Finite Group Databasebeta

← #11858523

Subgroups — #11858523

Order 1152.

822 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 191 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
1C2×#64283C211yesmaximal, characteristic
2#10594969C211yesmaximal, characteristic
3C2×#63874C211yesmaximal, characteristic
4#10593507C214yesmaximal, complemented
5#10593394C214yesmaximal, complemented
6#10593389C214yesmaximal, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×#3792C2212yes—
9#64283C418yescomplemented
10C2×#3788C2212yes—
11C2×#3787C2212yes—
12C3×#926—21no—
13C2×C3×C4×Dic3—21no—
14#63974—21no—
15C2×#3724C2212yes—
16C2×#3722—21no—
17#63957C2212yes—
18#63900C2212yes—
19C4×#624—21no—
20#63874—21no—
21#63874—21no—
22#63874C2212yes—
23#63874C2212yes—
24#63874C2212yes—
25#63849—21no—
26#63743C2218yescomplemented
27#63742C2218yescomplemented
28D3×#117—61no—
29C2×#872—61no—
30C23×C3⋊D3D411yescharacteristic
31C22×C32×C4D411yescharacteristic
32C22×C3⋊Dic3C2311yescharacteristic
33C2×C4×C3⋊D3C2×C414yes—
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3Q814yes—
37C2×C4×C3⋊D3C2311yescharacteristic
38C2×C4×C3⋊D3C2311yescharacteristic
39C22×C3×Dic3—22no—
40C2×#624—22no—
41#3792C2×C418yescomplemented
42C2×#622C2314yes—
43#3788C2×C418yescomplemented
44#3787C2×C418yescomplemented
45C3×#217—22no—
46C3×C4⋊Dic3—22no—
47C3×C4×Dic3—22no—
48C3×C4×Dic3—22no—
49C3×C4×Dic3—22no—
50#3724—22no—
51#3724C2314yes—
52#3724C2314yes—
53#3722—22no—
54#3722—22no—
55#3722—22no—
56Dic32—22no—
57#2911—91nomaximal, Sylow
58C22×C4×D3—61no—
59C22×C4×D3—61no—
60C3×#117—61no—
61C2×C3×C42—61no—
62C2×(C2×D3)⋊C4—62no—
63#926—21no—
64C2×Dic3⋊C4—62no—
65C2×C4×Dic3—21no—
66#892—62no—
67D3×C4⋊C4—62no—
68D3×C22⋊C4—62no—
69#877—62no—
70#872—62no—
71#872—62no—
72#872—62no—
73#872—62no—
74#872—62no—
75C42×D3—62no—
76C23×C32C2×D411yescharacteristic
77C22×C3⋊D3—42no—
78C22×C3⋊D3C4⋊C414yes—
79C22×C3⋊D3C2×D411yescharacteristic
80C22×C3⋊D3C2×D411yescharacteristic
81C2×C32×C4C4⋊C414yes—
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C3⋊Dic3C22×C412yes—
85C2×C3⋊Dic3C2×D411yescharacteristic
86C2×C3⋊Dic3C2×Q812yes—
87C2×C3⋊Dic3C2411yescharacteristic
88C4×C3⋊D3C4⋊C414yes—
89C4×C3⋊D3C4⋊C414yes—
90C4×C3⋊D3C22×C412yes—
91C4×C3⋊D3C22×C412yes—
92C4×C3⋊D3C2×Q812yes—
93C4×C3⋊D3C2×Q812yes—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—24no—
96C2×C3×Dic3—44no—
97#624—44no—
98#622C22×C418yes—
99C22×M16—91no—
100C2×#117—91no—
101C2×#117—91no—
102#428—94no—
103#428—94no—
104#427—94no—
105C23×D3—61no—
106C23×D3—61no—
107C22×C3×C4—21no—
108C22×C3×C4—21no—
109C22×C3×C4—62no—
110C22×Dic3—22no—
111C22×Dic3—61no—
112C22×Dic3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—61no—
120C2×C4×D3—61no—
121C2×C4×D3—64no—
122C2×C4×D3—64no—
123C2×C4×D3—64no—
124C2×C4×D3—64no—
125C2×C4×D3—64no—
126C3×C4⋊C4—62no—
127C3×C22⋊C4—62no—
128C3×C42—62no—
129C3×C42—62no—
130C3×C42—62no—
131#217—22no—
132(C2×D3)⋊C4—64no—
133(C2×D3)⋊C4—64no—
134(C2×D3)⋊C4—64no—
135C4⋊Dic3—22no—
136Dic3⋊C4—64no—
137Dic3⋊C4—64no—
138Dic3⋊C4—64no—
139C4×Dic3—22no—
140C4×Dic3—22no—
141C4×Dic3—22no—
142C4×Dic3—64no—
143C22×C32—22no—
144C22×C32C2×C4⋊C412yes—
145C22×C32C22×D411yescharacteristic
146C2×C3⋊D3—22no—
147C2×C3⋊D3—22no—
148C2×C3⋊D3—44no—
149C2×C3⋊D3C2×C4⋊C412yes—
150C2×C3⋊D3C2×C4⋊C412yes—
151C32×C4C2×C4⋊C412yes—
152C32×C4C2×C4⋊C412yes—
153C3⋊Dic3C2×C4⋊C412yes—
154C3⋊Dic3C23×C411yescharacteristic
155C3⋊Dic3C22×Q811yescharacteristic
156C3×Dic3—44no—
157C3×Dic3—44no—
158C23×C4—91no—
159C2×M16—92no—
160C2×M16—98no—
161C2×M16—92no—
