Finite Group Databasebeta

← C2×#10590370 #11874255

Subgroups — C2×#10590370 #11874255

Order 1152.

1349 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64084C211yesmaximal, characteristic, complemented
2C2×C3×#875C211yesmaximal, characteristic, complemented
3C22×#3719C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C22×#3716C211yesmaximal, characteristic, complemented
6C22×#3714C211yesmaximal, characteristic
7C2×C3×C4×C3⋊C8C211yesmaximal, characteristic, complemented
8#10590370C218yesmaximal, direct product factor
9C2×#5059—31nomaximal
10C2×#4696—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×#3752—22no—
17#64084—22no—
18#64084C2214yescomplemented
19C2×C3×(C2×D3)⋊C4—22no—
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#875—22no—
23C3×#875C2214yescomplemented
24C2×#3719—24no—
25C2×#3719C2214yescomplemented
26C2×#3717—24no—
27C2×#3717C2214yescomplemented
28C2×#3716—24no—
29C2×#3716C2214yescomplemented
30C2×#3714—24no—
31C2×#3714C2214yes—
32C3×C4×C3⋊C8C2214yescomplemented
33C2×C3×#124—31no—
34C22×#216—31no—
35C22×#215—31no—
36C22×#214—31no—
37C22×#213—31no—
38C22×Dic12—31no—
39C22×D24—31no—
40C22×#204—31no—
41C22×#204—31no—
42C2×#875—31no—
43C2×#875—31no—
44C2×#875—61no—
45C2×#875D311yescharacteristic, complemented
46C2×C3×C4×C8—31no—
47#5059—38no—
48C2×C4×C3⋊C8D311yescharacteristic, complemented
49#4696—38no—
50C23×C3⋊D3—21no—
51C23×C3×D3—21no—
52C22×C32×C4D412yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×#634—22no—
60C2×#634—22no—
61C2×#634—21no—
62C2×#634C2312yes—
63C22×C3×Dic3—21no—
64C2×C3×D12—22no—
65C2×C3×D12—22no—
66C2×C3×D12—21no—
67C2×C3×D12C2312yes—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2312yes—
72C32×C42D412yes—
73C32×C42C2312yes—
74#3752—28no—
75C3×(C2×D3)⋊C4—28no—
76C2×C3×C3⋊C8D414yes—
77C2×C3×C3⋊C8D414yes—
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2312yes—
80#3719—28no—
81#3717—28no—
82#3716—28no—
83#3714—28no—
84C2×#495—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×D12—31no—
88C22×D12—31no—
89C22×D12—61no—
90C22×D12C2×D311yescharacteristic
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C22×Dic6C2×D311yescharacteristic
95C22×C3×C8—31no—
96C22×C3×C8—31no—
97C3×#124—34no—
98C3×#124—62no—
99C2×C3×C22⋊C4—62no—
100C2×C3×C42—21no—
101C2×C3×C42C2×D311yescharacteristic
102C2×C3×C42C2×D311yescharacteristic
103C2×#216—34no—
104C2×#216—64no—
105C2×#215—34no—
106C2×#215—64no—
107C2×#214—34no—
108C2×#214—64no—
109C2×#213—34no—
110C2×#213—64no—
111C2×(C2×D3)⋊C4—22no—
112C2×(C2×D3)⋊C4—64no—
113C2×(C2×D3)⋊C4—62no—
114C2×(C2×D3)⋊C4—62no—
115C22×C3⋊C8C2×D311yescharacteristic
116C22×C3⋊C8C2×D311yescharacteristic
117C2×Dic12—34no—
118C2×Dic12—64no—
119C2×D24—34no—
120C2×D24—64no—
121C2×#204—34no—
