Finite Group Databasebeta

← #11780723

Subgroups — #11780723

Order 1152.

374 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 70 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#10593868C211yesmaximal, characteristic
2C3×#4703C211yesmaximal, characteristic
3#10590315C211yesmaximal, characteristic
4#10590305C211yesmaximal, characteristic
5#10589331C211yesmaximal, characteristic
6C3×#4465C211yesmaximal, characteristic
7#10589088C211yesmaximal, characteristic
8#71252—31nomaximal
9#68376—31nomaximal
10#64079C2211yescharacteristic
11C3×#870C2211yescharacteristic
12C3×#870C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63847—21no—
15#63847—21no—
16#63846—21no—
17#63846—21no—
18#63845—21no—
19#63845—21no—
20C32×#97C2211yescharacteristic
21#63630C2211yescharacteristic
22C3×#816—21no—
23C3×#816—21no—
24C3×#803C2211yescharacteristic
25#63576—21no—
26#63575—21no—
27#63574—21no—
28#63573—21no—
29C3⋊#564—31no—
30C3⋊#564—31no—
31C3×#491—31no—
32#5081—31no—
33#5081—31no—
34#5064—31no—
35#4703D311yescharacteristic
36#4702—31no—
37C3×#330—31no—
38#4543—31no—
39#4465—31no—
40#4465—31no—
41#4465—31no—
42#4465—61no—
43#4465D311yescharacteristic
44C2×C3×Dic6—21no—
45C2×C32×C8—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)D411yescharacteristic
48C4⋊(C3⋊Dic3)D411yescharacteristic
49#3750—21no—
50#3750—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C3×C4⋊Dic3D411yescharacteristic
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C2×C3×C3⋊C8—21no—
63#3724—21no—
64#3724—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic32—21no—
70Dic32—21no—
71#1663—91noSylow
72C3×C4⋊Q8—31no—
73C3×#125—31no—
74C3×#125—31no—
75#890—61no—
76#890—61no—
77#890—61no—
78#890—61no—
79#889—61no—
80#889—61no—
81#889—61no—
82#889—61no—
83#889—61no—
84#889—61no—
85#889—61no—
86#889—61no—
87#870—31no—
88#870—31no—
89#870—61no—
90#870C2×D311yescharacteristic
91#870C2×D311yescharacteristic
92#869C2×D311yescharacteristic
93C3×#103—61no—
94C3×#103—61no—
95C3×#97—21no—
96C3×#97—31no—
97C3×#97C2×D311yescharacteristic
98C3×#97C2×D311yescharacteristic
99#818—61no—
100#817—61no—
101#816—21no—
102#816—21no—
103#808—61no—
104#808—61no—
105#808—61no—
106#807—61no—
107#807—61no—
108#807—61no—
109#803—31no—
110#803—31no—
111#803—61no—
112#803C2×D311yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—21no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—41no—
123C3×Dic6—42no—
124C32×C8—41no—
125C3⋊(C3⋊C8)—22no—
126C3×C3⋊C8—22no—
127#564—91no—
128#501—91no—
129#501—91no—
130#491—31no—
131#330—31no—
132#330—91no—
133#330—91no—
134C2×C3×Q8—61no—
135C2×Dic6—21no—
136C2×C3×C8—21no—
137C2×C3×C8—21no—
138C2×C3×C8—41no—
139C2×C3×C8—61no—
140C3×C4⋊C4—31no—
141C3×C4⋊C4—31no—
142C3×C4⋊C4—31no—
143C3×C4⋊C4—31no—
144C3×C4⋊C4—61no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
150C3×C42—21no—
151C3×C42C22×D311yescharacteristic
152C3×C42C22×D311yescharacteristic
153C4⋊Dic3—21no—
154C4⋊Dic3—21no—
155C4⋊Dic3—31no—
156C4⋊Dic3—31no—
157C4⋊Dic3—31no—
158C4⋊Dic3—31no—
159C4⋊Dic3—61no—
160C4⋊Dic3—61no—
161C4⋊Dic3—61no—
162C4⋊Dic3—61no—
163C4⋊Dic3—61no—
164C4⋊Dic3—61no—
165C4⋊Dic3D1211yescharacteristic
166C4⋊Dic3D1211yescharacteristic
167C4⋊Dic3#6711yescharacteristic
168C4⋊Dic3#6711yescharacteristic
169Dic3⋊C4—21no—
170Dic3⋊C4—21no—
171Dic3⋊C4—21no—
172Dic3⋊C4—21no—
173Dic3⋊C4—61no—
174Dic3⋊C4—61no—
175Dic3⋊C4—61no—
176Dic3⋊C4—61no—
177Dic3⋊C4—61no—
178Dic3⋊C4—61no—
179Dic3⋊C4—61no—
