Finite Group Databasebeta

← #29589618

Subgroups — #29589618

Order 15616.

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

normal subgroups only

This group has 532 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#21450705C211yesmaximal, characteristic
2#21444140C211yesmaximal, characteristic, complemented
3#21443748C212yesmaximal, complemented
4#21443746C212yesmaximal, complemented
5C61×#1465C211yesmaximal, characteristic, complemented
6C2×#14519758C411yescharacteristic
7C2×#14519745C411yescharacteristic
8C22×#11758198C411yescharacteristic
9#16839815—21no—
10#16839684—21no—
11#16839678—21no—
12#16839653—21no—
13#16839641—21no—
14#16839623C2211yescharacteristic
15#16839622C411yescharacteristic
16#16839617C2211yescharacteristic
17#16839486—21no—
18#16839486C2212yes—
19C2×C4×D4×C61C2211yescharacteristic
20C61×#407—21no—
21C61×#324—21no—
22C61×#323C2212yes—
23C24×D61C2×C411yescharacteristic
24C22×C22⋊D61—21no—
25C23×Dic61C2×C411yescharacteristic
26#14519758—42no—
27#14519745—42no—
28C2×C4⋊Dic61—21no—
29C2×#11758196—21no—
30C2×C22⋊Dic61—21no—
31C2×C22⋊Dic61C2×C411yescharacteristic
32C2×C22⋊Dic61C2×C411yescharacteristic
33C2×#11758198—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—41no—
39C2×#11758198—41no—
40C4⋊#92418—41no—
41C22⋊#92418—22no—
42C4×#92418—41no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46C22×D4×C61C2×C411yescharacteristic
47C23×C4×C61C2×C411yescharacteristic
48C23×C4×C61D411yescharacteristic
49C2×M16×C61—41no—
50C4×D4×C61—41no—
51C4×D4×C61—41no—
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C22⋊C4×C61D411yescharacteristic
54C2×C22⋊C4×C61C2311yescharacteristic
55C2×C42×C61D411yescharacteristic
56C22⋊C8×C61—22no—
57C22⋊C8×C61—41no—
58C24×C61C22⋊C411yescharacteristic
59C24×C61C22×C411yescharacteristic
60C23×D61—21no—
61C23×D61—22no—
62C23×D61—42no—
63C23×D61—41no—
64C23×D61—41no—
65C23×D61—81no—
66C2×D4×C61—22no—
67C2×D4×C61—22no—
68C2×D4×C61—41no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—81no—
74C22×C4×C61—81no—
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C2×C22⋊D61—42no—
81C2×C22⋊D61—42no—
82C2×C22⋊D61—81no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—22no—
87C22×Dic61—41no—
88C22×Dic61—41no—
89M16×C61—82no—
90C2×C8×C61—42no—
91C4⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C42×C61—21no—
95C42×C61—21no—
96C22⋊Dic61—42no—
97C22⋊Dic61—41no—
98C22⋊Dic61—41no—
99#11758198—42no—
100#11758198—42no—
101#11758198—41no—
102#11758198—41no—
103#11758198—42no—
104#11758198—81no—
105C4⋊Dic61—81no—
106#11758196—42no—
107C2×#92418—42no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61C2×C22⋊C411yescharacteristic
118C23×C61#13112yes—
119C22×D61—22no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—42no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—42no—
128C22×D61—84no—
129C22×D61—84no—
130C22×D61—82no—
131C22×D61—82no—
132D4×C61—44no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—41no—
139C2×C4×C61—42no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—81no—
144C2×C4×C61—81no—
145C2×C4×C61—81no—
146C2×C4×C61#9911yescharacteristic
147C2×C4×C61#9911yescharacteristic
148C2×C4×C61#10012yes—
149C22⋊D61—84no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—82no—
160C8×C61—82no—
161#92418—82no—
162#11559—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—22no—
166C22×C61—42no—
167C22×C61—42no—
168C22×C61—42no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—81no—
175C22×C61#40811yescharacteristic
176C22×C61C2×#9911yescharacteristic
177C22×C61C2×#10011yescharacteristic
178C2×D61—42no—
179C2×D61—42no—
180C2×D61—42no—
181C2×D61—81no—
182C2×D61—81no—
183C2×D61—84no—
184C2×D61—81no—
185C2×D61—81no—
186C2×D61—84no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—22no—
190C4×C61—41no—
191C4×C61—41no—
192C4×C61—41no—
193Dic61—81no—
194Dic61—81no—
195Dic61—81no—
196#2534—611no—
197#1465D6111yescharacteristic, complemented
198#1460—611no—
199#1317—612no—
