Finite Group Databasebeta

← D11×#3238 #15625890

Subgroups — D11×#3238 #15625890

Order 2816.

2018 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2D11×#529C211yesmaximal, characteristic
3#13079841C212yesmaximal, complemented
4#13079840C212yesmaximal, complemented
5#13079839C211yesmaximal, characteristic, complemented
6#13079838C212yesmaximal, complemented
7#13079837C211yesmaximal, characteristic, complemented
8#13079836C212yesmaximal, complemented
9#13079835C212yesmaximal, complemented
10#13079834C211yesmaximal, characteristic, complemented
11#13079833C212yesmaximal, complemented
12D11×#501C212yesmaximal, complemented
13D11×#489C212yesmaximal, complemented
14D11×#483C212yesmaximal, complemented
15D11×#480C212yesmaximal
16D11×#477C212yesmaximal, complemented
17D11×#476C212yesmaximal, complemented
18D11×#432C211yesmaximal, characteristic, complemented
19C11×#3238C211yesmaximal, characteristic, complemented
20C22×Q8×D11—21no—
21C2×C11×C4⋊Q8C2211yescharacteristic, complemented
22C11×#529C2211yescharacteristic
23C2×#66997—21no—
24D11×C4⋊Q8—21no—
25D11×C4⋊Q8—21no—
26D11×C4⋊Q8—21no—
27D11×C4⋊Q8—21no—
28D11×C4⋊Q8C2212yes—
29D11×C4⋊Q8C2212yes—
30D11×C4⋊Q8C2212yescomplemented
31D11×C4⋊Q8C2212yescomplemented
32#10623237—21no—
33D11×#126—21no—
34#10623222C2211yescharacteristic
35D11×#125C2211yescharacteristic
36#10623211C2211yescharacteristic
37D11×#124C2211yescharacteristic
38D11×#123—21no—
39#10623180—21no—
40D11×C22⋊Q8C2211yescharacteristic
41#10623155C2211yescharacteristic
42D11×#121C2211yescharacteristic
43#10623131C2211yescharacteristic
44#10623111C2211yescharacteristic
45C4×Q8×D11C2211yescharacteristic
46#10623088C2211yescharacteristic
47C4×D4×D11—21no—
48C4×D4×D11C2211yescharacteristic
49#10623069—21no—
50#10623059—21no—
51D11×#117—21no—
52C2×C4⋊C4×D11—21no—
53C2×C4⋊C4×D11C2212yes—
54C2×#66941—21no—
55C2×#66941C2212yescomplemented
56#10623010C2211yescharacteristic
57C2×C42×D11C2211yescharacteristic
58C2×#66922C2211yescharacteristic, complemented
59C11×#501C2212yescomplemented
60C11×#489C2212yescomplemented
61C11×#483C2212yescomplemented
62C11×#480C2212yes—
63C11×#477C2212yescomplemented
64C11×#476C2212yescomplemented
65C11×#432C2211yescharacteristic, complemented
66#10622704C2212yescomplemented
67#10622702C2212yescomplemented
68#10622697C2212yescomplemented
69#10622693C2212yescomplemented
70#10622678C2212yescomplemented
71#10622668C2212yescomplemented
72#10622656C2212yescomplemented
73#10622646C2212yes—
74#10622634C2212yescomplemented
75#10622621C2212yescomplemented
76#10622584C2212yescomplemented
77#10622580C2212yes—
78#10622539C2211yescharacteristic, complemented
79#10622495C2214yes—
80D11×#107C2214yes—
81#10622489C2214yescomplemented
82#10622488C2214yescomplemented
83#10622483C2214yescomplemented
84#10622475C2214yescomplemented
85D11×#106C2214yes—
86#10622469C2214yescomplemented
87#10622463C2212yescomplemented
88#10622455C2212yescomplemented
89#10622448C2212yescomplemented
90D11×C4⋊C8C2212yes—
91#10622418C2214yescomplemented
92D11×#103C2214yes—
93#10622408C2214yescomplemented
94#10622407C2214yescomplemented
