Finite Group Databasebeta

← #11773836

Subgroups — #11773836

Order 1152.

555 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 555 conjugacy classes of subgroups — too many to draw. Only its 112 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×#63838C211yesmaximal, characteristic
2#10592417C211yesmaximal, characteristic
3#10591061C211yesmaximal, characteristic
4C3×#4469C212yesmaximal
5#10589147C212yesmaximal
6#68125—32nomaximal
7C22×#627C411yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C2×C3×Dic3⋊C4C2212yes—
10C2×#3724C411yescharacteristic
11C2×Dic32C412yes—
12#63838—21no—
13#63838—21no—
14#63838—21no—
15#63838—21no—
16C32×C22⋊C8C2211yescharacteristic
17#63657C2211yescharacteristic
18#63641—21no—
19C8×C3⋊Dic3—21no—
20C3×#830C2212yes—
21#63572—21no—
22#63553—21no—
23C2×#887—32no—
24#4718—32no—
25#4718—32no—
26#4718—61no—
27C3×#324—32no—
28#4528—32no—
29#4469—32no—
30#4469D312yes—
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3C2×C411yescharacteristic
33C22×C3⋊Dic3C2×C411yescharacteristic
34C22×C3×Dic3C2×C412yes—
35C22×C3×Dic3C2×C412yes—
36C2×#627—21no—
37C2×#627—21no—
38C2×#627—22no—
39C2×#627C814yescomplemented
40C2×C32×C8—21no—
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44C4×C3⋊Dic3D411yescharacteristic
45C2×C3⋊(C3⋊C8)—21no—
46C3×Dic3⋊C4—22no—
47C3×Dic3⋊C4—22no—
48C2×C3×C3⋊C8—22no—
49#3724—21no—
50#3724—21no—
51Dic32—22no—
52Dic32—22no—
53#1461—91noSylow
54C22×Dic6—32no—
55C2×C3×C4⋊C4—32no—
56C2×Dic3⋊C4—32no—
57C2×Dic3⋊C4C2×D312yes—
58C2×C4×Dic3—32no—
59C2×C4×Dic3—32no—
60C2×C4×Dic3—32no—
61C2×C4×Dic3—61no—
62#887—62no—
63#887—62no—
64#887—62no—
65#887—62no—
66C3×C22⋊C8—21no—
67C3×C22⋊C8—32no—
68C3×C22⋊C8C2×D312yes—
69#830—32no—
70#830—61no—
71#830C2×D312yes—
72Dic3⋊C8—62no—
73Dic3⋊C8—62no—
74Dic3⋊C8—62no—
75C8×Dic3—62no—
76C8×Dic3—62no—
77C8×Dic3—62no—
78C23×C32C22×C411yescharacteristic
79C2×C32×C4—41no—
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C2×C812yes—
88C2×C3⋊Dic3M1612yes—
89C2×C3×Dic3—22no—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—22no—
92C2×C3×Dic3—42no—
93C2×C3×Dic3C2×C814yes—
94#627—24no—
95#627—24no—
96C32×C8—41no—
97C3⋊(C3⋊C8)—41no—
98C3×C3⋊C8—42no—
99C2×C4×Q8—91no—
100#431—91no—
101#431—91no—
102#324—32no—
103#324—92no—
104C22×C3×C4—21no—
105C22×C3×C4—32no—
106C22×C3×C4—32no—
107C22×C3×C4C22×D312yes—
108C22×Dic3—32no—
109C22×Dic3—32no—
110C22×Dic3—61no—
111C22×Dic3—61no—
112C22×Dic3C4×D312yes—
113C22×Dic3C4×D312yes—
114C2×Dic6—38no—
115C2×Dic6—62no—
116C2×Dic6—62no—
117C2×Dic6—64no—
118C2×C3×C8—22no—
119C2×C3×C8—22no—
120C2×C3×C8—62no—
121C3×C4⋊C4—62no—
122C3×C4⋊C4—62no—
123Dic3⋊C4—22no—
124Dic3⋊C4—22no—
125Dic3⋊C4—62no—
126Dic3⋊C4—62no—
127C4×Dic3—32no—
128C4×Dic3—32no—
129C4×Dic3—32no—
130C4×Dic3—32no—
131C4×Dic3—61no—
132C4×Dic3—61no—
133C4×Dic3—61no—
134C4×Dic3—61no—
135C4×Dic3—62no—
136C4×Dic3—62no—
137C4×Dic3—62no—
138C4×Dic3—62no—
139C2×C3⋊C8—22no—
140C2×C3⋊C8—62no—
141C2×C3⋊C8—62no—
142C22×C32—21no—
143C22×C32—21no—
144C22×C32C2×C22⋊C411yescharacteristic
145C22×C32C22×C811yescharacteristic
146C22×C32C2×M1611yescharacteristic
147C32×C4—21no—
148C32×C4—21no—
149C3⋊Dic3—21no—
150C3⋊Dic3C22⋊C812yes—
151C3⋊Dic3C22⋊C812yes—
152C3⋊Dic3#10112yes—
153C3×Dic3—24no—
154C3×Dic3—42no—
