Finite Group Databasebeta

← #11775089

Subgroups — #11775089

Order 1152.

591 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 591 conjugacy classes of subgroups — too many to draw. Only its 102 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
1#10596093C211yesmaximal, characteristic
2#10591257C211yesmaximal, characteristic
3#10591061C211yesmaximal, characteristic
4C3×#4538C212yesmaximal
5#10589154C212yesmaximal
6#68309—32nomaximal
7C32×C22⋊Q8C2211yescharacteristic
8Q8×C3⋊Dic3C411yescharacteristic, complemented
9#64153C411yescharacteristic, complemented
10#64133C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64098—21no—
13#64097C411yescharacteristic, complemented
14#64096—21no—
15#64096C411yescharacteristic, complemented
16#64087—21no—
17#64086—21no—
18C2×#3724—21no—
19C2×Dic32—21no—
20C3×C3⋊#95C2212yes—
21C3×#830C2212yes—
22#63572—21no—
23#63553—21no—
24#5622—32no—
25#5622—61no—
26#4718—32no—
27#4649—32no—
28C3×#328—32no—
29#4538D312yes—
30#4467—32no—
31#4452—32no—
32C2×C32×Q8C2×C411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36C2×#634—21no—
37C2×#634C2×C411yescharacteristic
38C22×C3×Dic3—22no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4C2×C411yescharacteristic
41C32×C22⋊C4—21no—
42#3757—21no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)C2×C411yescharacteristic
45#3750—21no—
46#3750—21no—
47#3750—21no—
48#3750—21no—
49#3750—21no—
50C4×C3⋊Dic3—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3C2×C411yescharacteristic
53C4×C3⋊Dic3C2×C411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C2×C3×C3⋊C8—22no—
57#3724—24no—
58Dic32—42no—
59#1503—91noSylow
60C3×C22⋊Q8—21no—
61C3×C22⋊Q8C2×D312yes—
62Q8×Dic3—32no—
63Q8×Dic3—61no—
64#944—32no—
65#944—61no—
66#924—32no—
67#924—61no—
68C2×Dic3⋊C4—62no—
69C2×C4×Dic3—32no—
70C2×C4×Dic3—61no—
71C2×C4×Dic3—62no—
72#889—62no—
73#889—62no—
74#888—32no—
75#888—61no—
76#887—32no—
77#887—61no—
78#887—62no—
79#887—62no—
80#878—62no—
81#878—62no—
82#877—62no—
83#877—62no—
84C3×C22⋊C8—32no—
85C3×#95—32no—
86C3⋊#95C2×D312yes—
87#830C2×D312yes—
88Dic3⋊C8—62no—
89C8×Dic3—62no—
90C23×C32C2×D411yescharacteristic
91C32×Q8—41no—
92C2×C32×C4—21no—
93C2×C32×C4—21no—
94C2×C32×C4—41no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3C22⋊C411yescharacteristic
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C2×C3⋊Dic3C22⋊C411yescharacteristic
104C2×C3⋊Dic3SD1612yes—
105C2×C3⋊Dic3Q1612yes—
106#634—42no—
107#634—41no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3—42no—
110C2×C3×Dic3—42no—
111C3×C3⋊C8—42no—
112#533—91no—
113#431—91no—
114C4×C4⋊C4—91no—
115#328—32no—
116#328—92no—
117C2×C3×Q8—21no—
118C2×C3×Q8C4×D312yes—
119C22×C3×C4—21no—
120C22×C3×C4—62no—
121C22×C3×C4C22×D312yes—
122C22×Dic3—22no—
123C22×Dic3—32no—
124C22×Dic3—32no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C2×Dic6—32no—
128C2×Dic6—61no—
129C2×Dic6—62no—
130C2×Dic6—62no—
131C2×C3×C8—62no—
132C3×C4⋊C4—22no—
133C3×C4⋊C4—22no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4C4×D312yes—
136C3×C22⋊C4—22no—
137C3×C22⋊C4—22no—
138#217—62no—
139#217—62no—
140C4⋊Dic3—32no—
141C4⋊Dic3—61no—
142C4⋊Dic3—62no—
143C4⋊Dic3—62no—
144Dic3⋊C4—68no—
145Dic3⋊C4—62no—
146Dic3⋊C4—62no—
147Dic3⋊C4—62no—
148Dic3⋊C4—62no—
149Dic3⋊C4—62no—
150Dic3⋊C4—62no—
151Dic3⋊C4—62no—
152Dic3⋊C4—62no—
153Dic3⋊C4—62no—
154Dic3⋊C4—62no—
155C4×Dic3—32no—
156C4×Dic3—32no—
157C4×Dic3—32no—
158C4×Dic3—32no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C4×Dic3—61no—
162C4×Dic3—61no—
163C4×Dic3—62no—
164C4×Dic3—62no—
165C4×Dic3—62no—
166C4×Dic3—62no—
167C4×Dic3—124no—
168C2×C3⋊C8—22no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32C2×C22⋊C411yescharacteristic
172C22×C32C2×SD1611yescharacteristic
173C22×C32C2×Q1611yescharacteristic
174C32×C4—21no—
