Finite Group Databasebeta

← #11781680

Subgroups — #11781680

Order 1152.

400 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 86 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#10592547C211yesmaximal, characteristic
2#10590373C211yesmaximal, characteristic
3#10590307C211yesmaximal, characteristic, complemented
4#10590296C211yesmaximal, characteristic, complemented
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4479C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic
8#68592—31nomaximal
9#68472—31nomaximal
10C2×#3744—21no—
11#64083C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3717—21no—
15C2×#3717—21no—
16C32×C4⋊C8C2211yescharacteristic
17#63648—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63573—21no—
22#63572—21no—
23#63567—21no—
24#63555—21no—
25#5094—31no—
26#5085—31no—
27#4851—31no—
28#4848—31no—
29#4848—31no—
30#4848—61no—
31#4831—31no—
32#4693—31no—
33#4679—31no—
34C3×#335—31no—
35C3×#332—31no—
36#4486D311yescharacteristic, complemented
37#4485—31no—
38#4485—31no—
39#4479D311yescharacteristic, complemented
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×#634D411yescharacteristic
44C2×C3×Dic6—21no—
45C2×C32×C8—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)D411yescharacteristic
48#3750—21no—
49C4×C3⋊Dic3—21no—
50#3744—42no—
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—
61C2×#215—61no—
62C2×#215—61no—
63C2×#204—61no—
64C2×#204—61no—
65C2×#204—62no—
66C2×#204—61no—
67C2×#204—61no—
68#874—31no—
69#874—31no—
70#874—61no—
71#869C2×D311yescharacteristic
72C4×Dic6—31no—
73C4×Dic6—31no—
74C4×Dic6—61no—
75C3×C4⋊C8—21no—
76C3×C4⋊C8—31no—
77C3×C4⋊C8—31no—
78C3×C4⋊C8C2×D311yescharacteristic
79C3×C4⋊C8C2×D311yescharacteristic
80C3×C4×C8—31no—
81#821—61no—
82#821—61no—
83#821—62no—
84#817—61no—
85#816—61no—
86#815—61no—
87#815—61no—
88Dic3⋊C8—61no—
89Dic3⋊C8—61no—
90#810—61no—
91#808—61no—
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94C4×C3⋊C8C2×D311yescharacteristic
95C22×C3⋊D3—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101C4⋊(C3⋊D3)—41no—
102C4⋊(C3⋊D3)—41no—
103C4⋊(C3⋊D3)—41no—
104C4⋊(C3⋊D3)—41no—
105C4⋊(C3⋊D3)—81no—
106#634—21no—
107#634—21no—
108C2×C3×Dic3—41no—
109C3×Dic6—41no—
110C3×Dic6—41no—
111C32×C8—41no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8SD1612yescomplemented
116#492—91no—
117#475—91no—
118#460—91no—
119#446—91no—
120#335—31no—
121#332—31no—
122#331—91no—
123C2×C3×Q8—61no—
124C2×D12—62no—
125C2×D12—61no—
126C2×D12—61no—
127C2×D12—61no—
128C2×D12—61no—
129C2×D12—61no—
130C2×D12—61no—
131C2×D12—121no—
132C2×D12—121no—
133C2×Dic6—21no—
134C2×Dic6—31no—
135C2×Dic6—31no—
136C2×Dic6—61no—
137C2×C3×C8—22no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
140C2×C3×C8—31no—
141C2×C3×C8—31no—
142C2×C3×C8—61no—
143C2×C3×C8—61no—
144C3×C4⋊C4—61no—
145C3×C4⋊C4—61no—
146C3×C42—21no—
147C3×C42C22×D311yescharacteristic
148C3×C42C22×D311yescharacteristic
149#215—122no—
150#215—122no—
151C4⋊Dic3—21no—
152C4⋊Dic3—21no—
153C4⋊Dic3—31no—
154C4⋊Dic3—31no—
155C4⋊Dic3—61no—
156Dic3⋊C4—61no—
157Dic3⋊C4—61no—
158Dic3⋊C4—121no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C4×Dic3—121no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—21no—
164C2×C3⋊C8D1211yescharacteristic
165C2×C3⋊C8D1211yescharacteristic
166#204—122no—
167#204—124no—
168#204—122no—
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×C4C2×SD1611yescharacteristic
177C32×C4AGL(1,ℤ/8)11yescharacteristic
178C32×C4AGL(1,ℤ/8)11yescharacteristic
179C32×C4#13711yescharacteristic
180C3⋊Dic3—41no—
181C3⋊Dic3—41no—
182C3×Dic3—81no—
183C2×SD16—181no—
184C2×SD16—181no—
185C2×SD16—181no—
186C4⋊Q8—31no—
187#127—91no—
188C4×Q8—91no—
189#106—181no—
190C4⋊C8—31no—
