Finite Group Databasebeta

← #11772637

Subgroups — #11772637

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#10592933C211yesmaximal, characteristic
2C3×#5240C211yesmaximal, characteristic
3C3×#5237C211yesmaximal, characteristic
4#67701—31nomaximal
5#67697—31nomaximal
6C2×C32×#41C2211yescharacteristic
7C2×#3748C411yescharacteristic, complemented
8C22×C3⋊(C3⋊C8)C411yescharacteristic, complemented
9C3×#926—21no—
10C2×C3×#208—21no—
11#63657—21no—
12#63657—21no—
13C3×#836C412yescomplemented
14C3×#834—21no—
15C3×#834C412yes—
16C3×#833—21no—
17C3×#413—31no—
18C3×#410—31no—
19#5240D311yescharacteristic
20#5237D311yescharacteristic
21#5234—31no—
22#5234—31no—
23#5234—61no—
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#3748—41no—
34C2×C3⋊(C3⋊C8)—21no—
35C2×C3⋊(C3⋊C8)—21no—
36C2×C3⋊(C3⋊C8)—41no—
37C3×#217—22no—
38C3×C4⋊Dic3—41no—
39C3×C4×Dic3—41no—
40C3×#208—22no—
41C3×#208—41no—
42C2×C3×C3⋊C8—41no—
43#1395—91noSylow
44C2×C3×#41—21no—
45C2×C3×#41C2×D311yescharacteristic
46C2×C3×#41C2×D311yescharacteristic
47C2×C3×M16—61no—
48C3×#117—61no—
49#926—21no—
50C2×#208—21no—
51C2×#208—31no—
52C2×#208—31no—
53C2×#208—61no—
54C22×C3⋊C8—31no—
55C22×C3⋊C8—31no—
56C22×C3⋊C8—61no—
57C3×#101—32no—
58C3×#100—61no—
59C3×#99—32no—
60C3×#99—61no—
61#836Dic312yescomplemented
62#834—21no—
63#834Dic312yes—
64#833—21no—
65#830—62no—
66#830—62no—
67#830—61no—
68#830—61no—
69#830—61no—
70#830—61no—
71C23×C32C22⋊C411yescharacteristic
72C23×C32C4⋊C411yescharacteristic
73C23×C32C4⋊C411yescharacteristic
74C32×Q8—41no—
75C32×D4—41no—
76C32×D4—41no—
77C32×D4—41no—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4—21no—
81C2×C32×C4—21no—
82C2×C32×C4—21no—
83C2×C32×C4—21no—
84C2×C32×C4C4211yescharacteristic
85C2×C32×C4C22⋊C411yescharacteristic
86C2×C32×C4C22⋊C411yescharacteristic
87C2×C32×C4C4⋊C411yescharacteristic
88C2×C3×Dic3—42no—
89C3⋊(C3⋊C8)—41no—
90C3⋊(C3⋊C8)—41no—
91C3×C3⋊C8—42no—
92#413—31no—
93#410—31no—
94#408—91no—
95C3×#41—41no—
96C3×#41—41no—
97C3×#41—41no—
98C3×#41—41no—
99C3×#41—42no—
100C3×#41—42no—
101C2×C3×Q8—21no—
102C2×C3×Q8C4×D311yescharacteristic
103C2×C3×Q8C2×Dic311yescharacteristic
104C2×C3×D4—21no—
105C2×C3×D4—21no—
106C2×C3×D4—21no—
107C2×C3×D4Dic611yescharacteristic
108C2×C3×D4Dic611yescharacteristic
109C2×C3×D4C4×D311yescharacteristic
110C2×C3×D4C2×Dic311yescharacteristic
111C2×C3×D4#6711yescharacteristic
112C2×C3×D4#6711yescharacteristic
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4C4×D311yescharacteristic
117C22×C3×C4C4×D311yescharacteristic
118C22×C3×C4D1211yescharacteristic
119C22×C3×C4D1211yescharacteristic
120C22×C3×C4#6711yescharacteristic
121C22×C3×C4#6711yescharacteristic
122C3×M16—62no—
123C3×M16—121no—
124C2×C3×C8—121no—
125C3×C4⋊C4—121no—
126C3×C22⋊C4—62no—
127C3×C42—121no—
128#217—22no—
129C4⋊Dic3—41no—
130C4×Dic3—41no—
131#208—22no—
132#208—41no—
133#208—122no—
134#208—121no—
135#208—121no—
136C2×C3⋊C8—41no—
137C2×C3⋊C8—62no—
138C2×C3⋊C8—62no—
139C2×C3⋊C8—61no—
140C2×C3⋊C8—61no—
141C2×C3⋊C8—61no—
142C2×C3⋊C8—61no—
143C2×C3⋊C8—122no—
144C2×C3⋊C8—121no—
145C2×C3⋊C8—121no—
146C22×C32—21no—
147C22×C32—21no—
148C22×C32—21no—
149C22×C32—41no—
150C22×C32—41no—
151C22×C32—41no—
152C22×C32#9511yescharacteristic
153C32×C4—21no—
154C32×C4—21no—
155C32×C4—21no—
156C32×C4#9911yescharacteristic
157C32×C4#9911yescharacteristic
158C3×Dic3—82no—
159C2×#41D3211yescharacteristic
160C2×M16—61no—
161C2×M16—91no—
162C22×C8—91no—
163#117—61no—
164#101—32no—
165#100—61no—
166#99—32no—
167#99—61no—
