Finite Group Databasebeta

← #15631145

Subgroups — #15631145

Order 2816.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082353C211yesmaximal, characteristic, complemented
2#13080802C212yesmaximal, complemented
3#13080787C212yesmaximal, complemented
4#13080592C212yesmaximal, complemented
5#13080577C212yesmaximal, complemented
6#13080544C212yesmaximal, complemented
7#13080518C212yesmaximal, complemented
8#13080481C212yesmaximal, complemented
9#13080466C212yesmaximal, complemented
10#13078981C211yesmaximal, characteristic, complemented
11#13078601C211yesmaximal, characteristic, complemented
12#13078560C211yesmaximal, characteristic, complemented
13#13078478C211yesmaximal, characteristic, complemented
14#13078298C211yesmaximal, characteristic, complemented
15C2×#10622661C211yesmaximal, characteristic, complemented
16#13078124C211yesmaximal, characteristic, complemented
17#13077902C211yesmaximal, characteristic, complemented
18#13077868C211yesmaximal, characteristic, complemented
19#13077444C211yesmaximal, characteristic, complemented
20#13077311C211yesmaximal, characteristic, complemented
21#13077149C211yesmaximal, characteristic, complemented
22C2×#10622846C211yesmaximal, characteristic, complemented
23C11×#3489C211yesmaximal, characteristic, complemented
24C2×C11×2−1+4C2211yescharacteristic
25C22×C11×#41C2211yescharacteristic
26D4×Q8×C11C2212yescomplemented
27C11×#548C2212yescomplemented
28C11×#547—22no—
29C11×#547C2212yescomplemented
30C11×#546—22no—
31C11×#546C2212yescomplemented
32C11×#537—21no—
33C11×#537C2211yescharacteristic
34C11×#536—21no—
35C11×#536C2211yescharacteristic
36C11×#525—21no—
37C11×#525C2211yescharacteristic
38C2×C11×C22⋊Q8—21no—
39C2×C11×C22⋊Q8C2211yescharacteristic
40C11×#520C2211yescharacteristic
41#10623361C2211yescharacteristic, complemented
42#10623358C2211yescharacteristic, complemented
43C2×#67002C2211yescharacteristic
44C2×#67002C2211yescharacteristic
45C2×#67001C2211yescharacteristic, complemented
46C22×#4325C2211yescharacteristic, complemented
47C2×#66983C2211yescharacteristic
48C2×#66979C2211yescharacteristic
49C23×C11⋊C8C2211yescharacteristic
50#10623189—22no—
51#10623174—21no—
52#10623155—21no—
53#10623150—21no—
54#10623127—21no—
55#10623122—22no—
56#10623096C2212yes—
57#10623096C2212yescomplemented
58#10623094C2212yescomplemented
59#10623086C2212yes—
60#10623052C2211yescharacteristic, complemented
61#10623050C2211yescharacteristic, complemented
62#10622851C2212yes—
63#10622851C2212yes—
64#10622851C2212yescomplemented
65#10622851C2212yescomplemented
66#10622847C2211yescharacteristic, complemented
67#10622846C2211yescharacteristic
68#10622846C2211yescharacteristic
69#10622846C2211yescharacteristic
70#10622846C2211yescharacteristic
71#10622846C2211yescharacteristic, complemented
72#10622846C2211yescharacteristic, complemented
73#10622846C2211yescharacteristic, complemented
74#10622846C2211yescharacteristic, complemented
75#10622846C2212yescomplemented
76#10622845C2211yescharacteristic
77#10622845C2211yescharacteristic
78#10622845C2212yescomplemented
79#10622840C2212yes—
80#10622840C2212yescomplemented
81#10622840C2212yescomplemented
82#10622838C2211yescharacteristic, complemented
83#10622838C2211yescharacteristic, complemented
84#10622838C2212yescomplemented
85C2×#66899C2211yescharacteristic, complemented
86C2×#66899C2211yescharacteristic, complemented
87C2×#66899C2212yescomplemented
88C2×#66899C2211yescharacteristic, complemented
89#10622830C2212yes—
90C2×#66896C2211yescharacteristic, complemented
91C2×#66896C2211yescharacteristic, complemented
92#10622820C2211yescharacteristic
93#10622696C2212yescomplemented
94#10622696C2212yescomplemented
95#10622695C2212yescomplemented
96#10622694C2212yescomplemented
97#10622670C2212yescomplemented
98#10622670C2212yescomplemented
