Finite Group Databasebeta

← #68954

Subgroups — #68954

Order 384.

378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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×#886C211yesmaximal, characteristic
2C2×#877C211yesmaximal, characteristic, complemented
3C2×#806C211yesmaximal, characteristic
4C2×#806C211yesmaximal, characteristic
5#4943C211yesmaximal, characteristic, complemented
6C3×#342C211yesmaximal, characteristic, complemented
7#4526C211yesmaximal, characteristic, complemented
8#1899—31nomaximal, Sylow
9C22×#67C2211yescharacteristic
10C23×Dic3C2211yescharacteristic
11C2×C3×C22⋊C4C2211yescharacteristic
12C2×C3×C22⋊C4C2211yescharacteristic
13C2×C3×C22⋊C4C2211yescharacteristic
14C2×#217C2211yescharacteristic
15C2×#217C2211yescharacteristic
16C2×(C2×D3)⋊C4C412yescomplemented
17C2×C4⋊Dic3C412yescomplemented
18C2×Dic3⋊C4—21no—
19C2×C4×Dic3—21no—
20#886—22no—
21#886—21no—
22#886—21no—
23#877—22no—
24#877—22no—
25C3⋊#95—22no—
26#806—22no—
27#806—22no—
28C2×#123—31no—
29C2×#117—31no—
30C2×#99—31no—
31C2×#99—31no—
32#381—31no—
33#342—31no—
34#342D311yescharacteristic, complemented
35C24×C3C2311yescharacteristic
36C23×D3C2×C411yescharacteristic
37C22×C3×C4—21no—
38C22×C3×C4—21no—
39C22×C3×C4C2×C412yes—
40C2×#67—21no—
41C2×#67—21no—
42C2×#67—21no—
43C2×#67—21no—
44C2×#67—21no—
45C2×#67—21no—
46C22×Dic3—21no—
47C22×Dic3—21no—
48C22×Dic3—21no—
49C22×Dic3—21no—
50C22×Dic3—21no—
51C22×Dic3—21no—
52C22×Dic3C2×C411yescharacteristic
53C22×Dic3C2×C412yes—
54C22×Dic3D412yes—
55C22×Dic3D411yescharacteristic
56C22×Dic3D411yescharacteristic
57C3×C22⋊C4—21no—
58C3×C22⋊C4—21no—
59C3×C22⋊C4—21no—
60C3×C22⋊C4—21no—
61C3×C22⋊C4—21no—
62C3×C22⋊C4D412yes—
63#217—21no—
64#217—21no—
65#217—21no—
66#217D412yes—
67(C2×D3)⋊C4—22no—
68(C2×D3)⋊C4—22no—
69C4⋊Dic3—22no—
70C4⋊Dic3—22no—
71Dic3⋊C4—24no—
72C4×Dic3—24no—
73C22×D4—31no—
74C23×C4—31no—
75#123—62no—
76#123—61no—
77#123—61no—
78#117—62no—
79#117—62no—
80C2×C4⋊C4—32no—
81C2×C4⋊C4—61no—
82C2×C22⋊C4—31no—
83C2×C22⋊C4—32no—
84C2×C22⋊C4—31no—
85C2×C22⋊C4C2×D311yescharacteristic
86C2×C22⋊C4C2×D311yescharacteristic
87C2×C22⋊C4C2×D311yescharacteristic
88C2×C42—61no—
89#99—62no—
90#99—62no—
91#95—62no—
92C23×C3—42no—
93C23×C3C22×C411yescharacteristic
94C23×C3C2×D411yescharacteristic
95C23×C3C2×D411yescharacteristic
96C23×C3C2×D411yescharacteristic
97C23×C3C2×D411yescharacteristic
98C23×C3#4111yescharacteristic
99C23×C3#4111yescharacteristic
100C22×D3—21no—
101C22×D3—21no—
102C22×D3—21no—
103C22×D3—42no—
104C2×C3×C4—22no—
105C2×C3×C4—22no—
106C2×C3×C4—42no—
107C2×C3×C4—42no—
108C2×C3×C4—42no—
109C2×C3×C4—41no—
110#67—41no—
111#67—41no—
112#67—41no—
113#67—41no—
114C2×Dic3—22no—
115C2×Dic3—22no—
116C2×Dic3—21no—
117C2×Dic3—21no—
118C2×Dic3—22no—
119C2×Dic3—22no—
120C2×Dic3—21no—
121C2×Dic3—21no—
122C2×Dic3—21no—
123C2×Dic3—21no—
124C2×Dic3—21no—
125C2×Dic3—22no—
126C2×Dic3—42no—
127C2×Dic3—42no—
128C2×Dic3—41no—
129C2×Dic3C22⋊C412yes—
130C2×Dic3C22⋊C412yes—
131C24—31no—
132C24C22×D311yescharacteristic
133C2×D4—61no—
134C2×D4—61no—
135C2×D4—61no—
