Finite Group Databasebeta

← #29569349

Subgroups — #29569349

Order 15616.

378 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21453781C211yesmaximal, characteristic
2#21447358C211yesmaximal, characteristic
3#21447358C211yesmaximal, characteristic
4#21443644C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic
6#21443642C211yesmaximal, characteristic
7C61×#2100C211yesmaximal, characteristic
8C2×#14519710—21no—
9C2×#14519710—21no—
10C2×#14519700—21no—
11C2×#14519700—21no—
12#16839695—21no—
13#16839694—21no—
14#16839682—21no—
15#16839668C2211yescharacteristic
16#16839668C2211yescharacteristic
17#16839666—21no—
18#16839661—21no—
19#16839648—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C61×#389C2211yescharacteristic
23C61×#384C2211yescharacteristic
24C61×#340—21no—
25C61×#340—21no—
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×Dic122D411yescharacteristic
29C22×#92418—21no—
30C22×#92418—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61D411yescharacteristic
34C2×C4⋊Dic61D411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×C4×Dic61—21no—
38#14519710—42no—
39#14519710—42no—
40#14519700—42no—
41#14519700—42no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C22×C8×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C42×C61C2311yescharacteristic
57#95×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—41no—
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C2×Dic122—21no—
69C2×Dic122—21no—
70C2×Dic122—21no—
71C2×Dic122—41no—
72C2×Dic122—41no—
73C2×Dic122—41no—
74C2×Dic122—41no—
75C2×Dic122Q1612yes—
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—42no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61Q1612yes—
89C42×C61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—81no—
93C4⋊Dic61—81no—
94#11758196—81no—
95#11758196—81no—
96C4×Dic61—81no—
97C2×#92418—22no—
98C2×#92418—22no—
99C2×#92418—41no—
100C2×#92418—41no—
101C2×#92418—41no—
102C2×#92418—41no—
103C23×C61#12011yescharacteristic
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—22no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—81no—
117C2×C4×C61—81no—
118C2×C4×C61—81no—
119C2×C4×C61C2×Q1611yescharacteristic
120C2×C4×C61C2×Q1611yescharacteristic
121C2×C4×C61#13511yescharacteristic
122C2×C4×C61#13711yescharacteristic
123C2×C4×C61#13711yescharacteristic
124C2×C4×C61#13711yescharacteristic
125C2×Dic61—22no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137Dic122—42no—
138Dic122—42no—
139Dic122—81no—
140Dic122—81no—
141C8×C61—81no—
142#92418—42no—
143#92418—42no—
144#7836—611nomaximal, Sylow
145C22×C61#45111yescharacteristic
146C22×C61#45111yescharacteristic
147C22×C61#45211yescharacteristic
148C22×C61#45311yescharacteristic
149C22×C61#45311yescharacteristic
150C22×C61#45411yescharacteristic
151C22×C61#45811yescharacteristic
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—42no—
159C4×C61—81no—
160C4×C61—161no—
161Dic61—42no—
162Dic61—81no—
163Dic61—81no—
164Dic61—81no—
165#2806—611no—
166#2100D6111yescharacteristic
167#2095—611no—
168#2095—611no—
169#1272—611no—
170#1272—611no—
171#1271—611no—
172C2×C61#161411yescharacteristic
173C2×C61#161711yescharacteristic
174C2×C61#161811yescharacteristic
175C2×C61#163211yescharacteristic
176C2×C61#163311yescharacteristic
177C2×C61#163611yescharacteristic
178C2×C61#165611yescharacteristic
179C2×#107—1221no—
180C2×#107—1221no—
181C2×#103—1221no—
182C2×#103—1221no—
183#398—1221no—
184#398—1221no—
185#395—1221no—
186#391—611no—
187#391—611no—
188#391—1221no—
189#389—1221no—
190#389C2×D6111yescharacteristic
191#387—1221no—
192#384C2×D6111yescharacteristic
193#340—21no—
194#340—21no—
195#336—611no—
196#336—611no—
197#336C2×D6111yescharacteristic
198C61#783611yescharacteristic, complemented, Sylow
199C22×Q8—611no—
200C22×Q8—611no—
201C22×C8—21no—
202C22×C8—1221no—
203C22×C8—1221no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4C22⋊D6111yescharacteristic
215C2×C4⋊C4C22⋊D6111yescharacteristic
216C2×C42—1221no—
217C2×C42C22×D6111yescharacteristic
218#107—2442no—
219#107—2442no—
220#103—2442no—
221#103—2442no—
222#95—21no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230C2×Q8—612no—
231C2×Q8—1221no—
232C2×Q8—1221no—
233C2×Q8—1221no—
234C2×Q8—2441no—
235C2×Q8—2441no—
236C2×Q8—2441no—
237C2×Q8—2441no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4D4×D6111yescharacteristic
246C22×C4D4×D6111yescharacteristic
247C22×C4C2×C22⋊D6111yescharacteristic
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—1222no—
252C2×C8—1222no—
253C2×C8—2441no—
254C2×C8—2441no—
255C2×C8—2441no—
256C2×C8—2441no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—42no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—4881no—
267C4⋊C4—4881no—
268C4⋊C4—4881no—
269C4⋊C4—4881no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4#1175820212yes—
273C42—41no—
274C42—4881no—
275C23#1451974511yescharacteristic
276Q8—4881no—
277Q8—4881no—
278Q8—2442no—
279Q8—2442no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—1222no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4Q16×D6111yescharacteristic
308C2×C4C2×#1175820211yescharacteristic
309C2×C4#1451979811yescharacteristic
310C2×C4#1451980611yescharacteristic
311C2×C4#1451980711yescharacteristic
312C2×C4#1451980911yescharacteristic
313C8—81no—
314C8—2442no—
315C8—2442no—
316C22#1683991611yescharacteristic
317C22#1683991711yescharacteristic
318C22#1683992111yescharacteristic
319C22#1683992811yescharacteristic
320C22#1683992811yescharacteristic
321C22#1683993411yescharacteristic
322C22#1683995111yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—42no—
330C4—81no—
331C4—161no—
332C4—4881no—
333C4—4881no—
334C4—4881no—
335C4—2442no—
336C2#2144484211yescharacteristic
337C2#2144486011yescharacteristic
338C2#2144486411yescharacteristic
339C2#2144495111yescharacteristic
340C2#2144495811yescharacteristic
341C2#2144497411yescharacteristic
342C2#2144511111yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2100C2
socle, prime radicalC23×C61#120
hypercenter#2100D61
hypocenterC61#7836
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
198. C61#7836semidirect

Maximal subgroups

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

subgroupindex
#214537812
#214473582
#214436442
#214436422
C61×#21002
#783661