Finite Group Databasebeta

← C2×#10591552 #11857756

Subgroups — C2×#10591552 #11857756

Order 1152.

2057 conjugacy classes of subgroups.

The subgroup lattice has 425 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C22×#3710C211yesmaximal, characteristic
4C2×C3×#835C212yesmaximal, complemented
5#10591552C218yesmaximal, direct product factor
6C2×#63567C212yesmaximal, complemented
7C2×D3×#103—32nomaximal
8C22×C32×Q8C2211yescharacteristic
9C2×Q8×C3⋊D3—24no—
10C2×Q8×C3⋊D3—22no—
11C2×Q8×C3⋊D3C418yescomplemented
12C2×Q8×C3⋊D3C2214yes—
13C22×C4×C3⋊D3—21no—
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×#634—21no—
16C22×#634C2211yescharacteristic
17C22×#624—21no—
18C2×C3×C4⋊Dic3C2212yes—
19C22×C3×C3⋊C8C2212yes—
20C2×#3724—21no—
21#63900—22no—
22#63900C2214yes—
23C2×#3710—24no—
24C2×#3710C2214yes—
25C3×#835C2218yescomplemented
26#63567C2218yescomplemented
27C22×D3×Q8—32no—
28C22×D3×Q8—61no—
29C22×D3×C8—32no—
30C2×D3×C4⋊C4—32no—
31C2×C3×#103—32no—
32C2×#835D312yescomplemented
33C2×#816—32no—
34C2×#810—32no—
35D3×#103—316no—
36C23×C3⋊D3D411yescharacteristic
37C2×C32×Q8—22no—
38C2×C32×Q8—21no—
39C2×C32×Q8C2×C414yescomplemented
40C2×C32×Q8C2312yes—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3D411yescharacteristic
45Q8×C3⋊D3—216no—
46Q8×C3⋊D3—28no—
47Q8×C3⋊D3C2×C4116yescomplemented
48C2×C4×C3⋊D3—28no—
49C2×C4×C3⋊D3—24no—
50C2×C4×C3⋊D3C2×C414yes—
51C2×C4×C3⋊D3D412yes—
52C2×C4×C3⋊D3D414yes—
53C2×C4×C3⋊D3C2312yes—
54C2×#634—21no—
55C2×#634—22no—
56C2×#634—28no—
57C2×#634—24no—
58C2×#634C2×C414yescomplemented
59C2×#634C2312yes—
60C22×C3×Dic3—22no—
61C2×#624—24no—
62C2×#624—44no—
63C3×C4⋊Dic3—22no—
64C3×C4⋊Dic3C2314yes—
65C2×C3×C3⋊C8—24no—
66C2×C3×C3⋊C8C2314yes—
67#3724—24no—
68#3710—28no—
69C22×#103—91noSylow
70C22×C3×Q8—21no—
71C22×C3×Q8C2×D312yes—
72C2×D3×Q8—316no—
73C2×D3×Q8—38no—
74C2×D3×Q8—68no—
75C2×D3×Q8—64no—
76C2×D3×Q8—64no—
77C2×D3×Q8—68no—
78C2×D3×Q8—64no—
79C2×D3×Q8—68no—
80C22×C4×D3—32no—
81C22×C4×D3—61no—
82C22×C4×D3—62no—
83C22×C4×D3—62no—
84C22×C4×D3—62no—
85C22×Dic6—32no—
86C22×Dic6—61no—
87C22×Dic6—62no—
88C22×Dic6—62no—
89C22×C3×C8—32no—
90C2×C3×C4⋊C4—32no—
91C2×C4⋊Dic3C2×D312yes—
92C2×Dic3⋊C4—62no—
93C22×C3⋊C8C2×D312yes—
94C2×D3×C8—38no—
95C2×D3×C8—68no—
96D3×C4⋊C4—38no—
97D3×C4⋊C4—64no—
98C3×#103—38no—
99#835C2×D318yescomplemented
100#816—38no—
101#810—38no—
102C23×C32C2×D411yescharacteristic
