Finite Group Databasebeta

← #11806042

Subgroups — #11806042

Order 1152.

986 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×C3⋊D3C211yesmaximal, characteristic
2#10593827C212yesmaximal
3#10593811C212yesmaximal, complemented
4C4×C22⋊#157C212yesmaximal, complemented
5C4⋊C4×#157C212yesmaximal, complemented
6#10593747C214yesmaximal, complemented
7#10593736C211yesmaximal, characteristic, complemented
8C4×C4⋊#157C211yesmaximal, characteristic, complemented
9C2×D4×C3⋊D3C2211yescharacteristic
10C22×C4×C3⋊D3C2212yes—
11C2×C22⋊#157C2214yes—
12C2×C22⋊#157C2214yes—
13C2×C4⋊#157C2212yes—
14C2×C4⋊#157C2212yes—
15C2×C4×#157C2212yes—
16C2×C4×#157C2214yes—
17C32×C4×D4C411yescharacteristic, complemented
18D4×C3⋊Dic3C411yescharacteristic, complemented
19C4×#638C412yescomplemented
20#64102C411yescharacteristic, complemented
21C4⋊C4×C3⋊D3C2211yescharacteristic
22#64090C412yescomplemented
23C22⋊C4×C3⋊D3C2212yes—
24C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
25C42×C3⋊D3C2211yescharacteristic
26#63781C2211yescharacteristic
27#63781C2212yes—
28#63781C2211yescharacteristic
29#63781C2214yes—
30#63781C2212yes—
31C4×D3×D4—62no—
32C23×C3⋊D3C2312yes—
33C22×#157C2312yes—
34C22×#157C2314yes—
35C22×#157C2312yes—
36C2×C32×D4C2×C411yescharacteristic
37C22×C32×C4C2×C412yes—
38C2×#638C2×C412yes—
39C22×C3⋊Dic3C2×C412yes—
40D4×C3⋊D3—22no—
41D4×C3⋊D3—22no—
42C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
43C2×C4×C3⋊D3—44no—
44C2×C4×C3⋊D3C2×C412yes—
45C2×C4×C3⋊D3C2×C412yes—
46C2×C4×C3⋊D3C2312yes—
47C2×C4×C3⋊D3C2311yescharacteristic
48C2×C4×C3⋊D3C2311yescharacteristic
49C2×C4×C3⋊D3C2311yescharacteristic
50C22⋊#157—28no—
51C22⋊#157—44no—
52C4⋊#157—24no—
53C4⋊#157—24no—
54C4×#157—24no—
55C4×#157—44no—
56C32×C4⋊C4C2×C411yescharacteristic
57C32×C22⋊C4C2×C412yes—
58C32×C42C2×C411yescharacteristic
59#3757C2×C412yes—
60#3752C2×C412yes—
61#3752C2×C412yes—
62C4⋊(C3⋊Dic3)C2×C411yescharacteristic
63#3750C2×C412yes—
64C4×C3⋊Dic3C2×C411yescharacteristic
65C4×C3⋊Dic3C2×C411yescharacteristic
66C4×C3⋊Dic3C2×C411yescharacteristic
67#2357—91nomaximal, Sylow
68C2×D3×D4—62no—
69C22×C4×D3—64no—
70C3×C4×D4—22no—
71D4×Dic3—62no—
72C4×#67—64no—
73#893—62no—
74D3×C4⋊C4—62no—
75#67⋊C4—64no—
76D3×C22⋊C4—64no—
77C4×D12—62no—
78C42×D3—62no—
79C23×C32C22×C412yes—
80C22×C3⋊D3—22no—
81C22×C3⋊D3—22no—
82C22×C3⋊D3—24no—
83C22×C3⋊D3—24no—
84C22×C3⋊D3C22×C412yes—
85C22×C3⋊D3C2411yescharacteristic
86C2×#157—22no—
87C2×#157—22no—
88C2×#157—22no—
89C2×#157—22no—
90C2×#157—24no—
91C2×#157—24no—
92C2×#157—24no—
93C2×#157—22no—
94C2×#157#4114yes—
95C32×D4—22no—
96C2×C32×C4—42no—
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C22×C412yes—
