Finite Group Databasebeta

← #15624635

Subgroups — #15624635

Order 2816.

2186 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082280C211yesmaximal, characteristic
2D11×#536C211yesmaximal, characteristic, complemented
3#13079501C212yesmaximal, complemented
4#13079499C212yesmaximal, complemented
5#13079484C212yesmaximal, complemented
6#13079482C212yesmaximal, complemented
7#13079447C212yesmaximal, complemented
8#13079417C212yesmaximal, complemented
9#13079398C212yesmaximal, complemented
10#13079368C212yesmaximal, complemented
11#13078587C211yesmaximal, characteristic, complemented
12#13078581C211yesmaximal, characteristic, complemented
13#13078558C211yesmaximal, characteristic, complemented
14#13078527C211yesmaximal, characteristic, complemented
15#13078309C211yesmaximal, characteristic, complemented
16#13078257C211yesmaximal, characteristic, complemented
17#13078255C211yesmaximal, characteristic, complemented
18#13077896C211yesmaximal, characteristic, complemented
19#13077892C211yesmaximal, characteristic, complemented
20#13077848C211yesmaximal, characteristic, complemented
21C2×#10622419C211yesmaximal, characteristic, complemented
22#13077063C211yesmaximal, characteristic, complemented
23C11×#3063C211yesmaximal, characteristic, complemented
24C2×#67042C2211yescharacteristic
25C2×#41×D11C2211yescharacteristic
26C22×Q8×D11C2211yescharacteristic, complemented
27C2×C11×#137C2211yescharacteristic, complemented
28C2×C11×#131C2211yescharacteristic, complemented
29C11×#537C2211yescharacteristic
30C11×#536C2211yescharacteristic, complemented
31#10623361C2211yescharacteristic
32#10623359C2211yescharacteristic
33#10623356C2211yescharacteristic, complemented
34C2×#67004C2211yescharacteristic, complemented
35C2×#67001C2211yescharacteristic, complemented
36#10623347C2211yescharacteristic
37C22×#4325C2211yescharacteristic, complemented
38C22×#4314C2211yescharacteristic, complemented
39#10623255—21no—
40D11×C4⋊Q8—21no—
41#10623206—21no—
42D11×#124—21no—
43D11×#123—22no—
44#10623179—22no—
45#10623164—21no—
46#10623161—21no—
47#10623160C2212yes—
48#10623159C2212yescomplemented
49#10623159C2212yescomplemented
50#10623158C2212yes—
51D11×C22⋊Q8C2212yescomplemented
52D11×C22⋊Q8C2212yescomplemented
53#10623141—22no—
54#10623140—21no—
55#10623140—22no—
56#10623138C2212yes—
57D11×#121C2212yes—
58#10623130—21no—
59#10623057C2211yescharacteristic
60D11×#117C2211yescharacteristic, complemented
61C2×#66948C2211yescharacteristic
62#10623035C2211yescharacteristic
63C11×#470C2212yescomplemented
64C11×#468C2212yescomplemented
65C11×#467C2212yescomplemented
66C11×#465C2212yescomplemented
67C11×#428C2211yescharacteristic, complemented
68C11×#416C2211yescharacteristic, complemented
69C2×C11×#103C2211yescharacteristic, complemented
70#10622846C2211yescharacteristic, complemented
71#10622838C2211yescharacteristic, complemented
72#10622800C2212yescomplemented
73#10622800C2212yescomplemented
74#10622799C2212yescomplemented
75#10622799C2212yescomplemented
76#10622783C2212yescomplemented
77#10622783C2212yescomplemented
78#10622782C2212yescomplemented
79#10622782C2212yescomplemented
80#10622747C2212yescomplemented
81#10622747C2212yescomplemented
82#10622744C2211yescharacteristic, complemented
83#10622742C2211yescharacteristic
84#10622742C2212yescomplemented
85#10622739C2211yescharacteristic, complemented
86#10622739C2212yescomplemented
87#10622733C2211yescharacteristic, complemented
88#10622727C2212yescomplemented
89#10622727C2212yescomplemented
90#10622723C2211yescharacteristic
91#10622723C2212yescomplemented
92C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
93C2×(C2×D11)⋊C8C2212yescomplemented
94#10622719C2211yescharacteristic, complemented
95#10622665C2212yescomplemented
96#10622664C2212yescomplemented
97#10622662C2212yescomplemented
98#10622662C2212yescomplemented
99#10622661C2212yescomplemented
100#10622661C2212yescomplemented
