Finite Group Databasebeta

← #11858873

Subgroups — #11858873

Order 1152.

855 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 855 conjugacy classes of subgroups — too many to draw. Only its 212 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#10593992C211yesmaximal, characteristic
2C4×#3743C211yesmaximal, characteristic, complemented
3C3×#4690C212yesmaximal, complemented
4#10590937C212yesmaximal
5#10590699C214yesmaximal, complemented
6#10590666C212yesmaximal, complemented
7#10590265C212yesmaximal, complemented
8#10590247C211yesmaximal, characteristic, complemented
9#79371—32nomaximal
10C2×C4×D32C2211yescharacteristic
11C2×#3743C2212yes—
12C42×C3⋊D3C2211yescharacteristic
13C3×#872C2212yes—
14#63921C412yes—
15#63883C412yes—
16C4×#624C2211yescharacteristic
17#63878C414yes—
18#63855C2212yes—
19C2×#3712C2212yes—
20C32×C4×C8C2211yescharacteristic, complemented
21#63642C2212yescomplemented
22C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C3×(C2×D3)⋊C8C2214yes—
24C3×Dic3⋊C8C2214yescomplemented
25C3×#803C2212yescomplemented
26Dic3⋊(C3⋊C8)C2214yescomplemented
27(C2×D3)⋊(C3⋊C8)C2214yes—
28#63553C2212yescomplemented
29D3×#117—32no—
30C3×#433—32no—
31#5000—32no—
32#4840—34no—
33#4837—34no—
34#4726—34no—
35#4720—34no—
36#4709—32no—
37#4707—32no—
38#4690D312yescomplemented
39C4×ΓL(1,𝔽25)—32no—
40C4×ΓL(1,𝔽25)—61no—
41C22×D32C2×C411yescharacteristic
42C2×C4×C3⋊D3C2×C412yes—
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×C3×C4×D3C2312yes—
45C2×#624C2×C411yescharacteristic
46C2×#624C2×C412yes—
47C2×D3×Dic3C2×C412yes—
48C4×D32—24no—
49C2×C32×C8C2312yes—
50C32×C42C2311yescharacteristic
51C4×C3⋊Dic3C2×C412yes—
52C4×C3⋊Dic3C2311yescharacteristic
53C2×C3⋊(C3⋊C8)C2312yes—
54#3743—24no—
55C3×(C2×D3)⋊C4C2×C414yes—
56C3×Dic3⋊C4C2×C414yes—
57C3×C4×Dic3C2312yes—
58C2×C3×C3⋊C8C2314yes—
59Dic3⋊Dic3C2×C414yes—
60(C2×D3)⋊Dic3C2×C414yes—
61Dic32C2×C412yes—
62#3712—24no—
63#2921—91noSylow
64C22×C4×D3—32no—
65C3×#117—32no—
66#926—32no—
67C2×ΓL(1,𝔽25)—34no—
68C2×ΓL(1,𝔽25)—34no—
69C2×ΓL(1,𝔽25)—62no—
70#892—34no—
71D3×C4⋊C4—34no—
72D3×C22⋊C4—34no—
73#877—34no—
74#872—32no—
75#872C2×D312yes—
76C42×D3—32no—
77C42×D3—32no—
78C42×D3—61no—
79C3×C4⋊C8—34no—
80C3×C22⋊C8—34no—
81C3×#97—32no—
82C3×C4×C8—21no—
83C3×C4×C8C2×D312yescomplemented
84#830—34no—
85(C2×D3)⋊C8—34no—
86(C2×D3)⋊C8C2×D314yes—
87#815—34no—
88#815—62no—
89Dic3⋊C8—34no—
90Dic3⋊C8C2×D314yescomplemented
91C8×Dic3—34no—
92C4⋊(C3⋊C8)—34no—
93#803C2×D312yescomplemented
