Finite Group Databasebeta

← #15630971

Subgroups — #15630971

Order 2816.

2182 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C211yesmaximal, characteristic, complemented
2#41×D44C211yesmaximal, characteristic, complemented
3#13080912C212yesmaximal, complemented
4#13080860C212yesmaximal, complemented
5#13080807C214yesmaximal, complemented
6#13080777C214yesmaximal, complemented
7#13080568C212yesmaximal, complemented
8#13080546C212yesmaximal, complemented
9#13079010C211yesmaximal, characteristic, complemented
10#13078550C212yesmaximal, complemented
11#13078431C211yesmaximal, characteristic, complemented
12#13078233C212yesmaximal, complemented
13#13078080C211yesmaximal, characteristic, complemented
14#13077864C212yesmaximal, complemented
15M16×D44C211yesmaximal, characteristic, complemented
16#13077132C212yesmaximal, complemented
17C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
18C2×#41×D11C2212yes—
19C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
20C4×C11×#41C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic, complemented
22C2×#66991C2212yescomplemented
23C2×#66985C2212yescomplemented
24C2×#66983—21no—
25C2×#66979—21no—
26C2×M16×D11C2212yescomplemented
27#10623108C2211yescharacteristic, complemented
28#10623107C2212yescomplemented
29Q8×D44C2211yescharacteristic, complemented
30#10623094—21no—
31#10623094—21no—
32#10623094—22no—
33#10623094C2212yes—
34#10623094C2214yescomplemented
35#10623094C2212yescomplemented
36#10623086—21no—
37#10623086C2211yescharacteristic, complemented
38#10623085—22no—
39#10623085C2212yescomplemented
40D4×D44—21no—
41D4×D44C2211yescharacteristic, complemented
42#10623055—22no—
43#10623055C2212yes—
44C2×#66945C2212yescomplemented
45C2×#66938—22no—
46#10623008—21no—
47#10623008C2211yescharacteristic
48C2×C4×D44—21no—
49C2×C4×D44C2211yescharacteristic
50C2×#66922C2211yescharacteristic, complemented
51C11×#442C2212yescomplemented
52C11×#440C2212yescomplemented
53C4×C11×SD16C2212yescomplemented
54C4×C11×D8C2212yescomplemented
55C11×#428C2211yescharacteristic, complemented
56C11×#418C2211yescharacteristic, complemented
57C11×#417C2211yescharacteristic
58C4×C11×M16C2211yescharacteristic, complemented
59#10622845C2212yes—
60#10622785C2214yescomplemented
61#10622783C2214yescomplemented
62#10622771C2214yescomplemented
63#10622769C2214yescomplemented
64#10622746C2212yescomplemented
65#10622746C2212yescomplemented
66#10622739C2212yescomplemented
67#10622634C2212yescomplemented
68#10622633C2212yescomplemented
69#10622632C2212yescomplemented
70#10622629C2214yescomplemented
71#10622628C2212yescomplemented
72#10622621C2212yescomplemented
73#10622620C2212yescomplemented
74#10622608C2212yescomplemented
75#10622579C2212yescomplemented
76#10622537C2211yescharacteristic, complemented
77#10622501C2214yescomplemented
