Finite Group Databasebeta

← #29584474

Subgroups — #29584474

Order 15616.

390 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446582C211yesmaximal, characteristic
2#21446577C211yesmaximal, characteristic
3#21445946C211yesmaximal, characteristic
4#21443702C211yesmaximal, characteristic
5#21443660C211yesmaximal, characteristic
6#21443660C211yesmaximal, characteristic
7C61×#2571C211yesmaximal, characteristic
8C2×#14519710—21no—
9C2×#14519708—21no—
10C2×C4⋊#92418C2211yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12C2×C4×#92418C2211yescharacteristic
13#16839632C2211yescharacteristic
14#16839524—22no—
15#16839524—21no—
16#16839524—21no—
17C61×#400—22no—
18C61×#389—21no—
19C61×#389—21no—
20C61×#384C2211yescharacteristic
21C61×#382—21no—
22C61×#382—21no—
23C4×C4⋊C4×C61C2211yescharacteristic
24C4×C4⋊C4×C61C2211yescharacteristic
25C22×#92418—21no—
26C22×#92418—21no—
27C22×#92418—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31#14519710—42no—
32#14519708—42no—
33C4⋊#92418—21no—
34C4⋊#92418—21no—
35C4⋊#92418Q812yes—
36C4⋊#92418Q812yes—
37C4×#92418—21no—
38C4×#92418Q812yes—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61—21no—
41C2×C4⋊C4×C61—22no—
42C2×C4⋊C4×C61D411yescharacteristic
43C2×C4⋊C4×C61D411yescharacteristic
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C4⋊C4×C61D412yes—
47C2×C42×C61—21no—
48C2×C42×C61—21no—
49C2×C42×C61C2311yescharacteristic
50#95×C61—22no—
51#95×C61—22no—
52#95×C61—22no—
53#95×C61—21no—
54#95×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—22no—
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×Dic61—41no—
64C4⋊C4×C61—21no—
65C4⋊C4×C61—21no—
66C4⋊C4×C61—21no—
67C4⋊C4×C61—21no—
68C4⋊C4×C61—21no—
69C4⋊C4×C61—21no—
70C4⋊C4×C61—21no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—42no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—82no—
78C42×C61—41no—
79C42×C61—41no—
80C42×C61—41no—
81C42×C61—41no—
82C42×C61C2×Q811yescharacteristic
83C42×C61C2×Q811yescharacteristic
84C42×C61C2×Q811yescharacteristic
85C42×C61#4111yescharacteristic
86C4⋊Dic61—42no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91C2×#92418—22no—
92C2×#92418—22no—
93C2×#92418—22no—
94C2×#92418—41no—
95C2×#92418—41no—
96C2×#92418—41no—
97C2×#92418—41no—
98C2×#92418—41no—
99C2×#92418—41no—
100C23×C61#12011yescharacteristic
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—42no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—42no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—42no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61C22⋊Q811yescharacteristic
119C2×C4×C61C22⋊Q811yescharacteristic
120C2×C4×C61C22⋊Q811yescharacteristic
121C2×C4×C61C4⋊Q811yescharacteristic
122C2×C4×C61C4⋊Q811yescharacteristic
123C2×C4×C61C4⋊Q811yescharacteristic
124C2×C4×C61#13511yescharacteristic
125C2×C4×C61#13511yescharacteristic
126C2×C4×C61#13511yescharacteristic
127C2×C4×C61#13511yescharacteristic
128C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C61#13711yescharacteristic
131C2×C4×C61#13711yescharacteristic
132C2×Dic61—81no—
133C2×Dic61—81no—
134C2×Dic61—81no—
135#92418—42no—
136#92418—42no—
137#92418—42no—
138#10578—611nomaximal, Sylow
139C22×C61#39511yescharacteristic
140C22×C61#44911yescharacteristic
141C22×C61#44911yescharacteristic
142C22×C61#45211yescharacteristic
143C22×C61#45211yescharacteristic
144C22×C61#45411yescharacteristic
145C22×C61#45511yescharacteristic
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—81no—
149C4×C61—81no—
150C4×C61—82no—
151C4×C61—81no—
152C4×C61—81no—
153C4×C61#47811yescharacteristic
154C4×C61#47811yescharacteristic
155C4×C61#47911yescharacteristic
156C4×C61#47911yescharacteristic
157C4×C61#49911yescharacteristic
158C4×C61#49911yescharacteristic
159C4×C61#50111yescharacteristic
160C4×C61#50111yescharacteristic
161Dic61—161no—
162#2571D6111yescharacteristic
163#1948—611no—
164#1947—611no—
