Finite Group Databasebeta

← #11780985

Subgroups — #11780985

Order 1152.

373 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 373 conjugacy classes of subgroups — too many to draw. Only its 88 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#10592791C211yesmaximal, characteristic
2C3×#5094C211yesmaximal, characteristic
3#10590301C211yesmaximal, characteristic
4#10590250C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic
6#10589100C211yesmaximal, characteristic
7#10589094C211yesmaximal, characteristic
8#71117—31nomaximal
9#68465—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3756—21no—
12C2×#3756—21no—
13#64078C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#810—21no—
17C3×#808—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21#63573—21no—
22Dic3⋊(C3⋊C8)—21no—
23#63566—21no—
24Dic3×C3⋊C8—21no—
25C3×#475—31no—
26#5094D311yescharacteristic
27#5092—31no—
28#5092—31no—
29#5092—61no—
30Q8×C3⋊C8—31no—
31#5020—31no—
32#4851—31no—
33#4830—31no—
34C3×#332—31no—
35#4547D311yescharacteristic
36#4486—31no—
37#4482—31no—
38#4479—31no—
39#4479—31no—
40C2×C32×Q8—21no—
41C2×#634—21no—
42C2×C3×Dic6D411yescharacteristic
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C42C2311yescharacteristic
46#3756—42no—
47#3756—42no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C2×C3⋊(C3⋊C8)D411yescharacteristic
51C2×C3⋊(C3⋊C8)D411yescharacteristic
52C3×C4⋊Dic3D411yescharacteristic
53C3×Dic3⋊C4—21no—
54C3×C4×Dic3—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58#1670—91noSylow
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4×Q8—31no—
63C2×#216—61no—
64C2×#216—61no—
65C2×#216—61no—
66C2×#216—61no—
67C2×#216—62no—
68C2×#216—62no—
69#869—31no—
70#869—31no—
71#869—61no—
72C4×Dic6C2×D311yescharacteristic
73C3×#106—61no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8—31no—
77C3×#103—61no—
78#835—61no—
79#817—61no—
80#816—61no—
81Dic3⋊C8—61no—
82C8×Dic3—61no—
83#810—21no—
84#808—21no—
85#808—61no—
86C4⋊(C3⋊C8)—61no—
87C4⋊(C3⋊C8)C2×D311yescharacteristic
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C4×C3⋊C8—61no—
94C32×Q8—41no—
95C32×Q8—41no—
96C2×C32×C4—41no—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C3⋊Dic3—41no—
101#634—41no—
102#634—41no—
103C2×C3×Dic3—21no—
104C2×C3×Dic3—21no—
105C3×Dic6—21no—
106C3×Dic6Q1612yescomplemented
107C3⋊(C3⋊C8)—21no—
108C3⋊(C3⋊C8)SD1612yes—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112#494—91no—
113#475—31no—
114#475—91no—
115C8×Q8—91no—
116#335—91no—
117#332—31no—
118#332—91no—
119C2×C3×Q8—22no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×Q8—31no—
123C2×Dic6—62no—
124C2×Dic6—61no—
125C2×Dic6—61no—
126C2×Dic6#6711yescharacteristic
127C2×C3×C8—61no—
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—31no—
135C3×C4⋊C4—41no—
136C3×C4⋊C4—41no—
137C3×C4⋊C4—61no—
138C3×C42—21no—
139C3×C42—61no—
140C3×C42C22×D311yescharacteristic
141C3×C42C22×D311yescharacteristic
142#216—122no—
143#216—122no—
144#216—124no—
145#216—124no—
146#216—122no—
147#216—122no—
148C4⋊Dic3—61no—
149C4⋊Dic3—61no—
150C4⋊Dic3—61no—
151C4⋊Dic3—61no—
152C4⋊Dic3—121no—
153C4⋊Dic3—121no—
154C4⋊Dic3#6711yescharacteristic
155Dic3⋊C4—21no—
156C4×Dic3—21no—
157C2×C3⋊C8—21no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—31no—
161C2×C3⋊C8—31no—
162C2×C3⋊C8—31no—
163C2×C3⋊C8—31no—
164C2×C3⋊C8—61no—
165C2×C3⋊C8—61no—
166C22×C32#12111yescharacteristic
167C32×C4—21no—
168C32×C4—81no—
169C32×C4C2×SD1611yescharacteristic
170C32×C4C2×Q1611yescharacteristic
171C32×C4#13511yescharacteristic
172C32×C4AGL(1,ℤ/8)11yescharacteristic
