Finite Group Databasebeta

← D4×#66930 #14913166

Subgroups — D4×#66930 #14913166

Order 2816.

3562 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic
2C22×#66930C212yesmaximal, complemented
3#13071564C212yesmaximal, complemented
4#13071543C214yesmaximal, complemented
5D4×Dic11⋊C4C212yesmaximal, complemented
6#13071487C211yesmaximal, characteristic, complemented
7#13071483C211yesmaximal, characteristic, complemented
8#13071467C212yesmaximal, complemented
9#13071461C212yesmaximal, complemented
10D4×C22⋊Dic11C211yesmaximal, characteristic
11#13071078C212yesmaximal, complemented
12#13071056C214yesmaximal, complemented
13#13071018C211yesmaximal, characteristic, complemented
14#13070994C212yesmaximal, complemented
15C4×D4×Dic11C212yesmaximal, complemented
16C4×#66930C211yesmaximal, characteristic, complemented
17D4×C11×C22⋊C4C211yesmaximal, characteristic
18C23×D4×C11C2211yescharacteristic
19C24×Dic11C2212yes—
20C2×C4×D4×C11C2212yes—
21C22×C11×C22⋊C4C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C2×D4×Dic11C4116yescomplemented
25C2×D4×Dic11C2212yes—
26C2×D4×Dic11C2211yescharacteristic
27C2×D4×Dic11C2211yescharacteristic
28C2×D4×Dic11C2212yes—
29C2×D4×Dic11C2211yescharacteristic
30C2×D4×Dic11C2212yes—
31C2×D4×Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2214yescomplemented
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2214yescomplemented
36C2×#66930—216no—
37C2×#66930C2212yes—
38C2×#66930C2211yescharacteristic
39C2×#66930C2212yes—
40C2×#66930C2212yes—
41C2×#66930C2211yescharacteristic
42C2×#66930C2214yescomplemented
43C2×#66930C2214yescomplemented
44C11×#390C2212yes—
45C11×#386C2214yes—
46C11×#380C2211yescharacteristic
47C11×#379C2212yes—
48C4×C11×C22⋊C4C2211yescharacteristic
49#10622860C2212yes—
50#10622834C2212yes—
51#10622833C2214yes—
52#10622825C2211yescharacteristic
53#10622823C2214yescomplemented
54C4×C22⋊Dic11C2211yescharacteristic
55C4×C22⋊Dic11C2214yescomplemented
56#10622589C2212yescomplemented
57C4⋊C4×Dic11C2212yescomplemented
58C4⋊C4×Dic11C2212yescomplemented
59#10622586C2212yescomplemented
60#10622559C2214yescomplemented
61#10622558C2214yescomplemented
62#10622558C2214yescomplemented
63#10622557C2214yescomplemented
64#10622557C2214yescomplemented
65#10622556C2212yes—
66#10622556C2212yes—
67#10622555C2212yes—
68#10622555C2214yescomplemented
69#10622555C2214yescomplemented
70C22⋊C4×Dic11C2211yescharacteristic
71C22⋊C4×Dic11C2211yescharacteristic
72C22⋊C4×Dic11C2214yescomplemented
73C22⋊C4×Dic11C2214yescomplemented
74C22⋊C4×Dic11C2214yescomplemented
75C4×C4⋊Dic11C2212yescomplemented
76C4×Dic11⋊C4C2212yescomplemented
77C42×Dic11C2212yescomplemented
78#10622541C2212yescomplemented
