Finite Group Databasebeta

← #15622176

Subgroups — #15622176

Order 2816.

2170 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic, complemented
2#13078778C212yesmaximal, complemented
3#13078767C212yesmaximal, complemented
4#13078725C214yesmaximal, complemented
5#13078687C212yesmaximal, complemented
6#13078676C212yesmaximal, complemented
7#13078634C214yesmaximal, complemented
8#13078547C212yesmaximal, complemented
9#13078421C211yesmaximal, characteristic, complemented
10#13078413C211yesmaximal, characteristic, complemented
11#13078088C211yesmaximal, characteristic, complemented
12#13078080C211yesmaximal, characteristic, complemented
13#13077858C212yesmaximal, complemented
14C4×#66995C212yesmaximal, complemented
15C4×#66985C212yesmaximal, complemented
16#13077249C211yesmaximal, characteristic, complemented
17C2×C4×C11×#41C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic
19C4×C11×#41—21no—
20C4×C11×#41—21no—
21C4×C11×#41—21no—
22C4×C11×#41—21no—
23C4×C11×#41C2212yes—
24C4×C11×#41C2212yes—
25C4×C11×#41C2212yes—
26C4×C11×#41C2212yes—
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11—21no—
30C2×C4×D4×C11—21no—
31C2×C4×D4×C11C2211yescharacteristic
32C2×C4×D4×C11C2211yescharacteristic
33C2×C11×#117—21no—
34C2×C11×#117C2211yescharacteristic
35C22×C42×C11—21no—
36C22×C42×C11C2211yescharacteristic
37C2×#66995C2212yes—
38C2×#66985C2212yes—
39#10623322—21no—
40#10623322—21no—
41#10623322C2212yes—
42#10623010—21no—
43#10623010—21no—
44#10623010—21no—
45#10623010—21no—
46#10623010C2212yescomplemented
47#10623010C2212yescomplemented
48#10623008C2211yescharacteristic
49#10623008C2211yescharacteristic, complemented
50#10623008C2211yescharacteristic, complemented
51C4×#4339—21no—
52C4×#4339—21no—
53C4×#4339C2212yes—
54#10623001C2211yescharacteristic
55#10623001C2211yescharacteristic, complemented
56#10623001C2211yescharacteristic, complemented
57#10622852C2214yes—
58#10622852C2214yes—
59#10622851C2214yes—
60#10622851C2214yes—
61#10622838C2212yes—
62#10622828C2212yes—
63#10622820C2212yes—
64#10622644C2212yescomplemented
65#10622643C2214yescomplemented
66C4×#4326C2214yescomplemented
67#10622641C2214yescomplemented
68#10622640C2212yescomplemented
69#10622639C2214yescomplemented
70C4×#4325C2214yescomplemented
71#10622635C2214yescomplemented
72#10622634C2212yescomplemented
73#10622633C2212yescomplemented
74#10622632C2212yescomplemented
75#10622631C2214yescomplemented
76C4×#4324C2214yescomplemented
77#10622629C2214yescomplemented
78#10622628C2212yescomplemented
79#10622627C2214yescomplemented
80C4×#4323C2214yescomplemented
81#10622622C2214yescomplemented
82#10622621C2212yescomplemented
83#10622620C2212yescomplemented
84#10622616C2214yescomplemented
85#10622616C2214yescomplemented
86#10622609C2214yescomplemented
87#10622609C2214yescomplemented
88#10622579C2212yes—
89#10622579C2212yes—
90#10622577C2212yes—
91#10622577C2212yes—
92#10622539C2212yescomplemented
