Finite Group Databasebeta

← #15626601

Subgroups — #15626601

Order 2816.

1942 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic, complemented
2#13079963C214yesmaximal, complemented
3#13079958C211yesmaximal, characteristic, complemented
4#13079953C212yesmaximal, complemented
5#13079947C212yesmaximal, complemented
6#13079942C212yesmaximal, complemented
7#13079936C212yesmaximal, complemented
8#13079932C211yesmaximal, characteristic, complemented
9#13079928C211yesmaximal, characteristic, complemented
10#13079923C211yesmaximal, characteristic, complemented
11#13078404C212yesmaximal, complemented
12#13078398C212yesmaximal, complemented
13#13078194C214yesmaximal, complemented
14#13078071C212yesmaximal, complemented
15#13078065C212yesmaximal, complemented
16C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
17C11×#3444C211yesmaximal, characteristic, complemented
18C11×#533C2211yescharacteristic
19C11×#533C2211yescharacteristic
20C11×#533C2211yescharacteristic
21C11×#532C2211yescharacteristic
22C11×#532C2211yescharacteristic
23C11×#532C2211yescharacteristic
24C11×#529—21no—
25C11×#529—21no—
26C11×#529—21no—
27C11×#529—21no—
28C11×#529C2212yes—
29C11×#529C2212yes—
30C11×#525—21no—
31C11×#525—21no—
32C11×#525C2212yes—
33C4×C11×#41—21no—
34C4×C11×#41—21no—
35C4×C11×#41C2212yes—
36C22×C42×C11C2211yescharacteristic
37C2×#67003C2214yes—
38#10623322—21no—
39#10623322—21no—
40#10623322C2212yes—
41C23×C11⋊C8C2212yes—
42#10623010—21no—
43#10623010—21no—
44#10623010—21no—
45#10623010—21no—
46#10623010C2212yes—
47#10623010C2212yes—
48#10623008C2211yescharacteristic
49#10623008C2211yescharacteristic
50#10623008C2211yescharacteristic
51C4×#4339—21no—
52C4×#4339—21no—
53C4×#4339C2212yes—
54#10623001C2211yescharacteristic
55#10623001C2211yescharacteristic
56#10623001C2211yescharacteristic
57#10622846C2214yes—
58#10622707C2212yescomplemented
59#10622704C2212yescomplemented
60#10622703C2212yescomplemented
61#10622700C2212yescomplemented
62#10622697C2212yescomplemented
63#10622696C2212yescomplemented
64#10622688C2212yescomplemented
65#10622685C2212yescomplemented
66#10622679C2214yescomplemented
67#10622676C2214yescomplemented
68#10622670C2214yescomplemented
69#10622667C2214yescomplemented
70#10622664C2214yes—
71#10622664C2214yes—
72#10622661C2214yes—
73#10622661C2214yes—
74#10622654C2214yes—
75#10622654C2214yes—
76#10622651C2214yes—
77#10622651C2214yes—
78#10622644C2212yescomplemented
79#10622641C2214yescomplemented
80#10622640C2212yescomplemented
81#10622635C2214yescomplemented
82#10622634C2212yescomplemented
83#10622633C2212yescomplemented
84#10622632C2212yescomplemented
85#10622629C2214yescomplemented
86#10622628C2212yescomplemented
87#10622622C2214yescomplemented
88#10622621C2212yescomplemented
89#10622620C2212yescomplemented
90#10622615C2214yes—
91#10622611C2214yes—
92C2×C4⋊(C11⋊C8)C2212yes—
93C2×C4⋊(C11⋊C8)C2212yes—
94C2×C4⋊(C11⋊C8)C2211yescharacteristic
95C2×C4⋊(C11⋊C8)C2211yescharacteristic
96C2×C4⋊(C11⋊C8)C2212yes—
97C2×C4⋊(C11⋊C8)C2212yes—
98C2×C4⋊(C11⋊C8)C2212yes—
99C2×C11×#41—21no—