101#10622655C2212yescomplemented
102#10622654C2212yescomplemented
103#10622614C2211yescharacteristic, complemented
104#10622611C2211yescharacteristic, complemented
105C2×#66874C2211yescharacteristic, complemented
106#10622577C2211yescharacteristic, complemented
107#10622501C2212yescomplemented
108#10622498C2212yescomplemented
109#10622497C2212yescomplemented
110#10622495C2212yescomplemented
111#10622480C2212yescomplemented
112#10622479C2212yescomplemented
113#10622476C2212yescomplemented
114#10622475C2212yescomplemented
115#10622428C2212yescomplemented
116#10622428C2211yescharacteristic, complemented
117#10622427C2212yescomplemented
118#10622427C2211yescharacteristic, complemented
119#10622423C2212yescomplemented
120#10622423C2212yescomplemented
121#10622422C2212yescomplemented
122#10622422C2211yescharacteristic, complemented
123#10622419C2212yescomplemented
124#10622419C2212yescomplemented
125#10622419C2212yescomplemented
126#10622419C2212yescomplemented
127#10622418C2212yescomplemented
128#10622418C2211yescharacteristic, complemented
129#10622397C2211yescharacteristic, complemented
130#10622392C2211yescharacteristic, complemented
131#10622390C2211yescharacteristic, complemented
132#10622389C2212yescomplemented
133#10622389C2212yescomplemented
134#10622387C2211yescharacteristic, complemented
135C2×C11×#41C2311yescharacteristic
136C2×C11×#41C2311yescharacteristic
137C22×Q8×C11C2311yescharacteristic
138#67042—42no—
139#67042—42no—
140#41×D11—42no—
141#41×D11—42no—
142C2×#4343D411yescharacteristic
143C2×#4343C2312yes—
144C2×Q8×D11—21no—
145C2×Q8×D11—21no—
146C2×Q8×D11—42no—
147C2×Q8×D11—42no—
148C2×Q8×D11D411yescharacteristic
149C2×Q8×D11C2312yes—
150C2×Q8×D11C2312yes—
151C2×#4341D411yescharacteristic
152C2×#4341D412yes—
153C2×D4×D11—22no—
154C2×D4×D11—22no—
155C2×D4×D11D412yes—
156C2×D4×D11D411yescharacteristic
157C2×D4×D11C2312yes—
158C2×#4339—21no—
159C2×#4339C2311yescharacteristic
160C2×#4339C2312yes—
161C22×D44—21no—
162C22×D44—21no—
163C22×D44C2311yescharacteristic
164C22×C4×D11—21no—
165C22×C4×D11C2311yescharacteristic
166C22×C4×D11C2312yes—
167C22×Dic22—21no—
168C22×Dic22C2311yescharacteristic
169C11×#137—42no—
170C2×C11×Q16C2312yes—
171C2×C11×SD16C2312yes—
172C11×#131—42no—
173C2×C11×M16C2311yescharacteristic
174C2×C11×M16C2312yes—
175C22×C8×C11C2311yescharacteristic
176C22×C8×C11C2312yes—
177C11×C4⋊Q8—21no—
178C11×#124—21no—
179C11×#123—22no—
180C11×C22⋊Q8—21no—
181C11×C22⋊Q8C2312yes—
182C11×C22⋊Q8C2312yes—
183C11×C22⋊Q8C2312yes—
184C11×#121—21no—
185C11×#121—22no—
186C11×#121C2312yes—
187C11×#117C2311yescharacteristic
188C2×C11×C4⋊C4C2311yescharacteristic
189#67004—42no—
190#67001—42no—
191#67000—21no—
192#67000—21no—
193#66999C2312yes—
194#66999C2312yes—
195#66999C2311yescharacteristic
196#66999C2311yescharacteristic
197#66997—21no—
198#66997—21no—
199C2×#4326C2312yes—
200C2×#4325—42no—
201C2×#4325C2312yes—
202C2×#4325C2312yes—
203#66993—21no—
204#66993—22no—
205#66992—22no—
206#66991C2311yescharacteristic
207#66991C2311yescharacteristic
208#66990—21no—
209#66990—22no—
210#66990—22no—
211#66989—21no—
212#66988—22no—
213#66988—21no—
214C2×#4324C2312yes—
215#66983C2312yes—
216#66983C2312yes—
217#66982—22no—
218C4×C22⋊D11—22no—
219C4×C22⋊D11—21no—
220C4×C22⋊D11—21no—
221C2×(C2×D11)⋊C4—21no—
222#66979C2311yescharacteristic
223#66979C2311yescharacteristic
224#66977C2312yes—
225#66977C2312yes—
226C2×#4318C2311yescharacteristic
227C2×#4318C2312yes—
228C22×C11⋊C8C2311yescharacteristic
229C22×C11⋊C8C2312yes—
230C2×#4314—42no—
231C2×#4314C2312yes—
232C2×#4314C2312yes—
233#66950C2312yes—
234#66950C2312yes—
235#66949—22no—
236#66949—22no—
237#66949—22no—
238#66948—22no—
239#66948—21no—
240#66948—21no—
241#66948C2312yes—
242#66948C2312yes—
243#66947—22no—
244#66947—22no—
245#66947—22no—
246#66946—21no—
247#66946—22no—
248#66945C2311yescharacteristic
249#66945C2312yes—
250#66945C2311yescharacteristic
