Finite Group Databasebeta

← #11787280

Subgroups — #11787280

Order 1152.

682 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 78 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×#64286C211yesmaximal, characteristic
2C3⋊D3×C22⋊Q8C211yesmaximal, characteristic
3C2×#63784C212yesmaximal, complemented
4#10593800C211yesmaximal, characteristic
5#10590163C212yesmaximal, complemented
6C2×Q8×C3⋊D3C2211yescharacteristic
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157—21no—
9#64286—24no—
10C2×C4⋊#157C2212yes—
11C2×C4×#157—21no—
12C2×#3787C2212yes—
13C32×C22⋊Q8C411yescharacteristic, complemented
14#64155C411yescharacteristic, complemented
15#64133C411yescharacteristic, complemented
16#64106C411yescharacteristic, complemented
17#64105—21no—
18C4⋊C4×C3⋊D3—21no—
19C4⋊C4×C3⋊D3C2211yescharacteristic
20C22⋊C4×C3⋊D3—21no—
21#64087—21no—
22C22⋊#622—21no—
23#63784—24no—
24#63778—21no—
25D3×C22⋊Q8—62no—
26C23×C3⋊D3D411yescharacteristic
27C22×#157—22no—
28C2×C32×Q8C2×C411yescharacteristic
29C22×C32×C4C2×C411yescharacteristic
30C22×C3⋊Dic3D411yescharacteristic
31Q8×C3⋊D3—22no—
32Q8×C3⋊D3—22no—
33C2×C4×C3⋊D3—22no—
34C2×C4×C3⋊D3—22no—
35C2×C4×C3⋊D3—21no—
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3C2×C411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3C2311yescharacteristic
41C2×#634—21no—
42C2×#634C2×C411yescharacteristic
43C22⋊#157—24no—
44C2×#622—22no—
45C4⋊#157—22no—
46C4⋊#157D414yes—
47C4×#157—24no—
48#3787—22no—
49#3787—22no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4C2×C411yescharacteristic
52C32×C22⋊C4—21no—
53#3757—21no—
54#3752—21no—
55#3752—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)C2×C411yescharacteristic
58#3750—21no—
59#3750—21no—
60#3750—21no—
61#1873—91nomaximal, Sylow
62C2×D3×Q8—62no—
63C22×C4×D3—62no—
64C3×C22⋊Q8—22no—
65#946—62no—
66#924—62no—
67#897—62no—
68#896—64no—
69D3×C4⋊C4—62no—
70D3×C4⋊C4—64no—
71D3×C22⋊C4—64no—
72#878—64no—
73C23×C32C22⋊C411yescharacteristic
74C22×C3⋊D3—22no—
75C22×C3⋊D3—21no—
76C22×C3⋊D3—21no—
77C22×C3⋊D3—22no—
78C22×C3⋊D3C22⋊C411yescharacteristic
79C22×C3⋊D3C2×D411yescharacteristic
80C2×#157—24no—
81C2×#157—42no—
82C2×#157—42no—
83C32×Q8—22no—
84C2×C32×C4—21no—
85C2×C32×C4—21no—
86C2×C32×C4—22no—
87C2×C32×C4C22⋊C411yescharacteristic
88C2×C32×C4C22×C411yescharacteristic
89C2×C3⋊Dic3—21no—
90C2×C3⋊Dic3—21no—
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C2×C3⋊Dic3C2×D411yescharacteristic
94C4×C3⋊D3—21no—
95C4×C3⋊D3—21no—
96C4×C3⋊D3—22no—
97C4×C3⋊D3—22no—
98C4×C3⋊D3—41no—
99C4×C3⋊D3—41no—
100C4×C3⋊D3—42no—
101C4×C3⋊D3C2×D412yes—
102C4×C3⋊D3#4112yes—
103#634—22no—
104#634—42no—
105#622—42no—
106C2×C22⋊Q8—91no—
107C2×#117—91no—
108C2×#103—92no—
109C2×C22⋊C8—91no—
110#340—92no—
111C23×D3—62no—
112C2×C3×Q8—22no—
113C22×C3×C4—22no—
114C22×Dic3—62no—
115D3×Q8—124no—
116D3×Q8—124no—
117C2×C4×D3—62no—
118C2×C4×D3—62no—
119C2×C4×D3—62no—
120C2×C4×D3—62no—
121C2×C4×D3—64no—
122C2×C4×D3—64no—
123C2×C4×D3—124no—
124C2×C4×D3—124no—
125C2×Dic6—62no—
126C2×Dic6—64no—
127C3×C4⋊C4—24no—
128C3×C4⋊C4—22no—
129C3×C22⋊C4—24no—
130#217—64no—
131(C2×D3)⋊C4—64no—
132(C2×D3)⋊C4—64no—
133C4⋊Dic3—62no—
134C4⋊Dic3—64no—
135Dic3⋊C4—64no—
136Dic3⋊C4—64no—
137Dic3⋊C4—64no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32—21no—
141C22×C32C2×C22⋊C411yescharacteristic
142C2×C3⋊D3—21no—
143C2×C3⋊D3—21no—
144C2×C3⋊D3—21no—
145C2×C3⋊D3—42no—
146C2×C3⋊D3—42no—
147C2×C3⋊D3#12011yescharacteristic
148C2×C3⋊D3#12311yescharacteristic
149C2×C3⋊D3#13512yes—
150C2×C3⋊D3#13712yes—
151#157—44no—
152C32×C4—21no—
153C32×C4—41no—
154C32×C4—41no—
155C32×C4C4×D412yes—
156C3⋊Dic3—21no—
157C3⋊Dic3—41no—
158C3⋊Dic3—41no—
