Finite Group Databasebeta

← #11781891

Subgroups — #11781891

Order 1152.

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

normal subgroups only

This group has 341 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#10592779C211yesmaximal, characteristic
2C3×#5090C211yesmaximal, characteristic
3#10590283C211yesmaximal, characteristic
4#10590259C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic
6#10589100C211yesmaximal, characteristic
7#10589096C211yesmaximal, characteristic
8#71056—31nomaximal
9#68474—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×#216—21no—
13C3×C4×Dic6C2211yescharacteristic
14#63635—21no—
15#63635—21no—
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#835—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×#462—31no—
26#5090D311yescharacteristic
27#5080—31no—
28#5080—31no—
29#5080—61no—
30#5024—31no—
31#5021—31no—
32#4850—31no—
33#4831—31no—
34C3×#332—31no—
35#4547D311yescharacteristic
36#4481—31no—
37#4481—31no—
38#4479—31no—
39#4479—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×#216—42no—
51C3×C4⋊Dic3D411yescharacteristic
52C3×Dic3⋊C4—21no—
53C3×C4×Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57#1692—91noSylow
58C2×C3×Q16—61no—
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4×Q8—31no—
63C2×#216—21no—
64#869—31no—
65#869—31no—
66#869—61no—
67C4×Dic6C2×D311yescharacteristic
68C3×C4⋊C8—31no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×#103—61no—
72#835—21no—
73#835—61no—
74#818—61no—
75#816—61no—
76#815—61no—
77Dic3⋊C8—61no—
78#808—61no—
79#808—61no—
80#808—61no—
81#808—61no—
82#808—62no—
83#808—62no—
84#807—61no—
85C4⋊(C3⋊C8)—61no—
86C4⋊(C3⋊C8)C2×D311yescharacteristic
87C4⋊(C3⋊C8)C2×D311yescharacteristic
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89#803—61no—
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C32×Q8—41no—
94C32×Q8—41no—
95C2×C32×C4—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3⋊Dic3—41no—
100#634—81no—
101C2×C3×Dic3—21no—
102C2×C3×Dic3—21no—
103C3×Dic6—21no—
104C3×Dic6—21no—
105C3⋊(C3⋊C8)—21no—
106C3⋊(C3⋊C8)Q1612yescomplemented
107C3×C3⋊C8—41no—
108C3×C3⋊C8—41no—
109C3×C3⋊C8—41no—
110#498—91no—
111#477—91no—
112#462—31no—
113#446—91no—
114#335—91no—
115#333—91no—
116#332—31no—
117C2×C3×Q8—21no—
118C2×C3×Q8—21no—
119C2×C3×Q8—31no—
120C2×C3×Q8—41no—
121C2×Dic6—61no—
122C2×Dic6—61no—
123C2×Dic6—121no—
124C2×Dic6#6711yescharacteristic
125C3×Q16—122no—
126C2×C3×C8—61no—
127C2×C3×C8—61no—
128C2×C3×C8—61no—
129C3×C4⋊C4—22no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—31no—
135C3×C4⋊C4—41no—
136C3×C4⋊C4—61no—
137C3×C42—21no—
138C3×C42—61no—
139C3×C42C22×D311yescharacteristic
140C3×C42C22×D311yescharacteristic
141#216—42no—
142C4⋊Dic3—62no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—121no—
148C4⋊Dic3#6711yescharacteristic
149Dic3⋊C4—21no—
150C4×Dic3—21no—
151C2×C3⋊C8—21no—
152C2×C3⋊C8—21no—
153C2×C3⋊C8—21no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—31no—
157C2×C3⋊C8—31no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—61no—
160C22×C32#12111yescharacteristic
161C32×C4—21no—
162C32×C4—81no—
163C32×C4C2×Q1611yescharacteristic
164C32×C4AGL(1,ℤ/8)11yescharacteristic
165C32×C4#13711yescharacteristic
166C32×C4#13711yescharacteristic
167C3⋊Dic3—81no—
168C3×Dic3—41no—
169C3×Dic3—41no—
170C2×Q16—61no—
171C4⋊Q8—91no—
172C4⋊Q8D3211yescharacteristic