99#10622669C2212yescomplemented
100#10622668C2212yescomplemented
101#10622662C2212yescomplemented
102#10622661C2212yes—
103#10622661C2212yes—
104#10622661C2212yescomplemented
105#10622661C2212yescomplemented
106#10622661C2212yescomplemented
107#10622658C2212yescomplemented
108#10622658C2212yescomplemented
109#10622658C2212yescomplemented
110#10622657C2212yescomplemented
111#10622656C2212yescomplemented
112#10622656C2212yescomplemented
113#10622652C2212yescomplemented
114#10622651C2212yescomplemented
115#10622648C2212yescomplemented
116#10622647C2212yescomplemented
117#10622639C2212yescomplemented
118C4×#4325C2212yescomplemented
119#10622635C2212yescomplemented
120#10622633C2212yescomplemented
121#10622627C2212yescomplemented
122C4×#4323C2212yescomplemented
123#10622624C2212yescomplemented
124#10622624C2212yescomplemented
125D4×C11⋊C8C2212yescomplemented
126D4×C11⋊C8C2212yescomplemented
127#10622622C2212yescomplemented
128#10622621C2212yescomplemented
129#10622612C2211yescharacteristic, complemented
130#10622610C2211yescharacteristic, complemented
131C2×#66873C2211yescharacteristic, complemented
132#10622577C2211yescharacteristic, complemented
133#10622577C2211yescharacteristic, complemented
134C2×#66872C2211yescharacteristic, complemented
135C11×2−1+4—24no—
136C11×2−1+4—42no—
137C2×C11×#41—21no—
138C2×C11×#41—22no—
139C2×C11×#41—21no—
140C2×C11×#41—21no—
141C2×C11×#41—24no—
142C2×C11×#41—42no—
143C2×C11×#41C2311yescharacteristic
144C2×C11×#41C2312yes—
145C2×C11×#41C2311yescharacteristic
146C2×C11×#41C2311yescharacteristic
147C2×C11×#41C2311yescharacteristic
148C2×C11×#41C2311yescharacteristic
149C22×Q8×C11—21no—
150C22×Q8×C11C2311yescharacteristic
151C22×Q8×C11C2311yescharacteristic
152C22×Q8×C11C2312yes—
153C22×D4×C11—21no—
154C22×D4×C11C2311yescharacteristic
155C23×C4×C11—21no—
156C23×C4×C11C2311yescharacteristic
157C22×C22⋊D11—21no—
158C2×#4341—22no—
159C22×D44C2311yescharacteristic
160C11×C4⋊Q8—22no—
161C11×C4⋊Q8C2312yes—
162C11×#124—22no—
163C11×#124C2312yes—
164C11×#123—22no—
165C11×#123—22no—
166C11×#123—22no—
167C11×#123—22no—
168C11×#123D412yes—
169C11×C22⋊Q8—21no—
170C11×C22⋊Q8—21no—
171C11×C22⋊Q8—21no—
172C11×C22⋊Q8—21no—
173C11×C22⋊Q8—22no—
174C11×C22⋊Q8—21no—
175C11×C22⋊Q8—22no—
176C11×C22⋊Q8—22no—
177C11×C22⋊Q8D411yescharacteristic
178C11×C22⋊Q8D411yescharacteristic
179C11×C22⋊Q8C2312yes—
180C11×C22⋊Q8C2312yes—
181C11×C22⋊Q8C2312yes—
182C11×#121—21no—
183C11×#121—22no—
184C11×#121—22no—
185C11×#121—22no—
186C11×#121—22no—
187C11×#121D411yescharacteristic
188C11×#121D411yescharacteristic
189C11×#121C2312yes—
190C11×#120—22no—
191C11×#120D412yes—
192C4×Q8×C11C2312yes—
193C4×D4×C11—22no—
194C4×D4×C11—22no—
195C4×D4×C11—22no—
196C4×D4×C11C2312yes—
197C4×D4×C11C2312yes—
198C4×D4×C11C2312yes—
199C11×#117—21no—
200C11×#117C2311yescharacteristic
201C2×C11×C4⋊C4—21no—
202C2×C11×C4⋊C4—21no—
203C2×C11×C4⋊C4—22no—
204C2×C11×C4⋊C4C2311yescharacteristic
205C2×C11×C22⋊C4—21no—
206C2×C11×C22⋊C4—22no—
207C2×C22⋊Dic11—21no—
208#67002—24no—
209#67002—42no—
210#67001—42no—
211#67000—21no—
212Q8×Dic11—21no—
213C2×#4325—42no—
214C2×#4325C2312yes—
215C2×#4325C2312yes—
216C2×#4325C2312yes—
217C2×#4325C2312yes—
218#66993—21no—
219#66992—22no—
220#66992—22no—
221#66991—22no—
222#66990—22no—
223D4×Dic11—22no—
224D4×Dic11—21no—
225C2×#4323C2312yes—
226C2×#4323C2312yes—
227#66983—21no—
228#66983—21no—
229#66983C2312yes—
230#66983C2312yes—
231#66983C2312yes—
232#66983C2312yes—
233C2×(C2×D11)⋊C4—21no—
234#66979—21no—
235#66979—21no—
236#66979C2311yescharacteristic
237#66979C2311yescharacteristic
238#66979C2311yescharacteristic
239#66979C2311yescharacteristic
240#66979C2312yes—
241C2×C4⋊Dic11C2311yescharacteristic
242C2×C4⋊Dic11C2311yescharacteristic
243C2×C4⋊Dic11C2311yescharacteristic
244C2×C4⋊Dic11C2312yes—
245C2×C4×Dic11—21no—
