Finite Group Databasebeta

← #11791636

Subgroups — #11791636

Order 1152.

729 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 729 conjugacy classes of subgroups — too many to draw. Only its 172 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×#64097C211yesmaximal, characteristic
2#10591274C211yesmaximal, characteristic
3C2×#63572C211yesmaximal, characteristic
4C3×#4529C212yesmaximal
5#10589164C212yesmaximal
6#68800—32nomaximal
7C22×#634—21no—
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×#3750—21no—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64097—22no—
13#64097C414yescomplemented
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×Dic32—21no—
17#63579—21no—
18#63572—22no—
19C2×#888—32no—
20C2×#888—61no—
21C2×Dic3⋊C8—32no—
22Dic3×C4⋊C4—32no—
23C3×#340—32no—
24#4551—32no—
25#4529—32no—
26#4529D312yes—
27C22×C32×C4—21no—
28C22×C32×C4C2311yescharacteristic
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3D411yescharacteristic
31C22×C3⋊Dic3D411yescharacteristic
32C2×#634—24no—
33C2×#634—42no—
34C2×#634—42no—
35C22×C3×Dic3—22no—
36C32×C4⋊C4—21no—
37C32×C4⋊C4C2×C412yes—
38C4⋊(C3⋊Dic3)—21no—
39C4⋊(C3⋊Dic3)C2×C412yes—
40#3750—24no—
41C4×C3⋊Dic3C2×C412yes—
42C4×C3⋊Dic3D412yes—
43C3×C4⋊Dic3—22no—
44C3×C4⋊Dic3Q814yescomplemented
45C2×C3×C3⋊C8—22no—
46C2×C3×C3⋊C8—22no—
47C2×C3×C3⋊C8—22no—
48Dic32—42no—
49#1988—91noSylow
50C22×Dic6—62no—
51C22×Dic6—62no—
52C22×C3×C8—32no—
53C2×C3×C4⋊C4—21no—
54C2×C3×C4⋊C4—32no—
55C2×C3×C4⋊C4C2×D312yes—
56C2×C4⋊Dic3—32no—
57C2×C4⋊Dic3—61no—
58C2×C4⋊Dic3C2×D312yes—
59C2×Dic3⋊C4—62no—
60C2×Dic3⋊C4—62no—
61C2×C4×Dic3—32no—
62C2×C4×Dic3—61no—
63C2×C4×Dic3—62no—
64C22×C3⋊C8C2×D312yes—
65#888—38no—
66#888—64no—
67#888—64no—
68#888—64no—
69C3⋊#95—62no—
70Dic3⋊C8—64no—
71C23×C32C2×D411yescharacteristic
72C2×C32×C4—22no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4C22×C411yescharacteristic
76C2×C32×C4C2×D411yescharacteristic
77C2×C32×C4C2×Q812yes—
78C2×C32×C4#4112yes—
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3—22no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3—41no—
83C2×C3⋊Dic3C22⋊C412yes—
84C2×C3⋊Dic3C22⋊C412yes—
85C2×C3⋊Dic3D812yes—
86C2×C3⋊Dic3SD1612yes—
87#634—48no—
88C2×C3×Dic3—24no—
89C2×C3×Dic3—42no—
90C2×C3×Dic3—42no—
91C3×C3⋊C8—42no—
92C2×C4⋊Q8—91no—
93C2×C4⋊C8—91no—
94C4×C4⋊C4—91no—
95#340—32no—
96#340—92no—
97C22×C3×C4—22no—
98C22×C3×C4—22no—
99C22×C3×C4—21no—
100C22×C3×C4—62no—
101C22×C3×C4C22×D312yes—
102C22×Dic3—22no—
103C22×Dic3—32no—
104C22×Dic3—32no—
105C22×Dic3—61no—
106C22×Dic3—61no—
107C22×Dic3—62no—
108C22×Dic3—62no—
109C2×Dic6—68no—
110C2×Dic6—68no—
111C2×Dic6—124no—
112C2×Dic6—124no—
113C2×Dic6—124no—
114C2×Dic6—124no—
115C2×C3×C8—62no—
116C2×C3×C8—62no—
117C2×C3×C8—62no—
118C3×C4⋊C4—22no—
119C3×C4⋊C4—22no—
120C3×C4⋊C4—22no—
121C3×C4⋊C4—34no—
122C3×C4⋊C4—62no—
123C3×C4⋊C4C4×D314yes—
124C4⋊Dic3—22no—
125C4⋊Dic3—34no—
126C4⋊Dic3—62no—
127C4⋊Dic3—62no—
128C4⋊Dic3—62no—
129C4⋊Dic3Dic614yescomplemented
130Dic3⋊C4—68no—
131Dic3⋊C4—68no—
132C4×Dic3—34no—
133C4×Dic3—34no—
134C4×Dic3—62no—
135C4×Dic3—62no—
136C4×Dic3—124no—
137C2×C3⋊C8—22no—
138C2×C3⋊C8—22no—
139C2×C3⋊C8—22no—
140C22×C32C2×C22⋊C411yescharacteristic
141C22×C32C22⋊Q812yes—
142C22×C32C2×D811yescharacteristic
143C22×C32C2×SD1611yescharacteristic
144C22×C32#13712yes—
145C32×C4—42no—
146C32×C4C4×Q812yes—
147C32×C4#12411yescharacteristic
148C32×C4C4⋊Q811yescharacteristic
149C3⋊Dic3—22no—
150C3⋊Dic3—42no—
151C3⋊Dic3#10214yes—
152C3×Dic3—44no—
153C22×Q8—181no—
