Finite Group Databasebeta

← #11794295

Subgroups — #11794295

Order 1152.

410 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 55 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#10594813C211yesmaximal, characteristic
2#10593507C212yesmaximal
3#10591247C211yesmaximal, characteristic
4#10590208C211yesmaximal, characteristic
5#10590074C212yesmaximal
6C2×#3792C2212yes—
7C2×#3750C2211yescharacteristic
8C3×#924—21no—
9#63982—21no—
10C2×#3724C2211yescharacteristic
11#63957C2212yes—
12C2×Dic32C2211yescharacteristic
13#63847—22no—
14#63839—22no—
15#63743—22no—
16#63742—22no—
17C3×C3⋊#95—21no—
18#63579—21no—
19#5623—61no—
20#4650—61no—
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3D411yescharacteristic
23C22×C3⋊Dic3C2311yescharacteristic
24C22×C3×Dic3—21no—
25C22×C3×Dic3—21no—
26C2×C3×Dic6—21no—
27C2×#627—21no—
28#3792—22no—
29#3792Q814yescomplemented
30C2×#622—22no—
31#3750—22no—
32C3×#217—22no—
33C3×C4⋊Dic3—21no—
34C3×Dic3⋊C4—22no—
35#3724—21no—
36#3724—22no—
37#3724D412yes—
38#3724D412yes—
39Dic3⋊Dic3—22no—
40Dic32—22no—
41Dic32—21no—
42Dic32Q812yescomplemented
43#2061—91nomaximal, Sylow
44C3×C22⋊Q8—61no—
45#944—62no—
46#924—21no—
47C2×Dic3⋊C4—61no—
48C2×Dic3⋊C4—61no—
49C2×Dic3⋊C4—61no—
50C2×C4×Dic3—61no—
51#889—62no—
52#889—62no—
53#888—62no—
54#878—62no—
55#877—62no—
56C3×#95—61no—
57C3⋊#95—21no—
58C3⋊#95—61no—
59C3⋊#95—61no—
60C23×C32C2×D411yescharacteristic
61C2×C32×C4—21no—
62C2×C32×C4—41no—
63C2×C3⋊Dic3—21no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3C2×D412yes—
66C2×C3⋊Dic3C2×Q812yes—
67C2×C3⋊Dic3C2×Q811yescharacteristic
68C2×C3⋊Dic3#4111yescharacteristic
69C2×C3×Dic3—22no—
70C2×C3×Dic3—22no—
71C2×C3×Dic3—22no—
72C2×C3×Dic3—41no—
73C2×C3×Dic3—41no—
74C2×C3×Dic3—41no—
75C2×C3×Dic3—41no—
76C2×C3×Dic3—41no—
77C3×Dic6—81no—
78#627—81no—
79#622—24no—
80#544—91no—
81#428—92no—
82#382—91no—
83#343—91no—
84#339—92no—
85C2×C3×Q8—61no—
86C22×C3×C4—21no—
87C22×C3×C4—21no—
88C22×C3×C4—61no—
89C22×C3×C4—61no—
90C22×Dic3—21no—
91C22×Dic3—21no—
92C22×Dic3—61no—
93C22×Dic3—61no—
94C22×Dic3—61no—
95C22×Dic3—61no—
96C2×Dic6—21no—
97C2×Dic6—62no—
98C3×C4⋊C4—62no—
99C3×C4⋊C4—61no—
100C3×C22⋊C4—62no—
101#217—22no—
102C4⋊Dic3—21no—
103C4⋊Dic3—62no—
104Dic3⋊C4—22no—
105Dic3⋊C4—62no—
106Dic3⋊C4—62no—
107Dic3⋊C4—62no—
108Dic3⋊C4—62no—
109Dic3⋊C4—62no—
110Dic3⋊C4—62no—
111Dic3⋊C4—122no—
112Dic3⋊C4—122no—
113C4×Dic3—62no—
114C4×Dic3—62no—
115C4×Dic3—62no—
116C4×Dic3—62no—
117C22×C32—21no—
118C22×C32—21no—
119C22×C32#12011yescharacteristic
120C22×C32C22⋊Q811yescharacteristic
121C22×C32C4⋊Q811yescharacteristic
122C32×C4—41no—
123C3⋊Dic3—41no—
124C3⋊Dic3C22⋊Q812yes—
125C3⋊Dic3C4⋊Q812yes—
126C3×Dic3—42no—
127C3×Dic3—42no—
128C3×Dic3—42no—
129C3×Dic3—81no—
130C2×M16—92no—
131C4⋊Q8—182no—
132#125—182no—
133C22⋊Q8—61no—
134C22⋊Q8—181no—
135#117—92no—
136C2×C4⋊C4—91no—
137C2×C4⋊C4—91no—
138C2×C42—91no—
139#107—182no—
140#106—182no—
141#95—61no—
