Finite Group Databasebeta

← #11877025

Subgroups — #11877025

Order 1152.

1074 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 237 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#10596199C211yesmaximal, characteristic
2#10596199C211yesmaximal, characteristic
3C32×#487C211yesmaximal, characteristic, complemented
4#10592791C211yesmaximal, characteristic, complemented
5#10592779C211yesmaximal, characteristic, complemented
6#10592515C214yesmaximal
7#10592488C214yesmaximal, complemented
8C4×#3743C211yesmaximal, characteristic
9#10592380C211yesmaximal, characteristic, complemented
10#81596—34nomaximal
11C32×C4⋊Q8C2211yescharacteristic
12C32×C4⋊Q8C2211yescharacteristic
13#64155—21no—
14#64155C2212yes—
15Q8×C3⋊Dic3—21no—
16Q8×C3⋊Dic3C2212yes—
17C2×#3756C2214yes—
18C2×#3743C2212yes—
19#64106—21no—
20#64106C2212yes—
21#64101—21no—
22#64101—21no—
23#64099—21no—
24#64099—21no—
25#64096—21no—
26#64096C2212yes—
27C42×C3⋊D3C2211yescharacteristic
28#64078C2211yescharacteristic
29#64078C2211yescharacteristic
30C32×#103C2214yes—
31C32×C4×C8C2211yescharacteristic
32#63643C2214yes—
33#63642C2212yes—
34#63635C2214yes—
35C4×C3⋊(C3⋊C8)C2211yescharacteristic
36#5728—34no—
37#5728—34no—
38C3×#487D314yescomplemented
39#5092—34no—
40#5080—34no—
41#4816—316no—
42#4789—316no—
43C4×ΓL(1,𝔽25)—34no—
44#4681—34no—
45C2×C32×Q8—21no—
46C2×C32×Q8C2312yes—
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3D411yescharacteristic
49C2×C4×C3⋊D3C2311yescharacteristic
50C2×#634—21no—
51C2×#634C2312yes—
52C2×C32×C8C2312yes—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4C2312yes—
57C32×C42C2311yescharacteristic
58#3756—28no—
59#3752—22no—
60#3752—22no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—22no—
65C4⋊(C3⋊Dic3)—22no—
66C4⋊(C3⋊Dic3)C2312yes—
67#3750—22no—
68#3750—22no—
69C4×C3⋊Dic3—22no—
70C4×C3⋊Dic3—22no—
71C4×C3⋊Dic3D411yescharacteristic
72C4×C3⋊Dic3D411yescharacteristic
73C4×C3⋊Dic3C2311yescharacteristic
74C2×C3⋊(C3⋊C8)C2312yes—
75#3743—24no—
76#3185—91noSylow
77C3×C4⋊Q8C2×D314yes—
78C3×C4⋊Q8C2×D314yes—
79#946—38no—
80#946—64no—
81Q8×Dic3—38no—
82Q8×Dic3—64no—
83C2×#216—316no—
84C2×ΓL(1,𝔽25)—38no—
85#897—38no—
86#897—64no—
87#892—64no—
88#892—64no—
89#890—64no—
90#890—64no—
91#887—38no—
92#887—64no—
93C42×D3—34no—
94#869—34no—
95#869—34no—
96C3×#103C2×D3116yes—
97C3×C4×C8C2×D314yes—
98#816—316no—
99#815—38no—
100#808—316no—
101C4×C3⋊C8—34no—
102C22×C3⋊D3C2×D411yescharacteristic
103C32×Q8—24no—
104C32×Q8—42no—
105C2×C32×C4—22no—
106C2×C32×C4—22no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2411yescharacteristic
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3C2×D411yescharacteristic
113C2×C3⋊Dic3C2×D411yescharacteristic
114C2×C3⋊Dic3C2×D411yescharacteristic
115C4×C3⋊D3—22no—
116C4×C3⋊D3—22no—
117C4×C3⋊D3—22no—
118#634—24no—
119#634—42no—
120C32×C8—22no—
121C3⋊(C3⋊C8)#4114yes—
122#533—91no—
123#533—91no—
124#498—91no—
125#494—91no—
126#487—91no—
127#487C3⋊D311yescharacteristic, complemented
128#470—94no—
129#441—94no—
130C4×M16—91no—
131C2×C3×Q8—24no—
132C2×C3×Q8C22×D318yes—
133C2×C4×D3—34no—
134C2×C4×D3—34no—
135C2×C4×D3—34no—
136C2×Dic6—38no—
137C2×Dic6—64no—
138C2×C3×C8C22×D318yes—
139C3×C4⋊C4—24no—
140C3×C4⋊C4—24no—
141C3×C4⋊C4—24no—
142C3×C4⋊C4C22×D318yes—
143C3×C42C22×D314yes—
144#216—632no—
145(C2×D3)⋊C4—68no—
146(C2×D3)⋊C4—68no—
147C4⋊Dic3—38no—
148C4⋊Dic3—68no—
149C4⋊Dic3—68no—
150C4⋊Dic3—64no—
151C4⋊Dic3—64no—
152C4⋊Dic3—64no—
153Dic3⋊C4—68no—