251C4⋊C4×D11—22no—
252C4⋊C4×D11—22no—
253C4⋊C4×D11C2312yes—
254C4⋊C4×D11C2311yescharacteristic
255C4⋊C4×D11C2311yescharacteristic
256#66941—22no—
257#66941—22no—
258#66940—21no—
259#66939—22no—
260#66938—22no—
261#66938—22no—
262#66938—22no—
263#66937—22no—
264#66937—22no—
265#66937—22no—
266#66936—22no—
267#66936—22no—
268#66935—22no—
269#66935—22no—
270(C22⋊D11)⋊C4—22no—
271C22⋊C4×D11—21no—
272C22⋊C4×D11—22no—
273C22⋊C4×D11—22no—
274C22⋊C4×D11—22no—
275#66931—22no—
276#66931—22no—
277#66930—21no—
278#66928—21no—
279#66925—21no—
280C42×D11—21no—
281#66922—21no—
282C11×#107C2312yes—
283C11×#106C2312yes—
284C11×#103C2312yes—
285C11×#103C2312yes—
286C11×#103C2311yescharacteristic
287C11×#103C2311yescharacteristic
288C11×#102C2311yescharacteristic
289C11×#102C2311yescharacteristic
290#66899C2312yes—
291#66899C2312yes—
292#66899C2311yescharacteristic
293#66899C2311yescharacteristic
294#66896C2311yescharacteristic
295#66896C2311yescharacteristic
296#66885C2312yes—
297#66885C2312yes—
298(C2×D11)⋊C8C2311yescharacteristic
299(C2×D11)⋊C8C2312yes—
300(C2×D11)⋊C8C2311yescharacteristic
301(C2×D11)⋊C8C2312yes—
302(C2×D11)⋊C8C2312yes—
303(C2×D11)⋊C8C2311yescharacteristic
304(C2×D11)⋊C8C2311yescharacteristic
305(C2×D11)⋊C8C2312yes—
306(C2×D11)⋊C8C2312yes—
307(C2×D11)⋊C8C2312yes—
308#66882C2311yescharacteristic
309#66882C2311yescharacteristic
310#66881C2311yescharacteristic
311#66881C2311yescharacteristic
312#66880C2312yes—
313#66880C2312yes—
314#66874C2312yes—
315#66874C2312yes—
316#66873C2312yes—
317#66873C2312yes—
318#66872C2311yescharacteristic
319#66872C2312yes—
320#66872C2311yescharacteristic
321#66871C2312yes—
322#66871C2311yescharacteristic
323#66871C2311yescharacteristic
324#60758—111nomaximal, Sylow
325C23×D11—21no—
326C23×D11—22no—
327C23×D11C2×D411yescharacteristic
328C23×D11C2×D412yes—
329C11×#41—22no—
330C11×#41—22no—
331C11×#41—22no—
332C11×#41—22no—
333C2×Q8×C11—21no—
334C2×Q8×C11—22no—
335C2×Q8×C11—22no—
336C2×Q8×C11C2×D411yescharacteristic
337C2×Q8×C11C2412yes—
338C2×Q8×C11C2411yescharacteristic
339C2×D4×C11—21no—
340C2×D4×C11—22no—
341C2×D4×C11C2×D412yes—
342C2×D4×C11C2×D411yescharacteristic
343C2×D4×C11C2411yescharacteristic
344C22×C4×C11—21no—
345C22×C4×C11—21no—
346C22×C4×C11—21no—
347C22×C4×C11C2412yes—
348C22×C4×C11C2411yescharacteristic
349C2×C22⋊D11—22no—
350C2×C22⋊D11—22no—
351C2×C22⋊D11—22no—
352C2×C22⋊D11—21no—
353C2×C22⋊D11—21no—
354C2×C22⋊D11C2×D412yes—
355C2×C22⋊D11C2×D412yes—
356C2×C22⋊D11C2×D412yes—
357C22×Dic11—21no—
358C22×Dic11C2×D411yescharacteristic
359C22×Dic11C2×D412yes—
360#4343—42no—
361#4343—42no—
362#4343—42no—
363Q8×D11—42no—
364Q8×D11—42no—
365Q8×D11—42no—
366Q8×D11—42no—
367Q8×D11—42no—
368Q8×D11—44no—
369Q8×D11—44no—
370#4341—42no—
371#4341—44no—
372D4×D11—44no—
373D4×D11—42no—
374D4×D11—42no—
375D4×D11—42no—
376D4×D11—48no—
377D4×D11—84no—
378#4339—22no—
379#4339—22no—
380#4339—42no—
381#4339—42no—
382#4339—44no—
383C2×D44—22no—
384C2×D44—22no—
385C2×D44—22no—
386C2×D44—21no—
387C2×D44—22no—
388C2×D44—22no—
389C2×D44—44no—
390C2×D44—82no—
391C2×D44C2×D411yescharacteristic
392C2×D44C2×D412yes—
393C2×D44C2412yes—
394C2×C4×D11—22no—
395C2×C4×D11—21no—
396C2×C4×D11—21no—
397C2×C4×D11—22no—
398C2×C4×D11—22no—
399C2×C4×D11—22no—
400C2×C4×D11—22no—
401C2×C4×D11—22no—
402C2×C4×D11—42no—
403C2×C4×D11—42no—
404C2×C4×D11—44no—
405C2×C4×D11C2×D411yescharacteristic
406C2×C4×D11C2×D411yescharacteristic
407C2×C4×D11C2×D412yes—
408C2×C4×D11C2×D412yes—
409C2×C4×D11C2411yescharacteristic
410C2×C4×D11C2412yes—
411C2×C4×D11C2411yescharacteristic
412C2×Dic22—22no—
413C2×Dic22—22no—
414C2×Dic22—21no—
415C2×Dic22—22no—
416C2×Dic22—22no—
417C2×Dic22—44no—
418C2×Dic22C2×D411yescharacteristic
419C2×Dic22C2×D412yes—
420C2×Dic22C2412yes—
421C11×Q16—42no—
422C11×SD16—42no—
423C11×M16—22no—
424C11×M16—42no—
425C2×C8×C11—22no—
426C2×C8×C11—42no—
427C2×C8×C11C2412yes—
