Finite Group Databasebeta

← C2×#13082239 #15660874

Subgroups — C2×#13082239 #15660874

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#13082239C2132yesmaximal, direct product factor
2C2×Q8×Dic22C211yesmaximal, characteristic, complemented
3C2×#10623094C213yesmaximal, complemented
4C2×#10623147C216yesmaximal, complemented
5C2×#10623249C213yesmaximal, complemented
6C2×#10623365C212yesmaximal, complemented
7C2×#10623247C213yesmaximal, complemented
8C2×#10623127C216yesmaximal, complemented
9C2×#41×Dic11C212yesmaximal, complemented
10C2×C4×#4343C211yesmaximal, characteristic, complemented
11C2×C4×#4341C213yesmaximal, complemented
12C2×C11×#550C211yesmaximal, characteristic, complemented
13C22×C11×#41C2212yes—
14C22×#4343C2211yescharacteristic
15C22×#4341C2213yes—
16C22×#4341C2216yes—
17C11×#550C22116yescomplemented
18C2×C11×#127C2213yes—
19C2×C11×#121C2216yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2213yes—
22#10623365C22132yescomplemented
23#41×Dic11C22132yescomplemented
24C2×Q8×Dic11C2212yes—
25C2×Q8×Dic11C2211yescharacteristic
26C2×#66993C2216yes—
27C2×#66992C22112yes—
28C2×#66991C2216yes—
29C2×#66991C2216yes—
30C2×#66989C2216yes—
31C2×D4×Dic11C2216yes—
32C2×D4×Dic11C2213yes—
33C2×D4×Dic11C2216yes—
34C2×#66983C2216yes—
35C2×C4×C22⋊D11C2216yes—
36C2×#66979C2216yes—
37C22×C4×Dic11C2216yes—
38#10623249C22148yescomplemented
39#10623247C22148yescomplemented
40#10623147C22196yescomplemented
41#10623127C22196yescomplemented
42C4×#4343C22116yescomplemented
43Q8×Dic22C22116yescomplemented
44#10623094C22148yescomplemented
45C4×#4341C22148yescomplemented
46C2×#66946C2213yes—
47C2×#66945C2213yes—
48C2×#66945C2213yes—
49C2×#66941C2216yes—
50C2×#66940C2211yescharacteristic
51C2×#66938C22112yes—
52C2×(C22⋊D11)⋊C4C2216yes—
53C2×#66930C2216yes—
54C2×C4×D44C2213yes—
55C2×C42×D11C2213yes—
56C2×#66922C2213yes—
57C2×C4×Dic22C2213yes—
58C2×C11×#41—216no—
59C2×C11×#41C23116yes—
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2316yes—
62C22×D4×C11C2313yes—
63C22×D4×C11C2316yes—
64C23×C4×C11C2316yes—
65C22×C22⋊D11C2316yes—
66C22×C22⋊D11C23112yes—
67C23×Dic11C2316yes—
68C23×Dic11C2316yes—
69C2×#4343—28no—
70C2×#4343C2318yes—
71C2×#4341—224no—
72C2×#4341—424no—
73C2×#4341C23124yes—
74C2×#4341C23148yes—
75C22×D44C2313yes—
76C22×C4×D11C2313yes—
77C22×C4×D11C2313yes—
78C22×C4×D11C2313yes—
79C22×Dic22C2316yes—
80C22×Dic22C2311yescharacteristic
81C11×#127C23124yes—
82C11×#121C23148yes—
83C4×Q8×C11C2318yes—
84C4×D4×C11C23124yes—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2313yes—
87C2×C11×C22⋊C4C2316yes—
