Finite Group Databasebeta

← #11785747

Subgroups — #11785747

Order 1152.

593 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 593 conjugacy classes of subgroups — too many to draw. Only its 140 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×C3×#892C211yesmaximal, characteristic
2#10591069C212yesmaximal
3#10589396C211yesmaximal, characteristic, complemented
4C3×#4530C211yesmaximal, characteristic, complemented
5#10589167C212yesmaximal, complemented
6#71589—31nomaximal
7#68991—31nomaximal
8C22×C3×C4×D3C2211yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×#3748C2212yes—
11C2×C3×(C2×D3)⋊C4C412yes—
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C2×C3×C4×Dic3C412yes—
14C2×C3×#208C2212yes—
15C3×#892—24no—
16(C2×D3)⋊(C3⋊C8)—24no—
17C2×C3×#117—31no—
18C2×#892D311yescharacteristic
19#5207—32no—
20#5126—32no—
21C3×#343—31no—
22#4554—32no—
23#4530—31no—
24#4530—31no—
25#4530—32no—
26#4530—61no—
27#4530D311yescharacteristic, complemented
28C23×C3×D3C2×C411yescharacteristic
29C22×C32×C4C2×C412yes—
30C22×C32×C4C2311yescharacteristic
31C22×C3×Dic3C2×C411yescharacteristic
32C22×C3×Dic3C2×C412yes—
33C2×C3×C4×D3—22no—
34C2×C3×C4×D3—21no—
35C2×C3×C4×D3—21no—
36C2×C3×C4×D3D414yes—
37C32×C4⋊C4—22no—
38#3748—22no—
39#3748—22no—
40C2×C3⋊(C3⋊C8)—22no—
41C3×(C2×D3)⋊C4—24no—
42C3×C4⋊Dic3—22no—
43C3×C4×Dic3—24no—
44C3×#208—22no—
45C3×#208—22no—
46C2×C3×C3⋊C8—22no—
47#1822—91noSylow
48C23×C3×C4—31no—
49C22×C4×D3C2×D311yescharacteristic
50C2×C3×M16—32no—
51C3×#117—64no—
52C2×C3×C4⋊C4—21no—
53C2×C3×C4⋊C4—31no—
54C2×C3×C4⋊C4C2×D311yescharacteristic
55C2×C3×C4⋊C4C2×D311yescharacteristic
56C2×C3×C22⋊C4—32no—
57C2×C3×C42—32no—
58C2×(C2×D3)⋊C4Dic312yes—
59C2×C4⋊Dic3C2×D311yescharacteristic
60C2×C4×Dic3Dic312yes—
61C2×#208—32no—
62C2×#208—32no—
63C2×#208—62no—
64C2×#208C2×D312yes—
65#892—24no—
66#830—64no—
67(C2×D3)⋊C8—64no—
68C23×C32C22×C411yescharacteristic
69C22×C3×D3—21no—
70C22×C3×D3—21no—
71C22×C3×D3—41no—
72C22×C3×D3—41no—
73C22×C3×D3C22⋊C412yes—
74C2×C32×C4—22no—
75C2×C32×C4—42no—
76C2×C32×C4C2×D412yes—
77C2×C32×C4#4112yes—
78C2×C32×C4#4111yescharacteristic
79C2×C32×C4#4111yescharacteristic
80C2×C3×Dic3—21no—
81C2×C3×Dic3—21no—
82C2×C3×Dic3—22no—
83C2×C3×Dic3—42no—
84C2×C3×Dic3C22⋊C412yes—
85C3×C4×D3—24no—
86C3×C4×D3—24no—
87C3⋊(C3⋊C8)—42no—
88C3×C3⋊C8—42no—
89C2×#117—31no—
90#407—92no—
91#343—31no—
92#343—92no—
93#343—91no—
94C24×C3—31no—
95C23×D3C2×Dic311yescharacteristic
96C22×C3×C4—22no—
97C22×C3×C4—21no—
98C22×C3×C4—31no—
99C22×C3×C4—34no—
100C22×C3×C4—32no—
101C22×C3×C4—62no—
102C22×C3×C4—61no—
103C22×C3×C4—61no—
104C22×C3×C4C4×D312yes—
105C22×C3×C4C2×Dic312yes—
106C22×C3×C4C22×D311yescharacteristic
107C22×C3×C4C22×D311yescharacteristic
108C22×Dic3C2×Dic311yescharacteristic
109C22×Dic3C2×Dic312yes—
110C2×C4×D3—21no—
111C2×C4×D3—22no—
112C2×C4×D3—21no—
113C2×C4×D3#6714yes—
114C3×M16—62no—
115C3×M16—62no—
116C2×C3×C8—62no—
117C3×C4⋊C4—22no—
118C3×C4⋊C4—22no—
119C3×C4⋊C4—42no—
120C3×C4⋊C4—62no—
121C3×C22⋊C4—64no—
122C3×C42—64no—
123(C2×D3)⋊C4—24no—
124C4⋊Dic3—22no—
125C4×Dic3—24no—
126#208—22no—
127#208—22no—
128#208—64no—
129#208—62no—
130#208—62no—
131#208—62no—
132#208—62no—
133#208—122no—
134C2×C3⋊C8—22no—
135C2×C3⋊C8—62no—
136C2×C3⋊C8—62no—
137C2×C3⋊C8—122no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32C2×C22⋊C411yescharacteristic
141C22×C32#11711yescharacteristic
142C22×C32#11711yescharacteristic
143C2×C3×D3—22no—
144C2×C3×D3—22no—
145C2×C3×D3—22no—
146C2×C3×D3—42no—
147C2×C3×D3—42no—
148C32×C4—42no—
149C32×C4#12312yes—
150C32×C4#12312yes—
151C3×Dic3—22no—
152C3×Dic3—42no—
153C23×C4—31no—
154C2×M16—32no—
155C2×M16—92no—
156#117—64no—
157C2×C4⋊C4—31no—
158C2×C4⋊C4D3211yescharacteristic
159C2×C22⋊C4—32no—
160C2×C42—32no—
