Finite Group Databasebeta

← #11780719

Subgroups — #11780719

Order 1152.

389 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 389 conjugacy classes of subgroups — too many to draw. Only its 76 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×C3⋊#564C211yesmaximal, characteristic
2#10592763C211yesmaximal, characteristic
3#10590306C211yesmaximal, characteristic
4#10590295C211yesmaximal, characteristic
5C3×#4543C211yesmaximal, characteristic
6#10589088C211yesmaximal, characteristic
7#10589088C211yesmaximal, characteristic
8#71961—31nomaximal
9#68376—31nomaximal
10C32×#125C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#890—21no—
13C3×#890—21no—
14C3×#889—21no—
15C3×#889—21no—
16C3×#889—21no—
17C3×#889—21no—
18C3×#870C2211yescharacteristic
19C3×#870C2211yescharacteristic
20#63635—21no—
21#63634—21no—
22#63630C2211yescharacteristic
23C3×#803C2211yescharacteristic
24C3×#803C2211yescharacteristic
25#63575—21no—
26#63573—21no—
27#63567—21no—
28#63567—21no—
29C3×#564—31no—
30C3⋊#564D311yescharacteristic
31#5069—31no—
32#5064—31no—
33#5064—31no—
34#5064—31no—
35#5064—61no—
36#4703—31no—
37#4702—31no—
38C3×#330—31no—
39#4543—31no—
40#4543—31no—
41#4543D311yescharacteristic
42#4465—31no—
43#4465—31no—
44C2×#634—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4D411yescharacteristic
48C32×C4⋊C4D411yescharacteristic
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3D411yescharacteristic
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4⋊Dic3D411yescharacteristic
58C3×C4⋊Dic3D411yescharacteristic
59C3×Dic3⋊C4—21no—
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#1663—91noSylow
72C3×#125—21no—
73C3×#125—31no—
74C3×#125—31no—
75C3×#125—61no—
76C3×#125—61no—
77C3×#125—61no—
78C3×#125—61no—
79C3×#125—61no—
80C3×#125—61no—
81C3×#125C2×D311yescharacteristic
82C3×#125C2×D311yescharacteristic
83#890—21no—
84#890—21no—
85#889—21no—
86#889—21no—
87#889—21no—
88#889—21no—
89#870C2×D311yescharacteristic
90#870C2×D311yescharacteristic
91#869—31no—
92#869—31no—
93#869—61no—
94C3×#97—31no—
95C3×#97—31no—
96#818—61no—
97#817—61no—
98#816—61no—
99#816—61no—
100#810—61no—
101#810—61no—
102#808—61no—
103#808—62no—
104#808—61no—
105#808—61no—
106#807—61no—
107#807—62no—
108#807—61no—
109#807—61no—
110#803—31no—
111#803—31no—
112#803—61no—
113#803C2×D311yescharacteristic
114#803C2×D311yescharacteristic
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3—41no—
121#634—42no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C3⋊(C3⋊C8)—22no—
127C3×C3⋊C8—22no—
128C3×C3⋊C8—41no—
129#564—31no—
130#501—91no—
131#501—91no—
132#491—91no—
133#330—31no—
134#330—91no—
135#330—91no—
136C2×Dic6—61no—
137C2×Dic6—61no—
138C2×Dic6—121no—
139C2×C3×C8—61no—
140C2×C3×C8—61no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4—31no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4—31no—
151C3×C4⋊C4—41no—
152C3×C4⋊C4—41no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4D1211yescharacteristic
164C3×C4⋊C4D1211yescharacteristic
165C3×C4⋊C4#6711yescharacteristic
166C3×C4⋊C4#6711yescharacteristic
167C3×C42—21no—
168C3×C42—61no—
169C3×C42—61no—
170C3×C42C22×D311yescharacteristic
171C3×C42C22×D311yescharacteristic
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3—62no—
175C4⋊Dic3—61no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—121no—
180C4⋊Dic3#6711yescharacteristic
181C4⋊Dic3#6711yescharacteristic
182C4⋊Dic3#6711yescharacteristic
183C4⋊Dic3#6711yescharacteristic
184Dic3⋊C4—21no—
185Dic3⋊C4—21no—
186Dic3⋊C4—21no—
187Dic3⋊C4—21no—
188Dic3⋊C4—21no—