100C2×C11×#41—21no—
101C2×C11×#41C2312yes—
102C23×C4×C11D411yescharacteristic
103C23×C4×C11D411yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C2×#4339—21no—
106C2×#4339—21no—
107C2×#4339C2312yes—
108C11×C4⋊Q8C2311yescharacteristic
109C11×C4⋊Q8C2311yescharacteristic
110C11×C4⋊Q8C2311yescharacteristic
111C11×#127C2311yescharacteristic
112C11×#126—22no—
113C11×#126—22no—
114C11×#125—21no—
115C11×#125—21no—
116C11×#125C2312yes—
117C11×#124—21no—
118C11×#124—21no—
119C11×#124C2312yes—
120C11×#123—22no—
121C11×#123—22no—
122C11×#123—22no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8—21no—
125C11×C22⋊Q8—21no—
126C11×C22⋊Q8—21no—
127C11×C22⋊Q8C2312yes—
128C11×C22⋊Q8C2312yes—
129C11×#121—21no—
130C11×#121—21no—
131C11×#121—21no—
132C11×#121—21no—
133C11×#121C2312yes—
134C11×#121C2312yes—
135C11×#120—22no—
136C4×Q8×C11—21no—
137C4×Q8×C11—21no—
138C4×Q8×C11—21no—
139C4×Q8×C11—21no—
140C4×Q8×C11C2312yes—
141C4×Q8×C11C2312yes—
142C4×D4×C11—22no—
143C4×D4×C11—22no—
144C4×D4×C11—22no—
145C4×D4×C11—22no—
146C4×D4×C11—22no—
147C4×D4×C11—22no—
148C4×D4×C11—21no—
149C4×D4×C11—21no—
150C4×D4×C11—21no—
151C4×D4×C11—21no—
152C4×D4×C11C2312yes—
153C4×D4×C11C2312yes—
154C11×#117—21no—
155C11×#117—21no—
156C11×#117—22no—
157C11×#117—22no—
158C11×#117—22no—
159C11×#117C2312yes—
160C2×C42×C11—22no—
161C2×C42×C11D411yescharacteristic
162C2×C42×C11D411yescharacteristic
163C2×C42×C11D411yescharacteristic
164C2×C42×C11D411yescharacteristic
165C2×C42×C11D411yescharacteristic
166C2×C42×C11D411yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2311yescharacteristic
173#67006—22no—
174#67003—48no—
175C2×#4326C2314yes—
176C2×#4325C2314yes—
177C2×#4324C2314yes—
178C2×#4323C2314yes—
179#66983—21no—
180#66983—21no—
181#66983—21no—
182#66983—21no—
183#66983C2312yes—
184#66983C2312yes—
185#66982—22no—
186#66982—22no—
187#66982—22no—
188C4×C22⋊D11—22no—
189C4×C22⋊D11—22no—
190C4×C22⋊D11—22no—
191C4×C22⋊D11—22no—
192C4×C22⋊D11—22no—
193C4×C22⋊D11—22no—
194#66979—21no—
195#66979—21no—
196#66979C2312yes—
197#66977—21no—
198#66977—21no—
199#66977—21no—
200#66977—21no—
201#66977C2312yes—
202#66977C2312yes—
203C22×C11⋊C8—44no—
204C22×C11⋊C8C2314yes—
205C22×C11⋊C8C2312yes—
206C22×C11⋊C8C2314yes—
207C22×C11⋊C8C2312yes—
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—
240#66874C2314yes—
241#66874C2314yes—
242#66873C2314yes—
243#66873C2314yes—
244#66872C2314yes—
245#66872C2314yes—
246#66871C2314yes—
247#66871C2314yes—
248C4⋊(C11⋊C8)C2312yes—
249C4⋊(C11⋊C8)C2312yes—
250C4⋊(C11⋊C8)C2314yes—
251C4⋊(C11⋊C8)C2314yes—
252C4⋊(C11⋊C8)C2312yes—
253C4⋊(C11⋊C8)C2312yes—
254#60900—111nomaximal, Sylow
255C24×C11C2×D411yescharacteristic
256C11×#41—24no—
257C11×#41—24no—
258C11×#41—44no—
259C11×#41—44no—
260C2×Q8×C11—21no—
261C2×Q8×C11—21no—
262C2×Q8×C11C2412yes—
263C2×D4×C11—22no—
264C2×D4×C11—22no—
265C2×D4×C11—22no—
266C2×D4×C11—21no—
267C2×D4×C11—21no—
268C2×D4×C11C2412yes—
269C22×C4×C11—24no—
270C22×C4×C11—22no—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11—22no—
274C22×C4×C11—22no—
275C22×C4×C11—42no—
