Finite Group Databasebeta

← #11773206

Subgroups — #11773206

Order 1152.

1074 conjugacy classes of subgroups.

The subgroup lattice has 361 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊#157C211yesmaximal, characteristic
2C22×C4×#157C211yesmaximal, characteristic
3C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
4C2×#63781C214yesmaximal
5C23×#157C2212yes—
6C23×#157C2212yes—
7C22×C4×C3⋊D3C2212yes—
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C4⋊#157—22no—
10C2×C4⋊#157—22no—
11C2×C4⋊#157C414yescomplemented
12C2×C4×#157—22no—
13C2×C4×#157—22no—
14C2×C4×#157C414yescomplemented
15C2×C32×C4⋊C4C411yescharacteristic, complemented
16C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
17C2×#3750C412yescomplemented
18C4⋊C4×C3⋊D3—22no—
19C4⋊C4×C3⋊D3—22no—
20#63781—28no—
21C2×D3×C4⋊C4—62no—
22C23×C3⋊D3C2311yescharacteristic
23C22×#157—22no—
24C22×#157—22no—
25C22×#157—22no—
26C22×#157—22no—
27C22×#157—22no—
28C22×#157—22no—
29C22×#157—24no—
30C22×#157—24no—
31C22×#157C2×C414yes—
32C22×#157C2×C414yes—
33C22×#157D414yes—
34C22×#157Q814yes—
35C22×C32×C4C2×C412yes—
36C22×C32×C4C2×C411yescharacteristic
37C22×C3⋊Dic3C2×C412yes—
38C22×C3⋊Dic3C2×C411yescharacteristic
39C2×C4×C3⋊D3—22no—
40C2×C4×C3⋊D3—22no—
41C2×C4×C3⋊D3—24no—
42C2×C4×C3⋊D3—24no—
43C2×C4×C3⋊D3C2×C412yes—
44C2×C4×C3⋊D3C2×C412yes—
45C2×C4×C3⋊D3D412yes—
46C2×C4×C3⋊D3D412yes—
47C2×C4×C3⋊D3D412yes—
48C2×C4×C3⋊D3Q812yes—
49C4⋊#157—28no—
50C4×#157—28no—
51C32×C4⋊C4—22no—
52C4⋊(C3⋊Dic3)—22no—
53#3750—24no—
54C4⋊#95—91nomaximal, Sylow
55C22×C4×D3—62no—
56C22×C4×D3—64no—
57C2×C3×C4⋊C4—22no—
58C2×C4⋊Dic3—62no—
59C2×Dic3⋊C4—64no—
60D3×C4⋊C4—68no—
61D3×C4⋊C4—68no—
62C23×C32C22×C411yescharacteristic
63C22×C3⋊D3C22×C411yescharacteristic
64C22×C3⋊D3C22×C411yescharacteristic
65C22×C3⋊D3C2×D411yescharacteristic
66C22×C3⋊D3C2×D411yescharacteristic
67C22×C3⋊D3C2×D411yescharacteristic
68C22×C3⋊D3C2×D412yes—
69C22×C3⋊D3C2×Q811yescharacteristic
70C22×C3⋊D3C2×Q812yes—
71C22×C3⋊D3#4112yes—
72C22×C3⋊D3#4112yes—
73C2×#157—24no—
74C2×#157—24no—
75C2×#157—24no—
76C2×#157—24no—
77C2×#157—24no—
78C2×#157—24no—
79C2×#157—24no—
80C2×#157—28no—
81C2×#157—44no—
82C2×#157—42no—
83C2×#157—42no—
84C2×#157C4⋊C418yescomplemented
85C2×C32×C4—22no—
86C2×C32×C4—24no—
87C2×C32×C4C4212yes—
88C2×C32×C4C22⋊C412yes—
89C2×C32×C4C4⋊C412yes—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—24no—
92C2×C3⋊Dic3C4212yes—
93C2×C3⋊Dic3C22⋊C412yes—
94C2×C3⋊Dic3C4⋊C412yes—
95C4×C3⋊D3—44no—
96C4×C3⋊D3—42no—
97C4×C3⋊D3—42no—
98C4×C3⋊D3C22⋊C414yes—
99C4×C3⋊D3C22⋊C414yes—
100C4×C3⋊D3C4⋊C414yes—
101C4×C3⋊D3C4⋊C414yes—
102C22×C4⋊C4—91no—
103C22×C4⋊C4—91no—
104C22×C42—91no—
105C2×#95—94no—
106C23×D3—62no—