93#10622539C2212yescomplemented
94#10622538C2212yescomplemented
95#10622538C2212yescomplemented
96#10622537C2211yescharacteristic
97#10622537C2211yescharacteristic
98C4×#4318C2212yes—
99C2×C11×#41—24no—
100C2×C11×#41—24no—
101C2×C11×#41—21no—
102C2×C11×#41—21no—
103C2×C11×#41C2312yes—
104C2×C11×#41C2312yes—
105C22×Q8×C11C2311yescharacteristic
106C22×D4×C11—21no—
107C22×D4×C11C2311yescharacteristic
108C23×C4×C11—21no—
109C23×C4×C11—21no—
110C23×C4×C11—21no—
111C23×C4×C11D411yescharacteristic
112C23×C4×C11D411yescharacteristic
113C23×C4×C11C2311yescharacteristic
114C2×#4339—21no—
115C2×#4339—21no—
116C2×#4339C2312yes—
117C4×Q8×C11—21no—
118C4×Q8×C11—21no—
119C4×Q8×C11—21no—
120C4×Q8×C11—21no—
121C4×Q8×C11C2312yes—
122C4×Q8×C11C2312yes—
123C4×Q8×C11C2312yes—
124C4×Q8×C11C2312yes—
125C4×D4×C11—22no—
126C4×D4×C11—22no—
127C4×D4×C11—22no—
128C4×D4×C11—22no—
129C4×D4×C11—22no—
130C4×D4×C11—22no—
131C4×D4×C11—22no—
132C4×D4×C11—22no—
133C4×D4×C11—21no—
134C4×D4×C11—21no—
135C4×D4×C11—21no—
136C4×D4×C11—21no—
137C4×D4×C11C2312yes—
138C4×D4×C11C2312yes—
139C4×D4×C11C2312yes—
140C4×D4×C11C2312yes—
141C11×#117—21no—
142C11×#117—21no—
143C11×#117—22no—
144C11×#117—22no—
145C11×#117—22no—
146C11×#117—22no—
147C11×#117C2312yes—
148C11×#117C2312yes—
149C2×C11×C4⋊C4—21no—
150C2×C11×C4⋊C4—21no—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C22⋊C4—21no—
154C2×C11×C22⋊C4—21no—
155C2×C11×C22⋊C4—21no—
156C2×C42×C11—21no—
157C2×C42×C11—21no—
158C2×C42×C11—21no—
159C2×C42×C11—22no—
160C2×C42×C11—22no—
161C2×C42×C11—22no—
162C2×C42×C11—22no—
163C2×C42×C11D411yescharacteristic
164C2×C42×C11D411yescharacteristic
165C2×C42×C11D411yescharacteristic
166C2×C42×C11D411yescharacteristic
167C2×C42×C11D411yescharacteristic
168C2×C42×C11D411yescharacteristic
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2311yescharacteristic
173C2×C42×C11C2311yescharacteristic
174C2×C42×C11C2311yescharacteristic
175#67006—22no—
176C2×#4326C2314yes—
177#66995—28no—
178C2×#4325C2314yes—
179C2×#4324C2314yes—
180#66985—28no—
181C2×#4323C2314yes—
182#66983—21no—
183#66983—21no—
184#66983—21no—
185#66983—21no—
186#66983C2312yes—
187#66983C2312yes—
188#66982—22no—
189#66982—22no—
190#66982—22no—
191C4×C22⋊D11—22no—
192C4×C22⋊D11—22no—
193C4×C22⋊D11—22no—
194C4×C22⋊D11—22no—
195C4×C22⋊D11—22no—
196C4×C22⋊D11—22no—
197#66979—21no—
198#66979—21no—
199#66979C2312yes—
200#66977—21no—
201#66977—21no—
202#66977—21no—
203#66977—21no—
204#66977C2312yes—
205#66977C2312yes—
206C2×#4318C2312yes—
207C2×#4318C2312yes—
208#66929—22no—
209#66929—22no—
210#66928—21no—
211#66928—21no—
212#66928C2312yes—
213#66927C2311yescharacteristic
214C4×D44—21no—
215C4×D44—21no—
216C4×D44—21no—
217C4×D44—21no—
218C4×D44C2312yes—
219C4×D44C2312yes—
220#66925—22no—
221#66925—22no—
222#66925—22no—
223C42×D11—22no—
224#66923—21no—
225#66923—21no—
226#66923C2312yes—
227#66922C2311yescharacteristic
228#66922C2311yescharacteristic
