Finite Group Databasebeta

← #15622804

Subgroups — #15622804

Order 2816.

1990 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#67043C211yesmaximal, characteristic
2#13078911C214yesmaximal, complemented
3#13078824C214yesmaximal, complemented
4#13078772C212yesmaximal, complemented
5#13078742C212yesmaximal, complemented
6#13078681C212yesmaximal, complemented
7#13078651C212yesmaximal, complemented
8#13078579C212yesmaximal, complemented
9#13078417C211yesmaximal, characteristic, complemented
10#13078398C211yesmaximal, characteristic, complemented
11#13078099C211yesmaximal, characteristic, complemented
12C2×#10622703C211yesmaximal, characteristic, complemented
13#13077909C212yesmaximal
14#13077482C212yesmaximal, complemented
15#13077459C212yesmaximal, complemented
16#13077282C211yesmaximal, characteristic, complemented
17C11×#3509C211yesmaximal, characteristic, complemented
18C2×#67043C2211yescharacteristic
19C11×#557—21no—
20C11×#557—21no—
21C11×#556—21no—
22C11×#556—21no—
23C11×#552—22no—
24C11×#552—22no—
25C11×#541C2214yes—
26C11×#536C2212yes—
27C11×#533C2212yes—
28C11×#533C2212yes—
29C11×#533C2211yescharacteristic
30C2×C11×C4⋊Q8C2211yescharacteristic
31C11×#519C2212yes—
32C4×C11×#41C2211yescharacteristic
33#10623358C2211yescharacteristic
34C22×#4326C2212yes—
35C2×#66995C2212yes—
36#10623103—21no—
37C4×Q8×D11—21no—
38#10623077—22no—
39#10623077—21no—
40C4×#4341—22no—
41C4×#4341—21no—
42#10623054C2212yes—
43#10623054C2211yescharacteristic
44#10623047C2212yes—
45#10623047C2211yescharacteristic
46C4×#4339C2211yescharacteristic
47C4×#4339C2212yes—
48C2×C4×Dic22C2211yescharacteristic
49C2×C4×Dic22C2212yes—
50#10622847C2212yes—
51#10622838C2212yes—
52C2×#66899C2212yes—
53#10622707C2211yescharacteristic
54#10622707C2212yes—
55#10622704C2211yescharacteristic
56#10622704C2212yes—
57#10622703C2214yes—
58#10622703C2212yes—
59#10622703C2212yes—
60#10622703C2212yes—
61#10622703C2212yes—
62#10622700C2211yescharacteristic
63#10622697C2211yescharacteristic
64#10622696C2212yes—
65#10622696C2212yes—
66#10622679C2212yes—
67#10622676C2214yes—
68#10622676C2212yes—
69#10622663C2214yes—
70#10622663C2214yes—
71#10622660C2214yes—
72#10622660C2214yes—
73#10622658C2214yes—
74#10622658C2214yes—
75#10622657C2214yes—
76#10622656C2214yes—
77#10622643C2214yes—
78#10622643C2214yes—
79#10622643C2214yes—
80C4×#4326C2214yes—
81C4×#4326C2214yes—
82C4×#4326C2214yes—
83#10622639C2214yes—
84C4×#4325C2214yes—
85#10622617C2212yes—
86#10622615C2212yes—
87#10622613C2214yes—
88#10622611C2212yes—
89#10622610C2212yes—
90#10622608C2212yes—
91#10622539C2212yes—
92#10622538C2212yes—
93#10622537C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2211yescharacteristic
