Finite Group Databasebeta

← #11901192

Subgroups — #11901192

Order 1152.

4668 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C212yesmaximal, complemented
2C2×C32×#117C211yesmaximal, characteristic, complemented
3#10595997C214yesmaximal, complemented
4#10595996C214yesmaximal, complemented
5#10595995C218yesmaximal, complemented
6#10595981C214yesmaximal, complemented
7#10595964C214yesmaximal, complemented
8#10595948C214yesmaximal, complemented
9#85735—34nomaximal
10C23×C32×C4C2211yescharacteristic
11C22×#638C2214yes—
12C2×#3828—216no—
13C2×#3828C2214yes—
14C2×#3828C2214yes—
15C2×#3828C2214yescomplemented
16C2×#3828C2214yescomplemented
17C22×C4⋊(C3⋊D3)C2212yescomplemented
18C22×C4×C3⋊D3C2214yescomplemented
19C22×#634C2212yescomplemented
20C32×#117C2214yescomplemented
21C32×#117C2214yescomplemented
22C2×C32×C4⋊C4C2212yescomplemented
23C2×C32×C22⋊C4C2212yes—
24C2×C32×C42C2212yescomplemented
25#64139C22116yescomplemented
26#64106C22116yescomplemented
27#64104C22116yescomplemented
28#64095C22116yescomplemented
29#64091C22116yescomplemented
30#64084C2218yescomplemented
31#64083C2214yescomplemented
32C4×C4⋊(C3⋊D3)C22116yescomplemented
33#64078C2214yescomplemented
34C22×#235—38no—
35C2×C3×#117D314yescomplemented
36#5526—316no—
37#5525—316no—
38#5524—332no—
39#5510—316no—
40#5493—316no—
41#5477—316no—
42C24×C32C2311yescharacteristic
43C23×C3⋊D3C2314yes—
44C22×C32×C4D418yescomplemented
45C22×C32×C4C2314yes—
46C22×C32×C4C2312yes—
47C22×C32×C4C2312yes—
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C2×#638—216no—
51C2×#638C2318yes—
52C2×#638C2318yes—
53C22×C3⋊Dic3C2314yes—
54#3828—216no—
55#3828—216no—
56#3828—216no—
57#3828—216no—
58C2×C4⋊(C3⋊D3)—28no—
59C2×C4⋊(C3⋊D3)C2314yes—
60C2×C4⋊(C3⋊D3)C2314yes—
61C2×C4⋊(C3⋊D3)C23116yes—
62C2×C4×C3⋊D3—216no—
63C2×C4×C3⋊D3C2318yes—
64C2×C4×C3⋊D3C2318yes—
65C2×#634—28no—
66C2×#634C2314yes—
67C2×#634C2314yes—
68C32×C4⋊C4C2318yes—
69C32×C22⋊C4C2318yes—
70C32×C42C2314yes—
71C32×C42C2314yes—
72#3752C23132yes—
73C4⋊(C3⋊Dic3)C23116yes—
74#3449—91noSylow
75C23×C3×C4C2×D314yes—
76C22×#67—316no—
77C2×#235—316no—
78C2×#235—316no—
79C2×#235—316no—
80C2×#235—316no—
81C2×#235—664no—
82C22×D12—38no—
83C22×C4×D3—316no—
84C22×Dic6—38no—
85C3×#117C2×D3116yescomplemented
86C3×#117C2×D3116yescomplemented
87C2×C3×C4⋊C4C2×D318yescomplemented
88C2×C3×C22⋊C4C2×D318yes—
89C2×C3×C42C2×D318yescomplemented
90#930—364no—
91#897—364no—
92#895—364no—
93#886—364no—
94#882—364no—
95#875—332no—
96#874—316no—
97C4×D12—364no—
98#869—316no—
99C23×C32—42no—
100C23×C32C2×D414yes—
101C23×C32C2412yes—
102C23×C32C2411yescharacteristic
103C22×C3⋊D3—28no—
104C22×C3⋊D3—48no—
105C22×C3⋊D3C2418yes—
106C2×C32×C4—44no—
107C2×C32×C4C2×D418yes—
108C2×C32×C4C2×D418yes—
109C2×C32×C4C2×D414yes—
110C2×C32×C4C2×D414yes—
111C2×C32×C4C2418yes—
112C2×C32×C4C2411yescharacteristic
113C2×C32×C4C2411yescharacteristic
114C2×C32×C4C2412yes—
115#638—216no—
