Finite Group Databasebeta

← C2×#10591565 #11865489

Subgroups — C2×#10591565 #11865489

Order 1152.

1237 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
1C22×#3755C211yesmaximal, characteristic
2C2×C3×#944C211yesmaximal, characteristic, complemented
3C2×#63894C211yesmaximal, characteristic
4C22×#3717C211yesmaximal, characteristic
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591565C218yesmaximal, direct product factor
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C2×#63565C211yesmaximal, characteristic, complemented
9C2×#5083—31nomaximal
10C2×#4818—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#624—21no—
15C2×#3755—24no—
16C2×#3755C2214yes—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#944—22no—
19C3×#944C2214yescomplemented
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4—21no—
22C2×C3×Dic3⋊C4—21no—
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×#3722—21no—
26#63894—22no—
27#63894C2214yes—
28C2×#3717—24no—
29C2×#3717C2214yes—
30C3×#835C2214yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63565C2214yescomplemented
33C2×C3×C4⋊Q8—31no—
34C2×#944D311yescharacteristic, complemented
35C22×#215—31no—
36C22×#215—31no—
37C22×#215—31no—
38C22×#215—61no—
39C22×#204—31no—
40C2×#893—31no—
41C2×C4×D12—31no—
42C2×C3×#103—31no—
43C2×#835—31no—
44C2×#835D311yescharacteristic, complemented
45C2×Dic3⋊C8—31no—
46#5083—38no—
47C2×#810—31no—
48C2×C4⋊(C3⋊C8)—31no—
49#4818—38no—
50C23×C3⋊D3—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—22no—
53C2×C32×Q8—22no—
54C2×C32×Q8C2312yes—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)D414yes—
60C2×C4⋊(C3⋊D3)C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D411yescharacteristic
64C22×C3×Dic3D411yescharacteristic
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C2×#624—24no—
70C2×#624—44no—
71#3755—28no—
72C2×C3⋊(C3⋊C8)—22no—
73C2×C3⋊(C3⋊C8)C2312yes—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3C2312yes—
76C3×Dic3⋊C4—24no—
77C3×Dic3⋊C4—24no—
78C3×C4×Dic3D412yes—
79C3×C4×Dic3C2312yes—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8C2312yes—
82#3722—24no—
83#3717—28no—
84C2×#461—91noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8—31no—
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×Q8C2×D311yescharacteristic
89C22×D12—31no—
90C22×D12—31no—
91C22×D12—61no—
92C22×C4×D3—61no—
93C22×C4×D3—61no—
94C22×Dic6C2×D311yescharacteristic
95C22×C3×C8—31no—
96C3×C4⋊Q8—34no—
97C3×C4⋊Q8—62no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—61no—
100C2×C3×C4⋊C4—61no—
101C2×C3×C42—31no—
102#944—22no—
103#944C2×D314yescomplemented
104C2×#215—34no—
105C2×#215—34no—
106C2×#215—34no—
107C2×#215—64no—
108C2×#215—64no—
109C2×#215—64no—
110C2×#215—64no—
111C2×#215—68no—
112C2×(C2×D3)⋊C4—61no—
113C2×(C2×D3)⋊C4—61no—
114C2×C4⋊Dic3C2×D311yescharacteristic
115C2×Dic3⋊C4—21no—
116C2×Dic3⋊C4—21no—
117C2×C4×Dic3C2×D311yescharacteristic
