Finite Group Databasebeta

← #11878401

Subgroups — #11878401

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×#467C211yesmaximal, characteristic, complemented
3#10592885C212yesmaximal, complemented
4#10592815C211yesmaximal, characteristic, complemented
5#10592809C211yesmaximal, characteristic
6#10592751C212yesmaximal, complemented
7#10592587C212yesmaximal, complemented
8#10592513C212yesmaximal, complemented
9#10592508C212yesmaximal, complemented
10#80767—34nomaximal
11C2×Q8×C3⋊D3C2212yes—
12C2×#3828C2211yescharacteristic
13C2×C32×Q16C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C32×C22⋊Q8C2212yes—
16#64155C2212yes—
17C2×#3756C2212yes—
18#64133C2212yes—
19C2×#3748C2211yescharacteristic
20C2×#3746C2211yescharacteristic
21#64106C2212yes—
22#64103—22no—
23#64101C2212yes—
24#64097—22no—
25#64094—22no—
26#64092—22no—
27C32×#107C2211yescharacteristic
28C32×#103C2212yes—
29#63662C2212yes—
30#63647C2212yes—
31#63647C2212yes—
32#63645C2211yescharacteristic
33#63643C2212yes—
34#63637C2212yes—
35#63635C2212yes—
36#5628—38no—
37C3×#467D314yescomplemented
38#5186—38no—
39#5116—34no—
40#5110—34no—
41#5052—38no—
42#4888—38no—
43#4814—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—
59C2×C32×C8—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—
75#3748—41no—
76C2×C3⋊(C3⋊C8)C2312yes—
77#3746—41no—
78#3202—91noSylow
79C2×D3×Q8—38no—
80C2×#235—34no—
81C2×C3×Q16C2×D314yes—
82C22×C3×C8C2×D314yes—
83C3×C22⋊Q8C2×D318yes—
84#946—38no—
85C2×#216—38no—
86#924—38no—
87C2×#208—34no—
88C2×Dic12—34no—
89#897—38no—
90#894—68no—
91#892—38no—
92#888—68no—
93#885—68no—
94#883—68no—
95C3×#107C2×D314yes—
96C3×#103C2×D318yes—
97#835—38no—
98(C2×D3)⋊C8—38no—
99(C2×D3)⋊C8—38no—
100#818—34no—
101#816—38no—
102#810—38no—
103#808—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—92no—
133#467—91no—
134#467C3⋊D311yescharacteristic, complemented
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—
152C2×C3×C8—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—
168#208—124no—
169C2×C3⋊C8—38no—
170Dic12—124no—
171C22×C32—21no—
172C22×C32—21no—
173C22×C32—21no—
174C22×C32C22×D411yescharacteristic
175C2×C3⋊D3—22no—
176C2×C3⋊D3—22no—
177C2×C3⋊D3—22no—
178C32×C4—21no—
179C32×C4—42no—
180C32×C4—42no—
181C32×C4H(5,𝔽2)11yescharacteristic
182C32×C4H(5,𝔽2)11yescharacteristic
183C3⋊Dic3—22no—
184C3⋊Dic3—42no—
185C3⋊Dic3—42no—
186C2×#41—91no—
187C22×Q8—92no—
188C2×Q16—92no—
189C2×Q16—91no—
190C2×Q16C2×C3⋊D311yescharacteristic
191C2×M16—91no—
192C22×C8C2×C3⋊D311yescharacteristic
193C4⋊Q8—182no—
194#124—182no—
195#123—182no—
196#123—182no—
197C22⋊Q8—92no—
198C22⋊Q8—92no—
199C22⋊Q8—92no—
200C22⋊Q8C2×C3⋊D312yes—
201#117—92no—
202#107—91no—
203#107C2×C3⋊D311yescharacteristic
204#106—92no—
205#103—92no—
206#103—92no—
207#103—92no—
208#103C2×C3⋊D312yes—
209C22⋊C8—92no—
210C22⋊C8—92no—
211C23×C3D3×D414yes—
212C22×D3—38no—
213C3×Q8—28no—
214C3×Q8—28no—
215C2×C3×C4—24no—
