Finite Group Databasebeta

← C2×#13082242 #15660877

Subgroups — C2×#13082242 #15660877

Order 2816.

8418 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082242C2132yesmaximal, direct product factor
2C2×Q8×Dic22C211yesmaximal, characteristic, complemented
3C2×#10623094C213yesmaximal, complemented
4C2×#10623063C216yesmaximal, complemented
5C2×#10623108C211yesmaximal, characteristic, complemented
6C2×#10623084C213yesmaximal, complemented
7C2×#10623365C212yesmaximal, complemented
8C2×#10623008C213yesmaximal, complemented
9C2×#10623079C216yesmaximal, complemented
10C2×C4×#4343C212yesmaximal, complemented
11C2×C4×#4339C213yesmaximal, complemented
12C2×C4×C11×#41C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C22×#4343C2212yes—
15C22×#4339C2213yes—
16C22×#4339C2216yes—
17C4×C11×#41C22116yescomplemented
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2213yes—
21C2×C4×D4×C11C2213yes—
22C2×C11×#117C2213yes—
23C22×C42×C11C2213yes—
24#10623365C22132yescomplemented
25C2×Q8×Dic11C2212yes—
26C2×#66993C2216yes—
27C2×#66991C2216yes—
28C2×#66983C2216yes—
29C2×#66983C2216yes—
30C2×C4×C22⋊D11C2216yes—
31C2×C4×C22⋊D11C2216yes—
32C2×#66979C2213yes—
33#10623108C22116yescomplemented
34C4×#4343C22132yescomplemented
35Q8×Dic22C22116yescomplemented
36#10623094C22148yescomplemented
37#10623084C22148yescomplemented
38#10623079C22196yescomplemented
39#10623063C22196yescomplemented
40C2×#66948C2216yes—
41C2×#66946C2216yes—
42C2×#66945C2216yes—
43C2×#66941C2216yes—
44C2×#66938C22112yes—
45C2×#66937C22112yes—
46#10623008C22148yescomplemented
47C2×#66928C2216yes—
48C2×#66927C2213yes—
49C4×#4339C22148yescomplemented
50C2×C4×D44C2216yes—
51C2×C4×D44C2213yes—
52C2×C4×D44C2213yes—
53C2×#66925C2216yes—
54C2×C42×D11C2216yes—
55C2×#66922C2213yes—
56C2×C4×Dic22C2213yes—
57C2×C4×Dic22C2211yescharacteristic
58C2×C11×#41—28no—
59C2×C11×#41C2318yes—
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2313yes—
62C23×C4×C11C2313yes—
63C23×C4×C11C2313yes—
64C23×C4×C11C2313yes—
65C22×C22⋊D11C2316yes—
66C22×C22⋊D11C23112yes—
67C2×#4343—216no—
68C2×#4343C23116yes—
69C2×#4339—224no—
70C2×#4339—424no—
71C2×#4339C23124yes—
72C2×#4339C23148yes—
73C22×D44C2313yes—
74C22×D44C2316yes—
75C22×D44C2316yes—
76C22×C4×D11C2316yes—
77C22×C4×D11C2316yes—
78C22×C4×D11C2316yes—
79C22×Dic22C2316yes—
80C22×Dic22C2311yescharacteristic
81C4×Q8×C11C2318yes—
82C4×Q8×C11C2318yes—
83C4×D4×C11C23124yes—
84C4×D4×C11C23124yes—
85C11×#117C23124yes—
86C2×C11×C4⋊C4C2313yes—
87C2×C11×C4⋊C4C2313yes—
88C2×C11×C22⋊C4C2316yes—
89C2×C42×C11C2313yes—
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2313yes—
