Finite Group Databasebeta

← #11878934

Subgroups — #11878934

Order 1152.

1182 conjugacy classes of subgroups.

The subgroup lattice has 339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#533C211yesmaximal, characteristic, complemented
2#10595948C211yesmaximal, characteristic
3#10592792C211yesmaximal, characteristic, complemented
4#10592791C211yesmaximal, characteristic, complemented
5#10592787C211yesmaximal, characteristic, complemented
6#10592784C211yesmaximal, characteristic, complemented
7#10592746C214yesmaximal, complemented
8#10592727C214yesmaximal, complemented
9#10592624C211yesmaximal, characteristic, complemented
10#83356—34nomaximal
11C2×#3828C2212yes—
12C32×C4⋊Q8C2211yescharacteristic
13C32×C4⋊Q8C2211yescharacteristic
14C32×#125—21no—
15C32×C22⋊Q8—21no—
16C32×C22⋊Q8C2212yes—
17C32×C4×Q8—21no—
18C32×C4×Q8C2212yes—
19C32×#117—21no—
20C2×C32×C42C2211yescharacteristic
21C2×#3756C2214yes—
22C2×#3755C2214yes—
23#64139—21no—
24#64139—21no—
25#64084C2212yes—
26#64083C2211yescharacteristic
27C4×C4⋊(C3⋊D3)—21no—
28C4×C4⋊(C3⋊D3)—21no—
29#64078C2211yescharacteristic
30#63657C2212yes—
31#63637C2214yes—
32#63636C2214yes—
33C4⋊(C3⋊(C3⋊C8))C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C4×C3⋊(C3⋊C8)C2211yescharacteristic
36C3×#533D314yescomplemented
37#5477—34no—
38#5093—34no—
39#5092—34no—
40#5088—34no—
41#5085—34no—
42#5047—316no—
43#5028—316no—
44#4925—34no—
45C2×C32×Q8—21no—
46C2×C32×Q8C2312yes—
47C22×C32×C4D411yescharacteristic
48C22×C32×C4D411yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C2×#638—22no—
51#3828—44no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)C2312yes—
55C2×C4×C3⋊D3—22no—
56C2×#634C2312yes—
57C32×C4⋊C4—21no—
58C32×C4⋊C4—21no—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—22no—
61C32×C4⋊C4—22no—
62C32×C4⋊C4C2312yes—
63C32×C22⋊C4—22no—
64C32×C42—22no—
65C32×C42D411yescharacteristic
66C32×C42D411yescharacteristic
67C32×C42C2311yescharacteristic
68C32×C42C2311yescharacteristic
69#3756—44no—
70#3755—44no—
71#3752—22no—
72#3752—22no—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)—21no—
75C2×C3⋊(C3⋊C8)C2312yes—
76C2×C3⋊(C3⋊C8)C2312yes—
77#3210—91noSylow
78C2×#235—38no—
79C3×C4⋊Q8C2×D314yes—
80C3×C4⋊Q8C2×D314yes—
81C3×#125—24no—
82C3×C22⋊Q8—24no—
83C3×C22⋊Q8C2×D318yes—
84C3×C4×Q8—24no—
85C3×C4×Q8C2×D318yes—
86C3×#117—24no—
87C2×C3×C42C2×D314yes—
88C2×#216—316no—
89C2×#215—316no—
90#930—64no—
91#930—64no—
92#875—38no—
93#874—34no—
94C4×D12—64no—
95C4×D12—64no—
96#869—34no—
97#830—38no—
98#810—316no—
99#809—316no—
100C4⋊(C3⋊C8)—38no—
101C4×C3⋊C8—34no—
102C4×C3⋊C8—34no—
103C23×C32C2×D411yescharacteristic
104C22×C3⋊D3—22no—
105C32×Q8—24no—
106C32×Q8—42no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2411yescharacteristic
118#638—44no—
119C2×C3⋊Dic3—22no—
120C4⋊(C3⋊D3)—24no—
121C4⋊(C3⋊D3)—42no—
122C4⋊(C3⋊D3)—42no—
123C4×C3⋊D3—44no—
124#634—24no—
125C3⋊(C3⋊C8)—22no—
126C3⋊(C3⋊C8)—22no—
127#533C3⋊D311yescharacteristic, complemented
128#532—91no—
129#494—91no—
130#492—91no—
131#487—91no—
132#486—91no—
133#464—94no—
134#452—94no—
135#431—91no—
136C2×C3×Q8—24no—
137C2×C3×Q8C22×D318yes—
138C22×C3×C4#6714yes—
139C22×C3×C4#6714yes—
140C22×C3×C4C22×D314yes—
141C2×#67—68no—
142#235—1216no—
143C2×D12—38no—
144C2×D12—64no—
145C2×D12—64no—
146C2×C4×D3—68no—
147C2×Dic6—38no—
148C3×C4⋊C4—24no—
149C3×C4⋊C4—24no—
150C3×C4⋊C4—24no—
151C3×C4⋊C4—28no—
152C3×C4⋊C4—28no—
153C3×C4⋊C4C22×D318yes—
154C3×C22⋊C4—28no—
155C3×C42—28no—
156C3×C42#6714yes—
157C3×C42#6714yes—
158C3×C42C22×D314yes—
159C3×C42C22×D314yes—
160#216—1216no—
161#215—1216no—
162(C2×D3)⋊C4—68no—
163(C2×D3)⋊C4—68no—
164C4⋊Dic3—64no—
165C4⋊Dic3—64no—
166C2×C3⋊C8—38no—
167C2×C3⋊C8—38no—
168C22×C32—21no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32C22×D411yescharacteristic
172C2×C3⋊D3—42no—