107C22×C3×C4—22no—
108C22×C3×C4—24no—
109C22×Dic3—62no—
110C22×Dic3—64no—
111C2×C4×D3—64no—
112C2×C4×D3—64no—
113C2×C4×D3—64no—
114C2×C4×D3—64no—
115C2×C4×D3—64no—
116C2×C4×D3—64no—
117C2×C4×D3—68no—
118C2×C4×D3—68no—
119C2×C4×D3—128no—
120C2×C4×D3—128no—
121C3×C4⋊C4—28no—
122C4⋊Dic3—68no—
123Dic3⋊C4—616no—
124C22×C32C2×C4211yescharacteristic
125C22×C32C2×C22⋊C411yescharacteristic
126C22×C32C2×C4⋊C411yescharacteristic
127C22×C32C4×D412yes—
128C22×C32C4×Q812yes—
129C2×C3⋊D3C2×C22⋊C411yescharacteristic
130C2×C3⋊D3C2×C22⋊C411yescharacteristic
131C2×C3⋊D3C2×C4⋊C412yes—
132C2×C3⋊D3C2×C4⋊C411yescharacteristic
133C2×C3⋊D3C2×C4⋊C411yescharacteristic
134C2×C3⋊D3#11712yes—
135C2×C3⋊D3C4×D412yes—
136C2×C3⋊D3C4×Q812yes—
137C2×C3⋊D3#12112yes—
138C2×C3⋊D3#12112yes—
139C2×C3⋊D3C22⋊Q812yes—
140C2×C3⋊D3C22⋊Q812yes—
141C2×C3⋊D3#12411yescharacteristic
142C2×C3⋊D3#12411yescharacteristic
143C2×C3⋊D3#12512yes—
144C2×C3⋊D3#12711yescharacteristic
145C2×C3⋊D3C4⋊Q812yes—
146C2×C3⋊D3C4⋊Q811yescharacteristic
147#157—28no—
148#157—44no—
149C32×C4—42no—
150C32×C4#9514yescomplemented
151C3⋊Dic3—42no—
152C3⋊Dic3#9514yescomplemented
153C23×C4—91no—
154C23×C4—92no—
155C23×C4—92no—
156C23×C4—92no—
157C2×C4⋊C4—94no—
158C2×C4⋊C4—92no—
159C2×C4⋊C4—91no—
160C2×C4⋊C4—182no—
161C2×C4⋊C4—182no—
162C2×C4⋊C4—182no—
163C2×C4⋊C4—182no—
164C2×C4⋊C4#15711yescharacteristic, complemented
165C2×C42—94no—
166C2×C42—182no—
167C2×C42—182no—
168#95—188no—
169C23×C3—22no—
170C22×D3—62no—
171C22×D3—62no—
172C22×D3—62no—
173C22×D3—62no—
174C22×D3—62no—
175C22×D3—64no—
176C22×D3—62no—
177C22×D3—64no—
178C22×D3—64no—
179C22×D3—64no—
180C2×C3×C4—28no—
181C2×C3×C4—24no—
182C2×C3×C4—24no—
183C2×C3×C4—24no—
184C2×C3×C4—48no—
185C2×Dic3—64no—
186C2×Dic3—64no—
187C2×Dic3—64no—
188C2×Dic3—68no—
189C2×Dic3—128no—
190C4×D3—68no—
191C4×D3—68no—
192C4×D3—68no—
193C4×D3—68no—
194C4×D3—1216no—
195C4×D3—128no—
196C4×D3—128no—
197C2×C32C2×#9511yescharacteristic
198C2×C32C4×C4⋊C412yes—
199C2×C32#38912yes—
200C2×C32#39011yescharacteristic
201C2×C32#39111yescharacteristic
202C3⋊D3#38012yes—
203C3⋊D3#38211yescharacteristic
204C3⋊D3#38411yescharacteristic
205C3⋊D3#38912yes—
206C3⋊D3#39011yescharacteristic
207C3⋊D3#39111yescharacteristic
208C24—91no—
209C22×C4—91no—
210C22×C4—92no—
211C22×C4—92no—
212C22×C4—92no—
213C22×C4—92no—
214C22×C4—92no—
215C22×C4—92no—
216C22×C4—94no—
217C22×C4—94no—
218C22×C4—94no—
219C22×C4—94no—
220C22×C4—92no—
221C22×C4—184no—
222C22×C4—182no—
223C22×C4—182no—
224C22×C4—184no—
225C22×C4—182no—
226C22×C4—182no—
227C22×C4—182no—
228C22×C4—182no—
229C22×C4—184no—
230C22×C4—182no—
231C22×C4—182no—
232C22×C4—184no—
233C22×C4C2×#15712yes—
234C22×C4C2×#15711yescharacteristic
