Finite Group Databasebeta

← C2×#10590672 #11857758

Subgroups — C2×#10590672 #11857758

Order 1152.

1801 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic
2C22×C8×C3⋊D3C211yesmaximal, characteristic
3C2×#63900C211yesmaximal, characteristic
4C2×C3×#816C212yesmaximal, complemented
5C2×#63565C212yesmaximal, complemented
6#10590672C218yesmaximal, direct product factor
7C2×D3×#103—32nomaximal
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×C3×Dic6C2212yes—
10C22×#627—21no—
11C22×#624—21no—
12C22×#624—21no—
13C2×#3797—22no—
14C2×#3797—24no—
15C2×#3797C418yescomplemented
16C2×#3797C2214yes—
17C22×C32×C8C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C2×C8×C3⋊D3—24no—
20C2×C8×C3⋊D3C2214yes—
21C2×C3×C4⋊Dic3C2212yes—
22C2×#3724—21no—
23#63900—22no—
24#63900C2214yes—
25C3×#816C2218yescomplemented
26#63565C2218yescomplemented
27C22×D3×Q8—32no—
28C22×D3×C8—32no—
29C22×D3×C8—61no—
30C2×D3×C4⋊C4—32no—
31C2×C3×#103—32no—
32C2×#835—32no—
33C2×#816D312yescomplemented
34C2×#810—32no—
35D3×#103—316no—
36C23×C3⋊D3D411yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C2×C4×C3⋊D3C2×C414yes—
40C2×C4×C3⋊D3D412yes—
41C2×C4×C3⋊D3D414yes—
42C2×C4×C3⋊D3C2312yes—
43C22×C3×Dic3—22no—
44C22×C3×Dic3—22no—
45C2×C3×Dic6—22no—
46C2×C3×Dic6—24no—
47C2×C3×Dic6C2×C418yescomplemented
48C2×C3×Dic6C2314yes—
49C2×#627—28no—
50C2×#627—24no—
51C2×#624—28no—
52C2×#624—24no—
53C2×#624—24no—
54C2×#624—44no—
55#3797—216no—
56#3797—28no—
57#3797C2×C4116yescomplemented
58C2×C32×C8—22no—
59C2×C32×C8C2312yes—
60C2×C3⋊(C3⋊C8)—22no—
61C2×C3⋊(C3⋊C8)C2312yes—
62C8×C3⋊D3—28no—
63C3×C4⋊Dic3—22no—
64C3×C4⋊Dic3C2314yes—
65#3724—24no—
66C22×#103—91noSylow
67C22×C3×Q8—32no—
68C2×D3×Q8—316no—
69C2×D3×Q8—38no—
70C2×D3×Q8—64no—
71C2×D3×Q8—68no—
72C22×C4×D3—32no—
73C22×C4×D3—61no—
74C22×C4×D3—62no—
75C22×C4×D3—62no—
76C22×Dic6—62no—
77C22×Dic6C2×D312yes—
78C22×C3×C8—21no—
79C22×C3×C8C2×D312yes—
80C2×C3×C4⋊C4—32no—
81C2×C4⋊Dic3C2×D312yes—
82C2×Dic3⋊C4—62no—
83C22×C3⋊C8—32no—
84C22×C3⋊C8—61no—
85C2×D3×C8—38no—
86C2×D3×C8—64no—
87C2×D3×C8—68no—
88C2×D3×C8—68no—
89D3×C4⋊C4—38no—
90D3×C4⋊C4—64no—
91C3×#103—38no—
92#835—38no—
93#816C2×D318yescomplemented
94#810—38no—
95C23×C32C2×D411yescharacteristic
96C22×C3⋊D3C22⋊C414yes—
97C22×C3⋊D3SD1614yes—
98C22×C3⋊D3Q1614yes—
99C22×C3⋊D3C2×D412yes—
100C2×C32×C4C22×C412yes—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D412yes—
103C2×C32×C4C2411yescharacteristic
104C2×C3⋊Dic3C22⋊C414yes—
105C2×C3⋊Dic3C2×D412yes—
106C4×C3⋊D3C22⋊C418yes—
107C4×C3⋊D3C22×C414yes—
108C4×C3⋊D3C2×D414yes—
109C2×C3×Dic3—28no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—24no—
112C2×C3×Dic3—44no—
113C3×Dic6—28no—
114C3×Dic6—24no—
115C3×Dic6C22×C418yescomplemented
116#627—216no—
117#624—216no—
118#624—48no—
119C32×C8—22no—
120C3⋊(C3⋊C8)—22no—
121C23×Q8—91no—
122C23×C8—91no—
123C22×C4⋊C4—91no—
