Finite Group Databasebeta

← #11807805

Subgroups — #11807805

Order 1152.

1392 conjugacy classes of subgroups.

The subgroup lattice has 333 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic
2#10592928C212yesmaximal, complemented
3#10592911C211yesmaximal, characteristic
4#10592910C211yesmaximal, characteristic
5#10592683C212yesmaximal, complemented
6#10592679C212yesmaximal, complemented
7#10592679C212yesmaximal, complemented
8#10592650C212yesmaximal
9#10592650C212yesmaximal
10#82750—34nomaximal
11C22×C32×Q8C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C32×C22⋊Q8C418yescomplemented
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C4⋊C4C2212yes—
16C2×C32×C22⋊C4C2212yes—
17C2×#3757C2212yes—
18C2×#3757C2211yescharacteristic
19C2×#3757C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2212yes—
21C2×C4⋊(C3⋊Dic3)C2212yes—
22C2×C4⋊(C3⋊Dic3)C2212yes—
23C2×C4×C3⋊Dic3C2212yes—
24C2×C4×C3⋊Dic3C2212yes—
25#63658C2212yes—
26#63658C2212yes—
27#63658C2212yes—
28#63658C2212yes—
29#63658C2212yes—
30#63658C2211yescharacteristic
31#63658C2211yescharacteristic
32#63658C2212yes—
33C2×C3×C22⋊Q8D314yes—
34#5229—38no—
35#5212—34no—
36#5211—34no—
37#4984—38no—
38#4980—38no—
39#4980—38no—
40#4951—38no—
41#4951—38no—
42C24×C32C2311yescharacteristic
43C2×C32×Q8—42no—
44C2×C32×Q8C2×C414yes—
45C22×C32×C4—42no—
46C22×C32×C4C2×C414yes—
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2312yes—
50C22×C32×C4C2312yes—
51C22×C3⋊Dic3C2312yes—
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2312yes—
54C22×C3⋊Dic3C2312yes—
55C32×C4⋊C4C2×C414yes—
56C32×C4⋊C4C2×C418yes—
57C32×C22⋊C4C2×C418yes—
58#3757—41no—
59#3757—42no—
60#3757—41no—
61C4⋊(C3⋊Dic3)—42no—
62C4⋊(C3⋊Dic3)—42no—
63C4⋊(C3⋊Dic3)—42no—
64C4×C3⋊Dic3—42no—
65C4×C3⋊Dic3—42no—
66#2378—91noSylow
67C22×C3×Q8C2×D314yes—
68C23×C3×C4C2×D314yes—
69C3×C22⋊Q8Dic3132yescomplemented
70C2×C3×C4⋊C4C2×D314yes—
71C2×C3×C4⋊C4C2×D318yes—
72C2×C3×C22⋊C4C2×D318yes—
73C2×#217—38no—
74C2×#217—34no—
75C2×#217—34no—
76C2×C4⋊Dic3—38no—
77C2×C4⋊Dic3—38no—
78C2×C4⋊Dic3—38no—
79C2×C4×Dic3—38no—
80C2×C4×Dic3—38no—
81C3⋊#95—38no—
82C3⋊#95—38no—
83C3⋊#95—38no—
84C3⋊#95—38no—
85C3⋊#95—38no—
86C3⋊#95—34no—
87C3⋊#95—34no—
88C3⋊#95—38no—
89C23×C32—21no—
90C23×C32—22no—
91C23×C32—22no—
92C23×C32—21no—
93C23×C32C22×C412yes—
94C23×C32C2411yescharacteristic
95C32×Q8—44no—
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—22no—
100C2×C32×C4—22no—
101C2×C32×C4—22no—
102C2×C32×C4—44no—
103C2×C32×C4C22×C414yes—
104C2×C32×C4C22×C414yes—
105C2×C32×C4C22×C412yes—
106C2×C32×C4C22×C412yes—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—22no—
119C2×C22⋊Q8C3⋊D311yescharacteristic
120#391—92no—
121#389—92no—
122#388—92no—
123#388—92no—
124#387—92no—
125#387—92no—
126#381—91no—
127#380—91no—
128C24×C3C22×D314yes—
129C2×C3×Q8—48no—
130C2×C3×Q8C2×Dic3116yes—
131C22×C3×C4—48no—
132C22×C3×C4C2×Dic3116yes—
133C22×C3×C4C22×D314yes—
134C22×C3×C4C22×D318yes—
135C22×C3×C4C22×D318yes—
136C22×C3×C4C22×D314yes—
137C22×Dic3—38no—
138C22×Dic3—38no—
139C22×Dic3—38no—
140C22×Dic3—38no—
141C3×C4⋊C4C2×Dic3116yes—
142C3×C4⋊C4C2×Dic3132yes—
143C3×C22⋊C4C2×Dic3132yes—
144#217—128no—
145#217—124no—
146#217—124no—
147C4⋊Dic3—128no—
148C4⋊Dic3—128no—
149C4⋊Dic3—128no—
150C4×Dic3—128no—
151C4×Dic3—128no—
152C22×C32—22no—
153C22×C32—22no—
154C22×C32—22no—
155C22×C32—42no—
156C22×C32—42no—
157C22×C32C23×C411yescharacteristic
158C22×C32H(5,𝔽2)12yes—
159C22×C32H(5,𝔽2)11yescharacteristic
160C22×C322−1+412yes—
161C22×C322−1+411yescharacteristic
162C32×C4—22no—
163C32×C4—22no—
164C32×C4—24no—
165C32×C4—24no—
166C3⋊Dic3—42no—
167C3⋊Dic3—42no—
168C3⋊Dic3—42no—
169C3⋊Dic3—42no—
170C22×Q8C2×C3⋊D311yescharacteristic
