Finite Group Databasebeta

← C2×#10590315 #11875040

Subgroups — C2×#10590315 #11875040

Order 1152.

841 conjugacy classes of subgroups.

The subgroup lattice has 337 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#870C211yesmaximal, characteristic
2C2×C3×#869C211yesmaximal, characteristic
3C2×#63630C211yesmaximal, characteristic
4C2×#63576C212yesmaximal
5C2×#63574C212yesmaximal
6#10590315C218yesmaximal, direct product factor
7C2×#5081—31nomaximal
8C2×#5064—31nomaximal
9C22×C3×Dic6—21no—
10C2×C32×C42C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2212yes—
12C2×C3×C4⋊Dic3—21no—
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×Dic3⋊C4—21no—
17C2×C3×Dic3⋊C4—21no—
18C3×#870—22no—
19C3×#870C2214yes—
20C3×#869—22no—
21C3×#869C2214yes—
22#63630C2214yes—
23#63576C2218yes—
24#63574C2218yes—
25C2×C3×C4⋊Q8—31no—
26C2×C3×#125—31no—
27C2×#870D311yescharacteristic
28C2×#869D311yescharacteristic
29#5081—38no—
30#5064—38no—
31C2×#808—32no—
32C2×#808—32no—
33C2×#807—32no—
34C2×#807—32no—
35C2×#803—31no—
36C2×#803—31no—
37C2×#803—61no—
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C32×C4C2311yescharacteristic
41C22×C3×Dic3—21no—
42C22×C3×Dic3—21no—
43C22×C3×Dic3—22no—
44C2×C3×Dic6—24no—
45C2×C3×Dic6—44no—
46C32×C42D412yes—
47C32×C42C2312yes—
48C2×C3⋊(C3⋊C8)Q818yescomplemented
49C2×C3⋊(C3⋊C8)C2314yes—
50C3×C4⋊Dic3—24no—
51C3×C4⋊Dic3—22no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3C2312yes—
55C3×C4⋊Dic3C2314yes—
56C3×C4⋊Dic3C2312yes—
57C3×Dic3⋊C4—24no—
58C3×Dic3⋊C4—24no—
59C2×#501—91noSylow
60C22×C3×Q8—61no—
61C22×Dic6—21no—
62C3×C4⋊Q8—34no—
63C3×C4⋊Q8—62no—
64C3×#125—34no—
65C3×#125—62no—
66C2×C3×C4⋊C4—31no—
67C2×C3×C4⋊C4—32no—
68C2×C3×C4⋊C4—31no—
69C2×C3×C4⋊C4—61no—
70C2×C3×C4⋊C4—61no—
71C2×C3×C4⋊C4—61no—
72C2×C3×C42—21no—
73C2×C3×C42C2×D311yescharacteristic
74C2×C3×C42C2×D311yescharacteristic
75C2×C4⋊Dic3—21no—
76C2×C4⋊Dic3C2×D312yes—
77C2×C4⋊Dic3C2×D311yescharacteristic
78C2×C4⋊Dic3C2×D311yescharacteristic
79C2×Dic3⋊C4—21no—
80C2×Dic3⋊C4—21no—
81C22×C3⋊C8—32no—
82C22×C3⋊C8—32no—
83C22×C3⋊C8—62no—
84#870—22no—
85#870C2×D314yes—
86#869—22no—
87#869C2×D314yes—
88#808—38no—
89#808—38no—
90#807—38no—
91#807—38no—
92#803—34no—
93#803—34no—
94#803—64no—
95C23×C32C2×D411yescharacteristic
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4C2×D412yes—
99C2×C32×C4C2×D412yes—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×Q814yes—
102C2×C32×C4C2411yescharacteristic
103C2×C3×Dic3—22no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—44no—
107C2×C3×Dic3—42no—
108C2×C3×Dic3—42no—
109C3×Dic6—48no—
110C3⋊(C3⋊C8)C2×Q818yescomplemented
111C2×C4⋊Q8—31no—
112C2×#125—31no—