142#95—181no—
143C23×C3—21no—
144C23×C3—21no—
145C3×Q8—241no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—41no—
149C2×C3×C4—41no—
150C2×C3×C4—41no—
151C2×C3×C4—62no—
152C2×C3×C4—62no—
153C2×C3×C4—62no—
154C2×C3×C4—81no—
155C2×C3×C4—121no—
156C2×C3×C4—121no—
157C2×C3×C4—121no—
158C2×C3×C4—121no—
159C2×C3×C4—121no—
160C2×Dic3—22no—
161C2×Dic3—22no—
162C2×Dic3—22no—
163C2×Dic3—41no—
164C2×Dic3—41no—
165C2×Dic3—41no—
166C2×Dic3—41no—
167C2×Dic3—41no—
168C2×Dic3—62no—
169C2×Dic3—62no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—62no—
173C2×Dic3—62no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—62no—
177C2×Dic3—121no—
178C2×Dic3—121no—
179C2×Dic3—121no—
180C2×Dic3—241no—
181Dic6—81no—
182Dic6—242no—
183C2×C32—21no—
184C2×C32—21no—
185C2×C32#39511yescharacteristic
186C2×C32#45411yescharacteristic
187C2×C32#45511yescharacteristic
188C2×Q8—61no—
189C2×Q8—181no—
190C22×C4—61no—
191C22×C4—61no—
192C22×C4—91no—
193C22×C4—91no—
194C22×C4GO+(4,𝔽2)11yescharacteristic
195M16—94no—
196M16—182no—
197C2×C8—182no—
198C4⋊C4—61no—
199C4⋊C4—62no—
200C4⋊C4—92no—
201C4⋊C4—92no—
202C4⋊C4—182no—
203C4⋊C4—181no—
204C4⋊C4—182no—
205C4⋊C4—182no—
206C22⋊C4—62no—
207C42—92no—
208C42—181no—
209C42—182no—
210C22×C3—21no—
211C22×C3—21no—
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—21no—
217C22×C3—21no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—41no—
221C22×C3—41no—
222C3×C4—41no—
223C3×C4—41no—
224C3×C4—81no—
225C3×C4—122no—
226C3×C4—122no—
227C3×C4—122no—
228C3×C4—241no—
229Dic3—42no—
230Dic3—42no—
231Dic3—42no—
232Dic3—62no—
233Dic3—62no—
234Dic3—62no—
235Dic3—62no—
236Dic3—81no—
237Dic3—122no—
238Dic3—241no—
239C32#206111yescharacteristic, complemented, Sylow
240C23C2×GO+(4,𝔽2)11yescharacteristic
241Q8—241no—
242Q8—721no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—62no—
246C2×C4—62no—
247C2×C4—62no—
248C2×C4—91no—
249C2×C4—91no—
250C2×C4—92no—
251C2×C4—92no—
252C2×C4—121no—
253C2×C4—121no—
254C2×C4—121no—
255C2×C4—121no—
256C2×C4—121no—
257C2×C4—181no—
258C2×C4—361no—
259C8—184no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—41no—
271C2×C3—41no—
272C22—21no—
273C22—21no—
274C22D32⋊Q811yescharacteristic
275C22#6422211yescharacteristic
276C22#6424111yescharacteristic
277C4—41no—
278C4—92no—
279C4—92no—
280C4—122no—
281C4—122no—
282C4—122no—
283C4—241no—
284C4—361no—
285C3—21no—
286C3—21no—
287C2—21no—
288C2—21no—
289C2#1059341111yescharacteristic
290C2#1059345111yescharacteristic
291C2#1059352911yescharacteristic
subgroupG/H
centerC22#64241
commutator, cosocleC22×C3⋊Dic3C23
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2061
LCSG ▷ C22×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
29. #3792Q8semidirect
42. Dic32Q8semidirect
239. C32#2061semidirect

Maximal subgroups

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

subgroupindex
#105948132
#105935072
#105912472
#105902082
#105900742
#20619