Finite Group Databasebeta

← #14914399

Subgroups — #14914399

Order 2816.

2186 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623131C211yesmaximal, characteristic
2#13071751C212yesmaximal, complemented
3#13071749C212yesmaximal, complemented
4#13071743C212yesmaximal, complemented
5#13071731C212yesmaximal, complemented
6#13071588C212yesmaximal, complemented
7#13071554C212yesmaximal, complemented
8#13071506C212yesmaximal, complemented
9#13071474C212yesmaximal, complemented
10#13071311C211yesmaximal, characteristic
11#13071298C211yesmaximal, characteristic, complemented
12#13071294C211yesmaximal, characteristic, complemented
13#13071263C211yesmaximal, characteristic, complemented
14#13071253C211yesmaximal, characteristic, complemented
15#13071175C211yesmaximal, characteristic, complemented
16C4×#66943C211yesmaximal, characteristic, complemented
17#13071163C211yesmaximal, characteristic, complemented
18C4×#66989C211yesmaximal, characteristic, complemented
19#13071011C211yesmaximal, characteristic, complemented
20#13070980C211yesmaximal, characteristic, complemented
21#13070977C211yesmaximal, characteristic, complemented
22#117×Dic11C211yesmaximal, characteristic, complemented
23C11×#2324C211yesmaximal, characteristic
24C2×C11×#121C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C11×#117C2211yescharacteristic
27C2×#66989C2211yescharacteristic
28C2×#66988C2212yes—
29C2×D4×Dic11C2211yescharacteristic
30C2×D4×Dic11C2211yescharacteristic
31C2×D4×Dic11C2212yes—
32C2×#66979C2211yescharacteristic
33C2×#66977C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35#10623131C4116yescomplemented
36C2×#66943C2211yescharacteristic
37C2×#66940C2211yescharacteristic
38C2×#66940C2211yescharacteristic
39C2×#66932C2212yes—
40C2×#66930C2212yes—
41C2×C4×Dic22C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#390C2212yes—
44C11×#389C2211yescharacteristic
45C11×#388C2212yes—
46C11×#386C2212yes—
47C11×#385C2212yes—
48C11×#380C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50#10622834C2211yescharacteristic
51#10622834C2212yes—
52#10622833C2212yes—
53#10622825C2211yescharacteristic
54C4×C22⋊Dic11C2212yes—
55C4×C22⋊Dic11C2212yes—
56C4×C22⋊Dic11C2212yes—
57C2×C11⋊#95C2212yes—
58#10622598C2211yescharacteristic
59#10622591C2212yes—
60#10622591C2212yes—
61#10622591C2212yes—
62#10622590C2211yescharacteristic
63#10622590C2211yescharacteristic
64#10622590C2212yes—
65C4⋊C4×Dic11C2212yes—
66C4⋊C4×Dic11C2211yescharacteristic
67C4⋊C4×Dic11C2211yescharacteristic
68C4⋊C4×Dic11C2211yescharacteristic
69C4⋊C4×Dic11C2211yescharacteristic
70C4⋊C4×Dic11C2211yescharacteristic
71C4⋊C4×Dic11C2211yescharacteristic
72C4⋊C4×Dic11C2211yescharacteristic
73C4⋊C4×Dic11C2211yescharacteristic
74#10622587C2211yescharacteristic
75#10622586C2211yescharacteristic
76#10622585C2212yes—
77#10622564C2212yes—
78#10622563C2212yes—
79#10622558C2212yes—
80#10622558C2212yes—
81#10622558C2212yes—
82#10622558C2212yes—
83#10622558C2212yes—
84#10622557C2212yes—
85#10622557C2212yes—
86#10622557C2212yes—
87#10622557C2212yes—
88#10622557C2212yes—
89#10622556C2212yes—
90#10622556C2212yes—
