Finite Group Databasebeta

← #11779344

Subgroups — #11779344

Order 1152.

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

normal subgroups only

This group has 471 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
2C3×#5021C211yesmaximal, characteristic, complemented
3#10590375C211yesmaximal, characteristic
4#10590310C211yesmaximal, characteristic, complemented
5#10589401C211yesmaximal, characteristic, complemented
6#10589090C211yesmaximal, characteristic
7#10589083C211yesmaximal, characteristic, complemented
8#71944—31nomaximal
9#71159—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C3×#947—21no—
12C3×#894—22no—
13C3×#893—21no—
14C3×#875—21no—
15C3×#874C2211yescharacteristic
16C3×C4×D12—21no—
17C3×#869C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C2×#3715—22no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#835—21no—
23C3×#807—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63576—21no—
26#63565—21no—
27C3×#559—31no—
28#5585D311yescharacteristic
29C3×#477—31no—
30#5091—31no—
31#5085—31no—
32#5076—31no—
33#5021—31no—
34#5021D311yescharacteristic, complemented
35#4544—31no—
36#4535—31no—
37#4535—31no—
38#4535—31no—
39#4535—61no—
40#4485—31no—
41#4484—31no—
42C2×C32×Q8D411yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12D412yes—
46C2×C3×C4×D3—22no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6D411yescharacteristic
49C32×C4⋊C4—21no—
50C32×C4⋊C4D411yescharacteristic
51C32×C42—21no—
52C32×C42C2311yescharacteristic
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×(C2×D3)⋊C4—22no—
56C3×(C2×D3)⋊C4—22no—
57C3×(C2×D3)⋊C4—22no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64#3715—44no—
65#1630—91noSylow
66C3×C4⋊Q8—31no—
67C3×#127—31no—
68C3×#124—61no—
69C3×#124—61no—
70C3×#123—62no—
71C3×C4×Q8—21no—
72C3×C4×Q8—31no—
73C3×C4×Q8C2×D311yescharacteristic
74C3×C4×Q8C2×D311yescharacteristic
75C3×C4×D4—61no—
76C3×C4×D4—61no—
77#947—21no—
78C2×#215—62no—
79C2×#214—62no—
80#894—22no—
81#893—21no—
82#875—21no—
83#874C2×D311yescharacteristic
84C4×D12—21no—
85#869C2×D311yescharacteristic
86C4×Dic6C2×D311yescharacteristic
87C3×#107—61no—
88C3×C4⋊C8—31no—
89C3×#103—61no—
90#835—21no—
91#835—61no—
92#810—61no—
93#807—21no—
94#807—61no—
95#807—61no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—61no—
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4×C3⋊C8—31no—
101C4×C3⋊C8—31no—
102C4×C3⋊C8—61no—
103C22×C3×D3—22no—
104C32×Q8—21no—
105C32×Q8—21no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—41no—
114C3×D12—42no—
115C3×D12—41no—
116C3×D12—41no—
117C3×D12—41no—
118C3×D12—41no—
119C3×C4×D3—82no—
120C3×Dic6—21no—
121C3×Dic6—21no—
122C3×Dic6—42no—
123C3⋊(C3⋊C8)—22no—
124C3⋊(C3⋊C8)—41no—
125C3×C3⋊C8—41no—
126#559—31no—
127#492—91no—
128#477—31no—
129#477—91no—
130#331—91no—
131Q8⋊C8—91no—
132Q8⋊C8—91no—
133C2×C3×Q8—21no—
134C2×C3×Q8—31no—
135C2×C3×Q8—61no—
136C2×C3×Q8#6711yescharacteristic
137C2×C3×Q8#6711yescharacteristic
138C2×C3×D4—32no—
139C2×C3×D4—61no—
140C2×C3×D4—61no—
141C22×C3×C4—62no—
142C2×D12—21no—
143C2×D12—21no—
144C2×D12#6712yes—
145C2×C4×D3—22no—
146C2×Dic6—21no—
147C2×Dic6#6711yescharacteristic
148C2×C3×C8—61no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—41no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4#6711yescharacteristic
158C3×C4⋊C4#6711yescharacteristic
159C3×C22⋊C4—62no—
160C3×C22⋊C4—62no—
161C3×C22⋊C4—62no—
162C3×C42—21no—
163C3×C42—21no—
164C3×C42—21no—
165C3×C42—41no—
166C3×C42—61no—
167C3×C42C22×D311yescharacteristic
168C3×C42C22×D311yescharacteristic
169#215—124no—
170#214—124no—
171(C2×D3)⋊C4—22no—
172(C2×D3)⋊C4—22no—
173(C2×D3)⋊C4—22no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3#6711yescharacteristic
177Dic3⋊C4—21no—
178C4×Dic3—21no—
179C2×C3⋊C8—21no—
180C2×C3⋊C8—61no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—121no—
185C2×C3⋊C8—121no—
186C22×C32#12011yescharacteristic
187C2×C3×D3—42no—
188C2×C3×D3—42no—
189C2×C3×D3—42no—
190C32×C4—21no—
191C32×C4—41no—
192C32×C4—41no—
193C32×C4#13511yescharacteristic
194C32×C4#13511yescharacteristic
195C32×C4#13711yescharacteristic
