Finite Group Databasebeta

← #27604212

Subgroups — #27604212

Order 13568.

1466 conjugacy classes of subgroups.

The subgroup lattice has 1274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283053C211yesmaximal, characteristic
2#20283022C211yesmaximal, characteristic
3#20282705C211yesmaximal, characteristic, complemented
4#20282698C211yesmaximal, characteristic, complemented
5#20282672C211yesmaximal, characteristic, complemented
6#20282663C211yesmaximal, characteristic, complemented
7#20282471C211yesmaximal, characteristic, complemented
8#20282470C211yesmaximal, characteristic, complemented
9#20282453C211yesmaximal, characteristic
10#20282441C211yesmaximal, characteristic
11#20281885C211yesmaximal, characteristic
12#20281877C211yesmaximal, characteristic
13#20281874C211yesmaximal, characteristic
14#20281866C211yesmaximal, characteristic
15#20281749C211yesmaximal, characteristic, complemented
16#20281704C211yesmaximal, characteristic
17#20281692C211yesmaximal, characteristic
18#20280813C211yesmaximal, characteristic, complemented
19#20280805C211yesmaximal, characteristic, complemented
20#20279554C211yesmaximal, characteristic
21#20279550C211yesmaximal, characteristic
22#20279522C211yesmaximal, characteristic, complemented
23#20279510C211yesmaximal, characteristic, complemented
24#20278735C211yesmaximal, characteristic
25#20278731C211yesmaximal, characteristic
26#20278702C211yesmaximal, characteristic, complemented
27#20278690C211yesmaximal, characteristic, complemented
28#20277433C211yesmaximal, characteristic, complemented
29#20277430C211yesmaximal, characteristic, complemented
30#20277249C211yesmaximal, characteristic
31C53×#2805C211yesmaximal, characteristic, complemented
32C2×#13133216C2211yescharacteristic
33C2×#13133215C2211yescharacteristic
34C2×#13133207C2211yescharacteristic
35C2×#13133197C2211yescharacteristic
36C2×#13133195C2211yescharacteristic
37C2×Q8×Dic53C2211yescharacteristic
38C2×C4×Dic106C2211yescharacteristic
39C2×#13133182C2211yescharacteristic
40C2×C42×D53C2211yescharacteristic
41C53⋊#401C2211yescharacteristic
42C53⋊#401C2211yescharacteristic
43C53⋊#401C2211yescharacteristic
44C53⋊#401C2211yescharacteristic
45#16810565C2211yescharacteristic
46#16810565C2211yescharacteristic
47#16810564C2211yescharacteristic
48#16810564C2211yescharacteristic
49#16810564C2211yescharacteristic
50#16810564C2211yescharacteristic
51#16810564C2211yescharacteristic
52#16810563C2211yescharacteristic
53#16810563C2211yescharacteristic
54#16810562C2211yescharacteristic
55#16810562C2211yescharacteristic
56#16810561C2211yescharacteristic
57#16810557C2211yescharacteristic
58#16810557C2211yescharacteristic
59#16810557C2211yescharacteristic
60#16810557C2211yescharacteristic
61#16810556C2211yescharacteristic
62#16810556C2211yescharacteristic
63#16810556C2211yescharacteristic
64#16810556C2211yescharacteristic
65#16810554C2211yescharacteristic
66#16810554C2211yescharacteristic
67#16810554C2211yescharacteristic
68#16810553C2211yescharacteristic
69#16810552C2211yescharacteristic
70#16810552C2211yescharacteristic
71#16810549C2211yescharacteristic
72#16810549C2211yescharacteristic
73#16810547C2211yescharacteristic
74#16810545C2211yescharacteristic
75#16810544C2211yescharacteristic
76#16810543C2211yescharacteristic
77#16810543C2211yescharacteristic
78#16810543C2211yescharacteristic
79#16810543C2211yescharacteristic
80#16810542C2211yescharacteristic
81#16810536C2211yescharacteristic
82#16810534C2211yescharacteristic
83#16810529C2211yescharacteristic
84#16810529C2211yescharacteristic
85#16810528C2211yescharacteristic
86#16810527C2211yescharacteristic
87#16810527C2211yescharacteristic
88#16810527C2211yescharacteristic
89#16810527C2211yescharacteristic
90#16810527C2211yescharacteristic
91#16810522C2211yescharacteristic
92#16810520C2211yescharacteristic
93#16810520C2211yescharacteristic
94#16810520C2211yescharacteristic
95#16810519C2211yescharacteristic