428C2×C8×C11C2411yescharacteristic
429C2×C8×C11C2411yescharacteristic
430C11×C4⋊C4—21no—
431C11×C4⋊C4—22no—
432C11×C4⋊C4—22no—
433C11×C4⋊C4—22no—
434C11×C4⋊C4C2411yescharacteristic
435C11×C4⋊C4C2411yescharacteristic
436C11×C4⋊C4C2412yes—
437C11×C22⋊C4—21no—
438C11×C22⋊C4—22no—
439C11×C22⋊C4—22no—
440C11×C22⋊C4—22no—
441C11×C22⋊C4—22no—
442C42×C11—21no—
443C22⋊Dic11—21no—
444C22⋊Dic11—21no—
445C22⋊Dic11—21no—
446C22⋊Dic11—22no—
447C22⋊Dic11—22no—
448C22⋊Dic11—21no—
449#4326—42no—
450#4325—42no—
451#4325—42no—
452#4324—42no—
453(C2×D11)⋊C4—22no—
454(C2×D11)⋊C4—22no—
455(C2×D11)⋊C4—21no—
456(C2×D11)⋊C4—21no—
457(C2×D11)⋊C4—22no—
458(C2×D11)⋊C4—22no—
459(C2×D11)⋊C4—22no—
460(C2×D11)⋊C4—22no—
461(C2×D11)⋊C4—22no—
462(C2×D11)⋊C4—21no—
463(C2×D11)⋊C4—21no—
464(C2×D11)⋊C4—22no—
465(C2×D11)⋊C4—22no—
466C4⋊Dic11—22no—
467C4⋊Dic11—22no—
468C4⋊Dic11C2411yescharacteristic
469C4⋊Dic11C2411yescharacteristic
470C4⋊Dic11C2411yescharacteristic
471C4⋊Dic11C2411yescharacteristic
472Dic11⋊C4—21no—
473Dic11⋊C4—21no—
474Dic11⋊C4—22no—
475Dic11⋊C4—22no—
476Dic11⋊C4—21no—
477Dic11⋊C4—22no—
478Dic11⋊C4—21no—
479Dic11⋊C4—22no—
480Dic11⋊C4—22no—
481C4×Dic11—21no—
482C4×Dic11—21no—
483C4×Dic11—22no—
484C4×Dic11—21no—
485C4×Dic11—21no—
486#4318—22no—
487#4318—42no—
488C2×C11⋊C8—22no—
489C2×C11⋊C8—42no—
490C2×C11⋊C8C2411yescharacteristic
491C2×C11⋊C8C2412yes—
492C2×C11⋊C8C2411yescharacteristic
493#4314—42no—
494#4314—42no—
495#3488—111no—
496C2×#536—111no—
497#3201—112no—
498#3201—112no—
499#3200—112no—
500#3200—112no—
501#3196—112no—
502#3193—112no—
503#3190—112no—
504#3187—112no—
505#3097—111no—
506#3097—111no—
507#3094—111no—
508#3091—111no—
509#3063—111no—
510#3063D1111yescharacteristic, complemented
511#3057—111no—
512#3057—111no—
513#3009—111no—
514#3009—111no—
515#3004—111no—
516C2×#448—111no—
517#2880—111no—
518C23×C11—21no—
519C23×C11C22×D412yes—
520C23×C11C22×D411yescharacteristic
521C22×D11—22no—
522C22×D11—22no—
523C22×D11—24no—
524C22×D11—22no—
525C22×D11—41no—
526C22×D11—42no—
527C22×D11—42no—
528C22×D11—44no—
529C22×D11—42no—
530C22×D11—82no—
531C22×D11—82no—
532C22×D11—81no—
533C22×D11—81no—
534C22×D11C22×D412yes—
535C22×D11C22×D411yescharacteristic
536C22×D11C22×D411yescharacteristic
537Q8×C11—22no—
538Q8×C11—22no—
539Q8×C11—21no—
540Q8×C11—22no—
541Q8×C11—21no—
542Q8×C11—42no—
543D4×C11—24no—
544D4×C11—22no—
545D4×C11—21no—
546D4×C11—21no—
547D4×C11—42no—
548D4×C11—82no—
549C2×C4×C11—22no—
550C2×C4×C11—22no—
551C2×C4×C11—21no—
552C2×C4×C11—21no—
553C2×C4×C11—22no—
554C2×C4×C11—22no—
555C2×C4×C11—21no—
556C2×C4×C11—42no—
557C2×C4×C11—42no—
558C2×C4×C11—81no—
559C2×C4×C11C22×D412yes—
560C2×C4×C11C22×D411yescharacteristic
561C2×C4×C11H(5,𝔽2)12yes—
562C2×C4×C11H(5,𝔽2)12yes—
563C2×C4×C11C2511yescharacteristic
564C22⋊D11—24no—
565C22⋊D11—42no—
566C22⋊D11—42no—
567C22⋊D11—44no—
568C22⋊D11—42no—
569C22⋊D11—81no—
570C22⋊D11—82no—
571C22⋊D11—82no—
572C2×Dic11—22no—
573C2×Dic11—21no—
574C2×Dic11—21no—
575C2×Dic11—21no—
576C2×Dic11—21no—
577C2×Dic11—22no—
578C2×Dic11—42no—
579C2×Dic11—42no—
580C2×Dic11C22×D411yescharacteristic
581C2×Dic11C22×D412yes—
582C2×Dic11C22×D411yescharacteristic
583D44—22no—
584D44—22no—
585D44—22no—
586D44—42no—
587D44—44no—
588D44—44no—
589D44—42no—
590D44—82no—
591C4×D11—22no—
592C4×D11—22no—
593C4×D11—21no—
594C4×D11—21no—
595C4×D11—21no—
596C4×D11—21no—
597C4×D11—22no—
598C4×D11—22no—
599C4×D11—42no—
600C4×D11—42no—
601C4×D11—44no—
602C4×D11—42no—
603C4×D11—44no—
604C4×D11—44no—
605C4×D11—42no—
606C4×D11—82no—
607Dic22—22no—
608Dic22—22no—
609Dic22—22no—
610Dic22—42no—
611Dic22—44no—
612Dic22—44no—
613Dic22—42no—
614C8×C11—21no—
615C8×C11—21no—
616C8×C11—22no—
617C11⋊C8—21no—
618C11⋊C8—21no—
619C11⋊C8—22no—
620C2×H(5,𝔽2)—111no—
621C22×#41—111no—
622C23×Q8—111no—
623C2×#137—111no—
624C2×#137C2×D1111yescharacteristic, complemented
625C22×SD16—111no—
626C22×SD16—111no—
627C2×#131—111no—
