Finite Group Databasebeta

← #11781909

Subgroups — #11781909

Order 1152.

319 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 319 conjugacy classes of subgroups — too many to draw. Only its 84 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×#4850C211yesmaximal, characteristic
2#10590384C211yesmaximal, characteristic
3#10590309C211yesmaximal, characteristic
4#10590259C211yesmaximal, characteristic
5#10589345C211yesmaximal, characteristic
6C3×#4482C211yesmaximal, characteristic
7#10589095C211yesmaximal, characteristic
8#71152—31nomaximal
9#68474—31nomaximal
10C3×#869C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3718—21no—
14C32×C4⋊C8C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#818—21no—
18C3×#816—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20#63574—21no—
21#63574—21no—
22Dic3⋊(C3⋊C8)—21no—
23#63565—21no—
24#63554—21no—
25C3×#477—31no—
26#5090—31no—
27#5080—31no—
28#5080—31no—
29#5031—31no—
30#5024—31no—
31#4850D311yescharacteristic
32#4831—31no—
33C3×#332—31no—
34#4546—31no—
35#4482D311yescharacteristic
36#4481—31no—
37#4479—31no—
38#4479—31no—
39#4479—61no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6D411yescharacteristic
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C3×Dic3⋊C4—21no—
54C3×C4×Dic3—21no—
55C2×C3×C3⋊C8—21no—
56#3718—42no—
57#1692—91noSylow
58C3×C4⋊Q8—31no—
59C3×C4⋊Q8—31no—
60C3×C4×Q8—31no—
61C2×#216—61no—
62C2×#216—61no—
63#869C2×D311yescharacteristic
64#869C2×D311yescharacteristic
65C4×Dic6C2×D311yescharacteristic
66C3×#107—61no—
67C3×C4⋊C8—21no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8C2×D311yescharacteristic
70C3×C4⋊C8C2×D311yescharacteristic
71C3×#103—61no—
72#835—61no—
73#818—21no—
74#816—21no—
75#815—61no—
76Dic3⋊C8—61no—
77#810—61no—
78#808—61no—
79#808—61no—
80#808—61no—
81#808—61no—
82C4⋊(C3⋊C8)—31no—
83C4⋊(C3⋊C8)—31no—
84C4⋊(C3⋊C8)—61no—
85C4⋊(C3⋊C8)—61no—
86C4⋊(C3⋊C8)C2×D311yescharacteristic
87#803—61no—
88C4×C3⋊C8—31no—
89C4×C3⋊C8—31no—
90C4×C3⋊C8—61no—
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C3×Dic3—21no—
95C2×C3×Dic3—21no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98C3×Dic6—21no—
99C3×Dic6—21no—
100C3×Dic6—41no—
101C3×Dic6—41no—
102C3×Dic6—81no—
103C32×C8—41no—
104C3⋊(C3⋊C8)—21no—
105C3⋊(C3⋊C8)—41no—
106C3⋊(C3⋊C8)Q1612yescomplemented
107C3×C3⋊C8—41no—
108#498—91no—
109#477—31no—
110#462—91no—
111#446—91no—
112#335—91no—
113#333—91no—
114#332—31no—
115C2×C3×Q8—31no—
116C2×C3×Q8—61no—
117C2×C3×Q8—61no—
118C2×Dic6—21no—
119C2×Dic6—21no—
120C2×Dic6#6711yescharacteristic
121C2×C3×C8—21no—
122C2×C3×C8—21no—
123C2×C3×C8—41no—
124C2×C3×C8—61no—
125C3×C4⋊C4—31no—
126C3×C4⋊C4—61no—
127C3×C4⋊C4—61no—
128C3×C4⋊C4—61no—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—61no—
131C3×C42—21no—
132C3×C42—61no—
133C3×C42C22×D311yescharacteristic
134C3×C42C22×D311yescharacteristic
135#216—122no—
136#216—122no—
137C4⋊Dic3—21no—
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—21no—
141C4⋊Dic3#6711yescharacteristic
142Dic3⋊C4—21no—
143C4×Dic3—21no—
144C2×C3⋊C8—21no—
145C2×C3⋊C8—31no—
146C2×C3⋊C8—31no—
147C2×C3⋊C8—31no—
148C2×C3⋊C8—31no—
149C2×C3⋊C8—61no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—121no—
154C22×C32#12111yescharacteristic
155C32×C4—21no—
156C32×C4C2×Q1611yescharacteristic
157C32×C4AGL(1,ℤ/8)11yescharacteristic