79#10622267C2214yescomplemented
80#10622266C2214yescomplemented
81#10622263C2212yescomplemented
82#10622262C2212yescomplemented
83#10622262C2212yescomplemented
84#10622261C2212yescomplemented
85C25×C11C2312yes—
86C22×D4×C11—28no—
87C22×D4×C11C2×C418yes—
88C22×D4×C11C2312yes—
89C22×D4×C11C2311yescharacteristic
90C22×D4×C11C2311yescharacteristic
91C23×C4×C11C2314yes—
92C23×C4×C11C2311yescharacteristic
93C23×Dic11—28no—
94C23×Dic11—28no—
95C23×Dic11C2×C4116yescomplemented
96C23×Dic11C2314yes—
97C23×Dic11C2312yes—
98C23×Dic11C2312yes—
99C23×Dic11C2312yes—
100C23×Dic11C2312yes—
101C23×Dic11C2312yes—
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C4×D4×C11—28no—
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C22⋊C4—28no—
107C2×C11×C22⋊C4C2312yes—
108C2×C11×C22⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C11×C22⋊C4C2311yescharacteristic
113C2×C42×C11C2312yes—
114C2×C22⋊Dic11—28no—
115C2×C22⋊Dic11C2×C4116yescomplemented
116C2×C22⋊Dic11C2312yes—
117C2×C22⋊Dic11C2311yescharacteristic
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2311yescharacteristic
126D4×Dic11—28no—
127D4×Dic11C2×C418yes—
128D4×Dic11C2×C418yes—
129D4×Dic11C2×C418yescomplemented
130D4×Dic11C2×C418yescomplemented
131D4×Dic11C2×C4116yescomplemented
132D4×Dic11C2×C4116yescomplemented
133C2×C4⋊Dic11C2×C418yescomplemented
134C2×C4⋊Dic11C2312yes—
135C2×C4⋊Dic11C2312yes—
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2311yescharacteristic
138C2×Dic11⋊C4—216no—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2312yes—
145C2×C4×Dic11—216no—
146C2×C4×Dic11C2×C418yescomplemented
147C2×C4×Dic11C2314yes—
148C2×C4×Dic11C2314yes—
149C2×C4×Dic11C2314yes—
150C2×C4×Dic11C2312yes—
151C2×C4×Dic11C2312yes—
152C2×C4×Dic11C2312yes—
153C2×C4×Dic11C2312yes—
154C2×C4×Dic11C2311yescharacteristic
155C2×C4×Dic11C2311yescharacteristic
156C2×C4×Dic11C2311yescharacteristic
157C2×C4×Dic11C2311yescharacteristic
158C2×C4×Dic11C2312yes—
159#66930—28no—
160#66930—24no—
161#66930—28no—
162#66930—28no—
163#66930—216no—
164#66930—216no—
165#66930D418yesdirect product factor
166C11×#95C2312yes—
167C11×#95C2312yes—
168C11⋊#95C2312yes—
169C11⋊#95C2312yes—
170C11⋊#95C2312yes—
171C11⋊#95C2312yes—
172C11⋊#95C2314yes—
173C11⋊#95C2314yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2314yes—
177D4×#117—111nomaximal, Sylow
178C24×C11—24no—
179C24×C11—24no—
180C24×C11—28no—
181C24×C11—44no—
182C24×C11C22×C418yes—
183C24×C11C2412yes—
184C24×C11C2411yescharacteristic
185C24×C11C2412yes—
186C2×D4×C11—28no—
187C2×D4×C11—232no—
188C2×D4×C11—24no—
189C2×D4×C11C22×C418yes—
190C2×D4×C11C22×C414yes—
191C2×D4×C11C22×C414yes—
192C2×D4×C11#4118yes—
193C22×C4×C11—24no—
194C22×C4×C11—28no—
