Finite Group Databasebeta

← #15630788

Subgroups — #15630788

Order 2816.

2088 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic22C211yesmaximal, characteristic, complemented
2#13080904C212yesmaximal, complemented
3#13080893C212yesmaximal, complemented
4#13080781C214yesmaximal, complemented
5#13080661C214yesmaximal, complemented
6#13080486C212yesmaximal, complemented
7#13080475C212yesmaximal, complemented
8#13078998C211yesmaximal, characteristic, complemented
9#13078564C212yesmaximal, complemented
10#13078417C211yesmaximal, characteristic, complemented
11#13078248C212yesmaximal, complemented
12#13078103C211yesmaximal, characteristic, complemented
13#13077849C212yesmaximal, complemented
14C4×#67004C211yesmaximal, characteristic, complemented
15D4×#4318C211yesmaximal, characteristic, complemented
16C2×#10622617C212yesmaximal, complemented
17C11×#3475C211yesmaximal, characteristic
18C23×Dic22C2212yes—
19C11×#556C2211yescharacteristic
20C11×#555C2211yescharacteristic
21C11×#554C2211yescharacteristic
22C11×#553C2212yes—
23C11×#552—21no—
24C11×#552C2212yes—
25C11×#551—22no—
26C11×#547C2211yescharacteristic
27C11×#546—21no—
28C11×#533C2211yescharacteristic
29C11×#529—22no—
30C11×#529—21no—
31C11×#525C2212yes—
32C4×C11×#41—21no—
33C4×C11×#41C2211yescharacteristic
34C2×C4×D4×C11C2211yescharacteristic
35C2×C11×#117C2212yes—
36C2×#67004C2211yescharacteristic
37C2×#67004C2212yes—
38C2×D4×Dic11—21no—
39C2×#66977C2212yes—
40C22×#4318C2212yes—
41D4×Dic22—21no—
42D4×Dic22—21no—
43D4×Dic22—22no—
44D4×Dic22C2212yes—
45D4×Dic22C2214yes—
46D4×Dic22C2212yes—
47C2×#66941—21no—
48C2×#66931—22no—
49C2×#66922C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51#10622845C2211yescharacteristic
52#10622820C2212yes—
53#10622707C2212yescomplemented
54#10622706C2212yescomplemented
55#10622706C2212yescomplemented
56#10622704C2212yescomplemented
57#10622682C2214yescomplemented
58#10622676C2214yescomplemented
59#10622665C2214yescomplemented
60#10622664C2214yescomplemented
61#10622663C2214yescomplemented
62#10622663C2214yescomplemented
63#10622655C2214yescomplemented
64#10622654C2214yescomplemented
65#10622653C2214yescomplemented
66#10622653C2214yescomplemented
67#10622644C2212yescomplemented
68#10622644C2212yescomplemented
69#10622643C2212yescomplemented
70C4×#4326C2212yescomplemented
71#10622632C2212yescomplemented
72#10622632C2212yescomplemented
73#10622631C2212yescomplemented
74C4×#4324C2212yescomplemented
75#10622625C2212yes—
76#10622624C2214yes—
77D4×C11⋊C8C2212yes—
78#10622617C2212yes—
79#10622617C2212yes—
80#10622617C2212yes—
81#10622617C2211yescharacteristic
82#10622617C2212yes—
83#10622617C2214yescomplemented
84#10622617C2214yescomplemented
85#10622609C2214yescomplemented
86#10622609C2214yescomplemented
87#10622608C2211yescharacteristic
88#10622608C2212yes—
89#10622584C2214yescomplemented
90#10622583C2214yescomplemented
91C2×#66874C2214yescomplemented
92C2×#66874C2214yescomplemented
