Finite Group Databasebeta

← #29590200

Subgroups — #29590200

Order 15616.

468 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 83 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#21451584C211yesmaximal, characteristic
2#21445550C211yesmaximal, characteristic
3#21444130C211yesmaximal, characteristic
4#21443820C211yesmaximal, characteristic
5#21443819C211yesmaximal, characteristic
6#21443818C211yesmaximal, characteristic
7C61×#1344C211yesmaximal, characteristic
8C2×#14519776C411yescharacteristic, complemented
9C2×#14519754—21no—
10C2×#14519733—21no—
11C2×#14519733C2211yescharacteristic
12#16839812—21no—
13#16839696—21no—
14#16839694C411yescharacteristic, complemented
15#16839693C411yescharacteristic, complemented
16#16839690—21no—
17#16839687C2211yescharacteristic
18#16839666—21no—
19#16839626C411yescharacteristic, complemented
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#397C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×Dic122—21no—
28C23×Dic61D411yescharacteristic
29#14519776—41no—
30#14519776—41no—
31#14519754—42no—
32#14519754—42no—
33#14519733—24no—
34#14519733—41no—
35#14519733—41no—
36#14519733—42no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—41no—
43C2×#11758196C2×C411yescharacteristic
44C2×#11758196D411yescharacteristic
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61D411yescharacteristic
48C2×C4×Dic61—41no—
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51#14519706—41no—
52C22⋊#92418—21no—
53C8×Dic61—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684C2×C411yescharacteristic
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61C2311yescharacteristic
63C22⋊C8×C61—21no—
64#95×C61—21no—
65#95×C61C2×C411yescharacteristic
66C24×C61C2×D411yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—41no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—22no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—41no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61D812yes—
83C22×Dic61SD1612yes—
84C2×Dic122—41no—
85C2×Dic122—41no—
86C2×Dic122—42no—
87C2×Dic122—42no—
88C2×C8×C61—41no—
89C4⋊C4×C61—41no—
90C22⋊C4×C61—22no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—41no—
95C22⋊Dic61—22no—
96C22⋊Dic61—41no—
97C22⋊Dic61—41no—
98C22⋊Dic61—41no—
99C22⋊Dic61—41no—
100C4⋊Dic61—42no—
101C4⋊Dic61—41no—
102#11758196—41no—
103#11758196—41no—
104#11758196—42no—
105#11758196—44no—
106#11758196—42no—
107#11758196—42no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C4×Dic61—44no—
113C2×#92418—41no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61C2×C22⋊C411yescharacteristic
119C23×C61C2×D811yescharacteristic
120C23×C61C2×SD1611yescharacteristic
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—42no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—81no—
133C2×C4×C61—81no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—22no—
137C2×Dic61—22no—
138C2×Dic61—22no—
139C2×Dic61—22no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—42no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—81no—
152C2×Dic61—81no—
153C2×Dic61#9911yescharacteristic
154C2×Dic61#9911yescharacteristic
155C2×Dic61#10212yes—
156C2×Dic61#10212yes—
157C2×Dic61#10412yes—
158Dic122—82no—
159Dic122—82no—
160C8×C61—81no—
161#92418—81no—
162#11694—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—81no—
172C22×C61C2×#9911yescharacteristic
173C22×C61C2×#10211yescharacteristic
174C22×C61C2×#10411yescharacteristic
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—81no—
178C4×C61—82no—
179C4×C61—81no—
180Dic61—22no—
181Dic61—41no—
182Dic61—41no—
183Dic61—81no—
184Dic61—82no—
185Dic61—81no—
186Dic61#32712yes—
187Dic61#32712yes—
188#2621—611no—
189#1740—611no—
190#1458—611no—
191#1344—611no—
192#1344—611no—
193#1344—611no—
194#1344D6111yescharacteristic
195C2×C61—21no—
196C2×C61—21no—
197C2×C61—41no—
198C2×C61—41no—
199C2×C61C2×#32711yescharacteristic
200C2×C61#212311yescharacteristic
201C2×C61#212911yescharacteristic
202C2×C4⋊Q8—611no—
203C2×C22⋊Q8—1221no—
204C2×#117—611no—
205C2×#117—1221no—
206#431—1221no—
207#398—611no—
208#398—611no—
209#398—1221no—
210#397—611no—
211#397—1221no—
212#397C2×D6111yescharacteristic
213#391—1221no—
214#382—611no—
215#342—611no—
216#342—1221no—
217#342C2×D6111yescharacteristic
218#324—1221no—
219#323—611no—
220#323C2×D6111yescharacteristic
221C61#1169411yescharacteristic, complemented, Sylow
222C22×Q8—1221no—
223C23×C4—611no—
224C4⋊Q8—2441no—
225C4⋊Q8—2441no—
226C22⋊Q8—2442no—
227C22⋊Q8—2442no—
228#117—1224no—
229#117—2441no—
230#117—2441no—
231#117—2442no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—2441no—
240C2×C4⋊C4C4×D6111yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—611no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4C22×D6111yescharacteristic
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—2441no—
250C4⋊C8—2441no—
251C22⋊C8—21no—
252C22⋊C8—1221no—
253C4×C8—2441no—
254#95—21no—
255#95—611no—
256#95—1221no—
257#95—1221no—
258#95—1221no—
259#95—1221no—
260#95C4×D6111yescharacteristic
261C24D4×D6111yescharacteristic
262C2×Q8—2442no—
263C2×Q8—2441no—
264C2×Q8—2441no—
265C2×Q8—2442no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—612no—
272C22×C4—612no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1222no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—2441no—
281C22×C4C2×C4×D6111yescharacteristic
282C22×C4D4×D6111yescharacteristic
283C2×C8—41no—
284C2×C8—2441no—
285C4⋊C4—41no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4—2442no—
290C4⋊C4—2442no—
291C4⋊C4—2442no—
292C4⋊C4—2442no—
293C4⋊C4—2444no—
294C22⋊C4—22no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—1222no—
300C22⋊C4—2441no—
301C22⋊C4—2441no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C42—1221no—
305C42—1221no—
306C42—1221no—
307C42—1221no—
308C42—2444no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23C22⋊C4×D6111yescharacteristic
314C23D8×D6111yescharacteristic
315C23SD16×D6111yescharacteristic
316Q8—4882no—
317Q8—4882no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—612no—
334C2×C4—612no—
335C2×C4—612no—
336C2×C4—1222no—
337C2×C4—1222no—
338C2×C4—1222no—
339C2×C4—1222no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—4881no—
345C2×C4—4881no—
346C2×C4—2442no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C8—81no—
356C8—4881no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22#99×D6111yescharacteristic
367C22#102×D6111yescharacteristic
368C22#104×D6111yescharacteristic
369C4—41no—
370C4—41no—
371C4—81no—
372C4—82no—
373C4—81no—
374C4—612no—
375C4—612no—
376C4—1222no—
377C4—4881no—
378C4—4882no—
379C4—4881no—
380C4—2441no—
381C4—2441no—
382C2—21no—
383C2—21no—
384C2—41no—
385C2—41no—
386C2#327×D6111yescharacteristic
387C2#2144747111yescharacteristic
388C2#2144749211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1344C2
socleC22×C61C2×#99
prime radicalC24×C61C2×D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1344D61
hypocenterC61#11694
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
8. C2×#14519776C4semidirect
14. #16839694C4semidirect
15. #16839693C4semidirect
19. #16839626C4semidirect
221. C61#11694semidirect

Maximal subgroups

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

subgroupindex
#214515842
#214455502
#214441302
#214438202
#214438192
#214438182
C61×#13442
#1169461