Finite Group Databasebeta

← #11781390

Subgroups — #11781390

Order 1152.

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

normal subgroups only

This group has 349 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#10592778C211yesmaximal, characteristic
2C3×#5094C211yesmaximal, characteristic
3#10590385C211yesmaximal, characteristic
4#10590250C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic
6#10589098C211yesmaximal, characteristic
7#10589094C211yesmaximal, characteristic
8#71118—31nomaximal
9#68468—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3719—21no—
14#63662—21no—
15#63662—21no—
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#810—21no—
18C3×#808—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22Dic3⋊(C3⋊C8)—21no—
23#63567—21no—
24Dic3×C3⋊C8—21no—
25C3×#475—31no—
26#5094D311yescharacteristic
27#5079—31no—
28#5079—31no—
29#5079—61no—
30#5031—31no—
31Q8×C3⋊C8—31no—
32#4849—31no—
33#4830—31no—
34C3×#332—31no—
35#4547D311yescharacteristic
36#4486—31no—
37#4482—31no—
38#4480—31no—
39#4480—31no—
40C2×C32×Q8—21no—
41C2×#634—21no—
42C2×C3×Dic6D411yescharacteristic
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C3×C4⋊Dic3D411yescharacteristic
51C3×Dic3⋊C4—21no—
52C3×C4×Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#3719—42no—
57#1680—91noSylow
58C3×C4⋊Q8—21no—
59C3×C4⋊Q8C2×D311yescharacteristic
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4×Q8—31no—
62C2×#216—61no—
63C2×Dic12—61no—
64#869—31no—
65#869—31no—
66#869—61no—
67C4×Dic6C2×D311yescharacteristic
68C3×#106—61no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8—31no—
72C3×#103—61no—
73#835—61no—
74#835—61no—
75#835—61no—
76#835—61no—
77#835—62no—
78#835—62no—
79#816—61no—
80Dic3⋊C8—61no—
81C8×Dic3—61no—
82#810—21no—
83#810—61no—
84#808—21no—
85C4⋊(C3⋊C8)—61no—
86C4⋊(C3⋊C8)C2×D311yescharacteristic
87C4⋊(C3⋊C8)C2×D311yescharacteristic
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4×C3⋊C8—31no—
90C4×C3⋊C8—31no—
91C4×C3⋊C8—61no—
92C4×C3⋊C8—61no—
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—41no—
100#634—41no—
101#634—41no—
102C2×C3×Dic3—21no—
103C2×C3×Dic3—21no—
104C3×Dic6—21no—
105C3×Dic6SD1612yes—
106C3⋊(C3⋊C8)—21no—
107C3⋊(C3⋊C8)—21no—
108C3×C3⋊C8—41no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111#487—91no—
112#475—31no—
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—31no—
122C2×Dic6—61no—
123C2×Dic6—61no—
124C2×Dic6—121no—
125C2×Dic6#6711yescharacteristic
126C2×C3×C8—61no—
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—31no—
134C3×C4⋊C4—41no—
135C3×C4⋊C4—41no—
136C3×C4⋊C4—61no—
137C3×C42—21no—
138C3×C42—61no—
139C3×C42C22×D311yescharacteristic
140C3×C42C22×D311yescharacteristic
141#216—122no—
142C4⋊Dic3—62no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—121no—
148C4⋊Dic3#6711yescharacteristic
149Dic3⋊C4—21no—
150C4×Dic3—21no—
151C2×C3⋊C8—21no—
152C2×C3⋊C8—21no—
153C2×C3⋊C8—21no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—31no—
157C2×C3⋊C8—31no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—61no—
160Dic12—122no—
161C22×C32#12111yescharacteristic
162C32×C4—21no—
163C32×C4—81no—
164C32×C4C2×SD1611yescharacteristic
165C32×C4#13511yescharacteristic
166C32×C4#13511yescharacteristic
167C32×C4#13711yescharacteristic
168C3⋊Dic3—81no—
