Finite Group Databasebeta

← #11785311

Subgroups — #11785311

Order 1152.

936 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic
2C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#63632C212yesmaximal
4#10592623C211yesmaximal, characteristic, complemented
5#10589389C212yesmaximal, complemented
6#69494—34nomaximal
7C2×#3828C2211yescharacteristic
8C2×C32×C4⋊C4—21no—
9C2×C32×C42C2212yes—
10C2×C32×C42C2211yescharacteristic
11C4×#638—21no—
12C4×#638—21no—
13#64135C2211yescharacteristic
14C2×#3748C2212yes—
15C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
16C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
17#64081—21no—
18C42×C3⋊D3—21no—
19C4×#634C411yescharacteristic, complemented
20C4×#634C411yescharacteristic, complemented
21C32×#95—21no—
22#63632—24no—
23C4⋊(C3⋊(C3⋊C8))—21no—
24C4⋊(C3⋊(C3⋊C8))—21no—
25C4×#235—34no—
26C3×C4×C4⋊C4D314yescomplemented
27C2×#805—38no—
28#4924—34no—
29#4523—38no—
30C22×C32×C4—22no—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C2×#638—21no—
35#3828—21no—
36#3828—21no—
37#3828D412yes—
38#3828Q812yes—
39C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
40C2×C4×C3⋊D3—21no—
41C2×C4×C3⋊D3—21no—
42C2×C4×C3⋊D3—21no—
43C2×#634C2×C411yescharacteristic
44C32×C4⋊C4—24no—
45C32×C42—22no—
46C32×C42—22no—
47C32×C42C2×C411yescharacteristic
48C32×C42C2×C411yescharacteristic
49C32×C42D411yescharacteristic
50C32×C42D411yescharacteristic
51#3757—21no—
52#3752—21no—
53#3752—21no—
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55C4⋊(C3⋊Dic3)C2×C411yescharacteristic
56#3750—21no—
57#3750—21no—
58C4×C3⋊Dic3—21no—
59C4×C3⋊Dic3—21no—
60C4×C3⋊Dic3—21no—
61#3748—22no—
62#3748—22no—
63C2×C3⋊(C3⋊C8)—22no—
64#1806—91noSylow
65C2×#235—34no—
66C2×C3×C4⋊C4—24no—
67C2×C3×C42C2×D318yes—
68C2×C3×C42C2×D314yes—
69C4×#67—64no—
70C4×#67—64no—
71#926—34no—
72C2×#208—38no—
73C4×D12—34no—
74C4×D12—34no—
75#872—64no—
76C42×D3—64no—
77C4×Dic6—34no—
78C4×Dic6—34no—
79C3×#95—24no—
80#805—616no—
81C4⋊(C3⋊C8)—64no—
82C4⋊(C3⋊C8)—64no—
83C23×C32C2×D411yescharacteristic
84C22×C3⋊D3—21no—
85C2×C32×C4—22no—
86C2×C32×C4—24no—
87C2×C32×C4—41no—
88C2×C32×C4—42no—
89C2×C32×C4—42no—
90C2×C32×C4C22⋊C411yescharacteristic
91C2×C32×C4C22⋊C411yescharacteristic
92C2×C32×C4C22⋊C411yescharacteristic
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×Q811yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C32×C4#4111yescharacteristic
100#638—22no—
101#638—22no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—21no—
104C2×C3⋊Dic3—21no—
105C4⋊(C3⋊D3)—21no—
106C4⋊(C3⋊D3)C4⋊C412yescomplemented
107C4×C3⋊D3—22no—
108C4×C3⋊D3—22no—
109C4×C3⋊D3—42no—
110C4×C3⋊D3—42no—
111#634—21no—
112#634C4⋊C412yescomplemented
113C3⋊(C3⋊C8)—42no—
114C4×#41—91no—
115#423—91no—
