Finite Group Databasebeta

← #11777595

Subgroups — #11777595

Order 1152.

383 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
1#10592723C211yesmaximal, characteristic, complemented
2C3×C4×#215C211yesmaximal, characteristic
3#10590329C211yesmaximal, characteristic
4C3×#4535C211yesmaximal, characteristic, complemented
5#10589099C211yesmaximal, characteristic, complemented
6#10589081C211yesmaximal, characteristic
7#10589078C211yesmaximal, characteristic, complemented
8#70897—31nomaximal
9#68220—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C2×C3×#215C411yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C2×D3×C3⋊C8—21no—
14C4⋊(C3⋊(C3⋊C8))—21no—
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16#63630—21no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#835C411yescharacteristic
19C3×#809C411yescharacteristic
20C3×#808C411yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×C4×SD16—31no—
26C4×#215D311yescharacteristic
27#5024—31no—
28#5024—31no—
29#5024—61no—
30D4×C3⋊C8—31no—
31#4834—31no—
32C3×Q8⋊C8—31no—
33#4535D311yescharacteristic, complemented
34D4⋊(C3⋊C8)—31no—
35#4479—31no—
36#4459—31no—
37#4458—31no—
38#4455—31no—
39#4454—31no—
40C2×C32×Q8C2×C411yescharacteristic
41C2×C3×D12C2×C411yescharacteristic
42C2×C3×C4×D3—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4C2×C411yescharacteristic
45C32×C42—21no—
46C32×C42C2311yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C3×#215—22no—
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3C2×C411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8C2×C411yescharacteristic
56C2×C3×C3⋊C8C2×C411yescharacteristic
57D3×C3⋊C8—42no—
58#1585—91noSylow
59C2×C3×SD16—31no—
60C3×C4×Q8—21no—
61C3×C4×Q8C2×D311yescharacteristic
62C3×C4×Q8C2×D311yescharacteristic
63C3×C4×D4—31no—
64C2×#215Dic311yescharacteristic
65C22×C3⋊C8—61no—
66C2×D3×C8—61no—
67C4×D12C2×D311yescharacteristic
68C3×#106—31no—
69C3×C4⋊C8—31no—
70C3×#103—31no—
71C3×#102—31no—
72C3×C4×C8—31no—
73C3×C4×C8—31no—
74#835Dic311yescharacteristic
75#830—61no—
76(C2×D3)⋊C8—61no—
77#809Dic311yescharacteristic
78#808Dic311yescharacteristic
79C4⋊(C3⋊C8)—31no—
80C4⋊(C3⋊C8)—31no—
81C4⋊(C3⋊C8)—61no—
82C4⋊(C3⋊C8)—61no—
83C4⋊(C3⋊C8)—61no—
84C4⋊(C3⋊C8)—62no—
85C4⋊(C3⋊C8)C2×D311yescharacteristic
86#803—61no—
87#803—61no—
88#803—62no—
89C4×C3⋊C8—31no—
90C4×C3⋊C8—31no—
91C4×C3⋊C8—61no—
92C4×C3⋊C8C2×D311yescharacteristic
93C4×C3⋊C8C2×D311yescharacteristic
94C22×C3×D3—21no—
95C32×Q8—21no—
96C32×Q8—21no—
97C2×C32×C4—21no—
98C2×C32×C4—21no—
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3×Dic3—21no—
103C3×D12—21no—
104C3×D12M1612yes—
105C3×C4×D3—41no—
106C3×C4×D3—41no—
107C3⋊(C3⋊C8)—21no—
108C3⋊(C3⋊C8)—21no—
109C3⋊(C3⋊C8)—41no—
110C3×C3⋊C8—22no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114#446—91no—
115C4×SD16—31no—
116C8×D4—91no—
117#335—91no—
118Q8⋊C8—31no—
119D4⋊C8—91no—
120#322—91no—
121C2×C3×Q8—21no—
122C2×C3×Q8C4×D311yescharacteristic
123C2×C3×Q8C2×Dic311yescharacteristic
124C2×C3×D4—31no—
125C22×C3×C4—61no—
126C2×D12C2×Dic311yescharacteristic
127C2×C4×D3—21no—
128C3×SD16—62no—
129C2×C3×C8—31no—
130C2×C3×C8—31no—
131C2×C3×C8—61no—
132C2×C3×C8—61no—
133C3×C4⋊C4—22no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4—31no—
138C3×C4⋊C4C4×D311yescharacteristic
139C3×C4⋊C4C2×Dic311yescharacteristic
140C3×C22⋊C4—61no—
141C3×C42—22no—
142C3×C42—21no—
143C3×C42—21no—
144C3×C42—21no—
145C3×C42C22×D311yescharacteristic
146C3×C42C22×D311yescharacteristic
147#215—22no—
148(C2×D3)⋊C4—21no—
149C4⋊Dic3C2×Dic311yescharacteristic
150C2×C3⋊C8—21no—
151C2×C3⋊C8—21no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—62no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8—122no—
162C2×C3⋊C8C2×Dic311yescharacteristic
163C2×C3⋊C8C2×Dic311yescharacteristic
164D3×C8—122no—
165C22×C32C4×D411yescharacteristic
166C2×C3×D3—22no—
167C2×C3×D3—41no—
168C2×C3×D3—41no—
169C32×C4—21no—
170C32×C4—41no—
171C32×C4—41no—
172C32×C4C2×M1611yescharacteristic
