Finite Group Databasebeta

← #15639264

Subgroups — #15639264

Order 2816.

2112 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4339C211yesmaximal, characteristic
2#13080948C211yesmaximal, characteristic, complemented
3#13080926C211yesmaximal, characteristic, complemented
4#13080721C212yesmaximal, complemented
5#13080691C212yesmaximal, complemented
6#13080486C211yesmaximal, characteristic, complemented
7#13080434C211yesmaximal, characteristic, complemented
8D4×#4326C211yesmaximal, characteristic, complemented
9D4×#4325C211yesmaximal, characteristic, complemented
10#13080278C211yesmaximal, characteristic, complemented
11#13080262C211yesmaximal, characteristic, complemented
12#13080187C212yesmaximal, complemented
13#13080127C212yesmaximal, complemented
14#13079623C211yesmaximal, characteristic, complemented
15#13079568C211yesmaximal, characteristic, complemented
16#13079446C212yesmaximal, complemented
17#13079397C212yesmaximal, complemented
18#13078772C211yesmaximal, characteristic, complemented
19#13078681C211yesmaximal, characteristic, complemented
20#13077874C212yesmaximal, complemented
21C2×#10622660C212yesmaximal, complemented
22#13077651C211yesmaximal, characteristic, complemented
23C11×#3501C211yesmaximal, characteristic, complemented
24C22×#4339C2212yes—
25C11×#554—21no—
26C11×#554—22no—
27C11×#554—21no—
28C11×#554C2211yescharacteristic
29C11×#554C2211yescharacteristic, complemented
30C11×#554C2212yescomplemented
31D4×Q8×C11C2211yescharacteristic
32D4×Q8×C11C2212yescomplemented
33D4×Q8×C11C2211yescharacteristic, complemented
34C11×#544—21no—
35C11×#543—22no—
36C11×#533C2211yescharacteristic, complemented
37C11×#533C2211yescharacteristic, complemented
38C2×C11×C22⋊Q8C2212yescomplemented
39C2×C11×C22⋊Q8C2212yescomplemented
40C11×#518—21no—
41C2×C4×D4×C11C2211yescharacteristic
42C22×#4326C2212yescomplemented
43C2×#66995C2212yescomplemented
44C2×#66995C2212yescomplemented
45C22×#4325C2212yescomplemented
46D4×C22⋊D11—21no—
47#10623322C2212yes—
48#10623084C2211yescharacteristic
49#10623083C2212yes—
50#10623082C2211yescharacteristic
51#10623081C2212yes—
52D4×D44C2211yescharacteristic
53#10623079—21no—
54#10623078—22no—
55C4×D4×D11—21no—
56D4×Dic22C2211yescharacteristic
57#10623038—21no—
58#10623021—22no—
59#10623008C2211yescharacteristic
60C4×#4339C2211yescharacteristic
61#10622841C2212yescomplemented
62#10622841C2212yescomplemented
63#10622840C2212yescomplemented
64#10622840C2212yescomplemented
65#10622820C2212yescomplemented
66C2×C22⋊(C11⋊C8)C2212yescomplemented
67#10622707C2211yescharacteristic, complemented
68#10622706C2211yescharacteristic, complemented
69#10622705C2211yescharacteristic, complemented
70#10622704C2211yescharacteristic, complemented
71#10622703C2211yescharacteristic, complemented
72#10622703C2211yescharacteristic, complemented
73#10622702C2212yescomplemented
74#10622701C2211yescharacteristic, complemented
75#10622700C2211yescharacteristic, complemented
76#10622699C2212yescomplemented
77#10622698C2211yescharacteristic, complemented
78#10622697C2211yescharacteristic, complemented
79#10622696C2211yescharacteristic, complemented
80#10622696C2211yescharacteristic, complemented
81#10622665C2212yescomplemented
82#10622665C2212yescomplemented
83#10622664C2212yescomplemented
84#10622664C2212yescomplemented
85#10622663C2212yescomplemented
86#10622663C2212yescomplemented
87#10622662C2212yescomplemented
88#10622662C2212yescomplemented
89#10622661C2212yescomplemented
90#10622661C2212yescomplemented
91#10622660C2211yescharacteristic
92#10622660C2212yes—
93#10622660C2211yescharacteristic
94#10622660C2212yescomplemented
95#10622660C2212yescomplemented
96#10622660C2212yescomplemented
97#10622660C2212yescomplemented
98#10622660C2212yescomplemented
