Finite Group Databasebeta

← C2×#10593857 #11910317

Subgroups — C2×#10593857 #11910317

Order 1152.

2213 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64084C211yesmaximal, characteristic
2C2×C3×#870C212yesmaximal, complemented
3C2×#63897C212yesmaximal
4C2×#63895C214yesmaximal, complemented
5C2×#63848C214yesmaximal, complemented
6C2×#63840C212yesmaximal, complemented
7#10593857C2116yesmaximal, direct product factor
8C2×#5699—32nomaximal
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C22×#627C2212yes—
12C22×#624C2212yes—
13C2×C32×C42C2211yescharacteristic
14C2×#3752C2214yes—
15#64084C2218yes—
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×Dic3⋊C4C2214yes—
19C2×C3×Dic3⋊C4C2214yes—
20C3×#870C22116yescomplemented
21C2×Dic3⋊Dic3C2214yes—
22C2×#3722C2212yes—
23C2×#3722C2214yes—
24C2×Dic32C2212yes—
25#63897C22116yes—
26#63895C22132yescomplemented
27#63848C22132yescomplemented
28#63840C22116yescomplemented
29C2×C3×#125—32no—
30#5699—332no—
31C2×#898—34no—
32C2×#898—34no—
33C2×#897—34no—
34C2×#896—34no—
35C2×#894—34no—
36C2×#888—34no—
37C2×#875—32no—
38C2×#875—61no—
39C2×#870D312yescomplemented
40C23×C3⋊D3C2312yes—
41C22×C32×C4C2311yescharacteristic
42C22×C32×C4C2312yes—
43C22×C3⋊Dic3C2312yes—
44C2×C4⋊(C3⋊D3)—42no—
45C2×C4⋊(C3⋊D3)C2314yes—
46C2×#634—42no—
47C2×#634C2314yes—
48C22×C3×Dic3C2314yes—
49C22×C3×Dic3C2314yes—
50C2×#627—44no—
51C2×#627C2318yes—
52C2×#624—44no—
53C2×#624C2318yes—
54C32×C42C2314yes—
55#3752C23116yes—
56C3×C4⋊Dic3C2318yes—
57C3×C4⋊Dic3C2318yes—
58C3×Dic3⋊C4C23116yes—
59C3×Dic3⋊C4C23116yes—
60Dic3⋊Dic3C23116yes—
61#3722C2318yes—
62#3722C23116yes—
63Dic32C2318yes—
64C2×#563—91noSylow
65C22×D12—32no—
66C22×D12—61no—
67C22×C4×D3—34no—
68C22×Dic6—32no—
69C22×Dic6—34no—
70C22×Dic6—61no—
71C3×#125—316no—
72C2×C3×C4⋊C4—34no—
73C2×C3×C4⋊C4—34no—
74C2×C3×C4⋊C4—32no—
75C2×C3×C4⋊C4—32no—
76C2×C3×C42—21no—
77C2×C3×C42C2×D312yes—
78C2×(C2×D3)⋊C4—34no—
79C2×(C2×D3)⋊C4—34no—
80C2×(C2×D3)⋊C4—34no—
81C2×(C2×D3)⋊C4—34no—
82C2×(C2×D3)⋊C4—34no—
83C2×(C2×D3)⋊C4—64no—
84C2×C4⋊Dic3—34no—
85C2×C4⋊Dic3C2×D312yes—
86C2×C4⋊Dic3C2×D312yes—
87C2×Dic3⋊C4—34no—
88C2×Dic3⋊C4C2×D314yes—
89C2×Dic3⋊C4C2×D314yes—
90C2×C4×Dic3—34no—
91#898—332no—
92#898—332no—
93#897—332no—
94#896—332no—
95#894—332no—
96#888—332no—
97#875—316no—
98#875—68no—
99#870C2×D3116yescomplemented
100C23×C32C2411yescharacteristic
101C22×C3⋊D3—24no—
102C22×C3⋊D3—28no—
103C22×C3⋊D3C2414yes—
104C2×C32×C4—22no—