95#10622387C2214yes—
96D11×#102C2214yes—
97#10622378C2214yescomplemented
98#10622374C2214yescomplemented
99#10622349C2212yes—
100D11×C22⋊C8C2212yes—
101#10622334C2212yescomplemented
102#10622332C2212yescomplemented
103#10622327C2212yescomplemented
104#10622318C2212yescomplemented
105D11×#97C2212yes—
106#10622315C2212yescomplemented
107C22×Q8×C11—21no—
108C2×Q8×D11—22no—
109C2×Q8×D11—22no—
110C2×Q8×D11—22no—
111C2×Q8×D11—22no—
112C2×Q8×D11—48no—
113C2×Q8×D11C2311yescharacteristic
114C2×D4×D11—21no—
115C2×D4×D11C2311yescharacteristic
116C22×C4×D11—22no—
117C22×C4×D11—21no—
118C22×C4×D11D411yescharacteristic
119C22×C4×D11D411yescharacteristic
120C22×C4×D11C2311yescharacteristic
121C22×Dic22—21no—
122C22×Dic22—22no—
123C11×C4⋊Q8—21no—
124C11×C4⋊Q8—21no—
125C11×C4⋊Q8C2312yes—
126C11×C4⋊Q8C2312yes—
127C11×#126—21no—
128C11×#125C2311yescharacteristic
129C11×#124C2311yescharacteristic
130C11×#123—21no—
131C11×C22⋊Q8C2311yescharacteristic
132C11×#121C2311yescharacteristic
133C4×Q8×C11C2311yescharacteristic
134C4×D4×C11—21no—
135C4×D4×C11C2311yescharacteristic
136C11×#117—21no—
137C2×C11×C4⋊C4—21no—
138C2×C11×C4⋊C4C2312yes—
139C2×C42×C11C2311yescharacteristic
140#67000C2311yescharacteristic
141#66999C2311yescharacteristic
142Q8×Dic11C2311yescharacteristic
143#66997—22no—
144#66997—22no—
145#66997—22no—
146#66997—22no—
147#66992—21no—
148#66991C2311yescharacteristic
149#66989C2311yescharacteristic
150#66988—21no—
151D4×Dic11—21no—
152D4×Dic11C2311yescharacteristic
153#66983C2311yescharacteristic
154#66982—21no—
155C4×C22⋊D11—21no—
156C4×C22⋊D11—21no—
157C4×C22⋊D11—21no—
158#66979—21no—
159C2×C4⋊Dic11—21no—
160C2×C4⋊Dic11C2312yes—
161#66977C2311yescharacteristic
162C2×Dic11⋊C4—22no—
163C2×Dic11⋊C4—22no—
164C2×C4×Dic11D411yescharacteristic
165C2×C4×Dic11D411yescharacteristic
166C2×C4×Dic11C2311yescharacteristic
167C2×C8×D11C2314yes—
168#66951—21no—
169#66951—21no—
170#66951—21no—
171#66950C2311yescharacteristic
172#66949—21no—
173#66948C2311yescharacteristic
174#66947—21no—
175#66947—21no—
176#66946—21no—
177#66946C2311yescharacteristic
178#66945—21no—
179#66945—21no—
180C4⋊C4×D11—21no—
181C4⋊C4×D11—21no—
182C4⋊C4×D11—21no—
183C4⋊C4×D11—22no—
184C4⋊C4×D11—22no—
185C4⋊C4×D11—22no—
186C4⋊C4×D11—22no—
187C4⋊C4×D11—22no—
188C4⋊C4×D11—22no—
189C4⋊C4×D11—21no—
190C4⋊C4×D11C2311yescharacteristic
191C4⋊C4×D11C2314yes—
192C4⋊C4×D11C2314yes—
193C4⋊C4×D11C2311yescharacteristic
194#66943C2311yescharacteristic
195#66943C2311yescharacteristic
196#66942—21no—
197#66942—21no—
198#66941—22no—
199#66941—22no—
200#66941—22no—
201#66941—22no—
202#66941—22no—
203#66941—22no—
204#66941C2314yes—
205#66941C2314yes—
206#66940—21no—
207#66940C2311yescharacteristic
208#66939—21no—
209#66938—21no—
210#66938—21no—
211#66937—21no—
212#66936—21no—
213#66936—21no—
214(C22⋊D11)⋊C4—21no—
215(C22⋊D11)⋊C4—21no—
216(C22⋊D11)⋊C4—21no—
217C22⋊C4×D11—21no—
218C22⋊C4×D11—21no—
219C22⋊C4×D11—21no—
220C22⋊C4×D11—21no—
221C22⋊C4×D11—21no—
222#66932—21no—
223#66932—21no—
224#66932—21no—
225#66931—21no—
226#66930—21no—
227#66930—21no—
228#66929—21no—
229#66928C2311yescharacteristic
