Finite Group Databasebeta

← #14917435

Subgroups — #14917435

Order 2816.

2182 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623134C211yesmaximal, characteristic
2#13071804C212yesmaximal, complemented
3#13071783C212yesmaximal, complemented
4#13071733C212yesmaximal, complemented
5#13071703C211yesmaximal, characteristic, complemented
6#13071689C211yesmaximal, characteristic, complemented
7#13071686C211yesmaximal, characteristic, complemented
8#13071669C211yesmaximal, characteristic, complemented
9#13071616C212yesmaximal, complemented
10#13071588C211yesmaximal, characteristic, complemented
11#13071577C211yesmaximal, characteristic, complemented
12#13071530C211yesmaximal, characteristic, complemented
13D4×Dic11⋊C4C211yesmaximal, characteristic, complemented
14#13071425C212yesmaximal, complemented
15#13071403C212yesmaximal, complemented
16#13071326C212yesmaximal, complemented
17#13071298C211yesmaximal, characteristic, complemented
18#13071290C212yesmaximal, complemented
19#13071223C211yesmaximal, characteristic, complemented
20#13071144C211yesmaximal, characteristic, complemented
21#121×Dic11C211yesmaximal, characteristic
22#13071098C211yesmaximal, characteristic, complemented
23C11×#2324C211yesmaximal, characteristic
24C2×C11×#121C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C11×#117C2211yescharacteristic
27C2×#66989C2212yes—
28C2×#66989C2211yescharacteristic
29C2×#66988C2212yes—
30C2×D4×Dic11C2211yescharacteristic
31C2×D4×Dic11C2212yes—
32C2×D4×Dic11C2211yescharacteristic
33C2×#66979C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C22×Dic11⋊C4C2212yes—
36C22×C4×Dic11C2211yescharacteristic
37#10623134C4116yescomplemented
38C2×#66941C2211yescharacteristic
39C2×#66940C2212yes—
40C2×#66940C2211yescharacteristic
41C2×#66940C2211yescharacteristic
42C2×#66932C2212yes—
43C2×#66931C2212yes—
44C2×C4×Dic22C2211yescharacteristic
45C11×#390C2212yes—
46C11×#390C2211yescharacteristic
47C11×#389C2211yescharacteristic
48C11×#388C2212yes—
49C11×#386C2212yes—
50C11×#385C2212yes—
51C11×#380C2211yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
53#10622834C2211yescharacteristic
54#10622833C2212yes—
55#10622825C2211yescharacteristic
56#10622823C2212yes—
57#10622823C2212yes—
58C4×C22⋊Dic11C2212yes—
59#10622598C2211yescharacteristic
60#10622591C2212yes—
61#10622591C2212yes—
62#10622590C2211yescharacteristic
63#10622589C2211yescharacteristic
64#10622589C2212yes—
65C4⋊C4×Dic11C2211yescharacteristic
66C4⋊C4×Dic11C2211yescharacteristic
67C4⋊C4×Dic11C2211yescharacteristic
68C4⋊C4×Dic11C2211yescharacteristic
69#10622587C2211yescharacteristic
70#10622586C2211yescharacteristic
71#10622586C2211yescharacteristic
72#10622586C2211yescharacteristic
73#10622586C2211yescharacteristic
74#10622586C2211yescharacteristic
75#10622585C2212yes—
76#10622585C2212yes—
77#10622564C2212yes—
78#10622559C2212yes—
79#10622559C2212yes—
80#10622559C2211yescharacteristic
81#10622559C2211yescharacteristic
82#10622559C2212yes—
83#10622559C2211yescharacteristic
84#10622559C2211yescharacteristic
85#10622558C2212yes—
86#10622558C2212yes—
87#10622558C2212yes—
88#10622558C2212yes—
89#10622558C2212yes—
90#10622557C2212yes—
