Finite Group Databasebeta

← #70029

Subgroups — #70029

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×#935C211yesmaximal, characteristic
2C2×#877C211yesmaximal, characteristic, complemented
3C2×C3×#99C211yesmaximal, characteristic
4C2×#834C211yesmaximal, characteristic
5#4943C211yesmaximal, characteristic, complemented
6#4527C211yesmaximal, characteristic, complemented
7#4527C211yesmaximal, characteristic, complemented
8#1899—31nomaximal, Sylow
9C22×C3×D4C2211yescharacteristic
10C23×Dic3C2211yescharacteristic
11C2×C3×C22⋊C4C2211yescharacteristic
12C2×C3×C22⋊C4C2211yescharacteristic
13C2×#217C412yescomplemented
14C2×#217C2211yescharacteristic
15C2×#217C2211yescharacteristic
16C2×#217C2211yescharacteristic
17#935—22no—
18#935—21no—
19#935—21no—
20C2×Dic3⋊C4—21no—
21C2×Dic3⋊C4C412yescomplemented
22C2×C4×Dic3—21no—
23#877—22no—
24#877—22no—
25C3×#99—22no—
26#834—22no—
27C3⋊#95—22no—
28C2×#123—31no—
29C2×#117—31no—
30C2×#99—31no—
31C2×#99D311yescharacteristic
32#381—31no—
33#342—31no—
34#342—31no—
35C24×C3C2×C411yescharacteristic
36C24×C3C2311yescharacteristic
37C2×C3×D4—21no—
38C2×C3×D4—21no—
39C2×C3×D4—21no—
40C2×C3×D4—21no—
41C2×C3×D4—21no—
42C2×C3×D4—21no—
43C22×C3×C4—21no—
44C22×C3×C4—21no—
45C22×C3×C4C2×C411yescharacteristic
46C22×Dic3—21no—
47C22×Dic3—21no—
48C22×Dic3—21no—
49C22×Dic3—21no—
50C22×Dic3—21no—
51C22×Dic3—21no—
52C22×Dic3C2×C412yes—
53C22×Dic3C2×C412yes—
54C22×Dic3D412yes—
55C22×Dic3D411yescharacteristic
56C22×Dic3D411yescharacteristic
57C3×C22⋊C4—21no—
58C3×C22⋊C4—21no—
59C3×C22⋊C4—21no—
60C3×C22⋊C4D412yes—
61#217—21no—
62#217—21no—
63#217—21no—
64#217—22no—
65#217—22no—
66#217—21no—
67#217—21no—
68#217D412yes—
69Dic3⋊C4—24no—
70Dic3⋊C4—22no—
71Dic3⋊C4—22no—
72C4×Dic3—24no—
73C22×D4C2×D311yescharacteristic
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⋊C4—31no—
86C2×C22⋊C4C2×D311yescharacteristic
87C2×C22⋊C4C2×D311yescharacteristic
88C2×C42—61no—
89#99—22no—
90#99—62no—
91#95—62no—
92C23×C3—21no—
93C23×C3—21no—
94C23×C3—21no—
95C23×C3—42no—
96C23×C3—42no—
97C23×C3C22×C411yescharacteristic
98C23×C3C2×D411yescharacteristic
99C23×C3C2×D411yescharacteristic
100C23×C3C2×D411yescharacteristic
101C23×C3C2×D411yescharacteristic
102C23×C3#4111yescharacteristic
103C23×C3#4111yescharacteristic
104C3×D4—41no—
105C3×D4—41no—
106C3×D4—41no—
107C3×D4—41no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—22no—
112C2×C3×C4—42no—
113C2×C3×C4—42no—
114C2×C3×C4—41no—
115C2×Dic3—22no—
116C2×Dic3—22no—
117C2×Dic3—21no—
118C2×Dic3—21no—
119C2×Dic3—22no—
120C2×Dic3—22no—
121C2×Dic3—21no—
122C2×Dic3—21no—
123C2×Dic3—22no—
124C2×Dic3—22no—
125C2×Dic3—42no—
126C2×Dic3—42no—
127C2×Dic3—42no—
128C2×Dic3—41no—
129C2×Dic3C22⋊C412yes—
130C2×Dic3C22⋊C412yes—
131C24C4×D311yescharacteristic
132C24C22×D311yescharacteristic
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—32no—
142C22×C4—32no—