105C2×C32×C4—24no—
106C2×C32×C4C2412yes—
107C2×C32×C4C2414yes—
108C2×C3⋊Dic3—24no—
109C2×C3⋊Dic3C2414yes—
110C4⋊(C3⋊D3)—44no—
111#634—44no—
112C2×C3×Dic3—28no—
113C2×C3×Dic3—28no—
114C2×C3×Dic3C2418yes—
115C2×C3×Dic3C2418yes—
116#627—48no—
117#624—48no—
118#563—916no—
119C2×C4⋊Q8—92no—
120C2×#126—94no—
121C2×#125—32no—
122C2×#124—91no—
123C2×#123—92no—
124C2×C22⋊Q8—94no—
125C23×D3—34no—
126C23×D3—62no—
127C22×C3×C4—21no—
128C22×C3×C4—22no—
129C22×C3×C4—34no—
130C22×C3×C4—34no—
131C22×C3×C4C22×D312yes—
132C22×C3×C4C22×D312yes—
133C22×C3×C4C22×D312yes—
134C22×Dic3—34no—
135C22×Dic3—62no—
136C22×Dic3C22×D314yes—
137C22×Dic3C22×D314yes—
138C2×D12—38no—
139C2×D12—64no—
140C2×D12—124no—
141C2×D12—124no—
142C2×C4×D3—316no—
143C2×C4×D3—128no—
144C2×Dic6—38no—
145C2×Dic6—316no—
146C2×Dic6—64no—
147C2×Dic6—128no—
148C2×Dic6—124no—
149C2×Dic6—124no—
150C3×C4⋊C4—316no—
151C3×C4⋊C4—38no—
152C3×C4⋊C4—316no—
153C3×C4⋊C4—38no—
154C3×C42—24no—
155C3×C42C22×D318yes—
156(C2×D3)⋊C4—316no—
157(C2×D3)⋊C4—316no—
158(C2×D3)⋊C4—316no—
159(C2×D3)⋊C4—316no—
160(C2×D3)⋊C4—316no—
161(C2×D3)⋊C4—616no—
162C4⋊Dic3—316no—
163C4⋊Dic3C22×D318yes—
164C4⋊Dic3C22×D318yes—
165Dic3⋊C4—316no—
166Dic3⋊C4C22×D3116yes—
167Dic3⋊C4C22×D3116yes—
168C4×Dic3—316no—
169C22×C32H(5,𝔽2)12yes—
170C22×C322−1+414yes—
171C22×C32C2511yescharacteristic
172C2×C3⋊D3—24no—
173C2×C3⋊D3—28no—
174C2×C3⋊D3—48no—
175C32×C4—22no—
176C32×C4—24no—
177C3⋊Dic3—24no—
178C3×Dic3—28no—
179C3×Dic3—28no—
180C22×Q8—92no—
181C22×Q8—91no—
182C22×D4—91no—
183C23×C4—92no—
184C4⋊Q8—916no—
185#126—932no—
186#125—316no—
187#124—98no—
188#123—916no—
189C22⋊Q8—932no—
190C2×C4⋊C4—32no—
191C2×C4⋊C4—34no—
192C2×C4⋊C4—34no—
193C2×C4⋊C4—32no—
194C2×C4⋊C4—94no—
195C2×C22⋊C4—94no—
196C2×C22⋊C4—92no—
197C2×C22⋊C4—94no—
198C2×C42—92no—
199C2×C42D3211yescharacteristic
200C23×C3—21no—
201C23×C3C23×D312yes—
202C22×D3—38no—
203C22×D3—64no—
204C22×D3—68no—
205C22×D3—68no—
206C22×D3—68no—
207C22×D3—124no—
208C22×D3—128no—
209C2×C3×C4—24no—
210C2×C3×C4—24no—
211C2×C3×C4—24no—
212C2×C3×C4—24no—
213C2×C3×C4—22no—
214C2×C3×C4—24no—
215C2×C3×C4—38no—
216C2×C3×C4—38no—
217C2×C3×C4—44no—
218C2×C3×C4—68no—
219C2×C3×C4—68no—
220C2×C3×C4C23×D314yes—
221C2×C3×C4C23×D314yes—
222C2×C3×C4C23×D314yes—
223C2×Dic3—28no—
224C2×Dic3—28no—
225C2×Dic3—38no—
226C2×Dic3—64no—
227C2×Dic3—68no—
228C2×Dic3—124no—
229C2×Dic3C23×D318yes—
230C2×Dic3C23×D318yes—
231D12—128no—
232D12—128no—
233C4×D3—1216no—
234Dic6—1216no—
