Finite Group Databasebeta

← #11781908

Subgroups — #11781908

Order 1152.

324 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 88 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×#4831C211yesmaximal, characteristic
2#10590384C211yesmaximal, characteristic
3#10590303C211yesmaximal, characteristic
4#10590283C211yesmaximal, characteristic
5#10589347C211yesmaximal, characteristic
6C3×#4486C211yesmaximal, characteristic
7#10589099C211yesmaximal, characteristic
8#70963—31nomaximal
9#68474—31nomaximal
10#64078C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3718—21no—
14C32×C4⋊C8C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×#815—21no—
17C3×Dic3⋊C8—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63575—21no—
21#63573—21no—
22#63573—21no—
23#63566—21no—
24#63565—21no—
25C3×#446—31no—
26#5090—31no—
27#5080—31no—
28#5031—31no—
29#5021—31no—
30#4850—31no—
31#4831D311yescharacteristic
32#4680—31no—
33C3×#332—31no—
34#4486D311yescharacteristic
35#4481—31no—
36#4481—31no—
37#4481—61no—
38#4479—31no—
39#4458—31no—
40C2×#634—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6D411yescharacteristic
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C2×C3⋊(C3⋊C8)—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3D411yescharacteristic
51C3×Dic3⋊C4—21no—
52C3×C4×Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#3718—42no—
57#1692—91noSylow
58C3×C4⋊Q8—31no—
59C3×C4×Q8—31no—
60C2×#216—61no—
61C2×#216—61no—
62#869—31no—
63#869—31no—
64#869—61no—
65#869C2×D311yescharacteristic
66C4×Dic6C2×D311yescharacteristic
67C3×C4⋊C8—21no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8—61no—
70C3×C4⋊C8C2×D311yescharacteristic
71C3×C4⋊C8C2×D311yescharacteristic
72C3×#97—61no—
73C3×C4×C8—31no—
74#835—61no—
75#835—61no—
76#818—61no—
77#817—61no—
78#817—61no—
79#816—61no—
80#815—21no—
81Dic3⋊C8—21no—
82#810—61no—
83#808—61no—
84#808—61no—
85#807—61no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8C2×D311yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C3⋊Dic3—41no—
95#634—81no—
96C2×C3×Dic3—21no—
97C2×C3×Dic3—21no—
98C2×C3×Dic3—41no—
99C3×Dic6—21no—
100C3×Dic6—21no—
101C3×Dic6—41no—
102C3×Dic6—41no—
103C32×C8—41no—
104C3⋊(C3⋊C8)—41no—
105C3×C3⋊C8—21no—
106C3×C3⋊C8—41no—
107C3×C3⋊C8Q1612yescomplemented
108#498—91no—
109#477—91no—
110#462—91no—
111#446—31no—
112#335—91no—
113#333—91no—
114#332—31no—
115C2×C3×Q8—31no—
116C2×C3×Q8—61no—
117C2×Dic6—21no—
118C2×Dic6—62no—
119C2×Dic6—61no—
120C2×Dic6—61no—
121C2×Dic6D1211yescharacteristic
122C2×C3×C8—21no—
123C2×C3×C8—21no—
124C2×C3×C8—31no—
125C2×C3×C8—31no—
126C2×C3×C8—41no—
127C2×C3×C8—61no—
128C3×C4⋊C4—31no—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C42—21no—
133C3×C42—61no—
134C3×C42C22×D311yescharacteristic
135C3×C42C22×D311yescharacteristic
136#216—122no—
137#216—122no—
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—61no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—61no—
144C4⋊Dic3—121no—
145C4⋊Dic3—121no—
146C4⋊Dic3D1211yescharacteristic
147Dic3⋊C4—21no—
148C4×Dic3—21no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—121no—
153C2×C3⋊C8#6711yescharacteristic
154C2×C3⋊C8#6711yescharacteristic
155C22×C32#12111yescharacteristic
156C32×C4—21no—
157C32×C4C2×Q1611yescharacteristic
158C32×C4AGL(1,ℤ/8)11yescharacteristic
159C32×C4#13711yescharacteristic
160C32×C4#13711yescharacteristic
161C3⋊Dic3—81no—
162C3×Dic3—41no—
163C3×Dic3—41no—
164C3×Dic3—81no—
