Finite Group Databasebeta

← #11895457

Subgroups — #11895457

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#10596192C211yesmaximal, characteristic
3C32×#487C211yesmaximal, characteristic
4#10592790C211yesmaximal, characteristic
5#10592789C211yesmaximal, characteristic
6#10592494C212yesmaximal
7#10592492C212yesmaximal
8#10592491C212yesmaximal
9#10592489C212yesmaximal
10C4×#3746C211yesmaximal, characteristic
11C8×#634C211yesmaximal, characteristic
12#81624—34nomaximal
13C32×C4⋊Q8C2211yescharacteristic
14C32×C4⋊Q8C2211yescharacteristic
15Q8×C3⋊Dic3C2212yes—
16#64153—22no—
17#64153C2212yes—
18C2×#3756C2212yes—
19C2×#3746C2211yescharacteristic
20#64099—21no—
21#64098—22no—
22#64097—21no—
23#64097C2212yes—
24#64096—21no—
25#64096—21no—
26#64096C2212yes—
27C4×#634C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×#103C2212yes—
31C32×#103C2212yes—
32C32×C4×C8C2211yescharacteristic
33#63662C2212yes—
34#63645C2211yescharacteristic
35#63643C2211yescharacteristic
36#63643C2211yescharacteristic
37#63641C2212yes—
38C8×C3⋊Dic3C2212yes—
39#63637C2212yes—
40#63634C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5722—34no—
43#5721—34no—
44C3×#487D314yes—
45#5091—34no—
46#5090—34no—
47#4795—38no—
48#4793—38no—
49#4792—38no—
50#4790—38no—
51C4×Dic12—34no—
52C8×Dic6—34no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2312yes—
55C2×#634—22no—
56C2×#634D411yescharacteristic
57C2×#634C2311yescharacteristic
58C2×#634C2311yescharacteristic
59C2×C32×C8C2311yescharacteristic
60C2×C32×C8C2311yescharacteristic
61C32×C4⋊C4—21no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C32×C4⋊C4C2312yes—
65C32×C42C2311yescharacteristic
66#3756—24no—
67C4⋊(C3⋊Dic3)—22no—
68C4⋊(C3⋊Dic3)D411yescharacteristic
69C4⋊(C3⋊Dic3)C2311yescharacteristic
70C4⋊(C3⋊Dic3)C2311yescharacteristic
71#3750—21no—
72#3750—21no—
73#3750—22no—
74#3750—22no—
75#3750—22no—
76#3750—22no—
77#3750D412yes—
78C4×C3⋊Dic3—21no—
79C4×C3⋊Dic3—21no—
80C4×C3⋊Dic3—22no—
81C4×C3⋊Dic3—22no—
82C4×C3⋊Dic3C2312yes—
83C2×C3⋊(C3⋊C8)C2312yes—
84#3746—22no—
85#3363—91noSylow
86C3×C4⋊Q8C2×D314yes—
87C3×C4⋊Q8C2×D314yes—
88Q8×Dic3—38no—
89#944—38no—
90#944—68no—
91C2×#216—38no—
92C2×Dic12—34no—
93#890—64no—
94#889—68no—
95#888—38no—
96#888—64no—
97#887—38no—
98#887—64no—
99#887—64no—
100C4×Dic6—34no—
101C4×Dic6—34no—
102C4×Dic6—34no—
103C3×#103C2×D318yes—
104C3×#103C2×D318yes—
105C3×C4×C8C2×D314yes—
106#835—38no—
107#818—34no—
108#816—34no—
109#816—34no—
110Dic3⋊C8—38no—
111C8×Dic3—38no—
112#810—38no—
113#807—38no—
114C4⋊(C3⋊C8)—34no—
115C32×Q8—22no—
116C32×Q8—22no—
117C32×Q8—81no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2411yescharacteristic
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3C2×D412yes—
128C2×C3⋊Dic3C2×D412yes—
129#634—21no—
130#634—21no—
131#634—21no—
132#634—82no—
133#634Q1614yescomplemented
134#634#4112yes—
135C32×C8—21no—
136C32×C8—21no—
137C3⋊(C3⋊C8)—22no—
138Q82—91no—
139#557—91no—
140#487—92no—
141#487C3⋊D311yescharacteristic
142#477—91no—
143#477—92no—
144#462—91no—
145#462—92no—
146C8×Q8—91no—
147C4×Q16—92no—
148C4×Q16—91no—
149C2×C3×Q8—24no—
150C2×C3×Q8C22×D318yes—
151C2×Dic6—34no—
152C2×Dic6—34no—
153C2×Dic6—34no—
154C2×Dic6—68no—
155C2×C3×C8C22×D314yes—
156C2×C3×C8C22×D314yes—
157C3×C4⋊C4—24no—
158C3×C4⋊C4—24no—
159C3×C4⋊C4—24no—
160C3×C4⋊C4C22×D318yes—
161C3×C42C22×D314yes—
162#216—616no—
163C4⋊Dic3—34no—
164C4⋊Dic3—34no—
165C4⋊Dic3—34no—
166C4⋊Dic3—68no—
167Dic3⋊C4—38no—
168Dic3⋊C4—68no—
169Dic3⋊C4—68no—
170Dic3⋊C4—68no—
171Dic3⋊C4—68no—
172Dic3⋊C4—64no—
173Dic3⋊C4—64no—
