Finite Group Databasebeta

← #11780725

Subgroups — #11780725

Order 1152.

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

normal subgroups only

This group has 389 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
2#10592401C211yesmaximal, characteristic
3#10590306C211yesmaximal, characteristic
4#10590295C211yesmaximal, characteristic
5C3×#4465C211yesmaximal, characteristic
6C3×#4465C211yesmaximal, characteristic
7#10589089C211yesmaximal, characteristic
8#68377—31nomaximal
9#68376—31nomaximal
10#64079C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#870C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63847—21no—
15#63847—21no—
16#63846—21no—
17#63846—21no—
18#63845—21no—
19#63845—21no—
20C32×#97C2211yescharacteristic
21#63645—21no—
22#63644—21no—
23C3×#803C2211yescharacteristic
24C3×#803C2211yescharacteristic
25#63575—21no—
26#63573—21no—
27#63567—21no—
28#63567—21no—
29C3⋊#564—31no—
30C3⋊#564—31no—
31#5069—31no—
32#5064—31no—
33#4703—31no—
34#4702—31no—
35#4702—31no—
36#4702—31no—
37#4702—61no—
38C3×#330—31no—
39C3×#330—31no—
40#4465—31no—
41#4465—31no—
42#4465D311yescharacteristic
43#4465D311yescharacteristic
44C2×#634—21no—
45C2×C32×C8—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)D411yescharacteristic
50C4⋊(C3⋊Dic3)D411yescharacteristic
51#3750—21no—
52#3750—21no—
53C3×C4⋊Dic3D411yescharacteristic
54C3×C4⋊Dic3D411yescharacteristic
55C3×C4⋊Dic3D411yescharacteristic
56C3×C4⋊Dic3D411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×Dic3⋊C4—21no—
61C2×C3×C3⋊C8—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×#125—31no—
73C3×#125—31no—
74#890—61no—
75#890—61no—
76#890—61no—
77#890—61no—
78#889—61no—
79#889—61no—
80#889—61no—
81#889—61no—
82#889—61no—
83#889—61no—
84#889—61no—
85#889—61no—
86#870—31no—
87#870—31no—
88#870—61no—
89#870C2×D311yescharacteristic
90#870C2×D311yescharacteristic
91#869—31no—
92#869—31no—
93#869—61no—
94C3×#97—21no—
95C3×#97—31no—
96C3×#97—31no—
97C3×#97C2×D311yescharacteristic
98C3×#97C2×D311yescharacteristic
99#818—61no—
100#818—61no—
101#818—62no—
102#818—61no—
103#817—61no—
104#817—61no—
105#817—62no—
106#817—61no—
107#816—61no—
108#816—61no—
109#810—61no—
110#810—61no—
111#808—61no—
112#807—61no—
113#803C2×D311yescharacteristic
114#803C2×D311yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—41no—
121#634—42no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C32×C8—22no—
127C3×C3⋊C8—22no—
128C3×C3⋊C8—41no—
129#564—91no—
130#501—91no—
131#501—91no—
132#491—91no—
133#330—31no—
134#330—31no—
135#330—91no—
136C2×Dic6—61no—
137C2×Dic6—61no—
138C2×Dic6—121no—
139C2×C3×C8—22no—
140C2×C3×C8—21no—
141C2×C3×C8—21no—
142C2×C3×C8—61no—
143C2×C3×C8—61no—
144C3×C4⋊C4—31no—
145C3×C4⋊C4—31no—
146C3×C4⋊C4—31no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—61no—
152C3×C42—21no—
153C3×C42C22×D311yescharacteristic
154C3×C42C22×D311yescharacteristic
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⋊Dic3—62no—
166C4⋊Dic3—61no—
167C4⋊Dic3—61no—
168C4⋊Dic3—61no—
169C4⋊Dic3—61no—
170C4⋊Dic3—121no—
171C4⋊Dic3D1211yescharacteristic
172C4⋊Dic3D1211yescharacteristic
173C4⋊Dic3D1211yescharacteristic
174C4⋊Dic3D1211yescharacteristic
175Dic3⋊C4—21no—
176Dic3⋊C4—21no—
177Dic3⋊C4—21no—
178Dic3⋊C4—21no—
179Dic3⋊C4—61no—
180Dic3⋊C4—61no—
181Dic3⋊C4—61no—
182Dic3⋊C4—61no—
183Dic3⋊C4—61no—
184Dic3⋊C4—61no—
