Finite Group Databasebeta

← #11873417

Subgroups — #11873417

Order 1152.

714 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 131 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#10593909C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic
3C4×#3787C211yesmaximal, characteristic
4#10593379C214yesmaximal, complemented
5#10593377C214yesmaximal, complemented
6#10593375C214yesmaximal
7C2×#3797—21no—
8C2×#3797C2212yes—
9C2×#3787C2212yes—
10C42×C3⋊D3C2211yescharacteristic
11C3×#869—21no—
12C3×#869—21no—
13#63919—21no—
14#63919C2212yes—
15#63919C2212yes—
16#63919C2212yes—
17#63900—21no—
18#63900—21no—
19#63900—21no—
20#63900C2212yes—
21#63873—21no—
22#63873C2212yes—
23C4×#622C2212yes—
24C4×#622C2212yes—
25#63740C22116yes—
26D3×C4⋊Q8—61no—
27D3×C4⋊Q8—61no—
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×C3×Dic6—22no—
32C2×C3×Dic6—22no—
33C2×#627—22no—
34C2×#627C2314yes—
35C2×#624—22no—
36C2×#624—22no—
37#3797—28no—
38#3797—44no—
39C2×#622C2314yes—
40#3787—24no—
41C32×C42D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C4×C3⋊Dic3C2311yescharacteristic
44C4×C3⋊Dic3C2311yescharacteristic
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3—22no—
47C3×C4⋊Dic3—22no—
48C3×C4⋊Dic3—22no—
49#3724—22no—
50#3724—22no—
51#3724—22no—
52#3724C2314yes—
53C2×#487—91nomaximal, Sylow
54C2×D3×Q8—62no—
55C2×D3×Q8—62no—
56C3×C4⋊Q8—61no—
57C3×C4⋊Q8—61no—
58#944—62no—
59#944—62no—
60D3×C4⋊C4—62no—
61D3×C4⋊C4—62no—
62D3×C4⋊C4—62no—
63D3×C4⋊C4—62no—
64#888—62no—
65#888—62no—
66#888—62no—
67#888—62no—
68C42×D3—61no—
69C42×D3—61no—
70#869—21no—
71#869—21no—
72C22×C3⋊D3C2×D411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4C2×D411yescharacteristic
75C2×C32×C4C2×D411yescharacteristic
76C2×C3⋊Dic3C2×D411yescharacteristic
77C2×C3⋊Dic3C2×D411yescharacteristic
78C2×C3⋊Dic3C2411yescharacteristic
79C4×C3⋊D3SD1614yes—
80C4×C3⋊D3Q1614yes—
81C4×C3⋊D3#4114yes—
82C2×C3×Dic3—24no—
83C2×C3×Dic3—24no—
84C3×Dic6—44no—
85C3×Dic6—44no—
86#627—28no—
87#627—44no—
88#624—44no—
89#624—44no—
90#622—24no—
91C2×C4⋊Q8—91no—
92C2×C4⋊Q8—91no—
93#487—94no—
94#487—94no—
95C2×#103—94no—
96C2×C4×C8—91no—
97C2×C3×Q8—62no—
98C2×C3×Q8—62no—
99D3×Q8—128no—
100D3×Q8—128no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×C4×D3—61no—
107C2×C4×D3—64no—
108C2×C4×D3—64no—
109C2×Dic6—22no—
110C2×Dic6—22no—
111C2×Dic6—64no—
112C2×Dic6—64no—
113C3×C4⋊C4—62no—
114C3×C4⋊C4—62no—
115C3×C4⋊C4—62no—
116C3×C4⋊C4—62no—
117C3×C42—21no—
118C3×C42—21no—
119C4⋊Dic3—22no—
120C4⋊Dic3—22no—
121C4⋊Dic3—22no—
122C4⋊Dic3—22no—
123Dic3⋊C4—64no—
124Dic3⋊C4—64no—
125Dic3⋊C4—64no—
126Dic3⋊C4—64no—
127C4×Dic3—61no—
128C4×Dic3—61no—
129C4×Dic3—61no—
130C4×Dic3—61no—
131C4×Dic3—61no—
132C4×Dic3—61no—
133C22×C32C22×D411yescharacteristic
134C2×C3⋊D3#12412yes—
135C2×C3⋊D3C2×SD1612yes—
136C2×C3⋊D3C2×Q1612yes—
137C32×C4#12412yes—
138C32×C4C2×SD1612yes—
139C32×C4C2×Q1612yes—