189Dic3⋊C4—21no—
190Dic3⋊C4—21no—
191Dic3⋊C4—21no—
192C4×Dic3—21no—
193C4×Dic3—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—62no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—61no—
199C22×C32#12011yescharacteristic
200C32×C4—21no—
201C32×C4—21no—
202C32×C4—21no—
203C32×C4—41no—
204C32×C4—41no—
205C3⋊Dic3—81no—
206C3×Dic3—41no—
207C3×Dic3—41no—
208C3×Dic3—41no—
209C3×Dic3—41no—
210C4⋊Q8—91no—
211#125—31no—
212#125—31no—
213#125—61no—
214#125—61no—
215#125—61no—
216#125—61no—
217#125—61no—
218#125—61no—
219#125D3211yescharacteristic
220#107—181no—
221#107—181no—
222#106—181no—
223#106—181no—
224#103—181no—
225#103—181no—
226#97—31no—
227#97—31no—
228#97—91no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—61no—
239C2×C3×C4—61no—
240C2×C3×C4—61no—
241C2×C3×C4—61no—
242C2×C3×C4C2×D1211yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4C2×#6711yescharacteristic
246C2×C3×C4C2×#6711yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248C2×Dic3—21no—
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—21no—
252C2×Dic3—122no—
253C2×Dic3—121no—
254C2×Dic3—121no—
255Dic6—122no—
256Dic6—122no—
257Dic6—242no—
258C3×C8—62no—
259C3×C8—121no—
260C3⋊C8—22no—
261C3⋊C8—41no—
262C3⋊C8—64no—
263C3⋊C8—62no—
264C3⋊C8—62no—
265C2×C32#45411yescharacteristic
266C2×C32#45611yescharacteristic
267C2×C32#45611yescharacteristic
268C2×Q8—181no—
269C2×C8—61no—
270C2×C8—61no—
271C2×C8—181no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—31no—
275C4⋊C4—31no—
276C4⋊C4—31no—
277C4⋊C4—31no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4—61no—
281C4⋊C4—61no—
282C4⋊C4—61no—
283C4⋊C4—61no—
284C4⋊C4—61no—
285C4⋊C4—61no—
286C4⋊C4—61no—
287C4⋊C4—61no—
288C4⋊C4—181no—
289C4⋊C4—181no—
290C4⋊C4#62611yescharacteristic
291C4⋊C4#62611yescharacteristic
292C42—61no—
293C42—61no—
294C42C2×D3211yescharacteristic
295C22×C3—21no—
296C22×C3#88211yescharacteristic
297C22×C3#95311yescharacteristic
298C3×C4—22no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—41no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—81no—
312C3×C4—81no—
313C3×C4—121no—
314C3×C4—121no—
315C3×C4—121no—
316C3×C4—121no—
317Dic3—41no—
318Dic3—41no—
319Dic3—41no—
320Dic3—41no—
321Dic3—242no—
322Dic3—241no—
323Dic3—241no—
324C32#166311yescharacteristic, complemented, Sylow
325Q8—362no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—61no—
331C2×C4—61no—
332C2×C4—361no—
333C2×C4C2×#62611yescharacteristic
334C2×C4D3×#6711yescharacteristic
335C2×C4D3×#6711yescharacteristic
336C8—62no—
337C8—121no—
338C8—182no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3#475211yescharacteristic
343C2×C3#482611yescharacteristic
344C2×C3#482711yescharacteristic
345C2×C3#524511yescharacteristic
346C2×C3#524611yescharacteristic
347C2×C3#524611yescharacteristic
348C22#6397711yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—121no—
355C4—121no—
356C4—121no—
357C4—121no—
358C4—721no—
359C3—21no—
360C3#6837611yescharacteristic, complemented
361C3#7196111yescharacteristic, complemented
362C2#1059164911yescharacteristic
363C2#1059168511yescharacteristic
364C2#1059168911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#125C22
socle, prime radicalC22×C32#120
hypercenter#125D32
hypocenterC32#1663
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
324. C32#1663semidirect
360. C3#68376semidirect
361. C3#71961semidirect

Maximal subgroups

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

subgroupindex
C3×C3⋊#5642
#105927632
#105903062
#105902952
C3×#45432
#105890882
#719613
#683763