Finite Group Databasebeta

← #14913740

Subgroups — #14913740

Order 2816.

2516 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic
2#13071712C212yesmaximal, complemented
3#13071705C211yesmaximal, characteristic, complemented
4#13071693C214yesmaximal, complemented
5#13071626C212yesmaximal, complemented
6#13071524C212yesmaximal
7#13071516C211yesmaximal, characteristic
8#13071489C212yesmaximal, complemented
9#13071183C211yesmaximal, characteristic, complemented
10#13071171C212yesmaximal, complemented
11#13071154C212yesmaximal, complemented
12#13071150C214yesmaximal, complemented
13C4×Q8×Dic11C211yesmaximal, characteristic, complemented
14C4×#66946C211yesmaximal, characteristic
15C4×#66946C212yesmaximal
16C4×C4⋊C4×D11C212yesmaximal, complemented
17C11×#2355C211yesmaximal, characteristic, complemented
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#66999C2212yes—
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22#10623110C4116yescomplemented
23C2×#66949C2214yes—
24C2×#66946C2212yes—
25C2×#66946C2211yescharacteristic
26C2×#66946C2211yescharacteristic
27C2×C4⋊C4×D11C2212yes—
28C2×C4⋊C4×D11C2212yes—
29C2×#66940C2212yes—
30C2×C4×D44C2211yescharacteristic
31C2×C4×D44C2212yes—
32C2×C42×D11C2212yes—
33C2×C42×D11C2214yes—
34C2×#66923C2212yes—
35C2×#66922C2211yescharacteristic
36C11×#391C2212yes—
37C11×#387C2214yes—
38C11×#384C2211yescharacteristic
39C11×#382C2212yes—
40C4×C11×C4⋊C4C2211yescharacteristic
41C4×C11×C4⋊C4C2212yes—
42C4×C11×C4⋊C4C2212yes—
43#10622602C2214yes—
44#10622600C2212yes—
45C4⋊C4×Dic11C2212yes—
46C4⋊C4×Dic11C2212yes—
47C4⋊C4×Dic11C2211yescharacteristic
48C4⋊C4×Dic11C2212yes—
49C4⋊C4×Dic11C2212yes—
50C4⋊C4×Dic11C2212yes—
51C4⋊C4×Dic11C2211yescharacteristic
52C4⋊C4×Dic11C2211yescharacteristic
53C4⋊C4×Dic11C2211yescharacteristic
54#10622587C2212yes—
55#10622586C2212yes—
56#10622586C2212yes—
57#10622586C2212yes—
58#10622586C2212yes—
59C4×(C2×D11)⋊C4C2212yes—
60C4×(C2×D11)⋊C4C2214yes—
61C4×C4⋊Dic11C2212yes—
62C4×C4⋊Dic11C2211yescharacteristic
63C4×C4⋊Dic11C2212yes—
64#10622546C2214yes—
65C4×Dic11⋊C4C2214yes—
66C42×Dic11C2212yes—
67C42×Dic11C2211yescharacteristic
68#10622541C2212yes—
69#10622281C2214yes—
70#10622281C2214yes—
71#10622280C2214yes—
72#10622279C2214yes—
73#10622279C2212yes—
74#10622279C2214yes—
75#10622279C2212yes—
76D11×#95C2214yes—
77#10622268C2214yes—
78#10622265C2214yes—
79#10622265C2214yes—
80#10622262C2214yes—
81#10622262C2214yes—
82#10622260C2214yes—
83#10622259C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C22×D44C2311yescharacteristic
86C22×C4×D11C2314yes—
87C22×C4×D11C2312yes—
88C22×C4×D11C2312yes—