628C2×#131C2×D1111yescharacteristic, complemented
629#550—221no—
630#548—221no—
631#546—222no—
632#546—221no—
633D42—222no—
634D42—221no—
635#537—112no—
636#537C2×D1111yescharacteristic
637#536—111no—
638#536—111no—
639#536—112no—
640#536—112no—
641#536—111no—
642#536—222no—
643#536—221no—
644#536—221no—
645#536C2×D1111yescharacteristic, complemented
646#535—111no—
647#535—112no—
648C2×C4⋊Q8—221no—
649C2×#124—221no—
650#525—111no—
651#525—112no—
652C2×#123—222no—
653C2×C22⋊Q8—112no—
654C2×C22⋊Q8—112no—
655C2×#121—112no—
656C2×#121—111no—
657#520—111no—
658C2×#117—111no—
659#485—112no—
660#485—112no—
661#485—111no—
662#485—111no—
663#485—112no—
664#485—112no—
665#484—112no—
666#484—111no—
667#484—112no—
668#483—112no—
669#483—111no—
670#483—112no—
671#482—112no—
672#482—112no—
673#482—111no—
674#482—111no—
675#481—112no—
676#481—111no—
677#480—112no—
678#480—111no—
679#470—112no—
680#470C2×D1112yescomplemented
681#468—112no—
682#468—112no—
683#468—112no—
684#468—112no—
685#468—112no—
686#468C2×D1112yescomplemented
687#467—112no—
688#467C2×D1112yescomplemented
689#465—112no—
690#465—112no—
691#465—112no—
692#465—112no—
693#465—112no—
694#465C2×D1112yescomplemented
695#452—112no—
696#452—112no—
697#452—112no—
698#452—112no—
699#451—112no—
700#451—112no—
701#450—112no—
702#450—112no—
703#450—112no—
704#450—112no—
705#448—112no—
706#448—112no—
707#448—112no—
708#448—112no—
709#448—112no—
710#448—112no—
711#428—111no—
712#428C2×D1111yescharacteristic, complemented
713#427—111no—
714#427—111no—
715#419—111no—
716#419—111no—
717#418—111no—
718#418—111no—
719#416—111no—
720#416C2×D1111yescharacteristic, complemented
721C2×#103—111no—
722C2×#103C2×D1111yescharacteristic, complemented
723#408—111no—
724#408—112no—
725#408—111no—
726#408—112no—
727#407—111no—
728#407—112no—
729C2×C22⋊C8—111no—
730C2×C22⋊C8—112no—
731C22×C11—21no—
732C22×C11—21no—
733C22×C11—22no—
734C22×C11—22no—
735C22×C11—22no—
736C22×C11—41no—
737C22×C11—41no—
738C22×C11—41no—
739C22×C11#53412yes—
740C22×C11C23×D411yescharacteristic
741C2×D11—21no—
742C2×D11—21no—
743C2×D11—22no—
744C2×D11—21no—
745C2×D11—21no—
746C2×D11—22no—
747C2×D11—22no—
748C2×D11—21no—
749C2×D11—44no—
750C2×D11—42no—
751C2×D11—42no—
752C2×D11—42no—
753C2×D11—84no—
754C2×D11—164no—
755C2×D11—162no—
756C2×D11#57712yes—
757C4×C11—22no—
758C4×C11—41no—
759C4×C11—41no—
760C4×C11—42no—
761C4×C11—42no—
762C4×C11—41no—
763C4×C11#53412yes—
764C4×C11C2×H(5,𝔽2)11yescharacteristic
765C4×C11C2×H(5,𝔽2)11yescharacteristic
766Dic11—22no—
767Dic11—21no—
768Dic11—21no—
769Dic11—41no—
770Dic11—41no—
771Dic11—42no—
772Dic11—41no—
773Dic11—41no—
774H(5,𝔽2)—442no—
775H(5,𝔽2)—442no—
776C2×#41—111no—
777C2×#41—112no—
778C2×#41—111no—
779C2×#41—111no—
780C2×#41—112no—
781C2×#41—112no—
782C2×#41—221no—
783C2×#41—442no—
784C2×#41—442no—
785C2×#41C22×D1111yescharacteristic
786C2×#41C22×D1111yescharacteristic
787C22×Q8—111no—
788C22×Q8—112no—
789C22×Q8—112no—
790C22×Q8—111no—
791C22×Q8—221no—
792C22×Q8—221no—
793C22×Q8—221no—
794C22×Q8—442no—
795C22×Q8—442no—
796C22×Q8C22×D1111yescharacteristic
797C22×D4—112no—
798C22×D4—111no—
799C22×D4—112no—
800C22×D4—111no—
801C22×D4—221no—
802C22×D4—221no—
803C22×D4—222no—
804C22×D4—222no—
805C23×C4—111no—
806C23×C4—112no—
807C23×C4—221no—
808#137—42no—
809#137—442no—
810C2×Q16—112no—
811C2×Q16C22×D1112yes—
812C2×SD16—112no—
813C2×SD16—112no—
814C2×SD16—112no—
815C2×SD16—112no—
816C2×SD16—112no—
817C2×SD16—442no—
818C2×SD16—442no—
819C2×SD16C22×D1112yes—
820#131—42no—
821#131—442no—
822C2×M16—111no—
823C2×M16—112no—
824C2×M16C22×D1111yescharacteristic
825C2×M16C22×D1112yes—
826C22×C8—111no—
827C22×C8—112no—
828C22×C8C22×D1111yescharacteristic
829C22×C8C22×D1112yes—
830C4⋊Q8—21no—
831C4⋊Q8—221no—
832C4⋊Q8—222no—
833C4⋊Q8—222no—
834C4⋊Q8—221no—
835C4⋊Q8—221no—
836#127—222no—
837#127—221no—
838#124—21no—
839#124—221no—
840#124—222no—
841#124—222no—
842#124—222no—
