Finite Group Databasebeta

← #11782709

Subgroups — #11782709

Order 1152.

385 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 385 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×#4681C211yesmaximal, characteristic
2C3×#4680C211yesmaximal, characteristic
3#10590387C211yesmaximal, characteristic
4#10590309C211yesmaximal, characteristic
5#10590309C211yesmaximal, characteristic
6#10590290C211yesmaximal, characteristic
7#10589320C211yesmaximal, characteristic
8#71337—31nomaximal
9#71217—31nomaximal
10C3×#869C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3718—22no—
15C32×C4×C8C2211yescharacteristic
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#817—22no—
19C3×#816—22no—
20#63574—22no—
21#63574—22no—
22#63565—22no—
23C3×#498—31no—
24C3×#487—31no—
25#5093—31no—
26#5092—31no—
27#5092—31no—
28#5080—31no—
29#5080—31no—
30#5080—31no—
31#5080—31no—
32#5079—31no—
33#4681D311yescharacteristic
34#4680D311yescharacteristic
35#4454—31no—
36#4454—31no—
37#4454—61no—
38C2×C3×Dic6—21no—
39C2×C3×Dic6—21no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—21no—
42C2×C32×C8D412yes—
43C32×C42C2311yescharacteristic
44C2×C3⋊(C3⋊C8)D412yes—
45C2×C3⋊(C3⋊C8)D412yes—
46C3×C4⋊Dic3—21no—
47C3×C4⋊Dic3—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54#3718—44no—
55#1716—91noSylow
56C3×C4⋊Q8—31no—
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8—31no—
59C3×C4⋊Q8—31no—
60C2×#216—62no—
61C2×#216—62no—
62#869C2×D311yescharacteristic
63#869C2×D311yescharacteristic
64#869C2×D311yescharacteristic
65#869C2×D311yescharacteristic
66C3×#106—62no—
67C3×#103—62no—
68C3×C4×C8—21no—
69C3×C4×C8C2×D311yescharacteristic
70C3×C4×C8C2×D311yescharacteristic
71#835—62no—
72#817—22no—
73#816—22no—
74#810—62no—
75#808—62no—
76#808—62no—
77#808—62no—
78#808—62no—
79C4×C3⋊C8—31no—
80C4×C3⋊C8—31no—
81C4×C3⋊C8—31no—
82C4×C3⋊C8—31no—
83C4×C3⋊C8—61no—
84C4×C3⋊C8—61no—
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C3×Dic3—41no—
89C2×C3×Dic3—41no—
90C2×C3×Dic3—41no—
91C2×C3×Dic3—41no—
92C3×Dic6—42no—
93C3×Dic6—42no—
94C3×Dic6—42no—
95C3×Dic6—42no—
96C32×C8—22no—
97C3⋊(C3⋊C8)—22no—
98C3⋊(C3⋊C8)SD1614yes—
99#498—31no—
100#498—91no—
101#498—91no—
102#494—91no—
103#487—31no—
104#487—91no—
105#322—91no—
106C2×C3×Q8—61no—
107C2×C3×Q8—61no—
108C2×C3×Q8—61no—
109C2×C3×Q8—61no—
110C2×Dic6—21no—
111C2×Dic6—21no—
112C2×Dic6—21no—
113C2×Dic6—21no—
114C2×C3×C8—22no—
115C2×C3×C8#6712yes—
116C2×C3×C8#6712yes—
117C3×C4⋊C4—61no—
118C3×C4⋊C4—61no—
119C3×C4⋊C4—61no—
120C3×C4⋊C4—61no—
121C3×C4⋊C4—61no—
122C3×C4⋊C4—61no—
123C3×C4⋊C4—61no—
124C3×C4⋊C4—61no—
125C3×C42—21no—
126C3×C42C22×D311yescharacteristic
127C3×C42C22×D311yescharacteristic
128#216—124no—
129#216—124no—
130C4⋊Dic3—21no—
131C4⋊Dic3—21no—
132C4⋊Dic3—21no—
133C4⋊Dic3—21no—
134C4⋊Dic3—21no—
135C4⋊Dic3—21no—
136C4⋊Dic3—21no—
137C4⋊Dic3—21no—
138C2×C3⋊C8—32no—
139C2×C3⋊C8—32no—
140C2×C3⋊C8—32no—
141C2×C3⋊C8—32no—
142C2×C3⋊C8—62no—
143C2×C3⋊C8—62no—
144C22×C32#12711yescharacteristic
145C32×C4C2×SD1612yes—
146C32×C4#13712yes—
