Finite Group Databasebeta

← #14914365

Subgroups — #14914365

Order 2816.

2194 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic
2#13071715C212yesmaximal, complemented
3#13071709C212yesmaximal, complemented
4#13071646C212yesmaximal
5#13071640C212yesmaximal
6#13071578C212yesmaximal, complemented
7#13071535C212yesmaximal, complemented
8#13071506C212yesmaximal
9#13071498C212yesmaximal
10#13071300C211yesmaximal, characteristic
11#13071298C211yesmaximal, characteristic
12#13071294C211yesmaximal, characteristic
13#13071263C211yesmaximal, characteristic, complemented
14#13071261C211yesmaximal, characteristic, complemented
15#13071187C211yesmaximal, characteristic, complemented
16C4×#66941C211yesmaximal, characteristic, complemented
17#13071185C211yesmaximal, characteristic, complemented
18C4×#66997C211yesmaximal, characteristic, complemented
19#13071018C211yesmaximal, characteristic
20#13070981C211yesmaximal, characteristic, complemented
21#13070980C211yesmaximal, characteristic, complemented
22#117×Dic11C211yesmaximal, characteristic
23C11×#2323C211yesmaximal, characteristic
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C11×#117C2211yescharacteristic
27C2×Q8×Dic11C2211yescharacteristic
28C2×Q8×Dic11C2211yescharacteristic
29C2×#66997C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33#10623153C4116yescomplemented
34C2×#66942C2212yes—
35C2×#66941C2211yescharacteristic
36C2×#66940C2211yescharacteristic
37C2×#66940C2212yes—
38C2×#66940C2211yescharacteristic
39C2×#66940C2212yes—
40C2×#66931C2212yes—
41C2×#66930C2212yes—
42C2×#66930C2212yes—
43C2×C4×Dic22C2211yescharacteristic
44C2×C4×Dic22C2212yes—
45C11×#391C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#389C2212yes—
48C11×#388C2212yes—
49C11×#388C2212yes—
50C11×#387C2212yes—
51C11×#380C2211yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
53#10622843C2211yescharacteristic
54#10622825C2211yescharacteristic
55#10622598C2211yescharacteristic
56#10622598C2212yes—
57#10622594C2212yes—
58#10622591C2212yes—
59#10622591C2212yes—
60#10622590C2212yes—
61#10622589C2211yescharacteristic
62#10622589C2211yescharacteristic
63C4⋊C4×Dic11C2212yes—
64C4⋊C4×Dic11C2211yescharacteristic
65C4⋊C4×Dic11C2211yescharacteristic
66C4⋊C4×Dic11C2211yescharacteristic
67C4⋊C4×Dic11C2211yescharacteristic
68C4⋊C4×Dic11C2211yescharacteristic
69C4⋊C4×Dic11C2211yescharacteristic
70C4⋊C4×Dic11C2211yescharacteristic
71C4⋊C4×Dic11C2212yes—
72C4⋊C4×Dic11C2211yescharacteristic
73#10622587C2211yescharacteristic
74#10622586C2211yescharacteristic
75#10622585C2212yes—
76#10622585C2212yes—
77#10622585C2212yes—
78#10622585C2212yes—
79#10622564C2212yes—
80#10622564C2212yes—
81#10622558C2212yes—
82#10622558C2212yes—
83#10622557C2212yes—
84#10622557C2212yes—
85#10622555C2212yes—
86C22⋊C4×Dic11C2211yescharacteristic
87C22⋊C4×Dic11C2211yescharacteristic
88C22⋊C4×Dic11C2211yescharacteristic