92C2×C42×C11C2313yes—
93C2×C42×C11C23124yes—
94C2×C22⋊Dic11C2316yes—
95Q8×Dic11C23116yes—
96#66993C23148yes—
97#66991C23148yes—
98#66983C23148yes—
99#66983C23148yes—
100C4×C22⋊D11C23148yes—
101C4×C22⋊D11C23148yes—
102C2×(C2×D11)⋊C4C2316yes—
103C2×(C2×D11)⋊C4C2316yes—
104C2×(C2×D11)⋊C4C23112yes—
105#66979C23124yes—
106C2×C4⋊Dic11C2313yes—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2316yes—
109C2×Dic11⋊C4C2312yes—
110C2×Dic11⋊C4C2316yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2316yes—
113C2×C4×Dic11C2316yes—
114#66948C23148yes—
115#66946C23148yes—
116#66945C23148yes—
117#66941C23148yes—
118#66938C23196yes—
119#66937C23196yes—
120#66928C23148yes—
121#66927C23124yes—
122C4×D44C23124yes—
123C4×D44C23124yes—
124C4×D44C23148yes—
125#66925C23148yes—
126C42×D11C23148yes—
127#66922C23124yes—
128C4×Dic22C2318yes—
129C4×Dic22C23124yes—
130C2×#3483—111nomaximal, Sylow
131C24×C11C2413yes—
132C23×D11C2416yes—
133C11×#41—232no—
134C2×Q8×C11#4118yescomplemented
135C2×Q8×C11C2414yes—
136C2×D4×C11—212no—
137C2×D4×C11C24112yes—
138C22×C4×C11—212no—
139C22×C4×C11—212no—
140C22×C4×C11—212no—
141C22×C4×C11C2413yes—
142C22×C4×C11C2411yescharacteristic
143C22×C4×C11C2413yes—
144C22×C4×C11C24112yes—
145C22×C4×C11C24112yes—
146C22×C4×C11C24112yes—
147C22×C4×C11C2413yes—
148C22×C4×C11C2411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—224no—
151C2×C22⋊D11—424no—
152C2×C22⋊D11C24124yes—
153C2×C22⋊D11C24148yes—
154C22×Dic11C2412yes—
155C22×Dic11C2416yes—
156C22×Dic11C2412yes—
157#4343—264no—
158#4339—296no—
159#4339—496no—
160C2×D44—212no—
161C2×D44—224no—
162C2×D44—412no—
163C2×D44C24112yes—
164C2×D44C24124yes—
165C2×D44C24124yes—
166C2×C4×D11—224no—
167C2×C4×D11—224no—
168C2×C4×D11—224no—
169C2×C4×D11C24124yes—
170C2×C4×D11C24124yes—
171C2×C4×D11C24124yes—
172C2×Dic22—412no—
173C2×Dic22#4118yescomplemented
174C2×Dic22C24124yes—
175C2×Dic22C2414yes—
176C11×C4⋊C4C24112yes—
177C11×C4⋊C4C24112yes—
178C11×C22⋊C4C24124yes—
179C42×C11C24112yes—
180C42×C11C2414yes—
181C42×C11C24112yes—
182C42×C11C24112yes—
183C22⋊Dic11C24124yes—
184(C2×D11)⋊C4C24124yes—
185(C2×D11)⋊C4C24124yes—
186(C2×D11)⋊C4C24148yes—
187C4⋊Dic11C24112yes—
188C4⋊Dic11C2414yes—
189C4⋊Dic11C24124yes—
190Dic11⋊C4C2418yes—
191Dic11⋊C4C24124yes—
192C4×Dic11C2418yes—
193C4×Dic11C24124yes—
194C4×Dic11C24124yes—
195#3483—1132no—
196C2×Q82—111no—
197C2×#555—113no—
198C2×#555—116no—
199C2×#550—112no—
200C2×#550—111no—
201C2×#550—113no—
202C2×#532—113no—
203C2×#532—116no—
204C2×C4×#41—113no—
205C2×C4×#41—112no—
206C2×C4×#41D1111yescharacteristic, complemented
