Finite Group Databasebeta

← #11782029

Subgroups — #11782029

Order 1152.

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

normal subgroups only

This group has 329 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
1#10592777C211yesmaximal, characteristic
2C3×#5091C211yesmaximal, characteristic
3#10590283C211yesmaximal, characteristic
4#10590259C211yesmaximal, characteristic
5C3×#4546C211yesmaximal, characteristic
6#10589098C211yesmaximal, characteristic
7#10589096C211yesmaximal, characteristic
8#71153—31nomaximal
9#68513—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13#63634—21no—
14#63634—21no—
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#810—21no—
17C3×#807—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21#63575—21no—
22Dic3⋊(C3⋊C8)—21no—
23#63566—21no—
24#63554—21no—
25C3×#477—31no—
26#5091D311yescharacteristic
27#5078—31no—
28#5078—31no—
29#5078—61no—
30#5024—31no—
31#5021—31no—
32#4850—31no—
33#4831—31no—
34C3×#333—31no—
35#4546D311yescharacteristic
36#4481—31no—
37#4481—31no—
38#4480—31no—
39#4480—31no—
40C2×C32×Q8—21no—
41C2×#634—21no—
42C2×C3×Dic6D411yescharacteristic
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C3×C4⋊Dic3D411yescharacteristic
51C3×Dic3⋊C4—21no—
52C3×C4×Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#1696—91noSylow
57C3×C4⋊Q8—21no—
58C3×C4⋊Q8C2×D311yescharacteristic
59C3×C4⋊Q8C2×D311yescharacteristic
60C3×C4×Q8—31no—
61#869—31no—
62#869—31no—
63#869—61no—
64C4×Dic6C2×D311yescharacteristic
65C3×#107—61no—
66C3×C4⋊C8—31no—
67C3×C4⋊C8—31no—
68C3×C4⋊C8—31no—
69C3×#103—61no—
70#835—61no—
71#818—61no—
72#816—61no—
73#815—61no—
74Dic3⋊C8—61no—
75#810—21no—
76#807—21no—
77#807—61no—
78#807—61no—
79#807—61no—
80#807—61no—
81#807—61no—
82#807—62no—
83#807—62no—
84C4⋊(C3⋊C8)—61no—
85C4⋊(C3⋊C8)C2×D311yescharacteristic
86C4⋊(C3⋊C8)C2×D311yescharacteristic
87C4⋊(C3⋊C8)C2×D311yescharacteristic
88#803—61no—
89C4×C3⋊C8—31no—
90C4×C3⋊C8—31no—
91C4×C3⋊C8—61no—
92C32×Q8—81no—
93C2×C32×C4—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—41no—
98#634—81no—
99C2×C3×Dic3—21no—
100C2×C3×Dic3—21no—
101C3×Dic6—21no—
102C3×Dic6—21no—
103C3⋊(C3⋊C8)—21no—
104C3⋊(C3⋊C8)Q1612yes—
105C3×C3⋊C8—41no—
106C3×C3⋊C8—41no—
107C3×C3⋊C8—41no—
108#500—91no—
109#477—31no—
110#477—91no—
111#446—91no—
112#334—91no—
113#333—31no—
114#333—91no—
115C2×C3×Q8—21no—
116C2×C3×Q8—21no—
117C2×C3×Q8—31no—
118C2×C3×Q8—41no—
119C2×Dic6—61no—
120C2×Dic6—61no—
121C2×Dic6—121no—
122C2×Dic6#6711yescharacteristic
123C2×C3×C8—61no—
124C2×C3×C8—61no—
125C2×C3×C8—61no—
126C3×C4⋊C4—22no—
127C3×C4⋊C4—21no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—31no—
132C3×C4⋊C4—41no—
133C3×C4⋊C4—61no—
134C3×C42—21no—
135C3×C42—61no—
136C3×C42C22×D311yescharacteristic
137C3×C42C22×D311yescharacteristic
138C4⋊Dic3—62no—
139C4⋊Dic3—61no—
140C4⋊Dic3—61no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—121no—
144C4⋊Dic3#6711yescharacteristic
145Dic3⋊C4—21no—
146C4×Dic3—21no—
147C2×C3⋊C8—21no—
148C2×C3⋊C8—21no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8—31no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8—61no—
156C22×C32#12111yescharacteristic
157C32×C4—21no—
158C32×C4—81no—
159C32×C4C2×Q1611yescharacteristic
160C32×C4#13711yescharacteristic
161C32×C4#13711yescharacteristic
162C32×C4#13711yescharacteristic
163C3⋊Dic3—81no—
164C3×Dic3—41no—
