Finite Group Databasebeta

← C2×#13079562 #15624962

Subgroups — C2×#13079562 #15624962

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic
2C22×#66997C211yesmaximal, characteristic
3#13079562C2116yesmaximal, direct product factor
4C2×#10622794C212yesmaximal, complemented
5C2×#10622405C212yesmaximal, complemented
6C2×#10622406C212yesmaximal, complemented
7C2×#10622795C212yesmaximal, complemented
8C2×#10622352C211yesmaximal, characteristic
9C2×#10622841C211yesmaximal, characteristic
10C2×#10622663C211yesmaximal, characteristic
11C2×#10622331C211yesmaximal, characteristic
12C2×C11×#451C211yesmaximal, characteristic
13C23×Q8×C11C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C22×C11×Q16C2212yes—
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×#66997—21no—
19C2×#66997—21no—
20C2×#66997—24no—
21C2×#66997C2218yes—
22C2×#66997C2212yes—
23C2×#66997C2212yes—
24C2×#66997C2211yescharacteristic
25C22×#4326C2212yes—
26C22×#4326C2212yes—
27C2×#66977C2211yescharacteristic
28C22×Dic11⋊C4—21no—
29C22×Dic11⋊C4—21no—
30C22×C4×Dic11C2211yescharacteristic
31C22×Dic44C2212yes—
32#10623153—24no—
33#10623153C2218yes—
34C2×#66942—21no—
35C2×#66941C2211yescharacteristic
36C2×#66940—21no—
37C2×#66940C2211yescharacteristic
38C2×#66931—21no—
39C2×#66930—21no—
40C11×#451C2218yes—
41C2×C11×#103C2212yes—
42C2×C11×C22⋊C8C2211yescharacteristic
43#10622841C2218yes—
44C2×#66899C2212yes—
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46#10622795C22116yescomplemented
47#10622794C22116yescomplemented
48C2×#66880C2212yes—
49C2×Dic11⋊C8C2212yes—
50C2×C8×Dic11C2212yes—
51#10622663C2218yes—
52C2×#66874C2212yes—
53#10622406C22116yescomplemented
54#10622405C22116yescomplemented
55#10622352C2218yes—
56#10622331C2218yes—
57C22×Q8×C11—21no—
58C22×Q8×C11—22no—
59C22×Q8×C11—44no—
60C22×Q8×C11C2311yescharacteristic
61C22×Q8×C11C2312yes—
62C22×Q8×C11C2314yes—
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C23×Dic11D411yescharacteristic
67C23×Dic11D411yescharacteristic
68C22×Dic22—21no—
69C22×Dic22—22no—
70C22×Dic22—21no—
71C22×Dic22—44no—
72C22×Dic22C2311yescharacteristic
73C22×Dic22C2312yes—
74C22×Dic22C2314yes—
75C2×C11×Q16—44no—
76C2×C11×Q16C2318yes—
77C22×C8×C11C2312yes—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8C2314yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C22⋊Dic11—21no—
84Q8×Dic11—22no—
85Q8×Dic11C2314yes—
86#66997—28no—
87#66997—24no—
88#66997—24no—
89#66997—28no—
90#66997—22no—
91#66997C2314yes—
92#66997C2318yes—
93#66997C2318yes—
94C2×#4326—44no—
95C2×#4326—44no—
96C2×#4326C2318yes—
97C2×#4326C2318yes—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100#66977—22no—
101#66977C2314yes—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—28no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—28no—
112C2×Dic11⋊C4—22no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11—21no—
115C2×C4×Dic11D411yescharacteristic
116C2×C4×Dic11D411yescharacteristic
117C2×C4×Dic11D414yes—
118C2×C4×Dic11C2311yescharacteristic
119C2×C4×Dic11C2311yescharacteristic
120C2×C4×Dic11C2314yes—
121C22×C11⋊C8C2312yes—