155C22×Q8—91no—
156C4×Q8—181no—
157C4×Q8—181no—
158C4×Q8—181no—
159C4×Q8—181no—
160C2×C4⋊C4—32no—
161C2×C4⋊C4—91no—
162C2×C42—91no—
163C2×C42—92no—
164C4⋊C8—181no—
165C4⋊C8—181no—
166C22⋊C8—32no—
167C22⋊C8—91no—
168C22⋊C8D3211yescharacteristic
169C4×C8—181no—
170C4×C8—181no—
171C23×C3—21no—
172C23×C3C2×C4×D312yes—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—34no—
176C2×C3×C4—42no—
177C2×C3×C4—42no—
178C2×C3×C4—62no—
179C2×C3×C4—62no—
180C2×C3×C4—62no—
181C2×C3×C4—122no—
182C2×C3×C4D3×D412yes—
183C2×C3×C4D3×D412yes—
184C2×Dic3—22no—
185C2×Dic3—22no—
186C2×Dic3—22no—
187C2×Dic3—32no—
188C2×Dic3—32no—
189C2×Dic3—32no—
190C2×Dic3—34no—
191C2×Dic3—34no—
192C2×Dic3—32no—
193C2×Dic3—42no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—62no—
198C2×Dic3—62no—
199C2×Dic3—61no—
200C2×Dic3—64no—
201C2×Dic3—122no—
202C2×Dic3D3×C814yes—
203Dic6—68no—
204Dic6—68no—
205C3×C8—42no—
206C3×C8—42no—
207C3×C8—122no—
208C3⋊C8—42no—
209C3⋊C8—122no—
210C3⋊C8—122no—
211C2×C32—21no—
212C2×C32—21no—
213C2×C32C2×C22⋊C811yescharacteristic
214C2×C32#41011yescharacteristic
215C2×C32C2×#10111yescharacteristic
216C2×Q8—94no—
217C2×Q8—181no—
218C2×Q8—181no—
219C2×Q8—182no—
220C22×C4—32no—
221C22×C4—32no—
222C22×C4—91no—
223C22×C4—91no—
224C22×C4C2×D3211yescharacteristic
225C2×C8—21no—
226C2×C8—62no—
227C2×C8—181no—
228C4⋊C4—62no—
229C4⋊C4—62no—
230C4⋊C4—181no—
231C4⋊C4—181no—
232C42—91no—
233C42—91no—
234C42—91no—
235C42—91no—
236C42—182no—
237C42—182no—
238C22×C3—22no—
239C22×C3—22no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—41no—
244C22×C3—41no—
245C22×C3D3×C22⋊C412yes—
246C22×C3C2×D3×C812yes—
247C22×C3D3×M1612yes—
248C3×C4—22no—
249C3×C4—22no—
250C3×C4—22no—
251C3×C4—41no—
252C3×C4—64no—
253C3×C4—122no—
254Dic3—24no—
255Dic3—34no—
256Dic3—34no—
257Dic3—34no—
258Dic3—42no—
259Dic3—62no—
260Dic3—62no—
261Dic3—62no—
262Dic3—62no—
263Dic3—121no—
264C32#146111yescharacteristic, complemented, Sylow
265C23C4×D3211yescharacteristic
266Q8—184no—
267Q8—184no—
268C2×C4—34no—
269C2×C4—41no—
270C2×C4—62no—
271C2×C4—62no—
272C2×C4—62no—
273C2×C4—92no—
274C2×C4—92no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—122no—
280C2×C4—182no—
281C2×C4#380211yescharacteristic
282C2×C4#381111yescharacteristic
283C8—41no—
284C8—122no—
285C8—361no—
286C2×C3—22no—
287C2×C3—22no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—41no—
292C2×C3—41no—
293C2×C3D3×C22⋊C812yes—
294C2×C3#474012yes—
295C2×C3D3×#10112yes—
296C22—21no—
297C22—21no—
298C22D32×C811yescharacteristic
299C22#6379111yescharacteristic
300C22#6392111yescharacteristic
301C4—21no—
302C4—21no—
303C4—64no—
304C4—92no—
305C4—92no—
306C4—92no—
307C4—122no—
308C4—181no—
309C3—21no—
310C3#6812512yescomplemented
311C2—21no—
312C2—21no—
313C2#1059040611yescharacteristic
314C2#1059093511yescharacteristic
315C2#1059100311yescharacteristic
subgroupG/H
centerC22#63921
commutatorC22×C32C22×C8
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1461
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
39. C2×#627C8semidirect
264. C32#1461semidirect
310. C3#68125semidirect

Maximal subgroups

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

subgroupindex
C2×#638382
#105924172
#105910612
C3×#44692
#105891472
#681253