99#10622660C2212yescomplemented
100#10622660C2212yescomplemented
101#10622660C2212yescomplemented
102#10622659C2212yescomplemented
103#10622659C2212yescomplemented
104#10622658C2211yescharacteristic, complemented
105#10622658C2212yescomplemented
106#10622658C2211yescharacteristic, complemented
107#10622644C2211yescharacteristic, complemented
108#10622644C2211yescharacteristic, complemented
109#10622643C2212yescomplemented
110C4×#4326C2211yescharacteristic, complemented
111C4×#4326C2211yescharacteristic, complemented
112#10622641C2212yescomplemented
113#10622641C2212yescomplemented
114#10622640C2211yescharacteristic, complemented
115#10622640C2211yescharacteristic, complemented
116#10622639C2212yescomplemented
117C4×#4325C2211yescharacteristic, complemented
118C4×#4325C2211yescharacteristic, complemented
119#10622625C2211yescharacteristic, complemented
120#10622625C2211yescharacteristic, complemented
121#10622624C2212yescomplemented
122#10622624C2212yescomplemented
123D4×C11⋊C8C2211yescharacteristic
124D4×C11⋊C8C2211yescharacteristic
125#10622584C2212yescomplemented
126#10622583C2212yescomplemented
127C2×#66874C2212yescomplemented
128#10622581C2212yescomplemented
129#10622580C2212yescomplemented
130#10622579C2212yescomplemented
131#10622579C2212yescomplemented
132C2×#66873C2212yescomplemented
133#10622539C2211yescharacteristic, complemented
134#10622538C2211yescharacteristic, complemented
135C22×Q8×C11C2312yes—
136C22×Q8×C11C2312yes—
137C22×D4×C11D411yescharacteristic
138C23×C4×C11C2312yes—
139C22×C22⋊D11—22no—
140C2×D4×D11—21no—
141C2×#4339—22no—
142C2×#4339—22no—
143C2×#4339—44no—
144C2×#4339—44no—
145C2×#4339C2311yescharacteristic
146C2×#4339C2312yes—
147C2×#4339C2312yes—
148C2×#4339C2312yes—
149C22×D44C2312yes—
150C22×C4×D11—22no—
151C22×Dic22C2312yes—
152C11×C4⋊Q8—21no—
153C11×C4⋊Q8—21no—
154C11×C4⋊Q8—22no—
155C11×C4⋊Q8C2311yescharacteristic
156C11×C4⋊Q8C2311yescharacteristic
157C11×C4⋊Q8C2311yescharacteristic
158C11×C4⋊Q8C2311yescharacteristic
159C11×#125—21no—
160C11×#125—21no—
161C11×#125—22no—
162C11×#125—21no—
163C11×#125—21no—
164C11×C22⋊Q8—22no—
165C11×C22⋊Q8—22no—
166C11×C22⋊Q8—22no—
167C11×C22⋊Q8—22no—
168C11×C22⋊Q8—21no—
169C11×C22⋊Q8—21no—
170C11×C22⋊Q8—22no—
171C11×C22⋊Q8—22no—
172C11×C22⋊Q8—22no—
173C11×C22⋊Q8—22no—
174C11×C22⋊Q8—22no—
175C11×C22⋊Q8—22no—
176C11×C22⋊Q8—22no—
177C11×C22⋊Q8—22no—
178C11×C22⋊Q8C2311yescharacteristic
179C11×C22⋊Q8C2312yes—
180C11×C22⋊Q8C2311yescharacteristic
181C11×C22⋊Q8C2312yes—
182C11×C22⋊Q8C2312yes—
183C11×C22⋊Q8C2312yes—
184C11×C22⋊Q8C2312yes—
185C4×Q8×C11—21no—
186C4×Q8×C11—21no—
187C4×Q8×C11C2311yescharacteristic
188C4×Q8×C11C2311yescharacteristic
189C4×Q8×C11C2312yes—
190C4×D4×C11—21no—
191C4×D4×C11—22no—
192C4×D4×C11—21no—
193C4×D4×C11—21no—
194C4×D4×C11—22no—
195C4×D4×C11—21no—
196C4×D4×C11D411yescharacteristic
197C4×D4×C11D412yes—
198C4×D4×C11D411yescharacteristic
199C4×D4×C11C2311yescharacteristic
200C4×D4×C11C2312yes—
201C4×D4×C11C2311yescharacteristic
202C11×#117—21no—
203C11×#117—21no—
204C2×C11×C4⋊C4—22no—
205C2×C11×C4⋊C4—22no—
206C2×C11×C4⋊C4D411yescharacteristic
207C2×C11×C4⋊C4C2312yes—
208C2×C11×C4⋊C4C2312yes—
209C2×C11×C22⋊C4—22no—
210C2×C11×C22⋊C4—22no—
211C2×C11×C22⋊C4D412yes—
212C2×C42×C11C2311yescharacteristic
213#67006—22no—
214C2×#4326—44no—
215C2×#4326C2311yescharacteristic
216C2×#4326C2312yes—
217C2×#4326C2311yescharacteristic
218C2×#4326C2312yes—
219C2×#4326C2312yes—
220C2×#4326C2312yes—
221C2×#4326C2312yes—
222#66995—44no—
223#66995—44no—
224C2×#4325—44no—
225C2×#4325C2311yescharacteristic
226C2×#4325C2312yes—
227C2×#4325C2311yescharacteristic
228C2×#4325C2312yes—
229C2×#4325C2312yes—
230C2×#4325C2312yes—
231C2×#4325C2312yes—
232#66993—21no—
233#66992—22no—
