Finite Group Databasebeta

← #14914205

Subgroups — #14914205

Order 2816.

2226 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×#10623109C211yesmaximal, characteristic
2#13071715C214yesmaximal, complemented
3#13071702C212yesmaximal, complemented
4#13071670C212yesmaximal, complemented
5#13071575C212yesmaximal, complemented
6#13071574C212yesmaximal, complemented
7#13071573C211yesmaximal, characteristic, complemented
8#13071571C211yesmaximal, characteristic, complemented
9#13071528C211yesmaximal, characteristic, complemented
10#13071350C214yesmaximal
11#13071237C212yesmaximal
12#13071146C212yesmaximal
13C4×#66999C212yesmaximal
14#13071021C211yesmaximal, characteristic
15#13070970C212yesmaximal
16C4×C4⋊C4×D11C211yesmaximal, characteristic
17Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×#66997C2211yescharacteristic
22#10623109C4116yescomplemented
23C2×#66950C2211yescharacteristic
24C2×#66949C2212yes—
25C2×#66945C2212yes—
26C2×C4⋊C4×D11C2211yescharacteristic
27C2×C4⋊C4×D11C2211yescharacteristic
28C2×#66942C2212yes—
29C2×#66941C2211yescharacteristic
30C2×#66940C2212yes—
31C2×#66925C2212yes—
32C2×C42×D11C2212yes—
33C2×C42×D11C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C2×C4×Dic22C2212yes—
36C11×#389C2212yes—
37C11×#389C2214yes—
38C11×#384C2212yes—
39C11×#384C2211yescharacteristic
40C4×C11×C4⋊C4C2211yescharacteristic
41C4×C11×C4⋊C4C2212yes—
42#10622843C2212yes—
43#10622602C2214yes—
44#10622602C2214yes—
45#10622600C2212yes—
46#10622600C2212yes—
47#10622594C2214yes—
48#10622591C2214yes—
49#10622591C2214yes—
50#10622590C2212yes—
51#10622590C2212yes—
52#10622589C2212yes—
53C4⋊C4×Dic11C2212yes—
54C4⋊C4×Dic11C2214yes—
55C4⋊C4×Dic11C2212yes—
56C4⋊C4×Dic11C2212yes—
57C4⋊C4×Dic11C2211yescharacteristic
58C4⋊C4×Dic11C2211yescharacteristic
59C4⋊C4×Dic11C2212yes—
60C4⋊C4×Dic11C2212yes—
61#10622587C2214yes—
62#10622586C2212yes—
63#10622585C2214yes—
64#10622585C2214yes—
65#10622585C2214yes—
66C4×(C2×D11)⋊C4C2214yes—
67#10622549C2212yes—
68#10622548C2211yescharacteristic
69C4×C4⋊Dic11C2212yes—
70C4×C4⋊Dic11C2211yescharacteristic
71C4×C4⋊Dic11C2212yes—
72#10622546C2214yes—
73C4×Dic11⋊C4C2214yes—
74C4×Dic11⋊C4C2212yes—
75C4×Dic11⋊C4C2214yes—
76#10622542C2212yes—
77#10622279C2214yes—
78D11×#95C2212yes—
79#10622268C2214yes—
80#10622267C2214yes—
81#10622262C2214yes—
82#10622262C2212yes—
83#10622259C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C22×C4×D11C2311yescharacteristic
86C22×C4×D11C2312yes—
87C22×C4×D11C2311yescharacteristic
88C22×C4×D11C2312yes—
89C22×C4×D11C2311yescharacteristic
90C22×Dic22C2311yescharacteristic
91C22×Dic22C2312yes—
92C4×Q8×C11—44no—
