Finite Group Databasebeta

← #11860691

Subgroups — #11860691

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#10592388C211yesmaximal, characteristic, complemented
4C3×C4×D24C212yesmaximal, complemented
5#10590941C212yesmaximal, complemented
6#10590777C212yesmaximal, complemented
7#10590741C212yesmaximal, complemented
8#10590714C211yesmaximal, characteristic, complemented
9#10590344C212yesmaximal, complemented
10#79588—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×C4×C8C2211yescharacteristic, complemented
24#63642C2211yescharacteristic, complemented
25C8×C3⋊Dic3C2211yescharacteristic, complemented
26#63630C2211yescharacteristic, complemented
27C3×#821C2214yescomplemented
28C3×#818C2212yescomplemented
29#63574C2212yescomplemented
30#63562C2214yescomplemented
31C2×D3×D8—32no—
32#5545—34no—
33C3×C4×D8—32no—
34Dic3×D8—32no—
35#5014—34no—
36#4880—32no—
37#4872—32no—
38#4785—34no—
39#4770—34no—
40C4×D24D312yescomplemented
41#4689—32no—
42#4689—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×#107—32no—
90C3×#102—34no—
91C3×C4×C8—21no—
92C3×C4×C8C2×D312yescomplemented
93#832—34no—
94#821C2×D314yescomplemented
95#818C2×D312yescomplemented
96#815—32no—
97#815—61no—
98C8×Dic3—32no—
99C8×Dic3—61no—
100#809—34no—
101#808—34no—
102#803—32no—
103#803—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—92no—
127#442—92no—
128C4×D8—32no—
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—32no—
158(C2×D3)⋊C4—32no—
159(C2×D3)⋊C4—62no—
160(C2×D3)⋊C4—64no—
161(C2×D3)⋊C4—64no—
162C4⋊Dic3C22×D314yes—
163Dic3⋊C4—32no—
164Dic3⋊C4—32no—
165Dic3⋊C4—62no—
166C4×Dic3—32no—
167C4×Dic3—61no—
168C4×Dic3—64no—
169C2×C3⋊C8—32no—
170C2×C3⋊C8—32no—
171C2×C3⋊C8—61no—
172C2×C3⋊C8—61no—
173D24C4×D318yescomplemented
174ΓL(1,𝔽25)—64no—
175ΓL(1,𝔽25)—64no—
176D3×C8—38no—
177D3×C8—64no—
178C22×C32C22×D411yescharacteristic
179C2×C3⋊D3—22no—
180C2×C3⋊D3C4×D412yes—
181C2×C3×D3—28no—
182C2×C3×D3—44no—
183C2×C3×D3—44no—
184D32—88no—
185C32×C4—22no—
186C32×C4C23×C411yescharacteristic
187C32×C4C2×#4111yescharacteristic
188C3⋊Dic3—22no—
189C3⋊Dic3C4×D412yes—
190C3×Dic3—44no—
191C22×D4—92no—
192C2×D8—32no—
193C2×D8—98no—
194C2×D8—92no—
195C2×M16—91no—
196C22×C8—91no—
197C4×D4—34no—
198C4×D4—94no—
199C4×D4—184no—
200#117—91no—
201#117—92no—
202C2×C22⋊C4—184no—
203#107—32no—
204#106—92no—
205#102—34no—
206#102—94no—
207#97—91no—
208#97—91no—
209C4×C8—91no—
210C4×C8D3211yescharacteristic, complemented
211C23×C3—64no—
212C22×D3—24no—
213C22×D3—32no—
214C22×D3—61no—
215C22×D3—616no—
216C22×D3—244no—
217C22×D3—244no—
218C3×D4—38no—
219C3×D4—64no—
220C2×C3×C4—21no—
221C2×C3×C4—22no—
222C2×C3×C4—64no—
223C2×C3×C4—244no—
224C2×C3×C4D3×D412yes—
225C2×C3×C4D3×D412yes—
226C2×C3×C4C23×D312yes—
227#67—616no—
228C2×Dic3—24no—
229C2×Dic3—32no—
230C2×Dic3—32no—
231C2×Dic3—32no—
232C2×Dic3—61no—
233C2×Dic3—62no—
234C2×Dic3—244no—
235D12—24no—
236D12C2×C4×D318yes—
237C4×D3—34no—
238C4×D3—34no—
239C4×D3—62no—
240C4×D3—62no—
241C4×D3—84no—
242C4×D3—244no—
243C3×C8—22no—
244C3×C8—22no—
245C3×C8—22no—