234#66991—21no—
235#66990—22no—
236D4×Dic11—21no—
237#66983—21no—
238#66983—21no—
239#66983C2312yes—
240#66983C2312yes—
241#66982—22no—
242C4×C22⋊D11—21no—
243C4×C22⋊D11—21no—
244C4×C22⋊D11—22no—
245C4×C22⋊D11—22no—
246#66979C2311yescharacteristic
247#66977C2312yes—
248#66977C2312yes—
249C2×#4318C2312yes—
250C2×#4318C2312yes—
251C22×C11⋊C8C2312yes—
252C22×C11⋊C8C2312yes—
253#66949—22no—
254#66948—21no—
255#66947—22no—
256#66946—21no—
257C4⋊C4×D11—21no—
258#66941—21no—
259#66938—22no—
260#66937—22no—
261#66937—22no—
262#66936—22no—
263#66935—22no—
264(C22⋊D11)⋊C4—22no—
265C22⋊C4×D11—22no—
266#66931—22no—
267#66928C2312yes—
268#66927C2311yescharacteristic
269C4×D44—21no—
270C4×D44—21no—
271C4×D44C2311yescharacteristic
272C4×D44C2311yescharacteristic
273#66925—21no—
274C42×D11—21no—
275#66922C2311yescharacteristic
276C4×Dic22C2311yescharacteristic
277C4×Dic22C2311yescharacteristic
278#66899C2311yescharacteristic
279#66899C2311yescharacteristic
280#66899C2312yes—
281#66899C2312yes—
282#66899C2311yescharacteristic
283#66899C2311yescharacteristic
284C22⋊(C11⋊C8)C2311yescharacteristic
285C22⋊(C11⋊C8)C2311yescharacteristic
286C22⋊(C11⋊C8)C2312yes—
287C22⋊(C11⋊C8)C2312yes—
288C22⋊(C11⋊C8)C2312yes—
289C22⋊(C11⋊C8)C2312yes—
290C22⋊(C11⋊C8)C2312yes—
291#66874C2311yescharacteristic
292#66874C2312yes—
293#66874C2312yes—
294#66874C2312yes—
295#66874C2311yescharacteristic
296#66874C2312yes—
297#66874C2312yes—
298#66873C2311yescharacteristic
299#66873C2312yes—
300#66873C2312yes—
301#66873C2312yes—
302#66873C2311yescharacteristic
303#66873C2312yes—
304#66873C2312yes—
305#66872C2311yescharacteristic
306#66872C2312yes—
307#66872C2311yescharacteristic
308#66871C2311yescharacteristic
309#66871C2312yes—
310#66871C2311yescharacteristic
311C4⋊(C11⋊C8)C2311yescharacteristic
312C4⋊(C11⋊C8)C2311yescharacteristic
313C4⋊(C11⋊C8)C2311yescharacteristic
314C4⋊(C11⋊C8)C2311yescharacteristic
315#66867C2312yes—
316C4×C11⋊C8C2311yescharacteristic
317C4×C11⋊C8C2311yescharacteristic
318#61607—111nomaximal, Sylow
319C24×C11C2×D412yes—
320C23×D11—22no—
321C2×Q8×C11—21no—
322C2×Q8×C11—21no—
323C2×Q8×C11—22no—
324C2×Q8×C11—22no—
325C2×Q8×C11—42no—
326C2×Q8×C11—42no—
327C2×Q8×C11—42no—
328C2×Q8×C11—42no—
329C2×Q8×C11C2411yescharacteristic
330C2×Q8×C11C2412yes—
331C2×Q8×C11C2411yescharacteristic
332C2×D4×C11—24no—
333C2×D4×C11C2×D412yes—
334C2×D4×C11C2×D411yescharacteristic
335C2×D4×C11C2×D411yescharacteristic
336C22×C4×C11—22no—
337C22×C4×C11—22no—
338C22×C4×C11—22no—
339C22×C4×C11—22no—
340C22×C4×C11—42no—
341C22×C4×C11—42no—
342C22×C4×C11C2×D411yescharacteristic
343C22×C4×C11C2×D411yescharacteristic
344C22×C4×C11C2×D412yes—
345C22×C4×C11C2×D412yes—
346C22×C4×C11C2×D412yes—
347C22×C4×C11C2411yescharacteristic
348C22×C4×C11C2412yes—
349C22×C4×C11C2412yes—
350C2×C22⋊D11—21no—
351C2×C22⋊D11—22no—
352C2×C22⋊D11—22no—
353C2×C22⋊D11—22no—
354C2×C22⋊D11—22no—
355C2×C22⋊D11—22no—
356C2×C22⋊D11—48no—
357C22×Dic11—22no—
358D4×D11—44no—
359#4339—22no—
360#4339—24no—
361#4339—22no—
362#4339—24no—
363#4339—42no—
364#4339—42no—
365#4339—42no—
366#4339—42no—
367#4339—48no—
368#4339—48no—
369C2×D44—24no—
370C2×D44—21no—
371C2×D44—22no—
372C2×D44—21no—
373C2×D44—42no—
374C2×D44C2412yes—
375C2×D44C2411yescharacteristic
376C2×C4×D11—21no—
377C2×C4×D11—21no—
378C2×C4×D11—22no—
379C2×C4×D11—22no—
380C2×C4×D11—22no—
381C2×C4×D11—21no—
382C2×C4×D11—48no—
383C2×Dic22—24no—
384C2×Dic22—22no—
385C2×Dic22—42no—
386C2×Dic22C2412yes—
387C2×Dic22C2411yescharacteristic
388C11×C4⋊C4—21no—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—21no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—22no—
397C11×C4⋊C4—21no—
398C11×C4⋊C4—21no—
399C11×C4⋊C4—21no—