91#10622557C2212yes—
92#10622557C2212yes—
93#10622557C2212yes—
94#10622557C2212yes—
95#10622556C2212yes—
96#10622555C2212yes—
97C22⋊C4×Dic11C2212yes—
98C22⋊C4×Dic11C2212yes—
99C22⋊C4×Dic11C2212yes—
100C22⋊C4×Dic11C2212yes—
101C4×C4⋊Dic11C2211yescharacteristic
102#10622546C2212yes—
103#10622545C2212yes—
104C4×Dic11⋊C4C2212yes—
105C4×Dic11⋊C4C2211yescharacteristic
106C4×Dic11⋊C4C2211yescharacteristic
107C4×Dic11⋊C4C2211yescharacteristic
108C4×Dic11⋊C4C2211yescharacteristic
109#10622542C2211yescharacteristic
110#10622542C2212yes—
111#10622541C2211yescharacteristic
112#10622267C2212yes—
113#10622266C2212yes—
114#10622265C2212yes—
115#10622265C2212yes—
116#10622265C2212yes—
117#10622264C2212yes—
118#10622262C2212yes—
119#10622262C2212yes—
120#10622260C2212yes—
121#10622260C2212yes—
122#10622259C2212yes—
123#10622259C2212yes—
124C22×D4×C11C2311yescharacteristic
125C22×D4×C11C2312yes—
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2312yes—
128C23×Dic11C2311yescharacteristic
129C23×Dic11C2311yescharacteristic
130C23×Dic11C2312yes—
131C23×Dic11C2312yes—
132C22×Dic22C2311yescharacteristic
133C22×Dic22C2312yes—
134C11×#121C2×C418yes—
135C4×D4×C11—42no—
136C11×#117—42no—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C2312yes—
147C2×C11×C22⋊C4C2311yescharacteristic
148C2×C11×C22⋊C4C2311yescharacteristic
149C2×C11×C22⋊C4C2312yes—
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C42×C11C2312yes—
153C2×C22⋊Dic11C2312yes—
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2312yes—
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2312yes—
159C2×C22⋊Dic11C2312yes—
160C2×C22⋊Dic11C2312yes—
161C2×C22⋊Dic11C2311yescharacteristic
162C2×C22⋊Dic11C2311yescharacteristic
163#66989C2×C4116yescomplemented
164#66989C2×C418yescomplemented
165#66988C2×C4116yescomplemented
166D4×Dic11—42no—
167D4×Dic11—44no—
168D4×Dic11C2×C418yescomplemented
169#66979C2×C418yescomplemented
170C2×C4⋊Dic11C2311yescharacteristic
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2312yes—
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2311yescharacteristic
176#66977C2×C418yescomplemented
177C2×Dic11⋊C4—44no—
178C2×Dic11⋊C4C2311yescharacteristic
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2311yescharacteristic
181C2×Dic11⋊C4C2311yescharacteristic
182C2×Dic11⋊C4C2311yescharacteristic
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2311yescharacteristic
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2311yescharacteristic
188C2×Dic11⋊C4C2312yes—
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2311yescharacteristic
191C2×Dic11⋊C4C2311yescharacteristic
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×C4×Dic11—42no—
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2312yes—
202C2×C4×Dic11C2312yes—
203C2×C4×Dic11C2312yes—
204C2×C4×Dic11C2312yes—
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210#66941C2×C418yescomplemented
211#66940—44no—
212#66940—42no—
213#66940C2×C418yescomplemented
214#66932C2×C4116yescomplemented
215#66931C2×C4116yescomplemented
216C4×Dic22—42no—
217C11×#95C2312yes—
218C11×#95C2312yes—
219C11×#95C2312yes—
220C11⋊#95C2311yescharacteristic