89C22⋊C4×Dic11C2211yescharacteristic
90C4×C4⋊Dic11C2212yes—
91C4×C4⋊Dic11C2211yescharacteristic
92#10622545C2211yescharacteristic
93#10622545C2211yescharacteristic
94#10622545C2212yes—
95C4×Dic11⋊C4C2212yes—
96C4×Dic11⋊C4C2212yes—
97C4×Dic11⋊C4C2212yes—
98C4×Dic11⋊C4C2212yes—
99C4×Dic11⋊C4C2212yes—
100C42×Dic11C2211yescharacteristic
101C42×Dic11C2211yescharacteristic
102#10622542C2211yescharacteristic
103#10622541C2211yescharacteristic
104#10622268C2212yes—
105#10622268C2212yes—
106#10622267C2212yes—
107#10622266C2212yes—
108#10622264C2212yes—
109#10622264C2212yes—
110#10622263C2212yes—
111#10622263C2212yes—
112#10622262C2212yes—
113#10622262C2212yes—
114#10622262C2212yes—
115#10622262C2212yes—
116#10622262C2212yes—
117#10622261C2212yes—
118#10622260C2212yes—
119#10622260C2212yes—
120#10622260C2212yes—
121#10622260C2212yes—
122#10622259C2212yes—
123#10622259C2212yes—
124C22×Q8×C11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C23×Dic11C2311yescharacteristic
127C23×Dic11C2311yescharacteristic
128C22×Dic22C2312yes—
129C22×Dic22C2311yescharacteristic
130C11×C22⋊Q8C2×C418yes—
131C4×Q8×C11—24no—
132C11×#117—24no—
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2312yes—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C22⋊C4C2311yescharacteristic
142C2×C11×C22⋊C4C2311yescharacteristic
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2312yes—
147C2×C42×C11C2312yes—
148C2×C42×C11C2311yescharacteristic
149C2×C22⋊Dic11C2311yescharacteristic
150C2×C22⋊Dic11C2311yescharacteristic
151C2×C22⋊Dic11C2312yes—
152C2×C22⋊Dic11C2312yes—
153Q8×Dic11—24no—
154Q8×Dic11C2×C418yes—
155#66997C2×C418yes—
156#66979—24no—
157C2×C4⋊Dic11C2311yescharacteristic
158C2×C4⋊Dic11C2312yes—
159C2×C4⋊Dic11C2311yescharacteristic
160C2×C4⋊Dic11C2311yescharacteristic
161C2×C4⋊Dic11C2311yescharacteristic
162C2×C4⋊Dic11C2312yes—
163C2×C4⋊Dic11C2312yes—
164C2×C4⋊Dic11C2311yescharacteristic
165#66977C2×C418yes—
166C2×Dic11⋊C4C2312yes—
167C2×Dic11⋊C4C2312yes—
168C2×Dic11⋊C4C2312yes—
169C2×Dic11⋊C4C2312yes—
170C2×Dic11⋊C4C2312yes—
171C2×Dic11⋊C4C2312yes—
172C2×Dic11⋊C4C2312yes—
173C2×Dic11⋊C4C2312yes—
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×C4×Dic11C2×C418yes—
180C2×C4×Dic11C2311yescharacteristic
181C2×C4×Dic11C2312yes—
182C2×C4×Dic11C2311yescharacteristic
183C2×C4×Dic11C2311yescharacteristic
184C2×C4×Dic11C2311yescharacteristic
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2311yescharacteristic
187C2×C4×Dic11C2311yescharacteristic
188C2×C4×Dic11C2311yescharacteristic
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2312yes—
194C2×C4×Dic11C2312yes—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204#66942C2×C4116yes—
205#66941C2×C418yes—
206#66940—24no—
207#66940—44no—
208#66940C2×C418yes—
209#66940C2×C4116yes—
210#66931C2×C4116yes—
211#66930—44no—
212#66930C2×C4116yes—