122C2×Dic44—44no—
123C2×Dic44C2318yes—
124#66942—28no—
125#66941—22no—
126#66941C2314yes—
127#66940—28no—
128#66940—22no—
129#66940C2314yes—
130#66931—28no—
131#66930—28no—
132C11×#103C2318yes—
133C11×C22⋊C8C2314yes—
134#66899C2318yes—
135C22⋊(C11⋊C8)C2314yes—
136#66880C2318yes—
137Dic11⋊C8C2318yes—
138C8×Dic11C2318yes—
139#66874C2318yes—
140C2×#3209—111nomaximal, Sylow
141C24×C11C2×D411yescharacteristic
142C2×Q8×C11—24no—
143C2×Q8×C11—22no—
144C2×Q8×C11—21no—
145C2×Q8×C11—24no—
146C2×Q8×C11—24no—
147C2×Q8×C11—24no—
148C2×Q8×C11—48no—
149C2×Q8×C11—44no—
150C2×Q8×C11—48no—
151C2×Q8×C11C2414yes—
152C2×Q8×C11C2412yes—
153C22×C4×C11—24no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—24no—
157C22×C4×C11—22no—
158C22×C4×C11—44no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—24no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—24no—
167C22×Dic11—22no—
168C22×Dic11—44no—
169C22×Dic11Q1618yescomplemented
170C22×Dic11C2×D414yes—
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D414yes—
175C22×Dic11C2×D411yescharacteristic
176C2×Dic22—24no—
177C2×Dic22—21no—
178C2×Dic22—24no—
179C2×Dic22—22no—
180C2×Dic22—24no—
181C2×Dic22—24no—
182C2×Dic22—24no—
183C2×Dic22—48no—
184C2×Dic22—44no—
185C2×Dic22—48no—
186C2×Dic22—44no—
187C2×Dic22C2414yes—
188C2×Dic22C2412yes—
189C11×Q16—48no—
190C2×C8×C11—24no—
191C2×C8×C11C2414yes—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4C2412yes—
195C11×C22⋊C4—24no—
196C22⋊Dic11—24no—
197#4326—48no—
198#4326—48no—
199C4⋊Dic11—24no—
200C4⋊Dic11—21no—
201C4⋊Dic11C2412yes—
202Dic11⋊C4—24no—
203Dic11⋊C4—24no—
204Dic11⋊C4—24no—
205Dic11⋊C4—24no—
206Dic11⋊C4—28no—
207Dic11⋊C4—28no—
208Dic11⋊C4—28no—
209Dic11⋊C4—28no—
210Dic11⋊C4—24no—
211C4×Dic11—24no—
212C4×Dic11—24no—
213C4×Dic11C2×D414yes—
214C4×Dic11C2×D412yes—
215C4×Dic11C2×D412yes—
216C4×Dic11C2×D414yes—
217C4×Dic11C2412yes—
218C4×Dic11C2412yes—
219C2×C11⋊C8—24no—
220C2×C11⋊C8C2414yes—
221Dic44—48no—
222C2×#533—111no—
223C22×C4⋊Q8—111no—
224#3209—1116no—
225C2×#494—112no—
226C2×#487—112no—
227C2×#462—112no—
228C2×#462—112no—
229C2×#451—111no—
230C2×#451—111no—
231C2×#451—111no—
232C2×#451D1111yescharacteristic
233C2×#431—111no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11C2×Q1614yes—
237C23×C11C22×D412yes—
238C23×C11C22×D411yescharacteristic
239Q8×C11—24no—
240Q8×C11—24no—
241Q8×C11—24no—
242Q8×C11—48no—
243Q8×C11—42no—
244Q8×C11—44no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—48no—
252C2×C4×C11—44no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11H(5,𝔽2)14yes—
258C2×C4×C11C2511yescharacteristic
259C2×Dic11—22no—
260C2×Dic11—28no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—48no—
265C2×Dic11—44no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11C2×Q1614yes—
269C2×Dic11C2×Q1614yes—
270C2×Dic11C2×Q16116yescomplemented
271C2×Dic11#13714yes—
272C2×Dic11C22×D412yes—
273C2×Dic11C22×D412yes—
274C2×Dic11C22×D412yes—
275C2×Dic11C22×D412yes—
276Dic22—24no—
277Dic22—24no—
278Dic22—24no—
279Dic22—48no—
280Dic22—42no—
281Dic22—44no—
282Dic22—48no—
283C8×C11—24no—
284C11⋊C8—24no—
285C23×Q8—111no—