89C22×C4×D11C2312yes—
90C22×C4×D11C2314yes—
91C22×Dic22C2312yes—
92C4×Q8×C11C2×C418yescomplemented
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C42×C11C2312yes—
101C2×C42×C11C2314yes—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2312yes—
104#66999C2×C4116yescomplemented
105Q8×Dic11—24no—
106Q8×Dic11—24no—
107C2×(C2×D11)⋊C4C2312yes—
108C2×(C2×D11)⋊C4C2314yes—
109C2×(C2×D11)⋊C4C2312yes—
110C2×(C2×D11)⋊C4C2314yes—
111C2×(C2×D11)⋊C4C2312yes—
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2312yes—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2314yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2311yescharacteristic
133C2×C4×Dic11C2311yescharacteristic
134C2×C4×Dic11C2314yes—
135C2×C4×Dic11C2312yes—
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2311yescharacteristic
138C2×C4×Dic11C2311yescharacteristic
139#66949C2×C4132yescomplemented
140#66946—28no—
141#66946—24no—
142#66946Q818yescomplemented
143C4⋊C4×D11—28no—
144C4⋊C4×D11C2×C4116yescomplemented
145#66940—44no—
146C4×D44C2×C4116yes—
147C4×D44C2×C418yes—
148C42×D11—28no—
149C42×D11—48no—
150#66923C2×C4116yescomplemented
151#66922C2×C418yescomplemented
152C11×#95C2312yes—
153C11×#95C2314yes—
154C11×#95C2314yes—
155C11×#95C2314yes—
156C11⋊#95C2312yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2312yes—
160C11⋊#95C2314yes—
161C11⋊#95C2312yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2312yes—
165C11⋊#95C2312yes—
166C4×#554—111nomaximal, Sylow
167C23×D11C2412yes—
168C2×Q8×C11—22no—
169C2×Q8×C11—22no—
170C2×Q8×C11C22×C414yes—
171C22×C4×C11C2412yes—
172C22×C4×C11C2414yes—
173C22×C4×C11C2412yes—
174C22×C4×C11C2411yescharacteristic
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2411yescharacteristic
179C22×Dic11C2412yes—
180C22×Dic11C2411yescharacteristic
181C22×Dic11C2412yes—
182C22×Dic11C2414yes—
183C22×Dic11C2411yescharacteristic
184C22×Dic11C2411yescharacteristic
185C22×Dic11C2412yes—
186C22×Dic11C2411yescharacteristic
187C2×D44C22×C414yes—
188C2×D44C2×Q814yes—
189C2×D44#4114yes—
190C2×C4×D11—24no—
191C2×C4×D11—24no—
192C2×C4×D11—24no—
193C2×C4×D11—28no—
194C2×C4×D11—28no—
195C2×C4×D11—24no—
196C2×C4×D11—24no—
197C2×C4×D11—24no—
198C2×C4×D11—44no—
199C2×C4×D11—44no—
200C2×C4×D11—44no—
201C2×C4×D11—42no—
202C2×C4×D11C22×C418yes—
203C2×C4×D11C22×C4116yes—
204C2×C4×D11C2×Q818yes—
205C2×Dic22—42no—
206C2×Dic22—42no—
207C2×Dic22C22×C418yes—
208C11×C4⋊C4—24no—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4C22×C414yes—
213C11×C4⋊C4C22×C418yes—
214C11×C4⋊C4C2×Q814yes—
215C42×C11—24no—
216C42×C11—44no—
217C42×C11C22×C414yes—
218C42×C11C22×C418yes—
