Finite Group Databasebeta

← C2×#10591629 #11874409

Subgroups — C2×#10591629 #11874409

Order 1152.

1293 conjugacy classes of subgroups; only the 244 normal subgroups are shown.

normal subgroups only

This group has 1293 conjugacy classes of subgroups — too many to draw. Only its 244 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64156C211yesmaximal, characteristic
2C22×C3×#216C212yesmaximal, complemented
3C2×#63873C211yesmaximal, characteristic, complemented
4C22×#3717C212yesmaximal
5#10591629C218yesmaximal, direct product factor
6C2×#63555C211yesmaximal, characteristic, complemented
7C2×#5190—32nomaximal
8C22×C32×Q8C2211yescharacteristic
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×C3×Dic6C2212yes—
11#64156—22no—
12#64156C2214yes—
13C2×#3752—22no—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×#216—28no—
16C2×C3×#216C2218yescomplemented
17C22×C3×C3⋊C8C2212yes—
18C2×#3724—22no—
19#63873—22no—
20#63873C2214yescomplemented
21C2×#3717—28no—
22C2×#3717C2218yes—
23#63555C2214yescomplemented
24C22×C3×Q16—32no—
25C2×#947—32no—
26C2×#947—61no—
27C2×#944—32no—
28C22×#216D312yescomplemented
29C22×#215—32no—
30C22×#204—32no—
31#5190—316no—
32C2×#815—32no—
33C23×C3⋊D3—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8—24no—
36C2×C32×Q8C2312yes—
37C22×C32×C4—21no—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3D412yes—
40C2×C4⋊(C3⋊D3)—24no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)C2312yes—
43C22×C3×Dic3—22no—
44C2×C3×Dic6—24no—
45C2×C3×Dic6—24no—
46C2×C3×Dic6—22no—
47C2×C3×Dic6C2314yes—
48#3752—28no—
49C4×C3⋊Dic3D412yes—
50C4×C3⋊Dic3C2312yes—
51C3×#216—216no—
52C2×C3×C3⋊C8D418yes—
53C2×C3×C3⋊C8C2314yes—
54#3724—28no—
55#3717—216no—
56C2×#497—91noSylow
57C22×C3×Q8—21no—
58C22×C3×Q8—32no—
59C22×C3×Q8C2×D312yes—
60C22×D12—32no—
61C22×D12—61no—
62C22×Dic6C2×D312yes—
63C2×C3×Q16—38no—
64C2×C3×Q16—68no—
65C22×C3×C8—32no—
66#947—38no—
67#947—64no—
68#947—64no—
69#947—64no—
70#944—38no—
71#944—64no—
72C2×#216—28no—
73C2×#216C2×D318yescomplemented
74C2×#215—38no—
75C2×#215—68no—
76C2×(C2×D3)⋊C4—64no—
77C2×(C2×D3)⋊C4—64no—
78C2×Dic3⋊C4—64no—
79C2×C4×Dic3—32no—
80C2×C4×Dic3—61no—
81C22×C3⋊C8C2×D312yes—
82C2×#204—38no—
83C2×#204—68no—
84#815—38no—
85C23×C32C2×D411yescharacteristic
86C22×C3⋊D3—22no—
87C22×C3⋊D3—42no—
88C22×C3⋊D3—44no—
89C32×Q8—24no—
90C32×Q8—42no—
91C2×C32×C4—22no—
92C2×C32×C4—42no—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D414yes—
95C2×C32×C4C2411yescharacteristic
96C2×C3⋊Dic3—24no—
97C2×C3⋊Dic3C2×D414yes—
98C4⋊(C3⋊D3)—24no—
99C4⋊(C3⋊D3)—42no—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—44no—
102C3×Dic6—24no—
103C3×Dic6—24no—
104C3×Dic6—44no—
105C3×C3⋊C8C2×D418yes—
106C22×Q16—32no—
107C22×SD16—92no—
108C2×C4⋊Q8—91no—
109C2×#124—91no—
110#497—98no—
111C2×#97—91no—
112C23×D3—62no—
113C23×D3—62no—
114C2×C3×Q8—22no—
115C2×C3×Q8—22no—
116C2×C3×Q8—24no—
117C2×C3×Q8—24no—
118C2×C3×Q8—22no—
119C2×C3×Q8—34no—
120C2×C3×Q8—44no—
121C2×C3×Q8—62no—
122C2×C3×Q8—64no—
123C2×C3×Q8—64no—
124C2×C3×Q8C22×D314yes—
125C22×C3×C4—22no—
126C22×C3×C4—22no—
127C22×C3×C4—21no—
128C22×C3×C4—62no—
129C22×C3×C4C22×D312yes—
130C22×Dic3—22no—
131C22×Dic3—34no—
132C22×Dic3—62no—
133C2×D12—34no—
134C2×D12—62no—
135C2×D12—64no—
136C2×D12—64no—
137C2×D12—62no—
138C2×D12—62no—
139C2×D12—124no—
140C2×Dic6—24no—
141C2×Dic6—24no—
142C2×Dic6—22no—
143C2×Dic6C22×D314yes—
144C3×Q16—616no—
145C2×C3×C8—38no—
146C2×C3×C8—34no—
147#216—216no—
148#215—616no—
149(C2×D3)⋊C4—616no—
150(C2×D3)⋊C4—616no—
151Dic3⋊C4—616no—
152C4×Dic3—34no—
153C4×Dic3—34no—
154C4×Dic3—62no—
155C4×Dic3—62no—
156C2×C3⋊C8#6718yes—
157C2×C3⋊C8C22×D314yes—
158#204—616no—
