Finite Group Databasebeta

← #11795352

Subgroups — #11795352

Order 1152.

298 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 51 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#10593394C211yesmaximal, characteristic
2#10593394C211yesmaximal, characteristic
3#10590701C211yesmaximal, characteristic
4#10590685C211yesmaximal, characteristic
5#10590185C211yesmaximal, characteristic
6#10590052C211yesmaximal, characteristic
7#10590052C211yesmaximal, characteristic
8C2×#3788C2211yescharacteristic
9C2×#3788C2211yescharacteristic
10C2×C8×C3⋊D3C2211yescharacteristic
11#63900C2211yescharacteristic
12#63900C2211yescharacteristic
13#63874C2211yescharacteristic
14C2×#3712C2211yescharacteristic
15#63743—21no—
16#63743—21no—
17#63742—21no—
18#63742—21no—
19C3×#817—21no—
20C3×Dic3⋊C8—21no—
21#63574—21no—
22Dic3⋊(C3⋊C8)—21no—
23D3×#106—61no—
24#4839—61no—
25C2×C4×C3⋊D3C2311yescharacteristic
26C2×#624—21no—
27C2×#624—21no—
28C2×#622—21no—
29C2×#622—21no—
30#3788—21no—
31#3788—21no—
32#3788Q812yes—
33#3788Q812yes—
34C2×C32×C8D411yescharacteristic
35C2×C3⋊(C3⋊C8)D411yescharacteristic
36C8×C3⋊D3—21no—
37C8×C3⋊D3—21no—
38C3×C4⋊Dic3—21no—
39C3×C4⋊Dic3—21no—
40C3×C4×Dic3—21no—
41C2×C3×C3⋊C8—21no—
42#3724—21no—
43#3724—21no—
44#3724D411yescharacteristic
45#3724D411yescharacteristic
46#3722—21no—
47#3712—21no—
48#3712—21no—
49#2090—91nomaximal, Sylow
50C2×ΓL(1,𝔽25)—61no—
51C2×D3×C8—61no—
52C2×D3×C8—61no—
53D3×C4⋊C4—61no—
54D3×C4⋊C4—61no—
55#872—61no—
56C3×#106—61no—
57C3×C4⋊C8—61no—
58#817—21no—
59Dic3⋊C8—21no—
60Dic3⋊C8—61no—
61#808—61no—
62#808—61no—
63C4⋊(C3⋊C8)—61no—
64C22×C3⋊D3#4111yescharacteristic
65C2×C32×C4C2×D411yescharacteristic
66C2×C3⋊Dic3C2×D411yescharacteristic
67C4×C3⋊D3C2×Q811yescharacteristic
68C4×C3⋊D3C2×Q811yescharacteristic
69C4×C3⋊D3#4111yescharacteristic
70C4×C3⋊D3#4111yescharacteristic
71C2×C3×Dic3—21no—
72C2×C3×Dic3—21no—
73C2×C3×Dic3—41no—
74C2×C3×Dic3—41no—
75#624—81no—
76#624—81no—
77#622—22no—
78#622—22no—
79C32×C8—21no—
80C3⋊(C3⋊C8)—21no—
81C3×C3⋊C8—41no—
82#428—91no—
83#428—91no—
84C2×#106—91no—
85#424—91no—
86#343—91no—
87#343—91no—
88#341—91no—
89C2×C4×D3—61no—
90C2×C4×D3—61no—
91C2×C4×D3—121no—
92C2×C4×D3—121no—
93C2×C3×C8—21no—
94C2×C3×C8—21no—
95C2×C3×C8—61no—
96C3×C4⋊C4—61no—
97C3×C4⋊C4—61no—
98C3×C42—61no—
99(C2×D3)⋊C4—61no—
100(C2×D3)⋊C4—61no—
101C4⋊Dic3—21no—
102C4⋊Dic3—21no—
103Dic3⋊C4—61no—
104Dic3⋊C4—61no—
105Dic3⋊C4—121no—
106Dic3⋊C4—121no—
107C4×Dic3—21no—
108C2×C3⋊C8—21no—
109C2×C3⋊C8—61no—
110C2×C3⋊C8—61no—
111ΓL(1,𝔽25)—121no—
112ΓL(1,𝔽25)—121no—
113D3×C8—62no—
114D3×C8—62no—
115D3×C8—121no—
116D3×C8—121no—
117C22×C32#12111yescharacteristic
118C2×C3⋊D3—21no—
119C2×C3⋊D3—21no—
120C2×C3⋊D3#12511yescharacteristic
121C2×C3⋊D3#12511yescharacteristic
122C32×C4#12311yescharacteristic
123C32×C4C4⋊Q811yescharacteristic
124C3⋊Dic3C22⋊Q811yescharacteristic
125C3⋊Dic3C22⋊Q811yescharacteristic