78#10622498C2214yescomplemented
79#10622480C2214yescomplemented
80#10622479C2214yescomplemented
81#10622417C2214yescomplemented
82#10622415C2214yescomplemented
83#10622395C2214yescomplemented
84#10622393C2214yescomplemented
85#10622391C2214yescomplemented
86#10622388C2214yescomplemented
87#10622385C2214yescomplemented
88#10622383C2214yescomplemented
89#10622327C2214yescomplemented
90#10622319C2214yescomplemented
91#10622307C2212yescomplemented
92#10622301C2212yescomplemented
93C8×D44C2212yescomplemented
94#10622294C2212yescomplemented
95C2×C11×#41C2311yescharacteristic
96C22×D4×C11C2311yescharacteristic
97C23×C4×C11—21no—
98C22×C22⋊D11—22no—
99#41×D11—28no—
100#41×D11—44no—
101C2×#4343C2312yes—
102C2×Q8×D11C2312yes—
103C2×#4341—22no—
104C2×#4341C2312yes—
105C2×D4×D11—22no—
106C2×D4×D11C2312yes—
107C2×#4339—22no—
108C2×#4339C2312yes—
109C22×D44—21no—
110C22×D44D411yescharacteristic
111C22×C4×D11—22no—
112C22×C4×D11C2312yes—
113C22×Dic22—21no—
114C11×AGL(1,ℤ/8)—24no—
115C2×C11×SD16C2312yes—
116C2×C11×D8C2312yes—
117C2×C11×M16C2311yescharacteristic
118C2×C11×M16C2311yescharacteristic
119C4×Q8×C11C2311yescharacteristic
120C4×Q8×C11C2311yescharacteristic
121C4×D4×C11—21no—
122C4×D4×C11—21no—
123C4×D4×C11—21no—
124C4×D4×C11—21no—
125C4×D4×C11C2311yescharacteristic
126C4×D4×C11C2311yescharacteristic
127C4×D4×C11C2312yes—
128C4×D4×C11C2312yes—
129C11×#117—21no—
130C11×#117C2311yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C22⋊C4—21no—
133C2×C42×C11—21no—
134C2×C42×C11C2311yescharacteristic
135C2×C22⋊Dic11—22no—
136#66991—22no—
137#66991—22no—
138#66991C2314yes—
139#66991C2314yes—
140C2×#4324C2314yes—
141#66985—44no—
142C2×#4323C2314yes—
143#66983—21no—
144#66983—21no—
145#66983—21no—
146#66983—22no—
147#66983—22no—
148#66983—24no—
149#66983—22no—
150#66983—21no—
151C2×(C2×D11)⋊C4—22no—
152C2×(C2×D11)⋊C4—22no—
153C2×(C2×D11)⋊C4D412yes—
154#66979—22no—
155#66979—22no—
156#66979—24no—
157C2×C4⋊Dic11—21no—
158C2×C4⋊Dic11—21no—
159C2×C4⋊Dic11D411yescharacteristic
160C2×C4⋊Dic11C2312yes—
161C2×C4×Dic11—22no—
162C2×#4318C2312yes—
163M16×D11—44no—
164C2×#4313C2314yes—
165C2×C8×D11C2314yes—
166#66950—22no—
167#66950—22no—
168#66950C2312yes—
169#66950C2312yes—
170#66948—22no—
171#66948—22no—
172#66948C2312yes—
173#66948C2312yes—
174#66945—22no—
175#66945—22no—
176#66945C2314yes—
177#66945C2314yes—
178#66939—22no—
179#66939—22no—
180#66939—22no—
181#66938—24no—
182#66938—24no—
183#66938—24no—
184#66938—24no—
185#66935—22no—
186#66935—22no—
187#66935—22no—
188#66928—22no—
189#66928C2312yes—
190#66927—21no—
191#66927C2311yescharacteristic
192C4×D44—21no—
193C4×D44—22no—
194C4×D44—22no—
195C4×D44—21no—
196C4×D44—21no—
197C4×D44—22no—
198C4×D44—21no—
199C4×D44D411yescharacteristic
200C4×D44D411yescharacteristic
201C4×D44D412yes—
202C4×D44C2311yescharacteristic
203C4×D44C2311yescharacteristic
