Finite Group Databasebeta

← #14925360

Subgroups — #14925360

Order 2816.

1826 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074164C212yesmaximal, complemented
2#13074149C212yesmaximal, complemented
3#13074134C212yesmaximal, complemented
4#13074119C212yesmaximal, complemented
5#13073216C211yesmaximal, characteristic, complemented
6#13073163C211yesmaximal, characteristic, complemented
7#13073018C211yesmaximal, characteristic, complemented
8#13072964C211yesmaximal, characteristic
9#13072480C211yesmaximal, characteristic, complemented
10#13072412C211yesmaximal, characteristic, complemented
11#13072184C211yesmaximal, characteristic
12#13072115C211yesmaximal, characteristic, complemented
13#13071917C212yesmaximal, complemented
14#13071876C212yesmaximal, complemented
15C4×#66943C211yesmaximal, characteristic, complemented
16C4×#67000C211yesmaximal, characteristic, complemented
17C4×#66983C211yesmaximal, characteristic
18#13071109C212yesmaximal, complemented
19#13071079C212yesmaximal, complemented
20#13071077C211yesmaximal, characteristic, complemented
21C4×Q8×Dic11C211yesmaximal, characteristic, complemented
22C4×#66979C211yesmaximal, characteristic, complemented
23C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
27C2×#67000C2211yescharacteristic
28C2×Q8×Dic11C2211yescharacteristic
29C2×Q8×Dic11C2211yescharacteristic
30C2×#66983C2211yescharacteristic
31C2×C4×C22⋊D11C2212yes—
32C2×#66979C2211yescharacteristic
33C2×#66979C2211yescharacteristic
34C2×#66943C2211yescharacteristic
35C2×C4×D44C2211yescharacteristic
36C2×#66925C2212yes—
37C11×#391C2211yescharacteristic
38C11×#389C2211yescharacteristic
39C11×#387C2212yes—
40C11×#385C2212yes—
41C11×#380C2211yescharacteristic
42C4×C11×C4⋊C4C2212yes—
43C4×C11×C4⋊C4C2211yescharacteristic
44C4×C11×C22⋊C4C2212yes—
45#10622843C2211yescharacteristic
46#10622826C2212yes—
47#10622825C2211yescharacteristic
48C4×C22⋊Dic11C2211yescharacteristic
49C4×C22⋊Dic11C2211yescharacteristic
50C4×C22⋊Dic11C2211yescharacteristic
51C4×C22⋊Dic11C2211yescharacteristic
52#10622607C2212yes—
53#10622606C2212yes—
54#10622603C2212yes—
55#10622603C2212yes—
56#10622603C2212yes—
57#10622603C2212yes—
58#10622601C2211yescharacteristic
59#10622601C2211yescharacteristic
60#10622601C2211yescharacteristic
61#10622599C2212yes—
62#10622598C2211yescharacteristic
63#10622595C2212yes—
64#10622591C2212yes—
65#10622591C2212yes—
66#10622590C2211yescharacteristic
67#10622590C2211yescharacteristic
68C4⋊C4×Dic11C2211yescharacteristic
69C4⋊C4×Dic11C2211yescharacteristic
70C4⋊C4×Dic11C2212yes—
71C4⋊C4×Dic11C2212yes—
72#10622586C2211yescharacteristic
73#10622586C2211yescharacteristic
74#10622586C2211yescharacteristic
75#10622574C2212yes—
76#10622574C2212yes—
77#10622570C2212yes—
78#10622570C2212yes—
79#10622566C2212yes—
80#10622566C2212yes—
81#10622557C2212yes—
82#10622557C2212yes—
83#10622553C2212yes—
