Finite Group Databasebeta

← #11781121

Subgroups — #11781121

Order 1152.

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

normal subgroups only

This group has 371 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
1C3×#4841C211yesmaximal, characteristic
2#10590363C211yesmaximal, characteristic
3#10590329C211yesmaximal, characteristic
4#10590312C211yesmaximal, characteristic, complemented
5#10589345C211yesmaximal, characteristic, complemented
6C3×#4482C211yesmaximal, characteristic, complemented
7#10589092C211yesmaximal, characteristic, complemented
8#71037—31nomaximal
9#68443—31nomaximal
10C2×C3×#204—21no—
11C3×C4×D12C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3715—21no—
15C2×D3×C3⋊C8—21no—
16C32×C4⋊C8C2211yescharacteristic
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C4×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#816—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21#63576—21no—
22#63576—21no—
23#63565—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#461—31no—
26#5083—31no—
27#5078—31no—
28#5078—31no—
29#5019—31no—
30D4×C3⋊C8—31no—
31#4841D311yescharacteristic
32#4834—31no—
33C3×#332—31no—
34#4547—31no—
35#4486—31no—
36#4482D311yescharacteristic, complemented
37#4479—31no—
38#4479—31no—
39#4479—61no—
40C2×C3×D12D411yescharacteristic
41C2×C3×C4×D3—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C32×C42C2311yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C3×(C2×D3)⋊C4—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56C3×#204—42no—
57#3715—42no—
58D3×C3⋊C8—42no—
59#1673—91noSylow
60C2×C3×SD16—61no—
61C3×C4⋊Q8—31no—
62C3×C4⋊Q8—31no—
63C3×C4×D4—31no—
64C2×#215—61no—
65C2×#214—61no—
66C22×C3⋊C8—61no—
67C2×#204—21no—
68C2×D3×C8—61no—
69C4×D12C2×D311yescharacteristic
70#869C2×D311yescharacteristic
71#869C2×D311yescharacteristic
72C3×C4⋊C8—21no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C2×D311yescharacteristic
76C3×#103—61no—
77#835—61no—
78#830—61no—
79(C2×D3)⋊C8—61no—
80#816—21no—
81#810—61no—
82#807—61no—
83#807—61no—
84#807—61no—
85#807—61no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C22×C3×D3—21no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3×Dic3—21no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3—41no—
100C3×D12—21no—
101C3×D12D812yes—
102C3×C4×D3—41no—
103C3×C4×D3—41no—
104C3×Dic6—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C3×Dic6—41no—
108C32×C8—41no—
109C3⋊(C3⋊C8)—21no—
110C3⋊(C3⋊C8)—41no—
111C3⋊(C3⋊C8)SD1612yescomplemented
112C3×C3⋊C8—41no—
113#500—91no—
114#461—31no—
115#461—91no—
116C8×D4—91no—
117#335—91no—
118#332—31no—
119#332—91no—
120C2×C3×Q8—61no—
121C2×C3×Q8—61no—
122C2×C3×D4—31no—
123C22×C3×C4—61no—
124C2×D12#6711yescharacteristic
125C2×C4×D3—21no—
126C2×Dic6—21no—
127C2×Dic6—21no—
128C3×SD16—122no—
129C2×C3×C8—21no—
130C2×C3×C8—21no—
131C2×C3×C8—41no—
132C2×C3×C8—61no—
133C3×C4⋊C4—31no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—61no—
138C3×C22⋊C4—61no—
139C3×C42—21no—
140C3×C42C22×D311yescharacteristic
141C3×C42C22×D311yescharacteristic
142#215—122no—
143#214—122no—
144(C2×D3)⋊C4—21no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3—21no—
148C4⋊Dic3—21no—
149C4⋊Dic3#6711yescharacteristic
150C2×C3⋊C8—21no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—121no—
160C2×C3⋊C8—122no—
161#204—42no—
162D3×C8—122no—
163C22×C32#12111yescharacteristic
164C2×C3×D3—22no—
165C2×C3×D3—41no—
166C2×C3×D3—41no—
167C32×C4—21no—
168C32×C4C2×D811yescharacteristic
169C32×C4C2×SD1611yescharacteristic
170C32×C4#13511yescharacteristic
171C32×C4#13711yescharacteristic
172C3×Dic3—41no—
173C3×Dic3—81no—
174C3×Dic3—81no—
175C2×SD16—61no—
176C2×SD16—181no—
