Finite Group Databasebeta

← #29592914

Subgroups — #29592914

Order 15616.

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

normal subgroups only

This group has 370 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#21454007C211yesmaximal, characteristic
2#21444810C211yesmaximal, characteristic
3#21444776C211yesmaximal, characteristic
4#21443839C211yesmaximal, characteristic
5#21443818C211yesmaximal, characteristic
6#21443767C211yesmaximal, characteristic
7C61×#2062C211yesmaximal, characteristic
8#16840090—21no—
9#16839917—21no—
10#16839704—21no—
11#16839703—21no—
12#16839700—21no—
13#16839690—21no—
14#16839687C2211yescharacteristic
15#16839682—21no—
16#16839674C2211yescharacteristic
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
27C22×Dic122D411yescharacteristic
28C2×#11758202—41no—
29C2×C4⋊Dic61D411yescharacteristic
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35#14519708—41no—
36#14519701—41no—
37#14519700—41no—
38C22⋊#92418—21no—
39C22⋊#92418—21no—
40#14519684—21no—
41#14519684—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×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—
78C2×Dic122—41no—
79C2×Dic122—81no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—81no—
85C4⋊C4×C61—82no—
86C22⋊C4×C61—22no—
87C22⋊C4×C61—21no—
88C22⋊C4×C61—21no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—81no—
96#11758202—82no—
97C4⋊Dic61—41no—
98#11758196—81no—
99#11758196—81no—
100#11758196—81no—
101C2×#92418—41no—
102C2×#92418—41no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61#12011yescharacteristic
108C23×C61#13511yescharacteristic
109C23×C61#13711yescharacteristic
110Q8×C61—81no—
111Q8×C61—81no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—42no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—42no—
122C2×C4×C61—41no—
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—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—
142C2×Dic61—41no—
143Dic122—42no—
144Dic122—81no—
145#92418—81no—
146#92418—81no—
147#12233—611nomaximal, Sylow
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—81no—
157C22×C61#45211yescharacteristic
158C22×C61#45611yescharacteristic
159C22×C61B(4,𝔽2)11yescharacteristic
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—81no—
163C4×C61—82no—
164C4×C61—81no—
165C4×C61—81no—
166C4×C61—81no—
167Dic61—81no—
168Dic61—81no—
169Dic61—81no—
170Dic61—81no—
171#2835—611no—
172#2062D6111yescharacteristic
173#1608—611no—
174#1602—611no—
175#1351—611no—
176#1344—611no—
177#1326—611no—
178C2×C61—21no—
179C2×C61—21no—
180C2×C61—41no—
181C2×C61—41no—
182C2×C61#160311yescharacteristic
183C2×C61#219911yescharacteristic
184C2×C61#220111yescharacteristic
185#543C2×D6111yescharacteristic
186#483—1221no—
187#451—1221no—
188#400—1221no—
189#400—1221no—
190#400—1221no—
191#397—611no—
192#397—1221no—
193#395—1221no—
194#393—611no—
195#385—21no—
196#385—1221no—
197#385C2×D6111yescharacteristic
198#342—21no—
199#342C2×D6111yescharacteristic
200#328—1221no—
201#328—1221no—
202#323—611no—
203#323—611no—
204C61#1223311yescharacteristic, complemented, Sylow
205C22×Q8—611no—
206C23×C4C22⋊D6111yescharacteristic
207C2×Q16—2441no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—41no—
211C22⋊Q8—41no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—41no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4—1221no—
222C2×C22⋊C4C22⋊D6111yescharacteristic
223C2×C22⋊C4C22×D6111yescharacteristic
224#106—2441no—
225#103—2441no—
226#103—2441no—
227C22⋊C8—1221no—
228C22⋊C8—1221no—
229#95—21no—
230#95—41no—
231#95—611no—
232#95—611no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240C24C2×C22⋊D6111yescharacteristic
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—4881no—
244C2×Q8—2441no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—81no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4D4×D6111yescharacteristic
257C22×C4D4×D6111yescharacteristic
258Q16—4882no—
259C2×C8—2441no—
260C2×C8—2441no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—81no—
266C4⋊C4—82no—
267C4⋊C4—4881no—
268C4⋊C4—4881no—
269C4⋊C4—4881no—
270C4⋊C4—2441no—
271C22⋊C4—22no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—4881no—
279C22⋊C4—2441no—
280C22⋊C4—2441no—
281C23—21no—
282C23—21no—
283C23—41no—
284C23—41no—
285C23#1451974511yescharacteristic
286C23#1451979711yescharacteristic
287C23#1451980811yescharacteristic
288Q8—81no—
289Q8—81no—
290Q8—4881no—
291Q8—2442no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C8—4881no—
324C8—4881no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22#1683992211yescharacteristic
335C22#1683994411yescharacteristic
336C22#1683994811yescharacteristic
337C4—41no—
338C4—41no—
339C4—81no—
340C4—82no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—4881no—
345C4—4881no—
346C4—4881no—
347C4—4881no—
348C2—21no—
349C2—21no—
350C2—41no—
351C2—41no—
352C2#2144478011yescharacteristic
353C2#2144781811yescharacteristic
354C2#2144783011yescharacteristic
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#12233
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
204. C61#12233semidirect

Maximal subgroups

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

subgroupindex
#214540072
#214448102
#214447762
#214438392
#214438182
#214437672
C61×#20622
#1223361