94C4×C3⋊C8—32no—
95C4×C3⋊C8—61no—
96C22×C3⋊D3C22×C411yescharacteristic
97C22×C3×D3C22×C412yes—
98C2×D32—22no—
99C2×D32—42no—
100C2×C32×C4C22×C412yes—
101C2×C32×C4C2411yescharacteristic
102C2×C3⋊Dic3C22×C412yes—
103C2×C3⋊Dic3C22×C411yescharacteristic
104C4×C3⋊D3—42no—
105C4×C3⋊D3#4114yes—
106C2×C3×Dic3C22×C414yes—
107C2×C3×Dic3C22×C412yes—
108C3×C4×D3—24no—
109#624—22no—
110#624—42no—
111D3×Dic3—24no—
112C32×C8—22no—
113C3⋊(C3⋊C8)—22no—
114C3×C3⋊C8—24no—
115C2×#117—91no—
116#433—32no—
117#433—92no—
118#433—94no—
119#423—92no—
120#407—92no—
121C4×M16—91no—
122C4×M16—91no—
123C23×D3—32no—
124C22×C3×C4—32no—
125C22×Dic3—32no—
126C2×C4×D3—32no—
127C2×C4×D3—32no—
128C2×C4×D3—32no—
129C2×C4×D3—34no—
130C2×C4×D3—34no—
131C2×C4×D3—61no—
132C2×C4×D3—62no—
133C2×C4×D3—68no—
134C2×C4×D3C22×D312yes—
135C2×C3×C8—22no—
136C2×C3×C8—34no—
137C2×C3×C8C22×D314yes—
138C3×C4⋊C4—34no—
139C3×C22⋊C4—34no—
140C3×C42—21no—
141C3×C42—32no—
142C3×C42C22×D312yes—
143#217—34no—
144(C2×D3)⋊C4—34no—
145(C2×D3)⋊C4C4×D314yes—
146C4⋊Dic3—34no—
147Dic3⋊C4—34no—
148Dic3⋊C4C4×D314yes—
149C4×Dic3—34no—
150C4×Dic3—32no—
151C4×Dic3—34no—
152C4×Dic3—61no—
153C4×Dic3—62no—
154C4×Dic3C22×D312yes—
155C2×C3⋊C8—34no—
156C2×C3⋊C8—62no—
157C2×C3⋊C8C22×D314yes—
158ΓL(1,𝔽25)—68no—
159ΓL(1,𝔽25)—68no—
160ΓL(1,𝔽25)—68no—
161C22×C32C23×C411yescharacteristic
162C2×C3⋊D3—22no—
163C2×C3⋊D3#11712yes—
164C2×C3×D3—22no—
165C2×C3×D3—24no—
166D32—44no—
167C32×C4—22no—
168C32×C4C2×#4112yes—
169C3⋊Dic3—22no—
170C3⋊Dic3#11712yes—
171C3×Dic3—22no—
172C3×Dic3—24no—
173C23×C4—91no—
174C2×M16—92no—
175C2×M16—92no—
176#117—32no—
177#117—92no—
178#117—94no—
179C2×C4⋊C4—92no—
180C2×C22⋊C4—92no—
181C2×C42—91no—
182C2×C42—91no—
183C4⋊C8—34no—
184C4⋊C8—94no—
185C22⋊C8—34no—
186C22⋊C8—94no—
187#97—32no—
188#97—92no—
189C4×C8—92no—
190C4×C8—91no—
191C4×C8D3211yescharacteristic, complemented
192C23×C3—32no—
193C22×D3—32no—
194C22×D3—61no—
195C22×D3—64no—
196C22×D3—124no—
197C22×D3C2×C4×D312yes—
198C2×C3×C4—21no—
199C2×C3×C4—22no—
200C2×C3×C4—34no—
201C2×C3×C4—32no—
202C2×C3×C4—64no—
203C2×C3×C4C2×C4×D314yes—
204C2×C3×C4C23×D312yes—
205C2×Dic3—32no—
206C2×Dic3—34no—
207C2×Dic3—61no—
208C2×Dic3—62no—
209C2×Dic3—64no—
210C2×Dic3C2×C4×D314yes—
211C2×Dic3C2×C4×D312yes—
212C4×D3—24no—
213C4×D3—38no—
214C4×D3—64no—
215C4×D3—64no—
216C4×D3—64no—
217C4×D3—124no—
218C4×D3—124no—
219C4×D3—124no—
220C3×C8—24no—
221C3×C8—24no—
222C3×C8—64no—
223C3⋊C8—24no—
224C3⋊C8—64no—
225C3⋊C8—64no—