88C2×C42×C11C2313yes—
89C2×C22⋊Dic11C2316yes—
90C2×C22⋊Dic11C23112yes—
91Q8×Dic11C23116yes—
92Q8×Dic11C2318yes—
93#66993C23148yes—
94#66992C23196yes—
95#66991C23148yes—
96#66991C23148yes—
97#66989C23148yes—
98D4×Dic11C23124yes—
99D4×Dic11C23148yes—
100D4×Dic11C23148yes—
101#66983C23148yes—
102C4×C22⋊D11C23148yes—
103C2×(C2×D11)⋊C4C2316yes—
104C2×(C2×D11)⋊C4C2316yes—
105#66979C23148yes—
106C2×C4⋊Dic11C2313yes—
107C2×C4⋊Dic11C2316yes—
108C2×C4⋊Dic11C2313yes—
109C2×Dic11⋊C4C2316yes—
110C2×Dic11⋊C4C2312yes—
111C2×C4×Dic11C2316yes—
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2313yes—
114C2×C4×Dic11C2313yes—
115C2×C4×Dic11C2316yes—
116C2×C4×Dic11C2312yes—
117C2×C4×Dic11C23148yes—
118#66946C23124yes—
119#66945C23124yes—
120#66945C23124yes—
121#66941C23148yes—
122#66940C2318yes—
123#66938C23196yes—
124(C22⋊D11)⋊C4C23148yes—
125#66930C23148yes—
126C4×D44C23124yes—
127C42×D11C23124yes—
128#66922C23124yes—
129C4×Dic22C23124yes—
130C2×#3483—111nomaximal, Sylow
131C24×C11C2416yes—
132C23×D11C2413yes—
133C11×#41—264no—
134C2×Q8×C11#4118yescomplemented
135C2×Q8×C11C2414yes—
136C2×D4×C11—212no—
137C2×D4×C11—224no—
138C2×D4×C11—412no—
139C2×D4×C11C24124yes—
140C2×D4×C11C24112yes—
141C2×D4×C11C24124yes—
142C22×C4×C11—224no—
143C22×C4×C11C2412yes—
144C22×C4×C11C24124yes—
145C22×C4×C11C2413yes—
146C22×C4×C11C2413yes—
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—224no—
149C2×C22⋊D11—424no—
150C2×C22⋊D11C24124yes—
151C2×C22⋊D11C24148yes—
152C22×Dic11—224no—
153C22×Dic11—224no—
154C22×Dic11C24124yes—
155C22×Dic11C24124yes—
156C22×Dic11C2411yescharacteristic
157C22×Dic11C2413yes—
158C22×Dic11C2416yes—
159C22×Dic11C2412yes—
160C22×Dic11C2411yescharacteristic
161#4343—232no—
162#4341—296no—
163#4341—496no—
164C2×D44—212no—
165C2×D44C24112yes—
166C2×C4×D11—212no—
167C2×C4×D11—212no—
168C2×C4×D11—212no—
169C2×C4×D11C24112yes—
170C2×C4×D11C24112yes—
171C2×C4×D11C24112yes—
172C2×Dic22—412no—
173C2×Dic22#4118yescomplemented
174C2×Dic22C24124yes—
175C2×Dic22C2414yes—
176C11×C4⋊C4C2414yes—
177C11×C4⋊C4C24112yes—
178C11×C22⋊C4C24124yes—
179C42×C11C24112yes—
180C22⋊Dic11C24124yes—
181C22⋊Dic11C24148yes—
182(C2×D11)⋊C4C24124yes—
183(C2×D11)⋊C4C24124yes—
184C4⋊Dic11C24112yes—
185C4⋊Dic11C24124yes—
186C4⋊Dic11C24112yes—
187Dic11⋊C4C24124yes—
188Dic11⋊C4C2418yes—
189C4×Dic11C24124yes—
190C4×Dic11C2414yes—
191C4×Dic11C24112yes—
192C4×Dic11C24112yes—
193C4×Dic11C24124yes—
194C4×Dic11C2418yes—
195#3483—1132no—
196C2×Q82—111no—
197C2×#555—116no—
198C2×#555—113no—
199C2×#550—112no—
200C2×#550—113no—
