Finite Group Databasebeta

← #14914290

Subgroups — #14914290

Order 2816.

2330 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623211C211yesmaximal, characteristic
2#13071743C212yesmaximal, complemented
3#13071731C212yesmaximal, complemented
4#13071611C212yesmaximal, complemented
5#13071607C212yesmaximal, complemented
6#13071551C212yesmaximal, complemented
7#13071522C212yesmaximal, complemented
8#13071498C212yesmaximal, complemented
9#13071474C212yesmaximal, complemented
10#13071357C211yesmaximal, characteristic, complemented
11#13071355C211yesmaximal, characteristic, complemented
12#13071329C211yesmaximal, characteristic, complemented
13#13071261C211yesmaximal, characteristic, complemented
14#13071253C211yesmaximal, characteristic, complemented
15#13071154C211yesmaximal, characteristic, complemented
16C4×#66999C211yesmaximal, characteristic, complemented
17#13071132C211yesmaximal, characteristic
18C4×#66991C211yesmaximal, characteristic
19#13071021C211yesmaximal, characteristic, complemented
20#13070981C211yesmaximal, characteristic, complemented
21#13070977C211yesmaximal, characteristic, complemented
22D11×#376C211yesmaximal, characteristic, complemented
23C11×#2326C211yesmaximal, characteristic, complemented
24C2×C11×#124C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×#66999C2211yescharacteristic
28C2×Q8×Dic11C2211yescharacteristic
29C2×Q8×Dic11C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×D4×Dic11C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C2×C4×C22⋊D11C2212yes—
34#10623211C4116yescomplemented
35C2×#66945C2212yes—
36C2×#66936C2212yes—
37C2×(C22⋊D11)⋊C4C2212yes—
38C2×(C22⋊D11)⋊C4C2212yes—
39C2×#66932C2212yes—
40C2×#66930C2212yes—
41C2×C42×D11C2211yescharacteristic
42C2×C42×D11C2211yescharacteristic
43C2×C42×D11C2211yescharacteristic
44C2×#66923C2211yescharacteristic
45C11×#391C2211yescharacteristic
46C11×#390C2211yescharacteristic
47C11×#388C2212yes—
48C11×#388C2212yes—
49C11×#385C2212yes—
50C11×#385C2212yes—
51C11×#384C2211yescharacteristic
52C11×#376C2211yescharacteristic
53#10622843C2211yescharacteristic
54#10622834C2211yescharacteristic
55C4×C22⋊Dic11C2212yes—
56C4×C22⋊Dic11C2212yes—
57C2×C11⋊#95C2212yes—
58#10622602C2212yes—
59#10622600C2211yescharacteristic
60#10622600C2211yescharacteristic
61#10622600C2212yes—
62#10622591C2212yes—
63#10622591C2212yes—
64#10622591C2212yes—
65#10622590C2212yes—
66C4⋊C4×Dic11C2211yescharacteristic
67C4⋊C4×Dic11C2211yescharacteristic
68C4⋊C4×Dic11C2212yes—
69C4⋊C4×Dic11C2212yes—
70C4⋊C4×Dic11C2212yes—
71C4⋊C4×Dic11C2211yescharacteristic
72C4⋊C4×Dic11C2211yescharacteristic
73#10622586C2211yescharacteristic
74#10622586C2211yescharacteristic
75#10622585C2212yes—
76#10622585C2212yes—
77#10622569C2212yes—
78#10622569C2212yes—