230C4×D44—21no—
231C4×D44C2311yescharacteristic
232#66925—21no—
233#66925—21no—
234C42×D11—21no—
235C42×D11D411yescharacteristic
236C42×D11D411yescharacteristic
237C42×D11D411yescharacteristic
238C42×D11D411yescharacteristic
239C42×D11C2311yescharacteristic
240C42×D11C2311yescharacteristic
241C42×D11C2311yescharacteristic
242C42×D11C2311yescharacteristic
243#66923C2311yescharacteristic
244#66922—21no—
245#66922—21no—
246#66922C2312yes—
247#66922C2312yes—
248C4×Dic22—21no—
249C4×Dic22C2311yescharacteristic
250C11×#107C2314yes—
251C11×#106C2314yes—
252C11×C4⋊C8C2312yes—
253C11×#103C2314yes—
254C11×#102C2314yes—
255C11×C22⋊C8C2312yes—
256C11×#97C2312yes—
257#66899C2314yes—
258#66896C2314yes—
259C22⋊(C11⋊C8)C2312yes—
260#66885C2314yes—
261(C2×D11)⋊C8C2314yes—
262#66882C2314yes—
263#66881C2314yes—
264#66880C2314yes—
265#66879C2314yes—
266Dic11⋊C8C2314yes—
267#66874C2314yes—
268#66873C2314yes—
269#66872C2314yes—
270#66872C2314yes—
271#66871C2314yes—
272#66871C2314yes—
273C4⋊(C11⋊C8)C2312yes—
274#66867C2312yes—
275C2×#3238—111nomaximal, Sylow
276C23×D11—21no—
277C23×D11C2×D411yescharacteristic
278C2×Q8×C11—22no—
279C2×Q8×C11—22no—
280C2×Q8×C11—44no—
281C2×Q8×C11C2411yescharacteristic
282C2×D4×C11—21no—
283C2×D4×C11C2411yescharacteristic
284C22×C4×C11—22no—
285C22×C4×C11—21no—
286C22×C4×C11C2×D411yescharacteristic
287C22×C4×C11C2×D411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C2×C22⋊D11—21no—
290C2×C22⋊D11—21no—
291C2×C22⋊D11—21no—
292C22×Dic11—21no—
293C22×Dic11—22no—
294C22×Dic11C2×D411yescharacteristic
295C22×Dic11C2×D411yescharacteristic
296C22×Dic11C2×D411yescharacteristic
297Q8×D11—24no—
298Q8×D11—48no—
299Q8×D11—48no—
300Q8×D11—48no—
301Q8×D11—48no—
302D4×D11—24no—
303D4×D11—44no—
304C2×D44—21no—
305C2×D44C2411yescharacteristic
306C2×C4×D11—24no—
307C2×C4×D11—24no—
308C2×C4×D11—21no—
309C2×C4×D11—24no—
310C2×C4×D11—21no—
311C2×C4×D11—21no—
312C2×C4×D11—21no—
313C2×C4×D11—24no—
314C2×C4×D11—24no—
315C2×C4×D11—21no—
316C2×C4×D11—44no—
317C2×C4×D11—48no—
318C2×C4×D11C2×D411yescharacteristic
319C2×C4×D11C2×D411yescharacteristic
320C2×C4×D11C2×D411yescharacteristic
321C2×C4×D11C2×D411yescharacteristic
322C2×C4×D11C2×D411yescharacteristic
323C2×C4×D11C2×D411yescharacteristic
324C2×C4×D11C2×D411yescharacteristic
325C2×C4×D11C2×D411yescharacteristic
326C2×C4×D11C2×D411yescharacteristic
327C2×C4×D11C2×D411yescharacteristic
328C2×C4×D11C2411yescharacteristic
329C2×C4×D11C2411yescharacteristic
330C2×Dic22—21no—
331C2×Dic22—24no—
332C2×Dic22—24no—
333C2×Dic22—22no—
334C2×Dic22—22no—
335C2×Dic22—44no—
336C2×Dic22—48no—
337C2×Dic22C2411yescharacteristic
338C2×C8×C11C2414yes—
339C11×C4⋊C4—21no—
340C11×C4⋊C4—22no—
341C11×C4⋊C4—22no—
342C11×C4⋊C4—22no—
343C11×C4⋊C4—21no—
344C11×C4⋊C4—21no—
345C11×C4⋊C4—21no—
346C11×C4⋊C4C2411yescharacteristic
347C11×C4⋊C4C2414yes—
348C11×C4⋊C4C2411yescharacteristic
349C11×C22⋊C4—21no—
350C11×C22⋊C4—21no—
351C11×C22⋊C4—21no—
352C11×C22⋊C4—21no—
353C11×C22⋊C4—21no—
354C42×C11—21no—
355C42×C11C2×D411yescharacteristic
356C42×C11C2×D411yescharacteristic
357C42×C11C2411yescharacteristic
