Finite Group Databasebeta

← #11783875

Subgroups — #11783875

Order 1152.

875 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 875 conjugacy classes of subgroups — too many to draw. Only its 160 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#10595993C211yesmaximal, characteristic
2C4×Dic32C211yesmaximal, characteristic, complemented
3C2×#63570C212yesmaximal
4#10591060C211yesmaximal, characteristic, complemented
5C3×#4532C212yesmaximal, complemented
6#68728—32nomaximal
7C2×#3828C2211yescharacteristic
8C32×#117C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10#64102C412yescomplemented
11#64096C412yescomplemented
12#64090—22no—
13#64081—21no—
14C42×C3⋊D3—21no—
15C2×C3×C4×Dic3C2212yes—
16C2×C3×#208C2212yes—
17C2×Dic32—22no—
18#63570C418yescomplemented
19#63555—21no—
20#63553—21no—
21#5522—32no—
22#5522—61no—
23C2×#825—32no—
24Dic3×M16—32no—
25C42×Dic3—32no—
26C2×#805—32no—
27C3×#339—32no—
28#4532D312yescomplemented
29C22×C32×C4C2311yescharacteristic
30C2×#638—21no—
31C22×C3⋊Dic3D412yes—
32#3828—22no—
33#3828C2×C414yes—
34C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
35C2×C4×C3⋊D3—21no—
36C2×C4×C3⋊D3—22no—
37C2×#634C2×C411yescharacteristic
38C22×C3×Dic3—22no—
39C32×C4⋊C4C2×C412yes—
40C32×C22⋊C4—21no—
41C32×C42—21no—
42#3752—22no—
43#3750—22no—
44C4×C3⋊Dic3—22no—
45C4×C3⋊Dic3C2×C412yes—
46C4×C3⋊Dic3D411yescharacteristic
47C4×C3⋊Dic3D411yescharacteristic
48C3×C4×Dic3—22no—
49C3×C4×Dic3C2×C414yescomplemented
50C3×#208—22no—
51C3×#208C2×C414yescomplemented
52C2×C3×C3⋊C8—22no—
53Dic32—28no—
54C4×#104—91noSylow
55C2×#235—32no—
56C2×#235—61no—
57C2×C3×M16—32no—
58C3×#117—21no—
59C3×#117C2×D312yes—
60C2×C3×C42—32no—
61C2×C4×Dic3—32no—
62C2×C4×Dic3—61no—
63C2×C4×Dic3—64no—
64C2×C4×Dic3C2×D312yes—
65C2×#208C2×D312yes—
66#893—34no—
67#893—62no—
68#887—34no—
69#887—62no—
70#67⋊C4—64no—
71#67⋊C4—64no—
72#872—62no—
73#872—62no—
74C42×D3—62no—
75C42×D3—62no—
76#825—38no—
77#815—62no—
78C8×Dic3—62no—
79#805—38no—
80C23×C32C2×D411yescharacteristic
81C22×C3⋊D3—21no—
82C2×C32×C4—22no—
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4C22×C412yes—
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4#4112yes—
87#638—24no—
88C2×C3⋊Dic3—21no—
89C2×C3⋊Dic3—24no—
90C2×C3⋊Dic3C22⋊C412yes—
91C2×C3⋊Dic3C22⋊C412yes—
92C4⋊(C3⋊D3)—21no—
93C4⋊(C3⋊D3)C4212yescomplemented
94C4×C3⋊D3—24no—
95C4×C3⋊D3—44no—
96#634—21no—
97#634C4212yescomplemented
98C2×C3×Dic3—28no—
99C2×C3×Dic3—24no—
100C3×C3⋊C8—24no—
101C4×#41—91no—
102C2×#104—92no—
103C4×M16—91no—
104C43—91no—
105#339—32no—
106C22×C3×C4—21no—
107C22×C3×C4—62no—
108C22×C3×C4C22×D312yes—
109C2×#67—62no—
110C2×#67—62no—
111C22×Dic3—22no—
112C22×Dic3—34no—
113C22×Dic3—62no—
114#235—34no—
115#235—34no—
116#235—64no—
117#235—64no—
118#235—62no—
119#235—62no—
120C2×D12—32no—
121C2×D12—61no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—64no—
125C2×C4×D3—64no—
126C2×Dic6—32no—
127C2×Dic6—61no—
128C3×M16—34no—
129C3×M16—62no—
130C2×C3×C8—62no—
131C3×C4⋊C4—22no—
132C3×C4⋊C4C4×D314yes—
133C3×C22⋊C4—22no—
134C3×C22⋊C4—22no—
135C3×C42—22no—
136C3×C42—22no—
137C3×C42—34no—
138C3×C42—62no—
139(C2×D3)⋊C4—64no—
140(C2×D3)⋊C4—64no—
141Dic3⋊C4—64no—
142Dic3⋊C4—64no—
143C4×Dic3—22no—
144C4×Dic3—34no—
145C4×Dic3—32no—
146C4×Dic3—32no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C4×Dic3—62no—
150C4×Dic3—616no—
151C4×Dic3—64no—
152C4×Dic3—64no—
153C4×Dic3C4×D314yescomplemented
154#208—22no—
155#208C4×D314yescomplemented
156C2×C3⋊C8—22no—
157C22×C32—22no—
158C22×C32C2×C22⋊C411yescharacteristic
159C22×C32C4×D412yes—
160C2×C3⋊D3—22no—
161C2×C3⋊D3—42no—
162C32×C4—42no—
163C32×C4C2×C4211yescharacteristic
164C32×C4#11711yescharacteristic
