Finite Group Databasebeta

← #11775159

Subgroups — #11775159

Order 1152.

599 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 599 conjugacy classes of subgroups — too many to draw. Only its 92 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#10592418C211yesmaximal, characteristic, complemented
3#10591252C211yesmaximal, characteristic, complemented
4C3×#4470C212yesmaximal, complemented
5#10589149C212yesmaximal, complemented
6#68278—32nomaximal
7C2×#3805—21no—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C3×#930C2212yes—
10#63980—21no—
11C2×Dic32—21no—
12#63919C411yescharacteristic, complemented
13#63915—21no—
14#63914C411yescharacteristic, complemented
15#63902—21no—
16#63898C412yescomplemented
17C32×C22⋊C8C2211yescharacteristic
18#63657C2211yescharacteristic
19#63642—21no—
20#63641—21no—
21C3×C3⋊#95C2212yes—
22#63579—21no—
23#5596—32no—
24#4719—32no—
25#4719—61no—
26#4648—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—44no—
41C2×D3×Dic3—22no—
42C2×C32×C8—21no—
43C4×C3⋊Dic3C2×C411yescharacteristic
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3D411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48C3×(C2×D3)⋊C4—22no—
49C3×C4⋊Dic3C2×C412yes—
50#3724—21no—
51(C2×D3)⋊Dic3—22no—
52Dic32—24no—
53#1505—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—
62C2×C4×Dic3—62no—
63#893—32no—
64#888—32no—
65#885—62no—
66#67⋊C4—62no—
67C3×C22⋊C8—21no—
68C3×C22⋊C8C2×D312yes—
69C3×#95—32no—
70C3⋊#95—62no—
71C3⋊#95C2×D312yes—
72#830—32no—
73#830—61no—
74#815—62no—
75#815—62no—
76Dic3⋊C8—62no—
77Dic3⋊C8—62no—
78C23×C32C2×D411yescharacteristic
79C22×C3×D3—22no—
80C2×C32×C4—41no—
81C2×C32×C4C22×C411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C22⋊C411yescharacteristic
88C2×C3⋊Dic3C22⋊C411yescharacteristic
89C3×#67—42no—
90C3×#67—42no—
91C2×C3×Dic3—24no—
92C2×C3×Dic3—22no—
93C2×C3×Dic3—42no—
94C2×C3×Dic3—42no—
95C3×D12—42no—
96#627—42no—
97#625—42no—
98#625—42no—
99D3×Dic3—44no—
100C32×C8—41no—
101C3⋊(C3⋊C8)—41no—
102#532—91no—
103#432—91no—
104#376—91no—
105#327—32no—
106#327—92no—
107C2×C3×D4—32no—
108C2×C3×D4—62no—
109C22×C3×C4—21no—
110C22×C3×C4—62no—
111C22×C3×C4C22×D312yes—
112C2×#67—22no—
113C2×#67—62no—
114C2×#67—62no—
115C22×Dic3—22no—
116C22×Dic3—32no—
117C22×Dic3—32no—
118C22×Dic3—61no—
119C22×Dic3—61no—
120C22×Dic3—62no—
121#237—124no—
122#237—124no—
123C2×D12C4×D312yes—
124C2×C4×D3—62no—
125C2×Dic6—62no—
126C2×C3×C8—22no—
127C2×C3×C8—22no—
128C3×C4⋊C4—32no—
129C3×C22⋊C4—62no—
130#217—62no—
131(C2×D3)⋊C4—22no—
132(C2×D3)⋊C4—62no—
133C4⋊Dic3C4×D312yes—
134Dic3⋊C4—62no—
135C4×Dic3—32no—
136C4×Dic3—32no—
137C4×Dic3—32no—
138C4×Dic3—32no—
139C4×Dic3—61no—
140C4×Dic3—61no—
141C4×Dic3—61no—
142C4×Dic3—61no—
143C4×Dic3—68no—
144C2×C3⋊C8—62no—
145C2×C3⋊C8—62no—
146C22×C32—21no—
147C22×C32—21no—
148C22×C32C2×C22⋊C411yescharacteristic
149C22×C32AGL(1,ℤ/8)12yes—
150C2×C3×D3—42no—
151C2×C3×D3—42no—
152C2×C3×D3—42no—
153C32×C4—21no—
154C32×C4—21no—
155C3⋊Dic3—21no—
156C3⋊Dic3—21no—
157C3⋊Dic3—21no—
158C3⋊Dic3#10412yes—
159C3×Dic3—44no—
160C3×Dic3—42no—
161C2×#41—181no—
162C4⋊Q8—91no—
163#127—91no—
164#124—181no—
165#121—32no—
166#121—181no—
167C4×D4—92no—
168C4×D4—181no—
169C2×C42—91no—
170C2×C42—181no—
171C4⋊C8—181no—
172C22⋊C8—91no—
173C22⋊C8D3211yescharacteristic
