Finite Group Databasebeta

← #11790473

Subgroups — #11790473

Order 1152.

314 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 65 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#10593748C211yesmaximal, characteristic
2#10593387C211yesmaximal, characteristic
3C2×#63733C211yesmaximal, characteristic
4#10590584C211yesmaximal, characteristic
5#10590582C211yesmaximal, characteristic
6#10590052C211yesmaximal, characteristic
7#10590052C211yesmaximal, characteristic
8C2×#3788C2211yescharacteristic
9C2×#3787C2211yescharacteristic
10#64101C2211yescharacteristic
11#63900C2211yescharacteristic
12#63900C2211yescharacteristic
13C2×#3712C2211yescharacteristic
14C2×#3712C2211yescharacteristic
15#63777—21no—
16C4×#622—21no—
17#63742—21no—
18#63742—21no—
19#63733C414yescomplemented
20C3×#808—21no—
21C3×#807—21no—
22#63575—21no—
23#63573—21no—
24#4881—61no—
25#4861—61no—
26C2×C4×C3⋊D3C2311yescharacteristic
27C2×#624—21no—
28C2×#624—21no—
29C2×#622—21no—
30C2×#622D411yescharacteristic
31C2×#622D411yescharacteristic
32#3788—21no—
33#3788Q812yes—
34#3787C2×C412yes—
35#3787Q812yes—
36C32×C4⋊C4D411yescharacteristic
37#3752—21no—
38C4⋊(C3⋊Dic3)D411yescharacteristic
39C4×C3⋊Dic3—21no—
40C3×C4⋊Dic3—21no—
41C3×C4⋊Dic3—21no—
42C2×C3×C3⋊C8—21no—
43C2×C3×C3⋊C8—21no—
44#3724—21no—
45#3724—21no—
46#3712—21no—
47#3712—21no—
48#3712C2×C412yes—
49#3712C2×C412yes—
50#1951—91nomaximal, Sylow
51C2×ΓL(1,𝔽25)—61no—
52C2×ΓL(1,𝔽25)—61no—
53#892—61no—
54#892—61no—
55D3×C4⋊C4—61no—
56D3×C4⋊C4—61no—
57C3×#107—61no—
58C3×#106—61no—
59#818—61no—
60#817—61no—
61#808—21no—
62#808—61no—
63#807—21no—
64#807—61no—
65C22×C3⋊D3#4111yescharacteristic
66C2×C32×C4—21no—
67C2×C32×C4C2×D411yescharacteristic
68C2×C3⋊Dic3—21no—
69C2×C3⋊Dic3C2×D411yescharacteristic
70C4×C3⋊D3C22×C411yescharacteristic
71C4×C3⋊D3C2×Q811yescharacteristic
72C4×C3⋊D3C2×Q811yescharacteristic
73C4×C3⋊D3#4111yescharacteristic
74C2×C3×Dic3—41no—
75C2×C3×Dic3—41no—
76#624—81no—
77#624—81no—
78#622—22no—
79#622C4⋊C412yes—
80#622C4⋊C412yes—
81C3×C3⋊C8—22no—
82C3×C3⋊C8—22no—
83C2×#108—91no—
84#428—91no—
85#428—91no—
86C2×#106—91no—
87#405—91no—
88#343—91no—
89#343—91no—
90C2×C4×D3—61no—
91C2×C4×D3—61no—
92C2×C4×D3—121no—
93C2×C4×D3—121no—
94C2×C3×C8—61no—
95C2×C3×C8—61no—
96C3×C4⋊C4—21no—
97C3×C4⋊C4—21no—
98C3×C4⋊C4—61no—
99C3×C4⋊C4—61no—
100(C2×D3)⋊C4—121no—
101(C2×D3)⋊C4—121no—
102C4⋊Dic3—21no—
103C4⋊Dic3—21no—
104C4⋊Dic3—61no—
105C4⋊Dic3—61no—
106Dic3⋊C4—121no—
107Dic3⋊C4—121no—
108C4×Dic3—121no—
109C4×Dic3—121no—
110C2×C3⋊C8—21no—
111C2×C3⋊C8—21no—
112ΓL(1,𝔽25)—62no—
113ΓL(1,𝔽25)—62no—
114ΓL(1,𝔽25)—62no—
115ΓL(1,𝔽25)—62no—
116C22×C32#12111yescharacteristic
117C2×C3⋊D3—21no—
118C2×C3⋊D3—21no—
119C2×C3⋊D3C4×Q811yescharacteristic
120C2×C3⋊D3#12511yescharacteristic
121C32×C4—41no—
122C32×C4C4×D411yescharacteristic
123C32×C4C4⋊Q811yescharacteristic
124C3⋊Dic3—41no—
125C3⋊Dic3C2×C4⋊C411yescharacteristic
126C3⋊Dic3C22⋊Q811yescharacteristic