118C22×C3⋊C8—31no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—61no—
121C22×C3⋊C8C2×D311yescharacteristic
122C2×#204—34no—
123C2×#204—64no—
124#893—34no—
125#893—62no—
126C4×D12—34no—
127C4×D12—62no—
128C3×#103—34no—
129#835—34no—
130#835C2×D314yescomplemented
131Dic3⋊C8—34no—
132#810—34no—
133C4⋊(C3⋊C8)—34no—
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—24no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C32×Q8—22no—
140C32×Q8—22no—
141C32×Q8—42no—
142C2×C32×C4—22no—
143C2×C32×C4—42no—
144C2×C32×C4C2×D412yes—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C4⋊(C3⋊D3)—24no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)C2×D414yes—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3SD1614yescomplemented
157C2×C3×Dic3C2×D412yes—
158C2×C3×Dic3C2×D412yes—
159C3×Dic6—22no—
160C3×Dic6—22no—
161C3×Dic6—42no—
162#624—48no—
163C3⋊(C3⋊C8)—22no—
164C3×C3⋊C8—22no—
165C22×SD16—91no—
166C22×SD16—91no—
167C2×C4⋊Q8—31no—
168C2×C4×D4—91no—
169#461—98no—
170C2×C4⋊C8—91no—
171C2×#103—31no—
172C2×#103—91no—
173C23×D3—61no—
174C23×D3—61no—
175C23×D3—121no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—24no—
179C2×C3×Q8—22no—
180C2×C3×Q8—22no—
181C2×C3×Q8—22no—
182C2×C3×Q8—22no—
183C2×C3×Q8—22no—
184C2×C3×Q8—32no—
185C2×C3×Q8—41no—
186C2×C3×Q8—42no—
187C2×C3×Q8—61no—
188C2×C3×Q8—62no—
189C2×C3×Q8—62no—
190C2×C3×Q8C22×D312yes—
191C2×C3×Q8C22×D312yes—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—41no—
198C22×C3×C4—61no—
199C22×C3×C4—61no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×Dic3—21no—
203C22×Dic3—21no—
204C22×Dic3#6711yescharacteristic
205C22×Dic3#6711yescharacteristic
206C2×D12—34no—
207C2×D12—34no—
208C2×D12—32no—
209C2×D12—32no—
210C2×D12—64no—
211C2×D12—62no—
212C2×D12—62no—
213C2×D12—61no—
214C2×D12—62no—
215C2×D12—61no—
216C2×D12—122no—
217C2×D12—121no—
218C2×C4×D3—64no—
219C2×C4×D3—64no—
220C2×C4×D3—124no—
221C2×C4×D3—124no—
222C2×Dic6—22no—
223C2×Dic6—22no—
224C2×Dic6—21no—
225C2×Dic6C22×D312yes—
226C2×C3×C8—32no—
227C2×C3×C8—62no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—64no—
230C3×C4⋊C4—64no—
231C3×C4⋊C4—61no—
232C3×C42—32no—
233C3×C42—32no—
234#215—68no—
235#215—68no—
236#215—68no—
237#215—616no—
238(C2×D3)⋊C4—64no—
239(C2×D3)⋊C4—64no—
240C4⋊Dic3—21no—
241C4⋊Dic3C22×D312yes—
242Dic3⋊C4—24no—
243Dic3⋊C4—24no—
244C4×Dic3#6712yes—
245C4×Dic3C22×D312yes—
246C2×C3⋊C8—22no—
247C2×C3⋊C8—32no—
248C2×C3⋊C8—32no—
249C2×C3⋊C8—62no—
250C2×C3⋊C8—64no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8C22×D312yes—
254#204—68no—
255C22×C32#12112yes—
256C22×C32C2×SD1612yes—
257C22×C32#13712yes—
258C22×C32C22×D411yescharacteristic
259C2×C3⋊D3—24no—
260C2×C3⋊D3—42no—
261C2×C3⋊D3—42no—
262C2×C3⋊D3—48no—
263C32×C4—42no—
264C32×C4#12112yes—
265C32×C4C22×D411yescharacteristic
266C32×C4C2×#4111yescharacteristic
267C3×Dic3—22no—
268C3×Dic3—42no—
269C3×Dic3—42no—
270C3×Dic3C2×SD1614yescomplemented