286C23×Q8C2×D1111yescharacteristic
287C22×Q16—112no—
288C22×Q16—112no—
289C22×Q16—112no—
290C22×Q16C2×D1112yes—
291#533—118no—
292#533—224no—
293C2×C4⋊Q8—111no—
294C2×C4⋊Q8—112no—
295C2×C4⋊Q8—111no—
296C2×C4⋊Q8—118no—
297C2×C4⋊Q8—112no—
298C2×C4⋊Q8—221no—
299C2×C4⋊Q8—221no—
300C2×C4⋊Q8—224no—
301C2×#125—221no—
302C2×C22⋊Q8—111no—
303C2×C22⋊Q8—221no—
304C2×C22⋊Q8C2×D1111yescharacteristic
305C2×C4×Q8—111no—
306C2×C4×Q8—111no—
307C2×C4×Q8—221no—
308C2×#117—221no—
309C22×C4⋊C4—221no—
310C22×C4⋊C4—221no—
311C22×C42—111no—
312#494—1116no—
313#487—1116no—
314#462—1116no—
315#462—1116no—
316#451—118no—
317#451—118no—
318#451—118no—
319#451C2×D1118yes—
320#431—118no—
321C2×C4⋊C8—112no—
322C2×#103—112no—
323C2×#103—112no—
324C2×#103—112no—
325C2×#103C2×D1112yes—
326C2×C22⋊C8—111no—
327C2×C22⋊C8C2×D1111yescharacteristic
328C2×C4×C8—112no—
329C22×C11—22no—
330C22×C11—28no—
331C22×C11—22no—
332C22×C11#53512yes—
333C22×C11C22×Q1614yes—
334C22×C11C22×Q1612yes—
335C22×C11C2×#13712yes—
336C22×C11C23×D411yescharacteristic
337C4×C11—22no—
338C4×C11—44no—
339C4×C11—42no—
340C4×C11—42no—
341C4×C11#53512yes—
342C4×C11C2×H(5,𝔽2)12yes—
343Dic11—22no—
344Dic11—44no—
345Dic11—42no—
346Dic11—42no—
347Dic11C22×Q1614yes—
348Dic11C22×Q1614yes—
349Dic11C2×#13714yes—
350C22×Q8—22no—
351C22×Q8—21no—
352C22×Q8—44no—
353C22×Q8—111no—
354C22×Q8—112no—
355C22×Q8—114no—
356C22×Q8—221no—
357C22×Q8—222no—
358C22×Q8—221no—
359C22×Q8—444no—
360C22×Q8C22×D1111yescharacteristic
361C22×Q8C22×D1112yes—
362C22×Q8C22×D1114yes—
363C23×C4—21no—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—221no—
367C23×C4C22×D1111yescharacteristic
368C2×Q16—44no—
369C2×Q16—118no—
370C2×Q16—118no—
371C2×Q16—118no—
372C2×Q16—444no—
373C2×Q16—444no—
374C2×Q16—444no—
375C2×Q16C22×D1118yes—
376C22×C8—112no—
377C22×C8C22×D1112yes—
378C4⋊Q8—114no—
379C4⋊Q8—118no—
380C4⋊Q8—118no—
381C4⋊Q8—114no—
382C4⋊Q8—222no—
383C4⋊Q8—228no—
384C4⋊Q8—224no—
385C4⋊Q8—228no—
386C4⋊Q8—224no—
387C4⋊Q8—222no—
388#125—228no—
389C22⋊Q8—22no—
390C22⋊Q8—114no—
391C22⋊Q8—228no—
392C22⋊Q8—222no—
393C22⋊Q8C22×D1114yes—
394C4×Q8—114no—
395C4×Q8—114no—
396C4×Q8—222no—
397C4×Q8—228no—
398C4×Q8—222no—
399#117—228no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—228no—
403C2×C4⋊C4—228no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—221no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—114no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42—114no—
423C2×C42—221no—
424C2×C42—221no—
425C4⋊C8—118no—
426#103—118no—
427#103—118no—
428#103—118no—
429#103C22×D1118yes—
430C22⋊C8—114no—
431C22⋊C8C22×D1114yes—
432C4×C8—118no—
433C2×C11—24no—
434C2×C11#320914yescomplemented
435C2×C11C2×#53511yescharacteristic
436C2×C11C23×Q1611yescharacteristic
437C2×C11C22×#13711yescharacteristic
438C24D4×D1111yescharacteristic
439C2×Q8—21no—
440C2×Q8—24no—
441C2×Q8—22no—
442C2×Q8—24no—
443C2×Q8—24no—
444C2×Q8—24no—
445C2×Q8—48no—
446C2×Q8—44no—
447C2×Q8—48no—
448C2×Q8—114no—
449C2×Q8—112no—
450C2×Q8—224no—
451C2×Q8—221no—
452C2×Q8—224no—
453C2×Q8—222no—
454C2×Q8—224no—
455C2×Q8—224no—
456C2×Q8—224no—
457C2×Q8—448no—