159C22×C32#12712yes—
160C22×C32#13714yes—
161C22×C32C22×D411yescharacteristic
162C2×C3⋊D3—42no—
163C2×C3⋊D3—44no—
164C2×C3⋊D3—84no—
165C32×C4—42no—
166C32×C4#12712yes—
167C32×C4C22×D412yes—
168C3⋊Dic3—24no—
169C3×Dic3—44no—
170C22×Q8—32no—
171C22×Q8D3211yescharacteristic
172C22×D4—91no—
173C2×Q16—38no—
174C2×Q16—68no—
175C2×SD16—98no—
176C2×SD16—188no—
177C22×C8—32no—
178C4⋊Q8—94no—
179C4⋊Q8—182no—
180#124—94no—
181#124—182no—
182C2×C4⋊C4—182no—
183C2×C22⋊C4—182no—
184C2×C42—91no—
185#97—94no—
186C23×C3—21no—
187C23×C3D3×D412yes—
188C22×D3—64no—
189C22×D3—64no—
190C22×D3—124no—
191C22×D3—128no—
192C22×D3—128no—
193C22×D3—124no—
194C3×Q8—24no—
195C3×Q8—24no—
196C3×Q8—44no—
197C3×Q8—44no—
198C3×Q8—44no—
199C3×Q8—64no—
200C3×Q8—64no—
201C3×Q8—124no—
202C2×C3×C4—24no—
203C2×C3×C4—24no—
204C2×C3×C4—21no—
205C2×C3×C4—24no—
206C2×C3×C4—21no—
207C2×C3×C4—44no—
208C2×C3×C4—44no—
209C2×C3×C4—64no—
210C2×C3×C4—124no—
211C2×C3×C4D3×D414yes—
212C2×C3×C4D3×D412yes—
213C2×C3×C4C2×#6714yes—
214C2×C3×C4C23×D312yes—
215C2×Dic3—24no—
216C2×Dic3—38no—
217C2×Dic3—44no—
218C2×Dic3—64no—
219C2×Dic3—68no—
220C2×Dic3—124no—
221D12—64no—
222D12—64no—
223D12—124no—
224D12—124no—
225D12—124no—
226Dic6—24no—
227Dic6—24no—
228Dic6—44no—
229C3×C8—38no—
230C3⋊C8C2×#6718yes—
231C2×C32#49714yescomplemented
232C2×C32C2×#12711yescharacteristic
233C2×C32C2×#13712yes—
234C3⋊D3—82no—
235C24—181no—
236C2×Q8—21no—
237C2×Q8—24no—
238C2×Q8—34no—
239C2×Q8—62no—
240C2×Q8—64no—
241C2×Q8—64no—
242C2×Q8C2×D3212yes—
243C2×D4—92no—
244C2×D4—184no—
245C2×D4—181no—
246C22×C4—21no—
247C22×C4—62no—
248C22×C4—92no—
249C22×C4C2×D3211yescharacteristic
250Q16—616no—
251SD16—1816no—
252C2×C8—34no—
253C2×C8—38no—
254C4⋊C4—188no—
255C22⋊C4—188no—
256C42—92no—
257C42—92no—
258C22×C3—21no—
259C22×C3—24no—
260C22×C3—22no—
261C22×C3#91818yes—
262C22×C3#94014yes—
263C22×C3C2×D3×D412yes—
264C2×D3—124no—
265C2×D3—128no—
266C2×D3—128no—
267C2×D3—124no—
268C2×D3—248no—
269C2×D3—248no—
270C3×C4—22no—
271C3×C4—22no—
272C3×C4—44no—
273C3×C4—44no—
274C3×C4—124no—
275C3×C4#94014yes—
276C3×C4C2×D3×D412yes—
277C3×C4C22×#6712yes—
278Dic3—44no—
279Dic3—68no—
280Dic3—124no—
281C32C2×#49711yescharacteristic, complemented, Sylow
282C23—182no—
283C23—364no—
284C23—362no—
285C23#381111yescharacteristic
286Q8—24no—
287Q8—42no—
288Q8—64no—
289Q8—64no—
290Q8—124no—
291D4—184no—
292D4—362no—
293C2×C4—22no—
294C2×C4—42no—
295C2×C4—64no—
296C2×C4—94no—
297C2×C4—124no—
298C2×C4—184no—
299C2×C4D3×#6714yes—
300C2×C4#381111yescharacteristic
301C2×C4C22×D3211yescharacteristic
302C8—38no—
303C2×C3—22no—
304C2×C3—24no—
305C2×C3—21no—
306C2×C3#519018yescomplemented
307C2×C3C2×#91814yes—
308C2×C3C2×#94012yes—
309D3—244no—
310D3—244no—
311C22—364no—
312C22—362no—
313C22—724no—
314C22#6394514yes—
315C22#6397912yes—
316C22C2×#381111yescharacteristic
317C4—42no—
318C4—124no—
319C4—184no—
320C4#6397912yes—
321C4C2×D3×#6712yes—
322C3—21no—
323C3C2×#519012yescomplemented
324C2—722no—
325C2#1059162914yesdirect product factor
326C2C2×#6394512yes—
327C2C2×#6397911yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×Q8D32
hypocenterC32C2×#497
LCSG ▷ C2×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
2. C22×C3×#216C2semidirect
3. C2×#63873C2semidirect
5. #10591629C2direct (N × H)
6. C2×#63555C2semidirect
16. C2×C3×#216C22semidirect
20. #63873C22semidirect
23. #63555C22semidirect
28. C22×#216D3semidirect
73. C2×#216C2×D3semidirect
231. C2×C32#497semidirect
281. C32C2×#497semidirect
306. C2×C3#5190semidirect
323. C3C2×#5190semidirect
325. C2#10591629direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641562
C22×C3×#2162
C2×#638732
C22×#37172
#105916292
C2×#635552
C2×#51903