185Dic3⋊C4—61no—
186Dic3⋊C4—61no—
187Dic3⋊C4—61no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—61no—
191Dic3⋊C4—121no—
192Dic3⋊C4—121no—
193C4×Dic3—61no—
194C4×Dic3—61no—
195C4×Dic3—61no—
196C4×Dic3—61no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C22×C32#12011yescharacteristic
200C32×C4—21no—
201C32×C4—21no—
202C32×C4—21no—
203C3⋊Dic3—41no—
204C3⋊Dic3—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—91no—
214#125—181no—
215#125—181no—
216#125—181no—
217#125—181no—
218#125—181no—
219#125—181no—
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#97D3211yescharacteristic
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—61no—
233C2×C3×C4—61no—
234C2×C3×C4—61no—
235C2×C3×C4—61no—
236C2×C3×C4C2×D1211yescharacteristic
237C2×C3×C4C2×D1211yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×Dic3—21no—
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—21no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—61no—
250C2×Dic3—121no—
251C2×Dic3—121no—
252C2×Dic3—122no—
253C2×Dic3—121no—
254C2×Dic3—121no—
255Dic6—122no—
256Dic6—122no—
257Dic6—242no—
258C3×C8—24no—
259C3×C8—22no—
260C3×C8—22no—
261C3×C8—62no—
262C3×C8—121no—
263C3⋊C8—22no—
264C3⋊C8—41no—
265C2×C32#45411yescharacteristic
266C2×C32#45611yescharacteristic
267C2×C32#45611yescharacteristic
268C2×Q8—181no—
269C2×C8—21no—
270C2×C8—61no—
271C2×C8—61no—
272C4⋊C4—31no—
273C4⋊C4—31no—
274C4⋊C4—31no—
275C4⋊C4—31no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4—91no—
281C4⋊C4—91no—
282C4⋊C4—181no—
283C4⋊C4—181no—
284C4⋊C4—181no—
285C4⋊C4—181no—
286C4⋊C4—181no—
287C4⋊C4—181no—
288C4⋊C4—181no—
289C4⋊C4—181no—
290C4⋊C4—181no—
291C4⋊C4—181no—
292C42—181no—
293C42—181no—
294C42C2×D3211yescharacteristic
295C22×C3—21no—
296C22×C3#88211yescharacteristic
297C22×C3#88211yescharacteristic
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—121no—
308C3×C4—121no—
309C3×C4—121no—
310C3×C4—121no—
311Dic3—41no—
312Dic3—41no—
313Dic3—41no—
314Dic3—41no—
315Dic3—121no—
316Dic3—121no—
317Dic3—121no—
318Dic3—121no—
319Dic3—241no—
320Dic3—241no—
321Dic3—242no—
322Dic3—241no—
323Dic3—241no—
324C32#166311yescharacteristic, complemented, Sylow
325Q8—362no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—181no—
331C2×C4—181no—
332C2×C4—361no—
333C2×C4D3×D1211yescharacteristic
334C2×C4D3×D1211yescharacteristic
335C2×C4#381111yescharacteristic
336C8—22no—
337C8—62no—
338C8—121no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3#475211yescharacteristic
343C2×C3#475311yescharacteristic
344C2×C3#482611yescharacteristic
345C2×C3#482611yescharacteristic
346C2×C3#482611yescharacteristic
347C2×C3#482711yescharacteristic
348C22#6392311yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—121no—
353C4—121no—
354C4—121no—
355C4—121no—
356C4—361no—
357C4—361no—
358C4—721no—
359C3—21no—
360C3#6837611yescharacteristic, complemented
361C3#6837711yescharacteristic, complemented
362C2#1059040111yescharacteristic
363C2#1059102111yescharacteristic
364C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
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
324. C32#1663semidirect
360. C3#68376semidirect
361. C3#68377semidirect

Maximal subgroups

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

subgroupindex
#105938682
#105924012
#105903062
#105902952
C3×#44652
#105890892
#683773
#683763