Finite Group Databasebeta

← #29590885

Subgroups — #29590885

Order 15616.

390 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 69 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#21451389C211yesmaximal, characteristic
2#21445895C211yesmaximal, characteristic
3#21444130C211yesmaximal, characteristic
4#21443840C211yesmaximal, characteristic
5#21443820C211yesmaximal, characteristic
6#21443818C211yesmaximal, characteristic
7C61×#1351C211yesmaximal, characteristic
8C2×Q8×Dic61C411yescharacteristic, complemented
9C2×#14519733C2211yescharacteristic
10#16839812—21no—
11#16839694C411yescharacteristic, complemented
12#16839687C2211yescharacteristic
13#16839681C411yescharacteristic, complemented
14#16839656—21no—
15#16839649—21no—
16#16839645—21no—
17#16839637—21no—
18#16839629C411yescharacteristic, complemented
19#16839623—21no—
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#393C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C23×Dic61D411yescharacteristic
28Q8×Dic61—41no—
29Q8×Dic61—41no—
30#14519733—41no—
31#14519733—41no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196C2×C411yescharacteristic
37C2×#11758196D411yescharacteristic
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61D411yescharacteristic
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44#14519706—41no—
45C22⋊#92418—21no—
46C8×Dic61—41no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—41no—
53#14519684—41no—
54#14519684C2×C411yescharacteristic
55C22×Q8×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61C2311yescharacteristic
59C22⋊C8×C61—21no—
60#95×C61—21no—
61#95×C61C2×C411yescharacteristic
62C24×C61C2×D411yescharacteristic
63C2×Q8×C61—42no—
64C2×Q8×C61—41no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—41no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C2×C8×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—42no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊Dic61—41no—
88C22⋊Dic61—41no—
89C22⋊Dic61—41no—
90C22⋊Dic61—41no—
91C22⋊Dic61—41no—
92C4⋊Dic61—42no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96#11758196—41no—
97#11758196—41no—
98#11758196—42no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—42no—
104C2×#92418—41no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61C2×C22⋊C411yescharacteristic
110C23×C61#13511yescharacteristic
111C23×C61#13511yescharacteristic
112Q8×C61—42no—
113Q8×C61—42no—
114C2×C4×C61—22no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—41no—
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×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
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—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148C2×Dic61—81no—
149C2×Dic61#9911yescharacteristic
150C2×Dic61#9911yescharacteristic
151C8×C61—81no—
152#92418—81no—
153#11842—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—81no—
163C22×C61C2×#9911yescharacteristic
164C22×C61#41611yescharacteristic
165C22×C61#42111yescharacteristic
166C4×C61—42no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—81no—
170C4×C61—161no—
171Dic61—21no—
172Dic61—21no—
173Dic61—41no—
174Dic61—41no—
175Dic61—41no—
176Dic61—81no—
177Dic61—81no—
178Dic61—161no—
179#2599—611no—
180#1820—611no—
181#1458—611no—
182#1351—611no—
183#1351D6111yescharacteristic
184#1344—611no—
185#1344—611no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—41no—
189C2×C61—41no—
190C2×C61#151611yescharacteristic
191C2×C61#212011yescharacteristic
192C2×C61#212911yescharacteristic
193C2×C4×Q8—611no—
194C2×#117—611no—
195#431—1221no—
196#398—611no—
197#397—611no—
198#395—611no—
199#393C2×D6111yescharacteristic
200#388—1221no—
201#387—1221no—
202#387—1221no—
203#385—1221no—
204#383—611no—
205#381—1221no—
206#342—611no—
207#342—1221no—
208#342C2×D6111yescharacteristic
209#324—1221no—
210#323—611no—
211#323C2×D6111yescharacteristic
212C61#1184211yescharacteristic, complemented, Sylow
213C22×Q8C4×D6111yescharacteristic
214C23×C4—611no—
215C4×Q8—2441no—
216C4×Q8—2441no—
217#117—2441no—
218#117—2441no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—611no—
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4C22×D6111yescharacteristic
231C2×C42—611no—
232C2×C42—611no—
233C2×C42—1221no—
234C4⋊C8—2441no—
235C22⋊C8—21no—
236C22⋊C8—1221no—
237C4×C8—2441no—
238#95—21no—
239#95—611no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95—2441no—
246#95—2441no—
247#95C4×D6111yescharacteristic
248C24D4×D6111yescharacteristic
249C2×Q8—42no—
250C2×Q8—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—2441no—
265C22×C4—2441no—
266C22×C4C2×C4×D6111yescharacteristic
267C22×C4D4×D6111yescharacteristic
268C2×C8—41no—
269C2×C8—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2442no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C4⋊C4—2442no—
277C22⋊C4—41no—
278C22⋊C4—42no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—2441no—
282C22⋊C4—2441no—
283C22⋊C4—2441no—
284C22⋊C4—2441no—
285C22⋊C4—2441no—
286C42—1221no—
287C42—1221no—
288C42—1221no—
289C42—1221no—
290C42—2442no—
291C23—21no—
292C23—21no—
293C23—41no—
294C23—41no—
295C23C22⋊C4×D6111yescharacteristic
296C23#1451979811yescharacteristic
297C23#1451980011yescharacteristic
298Q8—42no—
299Q8—42no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—4881no—
323C2×C4—4881no—
324C2×C4—4881no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C8—81no—
338C8—4881no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—81no—
348C22#99×D6111yescharacteristic
349C22#1683975711yescharacteristic
350C22#1683977711yescharacteristic
351C4—42no—
352C4—41no—
353C4—41no—
354C4—81no—
355C4—161no—
356C4—1221no—
357C4—1221no—
358C4—9761no—
359C4—4881no—
360C4—4881no—
361C4—2441no—
362C4—2441no—
363C4—2441no—
364C2—21no—
365C2—21no—
366C2—41no—
367C2—41no—
368C2#2144437411yescharacteristic
369C2#2144745711yescharacteristic
370C2#2144749211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1351C2
socleC22×C61C2×#99
prime radicalC24×C61C2×D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1351D61
hypocenterC61#11842
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
8. C2×Q8×Dic61C4semidirect
11. #16839694C4semidirect
13. #16839681C4semidirect
18. #16839629C4semidirect
212. C61#11842semidirect

Maximal subgroups

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

subgroupindex
#214513892
#214458952
#214441302
#214438402
#214438202
#214438182
C61×#13512
#1184261