204C4×D44C2312yes—
205#66922—21no—
206#66922—21no—
207#66922—21no—
208#66922C2311yescharacteristic
209#66922C2312yes—
210#66922C2312yes—
211C11×#107C2312yes—
212C11×#106C2312yes—
213C11×#103C2312yes—
214C11×#102C2312yes—
215C11×#102C2312yes—
216C11×#102C2312yes—
217C11×#97C2312yes—
218C4×C8×C11C2312yes—
219#66899C2314yes—
220#66896C2314yes—
221#66885C2314yes—
222#66885C2314yes—
223(C2×D11)⋊C8C2314yes—
224(C2×D11)⋊C8C2314yes—
225#66880C2314yes—
226#66880C2314yes—
227#66874C2314yes—
228#66873C2314yes—
229#66872C2314yes—
230#66871C2314yes—
231C4⋊(C11⋊C8)C2312yes—
232C4⋊(C11⋊C8)C2312yes—
233#61166—111nomaximal, Sylow
234C24×C11—21no—
235C23×D11—22no—
236C23×D11C2×D412yes—
237C11×#41—22no—
238C11×#41#4114yes—
239C2×Q8×C11C2411yescharacteristic
240C2×D4×C11—21no—
241C2×D4×C11—21no—
242C2×D4×C11—22no—
243C2×D4×C11—22no—
244C2×D4×C11C2412yes—
245C2×D4×C11C2411yescharacteristic
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—22no—
250C22×C4×C11—22no—
251C22×C4×C11—21no—
252C22×C4×C11—44no—
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C2×C22⋊D11—22no—
257C2×C22⋊D11—22no—
258C2×C22⋊D11—22no—
259C2×C22⋊D11—24no—
260C2×C22⋊D11—24no—
261C2×C22⋊D11—84no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11C2×D412yes—
265#4343—24no—
266#4343—42no—
267Q8×D11—24no—
268Q8×D11—42no—
269#4341—24no—
270#4341—42no—
271#4341—48no—
272D4×D11—24no—
273D4×D11—48no—
274D4×D11—42no—
275#4339—24no—
276#4339—24no—
277#4339—48no—
278C2×D44—22no—
279C2×D44—22no—
280C2×D44—22no—
281C2×D44—21no—
282C2×D44—21no—
283C2×D44—42no—
284C2×D44—44no—
285C2×D44C2×D411yescharacteristic
286C2×D44C2×D411yescharacteristic
287C2×D44C2×D412yes—
288C2×D44C2412yes—
289C2×C4×D11—22no—
290C2×C4×D11—22no—
291C2×C4×D11—22no—
292C2×C4×D11—24no—
293C2×C4×D11—24no—
294C2×C4×D11—48no—
295C2×C4×D11C2×D412yes—
296C2×C4×D11C2×D412yes—
297C2×C4×D11C2412yes—
298C2×C4×D11C2412yes—
299C2×Dic22—22no—
300C2×Dic22—22no—
301C2×Dic22—22no—
302C2×Dic22—82no—
303C2×Dic22C2412yes—
304C11×SD16—24no—
305C11×D8—24no—
306C11×M16—22no—
307C11×M16—22no—
308C2×C8×C11C2412yes—
309C2×C8×C11C2412yes—
310C11×C4⋊C4—21no—
311C11×C4⋊C4—21no—
312C11×C4⋊C4—21no—
313C11×C4⋊C4C2411yescharacteristic
314C11×C4⋊C4C2411yescharacteristic
315C11×C4⋊C4C2412yes—
316C11×C22⋊C4—21no—
317C11×C22⋊C4—21no—
318C11×C22⋊C4—21no—
319C11×C22⋊C4—22no—
320C11×C22⋊C4—22no—
321C42×C11—21no—
322C42×C11—21no—
323C42×C11—21no—
324C42×C11C2×D411yescharacteristic
325C42×C11C2×D411yescharacteristic
326C42×C11C2411yescharacteristic
327C42×C11C2411yescharacteristic
328C22⋊Dic11—24no—
329C22⋊Dic11—24no—
330#4324—44no—
331#4323—44no—
332(C2×D11)⋊C4—22no—
333(C2×D11)⋊C4—22no—
334(C2×D11)⋊C4—22no—
335(C2×D11)⋊C4—22no—
336(C2×D11)⋊C4—24no—
337(C2×D11)⋊C4—24no—
338(C2×D11)⋊C4—22no—
339(C2×D11)⋊C4—22no—
340(C2×D11)⋊C4C2×D412yes—
341(C2×D11)⋊C4C2×D412yes—
