Finite Group Databasebeta

← #11796536

Subgroups — #11796536

Order 1152.

595 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 595 conjugacy classes of subgroups — too many to draw. Only its 108 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#10596287C211yesmaximal, characteristic
2C2×C3×#836C212yesmaximal, complemented
3#10589185C212yesmaximal, complemented
4#10589183C212yesmaximal, complemented
5#70128—32nomaximal
6C22×C32×Q8C2211yescharacteristic
7C2×#3828C411yescharacteristic
8#64156C411yescharacteristic
9#64156C2211yescharacteristic
10#64155—22no—
11#64153C411yescharacteristic
12#64153C2211yescharacteristic
13#64138—22no—
14#64135C411yescharacteristic
15C2×C3×#208—22no—
16C3×#836—22no—
17C3×#836C2214yes—
18#5816—32no—
19#5816—61no—
20C2×C3×#101—32no—
21C2×#836D312yescomplemented
22#4478—34no—
23#4477—34no—
24C2×C32×Q8—42no—
25C2×C32×Q8C2×C411yescharacteristic
26C2×C32×Q8D412yes—
27C2×C32×Q8C2311yescharacteristic
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4D412yes—
30C2×#638—21no—
31#3828—42no—
32C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
33C2×C4×C3⋊D3—21no—
34C2×#634C2×C411yescharacteristic
35#3757—21no—
36#3752—22no—
37#3752—22no—
38C4⋊(C3⋊Dic3)—21no—
39#3750—22no—
40#3750—22no—
41C4×C3⋊Dic3C2×C411yescharacteristic
42C4×C3⋊Dic3C2×C411yescharacteristic
43C3×#208—24no—
44C3×#208—42no—
45C2×C3×C3⋊C8—42no—
46#2133—91noSylow
47C22×C3×Q8—21no—
48C22×C3×Q8C2×D312yes—
49C2×#235—32no—
50C2×#235—61no—
51C2×C3×M16—62no—
52#947—32no—
53#947—32no—
54#947—61no—
55#947—61no—
56#946—64no—
57#946—62no—
58#946—62no—
59#944—32no—
60#944—32no—
61#944—61no—
62#944—61no—
63#929—64no—
64#929—62no—
65#929—62no—
66#926—32no—
67#926—61no—
68C2×#208—22no—
69C3×#101—34no—
70C3×#101—62no—
71#836—22no—
72#836C2×D314yes—
73C23×C32C22⋊C411yescharacteristic
74C22×C3⋊D3—21no—
75C32×Q8—41no—
76C32×Q8—42no—
77C32×Q8—41no—
78C2×C32×C4—22no—
79C2×C32×C4—22no—
80C2×C32×C4—22no—
81C2×C32×C4C22⋊C412yes—
82C2×C32×C4C22⋊C411yescharacteristic
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4C2×D412yes—
85#638—42no—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—21no—
88C2×C3⋊Dic3—21no—
89C4⋊(C3⋊D3)—41no—
90C4×C3⋊D3—42no—
91#634—41no—
92C3×C3⋊C8—44no—
93#536—91no—
94C2×#101—32no—
95#356—92no—
96#355—92no—
97C2×C3×Q8—21no—
98C2×C3×Q8—22no—
99C2×C3×Q8—21no—
100C2×C3×Q8—42no—
101C2×C3×Q8—42no—
102C2×C3×Q8—44no—
103C2×C3×Q8C4×D312yes—
104C2×C3×Q8D1212yes—
105C2×C3×Q8#6712yes—
106C2×C3×Q8C22×D312yes—
107C22×C3×C4—21no—
108C22×C3×C4—22no—
109C22×C3×C4C4×D312yes—
110C22×C3×C4D1212yes—
111C22×C3×C4#6712yes—
112C2×#67—62no—
113C2×#67—62no—
114#235—124no—
115#235—122no—
116#235—122no—
117C2×D12—32no—
118C2×D12—61no—
119C2×C4×D3—62no—
120C2×C4×D3—62no—
121C2×Dic6—32no—
122C2×Dic6—61no—
123C3×M16—64no—
124C3×M16—122no—
125C2×C3×C8—122no—
126#217—62no—
127#217—62no—
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—
134C4⋊Dic3—62no—
135C4⋊Dic3—62no—
136Dic3⋊C4—64no—
137Dic3⋊C4—64no—
138Dic3⋊C4—62no—
139Dic3⋊C4—62no—
140Dic3⋊C4—62no—
141Dic3⋊C4—62no—
142C4×Dic3—32no—
143C4×Dic3—32no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146#208—24no—
147#208—42no—
148C2×C3⋊C8—42no—
149C22×C32—41no—
150C22×C32#9912yes—
151C22×C32C2×C22⋊C411yescharacteristic
152C2×C3⋊D3—42no—
153C2×C3⋊D3—41no—
154C32×C4—21no—
155C32×C4—21no—
156C32×C4—22no—
157C32×C4—22no—
