Finite Group Databasebeta

← #11780721

Subgroups — #11780721

Order 1152.

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

normal subgroups only

This group has 374 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
2C3×#5064C211yesmaximal, characteristic
3#10590315C211yesmaximal, characteristic
4#10590291C211yesmaximal, characteristic
5#10589409C211yesmaximal, characteristic
6#10589088C211yesmaximal, characteristic
7#10589088C211yesmaximal, characteristic
8#71961—31nomaximal
9#71393—31nomaximal
10C32×#125C2211yescharacteristic
11C3×#890—21no—
12C3×#890—21no—
13C3×#889—21no—
14C3×#889—21no—
15C3×#889—21no—
16C3×#889—21no—
17C3×#870C2211yescharacteristic
18C3×#870C2211yescharacteristic
19C3×#869C2211yescharacteristic
20#63630C2211yescharacteristic
21#63630C2211yescharacteristic
22C3×#808—21no—
23C3×#807—21no—
24C3×#803C2211yescharacteristic
25#63576—21no—
26#63574—21no—
27#63565—21no—
28#63565—21no—
29C3×#564—31no—
30C3⋊#564D311yescharacteristic
31C3×#501—31no—
32#5082—31no—
33#5081—31no—
34#5069—31no—
35#5064—31no—
36#5064D311yescharacteristic
37#4543—31no—
38#4543—31no—
39#4543—31no—
40#4543—31no—
41#4543—61no—
42#4465—31no—
43#4465—31no—
44C2×C3×Dic6—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4D411yescharacteristic
48C32×C4⋊C4D411yescharacteristic
49C32×C42C2311yescharacteristic
50C2×C3⋊(C3⋊C8)—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4⋊Dic3D411yescharacteristic
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
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×Dic3⋊C4—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71#1663—91noSylow
72C3×C4⋊Q8—31no—
73C3×#125—21no—
74C3×#125—31no—
75C3×#125—31no—
76C3×#125—61no—
77C3×#125—61no—
78C3×#125—61no—
79C3×#125—61no—
80C3×#125—61no—
81C3×#125—61no—
82C3×#125C2×D311yescharacteristic
83C3×#125C2×D311yescharacteristic
84#890—21no—
85#890—21no—
86#889—21no—
87#889—21no—
88#889—21no—
89#889—21no—
90#870C2×D311yescharacteristic
91#870C2×D311yescharacteristic
92#869C2×D311yescharacteristic
93C3×#107—61no—
94C3×#106—61no—
95C3×#97—31no—
96#835—61no—
97#835—61no—
98#810—61no—
99#810—61no—
100#808—21no—
101#808—61no—
102#808—61no—
103#807—21no—
104#807—61no—
105#807—61no—
106#803—31no—
107#803—31no—
108#803—31no—
109#803—31no—
110#803—61no—
111#803—61no—
112#803C2×D311yescharacteristic
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—41no—
123C3×Dic6—42no—
124C3⋊(C3⋊C8)—22no—
125C3⋊(C3⋊C8)—41no—
126C3×C3⋊C8—22no—
127#564—31no—
128#501—31no—
129#501—91no—
130#491—91no—
131#330—91no—
132#330—91no—
133#330—91no—
134C2×C3×Q8—61no—
135C2×Dic6—21no—
136C2×C3×C8—61no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—31no—
144C3×C4⋊C4—31no—
145C3×C4⋊C4—31no—
146C3×C4⋊C4—31no—
147C3×C4⋊C4—41no—
148C3×C4⋊C4—41no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4—61no—
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#6711yescharacteristic
162C3×C4⋊C4#6711yescharacteristic
163C3×C4⋊C4#6711yescharacteristic
164C3×C4⋊C4#6711yescharacteristic
165C3×C42—21no—
166C3×C42—61no—
167C3×C42—61no—
168C3×C42C22×D311yescharacteristic
169C3×C42C22×D311yescharacteristic
170C4⋊Dic3—21no—
171C4⋊Dic3—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3#6711yescharacteristic
175C4⋊Dic3#6711yescharacteristic
176C4⋊Dic3#6711yescharacteristic
177C4⋊Dic3#6711yescharacteristic
178Dic3⋊C4—21no—
179Dic3⋊C4—21no—
180Dic3⋊C4—21no—
