Finite Group Databasebeta

← Dic11×#554 #14913747

Subgroups — Dic11×#554 #14913747

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
1#13071716C212yesmaximal, complemented
2#13071706C211yesmaximal, characteristic, complemented
3#13071701C214yesmaximal, complemented
4#13071625C212yesmaximal, complemented
5#13071573C211yesmaximal, characteristic, complemented
6#13071526C212yesmaximal
7D4×C4⋊Dic11C211yesmaximal, characteristic
8#13071493C212yesmaximal, complemented
9C4⋊Q8×Dic11C211yesmaximal, characteristic, complemented
10#125×Dic11C212yesmaximal, complemented
11C22⋊Q8×Dic11C212yesmaximal, complemented
12C22⋊Q8×Dic11C214yesmaximal, complemented
13C4×Q8×Dic11C211yesmaximal, characteristic, complemented
14C4×D4×Dic11C212yesmaximal
15C4×D4×Dic11C211yesmaximal, characteristic
16C2×C4⋊C4×Dic11C212yesmaximal, complemented
17C2×C11×#554C211yesmaximal, characteristic
18C11×#554C4116yescomplemented
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#125C2212yes—
21C2×C11×C22⋊Q8C2212yes—
22C2×C11×C22⋊Q8C2214yes—
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2212yes—
26C22×C11×C4⋊C4C2212yes—
27C2×Q8×Dic11C2211yescharacteristic
28C2×Q8×Dic11C2211yescharacteristic
29C2×Q8×Dic11C2212yes—
30C2×D4×Dic11C2212yes—
31C2×D4×Dic11C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2212yes—
34C22×C4×Dic11C2212yes—
35C22×C4×Dic11C2214yes—
36#10622843C2212yes—
37#10622843C2214yes—
38#10622843C2212yes—
39#10622825C2212yes—
40#10622825C2214yes—
41C4×C22⋊Dic11C2212yes—
42C4×C22⋊Dic11C2214yes—
43C2×C11⋊#95C2214yes—
44#10622598C2214yes—
45#10622598C2212yes—
46#10622598C2212yes—
47#10622598C2212yes—
48#10622598C2212yes—
49#10622598C2212yes—
50#10622594C2214yes—
51#10622594C2214yes—
52#10622594C2214yes—
53#10622594C2214yes—
54#10622594C2214yes—
55C4⋊C4×Dic11C2212yes—
56C4⋊C4×Dic11C2214yes—
57C4⋊C4×Dic11C2212yes—
58C4⋊C4×Dic11C2214yes—
59C4⋊C4×Dic11C2212yes—
60C4⋊C4×Dic11C2211yescharacteristic
61C4⋊C4×Dic11C2212yes—
62C4⋊C4×Dic11C2212yes—
63C4⋊C4×Dic11C2214yes—
64C4⋊C4×Dic11C2212yes—
65C4⋊C4×Dic11C2211yescharacteristic
66C4⋊C4×Dic11C2211yescharacteristic
67C4⋊C4×Dic11C2212yes—
68C4⋊C4×Dic11C2211yescharacteristic
69#10622563C2214yes—
70#10622563C2214yes—
71#10622563C2214yes—
72C22⋊C4×Dic11C2214yes—
73C22⋊C4×Dic11C2212yes—
74C22⋊C4×Dic11C2214yes—
75C22⋊C4×Dic11C2212yes—
76#10622549C2212yes—
77#10622548C2211yescharacteristic
78C4×C4⋊Dic11C2211yescharacteristic
79C4×C4⋊Dic11C2211yescharacteristic
80C4×C4⋊Dic11C2212yes—
81C4×C4⋊Dic11C2212yes—
82C42×Dic11C2212yes—
83C42×Dic11C2211yescharacteristic
84C22×Q8×C11C2311yescharacteristic
85C22×Q8×C11C2312yes—
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11C2312yes—