219(C2×D11)⋊C4—24no—
220(C2×D11)⋊C4—28no—
221(C2×D11)⋊C4C22×C418yes—
222(C2×D11)⋊C4C22×C4116yes—
223(C2×D11)⋊C4C2×Q818yes—
224C4⋊Dic11—24no—
225C4⋊Dic11—24no—
226C4⋊Dic11—22no—
227C4⋊Dic11C22×C418yes—
228C4⋊Dic11C22×C418yes—
229C4⋊Dic11C22×C414yes—
230C4⋊Dic11#4114yes—
231Dic11⋊C4—28no—
232Dic11⋊C4—44no—
233Dic11⋊C4—44no—
234Dic11⋊C4C22×C4116yes—
235Dic11⋊C4C22×C4116yes—
236C4×Dic11—24no—
237C4×Dic11—24no—
238C4×Dic11—24no—
239C4×Dic11—24no—
240C4×Dic11—24no—
241C4×Dic11—28no—
242C4×Dic11—22no—
243C4×Dic11—22no—
244C4×Dic11—24no—
245C4×Dic11—22no—
246C4×Dic11—44no—
247C4×Dic11—41no—
248C4×Dic11—42no—
249C4×Dic11C2×Q814yes—
250C4×Dic11#4114yes—
251C2×#554—111no—
252#2370—112no—
253#2369—111no—
254#2368—114no—
255#2360—112no—
256#2355D1111yescharacteristic, complemented
257#2349—112no—
258D4×C4⋊C4—111no—
259#2345—112no—
260C4×C4⋊Q8—111no—
261C4×#125—112no—
262C4×C22⋊Q8—112no—
263C4×C22⋊Q8—114no—
264C42×Q8—111no—
265C42×D4—112no—
266C42×D4—111no—
267C2×C4×C4⋊C4—112no—
268C23×C11C2511yescharacteristic
269C22×D11—22no—
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—22no—
273C22×D11C23×C414yes—
274C22×D11C22×Q814yes—
275C22×D11C2×#4114yes—
276Q8×C11—28no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—21no—
282C2×C4×C11—22no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—24no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11C23×C414yes—
292C2×C4×C11C23×C414yes—
293C2×C4×C11C23×C412yes—
294C2×C4×C11C23×C412yes—
295C2×C4×C11C23×C412yes—
296C2×C4×C11C22×Q814yes—
297C2×C4×C11C22×Q812yes—
298C2×C4×C11C2×#4112yes—
299C2×C4×C11C2×#4112yes—
300C2×C4×C11C2×#4112yes—
301C2×Dic11—21no—
302C2×Dic11—22no—
303C2×Dic11—21no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—24no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—24no—
311C2×Dic11—22no—
312C2×Dic11—21no—
313C2×Dic11—22no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—22no—
317C2×Dic11C23×C414yes—
318C2×Dic11C23×C418yes—
319C2×Dic11C22×Q812yes—
320C2×Dic11C22×Q812yes—
321C2×Dic11C2×#4112yes—
322C2×Dic11C2×#4114yes—
323C2×Dic11C2×#4112yes—
324C2×Dic11H(5,𝔽2)12yes—
325D44C4×Q8116yescomplemented
326C4×D11—216no—
327C4×D11—216no—
328C4×D11—416no—
329C4×D11—48no—
330C4×D11—416no—
331Dic22—48no—
332#554—1116no—
333C2×C4⋊Q8—111no—
334C2×#125—112no—
335C2×C22⋊Q8—112no—
336C2×C22⋊Q8—114no—
337C2×C4×Q8—111no—
338C2×C4×Q8—111no—
339C2×C4×Q8—112no—
340C2×C4×Q8C2×D1111yescharacteristic
341C2×C4×D4—111no—
342C2×C4×D4—112no—
343C2×C4×D4—111no—
344C2×C4×D4—111no—
345C2×C4×D4—112no—
346C22×C4⋊C4—112no—
347C22×C4⋊C4—112no—
348C22×C42—112no—
349C22×C42—114no—
350#391—112no—
351#391—114no—
352#391C2×D1112yes—