165C3×Dic3—41no—
166C4⋊Q8—91no—
167C4⋊Q8D3211yescharacteristic
168C4×Q8—31no—
169#107—61no—
170#107—181no—
171#107—181no—
172#107—181no—
173C4⋊C8—31no—
174C4⋊C8—31no—
175C4⋊C8—31no—
176C4⋊C8—181no—
177#103—61no—
178#103—181no—
179#97—181no—
180C4×C8—91no—
181C3×Q8—61no—
182C3×Q8—61no—
183C3×Q8—81no—
184C3×Q8—81no—
185C3×Q8—82no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—42no—
190C2×C3×C4—41no—
191C2×C3×C4—41no—
192C2×C3×C4—61no—
193C2×C3×C4—61no—
194C2×C3×C4#23511yescharacteristic
195C2×C3×C4D3×D411yescharacteristic
196C2×C3×C4D3×D411yescharacteristic
197C2×C3×C4D3×D411yescharacteristic
198C2×C3×C4#23711yescharacteristic
199C2×C3×C4C2×#6711yescharacteristic
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—122no—
203C2×Dic3—121no—
204C2×Dic3—121no—
205Dic6—21no—
206Dic6—21no—
207Dic6—242no—
208Dic6—241no—
209Dic6—241no—
210C3×C8—121no—
211C3×C8—121no—
212C3×C8—121no—
213C3⋊C8—32no—
214C3⋊C8—32no—
215C3⋊C8—41no—
216C3⋊C8—41no—
217C3⋊C8—41no—
218C3⋊C8—62no—
219C3⋊C8—62no—
220C3⋊C8—61no—
221C3⋊C8—61no—
222C2×C32#46211yescharacteristic
223C2×C32#47011yescharacteristic
224C2×C32#47211yescharacteristic
225C2×Q8—21no—
226C2×Q8—31no—
227C2×Q8—181no—
228C2×C8—61no—
229C2×C8—61no—
230C2×C8—61no—
231C2×C8—91no—
232C2×C8—91no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—31no—
236C4⋊C4—61no—
237C4⋊C4—181no—
238C4⋊C4—181no—
239C42—61no—
240C42C2×D3211yescharacteristic
241C22×C3—21no—
242C22×C3#88411yescharacteristic
243C22×C3#93911yescharacteristic
244C3×C4—22no—
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—82no—
252C3×C4—81no—
253C3×C4—81no—
254C3×C4—121no—
255C3×C4—121no—
256C3×C4#91511yescharacteristic
257C3×C4#91511yescharacteristic
258C3×C4D3×Q1611yescharacteristic
259C3×C4D3×Q1611yescharacteristic
260C3×C4#91811yescharacteristic
261C3×C4#91811yescharacteristic
262C3×C4#94211yescharacteristic
263C3×C4#95111yescharacteristic
264Dic3—41no—
265Dic3—41no—
266Dic3—242no—
267Dic3—241no—
268Dic3—241no—
269C32#169611yescharacteristic, complemented, Sylow
270Q8—61no—
271Q8—61no—
272Q8—81no—
273Q8—721no—
274C2×C4—41no—
275C2×C4—61no—
276C2×C4—61no—
277C2×C4—361no—
278C2×C4#380411yescharacteristic
279C2×C4D3×#6711yescharacteristic
280C2×C4#381111yescharacteristic
281C8—92no—
282C8—121no—
283C8—121no—
284C8—121no—
285C8—181no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3#474911yescharacteristic
290C2×C3#479511yescharacteristic
291C2×C3#481611yescharacteristic
292C2×C3#505211yescharacteristic
293C2×C3#518211yescharacteristic
294C2×C3#519911yescharacteristic
295C22#6397111yescharacteristic
296C4—21no—
297C4—81no—
298C4—121no—
299C4—121no—
300C4—721no—
301C4#6394311yescharacteristic
302C4#6394411yescharacteristic
303C4#6394611yescharacteristic
304C4#6395111yescharacteristic
305C3—21no—
306C3#6851311yescharacteristic, complemented
307C3#7115311yescharacteristic, complemented
308C2#1059150811yescharacteristic
309C2#1059158011yescharacteristic
310C2#1059159811yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊Q8D32
hypocenterC32#1696
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
269. C32#1696semidirect
306. C3#68513semidirect
307. C3#71153semidirect

Maximal subgroups

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

subgroupindex
#105927772
C3×#50912
#105902832
#105902592
C3×#45462
#105890982
#105890962
#711533
#685133