88C23×C4×C11C2314yes—
89C23×Dic11C2314yes—
90C23×Dic11C2312yes—
91C23×Dic11C2312yes—
92C11×C4⋊Q8C2×C418yescomplemented
93C11×#125C2×C4116yescomplemented
94C11×C22⋊Q8C2×C4132yescomplemented
95C11×C22⋊Q8C2×C4116yescomplemented
96C4×Q8×C11C2×C418yescomplemented
97C4×D4×C11C2×C4116yes—
98C4×D4×C11C2×C418yes—
99C2×C11×C4⋊C4C2×C4116yescomplemented
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2312yes—
111C2×C22⋊Dic11C2312yes—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2312yes—
114Q8×Dic11—24no—
115Q8×Dic11—24no—
116Q8×Dic11—44no—
117D4×Dic11—28no—
118D4×Dic11—24no—
119D4×Dic11Q818yescomplemented
120C2×C4⋊Dic11—28no—
121C2×C4⋊Dic11C2312yes—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2312yes—
124C2×C4⋊Dic11C2312yes—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2312yes—
127C2×C4⋊Dic11C2314yes—
128C2×C4⋊Dic11C2312yes—
129C2×C4⋊Dic11C2314yes—
130C2×C4⋊Dic11C2314yes—
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4×Dic11—28no—
134C2×C4×Dic11—48no—
135C2×C4×Dic11C2312yes—
136C2×C4×Dic11C2312yes—
137C2×C4×Dic11C2311yescharacteristic
138C2×C4×Dic11C2311yescharacteristic
139C2×C4×Dic11C2312yes—
140C2×C4×Dic11C2312yes—
141C2×C4×Dic11C2311yescharacteristic
142C2×C4×Dic11C2312yes—
143C2×C4×Dic11C2314yes—
144C2×C4×Dic11C2312yes—
145C2×C4×Dic11C2312yes—
146C2×C4×Dic11C2311yescharacteristic
147C2×C4×Dic11C2312yes—
148C2×C4×Dic11C2314yes—
149C2×C4×Dic11C2314yes—
150C2×C4×Dic11C2311yescharacteristic
151C2×C4×Dic11C2311yescharacteristic
152C11⋊#95C2312yes—
153C11⋊#95C2314yes—
154C11⋊#95C2312yes—
155C11⋊#95C2312yes—
156C11⋊#95C2312yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2312yes—
162C11⋊#95C2312yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C4×#554—111nomaximal, Sylow
167C24×C11C2412yes—
168C2×Q8×C11—22no—
169C2×Q8×C11—22no—
170C2×Q8×C11—42no—
171C2×Q8×C11—42no—
172C2×Q8×C11C22×C414yes—
173C2×Q8×C11C22×C418yes—
174C2×D4×C11C22×C414yes—
175C2×D4×C11C2×Q814yes—
176C2×D4×C11#4114yes—
177C22×C4×C11—24no—
178C22×C4×C11—24no—
179C22×C4×C11—44no—
180C22×C4×C11—44no—
181C22×C4×C11C22×C418yes—
182C22×C4×C11C22×C4116yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2412yes—
187C22×C4×C11C2414yes—
188C22×C4×C11C2411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C22×Dic11—24no—
191C22×Dic11—24no—
192C22×Dic11—24no—
193C22×Dic11—28no—
194C22×Dic11—28no—
195C22×Dic11—24no—
196C22×Dic11—44no—
197C22×Dic11—42no—
198C22×Dic11C2×Q818yes—
199C22×Dic11C2412yes—
200C22×Dic11C2412yes—
201C22×Dic11C2414yes—
202C22×Dic11C2411yescharacteristic
203C22×Dic11C2411yescharacteristic
204C22×Dic11C2412yes—
205C22×Dic11C2411yescharacteristic
206C22×Dic11C2412yes—
