Finite Group Databasebeta

← #11860693

Subgroups — #11860693

Order 1152.

1121 conjugacy classes of subgroups; only the 226 normal subgroups are shown.

normal subgroups only

This group has 1121 conjugacy classes of subgroups — too many to draw. Only its 226 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
1C2×#63797C211yesmaximal, characteristic
2#10593996C212yesmaximal, complemented
3#10592407C211yesmaximal, characteristic, complemented
4C3×#4711C212yesmaximal, complemented
5#10590941C212yesmaximal, complemented
6#10590781C212yesmaximal, complemented
7#10590740C212yesmaximal, complemented
8#10590712C211yesmaximal, characteristic, complemented
9C4×#3713C212yesmaximal, complemented
10#79867—32nomaximal
11C2×#3802C2212yes—
12C2×#3743C2211yescharacteristic
13C2×C8×C3⋊D3C2211yescharacteristic
14#64081C2211yescharacteristic
15C2×C3×D24C2212yes—
16C3×C4×D12C2214yescomplemented
17D3×(C2×D3)⋊C4—24no—
18#63898C2214yescomplemented
19#63879—24no—
20#63849C2212yes—
21C2×#3713C2212yes—
22#63797C418yescomplemented
23C32×#97C2211yescharacteristic, complemented
24#63642C2211yescharacteristic, complemented
25C8×C3⋊Dic3C2211yescharacteristic, complemented
26C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
27C3×#821C2214yescomplemented
28C3×#817C2212yescomplemented
29#63576C2212yescomplemented
30#63562C2214yescomplemented
31C2×D3×D8—32no—
32#5545—34no—
33C3×#442—32no—
34#5152—32no—
35C4×#213—34no—
36#4869—32no—
37#4860—32no—
38#4770—34no—
39#4756—34no—
40#4711D312yescomplemented
41#4708—32no—
42#4708—61no—
43C22×D32—22no—
44C2×C4×C3⋊D3C2311yescharacteristic
45C2×C3×D12C2314yes—
46C2×C3×C4×D3—24no—
47C2×#625—22no—
48C2×D3×Dic3—24no—
49#3802—24no—
50#3802C2×C418yescomplemented
51C2×C32×C8C2311yescharacteristic
52C2×C32×C8C2311yescharacteristic
53C32×C42C2311yescharacteristic
54#3752D412yes—
55#3750D412yes—
56C4×C3⋊Dic3C2311yescharacteristic
57C2×C3⋊(C3⋊C8)C2311yescharacteristic
58C2×C3⋊(C3⋊C8)C2311yescharacteristic
59#3743—22no—
60C8×C3⋊D3C2×C414yescomplemented
61C3×(C2×D3)⋊C4—24no—
62C3×C4⋊Dic3C2314yes—
63C3×D24C2×C418yescomplemented
64#3722—22no—
65(C2×D3)⋊Dic3—24no—
66Dic32—22no—
67#3713C2×C418yescomplemented
68#2948—91noSylow
69C2×D3×D4—34no—
70C2×C3×D8—32no—
71C3×C4×D4—34no—
72D4×Dic3—34no—
73C2×#213—34no—
74C4×#67—64no—
75C2×(C2×D3)⋊C4—64no—
76D3×D8—316no—
77C2×D24C2×D312yes—
78C2×ΓL(1,𝔽25)—32no—
79C2×ΓL(1,𝔽25)—61no—
80C2×D3×C8—32no—
81C2×D3×C8—61no—
82#893—34no—
83#892—34no—
84#67⋊C4—64no—
85D3×C22⋊C4—64no—
86C4×D12C2×D314yescomplemented
87#872—32no—
88#872—61no—
89C3×#106—32no—
90C3×#102—34no—
91C3×#97—21no—
92C3×#97C2×D312yescomplemented
93#832—34no—
94#821C2×D314yescomplemented
95#817C2×D312yescomplemented
96#815—32no—
97#815—61no—
98C8×Dic3—32no—
99C8×Dic3—61no—
100#809—34no—
101#807—34no—
102C4×C3⋊C8—32no—