843#124—221no—
844#124—221no—
845#124—221no—
846#123—22no—
847#123—222no—
848#123—222no—
849#123—222no—
850#123—222no—
851#123—222no—
852#123—222no—
853#123—222no—
854#123—221no—
855#123—222no—
856C22⋊Q8—21no—
857C22⋊Q8—112no—
858C22⋊Q8—112no—
859C22⋊Q8—111no—
860C22⋊Q8—111no—
861C22⋊Q8—112no—
862C22⋊Q8—112no—
863C22⋊Q8—112no—
864C22⋊Q8—112no—
865C22⋊Q8—222no—
866C22⋊Q8—222no—
867C22⋊Q8—222no—
868C22⋊Q8—222no—
869C22⋊Q8—222no—
870C22⋊Q8C22×D1112yes—
871C22⋊Q8C22×D1112yes—
872C22⋊Q8C22×D1112yes—
873#121—22no—
874#121—21no—
875#121—111no—
876#121—111no—
877#121—112no—
878#121—112no—
879#121—112no—
880#121—112no—
881#121—222no—
882#121—222no—
883#121—222no—
884#121—221no—
885#121—221no—
886#121—222no—
887#121—222no—
888#121C22×D1112yes—
889#120—222no—
890#120—222no—
891#120—222no—
892#120—221no—
893#120—222no—
894C4×Q8—221no—
895C4×D4—222no—
896C4×D4—222no—
897C4×D4—221no—
898C4×D4—221no—
899C4×D4—221no—
900C4×D4—222no—
901#117—111no—
902#117—111no—
903#117—111no—
904#117—111no—
905#117—112no—
906#117—221no—
907#117—221no—
908#117C22×D1111yescharacteristic
909C2×C4⋊C4—111no—
910C2×C4⋊C4—111no—
911C2×C4⋊C4—112no—
912C2×C4⋊C4—222no—
913C2×C4⋊C4—222no—
914C2×C4⋊C4C22×D1111yescharacteristic
915C2×C22⋊C4—222no—
916C2×C22⋊C4—221no—
917C2×C22⋊C4—222no—
918C2×C22⋊C4—222no—
919C2×C22⋊C4—221no—
920C2×C42—221no—
921#107—111no—
922#107—111no—
923#107—111no—
924#107—111no—
925#107—112no—
926#107C22×D1112yes—
927#106—111no—
928#106—111no—
929#106—111no—
930#106—111no—
931#106—112no—
932#106C22×D1112yes—
933#103—111no—
934#103—111no—
935#103—112no—
936#103—112no—
937#103—112no—
938#103—112no—
939#103—112no—
940#103—112no—
941#103C22×D1112yes—
942#103C22×D1112yes—
943#103C22×D1111yescharacteristic
944#103C22×D1111yescharacteristic
945#102—111no—
946#102—111no—
947#102—112no—
948#102—112no—
949#102—112no—
950#102—112no—
951#102C22×D1111yescharacteristic
952#102C22×D1111yescharacteristic
953C22⋊C8—111no—
954C22⋊C8—111no—
955C22⋊C8—112no—
956C22⋊C8—111no—
957C22⋊C8—111no—
958C22⋊C8—112no—
959C22⋊C8—112no—
960C22⋊C8—112no—
961C22⋊C8—112no—
962C22⋊C8—112no—
963C2×C11—22no—
964C2×C11—42no—
965C2×C11—81no—
966C2×C11C2×#53411yescharacteristic
967C2×C11C2×#57711yescharacteristic
968C2×C11#358611yescharacteristic
969D11—22no—
970D11—41no—
971D11—42no—
972D11—82no—
973C24—111no—
974C24—112no—
975C24—222no—
976C24—221no—
977#41—22no—
978#41—22no—
979#41—22no—
980#41—22no—
981#41—222no—
982#41—222no—
983#41—442no—
984#41—442no—
985#41—444no—
986#41—444no—
987#41—442no—
988#41—442no—
989#41—442no—
990#41—442no—
991C2×Q8—21no—
992C2×Q8—22no—
993C2×Q8—22no—
994C2×Q8—111no—
995C2×Q8—112no—
996C2×Q8—112no—
997C2×Q8—222no—
998C2×Q8—222no—
999C2×Q8—221no—
1000C2×Q8—222no—
1001C2×Q8—222no—
1002C2×Q8—444no—
1003C2×Q8—442no—
1004C2×Q8—442no—
1005C2×Q8—442no—
1006C2×Q8—442no—
1007C2×Q8—442no—
1008C2×Q8—444no—
1009C2×Q8—444no—
1010C2×Q8D4×D1111yescharacteristic
1011C2×Q8C23×D1112yes—
1012C2×Q8C23×D1111yescharacteristic
1013C2×D4—21no—
1014C2×D4—22no—
1015C2×D4—112no—
1016C2×D4—112no—
1017C2×D4—112no—
1018C2×D4—111no—
1019C2×D4—112no—
1020C2×D4—112no—
1021C2×D4—222no—
1022C2×D4—222no—
1023C2×D4—222no—
1024C2×D4—222no—
1025C2×D4—221no—
1026C2×D4—221no—
1027C2×D4—222no—
1028C2×D4—222no—
1029C2×D4—221no—
1030C2×D4—222no—
1031C2×D4—222no—
1032C2×D4—444no—
1033C2×D4—442no—
1034C2×D4—442no—
1035C2×D4—442no—
1036C2×D4—444no—
1037C2×D4—448no—
1038C2×D4—882no—
1039C2×D4—884no—
1040C2×D4D4×D1112yes—
1041C2×D4D4×D1111yescharacteristic
1042C2×D4C23×D1111yescharacteristic
1043C22×C4—21no—
1044C22×C4—21no—
1045C22×C4—21no—
1046C22×C4—111no—
1047C22×C4—112no—
1048C22×C4—111no—
1049C22×C4—111no—
1050C22×C4—111no—
1051C22×C4—112no—
1052C22×C4—111no—
1053C22×C4—112no—
1054C22×C4—112no—
1055C22×C4—222no—
1056C22×C4—221no—
1057C22×C4—221no—
1058C22×C4—222no—
1059C22×C4—222no—
1060C22×C4—222no—
1061C22×C4—222no—
1062C22×C4—222no—
1063C22×C4—221no—
1064C22×C4—442no—
