Finite Group Databasebeta

← #11771926

Subgroups — #11771926

Order 1152.

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

normal subgroups only

This group has 395 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×#4947C211yesmaximal, characteristic
2#10589392C211yesmaximal, characteristic
3C3×#4525C211yesmaximal, characteristic
4#67646—31nomaximal
5#67449—31nomaximal
6C22×C3×Dic6C411yescharacteristic, complemented
7C2×C32×C22⋊C4C2211yescharacteristic
8C2×#3757—21no—
9C2×C3×#217—21no—
10C3×C3⋊#95—21no—
11C3×C3⋊#95C411yescharacteristic, complemented
12C3×#830—21no—
13C3×#393—31no—
14#4947D311yescharacteristic
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—
26C2×C3×Dic6—41no—
27C2×C3×Dic6—42no—
28C32×C22⋊C4—41no—
29#3757—22no—
30#3757—41no—
31C3×#217—42no—
32C2×C3×C3⋊C8—41no—
33#1351—91noSylow
34C22×C3×Q8—31no—
35C22×Dic6Dic311yescharacteristic, complemented
36C2×C3×C22⋊C4—21no—
37C2×C3×C22⋊C4—61no—
38C2×C3×C22⋊C4C2×D311yescharacteristic
39C2×C3×C22⋊C4C2×D311yescharacteristic
40C2×#217—21no—
41C2×#217—62no—
42C2×#217—61no—
43C2×#217—61no—
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×C32SD1611yescharacteristic
56C23×C32Q1611yescharacteristic
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—22no—
65C2×C3×Dic3—41no—
66C2×C3×Dic3—41no—
67C2×C3×Dic3—41no—
68C2×C3×Dic3—41no—
69C2×C3×Dic3—41no—
70C3×Dic6—42no—
71C3×Dic6—42no—
72C3×C3⋊C8—81no—
73#393—31no—
74#342—91no—
75#323—31no—
76C24×C3—21no—
77C24×C3D1211yescharacteristic
78C24×C3#6711yescharacteristic
79C2×C3×Q8—121no—
80C2×C3×Q8—122no—
81C22×C3×C4—21no—
82C22×C3×C4—21no—
83C22×C3×C4—61no—
84C22×C3×C4—61no—
85C22×C3×C4C4×D311yescharacteristic
86C22×C3×C4C2×Dic311yescharacteristic
87C22×C3×C4#6711yescharacteristic
88C22×C3×C4#6711yescharacteristic
89C22×Dic3—21no—
90C22×Dic3—21no—
91C22×Dic3—122no—
92C22×Dic3—121no—
93C22×Dic3—121no—
94C2×Dic6—41no—
95C2×Dic6—42no—
96C2×C3×C8—121no—
97C3×C22⋊C4—41no—
98C3×C22⋊C4—41no—
99C3×C22⋊C4—42no—
100C3×C22⋊C4—122no—
101#217—42no—
102#217—64no—
103#217—62no—
104#217—62no—
105#217—122no—
106#217—121no—
107#217—121no—
108C2×C3⋊C8—41no—
109C22×C32—21no—
110C22×C32—21no—
111C22×C32—21no—
112C22×C32—21no—
113C22×C32—41no—
114C22×C32—41no—
115C22×C32—41no—
116C22×C32—41no—
117C22×C32—81no—
118C22×C32#9911yescharacteristic
119C22×C32#10311yescharacteristic
120C22×C32#10411yescharacteristic
121C32×C4—41no—
122C32×C4—41no—
123C3⋊Dic3—82no—
124C3×Dic3—42no—
125C3×Dic3—81no—
126C22×Q8—31no—
127C2×C22⋊C4—61no—
128C2×C22⋊C4—181no—
129C2×C22⋊C4D3211yescharacteristic
130C22⋊C8—61no—
131#95—31no—
132#95—61no—
133C23×C3—22no—
134C23×C3—22no—
135C23×C3—21no—
136C23×C3—21no—
137C23×C3—21no—
138C23×C3—21no—
139C23×C3—21no—
140C23×C3—21no—
141C23×C3—21no—
142C23×C3—41no—
143C23×C3—41no—
144C23×C3—41no—
145C23×C3—41no—
146C23×C3—81no—
147C23×C3—81no—
148C23×C3#20411yescharacteristic
149C23×C3Dic1211yescharacteristic
150C23×C3(C2×D3)⋊C411yescharacteristic
151C23×C3#21511yescharacteristic
152C23×C3#21611yescharacteristic
153C23×C3#21711yescharacteristic
154C3×Q8—122no—
155C3×Q8—122no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—41no—
161C2×C3×C4—41no—
162C2×C3×C4—41no—
163C2×C3×C4—41no—
164C2×C3×C4—41no—
165C2×C3×C4—41no—
166C2×C3×C4—62no—
167C2×C3×C4—81no—
168C2×C3×C4—81no—
169C2×C3×C4—121no—
170C2×C3×C4—121no—
171C2×C3×C4—121no—