93C4×Q8×C11C2×C418yescomplemented
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2314yes—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C42×C11C2312yes—
104C2×C42×C11C2314yes—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2312yes—
107#66999C2×C418yes—
108#66997C2×C418yescomplemented
109C2×(C2×D11)⋊C4C2314yes—
110C2×(C2×D11)⋊C4C2312yes—
111C2×(C2×D11)⋊C4C2312yes—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2312yes—
114C2×C4⋊Dic11C2312yes—
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2312yes—
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4C2312yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2312yes—
123C2×Dic11⋊C4C2312yes—
124C2×Dic11⋊C4C2312yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2312yes—
127C2×Dic11⋊C4C2312yes—
128C2×C4×Dic11C2312yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2314yes—
133C2×C4×Dic11C2314yes—
134C2×C4×Dic11C2314yes—
135C2×C4×Dic11C2311yescharacteristic
136C2×C4×Dic11C2312yes—
137C2×C4×Dic11C2311yescharacteristic
138C2×C4×Dic11C2311yescharacteristic
139#66950C2×C418yes—
140#66949C2×C4116yes—
141#66945—28no—
142C4⋊C4×D11—24no—
143C4⋊C4×D11Q818yescomplemented
144#66942C2×C4116yescomplemented
145#66941C2×C418yescomplemented
146#66940—44no—
147#66925C2×C4116yes—
148C42×D11—44no—
149C42×D11C2×C418yes—
150C4×Dic22C2×C4116yescomplemented
151C4×Dic22C2×C418yescomplemented
152C11×#95C2314yes—
153C11×#95C2312yes—
154C11⋊#95C2312yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2312yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2312yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166#34213—111nomaximal, Sylow
167C23×D11C2411yescharacteristic
168C2×Q8×C11—22no—
169C2×Q8×C11—22no—
170C2×Q8×C11C22×C414yes—
171C22×C4×C11C2412yes—
172C22×C4×C11C2414yes—
173C22×C4×C11C2412yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2411yescharacteristic
176C22×C4×C11C2412yes—
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2411yescharacteristic
179C22×Dic11C2414yes—
180C22×Dic11C2412yes—
181C22×Dic11C2411yescharacteristic
182C22×Dic11C2411yescharacteristic
183C22×Dic11C2412yes—
184C22×Dic11C2412yes—
185C22×Dic11C2412yes—
186C22×Dic11C2411yescharacteristic
187C2×C4×D11—24no—
188C2×C4×D11—22no—
189C2×C4×D11—22no—
190C2×C4×D11—42no—
191C2×C4×D11—42no—
192C2×C4×D11—42no—
193C2×C4×D11—41no—
194C2×C4×D11—41no—
195C2×C4×D11—42no—
196C2×C4×D11C22×C414yes—
197C2×C4×D11C22×C414yes—
198C2×C4×D11C22×C414yes—
199C2×C4×D11C2×Q818yes—
200C2×C4×D11C2×Q814yes—
201C2×C4×D11#4114yes—
202C2×Dic22—22no—
203C2×Dic22—22no—
204C2×Dic22—42no—
205C2×Dic22—42no—
206C2×Dic22C22×C414yes—