207C23×C11—26no—
208C23×C11—26no—
209C23×C11—26no—
210C23×C11C2516yes—
211C23×C11C2511yescharacteristic
212C22×D11—212no—
213C22×D11—212no—
214C22×D11—212no—
215C22×D11C25112yes—
216Q8×C11C2×#41116yescomplemented
217D4×C11—224no—
218C2×C4×C11—26no—
219C2×C4×C11—22no—
220C2×C4×C11—26no—
221C2×C4×C11—224no—
222C2×C4×C11—224no—
223C2×C4×C11—224no—
224C2×C4×C11C2×#41112yes—
225C2×C4×C11C2×#4114yes—
226C2×C4×C11H(5,𝔽2)14yes—
227C2×C4×C11C2516yes—
228C2×C4×C11C2512yes—
229C2×C4×C11C2516yes—
230C2×C4×C11C2516yes—
231C2×C4×C11C2512yes—
232C2×C4×C11C2512yes—
233C22⋊D11—248no—
234C22⋊D11—448no—
235C2×Dic11—24no—
236C2×Dic11—212no—
237C2×Dic11C2×#4118yes—
238C2×Dic11C2514yes—
239C2×Dic11C25112yes—
240C2×Dic11C2514yes—
241D44—224no—
242D44—248no—
243D44—424no—
244C4×D11—248no—
245C4×D11—248no—
246C4×D11—248no—
247Dic22—424no—
248Dic22C2×#41116yescomplemented
249C22×#41—112no—
250C22×#41—113no—
251C22×#41—116no—
252C22×#41C2×D1111yescharacteristic
253Q82—1116no—
254#555—1148no—
255#555—1196no—
256#550—1132no—
257#550—1116no—
258#550—1148no—
259#532—1196no—
260#532—1148no—
261C2×C4⋊Q8—116no—
262C2×C4⋊Q8—113no—
263C2×#127—116no—
264C2×#127—113no—
265C2×#124—1112no—
266C2×#124—116no—
267C2×#121—116no—
268C2×#121—116no—
269C2×#121—116no—
270C2×#121—116no—
271C2×#121—1112no—
272C4×#41—1132no—
273C4×#41—1148no—
274C4×#41C2×D11116yescomplemented
275C2×C4×Q8—112no—
276C2×C4×Q8—111no—
277C2×C4×Q8—113no—
278C2×C4×Q8C2×D1111yescharacteristic
279C2×C4×Q8C2×D1111yescharacteristic
280C2×C4×D4—116no—
281C2×C4×D4—116no—
282C2×C4×D4—116no—
283C2×C4×D4—113no—
284C2×C4×D4—116no—
285C2×C4×D4—113no—
286C2×C4×D4C2×D1113yes—
287C2×C4×D4C2×D1113yes—
288C2×#117—113no—
289C2×#117—116no—
290C2×#117—116no—
291C2×#117C2×D1113yes—
292C22×C42—116no—
293C22×C42C2×D1113yes—
294C22×C11—26no—
295C22×C11—26no—
296C22×C11—26no—
297C22×C11—412no—
298C22×C11C22×#4112yes—
299C22×C11C22×#4112yes—
300C22×C11C2×H(5,𝔽2)12yes—
301C22×C11C2611yescharacteristic
302C2×D11—212no—
303C2×D11—212no—
304C2×D11—212no—
305C2×D11—424no—
306C4×C11—22no—
307C4×C11—26no—
308C4×C11—26no—
309C4×C11C22×#41112yes—
310C4×C11C22×#4114yes—
311C4×C11C2×H(5,𝔽2)14yes—
312Dic11—24no—
313Dic11—212no—
314Dic11C22×#4118yes—
315C2×#41—28no—
316C2×#41—1116no—
317C2×#41—1124no—
318C2×#41—1148no—
319C2×#41—2224no—
320C2×#41—2216no—
321C2×#41—4424no—
322C2×#41C22×D1118yes—
323C22×Q8—111no—
324C22×Q8—116no—
325C22×Q8C22×D1111yescharacteristic
326C22×D4—116no—
327C22×D4—1112no—
328C22×D4—116no—
329C22×D4—113no—
330C22×D4—116no—
331C22×D4C22×D1113yes—
332C23×C4—116no—
333C23×C4—116no—