96#16810519C2211yescharacteristic
97#16810518C2211yescharacteristic
98#16810518C2211yescharacteristic
99#16810518C2211yescharacteristic
100#16810515C2211yescharacteristic
101#16810515C2211yescharacteristic
102#16810514C2211yescharacteristic
103#16810514C2211yescharacteristic
104#16810513C2211yescharacteristic
105#16810513C2211yescharacteristic
106#16810512C2211yescharacteristic
107#16810512C2211yescharacteristic
108#16810510C2211yescharacteristic
109#16810510C2211yescharacteristic
110#16810510C2211yescharacteristic
111#16810510C2211yescharacteristic
112#16810510C2211yescharacteristic
113#16810509C2211yescharacteristic
114#16810509C2211yescharacteristic
115#16810509C2211yescharacteristic
116#16810509C2211yescharacteristic
117#16810508C2211yescharacteristic
118#16810508C2211yescharacteristic
119#16810508C2211yescharacteristic
120#16810508C2211yescharacteristic
121#16810507C2211yescharacteristic
122#16810507C2211yescharacteristic
123#16810507C2211yescharacteristic
124#16810507C2211yescharacteristic
125#16810507C2211yescharacteristic
126#16810506C2211yescharacteristic
127#16810506C2211yescharacteristic
128#16810506C2211yescharacteristic
129#16810506C2211yescharacteristic
130#16810506C2211yescharacteristic
131#16810506C2211yescharacteristic
132#16810505C2211yescharacteristic
133#16810505C2211yescharacteristic
134#16810505C2211yescharacteristic
135#16810505C2211yescharacteristic
136#16810505C2211yescharacteristic
137#16810505C2211yescharacteristic
138#16810505C2211yescharacteristic
139#16810505C2211yescharacteristic
140#16810504C2211yescharacteristic
141#16810504C2211yescharacteristic
142#16810504C2211yescharacteristic
143#16810504C2211yescharacteristic
144#16810504C2211yescharacteristic
145#16810504C2211yescharacteristic
146#16810504C2211yescharacteristic
147#16810504C2211yescharacteristic
148#16810497C2211yescharacteristic
149#16810497C2211yescharacteristic
150#16810497C2211yescharacteristic
151#16810494C2211yescharacteristic
152#16810494C2211yescharacteristic
153#16810494C2211yescharacteristic
154#16810494C2211yescharacteristic
155#16810494C2211yescharacteristic
156#16810488C2211yescharacteristic
157#16810487C2211yescharacteristic
158#16810487C2211yescharacteristic
159#16810485C2211yescharacteristic
160#16810485C2211yescharacteristic
161#16810482C2211yescharacteristic
162#16810482C2211yescharacteristic
163#16810482C2211yescharacteristic
164#16810480C2211yescharacteristic
165C4⋊C4×Dic53C2211yescharacteristic
166#16810474C2211yescharacteristic
167#16810474C2211yescharacteristic
168#16810470C2211yescharacteristic
169#16810470C2211yescharacteristic
170#16810469C2211yescharacteristic
171#16810468C2211yescharacteristic
172C53×#400C2211yescharacteristic
173C53×#400C2211yescharacteristic
174C53×#400C2211yescharacteristic
175C53×#400C2211yescharacteristic
176C53×#395C2211yescharacteristic
177C53×#395C2211yescharacteristic
178C53×#391C2211yescharacteristic
179C53×#389C2211yescharacteristic
180C53×#389C2211yescharacteristic
181C53×#389C2211yescharacteristic
182C53×#389C2211yescharacteristic
183C53×#387C2211yescharacteristic
184C53×#387C2211yescharacteristic
185C53×#387C2211yescharacteristic
186C53×#387C2211yescharacteristic
187C22×Dic106C2311yescharacteristic
188C22×Dic106C2311yescharacteristic
189C22×Dic106C2311yescharacteristic
190C22×C4×D53C2311yescharacteristic
191C22×C4×D53C2311yescharacteristic
192C22×C4×D53C2311yescharacteristic
193#13133216—24no—
194#13133215—24no—
195#13133207—42no—
196#13133197—42no—
197#13133195—24no—
198Q8×Dic53—42no—
199C4×Dic106—42no—
200#13133182—42no—
201C2×C4⋊Dic53C2311yescharacteristic
202C2×C4⋊Dic53C2311yescharacteristic
203C2×C4⋊Dic53C2311yescharacteristic
204C2×C4⋊Dic53C2311yescharacteristic
205C2×C4⋊Dic53C2311yescharacteristic
206C2×C4⋊Dic53C2311yescharacteristic
207C2×C4⋊Dic53C2311yescharacteristic
208C2×C4⋊Dic53C2311yescharacteristic
209C2×C4⋊Dic53C2311yescharacteristic
210C2×#11719919C2311yescharacteristic