79#10622564C2212yes—
80#10622564C2212yes—
81#10622563C2212yes—
82#10622563C2212yes—
83#10622558C2212yes—
84#10622558C2212yes—
85#10622557C2212yes—
86#10622557C2212yes—
87#10622556C2212yes—
88#10622555C2212yes—
89C22⋊C4×Dic11C2212yes—
90C22⋊C4×Dic11C2212yes—
91C22⋊C4×Dic11C2212yes—
92C4×(C2×D11)⋊C4C2212yes—
93#10622548C2211yescharacteristic
94C4×C4⋊Dic11C2211yescharacteristic
95C4×C4⋊Dic11C2211yescharacteristic
96C4×C4⋊Dic11C2212yes—
97#10622545C2211yescharacteristic
98#10622545C2211yescharacteristic
99#10622545C2211yescharacteristic
100#10622545C2212yes—
101C4×Dic11⋊C4C2212yes—
102#10622541C2211yescharacteristic
103#10622541C2211yescharacteristic
104#10622281C2212yes—
105#10622279C2212yes—
106D11×#95C2211yescharacteristic
107D11×#95C2211yescharacteristic
108D11×#95C2211yescharacteristic
109D11×#95C2211yescharacteristic
110#10622268C2212yes—
111#10622268C2212yes—
112#10622268C2212yes—
113#10622267C2212yes—
114#10622266C2212yes—
115#10622264C2212yes—
116#10622263C2212yes—
117#10622262C2212yes—
118#10622261C2211yescharacteristic
119#10622261C2211yescharacteristic
120#10622261C2211yescharacteristic
121#10622261C2211yescharacteristic
122#10622260C2212yes—
123#10622260C2212yes—
124C22×Q8×C11C2311yescharacteristic
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2312yes—
127C22×C22⋊D11C2312yes—
128C23×Dic11C2312yes—
129C23×Dic11C2312yes—
130C22×C4×D11C2311yescharacteristic
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×C4×D11C2311yescharacteristic
134C22×C4×D11C2311yescharacteristic
135C22×C4×D11C2311yescharacteristic
136C22×C4×D11C2311yescharacteristic
137C11×#124C2×C418yescomplemented
138C4×Q8×C11—24no—
139C4×D4×C11—24no—
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C2312yes—
147C2×C11×C22⋊C4C2312yes—
148C2×C11×C22⋊C4C2312yes—
149C2×C11×C22⋊C4C2312yes—
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2312yes—
152C2×C42×C11C2311yescharacteristic
153C2×C42×C11C2311yescharacteristic
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2312yes—
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2312yes—
159#66999C2×C418yescomplemented
160Q8×Dic11—24no—
161Q8×Dic11C2×C418yescomplemented
162#66991C2×C418yes—
163D4×Dic11—24no—
164D4×Dic11C2×C418yescomplemented
165C4×C22⋊D11—44no—
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2311yescharacteristic
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2312yes—
173C2×C4⋊Dic11C2312yes—
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2311yescharacteristic
176C2×C4⋊Dic11C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×C4×Dic11C2311yescharacteristic
185C2×C4×Dic11C2311yescharacteristic
186C2×C4×Dic11C2311yescharacteristic
187C2×C4×Dic11C2311yescharacteristic
188C2×C4×Dic11C2311yescharacteristic
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2312yes—
