Finite Group Databasebeta

← #11805230

Subgroups — #11805230

Order 1152.

966 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
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic
3#10593812C212yesmaximal
4C4×C22⋊#157C211yesmaximal, characteristic
5C4×C22⋊#157C212yesmaximal
6#10593759C212yesmaximal, complemented
7#10593758C214yesmaximal, complemented
8C4⋊C4×#157C212yesmaximal, complemented
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×C4×C3⋊D3C2212yes—
11C2×C22⋊#157C2211yescharacteristic
12C2×C22⋊#157C2212yes—
13C2×C22⋊#157C2211yescharacteristic
14C2×C4⋊#157C2212yes—
15C2×C4⋊#157C2214yes—
16C2×C4×#157C2212yes—
17C2×C4×#157C2214yes—
18C2×C32×C4⋊C4C411yescharacteristic, complemented
19C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
20C2×#3750C412yescomplemented
21C4⋊C4×C3⋊D3C411yescharacteristic, complemented
22C4⋊C4×C3⋊D3C411yescharacteristic, complemented
23C4⋊C4×C3⋊D3C412yescomplemented
24C4⋊C4×C3⋊D3C2211yescharacteristic
25C4⋊C4×C3⋊D3C2212yes—
26C4⋊C4×C3⋊D3C2211yescharacteristic
27#63781C2212yes—
28#63781C2214yes—
29#63781C2214yes—
30#63781C2212yes—
31C2×D3×C4⋊C4—62no—
32C23×C3⋊D3C2311yescharacteristic
33C22×#157C2312yes—
34C22×#157C2314yes—
35C22×#157C2312yes—
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4C2×C412yes—
38C22×C3⋊Dic3C2×C411yescharacteristic
39C22×C3⋊Dic3C2×C412yes—
40C2×C4×C3⋊D3—24no—
41C2×C4×C3⋊D3—44no—
42C2×C4×C3⋊D3C2×C411yescharacteristic
43C2×C4×C3⋊D3C2×C411yescharacteristic
44C2×C4×C3⋊D3C2×C412yes—
45C2×C4×C3⋊D3C2×C412yes—
46C2×C4×C3⋊D3C2312yes—
47C2×C4×C3⋊D3C2312yes—
48C2×C4×C3⋊D3C2311yescharacteristic
49C2×C4×C3⋊D3C2311yescharacteristic
50C22⋊#157—22no—
51C22⋊#157—24no—
52C22⋊#157Q814yes—
53C4⋊#157—24no—
54C4⋊#157—44no—
55C4×#157—24no—
56C4×#157—44no—
57C32×C4⋊C4C2×C412yes—
58C32×C4⋊C4C2×C411yescharacteristic
59C32×C4⋊C4C2×C411yescharacteristic
60C4⋊(C3⋊Dic3)C2×C412yes—
61C4⋊(C3⋊Dic3)C2×C411yescharacteristic
62C4⋊(C3⋊Dic3)C2×C411yescharacteristic
63#3750C2×C412yes—
64#3750C2×C412yes—
65#3750C2×C412yes—
66#3750C2×C412yes—
67#2345—91nomaximal, Sylow
68C22×C4×D3—62no—
69C22×C4×D3—64no—
70C2×C3×C4⋊C4—22no—
71C2×C4⋊Dic3—62no—
72C2×Dic3⋊C4—64no—
73D3×C4⋊C4—64no—
74D3×C4⋊C4—62no—
75D3×C4⋊C4—62no—
76D3×C4⋊C4—62no—
77D3×C4⋊C4—64no—
78D3×C4⋊C4—62no—
79C23×C32C22×C411yescharacteristic
80C22×C3⋊D3—22no—
81C22×C3⋊D3—22no—
82C22×C3⋊D3C22×C411yescharacteristic
83C22×C3⋊D3C2×Q812yes—
84C22×C3⋊D3#4112yes—
85C22×C3⋊D3C2411yescharacteristic
86C2×#157—22no—
87C2×#157—22no—
88C2×#157—22no—
89C2×#157—24no—
90C2×#157—22no—
91C2×#157—24no—
92C2×#157—24no—
93C2×#157—22no—
94C2×#157C2×Q814yes—
95C2×C32×C4—22no—
96C2×C32×C4—42no—
97C2×C32×C4C22×C412yes—
98C2×C32×C4C22×C412yes—