276C22×C4×C11C2×D411yescharacteristic
277C22×C4×C11C2×D411yescharacteristic
278C22×C4×C11C2×D411yescharacteristic
279C22×C4×C11C2×D411yescharacteristic
280C22×C4×C11C2×D411yescharacteristic
281C22×C4×C11C2×D411yescharacteristic
282C22×C4×C11C2×D411yescharacteristic
283C22×C4×C11C2×D411yescharacteristic
284C22×C4×C11C2×D411yescharacteristic
285C22×C4×C11C2×D411yescharacteristic
286C22×C4×C11C2×D411yescharacteristic
287C22×C4×C11C2×D411yescharacteristic
288C22×C4×C11C2×D411yescharacteristic
289C22×C4×C11C2×D411yescharacteristic
290C22×C4×C11C2×D411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C2×C22⋊D11—22no—
295C2×C22⋊D11—22no—
296C2×C22⋊D11—22no—
297#4339—24no—
298#4339—24no—
299#4339—44no—
300#4339—44no—
301C2×D44—21no—
302C2×D44—21no—
303C2×D44C2412yes—
304C2×C4×D11—22no—
305C2×C4×D11—22no—
306C2×C4×D11—22no—
307C2×Dic22—21no—
308C2×Dic22—21no—
309C2×Dic22C2412yes—
310C11×C4⋊C4—21no—
311C11×C4⋊C4—21no—
312C11×C4⋊C4—21no—
313C11×C4⋊C4—21no—
314C11×C4⋊C4—22no—
315C11×C4⋊C4—22no—
316C11×C4⋊C4—22no—
317C11×C4⋊C4—22no—
318C11×C4⋊C4—22no—
319C11×C4⋊C4—22no—
320C11×C4⋊C4C2412yes—
321C11×C4⋊C4C2412yes—
322C11×C22⋊C4—22no—
323C11×C22⋊C4—22no—
324C11×C22⋊C4—22no—
325C11×C22⋊C4—22no—
326C11×C22⋊C4—22no—
327C11×C22⋊C4—22no—
328C11×C22⋊C4—22no—
329C11×C22⋊C4—22no—
330C11×C22⋊C4—22no—
331C42×C11—22no—
332C42×C11—22no—
333C42×C11—22no—
334C42×C11C2×D411yescharacteristic
335C42×C11C2×D411yescharacteristic
336C42×C11C2×D411yescharacteristic
337C42×C11C2×D411yescharacteristic
338C42×C11C2×D411yescharacteristic
339C42×C11C2×D411yescharacteristic
340C42×C11C2×D411yescharacteristic
341C42×C11C2×D411yescharacteristic
342C42×C11C2×D411yescharacteristic
343C42×C11C2×D411yescharacteristic
344C42×C11C2×D411yescharacteristic
345C42×C11C2×D411yescharacteristic
346C42×C11C2411yescharacteristic
347C42×C11C2411yescharacteristic
348C42×C11C2411yescharacteristic
349C42×C11C2411yescharacteristic
350C22⋊Dic11—22no—
351C22⋊Dic11—22no—
352C22⋊Dic11—22no—
353#4326—44no—
354#4325—44no—
355#4324—44no—
356#4323—44no—
357(C2×D11)⋊C4—22no—
358(C2×D11)⋊C4—22no—
359(C2×D11)⋊C4—22no—
360(C2×D11)⋊C4—22no—
361(C2×D11)⋊C4—22no—
362(C2×D11)⋊C4—22no—
363C4⋊Dic11—21no—
364C4⋊Dic11—21no—
365C4⋊Dic11—21no—
366C4⋊Dic11—21no—
367C4⋊Dic11C2412yes—
368C4⋊Dic11C2412yes—
369Dic11⋊C4—22no—
370Dic11⋊C4—22no—
371Dic11⋊C4—22no—
372Dic11⋊C4—22no—
373Dic11⋊C4—22no—
374Dic11⋊C4—22no—
375C4×Dic11—22no—
376C4×Dic11—22no—
377C4×Dic11—22no—
378C2×C11⋊C8—28no—
379C2×C11⋊C8—42no—
380C2×C11⋊C8—44no—
381C2×C11⋊C8—42no—
382C2×C11⋊C8C2414yes—
383C2×C11⋊C8C2414yes—
384#3444—111no—
385#3444D1111yescharacteristic, complemented
386#3250—114no—
387#3249—111no—
388#3248—112no—
389#3248—112no—
390#3247—112no—
391#3247—112no—
392#3246—111no—
393#3246—111no—
394#3245—111no—
395#3076—112no—
396#3076—112no—
397#3050—114no—
398#3035—112no—
399#3035—112no—
400C22×C4⋊C8—111no—
401C23×C11—22no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11C22×D411yescharacteristic
406C23×C11C22×D411yescharacteristic
407C23×C11C22×D411yescharacteristic
408C22×D11—22no—