195C22×C4×C11—28no—
196C22×C4×C11—44no—
197C22×C4×C11C22×C414yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2414yes—
200C22×C4×C11C2411yescharacteristic
201C22×C4×C11C2412yes—
202C22×C4×C11C2411yescharacteristic
203C22×Dic11—264no—
204C22×Dic11—24no—
205C22×Dic11—24no—
206C22×Dic11—24no—
207C22×Dic11—24no—
208C22×Dic11—24no—
209C22×Dic11—24no—
210C22×Dic11—24no—
211C22×Dic11—24no—
212C22×Dic11—28no—
213C22×Dic11—24no—
214C22×Dic11—24no—
215C22×Dic11—28no—
216C22×Dic11—44no—
217C22×Dic11—42no—
218C22×Dic11C22×C418yes—
219C22×Dic11C22×C418yes—
220C22×Dic11C22×C418yes—
221C22×Dic11C22×C418yes—
222C22×Dic11C22×C418yes—
223C22×Dic11C22×C414yes—
224C22×Dic11C22×C414yes—
225C22×Dic11C2×D414yes—
226C22×Dic11#4114yes—
227C22×Dic11C2412yes—
228C22×Dic11C2414yes—
229C22×Dic11C2411yescharacteristic
230C22×Dic11C2412yes—
231C22×Dic11C2411yescharacteristic
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C22×Dic11C2411yescharacteristic
235C22×Dic11C2411yescharacteristic
236C11×C4⋊C4—24no—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—22no—
239C11×C22⋊C4—28no—
240C11×C22⋊C4—28no—
241C11×C22⋊C4—44no—
242C11×C22⋊C4C2×D414yes—
243C42×C11—24no—
244C22⋊Dic11—28no—
245C22⋊Dic11—24no—
246C22⋊Dic11—22no—
247C22⋊Dic11—28no—
248C22⋊Dic11—44no—
249C22⋊Dic11C22×C418yes—
250C22⋊Dic11C22×C418yes—
251C22⋊Dic11C22×C418yes—
252C22⋊Dic11C22×C418yes—
253C22⋊Dic11C2×D414yes—
254C4⋊Dic11—24no—
255C4⋊Dic11C22×C414yes—
256C4⋊Dic11C22×C414yes—
257C4⋊Dic11C22×C418yes—
258Dic11⋊C4—28no—
259Dic11⋊C4—28no—
260Dic11⋊C4—24no—
261Dic11⋊C4—28no—
262Dic11⋊C4—44no—
263Dic11⋊C4C2×D418yescomplemented
264C4×Dic11—28no—
265C4×Dic11—28no—
266C4×Dic11—24no—
267C4×Dic11—28no—
268C4×Dic11—24no—
269C4×Dic11—42no—
270C4×Dic11—42no—
271C4×Dic11C22×C414yes—
272C4×Dic11C22×C414yes—
273C4×Dic11C22×C414yes—
274C4×Dic11C22×C414yes—
275C4×Dic11C2×D418yescomplemented
276C22×C4×D4—111no—
277C22×#117—112no—
278#2354—112no—
279#2352—114no—
280D4×C4⋊C4—112no—
281#2344—111no—
282#2344—111no—
283#2342—112no—
284#2342—112no—
285D4×C22⋊C4—111no—
286D4×C22⋊C4D1111yescharacteristic
287#2293—112no—
288#2290—114no—
289#2285—111no—
290#2280—112no—
291C42×D4—112no—
292C4×#117—111no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—24no—
297C23×C11—22no—
298C23×C11—216no—
299C23×C11—216no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—24no—
303C23×C11—24no—
304C23×C11—48no—
305C23×C11—416no—
306C23×C11—416no—
307C23×C11C23×C414yes—
308C23×C11C23×C414yes—
309C23×C11C23×C412yes—
310C23×C11C22×D412yes—
311C23×C11C2×#4118yes—
312C23×C11C2×#4112yes—
313C23×C11C2511yescharacteristic
314D4×C11—216no—
315D4×C11—28no—
316D4×C11#117116yescomplemented
