Finite Group Databasebeta

← #11860859

Subgroups — #11860859

Order 1152.

1452 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64128C211yesmaximal, characteristic
2#10596045C212yesmaximal, complemented
3C32×C4×Q16C211yesmaximal, characteristic, complemented
4Q16×C3⋊Dic3C211yesmaximal, characteristic, complemented
5#10592725C212yesmaximal, complemented
6C3⋊D3×#107C211yesmaximal, characteristic, complemented
7#10592571C211yesmaximal, characteristic, complemented
8#10592516C212yesmaximal, complemented
9#10592502C212yesmaximal, complemented
10C4×#3745C211yesmaximal, characteristic, complemented
11#10592388C211yesmaximal, characteristic, complemented
12#79721—34nomaximal
13C2×#3832C2212yes—
14C2×C32×Q16C2211yescharacteristic
15C32×C4×Q8C2212yes—
16Q8×C3⋊Dic3C2212yes—
17C2×#3755C2212yes—
18#64128C418yescomplemented
19C2×#3745C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic
22#64102—22no—
23#64102C2212yes—
24C4⋊C4×C3⋊D3—22no—
25C4⋊C4×C3⋊D3C2212yes—
26C4×C4⋊(C3⋊D3)—22no—
27C4×C4⋊(C3⋊D3)C2212yes—
28#64081—22no—
29#64081C2211yescharacteristic
30C32×#107C2211yescharacteristic
31C32×#103C2212yes—
32C32×C4×C8C2211yescharacteristic
33#63662C2212yes—
34#63648C2212yes—
35#63645C2211yescharacteristic
36#63642C2211yescharacteristic
37C8×C3⋊Dic3C2211yescharacteristic
38#63636C2212yes—
39#63634C2212yes—
40#63630C2211yescharacteristic
41C2×#919—34no—
42#5574—38no—
43C3×C4×Q16D314yescomplemented
44Dic3×Q16—34no—
45#5026—38no—
46D3×#107—34no—
47#4872—34no—
48#4817—38no—
49#4803—38no—
50C4×D24—34no—
51#4689—34no—
52C2×C32×Q8C2312yes—
53#3832—24no—
54#3832C2×C418yescomplemented
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)C2312yes—
57C2×C4×C3⋊D3—22no—
58C2×C4×C3⋊D3—22no—
59C2×C4×C3⋊D3—22no—
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3C2311yescharacteristic
62C32×Q16C2×C414yescomplemented
63C2×C32×C8C2311yescharacteristic
64C2×C32×C8C2311yescharacteristic
65C32×C4⋊C4—22no—
66C32×C4⋊C4C2312yes—
67C32×C42—22no—
68C32×C42C2311yescharacteristic
69#3755C2×C418yescomplemented
70#3752—22no—
71#3752—22no—
72#3752D411yescharacteristic
73#3752D411yescharacteristic
74C4⋊(C3⋊Dic3)—22no—
75C4⋊(C3⋊Dic3)C2312yes—
76#3750—22no—
77#3750D411yescharacteristic
78#3750D411yescharacteristic
79C4×C3⋊Dic3—22no—
80C4×C3⋊Dic3C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83#3745C2×C414yescomplemented
84#3743—22no—
85C8×C3⋊D3C2×C414yescomplemented
86#2951—91noSylow
87C2×#239—38no—
88C2×C3×Q16C2×D314yes—
89C3×C4×Q8C2×D318yes—
90Q8×Dic3—38no—
91C2×#215—38no—
92#919—332no—
93C2×D24—34no—
94C2×ΓL(1,𝔽25)—34no—
95C2×D3×C8—34no—
96#893—38no—
97#893—68no—
98D3×C4⋊C4—38no—
99D3×C4⋊C4—68no—
100C4×D12—38no—
101C4×D12—68no—
102#872—34no—
103#872—68no—
104C3×#107C2×D314yes—
105C3×#103C2×D318yes—
106C3×C4×C8C2×D314yes—
107#835—38no—
108#821—38no—
109#818—34no—
110#815—34no—
111C8×Dic3—34no—
112#809—38no—
113#807—38no—
114#803—34no—
115C22×C3⋊D3—22no—