358C42×C11C2411yescharacteristic
359C22⋊Dic11—21no—
360C22⋊Dic11—21no—
361C22⋊Dic11—21no—
362C22⋊Dic11—21no—
363C22⋊Dic11—21no—
364(C2×D11)⋊C4—21no—
365(C2×D11)⋊C4—21no—
366(C2×D11)⋊C4—21no—
367(C2×D11)⋊C4—21no—
368(C2×D11)⋊C4—21no—
369(C2×D11)⋊C4—21no—
370(C2×D11)⋊C4—21no—
371(C2×D11)⋊C4—21no—
372(C2×D11)⋊C4—21no—
373(C2×D11)⋊C4—21no—
374C4⋊Dic11—21no—
375C4⋊Dic11—21no—
376C4⋊Dic11—21no—
377C4⋊Dic11—21no—
378C4⋊Dic11—22no—
379C4⋊Dic11—22no—
380C4⋊Dic11—22no—
381C4⋊Dic11C2411yescharacteristic
382C4⋊Dic11C2414yes—
383C4⋊Dic11C2411yescharacteristic
384Dic11⋊C4—21no—
385Dic11⋊C4—21no—
386Dic11⋊C4—21no—
387Dic11⋊C4—21no—
388Dic11⋊C4—21no—
389Dic11⋊C4—21no—
390Dic11⋊C4—24no—
391Dic11⋊C4—24no—
392Dic11⋊C4—24no—
393Dic11⋊C4—24no—
394Dic11⋊C4—21no—
395Dic11⋊C4—21no—
396Dic11⋊C4—21no—
397Dic11⋊C4—21no—
398C4×Dic11—21no—
399C4×Dic11—21no—
400C4×Dic11—21no—
401C4×Dic11C2×D411yescharacteristic
402C4×Dic11C2×D411yescharacteristic
403C4×Dic11C2×D411yescharacteristic
404C4×Dic11C2×D411yescharacteristic
405C4×Dic11C2×D411yescharacteristic
406C4×Dic11C2×D411yescharacteristic
407C4×Dic11C2×D411yescharacteristic
408C4×Dic11C2×D411yescharacteristic
409C4×Dic11C2×D411yescharacteristic
410C4×Dic11C2×D411yescharacteristic
411C4×Dic11C2411yescharacteristic
412C4×Dic11C2411yescharacteristic
413C2×C11⋊C8C2414yes—
414C8×D11—28no—
415C22×C4⋊Q8—111no—
416C2×#529—111no—
417#3238—112no—
418#3238—112no—
419#3238—112no—
420#3238—112no—
421#3238—112no—
422#3238—112no—
423#3238—111no—
424#3238—111no—
425#3238—111no—
426#3238D1111yescharacteristic, direct product factor
427C2×#501—112no—
428C2×#489—112no—
429C2×#483—112no—
430C2×#480—112no—
431C2×#477—112no—
432C2×#476—112no—
433C2×#432—111no—
434C23×C11—21no—
435C23×C11C22×D411yescharacteristic
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—21no—
439C22×D11—42no—
440C22×D11—42no—
441C22×D11—42no—
442C22×D11AGL(1,ℤ/8)14yes—
443C22×D11C22×D411yescharacteristic
444C22×D11C22×D411yescharacteristic
445Q8×C11—22no—
446Q8×C11—44no—
447Q8×C11—44no—
448D4×C11—22no—
449D4×C11—42no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—21no—
454C2×C4×C11—21no—
455C2×C4×C11—24no—
456C2×C4×C11—21no—
457C2×C4×C11—44no—
458C2×C4×C11—42no—
459C2×C4×C11C22×D411yescharacteristic
460C2×C4×C11C22×D411yescharacteristic
461C2×C4×C11C22×D411yescharacteristic
462C2×C4×C11C22×D411yescharacteristic
463C2×C4×C11C22×D411yescharacteristic
464C2×C4×C11C2511yescharacteristic
465C22⋊D11—42no—
466C22⋊D11—42no—
467C22⋊D11—42no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—21no—
472C2×Dic11—21no—
473C2×Dic11—21no—
474C2×Dic11—24no—
475C2×Dic11—44no—
476C2×Dic11—42no—
477C2×Dic11C22×D411yescharacteristic
478C2×Dic11C22×D411yescharacteristic
479C2×Dic11C22×D411yescharacteristic
480C2×Dic11C22×D411yescharacteristic
481C2×Dic11C22×D411yescharacteristic
482C2×Dic11C22×D411yescharacteristic
483D44—22no—
484D44—42no—
485C4×D11—22no—
486C4×D11—22no—
487C4×D11—22no—
488C4×D11—22no—
489C4×D11—22no—
490C4×D11—22no—
491C4×D11—22no—
492C4×D11—22no—
493C4×D11—22no—
494C4×D11—22no—
495C4×D11—42no—
496C4×D11—48no—
497C4×D11—48no—
498C4×D11—42no—
499C4×D11—42no—