207C2×Dic22C22×C418yes—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—44no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4—44no—
214C11×C4⋊C4C22×C414yes—
215C11×C4⋊C4C22×C418yes—
216C11×C4⋊C4C2×Q814yes—
217C42×C11—24no—
218C42×C11—44no—
219C42×C11C22×C414yes—
220C42×C11C22×C418yes—
221(C2×D11)⋊C4—28no—
222(C2×D11)⋊C4C22×C418yes—
223(C2×D11)⋊C4C22×C418yes—
224C4⋊Dic11—22no—
225C4⋊Dic11—24no—
226C4⋊Dic11—24no—
227C4⋊Dic11—42no—
228C4⋊Dic11C22×C414yes—
229C4⋊Dic11C22×C418yes—
230C4⋊Dic11C2×Q814yes—
231Dic11⋊C4—24no—
232Dic11⋊C4—44no—
233Dic11⋊C4—44no—
234Dic11⋊C4C22×C418yes—
235Dic11⋊C4C22×C418yes—
236Dic11⋊C4C22×C418yes—
237Dic11⋊C4C22×C418yes—
238Dic11⋊C4C22×C418yes—
239Dic11⋊C4C2×Q818yes—
240C4×Dic11—28no—
241C4×Dic11—24no—
242C4×Dic11—42no—
243C4×Dic11—42no—
244C4×Dic11—44no—
245C4×Dic11—44no—
246C4×Dic11—44no—
247C4×Dic11C22×C414yes—
248C4×Dic11C22×C418yes—
249C4×Dic11C22×C414yes—
250C4×Dic11C22×C414yes—
251C2×#533—111no—
252#2370—114no—
253#2369—112no—
254#2365—112no—
255#2355—112no—
256#2355—111no—
257#2355—112no—
258#2355—111no—
259Q8×C4⋊C4—111no—
260Q8×C4⋊C4D1111yescharacteristic, complemented
261#2329—114no—
262#2317—112no—
263C4×C22⋊Q8—112no—
264C4×C22⋊Q8—112no—
265#2285—111no—
266#2274—112no—
267C2×C4×C4⋊C4—111no—
268C23×C11C2511yescharacteristic
269C22×D11—21no—
270C22×D11—21no—
271C22×D11—21no—
272C22×D11—21no—
273C22×D11C23×C412yes—
274C22×D11C22×Q812yes—
275C22×D11C2×#4112yes—
276Q8×C11—28no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—21no—
283C2×C4×C11—22no—
284C2×C4×C11—21no—
285C2×C4×C11—24no—
286C2×C4×C11—22no—
287C2×C4×C11—24no—
288C2×C4×C11—22no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11C23×C412yes—
292C2×C4×C11C23×C414yes—
293C2×C4×C11C23×C414yes—
294C2×C4×C11C23×C412yes—
295C2×C4×C11C23×C412yes—
296C2×C4×C11C22×Q814yes—
297C2×C4×C11C22×Q812yes—
298C2×C4×C11C2×#4112yes—
299C2×C4×C11H(5,𝔽2)12yes—
300C2×C4×C112−1+412yes—
301C2×Dic11—22no—
302C2×Dic11—21no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—21no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—24no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—22no—
317C2×Dic11C23×C412yes—
318C2×Dic11C23×C412yes—
319C2×Dic11C23×C414yes—
320C2×Dic11C23×C414yes—
321C2×Dic11C23×C412yes—
322C2×Dic11C22×Q814yes—
323C2×Dic11C22×Q812yes—
324C2×Dic11C2×#4112yes—
325C4×D11—28no—
326C4×D11—44no—
327C4×D11—48no—
328C4×D11—48no—
329C4×D11C4×Q8116yescomplemented
330Dic22—28no—
331Dic22—48no—
332#533—1116no—
333C2×C4⋊Q8—111no—
334C2×C4⋊Q8—111no—
335C2×#125—112no—
336C2×C22⋊Q8—111no—
337C2×C22⋊Q8—112no—
338C2×C22⋊Q8—111no—
339C2×C4×Q8—112no—
340C2×C4×Q8—111no—
341C2×C4×Q8—112no—