342(C2×D11)⋊C4C2×D412yes—
343(C2×D11)⋊C4C2×D412yes—
344C4⋊Dic11—22no—
345C4⋊Dic11—22no—
346C4⋊Dic11—22no—
347C4⋊Dic11—21no—
348C4⋊Dic11—22no—
349C4⋊Dic11—22no—
350C4⋊Dic11—21no—
351C4⋊Dic11C2×D411yescharacteristic
352C4⋊Dic11C2×D411yescharacteristic
353C4⋊Dic11C2×D412yes—
354C4⋊Dic11C2414yes—
355C4×Dic11—24no—
356C4×Dic11—24no—
357#4318—24no—
358C2×C11⋊C8C2414yes—
359#4313—44no—
360C8×D11—44no—
361C2×#555—111no—
362D4×#41—111no—
363#3329—112no—
364#3325—112no—
365#3321—114no—
366#3319—114no—
367#3305—112no—
368#3303—112no—
369#3141—111no—
370#3093—112no—
371#3079—111no—
372#3055—112no—
373#3036—111no—
374#3006—112no—
375C4×AGL(1,ℤ/8)D1111yescharacteristic, complemented
376D4×M16—111no—
377#2896—112no—
378C23×C11—21no—
379C23×C11—22no—
380C23×C11—42no—
381C23×C11—42no—
382C23×C11—42no—
383C23×C11C22×D411yescharacteristic
384C22×D11—24no—
385C22×D11—22no—
386C22×D11—42no—
387C22×D11—42no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11—82no—
391C22×D11C22×D412yes—
392C22×D11C22×D412yes—
393Q8×C11—21no—
394Q8×C11C2×#4112yes—
395D4×C11—24no—
396D4×C11—22no—
397D4×C11—21no—
398D4×C11—22no—
399D4×C11—42no—
400D4×C11C2×#4112yes—
401C2×C4×C11—21no—
402C2×C4×C11—24no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—41no—
408C2×C4×C11—44no—
409C2×C4×C11—42no—
410C2×C4×C11—42no—
411C2×C4×C11—44no—
412C2×C4×C11—81no—
413C2×C4×C11C22×D411yescharacteristic
414C2×C4×C11C22×D411yescharacteristic
415C2×C4×C11C22×D411yescharacteristic
416C2×C4×C11C22×D411yescharacteristic
417C2×C4×C11C22×D411yescharacteristic
418C2×C4×C11C2×#4112yes—
419C2×C4×C11H(5,𝔽2)12yes—
420C2×C4×C11C2511yescharacteristic
421C22⋊D11—44no—
422C22⋊D11—44no—
423C22⋊D11—44no—
424C22⋊D11—84no—
425C22⋊D11—84no—
426C2×Dic11—24no—
427C2×Dic11—24no—
428C2×Dic11—22no—
429C2×Dic11—44no—
430C2×Dic11—44no—
431C2×Dic11C22×D412yes—
432C2×Dic11C22×D412yes—
433D44—22no—
434D44—22no—
435D44—22no—
436D44—22no—
437D44—42no—
438D44—44no—
439D44—44no—
440D44—42no—
441D44—81no—
442D44—82no—
443C4×D11—24no—
444C4×D11—24no—
445C4×D11—22no—
446C4×D11—22no—
447C4×D11—22no—
448C4×D11—22no—
449C4×D11—44no—
450C4×D11—44no—
451C4×D11—44no—
452Dic22—22no—
453Dic22—22no—
454Dic22—44no—
455Dic22—82no—
456Dic22—82no—
457C8×C11—22no—
458C8×C11—22no—
459C11⋊C8—24no—
460C22×#41—112no—
461C2×AGL(1,ℤ/8)—112no—
462C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
463C22×M16—112no—
464#555—112no—
465#555—112no—
466#555—114no—
467#555—221no—
468#555—222no—
469#555—221no—
470#550—111no—
471D4×Q8—111no—
472#548—112no—
473#547—111no—
474#547—221no—
475#546—112no—
476#546—222no—
477D42—111no—
478D42—221no—
479#532—111no—
480#532—221no—
481C2×C4⋊Q8—111no—
482C2×#124—222no—
483#525—112no—
484#525—222no—
485C2×#121—112no—
486C2×#121—221no—
487C4×#41C2×D1111yescharacteristic
488C2×C4×D4—111no—
489C2×C4×D4—221no—
490C2×C4×D4C2×D1111yescharacteristic, complemented
