Finite Group Databasebeta

← C2×#10594813 #11901928

Subgroups — C2×#10594813 #11901928

Order 1152.

2369 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C2×C3×#924C212yesmaximal
3C2×#63982C212yesmaximal
4C2×#63957C212yesmaximal
5C2×#63847C214yesmaximal, complemented
6#10594813C2116yesmaximal, direct product factor
7C2×#63839C214yesmaximal, complemented
8C2×#5623—32nomaximal
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C22×C3×Dic6C2212yes—
13C22×#627C2212yes—
14C2×#3750C2214yes—
15C2×#3750C2218yes—
16C2×C3×#217C2214yes—
17C2×C3×C4⋊Dic3C2212yes—
18C3×#924C22116yes—
19C2×C3×Dic3⋊C4C2214yes—
20#63982C22116yes—
21C2×#3724C2212yes—
22C2×#3724C2212yes—
23C2×#3724C2212yes—
24C2×Dic3⋊Dic3C2214yes—
25#63957C22116yes—
26C2×Dic32C2214yes—
27#63847C22132yescomplemented
28#63839C22132yescomplemented
29C2×C3×C22⋊Q8—32no—
30C2×#944—34no—
31C2×#924D312yes—
32C22×Dic3⋊C4—32no—
33C22×Dic3⋊C4—61no—
34#5623—332no—
35C2×#889—34no—
36C2×#889—34no—
37C2×#888—34no—
38C2×#878—34no—
39C2×#877—34no—
40C24×C32C2311yescharacteristic
41C22×C32×C4—42no—
42C22×C32×C4C2312yes—
43C22×C32×C4C2314yes—
44C22×C3⋊Dic3—42no—
45C22×C3⋊Dic3Q818yescomplemented
46C22×C3⋊Dic3C2312yes—
47C22×C3⋊Dic3C2314yes—
48C22×C3⋊Dic3C2312yes—
49C22×C3⋊Dic3C2314yes—
50C22×C3×Dic3C2314yes—
51C22×C3×Dic3C2314yes—
52C2×C3×Dic6—44no—
53C2×C3×Dic6C2318yes—
54C2×#627—44no—
55C2×#627C2318yes—
56#3750C23116yes—
57C3×#217C23116yes—
58C3×C4⋊Dic3C2318yes—
59C3×Dic3⋊C4C23116yes—
60#3724C2318yes—
61#3724C2318yes—
62#3724C2318yes—
63Dic3⋊Dic3C23116yes—
64Dic32C23116yes—
65C2×#544—91noSylow
66C22×C3×Q8—32no—
67C23×C3×C4—21no—
68C23×C3×C4C2×D312yes—
69C23×Dic3—32no—
70C23×Dic3—32no—
71C23×Dic3—61no—
72C23×Dic3—61no—
73C22×Dic6—34no—
74C22×Dic6C2×D312yes—
75C3×C22⋊Q8—316no—
76C2×C3×C4⋊C4—34no—
77C2×C3×C4⋊C4—32no—
78C2×C3×C22⋊C4—34no—
79C2×#217C2×D314yes—
80#944—332no—
81C2×C4⋊Dic3—34no—
82C2×C4⋊Dic3C2×D312yes—
83#924C2×D3116yes—
84C2×Dic3⋊C4—34no—
85C2×Dic3⋊C4—34no—
86C2×Dic3⋊C4—316no—
87C2×Dic3⋊C4—34no—
88C2×Dic3⋊C4—34no—
89C2×Dic3⋊C4—34no—
90C2×Dic3⋊C4—34no—
91C2×Dic3⋊C4—64no—
92C2×Dic3⋊C4—68no—
93C2×Dic3⋊C4C2×D314yes—
94C2×C4×Dic3—34no—
95C2×C4×Dic3—34no—
96#889—332no—
97#889—332no—
98#888—332no—
99#878—332no—
100#877—332no—
101C23×C32—22no—
102C23×C32—22no—
103C23×C32C2×Q814yes—
104C23×C32C2412yes—
105C23×C32C2411yescharacteristic
106C2×C32×C4—24no—
107C2×C32×C4—44no—
108C2×C32×C4C2414yes—
109C2×C3⋊Dic3—24no—
110C2×C3⋊Dic3—44no—
111C2×C3⋊Dic3C2×Q818yes—
112C2×C3⋊Dic3C2×Q8116yescomplemented
113C2×C3⋊Dic3C2414yes—
114C2×C3⋊Dic3C2414yes—