95C2×C11×#41C2311yescharacteristic
96C22×Q8×C11C2312yes—
97#67043—24no—
98#67043—24no—
99C2×Q8×D11—21no—
100C2×#4341—22no—
101C2×#4341—21no—
102C2×#4339C2312yes—
103C2×#4339C2311yescharacteristic
104C22×Dic22C2312yes—
105C22×Dic22C2311yescharacteristic
106C11×C4⋊Q8—22no—
107C11×C4⋊Q8—21no—
108C11×C4⋊Q8—21no—
109C11×C4⋊Q8C2312yes—
110C11×C4⋊Q8C2312yes—
111C11×C4⋊Q8C2311yescharacteristic
112C11×C4⋊Q8C2311yescharacteristic
113C11×#126—24no—
114C11×#126—24no—
115C11×#125—24no—
116C11×#125—24no—
117C11×#125—22no—
118C11×#125—22no—
119C11×#125C2312yes—
120C11×#124—22no—
121C11×#123—24no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8—22no—
125C11×C22⋊Q8—22no—
126C11×C22⋊Q8C2314yes—
127C11×C22⋊Q8C2314yes—
128C4×Q8×C11—22no—
129C4×Q8×C11—22no—
130C4×Q8×C11—22no—
131C4×Q8×C11—22no—
132C4×Q8×C11—21no—
133C4×Q8×C11—21no—
134C4×Q8×C11D411yescharacteristic
135C4×Q8×C11D411yescharacteristic
136C4×Q8×C11C2314yes—
137C4×Q8×C11C2314yes—
138C4×D4×C11D412yes—
139C4×D4×C11D411yescharacteristic
140C4×D4×C11D412yes—
141C4×D4×C11D411yescharacteristic
142C11×#117—22no—
143C11×#117—22no—
144C11×#117—24no—
145C11×#117C2312yes—
146C11×#117C2311yescharacteristic
147C11×#117C2312yes—
148C2×C11×C4⋊C4—21no—
149C2×C11×C4⋊C4—21no—
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2312yes—
152Q8×Dic11—21no—
153C2×#4326—28no—
154C2×#4326C2314yes—
155C2×#4326C2314yes—
156C2×#4326C2314yes—
157#66995—28no—
158C2×#4325C2314yes—
159D4×Dic11—22no—
160D4×Dic11—21no—
161C4×C22⋊D11—21no—
162C4×C22⋊D11—22no—
163C4×C22⋊D11—21no—
164C4×C22⋊D11—22no—
165#66979C2311yescharacteristic
166#66979C2312yes—
167C2×C4⋊Dic11C2311yescharacteristic
168C2×C4⋊Dic11C2312yes—
169C2×Dic11⋊C4—21no—
170C2×Dic11⋊C4—22no—
171C2×C4×Dic11—21no—
172C2×C4×Dic11—22no—
173C2×#4318C2312yes—
174C22×C11⋊C8C2312yes—
175#66945—21no—
176#66945—22no—
177C4⋊C4×D11—21no—
178C4⋊C4×D11—22no—
179#66940—21no—
180#66940—22no—
181#66940—21no—
182#66940—22no—
183(C22⋊D11)⋊C4—22no—
184(C22⋊D11)⋊C4—22no—
185(C22⋊D11)⋊C4—22no—
186#66930—22no—
187#66930—22no—
188#66930—22no—
189C4×D44C2311yescharacteristic
190C4×D44C2312yes—
191C4×D44C2311yescharacteristic
192#66925—22no—
193#66925—21no—
194C42×D11—22no—
195C42×D11—21no—
196C4×Dic22—22no—
197C4×Dic22—21no—
198C4×Dic22—22no—
199C4×Dic22—21no—
200C4×Dic22C2312yes—
201C4×Dic22C2311yescharacteristic
202C4×Dic22C2312yes—
203C4×Dic22C2312yes—
204C4×Dic22C2312yes—
205C4×Dic22C2312yes—
206C4×Dic22C2311yescharacteristic
207#66899C2314yes—
208#66899C2314yes—
209#66899C2314yes—
210#66899C2314yes—
211C22⋊(C11⋊C8)C2314yes—
212C22⋊(C11⋊C8)C2314yes—
213#66874C2312yes—
214#66874C2312yes—
