Finite Group Databasebeta

← C2×#10591598 #11867015

Subgroups — C2×#10591598 #11867015

Order 1152.

1113 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3756C211yesmaximal, characteristic, complemented
2C2×C3×#946C211yesmaximal, characteristic
3C2×#63857C211yesmaximal, characteristic
4C22×#3711C211yesmaximal, characteristic
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591598C218yesmaximal, direct product factor
7C2×#63574C211yesmaximal, characteristic, complemented
8C2×#63567C211yesmaximal, characteristic, complemented
9C2×#5052—31nomaximal
10C2×#4816—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C2×#3756—24no—
15C2×#3756C2214yescomplemented
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#946—22no—
18C3×#946C2214yes—
19C2×C3×(C2×D3)⋊C4—21no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×Dic3⋊C4—21no—
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×Dic3⋊Dic3—21no—
25C2×(C2×D3)⋊Dic3—21no—
26#63857—22no—
27#63857C2214yes—
28C2×#3711—24no—
29C2×#3711C2214yes—
30C3×#835C2214yescomplemented
31#63574C2214yescomplemented
32#63567C2214yescomplemented
33C2×C3×C22⋊Q8—31no—
34C2×#946D311yescharacteristic
35C22×#216—31no—
36C22×#216—31no—
37C22×#216—61no—
38C2×#924—31no—
39C22×#208—31no—
40C22×ΓL(1,𝔽25)—31no—
41C2×#897—31no—
42C2×C3×#103—31no—
43C2×#835D311yescharacteristic, complemented
44C2×#816—31no—
45#5052—38no—
46C2×#810—31no—
47C2×#808—31no—
48C2×#808—31no—
49#4816—38no—
50C23×C3×D3D411yescharacteristic
51C2×C32×Q8—21no—
52C2×C32×Q8—22no—
53C2×C32×Q8—22no—
54C2×C32×Q8C2312yes—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C2×#634—22no—
59C2×#634—22no—
60C2×#634—21no—
61C2×#634C2312yes—
62C22×C3×Dic3—21no—
63C22×C3×Dic3—21no—
64C22×C3×Dic3D411yescharacteristic
65C2×C3×C4×D3—22no—
66C2×C3×C4×D3—22no—
67C2×C3×C4×D3D412yes—
68C2×C3×C4×D3C2312yes—
69#3756—28no—
70C2×C3⋊(C3⋊C8)D414yes—
71C2×C3⋊(C3⋊C8)C2312yes—
72C3×(C2×D3)⋊C4—24no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3C2312yes—
76C3×C4⋊Dic3C2312yes—
77C3×Dic3⋊C4—24no—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2312yes—
80Dic3⋊Dic3—24no—
81(C2×D3)⋊Dic3—24no—
82#3711—28no—
83C2×#470—91noSylow
84C22×C3×Q8—21no—
85C22×C3×Q8C2×D311yescharacteristic
86C22×C3×Q8C2×D311yescharacteristic
87C23×C3×C4—31no—
88C22×C4×D3C2×D311yescharacteristic
89C22×Dic6—31no—
90C22×Dic6—31no—
91C22×Dic6—61no—
92C22×C3×C8—31no—
93C3×C22⋊Q8—34no—
94C3×C22⋊Q8—62no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—61no—
98C2×C3×C22⋊C4—61no—
99C2×#217—61no—
100#946—22no—
101#946C2×D314yes—
102C2×#216—34no—
103C2×#216—34no—
104C2×#216—64no—
105C2×#216—64no—
106C2×#216—64no—
107C2×#216—68no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—61no—
110C2×C4⋊Dic3—61no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×C4⋊Dic3C2×D311yescharacteristic
113#924—34no—
114#924—62no—
115C2×Dic3⋊C4—21no—
116C2×Dic3⋊C4—61no—
117C2×#208—34no—
118C2×#208—64no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—61no—
122C22×C3⋊C8C2×D311yescharacteristic
123C2×ΓL(1,𝔽25)—34no—
124C2×ΓL(1,𝔽25)—64no—
125#897—34no—
126#897—62no—
127C3×#103—34no—
128#835C2×D314yescomplemented
129#816—34no—
130#810—34no—
131#808—34no—
132#808—34no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—22no—
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3C2×D412yes—
138C32×Q8—22no—
139C32×Q8—22no—
140C32×Q8—42no—
141C2×C32×C4—22no—
142C2×C32×C4—42no—
143C2×C32×C4C2×D412yes—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—42no—
149#634—22no—
150#634—22no—
151#634—42no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3—42no—
157C2×C3×Dic3C2×D412yes—
158C3×C4×D3—24no—
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161C3⋊(C3⋊C8)C2×D414yes—
162C3×C3⋊C8—22no—
163C22×Q16—91no—
164C22×M16—91no—
