Finite Group Databasebeta

← #11777679

Subgroups — #11777679

Order 1152.

351 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 351 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592530C211yesmaximal, characteristic
2C4×#3719C211yesmaximal, characteristic
3#10590250C211yesmaximal, characteristic
4C3×#4484C211yesmaximal, characteristic
5C3×#4480C211yesmaximal, characteristic
6#10589085C211yesmaximal, characteristic
7#10589078C211yesmaximal, characteristic
8#68522—31nomaximal
9#68221—31nomaximal
10C4×#634C2211yescharacteristic
11C3×C4×Dic6C2211yescharacteristic
12C2×#3719C411yescharacteristic
13C32×C4⋊C8C2211yescharacteristic
14#63642—21no—
15#63641—21no—
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63575C411yescharacteristic
21Dic3⋊(C3⋊C8)—21no—
22#63567C411yescharacteristic
23#63566C411yescharacteristic
24Dic3×C3⋊C8—21no—
25C4×#216—31no—
26Q8×C3⋊C8—31no—
27#4831—31no—
28#4831—31no—
29#4831—61no—
30#4830—31no—
31C4×Dic12—31no—
32C3×#334—31no—
33C3×Q8⋊C8—31no—
34#4484—31no—
35#4484D311yescharacteristic
36#4480D311yescharacteristic
37#4456—31no—
38#4455—31no—
39#4454—31no—
40C2×#634C2×C411yescharacteristic
41C2×C3×Dic6C2×C411yescharacteristic
42C2×C32×C8—21no—
43C32×C42C2311yescharacteristic
44C4⋊(C3⋊Dic3)C2×C411yescharacteristic
45#3750—21no—
46C4×C3⋊Dic3—21no—
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C3×C4⋊Dic3C2×C411yescharacteristic
50C3×Dic3⋊C4—21no—
51C3×C4×Dic3—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8C2×C411yescharacteristic
55C2×C3×C3⋊C8C2×C411yescharacteristic
56#3719—22no—
57#1587—91noSylow
58C3×C4×Q8—31no—
59C2×#216—31no—
60C2×Dic12—31no—
61C4×Dic6—31no—
62C4×Dic6—31no—
63C4×Dic6—61no—
64C4×Dic6C2×D311yescharacteristic
65C3×C4⋊C8—21no—
66C3×C4⋊C8—31no—
67C3×C4⋊C8C2×D311yescharacteristic
68C3×C4⋊C8C2×D311yescharacteristic
69C3×C4×C8—31no—
70C3×C4×C8—31no—
71#835—31no—
72#818—31no—
73#816—31no—
74#816—31no—
75#815—61no—
76#815—61no—
77#815—62no—
78Dic3⋊C8—61no—
79Dic3⋊C8—61no—
80Dic3⋊C8—61no—
81Dic3⋊C8—62no—
82C8×Dic3—61no—
83#810—31no—
84#807—31no—
85C4⋊(C3⋊C8)—61no—
86C4⋊(C3⋊C8)C2×D311yescharacteristic
87C4×C3⋊C8—31no—
88C4×C3⋊C8—31no—
89C4×C3⋊C8—61no—
90C4×C3⋊C8—61no—
91C4×C3⋊C8C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—21no—
98#634—21no—
99#634—21no—
100C2×C3×Dic3—21no—
101C2×C3×Dic3—21no—
102C3×Dic6—21no—
103C3×Dic6M1612yes—
104C32×C8—41no—
105C3⋊(C3⋊C8)—21no—
106C3⋊(C3⋊C8)—21no—
107C3×C3⋊C8—22no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111#446—91no—
112C8×Q8—91no—
113C4×Q16—91no—
114#334—31no—
115Q8⋊C8—31no—
116Q8⋊C8—91no—
117#322—91no—
118C2×C3×Q8—31no—
119C2×Dic6—31no—
120C2×Dic6—31no—
121C2×Dic6—61no—
122C2×Dic6C4×D311yescharacteristic
123C2×C3×C8—22no—
124C2×C3×C8—21no—
125C2×C3×C8—21no—
126C2×C3×C8—31no—
127C2×C3×C8—31no—
128C2×C3×C8—61no—
129C2×C3×C8—61no—
130C3×C4⋊C4—31no—
131C3×C4⋊C4—61no—
132C3×C42—21no—
133C3×C42—61no—
134C3×C42C22×D311yescharacteristic
135C3×C42C22×D311yescharacteristic
136#216—62no—
137C4⋊Dic3—31no—
138C4⋊Dic3—31no—
139C4⋊Dic3—61no—
140C4⋊Dic3C4×D311yescharacteristic
141Dic3⋊C4—21no—
142Dic3⋊C4—62no—
143Dic3⋊C4—61no—
144Dic3⋊C4—61no—
145C4×Dic3—21no—
146C4×Dic3—62no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8—21no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8C4×D311yescharacteristic
158C2×C3⋊C8C4×D311yescharacteristic
159Dic12—62no—
160C22×C32C4×D411yescharacteristic
161C32×C4—21no—
162C32×C4C2×M1611yescharacteristic
163C32×C4#13111yescharacteristic
164C32×C4#13711yescharacteristic
165C32×C4#13711yescharacteristic
