Finite Group Databasebeta

← #11781892

Subgroups — #11781892

Order 1152.

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

normal subgroups only

This group has 346 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#10592789C211yesmaximal, characteristic
2C3×#5080C211yesmaximal, characteristic
3#10590296C211yesmaximal, characteristic
4#10590284C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic
6#10589099C211yesmaximal, characteristic
7#10589095C211yesmaximal, characteristic
8#71349—31nomaximal
9#68474—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3756—21no—
12C4×#634C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63662—21no—
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×#808—21no—
17C3×#808—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63575—21no—
22#63572—21no—
23#63567—21no—
24#63555—21no—
25C3×#498—31no—
26#5091—31no—
27#5090—31no—
28#5090—31no—
29#5090—61no—
30#5080D311yescharacteristic
31#4850—31no—
32#4831—31no—
33#4679—31no—
34C3×#332—31no—
35#4547D311yescharacteristic
36#4546—31no—
37#4481—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
46#3756—42no—
47C4⋊(C3⋊Dic3)D411yescharacteristic
48#3750—21no—
49C4×C3⋊Dic3—21no—
50C2×C3⋊(C3⋊C8)—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#1692—91noSylow
58C3×C4⋊Q8—21no—
59C3×C4⋊Q8—31no—
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4⋊Q8C2×D311yescharacteristic
62C2×#216—61no—
63C2×#216—61no—
64C2×#216—62no—
65#869C2×D311yescharacteristic
66C4×Dic6—31no—
67C4×Dic6—31no—
68C4×Dic6—61no—
69C3×#106—61no—
70C3×#106—61no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8—31no—
73C3×C4×C8—31no—
74#835—61no—
75#835—61no—
76#835—62no—
77#818—61no—
78#816—61no—
79#815—61no—
80#815—61no—
81Dic3⋊C8—61no—
82Dic3⋊C8—61no—
83#810—61no—
84#808—21no—
85#808—21no—
86#807—61no—
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—41no—
94C32×Q8—41no—
95C2×C32×C4—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101#634—21no—
102#634—21no—
103C2×C3×Dic3—41no—
104C3×Dic6—81no—
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—91no—
116#332—31no—
117C2×C3×Q8—22no—
118C2×C3×Q8—21no—
119C2×C3×Q8—21no—
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—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—41no—
134C3×C4⋊C4—41no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C42—21no—
138C3×C42C22×D311yescharacteristic
139C3×C42C22×D311yescharacteristic
140#216—124no—
141#216—122no—
142#216—122no—
143C4⋊Dic3—21no—
144C4⋊Dic3—21no—
145C4⋊Dic3—31no—
146C4⋊Dic3—31no—
147C4⋊Dic3—61no—
148Dic3⋊C4—61no—
149Dic3⋊C4—61no—
150Dic3⋊C4—121no—
151C4×Dic3—61no—
152C4×Dic3—61no—
153C4×Dic3—121no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—62no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8#6711yescharacteristic
160C2×C3⋊C8#6711yescharacteristic
161C22×C32#12111yescharacteristic
162C32×C4—21no—
163C32×C4—81no—
164C32×C4C2×Q1611yescharacteristic
165C32×C4AGL(1,ℤ/8)11yescharacteristic
166C32×C4#13711yescharacteristic
167C32×C4#13711yescharacteristic
168C3⋊Dic3—41no—
169C3⋊Dic3—41no—
170C3×Dic3—81no—
171C2×Q16—181no—
172C4⋊Q8—31no—
173C4⋊Q8D3211yescharacteristic
174C4×Q8—91no—
175#107—181no—
176#106—61no—