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C22×C411yescharacteristic
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—42no—
103C2×C3⋊Dic3C22×C411yescharacteristic
104C2×C3⋊Dic3C22×C412yes—
105C2×C3⋊Dic3C22×C412yes—
106C2×C3⋊Dic3C22×C411yescharacteristic
107C4×C3⋊D3—22no—
108C4×C3⋊D3—22no—
109C4×C3⋊D3—22no—
110C4×C3⋊D3—24no—
111C4×C3⋊D3—24no—
112C4×C3⋊D3—42no—
113C4×C3⋊D3—42no—
114C4×C3⋊D3#4114yes—
115C22×C4⋊C4—91no—
116#389—92no—
117#387—94no—
118#380—92no—
119#380—91no—
120C4×C4⋊C4—92no—
121C4×C22⋊C4—91no—
122C4×C22⋊C4—92no—
123C23×D3—62no—
124C22×C3×C4—22no—
125C22×C3×C4—24no—
126C22×Dic3—62no—
127C22×Dic3—64no—
128C2×C4×D3—62no—
129C2×C4×D3—62no—
130C2×C4×D3—62no—
131C2×C4×D3—62no—
132C2×C4×D3—64no—
133C2×C4×D3—64no—
134C2×C4×D3—64no—
135C2×C4×D3—64no—
136C2×C4×D3—616no—
137C2×C4×D3—1216no—
138C3×C4⋊C4—24no—
139C3×C4⋊C4—22no—
140C3×C4⋊C4—22no—
141C4⋊Dic3—64no—
142C4⋊Dic3—62no—
143C4⋊Dic3—62no—
144Dic3⋊C4—64no—
145Dic3⋊C4—64no—
146Dic3⋊C4—64no—
147Dic3⋊C4—64no—
148C22×C32—21no—
149C22×C32—21no—
150C22×C32C4×Q812yes—
151C22×C32C23×C411yescharacteristic
152C2×C3⋊D3—21no—
153C2×C3⋊D3—21no—
154C2×C3⋊D3—24no—
155C2×C3⋊D3—24no—
156C2×C3⋊D3C4×Q812yes—
157C2×C3⋊D3C22×Q811yescharacteristic
158C2×C3⋊D3C2×#4111yescharacteristic
159C2×C3⋊D3C2×#4112yes—
160C2×C3⋊D3H(5,𝔽2)12yes—
161#157—24no—
162#157—42no—
163#157—44no—
164C32×C4—21no—
165C32×C4—22no—
166C32×C4—22no—
167C32×C4#11712yes—
168C3⋊Dic3—21no—
169C3⋊Dic3—22no—
170C3⋊Dic3—22no—
171C3⋊Dic3#11712yes—
172C23×C4—91no—
173C23×C4—92no—
174C2×C4⋊C4—92no—
175C2×C4⋊C4—91no—
176C2×C4⋊C4—91no—
177C2×C4⋊C4—92no—
178C2×C4⋊C4—91no—
179C2×C4⋊C4—91no—
180C2×C4⋊C4—92no—
181C2×C4⋊C4—91no—
182C2×C4⋊C4—92no—
183C2×C4⋊C4—94no—
184C2×C4⋊C4#15711yescharacteristic, complemented
185C2×C22⋊C4—91no—
186C2×C22⋊C4—91no—
187C2×C22⋊C4—92no—
188C2×C42—92no—
189C2×C42—94no—
190#95—92no—
191#95—94no—
192#95—94no—
193#95—92no—
194C23×C3—22no—
195C22×D3—62no—
196C22×D3—64no—
197C22×D3—64no—
198C22×D3—62no—
199C22×D3—68no—
200C22×D3—68no—
201C2×C3×C4—28no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—24no—
205C2×C3×C4—24no—
206C2×C3×C4—48no—
207C2×Dic3—62no—
208C2×Dic3—62no—
209C2×Dic3—64no—
210C2×Dic3—64no—
211C2×Dic3—68no—
212C2×Dic3—128no—
213C4×D3—68no—
214C4×D3—68no—
215C4×D3—68no—
216C4×D3—68no—
217C4×D3—128no—
218C4×D3—128no—
219C4×D3—128no—
220C4×D3—128no—
221C2×C32—22no—
222C2×C32C2×#11711yescharacteristic
223C2×C32C2×C4×Q811yescharacteristic
224C2×C32#51811yescharacteristic
225C3⋊D3—22no—
226C3⋊D3#55312yes—
227C3⋊D3#55412yes—
228C24—91no—
229C22×C4—91no—
230C22×C4—92no—
231C22×C4—91no—
232C22×C4—92no—
233C22×C4—91no—
234C22×C4—92no—
235C22×C4—92no—
236C22×C4—91no—
237C22×C4—91no—
