Finite Group Databasebeta

← #11779342

Subgroups — #11779342

Order 1152.

484 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 92 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×#5585C211yesmaximal, characteristic
2#10592720C211yesmaximal, characteristic, complemented
3#10590369C211yesmaximal, characteristic
4#10590283C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589090C211yesmaximal, characteristic
7#10589084C211yesmaximal, characteristic, complemented
8#71944—31nomaximal
9#68260—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#947—21no—
13C3×#894—22no—
14C3×#893—21no—
15C3×#875—21no—
16C3×#874C2211yescharacteristic
17C3×C4×D12—21no—
18C3×C4×Dic6C2211yescharacteristic
19C2×#3716—22no—
20#63662—21no—
21#63634—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63575—21no—
26#63566—21no—
27C3×#559—31no—
28#5585D311yescharacteristic
29#5076—31no—
30#5021—31no—
31#5021—31no—
32#5021—31no—
33#5021—61no—
34#4850—31no—
35#4693—31no—
36C3×Q8⋊C8—31no—
37#4544—31no—
38#4535—31no—
39#4535D311yescharacteristic, complemented
40#4485—31no—
41#4456—31no—
42C2×C32×Q8D411yescharacteristic
43C2×#634—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D412yes—
47C2×C3×C4×D3—22no—
48C2×C3×Dic6D411yescharacteristic
49C32×C4⋊C4—21no—
50C32×C4⋊C4D411yescharacteristic
51C32×C42—21no—
52C32×C42C2311yescharacteristic
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×(C2×D3)⋊C4—22no—
57C3×(C2×D3)⋊C4—22no—
58C3×(C2×D3)⋊C4—22no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#3716—44no—
65#1630—91noSylow
66C3×#127—31no—
67C3×#124—61no—
68C3×#124—61no—
69C3×#123—62no—
70C3×C4×Q8—21no—
71C3×C4×Q8—31no—
72C3×C4×Q8C2×D311yescharacteristic
73C3×C4×Q8C2×D311yescharacteristic
74C3×C4×D4—61no—
75C3×C4×D4—61no—
76#947—21no—
77C2×#214—62no—
78C2×#204—62no—
79#894—22no—
80#893—21no—
81#875—21no—
82#874C2×D311yescharacteristic
83C4×D12—21no—
84#869—31no—
85#869—31no—
86#869—61no—
87C4×Dic6C2×D311yescharacteristic
88C3×C4⋊C8—31no—
89C3×C4×C8—31no—
90#835—61no—
91#835—62no—
92#835—61no—
93#835—61no—
94#818—61no—
95#816—61no—
96#807—61no—
97#807—62no—
98#807—61no—
99#807—61no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3×D3—22no—
106C32×Q8—21no—
107C32×Q8—21no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C3⋊Dic3—41no—
114#634—42no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C3×D12—42no—
118C3×D12—41no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×C4×D3—82no—
123C3×Dic6—21no—
124C3×Dic6—21no—
125C3⋊(C3⋊C8)—41no—
126C3×C3⋊C8—22no—
127C3×C3⋊C8—41no—
128#559—31no—
129#492—91no—
130#477—91no—
131#477—91no—
132#331—91no—
133Q8⋊C8—31no—
134Q8⋊C8—91no—
135C2×C3×Q8—21no—
136C2×C3×Q8—31no—
137C2×C3×Q8D1211yescharacteristic
138C2×C3×Q8#6711yescharacteristic
139C2×C3×D4—32no—
140C2×C3×D4—61no—
141C2×C3×D4—61no—
142C22×C3×C4—62no—
143C2×D12—21no—
144C2×D12—21no—
145C2×D12#6712yes—
146C2×C4×D3—22no—
147C2×Dic6—61no—
148C2×Dic6—61no—
149C2×Dic6—121no—
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—31no—
157C3×C4⋊C4—41no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4D1211yescharacteristic
160C3×C4⋊C4#6711yescharacteristic
161C3×C22⋊C4—62no—
162C3×C22⋊C4—62no—
163C3×C22⋊C4—62no—
164C3×C42—21no—
165C3×C42—21no—
166C3×C42—21no—
167C3×C42—41no—
168C3×C42—61no—
169C3×C42C22×D311yescharacteristic
170C3×C42C22×D311yescharacteristic
171#214—124no—
172(C2×D3)⋊C4—22no—
173(C2×D3)⋊C4—22no—
174(C2×D3)⋊C4—22no—
175C4⋊Dic3—62no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4⋊Dic3—121no—
181C4⋊Dic3#6711yescharacteristic
182Dic3⋊C4—21no—
183C4×Dic3—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—62no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—61no—
189#204—124no—
190C22×C32#12011yescharacteristic
191C2×C3×D3—42no—
192C2×C3×D3—42no—
193C2×C3×D3—42no—
194C32×C4—21no—
195C32×C4—41no—
196C32×C4—41no—
197C32×C4#13511yescharacteristic
198C32×C4#13511yescharacteristic
199C32×C4#13711yescharacteristic
200C32×C4#13711yescharacteristic
201C3⋊Dic3—81no—
202C3×Dic3—41no—
203C3×Dic3—41no—
204C2×SD16—182no—