166C3⋊Dic3—41no—
167C3⋊Dic3—41no—
168C3×Dic3—22no—
169C3×Dic3—41no—
170C2×Q16—91no—
171C4×Q8—31no—
172C4×Q8—91no—
173#107—91no—
174C4⋊C8—31no—
175C4⋊C8—181no—
176C4⋊C8—181no—
177C4⋊C8D3211yescharacteristic
178#103—91no—
179#103—91no—
180#97—181no—
181C4×C8—31no—
182C4×C8—31no—
183C4×C8—91no—
184C4×C8—181no—
185C3×Q8—32no—
186C3×Q8—61no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—61no—
191C2×C3×C4—61no—
192C2×C3×C4C2×C4×D311yescharacteristic
193C2×C3×C4C2×C4×D311yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×C3×C4D3×D411yescharacteristic
196C2×C3×C4#23711yescharacteristic
197C2×C3×C4#23911yescharacteristic
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—62no—
201C2×Dic3—62no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206Dic6—21no—
207Dic6—61no—
208Dic6—61no—
209Dic6—61no—
210Dic6—61no—
211Dic6—121no—
212Dic6—121no—
213Dic6ΓL(1,𝔽25)12yes—
214C3×C8—42no—
215C3×C8—41no—
216C3×C8—41no—
217C3×C8—62no—
218C3×C8—61no—
219C3×C8—61no—
220C3×C8—121no—
221C3⋊C8—22no—
222C3⋊C8—21no—
223C3⋊C8—21no—
224C3⋊C8—41no—
225C3⋊C8—62no—
226C3⋊C8—61no—
227C3⋊C8—61no—
228C3⋊C8—61no—
229C3⋊C8—61no—
230C3⋊C8—121no—
231C2×C32#43511yescharacteristic
232C2×C32#44111yescharacteristic
233C2×C32#44311yescharacteristic
234C2×Q8—31no—
235C2×Q8—91no—
236Q16—182no—
237C2×C8—21no—
238C2×C8—31no—
239C2×C8—31no—
240C2×C8—61no—
241C2×C8—61no—
242C2×C8—91no—
243C2×C8—91no—
244C4⋊C4—31no—
245C4⋊C4—61no—
246C4⋊C4—91no—
247C4⋊C4—181no—
248C42—61no—
249C42—181no—
250C42C2×D3211yescharacteristic
251C22×C3—21no—
252C22×C3#67⋊C411yescharacteristic
253C22×C3#89311yescharacteristic
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—41no—
261C3×C4—62no—
262C3×C4—121no—
263C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
264C3×C4#90111yescharacteristic
265C3×C4D3×M1611yescharacteristic
266C3×C4#90711yescharacteristic
267C3×C4#91511yescharacteristic
268C3×C4#91511yescharacteristic
269C3×C4#91511yescharacteristic
270C3×C4#91811yescharacteristic
271Dic3—22no—
272Dic3—41no—
273Dic3—122no—
274Dic3—122no—
275Dic3—121no—
276Dic3—121no—
277Dic3—121no—
278Dic3—121no—
279C32#158711yescharacteristic, complemented, Sylow
280Q8—32no—
281Q8—61no—
282Q8—181no—
283Q8—181no—
284C2×C4—61no—
285C2×C4—61no—
286C2×C4—181no—
287C2×C4—181no—
288C2×C4#379611yescharacteristic
289C2×C4C4×D3211yescharacteristic
290C2×C4#381111yescharacteristic
291C8—41no—
292C8—62no—
293C8—61no—
294C8—61no—
295C8—121no—
296C8—181no—
297C8—181no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3#473011yescharacteristic
302C2×C3#478911yescharacteristic
303C2×C3#482411yescharacteristic
304C2×C3#483611yescharacteristic
305C2×C3#485311yescharacteristic
306C2×C3#489511yescharacteristic
307C22#6388111yescharacteristic
308C4—21no—
309C4—62no—
310C4—121no—
311C4—361no—
312C4—361no—
313C4D3×ΓL(1,𝔽25)11yescharacteristic
314C4#6380411yescharacteristic
315C4#6393111yescharacteristic
316C4#6395111yescharacteristic
317C3—21no—
318C3#6822111yescharacteristic, complemented
319C3#6852211yescharacteristic, complemented
320C2#1059048511yescharacteristic
321C2#1059090711yescharacteristic
322C2#1059097711yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32C4×D4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1587
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
279. C32#1587semidirect
318. C3#68221semidirect
319. C3#68522semidirect

Maximal subgroups

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

subgroupindex
#105925302
C4×#37192
#105902502
C3×#44842
C3×#44802
#105890852
#105890782
#685223
#682213