Finite Group Databasebeta

← #11791670

Subgroups — #11791670

Order 1152.

633 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 633 conjugacy classes of subgroups — too many to draw. Only its 164 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×#64099C211yesmaximal, characteristic
2#10591274C211yesmaximal, characteristic
3C2×#63572C211yesmaximal, characteristic
4C3×#4529C212yesmaximal
5#10589164C212yesmaximal
6#68802—32nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C4⋊(C3⋊Dic3)—21no—
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×#3750—21no—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64099—22no—
13#64099C414yescomplemented
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×Dic32—21no—
17#63579—21no—
18#63572—22no—
19C2×#890—32no—
20C2×#890—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
32C22×C3×Dic3—22no—
33C32×C4⋊C4—21no—
34C32×C4⋊C4C2×C412yes—
35C4⋊(C3⋊Dic3)—21no—
36C4⋊(C3⋊Dic3)—24no—
37C4⋊(C3⋊Dic3)C2×C412yes—
38#3750—24no—
39C4×C3⋊Dic3C2×C412yes—
40C4×C3⋊Dic3D412yes—
41C3×C4⋊Dic3—22no—
42C3×C4⋊Dic3Q814yes—
43C2×C3×C3⋊C8—22no—
44C2×C3×C3⋊C8—22no—
45C2×C3×C3⋊C8—22no—
46Dic32—42no—
47#1989—91noSylow
48C22×C3×C8—32no—
49C2×C3×C4⋊C4—21no—
50C2×C3×C4⋊C4—32no—
51C2×C3×C4⋊C4C2×D312yes—
52C2×C4⋊Dic3—32no—
53C2×C4⋊Dic3—61no—
54C2×C4⋊Dic3—62no—
55C2×C4⋊Dic3—62no—
56C2×C4⋊Dic3C2×D312yes—
57C2×Dic3⋊C4—62no—
58C2×Dic3⋊C4—62no—
59C2×C4×Dic3—32no—
60C2×C4×Dic3—61no—
61C2×C4×Dic3—62no—
62C22×C3⋊C8C2×D312yes—
63#890—38no—
64#890—64no—
65#890—64no—
66#890—64no—
67C3⋊#95—62no—
68Dic3⋊C8—64no—
69C23×C32C2×D411yescharacteristic
70C2×C32×C4—22no—
71C2×C32×C4—42no—
72C2×C32×C4C22×C411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4C2×Q812yes—
75C2×C32×C4#4112yes—
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3—21no—
79C2×C3⋊Dic3—21no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3C22⋊C412yes—
83C2×C3⋊Dic3C22⋊C412yes—
84C2×C3×Dic3—24no—
85C2×C3×Dic3—42no—
86C2×C3×Dic3—42no—
87C3×C3⋊C8—42no—
88C2×#125—91no—
89C2×C4⋊C8—91no—
90C4×C4⋊C4—91no—
91#340—32no—
92#340—92no—
93C22×C3×C4—22no—
94C22×C3×C4—22no—
95C22×C3×C4—21no—
96C22×C3×C4—62no—
97C22×C3×C4C22×D312yes—
98C22×Dic3—22no—
99C22×Dic3—32no—
100C22×Dic3—32no—
101C22×Dic3—61no—
102C22×Dic3—61no—
103C22×Dic3—62no—
104C22×Dic3—62no—
105C2×C3×C8—62no—
106C2×C3×C8—62no—
107C2×C3×C8—62no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4—22no—
110C3×C4⋊C4—22no—
111C3×C4⋊C4—34no—
112C3×C4⋊C4—62no—
113C3×C4⋊C4C4×D314yes—
114C4⋊Dic3—22no—
115C4⋊Dic3—34no—
116C4⋊Dic3—62no—
117C4⋊Dic3—68no—
118C4⋊Dic3—68no—
119C4⋊Dic3—62no—
120C4⋊Dic3—62no—
121C4⋊Dic3Dic614yes—
122Dic3⋊C4—68no—
123Dic3⋊C4—68no—
124C4×Dic3—34no—
125C4×Dic3—34no—
126C4×Dic3—62no—
127C4×Dic3—62no—
128C4×Dic3—124no—
129C2×C3⋊C8—22no—
130C2×C3⋊C8—22no—
131C2×C3⋊C8—22no—
132C22×C32C2×C22⋊C411yescharacteristic
133C22×C32C22⋊Q812yes—
134C22×C32#13512yes—
135C22×C32AGL(1,ℤ/8)11yescharacteristic
136C22×C32#13711yescharacteristic
137C32×C4—42no—
138C32×C4C4×Q812yes—
139C32×C4#12411yescharacteristic
140C32×C4C4⋊Q811yescharacteristic
141C3⋊Dic3—22no—
142C3⋊Dic3—22no—
143C3⋊Dic3—42no—
144C3×Dic3—44no—
145C22×C8—32no—
146#125—94no—
147#125—182no—
148C2×C4⋊C4—32no—
149C2×C4⋊C4—91no—
150C2×C4⋊C4—181no—
151C2×C4⋊C4—181no—
