Finite Group Databasebeta

← #10591603

Subgroups — #10591603

Order 576.

374 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 70 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×Q8×C3⋊D3C211yesmaximal, characteristic
2C2×C3×#216C211yesmaximal, characteristic, complemented
3#63871C211yesmaximal, characteristic
4C2×#3719C211yesmaximal, characteristic, complemented
5C3×#835C211yesmaximal, characteristic, complemented
6#63567C211yesmaximal, characteristic, complemented
7#63557C211yesmaximal, characteristic
8#5186—31nomaximal
9#4809—31nomaximal
10C2×C32×Q8C2211yescharacteristic
11Q8×C3⋊D3—22no—
12Q8×C3⋊D3—22no—
13C2×C4×C3⋊D3—21no—
14C2×C4×C3⋊D3C2211yescharacteristic
15C2×#634—21no—
16C2×#634C2211yescharacteristic
17C2×C3×Dic6C2211yescharacteristic
18C3×#216—22no—
19C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C3⋊C8C2211yescharacteristic
21C2×C3×C3⋊C8C2211yescharacteristic
22Dic3⋊Dic3—21no—
23#3722—21no—
24#3719—22no—
25C2×D3×Q8—31no—
26C2×D3×Q8—31no—
27C2×D3×Q8—61no—
28C2×C3×Q16—31no—
29#946—31no—
30C2×#216—31no—
31C2×#216D311yescharacteristic, complemented
32C2×Dic12—31no—
33#897—31no—
34C3×#103—31no—
35#835D311yescharacteristic, complemented
36(C2×D3)⋊C8—31no—
37(C2×D3)⋊C8—31no—
38#816—31no—
39#810—31no—
40C22×C3⋊D3D411yescharacteristic
41C32×Q8—21no—
42C32×Q8D412yes—
43C2×C32×C4—21no—
44C2×C32×C4C2311yescharacteristic
45C2×C3⋊Dic3—21no—
46C2×C3⋊Dic3D411yescharacteristic
47C4×C3⋊D3—24no—
48C4×C3⋊D3—21no—
49C4×C3⋊D3—21no—
50#634—24no—
51#634—21no—
52#634D412yes—
53C2×C3×Dic3—21no—
54C2×C3×Dic3—21no—
55C3×Dic6—21no—
56C3×Dic6—21no—
57C3×C3⋊C8—21no—
58C3×C3⋊C8—21no—
59#451—91noSylow
60C2×C3×Q8—21no—
61C2×C3×Q8—31no—
62C2×C3×Q8C2×D311yescharacteristic
63C2×C3×Q8C2×D311yescharacteristic
64D3×Q8—62no—
65D3×Q8—62no—
66D3×Q8—64no—
67D3×Q8—64no—
68D3×Q8—62no—
69D3×Q8—62no—
70C2×C4×D3—31no—
71C2×C4×D3—31no—
72C2×C4×D3—61no—
73C2×C4×D3—61no—
74C2×C4×D3—61no—
75C2×C4×D3—62no—
76C2×Dic6—31no—
77C2×Dic6—31no—
78C2×Dic6—61no—
79C2×Dic6—61no—
80C2×Dic6—61no—
81C2×Dic6—62no—
82C2×Dic6C2×D311yescharacteristic
83C3×Q16—62no—
84C2×C3×C8—31no—
85C2×C3×C8—31no—
86C3×C4⋊C4—31no—
87#216—22no—
88#216—62no—
89(C2×D3)⋊C4—61no—
90(C2×D3)⋊C4—61no—
91C4⋊Dic3—61no—
92C4⋊Dic3C2×D311yescharacteristic
93Dic3⋊C4—61no—
94C2×C3⋊C8C2×D311yescharacteristic
95C2×C3⋊C8C2×D311yescharacteristic
96Dic12—62no—
97C22×C32C2×D411yescharacteristic
98C2×C3⋊D3—21no—
99C2×C3⋊D3—21no—
100C2×C3⋊D3Q1612yescomplemented
101C32×C4—22no—
102C32×C4C2×D411yescharacteristic
103C32×C4C2×D411yescharacteristic
104C3⋊Dic3—21no—
105C3⋊Dic3—22no—
106C3×Dic3—41no—
107C3×Dic3—41no—
108C22×Q8—91no—
109C2×Q16—31no—
110C2×Q16—91no—
111C22⋊Q8—91no—
112#103—31no—
113#103—91no—
114C22⋊C8—91no—
115C22×D3—31no—
116C22×D3—31no—
117C22×D3—61no—
118C3×Q8—22no—
119C3×Q8—21no—
120C3×Q8—21no—
121C3×Q8—22no—
122C3×Q8—61no—
123C3×Q8—61no—
124C3×Q8D1212yes—
125C3×Q8#6712yes—
126C2×C3×C4—22no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—61no—
131C2×C3×C4—61no—
132C2×C3×C4C22×D311yescharacteristic
133C2×C3×C4C22×D311yescharacteristic
