Finite Group Databasebeta

← #11781585

Subgroups — #11781585

Order 1152.

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

normal subgroups only

This group has 336 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#10592790C211yesmaximal, characteristic
2C3×#5093C211yesmaximal, characteristic
3#10590307C211yesmaximal, characteristic
4#10590254C211yesmaximal, characteristic
5C3×#4546C211yesmaximal, characteristic
6#10589099C211yesmaximal, characteristic
7#10589093C211yesmaximal, characteristic
8#71241—31nomaximal
9#68511—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C3×#869C2211yescharacteristic
13#63637—21no—
14#63634—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#5091—31no—
29#5091—31no—
30#5091—61no—
31#4851—31no—
32#4830—31no—
33C8×Dic6—31no—
34C3×#333—31no—
35#4547—31no—
36#4546D311yescharacteristic
37#4482—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#1684—91noSylow
57C3×C4⋊Q8—21no—
58C3×C4⋊Q8—31no—
59C3×C4⋊Q8C2×D311yescharacteristic
60C3×C4⋊Q8C2×D311yescharacteristic
61#869C2×D311yescharacteristic
62C4×Dic6—31no—
63C4×Dic6—31no—
64C4×Dic6—61no—
65C3×C4⋊C8—31no—
66C3×C4⋊C8—31no—
67C3×#103—61no—
68C3×#103—61no—
69C3×C4×C8—31no—
70#817—61no—
71#816—61no—
72Dic3⋊C8—61no—
73Dic3⋊C8—61no—
74C8×Dic3—61no—
75C8×Dic3—61no—
76#810—21no—
77#810—21no—
78#810—61no—
79#810—61no—
80#810—61no—
81#810—62no—
82#808—61no—
83#807—61no—
84#807—61no—
85#807—62no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4×C3⋊C8C2×D311yescharacteristic
92C32×Q8—81no—
93C2×C32×C4—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99#634—21no—
100#634Q1612yes—
101C2×C3×Dic3—41no—
102C3×Dic6—41no—
103C3×Dic6—41no—
104C3⋊(C3⋊C8)—41no—
105C3×C3⋊C8—21no—
106C3×C3⋊C8—21no—
107C3×C3⋊C8—41no—
108C3×C3⋊C8—41no—
109#487—31no—
110#477—91no—
111#475—91no—
112C8×Q8—91no—
113#335—91no—
114#333—31no—
115#332—91no—
116C2×C3×Q8—21no—
117C2×C3×Q8—21no—
118C2×C3×Q8—41no—
119C2×C3×Q8—61no—
120C2×Dic6—21no—
121C2×Dic6—31no—
122C2×Dic6—31no—
123C2×Dic6—61no—
124C2×C3×C8—31no—
125C2×C3×C8—31no—
126C2×C3×C8—61no—
127C2×C3×C8—61no—
128C3×C4⋊C4—22no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—41no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C42—21no—
137C3×C42C22×D311yescharacteristic
138C3×C42C22×D311yescharacteristic
139C4⋊Dic3—21no—
140C4⋊Dic3—21no—
141C4⋊Dic3—31no—
142C4⋊Dic3—31no—
143C4⋊Dic3—61no—
144Dic3⋊C4—61no—
145Dic3⋊C4—61no—
146Dic3⋊C4—121no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C4×Dic3—121no—
150C2×C3⋊C8—21no—
151C2×C3⋊C8—21no—
152C2×C3⋊C8—62no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8#6711yescharacteristic
156C2×C3⋊C8#6711yescharacteristic
157C22×C32#12111yescharacteristic
158C32×C4—21no—
159C32×C4—81no—
160C32×C4C2×Q1611yescharacteristic
161C32×C4#13511yescharacteristic
162C32×C4#13511yescharacteristic
163C32×C4#13711yescharacteristic
164C3⋊Dic3—22no—
165C3⋊Dic3—41no—
166C3×Dic3—81no—
167C4⋊Q8—31no—
168C4⋊Q8D3211yescharacteristic
169C4×Q8—91no—
170#107—181no—
171#106—181no—
172C4⋊C8—31no—
173C4⋊C8—31no—
174C4⋊C8—91no—
