Finite Group Databasebeta

← #11895463

Subgroups — #11895463

Order 1152.

1008 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
1#10596193C211yesmaximal, characteristic
2#10596038C211yesmaximal, characteristic
3C32×#477C211yesmaximal, characteristic
4#10592792C211yesmaximal, characteristic
5C4×#3756C211yesmaximal, characteristic
6#10592574C212yesmaximal
7#10592572C212yesmaximal
8#10592548C211yesmaximal, characteristic
9#10592529C211yesmaximal, characteristic
10#10592494C212yesmaximal
11#10592491C212yesmaximal
12#81138—34nomaximal
13C32×C4⋊Q8C2211yescharacteristic
14C32×C4×Q8C2211yescharacteristic
15#64153—22no—
16#64153C2212yes—
17C2×#3756C2211yescharacteristic
18C2×#3746C2212yes—
19#64098—22no—
20#64097—21no—
21#64097C2212yes—
22#64096—21no—
23#64096C2212yes—
24#64096C2212yes—
25#64079—21no—
26#64078C2211yescharacteristic
27C4×#634—21no—
28C4×#634C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×#107C2212yes—
31C32×C4⋊C8C2211yescharacteristic
32C32×#103C2212yes—
33#63662C2211yescharacteristic
34#63643C2212yes—
35#63641C2212yes—
36C8×C3⋊Dic3C2212yes—
37#63637C2212yes—
38#63637C2212yes—
39#63637C2211yescharacteristic
40#63634C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5722—34no—
43#5567—34no—
44C3×#477D314yes—
45#5093—34no—
46C4×#216—34no—
47#4875—38no—
48#4873—38no—
49#4849—34no—
50#4830—34no—
51#4795—38no—
52#4792—38no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2311yescharacteristic
55C2×#634—22no—
56C2×#634D411yescharacteristic
57C2×#634C2312yes—
58C2×#634C2311yescharacteristic
59C2×C32×C8C2312yes—
60C32×C4⋊C4—21no—
61C32×C4⋊C4—21no—
62C32×C4⋊C4C2311yescharacteristic
63C32×C4⋊C4C2312yes—
64C32×C42—21no—
65C32×C42C2311yescharacteristic
66#3756—22no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)D411yescharacteristic
70C4⋊(C3⋊Dic3)C2311yescharacteristic
71#3750—21no—
72#3750—22no—
73#3750—22no—
74#3750—22no—
75#3750—22no—
76#3750—22no—
77#3750D412yes—
78C4×C3⋊Dic3—21no—
79C4×C3⋊Dic3—22no—
80C4×C3⋊Dic3—22no—
81C4×C3⋊Dic3C2312yes—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84#3746—24no—
85#3363—91noSylow
86C3×C4⋊Q8C2×D314yes—
87C3×C4×Q8C2×D314yes—
88#944—38no—
89#944—68no—
90C2×#216—34no—
91C2×Dic12—38no—
92#889—68no—
93#888—38no—
94#888—64no—
95#887—38no—
96#887—38no—
97#887—64no—
98#870—64no—
99#869—34no—
100C4×Dic6—34no—
101C4×Dic6—34no—
102C4×Dic6—64no—
103C3×#107C2×D318yes—
104C3×C4⋊C8C2×D314yes—
105C3×#103C2×D318yes—
106#835—34no—
107#816—38no—
108Dic3⋊C8—38no—
109C8×Dic3—38no—
110#810—34no—
111#810—38no—
112#810—38no—
113#807—34no—
114C4×C3⋊C8—34no—
115C32×Q8—21no—
116C32×Q8—21no—
117C32×Q8—81no—
118C2×C32×C4—21no—
119C2×C32×C4—22no—
120C2×C32×C4—21no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2411yescharacteristic
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3C2×D412yes—
128C2×C3⋊Dic3C2×D412yes—
129#634—21no—
130#634—22no—
131#634—22no—
132#634—82no—
133#634Q1614yescomplemented
134#634#4112yes—
135C32×C8—22no—
136C3⋊(C3⋊C8)—21no—
137C3⋊(C3⋊C8)—21no—
138Q82—91no—
139#557—91no—
140#487—91no—
141#487—92no—
142#477—92no—
143#477C3⋊D311yescharacteristic
144#462—91no—
145#462—92no—
146C8×Q8—91no—
147C4×Q16—91no—
148C4×Q16—92no—
149C2×C3×Q8—24no—
150C2×C3×Q8C22×D314yes—
151C2×Dic6—34no—
152C2×Dic6—34no—
153C2×Dic6—38no—
154C2×Dic6—68no—
155C2×C3×C8C22×D318yes—
156C3×C4⋊C4—24no—
157C3×C4⋊C4—24no—
158C3×C4⋊C4C22×D314yes—
159C3×C4⋊C4C22×D318yes—
160C3×C42—24no—
161C3×C42C22×D314yes—
162#216—68no—
163C4⋊Dic3—34no—
164C4⋊Dic3—34no—
165C4⋊Dic3—64no—
166C4⋊Dic3—64no—
167Dic3⋊C4—38no—
168Dic3⋊C4—68no—
169Dic3⋊C4—68no—
170Dic3⋊C4—68no—
