Finite Group Databasebeta

← #11777678

Subgroups — #11777678

Order 1152.

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

normal subgroups only

This group has 339 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
1C3×#4831C211yesmaximal, characteristic
2C4×#3719C211yesmaximal, characteristic
3#10590254C211yesmaximal, characteristic
4#10589350C211yesmaximal, characteristic
5C3×#4480C211yesmaximal, characteristic
6#10589083C211yesmaximal, characteristic
7#10589079C211yesmaximal, characteristic
8#70957—31nomaximal
9#68522—31nomaximal
10C4×#634C2211yescharacteristic
11C3×C4×Dic6C2211yescharacteristic
12C2×#3719C411yescharacteristic
13C32×C4⋊C8C2211yescharacteristic
14C4×C3⋊(C3⋊C8)C2211yescharacteristic
15C3×#815—21no—
16C3×Dic3⋊C8—21no—
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63575C411yescharacteristic
21#63572—21no—
22#63567C411yescharacteristic
23#63566C411yescharacteristic
24#63553—21no—
25C3×#446—31no—
26C4×#216—31no—
27#4831D311yescharacteristic
28#4830—31no—
29C4×Dic12—31no—
30C8×Dic6—31no—
31C3×#334—31no—
32#4535—31no—
33#4484—31no—
34#4484—31no—
35#4484—31no—
36#4484—61no—
37#4480D311yescharacteristic
38#4454—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)—21no—
48C3×C4⋊Dic3C2×C411yescharacteristic
49C3×Dic3⋊C4—21no—
50C3×C4×Dic3—21no—
51C2×C3×C3⋊C8—21no—
52C2×C3×C3⋊C8C2×C411yescharacteristic
53C2×C3×C3⋊C8C2×C411yescharacteristic
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
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⋊C8—61no—
68C3×C4⋊C8C2×D311yescharacteristic
69C3×C4⋊C8C2×D311yescharacteristic
70C3×#97—61no—
71C3×C4×C8—31no—
72C3×C4×C8—31no—
73#835—31no—
74#818—31no—
75#816—31no—
76#816—31no—
77#815—21no—
78Dic3⋊C8—21no—
79Dic3⋊C8—61no—
80Dic3⋊C8—61no—
81C8×Dic3—61no—
82C8×Dic3—61no—
83#810—31no—
84#807—31no—
85C4⋊(C3⋊C8)C2×D311yescharacteristic
86C4×C3⋊C8—31no—
87C4×C3⋊C8—31no—
88C4×C3⋊C8—61no—
89C4×C3⋊C8C2×D311yescharacteristic
90C4×C3⋊C8C2×D311yescharacteristic
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C3⋊Dic3—21no—
95C2×C3⋊Dic3—21no—
96#634—21no—
97#634M1612yes—
98C2×C3×Dic3—21no—
99C2×C3×Dic3—21no—
100C3×Dic6—21no—
101C3×Dic6—21no—
102C32×C8—41no—
103C3⋊(C3⋊C8)—22no—
104C3×C3⋊C8—21no—
105C3×C3⋊C8—21no—
106C3×C3⋊C8—21no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—41no—
109#446—31no—
110C8×Q8—91no—
111C4×Q16—91no—
112#334—31no—
113Q8⋊C8—91no—
114Q8⋊C8—91no—
115#322—91no—
116C2×C3×Q8—31no—
117C2×Dic6—31no—
118C2×Dic6—31no—
119C2×Dic6—61no—
120C2×Dic6C4×D311yescharacteristic
121C2×C3×C8—21no—
122C2×C3×C8—21no—
123C2×C3×C8—31no—
124C2×C3×C8—31no—
125C2×C3×C8—31no—
126C2×C3×C8—31no—
127C2×C3×C8—41no—
128C2×C3×C8—61no—
129C3×C4⋊C4—31no—
130C3×C4⋊C4—61no—
131C3×C42—21no—
132C3×C42—61no—
133C3×C42C22×D311yescharacteristic
134C3×C42C22×D311yescharacteristic
135#216—62no—
136C4⋊Dic3—31no—
137C4⋊Dic3—31no—
138C4⋊Dic3—61no—
139C4⋊Dic3C4×D311yescharacteristic
140Dic3⋊C4—21no—
141Dic3⋊C4—61no—
142Dic3⋊C4—61no—
143Dic3⋊C4—121no—
144C4×Dic3—21no—
145C4×Dic3—61no—
146C4×Dic3—61no—
147C4×Dic3—121no—
148C2×C3⋊C8—21no—
149C2×C3⋊C8—61no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—121no—
152C2×C3⋊C8C4×D311yescharacteristic
153C2×C3⋊C8C4×D311yescharacteristic
154C2×C3⋊C8#6711yescharacteristic
155C2×C3⋊C8#6711yescharacteristic
156Dic12—62no—
157C22×C32C4×D411yescharacteristic
158C32×C4—21no—
159C32×C4C2×M1611yescharacteristic
160C32×C4#13111yescharacteristic
161C32×C4#13711yescharacteristic