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2311yescharacteristic
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2311yescharacteristic
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2312yes—
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2311yescharacteristic
243#34422—111nomaximal, Sylow
244C24×C11C2411yescharacteristic
245C24×C11C2412yes—
246C2×D4×C11—22no—
247C2×D4×C11—22no—
248C2×D4×C11—42no—
249C2×D4×C11—42no—
250C2×D4×C11C22×C414yes—
251C2×D4×C11C22×C418yes—
252C22×C4×C11—22no—
253C22×C4×C11—22no—
254C22×C4×C11—42no—
255C22×C4×C11—42no—
256C22×C4×C11—42no—
257C22×C4×C11C22×C414yes—
258C22×C4×C11C2412yes—
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2412yes—
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2411yescharacteristic
265C22×C4×C11C2412yes—
266C22×C4×C11C2411yescharacteristic
267C22×Dic11—22no—
268C22×Dic11—22no—
269C22×Dic11—24no—
270C22×Dic11—41no—
271C22×Dic11—41no—
272C22×Dic11—42no—
273C22×Dic11—41no—
274C22×Dic11—42no—
275C22×Dic11—41no—
276C22×Dic11—42no—
277C22×Dic11—42no—
278C22×Dic11C22×C418yes—
279C22×Dic11C2412yes—
280C22×Dic11C2411yescharacteristic
281C22×Dic11C2411yescharacteristic
282C22×Dic11C2412yes—
283C22×Dic11C2411yescharacteristic
284C22×Dic11C2411yescharacteristic
285C22×Dic11C2412yes—
286C22×Dic11C2411yescharacteristic
287C22×Dic11C2412yes—
288C22×Dic11C2411yescharacteristic
289C22×Dic11C2411yescharacteristic
290C22×Dic11C2411yescharacteristic
291C2×Dic22—22no—
292C2×Dic22—22no—
293C2×Dic22—42no—
294C2×Dic22—42no—
295C2×Dic22C22×C414yes—
296C2×Dic22C22×C418yes—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4—42no—
300C11×C4⋊C4—41no—
301C11×C4⋊C4—41no—
302C11×C4⋊C4C22×C414yes—
303C11×C22⋊C4—42no—
304C11×C22⋊C4—42no—
305C11×C22⋊C4—42no—
306C11×C22⋊C4—41no—
307C11×C22⋊C4—41no—
308C11×C22⋊C4—42no—
309C11×C22⋊C4C22×C418yes—
310C42×C11—22no—
311C42×C11—22no—
312C42×C11—42no—
313C22⋊Dic11—24no—
314C22⋊Dic11—42no—
315C22⋊Dic11—42no—
316C22⋊Dic11—42no—
317C22⋊Dic11C22×C418yes—
318C22⋊Dic11C22×C418yes—
319C22⋊Dic11C22×C418yes—
320C22⋊Dic11C22×C418yes—
321C22⋊Dic11C22×C414yes—
322C22⋊Dic11C22×C414yes—
323C4⋊Dic11—22no—
324C4⋊Dic11—22no—
325C4⋊Dic11—42no—
326C4⋊Dic11C22×C414yes—
327C4⋊Dic11C22×C414yes—
328C4⋊Dic11C22×C414yes—
329Dic11⋊C4—22no—
330Dic11⋊C4—24no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333Dic11⋊C4—22no—
334Dic11⋊C4—42no—
335Dic11⋊C4—42no—
336Dic11⋊C4—42no—
337Dic11⋊C4—42no—
338Dic11⋊C4—41no—
339Dic11⋊C4—41no—
340Dic11⋊C4—41no—
341Dic11⋊C4—42no—
342Dic11⋊C4—41no—
343Dic11⋊C4C22×C418yes—
344Dic11⋊C4C22×C418yes—
345Dic11⋊C4C22×C418yes—
346C4×Dic11—24no—
347C4×Dic11—22no—
348C4×Dic11—22no—
349C4×Dic11—42no—
350C4×Dic11—42no—
351C4×Dic11—42no—
352C4×Dic11—42no—
353C4×Dic11—41no—
354C4×Dic11—41no—
355C4×Dic11—42no—
356C4×Dic11—42no—
357C4×Dic11C22×C418yes—
358C4×Dic11C22×C414yes—
359C4×Dic11C22×C414yes—
360C2×#542—111no—
361#2383—112no—
362#2378—112no—
363#2373—112no—
364#2369—111no—
365#2367—111no—
366#2367—111no—
367#2365—111no—
368#2360—112no—
369#2357—111no—
370#2356—111no—
371Q8×C4⋊C4—111no—
372D4×C4⋊C4—111no—
373#2337—112no—
374#2335—112no—
375#2326—112no—
376#2324D1111yescharacteristic