215#66874C2314yes—
216#66874C2314yes—
217#66873C2312yes—
218#66873C2312yes—
219#66872C2314yes—
220#66872C2312yes—
221#66872C2312yes—
222#66871C2314yes—
223#66871C2312yes—
224#66871C2312yes—
225C4⋊(C11⋊C8)C2311yescharacteristic
226C4⋊(C11⋊C8)C2311yescharacteristic
227C4⋊(C11⋊C8)C2312yes—
228C4⋊(C11⋊C8)C2312yes—
229C4⋊(C11⋊C8)C2312yes—
230#66867C2314yes—
231C4×C11⋊C8C2314yes—
232#60594—111nomaximal, Sylow
233C11×#41—22no—
234C11×#41—22no—
235C2×Q8×C11—21no—
236C2×Q8×C11—21no—
237C2×Q8×C11—22no—
238C2×Q8×C11—24no—
239C2×Q8×C11—24no—
240C2×Q8×C11C2×D411yescharacteristic
241C2×Q8×C11C2414yes—
242C2×D4×C11C2×D412yes—
243C2×D4×C11C2×D411yescharacteristic
244C22×C4×C11—22no—
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2411yescharacteristic
251C2×C22⋊D11—22no—
252C2×C22⋊D11—21no—
253C22×Dic11—22no—
254C22×Dic11—21no—
255C22×Dic11—22no—
256C22×Dic11—21no—
257Q8×D11—28no—
258#4341—216no—
259#4341—28no—
260#4339—24no—
261#4339—24no—
262#4339—22no—
263#4339#4114yes—
264C2×D44C2411yescharacteristic
265C2×C4×D11—22no—
266C2×C4×D11—21no—
267C2×C4×D11—21no—
268C2×C4×D11—22no—
269C2×C4×D11—21no—
270C2×Dic22—24no—
271C2×Dic22—24no—
272C2×Dic22—22no—
273C2×Dic22—21no—
274C2×Dic22—22no—
275C2×Dic22#4114yes—
276C2×Dic22C2411yescharacteristic
277C2×Dic22C2412yes—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—24no—
285C11×C4⋊C4—24no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—24no—
289C11×C4⋊C4—24no—
290C11×C4⋊C4C2×D411yescharacteristic
291C11×C4⋊C4C2×D412yes—
292C11×C4⋊C4C2×D411yescharacteristic
293C11×C4⋊C4C2×D412yes—
294C11×C4⋊C4C2412yes—
295C11×C4⋊C4C2412yes—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—24no—
298C11×C22⋊C4—24no—
299C11×C22⋊C4C2×D412yes—
300C11×C22⋊C4C2×D412yes—
301C11×C22⋊C4C2×D412yes—
302C42×C11—24no—
303C42×C11—24no—
304C42×C11—22no—
305C42×C11C2×D412yes—
306C42×C11C2×D411yescharacteristic
307C42×C11C2×D412yes—
308C42×C11C2×D411yescharacteristic
309C42×C11C2412yes—
310C42×C11C2411yescharacteristic
311C42×C11C2411yescharacteristic
312C22⋊Dic11—22no—
313C22⋊Dic11—21no—
314#4326—28no—
315#4326—28no—
316#4326—28no—
317#4325—28no—
318(C2×D11)⋊C4—21no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—21no—
321C4⋊Dic11—22no—
322C4⋊Dic11—21no—
323C4⋊Dic11C2412yes—
324C4⋊Dic11C2411yescharacteristic
325C4⋊Dic11C2411yescharacteristic
326Dic11⋊C4—21no—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4—21no—
333C4×Dic11—21no—
334C4×Dic11—22no—
335C4×Dic11—22no—
336C4×Dic11—22no—
337C4×Dic11—22no—
338C4×Dic11—22no—
339C4×Dic11—21no—
340C4×Dic11—22no—
341C4×Dic11—21no—
342#4318—24no—
343C2×C11⋊C8—24no—
344C2×C11⋊C8C2412yes—
345C2×C11⋊C8C2414yes—
346C2×C11⋊C8C2412yes—