194C2×C4×Dic11C2312yes—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2311yescharacteristic
201#66945—44no—
202#66936C2×C4116yescomplemented
203(C22⋊D11)⋊C4—44no—
204(C22⋊D11)⋊C4C2×C4116yescomplemented
205#66932C2×C4116yescomplemented
206#66930C2×C4116yescomplemented
207C42×D11—24no—
208C42×D11—24no—
209C42×D11C2×C418yescomplemented
210#66923C2×C418yescomplemented
211C11×#95C2311yescharacteristic
212C11×#95C2311yescharacteristic
213C11×#95C2311yescharacteristic
214C11×#95C2311yescharacteristic
215C11×#95C2312yes—
216C11×#95C2312yes—
217C11⋊#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2311yescharacteristic
220C11⋊#95C2311yescharacteristic
221C11⋊#95C2311yescharacteristic
222C11⋊#95C2311yescharacteristic
223C11⋊#95C2311yescharacteristic
224C11⋊#95C2311yescharacteristic
225C11⋊#95C2311yescharacteristic
226C11⋊#95C2311yescharacteristic
227C11⋊#95C2311yescharacteristic
228C11⋊#95C2311yescharacteristic
229C11⋊#95C2311yescharacteristic
230C11⋊#95C2311yescharacteristic
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243#34220—111nomaximal, Sylow
244C24×C11C2412yes—
245C23×D11C2411yescharacteristic
246C2×Q8×C11—22no—
247C2×Q8×C11—22no—
248C2×Q8×C11C22×C414yes—
249C2×D4×C11—22no—
250C2×D4×C11—22no—
251C2×D4×C11C22×C414yes—
252C22×C4×C11—24no—
253C22×C4×C11—42no—
254C22×C4×C11—42no—
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2412yes—
257C22×C4×C11C2412yes—
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2412yes—
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2411yescharacteristic
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2411yescharacteristic
265C2×C22⋊D11—24no—
266C2×C22⋊D11—24no—
267C2×C22⋊D11C22×C418yes—
268C22×Dic11—24no—
269C22×Dic11—42no—
270C22×Dic11—42no—
271C22×Dic11—42no—
272C22×Dic11—42no—
273C22×Dic11C22×C418yes—
274C22×Dic11C2411yescharacteristic
275C22×Dic11C2411yescharacteristic
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2411yescharacteristic
279C22×Dic11C2411yescharacteristic
280C22×Dic11C2411yescharacteristic
281C22×Dic11C2412yes—
282C22×Dic11C2412yes—
283C22×Dic11C2411yescharacteristic
284C22×Dic11C2411yescharacteristic
285C2×C4×D11—22no—
286C2×C4×D11—22no—
287C2×C4×D11—22no—
288C2×C4×D11—22no—
289C2×C4×D11—22no—
290C2×C4×D11—22no—
291C2×C4×D11—22no—
292C2×C4×D11—22no—
293C2×C4×D11—22no—
294C2×C4×D11—22no—
295C2×C4×D11—22no—
296C2×C4×D11—22no—
297C2×C4×D11—41no—
298C2×C4×D11—41no—
299C2×C4×D11—41no—
300C2×C4×D11—41no—
301C2×C4×D11—41no—
302C2×C4×D11—41no—
303C2×C4×D11C22×C414yes—
304C2×C4×D11C22×C414yes—
305C2×C4×D11C22×C414yes—
306C11×C4⋊C4—22no—
307C11×C4⋊C4—24no—
308C11×C4⋊C4—22no—
309C11×C4⋊C4—42no—
310C11×C4⋊C4—42no—
311C11×C22⋊C4—24no—
312C11×C22⋊C4—42no—
313C11×C22⋊C4—42no—
314C11×C22⋊C4C22×C418yes—