377#2323—111no—
378#2322—112no—
379#2314—111no—
380C4×C22⋊Q8—111no—
381C4×#121—111no—
382#2296—111no—
383C23×C11—21no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—21no—
387C23×C11—22no—
388C23×C11—21no—
389C23×C11—21no—
390C23×C11—22no—
391C23×C11—21no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—21no—
395C23×C11C23×C412yes—
396C23×C11C23×C414yes—
397C23×C11C2511yescharacteristic
398D4×C11—28no—
399D4×C11—48no—
400C2×C4×C11—22no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—22no—
404C2×C4×C11—28no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—21no—
412C2×C4×C11—21no—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—22no—
422C2×C4×C11—21no—
423C2×C4×C11—84no—
424C2×C4×C11C23×C414yes—
425C2×C4×C11C23×C412yes—
426C2×C4×C11C23×C412yes—
427C2×C4×C11H(5,𝔽2)12yes—
428C2×C4×C112−1+412yes—
429C2×Dic11—21no—
430C2×Dic11—21no—
431C2×Dic11—21no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—21no—
435C2×Dic11—21no—
436C2×Dic11—21no—
437C2×Dic11—22no—
438C2×Dic11—21no—
439C2×Dic11—21no—
440C2×Dic11—22no—
441C2×Dic11—21no—
442C2×Dic11—21no—
443C2×Dic11—21no—
444C2×Dic11—21no—
445C2×Dic11—22no—
446C2×Dic11—21no—
447C2×Dic11—21no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—21no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—21no—
454C2×Dic11—22no—
455C2×Dic11—21no—
456C2×Dic11—21no—
457C2×Dic11—48no—
458C2×Dic11—44no—
459C2×Dic11—44no—
460C2×Dic11—84no—
461C2×Dic11C23×C412yes—
462C2×Dic11C23×C412yes—
463C2×Dic11C23×C412yes—
464C2×Dic11C23×C414yes—
465C2×Dic11C23×C412yes—
466C2×Dic11C23×C414yes—
467C2×Dic11H(5,𝔽2)12yes—
468C2×Dic112−1+412yes—
469Dic22—28no—
470Dic22—48no—
471#542—1116no—
472C2×C4⋊Q8—111no—
473C2×#126—112no—
474C2×#124—112no—
475C2×#124—111no—
476C2×#123—112no—
477C2×C22⋊Q8—111no—
478C2×C22⋊Q8—112no—
479C2×#121C2×D1111yescharacteristic
480C2×C4×Q8—111no—
481C2×C4×Q8—112no—
482C2×C4×Q8—111no—
483C2×C4×Q8—111no—
484C2×C4×D4—111no—
485C2×C4×D4—112no—
486C2×C4×D4—111no—
487C2×C4×D4C2×D1111yescharacteristic
488C2×#117—111no—
489C2×#117C2×D1111yescharacteristic
490C22×C4⋊C4—112no—
491C22×C42—111no—
492#391—111no—
493#391—111no—
494#391—112no—
495#391—112no—
496#391—112no—
497#390—111no—
498#390C2×D1112yes—
499#390C2×D1111yescharacteristic
500#389—112no—
501#389—112no—
502#389—111no—
503#389—111no—
504#389—111no—
505#389—111no—
506#389—111no—
507#389—111no—
508#389—111no—
509#389—112no—
510#389—112no—
511#389C2×D1111yescharacteristic
512#388—112no—
513#388—112no—
514#388—112no—
515#388—112no—
516#388—112no—
517#388—112no—
518#388—112no—
519#388—112no—
520#388—112no—
521#388—112no—
522#388—112no—
523#388C2×D1112yes—
524#387—112no—
525#387—112no—
526#387—112no—
527#387—112no—
528#387—112no—
529#387—112no—
530#387—112no—
531#387—112no—
532#386—112no—
533#386C2×D1112yes—
534#385—112no—
535#385—112no—
536#385—111no—
537#385—112no—
538#385—111no—
539#385—112no—
540#385—112no—
541#385—111no—
542#385—111no—
543#385C2×D1112yes—
544#384—111no—
545#384—112no—
546#383—112no—
547#382—111no—
548#381—112no—
549#380—111no—
550#380—112no—
551#380C2×D1111yescharacteristic
552C4×C4⋊C4—111no—
553C4×C4⋊C4—111no—
554C4×C4⋊C4—111no—
555C4×C4⋊C4—111no—
556C4×C4⋊C4—111no—