213C4×Dic22—24no—
214C4×Dic22—44no—
215C11×#95C2312yes—
216C11×#95C2312yes—
217C11×#95C2312yes—
218C11×#95C2312yes—
219C11×#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2311yescharacteristic
230C11⋊#95C2312yes—
231C11⋊#95C2311yescharacteristic
232C11⋊#95C2312yes—
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2311yescharacteristic
243#34225—111nomaximal, Sylow
244C24×C11C2411yescharacteristic
245C2×Q8×C11—22no—
246C2×Q8×C11—22no—
247C2×Q8×C11C22×C414yes—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11C22×C414yes—
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2412yes—
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11C22×C414yes—
266C22×Dic11C22×C414yes—
267C22×Dic11C2411yescharacteristic
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C22×Dic11C2411yescharacteristic
271C22×Dic11C2411yescharacteristic
272C22×Dic11C2411yescharacteristic
273C22×Dic11C2412yes—
274C22×Dic11C2412yes—
275C22×Dic11C2411yescharacteristic
276C22×Dic11C2411yescharacteristic
277C22×Dic11C2411yescharacteristic
278C22×Dic11C2411yescharacteristic
279C2×Dic22—24no—
280C2×Dic22—24no—
281C2×Dic22—22no—
282C2×Dic22—22no—
283C2×Dic22C22×C418yes—
284C2×Dic22C22×C414yes—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—24no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—42no—
291C11×C4⋊C4C22×C414yes—
292C11×C4⋊C4C22×C418yes—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—42no—
296C11×C22⋊C4C22×C418yes—
297C42×C11—22no—
298C42×C11—24no—
299C42×C11—42no—
300C42×C11#4114yes—
301C22⋊Dic11—22no—
302C22⋊Dic11—22no—
303C22⋊Dic11—42no—
304C22⋊Dic11C22×C418yes—
305C4⋊Dic11—22no—
306C4⋊Dic11—22no—
307C4⋊Dic11—24no—
308C4⋊Dic11—22no—
309C4⋊Dic11—22no—
310C4⋊Dic11—42no—
311C4⋊Dic11C22×C418yes—
312C4⋊Dic11C22×C414yes—
313Dic11⋊C4—24no—
314Dic11⋊C4—24no—
315Dic11⋊C4—24no—
316Dic11⋊C4—24no—
317Dic11⋊C4—24no—
318Dic11⋊C4—24no—
319Dic11⋊C4—42no—
320Dic11⋊C4—42no—
321Dic11⋊C4C22×C418yes—
322Dic11⋊C4C22×C418yes—
323Dic11⋊C4C22×C418yes—
324Dic11⋊C4C22×C418yes—
325Dic11⋊C4C22×C418yes—
326C4×Dic11—24no—
327C4×Dic11—24no—
328C4×Dic11—22no—
329C4×Dic11—22no—
330C4×Dic11—22no—
331C4×Dic11—22no—
332C4×Dic11—22no—
333C4×Dic11—22no—
334C4×Dic11—22no—
335C4×Dic11—22no—
336C4×Dic11—24no—
337C4×Dic11—22no—
338C4×Dic11—42no—
339C4×Dic11—42no—
340C4×Dic11—42no—
341C4×Dic11—42no—
342C4×Dic11—42no—
343C4×Dic11C22×C418yes—
344C4×Dic11C22×C418yes—
345C4×Dic11C22×C414yes—
346C4×Dic11C22×C414yes—
347C4×Dic11C22×C414yes—
348C4×Dic11C22×C414yes—
349C4×Dic11#4114yes—
350C2×#533—111no—
351#2370—112no—
352#2370—112no—
353#2362—112no—
354#2362—112no—
355#2356—112no—
356#2351—112no—
357#2347—112no—
358#2346—112no—
359#2323—111no—
360#2323—111no—
361#2323—111no—
362#2323D1111yescharacteristic
363#2320—111no—
364#2320—111no—
365C4×C4⋊Q8—111no—
366C4×C4⋊Q8—111no—
367C4×C4⋊Q8—111no—
368C4×C4⋊Q8—111no—
369#2285—111no—
370#2276—111no—