205C4⋊Q8—91no—
206#127—31no—
207#124—61no—
208#124—61no—
209#123—62no—
210C4×Q8—31no—
211C4×Q8D3211yescharacteristic
212C4×D4—61no—
213C4×D4—61no—
214#107—181no—
215#107—181no—
216C4⋊C8—31no—
217C4⋊C8—91no—
218#103—181no—
219#103—181no—
220C4×C8—31no—
221C23×C3—62no—
222C22×D3—22no—
223C3×Q8—22no—
224C3×Q8—21no—
225C3×Q8—21no—
226C3×Q8—21no—
227C3×Q8—21no—
228C3×Q8—41no—
229C3×Q8—61no—
230C3×Q8—61no—
231C3×D4—122no—
232C3×D4—121no—
233C3×D4—121no—
234C3×D4—121no—
235C3×D4—121no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—61no—
246C2×C3×C4—61no—
247C2×C3×C4—242no—
248C2×C3×C4C2×D1211yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4C2×#6711yescharacteristic
252C2×C3×C4C2×#6711yescharacteristic
253C2×C3×C4C2×#6711yescharacteristic
254C2×Dic3—21no—
255C2×Dic3—21no—
256C2×Dic3—122no—
257C2×Dic3—121no—
258C2×Dic3—121no—
259D12—42no—
260D12—41no—
261D12—41no—
262D12—41no—
263D12—41no—
264C4×D3—82no—
265Dic6—21no—
266Dic6—21no—
267Dic6—122no—
268Dic6—122no—
269Dic6—242no—
270C3×C8—62no—
271C3×C8—121no—
272C3⋊C8—22no—
273C3⋊C8—41no—
274C3⋊C8—122no—
275C3⋊C8—121no—
276C3⋊C8—121no—
277C2×C32#45211yescharacteristic
278C2×C32#45211yescharacteristic
279C2×C32#45311yescharacteristic
280C3×D3—82no—
281C2×Q8—31no—
282C2×Q8—181no—
283C2×Q8#62611yescharacteristic
284C2×D4—32no—
285C2×D4—61no—
286C2×D4—61no—
287C22×C4—62no—
288SD16—364no—
289C2×C8—61no—
290C2×C8—61no—
291C2×C8—181no—
292C4⋊C4—21no—
293C4⋊C4—31no—
294C4⋊C4—61no—
295C4⋊C4—181no—
296C4⋊C4—181no—
297C4⋊C4#62611yescharacteristic
298C22⋊C4—62no—
299C22⋊C4—62no—
300C22⋊C4—62no—
301C42—21no—
302C42—61no—
303C42C2×D3211yescharacteristic
304C22×C3—21no—
305C22×C3—122no—
306C22×C3—122no—
307C22×C3—122no—
308C22×C3#88211yescharacteristic
309C22×C3#95311yescharacteristic
310C2×D3—42no—
311C2×D3—42no—
312C2×D3—42no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—41no—
320C3×C4—42no—
321C3×C4—41no—
322C3×C4—41no—
323C3×C4—41no—
324C3×C4—41no—
325C3×C4—81no—
326C3×C4—121no—
327C3×C4—121no—
328C3×C4#90411yescharacteristic
329C3×C4#90911yescharacteristic
330C3×C4#91611yescharacteristic
331C3×C4#91811yescharacteristic
332C3×C4#95011yescharacteristic
333C3×C4#95011yescharacteristic
334C3×C4#95111yescharacteristic
335C3×C4#95111yescharacteristic
336Dic3—41no—
337Dic3—41no—
338Dic3—242no—
339Dic3—241no—
340Dic3—241no—
341C32#163011yescharacteristic, complemented, Sylow
342C23—62no—
343Q8—21no—
344Q8—21no—
345Q8—61no—
346Q8—61no—
347Q8—362no—
348D4—122no—
349D4—121no—
350D4—121no—
351D4—121no—
352D4—121no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—242no—
358C2×C4—361no—
359C2×C4C2×#62611yescharacteristic
360C2×C4D3×#6711yescharacteristic
361C2×C4D3×#6711yescharacteristic
362C8—62no—
363C8—121no—
364C8—361no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—242no—
369C2×C3#473311yescharacteristic
370C2×C3#480811yescharacteristic
371C2×C3#482211yescharacteristic
372C2×C3#523911yescharacteristic
373C2×C3#523911yescharacteristic
374C2×C3#524111yescharacteristic
375D3—82no—
376C22—122no—
377C22—122no—
378C22—122no—
379C22#6397711yescharacteristic
380C4—21no—
381C4—41no—
382C4—41no—
383C4—121no—
384C4—121no—
385C4—721no—
386C4#6382911yescharacteristic
387C4#6383111yescharacteristic
388C4#6394311yescharacteristic
389C4#6394711yescharacteristic
390C3—21no—
391C3#6826011yescharacteristic, complemented
392C3#7194411yescharacteristic, complemented
393C2—242no—
394C2#1059117311yescharacteristic
395C2#1059159911yescharacteristic
396C2#1059166611yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radicalC3×#874C22
hypercenterC4×Q8D32
hypocenterC32#1630
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10592720C2semidirect
4. #10590283C2semidirect
5. C3×#4535C2semidirect
7. #10589084C2semidirect
39. #4535D3semidirect
341. C32#1630semidirect
391. C3#68260semidirect
392. C3#71944semidirect

Maximal subgroups

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

subgroupindex
C3×#55852
#105927202
#105903692
#105902832
C3×#45352
#105890902
#105890842
#719443
#682603