347#3509D1111yescharacteristic, complemented
348C4×2−1+4—111no—
349#3127—114no—
350#3120—114no—
351#3116—112no—
352#3113—112no—
353#3107—112no—
354#3104—112no—
355#3097—112no—
356#3078—111no—
357#3076—111no—
358#3039—111no—
359C2×#462—111no—
360#3011—112no—
361#2950—112no—
362#2947—112no—
363#2925—111no—
364C23×C11C22×D412yes—
365C23×C11C22×D411yescharacteristic
366C22×D11—21no—
367Q8×C11—22no—
368Q8×C11—24no—
369Q8×C11—24no—
370Q8×C11—42no—
371Q8×C11—44no—
372Q8×C11—42no—
373D4×C11—24no—
374D4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—24no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—24no—
382C2×C4×C11—41no—
383C2×C4×C11—42no—
384C2×C4×C11—44no—
385C2×C4×C11C22×D412yes—
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11C22×D412yes—
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×D412yes—
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C2×#4112yes—
394C2×C4×C11C2×#4112yes—
395C2×C4×C11C2511yescharacteristic
396C22⋊D11—28no—
397C22⋊D11—24no—
398C2×Dic11—28no—
399C2×Dic11—24no—
400C2×Dic11—21no—
401C2×Dic11—22no—
402C2×Dic11—21no—
403C2×Dic11—21no—
404C2×Dic11—22no—
405C2×Dic11—81no—
406C2×Dic11—82no—
407D44—21no—
408D44C2×#4112yes—
409C4×D11—28no—
410C4×D11—24no—
411C4×D11—42no—
412C4×D11—82no—
413C4×D11—81no—
414Dic22—28no—
415Dic22—24no—
416Dic22—22no—
417Dic22—21no—
418Dic22C2×#4112yes—
419Dic22C2×#4114yes—
420C11⋊C8—22no—
421C11⋊C8—22no—
422C11⋊C8—24no—
423C2×2−1+4—111no—
424C2×#137—112no—
425C22×Q16—112no—
426#557—21no—
427#557—21no—
428#556—21no—
429#556—21no—
430#552—22no—
431#552—22no—
432#541C2×D1114yes—
433#536C2×D1112yes—
434#533C2×D1112yes—
435#533C2×D1112yes—
436#533C2×D1111yescharacteristic
437C2×C4⋊Q8C2×D1111yescharacteristic
438#520—111no—
439#520—112no—
440#520—111no—
441#520—222no—
442#520—221no—
443#519—112no—
444#519—111no—
445#519—221no—
446#519C2×D1112yes—
447C4×#41—111no—
448C4×#41—112no—
449C4×#41—222no—
450C4×#41—221no—
451C4×#41C2×D1111yescharacteristic
452C2×C4×Q8—111no—
453C2×C4×Q8—112no—
454C2×C4×Q8—221no—
455#485—114no—
456#485—114no—
457#484—114no—
458#483—114no—
459#479—112no—
460#479—114no—
461#478—112no—
462#477—111no—
463#477—112no—
464#476—111no—
465#475—111no—
466#475—112no—
467#474—111no—
468#462—112no—
469#462—112no—
470#462—112no—
471#462—114no—
472#462—112no—
473#461—112no—
474#461—112no—
475#452—114no—
476#452—114no—
477#451—114no—
478#451—114no—
479#441—114no—
480#441—114no—
481#441—114no—
482#440—114no—
483C4×Q16—114no—
484C4×Q16—114no—
485C4×Q16—114no—
486C4×SD16—114no—
487#433—114no—
488#432—112no—
489#431—112no—
490#428—112no—
491#427—112no—
492#423—111no—
493C2×C4⋊C8—111no—
494#419—112no—