173C32×C4#13111yescharacteristic
174C32×C4AGL(1,ℤ/8)11yescharacteristic
175C32×C4#13711yescharacteristic
176C3×Dic3—41no—
177C2×SD16—31no—
178C22×C8—181no—
179C4×Q8D3211yescharacteristic
180C4×D4—31no—
181#106—31no—
182C4⋊C8—31no—
183C4⋊C8—91no—
184C4⋊C8—181no—
185#103—31no—
186#102—31no—
187C22⋊C8—181no—
188#97—181no—
189C4×C8—31no—
190C4×C8—31no—
191C4×C8—91no—
192C23×C3—61no—
193C22×D3—21no—
194C3×Q8—21no—
195C3×Q8—21no—
196C3×Q8—21no—
197C3×Q8—21no—
198C3×Q8—41no—
199C3×Q8—41no—
200C3×D4—32no—
201C3×D4—61no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—61no—
212C2×C3×C4—121no—
213C2×C3×C4—121no—
214C2×C3×C4C2×C4×D311yescharacteristic
215C2×C3×C4D3×D411yescharacteristic
216C2×C3×C4D3×D411yescharacteristic
217C2×C3×C4#23711yescharacteristic
218C2×C3×C4#23711yescharacteristic
219C2×C3×C4C22×Dic311yescharacteristic
220C2×Dic3—21no—
221D12—21no—
222D12#20812yes—
223C4×D3—41no—
224C4×D3—41no—
225C3×C8—62no—
226C3×C8—61no—
227C3×C8—61no—
228C3×C8—121no—
229C3⋊C8—22no—
230C3⋊C8—21no—
231C3⋊C8—21no—
232C3⋊C8—41no—
233C3⋊C8—62no—
234C3⋊C8—61no—
235C3⋊C8—61no—
236C3⋊C8—61no—
237C3⋊C8—61no—
238C3⋊C8—121no—
239C3⋊C8—122no—
240C3⋊C8—121no—
241C3⋊C8—121no—
242C2×C32#43511yescharacteristic
243C2×C32#44011yescharacteristic
244C2×C32#44311yescharacteristic
245C3×D3—42no—
246C2×Q8D3×Dic311yescharacteristic
247C2×D4—31no—
248C22×C4—61no—
249SD16—62no—
250C2×C8—31no—
251C2×C8—31no—
252C2×C8—61no—
253C2×C8—61no—
254C2×C8—91no—
255C2×C8—91no—
256C2×C8—181no—
257C2×C8—362no—
258C4⋊C4—21no—
259C4⋊C4—31no—
260C4⋊C4D3×Dic311yescharacteristic
261C22⋊C4—61no—
262C42—21no—
263C42C2×D3211yescharacteristic
264C22×C3—21no—
265C22×C3—62no—
266C22×C3—121no—
267C22×C3—121no—
268C22×C3#67⋊C411yescharacteristic
269C22×C3D4×Dic311yescharacteristic
270C2×D3—22no—
271C2×D3—41no—
272C2×D3—41no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—41no—
280C3×C4—42no—
281C3×C4—42no—
282C3×C4—41no—
283C3×C4—41no—
284C3×C4—41no—
285C3×C4—41no—
286C3×C4—121no—
287C3×C4#90111yescharacteristic
288C3×C4D3×M1611yescharacteristic
289C3×C4#91411yescharacteristic
290C3×C4#91411yescharacteristic
291C3×C4#91511yescharacteristic
292C3×C4#91811yescharacteristic
293C3×C4C2×#20811yescharacteristic
294C3×C4#94811yescharacteristic
295Dic3—41no—
296C32#158511yescharacteristic, complemented, Sylow
297C23—61no—
298Q8—21no—
299Q8—21no—
300D4—32no—
301D4—61no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—61no—
305C2×C4—121no—
306C2×C4—121no—
307C2×C4C2×D3×Dic311yescharacteristic
308C2×C4#380511yescharacteristic
309C2×C4#381111yescharacteristic
310C8—62no—
311C8—61no—
312C8—61no—
313C8—121no—
314C8—181no—
315C8—181no—
316C8—361no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—122no—
321C2×C3#472811yescharacteristic
322C2×C3#481711yescharacteristic
323C2×C3#482411yescharacteristic
324C2×C3#501111yescharacteristic
325C2×C3#516411yescharacteristic
326C2×C3#519611yescharacteristic
327D3—42no—
328C22—62no—
329C22—121no—
330C22—121no—
331C22#67⋊Dic311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—121no—
336C4D3×#20811yescharacteristic
337C4#6381411yescharacteristic
338C4#6394111yescharacteristic
339C4#6395111yescharacteristic
340C3—21no—
341C3#6822011yescharacteristic, complemented
342C3#7089711yescharacteristic, complemented
343C2—122no—
344C2#1059115111yescharacteristic
345C2#1059157211yescharacteristic
346C2#1059167511yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32C4×D4
prime radicalC2×C3×D12C2×C4
cosocleC32×C42C23
hypercenterC4×Q8D32
hypocenterC32#1585
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10592723C2semidirect
4. C3×#4535C2semidirect
5. #10589099C2semidirect
7. #10589078C2semidirect
33. #4535D3semidirect
296. C32#1585semidirect
341. C3#68220semidirect
342. C3#70897semidirect

Maximal subgroups

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

subgroupindex
#105927232
C3×C4×#2152
#105903292
C3×#45352
#105890992
#105890812
#105890782
#708973
#682203