246C2×#4318C2311yescharacteristic
247C2×#4318C2311yescharacteristic
248C2×#4318C2312yes—
249C22×C11⋊C8—42no—
250C22×C11⋊C8C2311yescharacteristic
251C22×C11⋊C8C2311yescharacteristic
252C22×C11⋊C8C2311yescharacteristic
253C22×C11⋊C8C2311yescharacteristic
254C22×C11⋊C8C2311yescharacteristic
255C22×C11⋊C8C2311yescharacteristic
256C22×C11⋊C8C2312yes—
257#66951—22no—
258#66951—22no—
259#66950—22no—
260#66946—21no—
261#66946—21no—
262#66945—22no—
263#66943—21no—
264#66941—21no—
265#66939—22no—
266#66939—22no—
267#66938—22no—
268#66938—22no—
269#66936—22no—
270#66936—22no—
271(C22⋊D11)⋊C4—22no—
272(C22⋊D11)⋊C4—22no—
273C22⋊C4×D11—22no—
274#66931—22no—
275C4×D44C2312yes—
276C4×D44C2312yes—
277#66923C2312yes—
278#66922C2312yes—
279#66899C2311yescharacteristic
280#66899C2312yes—
281#66899C2311yescharacteristic
282#66899C2312yes—
283#66899C2312yes—
284#66899C2312yes—
285#66899C2311yescharacteristic
286#66899C2311yescharacteristic
287#66899C2311yescharacteristic
288#66899C2311yescharacteristic
289#66899C2311yescharacteristic
290#66899C2311yescharacteristic
291#66899C2312yes—
292#66899C2312yes—
293#66899C2312yes—
294#66899C2312yes—
295#66896C2311yescharacteristic
296#66896C2311yescharacteristic
297#66896C2311yescharacteristic
298#66896C2311yescharacteristic
299#66896C2311yescharacteristic
300#66896C2311yescharacteristic
301#66896C2311yescharacteristic
302#66896C2311yescharacteristic
303#66896C2312yes—
304#66896C2312yes—
305C22⋊(C11⋊C8)C2312yes—
306C22⋊(C11⋊C8)C2312yes—
307C22⋊(C11⋊C8)C2312yes—
308C22⋊(C11⋊C8)C2312yes—
309#66873C2312yes—
310#66873C2312yes—
311#66872C2312yes—
312#66872C2312yes—
313#66872C2312yes—
314#66872C2312yes—
315#66871C2312yes—
316#66871C2312yes—
317C4⋊(C11⋊C8)C2312yes—
318C4⋊(C11⋊C8)C2312yes—
319#66867C2312yes—
320C4×C11⋊C8C2312yes—
321#61174—111nomaximal, Sylow
322C24×C11—21no—
323C24×C11C2×D411yescharacteristic
324C23×D11—21no—
325C11×#41—22no—
326C11×#41—22no—
327C11×#41—22no—
328C11×#41—22no—
329C11×#41—22no—
330C11×#41—24no—
331C11×#41—22no—
332C11×#41—22no—
333C11×#41—44no—
334C11×#41—41no—
335C11×#41—41no—
336C11×#41—42no—
337C11×#41—44no—
338C11×#41—44no—
339C11×#41—48no—
340C11×#41#4114yescomplemented
341C2×Q8×C11—21no—
342C2×Q8×C11—22no—
343C2×Q8×C11—21no—
344C2×Q8×C11—22no—
345C2×Q8×C11—24no—
346C2×Q8×C11—22no—
347C2×Q8×C11—22no—
348C2×Q8×C11—41no—
349C2×Q8×C11—42no—
350C2×Q8×C11—44no—
351C2×Q8×C11C2×D411yescharacteristic
352C2×Q8×C11C2412yes—
353C2×Q8×C11C2411yescharacteristic
354C2×Q8×C11C2411yescharacteristic
355C2×D4×C11—21no—
356C2×D4×C11—22no—
357C2×D4×C11—22no—
358C2×D4×C11—21no—
359C2×D4×C11—21no—
360C2×D4×C11—21no—
361C2×D4×C11—22no—
362C2×D4×C11—21no—
363C2×D4×C11—41no—
364C2×D4×C11—44no—
365C2×D4×C11C2×D412yes—
366C2×D4×C11C2×D411yescharacteristic
367C2×D4×C11C2×D412yes—
368C2×D4×C11C2×D412yes—
369C2×D4×C11C2411yescharacteristic
370C2×D4×C11C2411yescharacteristic
371C22×C4×C11—21no—
372C22×C4×C11—22no—
373C22×C4×C11—22no—
374C22×C4×C11—21no—
375C22×C4×C11—22no—
376C22×C4×C11—21no—
377C22×C4×C11—21no—
378C22×C4×C11—22no—
379C22×C4×C11—21no—
380C22×C4×C11—21no—
381C22×C4×C11—21no—
382C22×C4×C11—22no—
383C22×C4×C11—44no—
384C22×C4×C11C2×D411yescharacteristic
385C22×C4×C11C2×D411yescharacteristic
386C22×C4×C11C2×D411yescharacteristic
387C22×C4×C11C2411yescharacteristic
388C22×C4×C11C2411yescharacteristic
389C22×C4×C11C2412yes—
390C22×C4×C11C2411yescharacteristic
391C2×C22⋊D11—22no—
392C2×C22⋊D11—22no—
393C2×C22⋊D11—22no—
394C2×C22⋊D11—22no—
395C2×C22⋊D11—82no—
396C22×Dic11—21no—
397C22×Dic11—21no—
398C22×Dic11—21no—
399C22×Dic11—22no—
400#4341—84no—
401C2×D44—21no—
402C2×D44—22no—
403C2×D44—22no—
404C2×D44C2412yes—
405C2×C4×D11—22no—
406C2×C4×D11—22no—
407C2×Dic22—22no—
408C11×C4⋊C4—22no—
409C11×C4⋊C4—21no—
410C11×C4⋊C4—22no—
411C11×C4⋊C4—22no—
412C11×C4⋊C4—22no—
413C11×C4⋊C4—22no—