334C23×C4—116no—
335C23×C4C22×D1113yes—
336C23×C4C22×D1113yes—
337C23×C4C22×D1113yes—
338C4⋊Q8—1148no—
339C4⋊Q8—1124no—
340#127—1148no—
341#127—1124no—
342#124—1196no—
343#124—1148no—
344#121—1148no—
345#121—1148no—
346#121—1148no—
347#121—1148no—
348#121—1196no—
349C4×Q8—1116no—
350C4×Q8—118no—
351C4×Q8—1124no—
352C4×Q8C22×D1118yes—
353C4×Q8C22×D1118yes—
354C4×D4—1148no—
355C4×D4—1148no—
356C4×D4—1148no—
357C4×D4—1148no—
358C4×D4—1124no—
359C4×D4—1124no—
360C4×D4C22×D11124yes—
361C4×D4C22×D11124yes—
362#117—1124no—
363#117—1148no—
364#117—1148no—
365#117C22×D11124yes—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—116no—
369C2×C4⋊C4—116no—
370C2×C4⋊C4—113no—
371C2×C4⋊C4C22×D1113yes—
372C2×C4⋊C4C22×D1113yes—
373C2×C22⋊C4—116no—
374C2×C22⋊C4—116no—
375C2×C22⋊C4—1112no—
376C2×C22⋊C4—116no—
377C2×C22⋊C4C22×D1116yes—
378C2×C42—116no—
379C2×C42—116no—
380C2×C42—112no—
381C2×C42—1148no—
382C2×C42C22×D1113yes—
383C2×C42C22×D1113yes—
384C2×C42C22×D11124yes—
385C2×C42C22×D1111yescharacteristic
386C2×C42C22×D1113yes—
387C2×C11—46no—
388C2×C11#348314yescomplemented
389C2×C11C23×#4111yescharacteristic
390C2×C11C23×#4111yescharacteristic
391C2×C11C22×H(5,𝔽2)11yescharacteristic
392D11—412no—
393C24—116no—
394C24C23×D1113yes—
395#41—232no—
396#41—2296no—
397#41—2264no—
398#41—4496no—
399C2×Q8—118no—
400C2×Q8—114no—
401C2×Q8—1124no—
402C2×Q8—4412no—
403C2×Q8#433918yescomplemented
404C2×Q8C23×D1114yes—
405C2×D4—212no—
406C2×D4—1124no—
407C2×D4—1148no—
408C2×D4—1124no—
409C2×D4—1112no—
410C2×D4—1124no—
411C2×D4—2224no—
412C2×D4—2224no—
413C2×D4—2212no—
414C2×D4—4412no—
415C2×D4—4424no—
416C2×D4C23×D11112yes—
417C22×C4—212no—
418C22×C4—212no—
419C22×C4—212no—
420C22×C4—112no—
421C22×C4—112no—
422C22×C4—116no—
423C22×C4—1124no—
424C22×C4—1124no—
425C22×C4—1124no—
426C22×C4—2224no—
427C22×C4—2224no—
428C22×C4—2224no—
429C22×C4C23×D1113yes—
430C22×C4C23×D1111yescharacteristic
431C22×C4C23×D1113yes—
432C22×C4C23×D11112yes—
433C22×C4C23×D11112yes—
434C22×C4C23×D11112yes—
435C22×C4C23×D1113yes—
436C22×C4C23×D1111yescharacteristic
437C22×C4C23×D1111yescharacteristic
438C4⋊C4—118no—
439C4⋊C4—114no—
440C4⋊C4—1124no—
441C4⋊C4—1124no—
442C4⋊C4—1112no—
443C4⋊C4C23×D11112yes—
444C4⋊C4C23×D11112yes—
445C22⋊C4—1124no—
446C22⋊C4—1124no—
447C22⋊C4—1148no—
448C22⋊C4—1124no—
449C22⋊C4C23×D11124yes—
450C42—118no—
451C42—1124no—
452C42—1124no—
453C42C23×D11112yes—
454C42C23×D1114yes—
455C42C23×D11112yes—
456C42C23×D11112yes—
457C11C2×#348311yescharacteristic, complemented, Sylow
458C23—26no—
459C23—26no—
460C23—26no—
461C23—1112no—
462C23—2212no—
