Finite Group Databasebeta

← #11860919

Subgroups — #11860919

Order 1152.

1452 conjugacy classes of subgroups.

The subgroup lattice has 345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64128C211yesmaximal, characteristic
2#10596045C212yesmaximal, complemented
3C32×#441C211yesmaximal, characteristic, complemented
4#10592883C211yesmaximal, characteristic, complemented
5C4×#3755C212yesmaximal, complemented
6#10592568C211yesmaximal, characteristic, complemented
7C3⋊D3×#106C211yesmaximal, characteristic, complemented
8#10592502C212yesmaximal, complemented
9#10592487C212yesmaximal, complemented
10#10592410C211yesmaximal, characteristic, complemented
11#10592407C211yesmaximal, characteristic, complemented
12#79832—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×#106C2211yescharacteristic
31C32×#103C2212yes—
32C32×#97C2211yescharacteristic
33#63662C2212yes—
34#63648C2212yes—
35#63644C2211yescharacteristic
36#63642C2211yescharacteristic
37C8×C3⋊Dic3C2211yescharacteristic
38#63636C2212yes—
39#63635C2212yes—
40C4×C3⋊(C3⋊C8)C2211yescharacteristic
41C2×#919—34no—
42#5574—38no—
43C3×#441D314yescomplemented
44#5184—34no—
45C4×#215—38no—
46#4869—34no—
47D3×#106—34no—
48#4803—38no—
49#4788—38no—
50#4711—34no—
51#4708—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#3752D412yes—
73C4⋊(C3⋊Dic3)—22no—
74C4⋊(C3⋊Dic3)C2312yes—
75#3750—22no—
76#3750D412yes—
77C4×C3⋊Dic3—22no—
78C4×C3⋊Dic3C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81#3745C2×C414yescomplemented
82#3743—22no—
83C8×C3⋊D3C2×C414yescomplemented
84#2952—91noSylow
85C2×#239—38no—
86C2×C3×Q16C2×D314yes—
87C3×C4×Q8C2×D318yes—
88Q8×Dic3—38no—
89C2×#215—38no—
90#919—332no—
91C2×D24—34no—
92C2×ΓL(1,𝔽25)—34no—
93C2×D3×C8—34no—
94#893—38no—
95#893—68no—
96D3×C4⋊C4—38no—
97D3×C4⋊C4—68no—
98C4×D12—38no—
99C4×D12—68no—
100#872—34no—
101#872—68no—
102C3×#106C2×D314yes—
103C3×#103C2×D318yes—
104C3×#97C2×D314yes—
105#835—38no—
106#821—38no—
107#817—34no—
108#815—34no—
109C8×Dic3—34no—
110#809—38no—
111#808—38no—
112C4×C3⋊C8—34no—
113C22×C3⋊D3—22no—
114C22×C3⋊D3C2×D411yescharacteristic
115C32×Q8—22no—
116C32×Q8C22×C414yes—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4C2×D412yes—
120C2×C32×C4C2411yescharacteristic
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3C2×D412yes—
123C2×C3⋊Dic3C2×D411yescharacteristic
124C4⋊(C3⋊D3)—28no—
125C4⋊(C3⋊D3)—22no—
126C4⋊(C3⋊D3)C22×C414yes—
127C4×C3⋊D3—28no—
128C4×C3⋊D3—82no—
129C4×C3⋊D3—82no—
130C4×C3⋊D3—82no—
131C4×C3⋊D3C22×C412yes—
132C4×C3⋊D3#4112yes—
133C32×C8—21no—
134C32×C8C22×C412yes—
135C3⋊(C3⋊C8)—21no—
136C3⋊(C3⋊C8)C22×C412yes—
137C2×#135—91no—
138#520—92no—
139#442—91no—
140#442—91no—
141#441—91no—
142#441C3⋊D311yescharacteristic, complemented
143C4×SD16—92no—
144C4×SD16—92no—
145C2×#106—91no—
146#417—92no—
147#405—91no—
148C2×C3×Q8C22×D318yes—
149#239—332no—
150#239—616no—
151C2×D12—38no—
152C2×D12—68no—
153C2×C4×D3—34no—
154C2×C4×D3—68no—
155C2×C4×D3—68no—
156C2×C4×D3—68no—
157C2×C4×D3—68no—
158C3×Q16C4×D3116yescomplemented
159C2×C3×C8C22×D314yes—
160C2×C3×C8C22×D314yes—
161C3×C4⋊C4—28no—
162C3×C4⋊C4C22×D318yes—
163C3×C42—28no—
164C3×C42C22×D314yes—
165#215—332no—
166(C2×D3)⋊C4—38no—
167(C2×D3)⋊C4—68no—
168(C2×D3)⋊C4—68no—
169C4⋊Dic3—38no—
170C4⋊Dic3—68no—
171Dic3⋊C4—38no—
172Dic3⋊C4—68no—
173C4×Dic3—34no—
174C4×Dic3—68no—
175C2×C3⋊C8—34no—
176C2×C3⋊C8—34no—
177D24—316no—
178ΓL(1,𝔽25)—68no—
179D3×C8—316no—
180C22×C32C22×D411yescharacteristic
181C2×C3⋊D3—22no—
182C2×C3⋊D3—24no—
183C2×C3⋊D3—42no—
184C2×C3⋊D3—42no—
185C2×C3⋊D3C4×D412yes—
186C32×C4—24no—
187C32×C4—22no—
188C32×C4—42no—
189C32×C4C23×C411yescharacteristic
190C32×C4C2×#4111yescharacteristic
191C3⋊Dic3—22no—
192C3⋊Dic3—42no—
193C3⋊Dic3C4×D412yes—