126C3×Dic3—41no—
127C3×Dic3—41no—
128C3×Dic3—81no—
129C3×Dic3—81no—
130C2×M16—91no—
131C2×M16—91no—
132C2×M16—91no—
133C22×C8—91no—
134#117—91no—
135C2×C4⋊C4—91no—
136C2×C4⋊C4—91no—
137#107—181no—
138#107—181no—
139#106—61no—
140#106—181no—
141#106—181no—
142#106—181no—
143C4⋊C8—61no—
144C4⋊C8—181no—
145C22×D3—61no—
146C22×D3—61no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—61no—
150C2×C3×C4—61no—
151C2×C3×C4—121no—
152C2×C3×C4—121no—
153C2×Dic3—21no—
154C2×Dic3—21no—
155C2×Dic3—41no—
156C2×Dic3—41no—
157C2×Dic3—61no—
158C2×Dic3—61no—
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—22no—
170C3×C8—41no—
171C3×C8—121no—
172C3⋊C8—41no—
173C3⋊C8—62no—
174C3⋊C8—121no—
175C2×C32#39811yescharacteristic
176C2×C32#47111yescharacteristic
177C2×C32#47111yescharacteristic
178C3⋊D3—21no—
179C3⋊D3—21no—
180C22×C4—91no—
181C22×C4—181no—
182C22×C4—181no—
183M16—92no—
184M16—92no—
185M16—181no—
186M16—181no—
187M16—181no—
188M16—181no—
189C2×C8—61no—
190C2×C8—91no—
191C2×C8—181no—
192C2×C8—181no—
193C2×C8—181no—
194C2×C8—181no—
195C2×C8GO+(4,𝔽2)11yescharacteristic
196C4⋊C4—61no—
197C4⋊C4—61no—
198C4⋊C4—91no—
199C4⋊C4—91no—
200C4⋊C4—181no—
201C4⋊C4—181no—
202C22⋊C4—181no—
203C42—61no—
204C22×C3—21no—
205C22×C3—21no—
206C2×D3—61no—
207C2×D3—61no—
208C2×D3—61no—
209C2×D3—61no—
210C2×D3—62no—
211C2×D3—62no—
212C2×D3—121no—
213C2×D3—121no—
214C3×C4—21no—
215C3×C4—21no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—121no—
219C3×C4—121no—
220C3×C4—241no—
221C3×C4—241no—
222Dic3—41no—
223Dic3—41no—
224Dic3—61no—
225Dic3—61no—
226Dic3—61no—
227Dic3—61no—
228Dic3—81no—
229Dic3—81no—
230C32#209011yescharacteristic, complemented, Sylow
231C23—91no—
232C2×C4—61no—
233C2×C4—61no—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—91no—
237C2×C4—91no—
238C2×C4—91no—
239C2×C4—121no—
240C2×C4—121no—
241C2×C4—721no—
242C2×C4—721no—
243C2×C4C2×GO+(4,𝔽2)11yescharacteristic
244C8—21no—
245C8—121no—
246C8—182no—
247C8—182no—
248C8—181no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—21no—
254C2×C3—21no—
255D3—62no—
256D3—62no—
257D3—121no—
258D3—121no—
259C22—91no—
260C22—91no—
261C22—181no—
262C22—181no—
263C22#6423011yescharacteristic
264C4—91no—
265C4—91no—
266C4—121no—
267C4—121no—
268C4—241no—
269C4—241no—
270C4#6422211yescharacteristic
271C4#6423311yescharacteristic
272C3—21no—
273C3—21no—
274C2—181no—
275C2—181no—
276C2#1059330011yescharacteristic
277C2#1059330211yescharacteristic
278C2#1059333911yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC2×C4×C3⋊D3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC22×C3⋊D3#41
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2090
LCSG ▷ C2×C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
230. C32#2090semidirect

Maximal subgroups

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

subgroupindex
#105933942
#105907012
#105906852
#105901852
#105900522
#20909