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—28no—
321C2×C4×C11—24no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—24no—
325C2×C4×C11—22no—
326C2×C4×C11—24no—
327C2×C4×C11—416no—
328C2×C4×C11C23×C412yes—
329C2×C4×C11C23×C412yes—
330C2×C4×C11C22×D414yes—
331C2×C4×C11C2×#4114yes—
332C2×Dic11—216no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—216no—
342C2×Dic11—216no—
343C2×Dic11—216no—
344C2×Dic11—216no—
345C2×Dic11—24no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—24no—
349C2×Dic11—22no—
350C2×Dic11—24no—
351C2×Dic11—44no—
352C2×Dic11—416no—
353C2×Dic11C4×D4116yescomplemented
354C2×Dic11C23×C412yes—
355C2×Dic11C23×C412yes—
356C2×Dic11C23×C414yes—
357C2×Dic11C23×C414yes—
358C2×Dic11C23×C412yes—
359C2×Dic11C23×C412yes—
360C2×Dic11C22×D414yes—
361C2×Dic11C22×D412yes—
362C2×Dic11C22×D412yes—
363C2×Dic11C2×#4112yes—
364C2×Dic11C2×#4112yes—
365C23×D4C2×D1111yescharacteristic
366C24×C4—112no—
367C2×C4×D4—111no—
368C2×C4×D4—112no—
369C2×C4×D4—111no—
370C2×C4×D4—111no—
371C2×C4×D4—112no—
372C2×C4×D4—111no—
373C2×C4×D4—1116no—
374C2×C4×D4—112no—
375C2×C4×D4C2×D1112yes—
376C2×#117—111no—
377C2×#117—112no—
378C2×#117—112no—
379C2×#117—112no—
380C2×#117—111no—
381C2×#117—114no—
382C2×#117—114no—
383C2×#117—2216no—
384C22×C4⋊C4—111no—
385C22×C4⋊C4—114no—
386C22×C22⋊C4—112no—
387C22×C22⋊C4—112no—
388C22×C22⋊C4C2×D1112yes—
389C22×C42—111no—
390C22×C42—114no—
391#390—112no—
392#390C2×D1112yes—
393#389—112no—
394#389—112no—
395#388—114no—
396#388—114no—
397#388—114no—
398#388—114no—
399#387—114no—
400#387—114no—
401#386—114no—
402#386C2×D1114yes—
403#385—114no—
404#385—114no—
405#384—112no—
406#382—112no—
407#381—112no—
408#381—112no—
409#380—111no—
410#380—112no—
411#380—114no—
412#380—114no—
413#380C2×D1111yescharacteristic
414#379—112no—
415#379C2×D1112yes—
416C4×C4⋊C4—112no—
417C4×C4⋊C4—112no—
418C4×C4⋊C4—112no—
419C4×C4⋊C4—112no—
420C4×C4⋊C4—112no—
421C4×C4⋊C4—112no—
422C4×C22⋊C4—111no—
423C4×C22⋊C4—114no—
424C4×C22⋊C4—111no—
425C4×C22⋊C4—111no—
426C4×C22⋊C4—114no—
427C4×C22⋊C4—114no—
428C4×C22⋊C4—114no—
429C4×C22⋊C4C2×D1111yescharacteristic
430#376—112no—
431C43—112no—
432C22×C11—22no—
433C22×C11—24no—
434C22×C11—22no—
435C22×C11—24no—
436C22×C11—28no—
437C22×C11—24no—
438C22×C11—24no—
439C22×C11—28no—
440C22×C11—24no—
441C22×C11—24no—
442C22×C11—24no—
443C22×C11—432no—
444C22×C11—44no—
445C22×C11—44no—
446C22×C11C2×#11718yescomplemented
447C22×C11C2×C4×D414yes—
448C22×C11C24×C411yescharacteristic
449C22×C11C23×D411yescharacteristic
450C22×C11C22×#4112yes—
451C22×C11C22×#4111yescharacteristic
452C22×C11#58512yes—
453C4×C11—22no—
454C4×C11—24no—
455C4×C11—44no—
456C4×C11—42no—
457C4×C11C2×#11714yescomplemented
458Dic11—24no—
