Finite Group Databasebeta

← #11781400

Subgroups — #11781400

Order 1152.

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

normal subgroups only

This group has 354 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#10592789C211yesmaximal, characteristic
2C3×#5093C211yesmaximal, characteristic
3#10590307C211yesmaximal, characteristic
4#10590254C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic
6#10589097C211yesmaximal, characteristic
7#10589093C211yesmaximal, characteristic
8#71240—31nomaximal
9#68469—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3756—21no—
12C4×#634C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63662—21no—
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×#810—21no—
17C3×#810—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63573—21no—
22#63572—21no—
23#63567—21no—
24#63553—21no—
25C3×#487—31no—
26#5094—31no—
27#5093D311yescharacteristic
28#5090—31no—
29#5090—31no—
30#5090—61no—
31#4851—31no—
32#4830—31no—
33C8×Dic6—31no—
34C3×#332—31no—
35#4547—31no—
36#4547D311yescharacteristic
37#4482—31no—
38#4480—31no—
39#4457—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#1680—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×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×#103—61no—
72C3×#103—61no—
73C3×C4×C8—31no—
74#835—61no—
75#835—61no—
76#835—62no—
77#817—61no—
78#816—61no—
79Dic3⋊C8—61no—
80Dic3⋊C8—61no—
81C8×Dic3—61no—
82C8×Dic3—61no—
83#810—21no—
84#810—21no—
85#810—61no—
86#808—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#634SD1612yes—
103C2×C3×Dic3—41no—
104C3×Dic6—41no—
105C3×Dic6—41no—
106C3⋊(C3⋊C8)—41no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111#487—31no—
112#475—91no—
113#462—91no—
114C8×Q8—91no—
115#334—91no—
116#332—31no—
117#332—91no—
118C2×C3×Q8—22no—
119C2×C3×Q8—21no—
120C2×C3×Q8—21no—
121C2×C3×Q8—61no—
122C2×Dic6—21no—
123C2×Dic6—31no—
124C2×Dic6—31no—
125C2×Dic6—61no—
126C2×C3×C8—31no—
127C2×C3×C8—31no—
128C2×C3×C8—61no—
129C2×C3×C8—61no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—41no—
135C3×C4⋊C4—41no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—61no—
138C3×C42—21no—
139C3×C42C22×D311yescharacteristic
140C3×C42C22×D311yescharacteristic
141#216—122no—
142#216—122no—
143#216—124no—
144C4⋊Dic3—21no—
145C4⋊Dic3—21no—
146C4⋊Dic3—31no—
147C4⋊Dic3—31no—
148C4⋊Dic3—61no—
149Dic3⋊C4—61no—
150Dic3⋊C4—61no—
151Dic3⋊C4—121no—
152C4×Dic3—61no—
153C4×Dic3—61no—
154C4×Dic3—121no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—62no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8#6711yescharacteristic
161C2×C3⋊C8#6711yescharacteristic
162C22×C32#12111yescharacteristic
163C32×C4—21no—
164C32×C4—81no—
165C32×C4C2×SD1611yescharacteristic
166C32×C4#13511yescharacteristic
167C32×C4#13511yescharacteristic
168C32×C4#13711yescharacteristic
169C3⋊Dic3—22no—
170C3⋊Dic3—41no—
171C3×Dic3—81no—
172C2×Q16—181no—
173C4⋊Q8—31no—
174C4⋊Q8D3211yescharacteristic
175C4×Q8—91no—
176#106—181no—
177C4⋊C8—31no—
178C4⋊C8—31no—
179C4⋊C8—91no—
180C4⋊C8—181no—
181#103—61no—
182#103—61no—
183#103—181no—
184#103—181no—
185C4×C8—31no—
186C4×C8—181no—
187C3×Q8—42no—
188C3×Q8—42no—
