Finite Group Databasebeta

← #29589495

Subgroups — #29589495

Order 15616.

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

normal subgroups only

This group has 504 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#21448541C211yesmaximal, characteristic
2#21444157C211yesmaximal, characteristic, complemented
3#21443762C212yesmaximal, complemented
4#21443750C212yesmaximal, complemented
5C61×#1465C211yesmaximal, characteristic, complemented
6C2×#14519773C411yescharacteristic
7C2×C4×D244C411yescharacteristic
8#16839726—21no—
9#16839665C411yescharacteristic
10#16839663C2211yescharacteristic
11#16839641—21no—
12#16839641—21no—
13#16839638—21no—
14#16839638—21no—
15#16839627C2211yescharacteristic
16#16839608C411yescharacteristic
17#16839488C2212yes—
18#16839486—21no—
19C2×C4×D4×C61C2211yescharacteristic
20C61×#407—21no—
21C61×#324C2212yes—
22C61×#323—21no—
23C22×D244C2×C411yescharacteristic
24C22×C22⋊D61—21no—
25C22×C22⋊D61—21no—
26C22×C4×D61—21no—
27C2×#11758194—41no—
28#14519773—22no—
29#14519773—22no—
30C4×D244—41no—
31C4×D244—41no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61C2×C411yescharacteristic
40C22⋊#92418—22no—
41C22⋊#92418—41no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46C22×D4×C61C2×C411yescharacteristic
47C23×C4×C61D411yescharacteristic
48C23×C4×C61D411yescharacteristic
49C2×M16×C61—41no—
50C4×D4×C61—41no—
51C4×D4×C61—41no—
52C2×C4⋊C4×C61C2311yescharacteristic
53C2×C22⋊C4×C61D411yescharacteristic
54C2×C22⋊C4×C61D411yescharacteristic
55C2×C42×C61C2×C411yescharacteristic
56C22⋊C8×C61—22no—
57C22⋊C8×C61—41no—
58C24×C61C22⋊C411yescharacteristic
59C24×C61C22⋊C411yescharacteristic
60C23×D61—21no—
61C2×D4×C61—21no—
62C2×D4×C61—21no—
63C2×D4×C61—41no—
64C2×D4×C61—41no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—81no—
70C22×C4×C61—81no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C2×C22⋊D61—24no—
77C2×C22⋊D61—24no—
78C2×C22⋊D61—81no—
79C2×C22⋊D61—81no—
80C2×C22⋊D61—81no—
81C2×C22⋊D61—81no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C2×D244—21no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244M1612yescomplemented
89C2×C4×D61—42no—
90C2×C4×D61—81no—
91C2×C4×D61—81no—
92M16×C61—82no—
93C2×C8×C61—42no—
94C4⋊C4×C61—41no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C42×C61—21no—
98C42×C61—21no—
99C22⋊Dic61—81no—
100C22⋊Dic61—81no—
101#11758198—41no—
102#11758198—41no—
103#11758198—81no—
104#11758198—81no—
105C4⋊Dic61—41no—
106C4×Dic61—21no—
107C4×Dic61—41no—
108C4×Dic61M1612yescomplemented
109#11758194—82no—
110C2×#92418—42no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61C2×C22⋊C411yescharacteristic
122C22×D61—22no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129D4×C61—42no—
130D4×C61—42no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—42no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—81no—
143C2×C4×C61—81no—
144C2×C4×C61#9911yescharacteristic
145C2×C4×C61#9911yescharacteristic
146C2×C4×C61C2×M1611yescharacteristic
147C2×C4×C61C2×M1611yescharacteristic
148C22⋊D61—84no—
149C22⋊D61—84no—
150C2×Dic61—22no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159D244—42no—
160D244—42no—
161C4×D61—84no—
162C8×C61—82no—
163#92418—82no—
164#11533—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—42no—
168C22×C61—42no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61#40711yescharacteristic
178C22×C61C2×#9911yescharacteristic
179C22×C61#41311yescharacteristic
180C2×D61—42no—
181C2×D61—42no—
182C2×D61—42no—
183C2×D61—81no—
184C2×D61—81no—
185C2×D61—81no—
186C2×D61—81no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—41no—
192C4×C61—41no—
193C4×C61—41no—
194Dic61—42no—
195Dic61—81no—
196Dic61—81no—
197#2328—611no—
198#1465—611no—
199#1465D6111yescharacteristic, complemented
200#1324—612no—
201#1318—612no—
202C2×C61—21no—
203C2×C61—21no—
204C2×C61—81no—
205C2×C61—81no—