171C23×C4C2×C3⋊D311yescharacteristic
172C22⋊Q8C3⋊Dic318yescomplemented
173C2×C4⋊C4—92no—
174C2×C4⋊C4—92no—
175C2×C4⋊C4—92no—
176C2×C4⋊C4C2×C3⋊D311yescharacteristic
177C2×C4⋊C4C2×C3⋊D312yes—
178C2×C22⋊C4—91no—
179C2×C22⋊C4—91no—
180C2×C22⋊C4—92no—
181C2×C22⋊C4C2×C3⋊D312yes—
182C2×C42—92no—
183C2×C42—92no—
184#95—92no—
185#95—91no—
186#95—92no—
187#95—91no—
188#95—92no—
189#95—92no—
190#95—92no—
191#95—92no—
192C23×C3—28no—
193C23×C3—28no—
194C23×C3—24no—
195C23×C3—24no—
196C23×C3C22×Dic318yes—
197C23×C3C23×D314yes—
198C3×Q8—416no—
199C2×C3×C4—28no—
200C2×C3×C4—28no—
201C2×C3×C4—28no—
202C2×C3×C4—28no—
203C2×C3×C4—28no—
204C2×C3×C4—28no—
205C2×C3×C4—416no—
206C2×C3×C4C22×Dic3116yes—
207C2×C3×C4C22×Dic3116yes—
208C2×C3×C4C22×Dic318yes—
209C2×C3×C4C22×Dic318yes—
210C2×Dic3—68no—
211C2×Dic3—68no—
212C2×Dic3—68no—
213C2×Dic3—68no—
214C2×Dic3—68no—
215C2×Dic3—68no—
216C2×Dic3—68no—
217C2×Dic3—68no—
218C2×Dic3—68no—
219C2×Dic3—68no—
220C2×Dic3—68no—
221C2×Dic3—68no—
222C2×C32—42no—
223C2×C32#51811yescharacteristic
224C2×C32#51911yescharacteristic
225C2×C32#52011yescharacteristic
226C2×C32#56212yes—
227C2×C32#56312yes—
228C24C22×C3⋊D311yescharacteristic
229C2×Q8—42no—
230C2×Q8C2×C3⋊Dic314yes—
231C22×C4—42no—
232C22×C4—92no—
233C22×C4—92no—
234C22×C4—92no—
235C22×C4—92no—
236C22×C4C2×C3⋊Dic314yes—
237C22×C4C22×C3⋊D311yescharacteristic
238C22×C4C22×C3⋊D312yes—
239C22×C4C22×C3⋊D312yes—
240C22×C4C22×C3⋊D311yescharacteristic
241C4⋊C4—362no—
242C4⋊C4—362no—
243C4⋊C4—362no—
244C4⋊C4C2×C3⋊Dic314yes—
245C4⋊C4C2×C3⋊Dic318yes—
246C22⋊C4—362no—
247C22⋊C4—361no—
248C22⋊C4—361no—
249C22⋊C4C2×C3⋊Dic318yes—
250C42—362no—
251C42—362no—
252C22×C3—28no—
253C22×C3—28no—
254C22×C3—28no—
255C22×C3—48no—
256C22×C3—48no—
257C22×C3#100418yes—
258C22×C3#100718yes—
259C22×C3#100914yes—
260C22×C3#101014yes—
261C22×C3C23×Dic314yes—
262C3×C4—28no—
263C3×C4—28no—
264C3×C4—216no—
265C3×C4—216no—
266Dic3—128no—
267Dic3—128no—
268Dic3—128no—
269Dic3—128no—
270C32#237811yescharacteristic, complemented, Sylow
271C23—22no—
272C23—22no—
273C23—21no—
274C23—21no—
275C23C22×C3⋊Dic312yes—
276C23C23×C3⋊D311yescharacteristic
277Q8—44no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—44no—
285C2×C4—182no—
286C2×C4—182no—
287C2×C4—182no—
288C2×C4—182no—
289C2×C4—182no—
290C2×C4—182no—
291C2×C4—182no—
292C2×C4—182no—
293C2×C4—182no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4—182no—
297C2×C4C22×C3⋊Dic314yes—
298C2×C4C22×C3⋊Dic314yes—
299C2×C4C22×C3⋊Dic312yes—
300C2×C4C22×C3⋊Dic312yes—
301C2×C3—48no—
302C2×C3#564618yes—
303C2×C3#564718yes—
304C2×C3#579814yes—
305C2×C3#581214yes—
306C2×C3#582714yes—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—42no—
311C22—42no—
312C22#6436112yes—
313C22#6436412yes—
314C22#6436611yescharacteristic
315C22#6436711yescharacteristic
316C22C23×C3⋊Dic311yescharacteristic
317C4—22no—
318C4—22no—
319C4—24no—
320C4—24no—
321C4—362no—
322C4—362no—
323C4—362no—
324C4—362no—
325C3#8275014yescomplemented
326C2—42no—
327C2#1059611712yes—
328C2#1059611812yes—
329C2#1059626911yescharacteristic
330C2#1059628311yescharacteristic
331C2#1059629811yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊Q8C2
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊Q8C3⋊D3
hypocenterC32#2378
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10592928C2semidirect
5. #10592683C2semidirect
6. #10592679C2semidirect
7. #10592679C2semidirect
13. C32×C22⋊Q8C4semidirect
69. C3×C22⋊Q8Dic3semidirect
172. C22⋊Q8C3⋊Dic3semidirect
270. C32#2378semidirect
325. C3#82750semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
#105929282
#105929112
#105929102
#105926832
#105926792
#105926502
#827503