84#10622552C2211yescharacteristic
85C4×(C2×D11)⋊C4C2212yes—
86C4×(C2×D11)⋊C4C2212yes—
87C4×(C2×D11)⋊C4C2212yes—
88C4×(C2×D11)⋊C4C2212yes—
89C4×C4⋊Dic11C2212yes—
90C4×C4⋊Dic11C2212yes—
91C4×C4⋊Dic11C2211yescharacteristic
92C4×C4⋊Dic11C2211yescharacteristic
93C4×C4⋊Dic11C2211yescharacteristic
94C4×C4⋊Dic11C2211yescharacteristic
95C4×C4⋊Dic11C2211yescharacteristic
96#10622545C2211yescharacteristic
97#10622545C2211yescharacteristic
98C4×Dic11⋊C4C2212yes—
99C42×Dic11C2212yes—
100C42×Dic11C2211yescharacteristic
101C42×Dic11C2211yescharacteristic
102#10622541C2211yescharacteristic
103#10622290C2212yes—
104#10622288C2212yes—
105#10622287C2212yes—
106#10622287C2212yes—
107#10622283C2212yes—
108#10622283C2212yes—
109#10622283C2212yes—
110#10622283C2212yes—
111#10622282C2212yes—
112#10622282C2212yes—
113C11⋊#401C2212yes—
114#10622274C2212yes—
115#10622273C2212yes—
116#10622272C2212yes—
117#10622268C2212yes—
118#10622268C2212yes—
119#10622268C2212yes—
120#10622267C2212yes—
121#10622260C2212yes—
122#10622260C2212yes—
123C22×Q8×C11C2311yescharacteristic
124C23×C4×C11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C22×C22⋊D11C2312yes—
128C22×D44C2311yescharacteristic
129C22×C4×D11C2312yes—
130C11×C22⋊Q8—24no—
131C4×Q8×C11—24no—
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2312yes—
136C2×C11×C4⋊C4C2312yes—
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C22⋊C4C2312yes—
139C2×C11×C22⋊C4C2312yes—
140C2×C42×C11—24no—
141C2×C42×C11C2312yes—
142C2×C42×C11C2311yescharacteristic
143C2×C42×C11C2312yes—
144C2×C42×C11C2311yescharacteristic
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C22⋊Dic11C2311yescharacteristic
148C2×C22⋊Dic11C2311yescharacteristic
149C2×C22⋊Dic11C2311yescharacteristic
150C2×C22⋊Dic11C2311yescharacteristic
151C2×C22⋊Dic11C2312yes—
152#67000—24no—
153Q8×Dic11—24no—
154Q8×Dic11—24no—
155#66983—24no—
156C4×C22⋊D11—28no—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2312yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169#66979—24no—
170#66979—24no—
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2311yescharacteristic
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2312yes—
175C2×C4⋊Dic11C2311yescharacteristic
176C2×C4⋊Dic11C2312yes—
177C2×C4⋊Dic11C2311yescharacteristic
178C2×C4⋊Dic11C2312yes—
179C2×C4⋊Dic11C2311yescharacteristic
180C2×C4⋊Dic11C2312yes—
181C2×C4⋊Dic11C2311yescharacteristic
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2311yescharacteristic
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×Dic11C2312yes—
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204#66943—24no—
205C4×D44—24no—
206#66925—28no—
207C11×#95C2312yes—
208C11×#95C2312yes—
209C11×#95C2312yes—
210C11×#95C2312yes—
211C11×#95C2312yes—
212C11⋊#95C2312yes—
213C11⋊#95C2312yes—
214C11⋊#95C2312yes—
215C11⋊#95C2312yes—
216C11⋊#95C2312yes—
217C11⋊#95C2311yescharacteristic