171Dic3⋊C4—68no—
172Dic3⋊C4—68no—
173Dic3⋊C4—64no—
174C4×Dic3—38no—
175C4×Dic3—68no—
176C4×Dic3—68no—
177C4×Dic3—64no—
178C2×C3⋊C8—34no—
179C2×C3⋊C8—34no—
180Dic12—616no—
181C22×C32C22×D411yescharacteristic
182C32×C4—21no—
183C32×C4—41no—
184C32×C4—42no—
185C32×C4—41no—
186C32×C4C2×Q1612yes—
187C32×C4C2×#4111yescharacteristic
188C32×C42−1+411yescharacteristic
189C3⋊Dic3—22no—
190C3⋊Dic3—22no—
191C3⋊Dic3—42no—
192C3⋊Dic3—41no—
193C3⋊Dic3C2×Q1614yes—
194C2×Q16—91no—
195C2×Q16—92no—
196C4⋊Q8—92no—
197C4⋊Q8—92no—
198C4⋊Q8—91no—
199C4⋊Q8—181no—
200C4⋊Q8—182no—
201C4⋊Q8C2×C3⋊D311yescharacteristic
202#125—181no—
203#125—182no—
204C4×Q8—91no—
205C4×Q8—92no—
206C4×Q8—92no—
207C4×Q8—91no—
208C4×Q8—181no—
209C4×Q8—181no—
210C4×Q8C2×C3⋊D311yescharacteristic
211#107—91no—
212#107C2×C3⋊D312yes—
213C4⋊C8—92no—
214C4⋊C8C2×C3⋊D311yescharacteristic
215#103—91no—
216#103—92no—
217#103—91no—
218#103—92no—
219#103—92no—
220#103C2×C3⋊D312yes—
221C4×C8—92no—
222C4×C8—91no—
223C3×Q8—24no—
224C3×Q8—24no—
225C3×Q8—84no—
226C2×C3×C4—24no—
227C2×C3×C4—28no—
228C2×C3×C4—24no—
229C2×C3×C4D3×D414yes—
230C2×C3×C4D3×D414yes—
231C2×C3×C4C23×D314yes—
232C2×Dic3—38no—
233C2×Dic3—38no—
234C2×Dic3—64no—
235C2×Dic3—64no—
236C2×Dic3—68no—
237Dic6—316no—
238Dic6—38no—
239Dic6—64no—
240Dic6—68no—
241Dic6—68no—
242Dic6—248no—
243C3×C8—28no—
244C3⋊C8—64no—
245C3⋊C8—64no—
246C2×C32#54811yescharacteristic
247C2×C32C22×Q1611yescharacteristic
248C2×C32#57711yescharacteristic
249C2×Q8—21no—
250C2×Q8—91no—
251C2×Q8—91no—
252C2×Q8—92no—
253C2×Q8—182no—
254C2×Q8C22×C3⋊D311yescharacteristic
255Q16—184no—
256Q16—182no—
257C2×C8—91no—
258C2×C8—91no—
259C2×C8C22×C3⋊D312yes—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—92no—
263C4⋊C4—91no—
264C4⋊C4—91no—
265C4⋊C4—182no—
266C4⋊C4—182no—
267C4⋊C4—182no—
268C4⋊C4—182no—
269C4⋊C4—182no—
270C4⋊C4—181no—
271C4⋊C4—181no—
272C4⋊C4—181no—
273C4⋊C4C22×C3⋊D312yes—
274C4⋊C4C22×C3⋊D311yescharacteristic
275C42—21no—
276C42—92no—
277C42—182no—
278C42—182no—
279C42—181no—
280C42C22×C3⋊D311yescharacteristic
281C22×C3C2×D3×D414yes—
282C3×C4—24no—
283C3×C4—44no—
284C3×C4—48no—
285C3×C4—44no—
286C3×C4D3×Q1618yes—
287C3×C4#100714yes—
288C3×C4D3×#4114yes—
289Dic3—316no—
290Dic3—68no—
291Dic3—68no—
292Dic3—128no—
293Dic3—124no—
294C32#336311yescharacteristic, complemented, Sylow
295Q8—21no—
296Q8—21no—
297Q8—81no—
298Q8—94no—
299Q8—92no—
300Q8—181no—
301Q8—182no—
302Q8—182no—
303Q8—722no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—92no—
308C2×C4—92no—
309C2×C4—181no—
310C2×C4—181no—
311C2×C4—182no—
312C2×C4D4×C3⋊D311yescharacteristic
313C2×C4D4×C3⋊D311yescharacteristic
314C2×C4C23×C3⋊D311yescharacteristic
315C8—22no—
316C8—181no—
317C8—181no—
318C2×C3#563314yes—
319C2×C3C2×D3×Q1614yes—
320C2×C3#577514yes—
321C22C2×D4×C3⋊D311yescharacteristic
322C4—21no—
323C4—41no—
324C4—42no—
325C4—41no—
326C4—94no—
327C4—182no—
328C4—182no—
329C4—362no—
330C4—361no—
331C4Q16×C3⋊D312yes—
332C4#6436411yescharacteristic
333C4#41×C3⋊D311yescharacteristic
334C3#8113814yescomplemented
335C2#1059610411yescharacteristic
336C2C2×Q16×C3⋊D311yescharacteristic
337C2#1059624611yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#477C2
socle, prime radicalC22×C32C22×D4
hypercenter#477C3⋊D3
hypocenterC32#3363
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
133. #634Q16semidirect
294. C32#3363semidirect
334. C3#81138semidirect

Maximal subgroups

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

subgroupindex
#105961932
#105960382
C32×#4772
#105927922
C4×#37562
#105925742
#105925722
#105925482
#105925292
#105924942
#105924912
#811383