158C3⋊Dic3—41no—
159C3⋊Dic3—41no—
160C3⋊Dic3—41no—
161C2×#41—91no—
162C22×Q8D3211yescharacteristic
163C2×M16—62no—
164C4⋊Q8—91no—
165C4⋊Q8—91no—
166#124—91no—
167#124—91no—
168#123—182no—
169C22⋊Q8—182no—
170#117—91no—
171#101—34no—
172#101—62no—
173C23×C3—21no—
174C23×C3(C2×D3)⋊C412yes—
175C22×D3—62no—
176C22×D3—62no—
177C3×Q8—42no—
178C3×Q8—42no—
179C3×Q8—42no—
180C3×Q8—42no—
181C3×Q8—42no—
182C3×Q8—44no—
183C3×Q8—42no—
184C2×C3×C4—24no—
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—21no—
192C2×C3×C4—22no—
193C2×C3×C4—21no—
194C2×C3×C4—22no—
195C2×C3×C4—42no—
196C2×C3×C4—42no—
197C2×C3×C4(C2×D3)⋊C412yes—
198C2×C3×C4(C2×D3)⋊C412yes—
199C2×C3×C4(C2×D3)⋊C412yes—
200C2×C3×C4C2×C4×D312yes—
201C2×C3×C4C2×D1212yes—
202C2×C3×C4C2×#6712yes—
203#67—124no—
204#67—122no—
205#67—122no—
206C2×Dic3—62no—
207C2×Dic3—62no—
208C2×Dic3—62no—
209C2×Dic3—62no—
210C2×Dic3—62no—
211C2×Dic3—62no—
212D12—122no—
213D12—122no—
214C4×D3—124no—
215C4×D3—124no—
216Dic6—122no—
217Dic6—122no—
218C3×C8—124no—
219C3⋊C8—44no—
220C2×C32—21no—
221C2×C32—22no—
222C2×C32C2×#9911yescharacteristic
223C3⋊D3—81no—
224#41—362no—
225C2×Q8—42no—
226C2×Q8—91no—
227C2×Q8#62411yescharacteristic
228C2×Q8#62612yes—
229C2×Q8C2×D3211yescharacteristic
230C2×D4—91no—
231C2×D4—181no—
232C22×C4—181no—
233C22×C4#62411yescharacteristic
234C22×C4#62612yes—
235M16—64no—
236M16—122no—
237C2×C8—122no—
238C4⋊C4—181no—
239C4⋊C4—182no—
240C4⋊C4—182no—
241C22⋊C4—181no—
242C22⋊C4—182no—
243C22⋊C4—182no—
244C42—91no—
245C42—91no—
246C22×C3—22no—
247C22×C3—21no—
248C22×C3—42no—
249C22×C3—42no—
250C22×C3#80612yes—
251C22×C3#80612yes—
252C22×C3C2×(C2×D3)⋊C412yes—
253C2×D3—122no—
254C2×D3—124no—
255C2×D3—124no—
256C2×D3—122no—
257C3×C4—22no—
258C3×C4—22no—
259C3×C4—22no—
260C3×C4—22no—
261C3×C4—22no—
262C3×C4—22no—
263C3×C4—22no—
264C3×C4—22no—
265C3×C4—42no—
266C3×C4—42no—
267Dic3—122no—
268Dic3—122no—
269Dic3—122no—
270Dic3—122no—
271Dic3—122no—
272Dic3—122no—
273C32#213311yescharacteristic, complemented, Sylow
274C23—181no—
275C23#372211yescharacteristic
276Q8—41no—
277Q8—42no—
278Q8—41no—
279Q8—361no—
280D4—361no—
281D4—362no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—181no—
286C2×C4—181no—
287C2×C4—181no—
288C2×C4—362no—
289C2×C4#372212yes—
290C2×C4#372211yescharacteristic
291C2×C4C2×#62411yescharacteristic
292C2×C4C2×#62612yes—
293C8—124no—
294C2×C3—22no—
295C2×C3—22no—
296C2×C3—22no—
297C2×C3—22no—
298C2×C3—21no—
299C2×C3—42no—
300C2×C3C2×#80612yes—
301D3—242no—
302D3—242no—
303C22—41no—
304C22—362no—
305C22—361no—
306C22#6358112yes—
307C22C2×#372211yescharacteristic
308C4—22no—
309C4—21no—
310C4—22no—
311C4—21no—
312C4—361no—
313C4—361no—
314C4—361no—
315C3—21no—
316C3#7012812yescomplemented
317C2—21no—
318C2—22no—
319C2—721no—
320C2C2×#6358111yescharacteristic
subgroupG/H
centerC2C2×#63581
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C2×D32
FittingC22×C32×Q8C22
socleC2×C32C2×#99
prime radicalC2×#3828C4
cosocleC2×C32×Q8C23
hypercenterC22×Q8D32
hypocenterC32#2133
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#836C2semidirect
3. #10589185C2semidirect
4. #10589183C2semidirect
21. C2×#836D3semidirect
273. C32#2133semidirect
316. C3#70128semidirect

Maximal subgroups

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

subgroupindex
#105962872
C2×C3×#8362
#105891852
#105891832
#701283