189C3×Q8—41no—
190C3×Q8—41no—
191C3×Q8—41no—
192C3×Q8—41no—
193C3×Q8—121no—
194C3×Q8—121no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—42no—
199C2×C3×C4—41no—
200C2×C3×C4—41no—
201C2×C3×C4—121no—
202C2×C3×C4#23511yescharacteristic
203C2×C3×C4D3×D411yescharacteristic
204C2×C3×C4D3×D411yescharacteristic
205C2×C3×C4D3×D411yescharacteristic
206C2×C3×C4#23711yescharacteristic
207C2×C3×C4C2×#6711yescharacteristic
208C2×Dic3—41no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—121no—
214C2×Dic3—121no—
215Dic6—32no—
216Dic6—32no—
217Dic6—41no—
218Dic6—41no—
219Dic6—62no—
220Dic6—61no—
221Dic6—61no—
222Dic6—121no—
223C3×C8—61no—
224C3×C8—61no—
225C3×C8—121no—
226C3×C8—121no—
227C3⋊C8—21no—
228C3⋊C8—21no—
229C3⋊C8—41no—
230C3⋊C8—41no—
231C3⋊C8—122no—
232C3⋊C8—121no—
233C3⋊C8—121no—
234C2×C32#46411yescharacteristic
235C2×C32#46511yescharacteristic
236C2×C32#47311yescharacteristic
237C2×Q8—21no—
238C2×Q8—61no—
239C2×Q8—91no—
240Q16—362no—
241C2×C8—31no—
242C2×C8—31no—
243C2×C8—61no—
244C2×C8—61no—
245C2×C8—181no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—61no—
249C4⋊C4—61no—
250C4⋊C4—91no—
251C4⋊C4—181no—
252C42—181no—
253C42C2×D3211yescharacteristic
254C22×C3—21no—
255C22×C3#88411yescharacteristic
256C22×C3#93811yescharacteristic
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—41no—
264C3×C4—82no—
265C3×C4—81no—
266C3×C4—81no—
267C3×C4—241no—
268C3×C4#91211yescharacteristic
269C3×C4D3×SD1611yescharacteristic
270C3×C4D3×SD1611yescharacteristic
271C3×C4#91611yescharacteristic
272C3×C4#91611yescharacteristic
273C3×C4#91811yescharacteristic
274C3×C4#95011yescharacteristic
275C3×C4#95111yescharacteristic
276Dic3—62no—
277Dic3—62no—
278Dic3—81no—
279Dic3—122no—
280Dic3—121no—
281Dic3—121no—
282Dic3—241no—
283C32#168011yescharacteristic, complemented, Sylow
284Q8—41no—
285Q8—41no—
286Q8—92no—
287Q8—121no—
288Q8—121no—
289Q8—181no—
290C2×C4—41no—
291C2×C4—121no—
292C2×C4—181no—
293C2×C4—181no—
294C2×C4#380411yescharacteristic
295C2×C4D3×#6711yescharacteristic
296C2×C4#381111yescharacteristic
297C8—61no—
298C8—61no—
299C8—121no—
300C8—121no—
301C8—361no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3#475511yescharacteristic
306C2×C3#477811yescharacteristic
307C2×C3#479811yescharacteristic
308C2×C3#505411yescharacteristic
309C2×C3#517111yescharacteristic
310C2×C3#519211yescharacteristic
311C22#6395811yescharacteristic
312C4—21no—
313C4—81no—
314C4—182no—
315C4—241no—
316C4—361no—
317C4#6393011yescharacteristic
318C4#6393611yescharacteristic
319C4#6394311yescharacteristic
320C4#6394711yescharacteristic
321C3—21no—
322C3#6846911yescharacteristic, complemented
323C3#7124011yescharacteristic, complemented
324C2#1059146511yescharacteristic
325C2#1059154311yescharacteristic
326C2#1059157711yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊Q8D32
hypocenterC32#1680
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
283. C32#1680semidirect
322. C3#68469semidirect
323. C3#71240semidirect

Maximal subgroups

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

subgroupindex
#105927892
C3×#50932
#105903072
#105902542
C3×#45472
#105890972
#105890932
#712403
#684693