Finite Group Databasebeta

← #11772636

Subgroups — #11772636

Order 1152.

403 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 403 conjugacy classes of subgroups — too many to draw. Only its 96 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#10592939C211yesmaximal, characteristic
2C3×#5237C211yesmaximal, characteristic
3C3×#5234C211yesmaximal, characteristic
4#67701—31nomaximal
5#67692—31nomaximal
6C2×C32×#41C2211yescharacteristic
7#64135—21no—
8C2×C3×#208—21no—
9C2×C3×#208C411yescharacteristic, complemented
10C22×C3×C3⋊C8C411yescharacteristic, complemented
11#63661—21no—
12#63661C412yes—
13C3×#836C412yescomplemented
14C3×#833—21no—
15C3×#830—21no—
16C3×#830—21no—
17C3×#413—31no—
18C3×#408—31no—
19#5240—31no—
20#5240—31no—
21#5240—61no—
22#5237D311yescharacteristic
23#5234D311yescharacteristic
24C32×#41—41no—
25C32×#41—41no—
26C2×C32×Q8C2×C411yescharacteristic
27C2×C32×D4C2×C411yescharacteristic
28C2×C32×D4D411yescharacteristic
29C2×C32×D4Q811yescharacteristic
30C22×C32×C4C2×C411yescharacteristic
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33#3757—22no—
34C4⋊(C3⋊Dic3)—41no—
35C4×C3⋊Dic3—41no—
36C3×#208—22no—
37C3×#208—41no—
38C3×#208—41no—
39C2×C3×C3⋊C8—21no—
40C2×C3×C3⋊C8—21no—
41C2×C3×C3⋊C8—41no—
42C2×C3×C3⋊C8—41no—
43#1395—91noSylow
44C2×C3×#41—21no—
45C2×C3×#41C2×D311yescharacteristic
46C2×C3×#41C2×D311yescharacteristic
47C2×C3×M16—31no—
48C2×C3×M16—61no—
49C22×C3×C8—31no—
50#926—62no—
51#926—61no—
52#926—61no—
53C2×#208—21no—
54C2×#208Dic311yescharacteristic, complemented
55C22×C3⋊C8Dic311yescharacteristic, complemented
56C3×#101—32no—
57C3×#100—61no—
58C3×C22⋊C8—61no—
59C3×C22⋊C8—61no—
60#836Dic312yescomplemented
61#834—32no—
62#834—32no—
63#834—62no—
64#834—62no—
65#834—61no—
66#834—61no—
67#833—21no—
68#830—21no—
69#830—21no—
70C23×C32C22⋊C411yescharacteristic
71C23×C32C4⋊C411yescharacteristic
72C23×C32C4⋊C411yescharacteristic
73C32×Q8—41no—
74C32×D4—41no—
75C32×D4—41no—
76C32×D4—41no—
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4—21no—
81C2×C32×C4—21no—
82C2×C32×C4—21no—
83C2×C32×C4C4211yescharacteristic
84C2×C32×C4C22⋊C411yescharacteristic
85C2×C32×C4C22⋊C411yescharacteristic
86C2×C32×C4C4⋊C411yescharacteristic
87C2×C3⋊Dic3—42no—
88C3×C3⋊C8—42no—
89C3×C3⋊C8—41no—
90C3×C3⋊C8—41no—
91#413—31no—
92#410—91no—
93#408—31no—
94C3×#41—41no—
95C3×#41—41no—
96C3×#41—41no—
97C3×#41—41no—
98C3×#41—42no—
99C3×#41—42no—
100C2×C3×Q8—21no—
101C2×C3×Q8C4×D311yescharacteristic
102C2×C3×Q8C2×Dic311yescharacteristic
103C2×C3×D4—21no—
104C2×C3×D4—21no—
105C2×C3×D4—21no—
106C2×C3×D4Dic611yescharacteristic
107C2×C3×D4Dic611yescharacteristic
108C2×C3×D4C4×D311yescharacteristic
109C2×C3×D4C4×D311yescharacteristic
110C2×C3×D4D1211yescharacteristic
111C2×C3×D4#6711yescharacteristic
112C22×C3×C4—21no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4C4×D311yescharacteristic
116C22×C3×C4D1211yescharacteristic
117C22×C3×C4C2×Dic311yescharacteristic
118C22×C3×C4#6711yescharacteristic
119C22×C3×C4#6711yescharacteristic
120C22×C3×C4#6711yescharacteristic
121C3×M16—62no—
122C3×M16—121no—
123C3×M16—121no—
124C2×C3×C8—61no—
125C2×C3×C8—61no—
126C2×C3×C8—121no—
127C2×C3×C8—121no—
128#217—64no—
129#217—62no—
130#217—62no—
131C4⋊Dic3—122no—
132C4⋊Dic3—121no—
133C4⋊Dic3—121no—
134C4×Dic3—122no—
135C4×Dic3—121no—
136C4×Dic3—121no—
137#208—22no—
138#208—41no—
139#208—41no—
140C2×C3⋊C8—21no—
141C2×C3⋊C8—21no—
142C2×C3⋊C8—41no—
143C2×C3⋊C8—41no—
144C22×C32—21no—
145C22×C32—21no—
146C22×C32—21no—
147C22×C32—41no—
148C22×C32—41no—
149C22×C32—41no—
150C22×C32#9511yescharacteristic
151C32×C4—21no—
152C32×C4—21no—
153C32×C4—21no—
154C32×C4#9911yescharacteristic
155C32×C4#9911yescharacteristic
156C3⋊Dic3—82no—
157C2×#41D3211yescharacteristic
