Finite Group Databasebeta

← #11878926

Subgroups — #11878926

Order 1152.

640 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 115 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#10595050C211yesmaximal, characteristic
2C2×#63919C211yesmaximal, characteristic
3#10593795C211yesmaximal, characteristic
4#10593499C214yesmaximal
5#10593450C212yesmaximal, complemented
6#10593447C214yesmaximal, complemented
7#10593379C212yesmaximal, complemented
8C22×#627C2212yes—
9C2×#3776C2218yes—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C3×#926—21no—
12C2×C3×C4⋊Dic3—21no—
13#63982—21no—
14#63982C2212yes—
15C2×#3724—21no—
16#63919—21no—
17#63919—21no—
18#63919C2212yes—
19#63919C2212yes—
20#63919C2211yescharacteristic
21#63919C2211yescharacteristic
22C4×#627—21no—
23C4×#627C2212yes—
24#63872—21no—
25C22⋊#622C2212yes—
26C4⋊#622C2212yes—
27C4×#622C2212yes—
28#63740C2218yes—
29#5517—61no—
30C2×#888—61no—
31C22×C32×C4D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C22×C3⋊Dic3C2311yescharacteristic
34C22×C3×Dic3—22no—
35C2×#627—22no—
36C2×#627—21no—
37C2×#627—44no—
38C2×#627C2314yes—
39C2×#627C2312yes—
40C2×#622C2314yes—
41#3776—48no—
42C4×C3⋊Dic3D411yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44C4×C3⋊Dic3C2311yescharacteristic
45C4×C3⋊Dic3C2311yescharacteristic
46C3×#217—22no—
47C3×C4⋊Dic3—22no—
48C3×C4⋊Dic3—22no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4×Dic3—22no—
52#3724—21no—
53#3724—22no—
54#3724—22no—
55#3724C2312yes—
56Dic3⋊Dic3—22no—
57Dic3⋊Dic3—22no—
58#3209—91nomaximal, Sylow
59C22×Dic6—62no—
60C3×#117—61no—
61C2×C3×C4⋊C4—61no—
62#926—21no—
63C2×C4⋊Dic3—21no—
64C2×Dic3⋊C4—62no—
65C2×C4×Dic3—61no—
66C2×C4×Dic3—61no—
67#890—61no—
68#890—61no—
69#888—62no—
70#888—62no—
71#888—61no—
72#888—61no—
73#888—62no—
74#888—62no—
75#878—62no—
76#878—62no—
77C4×Dic6—62no—
78C4×Dic6—62no—
79C23×C32C2×D411yescharacteristic
80C2×C32×C4Q1614yescomplemented
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3C2×D411yescharacteristic
86C2×C3⋊Dic3C2×D411yescharacteristic
87C2×C3⋊Dic3C2×D411yescharacteristic
88C2×C3⋊Dic3C2411yescharacteristic
89C2×C3×Dic3—22no—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—24no—
92C2×C3×Dic3—44no—
93#627—24no—
94#627—28no—
95#627—44no—
96#627—42no—
97#622—24no—
98#533—91no—
99C2×C4⋊Q8—91no—
100#494—92no—
101#487—92no—
102#462—94no—
103#451—94no—
104#431—91no—
105C22×C3×C4—21no—
106C22×C3×C4—21no—
107C22×C3×C4—62no—
108C22×Dic3—22no—
109C22×Dic3—61no—
110C22×Dic3—61no—
111C22×Dic3—61no—
112C22×Dic3—61no—
113C2×Dic6—62no—
114C2×Dic6—64no—
115C2×Dic6—62no—
116C2×Dic6—64no—
117C2×Dic6—128no—
118C3×C4⋊C4—62no—
119C3×C4⋊C4—62no—
120C3×C4⋊C4—61no—
121C3×C4⋊C4—61no—
122C3×C22⋊C4—62no—
123C3×C42—62no—
124#217—22no—
125C4⋊Dic3—22no—
126C4⋊Dic3—22no—
127C4⋊Dic3—21no—
128C4⋊Dic3—21no—
129C4⋊Dic3—62no—
130C4⋊Dic3—62no—
131Dic3⋊C4—62no—
132Dic3⋊C4—62no—
133Dic3⋊C4—62no—
134Dic3⋊C4—62no—
135Dic3⋊C4—64no—
136Dic3⋊C4—64no—
137C4×Dic3—22no—
138C4×Dic3—61no—
139C4×Dic3—61no—
140C4×Dic3—61no—
141C4×Dic3—61no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C22×C32—21no—
147C22×C32—21no—
148C22×C32C2×Q1612yes—