342C2×C4×Q8C2×D1112yes—
343C2×C4×Q8C2×D1111yescharacteristic
344C2×#117—112no—
345C2×#117—112no—
346C22×C4⋊C4—111no—
347C22×C4⋊C4—111no—
348C22×C42—111no—
349C22×C42—112no—
350#391—112no—
351#391—114no—
352#391—112no—
353#391—114no—
354#389—114no—
355#389—114no—
356#389—114no—
357#389—112no—
358#389C2×D1114yes—
359#389C2×D1112yes—
360#387—114no—
361#387—114no—
362#387—114no—
363#387—114no—
364#387—114no—
365#387—114no—
366#385—114no—
367#385—114no—
368#384—112no—
369#384—111no—
370#384C2×D1112yes—
371#384C2×D1111yescharacteristic
372#382—112no—
373#382—112no—
374#382—112no—
375#380—112no—
376#380—112no—
377C4×C4⋊C4—112no—
378C4×C4⋊C4—111no—
379C4×C4⋊C4—111no—
380C4×C4⋊C4—112no—
381C4×C4⋊C4—112no—
382C4×C4⋊C4—114no—
383C4×C4⋊C4—112no—
384C4×C4⋊C4—112no—
385C4×C4⋊C4—111no—
386C4×C4⋊C4—112no—
387C4×C4⋊C4—112no—
388C4×C4⋊C4—114no—
389C4×C4⋊C4—112no—
390C4×C4⋊C4—114no—
391C4×C4⋊C4—114no—
392C4×C4⋊C4—112no—
393C4×C4⋊C4C2×D1111yescharacteristic
394C4×C4⋊C4C2×D1112yes—
395C4×C22⋊C4—114no—
396C4×C22⋊C4—114no—
397C2×#95—112no—
398C22×C11C24×C411yescharacteristic
399C22×C11C23×Q811yescharacteristic
400C22×C11C22×#4111yescharacteristic
401C22×C11C2×H(5,𝔽2)11yescharacteristic
402C22×C11C2×2−1+411yescharacteristic
403C22×C11#58511yescharacteristic
404C22×C11#58511yescharacteristic
405C2×D11—22no—
406C2×D11—22no—
407C2×D11—22no—
408C2×D11—22no—
409C2×D11—22no—
410C2×D11—22no—
411C2×D11C2×C4×Q814yes—
412C4×C11—24no—
413C4×C11—24no—
414C4×C11—22no—
415C4×C11—24no—
416C4×C11—44no—
417C4×C11—42no—
418C4×C11C2×C4×Q814yes—
419C4×C11#52014yes—
420Dic11—24no—
421Dic11—22no—
422Dic11—22no—
423Dic11—24no—
424Dic11—24no—
425Dic11—42no—
426Dic11—44no—
427Dic11C2×C4×Q814yes—
428C22×Q8—111no—
429C22×Q8—112no—
430C22×Q8C22×D1111yescharacteristic
431C23×C4—111no—
432C23×C4—111no—
433C23×C4—112no—
434C23×C4—111no—
435C23×C4—112no—
436C4⋊Q8—118no—
437C4⋊Q8—118no—
438#125—1116no—
439C22⋊Q8—118no—
440C22⋊Q8—1116no—
441C22⋊Q8—118no—
442C4×Q8—44no—
443C4×Q8—1116no—
444C4×Q8—118no—
445C4×Q8—444no—
446C4×Q8C4×D1118yescomplemented
447#117—1116no—
448#117—228no—
449C2×C4⋊C4—112no—
450C2×C4⋊C4—111no—
451C2×C4⋊C4—112no—
452C2×C4⋊C4—112no—
453C2×C4⋊C4—112no—
454C2×C4⋊C4—112no—
455C2×C4⋊C4—112no—
456C2×C4⋊C4—111no—
457C2×C4⋊C4—112no—
458C2×C4⋊C4—118no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4—112no—
461C2×C4⋊C4—112no—
462C2×C4⋊C4—112no—
463C2×C4⋊C4—114no—
464C2×C4⋊C4—112no—
465C2×C4⋊C4—114no—
466C2×C4⋊C4—224no—
467C2×C4⋊C4C22×D1111yescharacteristic
468C2×C4⋊C4C22×D1112yes—
469C2×C4⋊C4C22×D1112yes—
470C2×C4⋊C4C22×D1114yes—
471C2×C4⋊C4C22×D1112yes—
472C2×C4⋊C4C22×D1114yes—