414C11×C4⋊C4—22no—
415C11×C4⋊C4C2×D411yescharacteristic
416C11×C4⋊C4C2×D411yescharacteristic
417C11×C4⋊C4C2×D412yes—
418C11×C4⋊C4C2×D412yes—
419C11×C4⋊C4C2412yes—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—22no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—22no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4C2×D412yes—
428C11×C22⋊C4C2×D412yes—
429C11×C22⋊C4C2×D412yes—
430C11×C22⋊C4C2×D412yes—
431C11×C22⋊C4C2×D412yes—
432C42×C11—22no—
433C42×C11C2412yes—
434C22⋊Dic11—21no—
435C22⋊Dic11—21no—
436C22⋊Dic11—21no—
437C22⋊Dic11—22no—
438C22⋊Dic11—21no—
439#4325—24no—
440#4325—42no—
441#4325—42no—
442#4325—42no—
443#4323—24no—
444#4323—42no—
445(C2×D11)⋊C4—22no—
446(C2×D11)⋊C4—22no—
447(C2×D11)⋊C4—22no—
448(C2×D11)⋊C4—22no—
449(C2×D11)⋊C4—22no—
450(C2×D11)⋊C4—22no—
451C4⋊Dic11—22no—
452C4⋊Dic11—21no—
453C4⋊Dic11—22no—
454C4⋊Dic11—21no—
455C4⋊Dic11—21no—
456C4⋊Dic11C2411yescharacteristic
457C4⋊Dic11C2411yescharacteristic
458C4⋊Dic11C2411yescharacteristic
459C4⋊Dic11C2412yes—
460C4⋊Dic11C2411yescharacteristic
461Dic11⋊C4—22no—
462Dic11⋊C4—22no—
463C4×Dic11—21no—
464C4×Dic11—22no—
465C4×Dic11—21no—
466C4×Dic11—21no—
467C4×Dic11—21no—
468#4318—22no—
469#4318—22no—
470#4318—42no—
471C2×C11⋊C8—22no—
472C2×C11⋊C8—22no—
473C2×C11⋊C8—41no—
474C2×C11⋊C8—41no—
475C2×C11⋊C8—41no—
476C2×C11⋊C8—41no—
477C2×C11⋊C8—42no—
478C2×C11⋊C8C2411yescharacteristic
479C2×C11⋊C8C2412yes—
480C2×C11⋊C8C2411yescharacteristic
481C2×C11⋊C8C2412yes—
482C2×C11⋊C8C2411yescharacteristic
483C2×C11⋊C8C2411yescharacteristic
484#3494—111no—
485#3489D1111yescharacteristic, complemented
486#3321—112no—
487#3320—112no—
488#3307—112no—
489#3306—112no—
490#3303—112no—
491#3301—112no—
492#3298—112no—
493#3297—112no—
494#3137—111no—
495#3099—111no—
496#3095—111no—
497#3084—111no—
498#3062—111no—
499C2×#465—111no—
500#3042—111no—
501#3010—111no—
502#3006—111no—
503#2946—111no—
504#2929—111no—
505#2898—111no—
506C2×#416—111no—
507C23×C11—22no—
508C23×C11—22no—
509C23×C11—21no—
510C23×C11—21no—
511C23×C11—41no—
512C23×C11—42no—
513C23×C11—42no—
514C23×C11—81no—
515C23×C11C22×D411yescharacteristic
516C23×C11C22×D412yes—
517C23×C11C22×D411yescharacteristic
518C23×C11C22×D411yescharacteristic
519C22×D11—22no—
520C22×D11—42no—
521C22×D11—81no—
522C22×D11—81no—
523Q8×C11—22no—
524Q8×C11—21no—
525Q8×C11—22no—
526Q8×C11—21no—
527Q8×C11—22no—
528Q8×C11—21no—
529Q8×C11—44no—
530Q8×C11—42no—
531Q8×C11—42no—
532Q8×C11C2×#4112yes—
533D4×C11—24no—
534D4×C11—24no—
535D4×C11—24no—
536D4×C11—22no—
537D4×C11—21no—
538D4×C11—21no—
539D4×C11—21no—
540D4×C11—42no—
541D4×C11—42no—
542D4×C11—42no—
543D4×C11—42no—
544D4×C11—44no—
545D4×C11—42no—
546D4×C11—82no—
547D4×C11C2×#4112yes—
548C2×C4×C11—22no—
549C2×C4×C11—21no—
550C2×C4×C11—22no—
551C2×C4×C11—22no—
552C2×C4×C11—24no—
553C2×C4×C11—21no—
554C2×C4×C11—21no—
555C2×C4×C11—22no—
556C2×C4×C11—21no—
557C2×C4×C11—21no—
558C2×C4×C11—22no—
559C2×C4×C11—22no—
560C2×C4×C11—22no—
561C2×C4×C11—21no—
562C2×C4×C11—42no—
563C2×C4×C11—42no—
564C2×C4×C11—42no—
565C2×C4×C11—44no—
566C2×C4×C11—44no—
567C2×C4×C11—42no—
568C2×C4×C11—42no—
569C2×C4×C11—82no—
570C2×C4×C11—81no—
571C2×C4×C11C22×D411yescharacteristic
572C2×C4×C11C22×D412yes—
573C2×C4×C11C22×D412yes—
574C2×C4×C11C22×D412yes—
575C2×C4×C11C22×D411yescharacteristic
576C2×C4×C11C22×D411yescharacteristic
577C2×C4×C11C2×#4112yes—
578C2×C4×C11H(5,𝔽2)12yes—
579C2×C4×C11C2511yescharacteristic
580C22⋊D11—44no—
581C22⋊D11—82no—
582C22⋊D11—82no—
583C22⋊D11—82no—
584C2×Dic11—21no—
585C2×Dic11—21no—
586C2×Dic11—21no—
587C2×Dic11—21no—
588C2×Dic11—22no—
589C2×Dic11—42no—
590C2×Dic11—82no—
591C2×Dic11—81no—
592C2×Dic11—81no—
593D44—22no—
594D44—22no—
595D44—42no—
596C4×D11—82no—
597C4×D11—82no—
598Dic22—82no—
599C11⋊C8—22no—
600C11⋊C8—21no—
601C11⋊C8—21no—
602C11⋊C8—21no—
603C11⋊C8—21no—
