Finite Group Databasebeta

← #11774060

Subgroups — #11774060

Order 1152.

521 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 521 conjugacy classes of subgroups — too many to draw. Only its 94 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×#64098C211yesmaximal, characteristic
2#10591066C211yesmaximal, characteristic
3#10591061C211yesmaximal, characteristic
4C3×#4528C212yesmaximal
5#10589148C212yesmaximal
6#68128—32nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C4⋊(C3⋊Dic3)C411yescharacteristic
9C2×#3750C411yescharacteristic
10C2×#3750C411yescharacteristic
11C2×#3750C411yescharacteristic
12C2×#3750C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64098—21no—
15#64098—21no—
16#64098—21no—
17#64098—21no—
18C3×#830C2212yes—
19C3×#830C2212yes—
20#63572—21no—
21#63572—21no—
22#63555—21no—
23#63553—21no—
24C2×#889—32no—
25C2×#889—61no—
26#4719—32no—
27#4718—32no—
28C3×#324—32no—
29#4528D312yes—
30#4469—32no—
31#4469—32no—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C22×C3⋊Dic3C2×C411yescharacteristic
38C22×C3⋊Dic3C2×C411yescharacteristic
39C32×C4⋊C4—21no—
40C32×C4⋊C4—21no—
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)—21no—
43#3750—21no—
44#3750—21no—
45#3750—21no—
46#3750—21no—
47#3750—21no—
48#3750—21no—
49#3750—21no—
50#3750—21no—
51C4×C3⋊Dic3D411yescharacteristic
52C4×C3⋊Dic3D411yescharacteristic
53C4×C3⋊Dic3D411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—22no—
56C2×C3×C3⋊C8—22no—
57#1470—91noSylow
58C2×C3×C4⋊C4—21no—
59C2×C3×C4⋊C4C2×D312yes—
60C2×C4⋊Dic3—32no—
61C2×C4⋊Dic3—61no—
62C2×Dic3⋊C4—32no—
63C2×Dic3⋊C4—32no—
64C2×Dic3⋊C4—32no—
65C2×Dic3⋊C4—32no—
66C2×Dic3⋊C4—61no—
67C2×Dic3⋊C4—61no—
68C2×Dic3⋊C4—61no—
69C2×Dic3⋊C4—61no—
70C2×C4×Dic3—32no—
71C2×C4×Dic3—61no—
72#889—62no—
73#889—62no—
74#889—62no—
75#889—62no—
76#889—62no—
77#889—62no—
78#889—62no—
79#889—62no—
80C3×C22⋊C8—32no—
81C3×C22⋊C8—32no—
82#830C2×D312yes—
83#830C2×D312yes—
84#815—62no—
85Dic3⋊C8—62no—
86Dic3⋊C8—62no—
87C8×Dic3—62no—
88C23×C32C22×C411yescharacteristic
89C2×C32×C4—21no—
90C2×C32×C4—21no—
91C2×C32×C4—22no—
92C2×C32×C4—41no—
93C2×C32×C4—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C2×C3⋊Dic3C22⋊C411yescharacteristic
104C2×C3⋊Dic3C22⋊C411yescharacteristic
105C2×C3⋊Dic3C22⋊C411yescharacteristic
106C3×C3⋊C8—42no—
107C3×C3⋊C8—42no—
108C2×#125—91no—
109#432—91no—
110#431—91no—
111#324—32no—
112#324—92no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4C4×D312yes—
117C22×C3×C4C4×D312yes—
118C22×C3×C4C22×D312yes—
119C22×Dic3—32no—
120C22×Dic3—32no—
121C22×Dic3—32no—
122C22×Dic3—32no—
123C22×Dic3—61no—
124C22×Dic3—61no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C2×C3×C8—62no—
128C2×C3×C8—62no—
129C3×C4⋊C4—22no—
130C3×C4⋊C4—22no—
131C3×C4⋊C4—22no—
132C3×C4⋊C4—22no—
133C4⋊Dic3—62no—
134C4⋊Dic3—62no—
135C4⋊Dic3—62no—
136C4⋊Dic3—62no—
137Dic3⋊C4—62no—
138Dic3⋊C4—62no—
139Dic3⋊C4—62no—
140Dic3⋊C4—62no—
141Dic3⋊C4—62no—
142Dic3⋊C4—62no—
143Dic3⋊C4—62no—
144Dic3⋊C4—62no—
145Dic3⋊C4—62no—
146Dic3⋊C4—62no—
147Dic3⋊C4—62no—
148Dic3⋊C4—62no—
149Dic3⋊C4—62no—
150Dic3⋊C4—62no—
151Dic3⋊C4—62no—
152Dic3⋊C4—62no—
153C4×Dic3—32no—
154C4×Dic3—32no—
155C4×Dic3—32no—
156C4×Dic3—32no—
157C4×Dic3—61no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C2×C3⋊C8—22no—
162C2×C3⋊C8—22no—
163C22×C32—21no—
164C22×C32—21no—
165C22×C32C2×C22⋊C411yescharacteristic