172C2×C3×C4—121no—
173C2×C3×C4—121no—
174C2×Dic3—22no—
175C2×Dic3—41no—
176C2×Dic3—41no—
177C2×Dic3—41no—
178C2×Dic3—41no—
179C2×Dic3—41no—
180C2×Dic3—124no—
181C2×Dic3—122no—
182C2×Dic3—122no—
183C2×Dic3—242no—
184C2×Dic3—242no—
185C2×Dic3—241no—
186C2×Dic3—241no—
187C2×Dic3—241no—
188C2×Dic3—241no—
189Dic6—42no—
190Dic6—42no—
191C3×C8—241no—
192C3⋊C8—81no—
193C2×C32—21no—
194C2×C32—21no—
195C2×C32—41no—
196C2×C32—41no—
197C2×C32#32811yescharacteristic
198C2×C32AΣL(1,𝔽16)11yescharacteristic
199C2×C32#35411yescharacteristic
200C24#62611yescharacteristic
201C2×Q8—121no—
202C2×Q8—122no—
203C22×C4—61no—
204C22×C4—61no—
205C22×C4—361no—
206C22×C4D3×Dic311yescharacteristic
207C22×C4#62511yescharacteristic
208C2×C8—121no—
209C22⋊C4—41no—
210C22⋊C4—122no—
211C22⋊C4—182no—
212C22⋊C4—361no—
213C22×C3—21no—
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—21no—
217C22×C3—22no—
218C22×C3—22no—
219C22×C3—21no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—41no—
227C22×C3—41no—
228C22×C3—41no—
229C22×C3—41no—
230C22×C3—41no—
231C22×C3—41no—
232C22×C3—42no—
233C22×C3—42no—
234C22×C3—41no—
235C22×C3—41no—
236C22×C3—41no—
237C22×C3—41no—
238C22×C3—81no—
239C22×C3—81no—
240C22×C3—81no—
241C22×C3—81no—
242C22×C3—82no—
243C22×C3#80611yescharacteristic
244C22×C3#81611yescharacteristic
245C22×C3#82511yescharacteristic
246C22×C3#83411yescharacteristic
247C22×C3#83511yescharacteristic
248C22×C3#83711yescharacteristic
249C3×C4—41no—
250C3×C4—41no—
251C3×C4—41no—
252C3×C4—41no—
253C3×C4—81no—
254C3×C4—81no—
255C3×C4—122no—
256C3×C4—241no—
257Dic3—42no—
258Dic3—81no—
259Dic3—244no—
260Dic3—242no—
261Dic3—242no—
262C32#135111yescharacteristic, complemented, Sylow
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23#371711yescharacteristic
268C23#371911yescharacteristic
269C23(C2×D3)⋊Dic311yescharacteristic
270Q8—122no—
271Q8—122no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—62no—
277C2×C4—121no—
278C2×C4—121no—
279C2×C4—121no—
280C2×C4—121no—
281C2×C4—121no—
282C2×C4—362no—
283C2×C4—721no—
284C2×C4—721no—
285C8—241no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—41no—
294C2×C3—41no—
295C2×C3—42no—
296C2×C3—42no—
297C2×C3—41no—
298C2×C3—41no—
299C2×C3—41no—
300C2×C3—41no—
301C2×C3#446711yescharacteristic
302C2×C3#447311yescharacteristic
303C2×C3#447511yescharacteristic
304C2×C3#453611yescharacteristic
305C2×C3#453811yescharacteristic
306C2×C3#454111yescharacteristic
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—81no—
316C22#6356611yescharacteristic
317C22#6356811yescharacteristic
318C22#6358011yescharacteristic
319C4—41no—
320C4—41no—
321C4—122no—
322C4—241no—
323C4—722no—
324C3—21no—
325C3#6744911yescharacteristic, complemented
326C3#6764611yescharacteristic, complemented
327C2—21no—
328C2—21no—
329C2—41no—
330C2—41no—
331C2#1058915211yescharacteristic
332C2#1058917311yescharacteristic
333C2#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#1351
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
6. C22×C3×Dic6C4semidirect
11. C3×C3⋊#95C4semidirect
35. C22×Dic6Dic3semidirect
48. C3⋊#95Dic3semidirect
262. C32#1351semidirect
325. C3#67449semidirect
326. C3#67646semidirect

Maximal subgroups

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

subgroupindex
C3×#49472
#105893922
C3×#45252
#676463
#674493