165#1834—611no—
166#1296—611no—
167#1279—611no—
168#1279—611no—
169C2×C61#162811yescharacteristic
170C2×C61#163811yescharacteristic
171C2×C61#164011yescharacteristic
172C2×C61#164611yescharacteristic
173C2×C61#205911yescharacteristic
174C2×C61#205911yescharacteristic
175C2×C61#206111yescharacteristic
176C2×#107—1221no—
177C2×#106—1221no—
178C2×C4⋊C8—611no—
179C2×C4⋊C8—611no—
180C2×C4×C8—611no—
181#400—22no—
182#389—21no—
183#389—21no—
184#384—611no—
185#384C2×D6111yescharacteristic
186#382—21no—
187#382—21no—
188C4×C4⋊C4C2×D6111yescharacteristic
189C4×C4⋊C4C2×D6111yescharacteristic
190#340—1222no—
191#340—1221no—
192#340—1221no—
193C61#1057811yescharacteristic, complemented, Sylow
194C22×C8—1221no—
195C22×C8—1221no—
196C22×C8—1221no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4C22⋊D6111yescharacteristic
204C2×C4⋊C4C22⋊D6111yescharacteristic
205C2×C4⋊C4C22⋊D6111yescharacteristic
206C2×C4⋊C4C22⋊D6111yescharacteristic
207C2×C4⋊C4C22⋊D6112yes—
208C2×C42—21no—
209C2×C42—21no—
210C2×C42C22×D6111yescharacteristic
211#107—2442no—
212#106—2442no—
213C4⋊C8—612no—
214C4⋊C8—612no—
215C4⋊C8—1221no—
216C4⋊C8—1221no—
217C4×C8—612no—
218C4×C8—1221no—
219#95—22no—
220#95—22no—
221#95—22no—
222#95—21no—
223#95—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—2441no—
230C22×C4C2×C22⋊D6111yescharacteristic
231C22×C4C2×C22⋊D6111yescharacteristic
232C22×C4C2×C22⋊D6111yescharacteristic
233C2×C8—1222no—
234C2×C8—1222no—
235C2×C8—1222no—
236C2×C8—2441no—
237C2×C8—2441no—
238C2×C8—2441no—
239C2×C8—2441no—
240C2×C8—2441no—
241C2×C8—2441no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—82no—
256C4⋊C4—2442no—
257C4⋊C4—2441no—
258C4⋊C4—2441no—
259C4⋊C4—2441no—
260C4⋊C4—2441no—
261C42—41no—
262C42—41no—
263C42—41no—
264C42—41no—
265C42Q8×D6111yescharacteristic
266C42Q8×D6111yescharacteristic
267C42Q8×D6111yescharacteristic
268C42#1175822611yescharacteristic
269C23#1451974611yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—4881no—
288C2×C4—4881no—
289C2×C4—4881no—
290C2×C4#1451975311yescharacteristic
291C2×C4#1451975311yescharacteristic
292C2×C4#1451975311yescharacteristic
293C2×C4#1451977511yescharacteristic
294C2×C4#1451977511yescharacteristic
295C2×C4#1451977511yescharacteristic
296C2×C4#1451979711yescharacteristic
297C2×C4#1451979711yescharacteristic
298C2×C4#1451979711yescharacteristic
299C2×C4#1451979711yescharacteristic
300C2×C4#1451980211yescharacteristic
301C2×C4#1451980211yescharacteristic
302C2×C4#1451980711yescharacteristic
303C2×C4#1451980711yescharacteristic
304C8—2442no—
305C8—2442no—
306C8—2442no—
307C22#1683968111yescharacteristic
308C22#1683990711yescharacteristic
309C22#1683990711yescharacteristic
310C22#1683992411yescharacteristic
311C22#1683992411yescharacteristic
312C22#1683993511yescharacteristic
313C22#1683994011yescharacteristic
314C4—21no—
315C4—21no—
316C4—81no—
317C4—81no—
318C4—82no—
319C4—81no—
320C4—81no—
321C4—9761no—
322C4#1684005911yescharacteristic
323C4#1684005911yescharacteristic
324C4#1684006611yescharacteristic
325C4#1684006611yescharacteristic
326C4#1684016111yescharacteristic
327C4#1684016111yescharacteristic
328C4#1684017211yescharacteristic
329C4#1684017211yescharacteristic
330C2#2144492911yescharacteristic
331C2#2144499111yescharacteristic
332C2#2144500511yescharacteristic
333C2#2144504711yescharacteristic
334C2#2144715411yescharacteristic
335C2#2144715411yescharacteristic
336C2#2144716611yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2571C2
socle, prime radicalC23×C61#120
hypercenter#2571D61
hypocenterC61#10578
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2571

Complements

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

NH ≅ G/Ntype
193. C61#10578semidirect

Maximal subgroups

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

subgroupindex
#214465822
#214465772
#214459462
#214437022
#214436602
C61×#25712
#1057861