211C2×#11719919C2311yescharacteristic
212C2×#11719919C2311yescharacteristic
213C2×#11719919C2311yescharacteristic
214C2×#11719919C2311yescharacteristic
215C2×#11719919C2311yescharacteristic
216C2×#11719919C2311yescharacteristic
217C2×#11719919C2311yescharacteristic
218C2×#11719919C2311yescharacteristic
219C2×#11719919C2311yescharacteristic
220C2×#11719919C2311yescharacteristic
221C2×#11719919C2311yescharacteristic
222C2×#11719919C2311yescharacteristic
223C2×#11719919C2311yescharacteristic
224C2×#11719919C2311yescharacteristic
225C2×#11719919C2311yescharacteristic
226C2×#11719919C2311yescharacteristic
227C2×#11719919C2311yescharacteristic
228C2×#11719919C2311yescharacteristic
229C2×#11719919C2311yescharacteristic
230C2×#11719919C2311yescharacteristic
231C2×#11719919C2311yescharacteristic
232C2×#11719919C2311yescharacteristic
233C2×#11719919C2311yescharacteristic
234C2×#11719919C2311yescharacteristic
235C2×#11719919C2311yescharacteristic
236C2×#11719921C2311yescharacteristic
237C2×#11719921C2311yescharacteristic
238C2×#11719921C2311yescharacteristic
239C2×#11719921C2311yescharacteristic
240C2×#11719921C2311yescharacteristic
241C2×#11719921C2311yescharacteristic
242C2×#11719921C2311yescharacteristic
243C2×#11719921C2311yescharacteristic
244C2×#11719921C2311yescharacteristic
245C2×#11719921C2311yescharacteristic
246C2×#11719921C2311yescharacteristic
247C2×#11719921C2311yescharacteristic
248C2×C4×Dic53C2311yescharacteristic
249C2×C4×Dic53C2311yescharacteristic
250C2×C4×Dic53C2311yescharacteristic
251C2×C4×Dic53C2311yescharacteristic
252C2×C4×Dic53C2311yescharacteristic
253C2×C4×Dic53C2311yescharacteristic
254C2×C4×Dic53C2311yescharacteristic
255C2×C4×Dic53C2311yescharacteristic
256C2×C4×Dic53C2311yescharacteristic
257C2×C4×Dic53C2311yescharacteristic
258C2×C4×Dic53C2311yescharacteristic
259C2×C4×Dic53C2311yescharacteristic
260C2×C4×Dic53C2311yescharacteristic
261C42×D53—42no—
262#13133124C2311yescharacteristic
263#13133124C2311yescharacteristic
264#13133124C2311yescharacteristic
265#13133124C2311yescharacteristic
266#13133124C2311yescharacteristic
267#13133124C2311yescharacteristic
268#13133124C2311yescharacteristic
269#13133124C2311yescharacteristic
270#13133124C2311yescharacteristic
271#13133124C2311yescharacteristic
272#13133124C2311yescharacteristic
273#13133124C2311yescharacteristic
274#13133124C2311yescharacteristic
275#13133124C2311yescharacteristic
276#13133124C2311yescharacteristic
277#13133124C2311yescharacteristic
278#13133124C2311yescharacteristic
279#13133124C2311yescharacteristic
280#13133124C2311yescharacteristic
281#13133124C2311yescharacteristic
282#13133124C2311yescharacteristic
283#13133124C2311yescharacteristic
284#13133124C2311yescharacteristic
285#13133124C2311yescharacteristic
286#13133124C2311yescharacteristic
287#13133124C2311yescharacteristic
288#13133124C2311yescharacteristic
289#13133124C2311yescharacteristic
290#13133124C2311yescharacteristic
291#13133124C2311yescharacteristic
292#13133124C2311yescharacteristic
293#13133124C2311yescharacteristic
294#13133124C2311yescharacteristic
295#13133124C2311yescharacteristic
296#13133124C2311yescharacteristic
297#13133124C2311yescharacteristic
298#13133124C2311yescharacteristic
299#13133124C2311yescharacteristic
300#13133124C2311yescharacteristic
301#13133124C2311yescharacteristic
302#13133124C2311yescharacteristic
303#13133124C2311yescharacteristic
304#13133124C2311yescharacteristic
305#13133124C2311yescharacteristic
306#13133124C2311yescharacteristic
307#13133124C2311yescharacteristic
308#13133124C2311yescharacteristic
309#13133124C2311yescharacteristic
310#13133124C2311yescharacteristic
311#13133124C2311yescharacteristic
312#13133124C2311yescharacteristic
313#13133124C2311yescharacteristic
314#13133124C2311yescharacteristic
315#13133124C2311yescharacteristic
316C22×Q8×C53C2311yescharacteristic
317C2×C4⋊C4×C53C2311yescharacteristic
318C2×C4⋊C4×C53C2311yescharacteristic
