Finite Group Databasebeta

← #11805909

Subgroups — #11805909

Order 1152.

778 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic
2#10593837C212yesmaximal
3#10593758C214yesmaximal
4C4⋊C4×#157C212yesmaximal
5#10593736C212yesmaximal
6#10593735C211yesmaximal, characteristic
7C4×C4⋊#157C211yesmaximal, characteristic
8C4×C4⋊#157C212yesmaximal
9C2×Q8×C3⋊D3C2211yescharacteristic
10C2×C4⋊#157C2212yes—
11C2×C4⋊#157C2212yes—
12C2×C4⋊#157C2211yescharacteristic
13C2×C4⋊#157C2212yes—
14C2×C4⋊#157C2211yescharacteristic
15C2×C4×#157C2212yes—
16C2×C4×#157C2214yes—
17C32×C4×Q8C411yescharacteristic, complemented
18Q8×C3⋊Dic3C411yescharacteristic, complemented
19C4⋊C4×C3⋊D3C2211yescharacteristic
20C4⋊C4×C3⋊D3C2212yes—
21#64096C411yescharacteristic, complemented
22#64096C412yescomplemented
23C42×C3⋊D3C2211yescharacteristic
24C42×C3⋊D3C2212yes—
25C4×#634C411yescharacteristic, complemented
26C4×#634C412yescomplemented
27#63781C2214yes—
28#63781C2214yes—
29#63781C2212yes—
30#63781C2214yes—
31C4×D3×Q8—62no—
32C22×#157C2314yes—
33C22×#157C2312yes—
34C22×#157C2312yes—
35C2×C32×Q8C2×C411yescharacteristic
36Q8×C3⋊D3—22no—
37Q8×C3⋊D3—22no—
38C2×C4×C3⋊D3C2312yes—
39C2×C4×C3⋊D3C2311yescharacteristic
40C2×C4×C3⋊D3C2312yes—
41C2×C4×C3⋊D3C2311yescharacteristic
42C2×C4×C3⋊D3C2311yescharacteristic
43C2×#634C2×C411yescharacteristic
44C2×#634C2×C412yes—
45C4⋊#157—24no—
46C4⋊#157—24no—
47C4⋊#157—22no—
48C4⋊#157—42no—
49C4⋊#157Q814yescomplemented
50C4×#157—24no—
51C4×#157—44no—
52C32×C4⋊C4C2×C412yes—
53C32×C4⋊C4C2×C411yescharacteristic
54C32×C42C2×C412yes—
55C32×C42C2×C411yescharacteristic
56C4⋊(C3⋊Dic3)C2×C412yes—
57C4⋊(C3⋊Dic3)C2×C411yescharacteristic
58#3750C2×C412yes—
59#3750C2×C412yes—
60#3750C2×C412yes—
61C4×C3⋊Dic3C2×C412yes—
62C4×C3⋊Dic3C2×C411yescharacteristic
63C4×C3⋊Dic3C2×C412yes—
64C4×C3⋊Dic3C2×C411yescharacteristic
65C4×C3⋊Dic3C2×C412yes—
66C4×C3⋊Dic3C2×C411yescharacteristic
67#2355—91nomaximal, Sylow
68C2×D3×Q8—62no—
69C3×C4×Q8—22no—
70Q8×Dic3—62no—
71D3×C4⋊C4—62no—
72D3×C4⋊C4—64no—
73#887—64no—
74#887—62no—
75C42×D3—64no—
76C42×D3—62no—
77C4×Dic6—64no—
78C4×Dic6—62no—
79C22×C3⋊D3C2411yescharacteristic
80C2×#157—22no—
81C2×#157—22no—
82C2×#157—22no—
83C2×#157—22no—
84C2×#157—24no—
85C2×#157—24no—
86C2×#157—24no—
87C2×#157—22no—
88C2×#157C2×Q814yes—
89C32×Q8—22no—
90C2×C32×C4C22×C412yes—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C22×C412yes—
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C22×C411yescharacteristic
95C2×C3⋊Dic3C22×C412yes—