103C22×C3⋊D3C22⋊C414yes—
104C22×C3⋊D3SD1614yes—
105C22×C3⋊D3Q1614yes—
106C22×C3⋊D3C2×D412yes—
107C32×Q8—24no—
108C32×Q8—22no—
109C32×Q8C22×C414yescomplemented
110C2×C32×C4—24no—
111C2×C32×C4—22no—
112C2×C32×C4C22×C412yes—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D412yes—
115C2×C32×C4C2411yescharacteristic
116C2×C3⋊Dic3—24no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3C22⋊C414yes—
119C2×C3⋊Dic3C2×D412yes—
120C4×C3⋊D3—216no—
121C4×C3⋊D3C22⋊C418yes—
122C4×C3⋊D3C22×C414yes—
123C4×C3⋊D3C2×D414yes—
124#634—24no—
125#634—22no—
126#634—216no—
127#634C22×C414yescomplemented
128C2×C3×Dic3—24no—
129C2×C3×Dic3—44no—
130#624—48no—
131C3×C3⋊C8—24no—
132C23×Q8—91no—
133C23×C8—91no—
134C22×C4⋊C4—91no—
135C2×#103—32no—
136C2×#103—98no—
137C2×#103—92no—
138C23×D3—32no—
139C23×D3—61no—
140C2×C3×Q8—22no—
141C2×C3×Q8—24no—
142C2×C3×Q8—24no—
143C2×C3×Q8—22no—
144C2×C3×Q8—24no—
145C2×C3×Q8—22no—
146C2×C3×Q8C4×D318yescomplemented
147C2×C3×Q8C22×D314yes—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—21no—
151C22×C3×C4—62no—
152C22×C3×C4C22×D312yes—
153C22×Dic3—22no—
154C22×Dic3—32no—
155C22×Dic3—61no—
156C22×Dic3—62no—
157C22×Dic3—62no—
158D3×Q8—332no—
159D3×Q8—616no—
160D3×Q8—632no—
161D3×Q8—616no—
162D3×Q8—632no—
163D3×Q8—616no—
164C2×C4×D3—38no—
165C2×C4×D3—34no—
166C2×C4×D3—38no—
167C2×C4×D3—34no—
168C2×C4×D3—64no—
169C2×C4×D3—62no—
170C2×C4×D3—64no—
171C2×C4×D3—62no—
172C2×C4×D3—616no—
173C2×C4×D3—68no—
174C2×C4×D3—616no—
175C2×C4×D3—68no—
176C2×C4×D3—68no—
177C2×C4×D3—128no—
178C2×Dic6—38no—
179C2×Dic6—34no—
180C2×Dic6—64no—
181C2×Dic6—62no—
182C2×Dic6—616no—
183C2×Dic6—68no—
184C2×Dic6—616no—
185C2×Dic6—68no—
186C2×Dic6—62no—
187C2×Dic6—64no—
188C2×Dic6—62no—
189C2×Dic6—64no—
190C2×C3×C8—34no—
191C2×C3×C8—64no—
192C3×C4⋊C4—34no—
193C3×C4⋊C4—62no—
194C4⋊Dic3—22no—
195C4⋊Dic3C22×D314yes—
196Dic3⋊C4—68no—
197C2×C3⋊C8—24no—
198C2×C3⋊C8C22×D314yes—
199D3×C8—616no—
200C22×C32C2×C22⋊C412yes—
201C22×C32C2×SD1612yes—
202C22×C32C2×Q1612yes—
203C22×C32C22×D411yescharacteristic
204C2×C3⋊D3#103116yescomplemented
205C2×C3⋊D3C2×C22⋊C414yes—
206C2×C3⋊D3C2×SD1614yes—
207C2×C3⋊D3C2×Q1614yes—
208C32×C4—24no—
209C32×C4C2×C22⋊C412yes—
210C32×C4C23×C411yescharacteristic
211C32×C4C22×D411yescharacteristic
212C3⋊Dic3—24no—
213C3⋊Dic3C2×C22⋊C414yes—
214C3×Dic3—44no—
215C22×Q8—98no—
216C22×Q8—94no—
217C22×Q8—91no—
218C22×Q8—181no—