604C11⋊C8—22no—
605C2×2−1+4C2×D1111yescharacteristic
606C22×#41C2×D1111yescharacteristic
607C2×AGL(1,ℤ/8)—111no—
608C2×AGL(1,ℤ/8)—111no—
609C22×SD16—111no—
610C2×#131—111no—
611C23×C8—111no—
612#555—112no—
613#553—112no—
614#553—112no—
615#551—222no—
616D4×Q8C2×D1112yescomplemented
617#548C2×D1112yescomplemented
618#547—22no—
619#547—112no—
620#547C2×D1112yescomplemented
621#546—22no—
622#546—222no—
623#546C2×D1112yescomplemented
624#544—111no—
625#542—221no—
626#540—221no—
627#537—21no—
628#537C2×D1111yescharacteristic
629#536—21no—
630#536C2×D1111yescharacteristic
631#535—111no—
632#532—221no—
633#529—221no—
634#525—21no—
635#525C2×D1111yescharacteristic
636C2×C22⋊Q8—21no—
637C2×C22⋊Q8C2×D1111yescharacteristic
638C2×#121—111no—
639#520—111no—
640#520C2×D1111yescharacteristic
641#518—111no—
642C2×#117—111no—
643#491—112no—
644#489—112no—
645#488—112no—
646#487—112no—
647#485—112no—
648#485—112no—
649#485—112no—
650#484—112no—
651#483—112no—
652#483—112no—
653#482—112no—
654#481—112no—
655#479—112no—
656#478—112no—
657#476—112no—
658#475—112no—
659#469—112no—
660#468—112no—
661#466—112no—
662#465—112no—
663#465—112no—
664#465—112no—
665#465—112no—
666#465—112no—
667#463—112no—
668#463—112no—
669#461—112no—
670#461—112no—
671#449—112no—
672#449—112no—
673#449—112no—
674#449—112no—
675#448—112no—
676#448—112no—
677#448—112no—
678#447—112no—
679#442—112no—
680#440—112no—
681C4×SD16—112no—
682C4×D8—112no—
683#435—112no—
684#435—112no—
685C8×D4—112no—
686C8×D4—112no—
687#428—111no—
688#428—111no—
689C2×#106—111no—
690#424—111no—
691#419—111no—
692#419—111no—
693#419—112no—
694#417—111no—
695#417—111no—
696#417—112no—
697#416—111no—
698#416—111no—
699#416—111no—
700#416—111no—
701#416—111no—
702#416—111no—
703#416—111no—
704#416—111no—
705#416—112no—
706C2×#103—111no—
707C2×#103—111no—
708C2×#103—111no—
709C2×#103—112no—
710C2×#102—111no—
711C2×#102—111no—
712C2×#102—111no—
713#408—111no—
714#407—111no—
715#405—111no—
716C22×C11—21no—
717C22×C11—21no—
718C22×C11—21no—
719C22×C11—21no—
720C22×C11—21no—
721C22×C11—22no—
722C22×C11—21no—
723C22×C11—22no—
724C22×C11—22no—
725C22×C11—22no—
726C22×C11—21no—
727C22×C11—44no—
728C22×C11—41no—
729C22×C11—41no—
730C22×C11—41no—
731C22×C11—41no—
732C22×C11—41no—
733C22×C11—84no—
734C22×C11#54612yes—
735C22×C11#57712yes—
736C22×C11C23×D411yescharacteristic
737C2×D11—42no—
738C2×D11—42no—
739C2×D11—42no—
740C2×D11—162no—
741C4×C11—22no—
742C4×C11—21no—
743C4×C11—21no—
744C4×C11—22no—
745C4×C11—22no—
746C4×C11—22no—
747C4×C11—42no—
748C4×C11—41no—
749C4×C11—42no—
750C4×C11#54612yes—
751C4×C11C22×#4111yescharacteristic
752C4×C11C2×H(5,𝔽2)11yescharacteristic
753Dic11—41no—
754Dic11—41no—
755Dic11—41no—
756Dic11—42no—
757Dic11—41no—
7582−1+4—24no—
7592−1+4—42no—
760C2×#41—21no—
761C2×#41—22no—
762C2×#41—21no—
763C2×#41—21no—
764C2×#41—24no—
765C2×#41—42no—
766C2×#41—222no—
767C2×#41C22×D1111yescharacteristic
768C2×#41C22×D1112yes—
769C2×#41C22×D1111yescharacteristic
770C2×#41C22×D1111yescharacteristic
771C2×#41C22×D1111yescharacteristic
772C2×#41C22×D1111yescharacteristic
773C22×Q8—21no—
774C22×Q8C22×D1111yescharacteristic
775C22×Q8C22×D1112yes—
776C22×Q8C22×D1111yescharacteristic
777C22×D4—21no—
778C22×D4—111no—
779C22×D4—221no—
780C22×D4C22×D1111yescharacteristic
781C23×C4—21no—
782C23×C4C22×D1111yescharacteristic
783AGL(1,ℤ/8)—224no—
784AGL(1,ℤ/8)—442no—
785C2×SD16—112no—
786C2×SD16—112no—
787C2×SD16—112no—
788C2×SD16—112no—
789C2×SD16—442no—
790C2×D8—112no—
791C2×D8—112no—
792#131—442no—
793C2×M16—111no—
794C2×M16—111no—
795C2×M16—112no—
796C22×C8—111no—
797C22×C8—111no—
798C22×C8—111no—
799C22×C8—111no—
800C22×C8—111no—
801C22×C8—111no—
802C22×C8—112no—
803C22×C8—442no—
804C4⋊Q8—22no—
805C4⋊Q8—112no—
806C4⋊Q8—221no—
807C4⋊Q8C22×D1112yes—
808#127—221no—
809#126—222no—
