Finite Group Databasebeta

← #29584541

Subgroups — #29584541

Order 15616.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446779C211yesmaximal, characteristic
2#21446767C211yesmaximal, characteristic
3#21446538C211yesmaximal, characteristic
4C2×#16839512C211yesmaximal, characteristic
5C2×#16839510C211yesmaximal, characteristic
6#21443702C211yesmaximal, characteristic
7C61×#1947C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9C2×C4⋊#92418—21no—
10C2×C4⋊#92418C2211yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12C2×C4×#92418C2211yescharacteristic
13#16839524—21no—
14#16839524—21no—
15#16839524—21no—
16#16839524—21no—
17#16839517—21no—
18#16839512—22no—
19#16839510—22no—
20C2×#107×C61—21no—
21C2×C4⋊C8×C61C2211yescharacteristic
22C61×#384C2211yescharacteristic
23C4×C4⋊C4×C61C2211yescharacteristic
24C61×#340—21no—
25C22×Dic122—21no—
26C22×#92418—21no—
27C22×#92418—21no—
28C22×#92418D411yescharacteristic
29C22×#92418D411yescharacteristic
30#14519777—21no—
31#14519777—21no—
32#14519777—21no—
33#14519777Q812yes—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C4⋊#92418—21no—
37C4⋊#92418—21no—
38C4⋊#92418—21no—
39C4⋊#92418—21no—
40C4⋊#92418—42no—
41C4×#92418—21no—
42C4×#92418—21no—
43C22×C8×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C42×C61—21no—
50C2×C42×C61C2311yescharacteristic
51#107×C61—42no—
52C4⋊C8×C61—21no—
53C4⋊C8×C61D412yes—
54#95×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—41no—
58C22×C4×C61C2×D411yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61#4111yescharacteristic
61C22×Dic61—41no—
62C2×Dic122—22no—
63C2×Dic122—41no—
64C2×Dic122—81no—
65C2×Dic122—81no—
66C2×C8×C61—22no—
67C2×C8×C61—41no—
68C2×C8×C61—41no—
69C4⋊C4×C61—21no—
70C4⋊C4×C61—21no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—81no—
77C4⋊C4×C61SD1612yes—
78C42×C61—41no—
79C42×C61—41no—
80C42×C61C2×D411yescharacteristic
81C42×C61C2×Q811yescharacteristic
82C42×C61#4111yescharacteristic
83C42×C61#4111yescharacteristic
84C4⋊Dic61—22no—
85C4⋊Dic61—22no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88C2×#92418—21no—
89C2×#92418—21no—
90C2×#92418—21no—
91C2×#92418—21no—
92C2×#92418—21no—
93C2×#92418—41no—
94C2×#92418—41no—
95C2×#92418—41no—
96C2×#92418—41no—
97C2×#92418—41no—
98C2×#92418—41no—
99C2×#92418Q1612yes—
100C23×C61#12111yescharacteristic
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—22no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—81no—
110C2×C4×C61—81no—
111C2×C4×C61—81no—
112C2×C4×C61#12111yescharacteristic
113C2×C4×C61#12111yescharacteristic
114C2×C4×C61C22⋊Q811yescharacteristic
115C2×C4×C61C22⋊Q811yescharacteristic
116C2×C4×C61C22⋊Q811yescharacteristic
117C2×C4×C61#12611yescharacteristic
118C2×C4×C61C2×SD1611yescharacteristic
119C2×C4×C61C2×Q1611yescharacteristic
120C2×C4×C61#13511yescharacteristic
121C2×C4×C61#13511yescharacteristic
122C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C61#13711yescharacteristic
124C2×C4×C61#13711yescharacteristic
125C2×C4×C61#13711yescharacteristic
126C2×Dic61—42no—
127C2×Dic61—81no—
128C2×Dic61—81no—
129Dic122—82no—
130Dic122—82no—
131C8×C61—42no—
132#92418—22no—
133#92418—41no—
134#92418—81no—
135#92418—81no—
136#10589—611nomaximal, Sylow
137C22×C61#39611yescharacteristic
138C22×C61#46211yescharacteristic
139C22×C61#46311yescharacteristic
140C22×C61#46511yescharacteristic
141C22×C61#47011yescharacteristic
142C22×C61#47111yescharacteristic
143C22×C61#47211yescharacteristic
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—42no—
147C4×C61—81no—
148C4×C61—161no—
149C4×C61#46111yescharacteristic
150C4×C61#46411yescharacteristic
151C4×C61#46711yescharacteristic
152C4×C61#46811yescharacteristic
153C4×C61#47511yescharacteristic
154C4×C61#47711yescharacteristic
155C4×C61#47911yescharacteristic
156C4×C61#47911yescharacteristic
157Dic61—82no—
158#1990—611no—
159#1987—611no—
160#1947D6111yescharacteristic
161#1939—611no—
162C2×#334—611no—
163C2×#333—611no—
164#1296—611no—
165C2×C61#167211yescharacteristic