201C2×#550D1111yescharacteristic, complemented
202C2×#532—113no—
203C2×#532—116no—
204C2×C4×#41—112no—
205C2×C4×#41—111no—
206C2×C4×#41—113no—
207C23×C11—212no—
208C23×C11—212no—
209C23×C11—212no—
210C23×C11C25112yes—
211C23×C11C2511yescharacteristic
212C22×D11—26no—
213C22×D11—26no—
214C22×D11—26no—
215C22×D11C2516yes—
216Q8×C11C2×#41116yescomplemented
217D4×C11—224no—
218D4×C11—248no—
219D4×C11—424no—
220C2×C4×C11—24no—
221C2×C4×C11—26no—
222C2×C4×C11—248no—
223C2×C4×C11C2×#41112yes—
224C2×C4×C11C2×#4114yes—
225C2×C4×C11C2514yes—
226C2×C4×C11C2516yes—
227C2×C4×C11C2516yes—
228C2×C4×C11C2512yes—
229C22⋊D11—248no—
230C22⋊D11—448no—
231C2×Dic11—22no—
232C2×Dic11—26no—
233C2×Dic11—212no—
234C2×Dic11—248no—
235C2×Dic11—248no—
236C2×Dic11C2×#4118yes—
237C2×Dic11H(5,𝔽2)14yes—
238C2×Dic11C2512yes—
239C2×Dic11C2516yes—
240C2×Dic11C25112yes—
241C2×Dic11C2514yes—
242C2×Dic11C2512yes—
243D44—224no—
244C4×D11—224no—
245C4×D11—224no—
246C4×D11—224no—
247Dic22—424no—
248Dic22C2×#41116yescomplemented
249C22×#41—111no—
250C22×#41—113no—
251C22×#41—116no—
252C22×#41C2×D1112yes—
253Q82—1116no—
254#555—1196no—
255#555—1148no—
256#550—1132no—
257#550—1148no—
258#550C2×D11116yescomplemented
259#532—1148no—
260#532—1196no—
261C2×C4⋊Q8—116no—
262C2×C4⋊Q8—113no—
263C2×#127—116no—
264C2×#127C2×D1113yes—
265C2×#124—116no—
266C2×#124—1112no—
267C2×#121—116no—
268C2×#121—116no—
269C2×#121—1112no—
270C2×#121—116no—
271C2×#121C2×D1116yes—
272C4×#41—1132no—
273C4×#41—1116no—
274C4×#41—1148no—
275C2×C4×Q8—111no—
276C2×C4×Q8—112no—
277C2×C4×Q8—111no—
278C2×C4×Q8—113no—
279C2×C4×Q8C2×D1111yescharacteristic
280C2×C4×D4—116no—
281C2×C4×D4—113no—
282C2×C4×D4—116no—
283C2×C4×D4—116no—
284C2×C4×D4—113no—
285C2×C4×D4—116no—
286C2×C4×D4—113no—
287C2×C4×D4C2×D1113yes—
288C2×#117—116no—
289C2×#117—113no—
290C2×#117—113no—
291C2×#117—116no—
292C22×C42—116no—
293C22×C42—113no—
294C22×C11—212no—
295C22×C11—212no—
296C22×C11—212no—
297C22×C11—424no—
298C22×C11C22×#4112yes—
299C22×C11C22×#4112yes—
300C22×C11C2×H(5,𝔽2)12yes—
301C22×C11C2611yescharacteristic
302C2×D11—26no—
303C2×D11—26no—
304C2×D11—26no—
305C2×D11—412no—
306C4×C11—24no—
307C4×C11—26no—
308C4×C11C22×#41112yes—
309C4×C11C22×#4114yes—
310Dic11—22no—
311Dic11—26no—
312Dic11—212no—
313Dic11C22×#4118yes—
314Dic11C2×H(5,𝔽2)14yes—
315C2×#41—216no—
316C2×#41—118no—
317C2×#41—1124no—
318C2×#41—1148no—
319C2×#41—2224no—
320C2×#41—228no—
321C2×#41—4424no—
322C2×#41C22×D11116yes—
323C22×Q8—111no—
324C22×Q8—116no—
325C22×Q8C22×D1111yescharacteristic
326C22×D4—116no—
327C22×D4—1112no—
328C22×D4—113no—
