Finite Group Databasebeta

← C2×#13078777 #15621910

Subgroups — C2×#13078777 #15621910

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×C4×#4343C211yesmaximal, characteristic
3#13078777C2116yesmaximal, direct product factor
4C2×#10622428C212yesmaximal, complemented
5C2×#10622634C211yesmaximal, characteristic, complemented
6C2×#10622455C211yesmaximal, characteristic, complemented
7C2×#10622696C211yesmaximal, characteristic, complemented
8C2×#10622800C212yesmaximal
9C2×#10622797C212yesmaximal, complemented
10C2×#10622430C212yesmaximal, complemented
11C2×#10622448C211yesmaximal, characteristic, complemented
12C2×C11×#462C211yesmaximal, characteristic, complemented
13C22×#4343C2211yescharacteristic
14C22×C11×Q16C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C2212yes—
18C2×Q8×Dic11C2212yes—
19C2×Q8×Dic11C2211yescharacteristic
20C22×#4325C2212yes—
21#10623259—24no—
22#10623259C2218yescomplemented
23C4×#4343—24no—
24C4×#4343C2218yes—
25C2×#66950—21no—
26C2×#66946—21no—
27C2×#66946C2211yescharacteristic
28C2×#66945—21no—
29C2×#66945—21no—
30C2×#66945C2211yescharacteristic
31C2×#66943—21no—
32C2×#66940—21no—
33C2×C4×D44—21no—
34C2×C4×D44C2211yescharacteristic
35C2×C42×D11—21no—
36C2×C42×D11C2211yescharacteristic
37C2×#66922C2211yescharacteristic
38C11×#462C2218yescomplemented
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×#103C2212yes—
41C2×#66899C2212yes—
42C2×#66899C2212yes—
43#10622800C22116yes—
44#10622797C22116yescomplemented
45C2×#66885C2212yes—
46C2×(C2×D11)⋊C8C2212yes—
47C2×#66881C2212yes—
48C2×#66879C2212yes—
49#10622696C2218yescomplemented
50#10622634C2218yescomplemented
51C2×#66871C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622455C2218yescomplemented
54#10622448C2218yescomplemented
55#10622430C22116yescomplemented
56#10622428C22116yescomplemented
57C22×Q8×C11C2312yes—
58C22×Q8×C11C2311yescharacteristic
59C2×#4343—24no—
60C2×#4343—24no—
61C2×#4343—22no—
62C2×#4343C2314yes—
63C22×D44—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C4×D11—21no—
68C22×C4×D11D411yescharacteristic
69C22×C4×D11D411yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×Dic22—21no—
72C2×C11×Q16—28no—
73C2×C11×Q16C2318yes—
74C22×C8×C11C2312yes—
75C11×C4⋊Q8—22no—
76C11×C4⋊Q8C2314yes—
77C4×Q8×C11—22no—
78C4×Q8×C11C2314yes—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85#66999—24no—
86#66999C2318yes—
87Q8×Dic11—24no—
88Q8×Dic11—22no—
89Q8×Dic11C2318yes—
90Q8×Dic11C2314yes—
91C2×#4325—28no—
92C2×#4325C2318yes—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—22no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11D411yescharacteristic
107C2×C4×Dic11D411yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8C2312yes—
110#66950—28no—
111#66946—28no—
112#66946—22no—
113#66946C2314yes—
114#66945—28no—
115#66945—22no—
116#66945—28no—
117#66945C2314yes—
118#66943—28no—
119#66940—28no—
120C4×D44—28no—
121C4×D44—22no—
122C4×D44C2314yes—
123C42×D11—28no—
124C42×D11D414yes—
125C42×D11C2314yes—
126#66922—22no—
127#66922C2314yes—
128C11×C4⋊C8C2314yes—
129C11×#103C2318yes—
130#66899C2318yes—
131#66899C2318yes—
132#66885C2318yes—