495#419—112no—
496#416—112no—
497C2×#103—112no—
498#408—112no—
499#405—112no—
500C22×C11—21no—
501C22×C11—21no—
502C22×C11—22no—
503C22×C11—22no—
504C22×C11—22no—
505C22×C11#52512yes—
506C22×C11C23×D411yescharacteristic
507C2×D11—22no—
508C2×D11—41no—
509C2×D11—41no—
510C4×C11—21no—
511C4×C11—22no—
512C4×C11—21no—
513C4×C11—22no—
514C4×C11—22no—
515C4×C11—21no—
516C4×C11—42no—
517C4×C11—44no—
518C4×C11—42no—
519C4×C11#52512yes—
520C4×C11#57812yes—
521C4×C11C22×#4111yescharacteristic
522C4×C11C22×#4111yescharacteristic
523Dic11—22no—
524Dic11—24no—
525Dic11—42no—
526Dic11—41no—
527Dic11—41no—
5282−1+4—224no—
5292−1+4—224no—
530C2×#41—111no—
531C2×#41—112no—
532C2×#41—222no—
533C2×#41—221no—
534C2×#41C22×D1111yescharacteristic
535C22×Q8—111no—
536C22×Q8—112no—
537C22×Q8—221no—
538C22×Q8C22×D1112yes—
539#137—228no—
540C2×Q16—114no—
541C2×Q16—114no—
542C2×Q16—114no—
543C2×Q16—228no—
544C2×SD16—114no—
545C2×M16—112no—
546C22×C8—112no—
547C4⋊Q8—22no—
548C4⋊Q8—21no—
549C4⋊Q8—21no—
550C4⋊Q8C22×D1112yes—
551C4⋊Q8C22×D1112yes—
552C4⋊Q8C22×D1111yescharacteristic
553C4⋊Q8C22×D1111yescharacteristic
554#126—24no—
555#126—24no—
556#125—24no—
557#125—24no—
558#125—22no—
559#125—22no—
560#125C22×D1112yes—
561#124—22no—
562#123—24no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8C22×D1114yes—
568C22⋊Q8C22×D1114yes—
569C4×Q8—22no—
570C4×Q8—22no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—21no—
574C4×Q8—21no—
575C4×Q8—112no—
576C4×Q8—111no—
577C4×Q8—112no—
578C4×Q8—112no—
579C4×Q8—112no—
580C4×Q8—112no—
581C4×Q8—111no—
582C4×Q8—221no—
583C4×Q8—221no—
584C4×Q8—222no—
585C4×Q8—221no—
586C4×Q8—222no—
587C4×Q8—222no—
588C4×Q8—221no—
589C4×Q8—222no—
590C4×Q8—221no—
591C4×Q8C22⋊D1111yescharacteristic
592C4×Q8C22⋊D1111yescharacteristic
593C4×Q8C22×D1114yes—
594C4×Q8C22×D1114yes—
595C4×D4—111no—
596C4×D4—112no—
597C4×D4—111no—
598C4×D4—222no—
599C4×D4—221no—
600C4×D4—221no—
601C4×D4—222no—
602C4×D4—221no—
603C4×D4—222no—
604C4×D4—222no—
605C4×D4—222no—
606C4×D4—222no—
607C4×D4C22⋊D1112yes—
608C4×D4C22⋊D1111yescharacteristic
609C4×D4C22⋊D1112yes—
610C4×D4C22⋊D1111yescharacteristic
611#117—22no—
612#117—22no—
613#117—24no—
614#117—111no—
615#117—112no—
616#117—221no—
617#117—222no—
618#117—222no—
619#117—222no—
620#117—222no—
621#117—222no—
622#117—221no—
623#117C22×D1112yes—
624#117C22×D1111yescharacteristic
625#117C22×D1112yes—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—111no—
629C2×C4⋊C4—112no—
630C2×C4⋊C4—221no—
631C2×C4⋊C4—222no—
632C2×C4⋊C4—221no—
633C2×C4⋊C4—222no—
634C2×C42—221no—
635C2×C42—222no—
636C2×C42—222no—
637C2×C42—221no—
638C2×C42C22×D1111yescharacteristic
639C2×C42C22×D1112yes—