1065C22×C4—442no—
1066C22×C4—444no—
1067C22×C4C23×D1112yes—
1068C22×C4C23×D1111yescharacteristic
1069Q16—42no—
1070Q16—442no—
1071SD16—42no—
1072SD16—442no—
1073SD16—442no—
1074SD16—442no—
1075SD16—442no—
1076SD16—442no—
1077M16—22no—
1078M16—42no—
1079M16—222no—
1080M16—442no—
1081C2×C8—22no—
1082C2×C8—42no—
1083C2×C8—112no—
1084C2×C8—111no—
1085C2×C8—111no—
1086C2×C8—222no—
1087C2×C8—442no—
1088C2×C8C23×D1112yes—
1089C2×C8C23×D1111yescharacteristic
1090C2×C8C23×D1111yescharacteristic
1091C4⋊C4—22no—
1092C4⋊C4—22no—
1093C4⋊C4—21no—
1094C4⋊C4—22no—
1095C4⋊C4—111no—
1096C4⋊C4—111no—
1097C4⋊C4—111no—
1098C4⋊C4—111no—
1099C4⋊C4—221no—
1100C4⋊C4—221no—
1101C4⋊C4—222no—
1102C4⋊C4—222no—
1103C4⋊C4—222no—
1104C4⋊C4—222no—
1105C4⋊C4—222no—
1106C4⋊C4—221no—
1107C4⋊C4—221no—
1108C4⋊C4—222no—
1109C4⋊C4—222no—
1110C4⋊C4C23×D1111yescharacteristic
1111C4⋊C4C23×D1111yescharacteristic
1112C4⋊C4C23×D1112yes—
1113C22⋊C4—21no—
1114C22⋊C4—22no—
1115C22⋊C4—22no—
1116C22⋊C4—22no—
1117C22⋊C4—22no—
1118C22⋊C4—222no—
1119C22⋊C4—222no—
1120C22⋊C4—221no—
1121C22⋊C4—221no—
1122C22⋊C4—222no—
1123C22⋊C4—222no—
1124C22⋊C4—222no—
1125C22⋊C4—222no—
1126C22⋊C4—222no—
1127C22⋊C4—221no—
1128C22⋊C4—221no—
1129C22⋊C4—221no—
1130C22⋊C4—221no—
1131C22⋊C4—221no—
1132C22⋊C4—222no—
1133C22⋊C4—222no—
1134C22⋊C4—221no—
1135C22⋊C4—222no—
1136C22⋊C4—222no—
1137C42—21no—
1138C42—221no—
1139C42—221no—
1140C42—222no—
1141C42—221no—
1142C42—221no—
1143C11#6075811yescharacteristic, complemented, Sylow
1144C23—21no—
1145C23—111no—
1146C23—112no—
1147C23—111no—
1148C23—222no—
1149C23—224no—
1150C23—222no—
1151C23—222no—
1152C23—441no—
1153C23—442no—
1154C23—442no—
1155C23—444no—
1156C23—442no—
1157C23—881no—
1158C23—881no—
1159C23—882no—
1160C23—882no—
1161C23C2×D4×D1112yes—
1162C23C2×D4×D1111yescharacteristic
1163Q8—22no—
1164Q8—22no—
1165Q8—21no—
1166Q8—22no—
1167Q8—21no—
1168Q8—42no—
1169Q8—222no—
1170Q8—222no—
1171Q8—222no—
1172Q8—442no—
1173Q8—444no—
1174Q8—444no—
1175Q8—442no—
1176D4—24no—
1177D4—22no—
1178D4—21no—
1179D4—21no—
1180D4—42no—
1181D4—82no—
1182D4—224no—
1183D4—222no—
1184D4—222no—
1185D4—222no—
1186D4—442no—
1187D4—444no—
1188D4—444no—
1189D4—442no—
1190D4—442no—
1191D4—444no—
1192D4—442no—
1193D4—442no—
1194D4—882no—
1195D4—882no—
1196D4—882no—
1197D4—881no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—81no—
1208C2×C4—111no—
1209C2×C4—112no—
1210C2×C4—111no—
1211C2×C4—222no—
1212C2×C4—222no—
1213C2×C4—222no—
1214C2×C4—221no—
1215C2×C4—221no—
1216C2×C4—222no—
1217C2×C4—221no—
1218C2×C4—221no—
1219C2×C4—222no—
1220C2×C4—221no—
1221C2×C4—221no—
1222C2×C4—221no—
1223C2×C4—221no—
1224C2×C4—222no—
1225C2×C4—442no—
1226C2×C4—442no—
1227C2×C4—444no—
1228C2×C4—442no—
1229C2×C4—444no—
1230C2×C4—444no—
1231C2×C4—442no—
1232C2×C4—442no—
1233C2×C4—442no—
1234C2×C4—882no—
1235C2×C4C2×D4×D1112yes—
1236C2×C4C2×D4×D1111yescharacteristic
1237C2×C4#6703712yes—
1238C2×C4#6704212yes—
1239C2×C4C24×D1111yescharacteristic
1240C8—21no—
1241C8—21no—
1242C8—22no—
1243C8—221no—
1244C8—221no—
1245C8—222no—
1246C22—21no—
1247C22—21no—
1248C22—22no—
1249C22—22no—
1250C22—22no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—112no—
1255C22—221no—
1256C22—221no—
1257C22—221no—
1258C22—222no—
1259C22—221no—
1260C22—222no—
1261C22—222no—
1262C22—221no—
1263C22—444no—
1264C22—442no—
1265C22—442no—
1266C22—442no—
1267C22—884no—
1268C22—1762no—
1269C22—1764no—
1270C22#1062313612yes—
1271C22C22×D4×D1111yescharacteristic
1272C4—22no—
1273C4—41no—
1274C4—41no—
1275C4—42no—
1276C4—42no—
1277C4—41no—
1278C4—221no—
1279C4—221no—
1280C4—222no—
1281C4—441no—
1282C4—441no—
1283C4—442no—
1284C4—441no—
1285C4—441no—
1286C4#1062313612yes—
1287C4C2×#6703711yescharacteristic
1288C4C2×#6704211yescharacteristic
1289C2—22no—
1290C2—42no—
1291C2—81no—
1292C2—222no—
1293C2—441no—
1294C2—442no—
1295C2—882no—
1296C2C2×#1062313611yescharacteristic
1297C2D11×#57711yescharacteristic