500C4×D11—42no—
501C4×D11—42no—
502C4×D11#13714yes—
503C4×D112−1+414yes—
504Dic22—22no—
505Dic22—48no—
506Dic22—48no—
507Dic22—44no—
508Dic22—44no—
509Dic22—42no—
510C8×C11—24no—
511C11⋊C8—24no—
512C23×Q8—221no—
513C2×C4⋊Q8—112no—
514C2×C4⋊Q8—112no—
515C2×C4⋊Q8—112no—
516C2×C4⋊Q8—112no—
517C2×C4⋊Q8—112no—
518C2×C4⋊Q8—111no—
519C2×C4⋊Q8—221no—
520C2×C4⋊Q8—221no—
521C2×C4⋊Q8—221no—
522C2×C4⋊Q8—221no—
523C2×C4⋊Q8—221no—
524C2×C4⋊Q8—221no—
525C2×C4⋊Q8C2×D1111yescharacteristic, complemented
526#529—111no—
527#529—111no—
528#529—111no—
529#529—111no—
530#529—111no—
531#529—111no—
532#529—111no—
533#529—221no—
534#529—221no—
535#529—221no—
536#529—221no—
537#529C2×D1111yescharacteristic
538C2×#126—221no—
539C2×#125—111no—
540C2×#124—111no—
541C2×#123—221no—
542C2×C22⋊Q8—111no—
543C2×#121—111no—
544C2×C4×Q8—111no—
545C2×C4×D4—111no—
546C2×C4×D4—221no—
547C2×#117—221no—
548C22×C4⋊C4—112no—
549C22×C4⋊C4—221no—
550C22×C42—111no—
551#501—112no—
552#501—112no—
553#501—114no—
554#501—114no—
555#501—112no—
556#501C2×D1112yescomplemented
557#489—112no—
558#489—112no—
559#489—114no—
560#489—114no—
561#489—112no—
562#489C2×D1112yescomplemented
563#483—112no—
564#483—112no—
565#483—114no—
566#483—114no—
567#483—112no—
568#483C2×D1112yescomplemented
569#480—112no—
570#480—112no—
571#480—114no—
572#480—114no—
573#480—112no—
574#480C2×D1112yes—
575#477—112no—
576#477—112no—
577#477—114no—
578#477—112no—
579#477—114no—
580#477C2×D1112yescomplemented
581#476—112no—
582#476—112no—
583#476—114no—
584#476—112no—
585#476—114no—
586#476C2×D1112yescomplemented
587#432—111no—
588#432—112no—
589#432—112no—
590#432—112no—
591#432C2×D1111yescharacteristic, complemented
592C2×#107—114no—
593C2×#106—114no—
594C2×C4⋊C8—112no—
595C2×#103—114no—
596C2×#102—114no—
597C2×C22⋊C8—112no—
598C2×#97—112no—
599C22×C11—21no—
600C22×C11—21no—
601C22×C11—41no—
602C22×C11—41no—
603C22×C11—41no—
604C22×C11C2×AGL(1,ℤ/8)12yes—
605C22×C11C23×D411yescharacteristic
606C2×D11—21no—
607C2×D11—21no—
608C2×D11—28no—
609C2×D11—41no—
610C2×D11—41no—
611C2×D11—41no—
612C2×D11—84no—
613C2×D11#53612yes—
614C2×D11C2×AGL(1,ℤ/8)12yes—
615C2×D11C2×AGL(1,ℤ/8)12yes—
616C2×D11C2×#13712yes—
617C4×C11—21no—
618C4×C11—21no—
619C4×C11—21no—
620C4×C11—21no—
621C4×C11—41no—
622C4×C11—44no—
623C4×C11—41no—
624C4×C11—41no—
625C4×C11C2×#13712yes—
626C4×C11C2×2−1+412yes—
627Dic11—21no—
628Dic11—21no—
629Dic11—21no—
630Dic11—21no—
631Dic11—41no—
632Dic11—44no—
633Dic11—41no—
634Dic11—41no—
635Dic11#53612yes—
636Dic11C2×#13712yes—
637C22×Q8—21no—
638C22×Q8—111no—
639C22×Q8—222no—
640C22×Q8—222no—
641C22×Q8—222no—
642C22×Q8—222no—
643C22×Q8—222no—
644C22×Q8—221no—
645C22×Q8—448no—
646C22×D4—111no—
647C22×D4—221no—
648C23×C4—111no—
649C23×C4—111no—
650C23×C4—111no—
651C23×C4—221no—
652C23×C4—222no—
653C22×C8—114no—
654C4⋊Q8—21no—
655C4⋊Q8—21no—
656C4⋊Q8—114no—
657C4⋊Q8—114no—
658C4⋊Q8—112no—
659C4⋊Q8—112no—
660C4⋊Q8—222no—
661C4⋊Q8—222no—
662C4⋊Q8—222no—
663C4⋊Q8—222no—
664C4⋊Q8—222no—
665C4⋊Q8—222no—
666C4⋊Q8—222no—
667C4⋊Q8—222no—
668C4⋊Q8—222no—
669C4⋊Q8—222no—
670C4⋊Q8—221no—
671C4⋊Q8—221no—