491C2×#117—112no—
492C2×#117—221no—
493#489—114no—
494#487—112no—
495#486—112no—
496#485—114no—
497#485—114no—
498#482—114no—
499#482—114no—
500#477—112no—
501#476—112no—
502#475—112no—
503#474—112no—
504#469—114no—
505#468—114no—
506#466—114no—
507#465—114no—
508#463—114no—
509#461—112no—
510#459—112no—
511#449—114no—
512#449—114no—
513#448—114no—
514#447—114no—
515#442C2×D1112yescomplemented
516#440C2×D1112yescomplemented
517C4×SD16C2×D1112yescomplemented
518C4×D8C2×D1112yescomplemented
519#436—112no—
520#435—114no—
521C8×D4—112no—
522#428—112no—
523#428C2×D1111yescharacteristic, complemented
524#423—111no—
525#419—114no—
526#418—114no—
527#418C2×D1111yescharacteristic, complemented
528#417—112no—
529#417—112no—
530#417—112no—
531#417—112no—
532#417C2×D1111yescharacteristic
533#416—114no—
534#416—114no—
535#407—112no—
536C4×M16C2×D1111yescharacteristic, complemented
537C22×C11—21no—
538C22×C11—21no—
539C22×C11—22no—
540C22×C11—41no—
541C22×C11—41no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—84no—
546C22×C11#54612yes—
547C22×C11C23×D411yescharacteristic
548C2×D11—22no—
549C2×D11—22no—
550C2×D11—22no—
551C2×D11—22no—
552C2×D11—22no—
553C2×D11—22no—
554C2×D11—42no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—84no—
558C2×D11—88no—
559C4×C11—21no—
560C4×C11—21no—
561C4×C11—22no—
562C4×C11—21no—
563C4×C11—41no—
564C4×C11—42no—
565C4×C11—41no—
566C4×C11#54612yes—
567C4×C11#57512yes—
568C4×C11C22×#4111yescharacteristic
569C4×C11C2×H(5,𝔽2)11yescharacteristic
570Dic11—22no—
571Dic11—22no—
572Dic11—44no—
573Dic11—42no—
574C2×#41—112no—
575C2×#41—112no—
576C2×#41—112no—
577C2×#41—222no—
578C2×#41—222no—
579C2×#41—228no—
580C2×#41—444no—
581C2×#41C22×D1111yescharacteristic
582C22×Q8—112no—
583C22×Q8—221no—
584C22×D4—112no—
585C22×D4—111no—
586C22×D4—221no—
587C22×D4—222no—
588C22×D4—222no—
589C22×D4C22×D1111yescharacteristic
590C23×C4—21no—
591C23×C4—112no—
592C23×C4—222no—
593AGL(1,ℤ/8)—24no—
594AGL(1,ℤ/8)—444no—
595C2×SD16—114no—
596C2×SD16C22×D1112yes—
597C2×D8—114no—
598C2×D8C22×D1112yes—
599C2×M16—112no—
600C2×M16—114no—
601C2×M16—444no—
602C2×M16C22×D1111yescharacteristic
603C2×M16C22×D1111yescharacteristic
604C22×C8—114no—
605C4⋊Q8—112no—
606C4⋊Q8—112no—
607C4⋊Q8—111no—
608C4⋊Q8—221no—
609C4⋊Q8—221no—
610C4⋊Q8—221no—
611#127—111no—
612#127—221no—
613#124—112no—
614#124—222no—
615#124—224no—
616#124—224no—
617#124—224no—
618#124—224no—
619#123—222no—
620#123—222no—
621#123—222no—
622C22⋊Q8—112no—
623C22⋊Q8—112no—
624C22⋊Q8—222no—
625C22⋊Q8—222no—
626#121—114no—
627#121—114no—
628#121—112no—
629#121—112no—
630#121—222no—
631#121—222no—
632#121—222no—
633#121—221no—
634#121—222no—
635#121—222no—
636#121—224no—
637#121—221no—
638#121—222no—
639#121—222no—
640#121—221no—
641#121—221no—
642#120—222no—
643#120—222no—