122C2×#204—34no—
123C2×#204—64no—
124C2×#204—64no—
125#875—22no—
126#875—34no—
127#875—34no—
128#875—64no—
129#875—64no—
130#875—62no—
131#875—62no—
132#875C2×D314yescomplemented
133C3×C4×C8—34no—
134C4×C3⋊C8C2×D314yescomplemented
135C23×C32C2×D411yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—44no—
139C22×C3×D3—22no—
140C22×C3×D3—42no—
141C22×C3×D3—44no—
142C2×C32×C4—24no—
143C2×C32×C4C2×D412yes—
144C2×C32×C4C2×D412yes—
145C2×C32×C4C2×D414yes—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—42no—
150C4⋊(C3⋊D3)—22no—
151C4⋊(C3⋊D3)—22no—
152C4⋊(C3⋊D3)—42no—
153#634—22no—
154#634—22no—
155#634—42no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—42no—
158C3×D12—22no—
159C3×D12—22no—
160C3×D12—42no—
161C3×Dic6—22no—
162C3×Dic6—22no—
163C3×Dic6—42no—
164C3×C3⋊C8C2×D414yes—
165C3×C3⋊C8C2×D414yes—
166C22×Q16—91no—
167C22×SD16—91no—
168C22×SD16—91no—
169C22×D8—91no—
170C2×#124—31no—
171C2×#124—91no—
172#495—98no—
173C2×C4×C8—31no—
174C24×C3—61no—
175C23×D3—21no—
176C23×D3—62no—
177C23×D3—61no—
178C23×D3—61no—
179C2×C3×Q8—32no—
180C2×C3×Q8—61no—
181C2×C3×Q8—62no—
182C2×C3×Q8—62no—
183C2×C3×D4—32no—
184C2×C3×D4—62no—
185C2×C3×D4—62no—
186C2×C3×D4—61no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—61no—
190C22×C3×C4D1212yes—
191C22×C3×C4#6712yes—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C22×Dic3—21no—
195C22×Dic3—62no—
196C22×Dic3—61no—
197C22×Dic3—61no—
198C2×D12—22no—
199C2×D12—22no—
200C2×D12—21no—
201C2×D12—32no—
202C2×D12—32no—
203C2×D12—62no—
204C2×D12—62no—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—122no—
212C2×D12—122no—
213C2×D12C22×D312yes—
214C2×Dic6—22no—
215C2×Dic6—22no—
216C2×Dic6—21no—
217C2×Dic6—32no—
218C2×Dic6—32no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—61no—
226C2×Dic6—61no—
227C2×Dic6—122no—
228C2×Dic6—122no—
229C2×Dic6C22×D312yes—
230C2×C3×C8—34no—
231C2×C3×C8—34no—
232C2×C3×C8—32no—
233C2×C3×C8—32no—
234C3×C22⋊C4—68no—
235C3×C42—22no—
236C3×C42—22no—
237C3×C42D1212yes—
238C3×C42#6712yes—
239C3×C42C22×D312yes—
240C3×C42C22×D312yes—
241#216—68no—
242#215—68no—
243#214—68no—
244#213—68no—
245(C2×D3)⋊C4—28no—
246(C2×D3)⋊C4—616no—
247(C2×D3)⋊C4—68no—
248(C2×D3)⋊C4—68no—
249C2×C3⋊C8D1214yes—
250C2×C3⋊C8D1214yes—
251C2×C3⋊C8C22×D312yes—
252C2×C3⋊C8C22×D312yes—
253Dic12—68no—
254D24—68no—
255#204—68no—
256#204—68no—
257C22×C32#12712yes—
258C22×C32#13514yes—
259C22×C32C22×D411yescharacteristic
260C2×C3⋊D3—42no—
261C2×C3⋊D3—44no—
262C2×C3⋊D3—84no—
263C2×C3×D3—42no—
264C2×C3×D3—44no—
265C2×C3×D3—84no—
266C32×C4—24no—
267C32×C4#12712yes—
268C32×C4C22×D411yescharacteristic
269C32×C4C22×D411yescharacteristic
270C3⋊Dic3—42no—
271C3×Dic3—42no—
272C22×Q8—31no—
273C22×Q8—91no—
274C22×D4—31no—
275C22×D4—91no—