133(C2×D11)⋊C8C2318yes—
134#66881C2318yes—
135#66879C2318yes—
136#66871C2318yes—
137C4⋊(C11⋊C8)C2314yes—
138C2×#3116—111nomaximal, Sylow
139C23×D11—21no—
140C23×D11C2×D411yescharacteristic
141C2×Q8×C11—21no—
142C2×Q8×C11—22no—
143C2×Q8×C11—22no—
144C2×Q8×C11—24no—
145C2×Q8×C11—24no—
146C2×Q8×C11#4114yes—
147C2×Q8×C11C2414yes—
148C2×Q8×C11C2412yes—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—22no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160#4343—216no—
161#4343—28no—
162#4343—28no—
163C2×D44—28no—
164C2×D44—24no—
165C2×D44—21no—
166C2×D44—22no—
167C2×D44#4114yes—
168C2×D44C2412yes—
169C2×C4×D11—28no—
170C2×C4×D11—24no—
171C2×C4×D11—24no—
172C2×C4×D11—24no—
173C2×C4×D11—24no—
174C2×C4×D11—22no—
175C2×C4×D11—22no—
176C2×C4×D11—42no—
177C2×C4×D11—44no—
178C2×C4×D11—44no—
179C2×C4×D11C2×D412yes—
180C2×C4×D11C2×D414yes—
181C2×C4×D11C2×D414yes—
182C2×C4×D11C2412yes—
183C2×Dic22—24no—
184C2×Dic22—44no—
185C11×Q16—216no—
186C2×C8×C11—24no—
187C2×C8×C11C2414yes—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C2412yes—
193C42×C11—24no—
194C42×C11C2×D412yes—
195C42×C11C2412yes—
196#4325—216no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—28no—
200(C2×D11)⋊C4—24no—
201C4⋊Dic11—24no—
202C4⋊Dic11—28no—
203C4⋊Dic11—22no—
204C4⋊Dic11—24no—
205C4⋊Dic11—21no—
206C4⋊Dic11C2414yes—
207C4⋊Dic11C2412yes—
208Dic11⋊C4—28no—
209C4×Dic11—24no—
210C4×Dic11—24no—
211C4×Dic11—28no—
212C4×Dic11C2×D414yes—
213C4×Dic11C2×D412yes—
214C4×Dic11C2×D414yes—
215C4×Dic11C2412yes—
216C2×C11⋊C8—24no—
217C2×C11⋊C8C2414yes—
218C2×#533—111no—
219C2×C4×#41—111no—
220#3116—1116no—
221C2×#485—112no—
222C2×#477—111no—
223C2×#476—111no—
224C2×#462D1111yescharacteristic, complemented
225C2×#461—111no—
226C2×#452—112no—
227C2×#441—112no—
228C2×#440—112no—
229C2×#432—111no—
230C23×C11C22×D411yescharacteristic
231C22×D11—22no—
232C22×D11—24no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—42no—
237C22×D11—42no—
238C22×D11C22×D412yes—
239Q8×C11—24no—
240Q8×C11—22no—
241Q8×C11—24no—
242Q8×C11—24no—
243Q8×C11—44no—
244Q8×C11C2×#4114yes—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—44no—
251C2×C4×C11—42no—
252C2×C4×C11#13714yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D412yes—
256C2×C4×C11C2×#4112yes—
257C2×C4×C11C2×#4112yes—
258C2×C4×C11C2511yescharacteristic
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—42no—
265C2×Dic11—44no—
266C2×Dic11C22×D412yes—
267C2×Dic11C22×D412yes—
268C2×Dic11C22×D412yes—
269D44—216no—
270D44—24no—
271D44—22no—
272D44C2×#4114yes—
273C4×D11—216no—
274C4×D11—24no—
275C4×D11—28no—
276C4×D11—22no—
277C4×D11—22no—
278C4×D11—44no—
279C4×D11—48no—
280C4×D11—48no—
281Dic22—48no—
282C8×C11—24no—
283C11⋊C8—24no—
284C22×#41—111no—
285C22×Q16C2×D1112yes—
286C22×SD16—112no—
287#533—118no—
288#533—224no—
289C2×C4⋊Q8—111no—
290C2×C4⋊Q8C2×D1111yescharacteristic
291C2×#125—221no—
292C2×C22⋊Q8—112no—
293C2×C22⋊Q8—221no—
294C4×#41—118no—
295C4×#41—224no—
296C2×C4×Q8—111no—
297C2×C4×Q8—112no—
298C2×C4×Q8—221no—
299C2×C4×Q8C2×D1111yescharacteristic
300C2×C4×D4—111no—
301C2×C4×D4—111no—
302C2×C4×D4—221no—
303C2×C4×D4—221no—