162C22×C8—92no—
163#117—61no—
164#117—92no—
165#117—92no—
166#117—92no—
167#117—92no—
168#117—181no—
169#117—181no—
170#117—181no—
171C2×C4⋊C4—92no—
172C2×C4⋊C4—92no—
173C2×C22⋊C4—181no—
174C2×C22⋊C4—181no—
175C2×C42—61no—
176C2×C42—181no—
177#107—98no—
178#106—98no—
179C23×C3—21no—
180C23×C3—21no—
181C22×D3—61no—
182C22×D3—64no—
183C22×D3—64no—
184C22×D3—61no—
185C22×D3—61no—
186C22×D3—61no—
187C22×D3—124no—
188C22×D3—124no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—24no—
194C2×C3×C4—24no—
195C2×C3×C4—64no—
196C2×C3×C4—64no—
197C2×C3×C4—124no—
198C2×Dic3—24no—
199C2×Dic3—24no—
200C2×Dic3—44no—
201C2×Dic3—62no—
202C2×Dic3—62no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—62no—
206C2×Dic3—62no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C4×D3—64no—
210C4×D3—64no—
211C4×D3—64no—
212C4×D3—64no—
213C4×D3—62no—
214C4×D3—62no—
215C4×D3—62no—
216C4×D3—62no—
217C4×D3—62no—
218C4×D3—62no—
219C4×D3—62no—
220C4×D3—62no—
221C4×D3—128no—
222C2×C32—22no—
223C2×C32C22×C4⋊C411yescharacteristic
224C2×C32#57512yes—
225C3⋊D3—22no—
226C3⋊D3—22no—
227C24—91no—
228C22×C4—62no—
229C22×C4—91no—
230C22×C4—91no—
231C22×C4—91no—
232C22×C4—91no—
233C22×C4—91no—
234C22×C4—94no—
235C22×C4—94no—
236C22×C4—182no—
237C22×C4GO+(4,𝔽2)11yescharacteristic
238M16—98no—
239M16—98no—
240C2×C8—94no—
241C2×C8—98no—
242C4⋊C4—62no—
243C4⋊C4—94no—
244C4⋊C4—94no—
245C4⋊C4—182no—
246C22⋊C4—62no—
247C22⋊C4—182no—
248C22⋊C4—182no—
249C22⋊C4—182no—
250C42—62no—
251C42—62no—
252C42—62no—
253C42—182no—
254C22×C3—24no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—22no—
258C22×C3—22no—
259C22×C3—42no—
260C2×D3—62no—
261C2×D3—62no—
262C2×D3—62no—
263C2×D3—62no—
264C2×D3—64no—
265C2×D3—122no—
266C2×D3—122no—
267C2×D3—122no—
268C2×D3—128no—
269C2×D3—128no—
270C3×C4—22no—
271C3×C4—22no—
272C3×C4—22no—
273C3×C4—22no—
274C3×C4—124no—
275C3×C4—124no—
276Dic3—44no—
277Dic3—44no—
278Dic3—62no—
279Dic3—62no—
280Dic3—61no—
281Dic3—61no—
282Dic3—61no—
283Dic3—61no—
284C32#291111yescharacteristic, complemented, Sylow
285C23—91no—
286C23—91no—
287C23—94no—
288C23—362no—
289C23C2×GO+(4,𝔽2)11yescharacteristic
290C2×C4—64no—
291C2×C4—64no—
292C2×C4—91no—
293C2×C4—91no—
294C2×C4—92no—
295C2×C4—92no—
296C2×C4—92no—
297C2×C4—92no—
298C2×C4—92no—
299C2×C4—94no—
300C2×C4—94no—
301C2×C4—92no—
302C2×C4—124no—
303C2×C4—364no—
304C2×C4#377314yes—
305C2×C4C2×GO+(4,𝔽2)11yescharacteristic
306C2×C4C2×GO+(4,𝔽2)11yescharacteristic
307C8—98no—
308C2×C3—24no—
309C2×C3—22no—
310C2×C3—22no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—42no—
314D3—64no—
315D3—122no—
316D3—122no—
317D3—122no—
318C22—22no—
319C22—92no—
320C22—92no—
321C22—182no—
322C22—182no—
323C22—364no—
324C22C2×#377312yes—
325C22C22×GO+(4,𝔽2)11yescharacteristic
326C4—91no—
327C4—92no—
328C4—91no—
329C4—124no—
330C4—124no—
331C4C2×#377312yes—
332C4C2×#377312yes—
333C3—21no—
334C3—21no—
335C2—22no—
336C2—182no—
337C2—182no—
338C2#1059649912yes—
339C2C22×#377311yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
cosocleC2×C3⋊Dic3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2911
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10593507C2semidirect
5. #10593394C2semidirect
6. #10593389C2semidirect
9. #64283C4semidirect
26. #63743C22semidirect
27. #63742C22semidirect
41. #3792C2×C4semidirect
43. #3788C2×C4semidirect
44. #3787C2×C4semidirect
284. C32#2911semidirect

Maximal subgroups

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

subgroupindex
C2×#642832
#105949692
C2×#638742
#105935072
#105933942
#105933892
#29119