672C4⋊Q8C22×D1112yes—
673C4⋊Q8C22×D1112yes—
674#126—21no—
675#126—221no—
676#126—221no—
677#126—221no—
678#126—221no—
679#126—221no—
680#126—221no—
681#126—221no—
682#125—111no—
683#125—111no—
684#125—111no—
685#125—221no—
686#125—221no—
687#125C22×D1111yescharacteristic
688#124—111no—
689#124—111no—
690#124—111no—
691#124—221no—
692#124—221no—
693#124C22×D1111yescharacteristic
694#123—21no—
695#123—221no—
696#123—221no—
697#123—221no—
698#123—221no—
699#123—221no—
700#123—221no—
701#123—221no—
702C22⋊Q8—111no—
703C22⋊Q8—111no—
704C22⋊Q8—111no—
705C22⋊Q8—221no—
706C22⋊Q8—221no—
707C22⋊Q8C22×D1111yescharacteristic
708#121—111no—
709#121—111no—
710#121—111no—
711#121—221no—
712#121—221no—
713#121C22×D1111yescharacteristic
714C4×Q8—111no—
715C4×Q8—111no—
716C4×Q8—111no—
717C4×Q8—221no—
718C4×Q8—221no—
719C4×Q8C22×D1111yescharacteristic
720C4×D4—21no—
721C4×D4—111no—
722C4×D4—111no—
723C4×D4—111no—
724C4×D4—221no—
725C4×D4—221no—
726C4×D4—221no—
727C4×D4—221no—
728C4×D4—221no—
729C4×D4—221no—
730C4×D4—221no—
731C4×D4—221no—
732C4×D4—221no—
733C4×D4C22×D1111yescharacteristic
734#117—21no—
735#117—221no—
736#117—221no—
737#117—221no—
738#117—221no—
739#117—221no—
740#117—221no—
741#117—221no—
742C2×C4⋊C4—21no—
743C2×C4⋊C4—112no—
744C2×C4⋊C4—114no—
745C2×C4⋊C4—114no—
746C2×C4⋊C4—111no—
747C2×C4⋊C4—111no—
748C2×C4⋊C4—222no—
749C2×C4⋊C4—222no—
750C2×C4⋊C4—222no—
751C2×C4⋊C4—222no—
752C2×C4⋊C4—222no—
753C2×C4⋊C4—222no—
754C2×C4⋊C4—221no—
755C2×C4⋊C4—221no—
756C2×C4⋊C4—221no—
757C2×C4⋊C4—221no—
758C2×C4⋊C4—222no—
759C2×C4⋊C4—222no—
760C2×C4⋊C4—221no—
761C2×C4⋊C4C22×D1112yes—
762C2×C22⋊C4—221no—
763C2×C22⋊C4—221no—
764C2×C22⋊C4—221no—
765C2×C22⋊C4—221no—
766C2×C22⋊C4—221no—
767C2×C42—111no—
768C2×C42—111no—
769C2×C42—111no—
770C2×C42—111no—
771C2×C42—111no—
772C2×C42—111no—
773C2×C42—111no—
774C2×C42—111no—
775C2×C42—111no—
776C2×C42—111no—
777C2×C42—111no—
778C2×C42—221no—
779C2×C42C22×D1111yescharacteristic
780#107—114no—
781#107—114no—
782#107—114no—
783#107C22×D1114yes—
784#106—114no—
785#106—114no—
786#106—114no—
787#106C22×D1114yes—
788C4⋊C8—114no—
789C4⋊C8—112no—
790C4⋊C8C22×D1112yes—
791#103—114no—
792#103—114no—
793#103—114no—
794#103C22×D1114yes—
795#102—114no—
796#102—114no—
797#102—114no—
798#102C22×D1114yes—
799C22⋊C8—112no—
800C22⋊C8—114no—
801C22⋊C8C22×D1112yes—
802#97—114no—
803#97—112no—
804#97C22×D1112yes—
805C2×C11—22no—
806C2×C11—81no—
807C2×C11C2×#53611yescharacteristic
808C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
809C2×C11C22×#13711yescharacteristic
810D11—22no—
811D11—81no—
812D11#323814yesdirect product factor
813C24—111no—
814C24—221no—
815C2×Q8—22no—
816C2×Q8—22no—
817C2×Q8—44no—
818C2×Q8—111no—
819C2×Q8—221no—
820C2×Q8—224no—
821C2×Q8—224no—
822C2×Q8—224no—
823C2×Q8—222no—
824C2×Q8—222no—
825C2×Q8—444no—
826C2×Q8—448no—
827C2×Q8—448no—
828C2×Q8—448no—
829C2×Q8—448no—
830C2×Q8—448no—
831C2×Q8C23×D1111yescharacteristic
832C2×D4—21no—
833C2×D4—111no—
834C2×D4—221no—
835C2×D4—224no—
836C2×D4—221no—
837C2×D4—221no—
838C2×D4—221no—
839C2×D4—444no—
840C2×D4C23×D1111yescharacteristic
841C22×C4—22no—