644#120—222no—
645C4×Q8C22×D1111yescharacteristic
646C4×Q8C22×D1111yescharacteristic
647C4×D4—21no—
648C4×D4—21no—
649C4×D4—21no—
650C4×D4—21no—
651C4×D4—111no—
652C4×D4—112no—
653C4×D4—111no—
654C4×D4—111no—
655C4×D4—112no—
656C4×D4—111no—
657C4×D4—222no—
658C4×D4—221no—
659C4×D4—222no—
660C4×D4—222no—
661C4×D4—221no—
662C4×D4—221no—
663C4×D4—221no—
664C4×D4C22×D1112yes—
665C4×D4C22×D1112yes—
666C4×D4C22×D1111yescharacteristic
667C4×D4C22×D1111yescharacteristic
668#117—21no—
669#117—114no—
670#117—114no—
671#117—222no—
672#117—222no—
673#117—222no—
674#117—222no—
675#117—224no—
676#117C22×D1111yescharacteristic
677C2×C4⋊C4—111no—
678C2×C4⋊C4—112no—
679C2×C4⋊C4—221no—
680C2×C4⋊C4—221no—
681C2×C4⋊C4C22×D1111yescharacteristic
682C2×C22⋊C4—21no—
683C2×C22⋊C4—112no—
684C2×C22⋊C4—222no—
685C2×C22⋊C4—222no—
686C2×C22⋊C4—222no—
687C2×C42—21no—
688C2×C42—222no—
689C2×C42C22×D1111yescharacteristic
690#107—114no—
691#107C22×D1112yes—
692#106—114no—
693#106C22×D1112yes—
694C4⋊C8—112no—
695C4⋊C8—112no—
696#103—114no—
697#103—114no—
698#103—114no—
699#103—114no—
700#103C22×D1112yes—
701#102—114no—
702#102—114no—
703#102—114no—
704#102—114no—
705#102C22×D1112yes—
706#102C22×D1112yes—
707#102C22×D1112yes—
708C22⋊C8—114no—
709C22⋊C8—114no—
710#97C22×D1112yes—
711C4×C8C22×D1112yes—
712C2×C11—22no—
713C2×C11—42no—
714C2×C11—82no—
715C2×C11C2×#54611yescharacteristic
716C2×C11C2×#57511yescharacteristic
717C2×C11#358511yescharacteristic
718D11—42no—
719D11—42no—
720D11—82no—
721C24—21no—
722C24—112no—
723C24—222no—
724#41—22no—
725#41—224no—
726#41—224no—
727#41—224no—
728#41—224no—
729#41—448no—
730#41—442no—
731#41—448no—
732#41—442no—
733#41#433914yes—
734C2×Q8—112no—
735C2×Q8—222no—
736C2×Q8—222no—
737C2×Q8—222no—
738C2×Q8—224no—
739C2×Q8—442no—
740C2×Q8—882no—
741C2×Q8C23×D1111yescharacteristic
742C2×D4—21no—
743C2×D4—22no—
744C2×D4—21no—
745C2×D4—22no—
746C2×D4—111no—
747C2×D4—111no—
748C2×D4—112no—
749C2×D4—112no—
750C2×D4—222no—
751C2×D4—222no—
752C2×D4—222no—
753C2×D4—222no—
754C2×D4—224no—
755C2×D4—222no—
756C2×D4—222no—
757C2×D4—224no—
758C2×D4—224no—
759C2×D4—221no—
760C2×D4—221no—
761C2×D4—442no—
762C2×D4—444no—
763C2×D4—442no—
764C2×D4—448no—
765C2×D4—884no—
766C2×D4C23×D1112yes—
767C2×D4C23×D1111yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—44no—
775C22×C4—112no—
776C22×C4—112no—
777C22×C4—112no—
778C22×C4—112no—
779C22×C4—112no—
780C22×C4—222no—
781C22×C4—222no—
782C22×C4—222no—
783C22×C4—224no—
784C22×C4—224no—
785C22×C4—222no—
786C22×C4—222no—
787C22×C4—448no—
788C22×C4D4×D1111yescharacteristic
789C22×C4D4×D1111yescharacteristic
790C22×C4C23×D1111yescharacteristic
791SD16—24no—
792SD16—444no—
793D8—24no—
794D8—444no—
795M16—22no—
796M16—22no—
797M16—224no—
798M16—444no—
799C2×C8—114no—
800C2×C8—444no—
801C2×C8C23×D1112yes—
