Finite Group Databasebeta

← C2×#10593120 #11919881

Subgroups — C2×#10593120 #11919881

Order 1152.

2333 conjugacy classes of subgroups; only the 341 normal subgroups are shown.

normal subgroups only

This group has 2333 conjugacy classes of subgroups — too many to draw. Only its 341 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
1#10593120C218yesmaximal, direct product factor
2C2×2−1+4⋊C9C213yesmaximal, complemented
3C2×#63700C211yesmaximal, characteristic, complemented
4C22×#41⋊C9C213yesmaximal, complemented
5C2×C3×#585C311yesmaximal, characteristic
6C2×C9×#41—41nomaximal
72−1+4⋊C9C22112yescomplemented
8#63700C2214yescomplemented
9C2×#41⋊C9C2211yescharacteristic, complemented
10C2×#41⋊C9C2213yescomplemented
11C2×#41⋊C9C22112yescomplemented
12C22×Q8⋊C9C2213yescomplemented
13C3×#585—38no—
14C3×#585C2×C318yes—
15C2×C3×2−1+4—31no—
16C2×C3×2−1+4C2×C313yes—
17C2×C3×H(5,𝔽2)—33no—
18C2×C3×H(5,𝔽2)C2×C311yescharacteristic
19C22×C3×#41—33no—
20C22×C3×#41—31no—
21C22×C3×#41C2×C313yes—
22C9×#41—48no—
23C2×Q8×C9—41no—
24C2×D4×C9—43no—
25C22×C4×C9—43no—
26#41⋊C9C2312yescomplemented
27#41⋊C9C2316yescomplemented
28C2×Q8⋊C9C2311yescharacteristic
29C2×Q8⋊C9C2316yescomplemented
30C2×#585C911yescharacteristic, complemented, Sylow
31C3×2−1+4—312no—
32C3×2−1+4—38no—
33C3×2−1+4—38no—
34C3×2−1+4C22×C3112yes—
35C3×H(5,𝔽2)—34no—
36C3×H(5,𝔽2)—324no—
37C3×H(5,𝔽2)—324no—
38C3×H(5,𝔽2)C22×C314yes—
39C2×C3×#41—324no—
40C2×C3×#41—36no—
41C2×C3×#41—324no—
42C2×C3×#41—38no—
43C2×C3×#41—38no—
44C2×C3×#41—31no—
45C2×C3×#41—33no—
46C2×C3×#41—36no—
47C2×C3×#41—33no—
48C2×C3×#41—33no—
49C2×C3×#41—33no—
50C2×C3×#41—312no—
51C2×C3×#41A411yescharacteristic
52C2×C3×#41C22×C311yescharacteristic
53C2×C3×#41C22×C313yes—
54C2×C3×#41C22×C3112yes—
55C22×C3×Q8—33no—
56C22×C3×Q8—31no—
57C22×C3×Q8C22×C313yes—
58C22×C3×D4—33no—
59C22×C3×D4—36no—
60C22×C3×D4—33no—
61C22×C3×D4—33no—
62C23×C3×C4—32no—
63C23×C3×C4—33no—
64C23×C9—43no—
65Q8×C9—44no—
66D4×C9—412no—
67C2×C4×C9—43no—
68C2×C4×C9—412no—
69C2×C4×C9—41no—
70Q8⋊C9C2411yescharacteristic
71#585—38no—
72#585C2×C918yescomplemented
73C2×2−1+4—31no—
74C2×2−1+4C2×C913yescomplemented
75C2×H(5,𝔽2)—33no—
76C2×H(5,𝔽2)C2×C911yescharacteristic, complemented
77C22×#41—33no—
78C22×#41—31no—
79C22×#41C2×C913yescomplemented
80C24×C3—32no—
81C24×C3—33no—
82C3×#41—312no—
83C3×#41—324no—
84C3×#41—348no—
85C3×#41—312no—
86C3×#41—34no—
87C3×#41—34no—
88C3×#41—312no—
89C3×#41—312no—
90C3×#41—324no—
91C3×#41—324no—
92C3×#41—32no—
93C3×#41—312no—
94C3×#41—36no—
95C3×#41—312no—
96C3×#41C2×A418yes—
97C3×#41C23×C312yes—
98C3×#41C23×C316yes—
99C2×C3×Q8—312no—
100C2×C3×Q8—312no—