158C32×C4#13711yescharacteristic
159C32×C4#13711yescharacteristic
160C3×Dic3—41no—
161C3×Dic3—41no—
162C3×Dic3—81no—
163C3×Dic3—81no—
164C2×Q16—181no—
165C4⋊Q8—31no—
166C4⋊Q8—31no—
167C4×Q8—31no—
168#107—61no—
169#106—181no—
170#106—181no—
171C4⋊C8—31no—
172C4⋊C8—91no—
173C4⋊C8—181no—
174C4⋊C8D3211yescharacteristic
175#103—61no—
176#103—181no—
177#97—181no—
178C4×C8—91no—
179C3×Q8—61no—
180C3×Q8—61no—
181C3×Q8—121no—
182C3×Q8—121no—
183C3×Q8—241no—
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×C4—121no—
191C2×C3×C4#23511yescharacteristic
192C2×C3×C4D3×D411yescharacteristic
193C2×C3×C4D3×D411yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×C3×C4#23711yescharacteristic
196C2×C3×C4C2×#6711yescharacteristic
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—41no—
200C2×Dic3—41no—
201Dic6—21no—
202Dic6—21no—
203Dic6—41no—
204Dic6—41no—
205Dic6—81no—
206C3×C8—41no—
207C3×C8—41no—
208C3×C8—81no—
209C3×C8—121no—
210C3⋊C8—32no—
211C3⋊C8—32no—
212C3⋊C8—41no—
213C3⋊C8—62no—
214C3⋊C8—61no—
215C3⋊C8—61no—
216C3⋊C8—121no—
217C3⋊C8—121no—
218C3⋊C8—121no—
219C3⋊C8—241no—
220C2×C32#46211yescharacteristic
221C2×C32#46811yescharacteristic
222C2×C32#47111yescharacteristic
223C2×Q8—31no—
224C2×Q8—61no—
225C2×Q8—61no—
226Q16—362no—
227C2×C8—21no—
228C2×C8—61no—
229C2×C8—91no—
230C2×C8—91no—
231C2×C8—181no—
232C4⋊C4—31no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C42—61no—
239C42C2×D3211yescharacteristic
240C22×C3—21no—
241C22×C3#88411yescharacteristic
242C22×C3#93911yescharacteristic
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—41no—
250C3×C4—121no—
251C3×C4—121no—
252C3×C4—241no—
253C3×C4—241no—
254C3×C4#91111yescharacteristic
255C3×C4#91511yescharacteristic
256C3×C4#91511yescharacteristic
257C3×C4D3×Q1611yescharacteristic
258C3×C4D3×Q1611yescharacteristic
259C3×C4#91811yescharacteristic
260C3×C4#94211yescharacteristic
261C3×C4#94911yescharacteristic
262Dic3—41no—
263Dic3—41no—
264Dic3—81no—
265Dic3—81no—
266C32#169211yescharacteristic, complemented, Sylow
267Q8—61no—
268Q8—61no—
269Q8—121no—
270Q8—121no—
271Q8—241no—
272C2×C4—61no—
273C2×C4—61no—
274C2×C4—121no—
275C2×C4—121no—
276C2×C4#379511yescharacteristic
277C2×C4#380211yescharacteristic
278C2×C4D3×#6711yescharacteristic
279C8—41no—
280C8—92no—
281C8—121no—
282C8—181no—
283C8—361no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3#475411yescharacteristic
288C2×C3#478011yescharacteristic
289C2×C3#479511yescharacteristic
290C2×C3#504911yescharacteristic
291C2×C3#518211yescharacteristic
292C2×C3#520011yescharacteristic
293C22#6388511yescharacteristic
294C4—21no—
295C4—121no—
296C4—121no—
297C4—241no—
298C4—241no—
299C4#6380211yescharacteristic
300C4#6381111yescharacteristic
301C4#6392511yescharacteristic
302C4#6394611yescharacteristic
303C3—21no—
304C3#6847411yescharacteristic, complemented
305C3#7115211yescharacteristic, complemented
306C2#1059050311yescharacteristic
307C2#1059079811yescharacteristic
308C2#1059098011yescharacteristic
subgroupG/H
centerC22#63885
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
106. C3⋊(C3⋊C8)Q16semidirect
266. C32#1692semidirect
304. C3#68474semidirect
305. C3#71152semidirect

Maximal subgroups

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

subgroupindex
C3×#48502
#105903842
#105903092
#105902592
#105893452
C3×#44822
#105890952
#711523
#684743