Finite Group Databasebeta

← #11780754

Subgroups — #11780754

Order 1152.

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

normal subgroups only

This group has 413 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×#5699C211yesmaximal, characteristic
2#10592768C211yesmaximal, characteristic, complemented
3#10590306C211yesmaximal, characteristic, complemented
4#10590276C211yesmaximal, characteristic
5C3×#4543C211yesmaximal, characteristic, complemented
6#10589088C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic
8#71957—31nomaximal
9#68379—31nomaximal
10C32×#125C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#898—21no—
13C3×#898—21no—
14C3×#897—21no—
15C3×#896—21no—
16C3×#894—21no—
17C3×#888—21no—
18C3×#875C2211yescharacteristic
19C3×#870C2211yescharacteristic
20#63637—21no—
21#63637—21no—
22#63630C2211yescharacteristic
23C3×#803C2211yescharacteristic
24C3×#803C2211yescharacteristic
25#63575—21no—
26#63573—21no—
27#63566—21no—
28#63563—21no—
29C3×#563—31no—
30#5699D311yescharacteristic
31#5069—31no—
32#5069—31no—
33#5069—61no—
34#5064—31no—
35#5055—31no—
36#4714—31no—
37#4702—31no—
38C3×#330—31no—
39#4543—31no—
40#4543D311yescharacteristic, complemented
41#4540—31no—
42#4465—31no—
43#4464—31no—
44C2×#634—21no—
45C2×C3×D12D411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6D411yescharacteristic
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4D411yescharacteristic
52C32×C4⋊C4D411yescharacteristic
53C32×C42C2311yescharacteristic
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×C4⋊Dic3D411yescharacteristic
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×C4×Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#1664—91noSylow
72C3×C4⋊Q8—61no—
73C3×#126—61no—
74C3×#126—61no—
75C3×#125—21no—
76C3×#125—31no—
77C3×#125C2×D311yescharacteristic
78C3×#125C2×D311yescharacteristic
79C3×#124—31no—
80C3×#123—61no—
81C3×C22⋊Q8—61no—
82C3×C22⋊Q8—61no—
83#898—21no—
84#898—21no—
85#897—21no—
86#896—21no—
87#894—21no—
88#888—21no—
89#875C2×D311yescharacteristic
90#870C2×D311yescharacteristic
91#869—31no—
92#869—31no—
93#869—61no—
94C3×#97—31no—
95C3×#97—31no—
96#835—61no—
97#832—61no—
98#821—61no—
99#818—61no—
100#817—61no—
101#816—61no—
102#810—62no—
103#810—62no—
104#810—61no—
105#810—61no—
106#810—61no—
107#810—61no—
108#808—61no—
109#807—61no—
110#803—31no—
111#803—31no—
112#803—61no—
113#803C2×D311yescharacteristic
114#803C2×D311yescharacteristic
115C22×C3×D3—21no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—41no—
122#634—42no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C3×D12—41no—
127C3×C4×D3—81no—
128C3×Dic6—41no—
129C3×Dic6—81no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—41no—
133#563—31no—
134#501—91no—
135#491—91no—
136#489—91no—
137#330—31no—
138#330—91no—
139#329—91no—
140C2×C3×Q8—31no—
141C2×C3×Q8—61no—
142C2×C3×D4—31no—
143C22×C3×C4—61no—
144C2×D12#6711yescharacteristic
145C2×C4×D3—21no—
146C2×Dic6—21no—
147C2×Dic6—62no—
148C2×Dic6—61no—
149C2×Dic6—61no—
150C2×Dic6#6711yescharacteristic
151C2×C3×C8—61no—
152C2×C3×C8—61no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—41no—
162C3×C4⋊C4—41no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4D1211yescharacteristic
168C3×C4⋊C4D1211yescharacteristic
169C3×C4⋊C4#6711yescharacteristic
170C3×C4⋊C4#6711yescharacteristic
171C3×C22⋊C4—61no—
172C3×C22⋊C4—61no—
173C3×C22⋊C4—61no—
174C3×C22⋊C4—61no—
175C3×C22⋊C4—61no—
176C3×C42—21no—
177C3×C42—61no—
178C3×C42C22×D311yescharacteristic
179C3×C42C22×D311yescharacteristic
180(C2×D3)⋊C4—21no—
181(C2×D3)⋊C4—21no—
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—21no—
184(C2×D3)⋊C4—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—121no—
191C4⋊Dic3—121no—
192C4⋊Dic3#6711yescharacteristic
193C4⋊Dic3#6711yescharacteristic
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196Dic3⋊C4—21no—
