Finite Group Databasebeta

← #11785310

Subgroups — #11785310

Order 1152.

468 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×#3697C211yesmaximal, characteristic
2C4×C9×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#63364C212yesmaximal
4#10588604C211yesmaximal, characteristic, complemented
5#10588201C212yesmaximal, complemented
6#69494—31nomaximal
7C2×#3697C2211yescharacteristic
8C2×C9×C4⋊C4—21no—
9C2×C42×C9C2212yes—
10C2×C42×C9C2211yescharacteristic
11C4×#611—21no—
12C4×#611—21no—
13#63488C2211yescharacteristic
14C2×#3667C2212yes—
15C4×D36C411yescharacteristic, complemented
16C4×D36C411yescharacteristic, complemented
17#63434—21no—
18C42×D9—21no—
19C4×Dic18C411yescharacteristic, complemented
20C4×Dic18C411yescharacteristic, complemented
21C9×#95—21no—
22#63364—24no—
23C4⋊(C9⋊C8)—21no—
24C4⋊(C9⋊C8)—21no—
25C4×#235—31no—
26C3×C4×C4⋊C4D311yescharacteristic
27C2×#805—32no—
28#4924—31no—
29#4523—32no—
30C22×C4×C9—22no—
31C22×C4×C9D411yescharacteristic
32C22×C4×C9D411yescharacteristic
33C22×C4×C9C2311yescharacteristic
34C2×#611—21no—
35#3697—21no—
36#3697—21no—
37#3697D412yes—
38#3697Q812yes—
39C2×D36C2×C411yescharacteristic
40C2×C4×D9—21no—
41C2×C4×D9—21no—
42C2×C4×D9—21no—
43C2×Dic18C2×C411yescharacteristic
44C9×C4⋊C4—24no—
45C42×C9—22no—
46C42×C9—22no—
47C42×C9C2×C411yescharacteristic
48C42×C9C2×C411yescharacteristic
49C42×C9D411yescharacteristic
50C42×C9D411yescharacteristic
51#3676—21no—
52(C2×D9)⋊C4—21no—
53(C2×D9)⋊C4—21no—
54C4⋊Dic9C2×C411yescharacteristic
55C4⋊Dic9C2×C411yescharacteristic
56Dic9⋊C4—21no—
57Dic9⋊C4—21no—
58C4×Dic9—21no—
59C4×Dic9—21no—
60C4×Dic9—21no—
61#3667—22no—
62#3667—22no—
63C2×C9⋊C8—22no—
64#1806—91noSylow
65C2×#235—31no—
66C2×C3×C4⋊C4—21no—
67C2×C3×C42C2×D312yes—
68C2×C3×C42C2×D311yescharacteristic
69C4×#67—61no—
70C4×#67—61no—
71#926—31no—
72C2×#208—32no—
73C4×D12—31no—
74C4×D12—31no—
75#872—61no—
76C42×D3—61no—
77C4×Dic6—31no—
78C4×Dic6—31no—
79C3×#95—21no—
80#805—64no—
81C4⋊(C3⋊C8)—61no—
82C4⋊(C3⋊C8)—61no—
83C23×C9C2×D411yescharacteristic
84C22×D9—21no—
85C2×C4×C9—22no—
86C2×C4×C9—24no—
87C2×C4×C9—41no—
88C2×C4×C9—42no—
89C2×C4×C9—42no—
90C2×C4×C9C22⋊C411yescharacteristic
91C2×C4×C9C22⋊C411yescharacteristic
92C2×C4×C9C22⋊C411yescharacteristic
93C2×C4×C9C22⋊C411yescharacteristic
94C2×C4×C9C22×C411yescharacteristic
95C2×C4×C9C2×D411yescharacteristic
96C2×C4×C9C2×D411yescharacteristic
97C2×C4×C9C2×Q811yescharacteristic
98C2×C4×C9#4111yescharacteristic
99C2×C4×C9#4111yescharacteristic
100#611—22no—
101#611—22no—
102C2×Dic9—21no—
103C2×Dic9—21no—
104C2×Dic9—21no—
105D36—21no—
106D36C4⋊C412yescomplemented
107C4×D9—22no—
108C4×D9—22no—
109C4×D9—42no—
110C4×D9—42no—
111Dic18—21no—
112Dic18C4⋊C412yescomplemented
113C9⋊C8—42no—
114C4×#41—91no—
115#423—91no—
116C2×#104—92no—
117C4×C4⋊C4D911yescharacteristic, complemented
118#339—92no—
119C22×C3×C4—22no—
120C22×C3×C4#6711yescharacteristic
121C22×C3×C4#6711yescharacteristic
122C22×C3×C4C22×D311yescharacteristic
123C2×#67—61no—
124#235—32no—
125#235—32no—
126#235—61no—
127#235—61no—
128C2×D12—31no—
129C2×C4×D3—61no—
130C2×C4×D3—61no—
131C2×C4×D3—61no—
132C2×Dic6—31no—
133C3×C4⋊C4—24no—
134C3×C42—22no—
135C3×C42—22no—
136C3×C42C4×D311yescharacteristic
137C3×C42C4×D311yescharacteristic
138C3×C42D1211yescharacteristic
139C3×C42D1211yescharacteristic
140#217—61no—
141(C2×D3)⋊C4—61no—
142(C2×D3)⋊C4—61no—
143C4⋊Dic3—31no—
144C4⋊Dic3—31no—
145Dic3⋊C4—61no—
146Dic3⋊C4—61no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C4×Dic3—61no—
150#208—62no—
151#208—62no—
152C2×C3⋊C8—62no—
153C22×C9—21no—
154C22×C9—21no—
155C22×C9C2×C22⋊C411yescharacteristic
156C22×C9#12111yescharacteristic
157C22×C9C22⋊Q811yescharacteristic
158C2×D9—22no—
159C2×D9—41no—
160C2×D9—41no—
161C4×C9—21no—
162C4×C9—21no—
163C4×C9—21no—
164C4×C9—44no—
165C4×C9#10412yescomplemented
166C4×C9C2×C4⋊C411yescharacteristic
167C4×C9#11711yescharacteristic