229#66922C2311yescharacteristic
230C4×Dic22—21no—
231C4×Dic22—21no—
232C4×Dic22—21no—
233C4×Dic22—21no—
234C4×Dic22C2312yes—
235C4×Dic22C2312yes—
236#66899C2314yes—
237#66899C2314yes—
238#66896C2314yes—
239#66896C2314yes—
240C22⋊(C11⋊C8)C2314yes—
241C22⋊(C11⋊C8)C2314yes—
242#66874C2314yes—
243#66874C2314yes—
244#66873C2314yes—
245#66873C2314yes—
246#66872C2314yes—
247#66872C2314yes—
248#66871C2314yes—
249#66871C2314yes—
250C4⋊(C11⋊C8)C2312yes—
251C4⋊(C11⋊C8)C2312yes—
252C4⋊(C11⋊C8)C2312yes—
253C4⋊(C11⋊C8)C2312yes—
254#66867C2314yes—
255C4×C11⋊C8C2314yes—
256#60559—111nomaximal, Sylow
257C24×C11—21no—
258C24×C11C2×D411yescharacteristic
259C11×#41—28no—
260C11×#41—28no—
261C11×#41—24no—
262C11×#41—24no—
263C11×#41—24no—
264C11×#41—24no—
265C2×Q8×C11—21no—
266C2×Q8×C11—22no—
267C2×Q8×C11#4114yescomplemented
268C2×Q8×C11C2412yes—
269C2×D4×C11—28no—
270C2×D4×C11—22no—
271C2×D4×C11—22no—
272C2×D4×C11—21no—
273C2×D4×C11—22no—
274C2×D4×C11#4114yescomplemented
275C2×D4×C11C2412yes—
276C22×C4×C11—28no—
277C22×C4×C11—21no—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—21no—
283C22×C4×C11—21no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—22no—
287C22×C4×C11—22no—
288C22×C4×C11—42no—
289C22×C4×C11—42no—
290C22×C4×C11—44no—
291C22×C4×C11—44no—
292C22×C4×C11C2×D411yescharacteristic
293C22×C4×C11C2×D411yescharacteristic
294C22×C4×C11C2×D411yescharacteristic
295C22×C4×C11C2×D411yescharacteristic
296C22×C4×C11C2×D411yescharacteristic
297C22×C4×C11C2×D411yescharacteristic
298C22×C4×C11C2×D411yescharacteristic
299C22×C4×C11C2×D411yescharacteristic
300C22×C4×C11C2×D411yescharacteristic
301C22×C4×C11C2×D411yescharacteristic
302C22×C4×C11C2×D411yescharacteristic
303C22×C4×C11C2×D411yescharacteristic
304C22×C4×C11C2×D411yescharacteristic
305C22×C4×C11C2×D411yescharacteristic
306C22×C4×C11C2×D411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2411yescharacteristic
309C22×C4×C11C2411yescharacteristic
310C2×C22⋊D11—22no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—22no—
313#4339—24no—
314#4339—24no—
315#4339—44no—
316#4339—44no—
317C2×D44—21no—
318C2×D44—21no—
319C2×D44C2412yes—
320C2×C4×D11—22no—
321C2×C4×D11—22no—
322C2×C4×D11—22no—
323C2×Dic22—21no—
324C2×Dic22—21no—
325C2×Dic22C2412yes—
326C11×C4⋊C4—22no—
327C11×C4⋊C4—22no—
328C11×C4⋊C4—22no—
329C11×C4⋊C4—22no—
330C11×C4⋊C4—21no—
331C11×C4⋊C4—21no—
332C11×C4⋊C4C2412yes—
333C11×C4⋊C4C2412yes—
334C11×C22⋊C4—22no—
335C11×C22⋊C4—22no—
336C11×C22⋊C4—22no—
337C11×C22⋊C4—22no—
338C11×C22⋊C4—22no—
339C11×C22⋊C4—22no—
340C42×C11—22no—
341C42×C11—22no—
342C42×C11—22no—
343C42×C11—22no—
344C42×C11—22no—
345C42×C11—22no—
346C42×C11C2×D411yescharacteristic
347C42×C11C2×D411yescharacteristic
348C42×C11C2×D411yescharacteristic
349C42×C11C2×D411yescharacteristic
350C42×C11C2×D411yescharacteristic
351C42×C11C2×D411yescharacteristic
352C42×C11C2×D411yescharacteristic
353C42×C11C2×D411yescharacteristic