173C4×Q8—31no—
174#107—181no—
175#106—181no—
176#106—181no—
177C4⋊C8—31no—
178C4⋊C8—31no—
179C4⋊C8—31no—
180C4⋊C8—181no—
181#103—61no—
182#103—181no—
183#97—181no—
184C4×C8—91no—
185C3×Q8—41no—
186C3×Q8—41no—
187C3×Q8—41no—
188C3×Q8—41no—
189C3×Q8—61no—
190C3×Q8—61no—
191C3×Q8—81no—
192C3×Q8—81no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—42no—
197C2×C3×C4—41no—
198C2×C3×C4—41no—
199C2×C3×C4—61no—
200C2×C3×C4—61no—
201C2×C3×C4#23511yescharacteristic
202C2×C3×C4D3×D411yescharacteristic
203C2×C3×C4D3×D411yescharacteristic
204C2×C3×C4D3×D411yescharacteristic
205C2×C3×C4#23711yescharacteristic
206C2×C3×C4C2×#6711yescharacteristic
207C2×Dic3—21no—
208C2×Dic3—21no—
209C2×Dic3—122no—
210C2×Dic3—121no—
211C2×Dic3—121no—
212Dic6—21no—
213Dic6—21no—
214Dic6—242no—
215Dic6—241no—
216Dic6—241no—
217C3×C8—121no—
218C3×C8—121no—
219C3×C8—121no—
220C3⋊C8—32no—
221C3⋊C8—32no—
222C3⋊C8—41no—
223C3⋊C8—41no—
224C3⋊C8—41no—
225C3⋊C8—62no—
226C3⋊C8—62no—
227C3⋊C8—61no—
228C3⋊C8—61no—
229C2×C32#46211yescharacteristic
230C2×C32#46811yescharacteristic
231C2×C32#47111yescharacteristic
232C2×Q8—21no—
233C2×Q8—31no—
234C2×Q8—181no—
235Q16—122no—
236C2×C8—61no—
237C2×C8—61no—
238C2×C8—61no—
239C2×C8—91no—
240C2×C8—91no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—31no—
244C4⋊C4—61no—
245C4⋊C4—181no—
246C4⋊C4—181no—
247C42—61no—
248C42C2×D3211yescharacteristic
249C22×C3—21no—
250C22×C3#88411yescharacteristic
251C22×C3#93911yescharacteristic
252C3×C4—22no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—82no—
260C3×C4—81no—
261C3×C4—81no—
262C3×C4—121no—
263C3×C4—121no—
264C3×C4#91111yescharacteristic
265C3×C4#91511yescharacteristic
266C3×C4#91511yescharacteristic
267C3×C4D3×Q1611yescharacteristic
268C3×C4D3×Q1611yescharacteristic
269C3×C4#91811yescharacteristic
270C3×C4#93211yescharacteristic
271C3×C4#95111yescharacteristic
272Dic3—41no—
273Dic3—41no—
274Dic3—242no—
275Dic3—241no—
276Dic3—241no—
277C32#169211yescharacteristic, complemented, Sylow
278Q8—41no—
279Q8—41no—
280Q8—61no—
281Q8—61no—
282Q8—721no—
283C2×C4—41no—
284C2×C4—61no—
285C2×C4—61no—
286C2×C4—361no—
287C2×C4#380411yescharacteristic
288C2×C4D3×#6711yescharacteristic
289C2×C4#381111yescharacteristic
290C8—92no—
291C8—121no—
292C8—121no—
293C8—121no—
294C8—181no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3#475411yescharacteristic
299C2×C3#478011yescharacteristic
300C2×C3#479511yescharacteristic
301C2×C3#504211yescharacteristic
302C2×C3#518211yescharacteristic
303C2×C3#520311yescharacteristic
304C22#6397111yescharacteristic
305C4—21no—
306C4—81no—
307C4—121no—
308C4—121no—
309C4—721no—
310C4#6392911yescharacteristic
311C4#6393211yescharacteristic
312C4#6394411yescharacteristic
313C4#6395111yescharacteristic
314C3—21no—
315C3#6847411yescharacteristic, complemented
316C3#7105611yescharacteristic, complemented
317C2#1059146211yescharacteristic
318C2#1059158011yescharacteristic
319C2#1059164311yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊Q8D32
hypocenterC32#1692
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
106. C3⋊(C3⋊C8)Q16semidirect
277. C32#1692semidirect
315. C3#68474semidirect
316. C3#71056semidirect

Maximal subgroups

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

subgroupindex
#105927792
C3×#50902
#105902832
#105902592
C3×#45472
#105891002
#105890962
#710563
#684743