166C2×C61#167711yescharacteristic
167C2×C61#169611yescharacteristic
168C2×C61#170311yescharacteristic
169C2×C61#206311yescharacteristic
170C2×C61#206611yescharacteristic
171C2×C61#206811yescharacteristic
172C2×C4⋊Q8—611no—
173C2×#107—21no—
174C2×C4⋊C8—611no—
175C2×C4⋊C8—611no—
176C2×C4⋊C8—1221no—
177C2×C4⋊C8C2×D6111yescharacteristic
178C2×C4×C8—611no—
179#384C2×D6111yescharacteristic
180C4×C4⋊C4C2×D6111yescharacteristic
181#340—21no—
182#340—1221no—
183#340—1221no—
184#340—1221no—
185#340—1221no—
186#336—1221no—
187#334—1222no—
188#333—1222no—
189C61#1058911yescharacteristic, complemented, Sylow
190C22×Q8—1221no—
191C22×C8—21no—
192C22×C8—611no—
193C22×C8—611no—
194C22×C8—1221no—
195C22×C8—1221no—
196C4⋊Q8—612no—
197C4⋊Q8—1221no—
198C4⋊Q8—1221no—
199C4⋊Q8—1221no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4C22⋊D6111yescharacteristic
206C2×C4⋊C4C22⋊D6111yescharacteristic
207C2×C42—21no—
208C2×C42C22×D6111yescharacteristic
209#107—42no—
210C4⋊C8—21no—
211C4⋊C8—1221no—
212C4⋊C8—1221no—
213C4⋊C8—1221no—
214C4⋊C8—1221no—
215C4⋊C8—2442no—
216C4⋊C8D24412yes—
217C4×C8—1221no—
218C4×C8—1221no—
219#95—21no—
220C2×Q8—1222no—
221C2×Q8—4881no—
222C2×Q8—4881no—
223C2×Q8—2441no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—41no—
227C22×C4—2441no—
228C22×C4D4×D6111yescharacteristic
229C22×C4#1175822411yescharacteristic
230C22×C4C2×C22⋊D6111yescharacteristic
231C2×C8—22no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—612no—
235C2×C8—1221no—
236C2×C8—1221no—
237C2×C8—1221no—
238C2×C8—1221no—
239C2×C8—1221no—
240C2×C8—2441no—
241C2×C8—2441no—
242C2×C8—2441no—
243C2×C8—2441no—
244C2×C8—2441no—
245C2×C8—2441no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—81no—
254C4⋊C4—1222no—
255C4⋊C4—1222no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C4⋊C4#1175820012yes—
259C42—41no—
260C42—41no—
261C42C2×D24411yescharacteristic
262C42#1175822211yescharacteristic
263C42Q8×D6111yescharacteristic
264C42#1175822611yescharacteristic
265C23#1451974911yescharacteristic
266Q8—4882no—
267Q8—4882no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—4881no—
280C2×C4—4881no—
281C2×C4—2442no—
282C2×C4#1451975111yescharacteristic
283C2×C4#1451975211yescharacteristic
284C2×C4#1451975311yescharacteristic
285C2×C4#1451975511yescharacteristic
286C2×C4#1451975711yescharacteristic
287C2×C4#1451977211yescharacteristic
288C2×C4C2×#1175820011yescharacteristic
289C2×C4Q16×D6111yescharacteristic
290C2×C4#1451979611yescharacteristic
291C2×C4#1451979711yescharacteristic
292C2×C4#1451980111yescharacteristic
293C2×C4#1451980711yescharacteristic
294C2×C4#1451980811yescharacteristic
295C2×C4#1451980911yescharacteristic
296C8—42no—
297C8—1222no—
298C8—4881no—
299C8—4881no—
300C8—2441no—
301C22#1683968411yescharacteristic
302C22#1683997011yescharacteristic
303C22#1683997511yescharacteristic
304C22#1683998911yescharacteristic
305C22#1684001811yescharacteristic
306C22#1684002711yescharacteristic
307C22#1684003011yescharacteristic
308C4—21no—
309C4—21no—
310C4—42no—
311C4—81no—
312C4—161no—
313C4—4882no—
314C4#1683996711yescharacteristic
315C4#1683998411yescharacteristic
316C4#1684000411yescharacteristic
317C4#1684000911yescharacteristic
318C4#1684004411yescharacteristic
319C4#1684005611yescharacteristic
320C4#1684006611yescharacteristic
321C4#1684006811yescharacteristic
322C2#2144519911yescharacteristic
323C2#2144522611yescharacteristic
324C2#2144534511yescharacteristic
325C2#2144539211yescharacteristic
326C2#2144717611yescharacteristic
327C2#2144719711yescharacteristic
328C2#2144720911yescharacteristic
subgroupG/H
centerC23#14519749
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1947C2
socle, prime radicalC23×C61#121
hypercenter#1947D61
hypocenterC61#10589
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
189. C61#10589semidirect

Maximal subgroups

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

subgroupindex
#214467792
#214467672
#214465382
C2×#168395122
C2×#168395102
#214437022
C61×#19472
#1058961