165C32×C4C4×D412yes—
166C3⋊Dic3—22no—
167C3⋊Dic3—22no—
168C3⋊Dic3#10414yescomplemented
169C3×Dic3—28no—
170C2×#41—91no—
171C2×M16—32no—
172C4×Q8—92no—
173C4×D4—92no—
174C4×D4—182no—
175#117—181no—
176#117D3211yescharacteristic
177C2×C42—32no—
178C2×C42—91no—
179C2×C42—181no—
180C2×C42—182no—
181#104—98no—
182#97—181no—
183C4×C8—181no—
184C23×C3—21no—
185C23×C3D3×D412yes—
186C22×D3—62no—
187C22×D3—62no—
188C2×C3×C4—24no—
189C2×C3×C4—24no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—68no—
195C2×C3×C4—64no—
196C2×C3×C4C2×C4×D312yes—
197C2×C3×C4C2×C4×D312yes—
198C2×C3×C4C2×C4×D312yes—
199C2×C3×C4D3×D412yes—
200C2×C3×C4#23712yes—
201C2×C3×C4#23912yes—
202#67—68no—
203#67—64no—
204#67—64no—
205C2×Dic3—28no—
206C2×Dic3—24no—
207C2×Dic3—34no—
208C2×Dic3—34no—
209C2×Dic3—62no—
210C2×Dic3—62no—
211C2×Dic3—68no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—124no—
215D12—34no—
216D12—62no—
217D12—62no—
218D12—62no—
219C4×D3—68no—
220C4×D3—64no—
221C4×D3—64no—
222C4×D3—128no—
223C4×D3—128no—
224Dic6—34no—
225Dic6—62no—
226Dic6—62no—
227Dic6—62no—
228C3×C8—64no—
229C3⋊C8—24no—
230C2×C32—22no—
231C2×C32C4×C22⋊C411yescharacteristic
232C2×C32C2×#10412yes—
233C3⋊D3—42no—
234#41—94no—
235#41—182no—
236C2×Q8—91no—
237C2×D4—91no—
238C2×D4—181no—
239C22×C4—62no—
240C22×C4—92no—
241C22×C4—182no—
242C22×C4—181no—
243C22×C4C2×D3211yescharacteristic
244M16—34no—
245M16—62no—
246C2×C8—62no—
247C4⋊C4—182no—
248C4⋊C4#62412yes—
249C22⋊C4—21no—
250C22⋊C4—182no—
251C42—21no—
252C42—34no—
253C42—62no—
254C42—92no—
255C42—91no—
256C42—91no—
257C42—182no—
258C42—188no—
259C22×C3—24no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—42no—
263C22×C3D3×C22⋊C412yes—
264C22×C3#67⋊C412yes—
265C22×C3#89312yes—
266C2×D3—64no—
267C2×D3—64no—
268C2×D3—124no—
269C2×D3—124no—
270C3×C4—21no—
271C3×C4—22no—
272C3×C4—21no—
273C3×C4—44no—
274C3×C4—44no—
275C3×C4—68no—
276C3×C4C42×D312yes—
277C3×C4#67⋊C412yes—
278C3×C4#89212yes—
279C3×C4#89312yes—
280Dic3—28no—
281Dic3—38no—
282Dic3—64no—
283Dic3—64no—
284Dic3—64no—
285Dic3—64no—
286Dic3—122no—
287C32C4×#10411yescharacteristic, complemented, Sylow
288C23—181no—
289C23#381111yescharacteristic
290Q8—92no—
291Q8—181no—
292D4—92no—
293D4—184no—
294D4—181no—
295C2×C4—22no—
296C2×C4—68no—
297C2×C4—64no—
298C2×C4—92no—
299C2×C4—92no—
300C2×C4—184no—
301C2×C4—181no—
302C2×C4—184no—
303C2×C4—364no—
304C2×C4#379612yes—
305C2×C4C4×D3212yes—
306C2×C4C2×#62411yescharacteristic
307C2×C4#381111yescharacteristic
308C8—64no—
309C2×C3—22no—
310C2×C3—22no—
311C2×C3—21no—
312C2×C3—22no—
313C2×C3—42no—
314C2×C3#466612yes—
315C2×C3D3×#10414yes—
316D3—124no—
317D3—124no—
318C22—22no—
319C22—182no—
320C22—362no—
321C22#6388112yes—
322C22#6397411yescharacteristic
323C4—42no—
324C4—68no—
325C4—94no—
326C4—182no—
327C4—182no—
328C4#6384911yescharacteristic
329C4#6388112yes—
330C4C4×#62411yescharacteristic
331C3—21no—
332C3#6872812yescomplemented
333C2—22no—
334C2—362no—
335C2#1059126011yescharacteristic
336C2#1059167112yes—
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32C4×#104
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C4×Dic32C2semidirect
4. #10591060C2semidirect
5. C3×#4532C2semidirect
10. #64102C4semidirect
11. #64096C4semidirect
18. #63570C4semidirect
28. #4532D3semidirect
49. C3×C4×Dic3C2×C4semidirect
51. C3×#208C2×C4semidirect
93. C4⋊(C3⋊D3)C42semidirect
97. #634C42semidirect
153. C4×Dic3C4×D3semidirect
155. #208C4×D3semidirect
168. C3⋊Dic3#104semidirect
287. C32C4×#104semidirect
332. C3#68728semidirect

Maximal subgroups

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

subgroupindex
#105959932
C4×Dic322
C2×#635702
#105910602
C3×#45322
#687283