116#638—216no—
117C2×C3⋊Dic3—28no—
118C2×C3⋊Dic3C2418yes—
119C4⋊(C3⋊D3)—28no—
120C4⋊(C3⋊D3)—28no—
121C4⋊(C3⋊D3)—416no—
122C4×C3⋊D3—216no—
123C4×C3⋊D3—216no—
124#634—28no—
125#634—28no—
126C22×#41—92no—
127#537—94no—
128#536—94no—
129#535—94no—
130#534—94no—
131#532—94no—
132#525—98no—
133C2×#117C3⋊D311yescharacteristic, complemented
134C24×C3C22×D314yes—
135C23×D3—316no—
136C22×C3×C4D12132yescomplemented
137C22×C3×C4C22×D3116yes—
138C22×C3×C4C22×D314yes—
139C22×C3×C4C22×D314yes—
140C22×C3×C4C22×D318yes—
141C22×C3×C4C22×D318yes—
142C2×#67—332no—
143C2×#67—332no—
144C2×#67—664no—
145C22×Dic3—316no—
146#235—664no—
147#235—664no—
148#235—664no—
149#235—664no—
150C2×D12—316no—
151C2×D12—316no—
152C2×D12—364no—
153C2×D12—632no—
154C2×C4×D3—332no—
155C2×C4×D3—332no—
156C2×C4×D3—664no—
157C2×Dic6—316no—
158C2×Dic6—316no—
159C2×Dic6—632no—
160C3×C4⋊C4C22×D3132yes—
161C3×C22⋊C4C22×D3132yes—
162C3×C42C22×D3116yes—
163C3×C42C22×D3116yes—
164(C2×D3)⋊C4—3128no—
165C4⋊Dic3—364no—
166C22×C32—22no—
167C22×C32—24no—
168C22×C32—44no—
169C22×C32C22×D414yes—
170C22×C32C22×D412yes—
171C22×C32C2511yescharacteristic
172C2×C3⋊D3—28no—
173C2×C3⋊D3—216no—
174C2×C3⋊D3—416no—
175C32×C4—28no—
176C32×C4C22×D412yes—
177C32×C4C22×D414yes—
178C32×C4C22×D412yes—
179C3⋊Dic3—28no—
180C2×#41—94no—
181C2×#41—94no—
182C2×#41—94no—
183C2×#41—94no—
184C2×#41—1816no—
185C22×Q8—92no—
186C22×D4—94no—
187C22×D4—92no—
188C23×C4—94no—
189C23×C4C2×C3⋊D311yescharacteristic
190C4⋊Q8—94no—
191#127—94no—
192#124—98no—
193#123—916no—
194C22⋊Q8—916no—
195#121—916no—
196#121—916no—
197#120—916no—
198C4×D4—916no—
199#117C2×C3⋊D314yescomplemented
200#117C2×C3⋊D314yescomplemented
201C2×C4⋊C4C2×C3⋊D312yescomplemented
202C2×C22⋊C4C2×C3⋊D312yes—
203C2×C42C2×C3⋊D312yescomplemented
204C23×C3—48no—
205C23×C3C2×D12116yes—
206C23×C3C23×D318yes—
207C23×C3C23×D314yes—
208C22×D3—332no—
209C22×D3—632no—
210C22×D3—1232no—
211C2×C3×C4—416no—
212C2×C3×C4C2×D12132yes—
213C2×C3×C4C2×D12132yes—
214C2×C3×C4C2×D12116yes—
215C2×C3×C4C2×D12116yes—
216C2×C3×C4C23×D3132yes—
217C2×C3×C4C23×D314yes—
218C2×C3×C4C23×D318yes—
219C2×C3×C4C23×D314yes—
220#67—664no—
221#67—664no—
222C2×Dic3—332no—
223C2×Dic3—632no—
224D12—632no—
225D12—632no—
226D12—1264no—
227C4×D3—664no—
228C4×D3—664no—
229Dic6—632no—
230Dic6—632no—
231C2×C32—24no—
232C2×C32—22no—
233C2×C32C23×D411yescharacteristic
234C2×C32#58512yes—
235C3⋊D3—48no—
236C24—94no—
237C24C22×C3⋊D311yescharacteristic
238#41—1816no—
239#41—1816no—
240#41—1816no—
241#41—1816no—
242C2×Q8—94no—
243C2×Q8—94no—
244C2×Q8—188no—
245C2×D4—98no—
246C2×D4—98no—
247C2×D4—94no—
248C2×D4—94no—
249C2×D4—916no—
250C2×D4—1816no—
251C2×D4—188no—
252C22×C4—94no—
253C22×C4—98no—
254C22×C4—98no—
255C22×C4—1816no—
256C22×C4C4⋊(C3⋊D3)18yescomplemented
257C22×C4C22×C3⋊D314yes—
258C22×C4C22×C3⋊D311yescharacteristic
259C22×C4C22×C3⋊D312yes—
260C22×C4C22×C3⋊D311yescharacteristic
261C22×C4C22×C3⋊D312yes—
