Finite Group Databasebeta

← #11785245

Subgroups — #11785245

Order 1152.

782 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 782 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C4×D4×C3⋊D3C211yesmaximal, characteristic
2C2×#63782C212yesmaximal
3#10593736C211yesmaximal, characteristic, complemented
4#10593726C211yesmaximal, characteristic, complemented
5#10590163C212yesmaximal, complemented
6C2×D4×C3⋊D3C2211yescharacteristic
7C22×C4×C3⋊D3—21no—
8C2×C4⋊#157C2212yes—
9C2×#3787C2212yes—
10C32×C4×D4C411yescharacteristic, complemented
11D4×C3⋊Dic3C411yescharacteristic, complemented
12C4×#638—21no—
13#64102C411yescharacteristic, complemented
14C4⋊C4×C3⋊D3C2211yescharacteristic
15#64090—21no—
16C22⋊C4×C3⋊D3—21no—
17C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
18C42×C3⋊D3C2211yescharacteristic
19#63782—24no—
20#63781—21no—
21#63781—21no—
22#63779—21no—
23C4⋊#622—21no—
24C4×D3×D4—62no—
25C23×C3⋊D3—21no—
26C22×#157—22no—
27C2×C32×D4C2×C411yescharacteristic
28C22×C32×C4—21no—
29C2×#638—21no—
30C22×C3⋊Dic3—21no—
31D4×C3⋊D3—21no—
32D4×C3⋊D3—21no—
33D4×C3⋊D3D412yes—
34D4×C3⋊D3Q812yes—
35C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3—21no—
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3—44no—
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3C2311yescharacteristic
43C2×#622—22no—
44C4⋊#157—22no—
45C4⋊#157—22no—
46#3787—22no—
47#3787—22no—
48C32×C4⋊C4C2×C411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C42C2×C411yescharacteristic
51#3757—21no—
52#3752—21no—
53#3752—21no—
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55#3750—21no—
56C4×C3⋊Dic3C2×C411yescharacteristic
57C4×C3⋊Dic3D411yescharacteristic
58C4×C3⋊Dic3D411yescharacteristic
59#1804—91nomaximal, Sylow
60C2×D3×D4—62no—
61C22×C4×D3—64no—
62C3×C4×D4—22no—
63D4×Dic3—62no—
64C4×#67—64no—
65#893—62no—
66D3×C4⋊C4—62no—
67#67⋊C4—64no—
68D3×C22⋊C4—64no—
69C4×D12—62no—
70C42×D3—62no—
71C23×C32—21no—
72C22×C3⋊D3—21no—
73C22×C3⋊D3—22no—
74C22×C3⋊D3—22no—
75C22×C3⋊D3—42no—
76C22×C3⋊D3—42no—
77C22×C3⋊D3C2×D411yescharacteristic
78C2×#157—42no—
79C2×#157—42no—
80C2×#157—42no—
81C32×D4—21no—
82C32×D4C4⋊C412yes—
83C2×C32×C4—21no—
84C2×C32×C4—42no—
85C2×C32×C4C22⋊C411yescharacteristic
86C2×C32×C4C22⋊C411yescharacteristic
87C2×C32×C4C22×C411yescharacteristic
88#638—22no—
89#638—22no—
90C2×C3⋊Dic3—21no—
91C2×C3⋊Dic3—42no—
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C2×C3⋊Dic3C22⋊C411yescharacteristic
94C2×C3⋊Dic3C2×D411yescharacteristic
95C4⋊(C3⋊D3)—21no—
96C4⋊(C3⋊D3)C4⋊C412yes—
97C4×C3⋊D3—22no—