173C2×C3⋊D3—42no—
174C2×C3⋊D3—42no—
175C32×C4—21no—
176C32×C4—21no—
177C32×C4—21no—
178C32×C4—42no—
179C32×C4—42no—
180C32×C4#13512yes—
181C32×C4#13712yes—
182C32×C4H(5,𝔽2)12yes—
183C3⋊Dic3—42no—
184C2×#41—92no—
185C2×Q16—94no—
186C2×SD16—94no—
187C4⋊Q8—91no—
188C4⋊Q8C2×C3⋊D311yescharacteristic
189C4⋊Q8C2×C3⋊D311yescharacteristic
190#127—91no—
191#125—21no—
192#124—92no—
193C22⋊Q8—21no—
194C22⋊Q8C2×C3⋊D312yes—
195#121—181no—
196#121—181no—
197C4×Q8—21no—
198C4×Q8C2×C3⋊D312yes—
199C4×D4—181no—
200C4×D4—181no—
201#117—21no—
202C2×C42C2×C3⋊D311yescharacteristic
203C4⋊C8—92no—
204#103—94no—
205#102—94no—
206C22⋊C8—92no—
207C4×C8—91no—
208C4×C8—91no—
209C23×C3C2×#6714yes—
210C22×D3—68no—
211C3×Q8—216no—
212C3×Q8—48no—
213C2×C3×C4—28no—
214C2×C3×C4—28no—
215C2×C3×C4—28no—
216C2×C3×C4—28no—
217C2×C3×C4—28no—
218C2×C3×C4C2×#6714yes—
219C2×C3×C4C2×#6714yes—
220C2×C3×C4C2×#6714yes—
221C2×C3×C4C2×#6714yes—
222C2×C3×C4C2×#6714yes—
223C2×C3×C4C23×D314yes—
224#67—1216no—
225C2×Dic3—68no—
226D12—616no—
227D12—128no—
228D12—128no—
229C4×D3—1216no—
230Dic6—616no—
231C3⋊C8—68no—
232C3⋊C8—68no—
233C2×C32—41no—
234C2×C32#53511yescharacteristic
235C2×C32C2×#13511yescharacteristic
236C2×C32C2×#13711yescharacteristic
237C3⋊D3—82no—
238#41—364no—
239C2×Q8—21no—
240C2×Q8—92no—
241C2×Q8C22×C3⋊D312yes—
242C2×D4—92no—
243C2×D4—182no—
244C2×D4—181no—
245C2×D4—181no—
246C22×C4—182no—
247C22×C4#63811yescharacteristic
248C22×C4#63811yescharacteristic
249C22×C4C22×C3⋊D311yescharacteristic
250Q16—364no—
251SD16—364no—
252C2×C8—92no—
253C2×C8—92no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—181no—
260C4⋊C4—181no—
261C4⋊C4C22×C3⋊D312yes—
262C22⋊C4—22no—
263C22⋊C4—182no—
264C22⋊C4—182no—
265C42—22no—
266C42#63811yescharacteristic
267C42#63811yescharacteristic
268C42C22×C3⋊D311yescharacteristic
269C42C22×C3⋊D311yescharacteristic
270C22×C3—24no—
271C22×C3—24no—
272C22×C3—24no—
273C22×C3C22×#6714yes—
274C2×D3—128no—
275C2×D3—128no—
276C2×D3—128no—
277C3×C4—24no—
278C3×C4—24no—
279C3×C4—24no—
280C3×C4—48no—
281C3×C4—48no—
282C3×C4#94218yes—
283C3×C4#95018yes—
284C3×C4#100918yes—
285Dic3—128no—
286C32#321011yescharacteristic, complemented, Sylow
287C23—182no—
288C23C2×#63811yescharacteristic
289Q8—24no—
290Q8—42no—
291Q8—184no—
292D4—184no—
293D4—364no—
294D4—362no—
295D4—362no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—182no—
302C2×C4—364no—
303C2×C4C2×#63811yescharacteristic
304C2×C4C2×#63811yescharacteristic
305C2×C4C2×#63811yescharacteristic
306C2×C4C2×#63811yescharacteristic
307C2×C4C2×#63811yescharacteristic
308C2×C4C23×C3⋊D311yescharacteristic
309C8—182no—
310C8—182no—
311C2×C3—44no—
312C2×C3C2×#94214yes—
313C2×C3C2×#95014yes—
314C2×C3#583014yes—
315D3—248no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—362no—
320C22—362no—
321C22—362no—
322C22C22×#63811yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—42no—
328C4—362no—
329C4#6415112yes—
330C4#6415912yes—
331C4#6436612yes—
332C3#8335614yescomplemented
333C2—41no—
334C2—722no—
335C2C2×#6415111yescharacteristic
336C2C2×#6415911yescharacteristic
337C2#1059630111yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#533C2
socleC22×C32C22×D4
prime radical#10595948C2
hypercenter#533C3⋊D3
hypocenterC32#3210
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C32×#533C2semidirect
3. #10592792C2semidirect
4. #10592791C2semidirect
5. #10592787C2semidirect
6. #10592784C2semidirect
7. #10592746C2semidirect
8. #10592727C2semidirect
9. #10592624C2semidirect
36. C3×#533D3semidirect
127. #533C3⋊D3semidirect
286. C32#3210semidirect
332. C3#83356semidirect

Maximal subgroups

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

subgroupindex
C32×#5332
#105959482
#105927922
#105927912
#105927872
#105927842
#105927462
#105927272
#105926242
#833563