Finite Group Databasebeta

← #29590304

Subgroups — #29590304

Order 15616.

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

normal subgroups only

This group has 448 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#21451645C211yesmaximal, characteristic
2#21445550C211yesmaximal, characteristic
3#21444130C211yesmaximal, characteristic
4#21443844C211yesmaximal, characteristic
5#21443843C211yesmaximal, characteristic
6#21443842C211yesmaximal, characteristic
7C61×#1352C211yesmaximal, characteristic
8C2×#14519776C411yescharacteristic, complemented
9C2×#14519733—21no—
10C2×#14519733C2211yescharacteristic
11#16839812—21no—
12#16839702C411yescharacteristic, complemented
13#16839700C411yescharacteristic, complemented
14#16839698C2211yescharacteristic
15#16839682—21no—
16#16839674—21no—
17#16839657—21no—
18#16839626C411yescharacteristic, complemented
19#16839620—21no—
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#399C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×Dic122—21no—
28C23×Dic61D411yescharacteristic
29#14519776—41no—
30#14519776—41no—
31#14519733—24no—
32#14519733—41no—
33#14519733—41no—
34#14519733—42no—
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—41no—
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48#14519706—41no—
49C22⋊#92418—21no—
50C8×Dic61—41no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61C2311yescharacteristic
62C22⋊C8×C61—21no—
63#95×C61C2×C411yescharacteristic
64C24×C61C2×D411yescharacteristic
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—22no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—41no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61SD1612yes—
81C22×Dic61Q1612yes—
82C2×Dic122—42no—
83C2×Dic122—81no—
84C2×Dic122—81no—
85C2×C8×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—81no—
88C22⋊C4×C61—22no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—81no—
92C22⋊Dic61—22no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—81no—
96C4⋊Dic61—41no—
97#11758196—41no—
98#11758196—41no—
99#11758196—44no—
100#11758196—41no—
101#11758196—41no—
102#11758196—42no—
103#11758196—81no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—44no—
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
117C2×C4×C61—21no—
118C2×C4×C61—21no—
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—41no—
127C2×C4×C61—41no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—22no—
133C2×Dic61—22no—
134C2×Dic61—22no—
135C2×Dic61—22no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—42no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—81no—
148C2×Dic61—81no—
149C2×Dic61#9911yescharacteristic
150C2×Dic61#9911yescharacteristic
151C2×Dic61#10312yes—
152C2×Dic61#10312yes—
153C2×Dic61#10412yes—
154Dic122—84no—
155C8×C61—81no—
156#92418—81no—
157#11718—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—81no—
167C22×C61C2×#9911yescharacteristic
168C22×C61C2×#10311yescharacteristic
169C22×C61C2×#10411yescharacteristic
170C4×C61—41no—
171C4×C61—41no—
172C4×C61—81no—
173C4×C61—82no—
174C4×C61—81no—
175Dic61—22no—
176Dic61—41no—
177Dic61—41no—
178Dic61—81no—
179Dic61—82no—
180Dic61—81no—
181Dic61#32812yes—
182Dic61#32812yes—
183#2628—611no—
184#1740—611no—
185#1458—611no—
186#1352—611no—
187#1352—611no—
188#1352—611no—
189#1352D6111yescharacteristic
190C2×C61—21no—
191C2×C61—21no—
192C2×C61—41no—
193C2×C61—41no—
194C2×C61C2×#32811yescharacteristic
195C2×C61#212311yescharacteristic
196C2×C61#212811yescharacteristic
197C2×C4⋊Q8—611no—
198C2×#117—611no—
199C2×#117—1221no—
200#431—1221no—
201#400—611no—
202#400—611no—
203#399—611no—
204#399C2×D6111yescharacteristic
205#395—1221no—
206#393—1221no—
207#389—1221no—
208#382—611no—
209#380—1221no—
210#342—611no—
211#342—1221no—
212#342C2×D6111yescharacteristic
213#324—1221no—
214#323—611no—
215#323C2×D6111yescharacteristic
216C61#1171811yescharacteristic, complemented, Sylow
217C22×Q8—1221no—
218C23×C4—611no—
219C4⋊Q8—2441no—
220C4⋊Q8—2441no—
221#117—1224no—
222#117—2441no—
223#117—2441no—
224#117—2442no—
225C2×C4⋊C4—21no—
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—2441no—
233C2×C4⋊C4C4×D6111yescharacteristic
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—2441no—
243C4⋊C8—2441no—
244C22⋊C8—21no—
245C22⋊C8—1221no—
246C4×C8—2441no—
247#95—611no—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251#95—1221no—
252#95—1221no—
253#95C4×D6111yescharacteristic
254C24D4×D6111yescharacteristic
255C2×Q8—4881no—
256C2×Q8—4881no—
257C2×Q8—2442no—
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—41no—
278C4⋊C4—81no—
279C4⋊C4—4881no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C4⋊C4—2442no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C4⋊C4—2444no—
287C22⋊C4—22no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—81no—
291C22⋊C4—1222no—
292C22⋊C4—4881no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C42—1221no—
296C42—1221no—
297C42—1221no—
298C42—1221no—
299C42—2444no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23C22⋊C4×D6111yescharacteristic
305C23SD16×D6111yescharacteristic
306C23Q16×D6111yescharacteristic
307Q8—4884no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—612no—
324C2×C4—612no—
325C2×C4—612no—
326C2×C4—1222no—
327C2×C4—1222no—
328C2×C4—1222no—
329C2×C4—1222no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—2442no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C8—81no—
346C8—4881no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—81no—
356C22#99×D6111yescharacteristic
357C22#103×D6111yescharacteristic
358C22#104×D6111yescharacteristic
359C4—41no—
360C4—41no—
361C4—81no—
362C4—82no—
363C4—81no—
364C4—612no—
365C4—612no—
366C4—1222no—
367C4—4881no—
368C4—4882no—
369C4—4881no—
370C4—2441no—
371C4—2441no—
372C2—21no—
373C2—21no—
374C2—41no—
375C2—41no—
376C2#328×D6111yescharacteristic
377C2#2144747111yescharacteristic
378C2#2144748911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1352C2
socleC22×C61C2×#99
prime radicalC24×C61C2×D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1352D61
hypocenterC61#11718
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
8. C2×#14519776C4semidirect
12. #16839702C4semidirect
13. #16839700C4semidirect
18. #16839626C4semidirect
216. C61#11718semidirect

Maximal subgroups

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

subgroupindex
#214516452
#214455502
#214441302
#214438442
#214438432
#214438422
C61×#13522
#1171861