Finite Group Databasebeta

← #11773768

Subgroups — #11773768

Order 1152.

693 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 693 conjugacy classes of subgroups — too many to draw. Only its 156 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
1C2×#64081C211yesmaximal, characteristic
2C3×#4925C212yesmaximal, complemented
3#10589148C212yesmaximal, complemented
4#10589146C212yesmaximal
5#70782—32nomaximal
6C22×C4×C3⋊D3C411yescharacteristic
7C2×C32×C42C2211yescharacteristic
8C2×#3752C411yescharacteristic
9C2×#3752C2211yescharacteristic
10C2×#3750C411yescharacteristic
11C2×#3750C2211yescharacteristic
12C2×C4×C3⋊Dic3C411yescharacteristic
13#64081—22no—
14#64081—22no—
15C3×#830C2214yes—
16C3×C4⋊(C3⋊C8)—22no—
17C3×C4×C3⋊C8—22no—
18C2×#872—32no—
19C2×#872—61no—
20C3×#431—32no—
21#4925D312yescomplemented
22#4469—34no—
23#4468—34no—
24C23×C3⋊D3C2×C411yescharacteristic
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3C2×C411yescharacteristic
31C2×C4×C3⋊D3—21no—
32C2×C4×C3⋊D3—21no—
33C2×C4×C3⋊D3—22no—
34C2×C4×C3⋊D3C814yescomplemented
35C32×C42D412yes—
36C32×C42D412yes—
37#3752—22no—
38#3752—22no—
39#3750—22no—
40#3750—22no—
41C4×C3⋊Dic3—21no—
42C4×C3⋊Dic3—21no—
43C2×C3×C3⋊C8—24no—
44#1458—91noSylow
45C22×C4×D3—32no—
46C22×C4×D3—61no—
47C2×C3×C42—21no—
48C2×C3×C42C2×D312yes—
49C2×(C2×D3)⋊C4—32no—
50C2×(C2×D3)⋊C4—32no—
51C2×(C2×D3)⋊C4—61no—
52C2×(C2×D3)⋊C4—61no—
53C2×Dic3⋊C4—32no—
54C2×Dic3⋊C4—32no—
55C2×Dic3⋊C4—61no—
56C2×Dic3⋊C4—61no—
57C2×C4×Dic3—32no—
58C2×C4×Dic3—61no—
59#872—64no—
60#872—64no—
61#872—62no—
62#872—62no—
63#872—62no—
64#872—62no—
65C3×C4⋊C8—62no—
66C3×C22⋊C8—34no—
67C3×C4×C8—62no—
68#830C2×D314yes—
69C4⋊(C3⋊C8)—22no—
70C4×C3⋊C8—22no—
71C23×C32C22×C411yescharacteristic
72C22×C3⋊D3—21no—
73C22×C3⋊D3—21no—
74C22×C3⋊D3—41no—
75C22×C3⋊D3—41no—
76C22×C3⋊D3C2×C812yes—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C32×C4C22⋊C412yes—
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22⋊C411yescharacteristic
82C2×C32×C4C2×C812yes—
83C2×C32×C4M1612yes—
84C2×C32×C4C2×D412yes—
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—21no—
88C2×C3⋊Dic3—21no—
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3C2×C812yes—
92C4×C3⋊D3—24no—
93C4×C3⋊D3—24no—
94C3×C3⋊C8—44no—
95C2×#117—91no—
96#431—32no—
97#324—92no—
98#323—92no—
99C23×D3—32no—
100C23×D3—61no—
101C22×C3×C4—21no—
102C22×C3×C4—21no—
103C22×C3×C4—21no—
104C22×C3×C4C4×D312yes—
105C22×C3×C4C4×D312yes—
106C22×C3×C4C22×D312yes—