152C2×C4⋊C4D3211yescharacteristic
153C2×C42—91no—
154C2×C42—181no—
155C4⋊C8—182no—
156#95—181no—
157C23×C3—21no—
158C23×C3D3×D412yes—
159C2×C3×C4—24no—
160C2×C3×C4—24no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—44no—
166C2×C3×C4—42no—
167C2×C3×C4—42no—
168C2×C3×C4—64no—
169C2×C3×C4—122no—
170C2×C3×C4—122no—
171C2×C3×C4C2×Dic612yes—
172C2×C3×C4C2×C4×D312yes—
173C2×C3×C4#23512yes—
174C2×C3×C4D3×D412yes—
175C2×C3×C4#23712yes—
176C2×C3×C4D3×Q812yes—
177C2×Dic3—24no—
178C2×Dic3—34no—
179C2×Dic3—34no—
180C2×Dic3—42no—
181C2×Dic3—42no—
182C2×Dic3—62no—
183C2×Dic3—62no—
184C2×Dic3—62no—
185C2×Dic3—62no—
186C2×Dic3—62no—
187C2×Dic3—62no—
188C2×Dic3—64no—
189C2×Dic3—64no—
190C2×Dic3—122no—
191C2×Dic3—121no—
192C2×Dic3—121no—
193C2×Dic3—122no—
194C2×Dic3—122no—
195C2×Dic3—122no—
196C2×Dic3—122no—
197C3×C8—122no—
198C3⋊C8—42no—
199C2×C32#39111yescharacteristic
200C2×C32#41611yescharacteristic
201C2×C32#41711yescharacteristic
202C2×C32#47812yes—
203C2×C32#47912yes—
204C22×C4—21no—
205C22×C4—62no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—181no—
209C22×C4C2×D3211yescharacteristic
210C2×C8—62no—
211C2×C8—62no—
212C2×C8—62no—
213C4⋊C4—21no—
214C4⋊C4—34no—
215C4⋊C4—62no—
216C4⋊C4—92no—
217C4⋊C4—184no—
218C4⋊C4—184no—
219C4⋊C4—181no—
220C4⋊C4#62412yes—
221C42—92no—
222C42—92no—
223C42—362no—
224C22×C3—22no—
225C22×C3—22no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—21no—
229C22×C3#87812yes—
230C22×C3D3×C22⋊C412yes—
231C22×C3#89612yes—
232C22×C3#91212yes—
233C22×C3#91412yes—
234C22×C3#91612yes—
235C22×C3#91812yes—
236C3×C4—21no—
237C3×C4—22no—
238C3×C4—21no—
239C3×C4—44no—
240C3×C4—44no—
241C3×C4—124no—
242C3×C4C4×Dic612yes—
243C3×C4#88512yes—
244C3×C4#88712yes—
245C3×C4#88812yes—
246Dic3—44no—
247Dic3—64no—
248Dic3—64no—
249Dic3—122no—
250Dic3—122no—
251Dic3—124no—
252Dic3—124no—
253C32#198911yescharacteristic, complemented, Sylow
254C23#381111yescharacteristic
255C2×C4—22no—
256C2×C4—42no—
257C2×C4—64no—
258C2×C4—92no—
259C2×C4—92no—
260C2×C4—122no—
261C2×C4—122no—
262C2×C4—182no—
263C2×C4—181no—
264C2×C4—181no—
265C2×C4—182no—
266C2×C4—361no—
267C2×C4—361no—
268C2×C4D3×Dic612yes—
269C2×C4#379512yes—
270C2×C4C2×#62411yescharacteristic
271C2×C4#381111yescharacteristic
272C8—122no—
273C2×C3—22no—
274C2×C3—22no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3#464612yes—
279C2×C3#476612yes—
280C2×C3#477212yes—
281C2×C3#479912yes—
282C2×C3#480312yes—
283C2×C3#487112yes—
284C2×C3#487712yes—
285C22#6389612yes—
286C22#6393612yes—
287C22#6394111yescharacteristic
288C22#6394511yescharacteristic
289C22#6397411yescharacteristic
290C4—42no—
291C4—124no—
292C4—182no—
293C4—182no—
294C4—362no—
295C4#6384011yescharacteristic
296C4#6384412yes—
297C4#6391311yescharacteristic
298C3—21no—
299C3#6880212yescomplemented
300C2#1059047412yes—
301C2#1059049412yes—
302C2#1059127311yescharacteristic
303C2#1059142411yescharacteristic
304C2#1059155411yescharacteristic
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#1989
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. #64099C4semidirect
253. C32#1989semidirect
299. C3#68802semidirect

Maximal subgroups

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

subgroupindex
C2×#640992
#105912742
C2×#635722
C3×#45292
#105891642
#688023