Finite Group Databasebeta

← #11775058

Subgroups — #11775058

Order 1152.

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

normal subgroups only

This group has 665 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#10592348C211yesmaximal, characteristic, complemented
3#10591061C211yesmaximal, characteristic, complemented
4C3×#4451C212yesmaximal, complemented
5#10589150C212yesmaximal, complemented
6#68277—32nomaximal
7C2×#3805—21no—
8C2×#3750—21no—
9C2×C4×C3⋊Dic3—21no—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C3×#930C2212yes—
12#63980—21no—
13#63919C411yescharacteristic, complemented
14#63915—21no—
15#63914C411yescharacteristic, complemented
16#63902—21no—
17#63898C412yescomplemented
18C32×#95C2211yescharacteristic
19#63658C2211yescharacteristic
20C3×#830C2212yes—
21#63572—21no—
22#63553—21no—
23#5596—32no—
24#4718—32no—
25#4649—32no—
26#4649—61no—
27C3×#327—32no—
28#4537—32no—
29#4470—32no—
30#4451D312yescomplemented
31C22×C32×C4—21no—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3D411yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36C2×C3×#67—22no—
37C2×C3×D12C2×C412yes—
38C2×#627—21no—
39C2×#625—21no—
40C2×#625—21no—
41#3805—42no—
42#3805—42no—
43C2×D3×Dic3—22no—
44#3750—24no—
45C4×C3⋊Dic3—42no—
46C4×C3⋊Dic3C2×C411yescharacteristic
47C4×C3⋊Dic3C2×C411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3D411yescharacteristic
50C3×(C2×D3)⋊C4—22no—
51C3×C4⋊Dic3C2×C412yes—
52C2×C3×C3⋊C8—22no—
53#3724—21no—
54(C2×D3)⋊Dic3—22no—
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×Dic3⋊C4—62no—
64C2×C4×Dic3—32no—
65C2×C4×Dic3—61no—
66C2×C4×Dic3—62no—
67C2×C4×Dic3—62no—
68#893—32no—
69#888—32no—
70#885—62no—
71#67⋊C4—62no—
72C3×C22⋊C8—32no—
73C3×#95—21no—
74C3×#95C2×D312yes—
75C3⋊#95—32no—
76C3⋊#95—61no—
77#830C2×D312yes—
78Dic3⋊C8—62no—
79C8×Dic3—62no—
80C23×C32C2×D411yescharacteristic
81C22×C3×D3—22no—
82C2×C32×C4—22no—
83C2×C32×C4—41no—
84C2×C32×C4—41no—
85C2×C32×C4—41no—
86C2×C32×C4C22×C411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3—41no—
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C2×C3⋊Dic3C22⋊C411yescharacteristic
94C2×C3⋊Dic3C22⋊C411yescharacteristic
95C2×C3⋊Dic3C22⋊C411yescharacteristic
96C2×C3⋊Dic3D812yes—
97C2×C3⋊Dic3SD1612yes—
98C3×#67—42no—
99C3×#67—42no—
100C2×C3×Dic3—22no—
101C3×D12—42no—
102#627—42no—
103#625—42no—
104#625—42no—
105D3×Dic3—44no—
106C3×C3⋊C8—42no—
107#532—91no—
108#431—91no—
109C4×C4⋊C4—91no—
110#327—32no—
111#327—92no—
112C2×C3×D4—32no—
113C2×C3×D4—62no—
114C22×C3×C4—22no—
115C22×C3×C4—22no—
116C22×C3×C4—21no—
117C22×C3×C4C22×D312yes—
118C2×#67—22no—
119C2×#67—62no—
120C2×#67—62no—
121C22×Dic3—32no—
122C22×Dic3—32no—
123C22×Dic3—61no—
124C22×Dic3—61no—
125C22×Dic3—62no—
126C22×Dic3—62no—
127C22×Dic3—62no—
128#237—124no—
129#237—124no—
130C2×D12C4×D312yes—
131C2×C4×D3—62no—
132C2×Dic6—62no—
133C2×C3×C8—62no—
134C3×C4⋊C4—32no—
135C3×C22⋊C4—62no—
136#217—62no—
137(C2×D3)⋊C4—22no—
138(C2×D3)⋊C4—62no—
139C4⋊Dic3C4×D312yes—
140Dic3⋊C4—62no—
141Dic3⋊C4—68no—
142Dic3⋊C4—68no—
143C4×Dic3—32no—
144C4×Dic3—32no—
145C4×Dic3—32no—
146C4×Dic3—32no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C4×Dic3—124no—
152C4×Dic3—124no—
153C2×C3⋊C8—22no—
154C22×C32—21no—
155C22×C32—21no—
156C22×C32C2×C22⋊C411yescharacteristic
157C22×C32C2×D811yescharacteristic
158C22×C32C2×SD1611yescharacteristic
159C2×C3×D3—42no—
160C2×C3×D3—42no—
161C2×C3×D3—42no—
162C32×C4—21no—
163C32×C4—21no—
164C32×C4—42no—
165C3⋊Dic3—21no—
166C3⋊Dic3—42no—
167C3⋊Dic3#10212yes—
168C3⋊Dic3#10212yes—
169C3⋊Dic3#10412yes—
170C3×Dic3—42no—
171C2×#41—181no—
172C4⋊Q8—91no—
173#127—91no—
174#124—181no—
175#121—32no—
176#121—181no—
177C4×D4—92no—
178C4×D4—181no—
179C2×C4⋊C4—181no—
180C2×C42—91no—
181C2×C42—181no—
182C4⋊C8—181no—