107C22×Dic3—32no—
108C22×Dic3—32no—
109C22×Dic3—32no—
110C22×Dic3—61no—
111C22×Dic3—61no—
112C22×Dic3—61no—
113C2×C4×D3—38no—
114C2×C4×D3—64no—
115C2×C4×D3—62no—
116C2×C4×D3—62no—
117C2×C4×D3—64no—
118C2×C4×D3—64no—
119C2×C4×D3—62no—
120C2×C4×D3—62no—
121C2×C3×C8—64no—
122C3×C42—22no—
123C3×C42—22no—
124C3×C42D1212yes—
125C3×C42D1212yes—
126C3×C42#6712yes—
127C3×C42#6712yes—
128(C2×D3)⋊C4—64no—
129(C2×D3)⋊C4—64no—
130(C2×D3)⋊C4—62no—
131(C2×D3)⋊C4—62no—
132(C2×D3)⋊C4—62no—
133(C2×D3)⋊C4—62no—
134Dic3⋊C4—64no—
135Dic3⋊C4—64no—
136Dic3⋊C4—62no—
137Dic3⋊C4—62no—
138Dic3⋊C4—62no—
139Dic3⋊C4—62no—
140C4×Dic3—62no—
141C4×Dic3—62no—
142C4×Dic3—62no—
143C4×Dic3—62no—
144C2×C3⋊C8—24no—
145C22×C32—21no—
146C22×C32—21no—
147C22×C32C2×C22⋊C411yescharacteristic
148C22×C32C22×C811yescharacteristic
149C22×C32C2×M1611yescharacteristic
150C2×C3⋊D3—22no—
151C2×C3⋊D3—42no—
152C2×C3⋊D3—41no—
153C2×C3⋊D3—41no—
154C2×C3⋊D3—42no—
155C32×C4—22no—
156C32×C4—22no—
157C32×C4C22⋊C812yes—
158C32×C4C22⋊C812yes—
159C3⋊Dic3—22no—
160C3⋊Dic3—41no—
161C3⋊Dic3—41no—
162C23×C4—91no—
163#117—182no—
164#117—182no—
165C2×C4⋊C4—91no—
166C2×C4⋊C4—91no—
167C2×C22⋊C4—91no—
168C2×C22⋊C4—91no—
169C2×C42—91no—
170C2×C42D3211yescharacteristic
171C4⋊C8—62no—
172C22⋊C8—34no—
173C4×C8—62no—
174C23×C3—21no—
175C23×C3C2×C4×D312yes—
176C22×D3—34no—
177C22×D3—62no—
178C22×D3—62no—
179C22×D3—62no—
180C22×D3—62no—
181C22×D3—62no—
182C22×D3—122no—
183C22×D3—122no—
184C22×D3—122no—
185C22×D3—122no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—21no—
189C2×C3×C4—22no—
190C2×C3×C4—21no—
191C2×C3×C4—22no—
192C2×C3×C4—42no—
193C2×C3×C4—42no—
194C2×C3×C4—42no—
195C2×C3×C4—42no—
196C2×C3×C4D3×C814yes—
197C2×C3×C4ΓL(1,𝔽25)14yes—
198C2×C3×C4(C2×D3)⋊C412yes—
199C2×C3×C4(C2×D3)⋊C412yes—
200C2×C3×C4(C2×D3)⋊C412yes—
201C2×C3×C4(C2×D3)⋊C412yes—
202C2×C3×C4C2×D1212yes—
203C2×C3×C4C2×#6712yes—
204C2×Dic3—34no—
205C2×Dic3—62no—
206C2×Dic3—62no—
207C2×Dic3—62no—
208C2×Dic3—62no—
209C2×Dic3—62no—
210C2×Dic3—62no—
211C2×Dic3—62no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—122no—
215C2×Dic3—122no—
216C2×Dic3—122no—
217C2×Dic3—122no—
218C4×D3—68no—
219C4×D3—68no—
220C4×D3—68no—
221C4×D3—68no—
222C3×C8—124no—
223C3⋊C8—44no—
224C2×C32—21no—
225C2×C32—21no—
226C2×C32C2×C22⋊C811yescharacteristic
227C2×C32#41011yescharacteristic
228C2×C32#41311yescharacteristic
229C3⋊D3—42no—
230C24—91no—
231C22×C4—91no—
232C22×C4—94no—
233C22×C4—91no—
234C22×C4—91no—
235C22×C4—182no—