218C11⋊#95C2311yescharacteristic
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2311yescharacteristic
228C11⋊#95C2312yes—
229C11⋊#95C2311yescharacteristic
230C11⋊#95C2312yes—
231C11⋊#95C2311yescharacteristic
232C11⋊#95C2311yescharacteristic
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2311yescharacteristic
235#34915—111nomaximal, Sylow
236C24×C11C2411yescharacteristic
237C23×D11C2412yes—
238C2×Q8×C11—22no—
239C2×Q8×C11—22no—
240C2×Q8×C11#4114yes—
241C22×C4×C11—22no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—22no—
247C22×C4×C11—41no—
248C22×C4×C11—41no—
249C22×C4×C11#4114yes—
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2412yes—
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C2×C22⋊D11—24no—
261C2×C22⋊D11—24no—
262C2×C22⋊D11—42no—
263C22×Dic11C2412yes—
264C22×Dic11C2411yescharacteristic
265C22×Dic11C2411yescharacteristic
266C22×Dic11C2411yescharacteristic
267C22×Dic11C2411yescharacteristic
268C22×Dic11C2411yescharacteristic
269C22×Dic11C2412yes—
270C22×Dic11C2411yescharacteristic
271C22×Dic11C2412yes—
272C22×Dic11C2411yescharacteristic
273C22×Dic11C2411yescharacteristic
274C2×D44—22no—
275C2×D44—22no—
276C2×D44—22no—
277C2×C4×D11—24no—
278C2×C4×D11—24no—
279C2×C4×D11—24no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—24no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—24no—
285C11×C4⋊C4—42no—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—42no—
288C42×C11—24no—
289C42×C11—22no—
290C42×C11—22no—
291C42×C11—22no—
292C42×C11—24no—
293C42×C11#4114yes—
294C22⋊Dic11—22no—
295C22⋊Dic11—22no—
296C22⋊Dic11—22no—
297C22⋊Dic11—22no—
298C22⋊Dic11—24no—
299(C2×D11)⋊C4—24no—
300(C2×D11)⋊C4—24no—
301(C2×D11)⋊C4—24no—
302(C2×D11)⋊C4—24no—
303(C2×D11)⋊C4—24no—
304(C2×D11)⋊C4—24no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4—42no—
307(C2×D11)⋊C4—42no—
308(C2×D11)⋊C4—42no—
309(C2×D11)⋊C4—42no—
310(C2×D11)⋊C4—42no—
311C4⋊Dic11—24no—
312C4⋊Dic11—22no—
313C4⋊Dic11—22no—
314C4⋊Dic11—24no—
315C4⋊Dic11—22no—
316C4⋊Dic11—22no—
317C4⋊Dic11—22no—
318C4⋊Dic11—24no—
319C4⋊Dic11—22no—
320C4⋊Dic11—42no—
321C4⋊Dic11#4114yes—
322Dic11⋊C4—24no—
323Dic11⋊C4—24no—
324Dic11⋊C4—24no—
325Dic11⋊C4—24no—
326Dic11⋊C4—42no—
327C4×Dic11—24no—
328C4×Dic11—22no—
329C4×Dic11—22no—
330C4×Dic11—22no—
331C4×Dic11—22no—
332C4×Dic11—24no—
333C4×Dic11—24no—
334C4×Dic11—22no—
335C4×Dic11—22no—
336C4×Dic11—22no—
337C4×Dic11—41no—
338C4×Dic11—41no—
339C4×Dic11—41no—
340C4×Dic11—41no—
341C4×Dic11—42no—
342C4×Dic11—42no—
343C4×Dic11#4114yes—
344#2597—112no—
345#2596—112no—
346#2595—112no—
347#2594—112no—
348#2513—111no—
349#2509—111no—
350#2494—111no—
351#2490—111no—
352#2453—111no—
353#2448—111no—
354#2426—111no—
355#2421—111no—
356#2401—112no—
357#2395—112no—
358C4×#125—111no—
359C4×#124—111no—
360C4×C22⋊Q8D1111yescharacteristic, complemented
361C4×#121—111no—
362#2298—112no—
363#2293—111no—
364#2293—112no—