458C2×Q8—444no—
459C2×Q8—448no—
460C2×Q8—444no—
461C2×Q8C23×D1114yes—
462C2×Q8C23×D1112yes—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—44no—
469C22×C4—118no—
470C22×C4—114no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—114no—
475C22×C4—111no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—222no—
481C22×C4—444no—
482C22×C4D4×D1112yes—
483C22×C4D4×D1111yescharacteristic
484C22×C4C23×D1112yes—
485C22×C4C23×D1111yescharacteristic
486Q16—48no—
487Q16—448no—
488Q16—448no—
489Q16—448no—
490C2×C8—24no—
491C2×C8—114no—
492C2×C8—224no—
493C2×C8C23×D1114yes—
494C4⋊C4—24no—
495C4⋊C4—21no—
496C4⋊C4—112no—
497C4⋊C4—228no—
498C4⋊C4—228no—
499C4⋊C4—228no—
500C4⋊C4—228no—
501C4⋊C4—224no—
502C4⋊C4—224no—
503C4⋊C4—224no—
504C4⋊C4—224no—
505C4⋊C4—224no—
506C4⋊C4—221no—
507C4⋊C4—224no—
508C4⋊C4C23×D1112yes—
509C22⋊C4—24no—
510C22⋊C4—224no—
511C42—114no—
512C42—112no—
513C42—114no—
514C42—112no—
515C42—112no—
516C42—112no—
517C42—224no—
518C42—224no—
519C11C2×#320911yescharacteristic, complemented, Sylow
520C23—22no—
521C23—22no—
522C23Q16×D1114yes—
523C23C2×D4×D1112yes—
524C23C2×D4×D1111yescharacteristic
525Q8—24no—
526Q8—24no—
527Q8—24no—
528Q8—48no—
529Q8—42no—
530Q8—44no—
531Q8—224no—
532Q8—224no—
533Q8—224no—
534Q8—448no—
535Q8—448no—
536Q8—444no—
537Q8—442no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—48no—
545C2×C4—42no—
546C2×C4—44no—
547C2×C4—42no—
548C2×C4—114no—
549C2×C4—114no—
550C2×C4—1116no—
551C2×C4—114no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—112no—
555C2×C4—112no—
556C2×C4—228no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—224no—
561C2×C4—448no—
562C2×C4—442no—
563C2×C4—444no—
564C2×C4—442no—
565C2×C4C2×D4×D1112yes—
566C2×C4C2×D4×D1111yescharacteristic
567C2×C4#6703714yes—
568C2×C4C24×D1111yescharacteristic
569C8—24no—
570C8—224no—
571C22—28no—
572C22—22no—
573C22—22no—
574C22#1062312312yes—
575C22C2×Q16×D1114yes—
576C22C2×Q16×D1112yes—
577C22D11×#13712yes—
578C22C22×D4×D1111yescharacteristic
579C4—22no—
580C4—44no—
581C4—42no—
582C4—42no—
583C4—114no—
584C4—114no—
585C4—114no—
586C4—222no—
587C4—444no—
588C4—442no—
589C4—442no—
590C4#1062312312yes—
591C4C2×#6703712yes—
592C2—24no—
593C2#1307956214yesdirect product factor
594C2C2×#1062312311yescharacteristic
595C2C22×Q16×D1111yescharacteristic
596C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#451C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#451D11
hypocenterC11C2×#3209
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #13079562C2direct (N × H)
4. C2×#10622794C2semidirect
5. C2×#10622405C2semidirect
6. C2×#10622406C2semidirect
7. C2×#10622795C2semidirect
46. #10622795C22semidirect
47. #10622794C22semidirect
53. #10622406C22semidirect
54. #10622405C22semidirect
169. C22×Dic11Q16semidirect
270. C2×Dic11C2×Q16semidirect
434. C2×C11#3209semidirect
519. C11C2×#3209semidirect
593. C2#13079562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231532
C22×#669972
#130795622
C2×#106227942
C2×#106224052
C2×#106224062
C2×#106227952
C2×#106223522
C2×#106228412
C2×#106226632
C2×#106223312
C2×C11×#4512
C2×#320911