149C22×C32C22×D411yescharacteristic
150C32×C4C2×Q1612yes—
151C32×C4C2×Q1612yes—
152C3⋊Dic3—21no—
153C3⋊Dic3—21no—
154C3⋊Dic3#13712yes—
155C3⋊Dic3H(5,𝔽2)12yes—
156C3×Dic3—44no—
157C3×Dic3—42no—
158C3×Dic3—42no—
159C22×Q8—92no—
160C2×Q16—98no—
161C4⋊Q8—91no—
162C4⋊Q8—92no—
163C4⋊Q8—92no—
164C4⋊Q8—91no—
165C4⋊Q8—181no—
166C4⋊Q8—181no—
167#125—181no—
168C22⋊Q8—92no—
169C22⋊Q8—181no—
170C4×Q8—92no—
171C4×Q8—181no—
172#117—61no—
173C2×C4⋊C4—61no—
174C2×C4⋊C4—181no—
175C2×C42—91no—
176C4⋊C8—92no—
177#103—98no—
178C22⋊C8—92no—
179C4×C8—92no—
180C23×C3—21no—
181C23×C3—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—24no—
187C2×C3×C4—24no—
188C2×C3×C4—62no—
189C2×C3×C4—62no—
190C2×C3×C4—64no—
191C2×C3×C4—124no—
192C2×Dic3—22no—
193C2×Dic3—22no—
194C2×Dic3—24no—
195C2×Dic3—44no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—64no—
205C2×Dic3—64no—
206C2×Dic3—122no—
207C2×Dic3—122no—
208Dic6—124no—
209Dic6—128no—
210Dic6—124no—
211Dic6—128no—
212C2×C32—22no—
213C2×C32#53511yescharacteristic
214C2×C32C22×Q1611yescharacteristic
215C2×C32C2×#13711yescharacteristic
216C2×Q8—94no—
217C2×Q8—92no—
218C2×Q8—181no—
219C2×Q8—182no—
220C2×Q8—364no—
221C22×C4—62no—
222C22×C4—91no—
223C22×C4—91no—
224C22×C4GO+(4,𝔽2)11yescharacteristic
225Q16—368no—
226C2×C8—94no—
227C4⋊C4—62no—
228C4⋊C4—62no—
229C4⋊C4—61no—
230C4⋊C4—61no—
231C4⋊C4—92no—
232C4⋊C4—182no—
233C4⋊C4—182no—
234C4⋊C4—182no—
235C4⋊C4—182no—
236C4⋊C4—181no—
237C22⋊C4—62no—
238C42—62no—
239C42—91no—
240C42—91no—
241C42—91no—
242C42—91no—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—41no—
250C22×C3—41no—
251C3×C4—22no—
252C3×C4—22no—
253C3×C4—22no—
254C3×C4—22no—
255C3×C4—124no—
256C3×C4—122no—
257C3×C4—122no—
258Dic3—44no—
259Dic3—42no—
260Dic3—42no—
261Dic3—62no—
262Dic3—62no—
263Dic3—62no—
264Dic3—62no—
265Dic3—62no—
266Dic3—62no—
267Dic3—121no—
268Dic3—121no—
269C32#320911yescharacteristic, complemented, Sylow
270C23C2×GO+(4,𝔽2)11yescharacteristic
271Q8—184no—
272Q8—188no—
273Q8—362no—
274Q8—364no—
275C2×C4—62no—
276C2×C4—62no—
277C2×C4—64no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—91no—
282C2×C4—124no—
283C2×C4—182no—
284C2×C4—182no—
285C2×C4#377614yescomplemented
286C2×C4C2×GO+(4,𝔽2)11yescharacteristic
287C2×C4C2×GO+(4,𝔽2)11yescharacteristic
288C8—184no—
289C2×C3—24no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—42no—
297C22—21no—
298C22—21no—
299C22C2×#377612yes—
300C22C22×GO+(4,𝔽2)11yescharacteristic
301C4—92no—
302C4—92no—
303C4—122no—
304C4—124no—
305C4—122no—
306C4—181no—
307C4—181no—
308C4C2×#377612yes—
309C4C2×#377612yes—
310C3—21no—
311C3—21no—
312C2—22no—
313C2#1059650511yescharacteristic
314C2#1059651211yescharacteristic
315C2C22×#377611yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#3209
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
5. #10593450C2semidirect
6. #10593447C2semidirect
7. #10593379C2semidirect
80. C2×C32×C4Q16semidirect
269. C32#3209semidirect
285. C2×C4#3776semidirect

Maximal subgroups

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

subgroupindex
#105950502
C2×#639192
#105937952
#105934992
#105934502
#105934472
#105933792
#32099