Finite Group Databasebeta

← #11781901

Subgroups — #11781901

Order 1152.

340 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 86 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#10592790C211yesmaximal, characteristic
2C3×#5080C211yesmaximal, characteristic
3#10590388C211yesmaximal, characteristic
4#10590296C211yesmaximal, characteristic
5C3×#4546C211yesmaximal, characteristic
6#10589099C211yesmaximal, characteristic
7#10589092C211yesmaximal, characteristic
8#71349—31nomaximal
9#68512—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3719—21no—
14#63637—21no—
15#63634—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#808—21no—
18C3×#808—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22#63572—21no—
23#63566—21no—
24#63555—21no—
25C3×#498—31no—
26#5091—31no—
27#5091—31no—
28#5091—61no—
29#5090—31no—
30#5080D311yescharacteristic
31#4849—31no—
32#4831—31no—
33#4679—31no—
34C3×#333—31no—
35#4547—31no—
36#4546D311yescharacteristic
37#4486—31no—
38#4479—31no—
39#4458—31no—
40C2×C32×Q8—21no—
41C2×#634D411yescharacteristic
42C2×C3×Dic6—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)D411yescharacteristic
47#3750—21no—
48C4×C3⋊Dic3—21no—
49C2×C3⋊(C3⋊C8)—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#3719—42no—
57#1692—91noSylow
58C3×C4⋊Q8—21no—
59C3×C4⋊Q8—31no—
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4⋊Q8C2×D311yescharacteristic
62C2×#216—61no—
63C2×Dic12—61no—
64#869C2×D311yescharacteristic
65C4×Dic6—31no—
66C4×Dic6—31no—
67C4×Dic6—61no—
68C3×#106—61no—
69C3×#106—61no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8—31no—
72C3×C4×C8—31no—
73#835—61no—
74#816—61no—
75#815—61no—
76#815—61no—
77Dic3⋊C8—61no—
78Dic3⋊C8—61no—
79#810—61no—
80#810—61no—
81#810—62no—
82#808—21no—
83#808—21no—
84#807—61no—
85#807—61no—
86#807—62no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C32×Q8—81no—
94C2×C32×C4—41no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100#634—21no—
101#634—21no—
102C2×C3×Dic3—41no—
103C3×Dic6—41no—
104C3×Dic6—41no—
105C3⋊(C3⋊C8)—41no—
106C3×C3⋊C8—21no—
107C3×C3⋊C8—41no—
108C3×C3⋊C8—41no—
109C3×C3⋊C8Q1612yescomplemented
110#498—31no—
111#477—91no—
112#462—91no—
113#446—91no—
114#335—91no—
115#333—31no—
116#332—91no—
117C2×C3×Q8—21no—
118C2×C3×Q8—21no—
119C2×C3×Q8—41no—
120C2×C3×Q8—61no—
121C2×Dic6—21no—
122C2×Dic6—31no—
123C2×Dic6—31no—
124C2×Dic6—61no—
125C2×C3×C8—31no—
126C2×C3×C8—31no—
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—41no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C42—21no—
138C3×C42C22×D311yescharacteristic
139C3×C42C22×D311yescharacteristic
140#216—122no—
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C4⋊Dic3—31no—
144C4⋊Dic3—31no—
145C4⋊Dic3—61no—
146Dic3⋊C4—61no—
147Dic3⋊C4—61no—
148Dic3⋊C4—121no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C4×Dic3—121no—
152C2×C3⋊C8—21no—
153C2×C3⋊C8—21no—
154C2×C3⋊C8—62no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8#6711yescharacteristic
158C2×C3⋊C8#6711yescharacteristic
159Dic12—122no—
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—41no—
168C3⋊Dic3—41no—
169C3×Dic3—81no—
170C2×Q16—181no—
171C4⋊Q8—31no—
172C4⋊Q8D3211yescharacteristic
173C4×Q8—91no—
174#107—181no—
175#106—61no—
176#106—61no—
177C4⋊C8—31no—