162C32×C4#13711yescharacteristic
163C3⋊Dic3—22no—
164C3⋊Dic3—41no—
165C3×Dic3—41no—
166C3×Dic3—41no—
167C2×Q16—91no—
168C4×Q8—31no—
169C4×Q8—91no—
170#107—91no—
171C4⋊C8—31no—
172C4⋊C8—61no—
173C4⋊C8—181no—
174C4⋊C8D3211yescharacteristic
175#103—91no—
176#103—91no—
177#97—61no—
178C4×C8—31no—
179C4×C8—31no—
180C4×C8—91no—
181C4×C8—181no—
182C3×Q8—61no—
183C3×Q8—61no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—61no—
188C2×C3×C4—61no—
189C2×C3×C4C2×C4×D311yescharacteristic
190C2×C3×C4C2×C4×D311yescharacteristic
191C2×C3×C4#23511yescharacteristic
192C2×C3×C4D3×D411yescharacteristic
193C2×C3×C4#23911yescharacteristic
194C2×C3×C4C2×#6711yescharacteristic
195C2×Dic3—21no—
196C2×Dic3—21no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—121no—
202C2×Dic3—121no—
203Dic6—21no—
204Dic6—21no—
205Dic6—32no—
206Dic6—32no—
207Dic6—62no—
208Dic6—61no—
209Dic6—61no—
210Dic6—121no—
211C3×C8—41no—
212C3×C8—41no—
213C3×C8—61no—
214C3×C8—61no—
215C3×C8—61no—
216C3×C8—61no—
217C3×C8—81no—
218C3×C8—121no—
219C3⋊C8—21no—
220C3⋊C8—21no—
221C3⋊C8—21no—
222C3⋊C8—21no—
223C3⋊C8—41no—
224C3⋊C8—62no—
225C3⋊C8—62no—
226C3⋊C8—122no—
227C2×C32#43511yescharacteristic
228C2×C32#44111yescharacteristic
229C2×C32#44311yescharacteristic
230C2×Q8—31no—
231C2×Q8—91no—
232Q16—182no—
233C2×C8—21no—
234C2×C8—31no—
235C2×C8—31no—
236C2×C8—31no—
237C2×C8—31no—
238C2×C8—61no—
239C2×C8—181no—
240C4⋊C4—31no—
241C4⋊C4—61no—
242C4⋊C4—91no—
243C4⋊C4—181no—
244C42—61no—
245C42—181no—
246C42C2×D3211yescharacteristic
247C22×C3—21no—
248C22×C3#89311yescharacteristic
249C22×C3C4×#6711yescharacteristic
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—41no—
257C3×C4—121no—
258C3×C4—121no—
259C3×C4#90111yescharacteristic
260C3×C4D3×M1611yescharacteristic
261C3×C4D3×M1611yescharacteristic
262C3×C4#90711yescharacteristic
263C3×C4#91511yescharacteristic
264C3×C4#91511yescharacteristic
265C3×C4#94211yescharacteristic
266C3×C4#95111yescharacteristic
267Dic3—41no—
268Dic3—41no—
269Dic3—62no—
270Dic3—62no—
271Dic3—122no—
272Dic3—121no—
273Dic3—121no—
274Dic3—241no—
275C32#158711yescharacteristic, complemented, Sylow
276Q8—61no—
277Q8—61no—
278Q8—92no—
279Q8—181no—
280C2×C4—61no—
281C2×C4—61no—
282C2×C4—181no—
283C2×C4—181no—
284C2×C4#379911yescharacteristic
285C2×C4C4×D3211yescharacteristic
286C2×C4D3×#6711yescharacteristic
287C8—41no—
288C8—61no—
289C8—61no—
290C8—61no—
291C8—61no—
292C8—121no—
293C8—182no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3#483611yescharacteristic
298C2×C3#485311yescharacteristic
299C2×C3#489511yescharacteristic
300C2×C3#503011yescharacteristic
301C2×C3#512711yescharacteristic
302C2×C3#514411yescharacteristic
303C22#6390411yescharacteristic
304C4—21no—
305C4—121no—
306C4—121no—
307C4—182no—
308C4—361no—
309C4#6379111yescharacteristic
310C4#6380411yescharacteristic
311C4#6392911yescharacteristic
312C4#6394611yescharacteristic
313C3—21no—
314C3#6852211yescharacteristic, complemented
315C3#7095711yescharacteristic, complemented
316C2#1059048011yescharacteristic
317C2#1059073811yescharacteristic
318C2#1059099511yescharacteristic
subgroupG/H
centerC2×C4D3×#67
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
275. C32#1587semidirect
314. C3#68522semidirect
315. C3#70957semidirect

Maximal subgroups

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

subgroupindex
C3×#48312
C4×#37192
#105902542
#105893502
C3×#44802
#105890832
#105890792
#709573
#685223