Finite Group Databasebeta

← #11878407

Subgroups — #11878407

Order 1152.

1134 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 209 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#10596099C212yesmaximal
2C32×#470C211yesmaximal, characteristic, complemented
3#10592885C212yesmaximal, complemented
4#10592836C211yesmaximal, characteristic, complemented
5#10592828C211yesmaximal, characteristic
6#10592750C212yesmaximal, complemented
7#10592567C212yesmaximal, complemented
8#10592514C212yesmaximal, complemented
9#10592508C212yesmaximal, complemented
10#80912—34nomaximal
11C2×Q8×C3⋊D3C2212yes—
12C2×#3828C2211yescharacteristic
13C2×C32×Q16C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C32×C22⋊Q8C2212yes—
16#64155C2212yes—
17C2×#3756C2212yes—
18#64133C2212yes—
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C2×#3746C2211yescharacteristic
21#64106C2212yes—
22#64103—22no—
23#64101C2212yes—
24#64097—22no—
25#64094—22no—
26#64092—22no—
27C32×#106C2211yescharacteristic
28C32×#103C2212yes—
29#63662C2212yes—
30#63647C2212yes—
31#63647C2212yes—
32#63644C2211yescharacteristic
33#63643C2212yes—
34#63637C2212yes—
35#63634C2212yes—
36#5628—38no—
37C3×#470D314yescomplemented
38#5186—38no—
39#5137—34no—
40#5129—34no—
41#5051—38no—
42#4868—38no—
43#4815—38no—
44#4809—38no—
45C2×C32×Q8C2312yes—
46C22×C32×C4C2311yescharacteristic
47C2×#638D412yes—
48Q8×C3⋊D3—42no—
49Q8×C3⋊D3—42no—
50#3828—41no—
51#3828—41no—
52C2×C4⋊(C3⋊D3)D411yescharacteristic
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3C2312yes—
55C2×#634—22no—
56C2×#634D411yescharacteristic
57C2×#634C2312yes—
58C32×Q16—41no—
59C32×M16—41no—
60C2×C32×C8C2311yescharacteristic
61C2×C32×C8C2311yescharacteristic
62C32×C4⋊C4—22no—
63C32×C4⋊C4C2312yes—
64C32×C22⋊C4—22no—
65#3757—22no—
66#3756—42no—
67#3752—22no—
68#3752—22no—
69#3752—22no—
70C4⋊(C3⋊Dic3)—22no—
71C4⋊(C3⋊Dic3)C2312yes—
72#3750—22no—
73#3750—22no—
74C4×C3⋊Dic3—22no—
75C2×C3⋊(C3⋊C8)—41no—
76C2×C3⋊(C3⋊C8)C2312yes—
77#3746—41no—
78#3202—91noSylow
79C2×D3×Q8—38no—
80C2×#235—34no—
81C2×C3×Q16C2×D314yes—
82C2×C3×M16C2×D314yes—
83C3×C22⋊Q8C2×D318yes—
84#946—38no—
85C2×#216—38no—
86#924—38no—
87C22×C3⋊C8—34no—
88C2×Dic12—34no—
89#897—38no—
90#894—68no—
91#892—38no—
92#888—68no—
93#885—68no—
94#883—68no—
95C3×#106C2×D314yes—
96C3×#103C2×D318yes—
97#835—38no—
98(C2×D3)⋊C8—38no—
99(C2×D3)⋊C8—38no—
100#817—34no—
101#816—38no—
102#810—38no—
103#807—38no—
104C23×C32C2×D411yescharacteristic
105C22×C3⋊D3C2×D412yes—
106C32×Q8—22no—
107C32×Q8—22no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2411yescharacteristic
114#638—42no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3C2×D412yes—
118C4⋊(C3⋊D3)—41no—
119C4×C3⋊D3—22no—
120C4×C3⋊D3—22no—
121C4×C3⋊D3—44no—
122#634—22no—
123#634—22no—
124#634—41no—
125#634—44no—
126C32×C8—21no—
127C32×C8—21no—
128C3⋊(C3⋊C8)—22no—
129#536—92no—
130#485—92no—
131#485—92no—
132#470—91no—
133#470C3⋊D311yescharacteristic, complemented
134#467—92no—
135#451—92no—
136#451—92no—
137#408—91no—
138C2×C3×Q8C22×D318yes—
139C22×C3×C4C22×D314yes—
140C2×#67—38no—
141D3×Q8—128no—
142D3×Q8—128no—
143#235—124no—
144#235—124no—
145C2×D12—34no—
146C2×C4×D3—38no—
147C2×C4×D3—68no—
148C2×Dic6—38no—
149C2×Dic6—34no—
150C2×Dic6—68no—
151C3×Q16—44no—
152C3×M16—44no—
153C2×C3×C8C22×D314yes—
154C2×C3×C8C22×D314yes—
155C3×C4⋊C4—28no—
156C3×C4⋊C4C22×D318yes—
157C3×C22⋊C4—28no—
158#217—68no—
159#216—128no—
160(C2×D3)⋊C4—68no—
161(C2×D3)⋊C4—68no—
162(C2×D3)⋊C4—68no—
163C4⋊Dic3—38no—
164C4⋊Dic3—68no—
165Dic3⋊C4—68no—
166Dic3⋊C4—68no—
167C4×Dic3—68no—
168C2×C3⋊C8—38no—
169C2×C3⋊C8—124no—