168C22⋊C8—181no—
169C22⋊C8—181no—
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—21no—
173C23×C3Dic3⋊C411yescharacteristic
174C23×C3Dic3⋊C411yescharacteristic
175C23×C3Dic3⋊C411yescharacteristic
176C23×C3C4⋊Dic311yescharacteristic
177C23×C3(C2×D3)⋊C411yescharacteristic
178C23×C3#21711yescharacteristic
179C3×Q8—41no—
180C3×Q8—41no—
181C3×Q8—42no—
182C3×D4—41no—
183C3×D4—41no—
184C3×D4—41no—
185C3×D4—41no—
186C3×D4—41no—
187C3×D4—41no—
188C3×D4—42no—
189C3×D4—42no—
190C3×D4—42no—
191C2×C3×C4—22no—
192C2×C3×C4—22no—
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—21no—
208C2×C3×C4—21no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—122no—
214C2×C3×C4C4×Dic311yescharacteristic
215C2×C3×C4C4×Dic311yescharacteristic
216C2×C3×C4Dic3⋊C411yescharacteristic
217C2×C3×C4C4⋊Dic311yescharacteristic
218C2×C3×C4(C2×D3)⋊C411yescharacteristic
219C2×C3×C4(C2×D3)⋊C411yescharacteristic
220C2×C3×C4(C2×D3)⋊C411yescharacteristic
221C2×C3×C4#21711yescharacteristic
222C2×Dic3—42no—
223C3×C8—122no—
224C3⋊C8—42no—
225C3⋊C8—122no—
226C3⋊C8—122no—
227C3⋊C8—121no—
228C3⋊C8—121no—
229C3⋊C8—121no—
230C3⋊C8—121no—
231C2×C32—21no—
232C2×C32—41no—
233C2×C32—41no—
234C2×C32—41no—
235C2×C32#34211yescharacteristic
236#41—41no—
237#41—41no—
238C2×Q8D3×Dic311yescharacteristic
239C2×D4D3×Dic311yescharacteristic
240C2×D4#62511yescharacteristic
241C2×D4#62711yescharacteristic
242C22×C4#62411yescharacteristic
243C22×C4#62611yescharacteristic
244C22×C4#62611yescharacteristic
245M16—62no—
246M16—121no—
247M16—361no—
248C2×C8—121no—
249C2×C8—181no—
250C2×C8—181no—
251C2×C8—361no—
252C4⋊C4—121no—
253C22⋊C4—62no—
254C42—121no—
255C22×C3—22no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—42no—
272C22×C3—42no—
273C22×C3—42no—
274C22×C3C3⋊#9511yescharacteristic
275C22×C3C3⋊#9511yescharacteristic
276C3×C4—22no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4—242no—
288C3×C4#80611yescharacteristic
289C3×C4#80611yescharacteristic
290C3×C4#80611yescharacteristic
291C3×C4#80611yescharacteristic
292Dic3—82no—
293C32#139511yescharacteristic, complemented, Sylow
294C23(C2×D3)⋊Dic311yescharacteristic
295C23Dic3⋊Dic311yescharacteristic
296C23#372411yescharacteristic
297Q8—41no—
298D4—41no—
299D4—41no—
300D4—41no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—122no—
308C2×C4Dic3211yescharacteristic
309C2×C4(C2×D3)⋊Dic311yescharacteristic
310C2×C4#372211yescharacteristic
311C2×C4Dic3⋊Dic311yescharacteristic
312C8—122no—
313C8—361no—
314C8—361no—
315C2×C3—22no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—42no—
320C2×C3—41no—
321C2×C3—41no—
322C2×C3—41no—
323C2×C3—41no—
324C2×C3—41no—
325C2×C3—41no—
326C2×C3—81no—
327C2×C3—81no—
328C2×C3#452711yescharacteristic
329C2×C3#452711yescharacteristic
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22#6357911yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—242no—
341C4#6358111yescharacteristic
342C4#6358111yescharacteristic
343C3—21no—
344C3#6769711yescharacteristic, complemented
345C3#6770111yescharacteristic, complemented
346C2—21no—
347C2—41no—
348C2—41no—
349C2—41no—
350C2#1058918711yescharacteristic
subgroupG/H
centerC4#63581
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
7. C2×#3748C4semidirect
8. C22×C3⋊(C3⋊C8)C4semidirect
13. C3×#836C4semidirect
61. #836Dic3semidirect
293. C32#1395semidirect
344. C3#67697semidirect
345. C3#67701semidirect

Maximal subgroups

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

subgroupindex
#105929332
C3×#52402
C3×#52372
#677013
#676973