557C4×C4⋊C4—112no—
558C4×C4⋊C4—111no—
559C4×C4⋊C4—111no—
560C4×C4⋊C4—111no—
561C4×C4⋊C4—111no—
562C4×C4⋊C4—112no—
563C4×C4⋊C4—112no—
564C4×C4⋊C4C2×D1111yescharacteristic
565C4×C22⋊C4—112no—
566C4×C22⋊C4—112no—
567C4×C22⋊C4—112no—
568C4×C22⋊C4—112no—
569C4×C22⋊C4—112no—
570#376—112no—
571C22×C11—22no—
572C22×C11—24no—
573C22×C11—22no—
574C22×C11—24no—
575C22×C11—24no—
576C22×C11—22no—
577C22×C11—42no—
578C22×C11—41no—
579C22×C11—42no—
580C22×C11—41no—
581C22×C11—41no—
582C22×C11—42no—
583C22×C11—41no—
584C22×C11—42no—
585C22×C11C24×C411yescharacteristic
586C22×C11C2×H(5,𝔽2)11yescharacteristic
587C22×C11C2×H(5,𝔽2)11yescharacteristic
588C22×C11C2×2−1+411yescharacteristic
589C22×C11C2×2−1+411yescharacteristic
590C22×C11#58511yescharacteristic
591C22×C11#58511yescharacteristic
592C4×C11—22no—
593C4×C11—24no—
594C4×C11—41no—
595C4×C11—41no—
596C4×C11—41no—
597C4×C11—42no—
598C4×C11—41no—
599C4×C11—42no—
600C4×C11#52014yes—
601Dic11—24no—
602Dic11—22no—
603Dic11—24no—
604Dic11—22no—
605Dic11—22no—
606Dic11—22no—
607Dic11—22no—
608Dic11—22no—
609Dic11—41no—
610Dic11—41no—
611Dic11—42no—
612Dic11—42no—
613C22×Q8—111no—
614C22×Q8—112no—
615C22×D4C22×D1111yescharacteristic
616C22×D4C22×D1112yes—
617C23×C4—112no—
618C23×C4—112no—
619C23×C4—111no—
620C23×C4—111no—
621C23×C4C22×D1111yescharacteristic
622C23×C4C22×D1112yes—
623C4⋊Q8—118no—
624#126—1116no—
625#124—118no—
626#124—1116no—
627#123—1116no—
628C22⋊Q8—118no—
629C22⋊Q8—1116no—
630#121C4×D1118yes—
631C4×Q8—118no—
632C4×Q8—442no—
633C4×Q8—442no—
634C4×Q8—444no—
635C4×D4—42no—
636C4×D4—118no—
637C4×D4—442no—
638C4×D4—444no—
639#117—42no—
640#117—118no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—111no—
643C2×C4⋊C4—111no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—112no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4—111no—
648C2×C4⋊C4—112no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—111no—
652C2×C4⋊C4—111no—
653C2×C4⋊C4—111no—
654C2×C4⋊C4—112no—
655C2×C4⋊C4—112no—
656C2×C4⋊C4—112no—
657C2×C4⋊C4—112no—
658C2×C4⋊C4—112no—
659C2×C4⋊C4—111no—
660C2×C4⋊C4—112no—
661C2×C4⋊C4—111no—
662C2×C4⋊C4—111no—
663C2×C4⋊C4—111no—
664C2×C4⋊C4—444no—
665C2×C4⋊C4C22×D1111yescharacteristic
666C2×C4⋊C4C22×D1111yescharacteristic
667C2×C4⋊C4C22×D1111yescharacteristic
668C2×C4⋊C4C22×D1111yescharacteristic
669C2×C4⋊C4C22×D1112yes—
670C2×C4⋊C4C22×D1111yescharacteristic
671C2×C22⋊C4—111no—
672C2×C22⋊C4—111no—
673C2×C22⋊C4—112no—
674C2×C22⋊C4—112no—
675C2×C22⋊C4—112no—
676C2×C22⋊C4—112no—
677C2×C22⋊C4—112no—
678C2×C22⋊C4—112no—
679C2×C22⋊C4—112no—
680C2×C22⋊C4—112no—
681C2×C22⋊C4C22×D1111yescharacteristic
682C2×C22⋊C4C22×D1111yescharacteristic
683C2×C22⋊C4C22×D1112yes—
684C2×C22⋊C4C22×D1112yes—
685C2×C22⋊C4C22×D1112yes—
686C2×C22⋊C4C22×D1112yes—
687C2×C22⋊C4C22×D1112yes—
688C2×C42—111no—
689C2×C42—111no—
690C2×C42—112no—
691C2×C42—112no—
692C2×C42—111no—
693C2×C42—111no—
694C2×C42—112no—
695C2×C42—112no—
696C2×C42—112no—
697C2×C42—112no—
698C2×C42—112no—
699C2×C42—111no—
700C2×C42—112no—
701C2×C42—111no—
702C2×C42—442no—
703C2×C42C22×D1111yescharacteristic
704C2×C42C22×D1111yescharacteristic
705C2×C42C22×D1112yes—
706#95—111no—
