251⋊C4C22semidirect
160. C4⋊C4×D251C22semidirect
161. C4⋊C4×D251C22semidirect
162. C4⋊C4×D251C22semidirect
163. C4⋊C4×D251C22semidirect
172. #125×C251C22semidirect
173. #124×C251C22semidirect
174. #124×C251C22semidirect
175. #123×C251C22semidirect
176. #123×C251C22semidirect
177. #123×C251C22semidirect
178. #123×C251C22semidirect
179. C22⋊Q8×C251C22semidirect
180. C22⋊Q8×C251C22semidirect
181. C22⋊Q8×C251C22semidirect
182. C22⋊Q8×C251C22semidirect
184. #121×C251C22semidirect
185. #121×C251C22semidirect
186. #121×C251C22semidirect
521. C251#3536semidirect
526. #562D251semidirect
575. #125C2×D251semidirect
584. #124C2×D251semidirect
585. #124C2×D251semidirect
600. #123C2×D251semidirect
601. #123C2×D251semidirect
602. #123C2×D251semidirect
603. #123C2×D251semidirect
636. C22⋊Q8C2×D251semidirect
637. C22⋊Q8C2×D251semidirect
638. C22⋊Q8C2×D251semidirect
639. C22⋊Q8C2×D251semidirect
669. #121C2×D251semidirect
670. #121C2×D251semidirect
671. #121C2×D251semidirect

Maximal subgroups

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

subgroupindex
#306324342
#306324332
#306324322
#306323932
#306323912
#306323472
#306323452
#306323392
#306323352
#306323342
#306323302
#306323292
#306323262
#306323122
#306323052
#306323012
#306322852
#306322802
#306322732
#306322712
#306322672
#306322662
#306322642
#306321952
C22⋊Q8×D2512
#121×D2512
#562×C2512
#3536251