207C22×Dic11C2411yescharacteristic
208C11×C4⋊C4C22×C414yes—
209C11×C4⋊C4C22×C4116yes—
210C11×C4⋊C4C22×C418yes—
211C11×C4⋊C4C22×C414yes—
212C11×C4⋊C4C22×C418yes—
213C11×C4⋊C4C22×C418yes—
214C11×C4⋊C4C22×C4116yes—
215C11×C22⋊C4C22×C4116yes—
216C11×C22⋊C4C22×C418yes—
217C42×C11C22×C418yes—
218C42×C11C22×C414yes—
219C22⋊Dic11—28no—
220C22⋊Dic11—24no—
221C22⋊Dic11C2×Q818yes—
222C4⋊Dic11—28no—
223C4⋊Dic11—24no—
224C4⋊Dic11—24no—
225C4⋊Dic11—24no—
226C4⋊Dic11—24no—
227C4⋊Dic11—22no—
228C4⋊Dic11—22no—
229C4⋊Dic11—44no—
230C4⋊Dic11—44no—
231C4⋊Dic11—42no—
232C4⋊Dic11C2×Q814yes—
233C4⋊Dic11#4114yes—
234C4×Dic11—24no—
235C4×Dic11—24no—
236C4×Dic11—24no—
237C4×Dic11—24no—
238C4×Dic11—24no—
239C4×Dic11—28no—
240C4×Dic11—22no—
241C4×Dic11—24no—
242C4×Dic11—22no—
243C4×Dic11—24no—
244C4×Dic11—22no—
245C4×Dic11—44no—
246C4×Dic11—44no—
247C4×Dic11—42no—
248C4×Dic11—41no—
249C4×Dic11C2×Q814yes—
250C4×Dic11#4114yes—
251C2×#554D1111yescharacteristic
252#2370—112no—
253#2369—111no—
254#2368—114no—
255#2360—112no—
256#2355—111no—
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×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11C23×C414yes—
273C23×C11C22×Q814yes—
274C23×C11C2×#4114yes—
275C23×C11C2511yescharacteristic
276Q8×C11—28no—
277Q8×C11—48no—
278D4×C11C4×Q8116yescomplemented
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—24no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—21no—
288C2×C4×C11—24no—
289C2×C4×C11—216no—
290C2×C4×C11—416no—
291C2×C4×C11C23×C414yes—
292C2×C4×C11C23×C412yes—
293C2×C4×C11C23×C414yes—
294C2×C4×C11C23×C414yes—
295C2×C4×C11C23×C418yes—
296C2×C4×C11C23×C412yes—
297C2×C4×C11C23×C412yes—
298C2×C4×C11C22×Q812yes—
299C2×C4×C11C2×#4112yes—
300C2×C4×C11C2×#4112yes—
301C2×C4×C11C2×#4112yes—
302C2×Dic11—21no—
303C2×Dic11—22no—
304C2×Dic11—21no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—216no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—21no—
314C2×Dic11—22no—
315C2×Dic11—21no—
316C2×Dic11—24no—
317C2×Dic11—22no—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—21no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—48no—
324C2×Dic11—416no—
325C2×Dic11C22×Q812yes—
326C2×Dic11C22×Q814yes—
327C2×Dic11C22×Q812yes—
328C2×Dic11C2×#4112yes—
329C2×Dic11C2×#4114yes—
330C2×Dic11C2×#4112yes—
331C2×Dic11H(5,𝔽2)12yes—
332#554Dic11116yesdirect product factor
333C2×C4⋊Q8C2×D1111yescharacteristic
334C2×#125C2×D1112yes—
335C2×C22⋊Q8C2×D1112yes—
336C2×C22⋊Q8C2×D1114yes—
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×D4C2×D1111yescharacteristic
345C2×C4×D4C2×D1112yes—
346C22×C4⋊C4—112no—
347C22×C4⋊C4C2×D1112yes—
348C22×C42—112no—
349C22×C42—114no—