354C42×C11C2×D411yescharacteristic
355C42×C11C2×D411yescharacteristic
356C42×C11C2×D411yescharacteristic
357C42×C11C2×D411yescharacteristic
358C42×C11C2411yescharacteristic
359C42×C11C2411yescharacteristic
360C42×C11C2411yescharacteristic
361C42×C11C2411yescharacteristic
362C22⋊Dic11—22no—
363C22⋊Dic11—22no—
364C22⋊Dic11—22no—
365#4326—28no—
366#4325—28no—
367#4324—28no—
368#4323—28no—
369(C2×D11)⋊C4—22no—
370(C2×D11)⋊C4—22no—
371(C2×D11)⋊C4—22no—
372(C2×D11)⋊C4—22no—
373(C2×D11)⋊C4—22no—
374(C2×D11)⋊C4—22no—
375C4⋊Dic11—21no—
376C4⋊Dic11—21no—
377C4⋊Dic11—21no—
378C4⋊Dic11—21no—
379C4⋊Dic11C2412yes—
380C4⋊Dic11C2412yes—
381Dic11⋊C4—22no—
382Dic11⋊C4—22no—
383Dic11⋊C4—22no—
384Dic11⋊C4—22no—
385Dic11⋊C4—22no—
386Dic11⋊C4—22no—
387C4×Dic11—22no—
388C4×Dic11—22no—
389C4×Dic11—22no—
390#4318—24no—
391#4318—24no—
392C2×C11⋊C8C2414yes—
393C2×C11⋊C8C2414yes—
394#3444—111no—
395C2×C4×#41D1111yescharacteristic, complemented
396#3116—112no—
397#3115—112no—
398#3111—114no—
399#3107—112no—
400#3106—112no—
401#3102—114no—
402#3093—112no—
403#3078—111no—
404#3077—111no—
405#3037—111no—
406#3036—111no—
407#3005—112no—
408C4×#137—112no—
409C4×AGL(1,ℤ/8)—112no—
410#2920—111no—
411C23×C11—22no—
412C23×C11—24no—
413C23×C11—22no—
414C23×C11—41no—
415C23×C11—41no—
416C23×C11—42no—
417C23×C11—42no—
418C23×C11C22×D411yescharacteristic
419C23×C11C22×D411yescharacteristic
420C23×C11C22×D411yescharacteristic
421C22×D11—22no—
422Q8×C11—24no—
423Q8×C11—22no—
424Q8×C11C2×#4114yes—
425D4×C11—28no—
426D4×C11—28no—
427D4×C11—24no—
428D4×C11—22no—
429D4×C11C2×#4114yes—
430C2×C4×C11—28no—
431C2×C4×C11—28no—
432C2×C4×C11—22no—
433C2×C4×C11—24no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—21no—
444C2×C4×C11—21no—
445C2×C4×C11—21no—
446C2×C4×C11—21no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—44no—
456C2×C4×C11—44no—
457C2×C4×C11—42no—
458C2×C4×C11—42no—
459C2×C4×C11—44no—
460C2×C4×C11—44no—
461C2×C4×C11C22×D411yescharacteristic
462C2×C4×C11C22×D411yescharacteristic
463C2×C4×C11C22×D411yescharacteristic
464C2×C4×C11C22×D411yescharacteristic
465C2×C4×C11C22×D411yescharacteristic
466C2×C4×C11C22×D411yescharacteristic
467C2×C4×C11C22×D411yescharacteristic
468C2×C4×C11C22×D411yescharacteristic
469C2×C4×C11C22×D411yescharacteristic
470C2×C4×C11C22×D411yescharacteristic
471C2×C4×C11C22×D411yescharacteristic
472C2×C4×C11C2×#4112yes—
473C2×C4×C11C2×#4112yes—
474C2×C4×C11C2511yescharacteristic
475C22⋊D11—44no—
476C22⋊D11—44no—
477C22⋊D11—44no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481D44—22no—
482D44—22no—
483D44—42no—
484D44—42no—
485C4×D11—44no—
486C4×D11—44no—
487C4×D11—44no—
488Dic22—22no—
489Dic22—22no—
490Dic22—42no—
491Dic22—42no—
492C11⋊C8—24no—
493C11⋊C8—24no—
494C22×#41C2×D1111yescharacteristic
495C2×#137—112no—
496C2×AGL(1,ℤ/8)—112no—
497#533—111no—
498#533—111no—
499#533—111no—
500#532—111no—
501#532—111no—
502#532—111no—
503#529—112no—
504#529—112no—
505#529—221no—
