Finite Group Databasebeta

← #11775428

Subgroups — #11775428

Order 1152.

573 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 573 conjugacy classes of subgroups — too many to draw. Only its 90 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#10592350C211yesmaximal, characteristic, complemented
3#10591066C211yesmaximal, characteristic, complemented
4C3×#4451C212yesmaximal, complemented
5#10589150C212yesmaximal, complemented
6#68281—32nomaximal
7C2×#3805—21no—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C3×#930C2212yes—
10#63980—21no—
11#63919C411yescharacteristic, complemented
12#63915—21no—
13#63914C411yescharacteristic, complemented
14#63902—21no—
15#63898C412yescomplemented
16C32×#95C2211yescharacteristic
17#63658—21no—
18#63658—21no—
19#63658C2211yescharacteristic
20C3×#830C2212yes—
21#63572—21no—
22#63555—21no—
23#5596—32no—
24#4719—32no—
25#4651—32no—
26#4651—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—
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3C2×C411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C4×C3⋊Dic3D411yescharacteristic
48C3×(C2×D3)⋊C4—22no—
49C3×C4⋊Dic3C2×C412yes—
50C2×C3×C3⋊C8—22no—
51#3724—21no—
52(C2×D3)⋊Dic3—22no—
53#1514—91noSylow
54C2×#237—62no—
55C3×#121—32no—
56#940—32no—
57#939—62no—
58D4×Dic3—32no—
59#930C2×D312yes—
60C2×C4×Dic3—32no—
61C2×C4×Dic3—61no—
62#893—32no—
63#888—32no—
64#885—62no—
65#67⋊C4—62no—
66C3×C22⋊C8—32no—
67C3×#95—21no—
68C3×#95C2×D312yes—
69C3⋊#95—32no—
70C3⋊#95—61no—
71C3⋊#95—62no—
72C3⋊#95—62no—
73C3⋊#95—62no—
74C3⋊#95—62no—
75#830C2×D312yes—
76#815—62no—
77Dic3⋊C8—62no—
78C23×C32C2×D411yescharacteristic
79C22×C3×D3—22no—
80C2×C32×C4—41no—
81C2×C32×C4—41no—
82C2×C32×C4—41no—
83C2×C32×C4—41no—
84C2×C32×C4C22×C411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—21no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3—41no—
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C2×C3⋊Dic3C22⋊C411yescharacteristic
94C2×C3⋊Dic3C22⋊C411yescharacteristic
95C2×C3⋊Dic3C22⋊C411yescharacteristic
96C3×#67—42no—
97C3×#67—42no—
98C2×C3×Dic3—22no—
99C3×D12—42no—
100#627—42no—
101#625—42no—
102#625—42no—
103D3×Dic3—44no—
104C3×C3⋊C8—42no—
105#532—91no—
106#432—91no—
107#383—91no—
108#327—32no—
109#327—92no—
110C2×C3×D4—32no—
111C2×C3×D4—62no—
112C22×C3×C4—22no—
113C22×C3×C4—22no—
114C22×C3×C4—21no—
115C22×C3×C4C22×D312yes—
116C2×#67—22no—
117C2×#67—62no—
118C2×#67—62no—
119C22×Dic3—32no—
120C22×Dic3—32no—
121C22×Dic3—61no—
122C22×Dic3—61no—
123C22×Dic3—62no—
124C22×Dic3—62no—
125C22×Dic3—62no—
126#237—124no—
127#237—124no—
128C2×D12C4×D312yes—
129C2×C4×D3—62no—
130C2×Dic6—62no—
131C2×C3×C8—62no—
132C3×C4⋊C4—32no—
133C3×C22⋊C4—62no—
134#217—62no—
135(C2×D3)⋊C4—22no—
136(C2×D3)⋊C4—62no—
137C4⋊Dic3C4×D312yes—
138Dic3⋊C4—62no—
139C4×Dic3—32no—
140C4×Dic3—32no—
141C4×Dic3—32no—
142C4×Dic3—32no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C4×Dic3—61no—
147C2×C3⋊C8—22no—
148C22×C32—21no—
149C22×C32—21no—
150C22×C32C2×C22⋊C411yescharacteristic
151C22×C32AGL(1,ℤ/8)11yescharacteristic
152C22×C32AGL(1,ℤ/8)11yescharacteristic
153C2×C3×D3—42no—
154C2×C3×D3—42no—
155C2×C3×D3—42no—
156C32×C4—21no—
157C32×C4—21no—
158C32×C4—81no—
159C3⋊Dic3—21no—
160C3⋊Dic3—21no—
161C3⋊Dic3—21no—
162C3⋊Dic3—21no—
163C3⋊Dic3—81no—
164C3×Dic3—42no—
165C2×#41—181no—
166C4⋊Q8—91no—
167#127—91no—
168#124—181no—
169#121—32no—
170#121—181no—
171C4×D4—92no—
172C4×D4—181no—
173C2×C42—91no—
174C4⋊C8—181no—
175C22⋊C8—32no—
176#97—181no—
177#95—91no—
178#95—181no—
