Finite Group Databasebeta

← #11860230

Subgroups — #11860230

Order 1152.

1057 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#235C212yesmaximal, complemented
2C2×#63822C211yesmaximal, characteristic
3C2×#63630C211yesmaximal, characteristic, complemented
4#10591138C211yesmaximal, characteristic, complemented
5#10591083C212yesmaximal, complemented
6#10590381C212yesmaximal, complemented
7#10590358C214yesmaximal, complemented
8#10590344C212yesmaximal, complemented
9#82506—32nomaximal
10C2×C3×#235C2212yes—
11C2×C32×C42C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×C4×#67—24no—
15C3×#926C2212yes—
16C3×C4×D12C2214yes—
17C3×#872—22no—
18C3×C42×D3—22no—
19C3×C4×Dic6C2214yes—
20C2×#3718C2211yescharacteristic
21C2×#3715C2212yes—
22#63822C418yescomplemented
23C2×#3713C2211yescharacteristic
24#63630C2212yes—
25#63630C2212yes—
26#63576C2212yes—
27#63574C2212yes—
28#63565C2214yes—
29#63562C2214yes—
30C3×C4×#41—32no—
31C2×#950—32no—
32C4×#235D312yescomplemented
33#5233—32no—
34#5030—34no—
35#5026—34no—
36#5018—34no—
37#5014—34no—
38#5002—32no—
39#4998—32no—
40C2×#803—32no—
41C2×#803—61no—
42C22×C32×C4D412yes—
43C22×C32×C4C2311yescharacteristic
44C2×C3×#67—22no—
45C3×#235—24no—
46C3×#235C2×C418yescomplemented
47C2×C3×D12C2312yes—
48C2×C3×C4×D3—22no—
49C2×C3×C4×D3—24no—
50C2×C3×Dic6C2312yes—
51C32×C42D412yes—
52C32×C42C2312yes—
53C2×C3⋊(C3⋊C8)—22no—
54C2×C3⋊(C3⋊C8)C2×C414yescomplemented
55C2×C3⋊(C3⋊C8)C2312yes—
56C2×C3⋊(C3⋊C8)C2311yescharacteristic
57C2×C3⋊(C3⋊C8)C2311yescharacteristic
58C3×#217—22no—
59C3×(C2×D3)⋊C4—24no—
60C3×C4⋊Dic3C2314yes—
61C3×Dic3⋊C4—24no—
62C3×C4×Dic3—22no—
63C3×C4×Dic3—24no—
64#3718C2×C414yescomplemented
65#3715C2×C418yescomplemented
66#3713C2×C414yescomplemented
67#2943—91noSylow
68C2×C3×#41—32no—
69C2×#235C2×D312yes—
70C3×C4×Q8—34no—
71C3×C4×D4—34no—
72C3×C4×D4—64no—
73C3×#117—32no—
74C3×#117—62no—
75C2×C3×C42—21no—
76C2×C3×C42—62no—
77C2×C3×C42C2×D312yes—
78#950—316no—
79C2×#216—32no—
80C2×#215—32no—
81C2×#214—32no—
82C2×#213—32no—
83C4×#67—24no—
84#926C2×D312yes—
85C22×C3⋊C8—32no—
86C22×C3⋊C8—32no—
87C22×C3⋊C8—61no—
88C22×C3⋊C8—61no—
89C4×D12C2×D314yes—
90#872—22no—
91C42×D3—22no—
92C4×Dic6C2×D314yes—
93#835—34no—
94#832—34no—
95#810—34no—
96#809—34no—
97#808—34no—
98#807—34no—
99#803—34no—
100#803—34no—
101#803—62no—
102#803—62no—
103C23×C32C2×D411yescharacteristic
104C22×C3×D3—22no—
105C2×C32×C4—42no—
106C2×C32×C4C22×C412yes—
107C2×C32×C4C2×D414yes—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4#4112yes—
110C2×C32×C4C2411yescharacteristic