183C22⋊C8—32no—
184C4×C8—181no—
185#95—91no—
186#95D3211yescharacteristic
187C23×C3—21no—
188C23×C3—62no—
189C23×C3D3×D412yes—
190C22×D3—22no—
191C3×D4—122no—
192C3×D4—122no—
193C3×D4—122no—
194C2×C3×C4—24no—
195C2×C3×C4—24no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—42no—
199C2×C3×C4—42no—
200C2×C3×C4—42no—
201C2×C3×C4—42no—
202C2×C3×C4—42no—
203C2×C3×C4—42no—
204C2×C3×C4—62no—
205C2×C3×C4C2×C4×D312yes—
206C2×C3×C4D3×D412yes—
207#67—42no—
208#67—42no—
209#67—124no—
210#67—124no—
211C2×Dic3—22no—
212C2×Dic3—32no—
213C2×Dic3—32no—
214C2×Dic3—32no—
215C2×Dic3—34no—
216C2×Dic3—34no—
217C2×Dic3—32no—
218C2×Dic3—61no—
219C2×Dic3—61no—
220C2×Dic3—61no—
221C2×Dic3—61no—
222C2×Dic3—62no—
223C2×Dic3—62no—
224C2×Dic3—64no—
225C2×Dic3—64no—
226C2×Dic3—64no—
227C2×Dic3—64no—
228C2×Dic3—124no—
229C2×Dic3—122no—
230C2×Dic3—122no—
231C2×Dic3—122no—
232C2×Dic3—122no—
233D12—42no—
234C4×D3—124no—
235Dic6—124no—
236C3×C8—122no—
237C3⋊C8—42no—
238C2×C32—21no—
239C2×C32—21no—
240C2×C32#41011yescharacteristic
241C2×C32C2×#10211yescharacteristic
242C2×C32C2×#10411yescharacteristic
243C3×D3—82no—
244#41—362no—
245#41—362no—
246C2×Q8—181no—
247C2×D4—32no—
248C2×D4—62no—
249C2×D4—181no—
250C2×D4—181no—
251C22×C4—21no—
252C22×C4—91no—
253C22×C4—91no—
254C22×C4—182no—
255C22×C4—181no—
256C22×C4C2×D3211yescharacteristic
257C2×C8—62no—
258C4⋊C4—32no—
259C4⋊C4—184no—
260C4⋊C4—181no—
261C22⋊C4—62no—
262C22⋊C4—182no—
263C42—91no—
264C42—91no—
265C42—91no—
266C42—91no—
267C42—362no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—22no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—122no—
276C22×C3—122no—
277C22×C3—122no—
278C22×C3D3×C22⋊C412yes—
279C22×C3D3×D812yes—
280C22×C3D3×SD1612yes—
281C2×D3—42no—
282C2×D3—42no—
283C2×D3—42no—
284C3×C4—22no—
285C3×C4—22no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4—44no—
289C3×C4—44no—
290C3×C4—122no—
291Dic3—34no—
292Dic3—34no—
293Dic3—34no—
294Dic3—42no—
295Dic3—62no—
296Dic3—62no—
297Dic3—62no—
298Dic3—62no—
299Dic3—62no—
300Dic3—124no—
301Dic3—124no—
302C32#150211yescharacteristic, complemented, Sylow
303C23—62no—
304C23#381111yescharacteristic
305Q8—362no—
306D4—122no—
307D4—122no—
308D4—122no—
309D4—362no—
310D4—362no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—62no—
316C2×C4—91no—
317C2×C4—91no—
318C2×C4—91no—
319C2×C4—92no—
320C2×C4—92no—
321C2×C4—91no—
322C2×C4—182no—
323C2×C4—182no—
324C2×C4—364no—
325C2×C4—361no—
326C2×C4—361no—
327C2×C4C4×D3211yescharacteristic
328C2×C4#380211yescharacteristic
329C8—122no—
330C2×C3—22no—
331C2×C3—22no—
332C2×C3—22no—
333C2×C3—22no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—242no—
338C2×C3#474012yes—
339C2×C3D3×#10212yes—
340C2×C3D3×#10412yes—
341D3—82no—
342C22—21no—
343C22—21no—
344C22—122no—
345C22—122no—
346C22—122no—
347C22#6392111yescharacteristic
348C22#6392611yescharacteristic
349C22#6394011yescharacteristic
350C4—21no—
351C4—21no—
352C4—42no—
353C4—92no—
354C4—92no—
355C4—92no—
356C4—122no—
357C4—181no—
358C4—362no—
359C3—21no—
360C3#6827712yescomplemented
361C2—21no—
362C2—21no—
363C2—242no—
364C2#1059039311yescharacteristic
365C2#1059040611yescharacteristic
366C2#1059059311yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32C2×C22⋊C4
prime radical#10594929C2
cosocleC22×C32×C4C23
hypercenter#95D32
hypocenterC32#1502
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592348C2semidirect
3. #10591061C2semidirect
4. C3×#4451C2semidirect
5. #10589150C2semidirect
13. #63919C4semidirect
15. #63914C4semidirect
17. #63898C4semidirect
30. #4451D3semidirect
302. C32#1502semidirect
360. C3#68277semidirect

Maximal subgroups

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

subgroupindex
#105949292
#105923482
#105910612
C3×#44512
#105891502
#682773