Finite Group Databasebeta

← #29593122

Subgroups — #29593122

Order 15616.

362 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 55 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#21453334C211yesmaximal, characteristic
2#21444844C211yesmaximal, characteristic
3#21444810C211yesmaximal, characteristic
4#21443842C211yesmaximal, characteristic
5#21443818C211yesmaximal, characteristic
6#21443749C211yesmaximal, characteristic
7C61×#2030C211yesmaximal, characteristic
8#16840095—21no—
9#16840090—21no—
10#16839704—21no—
11#16839703—21no—
12#16839698C2211yescharacteristic
13#16839687C2211yescharacteristic
14#16839659—21no—
15#16839650—21no—
16#16839644—21no—
17#16839635—21no—
18#16839499—21no—
19#16839499—21no—
20#16839486C2211yescharacteristic
21#16839486C2211yescharacteristic
22C61×#543C2211yescharacteristic
23C61×#381—21no—
24C61×#381C2211yescharacteristic
25C61×#342—21no—
26C61×#342C2211yescharacteristic
27C2×C4⋊Dic61D411yescharacteristic
28C2×C4⋊Dic61D411yescharacteristic
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C4×Dic61—21no—
36#14519710—41no—
37#14519708—41no—
38#14519701—41no—
39#14519701—41no—
40C22⋊#92418—21no—
41C22⋊#92418—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684D411yescharacteristic
48#14519684D411yescharacteristic
49C23×C4×C61D411yescharacteristic
50C22⋊Q8×C61—21no—
51C22⋊Q8×C61—21no—
52C22⋊Q8×C61—41no—
53C22⋊Q8×C61—41no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61D411yescharacteristic
57C2×C22⋊C4×C61C2311yescharacteristic
58#95×C61—21no—
59#95×C61—21no—
60#95×C61—41no—
61#95×C61—41no—
62C24×C61C2×D411yescharacteristic
63C2×Q8×C61—21no—
64C2×Q8×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊Dic61—42no—
91C22⋊Dic61—41no—
92C22⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95#11758196—42no—
96#11758196—42no—
97#11758196—81no—
98#11758196—81no—
99C4×Dic61—81no—
100C2×#92418—41no—
101C2×#92418—41no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61#12011yescharacteristic
107C23×C61#13511yescharacteristic
108C23×C61#13711yescharacteristic
109Q8×C61—81no—
110Q8×C61—81no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—42no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—81no—
125C2×C4×C61—81no—
126C2×C4×C61—81no—
127C2×C4×C61—81no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×Dic61—22no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142#92418—81no—
143#92418—81no—
144#12265—611nomaximal, Sylow
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—81no—
154C22×C61#45211yescharacteristic
155C22×C61#45511yescharacteristic
156C22×C61B(4,𝔽2)11yescharacteristic
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—81no—
160C4×C61—81no—
161C4×C61—81no—
162C4×C61—81no—
163C4×C61—161no—
164Dic61—42no—
165Dic61—81no—
166Dic61—81no—
167Dic61—81no—
168#2771—611no—
169#2030D6111yescharacteristic
170#1614—611no—
171#1608—611no—
172#1352—611no—
173#1344—611no—
174#1317—611no—
175C2×C61—21no—
176C2×C61—21no—
177C2×C61—41no—
178C2×C61—41no—
179C2×C61#160611yescharacteristic
180C2×C61#219811yescharacteristic
181C2×C61#220111yescharacteristic
182#543C2×D6111yescharacteristic
183#484—1221no—
184#483—1221no—
185#400—1221no—
186#400—1221no—
187#399—611no—
188#397—611no—
189#389—1221no—
190#388—1221no—
191#387—1221no—
192#385—1221no—
193#381—21no—
194#381C2×D6111yescharacteristic
195#342—21no—
196#342C2×D6111yescharacteristic
197#328—1221no—
198#328—1221no—
199#323—611no—
200#323—611no—
201C61#1226511yescharacteristic, complemented, Sylow
202C23×C4C22⋊D6111yescharacteristic
203C22⋊Q8—21no—
204C22⋊Q8—21no—
205C22⋊Q8—41no—
206C22⋊Q8—41no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—1221no—
216C2×C22⋊C4—1221no—
217C2×C22⋊C4C22⋊D6111yescharacteristic
218C2×C22⋊C4C22×D6111yescharacteristic
219C2×C42—1221no—
220#107—2441no—
221#106—2441no—
222#103—2441no—
223#103—2441no—
224C22⋊C8—1221no—
225C22⋊C8—1221no—
226#95—21no—
227#95—21no—
228#95—41no—
229#95—41no—
230#95—611no—
231#95—611no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237C24C2×C22⋊D6111yescharacteristic
238C2×Q8—21no—
239C2×Q8—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4D4×D6111yescharacteristic
254C22×C4D4×D6111yescharacteristic
255C2×C8—2441no—
256C2×C8—2441no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—4881no—
262C4⋊C4—4881no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2442no—
266C4⋊C4—2442no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—2442no—
274C22⋊C4—2441no—
275C22⋊C4—2441no—
276C42—4881no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23#1451974511yescharacteristic
282C23#1451979711yescharacteristic
283C23#1451980811yescharacteristic
284Q8—81no—
285Q8—81no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—1222no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C8—4881no—
318C8—4881no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22#1683992211yescharacteristic
329C22#1683993911yescharacteristic
330C22#1683994811yescharacteristic
331C4—41no—
332C4—41no—
333C4—81no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—161no—
338C4—4881no—
339C4—4881no—
340C4—4881no—
341C4—2442no—
342C2—21no—
343C2—21no—
344C2—41no—
345C2—41no—
346C2#2144479711yescharacteristic
347C2#2144781311yescharacteristic
348C2#2144783011yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2030C2
socleC22×C61B(4,𝔽2)
prime radicalC24×C61C2×D4
hypercenter#2030D61
hypocenterC61#12265
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2030

Complements

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

NH ≅ G/Ntype
201. C61#12265semidirect

Maximal subgroups

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

subgroupindex
#214533342
#214448442
#214448102
#214438422
#214438182
#214437492
C61×#20302
#1226561