271C22×Q8—31no—
272C22×Q8D3211yescharacteristic
273C22×D4—91no—
274C23×C4—181no—
275C2×SD16—94no—
276C2×SD16—94no—
277C2×SD16—184no—
278C2×SD16—184no—
279C22×C8—31no—
280C22×C8—91no—
281C4⋊Q8—34no—
282C4⋊Q8—62no—
283C4×D4—94no—
284C4×D4—182no—
285C2×C4⋊C4—31no—
286C2×C4⋊C4—61no—
287C2×C4⋊C4—61no—
288C2×C22⋊C4—181no—
289C2×C42—31no—
290C4⋊C8—94no—
291#103—34no—
292#103—94no—
293C23×C3—21no—
294C23×C3D3×D411yescharacteristic
295C23×C3C2×#6711yescharacteristic
296C22×D3—64no—
297C22×D3—64no—
298C22×D3—62no—
299C22×D3—62no—
300C22×D3—122no—
301C22×D3—124no—
302C22×D3—122no—
303C22×D3—122no—
304C22×D3—122no—
305C22×D3—122no—
306C22×D3—242no—
307C22×D3—242no—
308C3×Q8—24no—
309C3×Q8—22no—
310C3×Q8—22no—
311C3×Q8—22no—
312C3×Q8—22no—
313C3×Q8—42no—
314C3×Q8—44no—
315C3×Q8—42no—
316C3×Q8—42no—
317C3×Q8—62no—
318C3×Q8—62no—
319C3×Q8—122no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—34no—
327C2×C3×C4—32no—
328C2×C3×C4—32no—
329C2×C3×C4—42no—
330C2×C3×C4—44no—
331C2×C3×C4—42no—
332C2×C3×C4—42no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—122no—
337C2×C3×C4—122no—
338C2×C3×C4#23512yes—
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D412yes—
341C2×C3×C4D3×D412yes—
342C2×C3×C4#23712yes—
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345C2×C3×C4C23×D311yescharacteristic
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—42no—
350C2×Dic3—42no—
351C2×Dic3#21514yescomplemented
352C2×Dic3C2×#6712yes—
353C2×Dic3C2×#6712yes—
354D12—34no—
355D12—34no—
356D12—64no—
357D12—64no—
358D12—64no—
359D12—62no—
360D12—62no—
361D12—122no—
362D12—124no—
363C4×D3—128no—
364C4×D3—128no—
365Dic6—22no—
366Dic6—22no—
367Dic6—42no—
368C3×C8—62no—
369C3⋊C8—22no—
370C3⋊C8—64no—
371C3⋊C8—62no—
372C3⋊C8—62no—
373C2×C32#46114yescomplemented
374C2×C32C2×#12111yescharacteristic
375C2×C32C22×SD1611yescharacteristic
376C2×C32C2×#13711yescharacteristic
377C3⋊D3—44no—
378C24—181no—
379C2×Q8—21no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—32no—
383C2×Q8—61no—
384C2×Q8—62no—
385C2×Q8—62no—
386C2×Q8C2×D3212yes—
387C2×D4—92no—
388C2×D4—94no—
389C2×D4—182no—
390C2×D4—181no—
391C22×C4—21no—
392C22×C4—31no—
393C22×C4—31no—
394C22×C4—61no—
395C22×C4—61no—
396C22×C4—184no—
397C22×C4—364no—
398C22×C4C2×D3211yescharacteristic
399SD16—188no—
400SD16—188no—
401C2×C8—32no—
402C2×C8—62no—
403C2×C8—92no—
404C2×C8—182no—
405C4⋊C4—32no—
406C4⋊C4—64no—
407C4⋊C4—64no—
408C4⋊C4—61no—
409C22⋊C4—184no—
410C42—32no—
411C42—32no—
412C22×C3—21no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3#88412yes—
417C22×C3D3×SD1612yes—
418C22×C3#91812yes—
419C22×C3#93812yes—
420C22×C3C2×#21512yes—
421C22×C3#94212yes—
422C22×C3C2×D3×D411yescharacteristic
423C22×C3C22×#6711yescharacteristic
424C2×D3—64no—
425C2×D3—64no—
426C2×D3—124no—
427C2×D3—122no—
428C2×D3—122no—
429C2×D3—122no—
430C2×D3—122no—
431C2×D3—128no—
432C2×D3—128no—
433C2×D3—242no—
434C2×D3—248no—
