Finite Group Databasebeta

← #29584775

Subgroups — #29584775

Order 15616.

350 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
1#21446755C211yesmaximal, characteristic
2#21445821C211yesmaximal, characteristic
3#21445821C211yesmaximal, characteristic
4#21443702C211yesmaximal, characteristic
5#21443702C211yesmaximal, characteristic
6#21443654C211yesmaximal, characteristic
7C61×#1834C211yesmaximal, characteristic
8C2×C4×Dic122C2211yescharacteristic
9C2×C4⋊#92418C2211yescharacteristic
10C2×C4⋊#92418C2211yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12C2×#14519700—21no—
13C2×#14519700—21no—
14#16839524—21no—
15#16839524—21no—
16#16839516—21no—
17#16839516—21no—
18C2×C4×C8×C61C2211yescharacteristic
19C61×#384C2211yescharacteristic
20C61×#384C2211yescharacteristic
21C61×#340—21no—
22C61×#340—21no—
23C22×Dic122D411yescharacteristic
24C22×#92418—21no—
25C22×#92418—21no—
26C22×#92418—21no—
27C4×Dic122—21no—
28C4×Dic122—21no—
29C4×Dic122—21no—
30C4×Dic122—21no—
31C2×C4⋊Dic61D411yescharacteristic
32C2×#11758196—21no—
33C2×C4×Dic61—21no—
34C4⋊#92418—21no—
35C4⋊#92418—21no—
36C4⋊#92418—21no—
37C4⋊#92418—21no—
38C4⋊#92418—21no—
39C4⋊#92418—21no—
40#14519700—42no—
41#14519700—42no—
42C22×C8×C61D411yescharacteristic
43C22×C8×C61D411yescharacteristic
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C42×C61C2311yescharacteristic
51C4×C8×C61—21no—
52C4×C8×C61—21no—
53C22×C4×C61—41no—
54C22×C4×C61—41no—
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61#4111yescharacteristic
58C22×Dic61—21no—
59C22×Dic61—21no—
60C2×Dic122—21no—
61C2×Dic122—21no—
62C2×Dic122—21no—
63C2×Dic122—21no—
64C2×Dic122—21no—
65C2×Dic122SD1612yes—
66C2×C8×C61—21no—
67C2×C8×C61—21no—
68C2×C8×C61—21no—
69C2×C8×C61—21no—
70C2×C8×C61—21no—
71C2×C8×C61—21no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—81no—
81C4⋊C4×C61—81no—
82C42×C61#4111yescharacteristic
83C42×C61#4111yescharacteristic
84C42×C61#4111yescharacteristic
85C42×C61#4111yescharacteristic
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88#11758196—41no—
89#11758196—41no—
90C4×Dic61—41no—
91C4×Dic61—41no—
92C2×#92418—41no—
93C2×#92418—41no—
94C2×#92418—41no—
95C2×#92418—41no—
96C2×#92418—41no—
97C2×#92418—41no—
98C2×#92418—41no—
99C2×#92418—41no—
100C2×#92418—41no—
101C23×C61#12111yescharacteristic
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—81no—
105C2×C4×C61—81no—
106C2×C4×C61—81no—
107C2×C4×C61—81no—
108C2×C4×C61—81no—
109C2×C4×C61—81no—
110C2×C4×C61#12311yescharacteristic
111C2×C4×C61#12311yescharacteristic
112C2×C4×C61#12311yescharacteristic
113C2×C4×C61#12411yescharacteristic
114C2×C4×C61#12611yescharacteristic
115C2×C4×C61#12611yescharacteristic
116C2×C4×C61C2×SD1611yescharacteristic
117C2×C4×C61#13511yescharacteristic
118C2×C4×C61#13511yescharacteristic
119C2×C4×C61#13511yescharacteristic
120C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C61#13711yescharacteristic
122C2×C4×C61#13711yescharacteristic
123C2×C4×C61#13711yescharacteristic
124C2×Dic61—22no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130Dic122—22no—
131Dic122—22no—
132Dic122—41no—
133Dic122—41no—
134C8×C61—41no—
135C8×C61—41no—
136#92418—81no—
137#92418—81no—
138#92418—81no—
139#10626—611nomaximal, Sylow
140C22×C61#39711yescharacteristic
141C22×C61#46411yescharacteristic
142C22×C61#46411yescharacteristic
143C22×C61#46511yescharacteristic
144C22×C61#46811yescharacteristic
145C22×C61#47211yescharacteristic
146C22×C61#47311yescharacteristic
147C4×C61—21no—
148C4×C61—21no—
149C4×C61—161no—
150C4×C61—161no—
151C4×C61#48111yescharacteristic
152C4×C61#48211yescharacteristic
153C4×C61#48311yescharacteristic
154C4×C61#48511yescharacteristic
155C4×C61#48511yescharacteristic
156C4×C61#48511yescharacteristic
157C4×C61#48811yescharacteristic
158C4×C61#49111yescharacteristic
159Dic61—42no—
160Dic61—81no—
161#1984—611no—
162#1834D6111yescharacteristic
163#1803—611no—
164#1803—611no—
165#1296—611no—