91#10622555C2212yes—
92C22⋊C4×Dic11C2212yes—
93C22⋊C4×Dic11C2212yes—
94C22⋊C4×Dic11C2211yescharacteristic
95C22⋊C4×Dic11C2211yescharacteristic
96C22⋊C4×Dic11C2211yescharacteristic
97C22⋊C4×Dic11C2211yescharacteristic
98C22⋊C4×Dic11C2212yes—
99C22⋊C4×Dic11C2212yes—
100C22⋊C4×Dic11C2212yes—
101C4×C4⋊Dic11C2212yes—
102C4×C4⋊Dic11C2211yescharacteristic
103#10622545C2211yescharacteristic
104#10622545C2211yescharacteristic
105C4×Dic11⋊C4C2212yes—
106C4×Dic11⋊C4C2212yes—
107C4×Dic11⋊C4C2212yes—
108C42×Dic11C2211yescharacteristic
109C42×Dic11C2211yescharacteristic
110#10622542C2211yescharacteristic
111#10622541C2211yescharacteristic
112#10622268C2212yes—
113#10622268C2212yes—
114#10622268C2212yes—
115#10622267C2212yes—
116#10622266C2212yes—
117#10622264C2212yes—
118#10622264C2212yes—
119#10622262C2212yes—
120#10622262C2212yes—
121#10622261C2212yes—
122#10622261C2212yes—
123#10622260C2212yes—
124C22×D4×C11C2311yescharacteristic
125C22×D4×C11C2312yes—
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2312yes—
128C23×Dic11C2312yes—
129C23×Dic11C2312yes—
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C22×Dic22C2311yescharacteristic
133C11×#121C2×C418yes—
134C4×D4×C11—24no—
135C11×#117—24no—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C22⋊C4C2311yescharacteristic
143C2×C11×C22⋊C4C2311yescharacteristic
144C2×C11×C22⋊C4C2312yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C2312yes—
147C2×C11×C22⋊C4C2312yes—
148C2×C11×C22⋊C4C2312yes—
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2312yes—
151C2×C42×C11C2311yescharacteristic
152C2×C22⋊Dic11C2311yescharacteristic
153C2×C22⋊Dic11C2311yescharacteristic
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2312yes—
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2312yes—
159C2×C22⋊Dic11C2312yes—
160C2×C22⋊Dic11C2312yes—
161C2×C22⋊Dic11C2312yes—
162#66989C2×C418yes—
163#66988C2×C4116yescomplemented
164D4×Dic11—24no—
165D4×Dic11C2×C418yes—
166D4×Dic11C2×C4116yescomplemented
167#66979—24no—
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2311yescharacteristic
170C2×C4⋊Dic11C2311yescharacteristic
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2312yes—
173C2×C4⋊Dic11C2312yes—
174C2×C4⋊Dic11C2311yescharacteristic
175#66977C2×C418yescomplemented
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×C4×Dic11C2×C418yescomplemented
184C2×C4×Dic11C2312yes—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2311yescharacteristic
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2312yes—
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206#66943C2×C418yescomplemented
207#66940—24no—
208#66940C2×C418yescomplemented
209#66932C2×C4116yescomplemented
210#66930C2×C4116yescomplemented
211C4×Dic22—24no—
212C11×#95C2312yes—
213C11×#95C2312yes—
214C11×#95C2312yes—
215C11⋊#95C2312yes—
216C11⋊#95C2311yescharacteristic
217C11⋊#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2311yescharacteristic
223C11⋊#95C2312yes—
224C11⋊#95C2311yescharacteristic
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2311yescharacteristic
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2311yescharacteristic