158C2×M16—31no—
159C2×M16—61no—
160C22×C8—31no—
161#117—181no—
162#101—32no—
163#100—61no—
164#99—92no—
165#99—181no—
166C22⋊C8—61no—
167C22⋊C8—61no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3—21no—
171C23×C3Dic3⋊C411yescharacteristic
172C23×C3Dic3⋊C411yescharacteristic
173C23×C3Dic3⋊C411yescharacteristic
174C23×C3C4⋊Dic311yescharacteristic
175C23×C3(C2×D3)⋊C411yescharacteristic
176C23×C3(C2×D3)⋊C411yescharacteristic
177C3×Q8—41no—
178C3×Q8—41no—
179C3×Q8—42no—
180C3×D4—41no—
181C3×D4—41no—
182C3×D4—41no—
183C3×D4—41no—
184C3×D4—41no—
185C3×D4—41no—
186C3×D4—42no—
187C3×D4—42no—
188C3×D4—42no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4C4×Dic311yescharacteristic
212C2×C3×C4C4×Dic311yescharacteristic
213C2×C3×C4Dic3⋊C411yescharacteristic
214C2×C3×C4C4⋊Dic311yescharacteristic
215C2×C3×C4(C2×D3)⋊C411yescharacteristic
216C2×C3×C4(C2×D3)⋊C411yescharacteristic
217C2×C3×C4#21711yescharacteristic
218C2×C3×C4#21711yescharacteristic
219C2×Dic3—124no—
220C2×Dic3—122no—
221C2×Dic3—122no—
222C3×C8—122no—
223C3×C8—121no—
224C3×C8—121no—
225C3⋊C8—42no—
226C3⋊C8—41no—
227C3⋊C8—41no—
228C2×C32—21no—
229C2×C32—41no—
230C2×C32—41no—
231C2×C32—41no—
232C2×C32#34211yescharacteristic
233#41—41no—
234#41—41no—
235C2×Q8D3×Dic311yescharacteristic
236C2×D4#62411yescharacteristic
237C2×D4#62611yescharacteristic
238C2×D4#62711yescharacteristic
239C22×C4D3×Dic311yescharacteristic
240C22×C4#62511yescharacteristic
241C22×C4#62611yescharacteristic
242M16—62no—
243M16—121no—
244M16—121no—
245C2×C8—61no—
246C2×C8—61no—
247C2×C8—121no—
248C2×C8—121no—
249C4⋊C4—361no—
250C22⋊C4—182no—
251C42—361no—
252C22×C3—22no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—81no—
269C22×C3—81no—
270C22×C3—81no—
271C22×C3C3⋊#9511yescharacteristic
272C22×C3C3⋊#9511yescharacteristic
273C3×C4—22no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—41no—
283C3×C4—41no—
284C3×C4#80611yescharacteristic
285C3×C4#80611yescharacteristic
286C3×C4#83411yescharacteristic
287C3×C4#83411yescharacteristic
288Dic3—244no—
289Dic3—242no—
290Dic3—242no—
291C32#139511yescharacteristic, complemented, Sylow
292C23#372211yescharacteristic
293C23Dic3⋊Dic311yescharacteristic
294C23#372411yescharacteristic
295Q8—41no—
296D4—41no—
297D4—41no—
298D4—41no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—362no—
306C2×C4Dic3211yescharacteristic
307C2×C4(C2×D3)⋊Dic311yescharacteristic
308C2×C4(C2×D3)⋊Dic311yescharacteristic
309C2×C4Dic3⋊Dic311yescharacteristic
310C8—122no—
311C8—121no—
312C8—121no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—41no—
317C2×C3—42no—
318C2×C3—41no—
319C2×C3—41no—
320C2×C3—41no—
321C2×C3—41no—
322C2×C3—41no—
323C2×C3—41no—
324C2×C3—81no—
325C2×C3—81no—
326C2×C3#452611yescharacteristic
327C2×C3#452711yescharacteristic
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22#6357911yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—722no—
339C4#6358011yescharacteristic
340C4#6358011yescharacteristic
341C3—21no—
342C3#6769211yescharacteristic, complemented
343C3#6770111yescharacteristic, complemented
344C2—21no—
345C2—41no—
346C2—41no—
347C2—41no—
348C2#1058918611yescharacteristic
subgroupG/H
centerC4#63580
commutatorC2×C32×C4C42
Frattini, hypercenterC2×#41D32
Fitting, prime radical, cosocleC2×C32×#41C22
socleC2×C32#342
hypocenterC32#1395
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
9. C2×C3×#208C4semidirect
10. C22×C3×C3⋊C8C4semidirect
13. C3×#836C4semidirect
54. C2×#208Dic3semidirect
55. C22×C3⋊C8Dic3semidirect
60. #836Dic3semidirect
291. C32#1395semidirect
342. C3#67692semidirect
343. C3#67701semidirect

Maximal subgroups

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

subgroupindex
#105929392
C3×#52372
C3×#52342
#677013
#676923