319C2×C4⋊C4×C53C2311yescharacteristic
320C2×C4⋊C4×C53C2311yescharacteristic
321C2×C4⋊C4×C53C2311yescharacteristic
322C2×C4⋊C4×C53C2311yescharacteristic
323C2×C4⋊C4×C53C2311yescharacteristic
324C2×C4⋊C4×C53C2311yescharacteristic
325C2×C4⋊C4×C53C2311yescharacteristic
326C2×C4⋊C4×C53C2311yescharacteristic
327C2×C4⋊C4×C53C2311yescharacteristic
328C2×C4⋊C4×C53C2311yescharacteristic
329C2×C4⋊C4×C53C2311yescharacteristic
330C2×C42×C53C2311yescharacteristic
331C2×C42×C53C2311yescharacteristic
332C2×C42×C53C2311yescharacteristic
333#95×C53C2311yescharacteristic
334#95×C53C2311yescharacteristic
335#95×C53C2311yescharacteristic
336#95×C53C2311yescharacteristic
337#95×C53C2311yescharacteristic
338#95×C53C2311yescharacteristic
339#95×C53C2311yescharacteristic
340#95×C53C2311yescharacteristic
341#95×C53C2311yescharacteristic
342#95×C53C2311yescharacteristic
343#95×C53C2311yescharacteristic
344#95×C53C2311yescharacteristic
345#95×C53C2311yescharacteristic
346#95×C53C2311yescharacteristic
347#95×C53C2311yescharacteristic
348#95×C53C2311yescharacteristic
349#95×C53C2311yescharacteristic
350#95×C53C2311yescharacteristic
351C23×D53C2411yescharacteristic
352C2×Q8×C53—22no—
353C2×Q8×C53—41no—
354C2×Q8×C53—41no—
355C22×C4×C53C2411yescharacteristic
356C22×C4×C53C2411yescharacteristic
357C22×C4×C53C2411yescharacteristic
358C22×C4×C53C2411yescharacteristic
359C22×C4×C53C2411yescharacteristic
360C22×C4×C53C2411yescharacteristic
361C22×C4×C53C2411yescharacteristic
362C22×C4×C53C2411yescharacteristic
363C22×C4×C53C2411yescharacteristic
364C22×C4×C53C2411yescharacteristic
365C22×C4×C53C2411yescharacteristic
366C22×C4×C53C2411yescharacteristic
367C22×C4×C53C2411yescharacteristic
368C22×C4×C53C2411yescharacteristic
369C22×C4×C53C2411yescharacteristic
370C22×Dic53C2411yescharacteristic
371C22×Dic53C2411yescharacteristic
372C22×Dic53C2411yescharacteristic
373C22×Dic53C2411yescharacteristic
374C22×Dic53C2411yescharacteristic
375C22×Dic53C2411yescharacteristic
376C22×Dic53C2411yescharacteristic
377C22×Dic53C2411yescharacteristic
378C22×Dic53C2411yescharacteristic
379C22×Dic53C2411yescharacteristic
380C22×Dic53C2411yescharacteristic
381C22×Dic53C2411yescharacteristic
382C22×Dic53C2411yescharacteristic
383C22×Dic53C2411yescharacteristic
384C22×Dic53C2411yescharacteristic
385C2×C4×D53—22no—
386C2×C4×D53—22no—
387C2×C4×D53—22no—
388C2×C4×D53—22no—
389C2×C4×D53—22no—
390C2×C4×D53—41no—
391C2×C4×D53—41no—
392C2×C4×D53—41no—
393C2×C4×D53—41no—
394C2×Dic106—22no—
395C2×Dic106—22no—
396C2×Dic106—41no—
397C2×Dic106—41no—
398C2×Dic106—41no—
399C2×Dic106—41no—
400C2×Dic106—41no—
401C2×Dic106—41no—
402C2×Dic106#4114yes—
403C4⋊C4×C53—22no—
404C4⋊C4×C53—22no—
405C4⋊C4×C53—22no—
406C4⋊C4×C53—41no—
407C4⋊C4×C53—41no—
408C4⋊C4×C53—41no—
409C4⋊C4×C53—41no—
410C4⋊C4×C53—41no—
411C4⋊C4×C53—41no—
412C4⋊C4×C53—41no—
413C4⋊C4×C53—41no—
414C4⋊C4×C53—41no—
415C4⋊C4×C53—41no—
416C42×C53—41no—
417C42×C53—41no—
418C42×C53—41no—
419#11719921—22no—
420#11719921—22no—
421#11719921—22no—
422#11719921—22no—
423#11719921—22no—
424#11719921—22no—
425#11719921—41no—
426#11719921—41no—
427#11719921—41no—
428#11719921—41no—
429#11719921—41no—
430#11719921—41no—
431C4⋊Dic53—22no—
432C4⋊Dic53—22no—
433C4⋊Dic53—22no—
434C4⋊Dic53—22no—
435C4⋊Dic53—22no—
436C4⋊Dic53—22no—
437C4⋊Dic53—41no—
438C4⋊Dic53—41no—
439C4⋊Dic53—41no—
440#11719919—22no—
441#11719919—22no—
442#11719919—22no—
443#11719919—22no—
444#11719919—22no—
445#11719919—22no—
446#11719919—22no—
447#11719919—22no—
448#11719919—22no—
449#11719919—22no—
450#11719919—22no—
451#11719919—22no—
452#11719919—22no—
453#11719919—41no—
454#11719919—41no—
455#11719919—41no—
456#11719919—41no—
457#11719919—41no—
458#11719919—41no—
459#11719919—41no—
460#11719919—41no—
461#11719919—41no—
462#11719919—41no—
463#11719919—41no—
464#11719919—41no—
465#11719919—41no—
466C4×Dic53—22no—
467C4×Dic53—22no—
468C4×Dic53—22no—
469C4×Dic53—22no—
470C4×Dic53—22no—
