Finite Group Databasebeta

← #99×#157 #11783757

Subgroups — #99×#157 #11783757

Order 1152.

622 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C2×D4×#157C211yesmaximal, characteristic
2#10593817C211yesmaximal, characteristic
3C22⋊C4×#157C212yesmaximal, complemented
4C3⋊D3×#99C211yesmaximal, characteristic
5#10590155C212yesmaximal, complemented
6C23×#157C411yescharacteristic, complemented
7C23×#157C2211yescharacteristic
8C2×D4×C3⋊D3C2211yescharacteristic
9C2×C22⋊#157C411yescharacteristic, complemented
10C2×C22⋊#157C2212yes—
11C2×C22⋊#157C2211yescharacteristic
12D4×#157—22no—
13D4×#157—22no—
14C2×C4⋊#157C411yescharacteristic, complemented
15C2×C4×#157—22no—
16C2×C4×#157C411yescharacteristic, complemented
17C22⋊C4×C3⋊D3C2212yes—
18#63786C412yescomplemented
19#63781—22no—
20#63774C412yescomplemented
21C32×#99C411yescharacteristic, complemented
22#63661C411yescharacteristic, complemented
23#63633C412yescomplemented
24D3×#99—62no—
25C23×C3⋊D3C2×C411yescharacteristic
26C23×C3⋊D3C2311yescharacteristic
27C22×#157—22no—
28C22×#157—21no—
29C22×#157—21no—
30C22×#157—42no—
31C22×#157—42no—
32C22×#157C2×C411yescharacteristic
33C22×#157C2×C411yescharacteristic
34C22×#157C2×C411yescharacteristic
35C22×#157C2×C411yescharacteristic
36C22×#157D412yes—
37C22×#157D412yes—
38C2×C32×D4C2×C411yescharacteristic
39C2×#638C2×C411yescharacteristic
40C2×#638C2×C411yescharacteristic
41D4×C3⋊D3—22no—
42D4×C3⋊D3—22no—
43C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
44C2×C4×C3⋊D3—22no—
45C2×C4×C3⋊D3C2×C411yescharacteristic
46C22⋊#157—22no—
47C22⋊#157—22no—
48C22⋊#157—22no—
49C22⋊#157C2×C414yescomplemented
50C4⋊#157—22no—
51C4×#157—21no—
52C4×#157—21no—
53C4×#157—44no—
54C32×C22⋊C4C2×C412yescomplemented
55#3757C2×C412yescomplemented
56#3752—22no—
57C4×#99—91nomaximal, Sylow
58C2×D3×D4—62no—
59D3×C22⋊C4—64no—
60C3×#99—22no—
61#834—62no—
62#806—64no—
63C23×C32C4211yescharacteristic, complemented
64C23×C32C22×C411yescharacteristic
65C22×C3⋊D3—21no—
66C22×C3⋊D3—21no—
67C22×C3⋊D3—41no—
68C22×C3⋊D3—41no—
69C22×C3⋊D3—41no—
70C22×C3⋊D3—41no—
71C22×C3⋊D3C4211yescharacteristic, complemented
72C22×C3⋊D3C22×C411yescharacteristic
73C22×C3⋊D3C22×C411yescharacteristic
74C22×C3⋊D3C2×D412yes—
75C22×C3⋊D3#4112yes—
76C2×#157—22no—
77C2×#157—24no—
78C2×#157—21no—
79C2×#157—21no—
80C2×#157—24no—
81C2×#157—41no—
82C2×#157—42no—
83C2×#157—42no—
84C2×#157—42no—
85C2×#157—42no—
86C2×#157—42no—
87C2×#157—41no—
88C2×#157—41no—
89C2×#157C22⋊C411yescharacteristic
90C2×#157C22⋊C412yes—
91C2×#157C22⋊C411yescharacteristic
92C32×D4—22no—
93C2×C32×C4—22no—
94C2×C32×C4C4211yescharacteristic, complemented
95#638—22no—