506#529—221no—
507#529—221no—
508#529—221no—
509#525—112no—
510#525—221no—
511#525—221no—
512C4×#41—21no—
513C4×#41—21no—
514C4×#41—21no—
515C4×#41—21no—
516C4×#41—112no—
517C4×#41—221no—
518C4×#41—221no—
519C4×#41C2×D1112yes—
520C4×#41C2×D1112yes—
521C4×#41C2×D1112yes—
522C4×#41C2×D1112yes—
523C2×C4×Q8C2×D1111yescharacteristic
524C2×C4×Q8C2×D1111yescharacteristic
525C2×C4×D4—21no—
526C2×C4×D4—21no—
527C2×C4×D4C2×D1111yescharacteristic
528C2×C4×D4C2×D1111yescharacteristic
529C2×#117—21no—
530C2×#117C2×D1111yescharacteristic
531C22×C42—21no—
532C22×C42C2×D1111yescharacteristic
533#485—114no—
534#485—114no—
535#482—114no—
536#482—114no—
537#479—114no—
538#478—114no—
539#477—112no—
540#476—112no—
541#475—112no—
542#474—112no—
543#464—114no—
544#463—114no—
545#462—112no—
546#461—112no—
547#460—112no—
548#459—112no—
549#452—114no—
550#452—114no—
551#449—114no—
552#449—114no—
553#442—114no—
554#441—114no—
555#440—114no—
556#440—114no—
557C4×Q16—114no—
558C4×SD16—114no—
559C4×SD16—114no—
560C4×D8—114no—
561#432—112no—
562#432—112no—
563#431—112no—
564#431—112no—
565#428—112no—
566#428—112no—
567#423—111no—
568#423—111no—
569#419—112no—
570#418—112no—
571#417—112no—
572#417—112no—
573#407—112no—
574C4×M16—112no—
575C22×C11—21no—
576C22×C11—21no—
577C22×C11—21no—
578C22×C11—21no—
579C22×C11—24no—
580C22×C11—21no—
581C22×C11—21no—
582C22×C11—21no—
583C22×C11—21no—
584C22×C11—44no—
585C22×C11—48no—
586C22×C11—42no—
587C22×C11—42no—
588C22×C11#52512yes—
589C22×C11C23×D411yescharacteristic
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C4×C11—21no—
594C4×C11—21no—
595C4×C11—24no—
596C4×C11—21no—
597C4×C11—21no—
598C4×C11—21no—
599C4×C11—21no—
600C4×C11—21no—
601C4×C11—21no—
602C4×C11—42no—
603C4×C11—42no—
604C4×C11#52512yes—
605C4×C11#57512yes—
606C4×C11#57512yes—
607C4×C11C22×#4111yescharacteristic
608C4×C11C22×#4111yescharacteristic
609Dic11—42no—
610Dic11—42no—
611Dic11—42no—
612C2×#41—24no—
613C2×#41—24no—
614C2×#41—21no—
615C2×#41—21no—
616C2×#41—112no—
617C2×#41—221no—
618C2×#41—221no—
619C2×#41C22×D1112yes—
620C2×#41C22×D1112yes—
621C22×Q8C22×D1111yescharacteristic
622C22×D4—21no—
623C22×D4C22×D1111yescharacteristic
624C23×C4—21no—
625C23×C4—21no—
626C23×C4—21no—
627C23×C4C22⋊D1111yescharacteristic
628C23×C4C22⋊D1111yescharacteristic
629C23×C4C22×D1111yescharacteristic
630#137—228no—
631AGL(1,ℤ/8)—228no—
632C2×Q16—114no—
633C2×SD16—114no—
634C2×SD16—114no—
635C2×D8—114no—
636C2×M16—112no—
637C2×M16—112no—
638C4⋊Q8—111no—
639C4⋊Q8—111no—
640C4⋊Q8—111no—
641#127—111no—
642#126—222no—
643#126—222no—
644#125—112no—
645#125—221no—
646#125—221no—
647#124—112no—
648#124—221no—
649#124—221no—
650#123—222no—
651#123—222no—
652#123—222no—
653C22⋊Q8—112no—
654C22⋊Q8—112no—
655C22⋊Q8—221no—
656C22⋊Q8—221no—
657C22⋊Q8—221no—
658C22⋊Q8—221no—
659#121—112no—
660#121—112no—
661#121—221no—
662#121—221no—
663#121—221no—
664#121—221no—
665#120—222no—
666C4×Q8—21no—