166#1296—611no—
167#1277—611no—
168C2×C61#167811yescharacteristic
169C2×C61#168011yescharacteristic
170C2×C61#169811yescharacteristic
171C2×C61#170011yescharacteristic
172C2×C61#207411yescharacteristic
173C2×C61#207711yescharacteristic
174C2×C61#207811yescharacteristic
175C2×C4×Q8—611no—
176C2×C4⋊C8—611no—
177C2×C4⋊C8—611no—
178C2×C4⋊C8—611no—
179C2×#103—1221no—
180C2×#103—1221no—
181C2×C4×C8C2×D6111yescharacteristic
182#384C2×D6111yescharacteristic
183#384C2×D6111yescharacteristic
184#340—21no—
185#340—21no—
186#340—1221no—
187#340—1221no—
188#336—1221no—
189#336—1221no—
190C61#1062611yescharacteristic, complemented, Sylow
191C22×Q8—611no—
192C22×C8—1221no—
193C22×C8—1221no—
194C22×C8—1221no—
195C22×C8C22⋊D6111yescharacteristic
196C22×C8C22⋊D6111yescharacteristic
197C4×Q8—1221no—
198C4×Q8—1221no—
199C4×Q8—1221no—
200C4×Q8—1221no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—1221no—
209C2×C42—1221no—
210C2×C42C22×D6111yescharacteristic
211C4⋊C8—1221no—
212C4⋊C8—1221no—
213C4⋊C8—1221no—
214C4⋊C8—1221no—
215C4⋊C8—1221no—
216C4⋊C8—1221no—
217#103—2442no—
218#103—2442no—
219C4×C8—21no—
220C4×C8—21no—
221C2×Q8—612no—
222C2×Q8—1221no—
223C2×Q8—1221no—
224C2×Q8—1221no—
225C2×Q8—1221no—
226C2×Q8—1221no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4D4×D6111yescharacteristic
232C22×C4#1175822411yescharacteristic
233C22×C4C2×C22⋊D6111yescharacteristic
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—2441no—
241C2×C8—2441no—
242C2×C8—2441no—
243C2×C8—2441no—
244C2×C8—2441no—
245C2×C8—2441no—
246C2×C8—2441no—
247C2×C8—2441no—
248C2×C8—2441no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C4⋊C4—81no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4—2441no—
262C4⋊C4—2441no—
263C42—2441no—
264C42—2441no—
265C42#1175822211yescharacteristic
266C42#1175822211yescharacteristic
267C42#1175822611yescharacteristic
268C42#1175822611yescharacteristic
269C23#1451974811yescharacteristic
270Q8—1222no—
271Q8—1222no—
272Q8—2441no—
273Q8—2441no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—1222no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4#1451976011yescharacteristic
289C2×C4#1451976211yescharacteristic
290C2×C4#1451976211yescharacteristic
291C2×C4#1451976611yescharacteristic
292C2×C4#1451977211yescharacteristic
293C2×C4#1451977211yescharacteristic
294C2×C4SD16×D6111yescharacteristic
295C2×C4#1451979711yescharacteristic
296C2×C4#1451979711yescharacteristic
297C2×C4#1451979811yescharacteristic
298C2×C4#1451980411yescharacteristic
299C2×C4#1451980611yescharacteristic
300C2×C4#1451980711yescharacteristic
301C2×C4#1451980711yescharacteristic
302C8—41no—
303C8—41no—
304C8—4881no—
305C8—4881no—
306C8—4881no—
307C22#1683968811yescharacteristic
308C22#1683998111yescharacteristic
309C22#1683998111yescharacteristic
310C22#1683998811yescharacteristic
311C22#1684000511yescharacteristic
312C22#1684002911yescharacteristic
313C22#1684003411yescharacteristic
314C4—21no—
315C4—21no—
316C4—161no—
317C4—161no—
318C4—4881no—
319C4—2442no—
320C4#1684008211yescharacteristic
321C4#1684008811yescharacteristic
322C4#1684009411yescharacteristic
323C4#1684010311yescharacteristic
324C4#1684010311yescharacteristic
325C4#1684010611yescharacteristic
326C4#1684011911yescharacteristic
327C4#1684013211yescharacteristic
328C2#2144523211yescharacteristic
329C2#2144524611yescharacteristic
330C2#2144535611yescharacteristic
331C2#2144537011yescharacteristic
332C2#2144723811yescharacteristic
333C2#2144725311yescharacteristic
334C2#2144726011yescharacteristic
subgroupG/H
centerC23#14519748
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1834C2
socle, prime radicalC23×C61#121
hypercenter#1834D61
hypocenterC61#10626
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
190. C61#10626semidirect

Maximal subgroups

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

subgroupindex
#214467552
#214458212
#214437022
#214436542
C61×#18342
#1062661