Finite Group Databasebeta

← #11782921

Subgroups — #11782921

Order 1152.

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

normal subgroups only

This group has 543 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#10592393C211yesmaximal, characteristic, complemented
2C3×#4695C211yesmaximal, characteristic, complemented
3#10590369C211yesmaximal, characteristic, complemented
4#10590350C211yesmaximal, characteristic, complemented
5#10590350C211yesmaximal, characteristic, complemented
6#10590273C211yesmaximal, characteristic, complemented
7C3×#4454C211yesmaximal, characteristic, complemented
8#71279—31nomaximal
9#68094—31nomaximal
10#64083C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×D24—22no—
13C3×#874C2211yescharacteristic
14C3×#874C2211yescharacteristic
15C2×#3716—22no—
16C2×#3714—22no—
17C2×#3714—22no—
18C32×C4×C8C2211yescharacteristic
19#63648—22no—
20C3×C4×C3⋊C8C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22#63563—22no—
23C3×#493—31no—
24#5076—31no—
25#5073—31no—
26#5073—31no—
27#5070—31no—
28#4695—31no—
29#4695—31no—
30#4695D311yescharacteristic, complemented
31#4694—31no—
32#4694—31no—
33#4694—31no—
34#4694—61no—
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×#634—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C32×C8D412yes—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C2×C3×C3⋊C8D412yes—
53C2×C3×C3⋊C8D412yes—
54C3×D24—44no—
55#3716—44no—
56#3714—44no—
57#3714—44no—
58#1721—91noSylow
59C2×C3×D8—62no—
60C3×#127—31no—
61C3×#127—31no—
62C2×#214—62no—
63C2×#213—62no—
64C2×#213—62no—
65C2×D24—22no—
66C2×D24—62no—
67C2×D24—62no—
68C2×#204—62no—
69#874—31no—
70#874—31no—
71#874—61no—
72#874C2×D311yescharacteristic
73#874C2×D311yescharacteristic
74#869—31no—
75#869—31no—
76#869—61no—
77C3×C4×C8—21no—
78C3×C4×C8—31no—
79C3×C4×C8—31no—
80C3×C4×C8C2×D311yescharacteristic
81C3×C4×C8C2×D311yescharacteristic
82#832—62no—
83#821—64no—
84#821—62no—
85#821—62no—
86#821—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
95C2×C3⋊Dic3—41no—
96C4⋊(C3⋊D3)—42no—
97C4⋊(C3⋊D3)—42no—
98C4⋊(C3⋊D3)—42no—
99#634—42no—
100C3×D12—42no—
101C3×D12—42no—
102C3×D12—42no—
103C3×D12—42no—
104C3×D12—42no—
105C3×D12—42no—
106C32×C8—22no—
107C3×C3⋊C8—22no—
108C3×C3⋊C8D814yescomplemented
109#493—31no—
110#493—91no—
111#493—91no—
112#492—91no—
113#486—91no—
114#486—91no—
115#322—31no—
116C2×C3×D4—61no—
117C2×C3×D4—61no—
118C2×C3×D4—61no—
119C2×C3×D4—61no—
120C2×C3×D4—61no—
121C2×C3×D4—61no—
122C2×D12—21no—
123C2×D12—21no—
124C2×D12—21no—
125C2×D12—21no—
126C2×D12—21no—
127C2×D12—21no—
128C2×D12—62no—
129C2×D12—61no—
130C2×D12—61no—
131C2×D12—61no—
132C2×D12—61no—
133C2×D12—61no—
134C2×D12—61no—
135C2×D12—121no—
136C2×D12—121no—
137C2×Dic6—61no—
138C2×Dic6—61no—
139C2×Dic6—121no—
140C3×D8—124no—
141C2×C3×C8—22no—
142C2×C3×C8—32no—
143C2×C3×C8—32no—
144C2×C3×C8D1212yes—
145C2×C3×C8#6712yes—
146C3×C42—21no—
147C3×C42C22×D311yescharacteristic
148C3×C42C22×D311yescharacteristic
149#214—124no—
150#213—124no—
151#213—124no—
152C4⋊Dic3—62no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156C4⋊Dic3—61no—
157C4⋊Dic3—121no—
158C2×C3⋊C8D1212yes—
159C2×C3⋊C8D1212yes—
160D24—44no—
161D24—124no—
162D24—124no—
163#204—124no—
164C22×C32#12711yescharacteristic
165C2×C3⋊D3—81no—
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—
174C32×C4C2×D812yes—
175C32×C4AGL(1,ℤ/8)12yes—
176C32×C4AGL(1,ℤ/8)12yes—
177C3⋊Dic3—81no—
178C2×SD16—182no—
179C2×D8—62no—
180C2×D8—182no—
181C2×D8—182no—
182C4⋊Q8—91no—
183#127—31no—
184#127—31no—
185#127—91no—
186#102—182no—
187#102—182no—
188C4×C8—31no—
189C4×C8—31no—
