Finite Group Databasebeta

← #11788826

Subgroups — #11788826

Order 1152.

763 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 763 conjugacy classes of subgroups — too many to draw. Only its 124 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#10596296C211yesmaximal, characteristic
2#10594828C211yesmaximal, characteristic, complemented
3C3×#5236C212yesmaximal
4C2×#63561C211yesmaximal, characteristic, complemented
5#10589158C212yesmaximal, complemented
6#70411—32nomaximal
7C2×C32×#41C2211yescharacteristic
8C22×#634C2211yescharacteristic
9#64153C412yescomplemented
10#64145C412yescomplemented
11#64144—22no—
12#64135C2211yescharacteristic
13#64133—22no—
14C3×#926C2212yes—
15C2×C3×#208C2212yes—
16#63957—22no—
17#63844—24no—
18C3×#837—24no—
19#63561—22no—
20#5825—32no—
21#5825—61no—
22#5516—32no—
23C3×#421—32no—
24#5236D312yes—
25C2×#824—32no—
26#4557—32no—
27#4531—32no—
28C32×#41—22no—
29C32×#41—22no—
30C2×C32×Q8C2×C411yescharacteristic
31C2×C32×D4—21no—
32C2×C32×D4C2×C411yescharacteristic
33C22×C32×C4—21no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3D412yes—
36C2×#634—22no—
37C2×#634—22no—
38C2×#634C2×C412yes—
39C2×#634D412yes—
40#3757—21no—
41#3757—24no—
42C4⋊(C3⋊Dic3)—21no—
43#3750—24no—
44C4×C3⋊Dic3C2×C412yes—
45C3×#217—22no—
46C3×C4⋊Dic3—22no—
47C3×C4×Dic3D414yes—
48C3×#208—22no—
49C3×#208—22no—
50C2×C3×C3⋊C8—22no—
51#3724—24no—
52Dic32—24no—
53#1912—91noSylow
54C2×C3×#41—21no—
55C2×C3×#41C2×D312yes—
56C22×Dic6—32no—
57C22×Dic6—61no—
58C2×C3×M16—32no—
59C3×#117—32no—
60#944—34no—
61#944—62no—
62#936—34no—
63#936—62no—
64#935—64no—
65#935—64no—
66#926—32no—
67#926—61no—
68#926C2×D312yes—
69#924—64no—
70#924—64no—
71C2×#208C2×D312yes—
72#887—64no—
73#877—64no—
74C4×Dic6—64no—
75C3×#104—64no—
76#837—24no—
77#824—64no—
78C23×C32—21no—
79C23×C32C2×D411yescharacteristic
80C32×Q8—22no—
81C32×D4—22no—
82C32×D4—41no—
83C32×D4—41no—
84C2×C32×C4—21no—
85C2×C32×C4—42no—
86C2×C32×C4C22×C411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D412yes—
89C2×C32×C4#4112yes—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3C22⋊C414yes—
94#634—24no—
95#634—24no—
96C2×C3×Dic3—24no—
97C3×C3⋊C8—42no—
98#536—91no—
99#519—91no—
100#421—32no—
101C2×#101—91no—
102H(3,ℤ/4)—92no—
103C3×#41—22no—
104C3×#41—22no—
105C3×#41—22no—
106C3×#41—22no—
107C3×#41—42no—
108C3×#41—42no—
109C2×C3×Q8—21no—
110C2×C3×Q8C4×D312yes—
111C2×C3×D4—22no—
112C2×C3×D4—22no—
113C2×C3×D4—21no—
114C2×C3×D4C4×D312yes—
115C22×C3×C4—22no—
116C22×C3×C4—22no—
117C22×C3×C4—21no—
118C22×C3×C4C22×D312yes—
119C22×Dic3—34no—
120C22×Dic3—62no—
121C2×Dic6—34no—
122C2×Dic6—34no—
123C2×Dic6—62no—
124C2×Dic6—62no—
125C2×Dic6—62no—
126C2×Dic6—62no—
127C2×Dic6—62no—
128C2×Dic6—62no—
129C2×Dic6—122no—
130C2×Dic6—122no—
131C3×M16—62no—
132C3×M16—62no—
133C2×C3×C8—62no—
134C3×C4⋊C4—62no—
135C3×C22⋊C4—62no—
136C3×C42—34no—
137#217—22no—
138#217—68no—
139#217—68no—
140#217—62no—
141#217—62no—
142C4⋊Dic3—22no—
143C4⋊Dic3—62no—
144C4⋊Dic3—62no—
145Dic3⋊C4—68no—
146Dic3⋊C4—68no—
147Dic3⋊C4—68no—
148C4×Dic3—34no—
149C4×Dic3—62no—
150C4×Dic3—68no—
151C4×Dic3#6714yes—
152#208—22no—
153#208—22no—
154C2×C3⋊C8—22no—
155C22×C32—41no—
156C22×C32—42no—
157C22×C32—41no—
158C22×C32C2×C22⋊C411yescharacteristic
159C22×C32#12011yescharacteristic
160C22×C32#12311yescharacteristic
161C32×C4—41no—
162C32×C4C4×D412yes—
163C32×C4#12112yes—
164C3⋊Dic3—24no—
165C3⋊Dic3—42no—
166C3×Dic3—44no—
167C2×#41D3211yescharacteristic