165C2×Q16—181no—
166C4⋊Q8—31no—
167C4⋊Q8—91no—
168C4×Q8—31no—
169#107—181no—
170#106—181no—
171#106—181no—
172C4⋊C8—31no—
173C4⋊C8—61no—
174C4⋊C8—91no—
175C4⋊C8D3211yescharacteristic
176#103—181no—
177#103—181no—
178#97—61no—
179C4×C8—31no—
180C3×Q8—61no—
181C3×Q8—61no—
182C3×Q8—121no—
183C3×Q8—121no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—61no—
188C2×C3×C4—61no—
189C2×C3×C4—121no—
190C2×C3×C4C2×D1211yescharacteristic
191C2×C3×C4#23511yescharacteristic
192C2×C3×C4#23511yescharacteristic
193C2×C3×C4D3×D411yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×C3×C4C2×#6711yescharacteristic
196C2×Dic3—21no—
197C2×Dic3—21no—
198C2×Dic3—41no—
199C2×Dic3—122no—
200C2×Dic3—121no—
201C2×Dic3—121no—
202Dic6—21no—
203Dic6—21no—
204Dic6—41no—
205Dic6—41no—
206Dic6—241no—
207Dic6—241no—
208Dic6—242no—
209C3×C8—32no—
210C3×C8—41no—
211C3×C8—41no—
212C3×C8—61no—
213C3×C8—81no—
214C3×C8—121no—
215C3⋊C8—21no—
216C3⋊C8—41no—
217C3⋊C8—121no—
218C3⋊C8—121no—
219C3⋊C8—241no—
220C3⋊C8#21612yescomplemented
221C2×C32#46211yescharacteristic
222C2×C32#46811yescharacteristic
223C2×C32#47111yescharacteristic
224C2×Q8—31no—
225C2×Q8—61no—
226C2×Q8—181no—
227Q16—362no—
228C2×C8—21no—
229C2×C8—31no—
230C2×C8—31no—
231C2×C8—61no—
232C2×C8—181no—
233C4⋊C4—31no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—181no—
238C4⋊C4—181no—
239C42—61no—
240C42C2×D3211yescharacteristic
241C22×C3—21no—
242C22×C3#88411yescharacteristic
243C22×C3#93011yescharacteristic
244C3×C4—21no—
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—41no—
251C3×C4—121no—
252C3×C4—121no—
253C3×C4—241no—
254C3×C4#90811yescharacteristic
255C3×C4#90911yescharacteristic
256C3×C4#91111yescharacteristic
257C3×C4#91511yescharacteristic
258C3×C4#91511yescharacteristic
259C3×C4D3×Q1611yescharacteristic
260C3×C4C2×#21611yescharacteristic
261C3×C4#95111yescharacteristic
262Dic3—41no—
263Dic3—41no—
264Dic3—81no—
265Dic3—242no—
266Dic3—241no—
267Dic3—241no—
268C32#169211yescharacteristic, complemented, Sylow
269Q8—61no—
270Q8—61no—
271Q8—121no—
272Q8—121no—
273Q8—721no—
274C2×C4—61no—
275C2×C4—61no—
276C2×C4—121no—
277C2×C4—361no—
278C2×C4#379811yescharacteristic
279C2×C4D3×D1211yescharacteristic
280C2×C4D3×#6711yescharacteristic
281C8—32no—
282C8—41no—
283C8—61no—
284C8—121no—
285C8—361no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3#475411yescharacteristic
290C2×C3#478011yescharacteristic
291C2×C3#479511yescharacteristic
292C2×C3#503111yescharacteristic
293C2×C3#513411yescharacteristic
294C2×C3#514111yescharacteristic
295C22#6390611yescharacteristic
296C4—21no—
297C4—121no—
298C4—121no—
299C4—241no—
300C4—721no—
301C4#6379511yescharacteristic
302C4#6380011yescharacteristic
303C4#6392911yescharacteristic
304C4D3×#21611yescharacteristic
305C3—21no—
306C3#6847411yescharacteristic, complemented
307C3#7096311yescharacteristic, complemented
308C2#1059056111yescharacteristic
309C2#1059082811yescharacteristic
310C2#1059099811yescharacteristic
subgroupG/H
centerC22#63906
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1692
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
107. C3×C3⋊C8Q16semidirect
220. C3⋊C8#216semidirect
268. C32#1692semidirect
306. C3#68474semidirect
307. C3#70963semidirect

Maximal subgroups

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

subgroupindex
C3×#48312
#105903842
#105903032
#105902832
#105893472
C3×#44862
#105890992
#709633
#684743