159C3⋊Dic3#12112yes—
160C22×Q8—91no—
161C23×C4—91no—
162C22×C8—92no—
163C22⋊Q8—91no—
164C22⋊Q8—91no—
165C22⋊Q8—91no—
166C22⋊Q8—181no—
167C22⋊Q8—181no—
168C22⋊Q8#15711yescharacteristic, complemented
169#117—184no—
170C2×C4⋊C4—92no—
171C2×C4⋊C4—91no—
172C2×C4⋊C4—181no—
173C2×C22⋊C4—181no—
174C2×C22⋊C4—181no—
175C2×C42—181no—
176#103—184no—
177C22⋊C8—181no—
178C22⋊C8—181no—
179C23×C3—22no—
180C22×D3—62no—
181C22×D3—62no—
182C22×D3—68no—
183C22×D3—122no—
184C22×D3—122no—
185C22×D3—124no—
186C3×Q8—44no—
187C2×C3×C4—24no—
188C2×C3×C4—24no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—44no—
192C2×Dic3—62no—
193C2×Dic3—62no—
194C2×Dic3—64no—
195C2×Dic3—64no—
196C2×Dic3—124no—
197C4×D3—64no—
198C4×D3—64no—
199C4×D3—124no—
200C4×D3—124no—
201C4×D3—122no—
202C4×D3—122no—
203C4×D3—128no—
204C4×D3—124no—
205C4×D3—124no—
206Dic6—124no—
207Dic6—128no—
208C2×C32—41no—
209C2×C32#38611yescharacteristic
210C2×C32#41611yescharacteristic
211C2×C32#41911yescharacteristic
212C3⋊D3—41no—
213C3⋊D3#45212yes—
214C3⋊D3#48512yes—
215C24—91no—
216C2×Q8—91no—
217C2×Q8—181no—
218C2×Q8—182no—
219C2×Q8—182no—
220C2×Q8C2×#15711yescharacteristic
221C22×C4—91no—
222C22×C4—91no—
223C22×C4—91no—
224C22×C4—91no—
225C22×C4—91no—
226C22×C4—182no—
227C22×C4—182no—
228C22×C4—181no—
229C22×C4—181no—
230C22×C4—182no—
231C22×C4C2×#15711yescharacteristic
232C2×C8—182no—
233C2×C8—182no—
234C2×C8—182no—
235C4⋊C4—21no—
236C4⋊C4—94no—
237C4⋊C4—91no—
238C4⋊C4—181no—
239C4⋊C4—181no—
240C4⋊C4—181no—
241C4⋊C4—182no—
242C4⋊C4—181no—
243C4⋊C4C2×#15711yescharacteristic
244C22⋊C4—21no—
245C22⋊C4—181no—
246C22⋊C4—181no—
247C22⋊C4—184no—
248C22⋊C4—181no—
249C42—184no—
250C22×C3—24no—
251C22×C3—22no—
252C22×C3—42no—
253C22×C3—42no—
254C2×D3—62no—
255C2×D3—62no—
256C2×D3—64no—
257C2×D3—64no—
258C2×D3—64no—
259C2×D3—122no—
260C2×D3—122no—
261C2×D3—128no—
262C2×D3—128no—
263C3×C4—24no—
264C3×C4—42no—
265C3×C4—44no—
266C3×C4—44no—
267Dic3—64no—
268Dic3—122no—
269Dic3—124no—
270Dic3—124no—
271C32#187311yescharacteristic, complemented, Sylow
272C23—91no—
273C23—91no—
274C23—181no—
275C23—181no—
276C23—182no—
277C23—182no—
278C23C22⋊#15711yescharacteristic
279Q8—22no—
280Q8—182no—
281Q8—362no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—91no—
286C2×C4—92no—
287C2×C4—92no—
288C2×C4—91no—
289C2×C4—182no—
290C2×C4—181no—
291C2×C4—181no—
292C2×C4—182no—
293C2×C4—182no—
294C2×C4—184no—
295C2×C4—181no—
296C2×C4—181no—
297C2×C4—361no—
298C2×C4—361no—
299C2×C4—362no—
300C2×C4—362no—
301C2×C4—362no—
302C2×C4C22⋊#15711yescharacteristic
303C2×C4C22×#15711yescharacteristic
304C8—362no—
305C2×C3—22no—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3—44no—
309D3—64no—
310D3—64no—
311D3—124no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—91no—
316C22—91no—
317C22—92no—
318C22—92no—
319C22—181no—
320C22—181no—
321C22—181no—
322C22—362no—
323C22—362no—
324C22C2×C22⋊#15711yescharacteristic
325C4—21no—
326C4—41no—
327C4—41no—
328C4—92no—
329C4—181no—
330C4—364no—
331C4—361no—
332C4—361no—
333C4D4×#15712yes—
334C3—22no—
335C2—41no—
336C2—92no—
337C2—92no—
338C2—361no—
339C2#1059382611yescharacteristic
340C2#1059382911yescharacteristic
341C2#1059384111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C22⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22⋊Q8#157
hypocenterC32#1873
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#63784C2semidirect
5. #10590163C2semidirect
13. C32×C22⋊Q8C4semidirect
14. #64155C4semidirect
15. #64133C4semidirect
16. #64106C4semidirect
168. C22⋊Q8#157semidirect
271. C32#1873semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
C3⋊D3×C22⋊Q82
C2×#637842
#105938002
#105901632
#18739