365C42×Q8—111no—
366C4×#117—111no—
367C23×C11—21no—
368C23×C11—21no—
369C23×C11—21no—
370C23×C11—21no—
371C23×C11—21no—
372C23×C11—21no—
373C23×C11C2×#4112yes—
374C23×C11C2511yescharacteristic
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382Q8×C11—28no—
383C2×C4×C11—22no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—22no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—28no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—21no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—21no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—44no—
406C2×C4×C11—44no—
407C2×C4×C11C2×#4114yes—
408C2×C4×C11C2×#4112yes—
409C2×C4×C11C2×#4112yes—
410C2×C4×C11C2×#4112yes—
411C2×C4×C11C2×#4112yes—
412C2×C4×C11C2×#4112yes—
413C2×C4×C11C2×#4112yes—
414C2×C4×C11C2×#4112yes—
415C2×C4×C11C2×#4112yes—
416C22⋊D11—48no—
417C2×Dic11—21no—
418C2×Dic11—21no—
419C2×Dic11—22no—
420C2×Dic11—21no—
421C2×Dic11—21no—
422C2×Dic11—22no—
423C2×Dic11—21no—
424C2×Dic11—21no—
425C2×Dic11—22no—
426C2×Dic11—21no—
427C2×Dic11—21no—
428C2×Dic11—21no—
429C2×Dic11—21no—
430C2×Dic11—21no—
431C2×Dic11—21no—
432C2×Dic11—21no—
433C2×Dic11—21no—
434C2×Dic11—21no—
435C2×Dic11—21no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—21no—
441C2×Dic11—21no—
442C2×Dic11—22no—
443C2×Dic11—21no—
444C2×Dic11—21no—
445C2×Dic11—21no—
446C2×Dic11—21no—
447C2×Dic11C2×#4114yes—
448C2×Dic11C2×#4112yes—
449C2×Dic11C2×#4112yes—
450D44—44no—
451C4×D11—48no—
452C2×#125—111no—
453C2×#124—111no—
454C2×C22⋊Q8C2×D1111yescharacteristic
455C2×#121—111no—
456C2×C4×Q8—111no—
457C2×C4×Q8—111no—
458C2×C4×Q8C2×D1111yescharacteristic
459C2×C4×D4—112no—
460C2×C4×D4—111no—
461C2×#117—111no—
462C2×#117—111no—
463C2×#117—112no—
464C22×C42C2×D1111yescharacteristic
465#401—112no—
466#400—112no—
467#400—112no—
468#400—112no—
469#400—112no—
470#399—112no—
471#398—112no—
472#397—112no—
473#397—112no—
474#397—112no—
475#397—112no—
476#397—112no—
477#397—112no—
478#396—112no—
479#394—112no—
480#394—112no—
481#391—111no—
482#391C2×D1111yescharacteristic
483#390—111no—
484#390—111no—
485#390—111no—
486#390—112no—
487#390—112no—
488#390—111no—
489#389—111no—
490#389—111no—
491#389—111no—
492#389—111no—
493#389—111no—
494#389—112no—
495#389—112no—
496#389C2×D1111yescharacteristic
497#388—112no—
498#388—112no—
499#388—112no—
500#388—112no—
501#388—112no—
502#388—112no—
503#388—112no—
504#388—112no—
505#388—112no—
506#388—112no—
507#388—112no—
508#388—112no—
509#388—112no—
510#387—112no—
511#387—112no—
512#387—112no—
513#387—112no—
514#387—112no—
515#387—112no—
516#387C2×D1112yes—
517#386—112no—
518#385C2×D1112yes—
519#382—111no—
520#382—111no—
521#380—111no—
522#380C2×D1111yescharacteristic
523C4×C4⋊C4—112no—
524C4×C4⋊C4—112no—
525C4×C4⋊C4—111no—
526C4×C4⋊C4—111no—
527C4×C4⋊C4—112no—
528C4×C4⋊C4—112no—
529C4×C4⋊C4—111no—
530C4×C4⋊C4—111no—
531C4×C4⋊C4—111no—
