Finite Group Databasebeta

← #11780720

Subgroups — #11780720

Order 1152.

430 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 72 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#10596157C211yesmaximal, characteristic
2C3×#5064C211yesmaximal, characteristic
3#10590305C211yesmaximal, characteristic
4#10590289C211yesmaximal, characteristic
5C3×#4543C211yesmaximal, characteristic
6#10589089C211yesmaximal, characteristic
7#10589089C211yesmaximal, characteristic
8#71393—31nomaximal
9#68376—31nomaximal
10C32×#125C2211yescharacteristic
11#64099—21no—
12#64099—21no—
13#64098—21no—
14#64098—21no—
15#64098—21no—
16#64098—21no—
17#64079C2211yescharacteristic
18#64079C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×#808—21no—
21C3×#807—21no—
22C3×#803C2211yescharacteristic
23C3×#803C2211yescharacteristic
24C3×#803C2211yescharacteristic
25#63575—21no—
26#63573—21no—
27#63566—21no—
28#63566—21no—
29C3⋊#564—31no—
30C3⋊#564—31no—
31C3⋊#564—61no—
32C3×#501—31no—
33#5082—31no—
34#5081—31no—
35#5064D311yescharacteristic
36#4703—31no—
37#4702—31no—
38C3×#330—31no—
39#4543D311yescharacteristic
40#4465—31no—
41#4465—31no—
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
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)D411yescharacteristic
53C4⋊(C3⋊Dic3)D411yescharacteristic
54C4⋊(C3⋊Dic3)D411yescharacteristic
55C4⋊(C3⋊Dic3)D411yescharacteristic
56#3750—21no—
57#3750—21no—
58#3750—21no—
59#3750—21no—
60#3750—21no—
61#3750—21no—
62#3750—21no—
63#3750—21no—
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#1663—91noSylow
72C3×C4⋊Q8—31no—
73C3×#125—21no—
74C3×#125C2×D311yescharacteristic
75C3×#125C2×D311yescharacteristic
76#890—61no—
77#890—61no—
78#890—61no—
79#890—61no—
80#890—62no—
81#890—62no—
82#889—61no—
83#889—61no—
84#889—61no—
85#889—61no—
86#889—62no—
87#889—62no—
88#889—62no—
89#889—62no—
90#889—61no—
91#889—61no—
92#889—61no—
93#889—61no—
94#870—31no—
95#870—31no—
96#870—31no—
97#870—31no—
98#870—61no—
99#870—61no—
100#869C2×D311yescharacteristic
101C3×#107—61no—
102C3×#106—61no—
103C3×#97—31no—
104C3×#97—31no—
105C3×#97—31no—
106#835—61no—
107#835—61no—
108#818—61no—
109#817—61no—
110#816—61no—
111#816—61no—
112#808—21no—
113#808—61no—
114#807—21no—
115#807—61no—
116#803C2×D311yescharacteristic
117#803C2×D311yescharacteristic
118#803C2×D311yescharacteristic
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3×Dic3—41no—
129C3×Dic6—42no—
130C3×C3⋊C8—22no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—41no—
133#564—91no—
134#501—31no—
135#501—91no—
136#491—91no—
137#330—31no—
138#330—91no—
139#330—91no—
140C2×C3×Q8—61no—
141C2×Dic6—21no—
142C2×C3×C8—61no—
143C2×C3×C8—61no—
144C2×C3×C8—61no—
145C3×C4⋊C4—22no—
146C3×C4⋊C4—22no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4D1211yescharacteristic
156C3×C4⋊C4D1211yescharacteristic
157C3×C4⋊C4#6711yescharacteristic
158C3×C4⋊C4#6711yescharacteristic
159C3×C42—21no—
160C3×C42C22×D311yescharacteristic
161C3×C42C22×D311yescharacteristic
162C4⋊Dic3—21no—
163C4⋊Dic3—21no—
164C4⋊Dic3—31no—
165C4⋊Dic3—31no—
166C4⋊Dic3—31no—
167C4⋊Dic3—31no—
168C4⋊Dic3—31no—
169C4⋊Dic3—31no—
170C4⋊Dic3—31no—
171C4⋊Dic3—31no—
172C4⋊Dic3—61no—
173C4⋊Dic3—61no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—62no—
177C4⋊Dic3—62no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182Dic3⋊C4—62no—
183Dic3⋊C4—62no—
184Dic3⋊C4—62no—
185Dic3⋊C4—62no—
186Dic3⋊C4—62no—
187Dic3⋊C4—62no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—61no—