471C4×Dic53—22no—
472C4×Dic53—41no—
473C4×Dic53—41no—
474C4×Dic53—41no—
475C4×Dic53—41no—
476C4×Dic53—41no—
477C4×Dic53—41no—
478C4×Dic53—41no—
479C23×C53C2511yescharacteristic
480C22×D53—21no—
481C22×D53—21no—
482C22×D53—21no—
483C22×D53—21no—
484C22×D53—21no—
485C22×D53—21no—
486C22×D532−1+412yes—
487Q8×C53—44no—
488C2×C4×C53—21no—
489C2×C4×C53—21no—
490C2×C4×C53—21no—
491C2×C4×C53—21no—
492C2×C4×C53—21no—
493C2×C4×C53—21no—
494C2×C4×C53—21no—
495C2×C4×C53—21no—
496C2×C4×C53—21no—
497C2×C4×C53—21no—
498C2×C4×C53—21no—
499C2×C4×C53—21no—
500C2×C4×C53—21no—
501C2×C4×C53—21no—
502C2×C4×C53—21no—
503C2×C4×C53—21no—
504C2×C4×C53—21no—
505C2×C4×C53—21no—
506C2×C4×C53—21no—
507C2×C4×C53—21no—
508C2×C4×C53—21no—
509C2×C4×C53—21no—
510C2×C4×C53—21no—
511C2×C4×C53—21no—
512C2×C4×C53—21no—
513C2×C4×C53—21no—
514C2×C4×C53—21no—
515C2×C4×C53—21no—
516C2×C4×C53—21no—
517C2×C4×C53—21no—
518C2×C4×C53—21no—
519C2×C4×C53—21no—
520C2×C4×C53—21no—
521C2×C4×C53—21no—
522C2×C4×C53—21no—
523C2×C4×C53—21no—
524C2×C4×C53—21no—
525C2×C4×C53—21no—
526C2×C4×C53—21no—
527C2×C4×C53—21no—
528C2×C4×C53—21no—
529C2×C4×C53—21no—
530C2×C4×C53—21no—
531C2×C4×C53C2×#4112yes—
532C2×C4×C532−1+412yes—
533C2×Dic53—21no—
534C2×Dic53—21no—
535C2×Dic53—21no—
536C2×Dic53—21no—
537C2×Dic53—21no—
538C2×Dic53—21no—
539C2×Dic53—21no—
540C2×Dic53—21no—
541C2×Dic53—21no—
542C2×Dic53—21no—
543C2×Dic53—21no—
544C2×Dic53—21no—
545C2×Dic53—21no—
546C2×Dic53—21no—
547C2×Dic53—21no—
548C2×Dic53—21no—
549C2×Dic53—21no—
550C2×Dic53—21no—
551C2×Dic53—21no—
552C2×Dic53—21no—
553C2×Dic53—21no—
554C2×Dic53—21no—
555C2×Dic53—21no—
556C2×Dic53—21no—
557C2×Dic53—21no—
558C2×Dic53—21no—
559C2×Dic53—21no—
560C2×Dic53—21no—
561C2×Dic53—21no—
562C2×Dic53—21no—
563C2×Dic53—21no—
564C2×Dic53—21no—
565C2×Dic53—21no—
566C2×Dic53—21no—
567C2×Dic53—21no—
568C2×Dic53—21no—
569C2×Dic53—21no—
570C2×Dic53—21no—
571C2×Dic53—21no—
572C2×Dic53—21no—
573C2×Dic53—21no—
574C2×Dic53C2×#4112yes—
575C2×Dic53C2×#4112yes—
576C2×Dic53H(5,𝔽2)12yes—
577C2×Dic532−1+412yes—
578C4×D53—44no—
579C4×D53—44no—
580C4×D53—44no—
581Dic106—44no—
582Dic106—44no—
583Dic106—82no—
584#37212—531nomaximal, Sylow
585C22×C53C22×#4111yescharacteristic
586C22×C53C2×H(5,𝔽2)11yescharacteristic
587C22×C53C2×2−1+411yescharacteristic
588C22×C53C2×2−1+411yescharacteristic
589C22×C53C2×2−1+411yescharacteristic
590C22×C53#58511yescharacteristic
591C22×C53#58511yescharacteristic
592C2×D53—22no—
593C2×D53—22no—
594C2×D53—22no—
595C2×D53—41no—
596C2×D53—41no—
597C2×D53—41no—
598C2×D53—41no—
599C4×C53—22no—
600C4×C53—22no—
601C4×C53—41no—
602C4×C53—41no—
603C4×C53—41no—
604C4×C53—41no—
605C4×C53—41no—
606C4×C53—41no—
607C4×C53—41no—
608C4×C53—41no—
609C4×C53—41no—
610C4×C53—41no—
611C4×C53—41no—
612C4×C53—41no—
613C4×C53—41no—
614Dic53—22no—
615Dic53—22no—
616Dic53—22no—
617Dic53—22no—
618Dic53—41no—
619Dic53—41no—
620Dic53—41no—
621Dic53—41no—
622Dic53—41no—
623Dic53—41no—
624Dic53—41no—
625Dic53—41no—
626Dic53—41no—
627Dic53—41no—
628Dic53—41no—
629#2855—531no—
630#2851—531no—
631#2810—531no—
632#2809—531no—
633#2806—531no—
634#2805—531no—
635#2805D5311yescharacteristic, complemented
636#2789—531no—
637#2789—531no—
638#2787—531no—
639#2787—531no—
640#2745—531no—
641#2745—531no—
642#2744—531no—
643#2744—531no—
644#2734—531no—
645#2729—531no—
646#2729—531no—
647#2655—531no—
648#2655—531no—
649#2530—531no—
650#2530—531no—
651#2528—531no—
652#2528—531no—
653#2465—531no—
654#2465—531no—
655#2462—531no—
656#2462—531no—
657#2327—531no—
658#2327—531no—
659C4×C22⋊Q8—531no—
660C2×C53#345911yescharacteristic
661C2×C53#351811yescharacteristic
662C2×C53#352311yescharacteristic
663C2×C53#353511yescharacteristic
664C2×C53#353811yescharacteristic
665C2×C53#355311yescharacteristic
666C2×C53#355511yescharacteristic
667D53—42no—
668C2×C4⋊Q8—531no—
669C2×C4⋊Q8—531no—
670C2×#125—531no—
671C2×C22⋊Q8—531no—
672C2×C22⋊Q8—531no—
673C2×C4×Q8—531no—
674C2×C4×Q8—531no—
675C2×C4×Q8—531no—