473C2×C4⋊C4C22×D1112yes—
474C2×C4⋊C4C22×D1111yescharacteristic
475C2×C4⋊C4C22×D1111yescharacteristic
476C2×C22⋊C4—112no—
477C2×C22⋊C4—112no—
478C2×C22⋊C4—114no—
479C2×C42—112no—
480C2×C42—111no—
481C2×C42—111no—
482C2×C42—111no—
483C2×C42—118no—
484C2×C42—114no—
485C2×C42—112no—
486C2×C42—114no—
487C2×C42—114no—
488C2×C42—114no—
489C2×C42—112no—
490C2×C42—112no—
491C2×C42—444no—
492C2×C42C22×D1112yes—
493C2×C42C22×D1114yes—
494C2×C42C22×D1112yes—
495C2×C42C22×D1111yescharacteristic
496#95—112no—
497#95—112no—
498#95—112no—
499#95—114no—
500#95—114no—
501#95—114no—
502#95—114no—
503#95—114no—
504#95—114no—
505#95—114no—
506#95—114no—
507#95—114no—
508#95C22×D1112yes—
509#95C22×D1114yes—
510C2×C11C22×C4×Q811yescharacteristic
511C2×C11C2×#52011yescharacteristic
512C2×C11#342811yescharacteristic
513C2×C11#350111yescharacteristic
514C2×C11#350211yescharacteristic
515C2×C11#350611yescharacteristic
516C2×C11#350711yescharacteristic
517D11—24no—
518C24—111no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—114no—
522C2×Q8—118no—
523C2×Q8—222no—
524C2×Q8—222no—
525C2×Q8—442no—
526C2×Q8—442no—
527C2×Q8C2×C4×D1114yes—
528C22×C4—111no—
529C22×C4—114no—
530C22×C4—114no—
531C22×C4—114no—
532C22×C4—111no—
533C22×C4—112no—
534C22×C4—111no—
535C22×C4—112no—
536C22×C4—112no—
537C22×C4—114no—
538C22×C4—114no—
539C22×C4—118no—
540C22×C4—114no—
541C22×C4—112no—
542C22×C4—224no—
543C22×C4—222no—
544C22×C4—222no—
545C22×C4—442no—
546C22×C4—442no—
547C22×C4—441no—
548C22×C4—442no—
549C22×C4—441no—
550C22×C4—442no—
551C22×C4C23×D1112yes—
552C22×C4C23×D1114yes—
553C22×C4C23×D1112yes—
554C22×C4C23×D1112yes—
555C22×C4C23×D1111yescharacteristic
556C22×C4C23×D1112yes—
557C22×C4C23×D1111yescharacteristic
558C22×C4C23×D1111yescharacteristic
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—24no—
562C4⋊C4—44no—
563C4⋊C4—42no—
564C4⋊C4—44no—
565C4⋊C4—118no—
566C4⋊C4—118no—
567C4⋊C4—118no—
568C4⋊C4—118no—
569C4⋊C4—118no—
570C4⋊C4—118no—
571C4⋊C4—114no—
572C4⋊C4—118no—
573C4⋊C4—114no—
574C4⋊C4—224no—
575C4⋊C4—224no—
576C4⋊C4—222no—
577C4⋊C4—224no—
578C4⋊C4—444no—
579C4⋊C4—444no—
580C4⋊C4—442no—
581C4⋊C4C2×C4×D1118yes—
582C4⋊C4C2×C4×D1114yes—
583C4⋊C4Q8×D1114yes—
584C22⋊C4—118no—
585C22⋊C4—118no—
586C22⋊C4—228no—
587C42—24no—
588C42—44no—
589C42—114no—
590C42—114no—
591C42—114no—
592C42—118no—
593C42—228no—
594C42—224no—
595C42—442no—
596C42—442no—
597C42—444no—
598C42—444no—
599C42—444no—
600C42C2×C4×D1114yes—
601C42C2×C4×D1118yes—
602C11#3421311yescharacteristic, complemented, Sylow
603C23—112no—
604C23—112no—
605C23—112no—
606C23—221no—
607C23—221no—
608C23—221no—
609C23—221no—
