Finite Group Databasebeta

← #11859092

Subgroups — #11859092

Order 1152.

1176 conjugacy classes of subgroups.

The subgroup lattice has 327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic
2C32×#423C211yesmaximal, characteristic, complemented
3#10592828C212yesmaximal
4#10592821C212yesmaximal, complemented
5C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
6#10592539C214yesmaximal, complemented
7#10592534C212yesmaximal, complemented
8#10592532C212yesmaximal, complemented
9#79040—34nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2212yes—
12C2×C32×C42C2211yescharacteristic
13C4×#638C412yes—
14C4×#638C412yes—
15#64135C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2212yes—
17C4×C4⋊(C3⋊D3)C411yescharacteristic
18C4×C4⋊(C3⋊D3)C411yescharacteristic
19#64081C2212yes—
20C42×C3⋊D3C2212yes—
21C4×#634C411yescharacteristic
22C4×#634C411yescharacteristic
23C32×C4⋊C8C2212yes—
24C32×C4⋊C8C2212yes—
25#63647C2214yes—
26#63647C2214yes—
27#63642C2214yes—
28C8×C3⋊Dic3C2214yes—
29C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
30C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
31C4⋊(C3⋊(C3⋊C8))C2212yes—
32C4×#235—34no—
33C3×#423D314yescomplemented
34#5129—38no—
35#5122—38no—
36C2×C4⋊(C3⋊C8)—34no—
37#4840—316no—
38#4835—38no—
39#4833—38no—
40C22×C32×C4C2×C411yescharacteristic
41C22×C32×C4C2×C411yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C2×#638C2×C412yes—
44#3828—22no—
45#3828—22no—
46C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
47C2×C4×C3⋊D3C2×C412yes—
48C2×C4×C3⋊D3C2×C412yes—
49C2×C4×C3⋊D3C2312yes—
50C2×#634C2×C411yescharacteristic
51C32×M16—24no—
52C2×C32×C8C2314yes—
53C32×C42C2×C411yescharacteristic
54C32×C42C2×C411yescharacteristic
55C32×C42C2311yescharacteristic
56C32×C42C2311yescharacteristic
57#3757C2×C412yes—
58#3752C2×C412yes—
59#3752C2×C412yes—
60C4⋊(C3⋊Dic3)C2×C411yescharacteristic
61C4⋊(C3⋊Dic3)C2×C411yescharacteristic
62#3750C2×C412yes—
63#3750C2×C412yes—
64C4×C3⋊Dic3C2×C412yes—
65C4×C3⋊Dic3C2×C412yes—
66C4×C3⋊Dic3C2312yes—
67C2×C3⋊(C3⋊C8)—24no—
68C2×C3⋊(C3⋊C8)C2312yes—
69C2×C3⋊(C3⋊C8)C2312yes—
70#2925—91noSylow
71C2×#235—34no—
72C2×C3×M16C2×D318yes—
73C2×C3×C42C2×D314yes—
74C4×#67—38no—
75C4×#67—38no—
76#926—34no—
77C22×C3⋊C8—38no—
78C4×D12—34no—
79C4×D12—34no—
80#872—38no—
81C42×D3—38no—
82C4×Dic6—34no—
83C4×Dic6—34no—
84C3×C4⋊C8C2×D318yes—
85C3×C4⋊C8C2×D318yes—
86(C2×D3)⋊C8—316no—
87(C2×D3)⋊C8—316no—
88#815—316no—
89C8×Dic3—316no—
90C4⋊(C3⋊C8)—34no—
91C4⋊(C3⋊C8)—34no—
92C4⋊(C3⋊C8)—38no—
93C23×C32C22×C411yescharacteristic
94C22×C3⋊D3C22×C412yes—
95C2×C32×C4—22no—
96C2×C32×C4—41no—