116C2×#104—92no—
117C4×C4⋊C4C3⋊D311yescharacteristic, complemented
118#339—92no—
119C22×C3×C4—28no—
120C22×C3×C4#6714yes—
121C22×C3×C4#6714yes—
122C22×C3×C4C22×D314yes—
123C2×#67—64no—
124#235—38no—
125#235—38no—
126#235—64no—
127#235—64no—
128C2×D12—34no—
129C2×C4×D3—64no—
130C2×C4×D3—64no—
131C2×C4×D3—64no—
132C2×Dic6—34no—
133C3×C4⋊C4—216no—
134C3×C42—28no—
135C3×C42—28no—
136C3×C42C4×D314yes—
137C3×C42C4×D314yes—
138C3×C42D1214yes—
139C3×C42D1214yes—
140#217—64no—
141(C2×D3)⋊C4—64no—
142(C2×D3)⋊C4—64no—
143C4⋊Dic3—34no—
144C4⋊Dic3—34no—
145Dic3⋊C4—64no—
146Dic3⋊C4—64no—
147C4×Dic3—64no—
148C4×Dic3—64no—
149C4×Dic3—64no—
150#208—68no—
151#208—68no—
152C2×C3⋊C8—68no—
153C22×C32—21no—
154C22×C32—21no—
155C22×C32C2×C22⋊C411yescharacteristic
156C22×C32#12111yescharacteristic
157C22×C32C22⋊Q811yescharacteristic
158C2×C3⋊D3—22no—
159C2×C3⋊D3—41no—
160C2×C3⋊D3—41no—
161C32×C4—21no—
162C32×C4—21no—
163C32×C4—21no—
164C32×C4—44no—
165C32×C4#10412yescomplemented
166C32×C4C2×C4⋊C411yescharacteristic
167C32×C4#11711yescharacteristic
168C32×C4#12111yescharacteristic
169C32×C4C22⋊Q811yescharacteristic
170C3⋊Dic3—22no—
171C3⋊Dic3—41no—
172C3⋊Dic3—41no—
173C2×#41—91no—
174C2×M16—92no—
175C4×Q8—91no—
176C4×Q8—91no—
177C4×D4—91no—
178C4×D4—91no—
179C4×D4—181no—
180C4×D4—181no—
181#117—91no—
182#117—181no—
183C2×C4⋊C4—21no—
184C2×C42—181no—
185C2×C42C2×C3⋊D312yes—
186C2×C42C2×C3⋊D311yescharacteristic
187C4⋊C8—181no—
188C4⋊C8—181no—
189#104—184no—
190#95—21no—
191C23×C3C2×#6714yes—
192C22×D3—64no—
193C2×C3×C4—28no—
194C2×C3×C4—216no—
195C2×C3×C4—44no—
196C2×C3×C4—48no—
197C2×C3×C4—48no—
198C2×C3×C4(C2×D3)⋊C414yes—
199C2×C3×C4(C2×D3)⋊C414yes—
200C2×C3×C4(C2×D3)⋊C414yes—
201C2×C3×C4(C2×D3)⋊C414yes—
202C2×C3×C4C2×C4×D314yes—
203C2×C3×C4C2×D1214yes—
204C2×C3×C4D3×D414yes—
205C2×C3×C4#23714yes—
206C2×C3×C4D3×Q814yes—
207C2×C3×C4#23914yes—
208#67—68no—
209#67—68no—
210C2×Dic3—64no—
211C2×Dic3—64no—
212C2×Dic3—64no—
213D12—38no—
214D12—64no—
215C4×D3—68no—
216C4×D3—68no—
217C4×D3—128no—
218C4×D3—128no—
219Dic6—38no—
220Dic6—64no—
221C3⋊C8—128no—
222C2×C32—21no—
223C2×C32—21no—
224C2×C32#38011yescharacteristic
225C2×C32C2×#10411yescharacteristic
226C2×C32#42111yescharacteristic
227C3⋊D3—42no—
228#41—92no—
229#41—92no—
230#41—181no—
231#41—181no—
232C2×Q8—91no—
233C2×D4—91no—
234C2×D4—181no—
235C22×C4—22no—
236C22×C4—181no—
237C22×C4—181no—
238C22×C4—181no—
239C22×C4#63811yescharacteristic
240C22×C4#63811yescharacteristic
241C22×C4C22×C3⋊D311yescharacteristic
242M16—182no—
243M16—182no—
244C2×C8—182no—
245C4⋊C4—24no—
246C4⋊C4—91no—
247C4⋊C4—91no—
248C4⋊C4—181no—
249C4⋊C4—181no—
250C22⋊C4—181no—
251C22⋊C4—181no—
252C22⋊C4—181no—
253C42—22no—
254C42—22no—
255C42—181no—
256C42—181no—