810#126—222no—
811#125—112no—
812#125—221no—
813#124—22no—
814#124—221no—
815#124—222no—
816#124—222no—
817#124C22×D1112yes—
818#123—22no—
819#123—22no—
820#123—22no—
821#123—22no—
822#123—222no—
823#123—222no—
824#123—222no—
825#123—222no—
826#123C22⋊D1112yes—
827C22⋊Q8—21no—
828C22⋊Q8—21no—
829C22⋊Q8—21no—
830C22⋊Q8—21no—
831C22⋊Q8—22no—
832C22⋊Q8—21no—
833C22⋊Q8—22no—
834C22⋊Q8—22no—
835C22⋊Q8—222no—
836C22⋊Q8—222no—
837C22⋊Q8C22⋊D1111yescharacteristic
838C22⋊Q8C22⋊D1111yescharacteristic
839C22⋊Q8C22×D1112yes—
840C22⋊Q8C22×D1112yes—
841C22⋊Q8C22×D1112yes—
842#121—21no—
843#121—22no—
844#121—22no—
845#121—22no—
846#121—22no—
847#121—112no—
848#121—112no—
849#121—112no—
850#121—112no—
851#121—222no—
852#121—222no—
853#121—222no—
854#121—221no—
855#121—221no—
856#121C22⋊D1111yescharacteristic
857#121C22⋊D1111yescharacteristic
858#121C22×D1112yes—
859#120—22no—
860#120—222no—
861#120C22⋊D1112yes—
862C4×Q8—221no—
863C4×Q8C22×D1112yes—
864C4×D4—22no—
865C4×D4—22no—
866C4×D4—22no—
867C4×D4—112no—
868C4×D4—112no—
869C4×D4—221no—
870C4×D4—222no—
871C4×D4—221no—
872C4×D4—221no—
873C4×D4—222no—
874C4×D4—222no—
875C4×D4C22×D1112yes—
876C4×D4C22×D1112yes—
877C4×D4C22×D1112yes—
878#117—21no—
879#117—111no—
880#117—111no—
881#117—111no—
882#117—111no—
883#117—112no—
884#117—221no—
885#117—221no—
886#117—222no—
887#117C22×D1111yescharacteristic
888C2×C4⋊C4—21no—
889C2×C4⋊C4—21no—
890C2×C4⋊C4—22no—
891C2×C4⋊C4—111no—
892C2×C4⋊C4—111no—
893C2×C4⋊C4—111no—
894C2×C4⋊C4—112no—
895C2×C4⋊C4C22×D1111yescharacteristic
896C2×C22⋊C4—21no—
897C2×C22⋊C4—22no—
898C2×C22⋊C4—221no—
899C2×C22⋊C4—221no—
900C2×C22⋊C4—222no—
901C2×C42—221no—
902#107—112no—
903#107—112no—
904#106—112no—
905#106—112no—
906#106—112no—
907#106—112no—
908C4⋊C8—112no—
909C4⋊C8—112no—
910#103—111no—
911#103—112no—
912#103—111no—
913#103—111no—
914#103—111no—
915#103—111no—
916#103—111no—
917#103—111no—
918#103—111no—
919#103—112no—
920#103—112no—
921#103—112no—
922#103—112no—
923#103—112no—
924#103—112no—
925#103—112no—
926#102—111no—
927#102—111no—
928#102—111no—
929#102—111no—
930#102—111no—
931#102—111no—
932#102—111no—
933#102—111no—
934#102—112no—
935#102—112no—
936#102—112no—
937#102—112no—
938C22⋊C8—112no—
939C22⋊C8—112no—
940C22⋊C8—112no—
941C22⋊C8—112no—
942#97—112no—
943C4×C8—112no—
944C2×C11—22no—
945C2×C11—22no—
946C2×C11—42no—
947C2×C11—41no—
948C2×C11—42no—
949C2×C11—81no—
950C2×C11C2×#54611yescharacteristic
951C2×C11C2×#57711yescharacteristic
952C2×C11#358411yescharacteristic
953D11—82no—
954C24—21no—
955C24—221no—
956C24C2×C22⋊D1111yescharacteristic
957#41—22no—
958#41—22no—
959#41—22no—
960#41—22no—
961#41—22no—
962#41—24no—
963#41—22no—
964#41—22no—
965#41—44no—
966#41—41no—
967#41—41no—
968#41—42no—
969#41—44no—
970#41—44no—
971#41—48no—
972#41—884no—
973#41#434114yescomplemented
974C2×Q8—21no—
975C2×Q8—22no—
976C2×Q8—21no—
977C2×Q8—22no—
978C2×Q8—24no—
979C2×Q8—22no—
980C2×Q8—22no—
981C2×Q8—41no—
982C2×Q8—42no—
983C2×Q8—44no—
984C2×Q8—222no—
985C2×Q8C2×C22⋊D1111yescharacteristic
986C2×Q8C23×D1112yes—
987C2×Q8C23×D1111yescharacteristic
988C2×Q8C23×D1111yescharacteristic
989C2×D4—21no—
990C2×D4—22no—
991C2×D4—22no—
992C2×D4—21no—
993C2×D4—21no—
994C2×D4—21no—
995C2×D4—22no—
996C2×D4—21no—
997C2×D4—41no—
998C2×D4—44no—
999C2×D4—112no—
1000C2×D4—222no—
1001C2×D4—222no—
1002C2×D4—222no—
1003C2×D4—222no—
1004C2×D4—222no—
1005C2×D4—222no—
1006C2×D4—221no—
1007C2×D4—882no—
1008C2×D4C2×C22⋊D1112yes—
1009C2×D4C2×C22⋊D1112yes—
1010C2×D4C2×C22⋊D1111yescharacteristic
1011C2×D4C2×C22⋊D1112yes—
1012C2×D4C23×D1111yescharacteristic
1013C2×D4C23×D1111yescharacteristic
1014C22×C4—22no—
1015C22×C4—22no—
1016C22×C4—21no—
1017C22×C4—21no—
1018C22×C4—22no—
1019C22×C4—21no—
1020C22×C4—21no—
1021C22×C4—22no—
1022C22×C4—21no—
1023C22×C4—21no—
1024C22×C4—21no—
1025C22×C4—22no—