191C4⋊C8—31no—
192C4⋊C8—181no—
193C4⋊C8D3211yescharacteristic
194#103—181no—
195#102—181no—
196#97—181no—
197C4×C8—31no—
198C22×D3—122no—
199C22×D3—121no—
200C22×D3—121no—
201C3×Q8—121no—
202C3×Q8—121no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—121no—
207C2×C3×C4C2×D1211yescharacteristic
208C2×C3×C4#23511yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4D3×D411yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×C3×C4#23911yescharacteristic
213C2×Dic3—41no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C2×Dic3—121no—
219C2×Dic3—121no—
220D12—122no—
221D12—122no—
222D12—121no—
223D12—121no—
224D12—121no—
225D12—121no—
226D12—121no—
227D12—121no—
228D12—121no—
229D12—121no—
230D12—241no—
231D12—241no—
232D12—241no—
233D12—241no—
234D12—242no—
235Dic6—41no—
236Dic6—41no—
237Dic6—62no—
238Dic6—61no—
239Dic6—61no—
240Dic6—61no—
241Dic6—61no—
242Dic6—121no—
243C3×C8—32no—
244C3×C8—42no—
245C3×C8—41no—
246C3×C8—41no—
247C3×C8—61no—
248C3×C8—121no—
249C3×C8—121no—
250C3⋊C8—21no—
251C3⋊C8—41no—
252C3⋊C8—41no—
253C3⋊C8#20412yescomplemented
254C2×C32#46011yescharacteristic
255C2×C32#46811yescharacteristic
256C2×C32#47111yescharacteristic
257C3⋊D3—161no—
258C2×Q8—61no—
259C2×Q8—91no—
260C2×D4—181no—
261C2×D4—181no—
262C2×D4—181no—
263SD16—362no—
264SD16—362no—
265SD16—362no—
266C2×C8—21no—
267C2×C8—31no—
268C2×C8—31no—
269C2×C8—61no—
270C2×C8—61no—
271C4⋊C4—61no—
272C4⋊C4—61no—
273C4⋊C4—91no—
274C4⋊C4—181no—
275C42—181no—
276C42C2×D3211yescharacteristic
277C22×C3—21no—
278C22×C3#88411yescharacteristic
279C22×C3#89511yescharacteristic
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—241no—
297C3×C4C2×#20411yescharacteristic
298C3×C4#90811yescharacteristic
299C3×C4#91111yescharacteristic
300C3×C4#91111yescharacteristic
301C3×C4D3×SD1611yescharacteristic
302C3×C4#91411yescharacteristic
303C3×C4#91811yescharacteristic
304C3×C4#91811yescharacteristic
305Dic3—81no—
306Dic3—122no—
307Dic3—121no—
308Dic3—121no—
309Dic3—121no—
310Dic3—121no—
311Dic3—241no—
312C32#168611yescharacteristic, complemented, Sylow
313C23—361no—
314Q8—121no—
315Q8—121no—
316Q8—181no—
317Q8—181no—
318D4—361no—
319D4—361no—
320D4—361no—
321D4—361no—
322D4—721no—
323C2×C4—121no—
324C2×C4—181no—
325C2×C4—181no—
326C2×C4#379911yescharacteristic
327C2×C4D3×D1211yescharacteristic
328C2×C4#381111yescharacteristic
329C8—32no—
330C8—41no—
331C8—61no—
332C8—121no—
333C8—121no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3#475411yescharacteristic
338C2×C3#476211yescharacteristic
339C2×C3#481211yescharacteristic
340C2×C3#484811yescharacteristic
341C2×C3#488611yescharacteristic
342C2×C3#489811yescharacteristic
343D3—482no—
344D3—481no—
345D3—481no—
346C22—721no—
347C22—721no—
348C22—721no—
349C22#6391011yescharacteristic
350C4—21no—
351C4—241no—
352C4—361no—
353C4—361no—
354C4D3×#20411yescharacteristic
355C4#6379511yescharacteristic
356C4#6393711yescharacteristic
357C4#6394511yescharacteristic
358C3—21no—
359C3#6847211yescharacteristic, complemented
360C3#6859211yescharacteristic, complemented
361C2—1441no—
362C2#1059052211yescharacteristic
363C2#1059087911yescharacteristic
364C2#1059099011yescharacteristic
subgroupG/H
centerC22#63910
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
3. #10590307C2semidirect
4. #10590296C2semidirect
5. C3×#4486C2semidirect
6. C3×#4479C2semidirect
36. #4486D3semidirect
39. #4479D3semidirect
115. C3×C3⋊C8SD16semidirect
253. C3⋊C8#204semidirect
312. C32#1686semidirect
359. C3#68472semidirect
360. C3#68592semidirect

Maximal subgroups

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

subgroupindex
#105925472
#105903732
#105903072
#105902962
C3×#44862
C3×#44792
#105890912
#685923
#684723