329C22×D4C22×D1116yes—
330C22×D4C22×D1113yes—
331C22×D4C22×D1116yes—
332C23×C4—116no—
333C23×C4—116no—
334C23×C4—113no—
335C23×C4—113no—
336C23×C4—113no—
337C23×C4C22×D1116yes—
338C4⋊Q8—1148no—
339C4⋊Q8—1124no—
340#127—1148no—
341#127C22×D11124yes—
342#124—1148no—
343#124—1196no—
344#121—1148no—
345#121—1148no—
346#121—1196no—
347#121—1148no—
348#121C22×D11148yes—
349C4×Q8—118no—
350C4×Q8—1116no—
351C4×Q8—118no—
352C4×Q8—1124no—
353C4×Q8C22×D1118yes—
354C4×D4—1148no—
355C4×D4—1124no—
356C4×D4—1148no—
357C4×D4—1148no—
358C4×D4—1124no—
359C4×D4—1148no—
360C4×D4—1124no—
361C4×D4C22×D11124yes—
362#117—1148no—
363#117—1124no—
364#117—1124no—
365#117—1148no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—113no—
368C2×C4⋊C4—116no—
369C2×C4⋊C4—116no—
370C2×C4⋊C4—113no—
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1113yes—
373C2×C22⋊C4—1112no—
374C2×C22⋊C4—116no—
375C2×C22⋊C4—116no—
376C2×C22⋊C4—116no—
377C2×C22⋊C4C22×D1116yes—
378C2×C42—113no—
379C2×C42—116no—
380C2×C42—112no—
381C2×C42—113no—
382C2×C42—111no—
383C2×C42—116no—
384C2×C42—1148no—
385C2×C42—1124no—
386C2×C42C22×D1113yes—
387C2×C11—412no—
388C2×C11#348314yescomplemented
389C2×C11C23×#4111yescharacteristic
390C2×C11C23×#4111yescharacteristic
391C2×C11C22×H(5,𝔽2)11yescharacteristic
392D11—46no—
393C24—113no—
394C24C23×D1116yes—
395#41—264no—
396#41—2296no—
397#41—2232no—
398#41—4496no—
399C2×Q8—118no—
400C2×Q8—114no—
401C2×Q8—1124no—
402C2×Q8—4412no—
403C2×Q8#434118yescomplemented
404C2×Q8C23×D1114yes—
405C2×D4—224no—
406C2×D4—212no—
407C2×D4—412no—
408C2×D4—1124no—
409C2×D4—1148no—
410C2×D4—1112no—
411C2×D4—2224no—
412C2×D4—2212no—
413C2×D4—4424no—
414C2×D4C23×D11124yes—
415C2×D4C23×D11112yes—
416C2×D4C23×D11124yes—
417C22×C4—224no—
418C22×C4—111no—
419C22×C4—112no—
420C22×C4—1124no—
421C22×C4—1124no—
422C22×C4—111no—
423C22×C4—113no—
424C22×C4—116no—
425C22×C4—1112no—
426C22×C4—1112no—
427C22×C4—1112no—
428C22×C4—2212no—
429C22×C4—2224no—
430C22×C4—2224no—
431C22×C4—2212no—
432C22×C4—2212no—
433C22×C4C23×D11124yes—
434C22×C4C23×D1112yes—
435C22×C4C23×D1113yes—
436C22×C4C23×D1113yes—
437C22×C4C23×D1111yescharacteristic
438C4⋊C4—118no—
439C4⋊C4—1112no—
440C4⋊C4—1124no—
441C4⋊C4—1124no—
442C4⋊C4—1112no—
443C4⋊C4C23×D1114yes—
444C4⋊C4C23×D11112yes—
445C22⋊C4—1148no—
446C22⋊C4—1124no—
447C22⋊C4—1124no—
448C22⋊C4—1124no—
449C22⋊C4C23×D11124yes—
450C42—118no—
451C42—1112no—
452C42—114no—
453C42—1112no—
454C42—1124no—
455C42—1124no—
456C42C23×D11112yes—
457C11C2×#348311yescharacteristic, complemented, Sylow
458C23—212no—
459C23—212no—