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C22×C411yescharacteristic
102C2×C32×C4#4112yes—
103C2×C32×C4#4112yes—
104C2×C32×C4C2411yescharacteristic
105#638—24no—
106C2×C3⋊Dic3C22×C412yes—
107C2×C3⋊Dic3C22×C412yes—
108C2×C3⋊Dic3C22×C412yes—
109C4⋊(C3⋊D3)—22no—
110C4×C3⋊D3—24no—
111C4×C3⋊D3—22no—
112C4×C3⋊D3—22no—
113C4×C3⋊D3—42no—
114#634—22no—
115C32×C8—24no—
116C3⋊(C3⋊C8)—22no—
117C3⋊(C3⋊C8)—22no—
118C4×#41—91no—
119#433—94no—
120#432—92no—
121#431—92no—
122#423C3⋊D311yescharacteristic, complemented
123C2×C4⋊C8—91no—
124#408—92no—
125#405—92no—
126C22×C3×C4C4×D314yes—
127C22×C3×C4C4×D314yes—
128C22×C3×C4C22×D314yes—
129C2×#67—38no—
130#235—68no—
131#235—68no—
132C2×D12—34no—
133C2×C4×D3—38no—
134C2×C4×D3—38no—
135C2×C4×D3—38no—
136C2×Dic6—34no—
137C3×M16—216no—
138C2×C3×C8C22×D3116yes—
139C3×C42C4×D314yes—
140C3×C42C4×D314yes—
141C3×C42C22×D314yes—
142C3×C42C22×D314yes—
143#217—38no—
144(C2×D3)⋊C4—38no—
145(C2×D3)⋊C4—38no—
146C4⋊Dic3—34no—
147C4⋊Dic3—34no—
148Dic3⋊C4—38no—
149Dic3⋊C4—38no—
150C4×Dic3—38no—
151C4×Dic3—38no—
152C4×Dic3—38no—
153C2×C3⋊C8—38no—
154C2×C3⋊C8—38no—
155C2×C3⋊C8—616no—
156C22×C32—21no—
157C22×C32—21no—
158C22×C32#11712yes—
159C22×C32C23×C411yescharacteristic
160C2×C3⋊D3—22no—
161C2×C3⋊D3—22no—
162C2×C3⋊D3—22no—
163C32×C4—21no—
164C32×C4—21no—
165C32×C4—21no—
166C32×C4#11712yes—
167C32×C4#13112yes—
168C32×C4C2×#4111yescharacteristic
169C32×C4C2×#4111yescharacteristic
170C3⋊Dic3—22no—
171C3⋊Dic3—22no—
172C3⋊Dic3—22no—
173C2×#41—91no—
174C2×M16C2×C3⋊D312yes—
175C22×C8—92no—
176C4×Q8—91no—
177C4×Q8—91no—
178C4×D4—92no—
179C4×D4—92no—
180C4×D4—91no—
181C4×D4—91no—
182#117—91no—
183#117—92no—
184C2×C42—92no—
185C2×C42C2×C3⋊D311yescharacteristic
186C4⋊C8—91no—
187C4⋊C8—91no—
188C4⋊C8—92no—
189C4⋊C8C2×C3⋊D312yes—
190C4⋊C8C2×C3⋊D312yes—
191C22⋊C8—94no—
192C22⋊C8—94no—
193#97—94no—
194C4×C8—94no—
195C23×C3C2×C4×D314yes—
196C22×D3—38no—
197C2×C3×C4—28no—
198C2×C3×C4—44no—
199C2×C3×C4C2×C4×D314yes—
200C2×C3×C4C2×C4×D314yes—
201C2×C3×C4C2×C4×D314yes—
202C2×C3×C4C2×C4×D314yes—
203C2×C3×C4C2×C4×D314yes—
204C2×C3×C4#23718yes—
205C2×C3×C4#23918yes—
206C2×C3×C4C23×D314yes—
207#67—616no—
208C2×Dic3—38no—
209C2×Dic3—38no—
210C2×Dic3—38no—
211D12—68no—
212C4×D3—616no—
213C4×D3—68no—
214C4×D3—68no—
215C4×D3—128no—
216Dic6—68no—
217C3×C8—216no—
218C3⋊C8—68no—
219C3⋊C8—68no—
220C2×C32—22no—
221C2×C32C2×#11711yescharacteristic
222C2×C32C2×#13111yescharacteristic
223C2×C32#56811yescharacteristic
224C3⋊D3—42no—
225#41—182no—
226#41—182no—
227C2×Q8—91no—
228C2×D4—92no—
229C2×D4—91no—
230C22×C4—92no—
231C22×C4—92no—
232C22×C4—92no—
233C22×C4C4×C3⋊D311yescharacteristic