350#391—112no—
351#391—112no—
352#391—114no—
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#387—114no—
364#385—114no—
365#385—114no—
366#385—114no—
367#384—111no—
368#382—112no—
369#380—112no—
370#380—114no—
371C4×C4⋊C4—111no—
372C4×C4⋊C4—112no—
373C4×C4⋊C4—114no—
374C4×C4⋊C4—114no—
375C4×C4⋊C4—112no—
376C4×C4⋊C4—111no—
377C4×C4⋊C4—112no—
378C4×C4⋊C4—112no—
379C4×C4⋊C4—112no—
380C4×C4⋊C4—114no—
381C4×C4⋊C4—112no—
382C4×C4⋊C4—111no—
383C4×C4⋊C4—111no—
384C4×C4⋊C4—112no—
385C4×C4⋊C4—111no—
386C4×C4⋊C4—112no—
387C4×C4⋊C4—111no—
388C4×C4⋊C4—112no—
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×C11—24no—
399C22×C11—24no—
400C22×C11—24no—
401C22×C11—24no—
402C22×C11—24no—
403C22×C11—24no—
404C22×C11C2×C4×Q818yes—
405C22×C11C24×C411yescharacteristic
406C22×C11C23×Q811yescharacteristic
407C22×C11C22×#4111yescharacteristic
408C22×C11C22×#4111yescharacteristic
409C22×C11C22×#4111yescharacteristic
410C22×C11C2×H(5,𝔽2)11yescharacteristic
411C22×C11#58511yescharacteristic
412C4×C11—24no—
413C4×C11—24no—
414C4×C11—24no—
415C4×C11—28no—
416C4×C11—22no—
417C4×C11C2×C4×Q814yes—
418C4×C11C4×#4114yes—
419Dic11—24no—
420Dic11—22no—
421Dic11—22no—
422Dic11—24no—
423Dic11—42no—
424Dic11—42no—
425Dic11—41no—
426Dic11—44no—
427Dic11#55414yesdirect product factor
428C22×Q8C22×D1111yescharacteristic
429C22×Q8C22×D1112yes—
430C22×D4C22×D1111yescharacteristic
431C23×C4—112no—
432C23×C4—114no—
433C23×C4—112no—
434C23×C4C22×D1112yes—
435C23×C4C22×D1114yes—
436C4⋊Q8C2×Dic1118yescomplemented
437#125C2×Dic11116yescomplemented
438C22⋊Q8C2×Dic11132yescomplemented
439C22⋊Q8C2×Dic11116yescomplemented
440C4×Q8—224no—
441C4×Q8—224no—
442C4×Q8—444no—
443C4×Q8C2×Dic1118yescomplemented
444C4×D4—118no—
445C4×D4—228no—
446C4×D4—224no—
447C4×D4C2×Dic11116yes—
448C4×D4C2×Dic1118yes—
449C2×C4⋊C4—111no—
450C2×C4⋊C4—111no—
451C2×C4⋊C4—112no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—111no—
454C2×C4⋊C4—112no—
455C2×C4⋊C4—111no—
456C2×C4⋊C4—112no—
457C2×C4⋊C4—112no—
458C2×C4⋊C4—114no—
459C2×C4⋊C4—112no—
460C2×C4⋊C4—114no—
461C2×C4⋊C4—228no—
462C2×C4⋊C4C2×Dic11116yescomplemented
463C2×C4⋊C4C22×D1111yescharacteristic
464C2×C4⋊C4C22×D1114yes—
465C2×C4⋊C4C22×D1112yes—
466C2×C4⋊C4C22×D1111yescharacteristic
467C2×C4⋊C4C22×D1112yes—
468C2×C4⋊C4C22×D1112yes—
469C2×C4⋊C4C22×D1114yes—
470C2×C22⋊C4—112no—
471C2×C22⋊C4—112no—
472C2×C22⋊C4—114no—
473C2×C22⋊C4C22×D1114yes—
474C2×C22⋊C4C22×D1112yes—
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—112no—
489C2×C42—111no—
490C2×C42—114no—
491C2×C42—114no—
492C2×C42—228no—
493C2×C42—448no—
494C2×C42C22×D1112yes—
495C2×C42C22×D1111yescharacteristic
496#95—112no—