236C22×C4—181no—
237C22×C4—181no—
238C22×C4#62411yescharacteristic
239C22×C4#62411yescharacteristic
240C22×C4C2×D3211yescharacteristic
241C2×C8—64no—
242C4⋊C4—182no—
243C4⋊C4—182no—
244C22⋊C4—182no—
245C22⋊C4—182no—
246C42—181no—
247C42—181no—
248C42#62612yes—
249C42#62612yes—
250C22×C3—22no—
251C22×C3—22no—
252C22×C3—22no—
253C22×C3—22no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3C2×D3×C812yes—
258C22×C3C2×ΓL(1,𝔽25)12yes—
259C22×C3C2×(C2×D3)⋊C412yes—
260C2×D3—64no—
261C2×D3—64no—
262C2×D3—124no—
263C2×D3—124no—
264C2×D3—124no—
265C2×D3—122no—
266C2×D3—122no—
267C2×D3—122no—
268C2×D3—122no—
269C2×D3—124no—
270C3×C4—22no—
271C3×C4—22no—
272C3×C4—22no—
273C3×C4—22no—
274C3×C4—22no—
275C3×C4—22no—
276C3×C4—42no—
277C3×C4—42no—
278C3×C4(C2×D3)⋊C814yes—
279C3×C4(C2×D3)⋊C814yes—
280Dic3—64no—
281Dic3—64no—
282Dic3—122no—
283Dic3—122no—
284Dic3—122no—
285Dic3—122no—
286C32#145811yescharacteristic, complemented, Sylow
287C23—92no—
288C23—181no—
289C23—181no—
290C23—361no—
291C23—361no—
292C23C2×#62411yescharacteristic
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—92no—
296C2×C4—181no—
297C2×C4—181no—
298C2×C4—184no—
299C2×C4—184no—
300C2×C4—181no—
301C2×C4—181no—
302C2×C4—361no—
303C2×C4—361no—
304C2×C4#371012yes—
305C2×C4#371212yes—
306C2×C4#372212yes—
307C2×C4#372211yescharacteristic
308C2×C4#372211yescharacteristic
309C2×C4C2×#62612yes—
310C8—124no—
311C2×C3—22no—
312C2×C3—22no—
313C2×C3—22no—
314C2×C3—22no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3#500612yes—
319C2×C3C2×(C2×D3)⋊C812yes—
320C2×C3#513212yes—
321D3—124no—
322D3—124no—
323C22—21no—
324C22—21no—
325C22—182no—
326C22—362no—
327C22—362no—
328C22—361no—
329C22—361no—
330C22C2×#371011yescharacteristic
331C22C2×#371211yescharacteristic
332C22C2×#372211yescharacteristic
333C4—22no—
334C4—22no—
335C4—182no—
336C4—361no—
337C4—361no—
338C4#6355712yes—
339C4#6355712yes—
340C3—21no—
341C3#7078212yescomplemented
342C2—21no—
343C2—21no—
344C2—362no—
345C2C2×#6355711yescharacteristic
346C2#1059107811yescharacteristic
347C2#1059123211yescharacteristic
subgroupG/H
centerC2×C4#3722
commutatorC22×C32C22×C8
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1458
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4925C2semidirect
3. #10589148C2semidirect
21. #4925D3semidirect
34. C2×C4×C3⋊D3C8semidirect
286. C32#1458semidirect
341. C3#70782semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C3×#49252
#105891482
#105891462
#707823