168C22×Q8—91no—
169C2×M16—32no—
170C4⋊Q8—92no—
171#124—92no—
172#123—182no—
173C22⋊Q8—182no—
174C4×Q8—184no—
175#117—32no—
176#117—91no—
177#117—182no—
178#104—64no—
179#101—182no—
180C23×C3—22no—
181C23×C3—22no—
182C23×C3—21no—
183C23×C3D3×D412yes—
184C3×Q8—22no—
185C3×Q8—22no—
186C3×Q8—42no—
187C3×D4—22no—
188C3×D4—22no—
189C3×D4—42no—
190C3×D4—42no—
191C3×D4—42no—
192C3×D4—42no—
193C3×D4—42no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—22no—
197C2×C3×C4—21no—
198C2×C3×C4—22no—
199C2×C3×C4—21no—
200C2×C3×C4—44no—
201C2×C3×C4—42no—
202C2×C3×C4—42no—
203C2×C3×C4—64no—
204C2×C3×C4C2×C4×D312yes—
205C2×C3×C4#23512yes—
206C2×C3×C4D3×D412yes—
207C2×C3×C4D3×D412yes—
208C2×C3×C4#23712yes—
209C2×C3×C4C2×#6712yes—
210C2×Dic3—24no—
211C2×Dic3—38no—
212C2×Dic3—64no—
213C2×Dic3—64no—
214C2×Dic3—64no—
215C2×Dic3—64no—
216C2×Dic3—64no—
217C2×Dic3—122no—
218C2×Dic3—122no—
219Dic6—64no—
220Dic6—64no—
221Dic6—64no—
222Dic6—64no—
223Dic6—124no—
224Dic6—124no—
225C3×C8—122no—
226C3⋊C8—42no—
227C2×C32—21no—
228C2×C32—21no—
229C2×C32—21no—
230C2×C32—81no—
231C2×C32#38611yescharacteristic
232#41—22no—
233#41—22no—
234C2×Q8—92no—
235C2×Q8—92no—
236C2×Q8—182no—
237C2×Q8—182no—
238C2×Q8#62411yescharacteristic
239C2×D4—21no—
240C2×D4#62411yescharacteristic
241C22×C4—21no—
242C22×C4—92no—
243C22×C4C2×D3211yescharacteristic
244M16—62no—
245M16—62no—
246C2×C8—62no—
247C4⋊C4—62no—
248C4⋊C4—184no—
249C4⋊C4—184no—
250C4⋊C4—181no—
251C22⋊C4—62no—
252C22⋊C4—184no—
253C22⋊C4—181no—
254C42—34no—
255C42—92no—
256C42—184no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—42no—
261C22×C3—42no—
262C22×C3—42no—
263C22×C3—44no—
264C22×C3—44no—
265C22×C3—42no—
266C22×C3D3×C22⋊C412yes—
267C22×C3#88312yes—
268C22×C3#93712yes—
269C3×C4—22no—
270C3×C4—22no—
271C3×C4—42no—
272C3×C4—42no—
273C3×C4—124no—
274C3×C4#67⋊C412yes—
275C3×C4#88412yes—
276C3×C4C4×#6712yes—
277C3×C4#93812yes—
278Dic3—44no—
279Dic3—68no—
280Dic3—124no—
281Dic3—124no—
282Dic3—124no—
283C32#191211yescharacteristic, complemented, Sylow
284C23—21no—
285C23#381111yescharacteristic
286Q8—22no—
287Q8—184no—
288Q8—184no—
289D4—22no—
290D4—41no—
291D4—41no—
292C2×C4—21no—
293C2×C4—42no—
294C2×C4—64no—
295C2×C4—94no—
296C2×C4—182no—
297C2×C4—182no—
298C2×C4—182no—
299C2×C4#380412yes—
300C2×C4C2×#62411yescharacteristic
301C2×C4D3×#6712yes—
302C2×C4#381111yescharacteristic
303C8—122no—
304C2×C3—22no—
305C2×C3—22no—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3—21no—
309C2×C3—41no—
310C2×C3—41no—
311C2×C3—82no—
312C2×C3—82no—
313C2×C3#495612yes—
314C22—41no—
315C22—42no—
316C22—41no—
317C22#6397411yescharacteristic
318C22#6397511yescharacteristic
319C22#6398311yescharacteristic
320C4—41no—
321C4—124no—
322C4—184no—
323C4—362no—
324C4#6395212yes—
325C4#6395812yes—
326C3—21no—
327C3#7041112yescomplemented
328C2—21no—
329C2—21no—
330C2—21no—
331C2—81no—
332C2#1059172211yescharacteristic
subgroupG/H
centerC2#10591722
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC2×C32#386
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1912
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594828C2semidirect
4. C2×#63561C2semidirect
5. #10589158C2semidirect
9. #64153C4semidirect
10. #64145C4semidirect
283. C32#1912semidirect
327. C3#70411semidirect

Maximal subgroups

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

subgroupindex
#105962962
#105948282
C3×#52362
C2×#635612
#105891582
#704113