497#95—114no—
498#95—114no—
499#95—114no—
500#95—112no—
501#95—112no—
502#95—114no—
503#95—114no—
504#95—114no—
505#95—112no—
506#95—112no—
507#95—112no—
508#95—114no—
509#95—114no—
510C2×C11—28no—
511C2×C11C22×C4×Q811yescharacteristic
512C2×C11C2×C4×#4111yescharacteristic
513C2×C11C4×H(5,𝔽2)11yescharacteristic
514C2×C11C2×#55411yescharacteristic
515C2×C11#347511yescharacteristic
516C2×C11Q8×#4111yescharacteristic
517C2×C11#348111yescharacteristic
518C24C23×D1112yes—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—42no—
522C2×Q8—42no—
523C2×Q8C22×Dic1114yes—
524C2×Q8C22×Dic1118yes—
525C2×D4Q8×D1114yes—
526C2×D4#434314yes—
527C2×D4C22×Dic1114yes—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—111no—
533C22×C4—118no—
534C22×C4—111no—
535C22×C4—112no—
536C22×C4—111no—
537C22×C4—112no—
538C22×C4—112no—
539C22×C4—112no—
540C22×C4—114no—
541C22×C4—111no—
542C22×C4—224no—
543C22×C4—224no—
544C22×C4—224no—
545C22×C4—228no—
546C22×C4—228no—
547C22×C4—224no—
548C22×C4—444no—
549C22×C4—442no—
550C22×C4C22×Dic1118yes—
551C22×C4C22×Dic11116yes—
552C22×C4C23×D1112yes—
553C22×C4C23×D1112yes—
554C22×C4C23×D1111yescharacteristic
555C22×C4C23×D1112yes—
556C22×C4C23×D1114yes—
557C22×C4C23×D1111yescharacteristic
558C22×C4C23×D1111yescharacteristic
559C4⋊C4—114no—
560C4⋊C4—114no—
561C4⋊C4—228no—
562C4⋊C4—224no—
563C4⋊C4—224no—
564C4⋊C4—222no—
565C4⋊C4—224no—
566C4⋊C4—224no—
567C4⋊C4—222no—
568C4⋊C4—444no—
569C4⋊C4—442no—
570C4⋊C4—444no—
571C4⋊C4C22×Dic1114yes—
572C4⋊C4C22×Dic11116yes—
573C4⋊C4C22×Dic1118yes—
574C4⋊C4C22×Dic1114yes—
575C4⋊C4C22×Dic1118yes—
576C4⋊C4C22×Dic1118yes—
577C4⋊C4C22×Dic11116yes—
578C22⋊C4—118no—
579C22⋊C4—228no—
580C22⋊C4—224no—
581C22⋊C4C22×Dic11116yes—
582C22⋊C4C22×Dic1118yes—
583C42—114no—
584C42—114no—
585C42—224no—
586C42—224no—
587C42—224no—
588C42—228no—
589C42—224no—
590C42—224no—
591C42—222no—
592C42—222no—
593C42—224no—
594C42—224no—
595C42—222no—
596C42—444no—
597C42—444no—
598C42—442no—
599C42—441no—
600C42C22×Dic1118yes—
601C42C22×Dic1114yes—
602C11C4×#55411yescharacteristic, complemented, Sylow
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23C2×Q8×D1114yes—
608C23C2×#434314yes—
609C23C23×Dic1114yes—
610C23C24×D1111yescharacteristic
611Q8—28no—
612Q8—48no—
613D4Q8×Dic11116yescomplemented
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—24no—
624C2×C4—216no—
625C2×C4—416no—
626C2×C4—112no—
627C2×C4—112no—
628C2×C4—112no—
629C2×C4—112no—
630C2×C4—114no—
631C2×C4—112no—
632C2×C4—114no—
633C2×C4—2216no—
634C2×C4—221no—
635C2×C4—222no—
636C2×C4—221no—
637C2×C4—222no—
638C2×C4—222no—
639C2×C4—222no—
640C2×C4—221no—
641C2×C4—221no—
642C2×C4—222no—