315C11×C22⋊C4C22×C418yes—
316C42×C11—22no—
317C42×C11—24no—
318C42×C11C22×C414yes—
319C42×C11#4114yes—
320C22⋊Dic11—24no—
321C22⋊Dic11—42no—
322C22⋊Dic11—42no—
323C22⋊Dic11C22×C418yes—
324C22⋊Dic11C22×C418yes—
325(C2×D11)⋊C4—24no—
326(C2×D11)⋊C4—24no—
327(C2×D11)⋊C4C22×C418yes—
328C4⋊Dic11—24no—
329C4⋊Dic11—22no—
330C4⋊Dic11—22no—
331C4⋊Dic11—42no—
332C4⋊Dic11—42no—
333C4⋊Dic11C22×C414yes—
334C4⋊Dic11C22×C414yes—
335C4⋊Dic11C22×C418yes—
336Dic11⋊C4—42no—
337Dic11⋊C4—42no—
338Dic11⋊C4—42no—
339Dic11⋊C4—42no—
340Dic11⋊C4C22×C418yes—
341Dic11⋊C4C22×C418yes—
342Dic11⋊C4C22×C418yes—
343C4×Dic11—22no—
344C4×Dic11—22no—
345C4×Dic11—24no—
346C4×Dic11—22no—
347C4×Dic11—22no—
348C4×Dic11—22no—
349C4×Dic11—42no—
350C4×Dic11—42no—
351C4×Dic11—42no—
352C4×Dic11—42no—
353C4×Dic11—42no—
354C4×Dic11—42no—
355C4×Dic11C22×C414yes—
356C4×Dic11C22×C414yes—
357C4×Dic11C22×C414yes—
358C4×Dic11C22×C418yes—
359C4×Dic11#4114yes—
360C2×#529—111no—
361#2373—112no—
362#2373—112no—
363#2359—112no—
364#2359—112no—
365#2353—112no—
366#2349—112no—
367#2346—112no—
368#2343—112no—
369#2330—111no—
370#2330—111no—
371#2326—111no—
372#2326D1111yescharacteristic, complemented
373#2320—111no—
374#2319—111no—
375C4×C22⋊Q8—111no—
376C4×C22⋊Q8—111no—
377C4×#121—111no—
378C4×#121—111no—
379#2285—111no—
380#2276—111no—
381#2275—111no—
382C2×#376—111no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11C23×C414yes—
390C23×C11C2511yescharacteristic
391C22×D11—21no—
392C22×D11—21no—
393C22×D11—21no—
394C22×D11—21no—
395C22×D11C23×C412yes—
396C22×D11H(5,𝔽2)12yes—
397C22×D112−1+412yes—
398Q8×C11—28no—
399D4×C11—28no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—21no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—22no—
419C2×C4×C11—21no—
420C2×C4×C11—22no—
421C2×C4×C11—21no—
422C2×C4×C11—84no—
423C2×C4×C11C23×C412yes—
424C2×C4×C11C23×C412yes—
425C2×C4×C11C23×C414yes—
426C2×C4×C11C23×C412yes—
427C2×C4×C11C2×#4112yes—
428C2×C4×C11C2×#4112yes—
429C2×C4×C11C2×#4112yes—
430C2×C4×C11C2×#4112yes—
431C22⋊D11—216no—
432C2×Dic11—21no—
433C2×Dic11—21no—
434C2×Dic11—21no—
435C2×Dic11—22no—
436C2×Dic11—21no—
437C2×Dic11—21no—
438C2×Dic11—21no—
439C2×Dic11—22no—
440C2×Dic11—21no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—21no—
444C2×Dic11—21no—
445C2×Dic11—21no—
446C2×Dic11—21no—
447C2×Dic11—21no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—21no—
453C2×Dic11—21no—
454C2×Dic11—22no—
455C2×Dic11—21no—
456C2×Dic11—22no—
457C2×Dic11—21no—
458C2×Dic11—48no—
459C2×Dic11—84no—
460C2×Dic11C23×C412yes—
461C2×Dic11C23×C412yes—
462C2×Dic11C23×C412yes—
463C2×Dic11C23×C414yes—
464C2×Dic11C23×C414yes—
465C2×Dic11C2×#4112yes—
466C2×Dic11C2×#4112yes—
467C4×D11—28no—
468C4×D11—28no—
469C4×D11—44no—
470C4×D11—44no—
471C4×D11—44no—