154C22×C8—32no—
155C4⋊Q8—94no—
156C4⋊Q8—182no—
157C2×C4⋊C4—32no—
158C2×C4⋊C4—91no—
159C2×C4⋊C4—181no—
160C2×C4⋊C4D3211yescharacteristic
161C2×C42—91no—
162C2×C42—181no—
163C4⋊C8—182no—
164#95—181no—
165C23×C3—21no—
166C23×C3D3×D412yes—
167C2×C3×C4—24no—
168C2×C3×C4—24no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—42no—
174C2×C3×C4—42no—
175C2×C3×C4—42no—
176C2×C3×C4—42no—
177C2×C3×C4—64no—
178C2×C3×C4—122no—
179C2×C3×C4—122no—
180C2×C3×C4C2×Dic612yes—
181C2×C3×C4C2×C4×D312yes—
182C2×C3×C4#23512yes—
183C2×C3×C4D3×D412yes—
184C2×C3×C4#23712yes—
185C2×C3×C4D3×Q812yes—
186C2×Dic3—24no—
187C2×Dic3—34no—
188C2×Dic3—34no—
189C2×Dic3—34no—
190C2×Dic3—34no—
191C2×Dic3—42no—
192C2×Dic3—42no—
193C2×Dic3—62no—
194C2×Dic3—62no—
195C2×Dic3—62no—
196C2×Dic3—62no—
197C2×Dic3—64no—
198C2×Dic3—62no—
199C2×Dic3—62no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—122no—
203C2×Dic3—122no—
204C2×Dic3—122no—
205C2×Dic3—122no—
206Dic6—1216no—
207Dic6—1216no—
208C3×C8—122no—
209C3⋊C8—42no—
210C2×C32#39111yescharacteristic
211C2×C32C2×#10211yescharacteristic
212C2×C32#41911yescharacteristic
213C2×C32#47412yes—
214C2×C32#47512yes—
215C2×Q8—184no—
216C2×Q8—362no—
217C2×Q8—362no—
218C22×C4—21no—
219C22×C4—62no—
220C22×C4—91no—
221C22×C4—91no—
222C22×C4—181no—
223C22×C4C2×D3211yescharacteristic
224C2×C8—62no—
225C2×C8—62no—
226C2×C8—62no—
227C4⋊C4—21no—
228C4⋊C4—34no—
229C4⋊C4—62no—
230C4⋊C4—92no—
231C4⋊C4—184no—
232C4⋊C4—181no—
233C4⋊C4#62412yes—
234C42—92no—
235C42—92no—
236C42—362no—
237C22×C3—22no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—22no—
241C22×C3—21no—
242C22×C3#87812yes—
243C22×C3D3×C22⋊C412yes—
244C22×C3#89612yes—
245C22×C3D3×D812yes—
246C22×C3D3×SD1612yes—
247C22×C3#91512yes—
248C22×C3#91812yes—
249C3×C4—21no—
250C3×C4—22no—
251C3×C4—21no—
252C3×C4—44no—
253C3×C4—44no—
254C3×C4—124no—
255C3×C4C4×Dic612yes—
256C3×C4#88512yes—
257C3×C4#88712yes—
258C3×C4#88812yes—
259Dic3—38no—
260Dic3—44no—
261Dic3—64no—
262Dic3—64no—
263Dic3—64no—
264Dic3—124no—
265Dic3—124no—
266C32#198811yescharacteristic, complemented, Sylow
267C23#381111yescharacteristic
268Q8—368no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—64no—
273C2×C4—92no—
274C2×C4—92no—
275C2×C4—92no—
276C2×C4—92no—
277C2×C4—122no—
278C2×C4—122no—
279C2×C4—182no—
280C2×C4—182no—
281C2×C4—361no—
282C2×C4—361no—
283C2×C4D3×Dic612yes—
284C2×C4#379512yes—
285C2×C4C2×#62411yescharacteristic
286C2×C4#381111yescharacteristic
287C8—122no—
288C2×C3—22no—
289C2×C3—22no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3#464612yes—
294C2×C3#475912yes—
295C2×C3D3×#10212yes—
296C2×C3#479112yes—
297C2×C3#480212yes—
298C2×C3#485412yes—
299C2×C3#489012yes—
300C22#6389612yes—
301C22#6392611yescharacteristic
302C22#6393011yescharacteristic
303C22#6395112yes—
304C22#6397411yescharacteristic
305C4—42no—
306C4—94no—
307C4—124no—
308C4—182no—
309C4—362no—
310C4#6384011yescharacteristic
311C4#6384412yes—
312C4#6391311yescharacteristic
313C3—21no—
314C3#6880012yescomplemented
315C2#1059047112yes—
316C2#1059049712yes—
317C2#1059127311yescharacteristic
318C2#1059141611yescharacteristic
319C2#1059156211yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1988
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
13. #64097C4semidirect
44. C3×C4⋊Dic3Q8semidirect
129. C4⋊Dic3Dic6semidirect
266. C32#1988semidirect
314. C3#68800semidirect

Maximal subgroups

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

subgroupindex
C2×#640972
#105912742
C2×#635722
C3×#45292
#105891642
#688003