640#107—112no—
641#107—112no—
642#107—114no—
643#106—112no—
644#106—112no—
645#106—114no—
646C4⋊C8—111no—
647C4⋊C8—111no—
648C4⋊C8—112no—
649C4⋊C8—112no—
650C4⋊C8—112no—
651#103—114no—
652#103—114no—
653#103—114no—
654#103—114no—
655#103—112no—
656#103—112no—
657#103—114no—
658#103—114no—
659#102—112no—
660#102—112no—
661C22⋊C8—114no—
662C22⋊C8—114no—
663#97—114no—
664C4×C8—114no—
665C2×C11—22no—
666C2×C11—42no—
667C2×C11C2×#52511yescharacteristic
668C2×C11C2×#57811yescharacteristic
669C2×C11#358611yescharacteristic
670D11—42no—
671#41—22no—
672#41—22no—
673#41—114no—
674#41—224no—
675#41—224no—
676#41—2216no—
677#41—228no—
678#41—222no—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—22no—
682C2×Q8—24no—
683C2×Q8—24no—
684C2×Q8—114no—
685C2×Q8—112no—
686C2×Q8—111no—
687C2×Q8—224no—
688C2×Q8—224no—
689C2×Q8—228no—
690C2×Q8—222no—
691C2×Q8—222no—
692C2×Q8—221no—
693C2×Q8C2×C22⋊D1111yescharacteristic
694C2×Q8C23×D1114yes—
695C2×D4—111no—
696C2×D4—222no—
697C2×D4—221no—
698C2×D4C2×C22⋊D1112yes—
699C2×D4C2×C22⋊D1111yescharacteristic
700C22×C4—22no—
701C22×C4—222no—
702C22×C4—221no—
703C22×C4—222no—
704C22×C4—221no—
705C22×C4—222no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—222no—
709C22×C4—221no—
710C22×C4C2×C22⋊D1111yescharacteristic
711C22×C4C2×C22⋊D1112yes—
712C22×C4C2×C22⋊D1111yescharacteristic
713C22×C4C2×C22⋊D1112yes—
714C22×C4C23×D1112yes—
715C22×C4C23×D1111yescharacteristic
716Q16—228no—
717Q16—228no—
718Q16—228no—
719SD16—228no—
720M16—224no—
721C2×C8—112no—
722C2×C8—114no—
723C2×C8—112no—
724C2×C8—224no—
725C4⋊C4—22no—
726C4⋊C4—22no—
727C4⋊C4—22no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—24no—
732C4⋊C4—24no—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—112no—
738C4⋊C4—111no—
739C4⋊C4—111no—
740C4⋊C4—222no—
741C4⋊C4—221no—
742C4⋊C4—222no—
743C4⋊C4—222no—
744C4⋊C4—222no—
745C4⋊C4—222no—
746C4⋊C4—221no—
747C4⋊C4—222no—
748C4⋊C4—221no—
749C4⋊C4C2×C22⋊D1111yescharacteristic
750C4⋊C4C2×C22⋊D1112yes—
751C4⋊C4C2×C22⋊D1111yescharacteristic
752C4⋊C4C2×C22⋊D1112yes—
753C4⋊C4C23×D1112yes—
754C4⋊C4C23×D1112yes—
755C22⋊C4—22no—
756C22⋊C4—24no—
757C22⋊C4—24no—
758C22⋊C4—222no—
759C22⋊C4—221no—
760C22⋊C4—221no—
761C22⋊C4—222no—
762C22⋊C4—221no—
763C22⋊C4C2×C22⋊D1112yes—
764C22⋊C4C2×C22⋊D1112yes—
765C22⋊C4C2×C22⋊D1112yes—
766C42—24no—
767C42—24no—
768C42—22no—
769C42—222no—
770C42—221no—
771C42—222no—
772C42—221no—
773C42—222no—
774C42—221no—
775C42—222no—
776C42—222no—
777C42—222no—
778C42C2×C22⋊D1112yes—
779C42C2×C22⋊D1111yescharacteristic
780C42C2×C22⋊D1112yes—
781C42C2×C22⋊D1111yescharacteristic
782C42C23×D1112yes—
783C42C23×D1111yescharacteristic