409Q8×C11—22no—
410Q8×C11—22no—
411Q8×C11—42no—
412Q8×C11—42no—
413D4×C11—22no—
414D4×C11—22no—
415D4×C11—42no—
416D4×C11—44no—
417D4×C11—44no—
418D4×C11—44no—
419D4×C11—42no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—21no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—44no—
442C2×C4×C11—44no—
443C2×C4×C11—44no—
444C2×C4×C11#13514yescomplemented
445C2×C4×C11C22×D411yescharacteristic
446C2×C4×C11C22×D411yescharacteristic
447C2×C4×C11C22×D411yescharacteristic
448C2×C4×C11C22×D411yescharacteristic
449C2×C4×C11C22×D411yescharacteristic
450C2×C4×C11C22×D411yescharacteristic
451C2×C4×C11C22×D411yescharacteristic
452C2×C4×C11C22×D411yescharacteristic
453C2×C4×C11C22×D411yescharacteristic
454C2×C4×C11C22×D411yescharacteristic
455C2×C4×C11C22×D411yescharacteristic
456C2×C4×C11H(5,𝔽2)12yes—
457C2×C4×C112−1+412yes—
458C2×C4×C11C2511yescharacteristic
459C22⋊D11—44no—
460C22⋊D11—44no—
461C22⋊D11—44no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465D44—22no—
466D44—22no—
467D44—42no—
468D44—42no—
469C4×D11—44no—
470C4×D11—44no—
471C4×D11—44no—
472Dic22—22no—
473Dic22—22no—
474Dic22—42no—
475Dic22—42no—
476C11⋊C8—24no—
477C11⋊C8—24no—
478C2×#135—114no—
479C23×C8—112no—
480#533—111no—
481#533—111no—
482#533—111no—
483#533C2×D1111yescharacteristic
484#533C2×D1111yescharacteristic
485#533C2×D1111yescharacteristic
486#532—111no—
487#532—111no—
488#532—111no—
489#532C2×D1111yescharacteristic
490#532C2×D1111yescharacteristic
491#532C2×D1111yescharacteristic
492#529—21no—
493#529—21no—
494#529—21no—
495#529—21no—
496#529—112no—
497#529—112no—
498#529—221no—
499#529—221no—
500#529—221no—
501#529—221no—
502#529C2×D1112yes—
503#529C2×D1112yes—
504#525—21no—
505#525—21no—
506#525—112no—
507#525—221no—
508#525—221no—
509#525C2×D1112yes—
510C4×#41—21no—
511C4×#41—21no—
512C4×#41—112no—
513C4×#41—221no—
514C4×#41—221no—
515C4×#41C2×D1112yes—
516C22×C42C2×D1111yescharacteristic
517#479—114no—
518#479—114no—
519#478—114no—
520#478—114no—
521#477—112no—
522#477—112no—
523#476—112no—
524#476—112no—
525#475—112no—
526#475—112no—
527#474—112no—
528#474—112no—
529#467—114no—
530#467—114no—
531#466—114no—
532#466—114no—
533#465—114no—
534#465—114no—
535#465—114no—
536#465—114no—
537#464—114no—
538#464—114no—
539#463—114no—
540#463—114no—
541#462—112no—
542#462—112no—
543#461—112no—
544#461—112no—
545#460—112no—
546#460—112no—
547#459—112no—
548#459—112no—
549#427—114no—
550C2×C4⋊C8—112no—
551C2×C4⋊C8—112no—
552C2×C4⋊C8—111no—
553C2×C4⋊C8—111no—
554C2×C4⋊C8—112no—
555C2×C4⋊C8—112no—
556C2×C4⋊C8—112no—
557#416—114no—
558#416—114no—
559C22×C11—28no—
560C22×C11—21no—
561C22×C11—21no—
562C22×C11—21no—
563C22×C11—21no—
564C22×C11—21no—
565C22×C11—21no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11#53712yes—
570C22×C11C2×#13512yes—
571C22×C11#57512yes—
572C22×C11C23×D411yescharacteristic
573C2×D11—42no—
574C2×D11—42no—
575C2×D11—42no—
576C4×C11—21no—
577C4×C11—21no—
578C4×C11—21no—
579C4×C11—21no—
580C4×C11—21no—
581C4×C11—21no—
582C4×C11—21no—
583C4×C11—21no—
584C4×C11—42no—
585C4×C11—42no—
586C4×C11—42no—