353#389—112no—
354#389—112no—
355#389—112no—
356#389—112no—
357#389—112no—
358#389—114no—
359#387—114no—
360#387—114no—
361#387—114no—
362#387—114no—
363#387C2×D1114yes—
364#385—114no—
365#385—114no—
366#385—114no—
367#384C2×D1111yescharacteristic
368#382C2×D1112yes—
369#380—112no—
370#380—114no—
371C4×C4⋊C4—111no—
372C4×C4⋊C4—112no—
373C4×C4⋊C4—112no—
374C4×C4⋊C4—111no—
375C4×C4⋊C4—112no—
376C4×C4⋊C4—112no—
377C4×C4⋊C4—111no—
378C4×C4⋊C4—111no—
379C4×C4⋊C4—112no—
380C4×C4⋊C4—111no—
381C4×C4⋊C4—112no—
382C4×C4⋊C4—112no—
383C4×C4⋊C4—114no—
384C4×C4⋊C4—114no—
385C4×C4⋊C4—114no—
386C4×C4⋊C4C2×D1112yes—
387C4×C4⋊C4C2×D1111yescharacteristic
388C4×C4⋊C4C2×D1112yes—
389C4×C22⋊C4—112no—
390C4×C22⋊C4—114no—
391C4×C22⋊C4—114no—
392C4×C22⋊C4—112no—
393C4×C22⋊C4—112no—
394C4×C22⋊C4—114no—
395C2×#95—114no—
396C43—112no—
397C43—111no—
398C22×C11C24×C411yescharacteristic
399C22×C11C23×Q811yescharacteristic
400C22×C11C22×#4111yescharacteristic
401C22×C11C22×#4111yescharacteristic
402C22×C11C22×#4111yescharacteristic
403C22×C11C2×H(5,𝔽2)11yescharacteristic
404C22×C11#58511yescharacteristic
405C2×D11—24no—
406C2×D11—24no—
407C2×D11—24no—
408C2×D11—24no—
409C2×D11—24no—
410C2×D11—24no—
411C2×D11C2×C4×Q818yes—
412C4×C11—24no—
413C4×C11—22no—
414C4×C11—24no—
415C4×C11—24no—
416C4×C11—42no—
417C4×C11—44no—
418C4×C11C2×C4×Q814yes—
419C4×C11C4×#4114yes—
420Dic11—24no—
421Dic11—28no—
422Dic11—22no—
423Dic11—22no—
424Dic11—24no—
425Dic11—42no—
426Dic11—41no—
427Dic11#55414yescomplemented
428C22×Q8—112no—
429C22×Q8C22×D1111yescharacteristic
430C22×D4—111no—
431C23×C4—112no—
432C23×C4—112no—
433C23×C4—114no—
434C23×C4—114no—
435C23×C4—112no—
436C4⋊Q8—118no—
437#125—1116no—
438C22⋊Q8—1116no—
439C22⋊Q8—1132no—
440C4×Q8—224no—
441C4×Q8—224no—
442C4×Q8—444no—
443C4×Q8C4×D1118yescomplemented
444C4×D4—118no—
445C4×D4—1116no—
446C4×D4—118no—
447C4×D4—228no—
448C4×D4—224no—
449C2×C4⋊C4—111no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4—112no—
452C2×C4⋊C4—111no—
453C2×C4⋊C4—112no—
454C2×C4⋊C4—114no—
455C2×C4⋊C4—1116no—
456C2×C4⋊C4—114no—
457C2×C4⋊C4—111no—
458C2×C4⋊C4—112no—
459C2×C4⋊C4—112no—
460C2×C4⋊C4—114no—
461C2×C4⋊C4—114no—
462C2×C4⋊C4—228no—
463C2×C4⋊C4C22×D1112yes—
464C2×C4⋊C4C22×D1111yescharacteristic
465C2×C4⋊C4C22×D1112yes—
466C2×C4⋊C4C22×D1112yes—
467C2×C4⋊C4C22×D1111yescharacteristic
468C2×C4⋊C4C22×D1112yes—
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C22⋊C4—112no—
471C2×C22⋊C4—114no—
472C2×C22⋊C4—112no—
473C2×C22⋊C4—114no—
474C2×C22⋊C4—112no—
475C2×C42—111no—
476C2×C42—111no—
477C2×C42—111no—
478C2×C42—112no—
479C2×C42—111no—
480C2×C42—112no—