103C4×C3⋊C8—61no—
104C22×C3⋊D3C2×D411yescharacteristic
105C22×C3×D3—24no—
106C2×D32—28no—
107C2×D32—84no—
108C2×C32×C4C2×D412yes—
109C2×C32×C4C2411yescharacteristic
110C2×C3⋊Dic3C2×D412yes—
111C2×C3⋊Dic3C2×D411yescharacteristic
112C4×C3⋊D3C22×C412yes—
113C4×C3⋊D3#4112yes—
114C2×C3×Dic3—24no—
115C3×D12—24no—
116C3×D12C22×C418yes—
117C3×C4×D3—84no—
118#625—28no—
119D3×Dic3—84no—
120C32×C8—21no—
121C32×C8C22×C412yes—
122C3⋊(C3⋊C8)—21no—
123C3⋊(C3⋊C8)C22×C412yes—
124C22×D8—91no—
125#518—92no—
126#442—32no—
127#442—92no—
128C4×D8—92no—
129C4×D8—92no—
130#427—91no—
131#418—92no—
132#405—91no—
133C23×D3—64no—
134C2×C3×D4—34no—
135C22×C3×C4—64no—
136C2×#67—64no—
137C22×Dic3—64no—
138D3×D4—316no—
139D3×D4—68no—
140C2×D12C22×D314yes—
141C2×C4×D3—24no—
142C2×C4×D3—32no—
143C2×C4×D3—61no—
144C2×C4×D3—64no—
145C3×D8—38no—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8C22×D312yes—
149C2×C3×C8C22×D312yes—
150C3×C4⋊C4—34no—
151C3×C22⋊C4—64no—
152C3×C42—21no—
153C3×C42C22×D312yes—
154#217—64no—
155#213—316no—
156(C2×D3)⋊C4—24no—
157(C2×D3)⋊C4—34no—
158(C2×D3)⋊C4—62no—
159(C2×D3)⋊C4—64no—
160(C2×D3)⋊C4—64no—
161C4⋊Dic3C22×D314yes—
162Dic3⋊C4—34no—
163Dic3⋊C4—62no—
164C4×Dic3—32no—
165C4×Dic3—61no—
166C4×Dic3—64no—
167C2×C3⋊C8—32no—
168C2×C3⋊C8—32no—
169C2×C3⋊C8—61no—
170C2×C3⋊C8—61no—
171D24C4×D318yescomplemented
172ΓL(1,𝔽25)—64no—
173ΓL(1,𝔽25)—64no—
174D3×C8—38no—
175D3×C8—64no—
176C22×C32C22×D411yescharacteristic
177C2×C3⋊D3—22no—
178C2×C3⋊D3C4×D412yes—
179C2×C3×D3—28no—
180C2×C3×D3—44no—
181C2×C3×D3—44no—
182D32—88no—
183C32×C4—22no—
184C32×C4C23×C411yescharacteristic
185C32×C4C2×#4111yescharacteristic
186C3⋊Dic3—22no—
187C3⋊Dic3C4×D412yes—
188C3×Dic3—44no—
189C22×D4—92no—
190C2×D8—32no—
191C2×D8—98no—
192C2×D8—92no—
193C2×M16—91no—
194C22×C8—91no—
195C4×D4—34no—
196C4×D4—94no—
197C4×D4—184no—
198#117—91no—
199#117—92no—
200C2×C22⋊C4—184no—
201#107—92no—
202#106—32no—
203#102—34no—
204#102—94no—
205#97—91no—
206#97D3211yescharacteristic, complemented
207C4×C8—91no—
208C4×C8—91no—
209C23×C3—64no—
210C22×D3—24no—
211C22×D3—32no—
212C22×D3—61no—
213C22×D3—616no—
214C22×D3—244no—
215C22×D3—244no—
216C3×D4—38no—
217C3×D4—64no—
218C2×C3×C4—21no—
219C2×C3×C4—22no—
220C2×C3×C4—64no—
221C2×C3×C4—244no—
222C2×C3×C4D3×D414yes—
223C2×C3×C4C23×D312yes—
224#67—616no—
225C2×Dic3—24no—
226C2×Dic3—32no—
227C2×Dic3—34no—
228C2×Dic3—61no—
229C2×Dic3—62no—
230C2×Dic3—244no—
231D12—24no—
232D12C2×C4×D318yes—
233C4×D3—34no—
234C4×D3—34no—
235C4×D3—62no—
236C4×D3—62no—
237C4×D3—84no—
238C4×D3—244no—
239C3×C8—22no—
240C3×C8—22no—
241C3×C8—22no—
242C3×C8C2×C4×D314yes—
243C3⋊C8—34no—
244C3⋊C8—62no—
245C3⋊C8—62no—
246C3⋊C8—62no—
247C2×C32C2×C4×D411yescharacteristic
248C2×C32#57612yes—
249C3⋊D3—22no—
250C3×D3—48no—
251C24—182no—
252C2×D4—34no—