235Dic6—128no—
236Dic6—128no—
237C2×C32#56314yescomplemented
238C2×C32C2×H(5,𝔽2)11yescharacteristic
239C2×C32C2×2−1+412yes—
240C3⋊D3—44no—
241C24—92no—
242C2×Q8—98no—
243C2×Q8—94no—
244C2×Q8—362no—
245C2×Q8—364no—
246C2×D4—94no—
247C2×D4—362no—
248C22×C4—34no—
249C22×C4—34no—
250C22×C4—98no—
251C22×C4—92no—
252C22×C4—364no—
253C22×C4C2×D3212yes—
254C22×C4C2×D3211yescharacteristic
255C4⋊C4—38no—
256C4⋊C4—316no—
257C4⋊C4—316no—
258C4⋊C4—38no—
259C4⋊C4—916no—
260C22⋊C4—916no—
261C22⋊C4—98no—
262C22⋊C4—916no—
263C42—98no—
264C42C2×D3214yes—
265C22×C3—24no—
266C22×C3—22no—
267C22×C3—21no—
268C22×C3#100714yes—
269C22×C3#100914yes—
270C22×C3#101014yes—
271C22×C3C24×D312yes—
272C2×D3—68no—
273C2×D3—68no—
274C2×D3—68no—
275C2×D3—124no—
276C2×D3—128no—
277C2×D3—1216no—
278C2×D3—248no—
279C3×C4—24no—
280C3×C4—24no—
281C3×C4—24no—
282C3×C4—24no—
283C3×C4—44no—
284C3×C4—68no—
285C3×C4—68no—
286Dic3—28no—
287Dic3—28no—
288Dic3—68no—
289Dic3—124no—
290C32C2×#56311yescharacteristic, complemented, Sylow
291C23—94no—
292C23—188no—
293C23—184no—
294C23C22×D3211yescharacteristic
295Q8—364no—
296Q8—368no—
297D4—364no—
298C2×C4—24no—
299C2×C4—22no—
300C2×C4—38no—
301C2×C4—38no—
302C2×C4—68no—
303C2×C4—68no—
304C2×C4—94no—
305C2×C4—184no—
306C2×C4—368no—
307C2×C4C22×D3214yes—
308C2×C4C22×D3212yes—
309C2×C3—22no—
310C2×C3—21no—
311C2×C3—24no—
312C2×C3#569918yescomplemented
313C2×C3C2×#100712yes—
314C2×C3C2×#100912yes—
315C2×C3C2×#101012yes—
316D3—128no—
317D3—244no—
318C22—188no—
319C22—184no—
320C22—368no—
321C22#6429714yes—
322C22#6430812yes—
323C22C23×D3211yescharacteristic
324C4—24no—
325C4—22no—
326C4—68no—
327C4—68no—
328C4—184no—
329C3—21no—
330C3C2×#569912yescomplemented
331C2—364no—
332C2#1059385714yesdirect product factor
333C2C2×#6429712yes—
334C2C2×#6430811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32C2×#563
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#870C2semidirect
4. C2×#63895C2semidirect
5. C2×#63848C2semidirect
6. C2×#63840C2semidirect
7. #10593857C2direct (N × H)
20. C3×#870C22semidirect
26. #63895C22semidirect
27. #63848C22semidirect
28. #63840C22semidirect
39. C2×#870D3semidirect
99. #870C2×D3semidirect
237. C2×C32#563semidirect
290. C32C2×#563semidirect
312. C2×C3#5699semidirect
330. C3C2×#5699semidirect
332. C2#10593857direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640842
C2×C3×#8702
C2×#638972
C2×#638952
C2×#638482
C2×#638402
#105938572
C2×#56993