115C2×C3×Dic3—28no—
116C2×C3×Dic3—28no—
117C2×C3×Dic3C2418yes—
118C2×C3×Dic3C2418yes—
119C3×Dic6—48no—
120#627—48no—
121#544—916no—
122C2×C4⋊Q8—94no—
123C2×#125—94no—
124C2×C22⋊Q8—32no—
125C2×C22⋊Q8—92no—
126C2×#117—92no—
127C22×C4⋊C4—91no—
128C24×C3—21no—
129C24×C3C22×D312yes—
130C2×C3×Q8—38no—
131C2×C3×Q8—124no—
132C22×C3×C4—22no—
133C22×C3×C4—24no—
134C22×C3×C4—34no—
135C22×C3×C4—34no—
136C22×C3×C4—44no—
137C22×C3×C4—44no—
138C22×C3×C4C22×D312yes—
139C22×C3×C4C22×D312yes—
140C22×C3×C4C22×D318yes—
141C22×Dic3—316no—
142C22×Dic3—38no—
143C22×Dic3—34no—
144C22×Dic3—34no—
145C22×Dic3—38no—
146C22×Dic3—64no—
147C22×Dic3—62no—
148C22×Dic3—68no—
149C22×Dic3—62no—
150C22×Dic3—64no—
151C22×Dic3—124no—
152C22×Dic3—124no—
153C22×Dic3C22×D314yes—
154C22×Dic3C22×D314yes—
155C2×Dic6—316no—
156C2×Dic6—44no—
157C2×Dic6—128no—
158C2×Dic6C22×D318yes—
159C3×C4⋊C4—316no—
160C3×C4⋊C4—38no—
161C3×C22⋊C4—316no—
162#217C22×D3116yes—
163C4⋊Dic3—316no—
164C4⋊Dic3C22×D318yes—
165Dic3⋊C4—316no—
166Dic3⋊C4—316no—
167Dic3⋊C4—316no—
168Dic3⋊C4—316no—
169Dic3⋊C4—316no—
170Dic3⋊C4—316no—
171Dic3⋊C4—616no—
172Dic3⋊C4C22×D3116yes—
173C4×Dic3—316no—
174C4×Dic3—316no—
175C22×C32—28no—
176C22×C32—22no—
177C22×C32—22no—
178C22×C32C22×Q814yes—
179C22×C32C22×Q812yes—
180C22×C32H(5,𝔽2)12yes—
181C22×C322−1+412yes—
182C22×C32C2511yescharacteristic
183C32×C4—24no—
184C3⋊Dic3—24no—
185C3⋊Dic3C22×Q818yes—
186C3×Dic3—28no—
187C3×Dic3—28no—
188C22×Q8—32no—
189C22×Q8—92no—
190C23×C4—91no—
191C23×C4—91no—
192C23×C4D3211yescharacteristic
193C4⋊Q8—932no—
194#125—932no—
195C22⋊Q8—316no—
196C22⋊Q8—916no—
197#117—916no—
198C2×C4⋊C4—32no—
199C2×C4⋊C4—34no—
200C2×C4⋊C4—92no—
201C2×C4⋊C4—92no—
202C2×C4⋊C4—92no—
203C2×C4⋊C4—94no—
204C2×C4⋊C4—94no—
205C2×C4⋊C4—98no—
206C2×C22⋊C4—34no—
207C2×C42—94no—
208C23×C3—24no—
209C23×C3—24no—
210C23×C3—24no—
211C23×C3—24no—
212C23×C3—22no—
213C23×C3—21no—
214C23×C3—24no—
215C23×C3D3×Q818yes—
216C23×C3C23×D314yes—
217C23×C3C23×D312yes—
218C3×Q8—128no—
219C2×C3×C4—24no—
220C2×C3×C4—24no—
221C2×C3×C4—24no—
222C2×C3×C4—38no—
223C2×C3×C4—38no—
224C2×C3×C4—44no—
225C2×C3×C4—48no—
226C2×C3×C4—48no—
227C2×C3×C4—68no—
228C2×C3×C4—68no—
229C2×C3×C4C23×D314yes—
230C2×C3×C4C23×D314yes—
231C2×Dic3—28no—
232C2×Dic3—28no—
233C2×Dic3—316no—
234C2×Dic3—332no—
235C2×Dic3—38no—
236C2×Dic3—38no—
237C2×Dic3—68no—
238C2×Dic3—616no—
239C2×Dic3—64no—
240C2×Dic3—64no—
241C2×Dic3—68no—
242C2×Dic3—124no—
243C2×Dic3—128no—
244C2×Dic3—128no—
245C2×Dic3C23×D318yes—
246C2×Dic3C23×D318yes—
247Dic6—48no—
248Dic6—1216no—
249C2×C32—24no—