472C4×D11—44no—
473C4×D11—44no—
474#529—1116no—
475C2×#126—112no—
476C2×#125—111no—
477C2×#124C2×D1111yescharacteristic
478C2×#123—112no—
479C2×C22⋊Q8—111no—
480C2×#121—111no—
481C2×C4×Q8—111no—
482C2×C4×Q8—111no—
483C2×C4×Q8C2×D1111yescharacteristic
484C2×C4×D4—111no—
485C2×C4×D4—111no—
486C2×C4×D4—112no—
487C2×C4×D4—112no—
488C2×C4×D4—112no—
489C2×C4×D4C2×D1111yescharacteristic
490C2×#117—112no—
491C2×#117—112no—
492C22×C42—111no—
493C22×C42—111no—
494C22×C42—111no—
495#391—111no—
496#391C2×D1111yescharacteristic
497#390—111no—
498#390C2×D1111yescharacteristic
499#389—111no—
500#389—111no—
501#389—112no—
502#389—112no—
503#389—111no—
504#389—111no—
505#389—112no—
506#389—112no—
507#388—112no—
508#388—112no—
509#388—112no—
510#388—112no—
511#388—112no—
512#388—112no—
513#388C2×D1112yes—
514#388C2×D1112yes—
515#387—112no—
516#387—112no—
517#387—112no—
518#387—112no—
519#387—112no—
520#387—112no—
521#387—112no—
522#387—112no—
523#386—112no—
524#386—112no—
525#385—112no—
526#385—112no—
527#385—112no—
528#385—112no—
529#385C2×D1112yes—
530#385C2×D1112yes—
531#384—111no—
532#384C2×D1111yescharacteristic
533#383—112no—
534#382—112no—
535#382—112no—
536#381—112no—
537#380—112no—
538#380—111no—
539#380—111no—
540#380—112no—
541C4×C4⋊C4—111no—
542C4×C4⋊C4—111no—
543C4×C4⋊C4—111no—
544C4×C4⋊C4—111no—
545C4×C4⋊C4—112no—
546C4×C4⋊C4—112no—
547C4×C4⋊C4—112no—
548C4×C4⋊C4—111no—
549C4×C4⋊C4—111no—
550C4×C4⋊C4—112no—
551C4×C4⋊C4—112no—
552C4×C4⋊C4—112no—
553C4×C22⋊C4—112no—
554C4×C22⋊C4—112no—
555C4×C22⋊C4—112no—
556C4×C22⋊C4—112no—
557C4×C22⋊C4—112no—
558C4×C22⋊C4—112no—
559C4×C22⋊C4—112no—
560#376—111no—
561#376—111no—
562#376—112no—
563#376—111no—
564#376—111no—
565#376—111no—
566#376—111no—
567#376—111no—
568#376C2×D1111yescharacteristic
569C2×#95—112no—
570C2×#95—111no—
571C2×#95—111no—
572C2×#95—111no—
573C2×#95—111no—
574C22×C11—24no—
575C22×C11—24no—
576C22×C11—24no—
577C22×C11—42no—
578C22×C11—42no—
579C22×C11—42no—
580C22×C11—42no—
581C22×C11C24×C411yescharacteristic
582C22×C11C22×#4111yescharacteristic
583C22×C11C22×#4111yescharacteristic
584C22×C11C2×H(5,𝔽2)11yescharacteristic
585C22×C11C2×2−1+411yescharacteristic
586C22×C11#58511yescharacteristic
587C22×C11#58511yescharacteristic
588C2×D11—22no—
589C2×D11—22no—
590C2×D11—22no—
591C2×D11—22no—
592C2×D11—22no—
593C2×D11—22no—
594C2×D11#52014yes—
595C4×C11—24no—
596C4×C11—22no—
597C4×C11—22no—
598C4×C11—22no—
599C4×C11—22no—
600C4×C11—42no—
601C4×C11—42no—
602C4×C11—41no—
603C4×C11—41no—
604C4×C11C4×#4114yes—
605Dic11—22no—
606Dic11—22no—
607Dic11—24no—
608Dic11—22no—
609Dic11—24no—
610Dic11—22no—
611Dic11—22no—
612Dic11—41no—
613Dic11—42no—
614Dic11—42no—
615Dic11—41no—
616C22×Q8C22×D1111yescharacteristic
617C22×D4—112no—
618C22×D4C22×D1111yescharacteristic