173C3⋊Dic3—81no—
174C3×Dic3—22no—
175C3×Dic3—41no—
176C2×Q16—181no—
177C2×Q16—181no—
178C4⋊Q8—91no—
179C4⋊Q8D3211yescharacteristic
180C4×Q8—31no—
181#106—61no—
182#106—181no—
183C4⋊C8—31no—
184C4⋊C8—31no—
185C4⋊C8—31no—
186C4⋊C8—181no—
187#103—61no—
188#103—181no—
189C4×C8—91no—
190C4×C8—181no—
191C3×Q8—32no—
192C3×Q8—42no—
193C3×Q8—42no—
194C3×Q8—41no—
195C3×Q8—41no—
196C3×Q8—41no—
197C3×Q8—41no—
198C3×Q8—61no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—42no—
203C2×C3×C4—41no—
204C2×C3×C4—41no—
205C2×C3×C4—61no—
206C2×C3×C4—61no—
207C2×C3×C4#23511yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4D3×D411yescharacteristic
211C2×C3×C4#23711yescharacteristic
212C2×C3×C4C2×#6711yescharacteristic
213C2×Dic3—21no—
214C2×Dic3—21no—
215C2×Dic3—122no—
216C2×Dic3—121no—
217C2×Dic3—121no—
218Dic6—21no—
219Dic6—122no—
220Dic6—122no—
221Dic6—121no—
222Dic6—121no—
223Dic6—121no—
224Dic6—121no—
225Dic6#21612yescomplemented
226C3×C8—121no—
227C3×C8—121no—
228C3×C8—121no—
229C3⋊C8—32no—
230C3⋊C8—32no—
231C3⋊C8—41no—
232C3⋊C8—41no—
233C3⋊C8—41no—
234C3⋊C8—62no—
235C3⋊C8—62no—
236C3⋊C8—61no—
237C3⋊C8—61no—
238C2×C32#46011yescharacteristic
239C2×C32#46711yescharacteristic
240C2×C32#47311yescharacteristic
241C2×Q8—21no—
242C2×Q8—31no—
243C2×Q8—181no—
244Q16—362no—
245Q16—362no—
246C2×C8—61no—
247C2×C8—61no—
248C2×C8—61no—
249C2×C8—91no—
250C2×C8—91no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—31no—
254C4⋊C4—61no—
255C4⋊C4—181no—
256C4⋊C4—181no—
257C42—61no—
258C42C2×D3211yescharacteristic
259C22×C3—21no—
260C22×C3#88411yescharacteristic
261C22×C3#93911yescharacteristic
262C3×C4—22no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—62no—
270C3×C4—82no—
271C3×C4—81no—
272C3×C4—81no—
273C3×C4—121no—
274C3×C4#91111yescharacteristic
275C3×C4D3×SD1611yescharacteristic
276C3×C4D3×SD1611yescharacteristic
277C3×C4#91411yescharacteristic
278C3×C4#91611yescharacteristic
279C3×C4D3×Q1611yescharacteristic
280C3×C4C2×#21611yescharacteristic
281C3×C4#95011yescharacteristic
282Dic3—22no—
283Dic3—41no—
284Dic3—242no—
285Dic3—241no—
286Dic3—241no—
287C32#167011yescharacteristic, complemented, Sylow
288Q8—32no—
289Q8—41no—
290Q8—41no—
291Q8—61no—
292Q8—361no—
293Q8—361no—
294C2×C4—41no—
295C2×C4—61no—
296C2×C4—61no—
297C2×C4—361no—
298C2×C4#380411yescharacteristic
299C2×C4D3×#6711yescharacteristic
300C2×C4#381111yescharacteristic
301C8—92no—
302C8—121no—
303C8—121no—
304C8—121no—
305C8—181no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3#475511yescharacteristic
310C2×C3#476211yescharacteristic
311C2×C3#481311yescharacteristic
312C2×C3#505111yescharacteristic
313C2×C3#516311yescharacteristic
314C2×C3#520411yescharacteristic
315C22#6397111yescharacteristic
316C4—21no—
317C4—62no—
318C4—81no—
319C4—121no—
320C4—721no—
321C4#6393011yescharacteristic
322C4#6393711yescharacteristic
323C4D3×#21611yescharacteristic
324C4#6394711yescharacteristic
325C3—21no—
326C3#6846511yescharacteristic, complemented
327C3#7111711yescharacteristic, complemented
328C2#1059144411yescharacteristic
329C2#1059159611yescharacteristic
330C2#1059164411yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊Q8D32
hypocenterC32#1670
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
106. C3×Dic6Q16semidirect
225. Dic6#216semidirect
287. C32#1670semidirect
326. C3#68465semidirect
327. C3#71117semidirect

Maximal subgroups

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

subgroupindex
#105927912
C3×#50942
#105903012
#105902502
C3×#45472
#105891002
#105890942
#711173
#684653