219C22×Q8—182no—
220C22×Q8—184no—
221C22×Q8D3211yescharacteristic
222C23×C4—91no—
223C23×C4—181no—
224C23×C4—181no—
225C22×C8—32no—
226C22×C8—94no—
227C22×C8—184no—
228C2×C4⋊C4—32no—
229C2×C4⋊C4—94no—
230C2×C4⋊C4—182no—
231C2×C4⋊C4—181no—
232#103—38no—
233#103—98no—
234C23×C3—21no—
235C23×C3D3×D412yes—
236C22×D3—38no—
237C22×D3—38no—
238C22×D3—38no—
239C22×D3—34no—
240C22×D3—64no—
241C22×D3—64no—
242C22×D3—64no—
243C22×D3—62no—
244C3×Q8—24no—
245C3×Q8—28no—
246C3×Q8—28no—
247C3×Q8—24no—
248C3×Q8—24no—
249C3×Q8C2×C4×D318yescomplemented
250C2×C3×C4—24no—
251C2×C3×C4—28no—
252C2×C3×C4—28no—
253C2×C3×C4—24no—
254C2×C3×C4—21no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—21no—
258C2×C3×C4—64no—
259C2×C3×C4—124no—
260C2×C3×C4C2×C4×D314yes—
261C2×C3×C4D3×D412yes—
262C2×C3×C4D3×D414yes—
263C2×C3×C4C23×D312yes—
264C2×Dic3—24no—
265C2×Dic3—38no—
266C2×Dic3—34no—
267C2×Dic3—44no—
268C2×Dic3—64no—
269C2×Dic3—62no—
270C2×Dic3—64no—
271C2×Dic3—68no—
272C2×Dic3—68no—
273C2×Dic3—64no—
274C4×D3—316no—
275C4×D3—38no—
276C4×D3—38no—
277C4×D3—68no—
278C4×D3—64no—
279C4×D3—64no—
280C4×D3—632no—
281C4×D3—632no—
282C4×D3—1216no—
283Dic6—38no—
284Dic6—64no—
285Dic6—632no—
286Dic6—632no—
287Dic6—64no—
288Dic6—68no—
289Dic6—68no—
290Dic6—64no—
291C3×C8—64no—
292C3⋊C8—24no—
293C2×C32C2×#10314yescomplemented
294C2×C32C22×C22⋊C411yescharacteristic
295C2×C32C22×SD1611yescharacteristic
296C2×C32C22×Q1611yescharacteristic
297C3⋊D3C2×#10318yescomplemented
298C24—91no—
299C2×Q8—21no—
300C2×Q8—22no—
301C2×Q8—916no—
302C2×Q8—92no—
303C2×Q8—94no—
304C2×Q8—184no—
305C2×Q8—188no—
306C2×Q8—188no—
307C2×Q8—1816no—
308C2×Q8—181no—
309C2×Q8—182no—
310C2×Q8#62414yescomplemented
311C2×Q8C2×D3212yes—
312C22×C4—21no—
313C22×C4—62no—
314C22×C4—91no—
315C22×C4—92no—
316C22×C4—94no—
317C22×C4—92no—
318C22×C4—94no—
319C22×C4—184no—
320C22×C4—188no—
321C22×C4—184no—
322C22×C4—181no—
323C22×C4—364no—
324C22×C4C2×D3211yescharacteristic
325C2×C8—34no—
326C2×C8—64no—
327C2×C8—188no—
328C4⋊C4—34no—
329C4⋊C4—62no—
330C4⋊C4—184no—
331C22×C3—21no—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—22no—
335C22×C3D3×C22⋊C414yes—
336C22×C3D3×SD1614yes—
337C22×C3D3×Q1614yes—
338C22×C3C2×D3×D412yes—
339C2×D3—38no—
340C2×D3—38no—
341C2×D3—38no—
342C2×D3—332no—
343C2×D3—64no—
344C2×D3—616no—
345C2×D3—64no—
346C2×D3—64no—
347C3×C4—28no—
348C3×C4—28no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—22no—