96C2×C3⋊Dic3C22×C411yescharacteristic
97C2×C3⋊Dic3C22×C412yes—
98C2×C3⋊Dic3C22×C411yescharacteristic
99C2×C3⋊Dic3C22×C411yescharacteristic
100C4×C3⋊D3—22no—
101C4×C3⋊D3—22no—
102C4×C3⋊D3—22no—
103C4×C3⋊D3—21no—
104C4×C3⋊D3—22no—
105C4×C3⋊D3—21no—
106C4×C3⋊D3C2×Q812yes—
107C4×C3⋊D3#4112yes—
108C4×C3⋊D3#4112yes—
109C4×C3⋊D3#4112yes—
110#634—22no—
111#634—24no—
112C2×C4×Q8—91no—
113#391—92no—
114#387—94no—
115#384—91no—
116#382—92no—
117C4×C4⋊C4—91no—
118C4×C4⋊C4—92no—
119C4×C4⋊C4—92no—
120C2×C3×Q8—22no—
121D3×Q8—68no—
122D3×Q8—68no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—64no—
126C2×C4×D3—64no—
127C2×C4×D3—62no—
128C2×Dic6—64no—
129C2×Dic6—62no—
130C3×C4⋊C4—24no—
131C3×C4⋊C4—22no—
132C3×C42—24no—
133C3×C42—22no—
134C4⋊Dic3—64no—
135C4⋊Dic3—62no—
136Dic3⋊C4—64no—
137Dic3⋊C4—64no—
138Dic3⋊C4—64no—
139C4×Dic3—62no—
140C4×Dic3—64no—
141C4×Dic3—62no—
142C4×Dic3—64no—
143C4×Dic3—64no—
144C4×Dic3—62no—
145C22×C32C23×C411yescharacteristic
146C2×C3⋊D3C22×Q811yescharacteristic
147C2×C3⋊D3C2×#4111yescharacteristic
148C2×C3⋊D3C2×#4111yescharacteristic
149C2×C3⋊D3C2×#4111yescharacteristic
150C2×C3⋊D3H(5,𝔽2)11yescharacteristic
151C2×C3⋊D32−1+411yescharacteristic
152#157—24no—
153#157—42no—
154#157—44no—
155C32×C4—22no—
156C32×C4—22no—
157C32×C4—21no—
158C32×C4#11712yes—
159C32×C4C4×Q812yes—
160C3⋊Dic3—22no—
161C3⋊Dic3—22no—
162C3⋊Dic3—21no—
163C3⋊Dic3#11712yes—
164C3⋊Dic3C4×Q812yes—
165C22×Q8—91no—
166C4×Q8—91no—
167C4×Q8—92no—
168C4×Q8—91no—
169C4×Q8—92no—
170C4×Q8—91no—
171C4×Q8#15711yescharacteristic, complemented
172C2×C4⋊C4—91no—
173C2×C4⋊C4—91no—
174C2×C4⋊C4—92no—
175C2×C4⋊C4—91no—
176C2×C4⋊C4—92no—
177C2×C4⋊C4—92no—
178C2×C4⋊C4—92no—
179C2×C42—92no—
180C2×C42—91no—
181C2×C42—92no—
182C2×C42—94no—
183#95—94no—
184#95—92no—
185#95—94no—
186#95—94no—
187C22×D3—62no—
188C3×Q8—28no—
189C2×C3×C4—22no—
190C2×C3×C4—24no—
191C2×C3×C4—22no—
192C2×C3×C4—24no—
193C2×C3×C4—22no—
194C2×Dic3—62no—
195C2×Dic3—62no—
196C2×Dic3—64no—
197C2×Dic3—64no—
198C2×Dic3—62no—
199C4×D3—64no—
200C4×D3—64no—
201C4×D3—64no—
202C4×D3—64no—
203C4×D3—68no—
204C4×D3—68no—
205C4×D3—124no—
206C4×D3—122no—
207C4×D3—124no—
208C4×D3—122no—
209Dic6—616no—
210Dic6—68no—
211C2×C32C2×#11711yescharacteristic
212C2×C32C2×C4×Q811yescharacteristic
213C2×C32#52011yescharacteristic
214C3⋊D3#55411yescharacteristic
215C3⋊D3#55611yescharacteristic
216C3⋊D3#55711yescharacteristic
217C3⋊D3#55911yescharacteristic
218C2×Q8—92no—
219C2×Q8—91no—
220C2×Q8—182no—
221C2×Q8—182no—