435C2×D3—242no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—22no—
439C3×C4—34no—
440C3×C4—44no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—62no—
444C3×C4—122no—
445C3×C4—122no—
446C3×C4#88412yes—
447C3×C4#93812yes—
448C3×C4C2×#23511yescharacteristic
449C3×C4C2×D3×D411yescharacteristic
450C3×C4C2×D3×D411yescharacteristic
451C3×C4C2×#23711yescharacteristic
452Dic3—22no—
453Dic3—42no—
454Dic3—42no—
455Dic3C2×#21514yescomplemented
456C32C2×#46111yescharacteristic, complemented, Sylow
457C23—182no—
458C23—184no—
459C23—362no—
460C23—362no—
461C23D3×#6711yescharacteristic
462Q8—22no—
463Q8—22no—
464Q8—42no—
465Q8—62no—
466Q8—62no—
467Q8—122no—
468D4—94no—
469D4—182no—
470D4—184no—
471C2×C4—22no—
472C2×C4—32no—
473C2×C4—34no—
474C2×C4—32no—
475C2×C4—42no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—122no—
480C2×C4—122no—
481C2×C4—368no—
482C2×C4#380412yes—
483C2×C4D3×#6711yescharacteristic
484C2×C4#381112yes—
485C2×C4C22×D3211yescharacteristic
486C8—62no—
487C8—182no—
488C2×C3—21no—
489C2×C3—24no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3#481814yescomplemented
493C2×C3#508314yescomplemented
494C2×C3C2×#88411yescharacteristic
495C2×C3C2×D3×SD1611yescharacteristic
496C2×C3C2×#91811yescharacteristic
497C2×C3C2×#93811yescharacteristic
498C2×C3C22×#21511yescharacteristic
499C2×C3C2×#94211yescharacteristic
500D3—124no—
501D3—124no—
502D3—244no—
503C22—184no—
504C22—362no—
505C22—368no—
506C22—362no—
507C22D3×#21512yes—
508C22#6394812yes—
509C22#6395812yes—
510C22C2×D3×#6711yescharacteristic
511C4—34no—
512C4—42no—
513C4—62no—
514C4—122no—
515C4—122no—
516C4#6395812yes—
517C4C2×#380411yescharacteristic
518C4C2×#381111yescharacteristic
519C3—21no—
520C3C2×#481811yescharacteristic, complemented
521C3C2×#508311yescharacteristic, complemented
522C2—364no—
523C2#1059156514yesdirect product factor
524C2C2×D3×#21511yescharacteristic
525C2C2×#6394811yescharacteristic
526C2C2×#6395811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×Q8D32
hypocenterC32C2×#461
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
2. C2×C3×#944C2semidirect
5. C2×C3×#835C2semidirect
6. #10591565C2direct (N × H)
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. C2×#63565C2semidirect
19. C3×#944C22semidirect
30. C3×#835C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
32. #63565C22semidirect
34. C2×#944D3semidirect
44. C2×#835D3semidirect
103. #944C2×D3semidirect
130. #835C2×D3semidirect
156. C2×C3×Dic3SD16semidirect
270. C3×Dic3C2×SD16semidirect
351. C2×Dic3#215semidirect
373. C2×C32#461semidirect
455. Dic3C2×#215semidirect
456. C32C2×#461semidirect
492. C2×C3#4818semidirect
493. C2×C3#5083semidirect
520. C3C2×#4818semidirect
521. C3C2×#5083semidirect
523. C2#10591565direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37552
C2×C3×#9442
C2×#638942
C22×#37172
C2×C3×#8352
#105915652
C2×Dic3⋊(C3⋊C8)2
C2×#635652
C2×#50833
C2×#48183