240#34227—111nomaximal, Sylow
241C24×C11C2411yescharacteristic
242C24×C11C2412yes—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C2×D4×C11—42no—
246C2×D4×C11—42no—
247C2×D4×C11C22×C414yes—
248C2×D4×C11C22×C418yes—
249C22×C4×C11—22no—
250C22×C4×C11—22no—
251C22×C4×C11—24no—
252C22×C4×C11—42no—
253C22×C4×C11—42no—
254C22×C4×C11C22×C414yes—
255C22×C4×C11C2412yes—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2412yes—
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2412yes—
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2411yescharacteristic
263C22×C4×C11C2411yescharacteristic
264C22×Dic11—24no—
265C22×Dic11—41no—
266C22×Dic11—42no—
267C22×Dic11—41no—
268C22×Dic11—42no—
269C22×Dic11—41no—
270C22×Dic11—41no—
271C22×Dic11—42no—
272C22×Dic11—42no—
273C22×Dic11C22×C418yes—
274C22×Dic11C22×C414yes—
275C22×Dic11C22×C414yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2411yescharacteristic
279C22×Dic11C2411yescharacteristic
280C22×Dic11C2411yescharacteristic
281C22×Dic11C2411yescharacteristic
282C22×Dic11C2411yescharacteristic
283C22×Dic11C2411yescharacteristic
284C22×Dic11C2412yes—
285C22×Dic11C2412yes—
286C22×Dic11C2411yescharacteristic
287C22×Dic11C2411yescharacteristic
288C2×Dic22—22no—
289C2×Dic22—22no—
290C2×Dic22C22×C414yes—
291C11×C4⋊C4—22no—
292C11×C4⋊C4—22no—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—42no—
296C11×C4⋊C4C22×C414yes—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—24no—
300C11×C22⋊C4—42no—
301C11×C22⋊C4—42no—
302C11×C22⋊C4—42no—
303C11×C22⋊C4C22×C418yes—
304C42×C11—22no—
305C42×C11—42no—
306C42×C11#4114yes—
307C22⋊Dic11—22no—
308C22⋊Dic11—22no—
309C22⋊Dic11—24no—
310C22⋊Dic11—42no—
311C22⋊Dic11—42no—
312C22⋊Dic11—42no—
313C22⋊Dic11C22×C418yes—
314C22⋊Dic11C22×C418yes—
315C22⋊Dic11C22×C418yes—
316C22⋊Dic11C22×C418yes—
317C4⋊Dic11—22no—
318C4⋊Dic11—22no—
319C4⋊Dic11—22no—
320C4⋊Dic11—22no—
321C4⋊Dic11—42no—
322C4⋊Dic11C22×C418yes—
323C4⋊Dic11C22×C414yes—
324Dic11⋊C4—24no—
325Dic11⋊C4—24no—
326Dic11⋊C4—42no—
327Dic11⋊C4—42no—
328Dic11⋊C4C22×C418yes—
329Dic11⋊C4C22×C418yes—
330Dic11⋊C4C22×C418yes—
331C4×Dic11—24no—
332C4×Dic11—24no—
333C4×Dic11—22no—
334C4×Dic11—41no—
335C4×Dic11—42no—
336C4×Dic11—41no—
337C4×Dic11—42no—
338C4×Dic11—41no—
339C4×Dic11—41no—
340C4×Dic11—41no—
341C4×Dic11—42no—
342C4×Dic11—41no—
343C4×Dic11—41no—
344C4×Dic11—42no—
345C4×Dic11—41no—
346C4×Dic11—42no—
347C4×Dic11C22×C414yes—
348C4×Dic11C22×C418yes—
349C4×Dic11C22×C414yes—
350C4×Dic11C22×C414yes—
351C4×Dic11C22×C414yes—
352C4×Dic11#4114yes—
353C2×#529—111no—
354#2374—112no—
355#2374—112no—
356#2373—112no—
357#2373—112no—
358#2357—112no—
359#2353—112no—
360#2347—112no—
361#2343—112no—
362#2324—111no—
363#2324D1111yescharacteristic
364#2323—111no—
365#2323—111no—
366#2320—111no—
367#2319—111no—
368C4×#125—111no—
369C4×#125—111no—
370C4×#124—111no—
371C4×#124—111no—
372#2283—111no—
373#2276—111no—
374#2275—111no—
375C4×#117—111no—
376C23×C11—21no—
377C23×C11—22no—
378C23×C11—21no—
379C23×C11—22no—
380C23×C11—21no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—21no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—21no—