100C2×C32×C4C22×C411yescharacteristic
101#638—24no—
102C2×C3⋊Dic3—42no—
103C2×C3⋊Dic3C22×C411yescharacteristic
104C2×C3⋊Dic3C22×C411yescharacteristic
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—42no—
112C4×C3⋊D3—42no—
113C4×C3⋊D3#4112yes—
114C4×C3⋊D3#4112yes—
115C2×C4×D4—91no—
116#390—92no—
117#388—94no—
118#382—91no—
119#381—92no—
120C4×C4⋊C4—91no—
121C4×C4⋊C4—92no—
122C4×C22⋊C4—92no—
123C23×D3—64no—
124C2×C3×D4—22no—
125C22×C3×C4—24no—
126C2×#67—64no—
127C22×Dic3—64no—
128D3×D4—68no—
129D3×D4—68no—
130C2×D12—62no—
131C2×C4×D3—62no—
132C2×C4×D3—62no—
133C2×C4×D3—62no—
134C2×C4×D3—64no—
135C2×C4×D3—64no—
136C2×C4×D3—64no—
137C2×C4×D3—1216no—
138C3×C4⋊C4—22no—
139C3×C22⋊C4—24no—
140C3×C42—22no—
141#217—64no—
142(C2×D3)⋊C4—64no—
143(C2×D3)⋊C4—64no—
144C4⋊Dic3—62no—
145Dic3⋊C4—64no—
146C4×Dic3—62no—
147C4×Dic3—62no—
148C4×Dic3—62no—
149C22×C32—22no—
150C22×C32—22no—
151C22×C32—22no—
152C22×C32C23×C411yescharacteristic
153C2×C3⋊D3—22no—
154C2×C3⋊D3—22no—
155C2×C3⋊D3—22no—
156C2×C3⋊D3—44no—
157C2×C3⋊D3—44no—
158C2×C3⋊D3C2×#4111yescharacteristic
159C2×C3⋊D3C2×#4112yes—
160C2×C3⋊D3C2×#4111yescharacteristic
161C2×C3⋊D3H(5,𝔽2)12yes—
162#157—24no—
163#157—42no—
164#157—44no—
165C32×C4—21no—
166C32×C4—21no—
167C32×C4—22no—
168C32×C4#11712yes—
169C3⋊Dic3—21no—
170C3⋊Dic3—21no—
171C3⋊Dic3—22no—
172C3⋊Dic3#11712yes—
173C22×D4—91no—
174C23×C4—92no—
175C4×D4—91no—
176C4×D4—92no—
177C4×D4—91no—
178C4×D4—92no—
179C4×D4—91no—
180C4×D4#15711yescharacteristic, complemented
181C2×C4⋊C4—91no—
182C2×C4⋊C4—92no—
183C2×C4⋊C4—92no—
184C2×C22⋊C4—92no—
185C2×C22⋊C4—94no—
186C2×C22⋊C4—94no—
187C2×C42—91no—
188C2×C42—92no—
189C2×C42—94no—
190#95—91no—
191#95—92no—
192#95—91no—
193#95—94no—
194#95—92no—
195C23×C3—24no—
196C22×D3—62no—
197C22×D3—64no—
198C22×D3—68no—
199C22×D3—68no—
200C22×D3—128no—
201C22×D3—128no—
202C3×D4—28no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—24no—
207C2×C3×C4—48no—
208#67—616no—
209C2×Dic3—62no—
210C2×Dic3—62no—
211C2×Dic3—62no—
212C2×Dic3—64no—
213C2×Dic3—128no—
214D12—68no—
215C4×D3—64no—
216C4×D3—64no—
217C4×D3—68no—
218C4×D3—124no—
219C4×D3—128no—
220C4×D3—128no—
221C4×D3—128no—
222C2×C32—42no—
223C2×C32C2×#11711yescharacteristic
224C2×C32C4×#4111yescharacteristic
225C2×C32#51811yescharacteristic
226C3⋊D3—42no—
227C3⋊D3#55312yes—
228C3⋊D3#55912yes—
229C24—92no—
230C2×D4—92no—
231C2×D4—91no—
232C2×D4—182no—
233C2×D4—182no—
234C2×D4C2×#15711yescharacteristic
235C22×C4—91no—
236C22×C4—92no—
237C22×C4—92no—
238C22×C4—91no—
239C22×C4—92no—
240C22×C4—91no—
241C22×C4—92no—
242C22×C4—92no—
243C22×C4—92no—
244C22×C4—94no—
