Finite Group Databasebeta

← #11771808

Subgroups — #11771808

Order 1152.

377 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 377 conjugacy classes of subgroups — too many to draw. Only its 64 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#10592652C211yesmaximal, characteristic
2C3×#4526C211yesmaximal, characteristic
3C3×#4525C211yesmaximal, characteristic
4#67491—31nomaximal
5#67450—31nomaximal
6C2×C32×C22⋊C4C2211yescharacteristic
7C2×#3757—21no—
8C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
9C2×C3×#217—21no—
10#63658—21no—
11#63658C411yescharacteristic, complemented
12C3×#830—21no—
13#4953—31no—
14#4953—31no—
15#4953—61no—
16C3×#342—31no—
17C3×#323—31no—
18#4526D311yescharacteristic
19#4525D311yescharacteristic
20C24×C32D411yescharacteristic
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3—21no—
24C22×C3⋊Dic3—21no—
25C22×C3×Dic3—41no—
26C32×C22⋊C4—41no—
27#3757—41no—
28#3757—41no—
29C4⋊(C3⋊Dic3)—41no—
30C3×#217—22no—
31C3×#217—41no—
32C2×C3×C3⋊C8—41no—
33#1344—91noSylow
34C2×C3×C22⋊C4—21no—
35C2×C3×C22⋊C4—61no—
36C2×C3×C22⋊C4C2×D311yescharacteristic
37C2×C3×C22⋊C4C2×D311yescharacteristic
38C2×#217—21no—
39C2×#217—62no—
40C2×#217—61no—
41C2×#217—61no—
42C2×C4⋊Dic3—31no—
43C2×C4⋊Dic3—31no—
44C2×C4⋊Dic3—61no—
45C3×C22⋊C8—61no—
46C3⋊#95—31no—
47C3⋊#95—31no—
48C3⋊#95—61no—
49C3⋊#95—62no—
50C3⋊#95—61no—
51C3⋊#95—61no—
52#830—21no—
53C23×C32—21no—
54C23×C32—21no—
55C23×C32—41no—
56C23×C32—41no—
57C23×C32C22⋊C411yescharacteristic
58C23×C32D811yescharacteristic
59C23×C32SD1611yescharacteristic
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4—41no—
63C2×C32×C4—41no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3—41no—
66C2×C3⋊Dic3—41no—
67C2×C3⋊Dic3—41no—
68C2×C3⋊Dic3—41no—
69C2×C3⋊Dic3—41no—
70C2×C3×Dic3—42no—
71C2×C3×Dic3—81no—
72C2×C3×Dic3—81no—
73C3×C3⋊C8—81no—
74#397—91no—
75#342—31no—
76#323—31no—
77C24×C3—21no—
78C24×C3D1211yescharacteristic
79C24×C3#6711yescharacteristic
80C22×C3×C4—21no—
81C22×C3×C4—21no—
82C22×C3×C4—121no—
83C22×C3×C4C4×D311yescharacteristic
84C22×C3×C4C4×D311yescharacteristic
85C22×C3×C4D1211yescharacteristic
86C22×C3×C4#6711yescharacteristic
87C22×Dic3—41no—
88C22×Dic3—62no—
89C22×Dic3—62no—
90C22×Dic3—61no—
91C22×Dic3—61no—
92C22×Dic3—61no—
93C22×Dic3—61no—
94C2×C3×C8—121no—
95C3×C22⋊C4—41no—
96C3×C22⋊C4—41no—
97C3×C22⋊C4—42no—
98C3×C22⋊C4—62no—
99C3×C22⋊C4—121no—
100#217—22no—
101#217—41no—
102#217—122no—
103#217—122no—
104#217—121no—
105#217—121no—
106#217—121no—
107#217—121no—
108C4⋊Dic3—122no—
109C4⋊Dic3—121no—
110C4⋊Dic3—121no—
111C2×C3⋊C8—41no—
112C22×C32—21no—
113C22×C32—21no—
114C22×C32—21no—
115C22×C32—21no—
116C22×C32—41no—
117C22×C32—41no—
118C22×C32—41no—
119C22×C32—41no—
120C22×C32—81no—
121C22×C32#9911yescharacteristic
122C22×C32#10211yescharacteristic
123C22×C32#10411yescharacteristic
124C32×C4—41no—
125C32×C4—41no—
126C3⋊Dic3—81no—
127C3⋊Dic3—81no—
128C3×Dic3—82no—
129C2×C4⋊C4—91no—
130C2×C22⋊C4—61no—
131C2×C22⋊C4—181no—
132C2×C22⋊C4D3211yescharacteristic
133C22⋊C8—61no—
134#95—91no—
135#95—181no—
136C23×C3—21no—
137C23×C3—21no—
138C23×C3—21no—
139C23×C3—21no—
140C23×C3—21no—
141C23×C3—21no—
142C23×C3—21no—
143C23×C3—41no—
144C23×C3—41no—
145C23×C3—41no—
146C23×C3—41no—
147C23×C3—41no—
148C23×C3—41no—
149C23×C3—42no—
150C23×C3—42no—
151C23×C3#20411yescharacteristic
152C23×C3D2411yescharacteristic
153C23×C3(C2×D3)⋊C411yescharacteristic
154C23×C3(C2×D3)⋊C411yescharacteristic
155C23×C3#21311yescharacteristic
