Finite Group Databasebeta

← #11781576

Subgroups — #11781576

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#10592793C211yesmaximal, characteristic
2C3×#5079C211yesmaximal, characteristic
3#10590284C211yesmaximal, characteristic
4#10590254C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic
6#10589099C211yesmaximal, characteristic
7#10589095C211yesmaximal, characteristic
8#71241—31nomaximal
9#68471—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C3×#869C2211yescharacteristic
13#63637—21no—
14#63635—21no—
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×#835—21no—
17C3×#835—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#63553—21no—
25C3×#487—31no—
26#5094—31no—
27#5094—31no—
28#5094—61no—
29#5091—31no—
30#5079D311yescharacteristic
31#4850—31no—
32#4830—31no—
33C8×Dic6—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
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#835—21no—
71#835—21no—
72#818—61no—
73#816—61no—
74Dic3⋊C8—61no—
75Dic3⋊C8—61no—
76C8×Dic3—61no—
77C8×Dic3—61no—
78#810—61no—
79#810—61no—
80#810—61no—
81#810—62no—
82#808—61no—
83#808—61no—
84#808—62no—
85#807—61no—
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—41no—
93C32×Q8—41no—
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#634Q1612yes—
102C2×C3×Dic3—41no—
103C3×Dic6—81no—
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—91no—
115#332—31no—
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—41no—
183C3×Q8—41no—
184C3×Q8—41no—
185C3×Q8—41no—
186C3×Q8—81no—
187C3×Q8—81no—
188C3×Q8—241no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—42no—
193C2×C3×C4—41no—
194C2×C3×C4—41no—
195C2×C3×C4—121no—
196C2×C3×C4#23511yescharacteristic
197C2×C3×C4D3×D411yescharacteristic
198C2×C3×C4D3×D411yescharacteristic
199C2×C3×C4D3×D411yescharacteristic
200C2×C3×C4#23711yescharacteristic
201C2×C3×C4C2×#6711yescharacteristic
202C2×Dic3—41no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×Dic3—121no—
208C2×Dic3—121no—
209Dic6—32no—
210Dic6—32no—
211Dic6—62no—
212Dic6—61no—
213Dic6—61no—
214Dic6—81no—
215Dic6—121no—
216C3×C8—61no—
217C3×C8—61no—
218C3×C8—121no—
219C3×C8—121no—
220C3⋊C8—21no—
221C3⋊C8—21no—
222C3⋊C8—41no—
223C3⋊C8—41no—
224C3⋊C8—122no—
225C3⋊C8—121no—
226C3⋊C8—121no—
227C2×C32#46411yescharacteristic
228C2×C32#46711yescharacteristic
229C2×C32#47111yescharacteristic
230C2×Q8—21no—
231C2×Q8—61no—
232C2×Q8—91no—
233C2×C8—31no—
234C2×C8—31no—
235C2×C8—61no—
236C2×C8—61no—
237C2×C8—181no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C4⋊C4—91no—
243C4⋊C4—181no—
244C42—181no—
245C42C2×D3211yescharacteristic
246C22×C3—21no—
247C22×C3#88411yescharacteristic
248C22×C3#93811yescharacteristic
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—41no—
256C3×C4—82no—
257C3×C4—81no—
258C3×C4—81no—
259C3×C4—241no—
260C3×C4#91211yescharacteristic
261C3×C4#91511yescharacteristic
262C3×C4#91611yescharacteristic
263C3×C4D3×Q1611yescharacteristic
264C3×C4D3×Q1611yescharacteristic
265C3×C4#91911yescharacteristic
266C3×C4#95011yescharacteristic
267C3×C4#95111yescharacteristic
268Dic3—62no—
269Dic3—62no—
270Dic3—81no—
271Dic3—122no—
272Dic3—121no—
273Dic3—121no—
274Dic3—241no—
275C32#168411yescharacteristic, complemented, Sylow
276Q8—41no—
277Q8—41no—
278Q8—92no—
279Q8—181no—
280Q8—241no—
281C2×C4—41no—
282C2×C4—121no—
283C2×C4—181no—
284C2×C4—181no—
285C2×C4#380411yescharacteristic
286C2×C4D3×#6711yescharacteristic
287C2×C4#381111yescharacteristic
288C8—61no—
289C8—61no—
290C8—121no—
291C8—121no—
292C8—361no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3#475411yescharacteristic
297C2×C3#476711yescharacteristic
298C2×C3#481311yescharacteristic
299C2×C3#505411yescharacteristic
300C2×C3#517711yescharacteristic
301C2×C3#518811yescharacteristic
302C22#6395811yescharacteristic
303C4—21no—
304C4—81no—
305C4—182no—
306C4—241no—
307C4—361no—
308C4#6392911yescharacteristic
309C4#6393311yescharacteristic
310C4#6394411yescharacteristic
311C4#6395011yescharacteristic
312C3—21no—
313C3#6847111yescharacteristic, complemented
314C3#7124111yescharacteristic, complemented
315C2#1059144111yescharacteristic
316C2#1059154211yescharacteristic
317C2#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
275. C32#1684semidirect
313. C3#68471semidirect
314. C3#71241semidirect

Maximal subgroups

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

subgroupindex
#105927932
C3×#50792
#105902842
#105902542
C3×#45472
#105890992
#105890952
#712413
#684713