93#10622537C2211yescharacteristic
94C4×#4318C2211yescharacteristic
95C2×C11×#41—21no—
96C2×C11×#41C2311yescharacteristic
97C22×D4×C11D411yescharacteristic
98C23×C4×C11C2312yes—
99C23×Dic11—22no—
100C22×Dic22—28no—
101C22×Dic22—22no—
102C22×Dic22—22no—
103C22×Dic22—22no—
104C22×Dic22—44no—
105C22×Dic22C2312yes—
106C22×Dic22C2314yes—
107C22×Dic22C2314yes—
108C22×Dic22C2311yescharacteristic
109C11×C4⋊Q8C2311yescharacteristic
110C11×C4⋊Q8C2311yescharacteristic
111C11×#126—22no—
112C11×#126—22no—
113C11×#126—22no—
114C11×#125—22no—
115C11×#125—21no—
116C11×#125C2312yes—
117C11×#124—21no—
118C11×#124—22no—
119C11×#123—22no—
120C11×#123—22no—
121C11×#123—22no—
122C11×#123—22no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8—21no—
125C11×C22⋊Q8—21no—
126C11×C22⋊Q8—22no—
127C11×C22⋊Q8C2312yes—
128C11×C22⋊Q8C2312yes—
129C11×#121—22no—
130C11×#121—21no—
131C11×#121C2312yes—
132C11×#121C2312yes—
133C11×#120—22no—
134C4×Q8×C11—21no—
135C4×Q8×C11—21no—
136C4×Q8×C11—21no—
137C4×Q8×C11C2311yescharacteristic
138C4×Q8×C11C2311yescharacteristic
139C4×D4×C11—21no—
140C4×D4×C11—22no—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11—22no—
144C4×D4×C11—22no—
145C4×D4×C11D411yescharacteristic
146C4×D4×C11D411yescharacteristic
147C4×D4×C11D412yes—
148C4×D4×C11C2311yescharacteristic
149C4×D4×C11C2311yescharacteristic
150C4×D4×C11C2311yescharacteristic
151C4×D4×C11C2312yes—
152C4×D4×C11C2311yescharacteristic
153C11×#117—22no—
154C11×#117—22no—
155C11×#117—21no—
156C11×#117—22no—
157C11×#117—21no—
158C11×#117C2311yescharacteristic
159C11×#117C2312yes—
160C11×#117C2312yes—
161C11×#117C2312yes—
162C2×C11×C4⋊C4D411yescharacteristic
163C2×C11×C4⋊C4C2312yes—
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C22⋊C4—22no—
166C2×C11×C22⋊C4D412yes—
167C2×C42×C11—22no—
168C2×C42×C11—21no—
169C2×C42×C11C2311yescharacteristic
170C2×C22⋊Dic11—22no—
171#67004—24no—
172#67004—44no—
173C2×#4326C2312yes—
174C2×#4326C2314yes—
175D4×Dic11—24no—
176D4×Dic11—22no—
177D4×Dic11—22no—
178C2×#4324C2312yes—
179C2×#4324C2314yes—
180C2×C4⋊Dic11—21no—
181C2×C4⋊Dic11—21no—
182C2×C4⋊Dic11C2311yescharacteristic
183#66977—22no—
184#66977—22no—
185#66977C2314yes—
186#66977C2314yes—
187C2×Dic11⋊C4—21no—
188C2×Dic11⋊C4—22no—
189C2×C4×Dic11—21no—
190C2×#4318—44no—
191C2×#4318C2311yescharacteristic
192C2×#4318C2311yescharacteristic
193C2×#4318C2312yes—
194C2×#4318C2314yes—
195C22×C11⋊C8C2314yes—
196#66941—22no—
197#66941—22no—
198#66941—24no—
199#66931—24no—
200#66931—24no—
201#66931—24no—
202#66931—24no—
203#66922—21no—
204#66922—21no—
205#66922C2312yes—
206#66922C2312yes—
207C4×Dic22—21no—
208C4×Dic22—21no—
209C4×Dic22C2312yes—
210C4×Dic22C2312yes—
211#66899C2312yes—
212#66896C2312yes—
213C22⋊(C11⋊C8)C2314yes—
214C22⋊(C11⋊C8)C2314yes—
215#66874C2312yes—
216#66874C2312yes—
217#66874C2314yes—
218#66874C2314yes—
219#66874C2314yes—
220#66874C2314yes—
221#66874C2314yes—
222#66874C2314yes—
223#66874C2314yes—
224#66874C2314yes—