587C4×C11#53712yes—
588C4×C11C2×#13512yes—
589C4×C11C2×#13512yes—
590C4×C11C2×H(5,𝔽2)11yescharacteristic
591C4×C11C2×2−1+411yescharacteristic
592Dic11—42no—
593Dic11—42no—
594Dic11—42no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—112no—
598C2×#41—221no—
599C2×#41—221no—
600C2×#41C22×D1112yes—
601C23×C4C22⋊D1111yescharacteristic
602C23×C4C22⋊D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604#135—448no—
605C2×Q16—114no—
606C2×SD16—114no—
607C2×SD16—114no—
608C2×D8—114no—
609C22×C8—114no—
610C22×C8—112no—
611C22×C8—114no—
612C22×C8—112no—
613C22×C8—444no—
614C4⋊Q8—111no—
615C4⋊Q8—111no—
616C4⋊Q8—111no—
617C4⋊Q8C22×D1111yescharacteristic
618C4⋊Q8C22×D1111yescharacteristic
619C4⋊Q8C22×D1111yescharacteristic
620#127—111no—
621#127C22×D1111yescharacteristic
622#126—22no—
623#126—22no—
624#126—222no—
625#126—222no—
626#125—21no—
627#125—21no—
628#125—112no—
629#125—221no—
630#125—221no—
631#125C22×D1112yes—
632#124—21no—
633#124—21no—
634#124—112no—
635#124—221no—
636#124—221no—
637#124C22×D1112yes—
638#123—22no—
639#123—22no—
640#123—22no—
641#123—222no—
642#123—222no—
643#123—222no—
644C22⋊Q8—21no—
645C22⋊Q8—21no—
646C22⋊Q8—21no—
647C22⋊Q8—21no—
648C22⋊Q8—112no—
649C22⋊Q8—112no—
650C22⋊Q8—221no—
651C22⋊Q8—221no—
652C22⋊Q8—221no—
653C22⋊Q8—221no—
654C22⋊Q8C22×D1112yes—
655C22⋊Q8C22×D1112yes—
656#121—21no—
657#121—21no—
658#121—21no—
659#121—21no—
660#121—112no—
661#121—112no—
662#121—221no—
663#121—221no—
664#121—221no—
665#121—221no—
666#121C22×D1112yes—
667#121C22×D1112yes—
668#120—22no—
669#120—222no—
670C4×Q8—21no—
671C4×Q8—21no—
672C4×Q8—21no—
673C4×Q8—21no—
674C4×Q8—112no—
675C4×Q8—112no—
676C4×Q8—221no—
677C4×Q8—221no—
678C4×Q8—221no—
679C4×Q8—221no—
680C4×Q8C22×D1112yes—
681C4×Q8C22×D1112yes—
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—
706#117—21no—
707#117—21no—
708#117—22no—
709#117—22no—
710#117—22no—
711#117—112no—
712#117—221no—
713#117—221no—
714#117—222no—
715#117—222no—
716#117—222no—
717#117C22×D1112yes—
718C2×C42—22no—
719C2×C42—222no—
720C2×C42C22⋊D1111yescharacteristic
721C2×C42C22⋊D1111yescharacteristic
722C2×C42C22⋊D1111yescharacteristic
723C2×C42C22⋊D1111yescharacteristic
724C2×C42C22⋊D1111yescharacteristic
725C2×C42C22⋊D1111yescharacteristic
726C2×C42C22×D1111yescharacteristic
727C2×C42C22×D1111yescharacteristic
728C2×C42C22×D1111yescharacteristic
729C2×C42C22×D1111yescharacteristic
730C2×C42C22×D1111yescharacteristic
731C2×C42C22×D1111yescharacteristic
732#107—114no—
733#107—114no—
734#106—114no—
735#106—114no—
736C4⋊C8—112no—
737C4⋊C8—112no—
738C4⋊C8—112no—
739C4⋊C8—112no—
740C4⋊C8—114no—
741C4⋊C8—114no—
742#103—114no—
743#103—114no—
744#103—114no—
745#103—114no—
746#102—114no—
747#102—114no—
748#102—114no—
749#102—114no—
750C2×C11—22no—
751C2×C11—22no—
752C2×C11—22no—
753C2×C11—82no—
754C2×C11C2×#53711yescharacteristic
755C2×C11C22×#13511yescharacteristic
756C2×C11C2×#57511yescharacteristic
757D11—82no—
758C24C2×C22⋊D1111yescharacteristic
759#41—24no—
760#41—24no—
761#41—44no—
762#41—44no—
763#41—224no—
764#41—224no—
765#41—444no—