222C2×Q8C2×#15711yescharacteristic
223C22×C4—91no—
224C22×C4—91no—
225C22×C4—92no—
226C22×C4—92no—
227C22×C4—92no—
228C22×C4—91no—
229C22×C4—92no—
230C22×C4—94no—
231C4⋊C4—94no—
232C4⋊C4—92no—
233C4⋊C4—92no—
234C4⋊C4—92no—
235C4⋊C4—92no—
236C4⋊C4—91no—
237C4⋊C4—184no—
238C4⋊C4—182no—
239C4⋊C4—184no—
240C4⋊C4—362no—
241C4⋊C4C2×#15712yes—
242C4⋊C4C2×#15711yescharacteristic
243C42—91no—
244C42—92no—
245C42—91no—
246C42—92no—
247C42—91no—
248C42—92no—
249C42—184no—
250C42—364no—
251C42C2×#15712yes—
252C42C2×#15711yescharacteristic
253C22×C3—22no—
254C2×D3—62no—
255C2×D3—62no—
256C2×D3—62no—
257C2×D3—62no—
258C2×D3—62no—
259C2×D3—62no—
260C3×C4—28no—
261C3×C4—24no—
262C3×C4—24no—
263C3×C4—44no—
264C3×C4—42no—
265Dic3—64no—
266Dic3—64no—
267Dic3—68no—
268Dic3—124no—
269Dic3—122no—
270C32#235511yescharacteristic, complemented, Sylow
271C23—91no—
272Q8—22no—
273Q8—184no—
274Q8—182no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—92no—
278C2×C4—92no—
279C2×C4—92no—
280C2×C4—92no—
281C2×C4—94no—
282C2×C4—92no—
283C2×C4—91no—
284C2×C4—92no—
285C2×C4—182no—
286C2×C4—181no—
287C2×C4—182no—
288C2×C4—182no—
289C2×C4—182no—
290C2×C4—181no—
291C2×C4—182no—
292C2×C4—182no—
293C2×C4—182no—
294C2×C4—184no—
295C2×C4—184no—
296C2×C4—182no—
297C2×C4—184no—
298C2×C4—182no—
299C2×C4C22×#15712yes—
300C2×C4C22×#15711yescharacteristic
301C2×C4C22×#15712yes—
302C2×C4C22×#15711yescharacteristic
303C2×C4C22×#15711yescharacteristic
304C2×C3—22no—
305C2×C3—22no—
306C2×C3—22no—
307D3—62no—
308D3—62no—
309D3—62no—
310D3—62no—
311C22—91no—
312C22—91no—
313C22—91no—
314C22—91no—
315C22—91no—
316C22—91no—
317C22C23×#15711yescharacteristic
318C4—22no—
319C4—22no—
320C4—21no—
321C4—92no—
322C4—92no—
323C4—184no—
324C4—182no—
325C4—182no—
326C4—181no—
327C4—364no—
328C4—362no—
329C4#6428612yes—
330C4Q8×#15712yes—
331C3—22no—
332C2—91no—
333C2—91no—
334C2—91no—
335C2—91no—
336C2C2×#6428611yescharacteristic
337C2C2×Q8×#15711yescharacteristic
338C2#1059665011yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C4×Q8C4
prime radical, cosocleC22×C3⋊D3C24
hypercenterC4×Q8#157
hypocenterC32#2355
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
17. C32×C4×Q8C4semidirect
18. Q8×C3⋊Dic3C4semidirect
21. #64096C4semidirect
22. #64096C4semidirect
25. C4×#634C4semidirect
26. C4×#634C4semidirect
49. C4⋊#157Q8semidirect
171. C4×Q8#157semidirect
270. C32#2355semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
#105938372
#105937582
C4⋊C4×#1572
#105937362
#105937352
C4×C4⋊#1572
#23559