400C11×C4⋊C4—21no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—21no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4—21no—
405C11×C4⋊C4—21no—
406C11×C4⋊C4C2×D411yescharacteristic
407C11×C4⋊C4C2×D411yescharacteristic
408C11×C4⋊C4C2×D412yes—
409C11×C4⋊C4C2411yescharacteristic
410C11×C4⋊C4C2412yes—
411C11×C4⋊C4C2411yescharacteristic
412C11×C22⋊C4—21no—
413C11×C22⋊C4—22no—
414C11×C22⋊C4—21no—
415C11×C22⋊C4—22no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4C2×D412yes—
420C11×C22⋊C4C2×D412yes—
421C11×C22⋊C4C2×D412yes—
422C11×C22⋊C4C2×D412yes—
423C42×C11—22no—
424C42×C11—21no—
425C42×C11—21no—
426C42×C11C2×D411yescharacteristic
427C42×C11C2×D411yescharacteristic
428C42×C11C2411yescharacteristic
429C42×C11C2411yescharacteristic
430C22⋊Dic11—22no—
431C22⋊Dic11—22no—
432C22⋊Dic11—21no—
433#4326—22no—
434#4326—24no—
435#4326—22no—
436#4326—42no—
437#4326—42no—
438#4326—42no—
439#4326—42no—
440#4325—22no—
441#4325—24no—
442#4325—22no—
443#4325—42no—
444#4325—42no—
445#4325—42no—
446#4325—42no—
447(C2×D11)⋊C4—21no—
448(C2×D11)⋊C4—21no—
449(C2×D11)⋊C4—22no—
450(C2×D11)⋊C4—22no—
451(C2×D11)⋊C4—22no—
452(C2×D11)⋊C4—22no—
453C4⋊Dic11—21no—
454C4⋊Dic11—21no—
455C4⋊Dic11C2411yescharacteristic
456C4⋊Dic11C2411yescharacteristic
457Dic11⋊C4—21no—
458Dic11⋊C4—21no—
459Dic11⋊C4—22no—
460Dic11⋊C4—22no—
461C4×Dic11—21no—
462C4×Dic11—21no—
463C4×Dic11—21no—
464#4318—42no—
465#4318—42no—
466C2×C11⋊C8—42no—
467C2×C11⋊C8—42no—
468C2×C11⋊C8C2411yescharacteristic
469C2×C11⋊C8C2411yescharacteristic
470C2×C11⋊C8C2411yescharacteristic
471C2×C11⋊C8C2411yescharacteristic
472C2×C11⋊C8C2412yes—
473C2×C11⋊C8C2412yes—
474#3501D1111yescharacteristic, complemented
475D4×#41—111no—
476#3333—111no—
477#3331—111no—
478#3316—112no—
479#3314—112no—
480#3299—111no—
481#3295—111no—
482D4×Q16—111no—
483D4×SD16—111no—
484#3278—111no—
485#3276—111no—
486#3270—112no—
487#3266—112no—
488#3216—111no—
489#3210—111no—
490#3196—112no—
491#3190—112no—
492#3116—111no—
493#3107—111no—
494#3007—112no—
495C2×#452—112no—
496#2974—111no—
497C23×C11—24no—
498C23×C11—42no—
499C23×C11—42no—
500C23×C11C22×D411yescharacteristic
501C23×C11C22×D412yes—
502C23×C11C22×D412yes—
503C22×D11—21no—
504C22×D11—22no—
505C22×D11—44no—
506C22×D11—44no—
507C22×D11—82no—
508Q8×C11—21no—
509Q8×C11—22no—
510Q8×C11—21no—
511Q8×C11—21no—
512Q8×C11—22no—
513Q8×C11—21no—
514Q8×C11—81no—
515Q8×C11—81no—
516Q8×C11—82no—
517Q8×C11—82no—
518D4×C11—24no—
519D4×C11—22no—
520D4×C11#13714yescomplemented
521C2×C4×C11—22no—
522C2×C4×C11—22no—
523C2×C4×C11—22no—
524C2×C4×C11—22no—
525C2×C4×C11—22no—
526C2×C4×C11—21no—
527C2×C4×C11—21no—
528C2×C4×C11—22no—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
531C2×C4×C11—21no—
532C2×C4×C11—22no—
533C2×C4×C11—21no—
534C2×C4×C11—42no—
535C2×C4×C11—42no—
536C2×C4×C11—42no—
537C2×C4×C11—41no—
538C2×C4×C11—82no—
539C2×C4×C11—82no—
540C2×C4×C11—82no—
541C2×C4×C11—82no—
542C2×C4×C11C22×D411yescharacteristic
543C2×C4×C11C22×D411yescharacteristic
544C2×C4×C11C22×D411yescharacteristic
545C2×C4×C11C22×D411yescharacteristic
546C2×C4×C11C22×D412yes—
547C2×C4×C11C22×D412yes—
548C2×C4×C11C22×D411yescharacteristic
549C2×C4×C11C2511yescharacteristic
550C22⋊D11—24no—
551C22⋊D11—44no—
552C22⋊D11—44no—
553C22⋊D11—44no—
554C22⋊D11—44no—
555C22⋊D11—82no—
556C2×Dic11—21no—
557C2×Dic11—21no—
558C2×Dic11—21no—
559C2×Dic11—22no—
560C2×Dic11—44no—
561D44—21no—
562D44—22no—
563D44—22no—
564D44—44no—
565D44—42no—
566D44—81no—
567D44H(5,𝔽2)12yes—
568C4×D11—24no—
569C4×D11—44no—
570C4×D11—44no—
571C4×D11—44no—
572C4×D11—42no—
573C4×D11—81no—
574Dic22—21no—
575Dic22—22no—
576Dic22—22no—
577Dic22—44no—
578Dic22H(5,𝔽2)12yes—
579C11⋊C8—21no—
580C11⋊C8—21no—
581C11⋊C8—22no—
582C11⋊C8—22no—
583C11⋊C8—21no—
584C11⋊C8—21no—
585C22×#41—112no—
586C2×#137—112no—