619C23×C4—112no—
620C23×C4—111no—
621C23×C4—111no—
622C23×C4—111no—
623C23×C4—112no—
624C23×C4—111no—
625C23×C4—111no—
626C23×C4—111no—
627C23×C4—111no—
628C23×C4C22×D1112yes—
629#126—1116no—
630#125—118no—
631#124C4×D1118yescomplemented
632#123—1116no—
633C22⋊Q8—118no—
634#121—118no—
635C4×Q8—24no—
636C4×Q8—118no—
637C4×Q8—224no—
638C4×D4—24no—
639C4×D4—118no—
640C4×D4—1116no—
641C4×D4—224no—
642C4×D4—444no—
643C4×D4—444no—
644#117—1116no—
645#117—444no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4—112no—
648C2×C4⋊C4—111no—
649C2×C4⋊C4—112no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—112no—
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—112no—
660C2×C4⋊C4—112no—
661C2×C4⋊C4C22×D1111yescharacteristic
662C2×C4⋊C4C22×D1111yescharacteristic
663C2×C4⋊C4C22×D1112yes—
664C2×C4⋊C4C22×D1112yes—
665C2×C4⋊C4C22×D1112yes—
666C2×C22⋊C4—112no—
667C2×C22⋊C4—112no—
668C2×C22⋊C4—112no—
669C2×C22⋊C4—112no—
670C2×C22⋊C4—112no—
671C2×C22⋊C4—112no—
672C2×C22⋊C4—112no—
673C2×C22⋊C4—112no—
674C2×C22⋊C4C22×D1112yes—
675C2×C22⋊C4C22×D1112yes—
676C2×C22⋊C4C22×D1112yes—
677C2×C22⋊C4C22×D1112yes—
678C2×C22⋊C4C22×D1112yes—
679C2×C42—111no—
680C2×C42—112no—
681C2×C42—111no—
682C2×C42—111no—
683C2×C42—111no—
684C2×C42—118no—
685C2×C42—112no—
686C2×C42—111no—
687C2×C42—111no—
688C2×C42—111no—
689C2×C42—111no—
690C2×C42—111no—
691C2×C42—112no—
692C2×C42—112no—
693C2×C42—112no—
694C2×C42—112no—
695C2×C42—112no—
696C2×C42—112no—
697C2×C42—224no—
698C2×C42—224no—
699C2×C42C22×D1112yes—
700C2×C42C22×D1111yescharacteristic
701C2×C42C22×D1111yescharacteristic
702C2×C42C22×D1111yescharacteristic
703#95—111no—
704#95—111no—
705#95—111no—
706#95—111no—
707#95—111no—
708#95—111no—
709#95—111no—
710#95—111no—
711#95—111no—
712#95—111no—
713#95—111no—
714#95—111no—
715#95—112no—
716#95—112no—
717#95—112no—
718#95—112no—
719#95—112no—
720#95—112no—
721#95—112no—
722#95—112no—
723#95—112no—
724#95—112no—
725#95—112no—
726#95—112no—
727#95—112no—
728#95—112no—
729#95C22×D1111yescharacteristic
730#95C22×D1111yescharacteristic
731#95C22×D1111yescharacteristic
732#95C22×D1111yescharacteristic
733#95C22×D1112yes—
734#95C22×D1112yes—
735C2×C11—44no—
736C2×C11C2×C4×#4111yescharacteristic
737C2×C11C2×#52011yescharacteristic
738C2×C11#342811yescharacteristic
739C2×C11#349411yescharacteristic
740C2×C11#349411yescharacteristic
741C2×C11#349511yescharacteristic
742C2×C11#349511yescharacteristic
743D11—24no—
744C24—111no—
745C24C23×D1112yes—
746C2×Q8—22no—
747C2×Q8—22no—
748C2×Q8C2×C4×D1114yes—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—118no—
752C2×D4—224no—
753C2×D4—224no—
754C2×D4C2×C4×D1114yes—
755C22×C4—24no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—111no—
759C22×C4—111no—
760C22×C4—111no—
761C22×C4—111no—