147C32×C4#13712yes—
148C3×Dic3—81no—
149C3×Dic3—81no—
150C3×Dic3—81no—
151C3×Dic3—81no—
152C2×Q16—182no—
153C4⋊Q8—31no—
154C4⋊Q8—31no—
155C4⋊Q8—31no—
156C4⋊Q8—31no—
157#106—62no—
158#106—182no—
159#106—182no—
160#103—62no—
161#103—182no—
162C4×C8—91no—
163C4×C8—91no—
164C4×C8D3211yescharacteristic
165C3×Q8—122no—
166C3×Q8—122no—
167C3×Q8—122no—
168C3×Q8—122no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—121no—
173C2×C3×C4—121no—
174C2×C3×C4—121no—
175C2×C3×C4—121no—
176C2×C3×C4D3×D411yescharacteristic
177C2×C3×C4D3×D411yescharacteristic
178C2×C3×C4D3×D411yescharacteristic
179C2×C3×C4D3×D411yescharacteristic
180C2×C3×C4C2×#6711yescharacteristic
181C2×C3×C4C2×#6711yescharacteristic
182C2×Dic3—41no—
183C2×Dic3—41no—
184C2×Dic3—41no—
185C2×Dic3—41no—
186Dic6—42no—
187Dic6—42no—
188Dic6—42no—
189Dic6—42no—
190C3×C8—22no—
191C3×C8—22no—
192C3×C8—42no—
193C3⋊C8—34no—
194C3⋊C8—34no—
195C3⋊C8—64no—
196C3⋊C8—62no—
197C3⋊C8—62no—
198C3⋊C8—122no—
199C2×C32#49211yescharacteristic
200C2×C32#49711yescharacteristic
201C2×C32#49711yescharacteristic
202C2×Q8—61no—
203C2×Q8—61no—
204C2×Q8—61no—
205C2×Q8—61no—
206Q16—364no—
207C2×C8—92no—
208C2×C8—92no—
209C2×C8#62512yes—
210C4⋊C4—61no—
211C4⋊C4—61no—
212C4⋊C4—61no—
213C4⋊C4—61no—
214C4⋊C4—61no—
215C4⋊C4—61no—
216C4⋊C4—61no—
217C4⋊C4—61no—
218C42C2×D3211yescharacteristic
219C22×C3—21no—
220C22×C3#94011yescharacteristic
221C22×C3#94011yescharacteristic
222C3×C4—22no—
223C3×C4—22no—
224C3×C4—22no—
225C3×C4—241no—
226C3×C4—241no—
227C3×C4—241no—
228C3×C4—241no—
229C3×C4D3×SD1612yes—
230C3×C4D3×SD1612yes—
231C3×C4#91512yes—
232C3×C4#91812yes—
233C3×C4#94212yes—
234C3×C4#95112yes—
235Dic3—81no—
236Dic3—81no—
237Dic3—81no—
238Dic3—81no—
239C32#171611yescharacteristic, complemented, Sylow
240Q8—122no—
241Q8—122no—
242Q8—122no—
243Q8—122no—
244C2×C4—121no—
245C2×C4—121no—
246C2×C4—121no—
247C2×C4—121no—
248C2×C4#380211yescharacteristic
249C2×C4#380211yescharacteristic
250C2×C4C2×#62511yescharacteristic
251C8—22no—
252C8—94no—
253C8—182no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—21no—
257C2×C3#506011yescharacteristic
258C2×C3#508611yescharacteristic
259C2×C3#516711yescharacteristic
260C2×C3#517511yescharacteristic
261C2×C3#517511yescharacteristic
262C2×C3#519011yescharacteristic
263C22#6391411yescharacteristic
264C4—241no—
265C4—241no—
266C4—241no—
267C4—241no—
268C4#6379612yes—
269C4#6381112yes—
270C4#6382712yes—
271C3—21no—
272C3#7121711yescharacteristic, complemented
273C3#7133711yescharacteristic, complemented
274C2#1059037611yescharacteristic
275C2#1059087011yescharacteristic
276C2#1059088411yescharacteristic
subgroupG/H
centerC22#63914
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#127
hypercenterC4×C8D32
hypocenterC32#1716
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
239. C32#1716semidirect
272. C3#71217semidirect
273. C3#71337semidirect

Maximal subgroups

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

subgroupindex
C3×#46812
C3×#46802
#105903872
#105903092
#105902902
#105893202
#713373
#712173