587C2×#137—112no—
588C22×Q16—112no—
589C22×SD16—112no—
590#554—21no—
591#554—22no—
592#554—21no—
593#554C2×D1111yescharacteristic
594#554C2×D1111yescharacteristic, complemented
595#554C2×D1112yescomplemented
596#550—111no—
597D4×Q8—111no—
598D4×Q8C2×D1111yescharacteristic
599D4×Q8C2×D1112yescomplemented
600D4×Q8C2×D1111yescharacteristic, complemented
601#548—112no—
602#547—111no—
603#547—221no—
604#546—112no—
605#546—222no—
606D42—111no—
607D42—221no—
608#544—21no—
609#543—22no—
610#533C2×D1111yescharacteristic, complemented
611#533C2×D1111yescharacteristic, complemented
612#532—111no—
613#532—221no—
614#525—112no—
615#525—222no—
616C2×C22⋊Q8C2×D1112yescomplemented
617C2×C22⋊Q8C2×D1112yescomplemented
618#518—21no—
619C4×#41—111no—
620C2×C4×D4—221no—
621C2×C4×D4C2×D1111yescharacteristic
622#497—112no—
623#494—111no—
624#492—111no—
625#489—112no—
626#487—111no—
627#486—111no—
628#485—111no—
629#485—111no—
630#485—112no—
631#484—112no—
632#483—112no—
633#481—112no—
634#480—112no—
635#477—111no—
636#476—111no—
637#475—111no—
638#474—111no—
639#470—112no—
640#470—112no—
641#468—112no—
642#468—112no—
643#467—112no—
644#467—112no—
645#465—112no—
646#465—112no—
647#464—112no—
648#464—112no—
649#462—111no—
650#462—111no—
651#462—111no—
652#462—111no—
653#461—111no—
654#461—111no—
655#460—111no—
656#460—111no—
657#452—112no—
658#452—112no—
659#452—111no—
660#452—111no—
661#452—112no—
662#452—112no—
663#452—112no—
664#452—112no—
665#452—112no—
666#452—112no—
667#452—112no—
668#451—112no—
669#451—112no—
670#451—112no—
671#451—112no—
672#450—112no—
673#450—112no—
674#448—112no—
675#448—112no—
676#441—112no—
677#440—112no—
678C4×Q16—111no—
679C4×Q16—111no—
680C4×SD16—111no—
681C4×SD16—111no—
682#436—111no—
683#436—111no—
684#435—112no—
685#435—112no—
686C8×D4—111no—
687C8×D4—111no—
688#432—111no—
689#431—111no—
690#417—112no—
691#417—112no—
692C2×#103—112no—
693C2×#102—112no—
694#407—112no—
695C2×C22⋊C8—112no—
696C22×C11—22no—
697C22×C11—22no—
698C22×C11—21no—
699C22×C11—22no—
700C22×C11—21no—
701C22×C11—22no—
702C22×C11—21no—
703C22×C11—22no—
704C22×C11—84no—
705C22×C11C2×#13714yes—
706C22×C11C23×D411yescharacteristic
707C2×D11—22no—
708C2×D11—41no—
709C2×D11—41no—
710C2×D11—42no—
711C2×D11—42no—
712C2×D11—42no—
713C2×D11—88no—
714C4×C11—21no—
715C4×C11—21no—
716C4×C11—21no—
717C4×C11—22no—
718C4×C11—22no—
719C4×C11—21no—
720C4×C11—41no—
721C4×C11—42no—
722C4×C11—41no—
723C4×C11—41no—
724C4×C11—42no—
725C4×C11—41no—
726C4×C11C2×#13712yes—
727C4×C11C2×H(5,𝔽2)11yescharacteristic
728C4×C11C2×H(5,𝔽2)11yescharacteristic
729Dic11—22no—
730Dic11—41no—
731Dic11—42no—
732Dic11—41no—
733C2×#41—111no—
734C2×#41—112no—
735C2×#41—112no—
736C2×#41—112no—
737C2×#41—222no—
738C2×#41—222no—
739C2×#41—444no—
740C2×#41—444no—
741C22×Q8—112no—
742C22×Q8C22×D1112yes—
743C22×Q8C22×D1112yes—
744C22×D4—112no—
745C22×D4—222no—
746C22×D4—221no—
747C22×D4C22⋊D1111yescharacteristic
748C23×C4—222no—
749C23×C4C22×D1112yes—
750#137—444no—
751#137—444no—
752C2×Q16—111no—
753C2×Q16—112no—
754C2×Q16—111no—
755C2×Q16—112no—
756C2×Q16—112no—
757C2×Q16—112no—
758C2×Q16—112no—
759C2×Q16—444no—
760C2×SD16—111no—
761C2×SD16—112no—
762C2×SD16—111no—
763C2×SD16—112no—
764C2×SD16—112no—
765C2×SD16—112no—
766C2×SD16—112no—
767C2×SD16—444no—
768C2×M16—112no—
769C2×M16—112no—
770C22×C8—112no—
771C22×C8—112no—
772C4⋊Q8—21no—
773C4⋊Q8—21no—
774C4⋊Q8—22no—
775C4⋊Q8—111no—
776C4⋊Q8—221no—
777C4⋊Q8C22×D1111yescharacteristic
778C4⋊Q8C22×D1111yescharacteristic
779C4⋊Q8C22×D1111yescharacteristic
780C4⋊Q8C22×D1111yescharacteristic
781#127—111no—
782#127—221no—
783#125—21no—
784#125—21no—
785#125—22no—
786#125—21no—
787#125—21no—
788#124—112no—
789#124—222no—
790#123—222no—
791#123—222no—
792#123—222no—
