Finite Group Databasebeta

← #11771807

Subgroups — #11771807

Order 1152.

363 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 363 conjugacy classes of subgroups — too many to draw. Only its 66 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×#4953C211yesmaximal, characteristic
2#10589392C211yesmaximal, characteristic
3C3×#4525C211yesmaximal, characteristic
4#67649—31nomaximal
5#67450—31nomaximal
6C2×C32×C22⋊C4C2211yescharacteristic
7C2×#3757—21no—
8C2×C3×#217—21no—
9C2×C3×C4⋊Dic3C411yescharacteristic, complemented
10C3×C3⋊#95—21no—
11C3×C3⋊#95C411yescharacteristic, complemented
12C3×#830—21no—
13C3×#397—31no—
14#4953D311yescharacteristic
15C3×#323—31no—
16#4526—31no—
17#4526—31no—
18#4526—61no—
19#4525D311yescharacteristic
20C24×C32D411yescharacteristic
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3—41no—
24C22×C3×Dic3—21no—
25C22×C3×Dic3—21no—
26C32×C22⋊C4—41no—
27#3757—22no—
28#3757—41no—
29C3×#217—41no—
30C3×#217—41no—
31C3×C4⋊Dic3—41no—
32C2×C3×C3⋊C8—41no—
33#1344—91noSylow
34C2×C3×C4⋊C4—31no—
35C2×C3×C22⋊C4—21no—
36C2×C3×C22⋊C4—61no—
37C2×C3×C22⋊C4C2×D311yescharacteristic
38C2×C3×C22⋊C4C2×D311yescharacteristic
39C2×#217—21no—
40C2×#217—62no—
41C2×#217—61no—
42C2×#217—61no—
43C2×C4⋊Dic3Dic311yescharacteristic, complemented
44C3×C22⋊C8—61no—
45C3×#95—31no—
46C3×#95—61no—
47C3⋊#95—21no—
48C3⋊#95Dic311yescharacteristic, complemented
49#830—21no—
50C23×C32—21no—
51C23×C32—21no—
52C23×C32—41no—
53C23×C32—41no—
54C23×C32C22⋊C411yescharacteristic
55C23×C32D811yescharacteristic
56C23×C32SD1611yescharacteristic
57C2×C32×C4—21no—
58C2×C32×C4—21no—
59C2×C32×C4—41no—
60C2×C32×C4—41no—
61C2×C3⋊Dic3—42no—
62C2×C3⋊Dic3—81no—
63C2×C3⋊Dic3—81no—
64C2×C3×Dic3—41no—
65C2×C3×Dic3—41no—
66C2×C3×Dic3—41no—
67C2×C3×Dic3—41no—
68C2×C3×Dic3—41no—
69C2×C3×Dic3—41no—
70C3×C3⋊C8—81no—
71#397—31no—
72#342—91no—
73#323—31no—
74C24×C3—21no—
75C24×C3D1211yescharacteristic
76C24×C3#6711yescharacteristic
77C22×C3×C4—21no—
78C22×C3×C4—21no—
79C22×C3×C4—61no—
80C22×C3×C4—61no—
81C22×C3×C4C4×D311yescharacteristic
82C22×C3×C4C2×Dic311yescharacteristic
83C22×C3×C4#6711yescharacteristic
84C22×C3×C4#6711yescharacteristic
85C22×Dic3—21no—
86C22×Dic3—21no—
87C22×Dic3—122no—
88C22×Dic3—121no—
89C22×Dic3—121no—
90C2×C3×C8—121no—
91C3×C4⋊C4—121no—
92C3×C22⋊C4—41no—
93C3×C22⋊C4—41no—
94C3×C22⋊C4—42no—
95C3×C22⋊C4—121no—
96C3×C22⋊C4—121no—
97#217—41no—
98#217—41no—
99#217—64no—
100#217—62no—
101#217—62no—
102#217—122no—
103#217—121no—
104#217—121no—
105C4⋊Dic3—41no—
106C2×C3⋊C8—41no—
107C22×C32—21no—
108C22×C32—21no—
109C22×C32—21no—
110C22×C32—21no—
111C22×C32—41no—
112C22×C32—41no—
113C22×C32—41no—
114C22×C32—41no—
115C22×C32—81no—
116C22×C32#9911yescharacteristic
117C22×C32#10211yescharacteristic
118C22×C32#10411yescharacteristic
119C32×C4—41no—
120C32×C4—41no—
121C3⋊Dic3—82no—
122C3×Dic3—81no—
123C3×Dic3—81no—
124C2×C4⋊C4—31no—
125C2×C22⋊C4—61no—
126C2×C22⋊C4—181no—
127C2×C22⋊C4D3211yescharacteristic
128C22⋊C8—61no—
129#95—31no—
130#95—61no—
131C23×C3—22no—
132C23×C3—22no—
133C23×C3—21no—
134C23×C3—21no—
135C23×C3—21no—
136C23×C3—21no—
137C23×C3—21no—
138C23×C3—21no—
139C23×C3—21no—
140C23×C3—41no—
141C23×C3—41no—
142C23×C3—41no—
143C23×C3—41no—
144C23×C3—81no—
145C23×C3—81no—
146C23×C3#20411yescharacteristic
147C23×C3D2411yescharacteristic
148C23×C3(C2×D3)⋊C411yescharacteristic
149C23×C3#21311yescharacteristic
150C23×C3#21411yescharacteristic
151C23×C3#21711yescharacteristic
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—41no—
157C2×C3×C4—41no—
158C2×C3×C4—41no—
159C2×C3×C4—41no—
160C2×C3×C4—41no—