643C2×C4—221no—
644C2×C4—222no—
645C2×C4—224no—
646C2×C4—222no—
647C2×C4—222no—
648C2×C4—221no—
649C2×C4—224no—
650C2×C4—224no—
651C2×C4—221no—
652C2×C4—222no—
653C2×C4—222no—
654C2×C4—448no—
655C2×C4—4416no—
656C2×C4C2×Q8×D1112yes—
657C2×C4C2×#434312yes—
658C2×C4#41×D1112yes—
659C2×C4#41×D1112yes—
660C2×C4C23×Dic1114yes—
661C2×C4C23×Dic1112yes—
662C2×C4C23×Dic1114yes—
663C2×C4C23×Dic1114yes—
664C2×C4C23×Dic1118yes—
665C2×C4C23×Dic1112yes—
666C2×C4C23×Dic1112yes—
667C22—24no—
668C22—24no—
669C22—24no—
670C22—24no—
671C22—24no—
672C22—24no—
673C22C2×Q8×Dic1118yes—
674C22C22×Q8×D1111yescharacteristic
675C22C22×#434311yescharacteristic
676C22C2×#41×D1111yescharacteristic
677C22C2×#41×D1111yescharacteristic
678C22D11×H(5,𝔽2)11yescharacteristic
679C22#1062345511yescharacteristic
680C22C24×Dic1111yescharacteristic
681C4—24no—
682C4—24no—
683C4—24no—
684C4—28no—
685C4—22no—
686C4—114no—
687C4—224no—
688C4—222no—
689C4—222no—
690C4—224no—
691C4—442no—
692C4—442no—
693C4—444no—
694C4—441no—
695C4C2×Q8×Dic1114yes—
696C4#41×Dic1114yes—
697C2—28no—
698C2C22×Q8×Dic1111yescharacteristic
699C2C2×#41×Dic1111yescharacteristic
700C2H(5,𝔽2)×Dic1111yescharacteristic
701C2D11×#55411yescharacteristic
702C2#1308218211yescharacteristic
703C2#1308219511yescharacteristic
704C2#1308222711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#554C2
socle, cosocleC23×C11C25
prime radicalC22×D4×C11C23
hypercenterC2×#554D11
hypocenterC11C4×#554
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #13071716C2semidirect
2. #13071706C2semidirect
3. #13071701C2semidirect
4. #13071625C2semidirect
5. #13071573C2semidirect
8. #13071493C2semidirect
9. C4⋊Q8×Dic11C2semidirect
10. #125×Dic11C2semidirect
11. C22⋊Q8×Dic11C2semidirect
12. C22⋊Q8×Dic11C2semidirect
13. C4×Q8×Dic11C2semidirect
16. C2×C4⋊C4×Dic11C2semidirect
18. C11×#554C4semidirect
92. C11×C4⋊Q8C2×C4semidirect
93. C11×#125C2×C4semidirect
94. C11×C22⋊Q8C2×C4semidirect
95. C11×C22⋊Q8C2×C4semidirect
96. C4×Q8×C11C2×C4semidirect
99. C2×C11×C4⋊C4C2×C4semidirect
119. D4×Dic11Q8semidirect
278. D4×C11C4×Q8semidirect
332. #554Dic11direct (N × H)
427. Dic11#554direct (N × H)
436. C4⋊Q8C2×Dic11semidirect
437. #125C2×Dic11semidirect
438. C22⋊Q8C2×Dic11semidirect
439. C22⋊Q8C2×Dic11semidirect
443. C4×Q8C2×Dic11semidirect
462. C2×C4⋊C4C2×Dic11semidirect
602. C11C4×#554semidirect
613. D4Q8×Dic11semidirect

Maximal subgroups

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

subgroupindex
#130717162
#130717062
#130717012
#130716252
#130715732
#130715262
D4×C4⋊Dic112
#130714932
C4⋊Q8×Dic112
#125×Dic112
C22⋊Q8×Dic112
C4×Q8×Dic112
C4×D4×Dic112
C2×C4⋊C4×Dic112
C2×C11×#5542
C4×#55411