793C22⋊Q8—22no—
794C22⋊Q8—22no—
795C22⋊Q8—22no—
796C22⋊Q8—22no—
797C22⋊Q8—21no—
798C22⋊Q8—21no—
799C22⋊Q8—22no—
800C22⋊Q8—22no—
801C22⋊Q8—22no—
802C22⋊Q8—22no—
803C22⋊Q8—22no—
804C22⋊Q8—22no—
805C22⋊Q8—22no—
806C22⋊Q8—22no—
807C22⋊Q8—112no—
808C22⋊Q8—112no—
809C22⋊Q8—222no—
810C22⋊Q8—222no—
811C22⋊Q8C22×D1111yescharacteristic
812C22⋊Q8C22×D1112yes—
813C22⋊Q8C22×D1111yescharacteristic
814C22⋊Q8C22×D1112yes—
815C22⋊Q8C22×D1112yes—
816C22⋊Q8C22×D1112yes—
817C22⋊Q8C22×D1112yes—
818#121—112no—
819#121—112no—
820#121—222no—
821#121—221no—
822#121—221no—
823#121—221no—
824#121—221no—
825#121—222no—
826#121—222no—
827#120—222no—
828#120—222no—
829#120—222no—
830C4×Q8—21no—
831C4×Q8—21no—
832C4×Q8—111no—
833C4×Q8—111no—
834C4×Q8C22×D1111yescharacteristic
835C4×Q8C22×D1111yescharacteristic
836C4×Q8C22×D1112yes—
837C4×D4—21no—
838C4×D4—22no—
839C4×D4—21no—
840C4×D4—21no—
841C4×D4—22no—
842C4×D4—21no—
843C4×D4—111no—
844C4×D4—111no—
845C4×D4—221no—
846C4×D4—222no—
847C4×D4—221no—
848C4×D4—221no—
849C4×D4—222no—
850C4×D4—221no—
851C4×D4—222no—
852C4×D4—221no—
853C4×D4—221no—
854C4×D4C22⋊D1111yescharacteristic
855C4×D4C22⋊D1112yes—
856C4×D4C22⋊D1111yescharacteristic
857C4×D4C22×D1111yescharacteristic
858C4×D4C22×D1112yes—
859C4×D4C22×D1111yescharacteristic
860#117—21no—
861#117—21no—
862#117—111no—
863#117—221no—
864C2×C4⋊C4—22no—
865C2×C4⋊C4—22no—
866C2×C4⋊C4—221no—
867C2×C4⋊C4C22⋊D1111yescharacteristic
868C2×C4⋊C4C22×D1112yes—
869C2×C4⋊C4C22×D1112yes—
870C2×C22⋊C4—22no—
871C2×C22⋊C4—22no—
872C2×C22⋊C4—222no—
873C2×C22⋊C4C22⋊D1112yes—
874C2×C42—221no—
875C2×C42C22×D1111yescharacteristic
876#107—111no—
877#107—111no—
878#107—112no—
879#106—111no—
880#106—111no—
881#106—112no—
882C4⋊C8—111no—
883C4⋊C8—111no—
884C4⋊C8—111no—
885C4⋊C8—111no—
886#103—111no—
887#103—111no—
888#103—111no—
889#103—111no—
890#103—112no—
891#103—112no—
892#103—111no—
893#103—112no—
894#103—112no—
895#103—112no—
896#103—111no—
897#103—112no—
898#103—112no—
899#102—111no—
900#102—112no—
901#102—112no—
902#102—112no—
903#102—111no—
904#102—112no—
905#102—112no—
906C22⋊C8—111no—
907C22⋊C8—112no—
908C22⋊C8—112no—
909C22⋊C8—112no—
910C22⋊C8—111no—
911C22⋊C8—112no—
912C22⋊C8—112no—
913#97—112no—
914C4×C8—111no—
915C4×C8—111no—
916C2×C11—24no—
917C2×C11—42no—
918C2×C11—41no—
919C2×C11#348411yescharacteristic
920C2×C11C22×#13711yescharacteristic
921C2×C11#358411yescharacteristic
922D11—42no—
923D11—82no—
924C24—222no—
925C24C2×C22⋊D1112yes—
926#41—222no—
927#41—222no—
928#41—224no—
929#41—224no—
930#41—442no—
931#41—442no—
932#41—442no—
933#41—442no—
934#41—448no—
935#41—448no—
936C2×Q8—21no—
937C2×Q8—21no—
938C2×Q8—22no—
939C2×Q8—22no—
940C2×Q8—42no—
941C2×Q8—42no—
942C2×Q8—42no—
943C2×Q8—42no—
944C2×Q8—111no—
945C2×Q8—112no—
946C2×Q8—224no—
947C2×Q8—222no—
948C2×Q8—442no—
949C2×Q8C23×D1111yescharacteristic
950C2×Q8C23×D1112yes—
951C2×Q8C23×D1111yescharacteristic
952C2×D4—24no—
953C2×D4—111no—
954C2×D4—112no—
955C2×D4—224no—
956C2×D4—221no—
957C2×D4—222no—
958C2×D4—222no—
959C2×D4—222no—
960C2×D4—222no—
961C2×D4—222no—
962C2×D4—221no—
963C2×D4—222no—
964C2×D4—221no—
965C2×D4—442no—
966C2×D4—448no—
967C2×D4—444no—
968C2×D4C2×C22⋊D1112yes—
969C2×D4C2×C22⋊D1111yescharacteristic
970C2×D4C2×C22⋊D1111yescharacteristic
971C22×C4—22no—
972C22×C4—22no—
973C22×C4—22no—
974C22×C4—22no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—221no—
978C22×C4—222no—
979C22×C4—221no—
980C22×C4—222no—
981C22×C4—222no—
982C22×C4—222no—
983C22×C4—221no—
984C22×C4—448no—
985C22×C4C2×C22⋊D1111yescharacteristic
986C22×C4C2×C22⋊D1111yescharacteristic
987C22×C4C2×C22⋊D1112yes—
988C22×C4C2×C22⋊D1112yes—
989C22×C4C2×C22⋊D1112yes—
990C22×C4C23×D1111yescharacteristic
991C22×C4C23×D1112yes—
992C22×C4C23×D1112yes—
993Q16—222no—
