Finite Group Databasebeta

← #29590290

Subgroups — #29590290

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#21449086C211yesmaximal, characteristic
2#21445550C211yesmaximal, characteristic
3#21444130C211yesmaximal, characteristic
4#21443844C211yesmaximal, characteristic
5#21443842C211yesmaximal, characteristic
6#21443840C211yesmaximal, characteristic
7C61×#1351C211yesmaximal, characteristic
8C2×Q8×Dic61C411yescharacteristic, complemented
9C2×#14519733—21no—
10C2×#14519733C2211yescharacteristic
11#16839812—21no—
12#16839702C411yescharacteristic, complemented
13#16839698C2211yescharacteristic
14#16839696—21no—
15#16839685—21no—
16#16839681C411yescharacteristic, complemented
17#16839613—21no—
18#16839613C411yescharacteristic, complemented
19C22⋊C4×Dic61—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—24no—
31#14519733—41no—
32#14519733—41no—
33#14519733—42no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—41no—
40C2×#11758196C2×C411yescharacteristic
41C2×#11758196D411yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61D411yescharacteristic
45C2×C4×Dic61—21no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61—41no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519706—41no—
51C22⋊#92418—21no—
52C8×Dic61—41no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C22×Q8×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C24×C61C2×D411yescharacteristic
65C2×Q8×C61—42no—
66C2×Q8×C61—41no—
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×Dic61SD1612yes—
83C22×Dic61Q1612yes—
84C2×C8×C61—41no—
85C22⋊C4×C61—22no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—42no—
88C22⋊C4×C61—41no—
89C22⋊Dic61—22no—
90C22⋊Dic61—41no—
91C22⋊Dic61—42no—
92C22⋊Dic61—41no—
93C4⋊Dic61—42no—
94C4⋊Dic61—41no—
95#11758196—41no—
96#11758196—41no—
97#11758196—42no—
98#11758196—42no—
99#11758196—44no—
100#11758196—42no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—44no—
106C4×Dic61—41no—
107C4×Dic61—41no—
108C4×Dic61—42no—
109C2×#92418—41no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61C2×C22⋊C411yescharacteristic
115C23×C61C2×SD1611yescharacteristic
116C23×C61C2×Q1611yescharacteristic
117Q8×C61—42no—
118Q8×C61—42no—
119C2×C4×C61—22no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—42no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—22no—
135C2×Dic61—22no—
136C2×Dic61—22no—
137C2×Dic61—22no—
138C2×Dic61—22no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—81no—
150C2×Dic61—81no—
151C2×Dic61#9911yescharacteristic
152C2×Dic61#9911yescharacteristic
153C2×Dic61#10312yes—
154C2×Dic61#10312yes—
155C2×Dic61#10412yes—
156C8×C61—81no—
157#92418—81no—
158#11715—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—81no—
168C22×C61C2×#9911yescharacteristic
169C22×C61C2×#10311yescharacteristic
170C22×C61C2×#10411yescharacteristic
171C4×C61—42no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61—81no—
175C4×C61—82no—
176Dic61—22no—
177Dic61—42no—
178Dic61—41no—
179Dic61—41no—
180Dic61—82no—
181Dic61—81no—
182Dic61#32812yes—
183Dic61#32812yes—
184#2396—611no—
185#1740—611no—
186#1458—611no—
187#1352—611no—
188#1352—611no—
189#1351—611no—
190#1351D6111yescharacteristic
191C2×C61—21no—
192C2×C61—21no—
193C2×C61—41no—
194C2×C61—41no—
195C2×C61C2×#32811yescharacteristic
196C2×C61#212011yescharacteristic
197C2×C61#212611yescharacteristic
198C2×C4×Q8—611no—
199C2×#117—611no—
200C2×#117—1221no—
201#431—1221no—
202#400—611no—
203#399—611no—
204#398—1221no—
205#396—1221no—
206#395—611no—
207#393C2×D6111yescharacteristic
208C4×C4⋊C4—611no—
209C4×C4⋊C4—1221no—
210C4×C22⋊C4—1221no—
211#342—611no—
212#342—1221no—
213#342C2×D6111yescharacteristic
214#324—1221no—
215#323—611no—
216#323C2×D6111yescharacteristic
217C61#1171511yescharacteristic, complemented, Sylow
218C22×Q8C4×D6111yescharacteristic
219C23×C4—611no—
220C4×Q8—2441no—
221C4×Q8—2441no—
222#117—1224no—
223#117—2441no—
224#117—2441no—
225#117—2442no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—2441no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—611no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4C22×D6111yescharacteristic
240C2×C42—611no—
241C2×C42—611no—
242C2×C42—1221no—
243C2×C42—1221no—
244C2×C42—2441no—
245C4⋊C8—2441no—
246C22⋊C8—21no—
247C22⋊C8—1221no—
248C4×C8—2441no—
249#95—21no—
250#95—611no—
251#95—1221no—
252#95—1221no—
253#95—1221no—
254#95C4×D6111yescharacteristic
255C24D4×D6111yescharacteristic
256C2×Q8—42no—
257C2×Q8—41no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—612no—
264C22×C4—612no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1222no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—2441no—
273C22×C4C2×C4×D6111yescharacteristic
274C22×C4D4×D6111yescharacteristic
275C2×C8—41no—
276C2×C8—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2442no—
281C4⋊C4—2442no—
282C4⋊C4—2442no—
283C4⋊C4—2442no—
284C4⋊C4—2444no—
285C22⋊C4—22no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—41no—
289C22⋊C4—1222no—
290C22⋊C4—2441no—
291C22⋊C4—2442no—
292C22⋊C4—2441no—
293C42—1221no—
294C42—1221no—
295C42—1221no—
296C42—1221no—
297C42—2442no—
298C42—2441no—
299C42—2441no—
300C42—2444no—
301C23—21no—
302C23—21no—
303C23—41no—
304C23—41no—
305C23C22⋊C4×D6111yescharacteristic
306C23SD16×D6111yescharacteristic
307C23Q16×D6111yescharacteristic
308Q8—42no—
309Q8—42no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—612no—
326C2×C4—612no—
327C2×C4—612no—
328C2×C4—1222no—
329C2×C4—1222no—
330C2×C4—1222no—
331C2×C4—1222no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1222no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—4881no—
338C2×C4—4881no—
339C2×C4—2442no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C8—81no—
348C8—4881no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—81no—
358C22#99×D6111yescharacteristic
359C22#103×D6111yescharacteristic
360C22#104×D6111yescharacteristic
361C4—42no—
362C4—41no—
363C4—41no—
364C4—81no—
365C4—82no—
366C4—612no—
367C4—612no—
368C4—1222no—
369C4—4882no—
370C4—4881no—
371C4—2442no—
372C4—2441no—
373C4—2441no—
374C2—21no—
375C2—21no—
376C2—41no—
377C2—41no—
378C2#328×D6111yescharacteristic
379C2#2144745711yescharacteristic
380C2#2144748311yescharacteristic
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#11715
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
12. #16839702C4semidirect
16. #16839681C4semidirect
18. #16839613C4semidirect
217. C61#11715semidirect

Maximal subgroups

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

subgroupindex
#214490862
#214455502
#214441302
#214438442
#214438422
#214438402
C61×#13512
#1171561