387C23×C11—21no—
388C23×C11C23×C414yes—
389C23×C11C23×C412yes—
390C23×C11C2511yescharacteristic
391D4×C11—28no—
392D4×C11—48no—
393C2×C4×C11—21no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—22no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—22no—
401C2×C4×C11—28no—
402C2×C4×C11—22no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—22no—
406C2×C4×C11—21no—
407C2×C4×C11—22no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—22no—
411C2×C4×C11—21no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—84no—
415C2×C4×C11C23×C412yes—
416C2×C4×C11C23×C414yes—
417C2×C4×C11C23×C412yes—
418C2×C4×C11C2×#4112yes—
419C2×C4×C11C2×#4112yes—
420C2×C4×C11C2×#4112yes—
421C2×C4×C11C2×#4112yes—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—21no—
425C2×Dic11—21no—
426C2×Dic11—21no—
427C2×Dic11—21no—
428C2×Dic11—21no—
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—21no—
438C2×Dic11—22no—
439C2×Dic11—21no—
440C2×Dic11—21no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—21no—
444C2×Dic11—21no—
445C2×Dic11—22no—
446C2×Dic11—21no—
447C2×Dic11—21no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—48no—
451C2×Dic11—44no—
452C2×Dic11—44no—
453C2×Dic11—84no—
454C2×Dic11C23×C412yes—
455C2×Dic11C23×C412yes—
456C2×Dic11C23×C412yes—
457C2×Dic11C23×C412yes—
458C2×Dic11C23×C414yes—
459C2×Dic11C23×C414yes—
460C2×Dic11C2×#4112yes—
461C2×Dic11C2×#4112yes—
462Dic22—28no—
463#529—1116no—
464C2×#126—112no—
465C2×#125—111no—
466C2×#124—111no—
467C2×#123—112no—
468C2×C22⋊Q8—111no—
469C2×#121C2×D1111yescharacteristic
470C2×C4×Q8—111no—
471C2×C4×Q8—111no—
472C2×C4×Q8—111no—
473C2×C4×D4—111no—
474C2×C4×D4—112no—
475C2×C4×D4—111no—
476C2×C4×D4C2×D1111yescharacteristic
477C2×#117—111no—
478C2×#117—112no—
479C2×#117C2×D1111yescharacteristic
480C22×C42—111no—
481#391—111no—
482#391—111no—
483#390—111no—
484#390—112no—
485#390C2×D1111yescharacteristic
486#390C2×D1112yes—
487#389—111no—
488#389—111no—
489#389—112no—
490#389—111no—
491#389—112no—
492#389C2×D1111yescharacteristic
493#388—112no—
494#388—112no—
495#388—112no—
496#388—112no—
497#388—112no—
498#388—112no—
499#388—112no—
500#388—112no—
501#388—112no—
502#388—112no—
503#388—112no—
504#388C2×D1112yes—
505#387—112no—
506#387—112no—
507#387—112no—
508#387—112no—
509#387—112no—
510#387—112no—
511#387—112no—
512#387—112no—
513#386—112no—
514#386C2×D1112yes—
515#385—112no—
516#385C2×D1112yes—
517#383—112no—
518#383—112no—
519#382—111no—
520#382—111no—
521#382—112no—
522#381—112no—
523#381—112no—
524#380—111no—
525#380—112no—
526#380C2×D1111yescharacteristic
527C4×C4⋊C4—111no—
528C4×C4⋊C4—111no—
529C4×C4⋊C4—112no—
530C4×C4⋊C4—111no—
531C4×C4⋊C4—111no—
532C4×C4⋊C4—111no—
533C4×C4⋊C4—111no—
534C4×C4⋊C4—111no—
535C4×C4⋊C4—111no—
536C4×C4⋊C4—111no—
537C4×C4⋊C4—112no—
538C4×C4⋊C4—112no—
539C4×C4⋊C4—112no—
540C4×C4⋊C4—112no—
541C4×C4⋊C4—112no—
542C4×C4⋊C4—112no—
543C4×C4⋊C4C2×D1111yescharacteristic
544C4×C22⋊C4—112no—
545C4×C22⋊C4—112no—
546C4×C22⋊C4—112no—
547C4×C22⋊C4—112no—
548C4×C22⋊C4—112no—
549C4×C22⋊C4—111no—
550C4×C22⋊C4—112no—