459Dic11—24no—
460Dic11—22no—
461Dic11—22no—
462Dic11—24no—
463Dic11—44no—
464Dic11—42no—
465Dic11C2×C4×D414yes—
466Dic11C2×C4×D414yes—
467C25C22×D1112yes—
468C22×D4—28no—
469C22×D4C4×D1118yes—
470C22×D4C22×D1112yes—
471C22×D4C22×D1111yescharacteristic
472C22×D4C22×D1111yescharacteristic
473C23×C4—111no—
474C23×C4—1116no—
475C23×C4—112no—
476C23×C4—112no—
477C23×C4—112no—
478C23×C4—112no—
479C23×C4—112no—
480C23×C4—111no—
481C23×C4—114no—
482C23×C4—228no—
483C23×C4—228no—
484C23×C4C22×D1114yes—
485C23×C4C22×D1111yescharacteristic
486C4×D4—28no—
487C4×D4—118no—
488C4×D4—118no—
489C4×D4—1116no—
490C4×D4—118no—
491C4×D4—1116no—
492C4×D4—118no—
493C4×D4—228no—
494#117—118no—
495#117—2216no—
496#117—228no—
497#117—2216no—
498#117—228no—
499#117—224no—
500#117—228no—
501C2×C4⋊C4—118no—
502C2×C4⋊C4—112no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—112no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—114no—
507C2×C4⋊C4—114no—
508C2×C4⋊C4—114no—
509C2×C4⋊C4—112no—
510C2×C4⋊C4—112no—
511C2×C4⋊C4—114no—
512C2×C4⋊C4—2216no—
513C2×C4⋊C4C22×D1112yes—
514C2×C22⋊C4—28no—
515C2×C22⋊C4—1116no—
516C2×C22⋊C4—111no—
517C2×C22⋊C4—112no—
518C2×C22⋊C4—112no—
519C2×C22⋊C4—112no—
520C2×C22⋊C4—112no—
521C2×C22⋊C4—112no—
522C2×C22⋊C4—114no—
523C2×C22⋊C4—111no—
524C2×C22⋊C4—114no—
525C2×C22⋊C4—114no—
526C2×C22⋊C4—228no—
527C2×C22⋊C4C22×D1112yes—
528C2×C22⋊C4C22×D1114yes—
529C2×C22⋊C4C22×D1111yescharacteristic
530C2×C22⋊C4C22×D1114yes—
531C2×C22⋊C4C22×D1114yes—
532C2×C22⋊C4C22×D1111yescharacteristic
533C2×C42—118no—
534C2×C42—112no—
535C2×C42—111no—
536C2×C42—111no—
537C2×C42—111no—
538C2×C42—111no—
539C2×C42—114no—
540C2×C42—114no—
541C2×C42—114no—
542C2×C42—112no—
543C2×C42—112no—
544C2×C42—112no—
545C2×C42—112no—
546C2×C42—2216no—
547C2×C42C22×D1112yes—
548#95—112no—
549#95—112no—
550#95—112no—
551#95—114no—
552#95—114no—
553#95—114no—
554#95—114no—
555#95—114no—
556#95—112no—
557#95C22×D1112yes—
558#95C22×D1112yes—
559C2×C11—24no—
560C2×C11—28no—
561C2×C11—44no—
562C2×C11C22×#11711yescharacteristic
563C2×C11C22×C4×D411yescharacteristic
564C2×C11#342811yescharacteristic
565C2×C11D4×#4112yes—
566C2×C11#347512yes—
567C24—24no—
568C24—28no—
569C24—24no—
570C24—44no—
571C24C2×C4×D1118yes—
572C24C23×D1112yes—
573C24C23×D1111yescharacteristic
574C24C23×D1112yes—
575C2×D4—28no—
576C2×D4—232no—
577C2×D4—24no—
578C2×D4C2×C4×D1118yes—
579C2×D4C2×C4×D1114yes—
580C2×D4C2×C4×D1114yes—
581C2×D4#434118yes—
582C22×C4—24no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—44no—
586C22×C4—114no—
587C22×C4—114no—
588C22×C4—114no—
589C22×C4—111no—
590C22×C4—111no—
591C22×C4—118no—
592C22×C4—118no—
593C22×C4—118no—
594C22×C4—118no—
595C22×C4—118no—