194C2×#41—92no—
195#135—98no—
196C2×Q16C2×C3⋊D311yescharacteristic
197C2×SD16—92no—
198C2×D8—91no—
199C2×M16—91no—
200C22×C8—91no—
201C4×Q8—92no—
202C4×Q8C2×C3⋊D312yes—
203C4×D4—92no—
204C4×D4—92no—
205C4×D4—182no—
206C4×D4—182no—
207#117—91no—
208#117—182no—
209C2×C4⋊C4—92no—
210C2×C4⋊C4—182no—
211#106—91no—
212#106—92no—
213#106C2×C3⋊D311yescharacteristic
214#103—92no—
215#103C2×C3⋊D312yes—
216#102—92no—
217#102—92no—
218#97—91no—
219#97C2×C3⋊D311yescharacteristic
220C4×C8—91no—
221C4×C8—91no—
222C22×D3—34no—
223C22×D3—68no—
224C3×Q8—28no—
225C3×Q8C2×C4×D3116yes—
226C2×C3×C4—28no—
227C2×C3×C4—28no—
228C2×C3×C4D3×D418yes—
229C2×C3×C4C23×D314yes—
230C2×Dic3—34no—
231C2×Dic3—38no—
232C2×Dic3—68no—
233D12—316no—
234D12—632no—
235D12—68no—
236C4×D3—38no—
237C4×D3—38no—
238C4×D3—632no—
239C4×D3—248no—
240C4×D3—248no—
241C4×D3—248no—
242C3×C8—24no—
243C3×C8C2×C4×D318yes—
244C3⋊C8—38no—
245C3⋊C8—64no—
246C2×C32C2×C4×D411yescharacteristic
247C2×C32#57712yes—
248C3⋊D3—22no—
249C3⋊D3—44no—
250#41—98no—
251#41—184no—
252C2×Q8C22×C3⋊D312yes—
253C2×D4—92no—
254C2×D4—182no—
255C22×C4—91no—
256C22×C4—182no—
257C22×C4—182no—
258C22×C4—182no—
259C22×C4—182no—
260Q16C4×C3⋊D314yescomplemented
261SD16—98no—
262D8—94no—
263M16—182no—
264C2×C8—91no—
265C2×C8—94no—
266C2×C8—91no—
267C2×C8C22×C3⋊D311yescharacteristic
268C2×C8C22×C3⋊D311yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—92no—
271C4⋊C4—92no—
272C4⋊C4—182no—
273C4⋊C4—182no—
274C4⋊C4C22×C3⋊D312yes—
275C22⋊C4—92no—
276C22⋊C4—182no—
277C22⋊C4—182no—
278C42—22no—
279C42—91no—
280C42—182no—
281C42C22×C3⋊D311yescharacteristic
282C22×C3C2×D3×D414yes—
283C2×D3—38no—
284C2×D3—68no—
285C2×D3—616no—
286C2×D3—128no—
287C2×D3—128no—
288C3×C4—28no—
289C3×C4—216no—
290C3×C4—48no—
291C3×C4C22×C4×D314yes—
292C3×C4D3×#4114yes—
293Dic3—38no—
294Dic3—68no—
295Dic3—128no—
296C32#295211yescharacteristic, complemented, Sylow
297C23—91no—
298C23—182no—
299Q8—22no—
300Q8C2×C4×C3⋊D314yes—
301D4—94no—
302D4—188no—
303D4—182no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—91no—
307C2×C4—92no—
308C2×C4—92no—
309C2×C4—92no—
310C2×C4—188no—
311C2×C4—182no—
312C2×C4—722no—
313C2×C4—722no—
314C2×C4—722no—
315C2×C4D4×C3⋊D312yes—
316C2×C4C23×C3⋊D311yescharacteristic
317C8—21no—
318C8—92no—
319C8—181no—
320C8C2×C4×C3⋊D312yes—
321C2×C3C4×D3×D414yes—
322C2×C3#577818yes—
323D3—68no—
324D3—1216no—
325C22—92no—
326C22—182no—
327C22—184no—
328C22—362no—
329C22—362no—
330C22C2×D4×C3⋊D311yescharacteristic
331C4—22no—
332C4—24no—
333C4—42no—
334C4—92no—
335C4—182no—
336C4—362no—
337C4C22×C4×C3⋊D311yescharacteristic
338C4#41×C3⋊D311yescharacteristic
339C3#7983214yescomplemented
340C2—182no—
341C2—364no—
342C2C4×D4×C3⋊D311yescharacteristic
343C2#1059624912yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#441C2
socleC22×C32C22×D4
prime radicalC2×#64128C2
cosocleC2×C32×C4C24
hypercenter#441C3⋊D3
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. #10596045C2semidirect
3. C32×#441C2semidirect
4. #10592883C2semidirect
5. C4×#3755C2semidirect
6. #10592568C2semidirect
7. C3⋊D3×#106C2semidirect
8. #10592502C2semidirect
9. #10592487C2semidirect
10. #10592410C2semidirect
11. #10592407C2semidirect
18. #64128C4semidirect
43. C3×#441D3semidirect
54. #3832C2×C4semidirect
62. C32×Q16C2×C4semidirect
69. #3755C2×C4semidirect
81. #3745C2×C4semidirect
83. C8×C3⋊D3C2×C4semidirect
142. #441C3⋊D3semidirect
158. C3×Q16C4×D3semidirect
260. Q16C4×C3⋊D3semidirect
296. C32#2952semidirect
339. C3#79832semidirect

Maximal subgroups

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

subgroupindex
C2×#641282
#105960452
C32×#4412
#105928832
C4×#37552
#105925682
C3⋊D3×#1062
#105925022
#105924872
#105924102
#105924072
#798323