168C4×C9#12111yescharacteristic
169C4×C9C22⋊Q811yescharacteristic
170Dic9—22no—
171Dic9—41no—
172Dic9—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×D912yes—
186C2×C42C2×D911yescharacteristic
187C4⋊C8—181no—
188C4⋊C8—181no—
189#104—184no—
190#95—21no—
191C23×C3C2×#6711yescharacteristic
192C22×D3—61no—
193C2×C3×C4—22no—
194C2×C3×C4—24no—
195C2×C3×C4—41no—
196C2×C3×C4—42no—
197C2×C3×C4—42no—
198C2×C3×C4(C2×D3)⋊C411yescharacteristic
199C2×C3×C4(C2×D3)⋊C411yescharacteristic
200C2×C3×C4(C2×D3)⋊C411yescharacteristic
201C2×C3×C4(C2×D3)⋊C411yescharacteristic
202C2×C3×C4C2×C4×D311yescharacteristic
203C2×C3×C4C2×D1211yescharacteristic
204C2×C3×C4D3×D411yescharacteristic
205C2×C3×C4#23711yescharacteristic
206C2×C3×C4D3×Q811yescharacteristic
207C2×C3×C4#23911yescharacteristic
208#67—62no—
209#67—62no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213D12—32no—
214D12—61no—
215C4×D3—62no—
216C4×D3—62no—
217C4×D3—122no—
218C4×D3—122no—
219Dic6—32no—
220Dic6—61no—
221C3⋊C8—122no—
222C2×C9—21no—
223C2×C9—21no—
224C2×C9#38011yescharacteristic
225C2×C9C2×#10411yescharacteristic
226C2×C9#42111yescharacteristic
227D9—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#61111yescharacteristic
240C22×C4#61111yescharacteristic
241C22×C4C22×D911yescharacteristic
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×D911yescharacteristic
259C42C4×D911yescharacteristic
260C42D3611yescharacteristic
261C42D3611yescharacteristic
262C22×C3—21no—
263C22×C3—21no—
264C22×C3C2×(C2×D3)⋊C411yescharacteristic
265C22×C3#93811yescharacteristic
266C22×C3#94611yescharacteristic
267C2×D3—62no—
268C2×D3—121no—
269C2×D3—121no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—44no—
274C3×C4#80512yes—
275C3×C4D3×C4⋊C411yescharacteristic
276C3×C4#89211yescharacteristic
277C3×C4#89511yescharacteristic
278C3×C4#89711yescharacteristic
279Dic3—62no—
280Dic3—121no—
281Dic3—121no—
282C9#180611yescharacteristic, complemented, Sylow
283C23—181no—
284C23C2×#61111yescharacteristic
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(C2×D9)⋊C411yescharacteristic
304C2×C4(C2×D9)⋊C411yescharacteristic
305C2×C4(C2×D9)⋊C411yescharacteristic
306C2×C4(C2×D9)⋊C411yescharacteristic
307C2×C4C2×C4×D911yescharacteristic
308C2×C4C2×D3611yescharacteristic
309C2×C4D4×D911yescharacteristic
310C2×C4#369911yescharacteristic
311C2×C4Q8×D911yescharacteristic
312C2×C4#370111yescharacteristic
313C8—362no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3C2×#80511yescharacteristic
317C2×C3#498711yescharacteristic
318C2×C3#500511yescharacteristic
319D3—122no—
320C22—21no—
321C22—21no—
322C22—182no—
323C22—361no—
324C22—361no—
325C22C2×(C2×D9)⋊C411yescharacteristic
326C22#6350011yescharacteristic
327C22#6350811yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—44no—
332C4—182no—
333C4—361no—
334C4—361no—
335C4#6336412yescomplemented
336C4C4⋊C4×D911yescharacteristic
337C4#6345411yescharacteristic
338C4#6345711yescharacteristic
339C4#6345911yescharacteristic
340C3#6949411yescharacteristic
341C2—21no—
342C2—21no—
343C2—362no—
344C2C2×#6336411yescharacteristic
345C2#1058866711yescharacteristic
346C2#1058868511yescharacteristic
subgroupG/H
centerC2×C4C2×D36
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC4×C9×C4⋊C4C2
socleC22×C3C2×(C2×D3)⋊C4
prime radicalC2×#3697C22
cosocleC22×C4×C9C23
hypercenterC4×C4⋊C4D9
hypocenterC9#1806
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×C9×C4⋊C4C2semidirect
4. #10588604C2semidirect
5. #10588201C2semidirect
15. C4×D36C4semidirect
16. C4×D36C4semidirect
19. C4×Dic18C4semidirect
20. C4×Dic18C4semidirect
106. D36C4⋊C4semidirect
112. Dic18C4⋊C4semidirect
117. C4×C4⋊C4D9semidirect
165. C4×C9#104semidirect
282. C9#1806semidirect
335. C4#63364semidirect

Maximal subgroups

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

subgroupindex
C4×#36972
C4×C9×C4⋊C42
C2×#633642
#105886042
#105882012
#694943