596C22×C4—111no—
597C22×C4—112no—
598C22×C4—111no—
599C22×C4—112no—
600C22×C4—112no—
601C22×C4—114no—
602C22×C4—112no—
603C22×C4—114no—
604C22×C4—224no—
605C22×C4—224no—
606C22×C4—224no—
607C22×C4—224no—
608C22×C4—2264no—
609C22×C4—224no—
610C22×C4—224no—
611C22×C4—224no—
612C22×C4—224no—
613C22×C4—228no—
614C22×C4—224no—
615C22×C4—224no—
616C22×C4—228no—
617C22×C4—442no—
618C22×C4—444no—
619C22×C4C2×C4×D1114yes—
620C22×C4C23×D1112yes—
621C22×C4C23×D1114yes—
622C22×C4C23×D1111yescharacteristic
623C22×C4C23×D1112yes—
624C22×C4C23×D1111yescharacteristic
625C4⋊C4—24no—
626C4⋊C4—118no—
627C4⋊C4—114no—
628C4⋊C4—114no—
629C4⋊C4—118no—
630C4⋊C4—228no—
631C4⋊C4—228no—
632C4⋊C4—224no—
633C4⋊C4—228no—
634C4⋊C4—224no—
635C4⋊C4—444no—
636C22⋊C4—24no—
637C22⋊C4—28no—
638C22⋊C4—22no—
639C22⋊C4—28no—
640C22⋊C4—44no—
641C22⋊C4—118no—
642C22⋊C4—118no—
643C22⋊C4—118no—
644C22⋊C4—118no—
645C22⋊C4—114no—
646C22⋊C4—228no—
647C22⋊C4—224no—
648C22⋊C4—228no—
649C22⋊C4—222no—
650C22⋊C4—444no—
651C22⋊C4D4×D1114yes—
652C42—24no—
653C42—114no—
654C42—114no—
655C42—114no—
656C42—114no—
657C42—118no—
658C42—228no—
659C42—228no—
660C42—224no—
661C42—228no—
662C42—224no—
663C42—442no—
664C42—442no—
665C11D4×#11711yescharacteristic, complemented, Sylow
666C23—22no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—22no—
671C23—216no—
672C23—216no—
673C23—22no—
674C23—24no—
675C23—22no—
676C23—24no—
677C23—48no—
678C23—416no—
679C23—416no—
680C23C22×C4×D1114yes—
681C23C22×C4×D1114yes—
682C23C22×C4×D1112yes—
683C23C2×D4×D1112yes—
684C23C2×#434118yes—
685C23#41×D1112yes—
686C23C24×D1111yescharacteristic
687D4—216no—
688D4—28no—
689D4#66930116yesdirect product factor
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—28no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—416no—
701C2×C4—1116no—
702C2×C4—112no—
703C2×C4—112no—
704C2×C4—112no—
705C2×C4—112no—
706C2×C4—112no—
707C2×C4—112no—
708C2×C4—112no—
709C2×C4—112no—
710C2×C4—114no—
711C2×C4—114no—
712C2×C4—114no—
713C2×C4—2216no—
714C2×C4—2216no—
715C2×C4—2216no—
716C2×C4—2216no—
717C2×C4—2216no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—224no—
727C2×C4—222no—
728C2×C4—224no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—224no—
732C2×C4—444no—
733C2×C4—4416no—
734C2×C4C22×C4×D1112yes—
735C2×C4C22×C4×D1112yes—
736C2×C4C2×D4×D1114yes—
737C2×C4C2×#434114yes—
738C22—24no—
739C22—28no—
740C22—22no—
741C22—24no—
742C22—22no—
743C22—24no—
744C22—28no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—432no—
750C22—44no—
751C22—44no—
752C22C2×#6693018yescomplemented
753C22C4×D4×D1114yes—
754C22C23×C4×D1111yescharacteristic
755C22C22×D4×D1111yescharacteristic
756C22C22×#434112yes—