225#66872C2312yes—
226#66872C2314yes—
227#66871C2312yes—
228#66871C2314yes—
229C4⋊(C11⋊C8)C2312yes—
230C4⋊(C11⋊C8)C2312yes—
231#66867C2312yes—
232C4×C11⋊C8C2312yes—
233#61157—111nomaximal, Sylow
234C24×C11C2×D412yes—
235C11×#41—22no—
236C11×#41—22no—
237C11×#41—44no—
238C2×Q8×C11—21no—
239C2×Q8×C11—21no—
240C2×Q8×C11C2411yescharacteristic
241C2×D4×C11—24no—
242C2×D4×C11—21no—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C2×D4×C11C2×D412yes—
246C2×D4×C11C2×D411yescharacteristic
247C2×D4×C11C2×D411yescharacteristic
248C2×D4×C11C2411yescharacteristic
249C22×C4×C11—24no—
250C22×C4×C11—24no—
251C22×C4×C11—22no—
252C22×C4×C11—22no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D412yes—
259C22×C4×C11C2×D412yes—
260C22×C4×C11C2×D411yescharacteristic
261C22×C4×C11C2412yes—
262C22×C4×C11C2412yes—
263C22×C4×C11C2411yescharacteristic
264C22×Dic11—21no—
265C22×Dic11—24no—
266C22×Dic11—24no—
267C22×Dic11—21no—
268C22×Dic11—22no—
269C22×Dic11—48no—
270C2×Dic22—28no—
271C2×Dic22—28no—
272C2×Dic22—21no—
273C2×Dic22—22no—
274C2×Dic22—24no—
275C2×Dic22—24no—
276C2×Dic22—24no—
277C2×Dic22—22no—
278C2×Dic22—24no—
279C2×Dic22—44no—
280C2×Dic22—44no—
281C2×Dic22—48no—
282C2×Dic22—48no—
283C2×Dic22—48no—
284C2×Dic22#4114yescomplemented
285C2×Dic22C2414yes—
286C2×Dic22C2412yes—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—21no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4—22no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4—21no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—22no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4C2×D411yescharacteristic
298C11×C4⋊C4C2×D411yescharacteristic
299C11×C4⋊C4C2×D412yes—
300C11×C4⋊C4C2411yescharacteristic
301C11×C4⋊C4C2412yes—
302C11×C4⋊C4C2411yescharacteristic
303C11×C4⋊C4C2412yes—
304C11×C22⋊C4—21no—
305C11×C22⋊C4—22no—
306C11×C22⋊C4—22no—
307C11×C22⋊C4—22no—
308C11×C22⋊C4—22no—
309C11×C22⋊C4—22no—
310C11×C22⋊C4—22no—
311C11×C22⋊C4—21no—
312C11×C22⋊C4—21no—
313C11×C22⋊C4—22no—
314C11×C22⋊C4C2×D412yes—
315C11×C22⋊C4C2×D412yes—
316C11×C22⋊C4C2×D412yes—
317C11×C22⋊C4C2×D412yes—
318C42×C11—21no—
319C42×C11—22no—
320C42×C11—21no—
321C42×C11—22no—
322C42×C11—22no—
323C42×C11—21no—
324C42×C11C2×D411yescharacteristic
325C42×C11C2×D411yescharacteristic
326C42×C11C2411yescharacteristic
327C42×C11C2411yescharacteristic
328C22⋊Dic11—24no—
329C22⋊Dic11—24no—
330#4326—24no—
331#4326—44no—
332#4324—24no—
333#4324—44no—
334C4⋊Dic11—21no—
335C4⋊Dic11—22no—
336C4⋊Dic11—22no—
337C4⋊Dic11—22no—
338C4⋊Dic11—22no—
339C4⋊Dic11C2412yes—
340Dic11⋊C4—22no—
341Dic11⋊C4—22no—
342Dic11⋊C4—24no—
343Dic11⋊C4—24no—
344C4×Dic11—22no—
345C4×Dic11—22no—
346#4318—22no—
347#4318—22no—
348#4318—24no—
349#4318—44no—
350C2×C11⋊C8—44no—
351C2×C11⋊C8C2412yes—
352C2×C11⋊C8C2412yes—
353C2×C11⋊C8C2414yes—
354#3475D1111yescharacteristic
355C2×D4×Q8—111no—
356#3329—112no—
357#3328—112no—
358#3320—114no—
359#3312—114no—
360#3299—112no—
361#3298—112no—
362#3139—111no—
