Finite Group Databasebeta

← #29589469

Subgroups — #29589469

Order 15616.

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

normal subgroups only

This group has 530 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#21448473C211yesmaximal, characteristic
2#21444160C211yesmaximal, characteristic, complemented
3#21443768C212yesmaximal, complemented
4#21443746C212yesmaximal, complemented
5C61×#1465C211yesmaximal, characteristic, complemented
6C2×#14519745C411yescharacteristic
7C22×#11758198C411yescharacteristic
8#16839819—21no—
9#16839662—21no—
10#16839653—21no—
11#16839652—21no—
12#16839642C411yescharacteristic
13#16839641—21no—
14#16839634C2211yescharacteristic
15#16839617C2211yescharacteristic
16C4×C22⋊Dic61C411yescharacteristic
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#14519745—22no—
27#14519745—22no—
28C2×#11758196—21no—
29C2×C22⋊Dic61—21no—
30C2×C22⋊Dic61C2×C411yescharacteristic
31C2×C22⋊Dic61C2×C411yescharacteristic
32C2×#11758198—21no—
33C2×#11758198—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—41no—
38C2×#11758198—41no—
39C2×C4×Dic61—21no—
40C4⋊#92418—41no—
41C22⋊#92418—22no—
42#14519688—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—21no—
62C23×D61—41no—
63C23×D61—41no—
64C23×D61—81no—
65C23×D61—81no—
66C23×D61M1612yescomplemented
67C2×D4×C61—21no—
68C2×D4×C61—21no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—81no—
76C22×C4×C61—81no—
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C22⋊C411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C2×C22⋊D61—24no—
83C2×C22⋊D61—81no—
84C2×C22⋊D61—81no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—41no—
89C22×Dic61—81no—
90M16×C61—82no—
91C2×C8×C61—42no—
92C4⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—41no—
95C42×C61—21no—
96C42×C61—21no—
97C22⋊Dic61—21no—
98C22⋊Dic61—41no—
99C22⋊Dic61—81no—
100C22⋊Dic61M1612yescomplemented
101#11758198—24no—
102#11758198—42no—
103#11758198—41no—
104#11758198—41no—
105#11758198—81no—
106#11758198—81no—
107#11758196—81no—
108C4×Dic61—81no—
109C2×#92418—42no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61C2×C22⋊C411yescharacteristic
120C23×C61C2×M1611yescharacteristic
121C23×C61C2×M1611yescharacteristic
122C22×D61—22no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—42no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—42no—
131C22×D61—82no—
132C22×D61—82no—
133C22×D61—84no—
134C22×D61—82no—
135C22×D61—82no—
136D4×C61—42no—
137D4×C61—42no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—81no—
150C2×C4×C61—81no—
151C2×C4×C61—81no—
152C2×C4×C61#9911yescharacteristic
153C2×C4×C61#9911yescharacteristic
154C22⋊D61—84no—
155C2×Dic61—22no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—82no—
165C8×C61—82no—
166#92418—82no—
167#11527—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—42no—
175C22×C61—42no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—81no—
182C22×C61#40711yescharacteristic
183C22×C61C2×#9911yescharacteristic
184C22×C61#41311yescharacteristic
185C2×D61—42no—
186C2×D61—42no—
187C2×D61—42no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—84no—
191C2×D61—81no—
192C2×D61—81no—
193C2×D61—84no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—41no—
197C4×C61—41no—
198C4×C61—41no—
199C4×C61—41no—
200Dic61—42no—
201Dic61—81no—
202Dic61—81no—
203#2321—611no—
204#1466—611no—
205#1465D6111yescharacteristic, complemented
206#1326—612no—
207#1316—612no—
208C2×C61—21no—
209C2×C61—21no—
210C2×C61—41no—
211C2×C61—41no—
212C2×C61—81no—
213C2×C61#146511yescharacteristic
214C2×C61#212111yescharacteristic
215C2×C61#212211yescharacteristic
216D61—82no—
217C2×#120—611no—
218C2×C4×D4C2×D6111yescharacteristic