762C22×C4—111no—
763C22×C4—112no—
764C22×C4—112no—
765C22×C4—118no—
766C22×C4—114no—
767C22×C4—114no—
768C22×C4—114no—
769C22×C4—111no—
770C22×C4—111no—
771C22×C4—112no—
772C22×C4—112no—
773C22×C4—222no—
774C22×C4—222no—
775C22×C4—222no—
776C22×C4—222no—
777C22×C4—222no—
778C22×C4—222no—
779C22×C4—222no—
780C22×C4—222no—
781C22×C4—224no—
782C22×C4—222no—
783C22×C4—222no—
784C22×C4—222no—
785C22×C4—222no—
786C22×C4—441no—
787C22×C4—441no—
788C22×C4—441no—
789C22×C4—441no—
790C22×C4—441no—
791C22×C4—441no—
792C22×C4—442no—
793C22×C4—442no—
794C22×C4—442no—
795C22×C4—442no—
796C22×C4C23×D1111yescharacteristic
797C22×C4C23×D1112yes—
798C22×C4C23×D1112yes—
799C22×C4C23×D1111yescharacteristic
800C22×C4C23×D1112yes—
801C22×C4C23×D1111yescharacteristic
802C22×C4C23×D1111yescharacteristic
803C22×C4C23×D1111yescharacteristic
804C22×C4C23×D1111yescharacteristic
805C22×C4C23×D1111yescharacteristic
806C4⋊C4—22no—
807C4⋊C4—24no—
808C4⋊C4—22no—
809C4⋊C4—42no—
810C4⋊C4—42no—
811C4⋊C4—118no—
812C4⋊C4—118no—
813C4⋊C4—114no—
814C4⋊C4—118no—
815C4⋊C4—114no—
816C4⋊C4—118no—
817C4⋊C4—224no—
818C4⋊C4—222no—
819C4⋊C4—222no—
820C4⋊C4—442no—
821C4⋊C4—442no—
822C4⋊C4—442no—
823C4⋊C4—442no—
824C4⋊C4—442no—
825C4⋊C4—442no—
826C22⋊C4—24no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—118no—
830C22⋊C4—118no—
831C22⋊C4—118no—
832C22⋊C4—224no—
833C22⋊C4—224no—
834C22⋊C4—224no—
835C22⋊C4—442no—
836C22⋊C4—442no—
837C22⋊C4C2×C4×D1118yes—
838C22⋊C4C2×C4×D1118yes—
839C42—24no—
840C42—22no—
841C42—114no—
842C42—114no—
843C42—114no—
844C42—118no—
845C42—114no—
846C42—222no—
847C42—222no—
848C42—224no—
849C42—222no—
850C42—222no—
851C42—222no—
852C42—442no—
853C42—442no—
854C42—442no—
855C42—442no—
856C42—442no—
857C42—442no—
858C42C2×C4×D1114yes—
859C42#434114yes—
860C11#3422011yescharacteristic, complemented, Sylow
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—112no—
868C23—112no—
869C23—112no—
870C23—221no—
871C23—221no—
872C23—221no—
873C23—221no—
874C23C22×C4×D1114yes—
875C23C24×D1111yescharacteristic
876Q8—28no—
877D4—28no—
878D4—2216no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—21no—
896C2×C4—22no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—84no—
902C2×C4—112no—
903C2×C4—112no—
904C2×C4—112no—
905C2×C4—114no—
906C2×C4—114no—
907C2×C4—112no—
908C2×C4—112no—
909C2×C4—228no—
910C2×C4—221no—
911C2×C4—221no—
912C2×C4—221no—
913C2×C4—222no—
914C2×C4—221no—
915C2×C4—221no—
916C2×C4—222no—
917C2×C4—221no—
918C2×C4—221no—
919C2×C4—221no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—221no—
923C2×C4—221no—
924C2×C4—228no—
925C2×C4—221no—
926C2×C4—221no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—221no—
932C2×C4—221no—
933C2×C4—221no—
934C2×C4—222no—
935C2×C4—221no—
936C2×C4—222no—
937C2×C4—444no—