234C22×C4C4×C3⋊D311yescharacteristic
235C22×C4C22×C3⋊D311yescharacteristic
236M16—24no—
237C2×C8—92no—
238C2×C8—92no—
239C2×C8—184no—
240C2×C8C22×C3⋊D314yes—
241C4⋊C4—92no—
242C4⋊C4—92no—
243C4⋊C4—91no—
244C4⋊C4—91no—
245C22⋊C4—92no—
246C22⋊C4—92no—
247C22⋊C4—92no—
248C42—92no—
249C42—92no—
250C42—92no—
251C42C4×C3⋊D311yescharacteristic
252C42C4×C3⋊D311yescharacteristic
253C42C22×C3⋊D311yescharacteristic
254C42C22×C3⋊D311yescharacteristic
255C22×C3—24no—
256C22×C3—24no—
257C22×C3#89218yes—
258C22×C3C22×C4×D314yes—
259C2×D3—68no—
260C2×D3—68no—
261C2×D3—68no—
262C3×C4—24no—
263C3×C4—24no—
264C3×C4—24no—
265C3×C4#89218yes—
266C3×C4#90718yes—
267C3×C4C2×#23714yes—
268C3×C4C2×#23914yes—
269Dic3—68no—
270Dic3—68no—
271Dic3—68no—
272C32#292511yescharacteristic, complemented, Sylow
273C23—92no—
274C23C2×C4×C3⋊D311yescharacteristic
275Q8—182no—
276D4—184no—
277D4—182no—
278C2×C4—22no—
279C2×C4—41no—
280C2×C4—92no—
281C2×C4—92no—
282C2×C4—92no—
283C2×C4—182no—
284C2×C4—182no—
285C2×C4—184no—
286C2×C4—362no—
287C2×C4C2×C4×C3⋊D311yescharacteristic
288C2×C4C2×C4×C3⋊D311yescharacteristic
289C2×C4C2×C4×C3⋊D311yescharacteristic
290C2×C4C2×C4×C3⋊D311yescharacteristic
291C2×C4C2×C4×C3⋊D311yescharacteristic
292C2×C4#383012yes—
293C2×C4#383212yes—
294C2×C4C23×C3⋊D311yescharacteristic
295C8—24no—
296C8—182no—
297C8—182no—
298C2×C3—28no—
299C2×C3C2×#89214yes—
300C2×C3C2×#90714yes—
301C2×C3#574514yes—
302D3—128no—
303C22—21no—
304C22—21no—
305C22—182no—
306C22—182no—
307C22—182no—
308C22#6410112yes—
309C22C22×C4×C3⋊D311yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—182no—
314C4—182no—
315C4—182no—
316C4#6410112yes—
317C4#6411612yes—
318C4C2×#383011yescharacteristic
319C4C2×#383211yescharacteristic
320C3#7904014yescomplemented
321C2—22no—
322C2—362no—
323C2C2×#6410111yescharacteristic
324C2C2×#6411611yescharacteristic
325C2#1059621611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×C3⋊D3
commutator, socleC22×C32C23×C4
FittingC32×#423C2
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenter#423C3⋊D3
hypocenterC32#2925
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #423

Complements

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

NH ≅ G/Ntype
2. C32×#423C2semidirect
4. #10592821C2semidirect
5. C2×C4⋊(C3⋊(C3⋊C8))C2semidirect
6. #10592539C2semidirect
7. #10592534C2semidirect
8. #10592532C2semidirect
33. C3×#423D3semidirect
122. #423C3⋊D3semidirect
272. C32#2925semidirect
320. C3#79040semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C32×#4232
#105928282
#105928212
C2×C4⋊(C3⋊(C3⋊C8))2
#105925392
#105925342
#105925322
#790403