481C2×C42—112no—
482C2×C42—111no—
483C2×C42—114no—
484C2×C42—112no—
485C2×C42—112no—
486C2×C42—112no—
487C2×C42—112no—
488C2×C42—111no—
489C2×C42—114no—
490C2×C42—228no—
491C2×C42—448no—
492C2×C42C22×D1112yes—
493C2×C42C22×D1114yes—
494C2×C42C22×D1112yes—
495C2×C42C22×D1111yescharacteristic
496#95—112no—
497#95—114no—
498#95—114no—
499#95—112no—
500#95—112no—
501#95—114no—
502#95—114no—
503#95—112no—
504#95—112no—
505#95—114no—
506#95C22×D1114yes—
507#95C22×D1114yes—
508#95C22×D1112yes—
509#95C22×D1114yes—
510C2×C11C22×C4×Q811yescharacteristic
511C2×C11C2×C4×#4111yescharacteristic
512C2×C11C4×H(5,𝔽2)11yescharacteristic
513C2×C11C2×#55411yescharacteristic
514C2×C11#347511yescharacteristic
515C2×C11Q8×#4111yescharacteristic
516C2×C11#348111yescharacteristic
517D11—28no—
518C24—112no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—118no—
522C2×Q8—442no—
523C2×Q8—442no—
524C2×Q8C2×C4×D1114yes—
525C2×D4—114no—
526C2×D4—114no—
527C2×D4—114no—
528C22×C4—111no—
529C22×C4—111no—
530C22×C4—111no—
531C22×C4—112no—
532C22×C4—112no—
533C22×C4—114no—
534C22×C4—118no—
535C22×C4—118no—
536C22×C4—1116no—
537C22×C4—112no—
538C22×C4—111no—
539C22×C4—224no—
540C22×C4—224no—
541C22×C4—224no—
542C22×C4—228no—
543C22×C4—228no—
544C22×C4—224no—
545C22×C4—224no—
546C22×C4—224no—
547C22×C4—444no—
548C22×C4—444no—
549C22×C4—444no—
550C22×C4—442no—
551C22×C4C23×D1112yes—
552C22×C4C23×D1114yes—
553C22×C4C23×D1112yes—
554C22×C4C23×D1111yescharacteristic
555C22×C4C23×D1112yes—
556C22×C4C23×D1112yes—
557C22×C4C23×D1111yescharacteristic
558C22×C4C23×D1111yescharacteristic
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—24no—
562C4⋊C4—42no—
563C4⋊C4—1116no—
564C4⋊C4—118no—
565C4⋊C4—114no—
566C4⋊C4—118no—
567C4⋊C4—1116no—
568C4⋊C4—114no—
569C4⋊C4—228no—
570C4⋊C4—224no—
571C4⋊C4—224no—
572C4⋊C4—222no—
573C4⋊C4—444no—
574C4⋊C4—444no—
575C4⋊C4C2×C4×D1114yes—
576C4⋊C4C2×C4×D1118yes—
577C4⋊C4Q8×D1114yes—
578C22⋊C4—118no—
579C22⋊C4—1116no—
580C22⋊C4—118no—
581C22⋊C4—224no—
582C22⋊C4—228no—
583C42—24no—
584C42—44no—
585C42—114no—
586C42—114no—
587C42—224no—
588C42—224no—
589C42—224no—
590C42—228no—
591C42—224no—
592C42—224no—
593C42—222no—
594C42—222no—
595C42—224no—
596C42—222no—
597C42—444no—
598C42—442no—
599C42—441no—
600C42C2×C4×D1118yes—
601C42C2×C4×D1114yes—
602C11C4×#55411yescharacteristic, complemented, Sylow
603C23—114no—
604C23—114no—
605C23—114no—
606C23—222no—
607C23—222no—
608C23—222no—
609C23—222no—
610C23C24×D1111yescharacteristic
611Q8—28no—
612Q8—448no—
613D4—1116no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—112no—
629C2×C4—112no—
630C2×C4—112no—