676C22×C42—531no—
677#401—531no—
678#401—531no—
679#401—531no—
680#401—531no—
681#400—531no—
682#400—531no—
683#400—531no—
684#400—531no—
685#400—531no—
686#400—531no—
687#400—531no—
688#400—531no—
689#400—531no—
690#400—531no—
691#400—531no—
692#400—531no—
693#400C2×D5311yescharacteristic
694#400C2×D5311yescharacteristic
695#400C2×D5311yescharacteristic
696#400C2×D5311yescharacteristic
697#398—531no—
698#398—531no—
699#398—531no—
700#398—531no—
701#398—531no—
702#398—531no—
703#398—531no—
704#398—531no—
705#398—531no—
706#398—531no—
707#398—531no—
708#398—531no—
709#397—531no—
710#397—531no—
711#397—531no—
712#397—531no—
713#396—531no—
714#396—531no—
715#395—531no—
716#395—531no—
717#395—531no—
718#395—531no—
719#395—531no—
720#395—531no—
721#395C2×D5311yescharacteristic
722#395C2×D5311yescharacteristic
723#393—531no—
724#393—531no—
725#391—531no—
726#391—531no—
727#391—531no—
728#391—531no—
729#391—531no—
730#391—531no—
731#391—531no—
732#391—531no—
733#391C2×D5311yescharacteristic
734#389—531no—
735#389—531no—
736#389—531no—
737#389—531no—
738#389—531no—
739#389—531no—
740#389—531no—
741#389—531no—
742#389—531no—
743#389C2×D5311yescharacteristic
744#389C2×D5311yescharacteristic
745#389C2×D5311yescharacteristic
746#389C2×D5311yescharacteristic
747#388—531no—
748#388—531no—
749#388—531no—
750#388—531no—
751#388—531no—
752#388—531no—
753#388—531no—
754#388—531no—
755#387—531no—
756#387—531no—
757#387—531no—
758#387—531no—
759#387—531no—
760#387—531no—
761#387—531no—
762#387—531no—
763#387—531no—
764#387—531no—
765#387—531no—
766#387—531no—
767#387—531no—
768#387—531no—
769#387—531no—
770#387—531no—
771#387—531no—
772#387—531no—
773#387—531no—
774#387—531no—
775#387—531no—
776#387—531no—
777#387—531no—
778#387—531no—
779#387—531no—
780#387—531no—
781#387—531no—
782#387—531no—
783#387—531no—
784#387—531no—
785#387—531no—
786#387—531no—
787#387—531no—
788#387—531no—
789#387—531no—
790#387—531no—
791#387—531no—
792#387—531no—
793#387—531no—
794#387—531no—
795#387C2×D5311yescharacteristic
796#387C2×D5311yescharacteristic
797#387C2×D5311yescharacteristic
798#387C2×D5311yescharacteristic
799#385—531no—
800#385—531no—
801#385—531no—
802#385—531no—
803#385—531no—
804#385—531no—
805#385—531no—
806#385—531no—
807#382—531no—
808#382—531no—
809#382—531no—
810#381—531no—
811#381—531no—
812#380—531no—
813#380—531no—
814#380—531no—
815#380—531no—
816C4×C4⋊C4—531no—
817C4×C4⋊C4—531no—
818C4×C4⋊C4—531no—
819C4×C22⋊C4—531no—
820C4×C22⋊C4—531no—
821#376—531no—
822#376—531no—
823C53#3721211yescharacteristic, complemented, Sylow
824C22×Q8—531no—
825C22×Q8—531no—
826C22×Q8—531no—
827C22×Q8C22×D5311yescharacteristic
828C23×C4—531no—
829C23×C4—531no—
830C23×C4—531no—
831C4⋊Q8—1064no—
832C4⋊Q8—1064no—
833#125—2122no—
834C22⋊Q8—1064no—
835C22⋊Q8—2122no—
836C4×Q8—2122no—
837C4×Q8—2122no—
838C4×Q8—2122no—
839C2×C4⋊C4—531no—
840C2×C4⋊C4—531no—
841C2×C4⋊C4—531no—
842C2×C4⋊C4—531no—
843C2×C4⋊C4—531no—
844C2×C4⋊C4—531no—
845C2×C4⋊C4—531no—
846C2×C4⋊C4—531no—
847C2×C4⋊C4—531no—
848C2×C4⋊C4—531no—
849C2×C4⋊C4—531no—
850C2×C4⋊C4—531no—
851C2×C4⋊C4—531no—
852C2×C4⋊C4—531no—
853C2×C4⋊C4—531no—
854C2×C4⋊C4—531no—
855C2×C4⋊C4—531no—
856C2×C4⋊C4—531no—
857C2×C4⋊C4—531no—
858C2×C4⋊C4—531no—
859C2×C4⋊C4—531no—
860C2×C4⋊C4—531no—
861C2×C4⋊C4—531no—
862C2×C4⋊C4—531no—
863C2×C4⋊C4—531no—
864C2×C4⋊C4—531no—
865C2×C4⋊C4—531no—
866C2×C4⋊C4—531no—
867C2×C4⋊C4—531no—
868C2×C4⋊C4—531no—
869C2×C4⋊C4—531no—
870C2×C4⋊C4—531no—
871C2×C4⋊C4—531no—
872C2×C4⋊C4—531no—
873C2×C4⋊C4—531no—
874C2×C4⋊C4C22×D5311yescharacteristic
875C2×C4⋊C4C22×D5311yescharacteristic
876C2×C4⋊C4C22×D5311yescharacteristic
877C2×C4⋊C4C22×D5311yescharacteristic
878C2×C4⋊C4C22×D5311yescharacteristic
879C2×C4⋊C4C22×D5311yescharacteristic
880C2×C4⋊C4C22×D5311yescharacteristic
881C2×C4⋊C4C22×D5311yescharacteristic
882C2×C4⋊C4C22×D5311yescharacteristic
883C2×C4⋊C4C22×D5311yescharacteristic
884C2×C4⋊C4C22×D5311yescharacteristic
