Finite Group Databasebeta

← #14914218

Subgroups — #14914218

Order 2816.

2310 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2#13071620C212yesmaximal
3#13071618C214yesmaximal
4#13071617C212yesmaximal
5#13071575C211yesmaximal, characteristic, complemented
6#13071574C212yesmaximal, complemented
7#13071573C211yesmaximal, characteristic, complemented
8C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
9#13071528C212yesmaximal, complemented
10#13071354C214yesmaximal, complemented
11#13071237C212yesmaximal
12#13071187C212yesmaximal, complemented
13C4×#66997C212yesmaximal, complemented
14D11×#384C211yesmaximal, characteristic
15#13070970C212yesmaximal
16C4×#66945C211yesmaximal, 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×#66945C2211yescharacteristic
26C2×#66945C2211yescharacteristic
27C2×C4⋊C4×D11C2212yes—
28C2×C4⋊C4×D11C2212yes—
29C2×C4⋊C4×D11C2212yes—
30C2×#66942C2212yes—
31C2×#66941C2211yescharacteristic
32C2×#66940C2214yes—
33C2×#66925C2212yes—
34C2×C42×D11C2211yescharacteristic
35C2×C4×Dic22C2212yes—
36C2×C4×Dic22C2212yes—
37C2×C4×Dic22C2211yescharacteristic
38C11×#389C2214yes—
39C11×#389C2212yes—
40C11×#384C2212yes—
41C11×#384C2211yescharacteristic
42C4×C11×C4⋊C4C2211yescharacteristic
43C4×C11×C4⋊C4C2212yes—
44#10622843C2212yes—
45#10622602C2214yes—
46#10622602C2214yes—
47#10622594C2214yes—
48#10622591C2214yes—
49#10622590C2212yes—
50#10622589C2212yes—
51#10622589C2212yes—
52#10622589C2212yes—
53#10622589C2212yes—
54C4⋊C4×Dic11C2212yes—
55C4⋊C4×Dic11C2212yes—
56C4⋊C4×Dic11C2211yescharacteristic
57C4⋊C4×Dic11C2211yescharacteristic
58C4⋊C4×Dic11C2212yes—
59C4⋊C4×Dic11C2212yes—
60#10622587C2212yes—
61#10622586C2214yes—
62#10622585C2214yes—
63#10622585C2214yes—
64#10622585C2214yes—
65#10622585C2214yes—
66C4×(C2×D11)⋊C4C2214yes—
67C4×(C2×D11)⋊C4C2212yes—
68#10622549C2212yes—
69#10622548C2211yescharacteristic
70C4×C4⋊Dic11C2211yescharacteristic
71C4×C4⋊Dic11C2212yes—
72#10622546C2214yes—
73C4×Dic11⋊C4C2214yes—
74C4×Dic11⋊C4C2214yes—
75C42×Dic11C2212yes—
76#10622541C2212yes—
77#10622279C2212yes—
78#10622279C2214yes—
79#10622267C2214yes—
80#10622262C2214yes—
81#10622261C2212yes—
82#10622260C2214yes—
83#10622259C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C22×C4×D11C2311yescharacteristic
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2314yes—
88C22×C4×D11C2311yescharacteristic
89C22×Dic22C2311yescharacteristic
90C22×Dic22C2312yes—
91C4×Q8×C11—44no—
92C4×Q8×C11C2×C418yescomplemented
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2314yes—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C42×C11C2312yes—
103C2×C42×C11C2314yes—
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2312yes—
106#66999C2×C418yes—
107#66997C2×C418yescomplemented
108C2×(C2×D11)⋊C4C2312yes—
109C2×(C2×D11)⋊C4C2312yes—
110C2×(C2×D11)⋊C4C2312yes—
111C2×(C2×D11)⋊C4C2312yes—
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2312yes—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2312yes—
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2312yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2312yes—