156C23×C3#21511yescharacteristic
157C2×C3×C4—22no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—41no—
163C2×C3×C4—42no—
164C2×C3×C4—41no—
165C2×C3×C4—41no—
166C2×C3×C4—41no—
167C2×C3×C4—41no—
168C2×C3×C4—42no—
169C2×C3×C4—122no—
170C2×C3×C4—241no—
171C2×C3×C4—241no—
172C2×Dic3—42no—
173C2×Dic3—81no—
174C2×Dic3—81no—
175C2×Dic3—122no—
176C2×Dic3—122no—
177C2×Dic3—122no—
178C2×Dic3—122no—
179C2×Dic3—122no—
180C2×Dic3—121no—
181C2×Dic3—121no—
182C2×Dic3—121no—
183C2×Dic3—121no—
184C2×Dic3—122no—
185C2×Dic3—121no—
186C2×Dic3—121no—
187C2×Dic3—121no—
188C2×Dic3—121no—
189C2×Dic3—121no—
190C2×Dic3—121no—
191C2×Dic3—121no—
192C2×Dic3—121no—
193C3×C8—241no—
194C3⋊C8—81no—
195C2×C32—21no—
196C2×C32—21no—
197C2×C32—41no—
198C2×C32—41no—
199C2×C32#32711yescharacteristic
200C2×C32#35211yescharacteristic
201C2×C32#35411yescharacteristic
202C24#62611yescharacteristic
203C22×C4—121no—
204C22×C4—181no—
205C22×C4—181no—
206C22×C4#62411yescharacteristic
207C22×C4#62611yescharacteristic
208C2×C8—121no—
209C4⋊C4—361no—
210C22⋊C4—41no—
211C22⋊C4—62no—
212C22⋊C4—121no—
213C22⋊C4—361no—
214C22⋊C4—361no—
215C22×C3—22no—
216C22×C3—22no—
217C22×C3—21no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—41no—
229C22×C3—41no—
230C22×C3—41no—
231C22×C3—41no—
232C22×C3—41no—
233C22×C3—41no—
234C22×C3—42no—
235C22×C3—42no—
236C22×C3—41no—
237C22×C3—41no—
238C22×C3—41no—
239C22×C3—41no—
240C22×C3—81no—
241C22×C3—81no—
242C22×C3—81no—
243C22×C3—81no—
244C22×C3—82no—
245C22×C3#80511yescharacteristic
246C22×C3#80611yescharacteristic
247C22×C3#80611yescharacteristic
248C22×C3#80911yescharacteristic
249C22×C3#82111yescharacteristic
250C22×C3#82511yescharacteristic
251C3×C4—42no—
252C3×C4—41no—
253C3×C4—41no—
254C3×C4—41no—
255C3×C4—41no—
256C3×C4—81no—
257C3×C4—242no—
258Dic3—82no—
259Dic3—242no—
260Dic3—241no—
261Dic3—241no—
262Dic3—242no—
263Dic3—241no—
264Dic3—241no—
265C32#134411yescharacteristic, complemented, Sylow
266C23—21no—
267C23—21no—
268C23—41no—
269C23—41no—
270C23#371411yescharacteristic
271C23#371711yescharacteristic
272C23#372211yescharacteristic
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—122no—
278C2×C4—241no—
279C2×C4—241no—
280C2×C4—361no—
281C2×C4—361no—
282C2×C4—361no—
283C2×C4—361no—
284C2×C4—361no—
285C2×C4—361no—
286C8—241no—
287C2×C3—22no—
288C2×C3—22no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—41no—
297C2×C3—41no—
298C2×C3—41no—
299C2×C3—41no—
300C2×C3—81no—
301C2×C3—81no—
302C2×C3#445111yescharacteristic
303C2×C3#447011yescharacteristic
304C2×C3#447211yescharacteristic
305C2×C3#447311yescharacteristic
306C2×C3#447311yescharacteristic
307C2×C3#447611yescharacteristic
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22#6356411yescharacteristic
318C22#6357011yescharacteristic
319C22#6358111yescharacteristic
320C4—41no—
321C4—41no—
322C4—242no—
323C4—721no—
324C4—721no—
325C3—21no—
326C3#6745011yescharacteristic, complemented
327C3#6749111yescharacteristic, complemented
328C2—21no—
329C2—21no—
330C2—41no—
331C2—41no—
332C2#1058915111yescharacteristic
333C2#1058917711yescharacteristic
334C2#1058918111yescharacteristic
subgroupG/H
centerC22#63581
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
8. C2×C4⋊(C3⋊Dic3)C4semidirect
11. #63658C4semidirect
265. C32#1344semidirect
326. C3#67450semidirect
327. C3#67491semidirect

Maximal subgroups

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

subgroupindex
#105926522
C3×#45262
C3×#45252
#674913
#674503