111C3×#67—28no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—24no—
114C3×D12—22no—
115C3×D12C22×C414yes—
116C3×C4×D3—28no—
117C3×C4×D3—48no—
118C3×Dic6—22no—
119C3×Dic6C22×C414yes—
120C3⋊(C3⋊C8)—22no—
121C3⋊(C3⋊C8)C22×C412yes—
122C3⋊(C3⋊C8)C22×C412yes—
123C2×#135—91no—
124C4×#41—32no—
125#442—92no—
126#441—92no—
127#440—94no—
128#427—91no—
129#416—92no—
130C2×#97—91no—
131C3×#41—38no—
132C3×#41—64no—
133C2×C3×Q8—32no—
134C2×C3×D4—32no—
135C2×C3×D4—62no—
136C22×C3×C4—22no—
137C22×C3×C4—21no—
138C22×C3×C4—62no—
139C22×C3×C4—64no—
140C22×C3×C4#6714yes—
141C22×C3×C4C22×D312yes—
142C2×#67—22no—
143#235—24no—
144#235C4×D318yescomplemented
145C2×D12C22×D312yes—
146C2×C4×D3—22no—
147C2×C4×D3—24no—
148C2×Dic6C22×D312yes—
149C3×C4⋊C4—34no—
150C3×C4⋊C4—64no—
151C3×C22⋊C4—62no—
152C3×C22⋊C4—64no—
153C3×C42—22no—
154C3×C42—22no—
155C3×C42—62no—
156C3×C42—64no—
157C3×C42#6712yes—
158C3×C42#6712yes—
159C3×C42C22×D314yes—
160#217—22no—
161#216—38no—
162#215—38no—
163#214—38no—
164#213—38no—
165(C2×D3)⋊C4—24no—
166C4⋊Dic3C22×D314yes—
167Dic3⋊C4—24no—
168C4×Dic3—24no—
169C4×Dic3—22no—
170C2×C3⋊C8—38no—
171C2×C3⋊C8—32no—
172C2×C3⋊C8—32no—
173C2×C3⋊C8—34no—
174C2×C3⋊C8—61no—
175C2×C3⋊C8—61no—
176C2×C3⋊C8—62no—
177C2×C3⋊C8—64no—
178C2×C3⋊C8—64no—
179C2×C3⋊C8—64no—
180C22×C32—22no—
181C22×C32C4×D412yes—
182C22×C32C22×D411yescharacteristic
183C2×C3×D3—24no—
184C2×C3×D3—44no—
185C32×C4—24no—
186C32×C4C4×D412yes—
187C32×C4C23×C411yescharacteristic
188C32×C4C2×#4111yescharacteristic
189C3×Dic3—24no—
190C3×Dic3—44no—
191C2×#41—32no—
192#135—98no—
193C2×Q16—91no—
194C2×SD16—92no—
195C2×D8—91no—
196C22×C8—91no—
197C22×C8—91no—
198C4×Q8—34no—
199C4×D4—34no—
200C4×D4—64no—
201#117—32no—
202#117—62no—
203C2×C42—62no—
204C2×C42D3211yescharacteristic
205#107—92no—
206#106—92no—
207#103—94no—
208#102—94no—
209#97—92no—
210#97—92no—
211C23×C3—21no—
212C23×C3—62no—
213C23×C3C2×#6712yes—
214C22×D3—22no—
215C3×Q8—34no—
216C3×Q8—62no—
217C3×D4—34no—
218C3×D4—68no—
219C3×D4—62no—
220C2×C3×C4—21no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—24no—
224C2×C3×C4—21no—
225C2×C3×C4—44no—
226C2×C3×C4—44no—
227C2×C3×C4—62no—
228C2×C3×C4—68no—
229C2×C3×C4—64no—
230C2×C3×C4—128no—
231C2×C3×C4C2×C4×D314yes—
232C2×C3×C4#23514yes—
233C2×C3×C4C2×#6714yes—
234C2×C3×C4C2×#6714yes—
235C2×C3×C4C2×#6712yes—
236C2×C3×C4C23×D312yes—
237#67—28no—
238C2×Dic3—22no—
239C2×Dic3—24no—
240D12—22no—
241D12C2×C4×D314yes—
242C4×D3—28no—
243C4×D3—48no—
244Dic6—22no—
245Dic6C2×C4×D314yes—
246C3⋊C8—34no—
247C3⋊C8—34no—
248C3⋊C8—62no—
249C3⋊C8—62no—
250C3⋊C8—64no—
251C3⋊C8—64no—