842C22×C4—21no—
843C22×C4—111no—
844C22×C4—111no—
845C22×C4—111no—
846C22×C4—111no—
847C22×C4—111no—
848C22×C4—111no—
849C22×C4—111no—
850C22×C4—111no—
851C22×C4—111no—
852C22×C4—111no—
853C22×C4—111no—
854C22×C4—111no—
855C22×C4—111no—
856C22×C4—111no—
857C22×C4—111no—
858C22×C4—224no—
859C22×C4—224no—
860C22×C4—221no—
861C22×C4—224no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—224no—
866C22×C4—224no—
867C22×C4—221no—
868C22×C4—222no—
869C22×C4—221no—
870C22×C4—444no—
871C22×C4—448no—
872C22×C4D4×D1111yescharacteristic
873C22×C4D4×D1111yescharacteristic
874C22×C4C23×D1111yescharacteristic
875C2×C8—114no—
876C2×C8—228no—
877C2×C8C23×D1114yes—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—114no—
886C4⋊C4—111no—
887C4⋊C4—111no—
888C4⋊C4—224no—
889C4⋊C4—224no—
890C4⋊C4—221no—
891C4⋊C4—221no—
892C4⋊C4—224no—
893C4⋊C4—224no—
894C4⋊C4—221no—
895C4⋊C4—221no—
896C4⋊C4—221no—
897C4⋊C4—221no—
898C4⋊C4—221no—
899C4⋊C4—221no—
900C4⋊C4—221no—
901C4⋊C4—221no—
902C4⋊C4—222no—
903C4⋊C4—222no—
904C4⋊C4—222no—
905C4⋊C4—221no—
906C4⋊C4—221no—
907C4⋊C4—221no—
908C4⋊C4—221no—
909C4⋊C4C23×D1114yes—
910C4⋊C4C23×D1111yescharacteristic
911C4⋊C4C23×D1111yescharacteristic
912C22⋊C4—21no—
913C22⋊C4—21no—
914C22⋊C4—21no—
915C22⋊C4—21no—
916C22⋊C4—21no—
917C22⋊C4—221no—
918C22⋊C4—221no—
919C22⋊C4—221no—
920C22⋊C4—221no—
921C22⋊C4—221no—
922C22⋊C4—221no—
923C22⋊C4—221no—
924C22⋊C4—221no—
925C22⋊C4—221no—
926C22⋊C4—221no—
927C22⋊C4—221no—
928C22⋊C4—221no—
929C22⋊C4—221no—
930C22⋊C4—221no—
931C22⋊C4—221no—
932C42—21no—
933C42—111no—
934C42—111no—
935C42—111no—
936C42—111no—
937C42—111no—
938C42—111no—
939C42—111no—
940C42—111no—
941C42—111no—
942C42—111no—
943C42—111no—
944C42—111no—
945C42—221no—
946C42—221no—
947C42—221no—
948C42D4×D1111yescharacteristic
949C42D4×D1111yescharacteristic
950C42C23×D1111yescharacteristic
951C42C23×D1111yescharacteristic
952C11C2×#323811yescharacteristic, complemented, Sylow
953C23—21no—
954C23—111no—
955C23—114no—
956C23—111no—
957C23—222no—
958C23—222no—
959C23—221no—
960C23—442no—
961C23—442no—
962C23—442no—
963C23C2×D4×D1111yescharacteristic
964Q8—22no—
965Q8—44no—
966Q8—44no—
967Q8—222no—
968Q8—444no—
969Q8—444no—
970Q8—442no—
971Q8—448no—
972Q8—448no—
973D4—22no—
974D4—42no—
975D4—222no—
976D4—442no—
977D4—442no—
978D4—442no—
979D4—442no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—24no—
987C2×C4—44no—
988C2×C4—42no—
989C2×C4—111no—
990C2×C4—111no—
991C2×C4—114no—
992C2×C4—114no—
993C2×C4—111no—
994C2×C4—111no—
995C2×C4—111no—
996C2×C4—111no—
997C2×C4—222no—
998C2×C4—222no—
999C2×C4—222no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—221no—
1011C2×C4—221no—
1012C2×C4—221no—
1013C2×C4—224no—
1014C2×C4—442no—
1015C2×C4—448no—
1016C2×C4—448no—
1017C2×C4—442no—
1018C2×C4—442no—
1019C2×C4—442no—
1020C2×C4—442no—
1021C2×C4—444no—
1022C2×C4—442no—
1023C2×C4C2×D4×D1111yescharacteristic
1024C2×C4C2×D4×D1111yescharacteristic
1025C2×C4C2×D4×D1111yescharacteristic
1026C2×C4C2×D4×D1111yescharacteristic
1027C2×C4C2×D4×D1111yescharacteristic
1028C2×C4C24×D1111yescharacteristic
1029C8—24no—
1030C8—224no—