551C4×C22⋊C4—111no—
552C4×C22⋊C4—112no—
553C4×C22⋊C4—111no—
554C4×C22⋊C4—111no—
555C4×C22⋊C4—112no—
556#376—111no—
557#376—111no—
558#376—112no—
559#376—112no—
560C2×#95—112no—
561C43—111no—
562C43—111no—
563C22×C11—22no—
564C22×C11—24no—
565C22×C11—22no—
566C22×C11—24no—
567C22×C11—22no—
568C22×C11—24no—
569C22×C11—42no—
570C22×C11—41no—
571C22×C11—41no—
572C22×C11—42no—
573C22×C11—41no—
574C22×C11—42no—
575C22×C11—41no—
576C22×C11—42no—
577C22×C11C24×C411yescharacteristic
578C22×C11C22×#4111yescharacteristic
579C22×C11C22×#4111yescharacteristic
580C22×C11#58511yescharacteristic
581C22×C11#58511yescharacteristic
582C22×C11#58511yescharacteristic
583C22×C11#58511yescharacteristic
584C4×C11—22no—
585C4×C11—24no—
586C4×C11—22no—
587C4×C11—22no—
588C4×C11—41no—
589C4×C11—42no—
590C4×C11—42no—
591C4×C11—41no—
592C4×C11C4×#4114yes—
593Dic11—24no—
594Dic11—22no—
595Dic11—22no—
596Dic11—22no—
597Dic11—22no—
598Dic11—24no—
599Dic11—22no—
600Dic11—22no—
601Dic11—41no—
602Dic11—42no—
603Dic11—41no—
604Dic11—42no—
605C22×Q8—111no—
606C22×D4C22×D1111yescharacteristic
607C22×D4C22×D1112yes—
608C23×C4—112no—
609C23×C4—111no—
610C23×C4—111no—
611C23×C4—112no—
612C23×C4C22×D1111yescharacteristic
613C23×C4C22×D1112yes—
614#126—1116no—
615#125—118no—
616#124—118no—
617#123—1116no—
618C22⋊Q8—118no—
619#121C4×D1118yes—
620C4×Q8—118no—
621C4×Q8—224no—
622C4×Q8—224no—
623C4×D4—24no—
624C4×D4—118no—
625C4×D4—1116no—
626C4×D4—224no—
627#117—24no—
628#117—1116no—
629#117—224no—
630C2×C4⋊C4—112no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—111no—
633C2×C4⋊C4—112no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—111no—
636C2×C4⋊C4—111no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—111no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—112no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4C22×D1111yescharacteristic
645C2×C4⋊C4C22×D1111yescharacteristic
646C2×C4⋊C4C22×D1111yescharacteristic
647C2×C4⋊C4C22×D1111yescharacteristic
648C2×C4⋊C4C22×D1112yes—
649C2×C4⋊C4C22×D1111yescharacteristic
650C2×C22⋊C4—112no—
651C2×C22⋊C4—112no—
652C2×C22⋊C4—112no—
653C2×C22⋊C4—112no—
654C2×C22⋊C4—111no—
655C2×C22⋊C4—111no—
656C2×C22⋊C4—112no—
657C2×C22⋊C4—112no—
658C2×C22⋊C4—112no—
659C2×C22⋊C4—112no—
660C2×C22⋊C4C22×D1111yescharacteristic
661C2×C22⋊C4C22×D1111yescharacteristic
662C2×C22⋊C4C22×D1112yes—
663C2×C22⋊C4C22×D1112yes—
664C2×C22⋊C4C22×D1112yes—
665C2×C22⋊C4C22×D1112yes—
666C2×C22⋊C4C22×D1112yes—
667C2×C42—118no—
668C2×C42—111no—
669C2×C42—111no—
670C2×C42—112no—
671C2×C42—111no—
672C2×C42—111no—
673C2×C42—111no—
674C2×C42—111no—
675C2×C42—112no—
676C2×C42—112no—
677C2×C42—111no—
678C2×C42—111no—
679C2×C42—111no—
680C2×C42—111no—
681C2×C42—111no—
682C2×C42—111no—
683C2×C42—111no—
684C2×C42—111no—
685C2×C42—112no—
686C2×C42—112no—
687C2×C42—112no—
688C2×C42—112no—
689C2×C42—112no—
690C2×C42C22×D1111yescharacteristic
691C2×C42C22×D1112yes—
692C2×C42C22×D1111yescharacteristic
693#95—111no—
694#95—112no—
695#95—112no—
696#95—112no—
697#95—111no—
698#95—111no—
699#95—111no—
700#95—111no—
701#95—111no—
702#95—112no—
703#95—112no—