161C2×C3×C4—41no—
162C2×C3×C4—81no—
163C2×C3×C4—81no—
164C2×C3×C4—121no—
165C2×C3×C4—121no—
166C2×C3×C4—121no—
167C2×C3×C4—121no—
168C2×C3×C4—121no—
169C2×C3×C4—121no—
170C2×Dic3—41no—
171C2×Dic3—41no—
172C2×Dic3—41no—
173C2×Dic3—41no—
174C2×Dic3—41no—
175C2×Dic3—41no—
176C2×Dic3—124no—
177C2×Dic3—122no—
178C2×Dic3—122no—
179C2×Dic3—242no—
180C2×Dic3—242no—
181C2×Dic3—241no—
182C2×Dic3—241no—
183C2×Dic3—241no—
184C2×Dic3—241no—
185C3×C8—241no—
186C3⋊C8—81no—
187C2×C32—21no—
188C2×C32—21no—
189C2×C32—41no—
190C2×C32—41no—
191C2×C32#32711yescharacteristic
192C2×C32#35211yescharacteristic
193C2×C32#35411yescharacteristic
194C24#62611yescharacteristic
195C22×C4—61no—
196C22×C4—61no—
197C22×C4—361no—
198C22×C4D3×Dic311yescharacteristic
199C22×C4#62511yescharacteristic
200C2×C8—121no—
201C4⋊C4—121no—
202C22⋊C4—41no—
203C22⋊C4—121no—
204C22⋊C4—121no—
205C22⋊C4—182no—
206C22⋊C4—361no—
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—21no—
210C22×C3—21no—
211C22×C3—22no—
212C22×C3—22no—
213C22×C3—21no—
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—21no—
217C22×C3—21no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—41no—
221C22×C3—41no—
222C22×C3—41no—
223C22×C3—41no—
224C22×C3—41no—
225C22×C3—41no—
226C22×C3—42no—
227C22×C3—42no—
228C22×C3—41no—
229C22×C3—41no—
230C22×C3—41no—
231C22×C3—41no—
232C22×C3—81no—
233C22×C3—81no—
234C22×C3—81no—
235C22×C3—81no—
236C22×C3—82no—
237C22×C3#80611yescharacteristic
238C22×C3#82111yescharacteristic
239C22×C3#82511yescharacteristic
240C22×C3#83211yescharacteristic
241C22×C3#83411yescharacteristic
242C22×C3#83711yescharacteristic
243C3×C4—41no—
244C3×C4—41no—
245C3×C4—41no—
246C3×C4—41no—
247C3×C4—81no—
248C3×C4—81no—
249C3×C4—241no—
250C3×C4—241no—
251Dic3—81no—
252Dic3—81no—
253Dic3—244no—
254Dic3—242no—
255Dic3—242no—
256C32#134411yescharacteristic, complemented, Sylow
257C23—21no—
258C23—21no—
259C23—41no—
260C23—41no—
261C23#371411yescharacteristic
262C23#371611yescharacteristic
263C23(C2×D3)⋊Dic311yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—121no—
269C2×C4—121no—
270C2×C4—121no—
271C2×C4—121no—
272C2×C4—121no—
273C2×C4—121no—
274C2×C4—362no—
275C2×C4—721no—
276C2×C4—721no—
277C8—241no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—41no—
286C2×C3—41no—
287C2×C3—42no—
288C2×C3—42no—
289C2×C3—41no—
290C2×C3—41no—
291C2×C3—41no—
292C2×C3—41no—
293C2×C3#447011yescharacteristic
294C2×C3#447311yescharacteristic
295C2×C3#447611yescharacteristic
296C2×C3#453711yescharacteristic
297C2×C3#453911yescharacteristic
298C2×C3#454111yescharacteristic
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22#6356311yescharacteristic
309C22#6356811yescharacteristic
310C22#6358011yescharacteristic
311C4—41no—
312C4—41no—
313C4—241no—
314C4—241no—
315C4—722no—
316C3—21no—
317C3#6745011yescharacteristic, complemented
318C3#6764911yescharacteristic, complemented
319C2—21no—
320C2—21no—
321C2—41no—
322C2—41no—
323C2#1058915011yescharacteristic
324C2#1058917611yescharacteristic
325C2#1058918011yescharacteristic
subgroupG/H
centerC22#63580
commutatorC22×C32×C4C2×C4
Frattini, hypercenterC2×C22⋊C4D32
Fitting, cosocleC2×C32×C22⋊C4C22
socleC22×C32#99
prime radicalC24×C32D4
hypocenterC32#1344
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
9. C2×C3×C4⋊Dic3C4semidirect
11. C3×C3⋊#95C4semidirect
43. C2×C4⋊Dic3Dic3semidirect
48. C3⋊#95Dic3semidirect
256. C32#1344semidirect
317. C3#67450semidirect
318. C3#67649semidirect

Maximal subgroups

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

subgroupindex
C3×#49532
#105893922
C3×#45252
#676493
#674503