Finite Group Databasebeta

← #29593060

Subgroups — #29593060

Order 15616.

378 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 59 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#21453791C211yesmaximal, characteristic
2#21444844C211yesmaximal, characteristic
3#21444844C211yesmaximal, characteristic
4#21443842C211yesmaximal, characteristic
5#21443842C211yesmaximal, characteristic
6#21443767C211yesmaximal, characteristic
7C61×#2062C211yesmaximal, characteristic
8#16840095—21no—
9#16840095—21no—
10#16839704—21no—
11#16839698C2211yescharacteristic
12#16839698C2211yescharacteristic
13#16839695—21no—
14#16839659—21no—
15#16839658—21no—
16#16839655—21no—
17#16839635—21no—
18#16839499—21no—
19#16839499—21no—
20#16839486C2211yescharacteristic
21#16839486C2211yescharacteristic
22C61×#543C2211yescharacteristic
23C61×#385—21no—
24C61×#385C2211yescharacteristic
25C61×#342—21no—
26C61×#342C2211yescharacteristic
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61D411yescharacteristic
29C2×C4⋊Dic61D411yescharacteristic
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C4×Dic61—21no—
37#14519710—41no—
38#14519710—41no—
39#14519701—41no—
40#14519701—41no—
41C22⋊#92418—21no—
42C22⋊#92418—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×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—41no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61D411yescharacteristic
59C2×C22⋊C4×C61C2311yescharacteristic
60#95×C61—21no—
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—41no—
70C22×C4×C61—41no—
71C22×C4×C61—81no—
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—81no—
83C4⋊C4×C61—82no—
84C22⋊C4×C61—21no—
85C22⋊C4×C61—22no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61Q1612yes—
91C22⋊Dic61—42no—
92C22⋊Dic61—81no—
93C4⋊Dic61—42no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96#11758196—42no—
97#11758196—81no—
98#11758196—81no—
99#11758196—81no—
100C4×Dic61—81no—
101C2×#92418—41no—
102C2×#92418—41no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61#12011yescharacteristic
108C23×C61C2×Q1611yescharacteristic
109C23×C61#13711yescharacteristic
110Q8×C61—81no—
111Q8×C61—81no—
112C2×C4×C61—22no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—42no—
121C2×C4×C61—41no—
122C2×C4×C61—42no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—81no—
127C2×C4×C61—81no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61—81no—
131C2×Dic61—22no—
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—
142C2×Dic61—41no—
143#92418—81no—
144#92418—81no—
145#12255—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—81no—
155C22×C61#45111yescharacteristic
156C22×C61#45611yescharacteristic
157C22×C61B(4,𝔽2)11yescharacteristic
158C4×C61—42no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61—82no—
162C4×C61—81no—
163C4×C61—81no—
164C4×C61—81no—
165Dic61—42no—
166Dic61—81no—
167Dic61—81no—
168Dic61—81no—
169#2807—611no—
170#2062D6111yescharacteristic
171#1614—611no—
172#1614—611no—
173#1352—611no—
174#1352—611no—
175#1326—611no—
176C2×C61—21no—
177C2×C61—21no—
178C2×C61—41no—
179C2×C61—41no—
180C2×C61#160511yescharacteristic
181C2×C61#219811yescharacteristic
182C2×C61#220011yescharacteristic
183#543C2×D6111yescharacteristic
184#484—1221no—
185#484—1221no—
186#400—1221no—
187#399—611no—
188#399—611no—
189#398—1221no—
190#389—1221no—
191#389—1221no—
192#388—1221no—
193#385—21no—
194#385—1221no—
195#385C2×D6111yescharacteristic
196#342—21no—
197#342C2×D6111yescharacteristic
198#328—1221no—
199#328—1221no—
200#323—611no—
201#323—611no—
202C61#1225511yescharacteristic, complemented, Sylow
203C23×C4C22⋊D6111yescharacteristic
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206C22⋊Q8—41no—
207C22⋊Q8—41no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4C22⋊D6111yescharacteristic
222C2×C22⋊C4C22×D6111yescharacteristic
223C2×C42—1221no—
224#107—2441no—
225#107—2441no—
226#103—2441no—
227#103—2441no—
228C22⋊C8—1221no—
229C22⋊C8—1221no—
230#95—21no—
231#95—41no—
232#95—611no—
233#95—611no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237#95—1221no—
238C24C2×C22⋊D6111yescharacteristic
239C2×Q8—21no—
240C2×Q8—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—81no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4D4×D6111yescharacteristic
253C22×C4D4×D6111yescharacteristic
254C2×C8—2441no—
255C2×C8—2441no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—81no—
261C4⋊C4—82no—
262C4⋊C4—4881no—
263C4⋊C4—4881no—
264C4⋊C4—4881no—
265C4⋊C4—2441no—
266C4⋊C4—2441no—
267C4⋊C4—2442no—
268C4⋊C4—2442no—
269C22⋊C4—21no—
270C22⋊C4—22no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—4881no—
276C22⋊C4—2442no—
277C22⋊C4#1175820212yes—
278C42—4881no—
279C23—21no—
280C23—21no—
281C23—41no—
282C23—41no—
283C23#1451974511yescharacteristic
284C23C2×#1175820211yescharacteristic
285C23#1451980711yescharacteristic
286Q8—81no—
287Q8—81no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—1222no—
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—
317C2×C4—2441no—
318C2×C4—2441no—
319C8—4881no—
320C8—4881no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—81no—
330C22#1683991711yescharacteristic
331C22#1683994411yescharacteristic
332C22#1683994811yescharacteristic
333C4—42no—
334C4—41no—
335C4—41no—
336C4—82no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4—4881no—
341C4—4881no—
342C4—4881no—
343C4—2442no—
344C2—21no—
345C2—21no—
346C2—41no—
347C2—41no—
348C2#2144479211yescharacteristic
349C2#2144781311yescharacteristic
350C2#2144782411yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2062C2
socleC22×C61B(4,𝔽2)
prime radicalC24×C61C2×D4
hypercenter#2062D61
hypocenterC61#12255
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2062

Complements

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

NH ≅ G/Ntype
202. C61#12255semidirect

Maximal subgroups

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

subgroupindex
#214537912
#214448442
#214438422
#214437672
C61×#20622
#1225561