667C4×Q8—21no—
668C4×Q8—21no—
669C4×Q8—21no—
670C4×Q8—112no—
671C4×Q8—112no—
672C4×Q8—221no—
673C4×Q8—221no—
674C4×Q8—221no—
675C4×Q8—221no—
676C4×Q8C22×D1112yes—
677C4×Q8C22×D1112yes—
678C4×Q8C22×D1112yes—
679C4×Q8C22×D1112yes—
680C4×D4—22no—
681C4×D4—22no—
682C4×D4—22no—
683C4×D4—22no—
684C4×D4—22no—
685C4×D4—22no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—21no—
690C4×D4—21no—
691C4×D4—21no—
692C4×D4—112no—
693C4×D4—112no—
694C4×D4—222no—
695C4×D4—222no—
696C4×D4—222no—
697C4×D4—222no—
698C4×D4—222no—
699C4×D4—222no—
700C4×D4—221no—
701C4×D4—221no—
702C4×D4—221no—
703C4×D4—221no—
704C4×D4C22×D1112yes—
705C4×D4C22×D1112yes—
706C4×D4C22×D1112yes—
707C4×D4C22×D1112yes—
708#117—21no—
709#117—21no—
710#117—22no—
711#117—22no—
712#117—22no—
713#117—22no—
714#117—112no—
715#117—221no—
716#117—221no—
717#117—222no—
718#117—222no—
719#117—222no—
720#117C22×D1112yes—
721#117C22×D1112yes—
722C2×C4⋊C4—21no—
723C2×C4⋊C4—21no—
724C2×C4⋊C4C22×D1111yescharacteristic
725C2×C4⋊C4C22×D1111yescharacteristic
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—22no—
735C2×C42—22no—
736C2×C42—222no—
737C2×C42C22⋊D1111yescharacteristic
738C2×C42C22⋊D1111yescharacteristic
739C2×C42C22⋊D1111yescharacteristic
740C2×C42C22⋊D1111yescharacteristic
741C2×C42C22⋊D1111yescharacteristic
742C2×C42C22⋊D1111yescharacteristic
743C2×C42C22×D1111yescharacteristic
744C2×C42C22×D1111yescharacteristic
745C2×C42C22×D1111yescharacteristic
746C2×C42C22×D1111yescharacteristic
747C2×C42C22×D1111yescharacteristic
748C2×C42C22×D1111yescharacteristic
749#107—114no—
750#107—114no—
751#106—114no—
752#106—114no—
753C4⋊C8—112no—
754C4⋊C8—112no—
755C4⋊C8—112no—
756C4⋊C8—112no—
757#103—114no—
758#103—114no—
759#103—114no—
760#103—114no—
761#102—114no—
762#102—114no—
763#102—114no—
764#102—114no—
765C22⋊C8—114no—
766C22⋊C8—114no—
767#97—114no—
768C4×C8—114no—
769C2×C11—22no—
770C2×C11—41no—
771C2×C11—41no—
772C2×C11—44no—
773C2×C11C2×#52511yescharacteristic
774C2×C11C2×#57511yescharacteristic
775C2×C11C2×#57511yescharacteristic
776D11—82no—
777C24—21no—
778C24C2×C22⋊D1111yescharacteristic
779#41—28no—
780#41—28no—
781#41—24no—
782#41—24no—
783#41—24no—
784#41—24no—
785#41—224no—
786#41—224no—
787#41—444no—
788#41—444no—
789C2×Q8—22no—
790C2×Q8—21no—
791C2×Q8—112no—
792C2×Q8—221no—
793C2×Q8—221no—
794C2×Q8#433914yescomplemented
795C2×Q8C23×D1112yes—
796C2×D4—28no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—22no—
800C2×D4—21no—
801C2×D4—112no—
802C2×D4—222no—
803C2×D4—222no—
804C2×D4—222no—
805C2×D4—221no—
806C2×D4—221no—
807C2×D4#433914yescomplemented
808C2×D4C23×D1112yes—
809C22×C4—28no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—222no—
826C22×C4—222no—
827C22×C4—222no—
828C22×C4C2×C22⋊D1111yescharacteristic
829C22×C4C2×C22⋊D1111yescharacteristic
830C22×C4C2×C22⋊D1111yescharacteristic
831C22×C4C2×C22⋊D1111yescharacteristic
832C22×C4C2×C22⋊D1111yescharacteristic