363#3095—112no—
364#3078—111no—
365#3056—112no—
366#3039—111no—
367#3004—112no—
368C4×#137—111no—
369D4×M16—111no—
370C2×#419—112no—
371C23×C11—24no—
372C23×C11—24no—
373C23×C11—21no—
374C23×C11—42no—
375C23×C11C22×D412yes—
376C23×C11C22×D411yescharacteristic
377C23×C11C22×D412yes—
378Q8×C11—21no—
379Q8×C11—21no—
380Q8×C11—42no—
381Q8×C11—81no—
382D4×C11—24no—
383D4×C11—22no—
384D4×C11—21no—
385D4×C11—21no—
386D4×C11—42no—
387D4×C11—44no—
388D4×C11—82no—
389D4×C11#13714yescomplemented
390C2×C4×C11—24no—
391C2×C4×C11—24no—
392C2×C4×C11—24no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—41no—
404C2×C4×C11—44no—
405C2×C4×C11—42no—
406C2×C4×C11—42no—
407C2×C4×C11—81no—
408C2×C4×C11—82no—
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C22×D412yes—
413C2×C4×C11C22×D412yes—
414C2×C4×C11C22×D411yescharacteristic
415C2×C4×C11C22×D411yescharacteristic
416C2×C4×C11C2×#4112yes—
417C2×C4×C11H(5,𝔽2)12yes—
418C2×C4×C11C2511yescharacteristic
419C2×Dic11—24no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—24no—
423C2×Dic11—48no—
424C2×Dic11—48no—
425C2×Dic11—42no—
426C2×Dic11—44no—
427Dic22—24no—
428Dic22—22no—
429Dic22—24no—
430Dic22—24no—
431Dic22—48no—
432Dic22—48no—
433Dic22—44no—
434Dic22C2×#4114yes—
435C11⋊C8—22no—
436C11⋊C8—22no—
437C11⋊C8—24no—
438C23×Q8—112no—
439C2×#137—111no—
440C2×#137—112no—
441C22×M16—112no—
442#556C2×D1111yescharacteristic
443#555C2×D1111yescharacteristic
444#554C2×D1111yescharacteristic
445#553C2×D1112yes—
446#552—21no—
447#552C2×D1112yes—
448#551—22no—
449D4×Q8—112no—
450D4×Q8—112no—
451D4×Q8—114no—
452D4×Q8—221no—
453D4×Q8—222no—
454D4×Q8—221no—
455#547C2×D1111yescharacteristic
456#546—21no—
457#533C2×D1111yescharacteristic
458C2×C4⋊Q8—111no—
459C2×C4⋊Q8—221no—
460#529—22no—
461#529—21no—
462#525C2×D1112yes—
463C2×C22⋊Q8—112no—
464C2×C22⋊Q8—222no—
465C4×#41—21no—
466C4×#41C2×D1111yescharacteristic
467C2×C4×Q8—111no—
468C2×C4×D4—221no—
469C2×C4×D4C2×D1111yescharacteristic
470C2×#117C2×D1112yes—
471#491—114no—
472#487—112no—
473#487—112no—
474#485—114no—
475#485—114no—
476#484—114no—
477#483—114no—
478#479—114no—
479#477—112no—
480#475—112no—
481#470—114no—
482#468—114no—
483#467—114no—
484#465—114no—
485#462—112no—
486#462—112no—
487#461—112no—
488#461—112no—
489#451—114no—
490#451—114no—
491#448—114no—
492#448—114no—
493#441—112no—
494#440—112no—
495C4×Q16—112no—
496C4×SD16—112no—
497#436—112no—
498#435—114no—
499C8×D4—112no—
500#428—112no—
501#428—111no—
502#423—111no—
503#419—114no—
504#419—114no—
505#419—112no—
506#419—112no—
507#419—112no—
508#419—112no—
509#419—111no—
510#417—111no—
511C2×#103—114no—
512C2×#103—114no—
513#407—112no—
514C4×M16—111no—
515C22×C11—21no—
516C22×C11—22no—
517C22×C11—22no—
518C22×C11—21no—
519C22×C11—22no—
520C22×C11—22no—
521C22×C11—22no—
522C22×C11—48no—
523C22×C11—41no—
524C22×C11—41no—
525C22×C11—41no—
526C22×C11#54612yes—
527C22×C11C2×#13714yes—
528C22×C11C23×D411yescharacteristic