994Q16—224no—
995Q16—222no—
996Q16—442no—
997Q16—442no—
998Q16—442no—
999Q16—442no—
1000SD16—222no—
1001SD16—224no—
1002SD16—222no—
1003SD16—442no—
1004SD16—442no—
1005SD16—442no—
1006SD16—442no—
1007M16—442no—
1008M16—442no—
1009C2×C8—111no—
1010C2×C8—111no—
1011C2×C8—111no—
1012C2×C8—111no—
1013C2×C8—112no—
1014C2×C8—112no—
1015C2×C8—442no—
1016C2×C8—442no—
1017C4⋊C4—21no—
1018C4⋊C4—22no—
1019C4⋊C4—21no—
1020C4⋊C4—22no—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—22no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—111no—
1036C4⋊C4—111no—
1037C4⋊C4—221no—
1038C4⋊C4—222no—
1039C4⋊C4—221no—
1040C4⋊C4—221no—
1041C4⋊C4—222no—
1042C4⋊C4—221no—
1043C4⋊C4C2×C22⋊D1111yescharacteristic
1044C4⋊C4C2×C22⋊D1111yescharacteristic
1045C4⋊C4C2×C22⋊D1112yes—
1046C4⋊C4C23×D1111yescharacteristic
1047C4⋊C4C23×D1112yes—
1048C4⋊C4C23×D1111yescharacteristic
1049C22⋊C4—21no—
1050C22⋊C4—22no—
1051C22⋊C4—21no—
1052C22⋊C4—22no—
1053C22⋊C4—22no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—222no—
1057C22⋊C4—221no—
1058C22⋊C4—222no—
1059C22⋊C4—222no—
1060C22⋊C4—222no—
1061C22⋊C4—221no—
1062C22⋊C4—221no—
1063C22⋊C4—222no—
1064C22⋊C4—222no—
1065C22⋊C4C2×C22⋊D1112yes—
1066C22⋊C4C2×C22⋊D1112yes—
1067C22⋊C4C2×C22⋊D1112yes—
1068C22⋊C4C2×C22⋊D1112yes—
1069C42—22no—
1070C42—21no—
1071C42—21no—
1072C42—221no—
1073C42—221no—
1074C42—221no—
1075C42C2×C22⋊D1111yescharacteristic
1076C42C2×C22⋊D1111yescharacteristic
1077C42C23×D1111yescharacteristic
1078C42C23×D1111yescharacteristic
1079C11#6160711yescharacteristic, complemented, Sylow
1080C23—24no—
1081C23—42no—
1082C23—42no—
1083C23—221no—
1084C23—222no—
1085C23—444no—
1086C23—444no—
1087C23—882no—
1088C23C22×C22⋊D1111yescharacteristic
1089C23C22×C22⋊D1112yes—
1090C23C22×C22⋊D1112yes—
1091Q8—21no—
1092Q8—22no—
1093Q8—21no—
1094Q8—21no—
1095Q8—22no—
1096Q8—21no—
1097Q8—81no—
1098Q8—81no—
1099Q8—82no—
1100Q8—82no—
1101Q8—112no—
1102Q8—221no—
1103Q8—222no—
1104Q8—222no—
1105Q8—444no—
1106D4—24no—
1107D4—22no—
1108D4—112no—
1109D4—224no—
1110D4—221no—
1111D4—222no—
1112D4—222no—
1113D4—444no—
1114D4—444no—
1115D4—444no—
1116D4—444no—
1117D4—444no—
1118D4—442no—
1119D4—881no—
1120D4—882no—
1121D4#6699514yescomplemented
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—21no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—82no—
1140C2×C4—82no—
1141C2×C4—82no—
1142C2×C4—82no—
1143C2×C4—224no—
1144C2×C4—221no—
1145C2×C4—221no—
1146C2×C4—221no—
1147C2×C4—222no—
1148C2×C4—444no—
1149C2×C4—444no—
1150C2×C4—444no—
1151C2×C4—444no—
1152C2×C4—442no—
1153C2×C4—881no—
1154C2×C4C22×C22⋊D1111yescharacteristic
1155C2×C4C22×C22⋊D1111yescharacteristic
1156C2×C4C22×C22⋊D1111yescharacteristic
1157C2×C4C22×C22⋊D1111yescharacteristic
1158C2×C4C22×C22⋊D1112yes—
1159C2×C4C22×C22⋊D1112yes—
1160C2×C4C22×C22⋊D1111yescharacteristic
1161C2×C4C24×D1111yescharacteristic
1162C8—221no—
1163C8—221no—
1164C8—222no—
1165C8—222no—
1166C8—221no—
1167C8—221no—
1168C22—22no—
1169C22—22no—
1170C22—21no—
1171C22—22no—
1172C22—21no—
1173C22—22no—
1174C22—21no—
1175C22—22no—
1176C22—84no—
1177C22—222no—
1178C22—441no—
1179C22—441no—
1180C22—442no—
1181C22—442no—
1182C22—442no—
1183C22—888no—
1184C22C2×#6699514yes—
1185C22C23×C22⋊D1111yescharacteristic
1186C4—21no—
1187C4—22no—
1188C4—22no—
1189C4—21no—
1190C4—21no—
1191C4—21no—
1192C4—41no—
1193C4—42no—
1194C4—41no—
1195C4—41no—
1196C4—42no—
1197C4—41no—
1198C4—222no—
1199C4—442no—
1200C4—441no—
1201C4—441no—
1202C4C2×#6699512yes—
1203C4D11×H(5,𝔽2)11yescharacteristic
1204C4D11×H(5,𝔽2)11yescharacteristic
1205C2—24no—
1206C2—41no—
1207C2—42no—
1208C2—442no—
1209C2—882no—
1210C2#1308224711yescharacteristic
1211C2C22×#6699511yescharacteristic
1212C2#1308338711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3501C2