532C4×C4⋊C4—112no—
533C4×C4⋊C4—111no—
534C4×C4⋊C4—111no—
535C4×C4⋊C4C2×D1111yescharacteristic
536C4×C4⋊C4C2×D1112yes—
537C4×C22⋊C4—111no—
538C4×C22⋊C4—111no—
539C4×C22⋊C4—111no—
540C4×C22⋊C4—111no—
541C4×C22⋊C4—112no—
542C4×C22⋊C4—112no—
543C4×C22⋊C4—112no—
544C4×C22⋊C4—112no—
545C4×C22⋊C4C2×D1112yes—
546#376—111no—
547#376—111no—
548C43—111no—
549C43—111no—
550C43—112no—
551C22×C11—22no—
552C22×C11—22no—
553C22×C11—22no—
554C22×C11—41no—
555C22×C11—41no—
556C22×C11—41no—
557C22×C11—41no—
558C22×C11C22×#4111yescharacteristic
559C22×C11C22×#4111yescharacteristic
560C22×C11C22×#4111yescharacteristic
561C22×C11C22×#4111yescharacteristic
562C22×C11C22×#4111yescharacteristic
563C22×C11#58511yescharacteristic
564C22×C11#58511yescharacteristic
565C2×D11—42no—
566C2×D11—42no—
567C2×D11—42no—
568C2×D11—42no—
569C2×D11—42no—
570C2×D11—42no—
571C2×D11—42no—
572C4×C11—22no—
573C4×C11—24no—
574C4×C11—22no—
575C4×C11—41no—
576C4×C11—42no—
577C4×C11—41no—
578C4×C11—42no—
579C4×C11—42no—
580C4×C11#52914yes—
581C4×C11#52914yes—
582Dic11—24no—
583Dic11—22no—
584Dic11—22no—
585Dic11—42no—
586Dic11—41no—
587Dic11—41no—
588Dic11—41no—
589Dic11—41no—
590Dic11—42no—
591Dic11—41no—
592Dic11—41no—
593C22×Q8C22×D1111yescharacteristic
594C22×D4—112no—
595C22×D4—111no—
596C23×C4—112no—
597C23×C4C22×D1111yescharacteristic
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600#125—224no—
601#124—224no—
602C22⋊Q8—24no—
603#121—224no—
604C4×Q8—24no—
605C4×Q8—224no—
606C4×Q8—224no—
607C4×D4—228no—
608C4×D4—224no—
609#117—228no—
610#117—224no—
611#117—224no—
612C2×C4⋊C4—111no—
613C2×C4⋊C4—111no—
614C2×C4⋊C4—111no—
615C2×C4⋊C4—111no—
616C2×C4⋊C4—111no—
617C2×C4⋊C4—112no—
618C2×C4⋊C4—112no—
619C2×C4⋊C4—111no—
620C2×C4⋊C4—112no—
621C2×C4⋊C4—111no—
622C2×C4⋊C4—112no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—112no—
625C2×C4⋊C4—112no—
626C2×C4⋊C4—112no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4C22×D1111yescharacteristic
629C2×C4⋊C4C22×D1112yes—
630C2×C4⋊C4C22×D1111yescharacteristic
631C2×C4⋊C4C22×D1112yes—
632C2×C4⋊C4C22×D1111yescharacteristic
633C2×C4⋊C4C22×D1112yes—
634C2×C22⋊C4—111no—
635C2×C22⋊C4—111no—
636C2×C22⋊C4—111no—
637C2×C22⋊C4—111no—
638C2×C22⋊C4—112no—
639C2×C22⋊C4—112no—
640C2×C22⋊C4—112no—
641C2×C22⋊C4—112no—
642C2×C22⋊C4—112no—
643C2×C22⋊C4—112no—
644C2×C22⋊C4—112no—
645C2×C22⋊C4—112no—
646C2×C22⋊C4—112no—
647C2×C22⋊C4—112no—
648C2×C22⋊C4—112no—
649C2×C22⋊C4—112no—
650C2×C22⋊C4—112no—
651C2×C22⋊C4C22×D1112yes—
652C2×C22⋊C4C22×D1112yes—
653C2×C42—24no—
654C2×C42—111no—
655C2×C42—111no—
656C2×C42—111no—
657C2×C42—112no—
658C2×C42—112no—
659C2×C42—111no—
660C2×C42—111no—
661C2×C42—111no—
662C2×C42—111no—
663C2×C42—111no—
664C2×C42—112no—
665C2×C42—111no—
666C2×C42—111no—
667C2×C42—111no—
668C2×C42—111no—
669C2×C42—112no—
670C2×C42—112no—
671C2×C42C22×D1111yescharacteristic
672C2×C42C22×D1111yescharacteristic