246C3×C8C2×C4×D314yes—
247C3⋊C8—34no—
248C3⋊C8—62no—
249C3⋊C8—62no—
250C3⋊C8—62no—
251C2×C32C2×C4×D411yescharacteristic
252C2×C32#57612yes—
253C3⋊D3—22no—
254C3×D3—48no—
255C24—182no—
256C2×D4—34no—
257C2×D4—98no—
258C2×D4—184no—
259C2×D4—182no—
260C22×C4—64no—
261C22×C4—91no—
262C22×C4—184no—
263D8—38no—
264D8—98no—
265M16—182no—
266C2×C8—91no—
267C2×C8—94no—
268C2×C8—91no—
269C2×C8C2×D3211yescharacteristic
270C2×C8C2×D3211yescharacteristic
271C4⋊C4—34no—
272C4⋊C4—92no—
273C22⋊C4—64no—
274C22⋊C4—92no—
275C22⋊C4—182no—
276C22⋊C4—184no—
277C42—91no—
278C42—182no—
279C42C2×D3211yescharacteristic
280C22×C3—21no—
281C22×C3—68no—
282C22×C3—124no—
283C22×C3—124no—
284C22×C3C2×D3×D412yes—
285C2×D3—28no—
286C2×D3—34no—
287C2×D3—44no—
288C2×D3—44no—
289C2×D3—62no—
290C2×D3—62no—
291C2×D3—62no—
292C2×D3—122no—
293C2×D3—2416no—
294C3×C4—22no—
295C3×C4—22no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—42no—
299C3×C4—124no—
300C3×C4C22×C4×D312yes—
301C3×C4D3×#4112yes—
302Dic3—34no—
303Dic3—44no—
304Dic3—62no—
305Dic3—62no—
306Dic3—62no—
307Dic3—122no—
308C32#294811yescharacteristic, complemented, Sylow
309C23—64no—
310C23—91no—
311C23—188no—
312C23—724no—
313D4—38no—
314D4—64no—
315D4—188no—
316C2×C4—64no—
317C2×C4—91no—
318C2×C4—92no—
319C2×C4—92no—
320C2×C4—92no—
321C2×C4—244no—
322C2×C4—724no—
323C2×C4#380212yes—
324C2×C4C22×D3211yescharacteristic
325C8—21no—
326C8—92no—
327C8—181no—
328C8C4×D3212yes—
329C2×C3—22no—
330C2×C3—21no—
331C2×C3—128no—
332C2×C3C4×D3×D412yes—
333C2×C3#575712yes—
334C2×C3#576912yes—
335D3—48no—
336D3—64no—
337D3—122no—
338C22—68no—
339C22—92no—
340C22—124no—
341C22—124no—
342C22—182no—
343C22—728no—
344C22C2×#380211yescharacteristic
345C4—22no—
346C4—92no—
347C4—124no—
348C4—182no—
349C4C2×C4×D3211yescharacteristic
350C4#6430611yescharacteristic
351C3—21no—
352C3#7958812yescomplemented
353C2—128no—
354C2—182no—
355C2C4×#380211yescharacteristic
356C2#1059468712yes—
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#63797C2
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593996C2semidirect
3. #10592388C2semidirect
4. C3×C4×D24C2semidirect
5. #10590941C2semidirect
6. #10590777C2semidirect
7. #10590741C2semidirect
8. #10590714C2semidirect
9. #10590344C2semidirect
16. C3×C4×D12C22semidirect
18. #63898C22semidirect
22. #63797C4semidirect
23. C32×C4×C8C22semidirect
24. #63642C22semidirect
25. C8×C3⋊Dic3C22semidirect
26. #63630C22semidirect
27. C3×#821C22semidirect
28. C3×#818C22semidirect
29. #63574C22semidirect
30. #63562C22semidirect
40. C4×D24D3semidirect
50. #3802C2×C4semidirect
60. C8×C3⋊D3C2×C4semidirect
63. C3×D24C2×C4semidirect
67. #3713C2×C4semidirect
86. C4×D12C2×D3semidirect
92. C3×C4×C8C2×D3semidirect
94. #821C2×D3semidirect
95. #818C2×D3semidirect
173. D24C4×D3semidirect
210. C4×C8D32semidirect
308. C32#2948semidirect
352. C3#79588semidirect

Maximal subgroups

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

subgroupindex
C2×#637972
#105939962
#105923882
C3×C4×D242
#105909412
#105907772
#105907412
#105907142
#105903442
#795883