463C23—2212no—
464C23—2212no—
465C23C24×D1116yes—
466C23C24×D1111yescharacteristic
467Q8—1116no—
468Q8—4424no—
469Q8C2×#4339116yescomplemented
470D4—224no—
471D4—2248no—
472D4—2248no—
473D4—2224no—
474D4—4424no—
475D4—4448no—
476C2×C4—22no—
477C2×C4—26no—
478C2×C4—26no—
479C2×C4—224no—
480C2×C4—224no—
481C2×C4—224no—
482C2×C4—118no—
483C2×C4—114no—
484C2×C4—114no—
485C2×C4—1112no—
486C2×C4—2248no—
487C2×C4—224no—
488C2×C4—2212no—
489C2×C4—2248no—
490C2×C4—2248no—
491C2×C4C2×#4339112yes—
492C2×C4#41×D1114yes—
493C2×C4#6704214yes—
494C2×C4C24×D1116yes—
495C2×C4C24×D1112yes—
496C2×C4C24×D1116yes—
497C2×C4C24×D1116yes—
498C2×C4C24×D1112yes—
499C2×C4C24×D1112yes—
500C22—26no—
501C22—26no—
502C22—26no—
503C22—412no—
504C22—2212no—
505C22—2212no—
506C22—2212no—
507C22—4424no—
508C22C22×#433912yes—
509C22C2×#41×D1112yes—
510C22C2×#6704212yes—
511C22C25×D1111yescharacteristic
512C4—26no—
513C4—22no—
514C4—26no—
515C4—118no—
516C4—224no—
517C4—2212no—
518C4C22×#4339112yes—
519C4C2×#41×D1114yes—
520C4C2×#6704214yes—
521C2—46no—
522C2—4412no—
523C2#1308224214yesdirect product factor
524C2C22×#41×D1111yescharacteristic
525C2C23×#433911yescharacteristic
526C2C22×#6704211yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C4×C11×#41C2
socleC23×C11C25
hypercenterC2×C4×#41D11
hypocenterC11C2×#3483
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #13082242C2direct (N × H)
2. C2×Q8×Dic22C2semidirect
3. C2×#10623094C2semidirect
4. C2×#10623063C2semidirect
5. C2×#10623108C2semidirect
6. C2×#10623084C2semidirect
7. C2×#10623365C2semidirect
8. C2×#10623008C2semidirect
9. C2×#10623079C2semidirect
10. C2×C4×#4343C2semidirect
11. C2×C4×#4339C2semidirect
12. C2×C4×C11×#41C2semidirect
17. C4×C11×#41C22semidirect
24. #10623365C22semidirect
33. #10623108C22semidirect
34. C4×#4343C22semidirect
35. Q8×Dic22C22semidirect
36. #10623094C22semidirect
37. #10623084C22semidirect
38. #10623079C22semidirect
39. #10623063C22semidirect
46. #10623008C22semidirect
49. C4×#4339C22semidirect
134. C2×Q8×C11#41semidirect
173. C2×Dic22#41semidirect
206. C2×C4×#41D11semidirect
216. Q8×C11C2×#41semidirect
248. Dic22C2×#41semidirect
274. C4×#41C2×D11semidirect
388. C2×C11#3483semidirect
403. C2×Q8#4339semidirect
457. C11C2×#3483semidirect
469. Q8C2×#4339semidirect
523. C2#13082242direct (N × H)

Maximal subgroups

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

subgroupindex
#130822422
C2×Q8×Dic222
C2×#106230942
C2×#106230632
C2×#106231082
C2×#106230842
C2×#106233652
C2×#106230082
C2×#106230792
C2×C4×#43432
C2×C4×#43392
C2×C4×C11×#412
C2×#348311