304C2×#117—111no—
305C2×#117—221no—
306C2×#117—221no—
307C22×C42—111no—
308C22×C42—221no—
309#485—1116no—
310#477—118no—
311#476—118no—
312#462C2×D1118yescomplemented
313#461—118no—
314#452—1116no—
315#441—1116no—
316#440—1116no—
317#432—118no—
318C2×#107—112no—
319C2×#106—112no—
320C2×C4⋊C8—111no—
321C2×C4⋊C8C2×D1111yescharacteristic
322C2×#103—112no—
323C2×#103—112no—
324C2×#103C2×D1112yes—
325C2×#102—112no—
326C2×C22⋊C8—112no—
327C2×#97—112no—
328C22×C11#52512yes—
329C22×C11C2×#13712yes—
330C22×C11#57512yes—
331C22×C11C23×D411yescharacteristic
332C2×D11—24no—
333C2×D11—22no—
334C2×D11—22no—
335C2×D11—22no—
336C2×D11—44no—
337C2×D11—48no—
338C2×D11—42no—
339C2×D11—42no—
340C4×C11—24no—
341C4×C11—22no—
342C4×C11—44no—
343C4×C11—42no—
344C4×C11#52512yes—
345C4×C11C2×#13714yes—
346C4×C11C22×#4111yescharacteristic
347C4×C11C22×#4111yescharacteristic
348Dic11—22no—
349Dic11—22no—
350Dic11—22no—
351Dic11—42no—
352Dic11—44no—
353C2×#41—114no—
354C2×#41—222no—
355C2×#41—224no—
356C2×#41—224no—
357C22×Q8—221no—
358C22×Q8C22×D1112yes—
359C22×Q8C22×D1111yescharacteristic
360C22×D4—111no—
361C22×D4—221no—
362C23×C4—111no—
363C23×C4—111no—
364C23×C4—111no—
365C23×C4—221no—
366C23×C4—221no—
367C23×C4—221no—
368C2×Q16—28no—
369C2×Q16C22×D1118yes—
370C2×SD16—118no—
371C2×SD16—228no—
372C22×C8—112no—
373C22×C8C22×D1112yes—
374C4⋊Q8—22no—
375C4⋊Q8—114no—
376C4⋊Q8—222no—
377C4⋊Q8C22×D1114yes—
378#125—228no—
379C22⋊Q8—118no—
380C22⋊Q8—228no—
381C22⋊Q8—224no—
382C4×Q8—22no—
383C4×Q8—114no—
384C4×Q8—118no—
385C4×Q8—228no—
386C4×Q8—222no—
387C4×Q8—224no—
388C4×Q8C22×D1114yes—
389C4×D4—114no—
390C4×D4—114no—
391C4×D4—228no—
392C4×D4—222no—
393C4×D4—228no—
394C4×D4—222no—
395#117—114no—
396#117—228no—
397#117—222no—
398#117—228no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—222no—
412C2×C22⋊C4—221no—
413C2×C42—21no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—114no—
418C2×C42—114no—
419C2×C42—228no—
420C2×C42—221no—
421C2×C42—222no—
422C2×C42—221no—
423C2×C42C22×D1111yescharacteristic
424#107—118no—
425#106—118no—
426C4⋊C8—114no—
427C4⋊C8C22×D1114yes—
428#103—118no—
429#103—118no—
430#103C22×D1118yes—
431#102—118no—
432C22⋊C8—118no—
433#97—118no—
434C2×C11#311614yescomplemented
435C2×C11C2×#52511yescharacteristic
436C2×C11C22×#13711yescharacteristic
437C2×C11C2×#57511yescharacteristic
438D11—42no—
439D11—44no—
440C24—111no—
441C24—221no—
442#41—228no—
443#41—2216no—
444#41—228no—
445C2×Q8—21no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—24no—
449C2×Q8—24no—
450C2×Q8—224no—
451C2×Q8—444no—
452C2×Q8#434114yes—
453C2×Q8C23×D1114yes—
454C2×Q8C23×D1112yes—
455C2×D4—114no—
456C2×D4—112no—
457C2×D4—224no—
458C2×D4—228no—
459C2×D4—221no—
460C2×D4—222no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—114no—
468C22×C4—112no—
469C22×C4—112no—
470C22×C4—114no—
471C22×C4—224no—
472C22×C4—224no—
473C22×C4—228no—
474C22×C4—224no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—221no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—442no—
481C22×C4—444no—
482C22×C4—444no—
483C22×C4D4×D1111yescharacteristic
484C22×C4D4×D1111yescharacteristic