101C2×C3×Q8—38no—
102C2×C3×Q8—33no—
103C2×C3×Q8—33no—
104C2×C3×Q8—36no—
105C2×C3×Q8C2×A411yescharacteristic
106C2×C3×Q8C23×C311yescharacteristic
107C2×C3×Q8C23×C316yes—
108C2×C3×D4—31no—
109C2×C3×D4—33no—
110C2×C3×D4—312no—
111C2×C3×D4—36no—
112C2×C3×D4—348no—
113C2×C3×D4—312no—
114C2×C3×D4—312no—
115C2×C3×D4—36no—
116C2×C3×D4—324no—
117C2×C3×D4—312no—
118C2×C3×D4—33no—
119C2×C3×D4C2×A413yes—
120C22×C3×C4—36no—
121C22×C3×C4—316no—
122C22×C3×C4—33no—
123C22×C3×C4—33no—
124C22×C3×C4—33no—
125C22×C3×C4—312no—
126C22×C3×C4—312no—
127C22×C3×C4—33no—
128C22×C3×C4—31no—
129C22×C3×C4C2×A413yes—
130C22×C9—41no—
131C22×C9—46no—
132C22×C9—86no—
133C4×C9—42no—
134C4×C9—46no—
1352−1+4—312no—
1362−1+4—38no—
1372−1+4—38no—
1382−1+4C22×C9112yescomplemented
139H(5,𝔽2)—34no—
140H(5,𝔽2)—324no—
141H(5,𝔽2)—324no—
142H(5,𝔽2)C22×C914yescomplemented
143C2×#41—324no—
144C2×#41—36no—
145C2×#41—324no—
146C2×#41—38no—
147C2×#41—38no—
148C2×#41—31no—
149C2×#41—33no—
150C2×#41—36no—
151C2×#41—33no—
152C2×#41—33no—
153C2×#41—33no—
154C2×#41—312no—
155C2×#41C22⋊C911yescharacteristic
156C2×#41C22×C911yescharacteristic
157C2×#41C22×C913yes—
158C2×#41C22×C9112yescomplemented
159C22×Q8—33no—
160C22×Q8—31no—
161C22×Q8C22×C913yes—
162C22×D4—33no—
163C22×D4—36no—
164C22×D4—33no—
165C22×D4—33no—
166C23×C4—32no—
167C23×C4—33no—
168C23×C3—38no—
169C23×C3—33no—
170C23×C3—31no—
171C23×C3—312no—
172C23×C3—126no—
173C23×C3—124no—
174C23×C3C22×A413yes—
175C3×Q8—36no—
176C3×Q8—31no—
177C3×Q8—36no—
178C3×Q8—312no—
179C3×Q8C22×A414yes—
180C3×Q8C24×C311yescharacteristic
181C3×D4—32no—
182C3×D4—36no—
183C3×D4—36no—
184C3×D4—32no—
185C3×D4—324no—
186C3×D4—324no—
187C3×D4—312no—
188C3×D4C22×A4112yes—
189C2×C3×C4—324no—
190C2×C3×C4—33no—
191C2×C3×C4—31no—
192C2×C3×C4—36no—
193C2×C3×C4—36no—
194C2×C3×C4—312no—
195C2×C3×C4—32no—
196C2×C3×C4—32no—
197C2×C3×C4—312no—
198C2×C3×C4—36no—
199C2×C3×C4—36no—
200C2×C3×C4C22×A413yes—
201C2×C3×C4C22×A4112yes—
202C2×C3×C4C22×A411yescharacteristic
203C2×C9—42no—
204C2×C9—41no—
205C2×C9—86no—
206C24—32no—
207C24—33no—
208#41—312no—
209#41—324no—
210#41—348no—
211#41—312no—
212#41—34no—
213#41—34no—
214#41—312no—
215#41—312no—
216#41—324no—
217#41—324no—
218#41—32no—
219#41—312no—
220#41—36no—
221#41—312no—
222#41C2×C22⋊C918yes—
223#41C23×C912yes—
224#41C23×C916yes—
225C2×Q8—312no—
226C2×Q8—312no—
227C2×Q8—38no—
228C2×Q8—33no—
229C2×Q8—33no—
230C2×Q8—36no—
231C2×Q8C2×C22⋊C911yescharacteristic
232C2×Q8C23×C911yescharacteristic
233C2×Q8C23×C916yes—
234C2×D4—31no—
235C2×D4—33no—
236C2×D4—312no—
237C2×D4—36no—
238C2×D4—348no—
239C2×D4—312no—
240C2×D4—312no—
241C2×D4—36no—
242C2×D4—324no—
243C2×D4—312no—