226C2×C32C2×#11711yescharacteristic
227C2×C32#56812yes—
228C3⋊D3—22no—
229C3×D3—42no—
230C24—91no—
231C22×C4—32no—
232C22×C4—91no—
233C22×C4—92no—
234C22×C4—92no—
235C22×C4—91no—
236C22×C4—92no—
237C22×C4—184no—
238M16—184no—
239M16—184no—
240C2×C8—34no—
241C2×C8—92no—
242C2×C8C2×D3212yes—
243C4⋊C4—34no—
244C4⋊C4—94no—
245C22⋊C4—34no—
246C22⋊C4—94no—
247C42—32no—
248C42—92no—
249C42—91no—
250C42—92no—
251C42C2×D3211yescharacteristic
252C22×C3—21no—
253C22×C3—64no—
254C22×C3—62no—
255C22×C3C22×C4×D312yes—
256C2×D3—24no—
257C2×D3—22no—
258C2×D3—34no—
259C2×D3—62no—
260C2×D3—64no—
261C2×D3—122no—
262C2×D3—128no—
263C3×C4—24no—
264C3×C4—24no—
265C3×C4—22no—
266C3×C4—64no—
267C3×C4—62no—
268C3×C4D3×#4114yes—
269Dic3—24no—
270Dic3—22no—
271Dic3—34no—
272Dic3—62no—
273Dic3—64no—
274Dic3—122no—
275C32#292111yescharacteristic, complemented, Sylow
276C23—32no—
277C23—91no—
278C23—182no—
279C23—362no—
280C2×C4—34no—
281C2×C4—32no—
282C2×C4—64no—
283C2×C4—91no—
284C2×C4—94no—
285C2×C4—92no—
286C2×C4—182no—
287C2×C4—184no—
288C2×C4—362no—
289C2×C4—362no—
290C2×C4C4×D3212yes—
291C2×C4C22×D3211yescharacteristic
292C8—22no—
293C8—64no—
294C8—182no—
295C2×C3—22no—
296C2×C3—21no—
297C2×C3—122no—
298C2×C3D3×#11712yes—
299C2×C3#575014yes—
300D3—42no—
301D3—64no—
302D3—122no—
303C22—64no—
304C22—62no—
305C22—92no—
306C22—182no—
307C22—364no—
308C22C2×C4×D3211yescharacteristic
309C4—22no—
310C4—64no—
311C4—62no—
312C4—92no—
313C4—182no—
314C4#6430612yes—
315C3—21no—
316C3#7937112yescomplemented
317C2—122no—
318C2—182no—
319C2#1059399211yescharacteristic
320C2#1059467012yes—
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4×C8C22
prime radicalC22×D32C2×C4
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32#2921
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C4×#3743C2semidirect
3. C3×#4690C2semidirect
5. #10590699C2semidirect
6. #10590666C2semidirect
7. #10590265C2semidirect
8. #10590247C2semidirect
20. C32×C4×C8C22semidirect
21. #63642C22semidirect
22. C4×C3⋊(C3⋊C8)C22semidirect
24. C3×Dic3⋊C8C22semidirect
25. C3×#803C22semidirect
26. Dic3⋊(C3⋊C8)C22semidirect
28. #63553C22semidirect
38. #4690D3semidirect
83. C3×C4×C8C2×D3semidirect
90. Dic3⋊C8C2×D3semidirect
93. #803C2×D3semidirect
191. C4×C8D32semidirect
275. C32#2921semidirect
316. C3#79371semidirect

Maximal subgroups

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

subgroupindex
#105939922
C4×#37432
C3×#46902
#105909372
#105906992
#105906662
#105902652
#105902472
#793713