Finite Group Databasebeta

← #11791431

Subgroups — #11791431

Order 1152.

717 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 717 conjugacy classes of subgroups — too many to draw. Only its 170 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×#63873C211yesmaximal, characteristic
2C2×#63641C211yesmaximal, characteristic
3C2×C3×#816C212yesmaximal
4#10591274C211yesmaximal, characteristic
5C2×#63565C212yesmaximal
6#70229—32nomaximal
7C22×C3×Dic6C2212yes—
8C22×C32×C8C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C2×#3724—21no—
13C2×#3724—21no—
14C2×Dic32—21no—
15#63873—22no—
16#63873C414yescomplemented
17#63641—22no—
18C3×#816—24no—
19#63579—21no—
20#63565—24no—
21C2×#944—32no—
22C2×C3×#103—32no—
23C2×#835—32no—
24C2×#816D312yes—
25C2×Dic3⋊C8—32no—
26C2×Dic3⋊C8—61no—
27Dic3×C4⋊C4—32no—
28C2×#810—32no—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3D411yescharacteristic
31C22×C3⋊Dic3D411yescharacteristic
32C22×C3×Dic3—22no—
33C22×C3×Dic3—22no—
34C2×C3×Dic6—22no—
35C2×C3×Dic6—22no—
36C2×C3×Dic6—22no—
37C2×C3×Dic6—22no—
38C2×C3×Dic6—22no—
39C2×C3×Dic6C2×C414yes—
40C2×C32×C8—21no—
41C2×C32×C8—22no—
42C4×C3⋊Dic3C2×C412yes—
43C4×C3⋊Dic3D412yes—
44C2×C3⋊(C3⋊C8)—21no—
45C2×C3⋊(C3⋊C8)—22no—
46C3×C4⋊Dic3—22no—
47C3×C4⋊Dic3D414yes—
48#3724—24no—
49#3724—24no—
50Dic32—42no—
51#1981—91noSylow
52C22×C3×Q8—32no—
53C22×Dic6C2×D312yes—
54C22×C3×C8—21no—
55C22×C3×C8C2×D312yes—
56C2×C3×C4⋊C4—32no—
57#944—38no—
58#944—64no—
59C2×C4⋊Dic3C2×D312yes—
60C2×Dic3⋊C4—62no—
61C2×Dic3⋊C4—62no—
62C2×C4×Dic3—32no—
63C2×C4×Dic3—61no—
64C2×C4×Dic3—62no—
65C22×C3⋊C8—32no—
66C22×C3⋊C8—61no—
67C3×#103—64no—
68#835—64no—
69C3⋊#95—62no—
70#816—24no—
71Dic3⋊C8—64no—
72Dic3⋊C8—64no—
73#810—64no—
74C23×C32C2×D411yescharacteristic
75C2×C32×C4C22×C411yescharacteristic
76C2×C32×C4C2×D411yescharacteristic
77C2×C32×C4C2×D412yes—
78C2×C32×C4#4112yes—
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3C22⋊C412yes—
81C2×C3⋊Dic3C22⋊C412yes—
82C2×C3⋊Dic3SD1612yes—
83C2×C3⋊Dic3Q1612yes—
84C2×C3×Dic3—24no—
85C2×C3×Dic3—24no—
86C2×C3×Dic3—42no—
87C2×C3×Dic3—42no—
88C2×C3×Dic3—42no—
89C2×C3×Dic3—42no—
90C3×Dic6—24no—
91C3×Dic6—24no—
92C3×Dic6—42no—
93C3×Dic6—42no—
94C32×C8—41no—
95C3⋊(C3⋊C8)—41no—
96C2×C4⋊Q8—91no—
97C2×C4⋊C8—91no—
98C2×#103—32no—
99C2×#103—92no—
100C4×C4⋊C4—91no—
101C2×C3×Q8—34no—
102C2×C3×Q8—62no—
103C2×C3×Q8—62no—
104C2×C3×Q8—62no—
105C2×C3×Q8—62no—
106C2×C3×Q8—62no—
107C22×C3×C4—21no—
108C22×C3×C4—62no—
109C22×C3×C4—62no—
110C22×C3×C4C22×D312yes—
111C22×Dic3—22no—
112C22×Dic3—22no—
113C22×Dic3—32no—
114C22×Dic3—32no—
115C22×Dic3—61no—
116C22×Dic3—61no—
117C2×Dic6—22no—
118C2×Dic6—22no—
119C2×Dic6—22no—
120C2×Dic6—22no—
121C2×Dic6—22no—
122C2×Dic6C4×D314yes—
123C2×C3×C8—22no—
124C2×C3×C8—22no—
125C2×C3×C8—22no—
126C2×C3×C8—22no—
127C2×C3×C8—42no—
128C3×C4⋊C4—34no—
129C3×C4⋊C4—62no—
130C4⋊Dic3—22no—
131C4⋊Dic3#6714yes—
132Dic3⋊C4—68no—
133Dic3⋊C4—68no—
134C4×Dic3—34no—
135C4×Dic3—34no—
136C4×Dic3—62no—
137C4×Dic3—62no—
138C4×Dic3—124no—
139C2×C3⋊C8—62no—
140C2×C3⋊C8—62no—
141C2×C3⋊C8—62no—
142C2×C3⋊C8—62no—
143C2×C3⋊C8—122no—
144C22×C32C2×C22⋊C411yescharacteristic
145C22×C32#12112yes—
146C22×C32C2×SD1611yescharacteristic
147C22×C32C2×Q1611yescharacteristic
148C22×C32#13712yes—
149C32×C4C4×D412yes—
150C32×C4#12411yescharacteristic
151C32×C4#12711yescharacteristic
152C3⋊Dic3—22no—
153C3⋊Dic3#10314yescomplemented
154C3×Dic3—44no—
155C3×Dic3—44no—
156C22×Q8—32no—
157C22×C8—91no—