96#638—22no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3C4211yescharacteristic, complemented
99C4⋊(C3⋊D3)—22no—
100C4×C3⋊D3—21no—
101C4×C3⋊D3—21no—
102C4×C3⋊D3—42no—
103C4×C3⋊D3—42no—
104C2×C4×D4—91no—
105C2×#99—91no—
106C2×#99—91no—
107C4×C22⋊C4—92no—
108#342—92no—
109C23×D3—62no—
110C23×D3—62no—
111C2×C3×D4—22no—
112C2×#67—62no—
113C2×#67—62no—
114D3×D4—124no—
115D3×D4—124no—
116C2×D12—62no—
117C2×C4×D3—62no—
118C2×C4×D3—124no—
119C3×C22⋊C4—24no—
120#217—64no—
121(C2×D3)⋊C4—124no—
122C22×C32—21no—
123C22×C32—41no—
124C22×C32—41no—
125C22×C32C2×C4211yescharacteristic
126C22×C32C4×D412yes—
127C2×C3⋊D3—22no—
128C2×C3⋊D3—21no—
129C2×C3⋊D3—22no—
130C2×C3⋊D3—21no—
131C2×C3⋊D3—21no—
132C2×C3⋊D3—41no—
133C2×C3⋊D3—42no—
134C2×C3⋊D3—42no—
135C2×C3⋊D3—41no—
136C2×C3⋊D3—41no—
137C2×C3⋊D3—41no—
138C2×C3⋊D3C2×C22⋊C411yescharacteristic
139C2×C3⋊D3#11711yescharacteristic
140C2×C3⋊D3C4×D412yes—
141#157—21no—
142#157—22no—
143#157—44no—
144#157—41no—
145#157—41no—
146#157#9912yesdirect product factor
147C32×C4—21no—
148C32×C4—42no—
149C3⋊Dic3—21no—
150C3⋊Dic3—42no—
151C22×D4—91no—
152C23×C4—91no—
153C23×C4—91no—
154C4×D4—182no—
155C4×D4—182no—
156C2×C4⋊C4—91no—
157C2×C22⋊C4—92no—
158C2×C22⋊C4—92no—
159C2×C22⋊C4—91no—
160C2×C22⋊C4—91no—
161C2×C42—91no—
162C2×C42—182no—
163#99—92no—
164#99—92no—
165#99—91no—
166#99—92no—
167#99#15711yescharacteristic, direct product factor
168#95—182no—
169C23×C3—22no—
170C23×C3—22no—
171C22×D3—62no—
172C22×D3—64no—
173C22×D3—62no—
174C22×D3—64no—
175C22×D3—62no—
176C22×D3—122no—
177C22×D3—122no—
178C22×D3—242no—
179C22×D3—242no—
180C22×D3—242no—
181C22×D3—242no—
182C3×D4—44no—
183C2×C3×C4—22no—
184C2×C3×C4—44no—
185#67—124no—
186#67—124no—
187C2×Dic3—62no—
188C2×Dic3—124no—
189D12—124no—
190C4×D3—122no—
191C4×D3—122no—
192C4×D3—244no—
193C4×D3—244no—
194C2×C32—22no—
195C2×C32—21no—
196C2×C32—41no—
197C2×C32C4×C22⋊C411yescharacteristic
198C3⋊D3—22no—
199C3⋊D3—21no—
200C3⋊D3—41no—
201C3⋊D3C2×#9911yescharacteristic
202C3⋊D3#41011yescharacteristic
203C24—91no—
204C24—91no—
205C2×D4—91no—
206C2×D4—91no—
207C2×D4—91no—
208C2×D4—182no—
209C2×D4—182no—
210C2×D4C2×#15711yescharacteristic
211C22×C4—91no—
212C22×C4—92no—
213C22×C4—91no—
214C22×C4—92no—
215C22×C4—91no—
216C22×C4—91no—
217C22×C4—91no—
218C22×C4—182no—
219C22×C4—181no—
220C22×C4—181no—
221C22×C4—182no—
222C22×C4—362no—
223C22×C4—362no—
224C4⋊C4—182no—
225C22⋊C4—94no—
226C22⋊C4—92no—
227C22⋊C4—182no—
228C22⋊C4—182no—
229C22⋊C4—182no—
230C22⋊C4—182no—
231C22⋊C4C2×#15712yescomplemented
232C42—181no—
233C42—181no—
234C42—364no—
235C22×C3—22no—
236C22×C3—24no—
237C22×C3—42no—
238C22×C3—82no—
239C22×C3—82no—
240C2×D3—62no—
241C2×D3—62no—
242C2×D3—64no—
243C2×D3—124no—