206C2×C61#146511yescharacteristic
207C2×C61#212711yescharacteristic
208C2×C61#213411yescharacteristic
209D61—82no—
210C2×#127—611no—
211C2×C4×D4—611no—
212C2×C4×D4C2×D6111yescharacteristic
213#407—21no—
214#407—1221no—
215#390—611no—
216#390—611no—
217#386—1221no—
218#386—1221no—
219#386—1221no—
220#386—1221no—
221#382—611no—
222#376—611no—
223#324—612no—
224#324C2×D6112yes—
225#323—21no—
226#323—1221no—
227C61#1153311yescharacteristic, complemented, Sylow
228C22×D4—611no—
229C22×D4—1221no—
230C22×D4—1221no—
231C22×D4C4×D6111yescharacteristic
232C23×C4—1221no—
233C23×C4D24411yescharacteristic
234C23×C4C22⋊D6111yescharacteristic
235C2×M16—41no—
236C2×M16—2441no—
237#127—1222no—
238#127—1222no—
239C4×D4—41no—
240C4×D4—41no—
241C4×D4—2441no—
242C4×D4—2441no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4C22×D6111yescharacteristic
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4D24411yescharacteristic
251C2×C22⋊C4C22⋊D6111yescharacteristic
252C2×C42—611no—
253C2×C42—611no—
254C2×C42C4×D6111yescharacteristic
255C22⋊C8—22no—
256C22⋊C8—41no—
257C22⋊C8—1222no—
258C22⋊C8—2441no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263C24—1221no—
264C24#1175819811yescharacteristic
265C24#1175819811yescharacteristic
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—612no—
271C2×D4—1224no—
272C2×D4—1224no—
273C2×D4—1221no—
274C2×D4—4881no—
275C2×D4—4881no—
276C2×D4—4881no—
277C2×D4—4881no—
278C2×D4—2441no—
279C2×D4—2441no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—81no—
285C22×C4—81no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—4881no—
290C22×C4—4881no—
291C22×C4—2442no—
292C22×C4#1175819811yescharacteristic
293C22×C4#1175819811yescharacteristic
294C22×C4C2×C4×D6111yescharacteristic
295C22×C4C2×D24411yescharacteristic
296C22×C4C2×C22⋊D6111yescharacteristic
297M16—82no—
298M16—4882no—
299C2×C8—42no—
300C2×C8—2442no—
301C4⋊C4—41no—
302C4⋊C4—2441no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—4881no—
306C22⋊C4—4881no—
307C22⋊C4—4881no—
308C22⋊C4—4881no—
309C22⋊C4—2441no—
310C22⋊C4—2441no—
311C42—21no—
312C42—21no—
313C42—612no—
314C42—1221no—
315C42—2441no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—1222no—
327C23—2441no—
328C23—2441no—
329C23—2441no—
330C23—2441no—
331C23—2441no—
332C23—2441no—
333C23C2×#1175819811yescharacteristic
334D4—42no—
335D4—42no—
336D4—4884no—
337D4—4884no—
338D4—2442no—
339D4—2442no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—1222no—
354C2×C4—4884no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4#1451969111yescharacteristic
364C2×C4#1451969111yescharacteristic
365C2×C4M16×D6111yescharacteristic
366C2×C4M16×D6111yescharacteristic
367C8—82no—
368C8—4882no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—42no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—81no—
380C22—81no—
381C22—4881no—
382C22—4881no—
383C22—4881no—
384C22—4881no—
385C22—2442no—
386C22—2442no—
387C22—2442no—
388C22#1683972511yescharacteristic
389C22C2×#1451969111yescharacteristic
390C22#1683974411yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—4881no—
399C4—4881no—
400C4—2442no—
401C2—21no—
402C2—21no—
403C2—81no—
404C2—81no—
405C2—4882no—
406C2#2144415511yescharacteristic
407C2#2144748611yescharacteristic
408C2#2144751011yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1465C2
socleC22×C61C2×#99
prime radicalC2×#14519773C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1465D61
hypocenterC61#11533
LCSG ▷ C22×C4×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. #21444157C2semidirect
3. #21443762C2semidirect
4. #21443750C2semidirect
5. C61×#1465C2semidirect
88. C2×D244M16semidirect
108. C4×Dic61M16semidirect
199. #1465D61semidirect
227. C61#11533semidirect

Maximal subgroups

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

subgroupindex
#214485412
#214441572
#214437622
#214437502
C61×#14652
#1153361