885C2×C4⋊C4C22×D5311yescharacteristic
886C2×C4⋊C4C22×D5311yescharacteristic
887C2×C22⋊C4—531no—
888C2×C22⋊C4—531no—
889C2×C22⋊C4—531no—
890C2×C22⋊C4—531no—
891C2×C22⋊C4—531no—
892C2×C22⋊C4—531no—
893C2×C22⋊C4—531no—
894C2×C22⋊C4—531no—
895C2×C22⋊C4—531no—
896C2×C22⋊C4—531no—
897C2×C22⋊C4—531no—
898C2×C22⋊C4—531no—
899C2×C42—531no—
900C2×C42—531no—
901C2×C42—531no—
902C2×C42—531no—
903C2×C42—531no—
904C2×C42—531no—
905C2×C42—531no—
906C2×C42—531no—
907C2×C42—531no—
908C2×C42—531no—
909C2×C42—531no—
910C2×C42—531no—
911C2×C42—531no—
912C2×C42—2122no—
913C2×C42C22×D5311yescharacteristic
914C2×C42C22×D5311yescharacteristic
915C2×C42C22×D5311yescharacteristic
916#95—531no—
917#95—531no—
918#95—531no—
919#95—531no—
920#95—531no—
921#95—531no—
922#95—531no—
923#95—531no—
924#95—531no—
925#95—531no—
926#95—531no—
927#95—531no—
928#95—531no—
929#95—531no—
930#95—531no—
931#95—531no—
932#95—531no—
933#95—531no—
934#95—531no—
935#95—531no—
936#95—531no—
937#95—531no—
938#95—531no—
939#95—531no—
940#95—531no—
941#95—531no—
942#95—531no—
943#95—531no—
944#95—531no—
945#95—531no—
946#95—531no—
947#95—531no—
948#95—531no—
949#95—531no—
950#95—531no—
951#95—531no—
952#95—531no—
953#95—531no—
954#95—531no—
955#95—531no—
956#95—531no—
957#95—531no—
958#95—531no—
959#95—531no—
960#95—531no—
961#95—531no—
962#95—531no—
963#95—531no—
964#95—531no—
965#95—531no—
966#95—531no—
967#95—531no—
968#95—531no—
969#95—531no—
970#95C22×D5311yescharacteristic
971#95C22×D5311yescharacteristic
972#95C22×D5311yescharacteristic
973#95C22×D5311yescharacteristic
974#95C22×D5311yescharacteristic
975#95C22×D5311yescharacteristic
976#95C22×D5311yescharacteristic
977#95C22×D5311yescharacteristic
978#95C22×D5311yescharacteristic
979#95C22×D5311yescharacteristic
980#95C22×D5311yescharacteristic
981#95C22×D5311yescharacteristic
982#95C22×D5311yescharacteristic
983#95C22×D5311yescharacteristic
984#95C22×D5311yescharacteristic
985#95C22×D5311yescharacteristic
986#95C22×D5311yescharacteristic
987#95C22×D5311yescharacteristic
988C24—531no—
989C2×Q8—22no—
990C2×Q8—41no—
991C2×Q8—41no—
992C2×Q8—534no—
993C2×Q8—1062no—
994C2×Q8—1062no—
995C2×Q8—2121no—
996C2×Q8—2121no—
997C2×Q8—2121no—
998C2×Q8—2121no—
999C2×Q8—2121no—
1000C2×Q8—2121no—
1001C22×C4—531no—
1002C22×C4—531no—
1003C22×C4—531no—
1004C22×C4—531no—
1005C22×C4—531no—
1006C22×C4—531no—
1007C22×C4—531no—
1008C22×C4—531no—
1009C22×C4—531no—
1010C22×C4—531no—
1011C22×C4—531no—
1012C22×C4—531no—
1013C22×C4—531no—
1014C22×C4—531no—
1015C22×C4—531no—
1016C22×C4—1062no—
1017C22×C4—1062no—
1018C22×C4—1062no—
1019C22×C4—1062no—
1020C22×C4—1062no—
1021C22×C4—2121no—
1022C22×C4—2121no—
1023C22×C4—2121no—
1024C22×C4—2121no—
1025C22×C4C23×D5311yescharacteristic
1026C22×C4C23×D5311yescharacteristic
1027C22×C4C23×D5311yescharacteristic
1028C22×C4C23×D5311yescharacteristic
1029C22×C4C23×D5311yescharacteristic
1030C22×C4C23×D5311yescharacteristic
1031C22×C4C23×D5311yescharacteristic
1032C22×C4C23×D5311yescharacteristic
1033C22×C4C23×D5311yescharacteristic
1034C22×C4C23×D5311yescharacteristic
1035C22×C4C23×D5311yescharacteristic
1036C22×C4C23×D5311yescharacteristic
1037C22×C4C23×D5311yescharacteristic
1038C22×C4C23×D5311yescharacteristic
1039C22×C4C23×D5311yescharacteristic
1040C4⋊C4—22no—
1041C4⋊C4—22no—
1042C4⋊C4—22no—
1043C4⋊C4—41no—
1044C4⋊C4—41no—
1045C4⋊C4—41no—
1046C4⋊C4—41no—
1047C4⋊C4—41no—
1048C4⋊C4—41no—
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—1062no—
1054C4⋊C4—1062no—
1055C4⋊C4—1062no—
1056C4⋊C4—1062no—
1057C4⋊C4—1062no—
1058C4⋊C4—1062no—
1059C4⋊C4—1062no—
1060C4⋊C4—1062no—
1061C4⋊C4—1062no—
1062C4⋊C4—1062no—
1063C4⋊C4—1062no—
1064C4⋊C4—1062no—
1065C4⋊C4—1062no—
1066C4⋊C4—1062no—
1067C4⋊C4—1062no—
1068C4⋊C4—1062no—
1069C4⋊C4—1062no—
1070C4⋊C4—1062no—
1071C4⋊C4—1062no—
1072C4⋊C4—2121no—
1073C4⋊C4—2121no—
1074C4⋊C4—2121no—
1075C4⋊C4—2121no—
1076C4⋊C4—2121no—
1077C4⋊C4—2121no—
1078C4⋊C4—2121no—
1079C4⋊C4—2121no—