244C2×D3—124no—
245C2×D3—122no—
246C2×D3—122no—
247C2×D3—122no—
248C2×D3—242no—
249C2×D3—242no—
250C2×D3—244no—
251C2×D3—242no—
252C2×D3—244no—
253C2×D3—242no—
254C3×C4—42no—
255C3×C4—84no—
256Dic3—122no—
257Dic3—244no—
258C32C4×#9911yescharacteristic, complemented, Sylow
259C23—91no—
260C23—92no—
261C23—91no—
262C23—92no—
263C23—91no—
264C23—181no—
265C23—181no—
266C23—361no—
267C23—361no—
268C23—361no—
269C23—361no—
270C23C4×#15711yescharacteristic, complemented
271C23C22×#15711yescharacteristic
272D4—22no—
273D4—182no—
274D4—182no—
275D4—182no—
276C2×C4—22no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—92no—
280C2×C4—91no—
281C2×C4—181no—
282C2×C4—181no—
283C2×C4—184no—
284C2×C4—182no—
285C2×C4—181no—
286C2×C4—184no—
287C2×C4—181no—
288C2×C4—182no—
289C2×C4—362no—
290C2×C4—362no—
291C2×C4—362no—
292C2×C4—362no—
293C2×C4—361no—
294C2×C4—362no—
295C2×C4—362no—
296C2×C4—362no—
297C2×C4—361no—
298C2×C4—361no—
299C2×C4C4×#15711yescharacteristic, complemented
300C2×C3—22no—
301C2×C3—44no—
302C2×C3—42no—
303C2×C3—82no—
304D3—62no—
305D3—62no—
306D3—122no—
307D3—124no—
308D3—242no—
309C22—21no—
310C22—41no—
311C22—41no—
312C22—91no—
313C22—92no—
314C22—91no—
315C22—182no—
316C22—181no—
317C22—182no—
318C22—181no—
319C22—181no—
320C22—362no—
321C22—361no—
322C22—361no—
323C22—361no—
324C22—361no—
325C22—362no—
326C22C2×C4×#15711yescharacteristic
327C22D4×#15712yes—
328C4—21no—
329C4—42no—
330C4—92no—
331C4—181no—
332C4—182no—
333C4—181no—
334C4—362no—
335C4—361no—
336C4—361no—
337C4—364no—
338C3—22no—
339C2—22no—
340C2—21no—
341C2—41no—
342C2—91no—
343C2—91no—
344C2—182no—
345C2—181no—
346C2—361no—
347C2C22⋊C4×#15711yescharacteristic
subgroupG/H
centerC2C22⋊C4×#157
commutatorC22×C32C2×C42
FrattiniC23C22×#157
FittingC32×#99C4
socleC2×C32C4×C22⋊C4
prime radicalC2×D4×C3⋊D3C22
cosocleC23×C3⋊D3C23
hypercenter#99#157
hypocenterC32C4×#99
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
3. C22⋊C4×#157C2semidirect
5. #10590155C2semidirect
6. C23×#157C4semidirect
9. C2×C22⋊#157C4semidirect
14. C2×C4⋊#157C4semidirect
16. C2×C4×#157C4semidirect
18. #63786C4semidirect
20. #63774C4semidirect
21. C32×#99C4semidirect
22. #63661C4semidirect
23. #63633C4semidirect
49. C22⋊#157C2×C4semidirect
54. C32×C22⋊C4C2×C4semidirect
55. #3757C2×C4semidirect
63. C23×C32C42semidirect
71. C22×C3⋊D3C42semidirect
94. C2×C32×C4C42semidirect
98. C2×C3⋊Dic3C42semidirect
146. #157#99direct (N × H)
167. #99#157direct (N × H)
231. C22⋊C4C2×#157semidirect
258. C32C4×#99semidirect
270. C23C4×#157semidirect
299. C2×C4C4×#157semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#1572
#105938172
C22⋊C4×#1572
C3⋊D3×#992
#105901552
C4×#999