116C22×C3⋊D3C2×D411yescharacteristic
117C32×Q8—22no—
118C32×Q8C22×C414yes—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2411yescharacteristic
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3C2×D411yescharacteristic
126C2×C3⋊Dic3C2×D411yescharacteristic
127C2×C3⋊Dic3C2×D411yescharacteristic
128C4⋊(C3⋊D3)—28no—
129C4⋊(C3⋊D3)—22no—
130C4⋊(C3⋊D3)C22×C414yes—
131C4×C3⋊D3—28no—
132C4×C3⋊D3—82no—
133C4×C3⋊D3—82no—
134C4×C3⋊D3—82no—
135C4×C3⋊D3C22×C412yes—
136C4×C3⋊D3#4112yes—
137C32×C8—21no—
138C32×C8C22×C412yes—
139C3⋊(C3⋊C8)—21no—
140C3⋊(C3⋊C8)C22×C412yes—
141C2×#135—91no—
142#520—92no—
143#440—92no—
144#440—92no—
145C4×Q16—91no—
146C4×Q16C3⋊D311yescharacteristic, complemented
147C4×D8—91no—
148C4×D8—91no—
149C2×#107—91no—
150#417—92no—
151#405—91no—
152C2×C3×Q8C22×D318yes—
153#239—332no—
154#239—616no—
155C2×D12—38no—
156C2×D12—68no—
157C2×C4×D3—34no—
158C2×C4×D3—68no—
159C2×C4×D3—68no—
160C2×C4×D3—68no—
161C2×C4×D3—68no—
162C3×Q16C4×D3116yescomplemented
163C2×C3×C8C22×D314yes—
164C2×C3×C8C22×D314yes—
165C3×C4⋊C4—28no—
166C3×C4⋊C4C22×D318yes—
167C3×C42—28no—
168C3×C42C22×D314yes—
169#215—332no—
170(C2×D3)⋊C4—34no—
171(C2×D3)⋊C4—34no—
172(C2×D3)⋊C4—68no—
173(C2×D3)⋊C4—68no—
174C4⋊Dic3—38no—
175C4⋊Dic3—68no—
176Dic3⋊C4—34no—
177Dic3⋊C4—34no—
178Dic3⋊C4—68no—
179C4×Dic3—34no—
180C4×Dic3—68no—
181C2×C3⋊C8—34no—
182C2×C3⋊C8—34no—
183D24—316no—
184ΓL(1,𝔽25)—68no—
185D3×C8—316no—
186C22×C32C22×D411yescharacteristic
187C2×C3⋊D3—21no—
188C2×C3⋊D3—21no—
189C2×C3⋊D3—24no—
190C2×C3⋊D3—42no—
191C2×C3⋊D3—42no—
192C2×C3⋊D3C4×D412yes—
193C32×C4—24no—
194C32×C4—21no—
195C32×C4—21no—
196C32×C4—42no—
197C32×C4C23×C411yescharacteristic
198C32×C4C2×#4111yescharacteristic
199C3⋊Dic3—21no—
200C3⋊Dic3—21no—
201C3⋊Dic3—42no—
202C3⋊Dic3C4×D412yes—
203C2×#41—92no—
204#135—98no—
205C2×Q16C2×C3⋊D311yescharacteristic
206C2×SD16—92no—
207C2×D8—91no—
208C2×M16—91no—
209C22×C8—91no—
210C4×Q8—92no—
211C4×Q8C2×C3⋊D312yes—
212C4×D4—92no—
213C4×D4—92no—
214C4×D4—182no—
215C4×D4—182no—
216#117—91no—
217#117—182no—
218C2×C4⋊C4—92no—
219C2×C4⋊C4—182no—
220#107—91no—
221#107—92no—
222#107C2×C3⋊D311yescharacteristic
223#103—92no—
224#103C2×C3⋊D312yes—
225#102—92no—
226#102—92no—
227#97—91no—
228#97—91no—
229C4×C8—91no—
230C4×C8C2×C3⋊D311yescharacteristic
231C22×D3—34no—
232C22×D3—68no—
233C3×Q8—28no—
234C3×Q8C2×C4×D3116yes—
235C2×C3×C4—28no—
236C2×C3×C4—28no—
237C2×C3×C4D3×D414yes—
238C2×C3×C4D3×D414yes—
239C2×C3×C4C23×D314yes—
240C2×Dic3—34no—
241C2×Dic3—34no—
242C2×Dic3—34no—
243C2×Dic3—68no—
244D12—316no—
245D12—632no—
246D12—68no—
247C4×D3—38no—
248C4×D3—38no—
249C4×D3—632no—
250C4×D3—248no—
251C4×D3—248no—
252C4×D3—248no—
253C3×C8—24no—
254C3×C8C2×C4×D318yes—
255C3⋊C8—38no—
256C3⋊C8—64no—
257C2×C32C2×C4×D411yescharacteristic
258C2×C32#57611yescharacteristic
259C2×C32#57811yescharacteristic
260C3⋊D3—22no—
261C3⋊D3—44no—
262#41—98no—
263#41—184no—
264C2×Q8C22×C3⋊D312yes—