127C2×Dic11⋊C4C2312yes—
128C2×Dic11⋊C4C2312yes—
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2314yes—
134C2×C4×Dic11C2314yes—
135C2×C4×Dic11C2314yes—
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2312yes—
138C2×C4×Dic11C2311yescharacteristic
139C2×C4×Dic11C2311yescharacteristic
140C2×C4×Dic11C2312yes—
141#66950C2×C418yes—
142#66949C2×C4116yes—
143#66945—24no—
144#66945Q818yescomplemented
145C4⋊C4×D11—28no—
146C4⋊C4×D11—44no—
147C4⋊C4×D11—44no—
148#66942C2×C4116yescomplemented
149#66941C2×C418yescomplemented
150#66940—48no—
151#66925C2×C4116yes—
152C42×D11C2×C418yes—
153C4×Dic22—44no—
154C4×Dic22C2×C4116yescomplemented
155C4×Dic22C2×C418yescomplemented
156C11×#95C2314yes—
157C11×#95C2312yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2312yes—
162C11⋊#95C2312yes—
163C11⋊#95C2312yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168#34214—111nomaximal, Sylow
169C23×D11C2411yescharacteristic
170C2×Q8×C11—22no—
171C2×Q8×C11—22no—
172C2×Q8×C11C22×C414yes—
173C22×C4×C11C2414yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2412yes—
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C22×Dic11C2412yes—
182C22×Dic11C2414yes—
183C22×Dic11C2412yes—
184C22×Dic11C2412yes—
185C22×Dic11C2411yescharacteristic
186C22×Dic11C2412yes—
187C22×Dic11C2411yescharacteristic
188C22×Dic11C2411yescharacteristic
189C2×C4×D11—22no—
190C2×C4×D11—22no—
191C2×C4×D11—28no—
192C2×C4×D11—22no—
193C2×C4×D11—22no—
194C2×C4×D11—44no—
195C2×C4×D11—44no—
196C2×C4×D11C22×C414yes—
197C2×C4×D11C22×C414yes—
198C2×C4×D11C22×C414yes—
199C2×C4×D11C2×Q814yes—
200C2×C4×D11#4114yes—
201C2×Dic22—24no—
202C2×Dic22—24no—
203C2×Dic22—22no—
204C2×Dic22—22no—
205C2×Dic22C22×C418yes—
206C2×Dic22C22×C414yes—
207C11×C4⋊C4—24no—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—44no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4—44no—
213C11×C4⋊C4C22×C414yes—
214C11×C4⋊C4C22×C418yes—
215C11×C4⋊C4C2×Q814yes—
216C42×C11—24no—
217C42×C11—44no—
218C42×C11C22×C414yes—
219C42×C11C22×C418yes—
220(C2×D11)⋊C4—24no—
221(C2×D11)⋊C4C22×C418yes—
222(C2×D11)⋊C4C22×C418yes—
223(C2×D11)⋊C4C2×Q818yes—
224C4⋊Dic11—24no—
225C4⋊Dic11—22no—
226C4⋊Dic11—24no—
227C4⋊Dic11—42no—
228C4⋊Dic11C22×C414yes—
229C4⋊Dic11C22×C418yes—
230C4⋊Dic11C2×Q814yes—
231Dic11⋊C4—28no—
232Dic11⋊C4—28no—
233Dic11⋊C4—44no—
234Dic11⋊C4—44no—
235Dic11⋊C4—44no—
236Dic11⋊C4C22×C418yes—
237Dic11⋊C4C22×C418yes—
238Dic11⋊C4C22×C418yes—
239Dic11⋊C4C22×C418yes—
240Dic11⋊C4C22×C418yes—
241C4×Dic11—24no—
242C4×Dic11—24no—
243C4×Dic11—24no—
244C4×Dic11—24no—
245C4×Dic11—44no—
246C4×Dic11—44no—
247C4×Dic11—44no—
248C4×Dic11C22×C414yes—
249C4×Dic11C22×C418yes—
250C4×Dic11C22×C414yes—
251C4×Dic11C22×C414yes—
252C4×Dic11C2×Q818yes—
253C2×#533—111no—
254#2360—114no—
255#2360—112no—
256#2360—112no—
257#2355—111no—
258#2355—112no—
259#2355—111no—
260Q8×C4⋊C4—112no—
261Q8×C4⋊C4—111no—
262Q8×C4⋊C4D1111yescharacteristic, complemented
263#2330—114no—
264#2317—112no—
265C4×C4⋊Q8—112no—
266C4×C4⋊Q8—112no—