169C3×Dic3—22no—
170C3×Dic3—41no—
171C2×Q16—181no—
172C4⋊Q8—91no—
173C4⋊Q8D3211yescharacteristic
174C4×Q8—31no—
175#106—61no—
176C4⋊C8—31no—
177C4⋊C8—31no—
178C4⋊C8—31no—
179C4⋊C8—181no—
180#103—61no—
181#103—181no—
182#103—181no—
183#103—181no—
184C4×C8—91no—
185C4×C8—181no—
186C3×Q8—32no—
187C3×Q8—42no—
188C3×Q8—42no—
189C3×Q8—41no—
190C3×Q8—41no—
191C3×Q8—41no—
192C3×Q8—41no—
193C3×Q8—61no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—42no—
198C2×C3×C4—41no—
199C2×C3×C4—41no—
200C2×C3×C4—61no—
201C2×C3×C4—61no—
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—21no—
209C2×Dic3—21no—
210C2×Dic3—122no—
211C2×Dic3—121no—
212C2×Dic3—121no—
213Dic6—21no—
214Dic6—121no—
215Dic6—121no—
216Dic6—121no—
217Dic6—121no—
218Dic6—241no—
219Dic6—241no—
220Dic6#21512yes—
221C3×C8—121no—
222C3×C8—121no—
223C3×C8—121no—
224C3⋊C8—41no—
225C3⋊C8—41no—
226C3⋊C8—41no—
227C3⋊C8—61no—
228C3⋊C8—61no—
229C3⋊C8—61no—
230C3⋊C8—61no—
231C3⋊C8—121no—
232C3⋊C8—121no—
233C2×C32#46411yescharacteristic
234C2×C32#46511yescharacteristic
235C2×C32#47311yescharacteristic
236C2×Q8—21no—
237C2×Q8—31no—
238C2×Q8—181no—
239Q16—362no—
240C2×C8—61no—
241C2×C8—61no—
242C2×C8—61no—
243C2×C8—91no—
244C2×C8—91no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—31no—
248C4⋊C4—61no—
249C4⋊C4—181no—
250C4⋊C4—181no—
251C42—61no—
252C42C2×D3211yescharacteristic
253C22×C3—21no—
254C22×C3#88411yescharacteristic
255C22×C3#93911yescharacteristic
256C3×C4—22no—
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—62no—
264C3×C4—82no—
265C3×C4—81no—
266C3×C4—81no—
267C3×C4—121no—
268C3×C4#91211yescharacteristic
269C3×C4D3×SD1611yescharacteristic
270C3×C4#91511yescharacteristic
271C3×C4#91511yescharacteristic
272C3×C4#91611yescharacteristic
273C3×C4#91911yescharacteristic
274C3×C4C2×#21511yescharacteristic
275C3×C4#95011yescharacteristic
276Dic3—22no—
277Dic3—41no—
278Dic3—242no—
279Dic3—241no—
280Dic3—241no—
281C32#168011yescharacteristic, complemented, Sylow
282Q8—32no—
283Q8—41no—
284Q8—41no—
285Q8—61no—
286Q8—361no—
287Q8—361no—
288C2×C4—41no—
289C2×C4—61no—
290C2×C4—61no—
291C2×C4—361no—
292C2×C4#380411yescharacteristic
293C2×C4D3×#6711yescharacteristic
294C2×C4#381111yescharacteristic
295C8—121no—
296C8—121no—
297C8—121no—
298C8—181no—
299C8—181no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3#475511yescharacteristic
304C2×C3#476711yescharacteristic
305C2×C3#480711yescharacteristic
306C2×C3#504811yescharacteristic
307C2×C3#516611yescharacteristic
308C2×C3#520411yescharacteristic
309C22#6397111yescharacteristic
310C4—21no—
311C4—62no—
312C4—81no—
313C4—121no—
314C4—721no—
315C4#6393111yescharacteristic
316C4#6393611yescharacteristic
317C4D3×#21511yescharacteristic
318C4#6394911yescharacteristic
319C3—21no—
320C3#6846811yescharacteristic, complemented
321C3#7111811yescharacteristic, complemented
322C2#1059144311yescharacteristic
323C2#1059158511yescharacteristic
324C2#1059164411yescharacteristic
subgroupG/H
centerC22#63971
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
281. C32#1680semidirect
320. C3#68468semidirect
321. C3#71118semidirect

Maximal subgroups

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

subgroupindex
#105927782
C3×#50942
#105903852
#105902502
C3×#45472
#105890982
#105890942
#711183
#684683