Finite Group Databasebeta

← #11781682

Subgroups — #11781682

Order 1152.

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

normal subgroups only

This group has 378 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×#4831C211yesmaximal, characteristic, complemented
2#10590373C211yesmaximal, characteristic
3#10590367C211yesmaximal, characteristic
4#10590285C211yesmaximal, characteristic, complemented
5#10589351C211yesmaximal, characteristic
6C3×#4482C211yesmaximal, characteristic, complemented
7#10589099C211yesmaximal, characteristic, complemented
8#70958—31nomaximal
9#68472—31nomaximal
10#64083C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3717—21no—
14C2×#3717—21no—
15C2×#3717—21no—
16C32×C4⋊C8C2211yescharacteristic
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C3×#815—21no—
19C3×Dic3⋊C8—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22#63574—21no—
23#63565—21no—
24#63564—21no—
25C3×#446—31no—
26#5094—31no—
27#5085—31no—
28#5027—31no—
29#5020—31no—
30#4848—31no—
31#4831D311yescharacteristic, complemented
32#4693—31no—
33C3×#332—31no—
34#4485—31no—
35#4485—31no—
36#4485—61no—
37#4482D311yescharacteristic, complemented
38#4479—31no—
39#4458—31no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C3×Dic6—21no—
44C2×C3×Dic6D411yescharacteristic
45C2×C32×C8—21no—
46C32×C42C2311yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3D411yescharacteristic
51C3×Dic3⋊C4—21no—
52C3×C4×Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#3717—42no—
57#3717—42no—
58#3717—42no—
59#1686—91noSylow
60C3×C4⋊Q8—31no—
61C3×C4×Q8—31no—
62C2×#215—61no—
63C2×#215—61no—
64C2×#215—61no—
65C2×#204—61no—
66C2×#204—61no—
67C2×#204—61no—
68#874—31no—
69#874—31no—
70#874—61no—
71#869C2×D311yescharacteristic
72C4×Dic6C2×D311yescharacteristic
73C3×C4⋊C8—21no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8—61no—
76C3×C4⋊C8C2×D311yescharacteristic
77C3×C4⋊C8C2×D311yescharacteristic
78C3×#97—61no—
79C3×C4×C8—31no—
80#835—61no—
81#821—61no—
82#815—21no—
83Dic3⋊C8—21no—
84#810—61no—
85#809—61no—
86#808—61no—
87#808—61no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C22×C3⋊D3—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C4⋊(C3⋊D3)—41no—
98C4⋊(C3⋊D3)—41no—
99C4⋊(C3⋊D3)—41no—
100C4⋊(C3⋊D3)—41no—
101C4⋊(C3⋊D3)—81no—
102C2×C3×Dic3—21no—
103C2×C3×Dic3—21no—
104C2×C3×Dic3—41no—
105C3×Dic6—21no—
106C3×Dic6—21no—
107C3×Dic6—41no—
108C3×Dic6—41no—
109C32×C8—41no—
110C3⋊(C3⋊C8)—41no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8SD1612yescomplemented
114#492—91no—
115#475—91no—
116#460—91no—
117#446—31no—
118#335—91no—
119#332—31no—
120#331—91no—
121C2×C3×Q8—31no—
122C2×C3×Q8—61no—
123C2×D12—61no—
124C2×D12—61no—
125C2×D12—61no—
126C2×D12—61no—
127C2×D12—62no—
128C2×D12—61no—
129C2×D12—61no—
130C2×D12—121no—
131C2×D12—121no—
132C2×Dic6—21no—
133C2×Dic6D1211yescharacteristic
134C2×C3×C8—21no—
135C2×C3×C8—21no—
136C2×C3×C8—31no—
137C2×C3×C8—31no—
138C2×C3×C8—41no—
139C2×C3×C8—61no—
140C3×C4⋊C4—31no—
141C3×C4⋊C4—61no—
142C3×C4⋊C4—61no—
143C3×C4⋊C4—61no—
144C3×C42—21no—
145C3×C42—61no—
146C3×C42C22×D311yescharacteristic
147C3×C42C22×D311yescharacteristic
148#215—122no—
149#215—122no—
150#215—122no—
151C4⋊Dic3—21no—
152C4⋊Dic3—21no—
153C4⋊Dic3D1211yescharacteristic
154Dic3⋊C4—21no—
155C4×Dic3—21no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—121no—
160C2×C3⋊C8#6711yescharacteristic
161C2×C3⋊C8#6711yescharacteristic
162#204—122no—
163#204—122no—
164#204—122no—
165C22×C32#12111yescharacteristic
166C2×C3⋊D3—81no—
167C2×C3⋊D3—81no—
168C2×C3⋊D3—81no—
169C32×C4—21no—
170C32×C4C2×SD1611yescharacteristic
171C32×C4AGL(1,ℤ/8)11yescharacteristic
172C32×C4AGL(1,ℤ/8)11yescharacteristic
173C32×C4#13711yescharacteristic
174C3×Dic3—41no—
175C3×Dic3—41no—
176C3×Dic3—81no—
177C2×SD16—181no—
178C2×SD16—181no—
179C2×SD16—181no—
180C4⋊Q8—31no—
181#127—91no—
182C4×Q8—31no—
183#106—181no—
184C4⋊C8—31no—