610C23C24×D1111yescharacteristic
611Q8—28no—
612Q8—228no—
613Q8—448no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—112no—
629C2×C4—112no—
630C2×C4—112no—
631C2×C4—1116no—
632C2×C4—112no—
633C2×C4—112no—
634C2×C4—114no—
635C2×C4—114no—
636C2×C4—114no—
637C2×C4—222no—
638C2×C4—221no—
639C2×C4—222no—
640C2×C4—221no—
641C2×C4—222no—
642C2×C4—222no—
643C2×C4—221no—
644C2×C4—222no—
645C2×C4—222no—
646C2×C4—221no—
647C2×C4—228no—
648C2×C4—222no—
649C2×C4—224no—
650C2×C4—224no—
651C2×C4—222no—
652C2×C4—222no—
653C2×C4—224no—
654C2×C4—448no—
655C2×C4—444no—
656C2×C4—448no—
657C2×C4C22×C4×D1112yes—
658C2×C4C22×C4×D1114yes—
659C2×C4C22×C4×D1114yes—
660C2×C4C22×C4×D1112yes—
661C2×C4C22×C4×D1112yes—
662C2×C4#6703712yes—
663C2×C4C2×Q8×D1114yes—
664C2×C4C2×Q8×D1112yes—
665C2×C4#6704012yes—
666C2×C4#41×D1112yes—
667C22—114no—
668C22—222no—
669C22—222no—
670C22—222no—
671C22—222no—
672C22—222no—
673C22—222no—
674C22C23×C4×D1111yescharacteristic
675C22C2×#6703711yescharacteristic
676C22C22×Q8×D1111yescharacteristic
677C22C2×#6704011yescharacteristic
678C22C2×#41×D1111yescharacteristic
679C22#1062345511yescharacteristic
680C22#1062345711yescharacteristic
681C4—24no—
682C4—24no—
683C4—22no—
684C4—24no—
685C4—42no—
686C4—44no—
687C4—114no—
688C4—224no—
689C4—222no—
690C4—224no—
691C4—222no—
692C4—224no—
693C4—442no—
694C4—444no—
695C4#1062303514yes—
696C4C4×Q8×D1114yes—
697C2—224no—
698C2C2×C4×Q8×D1111yescharacteristic
699C2C2×#1062303511yescharacteristic
700C2#1308181611yescharacteristic
701C2#1308241111yescharacteristic
702C2#1308242511yescharacteristic
703C2#1308246011yescharacteristic
704C2#1308248211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingQ8×C11×C4⋊C4C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenterQ8×C4⋊C4D11
hypocenterC11#34213
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071715C2semidirect
3. #13071702C2semidirect
4. #13071670C2semidirect
5. #13071575C2semidirect
6. #13071574C2semidirect
7. #13071573C2semidirect
8. #13071571C2semidirect
9. #13071528C2semidirect
17. Q8×C11×C4⋊C4C2semidirect
22. #10623109C4semidirect
93. C4×Q8×C11C2×C4semidirect
108. #66997C2×C4semidirect
143. C4⋊C4×D11Q8semidirect
144. #66942C2×C4semidirect
145. #66941C2×C4semidirect
150. C4×Dic22C2×C4semidirect
151. C4×Dic22C2×C4semidirect
260. Q8×C4⋊C4D11semidirect
329. C4×D11C4×Q8semidirect
446. C4×Q8C4×D11semidirect
602. C11#34213semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
#130717152
#130717022
#130716702
#130715752
#130715742
#130715732
#130715712
#130715282
#130713502
#130712372
#130711462
C4×#669992
#130710212
#130709702
C4×C4⋊C4×D112
Q8×C11×C4⋊C42
#3421311