253C2×D4—98no—
254C2×D4—184no—
255C2×D4—182no—
256C22×C4—64no—
257C22×C4—91no—
258C22×C4—184no—
259D8—38no—
260D8—98no—
261M16—182no—
262C2×C8—91no—
263C2×C8—94no—
264C2×C8—91no—
265C2×C8C2×D3211yescharacteristic
266C2×C8C2×D3211yescharacteristic
267C4⋊C4—34no—
268C4⋊C4—92no—
269C22⋊C4—64no—
270C22⋊C4—92no—
271C22⋊C4—182no—
272C22⋊C4—184no—
273C42—91no—
274C42—182no—
275C42C2×D3211yescharacteristic
276C22×C3—21no—
277C22×C3—68no—
278C22×C3—124no—
279C22×C3—124no—
280C22×C3C2×D3×D412yes—
281C2×D3—28no—
282C2×D3—34no—
283C2×D3—44no—
284C2×D3—44no—
285C2×D3—62no—
286C2×D3—64no—
287C2×D3—122no—
288C2×D3—2416no—
289C3×C4—24no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—42no—
293C3×C4—124no—
294C3×C4C22×C4×D312yes—
295C3×C4D3×#4112yes—
296Dic3—34no—
297Dic3—44no—
298Dic3—62no—
299Dic3—64no—
300Dic3—122no—
301C32#294811yescharacteristic, complemented, Sylow
302C23—64no—
303C23—91no—
304C23—188no—
305C23—724no—
306D4—38no—
307D4—64no—
308D4—188no—
309C2×C4—64no—
310C2×C4—91no—
311C2×C4—92no—
312C2×C4—92no—
313C2×C4—92no—
314C2×C4—244no—
315C2×C4—724no—
316C2×C4#380212yes—
317C2×C4C22×D3211yescharacteristic
318C8—21no—
319C8—92no—
320C8—181no—
321C8C4×D3212yes—
322C2×C3—22no—
323C2×C3—21no—
324C2×C3—128no—
325C2×C3C4×D3×D412yes—
326C2×C3#577414yes—
327D3—48no—
328D3—64no—
329D3—122no—
330C22—68no—
331C22—92no—
332C22—124no—
333C22—124no—
334C22—182no—
335C22—728no—
336C22C2×#380211yescharacteristic
337C4—22no—
338C4—92no—
339C4—124no—
340C4—182no—
341C4C2×C4×D3211yescharacteristic
342C4#6430611yescharacteristic
343C3—21no—
344C3#7986712yescomplemented
345C2—128no—
346C2—182no—
347C2C4×#380211yescharacteristic
348C2#1059472012yes—
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#63797C2
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10593996C2semidirect
3. #10592407C2semidirect
4. C3×#4711C2semidirect
5. #10590941C2semidirect
6. #10590781C2semidirect
7. #10590740C2semidirect
8. #10590712C2semidirect
9. C4×#3713C2semidirect
16. C3×C4×D12C22semidirect
18. #63898C22semidirect
22. #63797C4semidirect
23. C32×#97C22semidirect
24. #63642C22semidirect
25. C8×C3⋊Dic3C22semidirect
26. C4×C3⋊(C3⋊C8)C22semidirect
27. C3×#821C22semidirect
28. C3×#817C22semidirect
29. #63576C22semidirect
30. #63562C22semidirect
40. #4711D3semidirect
50. #3802C2×C4semidirect
60. C8×C3⋊D3C2×C4semidirect
63. C3×D24C2×C4semidirect
67. #3713C2×C4semidirect
86. C4×D12C2×D3semidirect
92. C3×#97C2×D3semidirect
94. #821C2×D3semidirect
95. #817C2×D3semidirect
171. D24C4×D3semidirect
206. #97D32semidirect
301. C32#2948semidirect
344. C3#79867semidirect

Maximal subgroups

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

subgroupindex
C2×#637972
#105939962
#105924072
C3×#47112
#105909412
#105907812
#105907402
#105907122
C4×#37132
#798673