200#1316—612no—
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—42no—
204C2×C61—81no—
205C2×C61#147111yescharacteristic
206C2×C61#212011yescharacteristic
207C2×C61#212111yescharacteristic
208D61—82no—
209C2×#123—611no—
210C2×#120—611no—
211C2×C4×D4C2×D6111yescharacteristic
212C22×C22⋊C4—611no—
213#431—1221no—
214#407—21no—
215#396—1221no—
216#394—1221no—
217#388—1221no—
218#386—1221no—
219#381—611no—
220#380—611no—
221#379—611no—
222#324—21no—
223#323—612no—
224#323—1221no—
225#323C2×D6112yes—
226C61#1155911yescharacteristic, complemented, Sylow
227C25—611no—
228C22×D4—1221no—
229C22×D4C4×D6111yescharacteristic
230C23×C4—611no—
231C23×C4C4×D6111yescharacteristic
232C23×C4C22⋊D6111yescharacteristic
233C2×M16—41no—
234#123—2442no—
235#120—2442no—
236C4×D4—41no—
237C4×D4—41no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4C22⋊D6111yescharacteristic
241C2×C22⋊C4—611no—
242C2×C22⋊C4—611no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—2441no—
250C2×C22⋊C4—2441no—
251C2×C22⋊C4D24411yescharacteristic
252C2×C22⋊C4C22×D6111yescharacteristic
253C2×C42D24411yescharacteristic
254C4⋊C8—2441no—
255C22⋊C8—22no—
256C22⋊C8—41no—
257C22⋊C8—1222no—
258C4×C8—2441no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262C24—1221no—
263C24—1222no—
264C24—4881no—
265C24—2441no—
266C24—2441no—
267C24—2442no—
268C24#1175819811yescharacteristic
269C24C2×C4×D6111yescharacteristic
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—4881no—
274C2×D4—2442no—
275C2×D4—2442no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—81no—
281C22×C4—81no—
282C22×C4—1222no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—2441no—
287C22×C4—2441no—
288C22×C4#1175819811yescharacteristic
289C22×C4#1175819811yescharacteristic
290C22×C4#1175819811yescharacteristic
291C22×C4C2×D24411yescharacteristic
292C22×C4C2×C22⋊D6111yescharacteristic
293M16—82no—
294C2×C8—42no—
295C2×C8—2442no—
296C4⋊C4—41no—
297C4⋊C4—4881no—
298C4⋊C4—2442no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—4881no—
302C22⋊C4—2442no—
303C22⋊C4—2442no—
304C22⋊C4—2442no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2442no—
308C22⋊C4—2441no—
309C22⋊C4—2441no—
310C42—21no—
311C42—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—1222no—
322C23—4882no—
323C23—4882no—
324C23—4884no—
325C23—4884no—
326C23—2441no—
327C23—2441no—
328C23—2441no—
329C23—2442no—
330C23—2442no—
331C23—2441no—
332C23—2441no—
333C23—2441no—
334C23C2×#1175819811yescharacteristic
335C23#1451978512yes—
336D4—44no—
337D4—4884no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—4882no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4#1451969111yescharacteristic
362C2×C4#1451969111yescharacteristic
363C2×C4#1451969312yes—
364C8—82no—
365C8—4882no—
366C22—21no—
367C22—21no—
368C22—22no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—81no—
378C22—4881no—
379C22—4881no—
380C22—4884no—
381C22—4884no—
382C22—4881no—
383C22—4881no—
384C22—2442no—
385C22—2442no—
386C22—2442no—
387C22#1683973011yescharacteristic
388C22C2×#1451969111yescharacteristic
389C22C2×#1451969311yescharacteristic
390C4—21no—
391C4—21no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—4881no—
397C4—4881no—
398C4—4881no—
399C2—21no—
400C2—21no—
401C2—42no—
402C2—81no—
403C2—4882no—
404C2#2144418011yescharacteristic
405C2#2144746111yescharacteristic
406C2#2144746311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC24×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1465C2
socleC22×C61C2×#99
prime radicalC2×#14519745C4
cosocleC2×C22⋊C4×C61C23
hypercenter#1465D61
hypocenterC61#11559
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #21444140C2semidirect
3. #21443748C2semidirect
4. #21443746C2semidirect
5. C61×#1465C2semidirect
197. #1465D61semidirect
226. C61#11559semidirect

Maximal subgroups

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

subgroupindex
#214507052
#214441402
#214437482
#214437462
C61×#14652
#1155961