161C22⋊C8—184no—
162C23×C3—21no—
163C23×C3—32no—
164C23×C3—61no—
165C23×C3—61no—
166C23×C3—121no—
167C23×C3—121no—
168C23×C3C2×C4×D311yescharacteristic
169C23×C3C22×Dic311yescharacteristic
170C22×D3—21no—
171C22×D3—21no—
172C22×D3—41no—
173C22×D3—41no—
174C22×D3#21712yes—
175C2×C3×C4—22no—
176C2×C3×C4—22no—
177C2×C3×C4—21no—
178C2×C3×C4—22no—
179C2×C3×C4—21no—
180C2×C3×C4—22no—
181C2×C3×C4—32no—
182C2×C3×C4—42no—
183C2×C3×C4—42no—
184C2×C3×C4—42no—
185C2×C3×C4—61no—
186C2×C3×C4—61no—
187C2×C3×C4—64no—
188C2×C3×C4—64no—
189C2×C3×C4—62no—
190C2×C3×C4—82no—
191C2×C3×C4—122no—
192C2×C3×C4#23511yescharacteristic
193C2×C3×C4#23512yes—
194C2×C3×C4#23512yes—
195C2×C3×C4#23511yescharacteristic
196C2×C3×C4D3×D412yes—
197C2×C3×C4#23711yescharacteristic
198C2×C3×C4#23911yescharacteristic
199C2×C3×C4C2×#6712yes—
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—22no—
203C2×Dic3—42no—
204C2×Dic3#21712yes—
205C4×D3—24no—
206C4×D3—24no—
207C3×C8—122no—
208C3⋊C8—42no—
209C3⋊C8—124no—
210C3⋊C8—122no—
211C3⋊C8—122no—
212C2×C32—21no—
213C2×C32—21no—
214C2×C32#38111yescharacteristic
215C2×C32#41311yescharacteristic
216C2×C32#41311yescharacteristic
217C3×D3—42no—
218C24—31no—
219C22×C4—31no—
220C22×C4—34no—
221C22×C4—32no—
222C22×C4—61no—
223C22×C4—62no—
224C22×C4—61no—
225C22×C4D3×Dic312yes—
226C22×C4C2×D3211yescharacteristic
227M16—62no—
228M16—62no—
229M16—182no—
230M16—182no—
231C2×C8—62no—
232C2×C8—182no—
233C4⋊C4—22no—
234C4⋊C4—62no—
235C22⋊C4—64no—
236C42—64no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—41no—
245C22×C3—41no—
246C22×C3—62no—
247C22×C3—62no—
248C22×C3—62no—
249C22×C3—122no—
250C22×C3—122no—
251C22×C3#87211yescharacteristic
252C22×C3D3×C22⋊C411yescharacteristic
253C22×C3#89211yescharacteristic
254C22×C3#92611yescharacteristic
255C22×C3#92611yescharacteristic
256C22×C3C2×#21711yescharacteristic
257C2×D3—22no—
258C2×D3—22no—
259C2×D3—22no—
260C2×D3—42no—
261C2×D3—42no—
262C3×C4—22no—
263C3×C4—22no—
264C3×C4—42no—
265C3×C4—42no—
266C3×C4—62no—
267C3×C4—82no—
268C3×C4—122no—
269C3×C4#88312yes—
270C3×C4#89412yes—
271C3×C4#92912yes—
272C3×C4#92912yes—
273Dic3—22no—
274Dic3—42no—
275C32#182211yescharacteristic, complemented, Sylow
276C23—32no—
277C23—61no—
278C23—61no—
279C23—121no—
280C23—121no—
281C23C2×D3×Dic311yescharacteristic
282C2×C4—22no—
283C2×C4—32no—
284C2×C4—42no—
285C2×C4—61no—
286C2×C4—61no—
287C2×C4—64no—
288C2×C4—64no—
289C2×C4—62no—
290C2×C4—122no—
291C2×C4#379511yescharacteristic
292C2×C4#379812yes—
293C2×C4#379911yescharacteristic
294C2×C4D3×#6712yes—
295C8—122no—
296C8—362no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—41no—
305C2×C3—41no—
306C2×C3—122no—
307C2×C3#466411yescharacteristic
308C2×C3#474511yescharacteristic
309C2×C3#475111yescharacteristic
310C2×C3#521111yescharacteristic
311C2×C3#523711yescharacteristic
312C2×C3#523711yescharacteristic
313D3—42no—
314C22—21no—
315C22—21no—
316C22—62no—
317C22—62no—
318C22—62no—
319C22—122no—
320C22—122no—
321C22#6384111yescharacteristic
322C22#6385511yescharacteristic
323C22D3×#21711yescharacteristic
324C4—42no—
325C4—62no—
326C4—122no—
327C4#6385012yes—
328C4#6390512yes—
329C3—21no—
330C3#6899111yescharacteristic, complemented
331C3#7158911yescharacteristic, complemented
332C2—21no—
333C2—21no—
334C2—122no—
335C2#1059129411yescharacteristic
336C2#1059150111yescharacteristic
337C2#1059163711yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1822
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10589396C2semidirect
4. C3×#4530C2semidirect
5. #10589167C2semidirect
27. #4530D3semidirect
275. C32#1822semidirect
330. C3#68991semidirect
331. C3#71589semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
#105910692
#105893962
C3×#45302
#105891672
#715893
#689913