235C4⋊C4—22no—
236C4⋊C4—184no—
237C4⋊C4—188no—
238C4⋊C4—182no—
239C42—188no—
240C22×C3—22no—
241C22×C3—22no—
242C22×C3—24no—
243C22×C3—24no—
244C22×C3—22no—
245C2×D3—62no—
246C2×D3—62no—
247C2×D3—62no—
248C2×D3—62no—
249C2×D3—64no—
250C2×D3—62no—
251C2×D3—62no—
252C2×D3—64no—
253C2×D3—64no—
254C2×D3—64no—
255C2×D3—64no—
256C2×D3—64no—
257C2×D3—64no—
258C2×D3—64no—
259C2×D3—62no—
260C2×D3—64no—
261C2×D3—62no—
262C2×D3—64no—
263C3×C4—28no—
264C3×C4—48no—
265Dic3—68no—
266Dic3—128no—
267C32C4⋊#9511yescharacteristic, complemented, Sylow
268C23—91no—
269C23—91no—
270C23—91no—
271C23—91no—
272C23—92no—
273C23—92no—
274C23—92no—
275C23—92no—
276C23—91no—
277C23—91no—
278C23C22×#15711yescharacteristic
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—92no—
282C2×C4—92no—
283C2×C4—92no—
284C2×C4—94no—
285C2×C4—94no—
286C2×C4—94no—
287C2×C4—94no—
288C2×C4—98no—
289C2×C4—184no—
290C2×C4—184no—
291C2×C4—184no—
292C2×C4—184no—
293C2×C4—184no—
294C2×C4—184no—
295C2×C4—184no—
296C2×C4—188no—
297C2×C4—184no—
298C2×C4—182no—
299C2×C4—364no—
300C2×C4—362no—
301C2×C4—362no—
302C2×C4—362no—
303C2×C4—362no—
304C2×C4—364no—
305C2×C4C4×#15712yes—
306C2×C4C4⋊#15712yes—
307C2×C4C22⋊#15712yes—
308C2×C3—22no—
309C2×C3—22no—
310C2×C3—22no—
311C2×C3—24no—
312C2×C3—24no—
313D3—64no—
314D3—62no—
315D3—62no—
316D3—64no—
317D3—62no—
318D3—62no—
319C22—91no—
320C22—91no—
321C22—91no—
322C22—91no—
323C22—92no—
324C22—91no—
325C22—91no—
326C22—92no—
327C22—91no—
328C22—91no—
329C22—92no—
330C22—92no—
331C22—92no—
332C22—92no—
333C22—92no—
334C22—92no—
335C22—92no—
336C22—92no—
337C22C2×C4×#15711yescharacteristic
338C22C2×C4⋊#15711yescharacteristic
339C22D4×#15712yes—
340C22Q8×#15712yes—
341C22C2×C22⋊#15711yescharacteristic
342C4—42no—
343C4—94no—
344C4—188no—
345C4—364no—
346C4—362no—
347C4#6378114yescomplemented
348C3—22no—
349C2—92no—
350C2—91no—
351C2—91no—
352C2—92no—
353C2—91no—
354C2—91no—
355C2C4⋊C4×#15712yes—
356C2#1059375912yes—
357C2C2×#6378111yescharacteristic
358C2#1059382711yescharacteristic
359C2#1059383711yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C2×C42
FittingC2×C32×C4⋊C4C4
socleC23×C32C22×C4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC2×C4⋊C4#157
hypocenterC32C4⋊#95
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
11. C2×C4⋊#157C4semidirect
14. C2×C4×#157C4semidirect
15. C2×C32×C4⋊C4C4semidirect
16. C2×C4⋊(C3⋊Dic3)C4semidirect
17. C2×#3750C4semidirect
84. C2×#157C4⋊C4semidirect
150. C32×C4#95semidirect
152. C3⋊Dic3#95semidirect
164. C2×C4⋊C4#157semidirect
267. C32C4⋊#95semidirect
347. C4#63781semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#1572
C22×C4×#1572
C2×C4⋊C4×C3⋊D32
C2×#637812
C4⋊#959