244C2×D4—33no—
245C2×D4C2×C22⋊C913yes—
246C22×C4—36no—
247C22×C4—316no—
248C22×C4—33no—
249C22×C4—31no—
250C22×C4—33no—
251C22×C4—33no—
252C22×C4—33no—
253C22×C4—312no—
254C22×C4—312no—
255C22×C4C2×C22⋊C913yes—
256C22×C3—26no—
257C22×C3—36no—
258C22×C3—32no—
259C22×C3—62no—
260C22×C3—66no—
261C22×C3—1212no—
262C22×C3—128no—
263C22×C3C23×A416yes—
264C22×C3C23×A411yescharacteristic
265C3×C4—36no—
266C3×C4—31no—
267C3×C4—31no—
268C3×C4C23×A412yes—
269C3×C4C23×A416yes—
270C9—41noSylow
271C23—38no—
272C23—33no—
273C23—31no—
274C23—312no—
275C23—126no—
276C23—124no—
277C23C22×C22⋊C913yes—
278Q8—36no—
279Q8—31no—
280Q8—36no—
281Q8—312no—
282Q8C22×C22⋊C914yes—
283Q8C24×C911yescharacteristic
284D4—32no—
285D4—36no—
286D4—36no—
287D4—32no—
288D4—324no—
289D4—324no—
290D4—312no—
291D4C22×C22⋊C9112yes—
292C2×C4—324no—
293C2×C4—31no—
294C2×C4—33no—
295C2×C4—36no—
296C2×C4—36no—
297C2×C4—32no—
298C2×C4—312no—
299C2×C4—32no—
300C2×C4—36no—
301C2×C4—36no—
302C2×C4—312no—
303C2×C4C22×C22⋊C911yescharacteristic
304C2×C4C22×C22⋊C913yes—
305C2×C4C22×C22⋊C9112yes—
306C2×C3—26no—
307C2×C3—62no—
308C2×C3—66no—
309C2×C3#594512yes—
310C2×C3C24×A411yescharacteristic
311C22—26no—
312C22—36no—
313C22—32no—
314C22—62no—
315C22—66no—
316C22—1212no—
317C22—128no—
318C22C23×C22⋊C916yes—
319C22C23×C22⋊C911yescharacteristic
320C4—31no—
321C4—36no—
322C4—31no—
323C4C23×C22⋊C912yes—
324C4C23×C22⋊C916yes—
325C3C2×#594511yescharacteristic
326C2—26no—
327C2—62no—
328C2—66no—
329C2#1059312012yesdirect product factor
330C2C24×C22⋊C911yescharacteristic
subgroupG/H
centerC2×C3×C4C22×A4
commutator, hypocenterQ8C24×C9
FrattiniC2×C3C24×A4
Fitting, prime radicalC2×C3×#585C3
socleC22×C3C23×A4
cosocleC3×Q8C24×C3
hypercenterC2×C3×#41A4
LCSG ▷ Q8
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×#41

Complements

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

NH ≅ G/Ntype
1. #10593120C2direct (N × H)
2. C2×2−1+4⋊C9C2semidirect
3. C2×#63700C2semidirect
4. C22×#41⋊C9C2semidirect
7. 2−1+4⋊C9C22semidirect
8. #63700C22semidirect
9. C2×#41⋊C9C22semidirect
10. C2×#41⋊C9C22semidirect
11. C2×#41⋊C9C22semidirect
12. C22×Q8⋊C9C22semidirect
26. #41⋊C9C23semidirect
27. #41⋊C9C23semidirect
29. C2×Q8⋊C9C23semidirect
30. C2×#585C9semidirect
72. #585C2×C9semidirect
74. C2×2−1+4C2×C9semidirect
76. C2×H(5,𝔽2)C2×C9semidirect
79. C22×#41C2×C9semidirect
138. 2−1+4C22×C9semidirect
142. H(5,𝔽2)C22×C9semidirect
158. C2×#41C22×C9semidirect
329. C2#10593120direct (N × H)

Maximal subgroups

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

subgroupindex
#105931202
C2×2−1+4⋊C92
C2×#637002
C22×#41⋊C92
C2×C3×#5853
C2×C9×#414