Finite Group Databasebeta

← C2×#13078775 #15621908

Subgroups — C2×#13078775 #15621908

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×#4341C211yesmaximal, characteristic
3#13078775C2116yesmaximal, direct product factor
4C2×#10622427C212yesmaximal, complemented
5C2×#10622463C211yesmaximal, characteristic, complemented
6C2×#10622621C211yesmaximal, characteristic, complemented
7C2×#10622703C211yesmaximal, characteristic, complemented
8C2×#10622786C212yesmaximal
9C2×#10622402C212yesmaximal, complemented
10C2×#10622777C212yesmaximal, complemented
11C2×#10622448C211yesmaximal, characteristic, complemented
12C2×C11×#461C211yesmaximal, characteristic, complemented
13C22×#4341C2211yescharacteristic
14C22×C11×SD16C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66999C2212yes—
18C2×Q8×Dic11C2212yes—
19C22×#4326C2212yes—
20C2×D4×Dic11C2211yescharacteristic
21C2×C4×C22⋊D11—21no—
22C22×C4×Dic11—21no—
23#10623259—24no—
24#10623259C2218yescomplemented
25C4×#4341—24no—
26C4×#4341C2218yes—
27C2×#66950—21no—
28C2×#66945—21no—
29C2×#66945C2211yescharacteristic
30C2×#66943—21no—
31C2×#66940—21no—
32C2×#66940C2211yescharacteristic
33C2×(C22⋊D11)⋊C4—21no—
34C2×#66930—21no—
35C2×C42×D11C2211yescharacteristic
36C2×#66922C2211yescharacteristic
37C2×C4×Dic22C2211yescharacteristic
38C11×#461C2218yescomplemented
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×#103C2212yes—
41C2×#66899C2212yes—
42C2×#66896C2212yes—
43#10622786C22116yes—
44#10622777C22116yescomplemented
45C2×(C2×D11)⋊C8C2212yes—
46C2×#66882C2212yes—
47C2×#66880C2212yes—
48C2×#66879C2212yes—
49#10622703C2218yescomplemented
50#10622621C2218yescomplemented
51C2×#66872C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622463C2218yescomplemented
54#10622448C2218yescomplemented
55#10622427C22116yescomplemented
56#10622402C22116yescomplemented
57C22×Q8×C11C2312yes—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C23×Dic11—21no—
63C2×#4341—24no—
64C2×#4341—22no—
65C2×#4341—24no—
66C2×#4341C2314yes—
67C22×C4×D11D411yescharacteristic
68C22×C4×D11D411yescharacteristic
69C22×C4×D11C2311yescharacteristic
70C22×Dic22—21no—
71C22×Dic22C2311yescharacteristic
72C2×C11×SD16—28no—
73C2×C11×SD16C2318yes—
74C22×C8×C11C2312yes—
75C11×C4⋊Q8—22no—
76C11×C4⋊Q8C2314yes—
77C4×D4×C11—22no—
78C4×D4×C11C2314yes—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85#66999—24no—
86#66999C2318yes—
87Q8×Dic11—24no—
88Q8×Dic11C2318yes—
89C2×#4326—28no—
90C2×#4326C2318yes—
91D4×Dic11—22no—
92D4×Dic11C2314yes—
93C4×C22⋊D11—28no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—22no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2312yes—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—22no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—28no—
108C2×C4×Dic11D411yescharacteristic
109C2×C4×Dic11D411yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C22×C11⋊C8C2312yes—
112#66950—28no—
113#66945—28no—
114#66945—22no—
115#66945C2314yes—
116#66943—28no—
117#66940—28no—
118#66940—22no—
119#66940C2314yes—
120(C22⋊D11)⋊C4—28no—
121#66930—28no—
122C42×D11D414yes—
123C42×D11C2314yes—
124#66922—22no—
125#66922C2314yes—
126C4×Dic22—22no—
127C4×Dic22C2314yes—
128C11×C4⋊C8C2314yes—
129C11×#103C2318yes—
130#66899C2318yes—
131#66896C2318yes—
132(C2×D11)⋊C8C2318yes—
133#66882C2318yes—
134#66880C2318yes—
135#66879C2318yes—
136#66872C2318yes—
137C4⋊(C11⋊C8)C2314yes—
138C2×#3116—111nomaximal, Sylow
139C24×C11—21no—
140C23×D11C2×D411yescharacteristic
141C2×Q8×C11—22no—
142C2×Q8×C11—24no—
143C2×Q8×C11—24no—
144C2×Q8×C11C2414yes—
145C2×D4×C11—21no—
146C2×D4×C11—22no—
147C2×D4×C11#4114yes—
148C2×D4×C11C2412yes—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—24no—
152C22×C4×C11—44no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—28no—
157C2×C22⋊D11—24no—
158C22×Dic11—28no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—44no—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168#4341—216no—