177C22×C8—181no—
178C4⋊Q8—31no—
179C4⋊Q8—31no—
180C4×D4—31no—
181#107—181no—
182#107—181no—
183C4⋊C8—31no—
184C4⋊C8—91no—
185C4⋊C8D3211yescharacteristic
186#103—61no—
187#103—181no—
188C22⋊C8—181no—
189C4×C8—91no—
190C23×C3—61no—
191C22×D3—21no—
192C3×Q8—121no—
193C3×Q8—121no—
194C3×Q8—121no—
195C3×Q8—121no—
196C3×D4—32no—
197C3×D4—61no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—61no—
202C2×C3×C4—121no—
203C2×C3×C4—121no—
204C2×C3×C4—121no—
205C2×C3×C4—121no—
206C2×C3×C4#23511yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4#23711yescharacteristic
211C2×C3×C4C2×#6711yescharacteristic
212C2×Dic3—21no—
213C2×Dic3—41no—
214C2×Dic3—41no—
215D12—21no—
216D12#21312yes—
217C4×D3—41no—
218C4×D3—41no—
219Dic6—41no—
220Dic6—41no—
221Dic6—41no—
222Dic6—41no—
223C3×C8—41no—
224C3×C8—41no—
225C3×C8—81no—
226C3×C8—121no—
227C3⋊C8—32no—
228C3⋊C8—32no—
229C3⋊C8—41no—
230C3⋊C8—62no—
231C3⋊C8—61no—
232C3⋊C8—61no—
233C3⋊C8—121no—
234C3⋊C8—121no—
235C3⋊C8—121no—
236C3⋊C8—241no—
237C2×C32#46111yescharacteristic
238C2×C32#46611yescharacteristic
239C2×C32#47311yescharacteristic
240C3×D3—42no—
241C2×Q8—61no—
242C2×Q8—61no—
243C2×D4—31no—
244C22×C4—61no—
245SD16—122no—
246SD16—362no—
247C2×C8—21no—
248C2×C8—61no—
249C2×C8—91no—
250C2×C8—91no—
251C2×C8—181no—
252C2×C8—362no—
253C4⋊C4—31no—
254C4⋊C4—61no—
255C4⋊C4—61no—
256C4⋊C4—61no—
257C4⋊C4—61no—
258C22⋊C4—61no—
259C42C2×D3211yescharacteristic
260C22×C3—21no—
261C22×C3—62no—
262C22×C3—121no—
263C22×C3—121no—
264C22×C3#88411yescharacteristic
265C22×C3#93911yescharacteristic
266C2×D3—22no—
267C2×D3—41no—
268C2×D3—41no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—41no—
276C3×C4—121no—
277C3×C4—241no—
278C3×C4—241no—
279C3×C4D3×D811yescharacteristic
280C3×C4D3×SD1611yescharacteristic
281C3×C4D3×SD1611yescharacteristic
282C3×C4#91511yescharacteristic
283C3×C4#91611yescharacteristic
284C3×C4#91811yescharacteristic
285C3×C4C2×#21311yescharacteristic
286C3×C4#95011yescharacteristic
287Dic3—41no—
288Dic3—81no—
289Dic3—81no—
290C32#167311yescharacteristic, complemented, Sylow
291C23—61no—
292Q8—121no—
293Q8—121no—
294Q8—121no—
295Q8—121no—
296D4—32no—
297D4—61no—
298C2×C4—61no—
299C2×C4—121no—
300C2×C4—121no—
301C2×C4—121no—
302C2×C4—121no—
303C2×C4#379511yescharacteristic
304C2×C4#380211yescharacteristic
305C2×C4D3×#6711yescharacteristic
306C8—41no—
307C8—92no—
308C8—121no—
309C8—181no—
310C8—361no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—122no—
315C2×C3#475511yescharacteristic
316C2×C3#477511yescharacteristic
317C2×C3#481811yescharacteristic
318C2×C3#503811yescharacteristic
319C2×C3#516211yescharacteristic
320C2×C3#520411yescharacteristic
321D3—42no—
322C22—62no—
323C22—121no—
324C22—121no—
325C22#6388511yescharacteristic
326C4—21no—
327C4—121no—
328C4—241no—
329C4—241no—
330C4#6379611yescharacteristic
331C4#6381111yescharacteristic
332C4D3×#21311yescharacteristic
333C4#6394711yescharacteristic
334C3—21no—
335C3#6844311yescharacteristic, complemented
336C3#7103711yescharacteristic, complemented
337C2—122no—
338C2#1059049911yescharacteristic
339C2#1059074811yescharacteristic
340C2#1059098111yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC4⋊C8D32
hypocenterC32#1673
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
4. #10590312C2semidirect
5. #10589345C2semidirect
6. C3×#4482C2semidirect
7. #10589092C2semidirect
36. #4482D3semidirect
111. C3⋊(C3⋊C8)SD16semidirect
290. C32#1673semidirect
335. C3#68443semidirect
336. C3#71037semidirect

Maximal subgroups

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

subgroupindex
C3×#48412
#105903632
#105903292
#105903122
#105893452
C3×#44822
#105890922
#710373
#684433