174#97—181no—
175#95—32no—
176#95—181no—
177C23×C3—21no—
178C23×C3—62no—
179C23×C3D3×D412yes—
180C22×D3—22no—
181C3×D4—122no—
182C3×D4—122no—
183C3×D4—122no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—42no—
187C2×C3×C4—42no—
188C2×C3×C4—64no—
189C2×C3×C4—62no—
190C2×C3×C4—122no—
191C2×C3×C4—122no—
192C2×C3×C4C2×C4×D312yes—
193C2×C3×C4D3×D412yes—
194#67—42no—
195#67—42no—
196#67—124no—
197#67—124no—
198C2×Dic3—24no—
199C2×Dic3—22no—
200C2×Dic3—32no—
201C2×Dic3—32no—
202C2×Dic3—32no—
203C2×Dic3—32no—
204C2×Dic3—42no—
205C2×Dic3—42no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—64no—
211C2×Dic3—62no—
212C2×Dic3—62no—
213C2×Dic3—122no—
214C2×Dic3—122no—
215C2×Dic3—124no—
216D12—42no—
217C4×D3—124no—
218Dic6—124no—
219C3×C8—42no—
220C3×C8—42no—
221C3⋊C8—122no—
222C3⋊C8—122no—
223C2×C32—22no—
224C2×C32#41011yescharacteristic
225C2×C32#41811yescharacteristic
226C2×C32C2×#10411yescharacteristic
227C3×D3—82no—
228#41—364no—
229C2×Q8—181no—
230C2×D4—32no—
231C2×D4—62no—
232C2×D4—181no—
233C2×D4—181no—
234C22×C4—62no—
235C22×C4—91no—
236C22×C4—91no—
237C22×C4—182no—
238C22×C4C2×D3211yescharacteristic
239C2×C8—21no—
240C2×C8—181no—
241C4⋊C4—32no—
242C4⋊C4—181no—
243C22⋊C4—62no—
244C22⋊C4—182no—
245C42—91no—
246C42—91no—
247C42—91no—
248C42—91no—
249C42—184no—
250C22×C3—22no—
251C22×C3—22no—
252C22×C3—22no—
253C22×C3—21no—
254C22×C3—41no—
255C22×C3—41no—
256C22×C3—122no—
257C22×C3—122no—
258C22×C3—122no—
259C22×C3D3×C22⋊C412yes—
260C22×C3#91112yes—
261C22×C3#91412yes—
262C2×D3—42no—
263C2×D3—42no—
264C2×D3—42no—
265C3×C4—22no—
266C3×C4—22no—
267C3×C4—22no—
268C3×C4—41no—
269C3×C4—124no—
270C3×C4—122no—
271Dic3—34no—
272Dic3—44no—
273Dic3—42no—
274Dic3—62no—
275Dic3—62no—
276Dic3—62no—
277Dic3—62no—
278Dic3—121no—
279Dic3—121no—
280Dic3—121no—
281C32#150511yescharacteristic, complemented, Sylow
282C23—62no—
283C23#380211yescharacteristic
284Q8—362no—
285D4—122no—
286D4—122no—
287D4—122no—
288D4—362no—
289D4—362no—
290C2×C4—41no—
291C2×C4—64no—
292C2×C4—62no—
293C2×C4—91no—
294C2×C4—91no—
295C2×C4—91no—
296C2×C4—91no—
297C2×C4—122no—
298C2×C4—122no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4—364no—
302C2×C4C4×D3211yescharacteristic
303C2×C4#381111yescharacteristic
304C8—41no—
305C8—361no—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—42no—
312C2×C3—242no—
313C2×C3#474012yes—
314C2×C3#477012yes—
315C2×C3D3×#10412yes—
316D3—82no—
317C22—21no—
318C22—21no—
319C22—122no—
320C22—122no—
321C22—122no—
322C22#6379812yes—
323C22#6392111yescharacteristic
324C4—21no—
325C4—21no—
326C4—92no—
327C4—124no—
328C4—122no—
329C4—181no—
330C4—181no—
331C4—181no—
332C3—21no—
333C3#6827812yescomplemented
334C2—22no—
335C2—242no—
336C2#1059040611yescharacteristic
337C2#1059094111yescharacteristic
338C2#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#1505
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. #10592418C2semidirect
3. #10591252C2semidirect
4. C3×#4470C2semidirect
5. #10589149C2semidirect
12. #63919C4semidirect
14. #63914C4semidirect
16. #63898C4semidirect
29. #4470D3semidirect
281. C32#1505semidirect
333. C3#68278semidirect

Maximal subgroups

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

subgroupindex
#105949292
#105924182
#105912522
C3×#44702
#105891492
#682783