460C23—212no—
461C23—116no—
462C23—226no—
463C23—226no—
464C23—226no—
465C23C24×D11112yes—
466C23C24×D1111yescharacteristic
467Q8—1116no—
468Q8—4424no—
469Q8C2×#4341116yescomplemented
470D4—248no—
471D4—224no—
472D4—424no—
473D4—2248no—
474D4—2224no—
475D4—4448no—
476C2×C4—24no—
477C2×C4—26no—
478C2×C4—248no—
479C2×C4—118no—
480C2×C4—114no—
481C2×C4—112no—
482C2×C4—114no—
483C2×C4—116no—
484C2×C4—112no—
485C2×C4—1112no—
486C2×C4—2224no—
487C2×C4—2248no—
488C2×C4—2248no—
489C2×C4—222no—
490C2×C4—226no—
491C2×C4—2212no—
492C2×C4—2224no—
493C2×C4—2224no—
494C2×C4C2×#4341112yes—
495C2×C4#41×D1114yes—
496C2×C4C24×D1114yes—
497C2×C4C24×D1116yes—
498C2×C4C24×D1116yes—
499C2×C4C24×D1112yes—
500C22—212no—
501C22—212no—
502C22—212no—
503C22—424no—
504C22—226no—
505C22—226no—
506C22—226no—
507C22—4412no—
508C22C22×#434112yes—
509C22C2×#41×D1112yes—
510C22D11×H(5,𝔽2)12yes—
511C22C25×D1111yescharacteristic
512C4—24no—
513C4—26no—
514C4—118no—
515C4—114no—
516C4—226no—
517C4—222no—
518C4—2212no—
519C4C22×#4341112yes—
520C4C2×#41×D1114yes—
521C2—412no—
522C2—446no—
523C2#1308223914yesdirect product factor
524C2C22×#41×D1111yescharacteristic
525C2C23×#434111yescharacteristic
526C2C2×D11×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#550C2
socleC23×C11C25
hypercenterC2×#550D11
hypocenterC11C2×#3483
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #13082239C2direct (N × H)
2. C2×Q8×Dic22C2semidirect
3. C2×#10623094C2semidirect
4. C2×#10623147C2semidirect
5. C2×#10623249C2semidirect
6. C2×#10623365C2semidirect
7. C2×#10623247C2semidirect
8. C2×#10623127C2semidirect
9. C2×#41×Dic11C2semidirect
10. C2×C4×#4343C2semidirect
11. C2×C4×#4341C2semidirect
12. C2×C11×#550C2semidirect
17. C11×#550C22semidirect
22. #10623365C22semidirect
23. #41×Dic11C22semidirect
38. #10623249C22semidirect
39. #10623247C22semidirect
40. #10623147C22semidirect
41. #10623127C22semidirect
42. C4×#4343C22semidirect
43. Q8×Dic22C22semidirect
44. #10623094C22semidirect
45. C4×#4341C22semidirect
134. C2×Q8×C11#41semidirect
173. C2×Dic22#41semidirect
201. C2×#550D11semidirect
216. Q8×C11C2×#41semidirect
248. Dic22C2×#41semidirect
258. #550C2×D11semidirect
388. C2×C11#3483semidirect
403. C2×Q8#4341semidirect
457. C11C2×#3483semidirect
469. Q8C2×#4341semidirect
523. C2#13082239direct (N × H)

Maximal subgroups

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

subgroupindex
#130822392
C2×Q8×Dic222
C2×#106230942
C2×#106231472
C2×#106232492
C2×#106233652
C2×#106232472
C2×#106231272
C2×#41×Dic112
C2×C4×#43432
C2×C4×#43412
C2×C11×#5502
C2×#348311