Finite Group Databasebeta

← #11782919

Subgroups — #11782919

Order 1152.

565 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 565 conjugacy classes of subgroups — too many to draw. Only its 108 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#10592394C211yesmaximal, characteristic, complemented
2C3×#4694C211yesmaximal, characteristic, complemented
3#10590373C211yesmaximal, characteristic, complemented
4#10590350C211yesmaximal, characteristic, complemented
5#10590350C211yesmaximal, characteristic, complemented
6#10590281C211yesmaximal, characteristic, complemented
7C3×#4454C211yesmaximal, characteristic, complemented
8#71194—31nomaximal
9#68094—31nomaximal
10C2×#3745—22no—
11#64083C2211yescharacteristic
12#64083C2211yescharacteristic
13C3×#874C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C2×#3717—22no—
16C2×#3714—22no—
17C2×#3714—22no—
18C32×C4×C8C2211yescharacteristic
19C3×#821—22no—
20C3×C4×C3⋊C8C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22#63564—22no—
23C3×#486—31no—
24#5088—31no—
25#5085—31no—
26#5073—31no—
27#5073—31no—
28#4695—31no—
29#4695—31no—
30#4695—31no—
31#4695—31no—
32#4695—61no—
33#4694—31no—
34#4694D311yescharacteristic, complemented
35#4693—31no—
36C3×#322—31no—
37#4454D311yescharacteristic, complemented
38C2×C4⋊(C3⋊D3)—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×Dic6—21no—
48C2×C32×C8D412yes—
49C32×C42C2311yescharacteristic
50#3745—44no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8D412yes—
54C2×C3×C3⋊C8D412yes—
55#3717—44no—
56#3714—44no—
57#3714—44no—
58#1721—91noSylow
59C3×C4⋊Q8—31no—
60C3×#127—31no—
61C2×#215—62no—
62C2×#213—62no—
63C2×#213—62no—
64C2×D24—64no—
65C2×D24—62no—
66C2×D24—62no—
67C2×D24—62no—
68C2×D24—62no—
69C2×#204—62no—
70#874—31no—
71#874—31no—
72#874—31no—
73#874—31no—
74#874—61no—
75#874—61no—
76#874C2×D311yescharacteristic
77#869C2×D311yescharacteristic
78C3×#102—62no—
79C3×C4×C8—21no—
80C3×C4×C8—31no—
81C3×C4×C8—31no—
82C3×C4×C8C2×D311yescharacteristic
83C3×C4×C8C2×D311yescharacteristic
84#821—22no—
85#821—62no—
86#809—62no—
87C4×C3⋊C8C2×D311yescharacteristic
88C4×C3⋊C8C2×D311yescharacteristic
89C22×C3⋊D3—41no—
90C22×C3⋊D3—41no—
91C22×C3×D3—41no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C4⋊(C3⋊D3)—42no—
96C4⋊(C3⋊D3)—42no—
97C4⋊(C3⋊D3)—42no—
98C4⋊(C3⋊D3)—42no—
99C4⋊(C3⋊D3)—42no—
100C4⋊(C3⋊D3)—42no—
101C2×C3×Dic3—41no—
102C3×D12—42no—
103C3×D12—42no—
104C3×D12—42no—
105C3×Dic6—42no—
106C32×C8—22no—
107C3×C3⋊C8—22no—
108C3×C3⋊C8D814yescomplemented
109#493—91no—
110#493—91no—
111#493—91no—
112#492—91no—
113#486—31no—
114#486—91no—
115#322—31no—
116C2×C3×Q8—61no—
117C2×C3×D4—61no—
118C2×C3×D4—61no—
119C2×C3×D4—61no—
120C2×D12—21no—
121C2×D12—21no—
122C2×D12—21no—
123C2×D12—62no—
124C2×D12—62no—
125C2×D12—61no—
126C2×D12—61no—
127C2×D12—61no—
128C2×D12—61no—
129C2×D12—61no—
130C2×D12—61no—
131C2×D12—61no—
132C2×D12—61no—
133C2×D12—61no—
134C2×D12—61no—
135C2×D12—61no—
136C2×D12—61no—
137C2×D12—121no—
138C2×D12—121no—
139C2×D12—121no—
140C2×D12—121no—
141C2×Dic6—21no—
142C2×C3×C8—22no—
143C2×C3×C8—32no—
144C2×C3×C8—32no—
145C2×C3×C8D1212yes—
146C2×C3×C8#6712yes—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C42—21no—
150C3×C42C22×D311yescharacteristic
151C3×C42C22×D311yescharacteristic
152#215—124no—
153#213—124no—
154#213—124no—
155C4⋊Dic3—21no—
156C4⋊Dic3—21no—
157C2×C3⋊C8D1212yes—
158C2×C3⋊C8D1212yes—
159D24—128no—
160D24—124no—
161D24—124no—
162D24—124no—
163D24—124no—
164#204—124no—
165C22×C32#12711yescharacteristic
166C2×C3⋊D3—81no—
167C2×C3⋊D3—81no—
168C2×C3⋊D3—81no—
169C2×C3⋊D3—81no—
170C2×C3⋊D3—81no—
171C2×C3⋊D3—81no—
172C2×C3×D3—81no—
173C2×C3×D3—81no—
174C2×C3×D3—81no—
175C32×C4C2×D812yes—
176C32×C4AGL(1,ℤ/8)12yes—
177C32×C4AGL(1,ℤ/8)12yes—
178C3×Dic3—81no—
179C2×SD16—182no—
180C2×D8—182no—
181C2×D8—182no—
182C2×D8—182no—
183C4⋊Q8—31no—
184#127—31no—
185#127—91no—
186#127—91no—
187#102—62no—
188#102—182no—
189C4×C8—31no—
190C4×C8—31no—
191C4×C8D3211yescharacteristic