136C2×D4—61no—
137C2×D4—61no—
138C2×D4—61no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—32no—
142C22×C4—32no—
143C22×C4—31no—
144C22×C4—31no—
145C22×C4—31no—
146C22×C4—61no—
147C22×C4—61no—
148C22×C4—61no—
149C22×C4—61no—
150C22×C4—61no—
151C22×C4—61no—
152C22×C4C4×D312yes—
153C4⋊C4—62no—
154C4⋊C4—62no—
155C4⋊C4—64no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—32no—
162C22⋊C4—62no—
163C22⋊C4—62no—
164C22⋊C4—61no—
165C22⋊C4—61no—
166C22⋊C4—61no—
167C22⋊C4D1212yes—
168C42—64no—
169C22×C3—22no—
170C22×C3—22no—
171C22×C3—22no—
172C22×C3—41no—
173C22×C3—41no—
174C22×C3—41no—
175C22×C3—41no—
176C22×C3C2×C22⋊C411yescharacteristic
177C22×C3C4×D411yescharacteristic
178C22×C3C4×D411yescharacteristic
179C22×C3#12011yescharacteristic
180C22×C3#12111yescharacteristic
181C22×C3#12111yescharacteristic
182C22×C3#12311yescharacteristic
183C2×D3—41no—
184C2×D3—42no—
185C2×D3—81no—
186C2×D3—81no—
187C3×C4—42no—
188C3×C4—42no—
189C3×C4—81no—
190Dic3—22no—
191Dic3—22no—
192Dic3—42no—
193Dic3—41no—
194Dic3—81no—
195C23—42no—
196C23—61no—
197C23—61no—
198C23—61no—
199C23—122no—
200C23C2×C4×D311yescharacteristic
201C23C2×D1211yescharacteristic
202C23#23511yescharacteristic
203C23D3×D411yescharacteristic
204C23D3×D411yescharacteristic
205C23D3×D411yescharacteristic
206C23#23911yescharacteristic
207D4—121no—
208D4—121no—
209D4—121no—
210D4—121no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—32no—
214C2×C4—32no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—62no—
220C2×C4—61no—
221C2×C4—61no—
222C2×C4—62no—
223C2×C4—62no—
224C2×C4—61no—
225C2×C4—61no—
226C2×C4—62no—
227C2×C4—61no—
228C2×C4—61no—
229C2×C4—62no—
230C2×C4—61no—
231C2×C4—122no—
232C2×C4—122no—
233C2×C4—121no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3#38611yescharacteristic
241C2×C3#41012yes—
242D3—81no—
243C22—22no—
244C22—22no—
245C22—22no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—121no—
251C22—122no—
252C22—241no—
253C22—241no—
254C22C4×D1211yescharacteristic
255C22D3×C22⋊C411yescharacteristic
256C22#88211yescharacteristic
257C22#88411yescharacteristic
258C22#89311yescharacteristic
259C22#89411yescharacteristic
260C22#89511yescharacteristic
261C4—42no—
262C4—42no—
263C4—62no—
264C4—62no—
265C4—81no—
266C4—122no—
267C4—121no—
268C4—241no—
269C3#189911yescharacteristic, complemented, Sylow
270C2—21no—
271C2—21no—
272C2—21no—
273C2—21no—
274C2—21no—
275C2—21no—
276C2—241no—
277C2#466511yescharacteristic
278C2#474012yes—
subgroupG/H
centerC22D3×C22⋊C4
commutatorC23×C3C22×C4
FrattiniC24C22×D3
FittingC3×#342C2
socleC22×C3C2×C22⋊C4
prime radicalC22×#67C22
cosocleC24×C3C23
hypercenter#342D3
hypocenterC3#1899
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#877C2semidirect
5. #4943C2semidirect
6. C3×#342C2semidirect
7. #4526C2semidirect
16. C2×(C2×D3)⋊C4C4semidirect
17. C2×C4⋊Dic3C4semidirect
34. #342D3semidirect
269. C3#1899semidirect

Maximal subgroups

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

subgroupindex
C2×#8862
C2×#8772
C2×#8062
#49432
C3×#3422
#45262
#18993