166C22×C32#13112yes—
167C32×C4—21no—
168C32×C4—21no—
169C32×C4—41no—
170C32×C4—41no—
171C3⋊Dic3—21no—
172C3⋊Dic3—21no—
173C3⋊Dic3—21no—
174C3⋊Dic3—41no—
175C3⋊Dic3—41no—
176C3⋊Dic3#10112yes—
177#125—181no—
178#125—181no—
179#125—181no—
180#125—181no—
181C2×C4⋊C4—91no—
182C2×C4⋊C4—91no—
183C2×C4⋊C4—91no—
184C2×C4⋊C4—91no—
185C2×C4⋊C4—91no—
186C2×C4⋊C4D3211yescharacteristic
187C2×C42—91no—
188C4⋊C8—181no—
189C4⋊C8—181no—
190C22⋊C8—32no—
191C22⋊C8—32no—
192#97—181no—
193C4×C8—181no—
194C23×C3—21no—
195C23×C3C2×C4×D312yes—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—42no—
205C2×C3×C4—42no—
206C2×C3×C4—42no—
207C2×C3×C4—42no—
208C2×C3×C4—42no—
209C2×C3×C4D3×D412yes—
210C2×C3×C4D3×D412yes—
211C2×Dic3—32no—
212C2×Dic3—32no—
213C2×Dic3—32no—
214C2×Dic3—32no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C2×Dic3—64no—
220C2×Dic3—64no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227C2×Dic3—62no—
228C2×Dic3—62no—
229C2×Dic3—122no—
230C2×Dic3—122no—
231C2×Dic3—122no—
232C2×Dic3—122no—
233C3×C8—122no—
234C3×C8—122no—
235C3⋊C8—42no—
236C3⋊C8—42no—
237C2×C32—22no—
238C2×C32#40811yescharacteristic
239C2×C32#41011yescharacteristic
240C2×C32C2×#10111yescharacteristic
241C22×C4—91no—
242C22×C4—91no—
243C22×C4—91no—
244C22×C4—91no—
245C22×C4#62411yescharacteristic
246C22×C4#62411yescharacteristic
247C22×C4C2×D3211yescharacteristic
248C2×C8—62no—
249C2×C8—62no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—181no—
253C4⋊C4—181no—
254C4⋊C4—181no—
255C4⋊C4—181no—
256C4⋊C4—181no—
257C4⋊C4—181no—
258C4⋊C4—181no—
259C4⋊C4—181no—
260C4⋊C4—181no—
261C4⋊C4—181no—
262C42—91no—
263C42—91no—
264C42—91no—
265C42—91no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—21no—
272C22×C3D3×C22⋊C412yes—
273C22×C3#90112yes—
274C22×C3#90712yes—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—41no—
278C3×C4—41no—
279C3×C4—42no—
280C3×C4—42no—
281C3×C4—42no—
282C3×C4—42no—
283Dic3—34no—
284Dic3—62no—
285Dic3—62no—
286Dic3—62no—
287Dic3—62no—
288Dic3—62no—
289Dic3—121no—
290Dic3—121no—
291Dic3—122no—
292Dic3—122no—
293Dic3—122no—
294Dic3—122no—
295C32#147011yescharacteristic, complemented, Sylow
296C23C2×#62411yescharacteristic
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—91no—
303C2×C4—91no—
304C2×C4—91no—
305C2×C4—91no—
306C2×C4—182no—
307C2×C4—182no—
308C2×C4—182no—
309C2×C4—181no—
310C2×C4—181no—
311C2×C4—361no—
312C2×C4#381111yescharacteristic
313C2×C4#381111yescharacteristic
314C8—122no—
315C8—122no—
316C2×C3—24no—
317C2×C3—22no—
318C2×C3—22no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3#472712yes—
323C2×C3#474012yes—
324C2×C3D3×#10112yes—
325C22—21no—
326C22—21no—
327C22#6381712yes—
328C22#6397411yescharacteristic
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—92no—
334C4—181no—
335C4—181no—
336C4—181no—
337C4—361no—
338C4—361no—
339C3—21no—
340C3#6812812yescomplemented
341C2—22no—
342C2#1059115311yescharacteristic
343C2#1059152911yescharacteristic
344C2#1059163911yescharacteristic
subgroupG/H
centerC22#63974
commutator, prime radicalC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1470
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
295. C32#1470semidirect
340. C3#68128semidirect

Maximal subgroups

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

subgroupindex
C2×#640982
#105910662
#105910612
C3×#45282
#105891482
#681283