219C22×C22⋊C4—611no—
220#432—1221no—
221#407—21no—
222#390—1221no—
223#388—1221no—
224#388—1221no—
225#386—611no—
226#386—1221no—
227#385—611no—
228#379—611no—
229C4×C22⋊C4—611no—
230#324—21no—
231#323—612no—
232#323—1221no—
233#323C2×D6112yes—
234C61#1152711yescharacteristic, complemented, Sylow
235C25—611no—
236C22×D4—1221no—
237C22×D4C4×D6111yescharacteristic
238C23×C4—611no—
239C23×C4C4×D6111yescharacteristic
240C23×C4C22⋊D6111yescharacteristic
241C2×M16—41no—
242#120—1222no—
243#120—1222no—
244C4×D4—41no—
245C4×D4—41no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4C22⋊D6111yescharacteristic
248C2×C22⋊C4—611no—
249C2×C22⋊C4—611no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—2441no—
257C2×C22⋊C4—2441no—
258C2×C22⋊C4D24411yescharacteristic
259C2×C22⋊C4C22×D6111yescharacteristic
260C2×C42—1221no—
261C2×C42D24411yescharacteristic
262C4⋊C8—2441no—
263C22⋊C8—22no—
264C22⋊C8—41no—
265C22⋊C8—1222no—
266#97—2441no—
267#95—1221no—
268#95—1221no—
269#95—1221no—
270C24—612no—
271C24—1221no—
272C24—1221no—
273C24—4881no—
274C24—4881no—
275C24—2441no—
276C24—2441no—
277C24#1175819811yescharacteristic
278C24C2×C4×D6111yescharacteristic
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—1224no—
284C2×D4—4881no—
285C2×D4—4881no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—81no—
291C22×C4—81no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—4881no—
296C22×C4—2441no—
297C22×C4#1175819811yescharacteristic
298C22×C4#1175819811yescharacteristic
299C22×C4#1175819811yescharacteristic
300C22×C4C2×D24411yescharacteristic
301C22×C4C2×C22⋊D6111yescharacteristic
302M16—82no—
303C2×C8—42no—
304C2×C8—2442no—
305C4⋊C4—41no—
306C4⋊C4—4881no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—612no—
310C22⋊C4—1224no—
311C22⋊C4—1221no—
312C22⋊C4—4881no—
313C22⋊C4—4881no—
314C22⋊C4—4881no—
315C22⋊C4—2442no—
316C22⋊C4—2441no—
317C22⋊C4—2441no—
318C22⋊C4—2441no—
319C42—21no—
320C42—21no—
321C42—4881no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—1222no—
332C23—4882no—
333C23—4882no—
334C23—4884no—
335C23—4882no—
336C23—4882no—
337C23—2442no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23—2441no—
342C23—2442no—
343C23—2441no—
344C23—2441no—
345C23C2×#1175819811yescharacteristic
346C23M16×D6111yescharacteristic
347C23M16×D6111yescharacteristic
348D4—42no—
349D4—42no—
350D4—4884no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—1222no—
366C2×C4—4882no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4#1451969111yescharacteristic
376C2×C4#1451969111yescharacteristic
377C8—82no—
378C8—4882no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—42no—
386C22—42no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—81no—
393C22—4881no—
394C22—4881no—
395C22—4884no—
396C22—4884no—
397C22—4881no—
398C22—4881no—
399C22—2442no—
400C22—2442no—
401C22—2442no—
402C22#1683972511yescharacteristic
403C22C2×#1451969111yescharacteristic
404C22#1683974411yescharacteristic
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—4881no—
412C4—4881no—
413C4—2442no—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—41no—
418C2—81no—
419C2—4882no—
420C2#2144415511yescharacteristic
421C2#2144746311yescharacteristic
422C2#2144747011yescharacteristic
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#11527
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. #21444160C2semidirect
3. #21443768C2semidirect
4. #21443746C2semidirect
5. C61×#1465C2semidirect
66. C23×D61M16semidirect
100. C22⋊Dic61M16semidirect
205. #1465D61semidirect
234. C61#11527semidirect

Maximal subgroups

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

subgroupindex
#214484732
#214441602
#214437682
#214437462
C61×#14652
#1152761