143C22×C4—31no—
144C22×C4—31no—
145C22×C4—32no—
146C22×C4—61no—
147C22×C4—61no—
148C22×C4—61no—
149C22×C4—61no—
150C22×C4—61no—
151C22×C4—61no—
152C22×C4C4×D311yescharacteristic
153C4⋊C4—62no—
154C4⋊C4—62no—
155C4⋊C4—64no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—32no—
160C22⋊C4—62no—
161C22⋊C4—62no—
162C22⋊C4—61no—
163C22⋊C4—61no—
164C22⋊C4—61no—
165C22⋊C4—61no—
166C22⋊C4—61no—
167C22⋊C4#6712yes—
168C42—64no—
169C22×C3—22no—
170C22×C3—22no—
171C22×C3—22no—
172C22×C3—41no—
173C22×C3—41no—
174C22×C3—41no—
175C22×C3—41no—
176C22×C3—41no—
177C22×C3—42no—
178C22×C3—81no—
179C22×C3—81no—
180C22×C3C2×C22⋊C411yescharacteristic
181C22×C3C4×D411yescharacteristic
182C22×C3C4×D411yescharacteristic
183C22×C3#12011yescharacteristic
184C22×C3#12111yescharacteristic
185C22×C3#12111yescharacteristic
186C22×C3#12311yescharacteristic
187C3×C4—42no—
188C3×C4—41no—
189C3×C4—81no—
190Dic3—22no—
191Dic3—22no—
192Dic3—42no—
193Dic3—42no—
194Dic3—81no—
195C23—21no—
196C23—21no—
197C23—21no—
198C23—42no—
199C23—42no—
200C23C2×C4×D311yescharacteristic
201C23#23511yescharacteristic
202C23D3×D411yescharacteristic
203C23D3×D411yescharacteristic
204C23D3×D411yescharacteristic
205C23#23711yescharacteristic
206C23C2×#6711yescharacteristic
207D4—41no—
208D4—41no—
209D4—41no—
210D4—41no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—32no—
216C2×C4—32no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—62no—
221C2×C4—61no—
222C2×C4—61no—
223C2×C4—62no—
224C2×C4—62no—
225C2×C4—61no—
226C2×C4—61no—
227C2×C4—62no—
228C2×C4—62no—
229C2×C4—62no—
230C2×C4—122no—
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—81no—
241C2×C3#38611yescharacteristic
242C2×C3#41012yes—
243C22—22no—
244C22—22no—
245C22—22no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—42no—
252C22—81no—
253C22—81no—
254C22D3×C22⋊C411yescharacteristic
255C22#67⋊C411yescharacteristic
256C22#88311yescharacteristic
257C22#88411yescharacteristic
258C22C4×#6711yescharacteristic
259C22#93711yescharacteristic
260C22#93811yescharacteristic
261C4—42no—
262C4—41no—
263C4—62no—
264C4—62no—
265C4—81no—
266C4—122no—
267C4—122no—
268C4—241no—
269C3#189911yescharacteristic, complemented, Sylow
270C2—21no—
271C2—21no—
272C2—21no—
273C2—21no—
274C2—21no—
275C2—21no—
276C2—81no—
277C2#474012yes—
278C2#495611yescharacteristic
subgroupG/H
centerC22D3×C22⋊C4
commutatorC23×C3C22×C4
FrattiniC24C22×D3
FittingC2×C3×#99C2
socleC22×C3C2×C22⋊C4
prime radicalC22×C3×D4C22
cosocleC24×C3C23
hypercenterC2×#99D3
hypocenterC3#1899
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#877C2semidirect
5. #4943C2semidirect
6. #4527C2semidirect
7. #4527C2semidirect
13. C2×#217C4semidirect
21. C2×Dic3⋊C4C4semidirect
269. C3#1899semidirect

Maximal subgroups

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

subgroupindex
C2×#9352
C2×#8772
C2×C3×#992
C2×#8342
#49432
#45272
#18993