216C2×C3×C4—24no—
217C2×C3×C4—28no—
218C2×C3×C4—28no—
219C2×C3×C4D3×D414yes—
220C2×C3×C4C23×D314yes—
221#67—128no—
222C2×Dic3—38no—
223C2×Dic3—68no—
224C2×Dic3—68no—
225D12—124no—
226C4×D3—68no—
227C4×D3—68no—
228C4×D3—1216no—
229Dic6—68no—
230Dic6—68no—
231Dic6—124no—
232Dic6—1216no—
233C3×C8—24no—
234C3×C8—24no—
235C3⋊C8—68no—
236C2×C32—41no—
237C2×C32#53411yescharacteristic
238C2×C32#57811yescharacteristic
239C2×C32#57811yescharacteristic
240C3⋊D3—42no—
241#41—361no—
242#41—361no—
243C2×Q8—91no—
244C2×Q8—92no—
245C2×Q8—182no—
246C2×Q8—362no—
247C2×Q8—362no—
248C2×Q8C22×C3⋊D312yes—
249C2×D4—92no—
250C2×D4—91no—
251C22×C4—92no—
252C22×C4—182no—
253C22×C4C22×C3⋊D311yescharacteristic
254Q16—41no—
255Q16—361no—
256Q16—362no—
257M16—361no—
258C2×C8—41no—
259C2×C8—92no—
260C2×C8C22×C3⋊D311yescharacteristic
261C2×C8C22×C3⋊D311yescharacteristic
262C4⋊C4—22no—
263C4⋊C4—92no—
264C4⋊C4—182no—
265C4⋊C4—182no—
266C4⋊C4—182no—
267C4⋊C4C22×C3⋊D312yes—
268C22⋊C4—22no—
269C22⋊C4—182no—
270C22⋊C4—182no—
271C22⋊C4—182no—
272C22⋊C4—182no—
273C42—182no—
274C22×C3—24no—
275C22×C3—24no—
276C22×C3—24no—
277C22×C3C2×D3×D414yes—
278C2×D3—68no—
279C2×D3—68no—
280C2×D3—68no—
281C3×C4—24no—
282C3×C4—48no—
283C3×C4—48no—
284C3×C4#100414yes—
285C3×C4#100914yes—
286Dic3—68no—
287Dic3—128no—
288Dic3—128no—
289C32#320211yescharacteristic, complemented, Sylow
290C23—92no—
291C23D4×C3⋊D311yescharacteristic
292Q8—22no—
293Q8—22no—
294Q8—182no—
295Q8—182no—
296Q8—361no—
297Q8—364no—
298D4—361no—
299D4—362no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—92no—
305C2×C4—182no—
306C2×C4—182no—
307C2×C4—182no—
308C2×C4—182no—
309C2×C4—364no—
310C2×C4D4×C3⋊D311yescharacteristic
311C2×C4C23×C3⋊D311yescharacteristic
312C8—21no—
313C8—21no—
314C8—182no—
315C2×C3—44no—
316C2×C3#560514yes—
317C2×C3#576614yes—
318C2×C3#577114yes—
319D3—128no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—182no—
324C22—182no—
325C22—182no—
326C22C2×D4×C3⋊D311yescharacteristic
327C4—21no—
328C4—42no—
329C4—42no—
330C4—182no—
331C4—362no—
332C4—362no—
333C4#6436111yescharacteristic
334C4#6436611yescharacteristic
335C3#8076714yescomplemented
336C2—41no—
337C2—362no—
338C2#1059607611yescharacteristic
339C2#1059623711yescharacteristic
340C2#1059624211yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#467C2
socleC22×C32C22×D4
prime radicalC2×#3828C22
hypercenter#467C3⋊D3
hypocenterC32#3202
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. C32×#467C2semidirect
3. #10592885C2semidirect
4. #10592815C2semidirect
6. #10592751C2semidirect
7. #10592587C2semidirect
8. #10592513C2semidirect
9. #10592508C2semidirect
37. C3×#467D3semidirect
134. #467C3⋊D3semidirect
289. C32#3202semidirect
335. C3#80767semidirect

Maximal subgroups

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

subgroupindex
#105960992
C32×#4672
#105928852
#105928152
#105928092
#105927512
#105925872
#105925132
#105925082
#807673