485C22×C4C23×D1111yescharacteristic
486Q16—216no—
487SD16—2216no—
488C2×C8—24no—
489C2×C8—114no—
490C2×C8—224no—
491C2×C8C23×D1114yes—
492C4⋊C4—24no—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—21no—
496C4⋊C4—114no—
497C4⋊C4—112no—
498C4⋊C4—224no—
499C4⋊C4—228no—
500C4⋊C4—228no—
501C4⋊C4—221no—
502C4⋊C4—222no—
503C4⋊C4—224no—
504C4⋊C4C23×D1112yes—
505C22⋊C4—224no—
506C22⋊C4—224no—
507C22⋊C4—228no—
508C22⋊C4—224no—
509C42—24no—
510C42—114no—
511C42—114no—
512C42—112no—
513C42—112no—
514C42—224no—
515C42—224no—
516C42—228no—
517C42D4×D1112yes—
518C42C23×D1112yes—
519C11C2×#311611yescharacteristic, complemented, Sylow
520C23—112no—
521C23—222no—
522C23—222no—
523C23—224no—
524C23—222no—
525C23—222no—
526C23—442no—
527C23—442no—
528C23C2×D4×D1111yescharacteristic
529Q8—24no—
530Q8—22no—
531Q8—24no—
532Q8—24no—
533Q8—44no—
534Q8—448no—
535Q8C2×#434114yes—
536D4—114no—
537D4—2216no—
538D4—224no—
539D4—222no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—42no—
546C2×C4—44no—
547C2×C4—112no—
548C2×C4—112no—
549C2×C4—112no—
550C2×C4—2216no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—228no—
555C2×C4—224no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—224no—
560C2×C4—444no—
561C2×C4—448no—
562C2×C4—442no—
563C2×C4—444no—
564C2×C4—448no—
565C2×C4#6697114yes—
566C2×C4C2×D4×D1112yes—
567C2×C4C2×D4×D1112yes—
568C2×C4C2×D4×D1111yescharacteristic
569C2×C4C2×#434112yes—
570C2×C4#41×D1112yes—
571C2×C4C24×D1111yescharacteristic
572C8—24no—
573C8—224no—
574C22—224no—
575C22—222no—
576C22—222no—
577C22—222no—
578C22—442no—
579C22—442no—
580C22—444no—
581C22—448no—
582C22#1062313712yes—
583C22C2×#6697112yes—
584C22#1062330812yes—
585C22C22×D4×D1111yescharacteristic
586C4—24no—
587C4—22no—
588C4—44no—
589C4—42no—
590C4—222no—
591C4—222no—
592C4—222no—
593C4—442no—
594C4—444no—
595C4#1062313712yes—
596C4C2×#6697114yes—
597C4C22×#434111yescharacteristic
598C4C2×#41×D1111yescharacteristic
599C2—442no—
600C2—444no—
601C2#1307877714yesdirect product factor
602C2C2×#1062313711yescharacteristic
603C2C22×#6697111yescharacteristic
604C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
prime radicalC22×#4343C22
hypercenterC2×#462D11
hypocenterC11C2×#3116
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13078777C2direct (N × H)
4. C2×#10622428C2semidirect
5. C2×#10622634C2semidirect
6. C2×#10622455C2semidirect
7. C2×#10622696C2semidirect
9. C2×#10622797C2semidirect
10. C2×#10622430C2semidirect
11. C2×#10622448C2semidirect
12. C2×C11×#462C2semidirect
22. #10623259C22semidirect
38. C11×#462C22semidirect
44. #10622797C22semidirect
49. #10622696C22semidirect
50. #10622634C22semidirect
53. #10622455C22semidirect
54. #10622448C22semidirect
55. #10622430C22semidirect
56. #10622428C22semidirect
224. C2×#462D11semidirect
312. #462C2×D11semidirect
434. C2×C11#3116semidirect
519. C11C2×#3116semidirect
601. C2#13078777direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×C4×#43432
#130787772
C2×#106224282
C2×#106226342
C2×#106224552
C2×#106226962
C2×#106228002
C2×#106227972
C2×#106224302
C2×#106224482
C2×C11×#4622
C2×#311611