124C2×#103—32no—
125C2×#103—98no—
126C2×#103—92no—
127C23×D3—32no—
128C23×D3—61no—
129C2×C3×Q8—38no—
130C2×C3×Q8—34no—
131C2×C3×Q8—62no—
132C2×C3×Q8—64no—
133C22×C3×C4—21no—
134C22×C3×C4—62no—
135C22×C3×C4—62no—
136C22×C3×C4C22×D312yes—
137C22×Dic3—22no—
138C22×Dic3—22no—
139C22×Dic3—32no—
140C22×Dic3—61no—
141D3×Q8—332no—
142D3×Q8—632no—
143D3×Q8—616no—
144C2×C4×D3—38no—
145C2×C4×D3—34no—
146C2×C4×D3—38no—
147C2×C4×D3—34no—
148C2×C4×D3—64no—
149C2×C4×D3—62no—
150C2×C4×D3—64no—
151C2×C4×D3—62no—
152C2×C4×D3—616no—
153C2×C4×D3—68no—
154C2×C4×D3—68no—
155C2×C4×D3—128no—
156C2×Dic6—22no—
157C2×Dic6—24no—
158C2×Dic6—616no—
159C2×Dic6—68no—
160C2×Dic6C4×D318yescomplemented
161C2×Dic6C22×D314yes—
162C2×C3×C8—24no—
163C2×C3×C8—24no—
164C2×C3×C8—22no—
165C2×C3×C8C22×D314yes—
166C3×C4⋊C4—34no—
167C3×C4⋊C4—62no—
168C4⋊Dic3—22no—
169C4⋊Dic3C22×D314yes—
170Dic3⋊C4—68no—
171C2×C3⋊C8—34no—
172C2×C3⋊C8—62no—
173C2×C3⋊C8—64no—
174C2×C3⋊C8—64no—
175D3×C8—616no—
176D3×C8—616no—
177C22×C32C2×C22⋊C412yes—
178C22×C32C2×SD1612yes—
179C22×C32C2×Q1612yes—
180C22×C32C22×D411yescharacteristic
181C2×C3⋊D3#103116yescomplemented
182C2×C3⋊D3C2×C22⋊C414yes—
183C2×C3⋊D3C2×SD1614yes—
184C2×C3⋊D3C2×Q1614yes—
185C32×C4C2×C22⋊C412yes—
186C32×C4C23×C411yescharacteristic
187C32×C4C22×D411yescharacteristic
188C3⋊Dic3C2×C22⋊C414yes—
189C3×Dic3—28no—
190C3×Dic3—44no—
191C22×Q8—32no—
192C22×Q8—94no—
193C22×Q8—98no—
194C22×Q8—181no—
195C22×Q8—182no—
196C22×Q8—184no—
197C23×C4—91no—
198C23×C4—181no—
199C23×C4—181no—
200C22×C8—91no—
201C22×C8—94no—
202C22×C8—184no—
203C22×C8D3211yescharacteristic
204C2×C4⋊C4—32no—
205C2×C4⋊C4—94no—
206C2×C4⋊C4—182no—
207C2×C4⋊C4—181no—
208#103—38no—
209#103—98no—
210C23×C3—21no—
211C23×C3D3×D412yes—
212C22×D3—38no—
213C22×D3—38no—
214C22×D3—38no—
215C22×D3—34no—
216C22×D3—64no—
217C22×D3—64no—
218C22×D3—64no—
219C22×D3—62no—
220C3×Q8—38no—
221C3×Q8—68no—
222C3×Q8—64no—
223C2×C3×C4—21no—
224C2×C3×C4—22no—
225C2×C3×C4—21no—
226C2×C3×C4—22no—
227C2×C3×C4—68no—
228C2×C3×C4—64no—
229C2×C3×C4—64no—
230C2×C3×C4—124no—
231C2×C3×C4C2×C4×D314yes—
232C2×C3×C4D3×D412yes—
233C2×C3×C4D3×D414yes—
234C2×C3×C4C23×D312yes—
235C2×Dic3—28no—
236C2×Dic3—24no—
237C2×Dic3—24no—
238C2×Dic3—38no—
239C2×Dic3—34no—
240C2×Dic3—44no—
241C2×Dic3—64no—
242C2×Dic3—62no—
243C4×D3—316no—
244C4×D3—38no—
245C4×D3—38no—
246C4×D3—68no—
247C4×D3—64no—
248C4×D3—64no—
249C4×D3—632no—
250C4×D3—1216no—
251Dic6—28no—
252Dic6—24no—
253Dic6—632no—
254Dic6C2×C4×D318yescomplemented
255C3×C8—24no—
256C3×C8—24no—
257C3⋊C8—64no—
258C3⋊C8—64no—
259C2×C32C2×#10314yescomplemented
260C2×C32C22×C22⋊C411yescharacteristic
261C2×C32C22×SD1611yescharacteristic
262C2×C32C22×Q1611yescharacteristic
263C3⋊D3C2×#10318yescomplemented
264C24—91no—
265C2×Q8—34no—
266C2×Q8—38no—
267C2×Q8—62no—
268C2×Q8—64no—
269C2×Q8—916no—
270C2×Q8—184no—
271C2×Q8—188no—