267C2×#384—111no—
268#2274—112no—
269C4×#117—111no—
270C23×C11C2511yescharacteristic
271C22×D11—21no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11C23×C412yes—
276C22×D11C22×Q812yes—
277C22×D11C2×#4112yes—
278Q8×C11—28no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—21no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—22no—
290C2×C4×C11—24no—
291C2×C4×C11—22no—
292C2×C4×C11—24no—
293C2×C4×C11C23×C412yes—
294C2×C4×C11C23×C414yes—
295C2×C4×C11C23×C414yes—
296C2×C4×C11C23×C412yes—
297C2×C4×C11C23×C412yes—
298C2×C4×C11C22×Q814yes—
299C2×C4×C11C22×Q812yes—
300C2×C4×C11C2×#4112yes—
301C2×C4×C11H(5,𝔽2)12yes—
302C2×C4×C112−1+412yes—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—21no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—21no—
311C2×Dic11—22no—
312C2×Dic11—24no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11C23×C412yes—
318C2×Dic11C23×C414yes—
319C2×Dic11C23×C414yes—
320C2×Dic11C23×C412yes—
321C2×Dic11C23×C412yes—
322C2×Dic11C22×Q814yes—
323C2×Dic11C22×Q812yes—
324C2×Dic11C2×#4112yes—
325C2×Dic11H(5,𝔽2)12yes—
326C2×Dic112−1+412yes—
327C4×D11—28no—
328C4×D11—28no—
329C4×D11—88no—
330C4×D11C4×Q8116yescomplemented
331Dic22—28no—
332Dic22—216no—
333#533—1116no—
334C2×C4⋊Q8—111no—
335C2×C4⋊Q8—111no—
336C2×#125—112no—
337C2×C22⋊Q8—111no—
338C2×C22⋊Q8—112no—
339C2×C22⋊Q8—111no—
340C2×C4×Q8—114no—
341C2×C4×Q8—111no—
342C2×C4×Q8—112no—
343C2×C4×Q8—112no—
344C2×C4×Q8C2×D1112yes—
345C2×C4×Q8C2×D1111yescharacteristic
346C2×#117—111no—
347C2×#117—111no—
348C2×#117—112no—
349C22×C4⋊C4—112no—
350C22×C4⋊C4—112no—
351C22×C4⋊C4—112no—
352C22×C42—111no—
353#391—112no—
354#391—112no—
355#391—114no—
356#389—114no—
357#389—114no—
358#389—114no—
359#389—114no—
360#389—114no—
361#389—112no—
362#389—114no—
363#389C2×D1112yes—
364#389C2×D1114yes—
365#387—114no—
366#387—114no—
367#387—114no—
368#387—114no—
369#385—114no—
370#385—114no—
371#384—112no—
372#384—112no—
373#384—112no—
374#384—112no—
375#384—111no—
376#384C2×D1112yes—
377#384C2×D1111yescharacteristic
378#382—112no—
379#382—112no—
380C4×C4⋊C4—112no—
381C4×C4⋊C4—112no—
382C4×C4⋊C4—111no—
383C4×C4⋊C4—112no—
384C4×C4⋊C4—112no—
385C4×C4⋊C4—111no—
386C4×C4⋊C4—114no—
387C4×C4⋊C4—114no—
388C4×C4⋊C4—112no—
389C4×C4⋊C4—111no—
390C4×C4⋊C4—114no—
391C4×C4⋊C4C2×D1111yescharacteristic
392C4×C4⋊C4C2×D1112yes—
393C4×C22⋊C4—112no—
394C4×C22⋊C4—114no—
395C4×C22⋊C4—112no—
396C4×C22⋊C4—114no—
397#376—112no—
398C43—112no—
399C22×C11C24×C411yescharacteristic
400C22×C11C23×Q811yescharacteristic
401C22×C11C22×#4111yescharacteristic
402C22×C11C2×H(5,𝔽2)11yescharacteristic
403C22×C11C2×H(5,𝔽2)11yescharacteristic
404C22×C11C2×2−1+411yescharacteristic
405C22×C11C2×2−1+411yescharacteristic
406C2×D11—22no—
407C2×D11—22no—
408C2×D11—22no—
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—22no—
412C2×D11C2×C4×Q814yes—
413C4×C11—24no—
414C4×C11—24no—
415C4×C11—22no—
416C4×C11—24no—
417C4×C11—42no—
418C4×C11—44no—
419C4×C11C2×C4×Q814yes—
420C4×C11#52014yes—
421Dic11—24no—
422Dic11—24no—
423Dic11—22no—
424Dic11—24no—
425Dic11—44no—