371#2276—111no—
372C4×#117—111no—
373C23×C11—21no—
374C23×C11—21no—
375C23×C11—21no—
376C23×C11—21no—
377C23×C11—21no—
378C23×C11—21no—
379C23×C11C23×C412yes—
380C23×C11C2511yescharacteristic
381Q8×C11—28no—
382C2×C4×C11—22no—
383C2×C4×C11—21no—
384C2×C4×C11—22no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—22no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—22no—
392C2×C4×C11—28no—
393C2×C4×C11—22no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—22no—
397C2×C4×C11—21no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11C23×C412yes—
406C2×C4×C11C23×C414yes—
407C2×C4×C11C23×C414yes—
408C2×C4×C11C23×C412yes—
409C2×C4×C11C2×#4112yes—
410C2×C4×C11C2×#4112yes—
411C2×C4×C11C2×#4112yes—
412C2×C4×C11C2×#4112yes—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—21no—
416C2×Dic11—21no—
417C2×Dic11—22no—
418C2×Dic11—21no—
419C2×Dic11—21no—
420C2×Dic11—21no—
421C2×Dic11—22no—
422C2×Dic11—21no—
423C2×Dic11—21no—
424C2×Dic11—21no—
425C2×Dic11—28no—
426C2×Dic11—28no—
427C2×Dic11—22no—
428C2×Dic11—22no—
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—22no—
439C2×Dic11C23×C412yes—
440C2×Dic11C23×C412yes—
441C2×Dic11C23×C414yes—
442C2×Dic11C23×C414yes—
443C2×Dic11C23×C412yes—
444C2×Dic11C23×C412yes—
445C2×Dic11C2×#4112yes—
446C2×Dic11C2×#4112yes—
447C2×Dic11H(5,𝔽2)12yes—
448C2×Dic112−1+412yes—
449C2×Dic112−1+412yes—
450C2×Dic112−1+412yes—
451Dic22—28no—
452Dic22—216no—
453#533—1116no—
454C2×C4⋊Q8—111no—
455C2×C4⋊Q8—111no—
456C2×#125—112no—
457C2×C22⋊Q8—111no—
458C2×C22⋊Q8—112no—
459C2×C22⋊Q8C2×D1111yescharacteristic
460C2×C4×Q8—111no—
461C2×C4×Q8—111no—
462C2×C4×Q8—111no—
463C2×C4×Q8—112no—
464C2×C4×Q8—111no—
465C2×C4×Q8—112no—
466C2×C4×Q8—111no—
467C2×C4×Q8—112no—
468C2×C4×Q8C2×D1111yescharacteristic
469C2×#117—111no—
470C2×#117—112no—
471C2×#117—112no—
472C2×#117C2×D1111yescharacteristic
473C22×C42—111no—
474#391—111no—
475#391—111no—
476#391—111no—
477#391—112no—
478#391—112no—
479#391C2×D1111yescharacteristic
480#389—111no—
481#389—111no—
482#389—112no—
483#389—112no—
484#389—112no—
485#389—112no—
486#389—112no—
487#389—111no—
488#389—112no—
489#389—112no—
490#389—112no—
491#389—112no—
492#389C2×D1111yescharacteristic
493#389C2×D1112yes—
494#388—112no—
495#388—112no—
496#388—112no—
497#388—112no—
498#388—112no—
499#388—112no—
500#388C2×D1112yes—
501#388C2×D1112yes—
502#387—112no—
503#387—112no—
504#387—112no—
505#387—112no—
506#387—112no—
507#387—112no—
508#387—112no—
509#387C2×D1112yes—
510#384—111no—
511#384—111no—
512#383—112no—
513#383—112no—
514#382—112no—
515#382—112no—
516#382—112no—
517#380—111no—
518#380—112no—
519#380C2×D1111yescharacteristic
520C4×C4⋊C4—111no—
521C4×C4⋊C4—111no—
522C4×C4⋊C4—111no—
523C4×C4⋊C4—111no—
524C4×C4⋊C4—112no—
525C4×C4⋊C4—111no—
526C4×C4⋊C4—111no—
527C4×C4⋊C4—112no—
528C4×C4⋊C4—111no—
529C4×C4⋊C4—111no—
530C4×C4⋊C4—111no—
531C4×C4⋊C4—112no—