190C4×C8D3211yescharacteristic
191C23×C3—121no—
192C23×C3—121no—
193C22×D3—41no—
194C22×D3—41no—
195C22×D3—122no—
196C22×D3—121no—
197C22×D3—121no—
198C3×D4—122no—
199C3×D4—122no—
200C3×D4—122no—
201C3×D4—122no—
202C3×D4—122no—
203C3×D4—122no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4C2×D1211yescharacteristic
208C2×C3×C4C2×D1211yescharacteristic
209C2×C3×C4C2×D1211yescharacteristic
210C2×C3×C4D3×D411yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×C3×C4C2×#6711yescharacteristic
213C2×Dic3—122no—
214C2×Dic3—121no—
215C2×Dic3—121no—
216D12—42no—
217D12—42no—
218D12—42no—
219D12—42no—
220D12—42no—
221D12—42no—
222D12—124no—
223D12—122no—
224D12—122no—
225D12—122no—
226D12—122no—
227D12—122no—
228D12—122no—
229D12—242no—
230D12—242no—
231Dic6—122no—
232Dic6—122no—
233Dic6—242no—
234C3×C8—22no—
235C3×C8—22no—
236C3×C8—34no—
237C3×C8—42no—
238C3×C8—62no—
239C3⋊C8—22no—
240C3⋊C8D2414yescomplemented
241C2×C32#49311yescharacteristic
242C2×C32#49611yescharacteristic
243C2×C32#49611yescharacteristic
244C3⋊D3—161no—
245C3×D3—161no—
246C3×D3—161no—
247C2×Q8—181no—
248C2×D4—61no—
249C2×D4—61no—
250C2×D4—61no—
251C2×D4—61no—
252C2×D4—61no—
253C2×D4—61no—
254C2×D4—181no—
255C2×D4—181no—
256C2×D4—181no—
257SD16—364no—
258D8—124no—
259D8—364no—
260D8—364no—
261C2×C8—32no—
262C2×C8—32no—
263C2×C8#62612yes—
264C4⋊C4—181no—
265C4⋊C4—181no—
266C42C2×D3211yescharacteristic
267C22×C3—21no—
268C22×C3—241no—
269C22×C3—241no—
270C22×C3—241no—
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—81no—
280C2×D3—81no—
281C2×D3—81no—
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—
291C3×C4—22no—
292C3×C4—22no—
293C3×C4—22no—
294C3×C4C2×D2412yes—
295C3×C4#90812yes—
296C3×C4#90812yes—
297C3×C4D3×D812yes—
298C3×C4#91112yes—
299C3×C4#93212yes—
300Dic3—242no—
301Dic3—241no—
302Dic3—241no—
303C32#172111yescharacteristic, complemented, Sylow
304C23—121no—
305C23—121no—
306C23—361no—
307Q8—362no—
308D4—122no—
309D4—122no—
310D4—122no—
311D4—122no—
312D4—122no—
313D4—122no—
314D4—362no—
315D4—362no—
316D4—362no—
317C2×C4—361no—
318C2×C4D3×D1211yescharacteristic
319C2×C4D3×D1211yescharacteristic
320C2×C4C2×#62611yescharacteristic
321C8—22no—
322C8—34no—
323C8—62no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—481no—
328C2×C3—481no—
329C2×C3#469511yescharacteristic
330C2×C3#471211yescharacteristic
331C2×C3#471211yescharacteristic
332C2×C3#507411yescharacteristic
333C2×C3#515111yescharacteristic
334C2×C3#515411yescharacteristic
335D3—161no—
336D3—161no—
337D3—482no—
338D3—481no—
339D3—481no—
340C22—241no—
341C22—241no—
342C22—241no—
343C22—241no—
344C22—241no—
345C22—241no—
346C22—721no—
347C22—721no—
348C22—721no—
349C22#6391111yescharacteristic
350C4—721no—
351C4D3×D2412yes—
352C4#6379512yes—
353C4#6383012yes—
354C3—21no—
355C3#6809411yescharacteristic, complemented
356C3#7127911yescharacteristic, complemented
357C2—481no—
358C2—481no—
359C2—1441no—
360C2#1059037111yescharacteristic
361C2#1059088011yescharacteristic
362C2#1059088311yescharacteristic
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. #10592393C2semidirect
2. C3×#4695C2semidirect
3. #10590369C2semidirect
4. #10590350C2semidirect
5. #10590350C2semidirect
6. #10590273C2semidirect
7. C3×#4454C2semidirect
30. #4695D3semidirect
37. #4454D3semidirect
108. C3×C3⋊C8D8semidirect
240. C3⋊C8D24semidirect
303. C32#1721semidirect
355. C3#68094semidirect
356. C3#71279semidirect

Maximal subgroups

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

subgroupindex
#105923932
C3×#46952
#105903692
#105903502
#105902732
C3×#44542
#712793
#680943