272C2×Q8—188no—
273C2×Q8—1816no—
274C22×C4—62no—
275C22×C4—62no—
276C22×C4—91no—
277C22×C4—92no—
278C22×C4—94no—
279C22×C4—92no—
280C22×C4—94no—
281C22×C4—184no—
282C22×C4—188no—
283C22×C4—184no—
284C22×C4—364no—
285C22×C4C2×D3211yescharacteristic
286C2×C8—22no—
287C2×C8—92no—
288C2×C8—188no—
289C2×C8—182no—
290C2×C8C2×D3212yes—
291C4⋊C4—34no—
292C4⋊C4—62no—
293C4⋊C4—184no—
294C22×C3—21no—
295C22×C3—22no—
296C22×C3—22no—
297C22×C3—22no—
298C22×C3D3×C22⋊C414yes—
299C22×C3D3×SD1614yes—
300C22×C3D3×Q1614yes—
301C22×C3C2×D3×D412yes—
302C2×D3—38no—
303C2×D3—38no—
304C2×D3—38no—
305C2×D3—332no—
306C2×D3—64no—
307C2×D3—616no—
308C2×D3—64no—
309C2×D3—64no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—22no—
313C3×C4—68no—
314C3×C4—124no—
315C3×C4D3×C22⋊C414yes—
316C3×C4C22×C4×D312yes—
317C3×C4C2×D3×D412yes—
318Dic3—28no—
319Dic3—38no—
320Dic3—44no—
321Dic3—64no—
322C32C22×#10311yescharacteristic, complemented, Sylow
323C23—92no—
324C23—94no—
325C23—94no—
326C23—94no—
327C23#380211yescharacteristic
328Q8—38no—
329Q8—64no—
330Q8—68no—
331Q8—1816no—
332C2×C4—64no—
333C2×C4—68no—
334C2×C4—64no—
335C2×C4—92no—
336C2×C4—94no—
337C2×C4—94no—
338C2×C4—94no—
339C2×C4—98no—
340C2×C4—124no—
341C2×C4—1816no—
342C2×C4—368no—
343C2×C4C4×D3212yes—
344C2×C4#380211yescharacteristic
345C2×C4#381112yes—
346C2×C4C22×D3211yescharacteristic
347C8—22no—
348C8—182no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—24no—
352C2×C3—21no—
353C2×C3D3×#10318yescomplemented
354C2×C3C2×D3×C22⋊C412yes—
355C2×C3C2×D3×SD1612yes—
356C2×C3C2×D3×Q1612yes—
357D3—316no—
358D3—68no—
359C22—94no—
360C22—94no—
361C22—916no—
362C22—94no—
363C22#6379612yes—
364C22#6380212yes—
365C22#6392112yes—
366C22C2×#380211yescharacteristic
367C4—68no—
368C4—94no—
369C4—124no—
370C4#6392112yes—
371C4C2×C4×D3211yescharacteristic
372C4C2×#381111yescharacteristic
373C3—21no—
374C3C2×D3×#10312yescomplemented
375C2—98no—
376C2#1059067214yesdirect product factor
377C2C2×#6379611yescharacteristic
378C2C2×#6380211yescharacteristic
379C2C2×#6392111yescharacteristic
subgroupG/H
centerC23#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C22×#103
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×C3×#816C2semidirect
5. C2×#63565C2semidirect
6. #10590672C2direct (N × H)
15. C2×#3797C4semidirect
25. C3×#816C22semidirect
26. #63565C22semidirect
33. C2×#816D3semidirect
47. C2×C3×Dic6C2×C4semidirect
57. #3797C2×C4semidirect
93. #816C2×D3semidirect
115. C3×Dic6C22×C4semidirect
160. C2×Dic6C4×D3semidirect
181. C2×C3⋊D3#103semidirect
254. Dic6C2×C4×D3semidirect
259. C2×C32C2×#103semidirect
263. C3⋊D3C2×#103semidirect
322. C32C22×#103semidirect
353. C2×C3D3×#103semidirect
374. C3C2×D3×#103semidirect
376. C2#10590672direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C22×C8×C3⋊D32
C2×#639002
C2×C3×#8162
C2×#635652
#105906722
C2×D3×#1033