Finite Group Databasebeta

← #11781091

Subgroups — #11781091

Order 1152.

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

normal subgroups only

This group has 348 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#10592549C211yesmaximal, characteristic
2#10590388C211yesmaximal, characteristic
3#10590303C211yesmaximal, characteristic
4#10590254C211yesmaximal, characteristic
5C3×#4482C211yesmaximal, characteristic
6C3×#4480C211yesmaximal, characteristic
7#10589096C211yesmaximal, characteristic
8#68547—31nomaximal
9#68466—31nomaximal
10#64078C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3719—21no—
14C32×C4⋊C8C2211yescharacteristic
15#63645—21no—
16#63643—21no—
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63573—21no—
21#63573—21no—
22#63572—21no—
23#63566—21no—
24#63553—21no—
25#5090—31no—
26#5080—31no—
27#4850—31no—
28#4850—31no—
29#4850—61no—
30#4849—31no—
31#4830—31no—
32#4680—31no—
33C8×Dic6—31no—
34C3×#334—31no—
35C3×#332—31no—
36#4482D311yescharacteristic
37#4481—31no—
38#4481—31no—
39#4480D311yescharacteristic
40C2×#634—21no—
41C2×#634D411yescharacteristic
42C2×C3×Dic6—21no—
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)D411yescharacteristic
48#3750—21no—
49C4×C3⋊Dic3—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#3719—42no—
57#1672—91noSylow
58C3×C4⋊Q8—31no—
59C2×#216—61no—
60C2×Dic12—61no—
61#869—31no—
62#869—31no—
63#869—61no—
64#869C2×D311yescharacteristic
65C4×Dic6—31no—
66C4×Dic6—31no—
67C4×Dic6—61no—
68C3×C4⋊C8—21no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8C2×D311yescharacteristic
72C3×C4⋊C8C2×D311yescharacteristic
73C3×C4×C8—31no—
74#835—61no—
75#818—61no—
76#818—61no—
77#818—62no—
78#817—61no—
79#817—61no—
80#816—61no—
81#816—61no—
82#816—61no—
83#816—62no—
84Dic3⋊C8—61no—
85Dic3⋊C8—61no—
86C8×Dic3—61no—
87C8×Dic3—61no—
88#808—61no—
89#808—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—41no—
99#634—21no—
100#634—81no—
101#634SD1612yes—
102C2×C3×Dic3—41no—
103C3×Dic6—41no—
104C3×Dic6—41no—
105C32×C8—41no—
106C3×C3⋊C8—21no—
107C3×C3⋊C8—41no—
108C3×C3⋊C8—41no—
109C3×C3⋊C8Q1612yescomplemented
110#498—91no—
111#477—91no—
112#462—91no—
113C8×Q8—91no—
114#334—31no—
115#333—91no—
116#332—31no—
117C2×C3×Q8—61no—
118C2×Dic6—21no—
119C2×Dic6—31no—
120C2×Dic6—31no—
121C2×Dic6—61no—
122C2×Dic6—61no—
123C2×Dic6—61no—
124C2×Dic6—121no—
125C2×C3×C8—22no—
126C2×C3×C8—21no—
127C2×C3×C8—21no—
128C2×C3×C8—31no—
129C2×C3×C8—31no—
130C2×C3×C8—61no—
131C2×C3×C8—61no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C42—21no—
135C3×C42C22×D311yescharacteristic
136C3×C42C22×D311yescharacteristic
137#216—122no—
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—31no—
141C4⋊Dic3—31no—
142C4⋊Dic3—61no—
143C4⋊Dic3—62no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—61no—
148C4⋊Dic3—121no—
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⋊C8D1211yescharacteristic
158C2×C3⋊C8D1211yescharacteristic
159Dic12—122no—
160C22×C32#12111yescharacteristic
161C32×C4—21no—
162C32×C4C2×SD1611yescharacteristic
163C32×C4C2×Q1611yescharacteristic
164C32×C4#13511yescharacteristic
165C32×C4#13711yescharacteristic
166C3⋊Dic3—22no—
167C3⋊Dic3—41no—
168C3⋊Dic3—81no—
169C3×Dic3—81no—
170C2×Q16—181no—
171C4⋊Q8—31no—
172C4⋊Q8—91no—
173C4×Q8—91no—
174#107—181no—
175#106—181no—
176#106—181no—
177C4⋊C8—31no—