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—22no—
532C4×C11—22no—
533C4×C11—21no—
534C4×C11—41no—
535C4×C11—42no—
536C4×C11—41no—
537C4×C11—41no—
538C4×C11—42no—
539C4×C11#54612yes—
540C4×C11C2×#13712yes—
541C4×C11C22×#4111yescharacteristic
542C4×C11C2×H(5,𝔽2)11yescharacteristic
543Dic11—24no—
544Dic11—42no—
545Dic11—44no—
546C2×#41—21no—
547C2×#41C22×D1111yescharacteristic
548C22×Q8—111no—
549C22×Q8—112no—
550C22×Q8—114no—
551C22×Q8—114no—
552C22×Q8—228no—
553C22×Q8—222no—
554C22×Q8—222no—
555C22×Q8—222no—
556C22×Q8—444no—
557C22×D4C22⋊D1111yescharacteristic
558C23×C4—222no—
559C23×C4C22×D1112yes—
560#137—224no—
561#137—444no—
562C2×Q16—112no—
563C2×Q16—114no—
564C2×SD16—112no—
565C2×SD16—114no—
566C2×M16—111no—
567C2×M16—112no—
568C2×M16—111no—
569C2×M16—114no—
570C2×M16—444no—
571C22×C8—114no—
572C4⋊Q8—112no—
573C4⋊Q8—112no—
574C4⋊Q8—222no—
575C4⋊Q8—222no—
576C4⋊Q8—224no—
577C4⋊Q8—221no—
578C4⋊Q8—221no—
579C4⋊Q8C22×D1111yescharacteristic
580C4⋊Q8C22×D1111yescharacteristic
581#126—22no—
582#126—22no—
583#126—22no—
584#125—22no—
585#125—21no—
586#125C22×D1112yes—
587#124—21no—
588#124—22no—
589#123—22no—
590#123—22no—
591#123—22no—
592#123—22no—
593C22⋊Q8—21no—
594C22⋊Q8—21no—
595C22⋊Q8—21no—
596C22⋊Q8—22no—
597C22⋊Q8—114no—
598C22⋊Q8—114no—
599C22⋊Q8—222no—
600C22⋊Q8—222no—
601C22⋊Q8—224no—
602C22⋊Q8—224no—
603C22⋊Q8—224no—
604C22⋊Q8—224no—
605C22⋊Q8C22×D1112yes—
606C22⋊Q8C22×D1112yes—
607#121—22no—
608#121—21no—
609#121C22×D1112yes—
610#121C22×D1112yes—
611#120—22no—
612C4×Q8—21no—
613C4×Q8—21no—
614C4×Q8—21no—
615C4×Q8—112no—
616C4×Q8—112no—
617C4×Q8—221no—
618C4×Q8—221no—
619C4×Q8C22×D1111yescharacteristic
620C4×Q8C22×D1111yescharacteristic
621C4×D4—21no—
622C4×D4—22no—
623C4×D4—21no—
624C4×D4—21no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—224no—
628C4×D4—222no—
629C4×D4—222no—
630C4×D4C22⋊D1111yescharacteristic
631C4×D4C22⋊D1111yescharacteristic
632C4×D4C22⋊D1112yes—
633C4×D4C22×D1111yescharacteristic
634C4×D4C22×D1111yescharacteristic
635C4×D4C22×D1111yescharacteristic
636C4×D4C22×D1112yes—
637C4×D4C22×D1111yescharacteristic
638#117—22no—
639#117—22no—
640#117—21no—
641#117—22no—
642#117—21no—
643#117C22×D1111yescharacteristic
644#117C22×D1112yes—
645#117C22×D1112yes—
646#117C22×D1112yes—
647C2×C4⋊C4—111no—
648C2×C4⋊C4—221no—
649C2×C4⋊C4—221no—
650C2×C4⋊C4—222no—
651C2×C4⋊C4—221no—
652C2×C4⋊C4C22⋊D1111yescharacteristic
653C2×C4⋊C4C22×D1112yes—
654C2×C4⋊C4C22×D1112yes—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—222no—
657C2×C22⋊C4C22⋊D1112yes—
658C2×C42—22no—
659C2×C42—21no—
660C2×C42—221no—
661C2×C42C22×D1111yescharacteristic
662#107—112no—
663#107—114no—
664#106—112no—
665#106—114no—
666C4⋊C8—112no—
667C4⋊C8—112no—
668#103—112no—
669#103—112no—
670#103—112no—
671#103—114no—
672#103—114no—
673#103—114no—
674#103—114no—
675#103—114no—
676#103—114no—
677#103—114no—
678#103—114no—
679#102—112no—
680C22⋊C8—114no—
681C22⋊C8—114no—
682#97—112no—
683C4×C8—112no—