426Dic11—42no—
427Dic11C2×C4×Q814yes—
428Dic11#52014yes—
429C22×Q8—112no—
430C22×Q8—111no—
431C22×Q8C22×D1111yescharacteristic
432C23×C4—111no—
433C23×C4—111no—
434C23×C4—111no—
435C23×C4—114no—
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×Q8—448no—
447C4×Q8C4×D1118yescomplemented
448#117—118no—
449#117—1116no—
450#117—224no—
451C2×C4⋊C4—112no—
452C2×C4⋊C4—112no—
453C2×C4⋊C4—111no—
454C2×C4⋊C4—112no—
455C2×C4⋊C4—112no—
456C2×C4⋊C4—112no—
457C2×C4⋊C4—112no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—114no—
460C2×C4⋊C4—112no—
461C2×C4⋊C4—112no—
462C2×C4⋊C4—114no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—114no—
465C2×C4⋊C4—112no—
466C2×C4⋊C4—114no—
467C2×C4⋊C4—114no—
468C2×C4⋊C4—228no—
469C2×C4⋊C4—444no—
470C2×C4⋊C4—444no—
471C2×C4⋊C4C22×D1112yes—
472C2×C4⋊C4C22×D1112yes—
473C2×C4⋊C4C22×D1111yescharacteristic
474C2×C4⋊C4C22×D1112yes—
475C2×C4⋊C4C22×D1114yes—
476C2×C4⋊C4C22×D1114yes—
477C2×C4⋊C4C22×D1112yes—
478C2×C4⋊C4C22×D1111yescharacteristic
479C2×C4⋊C4C22×D1111yescharacteristic
480C2×C22⋊C4—112no—
481C2×C22⋊C4—112no—
482C2×C22⋊C4—112no—
483C2×C22⋊C4—112no—
484C2×C42—112no—
485C2×C42—112no—
486C2×C42—111no—
487C2×C42—111no—
488C2×C42—111no—
489C2×C42—118no—
490C2×C42—112no—
491C2×C42—112no—
492C2×C42—112no—
493C2×C42—112no—
494C2×C42—114no—
495C2×C42—114no—
496C2×C42—114no—
497C2×C42C22×D1112yes—
498C2×C42C22×D1114yes—
499C2×C42C22×D1112yes—
500C2×C42C22×D1111yescharacteristic
501#95—112no—
502#95—112no—
503#95—112no—
504#95—114no—
505#95—114no—
506#95—114no—
507#95—114no—
508#95—114no—
509#95—114no—
510#95—114no—
511#95C22×D1112yes—
512#95C22×D1114yes—
513C2×C11C22×C4×Q811yescharacteristic
514C2×C11C2×#52011yescharacteristic
515C2×C11C2×#52011yescharacteristic
516C2×C11#350311yescharacteristic
517C2×C11#350311yescharacteristic
518C2×C11#350811yescharacteristic
519C2×C11#350911yescharacteristic
520D11—24no—
521C24—111no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—118no—
525C2×Q8—114no—
526C2×Q8—224no—
527C2×Q8—224no—
528C2×Q8—222no—
529C2×Q8—222no—
530C2×Q8C2×C4×D1114yes—
531C22×C4—111no—
532C22×C4—111no—
533C22×C4—114no—
534C22×C4—114no—
535C22×C4—114no—
536C22×C4—112no—
537C22×C4—112no—
538C22×C4—112no—
539C22×C4—111no—
540C22×C4—114no—
541C22×C4—114no—
542C22×C4—112no—
543C22×C4—114no—
544C22×C4—222no—
545C22×C4—222no—
546C22×C4—228no—
547C22×C4—222no—
548C22×C4—222no—
549C22×C4—444no—
550C22×C4—444no—
551C22×C4C23×D1114yes—
552C22×C4C23×D1112yes—
553C22×C4C23×D1112yes—
554C22×C4C23×D1112yes—
555C22×C4C23×D1111yescharacteristic
556C22×C4C23×D1112yes—
557C22×C4C23×D1111yescharacteristic
558C22×C4C23×D1111yescharacteristic
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—22no—
562C4⋊C4—42no—
563C4⋊C4—44no—
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—114no—
573C4⋊C4—228no—
574C4⋊C4—228no—
575C4⋊C4—224no—
576C4⋊C4—224no—
577C4⋊C4—222no—
578C4⋊C4—444no—
579C4⋊C4—442no—
580C4⋊C4—444no—
581C4⋊C4—444no—
582C4⋊C4C2×C4×D1118yes—
583C4⋊C4C2×C4×D1114yes—
584C4⋊C4Q8×D1114yes—
585C22⋊C4—118no—
586C22⋊C4—118no—
587C22⋊C4—118no—
