Finite Group Databasebeta

← #29569211

Subgroups — #29569211

Order 15616.

398 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 87 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#21453812C211yesmaximal, characteristic
2#21447361C211yesmaximal, characteristic
3#21447229C211yesmaximal, characteristic
4#21447227C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic
6#21443644C211yesmaximal, characteristic
7C61×#1272C211yesmaximal, characteristic
8C2×#14519709—21no—
9C2×#14519702—21no—
10C2×#14519702—21no—
11C2×#14519701—21no—
12#16839683—21no—
13#16839683—21no—
14#16839682—21no—
15#16839669—21no—
16#16839668C2211yescharacteristic
17#16839668C2211yescharacteristic
18#16839666—21no—
19#16839666—21no—
20#16839632C2211yescharacteristic
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#391C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122D411yescharacteristic
29C22×Dic122D411yescharacteristic
30C22×#92418—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×C4×Dic61—21no—
40#14519709—42no—
41#14519702—42no—
42#14519702—42no—
43#14519701—42no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×Q8×C61D411yescharacteristic
52C22×C8×C61—21no—
53C22×C8×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56#95×C61—21no—
57#95×C61—21no—
58C2×Q8×C61—21no—
59C2×Q8×C61—41no—
60C2×Q8×C61—41no—
61C2×Q8×C61SD1612yes—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—41no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×Dic122—81no—
79C2×Dic122—81no—
80C2×Dic122—81no—
81C2×Dic122SD1612yes—
82C2×Dic122Q1612yes—
83C2×C8×C61—22no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C4⋊C4×C61—41no—
90C42×C61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61—81no—
100#11758196—81no—
101#11758196—81no—
102C4×Dic61—81no—
103C2×#92418—41no—
104C2×#92418—41no—
105C2×#92418—41no—
106C23×C61#12011yescharacteristic
107Q8×C61—42no—
108Q8×C61—81no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—22no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61C2×SD1611yescharacteristic
122C2×C4×C61C2×SD1611yescharacteristic
123C2×C4×C61C2×Q1611yescharacteristic
124C2×C4×C61#13711yescharacteristic
125C2×C4×C61#13711yescharacteristic
126C2×C4×C61#13711yescharacteristic
127C2×Dic61—22no—
128C2×Dic61—22no—
129C2×Dic61—41no—
130C2×Dic61—41no—
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—81no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142Dic122—42no—
143Dic122—42no—
144Dic122—81no—
145Dic122—81no—
146Dic122—84no—
147C8×C61—42no—
148C8×C61—81no—
149#92418—81no—
150#7812—611nomaximal, Sylow
151C22×C61#44811yescharacteristic
152C22×C61#44811yescharacteristic
153C22×C61#45111yescharacteristic
154C22×C61#45311yescharacteristic
155C22×C61#45511yescharacteristic
156C22×C61#45511yescharacteristic
157C22×C61#45811yescharacteristic
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—42no—
165C4×C61—81no—
166Dic61—42no—
167Dic61—42no—
168Dic61—81no—
169Dic61—81no—
170Dic61—161no—
171#2811—611no—
172#2096—611no—
173#2072—611no—
174#2072—611no—
175#1272—611no—
176#1272—611no—
177#1272D6111yescharacteristic
178C2×C61#160811yescharacteristic
179C2×C61#160811yescharacteristic
180C2×C61#161411yescharacteristic
181C2×C61#162311yescharacteristic
182C2×C61#164511yescharacteristic
183C2×C61#164511yescharacteristic
184C2×C61#165911yescharacteristic
185C2×#106—1221no—
186C2×#103—1221no—
187C2×#103—1221no—
188C2×#103—1221no—
189#395—1221no—
190#395—1221no—
191#395—1221no—
192#391—611no—
193#391—611no—
194#391—1221no—
195#391—1221no—
196#391—1221no—
197#391C2×D6111yescharacteristic
198#384—611no—
199#340—1221no—
200#340—1221no—
201#336—611no—
202#336C2×D6111yescharacteristic
203#336C2×D6111yescharacteristic
204C61#781211yescharacteristic, complemented, Sylow
205C22×Q8—611no—
206C22×Q8—611no—
207C22×Q8—1221no—
208C22×Q8D24411yescharacteristic
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—1221no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4D24411yescharacteristic
221C2×C42—1221no—
222C2×C42C22×D6111yescharacteristic
223#106—2442no—
224#103—2442no—
225#103—2442no—
226#103—2442no—
227#95—21no—
228#95—21no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236C2×Q8—21no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—612no—
240C2×Q8—612no—
241C2×Q8—1221no—
242C2×Q8—1221no—
243C2×Q8—4881no—
244C2×Q8—4881no—
245C2×Q8—4881no—
246C2×Q8—2441no—
247C2×Q8—2441no—
248C2×Q8—2441no—
249C2×Q8—2441no—
250C2×Q8#1175819012yes—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—2441no—
258C22×C4C2×D24411yescharacteristic
259C22×C4D4×D6111yescharacteristic
260C22×C4D4×D6111yescharacteristic
261C2×C8—22no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—2441no—
268C2×C8—2441no—
269C2×C8—2441no—
270C4⋊C4—41no—
271C4⋊C4—4881no—
272C4⋊C4—4881no—
273C4⋊C4—4881no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C42—41no—
283C42—4881no—
284C23#1451974711yescharacteristic
285Q8—42no—
286Q8—81no—
287Q8—4881no—
288Q8—4881no—
289Q8—4884no—
290Q8—2442no—
291Q8—2442no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—1222no—
305C2×C4—1222no—
306C2×C4—4881no—
307C2×C4—4881no—
308C2×C4—4881no—
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—
319C2×C4SD16×D6111yescharacteristic
320C2×C4C2×#1175819011yescharacteristic
321C2×C4Q16×D6111yescharacteristic
322C2×C4#1451980611yescharacteristic
323C2×C4#1451980911yescharacteristic
324C2×C4#1451981011yescharacteristic
325C8—42no—
326C8—81no—
327C8—4881no—
328C22#1683990211yescharacteristic
329C22#1683990311yescharacteristic
330C22#1683991911yescharacteristic
331C22#1683993111yescharacteristic
332C22#1683994111yescharacteristic
333C22#1683994211yescharacteristic
334C22#1683995311yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—81no—
343C4—9761no—
344C4—4881no—
345C4—4881no—
346C4—2442no—
347C4—2442no—
348C2#2144481111yescharacteristic
349C2#2144481211yescharacteristic
350C2#2144484511yescharacteristic
351C2#2144489911yescharacteristic
352C2#2144504111yescharacteristic
353C2#2144504211yescharacteristic
354C2#2144512711yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socle, prime radicalC23×C61#120
hypercenter#1272D61
hypocenterC61#7812
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
204. C61#7812semidirect

Maximal subgroups

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

subgroupindex
#214538122
#214473612
#214472292
#214472272
#214436442
C61×#12722
#781261