154Dic3⋊C4—68no—
155C4×Dic3—34no—
156C4×Dic3—34no—
157C4×Dic3—34no—
158C4×Dic3—68no—
159C4×Dic3—68no—
160C2×C3⋊C8—38no—
161ΓL(1,𝔽25)—616no—
162C22×C32C22×D411yescharacteristic
163C2×C3⋊D3—21no—
164C2×C3⋊D3—21no—
165C2×C3⋊D3—21no—
166C32×C4—42no—
167C32×C4—42no—
168C32×C4#13712yes—
169C32×C4#13712yes—
170C32×C4C2×#4112yes—
171C3⋊Dic3—21no—
172C3⋊Dic3—21no—
173C3⋊Dic3—21no—
174C3⋊Dic3—42no—
175C3⋊Dic3—42no—
176C2×Q16—94no—
177C2×M16—92no—
178C4⋊Q8—91no—
179C4⋊Q8—91no—
180C4⋊Q8C2×C3⋊D311yescharacteristic
181C4⋊Q8C2×C3⋊D311yescharacteristic
182#125—181no—
183#125—181no—
184C22⋊Q8—92no—
185C22⋊Q8—92no—
186C22⋊Q8—181no—
187C22⋊Q8—181no—
188C4×Q8—92no—
189C4×Q8—92no—
190C4×Q8—181no—
191C4×Q8—181no—
192#117—181no—
193#117—181no—
194C2×C42—91no—
195#106—94no—
196#103—94no—
197#103C2×C3⋊D314yes—
198#97—92no—
199C4×C8—91no—
200C4×C8C2×C3⋊D311yescharacteristic
201C22×D3—34no—
202C3×Q8—216no—
203C3×Q8—48no—
204C2×C3×C4—28no—
205C2×C3×C4—28no—
206C2×C3×C4D3×D414yes—
207C2×C3×C4D3×D414yes—
208C2×C3×C4C23×D314yes—
209C2×Dic3—34no—
210C2×Dic3—34no—
211C2×Dic3—34no—
212C2×Dic3—68no—
213C2×Dic3—68no—
214C4×D3—68no—
215C4×D3—68no—
216C4×D3—68no—
217Dic6—616no—
218Dic6—128no—
219C3×C8—28no—
220C3⋊C8—316no—
221C2×C32#53211yescharacteristic
222C2×C32C2×#13711yescharacteristic
223C2×C32C2×#13711yescharacteristic
224C3⋊D3—41no—
225C2×Q8—21no—
226C2×Q8—92no—
227C2×Q8—181no—
228C2×Q8C22×C3⋊D312yes—
229C22×C4—91no—
230C22×C4—91no—
231C22×C4—91no—
232Q16—188no—
233M16—184no—
234C2×C8—92no—
235C2×C8C22×C3⋊D312yes—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—92no—
240C4⋊C4—182no—
241C4⋊C4—182no—
242C4⋊C4—182no—
243C4⋊C4—182no—
244C4⋊C4—181no—
245C4⋊C4—181no—
246C4⋊C4—181no—
247C4⋊C4C22×C3⋊D312yes—
248C22⋊C4—182no—
249C22⋊C4—182no—
250C42—91no—
251C42—91no—
252C42—91no—
253C42—182no—
254C42—182no—
255C42C22×C3⋊D311yescharacteristic
256C22×C3C2×D3×D414yes—
257C2×D3—64no—
258C2×D3—64no—
259C2×D3—64no—
260C3×C4—48no—
261C3×C4—48no—
262C3×C4#91518yes—
263C3×C4#91818yes—
264C3×C4D3×#4118yes—
265Dic3—64no—
266Dic3—64no—
267Dic3—64no—
268Dic3—128no—
269Dic3—128no—
270C32#318511yescharacteristic, complemented, Sylow
271C23—91no—
272Q8—24no—
273Q8—42no—
274Q8—184no—
275Q8—362no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—182no—
282C2×C4—182no—
283C2×C4—182no—
284C2×C4—182no—
285C2×C4—182no—
286C2×C4D4×C3⋊D311yescharacteristic
287C2×C4D4×C3⋊D311yescharacteristic
288C2×C4C23×C3⋊D311yescharacteristic
289C8—22no—
290C8—94no—
291C2×C3#566814yes—
292C2×C3C2×#91514yes—
293C2×C3C2×#91814yes—
294D3—124no—
295C22—181no—
296C22—181no—
297C22—181no—
298C22C2×D4×C3⋊D311yescharacteristic
299C4—42no—
300C4—42no—
301C4—181no—
302C4—181no—
303C4—181no—
304C4—362no—
305C4—362no—
306C4#6412412yes—
307C4#6412712yes—
308C4#41×C3⋊D312yes—
309C3#8159614yescomplemented
310C2—361no—
311C2#1059613911yescharacteristic
312C2C2×#6412411yescharacteristic
313C2C2×#6412711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#487C3⋊D3
hypocenterC32#3185
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. C32×#487C2semidirect
4. #10592791C2semidirect
5. #10592779C2semidirect
7. #10592488C2semidirect
9. #10592380C2semidirect
38. C3×#487D3semidirect
127. #487C3⋊D3semidirect
270. C32#3185semidirect
309. C3#81596semidirect

Maximal subgroups

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

subgroupindex
#105961992
C32×#4872
#105927912
#105927792
#105925152
#105924882
C4×#37432
#105923802
#815963