707#95—112no—
708#95—112no—
709#95—112no—
710#95—111no—
711#95—111no—
712#95—111no—
713#95—112no—
714#95—112no—
715#95—112no—
716#95—112no—
717#95—112no—
718#95—112no—
719#95—112no—
720#95—111no—
721#95—112no—
722#95—112no—
723#95—111no—
724#95—112no—
725#95—112no—
726#95—111no—
727#95—112no—
728#95—111no—
729#95C22×D1112yes—
730#95C22×D1112yes—
731#95C22×D1112yes—
732C2×C11—42no—
733C2×C11—44no—
734C2×C11C2×#52011yescharacteristic
735C2×C11C4×H(5,𝔽2)11yescharacteristic
736C2×C11C4×2−1+411yescharacteristic
737C2×C11#354111yescharacteristic
738C2×C11#354211yescharacteristic
739C2×C11#355011yescharacteristic
740C2×C11#355711yescharacteristic
741C24C23×D1111yescharacteristic
742C24C23×D1112yes—
743C2×Q8—114no—
744C2×Q8—118no—
745C2×Q8—222no—
746C2×Q8—222no—
747C2×Q8—442no—
748C2×Q8—442no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4C2×C4×D1114yes—
754C2×D4C2×C4×D1118yes—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—111no—
761C22×C4—111no—
762C22×C4—111no—
763C22×C4—111no—
764C22×C4—112no—
765C22×C4—111no—
766C22×C4—112no—
767C22×C4—111no—
768C22×C4—118no—
769C22×C4—112no—
770C22×C4—111no—
771C22×C4—111no—
772C22×C4—112no—
773C22×C4—222no—
774C22×C4—222no—
775C22×C4—224no—
776C22×C4—441no—
777C22×C4—441no—
778C22×C4—442no—
779C22×C4—441no—
780C22×C4—442no—
781C22×C4—441no—
782C22×C4—442no—
783C22×C4—442no—
784C22×C4C2×C4×D1114yes—
785C22×C4C23×D1112yes—
786C22×C4C23×D1111yescharacteristic
787C22×C4C23×D1111yescharacteristic
788C22×C4C23×D1111yescharacteristic
789C22×C4C23×D1112yes—
790C22×C4C23×D1111yescharacteristic
791C22×C4C23×D1112yes—
792C22×C4C23×D1111yescharacteristic
793C22×C4C23×D1111yescharacteristic
794C4⋊C4—22no—
795C4⋊C4—22no—
796C4⋊C4—41no—
797C4⋊C4—41no—
798C4⋊C4—42no—
799C4⋊C4—114no—
800C4⋊C4—114no—
801C4⋊C4—114no—
802C4⋊C4—118no—
803C4⋊C4—118no—
804C4⋊C4—118no—
805C4⋊C4—222no—
806C4⋊C4—224no—
807C4⋊C4—222no—
808C4⋊C4—222no—
809C4⋊C4—222no—
810C4⋊C4—222no—
811C4⋊C4—222no—
812C4⋊C4—442no—
813C4⋊C4—442no—
814C4⋊C4—442no—
815C4⋊C4—442no—
816C4⋊C4—442no—
817C4⋊C4—441no—
818C4⋊C4—441no—
819C4⋊C4—441no—
820C4⋊C4—442no—
821C4⋊C4—441no—
822C4⋊C4C2×C4×D1114yes—
823C22⋊C4—41no—
824C22⋊C4—41no—
825C22⋊C4—42no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—114no—
830C22⋊C4—114no—
831C22⋊C4—118no—
832C22⋊C4—118no—
833C22⋊C4—118no—
834C22⋊C4—118no—
835C22⋊C4—224no—
836C22⋊C4—442no—
837C22⋊C4—442no—
838C22⋊C4—442no—
839C22⋊C4C2×C4×D1118yes—
840C42—22no—
841C42—22no—
842C42—42no—
843C42—114no—
844C42—114no—
845C42—118no—
846C42—224no—
847C42—222no—
848C42—222no—
849C42—441no—
850C42—441no—
851C42—442no—
852C42—442no—
853C42—442no—
854C42—442no—
855C42—442no—
856C42—442no—
857C11#3442211yescharacteristic, complemented, Sylow
858C23—21no—
859C23—22no—
860C23—21no—
861C23—22no—
862C23—21no—
863C23—22no—
864C23—21no—
865C23—22no—
866C23—22no—
867C23—21no—
868C23—22no—
869C23—21no—
870C23C22×C4×D1112yes—
871C23C22×C4×D1114yes—
872C23C24×D1111yescharacteristic
873Q8—228no—
874Q8—448no—
875D4—28no—
876D4—48no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—28no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—22no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—84no—