127C3×Dic3—81no—
128C3×Dic3—81no—
129C2×M16—91no—
130C2×M16—91no—
131C2×M16—91no—
132C22×C8—91no—
133#117—91no—
134C2×C4⋊C4—91no—
135C2×C4⋊C4—91no—
136#108—94no—
137#107—61no—
138#107—181no—
139#106—61no—
140#106—181no—
141#106—181no—
142#106—181no—
143#97—181no—
144C4×C8—181no—
145C22×D3—61no—
146C22×D3—61no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—41no—
150C2×C3×C4—41no—
151C2×C3×C4—121no—
152C2×C3×C4—121no—
153C2×Dic3—41no—
154C2×Dic3—41no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—121no—
158C2×Dic3—121no—
159C4×D3—61no—
160C4×D3—61no—
161C4×D3—61no—
162C4×D3—61no—
163C4×D3—61no—
164C4×D3—61no—
165C4×D3—61no—
166C4×D3—61no—
167C4×D3—242no—
168C4×D3—242no—
169C3×C8—62no—
170C3×C8—62no—
171C3⋊C8—22no—
172C3⋊C8—22no—
173C2×C32#38911yescharacteristic
174C2×C32#47111yescharacteristic
175C2×C32#47111yescharacteristic
176C3⋊D3—21no—
177C3⋊D3—21no—
178C22×C4—91no—
179C22×C4—181no—
180C22×C4—181no—
181M16—92no—
182M16—92no—
183M16—92no—
184M16—181no—
185M16—181no—
186M16—181no—
187C2×C8—61no—
188C2×C8—61no—
189C2×C8—91no—
190C2×C8—91no—
191C2×C8—92no—
192C2×C8—92no—
193C2×C8—181no—
194C4⋊C4—61no—
195C4⋊C4—61no—
196C4⋊C4—91no—
197C4⋊C4—181no—
198C4⋊C4—181no—
199C4⋊C4GO+(4,𝔽2)11yescharacteristic
200C22⋊C4—181no—
201C42—181no—
202C22×C3—21no—
203C22×C3—21no—
204C2×D3—61no—
205C2×D3—61no—
206C2×D3—61no—
207C2×D3—61no—
208C2×D3—121no—
209C2×D3—121no—
210C2×D3—121no—
211C2×D3—121no—
212C3×C4—21no—
213C3×C4—21no—
214C3×C4—21no—
215C3×C4—21no—
216C3×C4—81no—
217C3×C4—81no—
218C3×C4—241no—
219C3×C4—241no—
220Dic3—61no—
221Dic3—61no—
222Dic3—61no—
223Dic3—61no—
224Dic3—81no—
225Dic3—81no—
226Dic3—241no—
227Dic3—241no—
228C32#195111yescharacteristic, complemented, Sylow
229C23—91no—
230C2×C4—21no—
231C2×C4—91no—
232C2×C4—91no—
233C2×C4—91no—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—121no—
237C2×C4—121no—
238C2×C4—181no—
239C2×C4—721no—
240C2×C4—721no—
241C2×C4C2×GO+(4,𝔽2)11yescharacteristic
242C8—62no—
243C8—62no—
244C8—92no—
245C8—92no—
246C8—182no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253D3—121no—
254D3—121no—
255D3—121no—
256D3—121no—
257C22—91no—
258C22—91no—
259C22—181no—
260C22—181no—
261C22#6424211yescharacteristic
262C4—41no—
263C4—91no—
264C4—91no—
265C4—241no—
266C4—241no—
267C4—361no—
268C4#6422211yescharacteristic
269C4C4×GO+(4,𝔽2)11yescharacteristic
270C3—21no—
271C3—21no—
272C2—181no—
273C2—181no—
274C2#1059341011yescharacteristic
275C2#1059346711yescharacteristic
276C2#1059348111yescharacteristic
subgroupG/H
centerC22#64242
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#121
prime radicalC22×C3⋊D3#41
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#1951
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
19. #63733C4semidirect
228. C32#1951semidirect

Maximal subgroups

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

subgroupindex
#105937482
#105933872
C2×#637332
#105905842
#105905822
#105900522
#19519