Finite Group Databasebeta

← #11775065

Subgroups — #11775065

Order 1152.

627 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 627 conjugacy classes of subgroups — too many to draw. Only its 100 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#10594929C211yesmaximal, characteristic
2#10592417C211yesmaximal, characteristic, complemented
3#10591257C211yesmaximal, characteristic, complemented
4C3×#4470C212yesmaximal, complemented
5#10589149C212yesmaximal, complemented
6#68277—32nomaximal
7C2×#3805—21no—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C3×#930C2212yes—
10#63980—21no—
11C2×#3724—21no—
12C2×Dic32—21no—
13#63919C411yescharacteristic, complemented
14#63915—21no—
15#63914C411yescharacteristic, complemented
16#63902—21no—
17#63898C412yescomplemented
18C32×C22⋊C8C2211yescharacteristic
19#63657C2211yescharacteristic
20#63641—21no—
21C8×C3⋊Dic3—21no—
22C3×C3⋊#95C2212yes—
23#5596—32no—
24#4718—32no—
25#4718—61no—
26#4649—32no—
27C3×#327—32no—
28#4537—32no—
29#4470D312yescomplemented
30#4451—32no—
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C2×C3×#67—22no—
35C22×C3×Dic3—22no—
36C2×C3×D12C2×C412yes—
37C2×#627—21no—
38C2×#625—21no—
39C2×#625—21no—
40#3805—42no—
41#3805—42no—
42C2×D3×Dic3—22no—
43C2×C32×C8—21no—
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3C2×C411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C4×C3⋊Dic3D411yescharacteristic
48C2×C3⋊(C3⋊C8)—21no—
49C3×(C2×D3)⋊C4—22no—
50C3×C4⋊Dic3C2×C412yes—
51#3724—24no—
52#3724—21no—
53(C2×D3)⋊Dic3—22no—
54Dic32—42no—
55#1502—91noSylow
56C2×#237—62no—
57C3×#121—32no—
58#940—32no—
59#939—62no—
60D4×Dic3—32no—
61#930C2×D312yes—
62C2×Dic3⋊C4—62no—
63C2×C4×Dic3—32no—
64C2×C4×Dic3—61no—
65C2×C4×Dic3—62no—
66#893—32no—
67#888—32no—
68#885—62no—
69#67⋊C4—62no—
70C3×C22⋊C8—21no—
71C3×C22⋊C8C2×D312yes—
72C3×#95—32no—
73C3⋊#95C2×D312yes—
74#830—32no—
75#830—61no—
76Dic3⋊C8—62no—
77Dic3⋊C8—62no—
78C8×Dic3—62no—
79C8×Dic3—62no—
80C23×C32C2×D411yescharacteristic
81C22×C3×D3—22no—
82C2×C32×C4—41no—
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C22⋊C411yescharacteristic
88C2×C3⋊Dic3C22⋊C411yescharacteristic
89C2×C3⋊Dic3C22⋊C411yescharacteristic
90C2×C3⋊Dic3D812yes—
91C2×C3⋊Dic3SD1612yes—
92C3×#67—42no—
93C3×#67—42no—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—22no—
96C2×C3×Dic3—42no—
97C2×C3×Dic3—42no—
98C3×D12—42no—
99#627—42no—
100#625—42no—
101#625—42no—
102D3×Dic3—44no—
103C32×C8—41no—
104C3⋊(C3⋊C8)—41no—
105#532—91no—
106#431—91no—
107C4×C4⋊C4—91no—
108#327—32no—
109#327—92no—
110C2×C3×D4—32no—
111C2×C3×D4—62no—
112C22×C3×C4—21no—
113C22×C3×C4—62no—
114C22×C3×C4C22×D312yes—
115C2×#67—22no—
116C2×#67—62no—
117C2×#67—62no—
118C22×Dic3—22no—
119C22×Dic3—32no—
120C22×Dic3—32no—
121C22×Dic3—61no—
122C22×Dic3—61no—
123C22×Dic3—62no—
124#237—124no—
125#237—124no—
126C2×D12C4×D312yes—
127C2×C4×D3—62no—
128C2×Dic6—62no—
129C2×C3×C8—22no—
130C2×C3×C8—22no—
131C3×C4⋊C4—32no—
132C3×C22⋊C4—62no—
133#217—62no—
134(C2×D3)⋊C4—22no—
135(C2×D3)⋊C4—62no—
136C4⋊Dic3C4×D312yes—
137Dic3⋊C4—62no—
138Dic3⋊C4—68no—
139C4×Dic3—32no—
140C4×Dic3—32no—
141C4×Dic3—32no—
142C4×Dic3—32no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C4×Dic3—61no—
147C4×Dic3—124no—
148C2×C3⋊C8—62no—
149C2×C3⋊C8—62no—
150C22×C32—21no—
151C22×C32—21no—
152C22×C32C2×C22⋊C411yescharacteristic
153C22×C32C2×D811yescharacteristic
154C22×C32C2×SD1611yescharacteristic
155C2×C3×D3—42no—
156C2×C3×D3—42no—
157C2×C3×D3—42no—
158C32×C4—21no—
159C32×C4—21no—
160C3⋊Dic3—21no—
161C3⋊Dic3#10212yes—
162C3⋊Dic3#10212yes—
163C3⋊Dic3#10412yes—
164C3×Dic3—44no—
165C3×Dic3—42no—
166C2×#41—181no—
167C4⋊Q8—91no—
168#127—91no—
169#124—181no—