704#95—111no—
705#95—111no—
706#95—112no—
707#95—112no—
708#95—112no—
709#95—112no—
710#95—112no—
711#95—112no—
712#95—112no—
713#95—112no—
714#95—112no—
715#95—112no—
716#95—112no—
717#95—112no—
718#95C22×D1112yes—
719#95C22×D1112yes—
720#95C22×D1112yes—
721C2×C11—42no—
722C2×C11—44no—
723C2×C11C2×C4×#4111yescharacteristic
724C2×C11#342811yescharacteristic
725C2×C11#342811yescharacteristic
726C2×C11#351011yescharacteristic
727C2×C11#351011yescharacteristic
728C2×C11#351211yescharacteristic
729C2×C11#351211yescharacteristic
730C24C23×D1111yescharacteristic
731C24C23×D1112yes—
732C2×Q8—114no—
733C2×Q8—222no—
734C2×Q8—222no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4C2×C4×D1114yes—
740C2×D4C2×C4×D1118yes—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—24no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—111no—
747C22×C4—111no—
748C22×C4—111no—
749C22×C4—111no—
750C22×C4—111no—
751C22×C4—112no—
752C22×C4—112no—
753C22×C4—111no—
754C22×C4—114no—
755C22×C4—114no—
756C22×C4—118no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—111no—
760C22×C4—111no—
761C22×C4—224no—
762C22×C4—441no—
763C22×C4—441no—
764C22×C4—441no—
765C22×C4—442no—
766C22×C4—441no—
767C22×C4—442no—
768C22×C4—442no—
769C22×C4—442no—
770C22×C4C2×C4×D1114yes—
771C22×C4C23×D1112yes—
772C22×C4C23×D1111yescharacteristic
773C22×C4C23×D1111yescharacteristic
774C22×C4C23×D1112yes—
775C22×C4C23×D1112yes—
776C22×C4C23×D1111yescharacteristic
777C22×C4C23×D1111yescharacteristic
778C22×C4C23×D1111yescharacteristic
779C22×C4C23×D1111yescharacteristic
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—22no—
783C4⋊C4—22no—
784C4⋊C4—42no—
785C4⋊C4—118no—
786C4⋊C4—118no—
787C4⋊C4—114no—
788C4⋊C4—118no—
789C4⋊C4—118no—
790C4⋊C4—222no—
791C4⋊C4—222no—
792C4⋊C4—224no—
793C4⋊C4—224no—
794C4⋊C4—222no—
795C4⋊C4—222no—
796C4⋊C4—442no—
797C4⋊C4—442no—
798C4⋊C4—442no—
799C4⋊C4C2×C4×D1114yes—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—24no—
803C22⋊C4—42no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—118no—
807C22⋊C4—118no—
808C22⋊C4—118no—
809C22⋊C4—118no—
810C22⋊C4—222no—
811C22⋊C4—222no—
812C22⋊C4—224no—
813C22⋊C4—442no—
814C22⋊C4—442no—
815C22⋊C4—442no—
816C22⋊C4C2×C4×D1118yes—
817C42—22no—
818C42—42no—
819C42—114no—
820C42—114no—
821C42—114no—
822C42—114no—
823C42—118no—
824C42—114no—
825C42—224no—
826C42—224no—
827C42—222no—
828C42—441no—
829C42—442no—
830C42—441no—
831C42—441no—
832C42—441no—
833C42—442no—
834C42—442no—
835C42—441no—
836C42—441no—
837C42—442no—
838C42—441no—
839C42—442no—
840C42—441no—
841C42#434114yes—
842C11#3422711yescharacteristic, complemented, Sylow
843C23—21no—
844C23—22no—
845C23—21no—
846C23—22no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—22no—
855C23C22×C4×D1114yes—
856C23C22×C4×D1112yes—
857C23C24×D1111yescharacteristic
858Q8—228no—
859D4—28no—
860D4—48no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—22no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—22no—
868C2×C4—21no—
869C2×C4—28no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—84no—
883C2×C4—112no—
884C2×C4—112no—
885C2×C4—112no—