1026C22×C4—44no—
1027C22×C4—221no—
1028C22×C4—221no—
1029C22×C4—221no—
1030C22×C4—222no—
1031C22×C4—222no—
1032C22×C4—222no—
1033C22×C4C2×C22⋊D1111yescharacteristic
1034C22×C4C2×C22⋊D1111yescharacteristic
1035C22×C4C2×C22⋊D1111yescharacteristic
1036C22×C4C23×D1111yescharacteristic
1037C22×C4C23×D1112yes—
1038C22×C4C23×D1111yescharacteristic
1039C22×C4C23×D1111yescharacteristic
1040SD16—224no—
1041SD16—442no—
1042SD16—442no—
1043SD16—442no—
1044D8—224no—
1045D8—442no—
1046M16—222no—
1047M16—222no—
1048M16—442no—
1049C2×C8—111no—
1050C2×C8—112no—
1051C2×C8—111no—
1052C2×C8—111no—
1053C2×C8—111no—
1054C2×C8—112no—
1055C2×C8—222no—
1056C2×C8—222no—
1057C2×C8—441no—
1058C2×C8—441no—
1059C2×C8—441no—
1060C2×C8—441no—
1061C2×C8—442no—
1062C4⋊C4—22no—
1063C4⋊C4—21no—
1064C4⋊C4—22no—
1065C4⋊C4—22no—
1066C4⋊C4—22no—
1067C4⋊C4—22no—
1068C4⋊C4—22no—
1069C4⋊C4—111no—
1070C4⋊C4—112no—
1071C4⋊C4—111no—
1072C4⋊C4—111no—
1073C4⋊C4—111no—
1074C4⋊C4—221no—
1075C4⋊C4—221no—
1076C4⋊C4—221no—
1077C4⋊C4—222no—
1078C4⋊C4—222no—
1079C4⋊C4—222no—
1080C4⋊C4—222no—
1081C4⋊C4C2×C22⋊D1112yes—
1082C4⋊C4C2×C22⋊D1111yescharacteristic
1083C4⋊C4C2×C22⋊D1111yescharacteristic
1084C4⋊C4C2×C22⋊D1112yes—
1085C4⋊C4C23×D1112yes—
1086C22⋊C4—22no—
1087C22⋊C4—22no—
1088C22⋊C4—22no—
1089C22⋊C4—22no—
1090C22⋊C4—22no—
1091C22⋊C4—22no—
1092C22⋊C4—22no—
1093C22⋊C4—221no—
1094C22⋊C4—221no—
1095C22⋊C4—221no—
1096C22⋊C4—221no—
1097C22⋊C4—222no—
1098C22⋊C4—222no—
1099C22⋊C4—222no—
1100C22⋊C4—222no—
1101C22⋊C4—222no—
1102C22⋊C4—222no—
1103C22⋊C4—222no—
1104C22⋊C4C2×C22⋊D1112yes—
1105C22⋊C4C2×C22⋊D1112yes—
1106C22⋊C4C2×C22⋊D1112yes—
1107C22⋊C4C2×C22⋊D1112yes—
1108C22⋊C4C2×C22⋊D1112yes—
1109C42—22no—
1110C42—221no—
1111C42—221no—
1112C42—221no—
1113C42—221no—
1114C42—222no—
1115C42C23×D1112yes—
1116C11#6117411yescharacteristic, complemented, Sylow
1117C23—22no—
1118C23—22no—
1119C23—21no—
1120C23—21no—
1121C23—41no—
1122C23—42no—
1123C23—42no—
1124C23—81no—
1125C23—222no—
1126C23—442no—
1127C23—881no—
1128C23—881no—
1129C23C22×C22⋊D1111yescharacteristic
1130C23C22×C22⋊D1112yes—
1131C23C22×C22⋊D1111yescharacteristic
1132C23C22×C22⋊D1111yescharacteristic
1133Q8—22no—
1134Q8—21no—
1135Q8—22no—
1136Q8—21no—
1137Q8—22no—
1138Q8—21no—
1139Q8—44no—
1140Q8—42no—
1141Q8—42no—
1142Q8—882no—
1143Q8C2×#434112yes—
1144D4—24no—
1145D4—24no—
1146D4—24no—
1147D4—22no—
1148D4—21no—
1149D4—21no—
1150D4—21no—
1151D4—42no—
1152D4—42no—
1153D4—42no—
1154D4—42no—
1155D4—44no—
1156D4—42no—
1157D4—82no—
1158D4—222no—
1159D4—222no—
1160D4—444no—
1161D4—442no—
1162D4—882no—
1163D4—882no—
1164D4—882no—
1165D4C2×#434112yes—
1166C2×C4—22no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—21no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—44no—
1184C2×C4—44no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—82no—
1188C2×C4—81no—
1189C2×C4—221no—
1190C2×C4—221no—
1191C2×C4—221no—
1192C2×C4—221no—
1193C2×C4—222no—
1194C2×C4—442no—
1195C2×C4—882no—
1196C2×C4—882no—
1197C2×C4—881no—
1198C2×C4—882no—
1199C2×C4—881no—
1200C2×C4C2×#434112yes—
1201C2×C4#6703712yes—
1202C2×C4C22×C22⋊D1112yes—
1203C2×C4C22×C22⋊D1111yescharacteristic
1204C2×C4C22×C22⋊D1112yes—
1205C2×C4C22×C22⋊D1112yes—
1206C2×C4C22×C22⋊D1111yescharacteristic
1207C2×C4C22×C22⋊D1111yescharacteristic
1208C2×C4C24×D1111yescharacteristic
1209C8—222no—
1210C8—221no—
1211C8—221no—
1212C8—221no—
1213C8—221no—
1214C8—222no—
1215C22—21no—
1216C22—21no—
1217C22—21no—
1218C22—21no—
1219C22—21no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—21no—
1224C22—21no—
1225C22—22no—
1226C22—44no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—84no—
1233C22—442no—
1234C22—442no—
1235C22—442no—
1236C22—1762no—
1237C22#1062333712yes—
1238C22#1062336812yes—
1239C22C23×C22⋊D1111yescharacteristic
1240C4—21no—
1241C4—21no—
1242C4—22no—