170#121—32no—
171#121—181no—
172C4×D4—92no—
173C4×D4—181no—
174C2×C4⋊C4—181no—
175C2×C42—91no—
176C2×C42—181no—
177C4⋊C8—181no—
178C22⋊C8—91no—
179C22⋊C8D3211yescharacteristic
180C4×C8—181no—
181#95—32no—
182C23×C3—21no—
183C23×C3—62no—
184C23×C3D3×D412yes—
185C22×D3—22no—
186C3×D4—122no—
187C3×D4—122no—
188C3×D4—122no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—42no—
192C2×C3×C4—42no—
193C2×C3×C4—64no—
194C2×C3×C4—62no—
195C2×C3×C4—122no—
196C2×C3×C4—122no—
197C2×C3×C4C2×C4×D312yes—
198C2×C3×C4D3×D412yes—
199#67—42no—
200#67—42no—
201#67—124no—
202#67—124no—
203C2×Dic3—24no—
204C2×Dic3—22no—
205C2×Dic3—32no—
206C2×Dic3—32no—
207C2×Dic3—32no—
208C2×Dic3—34no—
209C2×Dic3—34no—
210C2×Dic3—32no—
211C2×Dic3—42no—
212C2×Dic3—42no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—62no—
217C2×Dic3—62no—
218C2×Dic3—61no—
219C2×Dic3—64no—
220C2×Dic3—122no—
221C2×Dic3—124no—
222D12—42no—
223C4×D3—124no—
224Dic6—124no—
225C3×C8—42no—
226C3×C8—42no—
227C3⋊C8—122no—
228C3⋊C8—122no—
229C2×C32—21no—
230C2×C32—21no—
231C2×C32#41011yescharacteristic
232C2×C32C2×#10211yescharacteristic
233C2×C32C2×#10411yescharacteristic
234C3×D3—82no—
235#41—362no—
236#41—362no—
237C2×Q8—181no—
238C2×D4—32no—
239C2×D4—62no—
240C2×D4—181no—
241C2×D4—181no—
242C22×C4—62no—
243C22×C4—91no—
244C22×C4—91no—
245C22×C4—182no—
246C22×C4C2×D3211yescharacteristic
247C2×C8—21no—
248C2×C8—181no—
249C4⋊C4—32no—
250C4⋊C4—181no—
251C4⋊C4—184no—
252C22⋊C4—62no—
253C22⋊C4—182no—
254C42—91no—
255C42—91no—
256C42—91no—
257C42—91no—
258C42—362no—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—122no—
267C22×C3—122no—
268C22×C3—122no—
269C22×C3D3×C22⋊C412yes—
270C22×C3D3×D812yes—
271C22×C3D3×SD1612yes—
272C2×D3—42no—
273C2×D3—42no—
274C2×D3—42no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—41no—
279C3×C4—124no—
280C3×C4—122no—
281Dic3—34no—
282Dic3—34no—
283Dic3—34no—
284Dic3—44no—
285Dic3—42no—
286Dic3—62no—
287Dic3—62no—
288Dic3—62no—
289Dic3—62no—
290Dic3—121no—
291C32#150211yescharacteristic, complemented, Sylow
292C23—62no—
293C23#380211yescharacteristic
294Q8—362no—
295D4—122no—
296D4—122no—
297D4—122no—
298D4—362no—
299D4—362no—
300C2×C4—41no—
301C2×C4—64no—
302C2×C4—62no—
303C2×C4—92no—
304C2×C4—92no—
305C2×C4—91no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—91no—
309C2×C4—122no—
310C2×C4—122no—
311C2×C4—182no—
312C2×C4—364no—
313C2×C4C4×D3211yescharacteristic
314C2×C4#381111yescharacteristic
315C8—41no—
316C8—361no—
317C2×C3—22no—
318C2×C3—22no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—41no—
323C2×C3—41no—
324C2×C3—242no—
325C2×C3#474012yes—
326C2×C3D3×#10212yes—
327C2×C3D3×#10412yes—
328D3—82no—
329C22—21no—
330C22—21no—
331C22—122no—
332C22—122no—
333C22—122no—
334C22#6379611yescharacteristic
335C22#6379711yescharacteristic
336C22#6392111yescharacteristic
337C4—21no—
338C4—21no—
339C4—92no—
340C4—92no—
341C4—92no—
342C4—124no—
343C4—122no—
344C4—181no—
345C3—21no—
346C3#6827712yescomplemented
347C2—21no—
348C2—21no—
349C2—242no—
350C2#1059040611yescharacteristic
351C2#1059094011yescharacteristic
352C2#1059100811yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10594929C2
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1502
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592417C2semidirect
3. #10591257C2semidirect
4. C3×#4470C2semidirect
5. #10589149C2semidirect
13. #63919C4semidirect
15. #63914C4semidirect
17. #63898C4semidirect
29. #4470D3semidirect
291. C32#1502semidirect
346. C3#68277semidirect

Maximal subgroups

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

subgroupindex
#105949292
#105924172
#105912572
C3×#44702
#105891492
#682773