784C42C23×D1111yescharacteristic
785C11#6059411yescharacteristic, complemented, Sylow
786C23—221no—
787C23C22×C22⋊D1112yes—
788C23C22×C22⋊D1111yescharacteristic
789Q8—22no—
790Q8—24no—
791Q8—24no—
792Q8—42no—
793Q8—44no—
794Q8—42no—
795Q8—114no—
796Q8—112no—
797Q8—228no—
798Q8—224no—
799Q8—222no—
800Q8—221no—
801D4—24no—
802D4—22no—
803D4—112no—
804D4—228no—
805D4—224no—
806D4—221no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—228no—
818C2×C4—228no—
819C2×C4—224no—
820C2×C4—222no—
821C2×C4—221no—
822C2×C4—224no—
823C2×C4—221no—
824C2×C4—222no—
825C2×C4—221no—
826C2×C4—442no—
827C2×C4—882no—
828C2×C4—881no—
829C2×C4—881no—
830C2×C4—882no—
831C2×C4#41×D1112yes—
832C2×C4#41×D1112yes—
833C2×C4C22×C22⋊D1112yes—
834C2×C4C22×C22⋊D1112yes—
835C2×C4C22×C22⋊D1111yescharacteristic
836C2×C4C22×C22⋊D1112yes—
837C2×C4C22×C22⋊D1111yescharacteristic
838C2×C4C22×C22⋊D1111yescharacteristic
839C2×C4C22×C22⋊D1111yescharacteristic
840C2×C4C22×C22⋊D1111yescharacteristic
841C2×C4C24×D1111yescharacteristic
842C8—222no—
843C8—222no—
844C8—224no—
845C22—21no—
846C22—21no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—222no—
851C22—441no—
852C22—441no—
853C22#1062335912yes—
854C22C23×C22⋊D1111yescharacteristic
855C4—21no—
856C4—22no—
857C4—21no—
858C4—22no—
859C4—21no—
860C4—22no—
861C4—42no—
862C4—42no—
863C4—44no—
864C4—224no—
865C4—222no—
866C4—442no—
867C4—441no—
868C4—441no—
869C4#1062335912yes—
870C4#1062336912yes—
871C4C2×#41×D1111yescharacteristic
872C4C2×#41×D1111yescharacteristic
873C2—22no—
874C2—42no—
875C2—442no—
876C2C2×#1062335911yescharacteristic
877C2C2×#1062336911yescharacteristic
878C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3509C2
socleC22×C11C23×D4
prime radicalC2×#67043C22
hypercenter#3509D11
hypocenterC11#60594
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3509

Complements

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

NH ≅ G/Ntype
2. #13078911C2semidirect
3. #13078824C2semidirect
4. #13078772C2semidirect
5. #13078742C2semidirect
6. #13078681C2semidirect
7. #13078651C2semidirect
8. #13078579C2semidirect
9. #13078417C2semidirect
10. #13078398C2semidirect
11. #13078099C2semidirect
12. C2×#10622703C2semidirect
14. #13077482C2semidirect
15. #13077459C2semidirect
16. #13077282C2semidirect
17. C11×#3509C2semidirect
347. #3509D11semidirect
785. C11#60594semidirect

Maximal subgroups

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

subgroupindex
C4×#670432
#130789112
#130788242
#130787722
#130787422
#130786812
#130786512
#130785792
#130784172
#130783982
#130780992
C2×#106227032
#130779092
#130774822
#130774592
#130772822
C11×#35092
#6059411