1298C2#1308340111yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3063C2
socleC22×C11C23×D4
prime radical#13082280C2
hypercenter#3063D11
hypocenterC11#60758
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3063

Complements

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

NH ≅ G/Ntype
2. D11×#536C2semidirect
3. #13079501C2semidirect
4. #13079499C2semidirect
5. #13079484C2semidirect
6. #13079482C2semidirect
7. #13079447C2semidirect
8. #13079417C2semidirect
9. #13079398C2semidirect
10. #13079368C2semidirect
11. #13078587C2semidirect
12. #13078581C2semidirect
13. #13078558C2semidirect
14. #13078527C2semidirect
15. #13078309C2semidirect
16. #13078257C2semidirect
17. #13078255C2semidirect
18. #13077896C2semidirect
19. #13077892C2semidirect
20. #13077848C2semidirect
21. C2×#10622419C2semidirect
22. #13077063C2semidirect
23. C11×#3063C2semidirect
26. C22×Q8×D11C22semidirect
27. C2×C11×#137C22semidirect
28. C2×C11×#131C22semidirect
30. C11×#536C22semidirect
33. #10623356C22semidirect
34. C2×#67004C22semidirect
35. C2×#67001C22semidirect
37. C22×#4325C22semidirect
38. C22×#4314C22semidirect
48. #10623159C22semidirect
49. #10623159C22semidirect
51. D11×C22⋊Q8C22semidirect
52. D11×C22⋊Q8C22semidirect
60. D11×#117C22semidirect
63. C11×#470C22semidirect
64. C11×#468C22semidirect
65. C11×#467C22semidirect
66. C11×#465C22semidirect
67. C11×#428C22semidirect
68. C11×#416C22semidirect
69. C2×C11×#103C22semidirect
70. #10622846C22semidirect
71. #10622838C22semidirect
72. #10622800C22semidirect
73. #10622800C22semidirect
74. #10622799C22semidirect
75. #10622799C22semidirect
76. #10622783C22semidirect
77. #10622783C22semidirect
78. #10622782C22semidirect
79. #10622782C22semidirect
80. #10622747C22semidirect
81. #10622747C22semidirect
82. #10622744C22semidirect
84. #10622742C22semidirect
85. #10622739C22semidirect
86. #10622739C22semidirect
87. #10622733C22semidirect
88. #10622727C22semidirect
89. #10622727C22semidirect
91. #10622723C22semidirect
92. C2×(C2×D11)⋊C8C22semidirect
93. C2×(C2×D11)⋊C8C22semidirect
94. #10622719C22semidirect
95. #10622665C22semidirect
96. #10622664C22semidirect
97. #10622662C22semidirect
98. #10622662C22semidirect
99. #10622661C22semidirect
100. #10622661C22semidirect
101. #10622655C22semidirect
102. #10622654C22semidirect
103. #10622614C22semidirect
104. #10622611C22semidirect
105. C2×#66874C22semidirect
106. #10622577C22semidirect
107. #10622501C22semidirect
108. #10622498C22semidirect
109. #10622497C22semidirect
110. #10622495C22semidirect
111. #10622480C22semidirect
112. #10622479C22semidirect
113. #10622476C22semidirect
114. #10622475C22semidirect
115. #10622428C22semidirect
116. #10622428C22semidirect
117. #10622427C22semidirect
118. #10622427C22semidirect
119. #10622423C22semidirect
120. #10622423C22semidirect
121. #10622422C22semidirect
122. #10622422C22semidirect
123. #10622419C22semidirect
124. #10622419C22semidirect
125. #10622419C22semidirect
126. #10622419C22semidirect
127. #10622418C22semidirect
128. #10622418C22semidirect
129. #10622397C22semidirect
130. #10622392C22semidirect
131. #10622390C22semidirect
132. #10622389C22semidirect
133. #10622389C22semidirect
134. #10622387C22semidirect
510. #3063D11semidirect
624. C2×#137C2×D11semidirect
628. C2×#131C2×D11semidirect
645. #536C2×D11semidirect
680. #470C2×D11semidirect
686. #468C2×D11semidirect
688. #467C2×D11semidirect
694. #465C2×D11semidirect
712. #428C2×D11semidirect
720. #416C2×D11semidirect
722. C2×#103C2×D11semidirect
1143. C11#60758semidirect

Maximal subgroups

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

subgroupindex
#130822802
D11×#5362
#130795012
#130794992
#130794842
#130794822
#130794472
#130794172
#130793982
#130793682
#130785872
#130785812
#130785582
#130785272
#130783092
#130782572
#130782552
#130778962
#130778922
#130778482
C2×#106224192
#130770632
C11×#30632
#6075811