252C2×C32—22no—
253C2×C32C2×C4×D411yescharacteristic
254C2×C32#57512yes—
255C3×D3—44no—
256#41—38no—
257#41—64no—
258C2×Q8—32no—
259C2×D4—32no—
260C2×D4—62no—
261C22×C4—62no—
262C22×C4—64no—
263C22×C4#62512yes—
264C22×C4C2×D3211yescharacteristic
265Q16—94no—
266SD16—98no—
267D8—94no—
268C2×C8—91no—
269C2×C8—91no—
270C2×C8—94no—
271C2×C8—92no—
272C2×C8—182no—
273C4⋊C4—34no—
274C4⋊C4—64no—
275C22⋊C4—62no—
276C22⋊C4—64no—
277C42—64no—
278C42—62no—
279C42#62512yes—
280C42C2×D3212yes—
281C22×C3—24no—
282C22×C3—24no—
283C22×C3—21no—
284C22×C3—22no—
285C22×C3—64no—
286C22×C3—124no—
287C22×C3C4×#6714yes—
288C22×C3C22×#6712yes—
289C2×D3—24no—
290C2×D3—44no—
291C3×C4—24no—
292C3×C4—24no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—22no—
296C3×C4—44no—
297C3×C4—64no—
298C3×C4—124no—
299C3×C4C4×#6714yes—
300C3×C4C22×C4×D312yes—
301C3×C4C2×#23512yes—
302Dic3—24no—
303Dic3—44no—
304C32#294311yescharacteristic, complemented, Sylow
305C23—62no—
306C23C2×#62511yescharacteristic
307Q8—34no—
308Q8—62no—
309D4—34no—
310D4—68no—
311D4—62no—
312C2×C4—42no—
313C2×C4—62no—
314C2×C4—68no—
315C2×C4—64no—
316C2×C4—128no—
317C2×C4#379812yes—
318C2×C4C4×D3212yes—
319C2×C4C2×#62514yes—
320C2×C4C2×#62511yescharacteristic
321C2×C4C22×D3211yescharacteristic
322C8—92no—
323C8—92no—
324C8—182no—
325C2×C3—24no—
326C2×C3—24no—
327C2×C3—21no—
328C2×C3—22no—
329C2×C3—124no—
330C2×C3C2×C4×#6712yes—
331C2×C3#582214yes—
332D3—44no—
333C22—22no—
334C22—64no—
335C22—124no—
336C22C4×#62512yes—
337C22C22×#62511yescharacteristic
338C4—24no—
339C4—64no—
340C4—124no—
341C4C4×#62512yes—
342C4C2×#379811yescharacteristic
343C4C2×C4×D3211yescharacteristic
344C3—21no—
345C3#8250612yescomplemented
346C2—22no—
347C2—124no—
348C2#1059478612yes—
349C2C2×C4×#62511yescharacteristic
subgroupG/H
centerC2×C4C2×#625
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radicalC2×#63822C2
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32#2943
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C3×C4×#235C2semidirect
3. C2×#63630C2semidirect
4. #10591138C2semidirect
5. #10591083C2semidirect
6. #10590381C2semidirect
7. #10590358C2semidirect
8. #10590344C2semidirect
22. #63822C4semidirect
32. C4×#235D3semidirect
46. C3×#235C2×C4semidirect
54. C2×C3⋊(C3⋊C8)C2×C4semidirect
64. #3718C2×C4semidirect
65. #3715C2×C4semidirect
66. #3713C2×C4semidirect
144. #235C4×D3semidirect
304. C32#2943semidirect
345. C3#82506semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2352
C2×#638222
C2×#636302
#105911382
#105910832
#105903812
#105903582
#105903442
#825063