socleC22×C11C23×D4
prime radicalD4×#4339C2
hypercenter#3501D11
hypocenterC11#61607
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3501

Complements

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

NH ≅ G/Ntype
2. #13080948C2semidirect
3. #13080926C2semidirect
4. #13080721C2semidirect
5. #13080691C2semidirect
6. #13080486C2semidirect
7. #13080434C2semidirect
8. D4×#4326C2semidirect
9. D4×#4325C2semidirect
10. #13080278C2semidirect
11. #13080262C2semidirect
12. #13080187C2semidirect
13. #13080127C2semidirect
14. #13079623C2semidirect
15. #13079568C2semidirect
16. #13079446C2semidirect
17. #13079397C2semidirect
18. #13078772C2semidirect
19. #13078681C2semidirect
20. #13077874C2semidirect
21. C2×#10622660C2semidirect
22. #13077651C2semidirect
23. C11×#3501C2semidirect
29. C11×#554C22semidirect
30. C11×#554C22semidirect
32. D4×Q8×C11C22semidirect
33. D4×Q8×C11C22semidirect
36. C11×#533C22semidirect
37. C11×#533C22semidirect
38. C2×C11×C22⋊Q8C22semidirect
39. C2×C11×C22⋊Q8C22semidirect
42. C22×#4326C22semidirect
43. C2×#66995C22semidirect
44. C2×#66995C22semidirect
45. C22×#4325C22semidirect
61. #10622841C22semidirect
62. #10622841C22semidirect
63. #10622840C22semidirect
64. #10622840C22semidirect
65. #10622820C22semidirect
66. C2×C22⋊(C11⋊C8)C22semidirect
67. #10622707C22semidirect
68. #10622706C22semidirect
69. #10622705C22semidirect
70. #10622704C22semidirect
71. #10622703C22semidirect
72. #10622703C22semidirect
73. #10622702C22semidirect
74. #10622701C22semidirect
75. #10622700C22semidirect
76. #10622699C22semidirect
77. #10622698C22semidirect
78. #10622697C22semidirect
79. #10622696C22semidirect
80. #10622696C22semidirect
81. #10622665C22semidirect
82. #10622665C22semidirect
83. #10622664C22semidirect
84. #10622664C22semidirect
85. #10622663C22semidirect
86. #10622663C22semidirect
87. #10622662C22semidirect
88. #10622662C22semidirect
89. #10622661C22semidirect
90. #10622661C22semidirect
94. #10622660C22semidirect
95. #10622660C22semidirect
96. #10622660C22semidirect
97. #10622660C22semidirect
98. #10622660C22semidirect
99. #10622660C22semidirect
100. #10622660C22semidirect
101. #10622660C22semidirect
102. #10622659C22semidirect
103. #10622659C22semidirect
104. #10622658C22semidirect
105. #10622658C22semidirect
106. #10622658C22semidirect
107. #10622644C22semidirect
108. #10622644C22semidirect
109. #10622643C22semidirect
110. C4×#4326C22semidirect
111. C4×#4326C22semidirect
112. #10622641C22semidirect
113. #10622641C22semidirect
114. #10622640C22semidirect
115. #10622640C22semidirect
116. #10622639C22semidirect
117. C4×#4325C22semidirect
118. C4×#4325C22semidirect
119. #10622625C22semidirect
120. #10622625C22semidirect
121. #10622624C22semidirect
122. #10622624C22semidirect
125. #10622584C22semidirect
126. #10622583C22semidirect
127. C2×#66874C22semidirect
128. #10622581C22semidirect
129. #10622580C22semidirect
130. #10622579C22semidirect
131. #10622579C22semidirect
132. C2×#66873C22semidirect
133. #10622539C22semidirect
134. #10622538C22semidirect
474. #3501D11semidirect
520. D4×C11#137semidirect
594. #554C2×D11semidirect
595. #554C2×D11semidirect
599. D4×Q8C2×D11semidirect
600. D4×Q8C2×D11semidirect
610. #533C2×D11semidirect
611. #533C2×D11semidirect
616. C2×C22⋊Q8C2×D11semidirect
617. C2×C22⋊Q8C2×D11semidirect
1079. C11#61607semidirect
1121. D4#66995semidirect

Maximal subgroups

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

subgroupindex
D4×#43392
#130809482
#130809262
#130807212
#130806912
#130804862
#130804342
D4×#43262
D4×#43252
#130802782
#130802622
#130801872
#130801272
#130796232
#130795682
#130794462
#130793972
#130787722
#130786812
#130778742
C2×#106226602
#130776512
C11×#35012
#6160711