177#106—61no—
178C4⋊C8—31no—
179C4⋊C8—31no—
180C4⋊C8—91no—
181C4⋊C8—181no—
182#103—181no—
183#103—181no—
184#97—181no—
185C4×C8—31no—
186C3×Q8—42no—
187C3×Q8—42no—
188C3×Q8—41no—
189C3×Q8—41no—
190C3×Q8—41no—
191C3×Q8—41no—
192C3×Q8—241no—
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—121no—
200C2×C3×C4#23511yescharacteristic
201C2×C3×C4D3×D411yescharacteristic
202C2×C3×C4D3×D411yescharacteristic
203C2×C3×C4D3×D411yescharacteristic
204C2×C3×C4#23711yescharacteristic
205C2×C3×C4C2×#6711yescharacteristic
206C2×Dic3—41no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—121no—
212C2×Dic3—121no—
213Dic6—62no—
214Dic6—61no—
215Dic6—61no—
216Dic6—61no—
217Dic6—61no—
218Dic6—81no—
219Dic6—121no—
220C3×C8—32no—
221C3×C8—61no—
222C3×C8—121no—
223C3×C8—121no—
224C3⋊C8—21no—
225C3⋊C8—41no—
226C3⋊C8—41no—
227C3⋊C8—122no—
228C3⋊C8—121no—
229C3⋊C8—121no—
230C3⋊C8#21612yescomplemented
231C2×C32#46211yescharacteristic
232C2×C32#46811yescharacteristic
233C2×C32#47111yescharacteristic
234C2×Q8—21no—
235C2×Q8—61no—
236C2×Q8—91no—
237Q16—362no—
238C2×C8—31no—
239C2×C8—31no—
240C2×C8—61no—
241C2×C8—61no—
242C2×C8—181no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4—91no—
248C4⋊C4—181no—
249C42—181no—
250C42C2×D3211yescharacteristic
251C22×C3—21no—
252C22×C3#88411yescharacteristic
253C22×C3#93811yescharacteristic
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—41no—
261C3×C4—82no—
262C3×C4—81no—
263C3×C4—81no—
264C3×C4—241no—
265C3×C4#91111yescharacteristic
266C3×C4#91411yescharacteristic
267C3×C4#91511yescharacteristic
268C3×C4#91511yescharacteristic
269C3×C4#91511yescharacteristic
270C3×C4D3×Q1611yescharacteristic
271C3×C4#94211yescharacteristic
272C3×C4C2×#21611yescharacteristic
273Dic3—81no—
274Dic3—122no—
275Dic3—121no—
276Dic3—121no—
277Dic3—121no—
278Dic3—121no—
279Dic3—241no—
280C32#169211yescharacteristic, complemented, Sylow
281Q8—41no—
282Q8—41no—
283Q8—181no—
284Q8—181no—
285Q8—241no—
286C2×C4—41no—
287C2×C4—121no—
288C2×C4—181no—
289C2×C4—181no—
290C2×C4#380411yescharacteristic
291C2×C4D3×#6711yescharacteristic
292C2×C4#381111yescharacteristic
293C8—32no—
294C8—61no—
295C8—121no—
296C8—121no—
297C8—361no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3#475411yescharacteristic
302C2×C3#478011yescharacteristic
303C2×C3#479511yescharacteristic
304C2×C3#509011yescharacteristic
305C2×C3#517411yescharacteristic
306C2×C3#517711yescharacteristic
307C22#6395811yescharacteristic
308C4—21no—
309C4—81no—
310C4—241no—
311C4—361no—
312C4—361no—
313C4#6393111yescharacteristic
314C4#6393711yescharacteristic
315C4D3×#21611yescharacteristic
316C4#6394611yescharacteristic
317C3—21no—
318C3#6847411yescharacteristic, complemented
319C3#7134911yescharacteristic, complemented
320C2#1059146411yescharacteristic
321C2#1059154211yescharacteristic
322C2#1059157511yescharacteristic
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
230. C3⋊C8#216semidirect
280. C32#1692semidirect
318. C3#68474semidirect
319. C3#71349semidirect

Maximal subgroups

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

subgroupindex
#105927892
C3×#50802
#105902962
#105902842
C3×#45472
#105890992
#105890952
#713493
#684743