532C4×C4⋊C4—112no—
533C4×C4⋊C4—112no—
534C4×C4⋊C4—112no—
535C4×C4⋊C4—112no—
536C4×C4⋊C4—112no—
537C4×C4⋊C4—112no—
538C4×C4⋊C4—112no—
539C4×C4⋊C4—112no—
540C4×C4⋊C4—112no—
541C4×C4⋊C4—112no—
542C4×C4⋊C4C2×D1111yescharacteristic
543C4×C22⋊C4—111no—
544C4×C22⋊C4—111no—
545C4×C22⋊C4—111no—
546C4×C22⋊C4—111no—
547#376—111no—
548#376—112no—
549#376—111no—
550#376—112no—
551C43—111no—
552C43—111no—
553C22×C11—22no—
554C22×C11—22no—
555C22×C11—22no—
556C22×C11—41no—
557C22×C11—41no—
558C22×C11—41no—
559C22×C11—41no—
560C22×C11C24×C411yescharacteristic
561C22×C11C22×#4111yescharacteristic
562C22×C11C22×#4111yescharacteristic
563C22×C11C2×H(5,𝔽2)11yescharacteristic
564C22×C11C2×2−1+411yescharacteristic
565C22×C11C2×2−1+411yescharacteristic
566C22×C11C2×2−1+411yescharacteristic
567C4×C11—22no—
568C4×C11—24no—
569C4×C11—24no—
570C4×C11—22no—
571C4×C11—22no—
572C4×C11—41no—
573C4×C11—42no—
574C4×C11—41no—
575C4×C11—42no—
576C4×C11C4×#4114yes—
577Dic11—24no—
578Dic11—22no—
579Dic11—24no—
580Dic11—22no—
581Dic11—22no—
582Dic11—22no—
583Dic11—41no—
584Dic11—42no—
585Dic11—41no—
586Dic11—42no—
587Dic11#51914yes—
588Dic11#52014yes—
589C22×Q8—112no—
590C22×Q8—111no—
591C22×Q8C22×D1111yescharacteristic
592C23×C4—111no—
593C23×C4—111no—
594C23×C4C22×D1111yescharacteristic
595C4⋊Q8—118no—
596C4⋊Q8—118no—
597#125—1116no—
598C22⋊Q8—118no—
599C22⋊Q8—1116no—
600C22⋊Q8C4×D1118yes—
601C4×Q8—24no—
602C4×Q8—118no—
603C4×Q8—118no—
604C4×Q8—1116no—
605C4×Q8—224no—
606C4×Q8—224no—
607C4×Q8—224no—
608C4×Q8—444no—
609C4×Q8—444no—
610#117—24no—
611#117—1116no—
612#117—224no—
613#117—444no—
614C2×C4⋊C4—112no—
615C2×C4⋊C4—112no—
616C2×C4⋊C4—112no—
617C2×C4⋊C4—112no—
618C2×C4⋊C4—112no—
619C2×C4⋊C4—112no—
620C2×C4⋊C4—111no—
621C2×C4⋊C4—112no—
622C2×C4⋊C4—112no—
623C2×C4⋊C4—111no—
624C2×C4⋊C4—111no—
625C2×C4⋊C4—111no—
626C2×C4⋊C4—111no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—112no—
630C2×C4⋊C4—112no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—112no—
633C2×C4⋊C4—112no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4C22×D1111yescharacteristic
636C2×C4⋊C4C22×D1111yescharacteristic
637C2×C4⋊C4C22×D1111yescharacteristic
638C2×C4⋊C4C22×D1111yescharacteristic
639C2×C4⋊C4C22×D1112yes—
640C2×C4⋊C4C22×D1112yes—
641C2×C4⋊C4C22×D1112yes—
642C2×C4⋊C4C22×D1111yescharacteristic
643C2×C22⋊C4—112no—
644C2×C22⋊C4—111no—
645C2×C22⋊C4—111no—
646C2×C22⋊C4—112no—
647C2×C22⋊C4C22×D1111yescharacteristic
648C2×C22⋊C4C22×D1111yescharacteristic
649C2×C22⋊C4C22×D1112yes—
650C2×C22⋊C4C22×D1112yes—
651C2×C42—118no—
652C2×C42—111no—
653C2×C42—112no—
654C2×C42—112no—
655C2×C42—111no—
656C2×C42—111no—
657C2×C42—111no—
658C2×C42—111no—
659C2×C42—111no—
660C2×C42—111no—
661C2×C42—111no—
662C2×C42—112no—
663C2×C42—112no—
664C2×C42—112no—
665C2×C42—111no—
666C2×C42—111no—
667C2×C42—111no—
668C2×C42—111no—
669C2×C42—111no—
670C2×C42—111no—