179#95—181no—
180#95D3211yescharacteristic
181C23×C3—21no—
182C23×C3—62no—
183C23×C3D3×D412yes—
184C22×D3—22no—
185C3×D4—122no—
186C3×D4—122no—
187C3×D4—122no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—42no—
191C2×C3×C4—42no—
192C2×C3×C4—42no—
193C2×C3×C4—42no—
194C2×C3×C4—42no—
195C2×C3×C4—42no—
196C2×C3×C4—42no—
197C2×C3×C4—42no—
198C2×C3×C4—62no—
199C2×C3×C4C2×C4×D312yes—
200C2×C3×C4D3×D412yes—
201#67—42no—
202#67—42no—
203#67—124no—
204#67—124no—
205C2×Dic3—22no—
206C2×Dic3—32no—
207C2×Dic3—32no—
208C2×Dic3—32no—
209C2×Dic3—32no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—121no—
217C2×Dic3—121no—
218C2×Dic3—124no—
219C2×Dic3—122no—
220C2×Dic3—122no—
221C2×Dic3—122no—
222C2×Dic3—122no—
223C2×Dic3—122no—
224C2×Dic3—122no—
225C2×Dic3—122no—
226C2×Dic3—122no—
227D12—42no—
228C4×D3—124no—
229Dic6—124no—
230C3×C8—122no—
231C3⋊C8—42no—
232C2×C32—21no—
233C2×C32—21no—
234C2×C32#41011yescharacteristic
235C2×C32#41811yescharacteristic
236C2×C32#42111yescharacteristic
237C3×D3—82no—
238#41—362no—
239#41—362no—
240C2×Q8—181no—
241C2×D4—32no—
242C2×D4—62no—
243C2×D4—181no—
244C2×D4—181no—
245C22×C4—21no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—182no—
249C22×C4—181no—
250C22×C4C2×D3211yescharacteristic
251C2×C8—62no—
252C4⋊C4—32no—
253C4⋊C4—181no—
254C22⋊C4—62no—
255C22⋊C4—182no—
256C42—91no—
257C42—91no—
258C42—91no—
259C42—91no—
260C22×C3—22no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—122no—
268C22×C3—122no—
269C22×C3—122no—
270C22×C3D3×C22⋊C412yes—
271C22×C3#91112yes—
272C22×C3#91412yes—
273C2×D3—42no—
274C2×D3—42no—
275C2×D3—42no—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4—82no—
281C3×C4—82no—
282C3×C4—122no—
283Dic3—42no—
284Dic3—62no—
285Dic3—62no—
286Dic3—62no—
287Dic3—62no—
288Dic3—121no—
289Dic3—121no—
290Dic3—121no—
291Dic3—121no—
292Dic3—242no—
293Dic3—242no—
294C32#151411yescharacteristic, complemented, Sylow
295C23—62no—
296C23#381111yescharacteristic
297Q8—362no—
298D4—122no—
299D4—122no—
300D4—122no—
301D4—362no—
302D4—362no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—62no—
308C2×C4—91no—
309C2×C4—91no—
310C2×C4—91no—
311C2×C4—91no—
312C2×C4—181no—
313C2×C4—181no—
314C2×C4—364no—
315C2×C4—361no—
316C2×C4—361no—
317C2×C4—361no—
318C2×C4—361no—
319C2×C4C4×D3211yescharacteristic
320C2×C4#380211yescharacteristic
321C8—122no—
322C2×C3—22no—
323C2×C3—22no—
324C2×C3—22no—
325C2×C3—22no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—242no—
330C2×C3#474012yes—
331C2×C3#477012yes—
332C2×C3#482112yes—
333D3—82no—
334C22—21no—
335C22—21no—
336C22—122no—
337C22—122no—
338C22—122no—
339C22#6392111yescharacteristic
340C22#6392711yescharacteristic
341C22#6394111yescharacteristic
342C4—21no—
343C4—21no—
344C4—81no—
345C4—122no—
346C4—181no—
347C4—181no—
348C4—181no—
349C4—181no—
350C4—721no—
351C3—21no—
352C3#6828112yescomplemented
353C2—21no—
354C2—21no—
355C2—242no—
356C2#1059039411yescharacteristic
357C2#1059040611yescharacteristic
358C2#1059059411yescharacteristic
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#1514
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. #10592350C2semidirect
3. #10591066C2semidirect
4. C3×#4451C2semidirect
5. #10589150C2semidirect
11. #63919C4semidirect
13. #63914C4semidirect
15. #63898C4semidirect
30. #4451D3semidirect
294. C32#1514semidirect
352. C3#68281semidirect

Maximal subgroups

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

subgroupindex
#105949292
#105923502
#105910662
C3×#44512
#105891502
#682813