140C3⋊Dic3C2×SD1612yes—
141C3⋊Dic3C2×Q1612yes—
142C3⋊Dic3C2×#4112yes—
143C3×Dic3—44no—
144C3×Dic3—44no—
145C22×Q8—92no—
146C22×Q8—181no—
147C22×C8—92no—
148C4⋊Q8—61no—
149C4⋊Q8—61no—
150C4⋊Q8—92no—
151C4⋊Q8—92no—
152C4⋊Q8—92no—
153C4⋊Q8—92no—
154C4⋊Q8—181no—
155C4⋊Q8—181no—
156C2×C4⋊C4—92no—
157C2×C4⋊C4—181no—
158C2×C4⋊C4—181no—
159C2×C4⋊C4—181no—
160C2×C42—91no—
161#103—916no—
162C4×C8—92no—
163C4×C8—92no—
164C22×D3—61no—
165C22×D3—61no—
166C3×Q8—124no—
167C3×Q8—124no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—64no—
175C2×C3×C4—64no—
176C2×Dic3—24no—
177C2×Dic3—24no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C4×D3—64no—
185C4×D3—64no—
186C4×D3—64no—
187C4×D3—64no—
188C4×D3—64no—
189C4×D3—64no—
190C4×D3—128no—
191C4×D3—128no—
192Dic6—44no—
193Dic6—44no—
194Dic6—128no—
195Dic6—128no—
196C2×C32C2×#12411yescharacteristic
197C2×C32C22×SD1611yescharacteristic
198C2×C32C22×Q1611yescharacteristic
199C3⋊D3#48714yescomplemented
200C2×Q8—62no—
201C2×Q8—62no—
202C2×Q8—94no—
203C2×Q8—182no—
204C2×Q8—188no—
205C2×Q8—364no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—182no—
210C22×C4—182no—
211C2×C8—94no—
212C2×C8—184no—
213C4⋊C4—62no—
214C4⋊C4—62no—
215C4⋊C4—62no—
216C4⋊C4—62no—
217C4⋊C4—94no—
218C4⋊C4—182no—
219C4⋊C4—182no—
220C4⋊C4—182no—
221C42—91no—
222C42—91no—
223C42—91no—
224C42GO+(4,𝔽2)11yescharacteristic
225C22×C3—21no—
226C22×C3—21no—
227C2×D3—62no—
228C2×D3—62no—
229C2×D3—62no—
230C2×D3—62no—
231C2×D3—62no—
232C2×D3—62no—
233C3×C4—22no—
234C3×C4—22no—
235C3×C4—22no—
236C3×C4—22no—
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—124no—
240C3×C4—124no—
241Dic3—44no—
242Dic3—44no—
243Dic3—62no—
244Dic3—62no—
245Dic3—62no—
246Dic3—62no—
247Dic3—62no—
248Dic3—62no—
249C32C2×#48711yescharacteristic, complemented, Sylow
250C23—91no—
251Q8—124no—
252Q8—124no—
253Q8—188no—
254Q8—364no—
255C2×C4—64no—
256C2×C4—64no—
257C2×C4—91no—
258C2×C4—91no—
259C2×C4—91no—
260C2×C4—94no—
261C2×C4—94no—
262C2×C4—94no—
263C2×C4—364no—
264C2×C4—364no—
265C2×C4C2×GO+(4,𝔽2)11yescharacteristic
266C2×C4C2×GO+(4,𝔽2)11yescharacteristic
267C2×C4C2×GO+(4,𝔽2)11yescharacteristic
268C8—184no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275D3—64no—
276D3—64no—
277C22—92no—
278C22—92no—
279C22—92no—
280C22C22×GO+(4,𝔽2)11yescharacteristic
281C4—92no—
282C4—92no—
283C4—92no—
284C4—124no—
285C4—124no—
286C4#6422112yes—
287C4#6422712yes—
288C4#6422812yes—
289C3—21no—
290C3—21no—
291C2—94no—
292C2C2×#6422111yescharacteristic
293C2C2×#6422711yescharacteristic
294C2C2×#6422811yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#487
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10593379C2semidirect
5. #10593377C2semidirect
199. C3⋊D3#487semidirect
249. C32C2×#487semidirect

Maximal subgroups

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

subgroupindex
#105939092
C4×#37872
#105933792
#105933772
#105933752
C2×#4879