684C2×C11—22no—
685C2×C11—24no—
686C2×C11—42no—
687C2×C11—81no—
688C2×C11C2×#54611yescharacteristic
689C2×C11C22×#13711yescharacteristic
690C2×C11#358611yescharacteristic
691C24C2×C22⋊D1112yes—
692#41—22no—
693#41—22no—
694#41—44no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—114no—
698C2×Q8—112no—
699C2×Q8—114no—
700C2×Q8—228no—
701C2×Q8—228no—
702C2×Q8—222no—
703C2×Q8—221no—
704C2×Q8—224no—
705C2×Q8—224no—
706C2×Q8—222no—
707C2×Q8—224no—
708C2×Q8—224no—
709C2×Q8—448no—
710C2×Q8—444no—
711C2×Q8—444no—
712C2×Q8—448no—
713C2×Q8—448no—
714C2×Q8C23×D1111yescharacteristic
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—22no—
718C2×D4—22no—
719C2×D4C2×C22⋊D1112yes—
720C2×D4C2×C22⋊D1111yescharacteristic
721C2×D4C2×C22⋊D1111yescharacteristic
722C2×D4C23×D1111yescharacteristic
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—222no—
733C22×C4—224no—
734C22×C4—224no—
735C22×C4—448no—
736C22×C4C2×C22⋊D1112yes—
737C22×C4C2×C22⋊D1111yescharacteristic
738C22×C4C2×C22⋊D1112yes—
739C22×C4C2×C22⋊D1112yes—
740C22×C4C2×C22⋊D1111yescharacteristic
741C22×C4C23×D1112yes—
742C22×C4C23×D1112yes—
743C22×C4C23×D1111yescharacteristic
744Q16—224no—
745Q16—444no—
746SD16—224no—
747SD16—444no—
748M16—222no—
749M16—222no—
750M16—224no—
751M16—444no—
752C2×C8—112no—
753C2×C8—112no—
754C2×C8—114no—
755C2×C8—444no—
756C4⋊C4—22no—
757C4⋊C4—22no—
758C4⋊C4—21no—
759C4⋊C4—22no—
760C4⋊C4—22no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—22no—
764C4⋊C4—22no—
765C4⋊C4—21no—
766C4⋊C4—112no—
767C4⋊C4—221no—
768C4⋊C4—222no—
769C4⋊C4—222no—
770C4⋊C4—222no—
771C4⋊C4—222no—
772C4⋊C4—224no—
773C4⋊C4—224no—
774C4⋊C4—222no—
775C4⋊C4—222no—
776C4⋊C4C2×C22⋊D1111yescharacteristic
777C4⋊C4C2×C22⋊D1111yescharacteristic
778C4⋊C4C2×C22⋊D1112yes—
779C4⋊C4C23×D1111yescharacteristic
780C4⋊C4C23×D1112yes—
781C4⋊C4C23×D1111yescharacteristic
782C4⋊C4C23×D1112yes—
783C22⋊C4—21no—
784C22⋊C4—22no—
785C22⋊C4—22no—
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—22no—
789C22⋊C4—22no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—22no—
793C22⋊C4—224no—
794C22⋊C4—224no—
795C22⋊C4C2×C22⋊D1112yes—
796C22⋊C4C2×C22⋊D1112yes—
797C22⋊C4C2×C22⋊D1112yes—
798C22⋊C4C2×C22⋊D1112yes—
799C42—21no—
800C42—22no—
801C42—21no—
802C42—22no—
803C42—22no—
804C42—21no—
805C42—222no—
806C42—222no—
807C42C2×C22⋊D1111yescharacteristic
808C42C2×C22⋊D1111yescharacteristic
809C42C23×D1111yescharacteristic
810C42C23×D1111yescharacteristic
811C11#6115711yescharacteristic, complemented, Sylow
812C23—24no—
813C23—24no—
814C23—21no—
815C23—42no—
816C23C22×C22⋊D1112yes—
817C23C22×C22⋊D1112yes—
818C23C22×C22⋊D1111yescharacteristic
819Q8—21no—
820Q8—21no—
821Q8—42no—
822Q8—81no—
823Q8—114no—
824Q8—224no—
825Q8—222no—
826Q8—224no—
827Q8—224no—
828Q8—448no—
829Q8—448no—
830Q8—444no—
831D4—24no—
832D4—22no—
833D4—21no—
834D4—21no—
835D4—44no—
836D4—42no—
837D4—82no—
838D4#6700414yescomplemented
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—41no—