673C2×C42C22×D1112yes—
674C2×C42C22×D1112yes—
675C2×C42C22×D1111yescharacteristic
676C2×C42C22×D1111yescharacteristic
677#95—111no—
678#95—111no—
679#95—111no—
680#95—111no—
681#95—111no—
682#95—111no—
683#95—111no—
684#95—111no—
685#95—112no—
686#95—112no—
687#95—112no—
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#95C22×D1112yes—
701#95C22×D1112yes—
702#95C22×D1112yes—
703#95C22×D1112yes—
704#95C22×D1112yes—
705C2×C11—42no—
706C2×C11C2×#52911yescharacteristic
707C2×C11C2×#52911yescharacteristic
708C2×C11#345511yescharacteristic
709C2×C11#347511yescharacteristic
710C2×C11#348011yescharacteristic
711C2×C11#348011yescharacteristic
712C2×C11#348011yescharacteristic
713D11—82no—
714C24—112no—
715C24C23×D1111yescharacteristic
716C2×Q8—22no—
717C2×Q8—22no—
718C2×Q8#433914yes—
719C2×D4—224no—
720C2×D4—224no—
721C2×D4—222no—
722C2×D4—222no—
723C2×D4—222no—
724C2×D4—442no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—41no—
732C22×C4—41no—
733C22×C4—112no—
734C22×C4—111no—
735C22×C4—111no—
736C22×C4—112no—
737C22×C4—111no—
738C22×C4—111no—
739C22×C4—112no—
740C22×C4—111no—
741C22×C4—111no—
742C22×C4—111no—
743C22×C4—111no—
744C22×C4—224no—
745C22×C4—224no—
746C22×C4—224no—
747C22×C4#434314yes—
748C22×C4C23×D1111yescharacteristic
749C22×C4C23×D1111yescharacteristic
750C22×C4C23×D1112yes—
751C22×C4C23×D1112yes—
752C22×C4C23×D1112yes—
753C22×C4C23×D1112yes—
754C22×C4C23×D1111yescharacteristic
755C22×C4C23×D1111yescharacteristic
756C22×C4C23×D1111yescharacteristic
757C22×C4C23×D1111yescharacteristic
758C4⋊C4—22no—
759C4⋊C4—24no—
760C4⋊C4—24no—
761C4⋊C4—22no—
762C4⋊C4—22no—
763C4⋊C4—42no—
764C4⋊C4—114no—
765C4⋊C4—224no—
766C4⋊C4—224no—
767C4⋊C4—222no—
768C4⋊C4—222no—
769C4⋊C4—224no—
770C4⋊C4—224no—
771C4⋊C4—224no—
772C4⋊C4—224no—
773C4⋊C4—222no—
774C4⋊C4—222no—
775C4⋊C4—222no—
776C4⋊C4—222no—
777C4⋊C4—224no—
778C4⋊C4—442no—
779C4⋊C4—442no—
780C22⋊C4—24no—
781C22⋊C4—42no—
782C22⋊C4—224no—
783C22⋊C4—224no—
784C22⋊C4—224no—
785C22⋊C4—222no—
786C22⋊C4—222no—
787C22⋊C4—222no—
788C22⋊C4—222no—
789C22⋊C4—224no—
790C22⋊C4—224no—
791C22⋊C4—224no—
792C22⋊C4—224no—
793C22⋊C4—224no—
794C22⋊C4—442no—
795C22⋊C4—442no—
796C22⋊C4—442no—
797C22⋊C4—442no—
798C22⋊C4—442no—
799C42—22no—
800C42—22no—
801C42—22no—
802C42—24no—
803C42—24no—
804C42—114no—
805C42—224no—
806C42—224no—
807C42—222no—
808C42—222no—
809C42—222no—
810C42—222no—
811C42—224no—
812C42—222no—
813C42—222no—
814C42—222no—
815C42—441no—
816C42—441no—
817C42—441no—
818C42—441no—
819C42—442no—
820C42—442no—
821C42#434114yes—
822C11#3491511yescharacteristic, complemented, Sylow
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—222no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23C2×#434312yes—
837C23C24×D1111yescharacteristic
838Q8—28no—
839D4—448no—
840D4—444no—
841C2×C4—21no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—28no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—44no—