197C4×Dic3—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—62no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C22×C32#12011yescharacteristic
204C2×C3×D3—41no—
205C2×C3×D3—41no—
206C2×C3×D3—41no—
207C32×C4—21no—
208C32×C4—21no—
209C32×C4—21no—
210C32×C4—41no—
211C32×C4—41no—
212C3⋊Dic3—81no—
213C3×Dic3—41no—
214C3×Dic3—41no—
215C3×Dic3—41no—
216C4⋊Q8—61no—
217C4⋊Q8—91no—
218#126—61no—
219#126—61no—
220#125—31no—
221#125D3211yescharacteristic
222#124—31no—
223#123—61no—
224C22⋊Q8—61no—
225C22⋊Q8—61no—
226#107—181no—
227#106—181no—
228#103—181no—
229#103—181no—
230#103—181no—
231#102—181no—
232#97—31no—
233#97—31no—
234#97—91no—
235C23×C3—61no—
236C22×D3—21no—
237C3×Q8—121no—
238C3×Q8—241no—
239C3×D4—121no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—61no—
250C2×C3×C4—61no—
251C2×C3×C4—61no—
252C2×C3×C4—241no—
253C2×C3×C4C2×D1211yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258C2×C3×C4C2×#6711yescharacteristic
259C2×Dic3—21no—
260C2×Dic3—21no—
261C2×Dic3—21no—
262C2×Dic3—122no—
263C2×Dic3—121no—
264C2×Dic3—121no—
265D12—41no—
266C4×D3—81no—
267Dic6—41no—
268Dic6—81no—
269Dic6—124no—
270Dic6—122no—
271Dic6—122no—
272C3×C8—62no—
273C3×C8—121no—
274C3⋊C8—22no—
275C3⋊C8—41no—
276C3⋊C8—122no—
277C3⋊C8—121no—
278C3⋊C8—121no—
279C2×C32#45411yescharacteristic
280C2×C32#45511yescharacteristic
281C2×C32#45611yescharacteristic
282C3×D3—81no—
283C2×Q8—31no—
284C2×Q8—61no—
285C2×Q8—181no—
286C2×D4—31no—
287C22×C4—61no—
288C2×C8—61no—
289C2×C8—61no—
290C2×C8—181no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—31no—
294C4⋊C4—31no—
295C4⋊C4—61no—
296C4⋊C4—61no—
297C4⋊C4—61no—
298C4⋊C4—61no—
299C4⋊C4—181no—
300C4⋊C4—181no—
301C4⋊C4#62611yescharacteristic
302C4⋊C4#62611yescharacteristic
303C22⋊C4—61no—
304C22⋊C4—61no—
305C22⋊C4—61no—
306C22⋊C4—61no—
307C22⋊C4—61no—
308C42—61no—
309C42C2×D3211yescharacteristic
310C22×C3—21no—
311C22×C3—121no—
312C22×C3—121no—
313C22×C3—121no—
314C22×C3#88211yescharacteristic
315C22×C3#95311yescharacteristic
316C2×D3—41no—
317C2×D3—41no—
318C2×D3—41no—
319C3×C4—22no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—41no—
327C3×C4—41no—
328C3×C4—41no—
329C3×C4—41no—
330C3×C4—41no—
331C3×C4—41no—
332C3×C4—81no—
333C3×C4—81no—
334C3×C4—121no—
335C3×C4—121no—
336C3×C4—121no—
337Dic3—41no—
338Dic3—41no—
339Dic3—41no—
340Dic3—242no—
341Dic3—241no—
342Dic3—241no—
343C32#166411yescharacteristic, complemented, Sylow
344C23—61no—
345Q8—121no—
346Q8—241no—
347Q8—362no—
348D4—121no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—61no—
352C2×C4—61no—
353C2×C4—61no—
354C2×C4—241no—
355C2×C4—361no—
356C2×C4C2×#62611yescharacteristic
357C2×C4D3×#6711yescharacteristic
358C2×C4D3×#6711yescharacteristic
359C8—62no—
360C8—121no—
361C8—361no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—241no—
366C2×C3#475311yescharacteristic
367C2×C3#482511yescharacteristic
368C2×C3#482611yescharacteristic
369C2×C3#524211yescharacteristic
370C2×C3#524511yescharacteristic
371C2×C3#524611yescharacteristic
372D3—81no—
373C22—121no—
374C22—121no—
375C22—121no—
376C22#6397711yescharacteristic
377C4—21no—
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—121no—
383C4—121no—
384C4—121no—
385C4—721no—
386C3—21no—
387C3#6837911yescharacteristic, complemented
388C3#7195711yescharacteristic, complemented
389C2—241no—
390C2#1059164611yescharacteristic
391C2#1059168811yescharacteristic
392C2#1059168911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#125C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenter#125D32
hypocenterC32#1664
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. #10592768C2semidirect
3. #10590306C2semidirect
5. C3×#4543C2semidirect
6. #10589088C2semidirect
40. #4543D3semidirect
343. C32#1664semidirect
387. C3#68379semidirect
388. C3#71957semidirect

Maximal subgroups

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

subgroupindex
C3×#56992
#105927682
#105903062
#105902762
C3×#45432
#105890882
#105890862
#719573
#683793