853C2×C4—44no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—81no—
857C2×C4—82no—
858C2×C4—224no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—224no—
862C2×C4—448no—
863C2×C4—448no—
864C2×C4—442no—
865C2×C4—444no—
866C2×C4#41×D1112yes—
867C2×C4#6704212yes—
868C2×C4C22×C22⋊D1112yes—
869C2×C4C22×C22⋊D1111yescharacteristic
870C2×C4C22×C22⋊D1111yescharacteristic
871C2×C4C22×C22⋊D1111yescharacteristic
872C2×C4C22×C22⋊D1112yes—
873C2×C4C22×C22⋊D1111yescharacteristic
874C2×C4C22×C22⋊D1111yescharacteristic
875C2×C4C24×D1111yescharacteristic
876C8—222no—
877C8—222no—
878C8—224no—
879C22—21no—
880C22—22no—
881C22—22no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—48no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22C2×#6700414yes—
891C22#1062336012yes—
892C22C23×C22⋊D1111yescharacteristic
893C4—21no—
894C4—21no—
895C4—22no—
896C4—22no—
897C4—21no—
898C4—41no—
899C4—42no—
900C4—41no—
901C4—41no—
902C4—42no—
903C4—224no—
904C4—442no—
905C4—444no—
906C4C2×#6700412yes—
907C4#1062336012yes—
908C4C2×#41×D1111yescharacteristic
909C4C2×#6704211yescharacteristic
910C2—22no—
911C2—24no—
912C2—42no—
913C2—81no—
914C2C2×#1062336011yescharacteristic
915C2C22×#6700411yescharacteristic
916C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3475C2
socleC22×C11C23×D4
hypercenter#3475D11
hypocenterC11#61157
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic22C2semidirect
2. #13080904C2semidirect
3. #13080893C2semidirect
4. #13080781C2semidirect
5. #13080661C2semidirect
6. #13080486C2semidirect
7. #13080475C2semidirect
8. #13078998C2semidirect
9. #13078564C2semidirect
10. #13078417C2semidirect
11. #13078248C2semidirect
12. #13078103C2semidirect
13. #13077849C2semidirect
14. C4×#67004C2semidirect
15. D4×#4318C2semidirect
16. C2×#10622617C2semidirect
53. #10622707C22semidirect
54. #10622706C22semidirect
55. #10622706C22semidirect
56. #10622704C22semidirect
57. #10622682C22semidirect
58. #10622676C22semidirect
59. #10622665C22semidirect
60. #10622664C22semidirect
61. #10622663C22semidirect
62. #10622663C22semidirect
63. #10622655C22semidirect
64. #10622654C22semidirect
65. #10622653C22semidirect
66. #10622653C22semidirect
67. #10622644C22semidirect
68. #10622644C22semidirect
69. #10622643C22semidirect
70. C4×#4326C22semidirect
71. #10622632C22semidirect
72. #10622632C22semidirect
73. #10622631C22semidirect
74. C4×#4324C22semidirect
83. #10622617C22semidirect
84. #10622617C22semidirect
85. #10622609C22semidirect
86. #10622609C22semidirect
89. #10622584C22semidirect
90. #10622583C22semidirect
91. C2×#66874C22semidirect
92. C2×#66874C22semidirect
284. C2×Dic22#41semidirect
389. D4×C11#137semidirect
811. C11#61157semidirect
838. D4#67004semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
#130809042
#130808932
#130807812
#130806612
#130804862
#130804752
#130789982
#130785642
#130784172
#130782482
#130781032
#130778492
C4×#670042
D4×#43182
C2×#106226172
C11×#34752
#6115711