191Dic3⋊C4—61no—
192Dic3⋊C4—62no—
193Dic3⋊C4—62no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206C4×Dic3—62no—
207C4×Dic3—62no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—21no—
214C2×C3⋊C8—21no—
215C22×C32#12011yescharacteristic
216C32×C4—21no—
217C32×C4—21no—
218C32×C4—21no—
219C32×C4—41no—
220C32×C4—41no—
221C3⋊Dic3—41no—
222C3⋊Dic3—41no—
223C3⋊Dic3—41no—
224C3⋊Dic3—41no—
225C3×Dic3—81no—
226C4⋊Q8—31no—
227#125—91no—
228#125—91no—
229#125—181no—
230#125—181no—
231#125—181no—
232#125—181no—
233#125—181no—
234#125—181no—
235#125D3211yescharacteristic
236#107—61no—
237#107—181no—
238#106—61no—
239#106—181no—
240#103—181no—
241#103—181no—
242#97—31no—
243#97—31no—
244#97—31no—
245C3×Q8—122no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—121no—
256C2×C3×C4C2×D1211yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4D3×D411yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4C2×#6711yescharacteristic
262C2×Dic3—41no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275Dic6—42no—
276C3×C8—62no—
277C3×C8—62no—
278C3×C8—121no—
279C3⋊C8—22no—
280C3⋊C8—22no—
281C3⋊C8—41no—
282C2×C32#45411yescharacteristic
283C2×C32#45611yescharacteristic
284C2×C32#45611yescharacteristic
285C2×Q8—61no—
286C2×C8—61no—
287C2×C8—61no—
288C2×C8—61no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—61no—
292C4⋊C4—61no—
293C4⋊C4—91no—
294C4⋊C4—91no—
295C4⋊C4—91no—
296C4⋊C4—91no—
297C4⋊C4—181no—
298C4⋊C4—181no—
299C4⋊C4—181no—
300C4⋊C4—181no—
301C4⋊C4—181no—
302C4⋊C4—181no—
303C4⋊C4—181no—
304C4⋊C4—181no—
305C4⋊C4—181no—
306C4⋊C4—181no—
307C4⋊C4#62611yescharacteristic
308C4⋊C4#62611yescharacteristic
309C42—181no—
310C42—181no—
311C42C2×D3211yescharacteristic
312C22×C3—21no—
313C22×C3#88211yescharacteristic
314C22×C3#93711yescharacteristic
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—41no—
322C3×C4—41no—
323C3×C4—41no—
324C3×C4—42no—
325C3×C4—42no—
326C3×C4—41no—
327C3×C4—41no—
328C3×C4—41no—
329C3×C4—41no—
330C3×C4—241no—
331Dic3—81no—
332Dic3—122no—
333Dic3—122no—
334Dic3—122no—
335Dic3—122no—
336Dic3—121no—
337Dic3—121no—
338Dic3—121no—
339Dic3—121no—
340Dic3—121no—
341Dic3—121no—
342Dic3—121no—
343Dic3—121no—
344C32#166311yescharacteristic, complemented, Sylow
345Q8—122no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—121no—
349C2×C4—181no—
350C2×C4—181no—
351C2×C4—181no—
352C2×C4—181no—
353C2×C4C2×#62611yescharacteristic
354C2×C4#381111yescharacteristic
355C2×C4#381111yescharacteristic
356C8—62no—
357C8—62no—
358C8—121no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3#475211yescharacteristic
363C2×C3#482611yescharacteristic
364C2×C3#482711yescharacteristic
365C2×C3#509511yescharacteristic
366C2×C3#520111yescharacteristic
367C2×C3#520511yescharacteristic
368C22#6398111yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—241no—
375C4—361no—
376C4—361no—
377C4—361no—
378C4—361no—
379C3—21no—
380C3#6837611yescharacteristic, complemented
381C3#7139311yescharacteristic, complemented
382C2#1059165011yescharacteristic
383C2#1059166811yescharacteristic
384C2#1059168611yescharacteristic
subgroupG/H
centerC22#63981
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
344. C32#1663semidirect
380. C3#68376semidirect
381. C3#71393semidirect

Maximal subgroups

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

subgroupindex
#105961572
C3×#50642
#105903052
#105902892
C3×#45432
#105890892
#713933
#683763