113#501—98no—
114C2×#107—92no—
115C2×#106—92no—
116C2×#97—91no—
117C2×C3×Q8—64no—
118C2×C3×Q8—124no—
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C22×C3×C4—21no—
122C22×C3×C4—61no—
123C22×C3×C4—61no—
124C22×C3×C4—62no—
125C22×C3×C4#6711yescharacteristic
126C22×C3×C4#6711yescharacteristic
127C22×C3×C4#6711yescharacteristic
128C22×C3×C4#6711yescharacteristic
129C22×C3×C4C22×D311yescharacteristic
130C22×C3×C4C22×D311yescharacteristic
131C22×Dic3—21no—
132C22×Dic3—21no—
133C22×Dic3—22no—
134C2×Dic6—24no—
135C2×Dic6—44no—
136C3×C4⋊C4—32no—
137C3×C4⋊C4—34no—
138C3×C4⋊C4—32no—
139C3×C4⋊C4—64no—
140C3×C4⋊C4—64no—
141C3×C4⋊C4—61no—
142C3×C4⋊C4—61no—
143C3×C4⋊C4—62no—
144C3×C4⋊C4—64no—
145C3×C42—22no—
146C3×C42—22no—
147C3×C42#6712yes—
148C3×C42#6712yes—
149C3×C42C22×D312yes—
150C3×C42C22×D312yes—
151C4⋊Dic3—22no—
152C4⋊Dic3—24no—
153C4⋊Dic3—21no—
154C4⋊Dic3—21no—
155C4⋊Dic3C22×D312yes—
156C4⋊Dic3C22×D314yes—
157C4⋊Dic3C22×D312yes—
158Dic3⋊C4—24no—
159Dic3⋊C4—24no—
160C2×C3⋊C8—38no—
161C2×C3⋊C8—38no—
162C2×C3⋊C8—34no—
163C2×C3⋊C8—34no—
164C2×C3⋊C8—64no—
165C2×C3⋊C8—68no—
166C22×C32C4⋊Q812yes—
167C22×C32AGL(1,ℤ/8)12yes—
168C22×C32#13712yes—
169C22×C32C22×D411yescharacteristic
170C32×C4—22no—
171C32×C4—22no—
172C32×C4C4⋊Q812yes—
173C32×C4C22×Q812yes—
174C3×Dic3—44no—
175C3×Dic3—42no—
176C3×Dic3—42no—
177C22×Q8—61no—
178C22×C8—92no—
179C4⋊Q8—34no—
180C4⋊Q8—62no—
181#125—34no—
182#125—62no—
183C2×C4⋊C4—31no—
184C2×C4⋊C4—31no—
185C2×C4⋊C4—32no—
186C2×C4⋊C4—61no—
187C2×C4⋊C4—61no—
188C2×C4⋊C4—61no—
189C2×C42D3211yescharacteristic
190#107—98no—
191#106—98no—
192#97—94no—
193C23×C3—21no—
194C23×C3C2×#6711yescharacteristic
195C23×C3C2×#6711yescharacteristic
196C3×Q8—128no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—22no—
201C2×C3×C4—21no—
202C2×C3×C4—24no—
203C2×C3×C4—21no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—42no—
207C2×C3×C4—42no—
208C2×C3×C4—62no—
209C2×C3×C4—62no—
210C2×C3×C4—64no—
211C2×C3×C4—122no—
212C2×C3×C4—122no—
213C2×C3×C4—124no—
214C2×C3×C4D3×Q814yes—
215C2×C3×C4D3×Q814yes—
216C2×C3×C4C2×#6712yes—
217C2×C3×C4C2×#6712yes—
218C2×C3×C4C2×#6712yes—
219C2×C3×C4C2×#6712yes—
220C2×C3×C4C2×#6711yescharacteristic
221C2×C3×C4C2×#6711yescharacteristic
222C2×C3×C4C23×D311yescharacteristic
223C2×C3×C4C23×D311yescharacteristic
224C2×Dic3—22no—
225C2×Dic3—22no—
226C2×Dic3—24no—
227C2×Dic3—44no—
228C2×Dic3—42no—
229C2×Dic3—42no—
230Dic6—48no—
231C3⋊C8—38no—
232C3⋊C8—38no—
233C3⋊C8—68no—
234C2×C32#50114yescomplemented
235C2×C32C2×C4⋊Q811yescharacteristic
236C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
237C2×C32C2×#13711yescharacteristic
238C2×Q8—64no—
239C2×Q8—124no—