802C2×C8C23×D1112yes—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—111no—
807C4⋊C4—111no—
808C4⋊C4—112no—
809C4⋊C4—114no—
810C4⋊C4—222no—
811C4⋊C4—222no—
812C4⋊C4—222no—
813C4⋊C4—222no—
814C4⋊C4—222no—
815C4⋊C4—221no—
816C4⋊C4—221no—
817C4⋊C4C23×D1112yes—
818C4⋊C4C23×D1111yescharacteristic
819C4⋊C4C23×D1111yescharacteristic
820C22⋊C4—21no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—112no—
826C22⋊C4—112no—
827C22⋊C4—112no—
828C22⋊C4—112no—
829C22⋊C4—222no—
830C22⋊C4—222no—
831C22⋊C4—224no—
832C22⋊C4—224no—
833C22⋊C4—222no—
834C22⋊C4—222no—
835C22⋊C4—224no—
836C22⋊C4—224no—
837C22⋊C4—222no—
838C22⋊C4—222no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—224no—
843C42—224no—
844C42D4×D1111yescharacteristic
845C42D4×D1111yescharacteristic
846C42C23×D1111yescharacteristic
847C42C23×D1111yescharacteristic
848C11#6116611yescharacteristic, complemented, Sylow
849C23—21no—
850C23—22no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—112no—
855C23—112no—
856C23—224no—
857C23—222no—
858C23—442no—
859C23—442no—
860C23—444no—
861C23—444no—
862C23—882no—
863C23C2×D4×D1111yescharacteristic
864Q8—21no—
865Q8—222no—
866Q8—222no—
867Q8—444no—
868Q8—882no—
869Q8—882no—
870Q8C2×#433912yes—
871D4—24no—
872D4—22no—
873D4—21no—
874D4—22no—
875D4—42no—
876D4—222no—
877D4—222no—
878D4—222no—
879D4—222no—
880D4—442no—
881D4—444no—
882D4—444no—
883D4—444no—
884D4—444no—
885D4—444no—
886D4—442no—
887D4—881no—
888D4—882no—
889D4—884no—
890D4—884no—
891D4C2×#433912yes—
892C2×C4—21no—
893C2×C4—22no—
894C2×C4—24no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—22no—
898C2×C4—41no—
899C2×C4—44no—
900C2×C4—42no—
901C2×C4—44no—
902C2×C4—42no—
903C2×C4—81no—
904C2×C4—112no—
905C2×C4—112no—
906C2×C4—224no—
907C2×C4—224no—
908C2×C4—224no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—224no—
914C2×C4—222no—
915C2×C4—444no—
916C2×C4—444no—
917C2×C4—444no—
918C2×C4—444no—
919C2×C4—444no—
920C2×C4C2×#433912yes—
921C2×C4C2×D4×D1111yescharacteristic
922C2×C4C2×D4×D1111yescharacteristic
923C2×C4C2×D4×D1111yescharacteristic
924C2×C4C2×D4×D1111yescharacteristic
925C2×C4C2×D4×D1111yescharacteristic
926C2×C4#6704212yes—
927C2×C4C24×D1111yescharacteristic
928C8—22no—
929C8—22no—
930C8—224no—
931C22—21no—
932C22—21no—
933C22—22no—
934C22—41no—
935C22—41no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—84no—
940C22—222no—
941C22—222no—
942C22—222no—
943C22—222no—
944C22—222no—
945C22—222no—
946C22—442no—
947C22—442no—
948C22—442no—
949C22—884no—
950C22—888no—
951C22#1062308112yes—
952C22C22×D4×D1111yescharacteristic
953C4—21no—
954C4—21no—
955C4—22no—
956C4—21no—
957C4—41no—
958C4—42no—
959C4—41no—
960C4—222no—
961C4—222no—
962C4—444no—
963C4—442no—
964C4#1062308112yes—
965C4#1062330412yes—
966C4C22×#433911yescharacteristic
967C4C2×#6704211yescharacteristic
968C2—22no—
969C2—42no—
970C2—82no—