766#41—444no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—112no—
770C2×Q8—221no—
771C2×Q8—221no—
772C2×Q8C23×D1112yes—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—112no—
779C2×D4—222no—
780C2×D4—222no—
781C2×D4—222no—
782C2×D4—221no—
783C2×D4—221no—
784C2×D4C23×D1112yes—
785C22×C4—24no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—42no—
792C22×C4—222no—
793C22×C4—222no—
794C22×C4—222no—
795C22×C4C2×C22⋊D1111yescharacteristic
796C22×C4C2×C22⋊D1111yescharacteristic
797C22×C4C2×C22⋊D1111yescharacteristic
798C22×C4C2×C22⋊D1111yescharacteristic
799C22×C4C2×C22⋊D1111yescharacteristic
800C22×C4C2×C22⋊D1111yescharacteristic
801C22×C4C2×C22⋊D1111yescharacteristic
802C22×C4C2×C22⋊D1111yescharacteristic
803C22×C4C2×C22⋊D1111yescharacteristic
804C22×C4C2×C22⋊D1111yescharacteristic
805C22×C4C2×C22⋊D1111yescharacteristic
806C22×C4C2×C22⋊D1111yescharacteristic
807C22×C4C2×C22⋊D1111yescharacteristic
808C22×C4C2×C22⋊D1111yescharacteristic
809C22×C4C2×C22⋊D1111yescharacteristic
810C22×C4C23×D1111yescharacteristic
811C22×C4C23×D1111yescharacteristic
812C22×C4C23×D1111yescharacteristic
813Q16—444no—
814SD16—444no—
815SD16—444no—
816D8—444no—
817C2×C8—114no—
818C2×C8—114no—
819C2×C8—228no—
820C2×C8—442no—
821C2×C8—444no—
822C2×C8—442no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—22no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—112no—
834C4⋊C4—112no—
835C4⋊C4—222no—
836C4⋊C4—222no—
837C4⋊C4—221no—
838C4⋊C4—221no—
839C4⋊C4—221no—
840C4⋊C4—221no—
841C4⋊C4—222no—
842C4⋊C4—222no—
843C4⋊C4—222no—
844C4⋊C4—222no—
845C4⋊C4C23×D1112yes—
846C4⋊C4C23×D1112yes—
847C22⋊C4—22no—
848C22⋊C4—22no—
849C22⋊C4—22no—
850C22⋊C4—22no—
851C22⋊C4—22no—
852C22⋊C4—22no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—22no—
856C22⋊C4—222no—
857C22⋊C4—222no—
858C22⋊C4—222no—
859C22⋊C4—222no—
860C22⋊C4—222no—
861C22⋊C4—222no—
862C22⋊C4—222no—
863C22⋊C4—222no—
864C22⋊C4—222no—
865C42—22no—
866C42—22no—
867C42—22no—
868C42—222no—
869C42—222no—
870C42—222no—
871C42C2×C22⋊D1111yescharacteristic
872C42C2×C22⋊D1111yescharacteristic
873C42C2×C22⋊D1111yescharacteristic
874C42C2×C22⋊D1111yescharacteristic
875C42C2×C22⋊D1111yescharacteristic
876C42C2×C22⋊D1111yescharacteristic
877C42C2×C22⋊D1111yescharacteristic
878C42C2×C22⋊D1111yescharacteristic
879C42C2×C22⋊D1111yescharacteristic
880C42C2×C22⋊D1111yescharacteristic
881C42C2×C22⋊D1111yescharacteristic
882C42C2×C22⋊D1111yescharacteristic
883C42C23×D1111yescharacteristic
884C42C23×D1111yescharacteristic
885C42C23×D1111yescharacteristic
886C42C23×D1111yescharacteristic
887C11#6090011yescharacteristic, complemented, Sylow
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—222no—
893C23C22×C22⋊D1111yescharacteristic
894C23C22×C22⋊D1111yescharacteristic
895C23C22×C22⋊D1111yescharacteristic
896Q8—22no—
897Q8—22no—
898Q8—42no—
899Q8—42no—
900Q8—222no—
901Q8—222no—
902Q8—442no—
903Q8—442no—
904D4—22no—
905D4—22no—
906D4—42no—
907D4—44no—
908D4—44no—
909D4—44no—
910D4—42no—
911D4—222no—
912D4—222no—
913D4—442no—
914D4—444no—
915D4—444no—