276C2×Q16—94no—
277C2×Q16—184no—
278C2×SD16—94no—
279C2×SD16—94no—
280C2×SD16—184no—
281C2×SD16—184no—
282C2×D8—94no—
283C2×D8—184no—
284C22×C8—31no—
285C22×C8—31no—
286#124—34no—
287#124—62no—
288#124—94no—
289#124—182no—
290C2×C22⋊C4—62no—
291C2×C22⋊C4—182no—
292C2×C42D3211yescharacteristic
293C4×C8—34no—
294C23×C3—21no—
295C23×C3—62no—
296C23×C3—122no—
297C23×C3—124no—
298C23×C3C2×D1211yescharacteristic
299C23×C3C2×#6711yescharacteristic
300C22×D3—22no—
301C22×D3—42no—
302C22×D3—44no—
303C22×D3—64no—
304C22×D3—62no—
305C22×D3—62no—
306C22×D3—124no—
307C22×D3—128no—
308C22×D3—122no—
309C22×D3—124no—
310C22×D3—122no—
311C22×D3—124no—
312C3×Q8—62no—
313C3×Q8—62no—
314C3×Q8—122no—
315C3×D4—62no—
316C3×D4—62no—
317C3×D4—122no—
318C2×C3×C4—24no—
319C2×C3×C4—24no—
320C2×C3×C4—21no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—24no—
325C2×C3×C4—44no—
326C2×C3×C4—62no—
327C2×C3×C4—122no—
328C2×C3×C4C2×D1212yes—
329C2×C3×C4C2×D1212yes—
330C2×C3×C4C2×D1214yes—
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4D3×D412yes—
333C2×C3×C4D3×D412yes—
334C2×C3×C4C2×#6714yes—
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338C2×Dic3—22no—
339C2×Dic3—42no—
340C2×Dic3—64no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—124no—
344C2×Dic3—122no—
345C2×Dic3—122no—
346D12—22no—
347D12—22no—
348D12—42no—
349D12—62no—
350D12—62no—
351D12—62no—
352D12—62no—
353D12—122no—
354D12—122no—
355D12—124no—
356D12—122no—
357D12—122no—
358Dic6—22no—
359Dic6—22no—
360Dic6—42no—
361Dic6—62no—
362Dic6—62no—
363Dic6—62no—
364Dic6—62no—
365Dic6—122no—
366Dic6—122no—
367Dic6—124no—
368Dic6—122no—
369Dic6—122no—
370C3×C8—34no—
371C3×C8—34no—
372C3⋊C8C2×D1214yes—
373C3⋊C8C2×D1214yes—
374C2×C32#49514yescomplemented
375C2×C32C2×#12711yescharacteristic
376C2×C32C2×#13512yes—
377C3⋊D3—82no—
378C3×D3—82no—
379C24—61no—
380C24—181no—
381C2×Q8—32no—
382C2×Q8—61no—
383C2×Q8—62no—
384C2×Q8—62no—
385C2×Q8—92no—
386C2×Q8—181no—
387C2×Q8—182no—
388C2×Q8—182no—
389C2×D4—32no—
390C2×D4—62no—
391C2×D4—62no—
392C2×D4—61no—
393C2×D4—92no—
394C2×D4—182no—
395C2×D4—182no—
396C2×D4—181no—
397C22×C4—61no—
398C22×C4—181no—
399C22×C4#62612yes—
400C22×C4C2×D3211yescharacteristic
401Q16—188no—
402SD16—188no—
403SD16—188no—
404D8—188no—
405C2×C8—32no—
406C2×C8—32no—
407C2×C8—34no—
408C2×C8—34no—
409C22⋊C4—68no—
410C22⋊C4—188no—
411C42#62612yes—
412C42C2×D3212yes—
413C22×C3—21no—
414C22×C3—24no—
415C22×C3—22no—
416C22×C3—122no—
417C22×C3—124no—
418C22×C3—244no—
419C22×C3#87412yes—
420C22×C3#90414yes—
421C22×C3#94012yes—
422C22×C3#95014yes—
423C22×C3C22×D1211yescharacteristic
424C22×C3C22×#6711yescharacteristic
425C2×D3—42no—
426C2×D3—44no—
427C2×D3—84no—
428C2×D3—124no—
429C2×D3—128no—
430C2×D3—122no—