178C4⋊C8—31no—
179C4⋊C8—91no—
180C4⋊C8—181no—
181#103—181no—
182#103—181no—
183#97—181no—
184C4×C8—31no—
185C3×Q8—81no—
186C3×Q8—81no—
187C3×Q8—82no—
188C3×Q8—121no—
189C3×Q8—121no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—42no—
194C2×C3×C4—41no—
195C2×C3×C4—41no—
196C2×C3×C4—121no—
197C2×C3×C4#23511yescharacteristic
198C2×C3×C4D3×D411yescharacteristic
199C2×C3×C4D3×D411yescharacteristic
200C2×C3×C4D3×D411yescharacteristic
201C2×C3×C4#23711yescharacteristic
202C2×C3×C4C2×#6711yescharacteristic
203C2×Dic3—41no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—121no—
209C2×Dic3—121no—
210Dic6—41no—
211Dic6—41no—
212Dic6—62no—
213Dic6—61no—
214Dic6—61no—
215Dic6—61no—
216Dic6—61no—
217Dic6—121no—
218C3×C8—32no—
219C3×C8—61no—
220C3×C8—121no—
221C3×C8—121no—
222C3⋊C8—21no—
223C3⋊C8—41no—
224C3⋊C8—41no—
225C3⋊C8—122no—
226C3⋊C8—121no—
227C3⋊C8—121no—
228C3⋊C8#21612yescomplemented
229C2×C32#46211yescharacteristic
230C2×C32#46811yescharacteristic
231C2×C32#47111yescharacteristic
232C2×Q8—21no—
233C2×Q8—61no—
234C2×Q8—91no—
235Q16—362no—
236C2×C8—31no—
237C2×C8—31no—
238C2×C8—61no—
239C2×C8—61no—
240C2×C8—181no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—91no—
246C4⋊C4—181no—
247C42—181no—
248C42C2×D3211yescharacteristic
249C22×C3—21no—
250C22×C3#88411yescharacteristic
251C22×C3#93811yescharacteristic
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—41no—
259C3×C4—82no—
260C3×C4—81no—
261C3×C4—81no—
262C3×C4—241no—
263C3×C4#91411yescharacteristic
264C3×C4#91411yescharacteristic
265C3×C4#91511yescharacteristic
266C3×C4#91511yescharacteristic
267C3×C4D3×Q1611yescharacteristic
268C3×C4#91811yescharacteristic
269C3×C4#94211yescharacteristic
270C3×C4C2×#21611yescharacteristic
271Dic3—81no—
272Dic3—122no—
273Dic3—121no—
274Dic3—121no—
275Dic3—121no—
276Dic3—121no—
277Dic3—241no—
278C32#169211yescharacteristic, complemented, Sylow
279Q8—81no—
280Q8—121no—
281Q8—121no—
282Q8—181no—
283Q8—181no—
284C2×C4—41no—
285C2×C4—121no—
286C2×C4—181no—
287C2×C4—181no—
288C2×C4#380411yescharacteristic
289C2×C4D3×#6711yescharacteristic
290C2×C4#381111yescharacteristic
291C8—32no—
292C8—61no—
293C8—121no—
294C8—121no—
295C8—361no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3#474811yescharacteristic
300C2×C3#479511yescharacteristic
301C2×C3#481211yescharacteristic
302C2×C3#509011yescharacteristic
303C2×C3#517411yescharacteristic
304C2×C3#517711yescharacteristic
305C22#6395811yescharacteristic
306C4—21no—
307C4—81no—
308C4—241no—
309C4—361no—
310C4—361no—
311C4#6394111yescharacteristic
312C4D3×#21611yescharacteristic
313C4#6394611yescharacteristic
314C4#6395111yescharacteristic
315C3—21no—
316C3#6851211yescharacteristic, complemented
317C3#7134911yescharacteristic, complemented
318C2#1059140711yescharacteristic
319C2#1059157511yescharacteristic
320C2#1059159011yescharacteristic
subgroupG/H
centerC22#63958
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
109. C3×C3⋊C8Q16semidirect
228. C3⋊C8#216semidirect
278. C32#1692semidirect
316. C3#68512semidirect
317. C3#71349semidirect

Maximal subgroups

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

subgroupindex
#105927902
C3×#50802
#105903882
#105902962
C3×#45462
#105890992
#105890922
#713493
#685123