265C2×D4—92no—
266C2×D4—182no—
267C22×C4—91no—
268C22×C4—182no—
269C22×C4—182no—
270C22×C4—182no—
271C22×C4—182no—
272Q16C4×C3⋊D314yescomplemented
273SD16—98no—
274D8—94no—
275M16—182no—
276C2×C8—91no—
277C2×C8—94no—
278C2×C8—91no—
279C2×C8C22×C3⋊D311yescharacteristic
280C2×C8C22×C3⋊D311yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—91no—
283C4⋊C4—91no—
284C4⋊C4—92no—
285C4⋊C4—182no—
286C4⋊C4—182no—
287C4⋊C4C22×C3⋊D312yes—
288C22⋊C4—91no—
289C22⋊C4—91no—
290C22⋊C4—182no—
291C22⋊C4—182no—
292C42—22no—
293C42—91no—
294C42—182no—
295C42C22×C3⋊D311yescharacteristic
296C22×C3C2×D3×D414yes—
297C2×D3—38no—
298C2×D3—64no—
299C2×D3—64no—
300C2×D3—616no—
301C2×D3—128no—
302C2×D3—128no—
303C3×C4—24no—
304C3×C4—24no—
305C3×C4—216no—
306C3×C4—48no—
307C3×C4C22×C4×D314yes—
308C3×C4D3×#4114yes—
309Dic3—38no—
310Dic3—64no—
311Dic3—64no—
312Dic3—128no—
313C32#295111yescharacteristic, complemented, Sylow
314C23—91no—
315C23—182no—
316Q8—22no—
317Q8C2×C4×C3⋊D314yes—
318D4—94no—
319D4—188no—
320D4—182no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—91no—
324C2×C4—92no—
325C2×C4—92no—
326C2×C4—91no—
327C2×C4—91no—
328C2×C4—188no—
329C2×C4—182no—
330C2×C4—722no—
331C2×C4—722no—
332C2×C4—722no—
333C2×C4D4×C3⋊D311yescharacteristic
334C2×C4D4×C3⋊D311yescharacteristic
335C2×C4C23×C3⋊D311yescharacteristic
336C8—21no—
337C8—92no—
338C8—181no—
339C8C2×C4×C3⋊D312yes—
340C2×C3C4×D3×D414yes—
341C2×C3#576614yes—
342C2×C3#576914yes—
343D3—68no—
344D3—1216no—
345C22—92no—
346C22—181no—
347C22—181no—
348C22—184no—
349C22—362no—
350C22—362no—
351C22C2×D4×C3⋊D311yescharacteristic
352C4—21no—
353C4—21no—
354C4—24no—
355C4—42no—
356C4—92no—
357C4—181no—
358C4—181no—
359C4—362no—
360C4C22×C4×C3⋊D311yescharacteristic
361C4#41×C3⋊D311yescharacteristic
362C3#7972114yescomplemented
363C2—182no—
364C2—364no—
365C2C4×D4×C3⋊D311yescharacteristic
366C2#1059623711yescharacteristic
367C2#1059624011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×Q16C2
socleC22×C32C22×D4
prime radicalC2×#64128C2
cosocleC2×C32×C4C24
hypercenterC4×Q16C3⋊D3
hypocenterC32#2951
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. #10596045C2semidirect
3. C32×C4×Q16C2semidirect
4. Q16×C3⋊Dic3C2semidirect
5. #10592725C2semidirect
6. C3⋊D3×#107C2semidirect
7. #10592571C2semidirect
8. #10592516C2semidirect
9. #10592502C2semidirect
10. C4×#3745C2semidirect
11. #10592388C2semidirect
18. #64128C4semidirect
43. C3×C4×Q16D3semidirect
54. #3832C2×C4semidirect
62. C32×Q16C2×C4semidirect
69. #3755C2×C4semidirect
83. #3745C2×C4semidirect
85. C8×C3⋊D3C2×C4semidirect
146. C4×Q16C3⋊D3semidirect
162. C3×Q16C4×D3semidirect
272. Q16C4×C3⋊D3semidirect
313. C32#2951semidirect
362. C3#79721semidirect

Maximal subgroups

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

subgroupindex
C2×#641282
#105960452
C32×C4×Q162
Q16×C3⋊Dic32
#105927252
C3⋊D3×#1072
#105925712
#105925162
#105925022
C4×#37452
#105923882
#797213