169#4341—28no—
170#4341—28no—
171C2×C4×D11—24no—
172C2×C4×D11—22no—
173C2×C4×D11—22no—
174C2×C4×D11—42no—
175C2×C4×D11C2×D412yes—
176C2×C4×D11C2×D414yes—
177C2×C4×D11C2×D414yes—
178C2×C4×D11C2412yes—
179C2×Dic22—21no—
180C2×Dic22—24no—
181C2×Dic22—22no—
182C2×Dic22—44no—
183C2×Dic22#4114yes—
184C2×Dic22C2412yes—
185C11×SD16—216no—
186C2×C8×C11—24no—
187C2×C8×C11C2414yes—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4C2412yes—
192C11×C22⋊C4—24no—
193C42×C11C2×D412yes—
194C42×C11C2412yes—
195C22⋊Dic11—24no—
196#4326—216no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—28no—
199C4⋊Dic11—28no—
200C4⋊Dic11—21no—
201C4⋊Dic11—22no—
202C4⋊Dic11—24no—
203C4⋊Dic11C2414yes—
204C4⋊Dic11C2412yes—
205Dic11⋊C4—24no—
206Dic11⋊C4—28no—
207Dic11⋊C4—24no—
208C4×Dic11—24no—
209C4×Dic11—24no—
210C4×Dic11—28no—
211C4×Dic11—24no—
212C4×Dic11C2×D412yes—
213C4×Dic11C2×D414yes—
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×#462—111no—
225C2×#461D1111yescharacteristic, complemented
226C2×#452—112no—
227C2×#441—112no—
228C2×#440—112no—
229C2×#432—111no—
230C23×C11—24no—
231C23×C11—22no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11C22×D411yescharacteristic
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—22no—
238C22×D11C22×D412yes—
239Q8×C11—24no—
240Q8×C11—24no—
241Q8×C11—44no—
242D4×C11—24no—
243D4×C11—22no—
244D4×C11C2×#4114yes—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—44no—
249C2×C4×C11—42no—
250C2×C4×C11—48no—
251C2×C4×C11#13714yes—
252C2×C4×C11C22×D412yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D412yes—
255C2×C4×C11C2×#4112yes—
256C2×C4×C11C2×#4112yes—
257C2×C4×C11C2511yescharacteristic
258C22⋊D11—216no—
259C2×Dic11—216no—
260C2×Dic11—24no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—48no—
268C2×Dic11—44no—
269C2×Dic11—42no—
270C2×Dic11C22×D412yes—
271C2×Dic11C22×D412yes—
272C2×Dic11C22×D412yes—
273C4×D11—24no—
274C4×D11—28no—
275C4×D11—22no—
276C4×D11—22no—
277C4×D11—44no—
278Dic22—24no—
279Dic22—22no—
280Dic22—48no—
281Dic22C2×#4114yes—
282C8×C11—24no—
283C11⋊C8—24no—
284C22×#41—111no—
285C22×Q16—112no—
286C22×SD16C2×D1112yes—
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—112no—
297C2×C4×Q8—111no—
298C2×C4×Q8—111no—
299C2×C4×Q8—221no—
300C2×C4×D4—111no—
301C2×C4×D4—221no—
302C2×C4×D4—221no—
303C2×C4×D4C2×D1111yescharacteristic
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#462—118no—
313#461C2×D1118yescomplemented
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—24no—
329C22×C11—48no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11#52512yes—
333C22×C11C2×#13712yes—
334C22×C11#57512yes—
335C22×C11C23×D411yescharacteristic
336C2×D11—22no—
337C2×D11—22no—
338C2×D11—22no—
339C2×D11—44no—
340C4×C11—22no—
341C4×C11—44no—
342C4×C11—42no—
343C4×C11#52512yes—
344C4×C11C2×#13714yes—
345C4×C11C22×#4111yescharacteristic
346C4×C11C22×#4111yescharacteristic
347Dic11—24no—
348Dic11—22no—
349Dic11—22no—
350Dic11—22no—
351Dic11—44no—
352Dic11—42no—
353C2×#41—114no—
354C2×#41—222no—
355C2×#41—224no—
356C2×#41—224no—
357C22×Q8—111no—
358C22×Q8—221no—
359C22×Q8C22×D1112yes—
360C22×D4—221no—
361C22×D4C22×D1111yescharacteristic
362C23×C4—21no—
363C23×C4—111no—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—221no—
367C23×C4—221no—
368C2×Q16—118no—
369C2×Q16—228no—
370C2×SD16—28no—
371C2×SD16C22×D1118yes—
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—118no—
383C4×Q8—114no—
384C4×Q8—114no—
385C4×Q8—222no—
386C4×Q8—228no—
387C4×Q8—224no—
388C4×Q8—222no—
389C4×D4—22no—
390C4×D4—114no—
391C4×D4—222no—
392C4×D4—228no—
393C4×D4—228no—
394C4×D4C22×D1114yes—
395#117—114no—
396#117—228no—
397#117—222no—
398#117—228no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—222no—
412C2×C22⋊C4—221no—
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—114no—
417C2×C42—114no—
418C2×C42—228no—
419C2×C42—221no—
420C2×C42—222no—
421C2×C42—221no—