238C22×C4—92no—
239C22×C4—92no—
240C22×C4—92no—
241C22×C4—94no—
242C22×C4—184no—
243C22×C4—364no—
244C22×C4C2×#15711yescharacteristic
245C22×C4C2×#15712yes—
246C4⋊C4—92no—
247C4⋊C4—92no—
248C4⋊C4—92no—
249C4⋊C4—92no—
250C4⋊C4—92no—
251C4⋊C4—91no—
252C4⋊C4—91no—
253C4⋊C4—184no—
254C4⋊C4—364no—
255C4⋊C4C2×#15712yes—
256C4⋊C4C2×#15711yescharacteristic
257C4⋊C4C2×#15711yescharacteristic
258C22⋊C4—94no—
259C22⋊C4—182no—
260C22⋊C4—184no—
261C42—184no—
262C42—364no—
263C22×C3—24no—
264C22×C3—24no—
265C22×C3—24no—
266C22×C3—22no—
267C2×D3—64no—
268C2×D3—64no—
269C2×D3—64no—
270C2×D3—62no—
271C2×D3—62no—
272C2×D3—64no—
273C2×D3—64no—
274C2×D3—616no—
275C2×D3—616no—
276C3×C4—24no—
277C3×C4—24no—
278C3×C4—44no—
279C3×C4—44no—
280Dic3—64no—
281Dic3—64no—
282Dic3—124no—
283Dic3—124no—
284C32#234511yescharacteristic, complemented, Sylow
285C23—91no—
286C23—92no—
287C23—92no—
288C23—91no—
289C23—182no—
290C23—182no—
291C23C22×#15711yescharacteristic
292C2×C4—22no—
293C2×C4—42no—
294C2×C4—91no—
295C2×C4—94no—
296C2×C4—94no—
297C2×C4—91no—
298C2×C4—92no—
299C2×C4—92no—
300C2×C4—182no—
301C2×C4—184no—
302C2×C4—184no—
303C2×C4—182no—
304C2×C4—182no—
305C2×C4—182no—
306C2×C4—182no—
307C2×C4—182no—
308C2×C4—182no—
309C2×C4—184no—
310C2×C4—182no—
311C2×C4—184no—
312C2×C4—184no—
313C2×C4—182no—
314C2×C4—362no—
315C2×C4—362no—
316C2×C4—362no—
317C2×C4C22×#15711yescharacteristic
318C2×C4C22×#15712yes—
319C2×C4C22×#15712yes—
320C2×C4C22×#15711yescharacteristic
321C2×C3—28no—
322C2×C3—22no—
323C2×C3—22no—
324C2×C3—22no—
325D3—64no—
326D3—64no—
327D3—68no—
328C22—21no—
329C22—21no—
330C22—92no—
331C22—92no—
332C22—91no—
333C22—91no—
334C22—92no—
335C22—184no—
336C22—184no—
337C22—181no—
338C22—181no—
339C22Q8×#15712yes—
340C22C23×#15711yescharacteristic
341C4—21no—
342C4—22no—
343C4—22no—
344C4—92no—
345C4—184no—
346C4—181no—
347C4—182no—
348C4—182no—
349C4—362no—
350C4—364no—
351C4#6428612yes—
352C3—22no—
353C2—22no—
354C2—92no—
355C2—92no—
356C2—182no—
357C2C2×#6428611yescharacteristic
358C2#1059664211yescharacteristic
359C2C2×Q8×#15711yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC2×C32×C4⋊C4C4
prime radicalC23×C3⋊D3C23
cosocleC22×C3⋊D3C24
hypercenterC2×C4⋊C4#157
hypocenterC32#2345
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #10593759C2semidirect
7. #10593758C2semidirect
8. C4⋊C4×#157C2semidirect
18. C2×C32×C4⋊C4C4semidirect
19. C2×C4⋊(C3⋊Dic3)C4semidirect
20. C2×#3750C4semidirect
21. C4⋊C4×C3⋊D3C4semidirect
22. C4⋊C4×C3⋊D3C4semidirect
23. C4⋊C4×C3⋊D3C4semidirect
184. C2×C4⋊C4#157semidirect
284. C32#2345semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
#105938122
C4×C22⋊#1572
#105937592
#105937582
C4⋊C4×#1572
#23459