196C32×C4#13711yescharacteristic
197C3×Dic3—41no—
198C3×Dic3—41no—
199C3×Dic3—81no—
200C2×SD16—182no—
201C4⋊Q8—31no—
202#127—31no—
203#124—61no—
204#124—61no—
205#123—62no—
206C4×Q8—31no—
207C4×Q8D3211yescharacteristic
208C4×D4—61no—
209C4×D4—61no—
210#107—61no—
211#107—181no—
212C4⋊C8—31no—
213C4⋊C8—91no—
214#103—61no—
215#103—181no—
216C4×C8—91no—
217C23×C3—62no—
218C22×D3—22no—
219C3×Q8—22no—
220C3×Q8—21no—
221C3×Q8—21no—
222C3×Q8—21no—
223C3×Q8—21no—
224C3×Q8—41no—
225C3×Q8—61no—
226C3×Q8—61no—
227C3×Q8—122no—
228C3×D4—122no—
229C3×D4—121no—
230C3×D4—121no—
231C3×D4—121no—
232C3×D4—121no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—61no—
243C2×C3×C4—61no—
244C2×C3×C4—121no—
245C2×C3×C4—242no—
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4C2×#6711yescharacteristic
249C2×C3×C4C2×#6711yescharacteristic
250C2×C3×C4C2×#6711yescharacteristic
251C2×C3×C4C2×#6711yescharacteristic
252C2×Dic3—21no—
253C2×Dic3—21no—
254C2×Dic3—41no—
255D12—42no—
256D12—41no—
257D12—41no—
258D12—41no—
259D12—41no—
260C4×D3—82no—
261Dic6—21no—
262Dic6—21no—
263Dic6—42no—
264C3×C8—121no—
265C3⋊C8—41no—
266C3⋊C8—62no—
267C3⋊C8—62no—
268C3⋊C8—122no—
269C3⋊C8—121no—
270C3⋊C8—121no—
271C3⋊C8—241no—
272C2×C32#45211yescharacteristic
273C2×C32#45211yescharacteristic
274C2×C32#45311yescharacteristic
275C3×D3—82no—
276C2×Q8—31no—
277C2×Q8—61no—
278C2×Q8#62511yescharacteristic
279C2×D4—32no—
280C2×D4—61no—
281C2×D4—61no—
282C22×C4—62no—
283SD16—364no—
284C2×C8—61no—
285C2×C8—181no—
286C2×C8—181no—
287C4⋊C4—21no—
288C4⋊C4—31no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4#62511yescharacteristic
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—62no—
296C42—21no—
297C42—61no—
298C42C2×D3211yescharacteristic
299C22×C3—21no—
300C22×C3—122no—
301C22×C3—122no—
302C22×C3—122no—
303C22×C3#93711yescharacteristic
304C22×C3#95311yescharacteristic
305C2×D3—42no—
306C2×D3—42no—
307C2×D3—42no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—41no—
315C3×C4—42no—
316C3×C4—41no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—41no—
320C3×C4—81no—
321C3×C4—121no—
322C3×C4—121no—
323C3×C4—241no—
324C3×C4#91811yescharacteristic
325C3×C4#91911yescharacteristic
326C3×C4#94211yescharacteristic
327C3×C4#95011yescharacteristic
328C3×C4#95011yescharacteristic
329C3×C4#95011yescharacteristic
330C3×C4#95111yescharacteristic
331C3×C4#95111yescharacteristic
332Dic3—41no—
333Dic3—41no—
334Dic3—81no—
335C32#163011yescharacteristic, complemented, Sylow
336C23—62no—
337Q8—21no—
338Q8—21no—
339Q8—61no—
340Q8—61no—
341Q8—122no—
342D4—122no—
343D4—121no—
344D4—121no—
345D4—121no—
346D4—121no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—121no—
352C2×C4—242no—
353C2×C4C2×#62511yescharacteristic
354C2×C4D3×#6711yescharacteristic
355C2×C4D3×#6711yescharacteristic
356C8—121no—
357C8—182no—
358C8—361no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—242no—
363C2×C3#504711yescharacteristic
364C2×C3#518711yescharacteristic
365C2×C3#519811yescharacteristic
366C2×C3#523911yescharacteristic
367C2×C3#523911yescharacteristic
368C2×C3#524111yescharacteristic
369D3—82no—
370C22—122no—
371C22—122no—
372C22—122no—
373C22#6397611yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—121no—
378C4—121no—
379C4—241no—
380C4#6382211yescharacteristic
381C4#6382711yescharacteristic
382C4#6394311yescharacteristic
383C4#6394911yescharacteristic
384C3—21no—
385C3#7115911yescharacteristic, complemented
386C3#7194411yescharacteristic, complemented
387C2—242no—
388C2#1059117011yescharacteristic
389C2#1059159711yescharacteristic
390C2#1059166511yescharacteristic
subgroupG/H
centerC22#63976
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. C3×#5021C2semidirect
4. #10590310C2semidirect
5. #10589401C2semidirect
7. #10589083C2semidirect
34. #5021D3semidirect
335. C32#1630semidirect
385. C3#71159semidirect
386. C3#71944semidirect

Maximal subgroups

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

subgroupindex
C3×#55852
C3×#50212
#105903752
#105903102
#105894012
#105890902
#105890832
#719443
#711593