262C4⋊C4—916no—
263C4⋊C4C22×C3⋊D318yes—
264C22⋊C4—932no—
265C22⋊C4C22×C3⋊D318yes—
266C42C22×C3⋊D314yes—
267C42C22×C3⋊D314yes—
268C22×C3—28no—
269C22×C3—216no—
270C22×C3—416no—
271C22×C3C22×D12116yes—
272C22×C3C22×D1218yes—
273C22×C3C24×D314yes—
274C2×D3—632no—
275C2×D3—664no—
276C2×D3—1264no—
277C3×C4—232no—
278C3×C4C22×D1218yes—
279C3×C4C22×D12116yes—
280C3×C4C22×D1218yes—
281Dic3—632no—
282C32#344911yescharacteristic, complemented, Sylow
283C23—42no—
284C23—98no—
285C23—188no—
286C23—368no—
287C23C2×C4⋊(C3⋊D3)14yes—
288C23C23×C3⋊D312yes—
289C23C23×C3⋊D311yescharacteristic
290Q8—188no—
291Q8—188no—
292D4—1816no—
293D4—1816no—
294D4—188no—
295D4—188no—
296D4—3616no—
297C2×C4—44no—
298C2×C4—98no—
299C2×C4—188no—
300C2×C4—1816no—
301C2×C4—1816no—
302C2×C4C2×C4⋊(C3⋊D3)18yes—
303C2×C4C2×C4⋊(C3⋊D3)18yes—
304C2×C4C2×C4⋊(C3⋊D3)14yes—
305C2×C4C2×C4⋊(C3⋊D3)14yes—
306C2×C4C23×C3⋊D318yes—
307C2×C4C23×C3⋊D311yescharacteristic
308C2×C4C23×C3⋊D312yes—
309C2×C4C23×C3⋊D311yescharacteristic
310C2×C3—216no—
311C2×C3—28no—
312C2×C3C23×D1214yes—
313C2×C3#596418yes—
314D3—1232no—
315C22—22no—
316C22—24no—
317C22—44no—
318C22—188no—
319C22—1816no—
320C22—3616no—
321C22C22×C4⋊(C3⋊D3)14yes—
322C22C22×C4⋊(C3⋊D3)12yes—
323C22C24×C3⋊D311yescharacteristic
324C4—28no—
325C4—188no—
326C4C22×C4⋊(C3⋊D3)12yes—
327C4C22×C4⋊(C3⋊D3)14yes—
328C4C22×C4⋊(C3⋊D3)12yes—
329C3#8573514yescomplemented
330C2—24no—
331C2—22no—
332C2—368no—
333C2C23×C4⋊(C3⋊D3)11yescharacteristic
334C2#1059675612yes—
subgroupG/H
centerC2×C4C23×C3⋊D3
commutator, socle, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×#117C2
hypercenterC2×#117C3⋊D3
hypocenterC32#3449
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C2×C32×#117C2semidirect
3. #10595997C2semidirect
4. #10595996C2semidirect
5. #10595995C2semidirect
6. #10595981C2semidirect
7. #10595964C2semidirect
8. #10595948C2semidirect
15. C2×#3828C22semidirect
16. C2×#3828C22semidirect
17. C22×C4⋊(C3⋊D3)C22semidirect
18. C22×C4×C3⋊D3C22semidirect
19. C22×#634C22semidirect
20. C32×#117C22semidirect
21. C32×#117C22semidirect
22. C2×C32×C4⋊C4C22semidirect
24. C2×C32×C42C22semidirect
25. #64139C22semidirect
26. #64106C22semidirect
27. #64104C22semidirect
28. #64095C22semidirect
29. #64091C22semidirect
30. #64084C22semidirect
31. #64083C22semidirect
32. C4×C4⋊(C3⋊D3)C22semidirect
33. #64078C22semidirect
35. C2×C3×#117D3semidirect
44. C22×C32×C4D4semidirect
85. C3×#117C2×D3semidirect
86. C3×#117C2×D3semidirect
87. C2×C3×C4⋊C4C2×D3semidirect
89. C2×C3×C42C2×D3semidirect
133. C2×#117C3⋊D3semidirect
136. C22×C3×C4D12semidirect
199. #117C2×C3⋊D3semidirect
200. #117C2×C3⋊D3semidirect
201. C2×C4⋊C4C2×C3⋊D3semidirect
203. C2×C42C2×C3⋊D3semidirect
256. C22×C4C4⋊(C3⋊D3)semidirect
282. C32#3449semidirect
329. C3#85735semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C2×C32×#1172
#105959972
#105959962
#105959952
#105959812
#105959642
#105959482
#857353