833C22×C4C2×C22⋊D1111yescharacteristic
834C22×C4C2×C22⋊D1111yescharacteristic
835C22×C4C2×C22⋊D1111yescharacteristic
836C22×C4C2×C22⋊D1111yescharacteristic
837C22×C4C2×C22⋊D1111yescharacteristic
838C22×C4C2×C22⋊D1111yescharacteristic
839C22×C4C2×C22⋊D1111yescharacteristic
840C22×C4C2×C22⋊D1111yescharacteristic
841C22×C4C2×C22⋊D1111yescharacteristic
842C22×C4C2×C22⋊D1111yescharacteristic
843C22×C4C23×D1111yescharacteristic
844C22×C4C23×D1111yescharacteristic
845C22×C4C23×D1111yescharacteristic
846Q16—228no—
847SD16—228no—
848SD16—228no—
849D8—228no—
850M16—224no—
851M16—224no—
852C2×C8—114no—
853C2×C8—114no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—112no—
861C4⋊C4—112no—
862C4⋊C4—222no—
863C4⋊C4—222no—
864C4⋊C4—221no—
865C4⋊C4—221no—
866C4⋊C4—221no—
867C4⋊C4—221no—
868C4⋊C4—222no—
869C4⋊C4—222no—
870C4⋊C4—222no—
871C4⋊C4—222no—
872C4⋊C4C23×D1112yes—
873C4⋊C4C23×D1112yes—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—222no—
881C22⋊C4—222no—
882C22⋊C4—222no—
883C22⋊C4—222no—
884C22⋊C4—222no—
885C22⋊C4—222no—
886C22⋊C4—222no—
887C22⋊C4—222no—
888C22⋊C4—222no—
889C42—22no—
890C42—22no—
891C42—22no—
892C42—22no—
893C42—22no—
894C42—22no—
895C42—222no—
896C42—222no—
897C42—222no—
898C42C2×C22⋊D1111yescharacteristic
899C42C2×C22⋊D1111yescharacteristic
900C42C2×C22⋊D1111yescharacteristic
901C42C2×C22⋊D1111yescharacteristic
902C42C2×C22⋊D1111yescharacteristic
903C42C2×C22⋊D1111yescharacteristic
904C42C2×C22⋊D1111yescharacteristic
905C42C2×C22⋊D1111yescharacteristic
906C42C2×C22⋊D1111yescharacteristic
907C42C2×C22⋊D1111yescharacteristic
908C42C2×C22⋊D1111yescharacteristic
909C42C2×C22⋊D1111yescharacteristic
910C42C23×D1111yescharacteristic
911C42C23×D1111yescharacteristic
912C42C23×D1111yescharacteristic
913C42C23×D1111yescharacteristic
914C11#6055911yescharacteristic, complemented, Sylow
915C23—22no—
916C23—24no—
917C23—22no—
918C23—41no—
919C23—41no—
920C23—42no—
921C23—42no—
922C23—222no—
923C23C22×C22⋊D1111yescharacteristic
924C23C22×C22⋊D1111yescharacteristic
925C23C22×C22⋊D1111yescharacteristic
926Q8—24no—
927Q8—22no—
928Q8—222no—
929Q8—222no—
930Q8—442no—
931Q8—442no—
932Q8C2×#433914yes—
933D4—28no—
934D4—28no—
935D4—24no—
936D4—22no—
937D4—222no—
938D4—222no—
939D4—442no—
940D4—444no—
941D4—444no—
942D4—444no—
943D4—442no—
944D4C2×#433914yes—
945C2×C4—28no—
946C2×C4—28no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—44no—
971C2×C4—44no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—44no—
975C2×C4—44no—
976C2×C4—222no—
977C2×C4—222no—
978C2×C4—222no—
979C2×C4—444no—
980C2×C4—444no—
981C2×C4—444no—
982C2×C4C2×#433912yes—
983C2×C4C2×#433912yes—
984C2×C4C22×C22⋊D1111yescharacteristic
985C2×C4C22×C22⋊D1111yescharacteristic
986C2×C4C22×C22⋊D1111yescharacteristic
987C2×C4C22×C22⋊D1111yescharacteristic
988C2×C4C22×C22⋊D1111yescharacteristic
989C2×C4C22×C22⋊D1111yescharacteristic
990C2×C4C22×C22⋊D1111yescharacteristic
991C2×C4C22×C22⋊D1111yescharacteristic