671C2×C42—112no—
672C2×C42—112no—
673C2×C42—112no—
674C2×C42—112no—
675C2×C42—112no—
676C2×C42C22×D1111yescharacteristic
677C2×C42C22×D1112yes—
678C2×C42C22×D1112yes—
679C2×C42C22×D1111yescharacteristic
680#95—111no—
681#95—111no—
682#95—111no—
683#95—111no—
684#95—111no—
685#95—111no—
686#95—111no—
687#95—111no—
688#95—112no—
689#95—112no—
690#95—112no—
691#95—112no—
692#95—112no—
693#95—112no—
694#95—112no—
695#95—112no—
696#95—112no—
697#95—112no—
698#95—112no—
699#95—112no—
700#95—112no—
701#95—112no—
702#95—112no—
703#95C22×D1112yes—
704#95C22×D1112yes—
705#95C22×D1112yes—
706#95C22×D1112yes—
707#95C22×D1112yes—
708C2×C11—42no—
709C2×C11C2×C4×#4111yescharacteristic
710C2×C11C2×#51911yescharacteristic
711C2×C11C2×#52011yescharacteristic
712C2×C11#350911yescharacteristic
713C2×C11#350911yescharacteristic
714C2×C11#351111yescharacteristic
715C2×C11#351111yescharacteristic
716C24C23×D1111yescharacteristic
717C2×Q8—22no—
718C2×Q8—22no—
719C2×Q8—118no—
720C2×Q8—114no—
721C2×Q8—224no—
722C2×Q8—224no—
723C2×Q8—222no—
724C2×Q8—222no—
725C2×Q8C2×C4×D1114yes—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—111no—
729C22×C4—111no—
730C22×C4—114no—
731C22×C4—114no—
732C22×C4—111no—
733C22×C4—111no—
734C22×C4—111no—
735C22×C4—112no—
736C22×C4—112no—
737C22×C4—111no—
738C22×C4—111no—
739C22×C4—112no—
740C22×C4—111no—
741C22×C4—112no—
742C22×C4—222no—
743C22×C4—222no—
744C22×C4—222no—
745C22×C4—222no—
746C22×C4C2×C4×D1114yes—
747C22×C4C23×D1111yescharacteristic
748C22×C4C23×D1111yescharacteristic
749C22×C4C23×D1112yes—
750C22×C4C23×D1112yes—
751C22×C4C23×D1112yes—
752C22×C4C23×D1112yes—
753C22×C4C23×D1111yescharacteristic
754C22×C4C23×D1111yescharacteristic
755C22×C4C23×D1111yescharacteristic
756C22×C4C23×D1111yescharacteristic
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—24no—
760C4⋊C4—22no—
761C4⋊C4—22no—
762C4⋊C4—42no—
763C4⋊C4—118no—
764C4⋊C4—118no—
765C4⋊C4—118no—
766C4⋊C4—118no—
767C4⋊C4—118no—
768C4⋊C4—118no—
769C4⋊C4—114no—
770C4⋊C4—222no—
771C4⋊C4—222no—
772C4⋊C4—224no—
773C4⋊C4—224no—
774C4⋊C4—224no—
775C4⋊C4—224no—
776C4⋊C4—224no—
777C4⋊C4—224no—
778C4⋊C4—224no—
779C4⋊C4—222no—
780C4⋊C4—222no—
781C4⋊C4—442no—
782C4⋊C4—442no—
783C4⋊C4—442no—
784C4⋊C4C2×C4×D1118yes—
785C4⋊C4C2×C4×D1114yes—
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—42no—
789C22⋊C4—118no—
790C22⋊C4—222no—
791C22⋊C4—222no—
792C22⋊C4—442no—
793C22⋊C4C2×C4×D1118yes—
794C42—22no—
795C42—24no—
796C42—42no—
797C42—114no—
798C42—114no—
799C42—114no—
800C42—114no—
801C42—118no—
802C42—118no—
803C42—114no—
804C42—224no—
805C42—224no—
806C42—222no—
807C42—222no—
808C42—222no—
809C42—222no—
810C42—222no—
811C42—222no—
812C42—222no—
813C42—222no—
814C42—224no—
815C42—222no—
816C42—442no—
817C42—442no—
818C42—442no—
819C42—442no—
820C42—442no—
821C42#434114yes—
822C11#3422511yescharacteristic, complemented, Sylow