158C22×C8D3211yescharacteristic
159C4⋊Q8—94no—
160C4⋊Q8—182no—
161C2×C4⋊C4—32no—
162C2×C4⋊C4—181no—
163C2×C4⋊C4—181no—
164C2×C42—91no—
165C2×C42—181no—
166C4⋊C8—182no—
167#103—64no—
168#103—184no—
169#95—181no—
170C23×C3—21no—
171C23×C3D3×D412yes—
172C3×Q8—64no—
173C3×Q8—64no—
174C3×Q8—122no—
175C3×Q8—122no—
176C2×C3×C4—22no—
177C2×C3×C4—21no—
178C2×C3×C4—22no—
179C2×C3×C4—21no—
180C2×C3×C4—64no—
181C2×C3×C4—64no—
182C2×C3×C4—122no—
183C2×C3×C4—122no—
184C2×C3×C4—122no—
185C2×C3×C4—122no—
186C2×C3×C4C2×C4×D312yes—
187C2×C3×C4#23512yes—
188C2×C3×C4D3×D412yes—
189C2×C3×C4D3×D412yes—
190C2×C3×C4#23712yes—
191C2×C3×C4C2×#6712yes—
192C2×Dic3—24no—
193C2×Dic3—24no—
194C2×Dic3—34no—
195C2×Dic3—34no—
196C2×Dic3—34no—
197C2×Dic3—34no—
198C2×Dic3—42no—
199C2×Dic3—42no—
200C2×Dic3—42no—
201C2×Dic3—42no—
202C2×Dic3—62no—
203C2×Dic3—62no—
204C2×Dic3—62no—
205C2×Dic3—62no—
206C2×Dic3—62no—
207C2×Dic3—62no—
208C2×Dic3—122no—
209Dic6—24no—
210Dic6—24no—
211Dic6—42no—
212Dic6—42no—
213C3×C8—42no—
214C3×C8—42no—
215C3⋊C8—122no—
216C3⋊C8—122no—
217C2×C32#39011yescharacteristic
218C2×C32C2×#10311yescharacteristic
219C2×C32#41911yescharacteristic
220C2×C32#46112yes—
221C2×C32#46212yes—
222C2×Q8—34no—
223C2×Q8—62no—
224C2×Q8—62no—
225C2×Q8—62no—
226C2×Q8—62no—
227C2×Q8—62no—
228C22×C4—62no—
229C22×C4—62no—
230C22×C4—91no—
231C22×C4—91no—
232C22×C4C2×D3211yescharacteristic
233C2×C8—22no—
234C2×C8—21no—
235C2×C8—182no—
236C2×C8—181no—
237C4⋊C4—34no—
238C4⋊C4—62no—
239C4⋊C4—184no—
240C4⋊C4—184no—
241C42—92no—
242C42—92no—
243C42—362no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—21no—
249C22×C3D3×C22⋊C412yes—
250C22×C3#88412yes—
251C22×C3D3×SD1612yes—
252C22×C3#91512yes—
253C22×C3D3×Q1612yes—
254C22×C3#91812yes—
255C22×C3#93912yes—
256C3×C4—22no—
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—124no—
260C3×C4—124no—
261C3×C4#67⋊C412yes—
262C3×C4#88512yes—
263C3×C4C4×#6712yes—
264C3×C4#94012yes—
265Dic3—38no—
266Dic3—44no—
267Dic3—44no—
268Dic3—64no—
269Dic3—64no—
270Dic3—122no—
271C32#198111yescharacteristic, complemented, Sylow
272C23#380211yescharacteristic
273Q8—64no—
274Q8—64no—
275Q8—122no—
276Q8—122no—
277C2×C4—64no—
278C2×C4—64no—
279C2×C4—92no—
280C2×C4—92no—
281C2×C4—92no—
282C2×C4—92no—
283C2×C4—122no—
284C2×C4—122no—
285C2×C4—122no—
286C2×C4—122no—
287C2×C4—182no—
288C2×C4#379512yes—
289C2×C4C4×D3211yescharacteristic
290C2×C4D3×#6712yes—
291C2×C4#381111yescharacteristic
292C8—41no—
293C8—361no—
294C2×C3—22no—
295C2×C3—22no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3#479512yes—
300C2×C3D3×#10312yes—
301C2×C3#480212yes—
302C2×C3#481812yes—
303C2×C3#495712yes—
304C2×C3#516212yes—
305C2×C3#518212yes—
306C22#6379611yescharacteristic
307C22#6380211yescharacteristic
308C22#6381112yes—
309C22#6388512yes—
310C22#6392111yescharacteristic
311C4—94no—
312C4—124no—
313C4—124no—
314C4—182no—
315C4#6387912yes—
316C4#6391311yescharacteristic
317C4#6397911yescharacteristic
318C3—21no—
319C3#7022912yescomplemented
320C2#1059067211yescharacteristic
321C2#1059069111yescharacteristic
322C2#1059074812yes—
323C2#1059079812yes—
324C2#1059138611yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1981
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
16. #63873C4semidirect
153. C3⋊Dic3#103semidirect
271. C32#1981semidirect
319. C3#70229semidirect

Maximal subgroups

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

subgroupindex
C2×#638732
C2×#636412
C2×C3×#8162
#105912742
C2×#635652
#702293