1031C22—21no—
1032C22—21no—
1033C22—41no—
1034C22—41no—
1035C22—41no—
1036C22—112no—
1037C22—112no—
1038C22—112no—
1039C22—112no—
1040C22—228no—
1041C22—221no—
1042C22—221no—
1043C22—441no—
1044C22—441no—
1045C22—441no—
1046C22—884no—
1047C22D11×AGL(1,ℤ/8)12yes—
1048C22C22×D4×D1111yescharacteristic
1049C4—21no—
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—41no—
1054C4—44no—
1055C4—41no—
1056C4—41no—
1057C4—112no—
1058C4—112no—
1059C4—221no—
1060C4—221no—
1061C4—221no—
1062C4—221no—
1063C4—441no—
1064C4—444no—
1065C4—441no—
1066C4—441no—
1067C4D11×#13712yes—
1068C4D11×2−1+412yes—
1069C2—22no—
1070C2—81no—
1071C2—114no—
1072C2—222no—
1073C2—881no—
1074C2D11×#53611yescharacteristic
1075C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
1076C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3238C2
socleC22×C11C23×D4
prime radicalD11×#121C22
hypercenter#3238D11
hypocenterC11C2×#3238
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3238

Complements

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

NH ≅ G/Ntype
1. C2×D11×C4⋊Q8C2semidirect
3. #13079841C2semidirect
4. #13079840C2semidirect
5. #13079839C2semidirect
6. #13079838C2semidirect
7. #13079837C2semidirect
8. #13079836C2semidirect
9. #13079835C2semidirect
10. #13079834C2semidirect
11. #13079833C2semidirect
12. D11×#501C2semidirect
13. D11×#489C2semidirect
14. D11×#483C2semidirect
16. D11×#477C2semidirect
17. D11×#476C2semidirect
18. D11×#432C2semidirect
19. C11×#3238C2semidirect
21. C2×C11×C4⋊Q8C22semidirect
30. D11×C4⋊Q8C22semidirect
31. D11×C4⋊Q8C22semidirect
55. C2×#66941C22semidirect
58. C2×#66922C22semidirect
59. C11×#501C22semidirect
60. C11×#489C22semidirect
61. C11×#483C22semidirect
63. C11×#477C22semidirect
64. C11×#476C22semidirect
65. C11×#432C22semidirect
66. #10622704C22semidirect
67. #10622702C22semidirect
68. #10622697C22semidirect
69. #10622693C22semidirect
70. #10622678C22semidirect
71. #10622668C22semidirect
72. #10622656C22semidirect
74. #10622634C22semidirect
75. #10622621C22semidirect
76. #10622584C22semidirect
78. #10622539C22semidirect
81. #10622489C22semidirect
82. #10622488C22semidirect
83. #10622483C22semidirect
84. #10622475C22semidirect
86. #10622469C22semidirect
87. #10622463C22semidirect
88. #10622455C22semidirect
89. #10622448C22semidirect
91. #10622418C22semidirect
93. #10622408C22semidirect
94. #10622407C22semidirect
97. #10622378C22semidirect
98. #10622374C22semidirect
101. #10622334C22semidirect
102. #10622332C22semidirect
103. #10622327C22semidirect
104. #10622318C22semidirect
106. #10622315C22semidirect
426. #3238D11direct (N × H)
525. C2×C4⋊Q8C2×D11semidirect
556. #501C2×D11semidirect
562. #489C2×D11semidirect
568. #483C2×D11semidirect
580. #477C2×D11semidirect
586. #476C2×D11semidirect
591. #432C2×D11semidirect
812. D11#3238direct (N × H)
952. C11C2×#3238semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
D11×#5292
#130798412
#130798402
#130798392
#130798382
#130798372
#130798362
#130798352
#130798342
#130798332
D11×#5012
D11×#4892
D11×#4832
D11×#4802
D11×#4772
D11×#4762
D11×#4322
C11×#32382
C2×#323811