245C22×C4—364no—
246C22×C4C2×#15712yes—
247C4⋊C4—92no—
248C4⋊C4—91no—
249C4⋊C4—184no—
250C4⋊C4—184no—
251C4⋊C4C2×#15711yescharacteristic
252C22⋊C4—92no—
253C22⋊C4—92no—
254C22⋊C4—92no—
255C22⋊C4—188no—
256C22⋊C4—364no—
257C22⋊C4C2×#15712yes—
258C42—91no—
259C42—91no—
260C42—91no—
261C42—184no—
262C42—364no—
263C42C2×#15711yescharacteristic
264C22×C3—28no—
265C22×C3—22no—
266C22×C3—44no—
267C22×C3—44no—
268C2×D3—64no—
269C2×D3—62no—
270C2×D3—62no—
271C2×D3—64no—
272C2×D3—68no—
273C2×D3—124no—
274C2×D3—124no—
275C2×D3—1216no—
276C2×D3—1216no—
277C3×C4—24no—
278C3×C4—24no—
279C3×C4—44no—
280C3×C4—42no—
281Dic3—64no—
282Dic3—64no—
283Dic3—124no—
284Dic3—122no—
285C32#235711yescharacteristic, complemented, Sylow
286C23—91no—
287C23—92no—
288C23—184no—
289C23—184no—
290C23—182no—
291C23—182no—
292C23C22×#15712yes—
293D4—22no—
294D4—184no—
295D4—182no—
296C2×C4—42no—
297C2×C4—91no—
298C2×C4—92no—
299C2×C4—92no—
300C2×C4—94no—
301C2×C4—91no—
302C2×C4—91no—
303C2×C4—92no—
304C2×C4—184no—
305C2×C4—182no—
306C2×C4—182no—
307C2×C4—182no—
308C2×C4—182no—
309C2×C4—182no—
310C2×C4—184no—
311C2×C4—184no—
312C2×C4—182no—
313C2×C4—184no—
314C2×C4—182no—
315C2×C4—362no—
316C2×C4—362no—
317C2×C4—362no—
318C2×C4C22×#15711yescharacteristic
319C2×C4C22×#15711yescharacteristic
320C2×C4C22×#15712yes—
321C2×C4C22×#15711yescharacteristic
322C2×C3—22no—
323C2×C3—22no—
324C2×C3—22no—
325C2×C3—48no—
326D3—64no—
327D3—64no—
328D3—128no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—91no—
333C22—91no—
334C22—92no—
335C22—92no—
336C22—182no—
337C22—182no—
338C22—182no—
339C22—364no—
340C22—364no—
341C22C23×#15711yescharacteristic
342C4—21no—
343C4—22no—
344C4—21no—
345C4—92no—
346C4—184no—
347C4—181no—
348C4—182no—
349C4—181no—
350C4—362no—
351C4—364no—
352C4#6428612yes—
353C3—22no—
354C2—42no—
355C2—92no—
356C2—92no—
357C2—362no—
358C2C2×#6428611yescharacteristic
359C2#1059664211yescharacteristic
360C2#41×#15711yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C4×D4C4
prime radicalC2×D4×C3⋊D3C22
cosocleC22×C3⋊D3C24
hypercenterC4×D4#157
hypocenterC32#2357
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10593811C2semidirect
4. C4×C22⋊#157C2semidirect
5. C4⋊C4×#157C2semidirect
6. #10593747C2semidirect
7. #10593736C2semidirect
8. C4×C4⋊#157C2semidirect
17. C32×C4×D4C4semidirect
18. D4×C3⋊Dic3C4semidirect
19. C4×#638C4semidirect
20. #64102C4semidirect
22. #64090C4semidirect
24. C4×C4⋊(C3⋊D3)C4semidirect
180. C4×D4#157semidirect
285. C32#2357semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
#105938272
#105938112
C4×C22⋊#1572
C4⋊C4×#1572
#105937472
#105937362
C4×C4⋊#1572
#23579