175C4⋊C8—181no—
176#103—61no—
177#103—61no—
178#103—181no—
179#103—181no—
180C4×C8—31no—
181C4×C8—181no—
182C3×Q8—81no—
183C3×Q8—81no—
184C3×Q8—82no—
185C3×Q8—121no—
186C3×Q8—121no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—42no—
191C2×C3×C4—41no—
192C2×C3×C4—41no—
193C2×C3×C4—121no—
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—41no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—121no—
206C2×Dic3—121no—
207Dic6—32no—
208Dic6—32no—
209Dic6—41no—
210Dic6—41no—
211Dic6—62no—
212Dic6—61no—
213Dic6—61no—
214Dic6—121no—
215C3×C8—61no—
216C3×C8—61no—
217C3×C8—121no—
218C3×C8—121no—
219C3⋊C8—21no—
220C3⋊C8—21no—
221C3⋊C8—41no—
222C3⋊C8—41no—
223C3⋊C8—122no—
224C3⋊C8—121no—
225C3⋊C8—121no—
226C2×C32#46411yescharacteristic
227C2×C32#46711yescharacteristic
228C2×C32#47111yescharacteristic
229C2×Q8—21no—
230C2×Q8—61no—
231C2×Q8—91no—
232C2×C8—31no—
233C2×C8—31no—
234C2×C8—61no—
235C2×C8—61no—
236C2×C8—181no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—61no—
240C4⋊C4—61no—
241C4⋊C4—91no—
242C4⋊C4—181no—
243C42—181no—
244C42C2×D3211yescharacteristic
245C22×C3—21no—
246C22×C3#88411yescharacteristic
247C22×C3#93811yescharacteristic
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—41no—
255C3×C4—82no—
256C3×C4—81no—
257C3×C4—81no—
258C3×C4—241no—
259C3×C4#91611yescharacteristic
260C3×C4#91611yescharacteristic
261C3×C4D3×Q1611yescharacteristic
262C3×C4D3×Q1611yescharacteristic
263C3×C4#91811yescharacteristic
264C3×C4#91911yescharacteristic
265C3×C4#95011yescharacteristic
266C3×C4#95111yescharacteristic
267Dic3—62no—
268Dic3—62no—
269Dic3—81no—
270Dic3—122no—
271Dic3—121no—
272Dic3—121no—
273Dic3—241no—
274C32#168411yescharacteristic, complemented, Sylow
275Q8—81no—
276Q8—92no—
277Q8—121no—
278Q8—121no—
279Q8—181no—
280C2×C4—41no—
281C2×C4—121no—
282C2×C4—181no—
283C2×C4—181no—
284C2×C4#380411yescharacteristic
285C2×C4D3×#6711yescharacteristic
286C2×C4#381111yescharacteristic
287C8—61no—
288C8—61no—
289C8—121no—
290C8—121no—
291C8—361no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3#474811yescharacteristic
296C2×C3#479811yescharacteristic
297C2×C3#481311yescharacteristic
298C2×C3#505411yescharacteristic
299C2×C3#517711yescharacteristic
300C2×C3#518811yescharacteristic
301C22#6395811yescharacteristic
302C4—21no—
303C4—81no—
304C4—182no—
305C4—241no—
306C4—361no—
307C4#6394311yescharacteristic
308C4#6394411yescharacteristic
309C4#6394711yescharacteristic
310C4#6395011yescharacteristic
311C3—21no—
312C3#6851111yescharacteristic, complemented
313C3#7124111yescharacteristic, complemented
314C2#1059140711yescharacteristic
315C2#1059157711yescharacteristic
316C2#1059160111yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊Q8D32
hypocenterC32#1684
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
274. C32#1684semidirect
312. C3#68511semidirect
313. C3#71241semidirect

Maximal subgroups

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

subgroupindex
#105927902
C3×#50932
#105903072
#105902542
C3×#45462
#105890992
#105890932
#712413
#685113