250C2×C32#54414yescomplemented
251C2×C32C23×Q811yescharacteristic
252C2×C32C2×H(5,𝔽2)11yescharacteristic
253C2×C32C2×2−1+411yescharacteristic
254C24C2×D3211yescharacteristic
255C2×Q8—38no—
256C2×Q8—98no—
257C2×Q8—124no—
258C2×Q8—364no—
259C22×C4—34no—
260C22×C4—34no—
261C22×C4—42no—
262C22×C4—94no—
263C22×C4—92no—
264C22×C4—98no—
265C22×C4—92no—
266C22×C4—94no—
267C22×C4—362no—
268C22×C4C2×D3212yes—
269C22×C4C2×D3214yes—
270C4⋊C4—38no—
271C4⋊C4—316no—
272C4⋊C4—98no—
273C4⋊C4—98no—
274C4⋊C4—98no—
275C4⋊C4—916no—
276C4⋊C4—916no—
277C22⋊C4—316no—
278C42—916no—
279C22×C3—24no—
280C22×C3—24no—
281C22×C3—216no—
282C22×C3—24no—
283C22×C3—24no—
284C22×C3—216no—
285C22×C3—22no—
286C22×C3—24no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—21no—
290C22×C3#100414yes—
291C22×C3C2×D3×Q818yes—
292C22×C3C2×D3×Q814yes—
293C22×C3#101014yes—
294C22×C3C24×D312yes—
295C3×C4—24no—
296C3×C4—24no—
297C3×C4—44no—
298C3×C4—68no—
299C3×C4—68no—
300Dic3—28no—
301Dic3—28no—
302Dic3—316no—
303Dic3—68no—
304Dic3—68no—
305Dic3—124no—
306C32C2×#54411yescharacteristic, complemented, Sylow
307C23—22no—
308C23—22no—
309C23#379714yes—
310C23C22×D3212yes—
311C23C22×D3211yescharacteristic
312Q8—128no—
313Q8—368no—
314C2×C4—24no—
315C2×C4—38no—
316C2×C4—38no—
317C2×C4—44no—
318C2×C4—68no—
319C2×C4—68no—
320C2×C4—916no—
321C2×C4—98no—
322C2×C4—94no—
323C2×C4—94no—
324C2×C4—184no—
325C2×C4—364no—
326C2×C4C22×D3214yes—
327C2×C3—28no—
328C2×C3—28no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—24no—
333C2×C3#562318yescomplemented
334C2×C3C2×#100412yes—
335C2×C3C22×D3×Q812yes—
336C2×C3C2×#101012yes—
337C22—22no—
338C22—22no—
339C22—28no—
340C22#6429812yes—
341C22C2×#379714yes—
342C22C2×#379712yes—
343C22#6433012yes—
344C22C23×D3211yescharacteristic
345C4—24no—
346C4—68no—
347C4—68no—
348C4—98no—
349C4—184no—
350C3—21no—
351C3C2×#562312yescomplemented
352C2—24no—
353C2#1059481314yesdirect product factor
354C2C2×#6429811yescharacteristic
355C2C22×#379711yescharacteristic
356C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32C2×#544
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
5. C2×#63847C2semidirect
6. #10594813C2direct (N × H)
7. C2×#63839C2semidirect
27. #63847C22semidirect
28. #63839C22semidirect
45. C22×C3⋊Dic3Q8semidirect
112. C2×C3⋊Dic3C2×Q8semidirect
250. C2×C32#544semidirect
306. C32C2×#544semidirect
333. C2×C3#5623semidirect
351. C3C2×#5623semidirect
353. C2#10594813direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37502
C2×C3×#9242
C2×#639822
C2×#639572
C2×#638472
#105948132
C2×#638392
C2×#56233