98C4×C3⋊D3—22no—
99C4×C3⋊D3—42no—
100C4×C3⋊D3—42no—
101C4×C3⋊D3—42no—
102C4×C3⋊D3C2×D411yescharacteristic
103C4×C3⋊D3C2×Q811yescharacteristic
104C4×C3⋊D3#4111yescharacteristic
105C4×C3⋊D3#4111yescharacteristic
106#622—42no—
107C2×C4×D4—91no—
108C2×C4⋊C8—91no—
109C2×#102—92no—
110#382—91no—
111#340—92no—
112C23×D3—64no—
113C2×C3×D4—22no—
114C22×C3×C4—24no—
115C2×#67—64no—
116C22×Dic3—64no—
117D3×D4—64no—
118D3×D4—64no—
119D3×D4—64no—
120D3×D4—64no—
121C2×D12—62no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—64no—
126C2×C4×D3—64no—
127C2×C4×D3—64no—
128C2×C4×D3—1216no—
129C3×C4⋊C4—22no—
130C3×C22⋊C4—24no—
131C3×C42—22no—
132#217—64no—
133(C2×D3)⋊C4—64no—
134(C2×D3)⋊C4—64no—
135C4⋊Dic3—62no—
136Dic3⋊C4—64no—
137C4×Dic3—62no—
138C4×Dic3—62no—
139C4×Dic3—62no—
140C22×C32—22no—
141C22×C32—41no—
142C22×C32—41no—
143C22×C32C2×C22⋊C411yescharacteristic
144C2×C3⋊D3—22no—
145C2×C3⋊D3—41no—
146C2×C3⋊D3—41no—
147C2×C3⋊D3—44no—
148C2×C3⋊D3—44no—
149C2×C3⋊D3#12111yescharacteristic
150C2×C3⋊D3C22⋊Q811yescharacteristic
151C2×C3⋊D3#13512yes—
152C2×C3⋊D3AGL(1,ℤ/8)12yes—
153#157—82no—
154C32×C4—21no—
155C32×C4—21no—
156C32×C4—41no—
157C32×C4C2×C4⋊C411yescharacteristic
158C32×C4#11711yescharacteristic
159C3⋊Dic3—21no—
160C3⋊Dic3—21no—
161C3⋊Dic3—41no—
162C3⋊Dic3#12111yescharacteristic
163C3⋊Dic3C22⋊Q811yescharacteristic
164C22×D4—91no—
165C23×C4—181no—
166C22×C8—92no—
167C4×D4—91no—
168C4×D4—91no—
169C4×D4—91no—
170C4×D4—181no—
171C4×D4—181no—
172C4×D4#15711yescharacteristic, complemented
173C2×C4⋊C4—91no—
174C2×C4⋊C4—92no—
175C2×C22⋊C4—181no—
176C2×C42—91no—
177C4⋊C8—181no—
178C4⋊C8—181no—
179#102—184no—
180#95—181no—
181#95—181no—
182C23×C3—24no—
183C22×D3—62no—
184C22×D3—64no—
185C22×D3—68no—
186C22×D3—68no—
187C22×D3—128no—
188C22×D3—128no—
189C3×D4—24no—
190C3×D4—24no—
191C2×C3×C4—24no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—48no—
196#67—68no—
197#67—68no—
198C2×Dic3—62no—
199C2×Dic3—62no—
200C2×Dic3—62no—
201C2×Dic3—64no—
202C2×Dic3—128no—
203D12—64no—
204D12—64no—
205C4×D3—62no—
206C4×D3—62no—
207C4×D3—62no—
208C4×D3—62no—
209C4×D3—68no—
210C4×D3—124no—
211C4×D3—128no—
212C4×D3—128no—
213C4×D3—128no—
214C2×C32—42no—
215C2×C32#38011yescharacteristic
216C2×C32#41611yescharacteristic
217C2×C32#41811yescharacteristic
218C3⋊D3—42no—
219C3⋊D3#46312yes—
220C3⋊D3#47812yes—
221C24—181no—
222C2×D4—92no—
223C2×D4—92no—
224C2×D4—91no—
225C2×D4—181no—
226C2×D4—181no—
227C2×D4—181no—
228C2×D4C2×#15711yescharacteristic
229C22×C4—21no—
230C22×C4—91no—
231C22×C4—91no—
232C22×C4—91no—
233C22×C4—181no—
