Finite Group Databasebeta

← #11781673

Subgroups — #11781673

Order 1152.

400 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 92 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#10592726C211yesmaximal, characteristic
2C3×#5024C211yesmaximal, characteristic, complemented
3C3×#5020C211yesmaximal, characteristic, complemented
4#10590373C211yesmaximal, characteristic
5#10589099C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic
8#71120—31nomaximal
9#70958—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C2×#3755—21no—
12#64083C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3717—21no—
15C2×#3717—21no—
16#63636—21no—
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C3×#835—21no—
19C3×#808—21no—
20C3×C4⋊(C3⋊C8)—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#803—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#475—31no—
26C3×#446—31no—
27#5085—31no—
28#5027—31no—
29#5027—31no—
30#5027—61no—
31#5024D311yescharacteristic, complemented
32#5020D311yescharacteristic, complemented
33#4693—31no—
34#4547—31no—
35#4485—31no—
36#4485—31no—
37#4482—31no—
38#4479—31no—
39#4458—31no—
40C2×C32×Q8D411yescharacteristic
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C3×Dic6—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4D411yescharacteristic
47C32×C42—21no—
48C32×C42C2311yescharacteristic
49#3755—42no—
50C2×C3⋊(C3⋊C8)—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#3717—42no—
58#3717—42no—
59#1686—91noSylow
60C3×C4⋊Q8—31no—
61C3×C4×Q8—21no—
62C3×C4×Q8C2×D311yescharacteristic
63C3×C4×Q8C2×D311yescharacteristic
64C2×#215—62no—
65C2×#215—61no—
66C2×#215—61no—
67C2×#215—61no—
68C2×#215—61no—
69C2×#204—61no—
70C2×#204—61no—
71#874—31no—
72#874—31no—
73#874—61no—
74#869C2×D311yescharacteristic
75C3×#106—61no—
76C3×C4⋊C8—31no—
77C3×C4⋊C8—31no—
78C3×C4⋊C8—61no—
79C3×#103—61no—
80C3×#97—61no—
81C3×C4×C8—31no—
82#835—21no—
83#809—62no—
84#809—61no—
85#809—61no—
86#808—21no—
87C4⋊(C3⋊C8)—21no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93#803—21no—
94C4×C3⋊C8C2×D311yescharacteristic
95C22×C3⋊D3—41no—
96C32×Q8—21no—
97C32×Q8—21no—
98C2×C32×C4—21no—
99C2×C32×C4—21no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C4⋊(C3⋊D3)—41no—
104C4⋊(C3⋊D3)—41no—
105C4⋊(C3⋊D3)—41no—
106C4⋊(C3⋊D3)—41no—
107C4⋊(C3⋊D3)—81no—
108C2×C3×Dic3—41no—
109C3×Dic6—41no—
110C3×Dic6—41no—
111C3⋊(C3⋊C8)—41no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8SD1612yescomplemented
116#492—91no—
117#475—31no—
118#460—91no—
119#446—31no—
120#335—91no—
121#332—91no—
122#331—91no—
123C2×C3×Q8—21no—
124C2×C3×Q8—61no—
125C2×C3×Q8D1211yescharacteristic
126C2×C3×Q8#6711yescharacteristic
127C2×D12—62no—
128C2×D12—61no—
129C2×D12—61no—
130C2×D12—61no—
131C2×D12—61no—
132C2×D12—61no—
133C2×D12—61no—
134C2×D12—121no—
135C2×D12—121no—
136C2×Dic6—21no—
137C2×C3×C8—31no—
138C2×C3×C8—31no—
139C2×C3×C8—61no—
140C2×C3×C8—61no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—41no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4D1211yescharacteristic
148C3×C4⋊C4#6711yescharacteristic
149C3×C42—21no—
150C3×C42—21no—
151C3×C42—21no—
152C3×C42—41no—
153C3×C42C22×D311yescharacteristic
154C3×C42C22×D311yescharacteristic
155#215—122no—
156#215—124no—
157#215—122no—
158#215—122no—
159#215—122no—
160C4⋊Dic3—21no—
161C4⋊Dic3—21no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—21no—
164C2×C3⋊C8—62no—
165C2×C3⋊C8—61no—
166C2×C3⋊C8—61no—
167C2×C3⋊C8#6711yescharacteristic
168C2×C3⋊C8#6711yescharacteristic
169#204—122no—
170#204—122no—
171C22×C32#12111yescharacteristic
172C2×C3⋊D3—81no—
173C2×C3⋊D3—81no—
174C2×C3⋊D3—81no—
175C32×C4—21no—
176C32×C4—41no—
177C32×C4—41no—
178C32×C4C2×SD1611yescharacteristic
179C32×C4AGL(1,ℤ/8)11yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C32×C4#13711yescharacteristic
182C3×Dic3—81no—
183C2×SD16—181no—
184C2×SD16—181no—
185C2×SD16—181no—
186C4⋊Q8—31no—
187#127—91no—
188C4×Q8D3211yescharacteristic