916D4—444no—
917D4—442no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—44no—
940C2×C4—44no—
941C2×C4—44no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—444no—
946C2×C4—444no—
947C2×C4—444no—
948C2×C4#6700314yescomplemented
949C2×C4#6704212yes—
950C2×C4#6704312yes—
951C2×C4C22×C22⋊D1111yescharacteristic
952C2×C4C22×C22⋊D1111yescharacteristic
953C2×C4C22×C22⋊D1111yescharacteristic
954C2×C4C22×C22⋊D1111yescharacteristic
955C2×C4C22×C22⋊D1111yescharacteristic
956C2×C4C22×C22⋊D1111yescharacteristic
957C2×C4C22×C22⋊D1111yescharacteristic
958C2×C4C22×C22⋊D1111yescharacteristic
959C2×C4C22×C22⋊D1111yescharacteristic
960C2×C4C22×C22⋊D1111yescharacteristic
961C2×C4C22×C22⋊D1111yescharacteristic
962C2×C4C24×D1111yescharacteristic
963C8—224no—
964C8—224no—
965C22—28no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—21no—
971C22—21no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—442no—
976C22—442no—
977C22—442no—
978C22C2×#6700312yes—
979C22#1062335312yes—
980C22#1062336412yes—
981C22C23×C22⋊D1111yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—442no—
994C4—442no—
995C4—442no—
996C4C2×#6700312yes—
997C4C2×#6700312yes—
998C4#1062336412yes—
999C4C2×#6704211yescharacteristic
1000C4C2×#6704311yescharacteristic
1001C2—22no—
1002C2—22no—
1003C2—22no—
1004C2—82no—
1005C2—882no—
1006C2C2×#1062336411yescharacteristic
1007C2C22×#6700311yescharacteristic
1008C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3444C2
socleC22×C11C23×D4
hypercenter#3444D11
hypocenterC11#60900
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #13081912C2semidirect
2. #13079963C2semidirect
3. #13079958C2semidirect
4. #13079953C2semidirect
5. #13079947C2semidirect
6. #13079942C2semidirect
7. #13079936C2semidirect
8. #13079932C2semidirect
9. #13079928C2semidirect
10. #13079923C2semidirect
11. #13078404C2semidirect
12. #13078398C2semidirect
13. #13078194C2semidirect
14. #13078071C2semidirect
15. #13078065C2semidirect
16. C22×C4⋊(C11⋊C8)C2semidirect
17. C11×#3444C2semidirect
58. #10622707C22semidirect
59. #10622704C22semidirect
60. #10622703C22semidirect
61. #10622700C22semidirect
62. #10622697C22semidirect
63. #10622696C22semidirect
64. #10622688C22semidirect
65. #10622685C22semidirect
66. #10622679C22semidirect
67. #10622676C22semidirect
68. #10622670C22semidirect
69. #10622667C22semidirect
78. #10622644C22semidirect
79. #10622641C22semidirect
80. #10622640C22semidirect
81. #10622635C22semidirect
82. #10622634C22semidirect
83. #10622633C22semidirect
84. #10622632C22semidirect
85. #10622629C22semidirect
86. #10622628C22semidirect
87. #10622622C22semidirect
88. #10622621C22semidirect
89. #10622620C22semidirect
385. #3444D11semidirect
444. C2×C4×C11#135semidirect
887. C11#60900semidirect
948. C2×C4#67003semidirect

Maximal subgroups

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

subgroupindex
#130819122
#130799632
#130799582
#130799532
#130799472
#130799422
#130799362
#130799322
#130799282
#130799232
#130784042
#130783982
#130781942
#130780712
#130780652
C22×C4⋊(C11⋊C8)2
C11×#34442
#6090011