257C42—181no—
258C42C4×C3⋊D311yescharacteristic
259C42C4×C3⋊D311yescharacteristic
260C42C4⋊(C3⋊D3)11yescharacteristic
261C42C4⋊(C3⋊D3)11yescharacteristic
262C22×C3—24no—
263C22×C3—24no—
264C22×C3C2×(C2×D3)⋊C414yes—
265C22×C3#93814yes—
266C22×C3#94614yes—
267C2×D3—68no—
268C2×D3—124no—
269C2×D3—124no—
270C3×C4—24no—
271C3×C4—24no—
272C3×C4—24no—
273C3×C4—416no—
274C3×C4#80518yescomplemented
275C3×C4D3×C4⋊C414yes—
276C3×C4#89214yes—
277C3×C4#89514yes—
278C3×C4#89714yes—
279Dic3—68no—
280Dic3—124no—
281Dic3—124no—
282C32#180611yescharacteristic, complemented, Sylow
283C23—181no—
284C23C2×#63811yescharacteristic
285Q8—92no—
286Q8—181no—
287D4—92no—
288D4—182no—
289D4—182no—
290D4—181no—
291C2×C4—22no—
292C2×C4—24no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—181no—
297C2×C4—182no—
298C2×C4—182no—
299C2×C4—181no—
300C2×C4—181no—
301C2×C4—362no—
302C2×C4—362no—
303C2×C4#375211yescharacteristic
304C2×C4#375211yescharacteristic
305C2×C4#375211yescharacteristic
306C2×C4#375211yescharacteristic
307C2×C4C2×C4×C3⋊D311yescharacteristic
308C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
309C2×C4D4×C3⋊D311yescharacteristic
310C2×C4#383011yescharacteristic
311C2×C4Q8×C3⋊D311yescharacteristic
312C2×C4#383211yescharacteristic
313C8—362no—
314C2×C3—24no—
315C2×C3—24no—
316C2×C3C2×#80514yes—
317C2×C3#498714yes—
318C2×C3#500514yes—
319D3—128no—
320C22—21no—
321C22—21no—
322C22—182no—
323C22—361no—
324C22—361no—
325C22C2×#375211yescharacteristic
326C22#6414711yescharacteristic
327C22#6415511yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—44no—
332C4—182no—
333C4—361no—
334C4—361no—
335C4#6363212yescomplemented
336C4C4⋊C4×C3⋊D311yescharacteristic
337C4#6410111yescharacteristic
338C4#6410411yescharacteristic
339C4#6410611yescharacteristic
340C3#6949414yescomplemented
341C2—21no—
342C2—21no—
343C2—362no—
344C2C2×#6363211yescharacteristic
345C2#1059268611yescharacteristic
346C2#1059270411yescharacteristic
subgroupG/H
centerC2×C4C2×C4⋊(C3⋊D3)
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×C4×C4⋊C4C2
socleC22×C32C2×C22⋊C4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC4×C4⋊C4C3⋊D3
hypocenterC32#1806
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×C4×C4⋊C4C2semidirect
4. #10592623C2semidirect
5. #10589389C2semidirect
15. C4×C4⋊(C3⋊D3)C4semidirect
16. C4×C4⋊(C3⋊D3)C4semidirect
19. C4×#634C4semidirect
20. C4×#634C4semidirect
26. C3×C4×C4⋊C4D3semidirect
106. C4⋊(C3⋊D3)C4⋊C4semidirect
112. #634C4⋊C4semidirect
117. C4×C4⋊C4C3⋊D3semidirect
165. C32×C4#104semidirect
274. C3×C4#805semidirect
282. C32#1806semidirect
335. C4#63632semidirect
340. C3#69494semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C32×C4×C4⋊C42
C2×#636322
#105926232
#105893892
#694943