757C22C2×#41×D1111yescharacteristic
758C22#1062345512yes—
759C4—22no—
760C4—24no—
761C4—42no—
762C4—44no—
763C4—114no—
764C4—114no—
765C4—224no—
766C4—224no—
767C4—222no—
768C4—222no—
769C4—224no—
770C4—442no—
771C4—444no—
772C4C2×#6693014yescomplemented
773C2—24no—
774C2—28no—
775C2—44no—
776C2C22×#6693011yescharacteristic
777C2C2×C4×D4×D1111yescharacteristic
778C2#1308181411yescharacteristic
779C2D4×#434112yes—
780C2#1308216712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingD4×C11×C22⋊C4C2
socle, cosocleC23×C11C25
prime radicalC23×D4×C11C22
hypercenterD4×C22⋊C4D11
hypocenterC11D4×#117
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#66930C2semidirect
3. #13071564C2semidirect
4. #13071543C2semidirect
5. D4×Dic11⋊C4C2semidirect
6. #13071487C2semidirect
7. #13071483C2semidirect
8. #13071467C2semidirect
9. #13071461C2semidirect
11. #13071078C2semidirect
12. #13071056C2semidirect
13. #13071018C2semidirect
14. #13070994C2semidirect
15. C4×D4×Dic11C2semidirect
16. C4×#66930C2semidirect
24. C2×D4×Dic11C4semidirect
33. C22×Dic11⋊C4C22semidirect
35. C22×C4×Dic11C22semidirect
42. C2×#66930C22semidirect
43. C2×#66930C22semidirect
53. #10622823C22semidirect
55. C4×C22⋊Dic11C22semidirect
56. #10622589C22semidirect
57. C4⋊C4×Dic11C22semidirect
58. C4⋊C4×Dic11C22semidirect
59. #10622586C22semidirect
60. #10622559C22semidirect
61. #10622558C22semidirect
62. #10622558C22semidirect
63. #10622557C22semidirect
64. #10622557C22semidirect
68. #10622555C22semidirect
69. #10622555C22semidirect
72. C22⋊C4×Dic11C22semidirect
73. C22⋊C4×Dic11C22semidirect
74. C22⋊C4×Dic11C22semidirect
75. C4×C4⋊Dic11C22semidirect
76. C4×Dic11⋊C4C22semidirect
77. C42×Dic11C22semidirect
78. #10622541C22semidirect
79. #10622267C22semidirect
80. #10622266C22semidirect
81. #10622263C22semidirect
82. #10622262C22semidirect
83. #10622262C22semidirect
84. #10622261C22semidirect
95. C23×Dic11C2×C4semidirect
115. C2×C22⋊Dic11C2×C4semidirect
129. D4×Dic11C2×C4semidirect
130. D4×Dic11C2×C4semidirect
131. D4×Dic11C2×C4semidirect
132. D4×Dic11C2×C4semidirect
133. C2×C4⋊Dic11C2×C4semidirect
146. C2×C4×Dic11C2×C4semidirect
165. #66930D4direct (N × H)
263. Dic11⋊C4C2×D4semidirect
275. C4×Dic11C2×D4semidirect
316. D4×C11#117semidirect
353. C2×Dic11C4×D4semidirect
446. C22×C11C2×#117semidirect
457. C4×C11C2×#117semidirect
665. C11D4×#117semidirect
689. D4#66930direct (N × H)
752. C22C2×#66930semidirect
772. C4C2×#66930semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C22×#669302
#130715642
#130715432
D4×Dic11⋊C42
#130714872
#130714832
#130714672
#130714612
D4×C22⋊Dic112
#130710782
#130710562
#130710182
#130709942
C4×D4×Dic112
C4×#669302
D4×C11×C22⋊C42
D4×#11711