170Dic12—124no—
171C22×C32—21no—
172C22×C32—22no—
173C22×C32C22×D411yescharacteristic
174C2×C3⋊D3—22no—
175C2×C3⋊D3—24no—
176C32×C4—21no—
177C32×C4—42no—
178C32×C4—42no—
179C32×C4H(5,𝔽2)11yescharacteristic
180C32×C4H(5,𝔽2)11yescharacteristic
181C3⋊Dic3—22no—
182C3⋊Dic3—42no—
183C3⋊Dic3—42no—
184C2×#41—91no—
185C22×Q8—92no—
186C2×Q16—92no—
187C2×Q16—91no—
188C2×Q16C2×C3⋊D311yescharacteristic
189C2×M16C2×C3⋊D311yescharacteristic
190C22×C8—91no—
191C4⋊Q8—182no—
192#124—182no—
193#123—182no—
194#123—182no—
195C22⋊Q8—92no—
196C22⋊Q8—92no—
197C22⋊Q8—92no—
198C22⋊Q8C2×C3⋊D312yes—
199#117—92no—
200#107—92no—
201#106—91no—
202#106C2×C3⋊D311yescharacteristic
203#103—92no—
204#103—92no—
205#103—92no—
206#103C2×C3⋊D312yes—
207C22⋊C8—92no—
208C22⋊C8—92no—
209C23×C3D3×D414yes—
210C22×D3—38no—
211C3×Q8—28no—
212C3×Q8—28no—
213C2×C3×C4—24no—
214C2×C3×C4—24no—
215C2×C3×C4—28no—
216C2×C3×C4—28no—
217C2×C3×C4D3×D414yes—
218C2×C3×C4C23×D314yes—
219#67—128no—
220C2×Dic3—38no—
221C2×Dic3—68no—
222C2×Dic3—68no—
223D12—124no—
224C4×D3—68no—
225C4×D3—68no—
226C4×D3—1216no—
227Dic6—68no—
228Dic6—68no—
229Dic6—124no—
230Dic6—1216no—
231C3×C8—24no—
232C3×C8—24no—
233C3⋊C8—68no—
234C2×C32—41no—
235C2×C32#53411yescharacteristic
236C2×C32#57812yes—
237C3⋊D3—42no—
238#41—361no—
239#41—361no—
240C2×Q8—91no—
241C2×Q8—92no—
242C2×Q8—182no—
243C2×Q8—362no—
244C2×Q8—362no—
245C2×Q8C22×C3⋊D312yes—
246C2×D4—92no—
247C2×D4—91no—
248C22×C4—92no—
249C22×C4—182no—
250C22×C4C22×C3⋊D311yescharacteristic
251Q16—41no—
252Q16—361no—
253Q16—362no—
254M16—41no—
255C2×C8—92no—
256C2×C8—361no—
257C2×C8C22×C3⋊D311yescharacteristic
258C2×C8C22×C3⋊D311yescharacteristic
259C4⋊C4—22no—
260C4⋊C4—92no—
261C4⋊C4—182no—
262C4⋊C4—182no—
263C4⋊C4—182no—
264C4⋊C4C22×C3⋊D312yes—
265C22⋊C4—22no—
266C22⋊C4—182no—
267C22⋊C4—182no—
268C22⋊C4—182no—
269C22⋊C4—182no—
270C42—182no—
271C22×C3—28no—
272C22×C3—24no—
273C22×C3C2×D3×D414yes—
274C2×D3—616no—
275C2×D3—68no—
276C3×C4—24no—
277C3×C4—48no—
278C3×C4—48no—
279C3×C4#100414yes—
280C3×C4#100914yes—
281Dic3—68no—
282Dic3—128no—
283Dic3—128no—
284C32#320211yescharacteristic, complemented, Sylow
285C23—92no—
286C23D4×C3⋊D311yescharacteristic
287Q8—22no—
288Q8—22no—
289Q8—182no—
290Q8—182no—
291Q8—361no—
292Q8—364no—
293D4—361no—
294D4—362no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—92no—
300C2×C4—182no—
301C2×C4—182no—
302C2×C4—182no—
303C2×C4—182no—
304C2×C4—364no—
305C2×C4D4×C3⋊D311yescharacteristic
306C2×C4C23×C3⋊D311yescharacteristic
307C8—21no—
308C8—21no—
309C8—182no—
310C2×C3—44no—
311C2×C3#560514yes—
312C2×C3#577918yes—
313D3—128no—
314C22—22no—
315C22—21no—
316C22—184no—
317C22—182no—
318C22C2×D4×C3⋊D311yescharacteristic
319C4—21no—
320C4—42no—
321C4—42no—
322C4—182no—
323C4—362no—
324C4—362no—
325C4#6436111yescharacteristic
326C4#6436611yescharacteristic
327C3#8091214yescomplemented
328C2—41no—
329C2—362no—
330C2#1059607611yescharacteristic
331C2#1059625012yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#470C2
socleC22×C32C22×D4
prime radicalC2×#3828C22
hypercenter#470C3⋊D3
hypocenterC32#3202
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. C32×#470C2semidirect
3. #10592885C2semidirect
4. #10592836C2semidirect
6. #10592750C2semidirect
7. #10592567C2semidirect
8. #10592514C2semidirect
9. #10592508C2semidirect
37. C3×#470D3semidirect
133. #470C3⋊D3semidirect
284. C32#3202semidirect
327. C3#80912semidirect

Maximal subgroups

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

subgroupindex
#105960992
C32×#4702
#105928852
#105928362
#105928282
#105927502
#105925672
#105925142
#105925082
#809123