901C2×C4—112no—
902C2×C4—112no—
903C2×C4—114no—
904C2×C4—112no—
905C2×C4—112no—
906C2×C4—114no—
907C2×C4—112no—
908C2×C4—112no—
909C2×C4—221no—
910C2×C4—221no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—221no—
914C2×C4—222no—
915C2×C4—221no—
916C2×C4—221no—
917C2×C4—221no—
918C2×C4—222no—
919C2×C4—221no—
920C2×C4—221no—
921C2×C4—221no—
922C2×C4—221no—
923C2×C4—221no—
924C2×C4—221no—
925C2×C4—221no—
926C2×C4—221no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—221no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—221no—
934C2×C4—221no—
935C2×C4—222no—
936C2×C4—221no—
937C2×C4—448no—
938C2×C4—444no—
939C2×C4—444no—
940C2×C4—884no—
941C2×C4C22×C4×D1114yes—
942C2×C4C22×C4×D1112yes—
943C2×C4C22×C4×D1112yes—
944C2×C4#6703712yes—
945C2×C4#6704312yes—
946C22—22no—
947C22—24no—
948C22—24no—
949C22—22no—
950C22—22no—
951C22—24no—
952C22—41no—
953C22—42no—
954C22—42no—
955C22—41no—
956C22—41no—
957C22—42no—
958C22—41no—
959C22—42no—
960C22C23×C4×D1111yescharacteristic
961C22C2×#6703711yescharacteristic
962C22C2×#6704311yescharacteristic
963C22D11×H(5,𝔽2)11yescharacteristic
964C22#1062345511yescharacteristic
965C22#1062345511yescharacteristic
966C22D11×2−1+411yescharacteristic
967C4—22no—
968C4—24no—
969C4—41no—
970C4—41no—
971C4—41no—
972C4—42no—
973C4—41no—
974C4—42no—
975C4—222no—
976C4—222no—
977C4—224no—
978C4—222no—
979C4—224no—
980C4—222no—
981C4—222no—
982C4—222no—
983C4—441no—
984C4—441no—
985C4—442no—
986C4—442no—
987C4#1062307714yes—
988C2—42no—
989C2—44no—
990C2C2×#1062307711yescharacteristic
991C2#1308182011yescharacteristic
992C2#1308182711yescharacteristic
993C2#1308289711yescharacteristic
994C2#1308293411yescharacteristic
995C2#1308302411yescharacteristic
996C2#1308312111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2324C2
socle, cosocleC23×C11C25
prime radicalC2×C11×#121C22
hypercenter#2324D11
hypocenterC11#34422
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. #13071804C2semidirect
3. #13071783C2semidirect
4. #13071733C2semidirect
5. #13071703C2semidirect
6. #13071689C2semidirect
7. #13071686C2semidirect
8. #13071669C2semidirect
9. #13071616C2semidirect
10. #13071588C2semidirect
11. #13071577C2semidirect
12. #13071530C2semidirect
13. D4×Dic11⋊C4C2semidirect
14. #13071425C2semidirect
15. #13071403C2semidirect
16. #13071326C2semidirect
17. #13071298C2semidirect
18. #13071290C2semidirect
19. #13071223C2semidirect
20. #13071144C2semidirect
22. #13071098C2semidirect
37. #10623134C4semidirect
163. #66989C2×C4semidirect
164. #66989C2×C4semidirect
165. #66988C2×C4semidirect
168. D4×Dic11C2×C4semidirect
169. #66979C2×C4semidirect
176. #66977C2×C4semidirect
210. #66941C2×C4semidirect
213. #66940C2×C4semidirect
214. #66932C2×C4semidirect
215. #66931C2×C4semidirect
857. C11#34422semidirect

Maximal subgroups

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

subgroupindex
C2×#106231342
#130718042
#130717832
#130717332
#130717032
#130716892
#130716862
#130716692
#130716162
#130715882
#130715772
#130715302
D4×Dic11⋊C42
#130714252
#130714032
#130713262
#130712982
#130712902
#130712232
#130711442
#121×Dic112
#130710982
C11×#23242
#3442211