189#106—61no—
190C4⋊C8—31no—
191C4⋊C8—31no—
192C4⋊C8—61no—
193C4⋊C8—91no—
194#103—61no—
195#102—181no—
196#97—61no—
197C4×C8—31no—
198C22×D3—122no—
199C22×D3—121no—
200C22×D3—121no—
201C3×Q8—22no—
202C3×Q8—21no—
203C3×Q8—21no—
204C3×Q8—21no—
205C3×Q8—21no—
206C3×Q8—41no—
207C3×Q8—121no—
208C3×Q8—121no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—121no—
219C2×C3×C4C2×D1211yescharacteristic
220C2×C3×C4#23511yescharacteristic
221C2×C3×C4D3×D411yescharacteristic
222C2×C3×C4#23711yescharacteristic
223C2×C3×C4C2×#6711yescharacteristic
224C2×C3×C4C2×#6711yescharacteristic
225C2×Dic3—41no—
226D12—122no—
227D12—122no—
228D12—121no—
229D12—121no—
230D12—121no—
231D12—121no—
232D12—121no—
233D12—121no—
234D12—121no—
235D12—121no—
236D12—241no—
237D12—241no—
238D12—241no—
239D12—241no—
240D12—242no—
241Dic6—41no—
242Dic6—41no—
243C3×C8—32no—
244C3×C8—61no—
245C3×C8—121no—
246C3×C8—121no—
247C3⋊C8—21no—
248C3⋊C8—41no—
249C3⋊C8—41no—
250C3⋊C8—122no—
251C3⋊C8—121no—
252C3⋊C8—121no—
253C3⋊C8#21512yescomplemented
254C2×C32#46011yescharacteristic
255C2×C32#46811yescharacteristic
256C2×C32#47111yescharacteristic
257C3⋊D3—161no—
258C2×Q8—61no—
259C2×Q8#62611yescharacteristic
260C2×D4—181no—
261C2×D4—181no—
262C2×D4—181no—
263SD16—362no—
264SD16—362no—
265SD16—362no—
266C2×C8—31no—
267C2×C8—31no—
268C2×C8—61no—
269C2×C8—61no—
270C2×C8—181no—
271C4⋊C4—21no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4#62611yescharacteristic
275C42—21no—
276C42C2×D3211yescharacteristic
277C22×C3—21no—
278C22×C3#93011yescharacteristic
279C22×C3#93911yescharacteristic
280C2×D3—242no—
281C2×D3—242no—
282C2×D3—242no—
283C2×D3—241no—
284C2×D3—241no—
285C2×D3—241no—
286C2×D3—241no—
287C2×D3—241no—
288C2×D3—241no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—41no—
296C3×C4—42no—
297C3×C4—41no—
298C3×C4—41no—
299C3×C4—41no—
300C3×C4—41no—
301C3×C4—81no—
302C3×C4—241no—
303C3×C4#90811yescharacteristic
304C3×C4#90911yescharacteristic
305C3×C4D3×SD1611yescharacteristic
306C3×C4#91411yescharacteristic
307C3×C4C2×#21511yescharacteristic
308C3×C4#94211yescharacteristic
309C3×C4#94911yescharacteristic
310C3×C4#94911yescharacteristic
311Dic3—81no—
312C32#168611yescharacteristic, complemented, Sylow
313C23—361no—
314Q8—21no—
315Q8—21no—
316Q8—121no—
317Q8—121no—
318D4—361no—
319D4—361no—
320D4—361no—
321D4—361no—
322D4—721no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—121no—
326C2×C4#380411yescharacteristic
327C2×C4C2×#62611yescharacteristic
328C2×C4D3×#6711yescharacteristic
329C8—32no—
330C8—61no—
331C8—121no—
332C8—121no—
333C8—361no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3#502711yescharacteristic
338C2×C3#504911yescharacteristic
339C2×C3#513411yescharacteristic
340C2×C3#514111yescharacteristic
341C2×C3#516311yescharacteristic
342C2×C3#520311yescharacteristic
343D3—482no—
344D3—481no—
345D3—481no—
346C22—721no—
347C22—721no—
348C22—721no—
349C22#6397811yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—241no—
354C4#6382511yescharacteristic
355C4#6383311yescharacteristic
356C4D3×#21511yescharacteristic
357C4#6393911yescharacteristic
358C3—21no—
359C3#7095811yescharacteristic, complemented
360C3#7112011yescharacteristic, complemented
361C2—1441no—
362C2#1059117811yescharacteristic
363C2#1059161711yescharacteristic
364C2#1059168011yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#121
prime radical#64083C22
hypercenterC4×Q8D32
hypocenterC32#1686
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
2. C3×#5024C2semidirect
3. C3×#5020C2semidirect
5. #10589099C2semidirect
6. #10589093C2semidirect
31. #5024D3semidirect
32. #5020D3semidirect
115. C3×C3⋊C8SD16semidirect
253. C3⋊C8#215semidirect
312. C32#1686semidirect
359. C3#70958semidirect
360. C3#71120semidirect

Maximal subgroups

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

subgroupindex
#105927262
C3×#50242
C3×#50202
#105903732
#105890992
#105890932
#105890912
#711203
#709583