938C2×C4—444no—
939C2×C4—444no—
940C2×C4—444no—
941C2×C4—444no—
942C2×C4—448no—
943C2×C4—884no—
944C2×C4C22×C4×D1112yes—
945C2×C4C22×C4×D1112yes—
946C2×C4C22×C4×D1114yes—
947C2×C4C22×C4×D1112yes—
948C2×C4C2×#434112yes—
949C2×C4C2×#434112yes—
950C2×C4C2×#434112yes—
951C2×C4#41×D1112yes—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—114no—
960C22—222no—
961C22—222no—
962C22—222no—
963C22—222no—
964C22—222no—
965C22—222no—
966C22C23×C4×D1111yescharacteristic
967C22C22×#434111yescharacteristic
968C22C2×#41×D1111yescharacteristic
969C22D11×H(5,𝔽2)11yescharacteristic
970C22#1062345511yescharacteristic
971C22D11×2−1+411yescharacteristic
972C22#1062345711yescharacteristic
973C4—24no—
974C4—22no—
975C4—22no—
976C4—22no—
977C4—22no—
978C4—42no—
979C4—42no—
980C4—41no—
981C4—41no—
982C4—222no—
983C4—222no—
984C4—224no—
985C4—222no—
986C4—224no—
987C4—222no—
988C4—222no—
989C4—441no—
990C4—442no—
991C4—442no—
992C4—441no—
993C4C4×#434114yes—
994C2—44no—
995C2—224no—
996C2C2×C4×#434111yescharacteristic
997C2D11×#52011yescharacteristic
998C2#1308181611yescharacteristic
999C2#1308234811yescharacteristic
1000C2#1308234911yescharacteristic
1001C2#1308236511yescharacteristic
1002C2#1308236611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2326C2
socle, cosocleC23×C11C25
prime radicalC2×#66991C22
hypercenter#2326D11
hypocenterC11#34220
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2326

Complements

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

NH ≅ G/Ntype
2. #13071743C2semidirect
3. #13071731C2semidirect
4. #13071611C2semidirect
5. #13071607C2semidirect
6. #13071551C2semidirect
7. #13071522C2semidirect
8. #13071498C2semidirect
9. #13071474C2semidirect
10. #13071357C2semidirect
11. #13071355C2semidirect
12. #13071329C2semidirect
13. #13071261C2semidirect
14. #13071253C2semidirect
15. #13071154C2semidirect
16. C4×#66999C2semidirect
19. #13071021C2semidirect
20. #13070981C2semidirect
21. #13070977C2semidirect
22. D11×#376C2semidirect
23. C11×#2326C2semidirect
34. #10623211C4semidirect
137. C11×#124C2×C4semidirect
159. #66999C2×C4semidirect
161. Q8×Dic11C2×C4semidirect
164. D4×Dic11C2×C4semidirect
202. #66936C2×C4semidirect
204. (C22⋊D11)⋊C4C2×C4semidirect
205. #66932C2×C4semidirect
206. #66930C2×C4semidirect
209. C42×D11C2×C4semidirect
210. #66923C2×C4semidirect
372. #2326D11semidirect
631. #124C4×D11semidirect
860. C11#34220semidirect

Maximal subgroups

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

subgroupindex
C2×#106232112
#130717432
#130717312
#130716112
#130716072
#130715512
#130715222
#130714982
#130714742
#130713572
#130713552
#130713292
#130712612
#130712532
#130711542
C4×#669992
#130711322
C4×#669912
#130710212
#130709812
#130709772
D11×#3762
C11×#23262
#3422011