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23C22×C4×D1112yes—
830C23C24×D1111yescharacteristic
831Q8—28no—
832Q8—2216no—
833Q8—228no—
834C2×C4—22no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—22no—
844C2×C4—28no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—112no—
858C2×C4—112no—
859C2×C4—112no—
860C2×C4—112no—
861C2×C4—112no—
862C2×C4—112no—
863C2×C4—112no—
864C2×C4—112no—
865C2×C4—114no—
866C2×C4—114no—
867C2×C4—112no—
868C2×C4—112no—
869C2×C4—228no—
870C2×C4—228no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—221no—
874C2×C4—221no—
875C2×C4—222no—
876C2×C4—221no—
877C2×C4—221no—
878C2×C4—221no—
879C2×C4—221no—
880C2×C4—221no—
881C2×C4—221no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—221no—
885C2×C4—221no—
886C2×C4—222no—
887C2×C4—221no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—221no—
891C2×C4—221no—
892C2×C4—221no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4C22×C4×D1112yes—
896C2×C4C22×C4×D1114yes—
897C2×C4C22×C4×D1114yes—
898C2×C4C22×C4×D1112yes—
899C2×C4C2×#434112yes—
900C2×C4C2×#434112yes—
901C2×C4C2×#434112yes—
902C2×C4#41×D1112yes—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22C23×C4×D1111yescharacteristic
911C22C22×#434111yescharacteristic
912C22C2×#41×D1111yescharacteristic
913C22D11×H(5,𝔽2)11yescharacteristic
914C22D11×2−1+411yescharacteristic
915C22D11×2−1+411yescharacteristic
916C22D11×2−1+411yescharacteristic
917C4—22no—
918C4—22no—
919C4—22no—
920C4—24no—
921C4—24no—
922C4—41no—
923C4—42no—
924C4—41no—
925C4—42no—
926C4—114no—
927C4—114no—
928C4—222no—
929C4—222no—
930C4—224no—
931C4—222no—
932C4—222no—
933C4—224no—
934C4—441no—
935C4—441no—
936C4—442no—
937C4—442no—
938C4C4×#434114yes—
939C2—42no—
940C2C2×C4×#434111yescharacteristic
941C2D11×#51911yescharacteristic
942C2D11×#52011yescharacteristic
943C2#1308249811yescharacteristic
944C2#1308250111yescharacteristic
945C2#1308252111yescharacteristic
946C2#1308252511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2323C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenter#2323D11
hypocenterC11#34225
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. #13071715C2semidirect
3. #13071709C2semidirect
6. #13071578C2semidirect
7. #13071535C2semidirect
13. #13071263C2semidirect
14. #13071261C2semidirect
15. #13071187C2semidirect
16. C4×#66941C2semidirect
17. #13071185C2semidirect
18. C4×#66997C2semidirect
20. #13070981C2semidirect
21. #13070980C2semidirect
33. #10623153C4semidirect
822. C11#34225semidirect

Maximal subgroups

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

subgroupindex
C2×#106231532
#130717152
#130717092
#130716462
#130716402
#130715782
#130715352
#130715062
#130714982
#130713002
#130712982
#130712942
#130712632
#130712612
#130711872
C4×#669412
#130711852
C4×#669972
#130710182
#130709812
#130709802
#117×Dic112
C11×#23232
#3422511