165C2×C22⋊Q8—31no—
166C2×C22⋊Q8—91no—
167#470—98no—
168C2×#106—91no—
169C2×#103—31no—
170C2×#103—91no—
171C24×C3—31no—
172C23×D3#6711yescharacteristic
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—24no—
176C2×C3×Q8—22no—
177C2×C3×Q8—22no—
178C2×C3×Q8—22no—
179C2×C3×Q8—22no—
180C2×C3×Q8—22no—
181C2×C3×Q8—41no—
182C2×C3×Q8—42no—
183C2×C3×Q8C22×D312yes—
184C2×C3×Q8C22×D312yes—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—31no—
189C22×C3×C4—32no—
190C22×C3×C4—32no—
191C22×C3×C4—41no—
192C22×C3×C4—62no—
193C22×C3×C4—62no—
194C22×C3×C4—61no—
195C22×C3×C4—61no—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C22×Dic3—21no—
199C22×Dic3—21no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3—121no—
203C22×Dic3#6711yescharacteristic
204C2×C4×D3—22no—
205C2×C4×D3—22no—
206C2×C4×D3#6712yes—
207C2×C4×D3C22×D312yes—
208C2×Dic6—32no—
209C2×Dic6—32no—
210C2×Dic6—62no—
211C2×Dic6—64no—
212C2×Dic6—62no—
213C2×Dic6—62no—
214C2×Dic6—62no—
215C2×Dic6—62no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—121no—
219C2×Dic6—122no—
220C2×C3×C8—32no—
221C2×C3×C8—62no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—64no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C22⋊C4—64no—
228#217—64no—
229#216—68no—
230#216—68no—
231#216—616no—
232(C2×D3)⋊C4—24no—
233(C2×D3)⋊C4—64no—
234C4⋊Dic3—21no—
235C4⋊Dic3—21no—
236C4⋊Dic3—64no—
237C4⋊Dic3C22×D312yes—
238C4⋊Dic3C22×D312yes—
239Dic3⋊C4—24no—
240Dic3⋊C4—64no—
241#208—68no—
242C2×C3⋊C8—22no—
243C2×C3⋊C8—34no—
244C2×C3⋊C8—34no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—32no—
247C2×C3⋊C8—64no—
248C2×C3⋊C8—62no—
249C2×C3⋊C8C22×D312yes—
250ΓL(1,𝔽25)—68no—
251C22×C32#12112yes—
252C22×C32#13712yes—
253C22×C32#13712yes—
254C22×C32C22×D411yescharacteristic
255C2×C3×D3—22no—
256C2×C3×D3—22no—
257C2×C3×D3—22no—
258C2×C3×D3—44no—
259C32×C4—42no—
260C32×C4#12112yes—
261C32×C4C22×D411yescharacteristic
262C32×C4C2×#4111yescharacteristic
263C3⋊Dic3—42no—
264C3×Dic3—22no—
265C3×Dic3—42no—
266C3×Dic3—42no—
267C22×Q8—91no—
268C22×Q8D3211yescharacteristic
269C23×C4—31no—
270C2×Q16—94no—
271C2×Q16—184no—
272C2×M16—94no—
273C2×M16—184no—
274C22×C8—31no—
275C22×C8—91no—
276C22⋊Q8—34no—
277C22⋊Q8—62no—
278C22⋊Q8—94no—
279C22⋊Q8—182no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—31no—
282C2×C4⋊C4—61no—
283C2×C4⋊C4—181no—
284C2×C22⋊C4—61no—
285C2×C22⋊C4—181no—
286#106—94no—
287#103—34no—
288#103—94no—
289C23×C3—21no—
290C23×C3—32no—
291C23×C3—62no—
292C23×C3—62no—
293C23×C3—62no—
294C23×C3D3×D411yescharacteristic
295C23×C3C2×#6711yescharacteristic
296C22×D3—22no—
297C22×D3—22no—
298C22×D3—22no—
299C22×D3C2×#6712yes—
300C3×Q8—24no—
301C3×Q8—22no—
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—42no—
306C3×Q8—44no—
307C3×Q8—42no—
308C3×Q8—42no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—22no—
313C2×C3×C4—21no—
314C2×C3×C4—22no—
315C2×C3×C4—32no—
316C2×C3×C4—42no—
317C2×C3×C4—44no—
318C2×C3×C4—42no—
319C2×C3×C4—42no—
320C2×C3×C4—62no—
321C2×C3×C4—64no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—122no—
327C2×C3×C4—122no—
328C2×C3×C4#23512yes—
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D412yes—
331C2×C3×C4D3×D412yes—
332C2×C3×C4#23712yes—
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×C3×C4C23×D311yescharacteristic
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—42no—
340C2×Dic3—42no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—122no—
344C2×Dic3—124no—
345C2×Dic3—122no—
346C2×Dic3—122no—
347C2×Dic3C2×#6712yes—
348C4×D3—24no—
349C4×D3—22no—
350C4×D3—22no—
351Dic6—64no—
352Dic6—62no—
353Dic6—62no—
354Dic6—62no—
355Dic6—62no—
356Dic6—122no—
357Dic6—124no—
358Dic6—122no—
359Dic6—122no—
360C3×C8—62no—
361C3⋊C8—22no—
362C3⋊C8—34no—
363C3⋊C8—34no—
364C3⋊C8—64no—