180Dic3⋊C4—61no—
181Dic3⋊C4—61no—
182Dic3⋊C4—61no—
183Dic3⋊C4—61no—
184Dic3⋊C4—61no—
185Dic3⋊C4—121no—
186Dic3⋊C4—121no—
187C4×Dic3—61no—
188C4×Dic3—61no—
189C4×Dic3—61no—
190C4×Dic3—61no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—121no—
195C22×C32#12011yescharacteristic
196C32×C4—21no—
197C32×C4—21no—
198C32×C4—21no—
199C3⋊Dic3—41no—
200C3⋊Dic3—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—91no—
210#125—181no—
211#125—181no—
212#125—181no—
213#125—181no—
214#125—181no—
215#125—181no—
216#107—181no—
217#107—181no—
218#106—181no—
219#106—181no—
220#103—61no—
221#103—61no—
222#97—31no—
223#97—91no—
224#97D3211yescharacteristic
225C3×Q8—122no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4—61no—
233C2×C3×C4—121no—
234C2×C3×C4C2×D1211yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4C2×#6711yescharacteristic
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—21no—
243C2×Dic3—21no—
244C2×Dic3—41no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—121no—
250C2×Dic3—121no—
251Dic6—42no—
252C3×C8—41no—
253C3×C8—41no—
254C3×C8—42no—
255C3×C8—62no—
256C3⋊C8—22no—
257C3⋊C8—62no—
258C3⋊C8—62no—
259C3⋊C8—122no—
260C2×C32#45411yescharacteristic
261C2×C32#45611yescharacteristic
262C2×C32#45611yescharacteristic
263C2×Q8—61no—
264C2×C8—21no—
265C2×C8—61no—
266C2×C8—181no—
267C4⋊C4—31no—
268C4⋊C4—31no—
269C4⋊C4—31no—
270C4⋊C4—31no—
271C4⋊C4—61no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—61no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4—91no—
278C4⋊C4—91no—
279C4⋊C4—181no—
280C4⋊C4—181no—
281C4⋊C4—181no—
282C4⋊C4—181no—
283C4⋊C4—181no—
284C4⋊C4—181no—
285C4⋊C4—181no—
286C4⋊C4—181no—
287C42—181no—
288C42—181no—
289C42C2×D3211yescharacteristic
290C22×C3—21no—
291C22×C3#88211yescharacteristic
292C22×C3#93711yescharacteristic
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—121no—
303C3×C4—121no—
304C3×C4—121no—
305C3×C4—121no—
306C3×C4—241no—
307Dic3—41no—
308Dic3—41no—
309Dic3—41no—
310Dic3—41no—
311Dic3—81no—
312Dic3—121no—
313Dic3—121no—
314Dic3—121no—
315Dic3—121no—
316Dic3—241no—
317Dic3—241no—
318C32#166311yescharacteristic, complemented, Sylow
319Q8—122no—
320C2×C4—61no—
321C2×C4—61no—
322C2×C4—61no—
323C2×C4—61no—
324C2×C4—121no—
325C2×C4—181no—
326C2×C4—181no—
327C2×C4D3×D1211yescharacteristic
328C2×C4#380211yescharacteristic
329C2×C4D3×#6711yescharacteristic
330C8—41no—
331C8—62no—
332C8—182no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3#475211yescharacteristic
337C2×C3#482611yescharacteristic
338C2×C3#482711yescharacteristic
339C2×C3#506211yescharacteristic
340C2×C3#520511yescharacteristic
341C2×C3#520511yescharacteristic
342C22#6392211yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—121no—
347C4—121no—
348C4—121no—
349C4—121no—
350C4—241no—
351C4—361no—
352C4—361no—
353C3—21no—
354C3#6837611yescharacteristic, complemented
355C3#7125211yescharacteristic, complemented
356C2#1059040011yescharacteristic
357C2#1059101711yescharacteristic
358C2#1059101811yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socle, prime radicalC22×C32#120
hypercenter#97D32
hypocenterC32#1663
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
318. C32#1663semidirect
354. C3#68376semidirect
355. C3#71252semidirect

Maximal subgroups

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

subgroupindex
#105938682
C3×#47032
#105903152
#105903052
#105893312
C3×#44652
#105890882
#712523
#683763