886C2×C4—112no—
887C2×C4—114no—
888C2×C4—114no—
889C2×C4—112no—
890C2×C4—112no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—221no—
894C2×C4—221no—
895C2×C4—221no—
896C2×C4—221no—
897C2×C4—221no—
898C2×C4—221no—
899C2×C4—221no—
900C2×C4—222no—
901C2×C4—221no—
902C2×C4—221no—
903C2×C4—221no—
904C2×C4—222no—
905C2×C4—221no—
906C2×C4—221no—
907C2×C4—222no—
908C2×C4—221no—
909C2×C4—221no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—221no—
913C2×C4—221no—
914C2×C4—221no—
915C2×C4—222no—
916C2×C4—221no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—444no—
920C2×C4—444no—
921C2×C4—448no—
922C2×C4—884no—
923C2×C4C22×C4×D1112yes—
924C2×C4C22×C4×D1114yes—
925C2×C4C22×C4×D1112yes—
926C2×C4C2×#434112yes—
927C2×C4C2×#434112yes—
928C2×C4C2×#434112yes—
929C2×C4#41×D1112yes—
930C22—22no—
931C22—24no—
932C22—22no—
933C22—24no—
934C22—22no—
935C22—24no—
936C22—42no—
937C22—41no—
938C22—42no—
939C22—41no—
940C22—41no—
941C22—42no—
942C22—41no—
943C22—42no—
944C22C23×C4×D1111yescharacteristic
945C22C22×#434111yescharacteristic
946C22C2×#41×D1111yescharacteristic
947C22#1062345511yescharacteristic
948C22#1062345511yescharacteristic
949C22#1062345511yescharacteristic
950C22#1062345711yescharacteristic
951C4—22no—
952C4—22no—
953C4—22no—
954C4—24no—
955C4—42no—
956C4—41no—
957C4—42no—
958C4—41no—
959C4—222no—
960C4—222no—
961C4—224no—
962C4—222no—
963C4—222no—
964C4—222no—
965C4—222no—
966C4—224no—
967C4—442no—
968C4—441no—
969C4—441no—
970C4—442no—
971C4C4×#434114yes—
972C2—42no—
973C2—44no—
974C2C2×C4×#434111yescharacteristic
975C2#1308181411yescharacteristic
976C2#1308181611yescharacteristic
977C2#1308250811yescharacteristic
978C2#1308251111yescharacteristic
979C2#1308253511yescharacteristic
980C2#1308253711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2324C2
socle, cosocleC23×C11C25
prime radicalC2×C11×#121C22
hypercenter#2324D11
hypocenterC11#34227
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. #13071751C2semidirect
3. #13071749C2semidirect
4. #13071743C2semidirect
5. #13071731C2semidirect
6. #13071588C2semidirect
7. #13071554C2semidirect
8. #13071506C2semidirect
9. #13071474C2semidirect
11. #13071298C2semidirect
12. #13071294C2semidirect
13. #13071263C2semidirect
14. #13071253C2semidirect
15. #13071175C2semidirect
16. C4×#66943C2semidirect
17. #13071163C2semidirect
18. C4×#66989C2semidirect
19. #13071011C2semidirect
20. #13070980C2semidirect
21. #13070977C2semidirect
22. #117×Dic11C2semidirect
35. #10623131C4semidirect
163. #66988C2×C4semidirect
166. D4×Dic11C2×C4semidirect
175. #66977C2×C4semidirect
183. C2×C4×Dic11C2×C4semidirect
206. #66943C2×C4semidirect
208. #66940C2×C4semidirect
209. #66932C2×C4semidirect
210. #66930C2×C4semidirect
842. C11#34227semidirect

Maximal subgroups

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

subgroupindex
C2×#106231312
#130717512
#130717492
#130717432
#130717312
#130715882
#130715542
#130715062
#130714742
#130713112
#130712982
#130712942
#130712632
#130712532
#130711752
C4×#669432
#130711632
C4×#669892
#130710112
#130709802
#130709772
#117×Dic112
C11×#23242
#3422711