178C4⋊C8—31no—
179C4⋊C8—181no—
180C4⋊C8D3211yescharacteristic
181#103—181no—
182#103—181no—
183C4×C8—31no—
184C4×C8—181no—
185C3×Q8—121no—
186C3×Q8—121no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—121no—
191C2×C3×C4C2×D1211yescharacteristic
192C2×C3×C4#23511yescharacteristic
193C2×C3×C4D3×D411yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×C3×C4D3×D411yescharacteristic
196C2×C3×C4#23911yescharacteristic
197C2×Dic3—41no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—121no—
203C2×Dic3—121no—
204C2×Dic3—122no—
205C2×Dic3—121no—
206C2×Dic3—121no—
207Dic6—32no—
208Dic6—32no—
209Dic6—41no—
210Dic6—41no—
211Dic6—62no—
212Dic6—61no—
213Dic6—61no—
214Dic6—121no—
215Dic6—242no—
216Dic6—241no—
217Dic6—241no—
218C3×C8—32no—
219C3×C8—42no—
220C3×C8—41no—
221C3×C8—41no—
222C3×C8—61no—
223C3×C8—121no—
224C3×C8—121no—
225C3⋊C8—21no—
226C3⋊C8—41no—
227C3⋊C8—41no—
228C3⋊C8Dic1212yescomplemented
229C2×C32#46211yescharacteristic
230C2×C32#46511yescharacteristic
231C2×C32#47111yescharacteristic
232C2×Q8—61no—
233C2×Q8—91no—
234C2×Q8—181no—
235Q16—362no—
236C2×C8—21no—
237C2×C8—31no—
238C2×C8—31no—
239C2×C8—61no—
240C2×C8—61no—
241C4⋊C4—61no—
242C4⋊C4—61no—
243C4⋊C4—91no—
244C4⋊C4—181no—
245C4⋊C4—181no—
246C4⋊C4—181no—
247C42—181no—
248C42C2×D3211yescharacteristic
249C22×C3—21no—
250C22×C3#88411yescharacteristic
251C22×C3#89511yescharacteristic
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—41no—
259C3×C4—241no—
260C3×C4C2×Dic1211yescharacteristic
261C3×C4#90911yescharacteristic
262C3×C4#91211yescharacteristic
263C3×C4D3×SD1611yescharacteristic
264C3×C4D3×SD1611yescharacteristic
265C3×C4#91511yescharacteristic
266C3×C4#91611yescharacteristic
267C3×C4D3×Q1611yescharacteristic
268Dic3—62no—
269Dic3—62no—
270Dic3—81no—
271Dic3—122no—
272Dic3—121no—
273Dic3—121no—
274Dic3—241no—
275Dic3—242no—
276Dic3—241no—
277Dic3—241no—
278C32#167211yescharacteristic, complemented, Sylow
279Q8—92no—
280Q8—121no—
281Q8—121no—
282Q8—181no—
283Q8—721no—
284C2×C4—121no—
285C2×C4—181no—
286C2×C4—181no—
287C2×C4—361no—
288C2×C4#379911yescharacteristic
289C2×C4D3×D1211yescharacteristic
290C2×C4#381111yescharacteristic
291C8—32no—
292C8—41no—
293C8—61no—
294C8—121no—
295C8—121no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3#475411yescharacteristic
300C2×C3#477811yescharacteristic
301C2×C3#479511yescharacteristic
302C2×C3#484911yescharacteristic
303C2×C3#486411yescharacteristic
304C2×C3#489811yescharacteristic
305C22#6391011yescharacteristic
306C4—21no—
307C4—182no—
308C4—241no—
309C4—361no—
310C4—721no—
311C4D3×Dic1211yescharacteristic
312C4#6380011yescharacteristic
313C4#6393611yescharacteristic
314C4#6394011yescharacteristic
315C3—21no—
316C3#6846611yescharacteristic, complemented
317C3#6854711yescharacteristic, complemented
318C2#1059050711yescharacteristic
319C2#1059080811yescharacteristic
320C2#1059099011yescharacteristic
subgroupG/H
centerC22#63910
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1672
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
109. C3×C3⋊C8Q16semidirect
228. C3⋊C8Dic12semidirect
278. C32#1672semidirect
316. C3#68466semidirect
317. C3#68547semidirect

Maximal subgroups

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

subgroupindex
#105925492
#105903882
#105903032
#105902542
C3×#44822
C3×#44802
#105890962
#685473
#684663