240C22×C4—61no—
241C22×C4—61no—
242C22×C4—62no—
243C22×C4#62511yescharacteristic
244C22×C4#62511yescharacteristic
245C22×C4C2×D3211yescharacteristic
246C2×C8—94no—
247C2×C8—98no—
248C4⋊C4—32no—
249C4⋊C4—34no—
250C4⋊C4—32no—
251C4⋊C4—61no—
252C4⋊C4—61no—
253C4⋊C4—62no—
254C4⋊C4—64no—
255C4⋊C4—64no—
256C4⋊C4—64no—
257C42#62512yes—
258C42C2×D3212yes—
259C22×C3—21no—
260C22×C3—22no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3#93212yes—
264C22×C3#94212yes—
265C22×C3#94412yes—
266C22×C3#94412yes—
267C22×C3#94912yes—
268C22×C3#95112yes—
269C22×C3C22×#6711yescharacteristic
270C22×C3C22×#6711yescharacteristic
271C3×C4—22no—
272C3×C4—22no—
273C3×C4—22no—
274C3×C4—22no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—42no—
278C3×C4—42no—
279C3×C4—122no—
280C3×C4—122no—
281C3×C4—124no—
282C3×C4#94412yes—
283C3×C4#94412yes—
284C3×C4C2×D3×Q812yes—
285C3×C4C2×D3×Q812yes—
286Dic3—44no—
287Dic3—42no—
288Dic3—42no—
289C32C2×#50111yescharacteristic, complemented, Sylow
290C23C2×#62511yescharacteristic
291Q8—128no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—62no—
295C2×C4—62no—
296C2×C4—64no—
297C2×C4—124no—
298C2×C4—122no—
299C2×C4—122no—
300C2×C4#379714yes—
301C2×C4C2×#62512yes—
302C2×C4C2×#62512yes—
303C2×C4C2×#62511yescharacteristic
304C2×C4C22×D3211yescharacteristic
305C8—98no—
306C2×C3—21no—
307C2×C3—24no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3#506414yescomplemented
311C2×C3#508114yescomplemented
312C2×C3C2×#93211yescharacteristic
313C2×C3C2×#94211yescharacteristic
314C2×C3C2×#94411yescharacteristic
315C2×C3C2×#94411yescharacteristic
316C2×C3C2×#94911yescharacteristic
317C2×C3C2×#95111yescharacteristic
318C22#6382312yes—
319C22#6382712yes—
320C22#6387312yes—
321C22C22×#62511yescharacteristic
322C4—22no—
323C4—22no—
324C4—124no—
325C4—122no—
326C4—122no—
327C4#6387312yes—
328C4C2×#379712yes—
329C3—21no—
330C3C2×#506411yescharacteristic, complemented
331C3C2×#508111yescharacteristic, complemented
332C2#1059031514yesdirect product factor
333C2C2×#6382311yescharacteristic
334C2C2×#6382711yescharacteristic
335C2C2×#6387311yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C2×D4
hypercenterC2×C42D32
hypocenterC32C2×#501
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
6. #10590315C2direct (N × H)
48. C2×C3⋊(C3⋊C8)Q8semidirect
110. C3⋊(C3⋊C8)C2×Q8semidirect
234. C2×C32#501semidirect
289. C32C2×#501semidirect
310. C2×C3#5064semidirect
311. C2×C3#5081semidirect
330. C3C2×#5064semidirect
331. C3C2×#5081semidirect
332. C2#10590315direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8702
C2×C3×#8692
C2×#636302
C2×#635762
C2×#635742
#105903152
C2×#50813
C2×#50643