185C4⋊C8—61no—
186C4⋊C8—91no—
187C4⋊C8D3211yescharacteristic
188#103—181no—
189#102—181no—
190#97—61no—
191C4×C8—31no—
192C22×D3—122no—
193C22×D3—121no—
194C22×D3—121no—
195C3×Q8—61no—
196C3×Q8—61no—
197C3×Q8—121no—
198C3×Q8—121no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—61no—
203C2×C3×C4—61no—
204C2×C3×C4—121no—
205C2×C3×C4C2×D1211yescharacteristic
206C2×C3×C4#23511yescharacteristic
207C2×C3×C4#23511yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4C2×#6711yescharacteristic
211C2×Dic3—21no—
212C2×Dic3—21no—
213C2×Dic3—41no—
214D12—121no—
215D12—121no—
216D12—121no—
217D12—121no—
218D12—121no—
219D12—121no—
220D12—121no—
221D12—121no—
222D12—241no—
223D12—241no—
224D12—241no—
225D12—241no—
226D12—241no—
227D12—241no—
228D12—242no—
229Dic6—21no—
230Dic6—21no—
231Dic6—41no—
232Dic6—41no—
233C3×C8—32no—
234C3×C8—41no—
235C3×C8—41no—
236C3×C8—61no—
237C3×C8—81no—
238C3×C8—121no—
239C3⋊C8—21no—
240C3⋊C8—41no—
241C3⋊C8—121no—
242C3⋊C8—121no—
243C3⋊C8—241no—
244C3⋊C8#21512yescomplemented
245C2×C32#46011yescharacteristic
246C2×C32#46811yescharacteristic
247C2×C32#47111yescharacteristic
248C3⋊D3—161no—
249C2×Q8—31no—
250C2×Q8—61no—
251C2×D4—181no—
252C2×D4—181no—
253C2×D4—181no—
254SD16—362no—
255SD16—362no—
256SD16—362no—
257C2×C8—21no—
258C2×C8—31no—
259C2×C8—31no—
260C2×C8—61no—
261C2×C8—181no—
262C4⋊C4—31no—
263C4⋊C4—61no—
264C4⋊C4—61no—
265C4⋊C4—61no—
266C42—61no—
267C42C2×D3211yescharacteristic
268C22×C3—21no—
269C22×C3#88411yescharacteristic
270C22×C3#93011yescharacteristic
271C2×D3—242no—
272C2×D3—242no—
273C2×D3—242no—
274C2×D3—241no—
275C2×D3—241no—
276C2×D3—241no—
277C2×D3—241no—
278C2×D3—241no—
279C2×D3—241no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—41no—
287C3×C4—121no—
288C3×C4—121no—
289C3×C4—241no—
290C3×C4#90811yescharacteristic
291C3×C4#90911yescharacteristic
292C3×C4#91111yescharacteristic
293C3×C4D3×SD1611yescharacteristic
294C3×C4#91411yescharacteristic
295C3×C4#91811yescharacteristic
296C3×C4C2×#21511yescharacteristic
297C3×C4#94911yescharacteristic
298Dic3—41no—
299Dic3—41no—
300Dic3—81no—
301C32#168611yescharacteristic, complemented, Sylow
302C23—361no—
303Q8—61no—
304Q8—61no—
305Q8—121no—
306Q8—121no—
307D4—361no—
308D4—361no—
309D4—361no—
310D4—361no—
311D4—721no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—121no—
315C2×C4#379811yescharacteristic
316C2×C4D3×D1211yescharacteristic
317C2×C4D3×#6711yescharacteristic
318C8—32no—
319C8—41no—
320C8—61no—
321C8—121no—
322C8—361no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3#475411yescharacteristic
327C2×C3#476211yescharacteristic
328C2×C3#481211yescharacteristic
329C2×C3#502711yescharacteristic
330C2×C3#513411yescharacteristic
331C2×C3#514111yescharacteristic
332D3—482no—
333D3—481no—
334D3—481no—
335C22—721no—
336C22—721no—
337C22—721no—
338C22#6390611yescharacteristic
339C4—21no—
340C4—121no—
341C4—121no—
342C4—241no—
343C4#6379411yescharacteristic
344C4#6380111yescharacteristic
345C4#6392511yescharacteristic
346C4D3×#21511yescharacteristic
347C3—21no—
348C3#6847211yescharacteristic, complemented
349C3#7095811yescharacteristic, complemented
350C2—1441no—
351C2#1059054911yescharacteristic
352C2#1059085011yescharacteristic
353C2#1059099811yescharacteristic
subgroupG/H
centerC22#63906
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radical#64083C22
hypercenterC4⋊C8D32
hypocenterC32#1686
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
1. C3×#4831C2semidirect
4. #10590285C2semidirect
6. C3×#4482C2semidirect
7. #10589099C2semidirect
31. #4831D3semidirect
37. #4482D3semidirect
113. C3×C3⋊C8SD16semidirect
244. C3⋊C8#215semidirect
301. C32#1686semidirect
348. C3#68472semidirect
349. C3#70958semidirect

Maximal subgroups

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

subgroupindex
C3×#48312
#105903732
#105903672
#105902852
#105893512
C3×#44822
#105890992
#709583
#684723