134C2×Dic3—21no—
135C2×Dic3—21no—
136C2×Dic3—31no—
137C2×Dic3—31no—
138C2×Dic3—61no—
139C2×Dic3—62no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142C4×D3—68no—
143C4×D3—64no—
144C4×D3—64no—
145C4×D3—62no—
146C4×D3—62no—
147C4×D3—61no—
148C4×D3—61no—
149C4×D3—61no—
150C4×D3—61no—
151Dic6—21no—
152Dic6—21no—
153Dic6—32no—
154Dic6—32no—
155Dic6—62no—
156Dic6—68no—
157Dic6—64no—
158Dic6—64no—
159Dic6—62no—
160Dic6—61no—
161Dic6—61no—
162C3×C8—61no—
163C3×C8—61no—
164C3⋊C8—21no—
165C3⋊C8—21no—
166C2×C32#12011yescharacteristic
167C2×C32C2×Q1611yescharacteristic
168C2×C32#13711yescharacteristic
169C3⋊D3—22no—
170C2×Q8—31no—
171C2×Q8—91no—
172C2×Q8—181no—
173C2×Q8—182no—
174C2×Q8—182no—
175C2×Q8D3211yescharacteristic
176C22×C4—91no—
177C22×C4—181no—
178Q16—62no—
179Q16—182no—
180C2×C8—31no—
181C2×C8—31no—
182C4⋊C4—31no—
183C4⋊C4—181no—
184C22⋊C4—181no—
185C22×C3—21no—
186C22×C3D3×D411yescharacteristic
187C22×C3D3×D411yescharacteristic
188C2×D3—32no—
189C2×D3—32no—
190C2×D3—62no—
191C2×D3—62no—
192C2×D3—62no—
193C2×D3—61no—
194C2×D3—61no—
195C2×D3—61no—
196C2×D3—61no—
197C3×C4—24no—
198C3×C4—22no—
199C3×C4—22no—
200C3×C4—21no—
201C3×C4—21no—
202C3×C4—121no—
203C3×C4—121no—
204C3×C4C2×D1211yescharacteristic
205C3×C4D3×D411yescharacteristic
206C3×C4D3×D411yescharacteristic
207C3×C4C2×#6711yescharacteristic
208Dic3—41no—
209Dic3—41no—
210Dic3—62no—
211Dic3—64no—
212Dic3—62no—
213Dic3—61no—
214Dic3—62no—
215Dic3—61no—
216C32#45111yescharacteristic, complemented, Sylow
217C23—91no—
218Q8—21no—
219Q8—61no—
220Q8—61no—
221Q8—92no—
222Q8—184no—
223Q8—181no—
224Q8#62612yes—
225C2×C4—21no—
226C2×C4—61no—
227C2×C4—61no—
228C2×C4—91no—
229C2×C4—184no—
230C2×C4—181no—
231C2×C4—181no—
232C2×C4—181no—
233C2×C4C2×D3211yescharacteristic
234C8—61no—
235C8—61no—
236C2×C3—21no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3#88211yescharacteristic
240C2×C3#91511yescharacteristic
241C2×C3D3×Q1611yescharacteristic
242C2×C3D3×Q1611yescharacteristic
243C2×C3#91811yescharacteristic
244C2×C3#93711yescharacteristic
245D3—64no—
246D3—62no—
247D3—62no—
248C22—92no—
249C22—181no—
250C22—181no—
251C22#381111yescharacteristic
252C4—22no—
253C4—121no—
254C4—121no—
255C4—181no—
256C4—182no—
257C4C2×#62611yescharacteristic
258C4#381111yescharacteristic
259C3—21no—
260C3#480911yescharacteristic, complemented
261C3#518611yescharacteristic, complemented
262C2—182no—
263C2#6394411yescharacteristic
264C2#6395111yescharacteristic
265C2#6398111yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC2×C32×Q8C22
socleC22×C32C2×D4
prime radicalC22×C3⋊D3D4
hypercenterC2×Q8D32
hypocenterC32#451
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#216C2semidirect
4. C2×#3719C2semidirect
5. C3×#835C2semidirect
6. #63567C2semidirect
31. C2×#216D3semidirect
35. #835D3semidirect
100. C2×C3⋊D3Q16semidirect
216. C32#451semidirect
260. C3#4809semidirect
261. C3#5186semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊D32
C2×C3×#2162
#638712
C2×#37192
C3×#8352
#635672
#635572
#51863
#48093