864C2×C4—44no—
865C2×C4—112no—
866C2×C4—112no—
867C2×C4—114no—
868C2×C4—221no—
869C2×C4—222no—
870C2×C4—221no—
871C2×C4—221no—
872C2×C4—221no—
873C2×C4—222no—
874C2×C4—221no—
875C2×C4—221no—
876C2×C4—222no—
877C2×C4—221no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—221no—
881C2×C4—221no—
882C2×C4—221no—
883C2×C4—221no—
884C2×C4—222no—
885C2×C4—221no—
886C2×C4—221no—
887C2×C4—221no—
888C2×C4—221no—
889C2×C4—221no—
890C2×C4—222no—
891C2×C4—221no—
892C2×C4—221no—
893C2×C4—221no—
894C2×C4—221no—
895C2×C4—222no—
896C2×C4—221no—
897C2×C4—221no—
898C2×C4—448no—
899C2×C4C2×#433914yes—
900C2×C4C2×#433912yes—
901C2×C4C2×#434112yes—
902C2×C4C2×#434112yes—
903C2×C4C2×#434112yes—
904C2×C4C2×#434312yes—
905C2×C4C2×#434312yes—
906C2×C4#41×D1112yes—
907C2×C4#41×D1112yes—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—442no—
916C22—442no—
917C22—442no—
918C22—442no—
919C22—442no—
920C22—442no—
921C22—442no—
922C22C22×#433911yescharacteristic
923C22C22×#434111yescharacteristic
924C22C22×#434311yescharacteristic
925C22C2×#41×D1111yescharacteristic
926C22C2×#41×D1111yescharacteristic
927C22#1062345311yescharacteristic
928C22#1062345311yescharacteristic
929C4—24no—
930C4—22no—
931C4—22no—
932C4—41no—
933C4—42no—
934C4—42no—
935C4—41no—
936C4—42no—
937C4—224no—
938C4—222no—
939C4—222no—
940C4—442no—
941C4—441no—
942C4—441no—
943C4—441no—
944C4—441no—
945C4—442no—
946C4—441no—
947C4—441no—
948C4#1062306914yes—
949C4#1062315514yes—
950C2—42no—
951C2—882no—
952C2C2×#1062306911yescharacteristic
953C2C2×#1062315511yescharacteristic
954C2#1308200411yescharacteristic
955C2#1308218311yescharacteristic
956C2#1308220711yescharacteristic
957C2#1308221111yescharacteristic
958C2#1308221411yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×C22⋊Q8C2
prime radicalC2×#66983C22
hypercenterC4×C22⋊Q8D11
hypocenterC11#34915
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #13074164C2semidirect
2. #13074149C2semidirect
3. #13074134C2semidirect
4. #13074119C2semidirect
5. #13073216C2semidirect
6. #13073163C2semidirect
7. #13073018C2semidirect
9. #13072480C2semidirect
10. #13072412C2semidirect
12. #13072115C2semidirect
13. #13071917C2semidirect
14. #13071876C2semidirect
15. C4×#66943C2semidirect
16. C4×#67000C2semidirect
18. #13071109C2semidirect
19. #13071079C2semidirect
20. #13071077C2semidirect
21. C4×Q8×Dic11C2semidirect
22. C4×#66979C2semidirect
23. C4×C11×C22⋊Q8C2semidirect
360. C4×C22⋊Q8D11semidirect
822. C11#34915semidirect

Maximal subgroups

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

subgroupindex
#130741642
#130741492
#130741342
#130741192
#130732162
#130731632
#130730182
#130729642
#130724802
#130724122
#130721842
#130721152
#130719172
#130718762
C4×#669432
C4×#670002
C4×#669832
#130711092
#130710792
#130710772
C4×Q8×Dic112
C4×#669792
C4×C11×C22⋊Q82
#3491511