175C32×C4—21no—
176C32×C4—41no—
177C32×C4—41no—
178C3⋊Dic3—21no—
179C3⋊Dic3—41no—
180C3⋊Dic3—41no—
181C3⋊Dic3#10312yes—
182C3⋊Dic3#10312yes—
183C3⋊Dic3#10412yes—
184C3×Dic3—44no—
185C4⋊Q8—91no—
186C4⋊Q8—91no—
187#125—181no—
188C22⋊Q8—91no—
189C22⋊Q8—181no—
190C22⋊Q8D3211yescharacteristic
191C4×Q8—91no—
192C4×Q8—91no—
193C4×Q8—181no—
194#117—181no—
195C2×C4⋊C4—181no—
196C2×C42—91no—
197C2×C42—181no—
198C4⋊C8—181no—
199C22⋊C8—32no—
200C4×C8—181no—
201#95—32no—
202C23×C3—21no—
203C23×C3D3×D412yes—
204C3×Q8—42no—
205C3×Q8—42no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—42no—
213C2×C3×C4—42no—
214C2×C3×C4—64no—
215C2×C3×C4—122no—
216C2×C3×C4—122no—
217C2×C3×C4C2×C4×D312yes—
218C2×C3×C4D3×D412yes—
219C2×Dic3—24no—
220C2×Dic3—32no—
221C2×Dic3—32no—
222C2×Dic3—32no—
223C2×Dic3—34no—
224C2×Dic3—34no—
225C2×Dic3—32no—
226C2×Dic3—42no—
227C2×Dic3—42no—
228C2×Dic3—61no—
229C2×Dic3—61no—
230C2×Dic3—61no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C2×Dic3—61no—
234C2×Dic3—64no—
235C2×Dic3—62no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—62no—
239C2×Dic3—122no—
240Dic6—124no—
241Dic6—124no—
242Dic6—122no—
243Dic6—122no—
244C3×C8—122no—
245C3⋊C8—42no—
246C2×C32—21no—
247C2×C32—21no—
248C2×C32#41011yescharacteristic
249C2×C32C2×#10311yescharacteristic
250C2×C32C2×#10411yescharacteristic
251C2×Q8—91no—
252C2×Q8—181no—
253C2×Q8#62411yescharacteristic
254C22×C4—62no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4C2×D3211yescharacteristic
258C2×C8—62no—
259C4⋊C4—21no—
260C4⋊C4—91no—
261C4⋊C4—181no—
262C4⋊C4—181no—
263C4⋊C4—181no—
264C4⋊C4—181no—
265C4⋊C4—181no—
266C4⋊C4—184no—
267C4⋊C4—181no—
268C4⋊C4#62411yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—181no—
271C42—91no—
272C42—91no—
273C42—91no—
274C42—91no—
275C42—181no—
276C42—181no—
277C42—362no—
278C22×C3—22no—
279C22×C3—22no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—41no—
284C22×C3—41no—
285C22×C3D3×C22⋊C412yes—
286C22×C3D3×SD1612yes—
287C22×C3D3×Q1612yes—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—41no—
292C3×C4—42no—
293C3×C4—42no—
294C3×C4—42no—
295C3×C4—42no—
296C3×C4—124no—
297Dic3—34no—
298Dic3—34no—
299Dic3—34no—
300Dic3—44no—
301Dic3—62no—
302Dic3—62no—
303Dic3—62no—
304Dic3—62no—
305Dic3—121no—
306Dic3—122no—
307Dic3—122no—
308Dic3—122no—
309Dic3—122no—
310C32#150311yescharacteristic, complemented, Sylow
311C23#381111yescharacteristic
312Q8—41no—
313Q8—361no—
314Q8—362no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—64no—
319C2×C4—92no—
320C2×C4—92no—
321C2×C4—91no—
322C2×C4—91no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—122no—
326C2×C4—122no—
327C2×C4—182no—
328C2×C4—181no—
329C2×C4—181no—
330C2×C4C2×#62411yescharacteristic
331C2×C4#381111yescharacteristic
332C8—122no—
333C2×C3—22no—
334C2×C3—22no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—41no—
339C2×C3—41no—
340C2×C3#474012yes—
341C2×C3D3×#10312yes—
342C2×C3D3×#10412yes—
343C22—21no—
344C22—21no—
345C22#6394011yescharacteristic
346C22#6394411yescharacteristic
347C22#6397411yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—92no—
353C4—92no—
354C4—92no—
355C4—124no—
356C4—181no—
357C4—361no—
358C4—361no—
359C3—21no—
360C3#6830912yescomplemented
361C2—21no—
362C2—21no—
363C2#1059152911yescharacteristic
364C2#1059155211yescharacteristic
365C2#1059167111yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22⋊Q8D32
hypocenterC32#1503
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
8. Q8×C3⋊Dic3C4semidirect
9. #64153C4semidirect
13. #64097C4semidirect
15. #64096C4semidirect
310. C32#1503semidirect
360. C3#68309semidirect

Maximal subgroups

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

subgroupindex
#105960932
#105912572
#105910612
C3×#45382
#105891542
#683093