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—44no—
435C2×C11#311614yescomplemented
436C2×C11C2×#52511yescharacteristic
437C2×C11C22×#13711yescharacteristic
438C2×C11C2×#57511yescharacteristic
439D11—42no—
440C24—21no—
441C24—111no—
442#41—228no—
443#41—2216no—
444#41—228no—
445C2×Q8—22no—
446C2×Q8—24no—
447C2×Q8—24no—
448C2×Q8—114no—
449C2×Q8—112no—
450C2×Q8—221no—
451C2×Q8—224no—
452C2×Q8—222no—
453C2×Q8—444no—
454C2×Q8C23×D1114yes—
455C2×D4—21no—
456C2×D4—22no—
457C2×D4—224no—
458C2×D4—228no—
459C2×D4#434114yes—
460C2×D4C23×D1112yes—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—44no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—114no—
469C22×C4—112no—
470C22×C4—112no—
471C22×C4—114no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—228no—
475C22×C4—221no—
476C22×C4—224no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—221no—
480C22×C4—222no—
481C22×C4—442no—
482C22×C4—444no—
483C22×C4D4×D1111yescharacteristic
484C22×C4D4×D1111yescharacteristic
485C22×C4C23×D1111yescharacteristic
486Q16—2216no—
487SD16—216no—
488C2×C8—24no—
489C2×C8—114no—
490C2×C8—224no—
491C2×C8C23×D1114yes—
492C4⋊C4—24no—
493C4⋊C4—24no—
494C4⋊C4—21no—
495C4⋊C4—114no—
496C4⋊C4—112no—
497C4⋊C4—224no—
498C4⋊C4—228no—
499C4⋊C4—228no—
500C4⋊C4—221no—
501C4⋊C4—222no—
502C4⋊C4—224no—
503C4⋊C4—224no—
504C4⋊C4C23×D1112yes—
505C22⋊C4—24no—
506C22⋊C4—224no—
507C22⋊C4—228no—
508C22⋊C4—224no—
509C42—114no—
510C42—114no—
511C42—112no—
512C42—112no—
513C42—224no—
514C42—224no—
515C42—228no—
516C42—224no—
517C42D4×D1112yes—
518C42C23×D1112yes—
519C11C2×#311611yescharacteristic, complemented, Sylow
520C23—24no—
521C23—22no—
522C23—42no—
523C23—42no—
524C23—112no—
525C23—222no—
526C23—222no—
527C23—222no—
528C23C2×D4×D1111yescharacteristic
529Q8—24no—
530Q8—24no—
531Q8—44no—
532Q8—114no—
533Q8—224no—
534Q8—222no—
535Q8—448no—
536D4—24no—
537D4—22no—
538D4—2216no—
539D4C2×#434114yes—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—42no—
544C2×C4—44no—
545C2×C4—48no—
546C2×C4—112no—
547C2×C4—112no—
548C2×C4—112no—
549C2×C4—2216no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—224no—
554C2×C4—222no—
555C2×C4—228no—
556C2×C4—224no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—224no—
561C2×C4—444no—
562C2×C4—448no—
563C2×C4—442no—
564C2×C4—444no—
565C2×C4#6696814yes—
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—24no—
575C22—42no—
576C22—42no—
577C22—48no—
578C22—222no—
579C22—222no—
580C22—222no—
581C22—444no—
582C22#1062313712yes—
583C22C2×#6696812yes—
584C22#1062330812yes—
585C22C22×D4×D1111yescharacteristic
586C4—22no—
587C4—44no—
588C4—42no—
589C4—222no—
590C4—224no—
591C4—222no—
592C4—222no—
593C4—442no—
594C4—444no—
595C4#1062313712yes—
596C4C2×#6696814yes—
597C4C22×#434111yescharacteristic
598C4C2×#41×D1111yescharacteristic
599C2—44no—
600C2—442no—
601C2#1307877514yesdirect product factor
602C2C2×#1062313711yescharacteristic
603C2C22×#6696811yescharacteristic
604C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
hypercenterC2×#461D11
hypocenterC11C2×#3116
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13078775C2direct (N × H)
4. C2×#10622427C2semidirect
5. C2×#10622463C2semidirect
6. C2×#10622621C2semidirect
7. C2×#10622703C2semidirect
9. C2×#10622402C2semidirect
10. C2×#10622777C2semidirect
11. C2×#10622448C2semidirect
12. C2×C11×#461C2semidirect
24. #10623259C22semidirect
38. C11×#461C22semidirect
44. #10622777C22semidirect
49. #10622703C22semidirect
50. #10622621C22semidirect
53. #10622463C22semidirect
54. #10622448C22semidirect
55. #10622427C22semidirect
56. #10622402C22semidirect
225. C2×#461D11semidirect
313. #461C2×D11semidirect
435. C2×C11#3116semidirect
519. C11C2×#3116semidirect
601. C2#13078775direct (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×#43412
#130787752
C2×#106224272
C2×#106224632
C2×#106226212
C2×#106227032
C2×#106227862
C2×#106224022
C2×#106227772
C2×#106224482
C2×C11×#4612
C2×#311611