365C2×C32#47014yescomplemented
366C2×C32C2×#12111yescharacteristic
367C2×C32C2×#13711yescharacteristic
368C2×C32C2×#13711yescharacteristic
369C3×D3—42no—
370C24—31no—
371C2×Q8—21no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—92no—
375C2×Q8—181no—
376C2×Q8—182no—
377C2×Q8—182no—
378C2×Q8C2×D3212yes—
379C22×C4—21no—
380C22×C4—31no—
381C22×C4—32no—
382C22×C4—32no—
383C22×C4—62no—
384C22×C4—62no—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4—181no—
388C22×C4C2×D3211yescharacteristic
389Q16—188no—
390M16—188no—
391C2×C8—32no—
392C2×C8—62no—
393C2×C8—92no—
394C2×C8—94no—
395C4⋊C4—32no—
396C4⋊C4—32no—
397C4⋊C4—64no—
398C4⋊C4—61no—
399C4⋊C4—61no—
400C4⋊C4—184no—
401C22⋊C4—64no—
402C22⋊C4—184no—
403C22×C3—21no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—62no—
408C22×C3—62no—
409C22×C3—62no—
410C22×C3—124no—
411C22×C3#88412yes—
412C22×C3#91512yes—
413C22×C3#91812yes—
414C22×C3#93912yes—
415C22×C3#94212yes—
416C22×C3#95112yes—
417C22×C3C2×D3×D411yescharacteristic
418C22×C3C22×#6711yescharacteristic
419C2×D3—22no—
420C2×D3—22no—
421C2×D3—22no—
422C2×D3—44no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—22no—
426C3×C4—44no—
427C3×C4—42no—
428C3×C4—42no—
429C3×C4—62no—
430C3×C4—122no—
431C3×C4—122no—
432C3×C4#88412yes—
433C3×C4#93912yes—
434C3×C4C2×#23511yescharacteristic
435C3×C4C2×D3×D411yescharacteristic
436C3×C4C2×D3×D411yescharacteristic
437C3×C4C2×#23711yescharacteristic
438Dic3—22no—
439Dic3—42no—
440Dic3—42no—
441Dic3—124no—
442Dic3—122no—
443Dic3—122no—
444C32C2×#47011yescharacteristic, complemented, Sylow
445C23—32no—
446C23—62no—
447C23—62no—
448C23—62no—
449C23D3×#6711yescharacteristic
450Q8—22no—
451Q8—22no—
452Q8—42no—
453Q8—182no—
454Q8—182no—
455Q8—362no—
456C2×C4—22no—
457C2×C4—32no—
458C2×C4—42no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—64no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—122no—
466C2×C4—122no—
467C2×C4—182no—
468C2×C4—362no—
469C2×C4#380412yes—
470C2×C4D3×#6711yescharacteristic
471C2×C4#381112yes—
472C2×C4C22×D3211yescharacteristic
473C8—62no—
474C8—94no—
475C2×C3—21no—
476C2×C3—24no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—122no—
480C2×C3#481614yescomplemented
481C2×C3#505214yescomplemented
482C2×C3C2×#88411yescharacteristic
483C2×C3C2×#91511yescharacteristic
484C2×C3C2×#91811yescharacteristic
485C2×C3C2×#93911yescharacteristic
486C2×C3C2×#94211yescharacteristic
487C2×C3C2×#95111yescharacteristic
488D3—42no—
489C22—62no—
490C22—62no—
491C22—62no—
492C22—124no—
493C22#6394312yes—
494C22#6394612yes—
495C22#6397112yes—
496C22C2×D3×#6711yescharacteristic
497C4—42no—
498C4—62no—
499C4—122no—
500C4—122no—
501C4—362no—
502C4#6397112yes—
503C4C2×#380411yescharacteristic
504C4C2×#381111yescharacteristic
505C3—21no—
506C3C2×#481611yescharacteristic, complemented
507C3C2×#505211yescharacteristic, complemented
508C2—122no—
509C2#1059159814yesdirect product factor
510C2C2×#6394311yescharacteristic
511C2C2×#6394611yescharacteristic
512C2C2×#6397111yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC22×Q8D32
hypocenterC32C2×#470
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3756C2semidirect
5. C2×C3×#835C2semidirect
6. #10591598C2direct (N × H)
7. C2×#63574C2semidirect
8. C2×#63567C2semidirect
15. C2×#3756C22semidirect
30. C3×#835C22semidirect
31. #63574C22semidirect
32. #63567C22semidirect
43. C2×#835D3semidirect
128. #835C2×D3semidirect
365. C2×C32#470semidirect
444. C32C2×#470semidirect
480. C2×C3#4816semidirect
481. C2×C3#5052semidirect
506. C3C2×#4816semidirect
507. C3C2×#5052semidirect
509. C2#10591598direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37562
C2×C3×#9462
C2×#638572
C22×#37112
C2×C3×#8352
#105915982
C2×#635742
C2×#635672
C2×#50523
C2×#48163