431C2×D3—124no—
432C2×D3—122no—
433C2×D3—124no—
434C2×D3—248no—
435C2×D3—244no—
436C2×D3—244no—
437C3×C4—24no—
438C3×C4—24no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—22no—
442C3×C4—44no—
443C3×C4—122no—
444C3×C4#87412yes—
445C3×C4#94012yes—
446C3×C4C22×D1211yescharacteristic
447C3×C4C22×D1211yescharacteristic
448C3×C4C2×D3×D411yescharacteristic
449C3×C4C2×D3×D411yescharacteristic
450Dic3—42no—
451Dic3—124no—
452Dic3—122no—
453Dic3—122no—
454C32C2×#49511yescharacteristic, complemented, Sylow
455C23—62no—
456C23—124no—
457C23—122no—
458C23—182no—
459C23—364no—
460C23—362no—
461C23C2×#62611yescharacteristic
462Q8—62no—
463Q8—62no—
464Q8—122no—
465Q8—182no—
466Q8—182no—
467Q8—362no—
468D4—62no—
469D4—62no—
470D4—122no—
471D4—182no—
472D4—182no—
473D4—362no—
474C2×C4—24no—
475C2×C4—62no—
476C2×C4—122no—
477C2×C4—182no—
478C2×C4—362no—
479C2×C4D3×D1212yes—
480C2×C4D3×D1212yes—
481C2×C4C2×#62614yes—
482C2×C4C2×#62611yescharacteristic
483C2×C4C22×D3211yescharacteristic
484C8—34no—
485C8—34no—
486C2×C3—24no—
487C2×C3—21no—
488C2×C3—22no—
489C2×C3—242no—
490C2×C3#469614yescomplemented
491C2×C3#505914yescomplemented
492C2×C3C2×#87411yescharacteristic
493C2×C3C2×#90412yes—
494C2×C3C2×#94011yescharacteristic
495C2×C3C2×#95012yes—
496D3—82no—
497D3—244no—
498D3—242no—
499D3—242no—
500C22—122no—
501C22—124no—
502C22—244no—
503C22—362no—
504C22—364no—
505C22—724no—
506C22#6382914yes—
507C22#6391112yes—
508C22C22×#62611yescharacteristic
509C4—24no—
510C4—122no—
511C4—362no—
512C4#6391112yes—
513C4C2×D3×D1211yescharacteristic
514C4C2×D3×D1211yescharacteristic
515C3—21no—
516C3C2×#469611yescharacteristic, complemented
517C3C2×#505911yescharacteristic, complemented
518C2—242no—
519C2—722no—
520C2#1059037014yesdirect product factor
521C2C2×#6382912yes—
522C2C2×#6391111yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
hypercenterC2×C42D32
hypocenterC32C2×#495
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64084C2semidirect
2. C2×C3×#875C2semidirect
3. C22×#3719C2semidirect
4. C22×#3717C2semidirect
5. C22×#3716C2semidirect
7. C2×C3×C4×C3⋊C8C2semidirect
8. #10590370C2direct (N × H)
18. #64084C22semidirect
23. C3×#875C22semidirect
25. C2×#3719C22semidirect
27. C2×#3717C22semidirect
29. C2×#3716C22semidirect
32. C3×C4×C3⋊C8C22semidirect
45. C2×#875D3semidirect
48. C2×C4×C3⋊C8D3semidirect
132. #875C2×D3semidirect
134. C4×C3⋊C8C2×D3semidirect
374. C2×C32#495semidirect
454. C32C2×#495semidirect
490. C2×C3#4696semidirect
491. C2×C3#5059semidirect
516. C3C2×#4696semidirect
517. C3C2×#5059semidirect
520. C2#10590370direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640842
C2×C3×#8752
C22×#37192
C22×#37172
C22×#37162
C22×#37142
C2×C3×C4×C3⋊C82
#105903702
C2×#50593
C2×#46963