1243C4—22no—
1244C4—22no—
1245C4—22no—
1246C4—41no—
1247C4—42no—
1248C4—42no—
1249C4—441no—
1250C4—441no—
1251C4—442no—
1252C4—441no—
1253C4—441no—
1254C4#1062333712yes—
1255C4C22×#434111yescharacteristic
1256C4C2×#6703711yescharacteristic
1257C2—22no—
1258C2—22no—
1259C2—41no—
1260C2—42no—
1261C2—42no—
1262C2—81no—
1263C2—882no—
1264C2C2×#1062333711yescharacteristic
1265C2C2×#1062336811yescharacteristic
1266C2#1308338711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3489C2
socleC22×C11C23×D4
hypercenter#3489D11
hypocenterC11#61174
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #525 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #13082353C2semidirect
2. #13080802C2semidirect
3. #13080787C2semidirect
4. #13080592C2semidirect
5. #13080577C2semidirect
6. #13080544C2semidirect
7. #13080518C2semidirect
8. #13080481C2semidirect
9. #13080466C2semidirect
10. #13078981C2semidirect
11. #13078601C2semidirect
12. #13078560C2semidirect
13. #13078478C2semidirect
14. #13078298C2semidirect
15. C2×#10622661C2semidirect
16. #13078124C2semidirect
17. #13077902C2semidirect
18. #13077868C2semidirect
19. #13077444C2semidirect
20. #13077311C2semidirect
21. #13077149C2semidirect
22. C2×#10622846C2semidirect
23. C11×#3489C2semidirect
26. D4×Q8×C11C22semidirect
27. C11×#548C22semidirect
29. C11×#547C22semidirect
31. C11×#546C22semidirect
41. #10623361C22semidirect
42. #10623358C22semidirect
45. C2×#67001C22semidirect
46. C22×#4325C22semidirect
57. #10623096C22semidirect
58. #10623094C22semidirect
60. #10623052C22semidirect
61. #10623050C22semidirect
64. #10622851C22semidirect
65. #10622851C22semidirect
66. #10622847C22semidirect
71. #10622846C22semidirect
72. #10622846C22semidirect
73. #10622846C22semidirect
74. #10622846C22semidirect
75. #10622846C22semidirect
78. #10622845C22semidirect
80. #10622840C22semidirect
81. #10622840C22semidirect
82. #10622838C22semidirect
83. #10622838C22semidirect
84. #10622838C22semidirect
85. C2×#66899C22semidirect
86. C2×#66899C22semidirect
87. C2×#66899C22semidirect
88. C2×#66899C22semidirect
90. C2×#66896C22semidirect
91. C2×#66896C22semidirect
93. #10622696C22semidirect
94. #10622696C22semidirect
95. #10622695C22semidirect
96. #10622694C22semidirect
97. #10622670C22semidirect
98. #10622670C22semidirect
99. #10622669C22semidirect
100. #10622668C22semidirect
101. #10622662C22semidirect
104. #10622661C22semidirect
105. #10622661C22semidirect
106. #10622661C22semidirect
107. #10622658C22semidirect
108. #10622658C22semidirect
109. #10622658C22semidirect
110. #10622657C22semidirect
111. #10622656C22semidirect
112. #10622656C22semidirect
113. #10622652C22semidirect
114. #10622651C22semidirect
115. #10622648C22semidirect
116. #10622647C22semidirect
117. #10622639C22semidirect
118. C4×#4325C22semidirect
119. #10622635C22semidirect
120. #10622633C22semidirect
121. #10622627C22semidirect
122. C4×#4323C22semidirect
123. #10622624C22semidirect
124. #10622624C22semidirect
125. D4×C11⋊C8C22semidirect
126. D4×C11⋊C8C22semidirect
127. #10622622C22semidirect
128. #10622621C22semidirect
129. #10622612C22semidirect
130. #10622610C22semidirect
131. C2×#66873C22semidirect
132. #10622577C22semidirect
133. #10622577C22semidirect
134. C2×#66872C22semidirect
340. C11×#41#41semidirect
485. #3489D11semidirect
616. D4×Q8C2×D11semidirect
617. #548C2×D11semidirect
620. #547C2×D11semidirect
623. #546C2×D11semidirect
973. #41#4341semidirect
1116. C11#61174semidirect

Maximal subgroups

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

subgroupindex
#130823532
#130808022
#130807872
#130805922
#130805772
#130805442
#130805182
#130804812
#130804662
#130789812
#130786012
#130785602
#130784782
#130782982
C2×#106226612
#130781242
#130779022
#130778682
#130774442
#130773112
#130771492
C2×#106228462
C11×#34892
#6117411