234C22×C4—181no—
235C22×C4—181no—
236C22×C4—181no—
237C22×C4—182no—
238C22×C4—364no—
239C2×C8—182no—
240C2×C8—182no—
241C2×C8—182no—
242C4⋊C4—91no—
243C4⋊C4—181no—
244C4⋊C4—182no—
245C4⋊C4—182no—
246C4⋊C4C2×#15711yescharacteristic
247C22⋊C4—21no—
248C22⋊C4—181no—
249C22⋊C4—181no—
250C22⋊C4—181no—
251C42—91no—
252C42—91no—
253C42—91no—
254C42C2×#15711yescharacteristic
255C22×C3—28no—
256C22×C3—22no—
257C22×C3—44no—
258C22×C3—44no—
259C2×D3—64no—
260C2×D3—62no—
261C2×D3—62no—
262C2×D3—64no—
263C2×D3—68no—
264C2×D3—1216no—
265C2×D3—1216no—
266C2×D3—124no—
267C2×D3—124no—
268C3×C4—24no—
269C3×C4—22no—
270C3×C4—22no—
271C3×C4—42no—
272C3×C4—44no—
273Dic3—62no—
274Dic3—62no—
275Dic3—64no—
276Dic3—122no—
277Dic3—124no—
278C32#180411yescharacteristic, complemented, Sylow
279C23—21no—
280C23—91no—
281C23—182no—
282C23—182no—
283C23—181no—
284C23—362no—
285C23—362no—
286D4—21no—
287D4—92no—
288D4—182no—
289D4—182no—
290D4—181no—
291D4C4⋊#15712yes—
292C2×C4—21no—
293C2×C4—42no—
294C2×C4—91no—
295C2×C4—91no—
296C2×C4—91no—
297C2×C4—91no—
298C2×C4—91no—
299C2×C4—91no—
300C2×C4—91no—
301C2×C4—182no—
302C2×C4—182no—
303C2×C4—181no—
304C2×C4—362no—
305C2×C4—362no—
306C2×C4—362no—
307C2×C4—362no—
308C2×C4—362no—
309C2×C4—362no—
310C2×C4—362no—
311C2×C4C22⋊#15711yescharacteristic
312C2×C4C22⋊#15711yescharacteristic
313C2×C4C22×#15711yescharacteristic
314C8—362no—
315C2×C3—22no—
316C2×C3—22no—
317C2×C3—22no—
318C2×C3—48no—
319D3—64no—
320D3—64no—
321D3—128no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22—91no—
326C22—91no—
327C22—92no—
328C22—92no—
329C22—182no—
330C22—364no—
331C22—364no—
332C22—361no—
333C22—361no—
334C22C2×C22⋊#15711yescharacteristic
335C4—21no—
336C4—21no—
337C4—41no—
338C4—91no—
339C4—91no—
340C4—181no—
341C4—181no—
342C4—361no—
343C4—722no—
344C4C2×C4⋊#15711yescharacteristic
345C4#6428611yescharacteristic
346C3—22no—
347C2—42no—
348C2—92no—
349C2—92no—
350C2—362no—
351C2#1059381211yescharacteristic
352C2#1059381411yescharacteristic
353C2#1059384111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4×D4C4
socleC22×C32C2×C22⋊C4
prime radicalC2×D4×C3⋊D3C22
cosocleC2×C4×C3⋊D3C23
hypercenterC4×D4#157
hypocenterC32#1804
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10593736C2semidirect
4. #10593726C2semidirect
5. #10590163C2semidirect
10. C32×C4×D4C4semidirect
11. D4×C3⋊Dic3C4semidirect
13. #64102C4semidirect
17. C4×C4⋊(C3⋊D3)C4semidirect
172. C4×D4#157semidirect
278. C32#1804semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
C2×#637822
#105937362
#105937262
#105901632
#18049