631C2×C4—114no—
632C2×C4—118no—
633C2×C4—112no—
634C2×C4—112no—
635C2×C4—114no—
636C2×C4—2216no—
637C2×C4—221no—
638C2×C4—222no—
639C2×C4—221no—
640C2×C4—222no—
641C2×C4—222no—
642C2×C4—222no—
643C2×C4—224no—
644C2×C4—221no—
645C2×C4—221no—
646C2×C4—224no—
647C2×C4—2216no—
648C2×C4—222no—
649C2×C4—221no—
650C2×C4—222no—
651C2×C4—221no—
652C2×C4—221no—
653C2×C4—222no—
654C2×C4—4416no—
655C2×C4—448no—
656C2×C4—4416no—
657C2×C4C22×C4×D1114yes—
658C2×C4C22×C4×D1112yes—
659C2×C4C22×C4×D1114yes—
660C2×C4C22×C4×D1112yes—
661C2×C4C22×C4×D1112yes—
662C2×C4C2×Q8×D1114yes—
663C2×C4C2×Q8×D1112yes—
664C2×C4#41×D1112yes—
665C2×C4#41×D1112yes—
666C2×C4#41×D1112yes—
667C22—118no—
668C22—224no—
669C22—224no—
670C22—224no—
671C22—224no—
672C22—224no—
673C22—224no—
674C22C23×C4×D1111yescharacteristic
675C22C22×Q8×D1111yescharacteristic
676C22C2×#41×D1111yescharacteristic
677C22C2×#41×D1111yescharacteristic
678C22C2×#41×D1111yescharacteristic
679C22D11×H(5,𝔽2)11yescharacteristic
680C22#1062345711yescharacteristic
681C4—24no—
682C4—24no—
683C4—24no—
684C4—22no—
685C4—42no—
686C4—44no—
687C4—114no—
688C4—222no—
689C4—222no—
690C4—224no—
691C4—224no—
692C4—228no—
693C4—442no—
694C4—441no—
695C4#1062305314yes—
696C4C4×Q8×D1114yes—
697C2—228no—
698C2C2×C4×Q8×D1111yescharacteristic
699C2C2×#1062305311yescharacteristic
700C2#1308182211yescharacteristic
701C2D11×#55411yescharacteristic
702C2#1308217711yescharacteristic
703C2#1308219811yescharacteristic
704C2#1308222511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2355C2
socle, cosocleC23×C11C25
prime radicalC22×D44C23
hypercenter#2355D11
hypocenterC11C4×#554
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. #13071712C2semidirect
3. #13071705C2semidirect
4. #13071693C2semidirect
5. #13071626C2semidirect
8. #13071489C2semidirect
9. #13071183C2semidirect
10. #13071171C2semidirect
11. #13071154C2semidirect
12. #13071150C2semidirect
13. C4×Q8×Dic11C2semidirect
16. C4×C4⋊C4×D11C2semidirect
17. C11×#2355C2semidirect
22. #10623110C4semidirect
92. C4×Q8×C11C2×C4semidirect
104. #66999C2×C4semidirect
139. #66949C2×C4semidirect
142. #66946Q8semidirect
144. C4⋊C4×D11C2×C4semidirect
150. #66923C2×C4semidirect
151. #66922C2×C4semidirect
256. #2355D11semidirect
325. D44C4×Q8semidirect
427. Dic11#554semidirect
443. C4×Q8C4×D11semidirect
602. C11C4×#554semidirect

Maximal subgroups

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

subgroupindex
C2×#106231102
#130717122
#130717052
#130716932
#130716262
#130715242
#130715162
#130714892
#130711832
#130711712
#130711542
#130711502
C4×Q8×Dic112
C4×#669462
C4×C4⋊C4×D112
C11×#23552
C4×#55411