174C4×Dic3—38no—
175C4×Dic3—68no—
176C4×Dic3—68no—
177C4×Dic3—64no—
178C4×Dic3—64no—
179C2×C3⋊C8—38no—
180Dic12—68no—
181C22×C32C22×D411yescharacteristic
182C32×C4—21no—
183C32×C4—42no—
184C32×C4—42no—
185C32×C4C2×Q1612yes—
186C32×C4C2×#4111yescharacteristic
187C32×C42−1+411yescharacteristic
188C3⋊Dic3—22no—
189C3⋊Dic3—22no—
190C3⋊Dic3—41no—
191C3⋊Dic3—41no—
192C3⋊Dic3—41no—
193C3⋊Dic3C2×Q1614yes—
194C2×Q16—92no—
195C2×Q16—91no—
196C4⋊Q8—92no—
197C4⋊Q8—92no—
198C4⋊Q8—181no—
199C4⋊Q8—182no—
200C4⋊Q8C2×C3⋊D311yescharacteristic
201C4⋊Q8C2×C3⋊D311yescharacteristic
202#125—182no—
203#125—181no—
204C4×Q8—91no—
205C4×Q8—92no—
206C4×Q8—92no—
207C4×Q8—91no—
208C4×Q8—91no—
209C4×Q8—181no—
210C4×Q8—181no—
211#107—91no—
212#107—92no—
213C4⋊C8—92no—
214C4⋊C8—91no—
215#103—92no—
216#103—91no—
217#103—91no—
218#103—92no—
219#103C2×C3⋊D312yes—
220#103C2×C3⋊D312yes—
221C4×C8—92no—
222C4×C8C2×C3⋊D311yescharacteristic
223C3×Q8—28no—
224C3×Q8—28no—
225C3×Q8—84no—
226C2×C3×C4—28no—
227C2×C3×C4—28no—
228C2×C3×C4D3×D414yes—
229C2×C3×C4D3×D414yes—
230C2×C3×C4C23×D314yes—
231C2×Dic3—38no—
232C2×Dic3—38no—
233C2×Dic3—64no—
234C2×Dic3—64no—
235C2×Dic3—64no—
236C2×Dic3—64no—
237Dic6—316no—
238Dic6—38no—
239Dic6—64no—
240Dic6—64no—
241Dic6—64no—
242Dic6—248no—
243C3×C8—24no—
244C3×C8—24no—
245C3⋊C8—68no—
246C2×C32#54811yescharacteristic
247C2×C32C22×Q1611yescharacteristic
248C2×C32#57711yescharacteristic
249C2×Q8—21no—
250C2×Q8—91no—
251C2×Q8—91no—
252C2×Q8—91no—
253C2×Q8—182no—
254C2×Q8C22×C3⋊D312yes—
255Q16—182no—
256Q16—184no—
257C2×C8—92no—
258C2×C8C22×C3⋊D311yescharacteristic
259C2×C8C22×C3⋊D311yescharacteristic
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—92no—
264C4⋊C4—91no—
265C4⋊C4—91no—
266C4⋊C4—91no—
267C4⋊C4—182no—
268C4⋊C4—182no—
269C4⋊C4—182no—
270C4⋊C4—182no—
271C4⋊C4—182no—
272C4⋊C4—181no—
273C4⋊C4—181no—
274C4⋊C4C22×C3⋊D312yes—
275C42—92no—
276C42—182no—
277C42—182no—
278C42—181no—
279C42—181no—
280C42C22×C3⋊D311yescharacteristic
281C22×C3C2×D3×D414yes—
282C3×C4—24no—
283C3×C4—48no—
284C3×C4—48no—
285C3×C4D3×Q1618yes—
286C3×C4D3×#4114yes—
287C3×C4#101014yes—
288Dic3—316no—
289Dic3—68no—
290Dic3—68no—
291Dic3—124no—
292Dic3—124no—
293Dic3—124no—
294C32#336311yescharacteristic, complemented, Sylow
295Q8—22no—
296Q8—22no—
297Q8—81no—
298Q8—94no—
299Q8—92no—
300Q8—181no—
301Q8—181no—
302Q8—181no—
303Q8—722no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—92no—
307C2×C4—92no—
308C2×C4—181no—
309C2×C4—181no—
310C2×C4—181no—
311C2×C4—181no—
312C2×C4D4×C3⋊D311yescharacteristic
313C2×C4D4×C3⋊D311yescharacteristic
314C2×C4C23×C3⋊D311yescharacteristic
315C8—21no—
316C8—21no—
317C8—182no—
318C2×C3#567714yes—
319C2×C3#576214yes—
320C2×C3C2×D3×Q1614yes—
321C22C2×D4×C3⋊D311yescharacteristic
322C4—21no—
323C4—42no—
324C4—42no—
325C4—94no—
326C4—182no—
327C4—182no—
328C4—361no—
329C4—361no—
330C4—361no—
331C4Q16×C3⋊D312yes—
332C4#41×C3⋊D311yescharacteristic
333C4#6436711yescharacteristic
334C3#8162414yescomplemented
335C2#1059614811yescharacteristic
336C2#1059623311yescharacteristic
337C2C2×Q16×C3⋊D311yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#487C2
socle, prime radicalC22×C32C22×D4
hypercenter#487C3⋊D3
hypocenterC32#3363
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
133. #634Q16semidirect
294. C32#3363semidirect
334. C3#81624semidirect

Maximal subgroups

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

subgroupindex
#105961932
#105961922
C32×#4872
#105927902
#105927892
#105924942
#105924922
#105924912
#105924892
C4×#37462
C8×#6342
#816243