352C3×C4—124no—
353C3×C4D3×C22⋊C414yes—
354C3×C4C22×C4×D312yes—
355C3×C4C2×D3×D412yes—
356Dic3—38no—
357Dic3—44no—
358Dic3—64no—
359Dic3—68no—
360Dic3—68no—
361C32C22×#10311yescharacteristic, complemented, Sylow
362C23—92no—
363C23—94no—
364C23—94no—
365C23—94no—
366C23#381111yescharacteristic
367Q8—22no—
368Q8—24no—
369Q8—94no—
370Q8—1816no—
371Q8—182no—
372Q8—184no—
373Q8C2×#62414yescomplemented
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—64no—
377C2×C4—92no—
378C2×C4—94no—
379C2×C4—94no—
380C2×C4—94no—
381C2×C4—98no—
382C2×C4—124no—
383C2×C4—1816no—
384C2×C4—182no—
385C2×C4—184no—
386C2×C4—368no—
387C2×C4C2×#62412yes—
388C2×C4#381112yes—
389C2×C4#381111yescharacteristic
390C2×C4C22×D3211yescharacteristic
391C8—64no—
392C2×C3—21no—
393C2×C3—24no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3D3×#10318yescomplemented
397C2×C3C2×D3×C22⋊C412yes—
398C2×C3C2×D3×SD1612yes—
399C2×C3C2×D3×Q1612yes—
400D3—316no—
401D3—68no—
402C22—94no—
403C22—916no—
404C22—94no—
405C22—94no—
406C22#6394012yes—
407C22#6394412yes—
408C22#6397412yes—
409C22C2×#381111yescharacteristic
410C4—24no—
411C4—94no—
412C4—124no—
413C4—184no—
414C4#6397412yes—
415C4C22×#62411yescharacteristic
416C4C2×#381111yescharacteristic
417C3—21no—
418C3C2×D3×#10312yescomplemented
419C2—98no—
420C2#1059155214yesdirect product factor
421C2C2×#6394011yescharacteristic
422C2C2×#6394411yescharacteristic
423C2C2×#6397411yescharacteristic
subgroupG/H
centerC23#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32C22×#103
LCSG ▷ 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
4. C2×C3×#835C2semidirect
5. #10591552C2direct (N × H)
6. C2×#63567C2semidirect
11. C2×Q8×C3⋊D3C4semidirect
25. C3×#835C22semidirect
26. #63567C22semidirect
32. C2×#835D3semidirect
39. C2×C32×Q8C2×C4semidirect
47. Q8×C3⋊D3C2×C4semidirect
58. C2×#634C2×C4semidirect
99. #835C2×D3semidirect
109. C32×Q8C22×C4semidirect
127. #634C22×C4semidirect
146. C2×C3×Q8C4×D3semidirect
204. C2×C3⋊D3#103semidirect
249. C3×Q8C2×C4×D3semidirect
293. C2×C32C2×#103semidirect
297. C3⋊D3C2×#103semidirect
310. C2×Q8#624semidirect
361. C32C22×#103semidirect
373. Q8C2×#624semidirect
396. C2×C3D3×#103semidirect
418. C3C2×D3×#103semidirect
420. C2#10591552direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C2×#639002
C22×#37102
C2×C3×#8352
#105915522
C2×#635672
C2×D3×#1033