181Dic3⋊C4—21no—
182Dic3⋊C4—21no—
183Dic3⋊C4—21no—
184Dic3⋊C4—21no—
185Dic3⋊C4—21no—
186C4×Dic3—21no—
187C4×Dic3—21no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—121no—
194C2×C3⋊C8—121no—
195C22×C32#12011yescharacteristic
196C32×C4—21no—
197C32×C4—21no—
198C32×C4—21no—
199C32×C4—41no—
200C32×C4—41no—
201C3×Dic3—41no—
202C3×Dic3—41no—
203C3×Dic3—41no—
204C3×Dic3—41no—
205C3×Dic3—81no—
206C4⋊Q8—31no—
207#125—31no—
208#125—31no—
209#125—61no—
210#125—61no—
211#125—61no—
212#125—61no—
213#125—61no—
214#125—61no—
215#125D3211yescharacteristic
216#107—61no—
217#107—181no—
218#106—61no—
219#106—181no—
220#103—181no—
221#103—181no—
222#97—31no—
223#97—91no—
224#97—91no—
225C3×Q8—122no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4—61no—
236C2×C3×C4—61no—
237C2×C3×C4—61no—
238C2×C3×C4—61no—
239C2×C3×C4—121no—
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4C2×#6711yescharacteristic
243C2×C3×C4C2×#6711yescharacteristic
244C2×C3×C4C2×#6711yescharacteristic
245C2×C3×C4C2×#6711yescharacteristic
246C2×Dic3—21no—
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—21no—
250C2×Dic3—41no—
251Dic6—42no—
252C3×C8—62no—
253C3⋊C8—22no—
254C3⋊C8—62no—
255C3⋊C8—62no—
256C3⋊C8—122no—
257C3⋊C8—121no—
258C3⋊C8—121no—
259C3⋊C8—122no—
260C2×C32#45411yescharacteristic
261C2×C32#45611yescharacteristic
262C2×C32#45611yescharacteristic
263C2×Q8—61no—
264C2×C8—61no—
265C2×C8—181no—
266C2×C8—181no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—31no—
270C4⋊C4—31no—
271C4⋊C4—31no—
272C4⋊C4—31no—
273C4⋊C4—61no—
274C4⋊C4—61no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4—61no—
281C4⋊C4—61no—
282C4⋊C4—61no—
283C4⋊C4—61no—
284C4⋊C4—61no—
285C4⋊C4#62511yescharacteristic
286C4⋊C4#62511yescharacteristic
287C42—61no—
288C42—61no—
289C42C2×D3211yescharacteristic
290C22×C3—21no—
291C22×C3#93711yescharacteristic
292C22×C3#95311yescharacteristic
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—41no—
300C3×C4—41no—
301C3×C4—41no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4—41no—
305C3×C4—41no—
306C3×C4—81no—
307C3×C4—81no—
308C3×C4—121no—
309C3×C4—121no—
310C3×C4—121no—
311C3×C4—121no—
312C3×C4—241no—
313Dic3—41no—
314Dic3—41no—
315Dic3—41no—
316Dic3—41no—
317Dic3—81no—
318C32#166311yescharacteristic, complemented, Sylow
319Q8—122no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—61no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—121no—
327C2×C4C2×#62511yescharacteristic
328C2×C4D3×#6711yescharacteristic
329C2×C4D3×#6711yescharacteristic
330C8—62no—
331C8—182no—
332C8—361no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3#509511yescharacteristic
337C2×C3#520111yescharacteristic
338C2×C3#520511yescharacteristic
339C2×C3#524511yescharacteristic
340C2×C3#524611yescharacteristic
341C2×C3#524611yescharacteristic
342C22#6397611yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—121no—
349C4—121no—
350C4—121no—
351C4—121no—
352C4—241no—
353C3—21no—
354C3#7139311yescharacteristic, complemented
355C3#7196111yescharacteristic, complemented
356C2#1059164811yescharacteristic
357C2#1059168411yescharacteristic
358C2#1059168711yescharacteristic
subgroupG/H
centerC22#63976
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
318. C32#1663semidirect
354. C3#71393semidirect
355. 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
C3×#50642
#105903152
#105902912
#105894092
#105890882
#719613
#713933