192C23×C3—121no—
193C22×D3—41no—
194C22×D3—122no—
195C22×D3—122no—
196C22×D3—121no—
197C22×D3—121no—
198C22×D3—121no—
199C22×D3—121no—
200C3×Q8—122no—
201C3×D4—122no—
202C3×D4—122no—
203C3×D4—122no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—121no—
208C2×C3×C4C2×D1211yescharacteristic
209C2×C3×C4C2×D1211yescharacteristic
210C2×C3×C4C2×D1211yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×C3×C4D3×D411yescharacteristic
213C2×C3×C4C2×#6711yescharacteristic
214C2×Dic3—41no—
215D12—42no—
216D12—42no—
217D12—42no—
218D12—124no—
219D12—124no—
220D12—122no—
221D12—122no—
222D12—122no—
223D12—122no—
224D12—122no—
225D12—122no—
226D12—122no—
227D12—122no—
228D12—122no—
229D12—122no—
230D12—122no—
231D12—122no—
232D12—242no—
233D12—242no—
234D12—242no—
235D12—242no—
236Dic6—42no—
237C3×C8—24no—
238C3×C8—22no—
239C3×C8—22no—
240C3×C8—34no—
241C3×C8—62no—
242C3⋊C8—22no—
243C3⋊C8D2414yescomplemented
244C2×C32#49311yescharacteristic
245C2×C32#49611yescharacteristic
246C2×C32#49611yescharacteristic
247C3⋊D3—161no—
248C3⋊D3—161no—
249C3×D3—161no—
250C2×Q8—61no—
251C2×D4—61no—
252C2×D4—61no—
253C2×D4—61no—
254C2×D4—181no—
255C2×D4—181no—
256C2×D4—181no—
257C2×D4—181no—
258C2×D4—181no—
259C2×D4—181no—
260SD16—364no—
261D8—364no—
262D8—364no—
263D8—364no—
264C2×C8—32no—
265C2×C8—32no—
266C2×C8#62612yes—
267C4⋊C4—61no—
268C4⋊C4—61no—
269C42C2×D3211yescharacteristic
270C22×C3—21no—
271C22×C3—241no—
272C22×C3—241no—
273C22×C3—241no—
274C22×C3#87411yescharacteristic
275C22×C3#94011yescharacteristic
276C2×D3—81no—
277C2×D3—81no—
278C2×D3—81no—
279C2×D3—242no—
280C2×D3—242no—
281C2×D3—242no—
282C2×D3—242no—
283C2×D3—242no—
284C2×D3—242no—
285C2×D3—241no—
286C2×D3—241no—
287C2×D3—241no—
288C2×D3—241no—
289C2×D3—241no—
290C2×D3—241no—
291C2×D3—241no—
292C2×D3—241no—
293C2×D3—241no—
294C2×D3—241no—
295C2×D3—241no—
296C2×D3—241no—
297C3×C4—22no—
298C3×C4—22no—
299C3×C4—22no—
300C3×C4—241no—
301C3×C4C2×D2412yes—
302C3×C4#90812yes—
303C3×C4#90812yes—
304C3×C4D3×D812yes—
305C3×C4#91412yes—
306C3×C4#94912yes—
307Dic3—81no—
308C32#172111yescharacteristic, complemented, Sylow
309C23—121no—
310C23—361no—
311C23—361no—
312Q8—122no—
313D4—122no—
314D4—122no—
315D4—122no—
316D4—362no—
317D4—362no—
318D4—362no—
319D4—362no—
320D4—362no—
321D4—362no—
322C2×C4—121no—
323C2×C4D3×D1211yescharacteristic
324C2×C4D3×D1211yescharacteristic
325C2×C4C2×#62611yescharacteristic
326C8—22no—
327C8—34no—
328C8—62no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—481no—
333C2×C3#469511yescharacteristic
334C2×C3#471211yescharacteristic
335C2×C3#471211yescharacteristic
336C2×C3#505811yescharacteristic
337C2×C3#515111yescharacteristic
338C2×C3#517611yescharacteristic
339D3—161no—
340D3—482no—
341D3—482no—
342D3—481no—
343D3—481no—
344D3—481no—
345D3—481no—
346C22—241no—
347C22—241no—
348C22—241no—
349C22—721no—
350C22—721no—
351C22—721no—
352C22—721no—
353C22—721no—
354C22—721no—
355C22#6391111yescharacteristic
356C4—241no—
357C4D3×D2412yes—
358C4#6379412yes—
359C4#6382512yes—
360C3—21no—
361C3#6809411yescharacteristic, complemented
362C3#7119411yescharacteristic, complemented
363C2—481no—
364C2—1441no—
365C2—1441no—
366C2#1059035111yescharacteristic
367C2#1059088011yescharacteristic
368C2#1059088111yescharacteristic
subgroupG/H
centerC22#63911
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#127
hypercenterC4×C8D32
hypocenterC32#1721
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. #10592394C2semidirect
2. C3×#4694C2semidirect
3. #10590373C2semidirect
4. #10590350C2semidirect
5. #10590350C2semidirect
6. #10590281C2semidirect
7. C3×#4454C2semidirect
34. #4694D3semidirect
37. #4454D3semidirect
108. C3×C3⋊C8D8semidirect
243. C3⋊C8D24semidirect
308. C32#1721semidirect
361. C3#68094semidirect
362. C3#71194semidirect

Maximal subgroups

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

subgroupindex
#105923942
C3×#46942
#105903732
#105903502
#105902812
C3×#44542
#711943
#680943