1080C4⋊C4—2121no—
1081C4⋊C4—2121no—
1082C4⋊C4—2121no—
1083C4⋊C4—2121no—
1084C4⋊C4—2121no—
1085C4⋊C4—2121no—
1086C4⋊C4—2121no—
1087C4⋊C4—2121no—
1088C22⋊C4—1062no—
1089C22⋊C4—1062no—
1090C22⋊C4—1062no—
1091C22⋊C4—1062no—
1092C22⋊C4—1062no—
1093C22⋊C4—1062no—
1094C22⋊C4—2121no—
1095C22⋊C4—2121no—
1096C22⋊C4—2121no—
1097C22⋊C4—2121no—
1098C22⋊C4—2121no—
1099C22⋊C4—2121no—
1100C42—41no—
1101C42—41no—
1102C42—41no—
1103C42—1062no—
1104C42—1062no—
1105C42—1062no—
1106C42—1062no—
1107C42—1062no—
1108C42—1062no—
1109C42—2121no—
1110C42—2121no—
1111C42—2121no—
1112C42—2121no—
1113C42—2121no—
1114C42—2121no—
1115C42—2121no—
1116C23—532no—
1117C23—1061no—
1118C23—1061no—
1119C23—1061no—
1120C23—1061no—
1121C23—1061no—
1122C23—1061no—
1123C23C24×D5311yescharacteristic
1124Q8—44no—
1125Q8—4242no—
1126Q8—2124no—
1127Q8—2124no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—532no—
1172C2×C4—532no—
1173C2×C4—532no—
1174C2×C4—532no—
1175C2×C4—1061no—
1176C2×C4—1061no—
1177C2×C4—1061no—
1178C2×C4—1061no—
1179C2×C4—1061no—
1180C2×C4—1061no—
1181C2×C4—1061no—
1182C2×C4—1061no—
1183C2×C4—1061no—
1184C2×C4—1061no—
1185C2×C4—1061no—
1186C2×C4—1061no—
1187C2×C4—1061no—
1188C2×C4—1061no—
1189C2×C4—1061no—
1190C2×C4—1061no—
1191C2×C4—1061no—
1192C2×C4—1061no—
1193C2×C4—1061no—
1194C2×C4—1061no—
1195C2×C4—1061no—
1196C2×C4—1061no—
1197C2×C4—1061no—
1198C2×C4—1061no—
1199C2×C4—1061no—
1200C2×C4—1061no—
1201C2×C4—1061no—
1202C2×C4—1061no—
1203C2×C4—1061no—
1204C2×C4—1061no—
1205C2×C4—1061no—
1206C2×C4—1061no—
1207C2×C4—1061no—
1208C2×C4—1061no—
1209C2×C4—1061no—
1210C2×C4—1061no—
1211C2×C4—1061no—
1212C2×C4—1061no—
1213C2×C4—1061no—
1214C2×C4—1061no—
1215C2×C4—1061no—
1216C2×C4—2124no—
1217C2×C4—2124no—
1218C2×C4—2124no—
1219C2×C4#41×D5312yes—
1220C2×C4#1313326512yes—
1221C22—1062no—
1222C22—1062no—
1223C22—1062no—
1224C22—2121no—
1225C22—2121no—
1226C22—2121no—
1227C22—2121no—
1228C22C2×#41×D5311yescharacteristic
1229C22H(5,𝔽2)×D5311yescharacteristic
1230C222−1+4×D5311yescharacteristic
1231C222−1+4×D5311yescharacteristic
1232C22C2×#1313326511yescharacteristic
1233C22#1681145811yescharacteristic
1234C22#1681145911yescharacteristic
1235C4—22no—
1236C4—22no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—1062no—
1251C4—1062no—
1252C4—1062no—
1253C4—1062no—
1254C4—2121no—
1255C4—2121no—
1256C4—2121no—
1257C4—2121no—
1258C4—2121no—
1259C4—2121no—
1260C4—2121no—
1261C4—2121no—
1262C4—2121no—
1263C4—2121no—
1264C4—2121no—
1265C2—2122no—
1266C2#2028812611yescharacteristic
1267C2#2028872511yescharacteristic
1268C2#2028880811yescharacteristic
1269C2#2028891911yescharacteristic
1270C2#2028895911yescharacteristic
1271C2#2028916411yescharacteristic
1272C2#2028920011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D53
commutator, socle, cosocleC23×C53C25
FittingC53×#2805C2
prime radicalC23×D53C24
hypercenter#2805D53
hypocenterC53#37212
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2805

Complements

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

NH ≅ G/Ntype
3. #20282705C2semidirect
4. #20282698C2semidirect
5. #20282672C2semidirect
6. #20282663C2semidirect
7. #20282471C2semidirect
8. #20282470C2semidirect
15. #20281749C2semidirect
18. #20280813C2semidirect
19. #20280805C2semidirect
22. #20279522C2semidirect
23. #20279510C2semidirect
26. #20278702C2semidirect
27. #20278690C2semidirect
28. #20277433C2semidirect
29. #20277430C2semidirect
31. C53×#2805C2semidirect
635. #2805D53semidirect
823. C53#37212semidirect

Maximal subgroups

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

subgroupindex
#202830532
#202830222
#202827052
#202826982
#202826722
#202826632
#202824712
#202824702
#202824532
#202824412
#202818852
#202818772
#202818742
#202818662
#202817492
#202817042
#202816922
#202808132
#202808052
#202795542
#202795502
#202795222
#202795102
#202787352
#202787312
#202787022
#202786902
#202774332
#202774302
#202772492
C53×#28052
#3721253