Finite Group Databasebeta

← #29589671

Subgroups — #29589671

Order 15616.

416 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 71 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#21451018C211yesmaximal, characteristic
2#21444156C211yesmaximal, characteristic
3#21444136C211yesmaximal, characteristic
4#21443764C211yesmaximal, characteristic, complemented
5#21443764C211yesmaximal, characteristic, complemented
6#21443763C211yesmaximal, characteristic, complemented
7C61×#1324C211yesmaximal, characteristic, complemented
8C2×#14519768C411yescharacteristic
9C2×#14519739C2211yescharacteristic
10#16839724—21no—
11C22⋊C8×D61—21no—
12#16839686—21no—
13#16839686—21no—
14#16839664C411yescharacteristic
15#16839663C411yescharacteristic
16#16839636—21no—
17#16839636—21no—
18#16839631C2211yescharacteristic
19C4×#11758196C411yescharacteristic
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22#16839485—21no—
23#16839485—21no—
24C61×#382C2211yescharacteristic
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C2×#11758189—41no—
31C2×C8×D61—41no—
32#14519768—41no—
33#14519768—41no—
34#14519739—41no—
35#14519739—41no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198D411yescharacteristic
47C2×#11758198D411yescharacteristic
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61C2×C411yescharacteristic
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52#14519689—41no—
53#14519689—41no—
54#14519684—21no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61C2311yescharacteristic
57C2×C42×C61C2×C411yescharacteristic
58C22⋊C8×C61—21no—
59C22⋊C8×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62C23×D61C22⋊C411yescharacteristic
63C23×D61C22⋊C411yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C2×D244—22no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—41no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—81no—
82C2×C4×D61—81no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C42×C61—21no—
88C42×C61—21no—
89#11758198—41no—
90#11758198—41no—
91#11758198—42no—
92#11758198—42no—
93#11758198—81no—
94#11758198—81no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98#11758196—42no—
99#11758196—42no—
100#11758196—81no—
101#11758196—81no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C2×#92418—41no—
107C2×#92418—41no—
108#11758189—82no—
109C8×D61—82no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61#10112yes—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—41no—
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—41no—
133C2×C4×C61#13111yescharacteristic
134C2×C4×C61#13111yescharacteristic
135C2×Dic61—22no—
136C2×Dic61—21no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61#9911yescharacteristic
145C2×Dic61#9911yescharacteristic
146D244—42no—
147D244—42no—
148C4×D61—42no—
149C4×D61—42no—
150C4×D61—81no—
151C4×D61—81no—
152C8×C61—81no—
153C8×C61—81no—
154#92418—81no—
155#92418—81no—
156#11572—611nomaximal, Sylow
157C22×C61—21no—
158C22×C61—21no—
159C22×C61#40811yescharacteristic
160C22×C61C2×#9911yescharacteristic
161C22×C61C2×#10111yescharacteristic
162C2×D61—22no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—42no—
166C2×D61—42no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—81no—
171C2×D61—81no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61—81no—
177C4×C61—81no—
178Dic61—21no—
179Dic61—21no—
180Dic61—42no—
181Dic61—41no—
182Dic61—81no—
183#2566—611no—
184#1465—611no—
185#1459—611no—
186#1325—611no—
187#1325—611no—
188#1324—611no—
189#1324D6111yescharacteristic, complemented
190C2×C61—21no—
191C2×C61—21no—
192C2×C61#147211yescharacteristic
193C2×C61#212711yescharacteristic
194C2×C61#213211yescharacteristic
195D61—42no—
196D61—81no—
197C2×#125—611no—
198C2×C4×D4—611no—
199#407—1221no—
200C2×C22⋊C8—1221no—
201#396—1221no—
202#396—1221no—
203#390—611no—
204#390—611no—
205#385—1221no—
206#385—1221no—
207#384—611no—
208#382C2×D6111yescharacteristic
209C4×C4⋊C4—611no—
210#324—611no—
211#324—611no—
212#324C2×D6111yescharacteristic
213#324C2×D6111yescharacteristic
214#323—1221no—
215#323—1221no—
216C61#1157211yescharacteristic, complemented, Sylow
217C22×D4—611no—
218C23×C4—611no—
219C23×C4—611no—
220C2×M16—2441no—
221C22×C8—2441no—
222#125—2441no—
223#125—2441no—
224C4×D4—2441no—
225C4×D4—2441no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4C4×D6111yescharacteristic
233C2×C4⋊C4C22×D6111yescharacteristic
234C2×C22⋊C4—611no—
235C2×C22⋊C4—611no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C42—611no—
241C2×C42—611no—
242C2×C42C4×D6111yescharacteristic
243C22⋊C8—21no—
244C22⋊C8—21no—
245C22⋊C8—1221no—
246C22⋊C8—1221no—
247C22⋊C8—2441no—
248C22⋊C8—2441no—
249#95—21no—
250#95—21no—
251#95—1221no—
252C24—611no—
253C24—611no—
254C2×D4—1222no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4—2441no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—4881no—
269C22×C4—4881no—
270C22×C4C2×C4×D6111yescharacteristic
271C22×C4D4×D6111yescharacteristic
272C22×C4D4×D6111yescharacteristic
273M16—4882no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—4882no—
277C2×C8—2441no—
278C2×C8—2441no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—4881no—
282C4⋊C4—4881no—
283C4⋊C4—2441no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C4⋊C4—2442no—
287C4⋊C4—2442no—
288C22⋊C4—4881no—
289C22⋊C4—4881no—
290C22⋊C4—2441no—
291C22⋊C4—2441no—
292C22⋊C4—2442no—
293C22⋊C4—2442no—
294C42—21no—
295C42—21no—
296C42—1221no—
297C42—1221no—
298C42—1221no—
299C42—1221no—
300C23—612no—
301C23—1221no—
302C23—1221no—
303C23—1221no—
304C23—1221no—
305C23—1221no—
306C23—2441no—
307C23—2441no—
308C23—2441no—
309C23—2441no—
310C23C22⋊C4×D6111yescharacteristic
311D4—2442no—
312D4—2442no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—1222no—
328C2×C4—1221no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4#1451978311yescharacteristic
341C2×C4#1451978511yescharacteristic
342C8—81no—
343C8—81no—
344C8—4881no—
345C8—4881no—
346C22—21no—
347C22—21no—
348C22—1222no—
349C22—4881no—
350C22—4881no—
351C22—2442no—
352C22—2442no—
353C22—2441no—
354C22—2441no—
355C22—2441no—
356C22—2441no—
357C22—2441no—
358C22#1683972711yescharacteristic
359C22#99×D6111yescharacteristic
360C22#101×D6111yescharacteristic
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—81no—
366C4—81no—
367C4—1221no—
368C4—1221no—
369C4—4881no—
370C4—2442no—
371C4—2441no—
372C2—21no—
373C2—21no—
374C2—4881no—
375C2—2442no—
376C2#2144418111yescharacteristic
377C2#2144748711yescharacteristic
378C2#2144750111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1324C2
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1324D61
hypocenterC61#11572
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
4. #21443764C2semidirect
5. #21443764C2semidirect
6. #21443763C2semidirect
7. C61×#1324C2semidirect
189. #1324D61semidirect
216. C61#11572semidirect

Maximal subgroups

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

subgroupindex
#214510182
#214441562
#214441362
#214437642
#214437632
C61×#13242
#1157261