588C22⋊C4—224no—
589C42—24no—
590C42—44no—
591C42—114no—
592C42—114no—
593C42—114no—
594C42—118no—
595C42—118no—
596C42—224no—
597C42—224no—
598C42—224no—
599C42—224no—
600C42—444no—
601C42—444no—
602C42—444no—
603C42C2×C4×D1114yes—
604C42C2×C4×D1118yes—
605C11#3421411yescharacteristic, complemented, Sylow
606C23—112no—
607C23—112no—
608C23—112no—
609C23—221no—
610C23—221no—
611C23—221no—
612C23—221no—
613C23C24×D1111yescharacteristic
614Q8—28no—
615Q8—2216no—
616Q8—228no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—112no—
632C2×C4—112no—
633C2×C4—112no—
634C2×C4—112no—
635C2×C4—112no—
636C2×C4—112no—
637C2×C4—1116no—
638C2×C4—112no—
639C2×C4—114no—
640C2×C4—114no—
641C2×C4—114no—
642C2×C4—228no—
643C2×C4—222no—
644C2×C4—221no—
645C2×C4—222no—
646C2×C4—221no—
647C2×C4—222no—
648C2×C4—222no—
649C2×C4—222no—
650C2×C4—222no—
651C2×C4—228no—
652C2×C4—224no—
653C2×C4—222no—
654C2×C4—222no—
655C2×C4—224no—
656C2×C4—224no—
657C2×C4—222no—
658C2×C4—888no—
659C2×C4C22×C4×D1112yes—
660C2×C4C22×C4×D1114yes—
661C2×C4C22×C4×D1114yes—
662C2×C4C22×C4×D1112yes—
663C2×C4C22×C4×D1112yes—
664C2×C4#6703712yes—
665C2×C4C2×Q8×D1114yes—
666C2×C4C2×Q8×D1112yes—
667C2×C4#6704012yes—
668C2×C4#41×D1112yes—
669C22—114no—
670C22—222no—
671C22—222no—
672C22—222no—
673C22—222no—
674C22—222no—
675C22—222no—
676C22C23×C4×D1111yescharacteristic
677C22C2×#6703711yescharacteristic
678C22C22×Q8×D1111yescharacteristic
679C22C2×#6704011yescharacteristic
680C22C2×#41×D1111yescharacteristic
681C22D11×H(5,𝔽2)11yescharacteristic
682C22D11×2−1+411yescharacteristic
683C4—24no—
684C4—22no—
685C4—24no—
686C4—24no—
687C4—44no—
688C4—42no—
689C4—114no—
690C4—114no—
691C4—224no—
692C4—224no—
693C4—222no—
694C4—224no—
695C4—444no—
696C4—442no—
697C4#1062303514yes—
698C4C4×Q8×D1114yes—
699C2—224no—
700C2C2×C4×Q8×D1111yescharacteristic
701C2D11×#52011yescharacteristic
702C2C2×#1062303511yescharacteristic
703C2#1308242711yescharacteristic
704C2#1308243411yescharacteristic
705C2#1308248611yescharacteristic
706C2#1308249911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingQ8×C11×C4⋊C4C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenterQ8×C4⋊C4D11
hypocenterC11#34214
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. #13071575C2semidirect
6. #13071574C2semidirect
7. #13071573C2semidirect
8. C4⋊C4×Dic22C2semidirect
9. #13071528C2semidirect
10. #13071354C2semidirect
12. #13071187C2semidirect
13. C4×#66997C2semidirect
17. Q8×C11×C4⋊C4C2semidirect
22. #10623109C4semidirect
92. C4×Q8×C11C2×C4semidirect
107. #66997C2×C4semidirect
144. #66945Q8semidirect
148. #66942C2×C4semidirect
149. #66941C2×C4semidirect
154. C4×Dic22C2×C4semidirect
155. C4×Dic22C2×C4semidirect
262. Q8×C4⋊C4D11semidirect
330. C4×D11C4×Q8semidirect
447. C4×Q8C4×D11semidirect
605. C11#34214semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
#130716202
#130716182
#130716172
#130715752
#130715742
#130715732
C4⋊C4×Dic222
#130715282
#130713542
#130712372
#130711872
C4×#669972
D11×#3842
#130709702
C4×#669452
Q8×C11×C4⋊C42
#3421411