971C2—442no—
972C2—442no—
973C2—882no—
974C2C2×#1062308111yescharacteristic
975C2C2×#1062330411yescharacteristic
976C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×AGL(1,ℤ/8)C2
socleC22×C11C23×D4
hypercenterC4×AGL(1,ℤ/8)D11
hypocenterC11#61166
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#10623094C2semidirect
2. #41×D44C2semidirect
3. #13080912C2semidirect
4. #13080860C2semidirect
5. #13080807C2semidirect
6. #13080777C2semidirect
7. #13080568C2semidirect
8. #13080546C2semidirect
9. #13079010C2semidirect
10. #13078550C2semidirect
11. #13078431C2semidirect
12. #13078233C2semidirect
13. #13078080C2semidirect
14. #13077864C2semidirect
15. M16×D44C2semidirect
16. #13077132C2semidirect
17. C4×C11×AGL(1,ℤ/8)C2semidirect
21. C2×C4×D4×C11C22semidirect
22. C2×#66991C22semidirect
23. C2×#66985C22semidirect
26. C2×M16×D11C22semidirect
27. #10623108C22semidirect
28. #10623107C22semidirect
29. Q8×D44C22semidirect
34. #10623094C22semidirect
35. #10623094C22semidirect
37. #10623086C22semidirect
39. #10623085C22semidirect
41. D4×D44C22semidirect
44. C2×#66945C22semidirect
50. C2×#66922C22semidirect
51. C11×#442C22semidirect
52. C11×#440C22semidirect
53. C4×C11×SD16C22semidirect
54. C4×C11×D8C22semidirect
55. C11×#428C22semidirect
56. C11×#418C22semidirect
58. C4×C11×M16C22semidirect
60. #10622785C22semidirect
61. #10622783C22semidirect
62. #10622771C22semidirect
63. #10622769C22semidirect
64. #10622746C22semidirect
65. #10622746C22semidirect
66. #10622739C22semidirect
67. #10622634C22semidirect
68. #10622633C22semidirect
69. #10622632C22semidirect
70. #10622629C22semidirect
71. #10622628C22semidirect
72. #10622621C22semidirect
73. #10622620C22semidirect
74. #10622608C22semidirect
75. #10622579C22semidirect
76. #10622537C22semidirect
77. #10622501C22semidirect
78. #10622498C22semidirect
79. #10622480C22semidirect
80. #10622479C22semidirect
81. #10622417C22semidirect
82. #10622415C22semidirect
83. #10622395C22semidirect
84. #10622393C22semidirect
85. #10622391C22semidirect
86. #10622388C22semidirect
87. #10622385C22semidirect
88. #10622383C22semidirect
89. #10622327C22semidirect
90. #10622319C22semidirect
91. #10622307C22semidirect
92. #10622301C22semidirect
93. C8×D44C22semidirect
94. #10622294C22semidirect
375. C4×AGL(1,ℤ/8)D11semidirect
490. C2×C4×D4C2×D11semidirect
515. #442C2×D11semidirect
516. #440C2×D11semidirect
517. C4×SD16C2×D11semidirect
518. C4×D8C2×D11semidirect
523. #428C2×D11semidirect
527. #418C2×D11semidirect
536. C4×M16C2×D11semidirect
848. C11#61166semidirect

Maximal subgroups

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

subgroupindex
C2×#106230942
#41×D442
#130809122
#130808602
#130808072
#130807772
#130805682
#130805462
#130790102
#130785502
#130784312
#130782332
#130780802
#130778642
M16×D442
#130771322
C4×C11×AGL(1,ℤ/8)2
#6116611