992C2×C4C22×C22⋊D1111yescharacteristic
993C2×C4C22×C22⋊D1111yescharacteristic
994C2×C4C22×C22⋊D1111yescharacteristic
995C2×C4C24×D1111yescharacteristic
996C8—224no—
997C8—224no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—24no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—44no—
1008C22—48no—
1009C22—42no—
1010C22—42no—
1011C22—442no—
1012C22—442no—
1013C22—442no—
1014C22#1062332212yes—
1015C22C23×C22⋊D1111yescharacteristic
1016C4—21no—
1017C4—21no—
1018C4—24no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—21no—
1023C4—21no—
1024C4—21no—
1025C4—42no—
1026C4—42no—
1027C4—442no—
1028C4—442no—
1029C4—442no—
1030C4#1062332212yes—
1031C4#1062335312yes—
1032C4#1062335312yes—
1033C4C22×#433911yescharacteristic
1034C4C22×#433911yescharacteristic
1035C2—22no—
1036C2—41no—
1037C2—41no—
1038C2—44no—
1039C2—882no—
1040C2C2×#1062332211yescharacteristic
1041C2C2×#1062335311yescharacteristic
1042C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×#41C2
socleC22×C11C23×D4
hypercenterC2×C4×#41D11
hypocenterC11#60559
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #13081912C2semidirect
2. #13078778C2semidirect
3. #13078767C2semidirect
4. #13078725C2semidirect
5. #13078687C2semidirect
6. #13078676C2semidirect
7. #13078634C2semidirect
8. #13078547C2semidirect
9. #13078421C2semidirect
10. #13078413C2semidirect
11. #13078088C2semidirect
12. #13078080C2semidirect
13. #13077858C2semidirect
14. C4×#66995C2semidirect
15. C4×#66985C2semidirect
16. #13077249C2semidirect
17. C2×C4×C11×#41C2semidirect
46. #10623010C22semidirect
47. #10623010C22semidirect
49. #10623008C22semidirect
50. #10623008C22semidirect
55. #10623001C22semidirect
56. #10623001C22semidirect
64. #10622644C22semidirect
65. #10622643C22semidirect
66. C4×#4326C22semidirect
67. #10622641C22semidirect
68. #10622640C22semidirect
69. #10622639C22semidirect
70. C4×#4325C22semidirect
71. #10622635C22semidirect
72. #10622634C22semidirect
73. #10622633C22semidirect
74. #10622632C22semidirect
75. #10622631C22semidirect
76. C4×#4324C22semidirect
77. #10622629C22semidirect
78. #10622628C22semidirect
79. #10622627C22semidirect
80. C4×#4323C22semidirect
81. #10622622C22semidirect
82. #10622621C22semidirect
83. #10622620C22semidirect
84. #10622616C22semidirect
85. #10622616C22semidirect
86. #10622609C22semidirect
87. #10622609C22semidirect
92. #10622539C22semidirect
93. #10622539C22semidirect
94. #10622538C22semidirect
95. #10622538C22semidirect
267. C2×Q8×C11#41semidirect
274. C2×D4×C11#41semidirect
395. C2×C4×#41D11semidirect
794. C2×Q8#4339semidirect
807. C2×D4#4339semidirect
914. C11#60559semidirect

Maximal subgroups

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

subgroupindex
#130819122
#130787782
#130787672
#130787252
#130786872
#130786762
#130786342
#130785472
#130784212
#130784132
#130780882
#130780802
#130778582
C4×#669952
C4×#669852
#130772492
C2×C4×C11×#412
#6055911