Finite Group Databasebeta

← #29590686

Subgroups — #29590686

Order 15616.

502 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 79 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#21451569C211yesmaximal, characteristic
2#21444153C211yesmaximal, characteristic, complemented
3#21443815C214yesmaximal, complemented
4C61×#1820C211yesmaximal, characteristic, complemented
5C2×#14519774C411yescharacteristic, complemented
6C2×#14519751—21no—
7#16839819—21no—
8#16839679—21no—
9#16839679C412yescomplemented
10#16839671—21no—
11#16839671C2212yes—
12#16839664—21no—
13#16839628C411yescharacteristic, complemented
14#16839488—21no—
15#16839486C2212yes—
16C2×#117×C61C2211yescharacteristic
17C61×#381—21no—
18C61×#342—21no—
19C61×#342C2212yes—
20C22×D244—21no—
21C22×D244—21no—
22C22×D244C2×C412yes—
23C22×C22⋊D61—22no—
24#14519774—41no—
25#14519774—41no—
26#14519751—44no—
27C2×C4⋊Dic61—21no—
28C2×#11758198—22no—
29C2×#11758198—22no—
30C2×#11758198—22no—
31C4⋊#92418—41no—
32C22⋊#92418—22no—
33#14519688—41no—
34#14519684—21no—
35#14519684C2×C412yes—
36C23×C4×C61D411yescharacteristic
37#117×C61—41no—
38#117×C61—41no—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C22⋊C4×C61—22no—
42C2×C22⋊C4×C61D411yescharacteristic
43C2×C22⋊C4×C61C2311yescharacteristic
44C2×C42×C61C2×C411yescharacteristic
45C2×C42×C61D411yescharacteristic
46#95×C61—41no—
47#95×C61—41no—
48C24×C61C2×D411yescharacteristic
49C23×D61—22no—
50C22×C4×C61—22no—
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—41no—
54C22×C4×C61—42no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C2×C22⋊D61—44no—
62C2×C22⋊D61—82no—
63C2×C22⋊D61—82no—
64C22×Dic61—22no—
65C2×D244—42no—
66C2×D244—42no—
67C2×D244—42no—
68C2×D244—42no—
69C2×D244—41no—
70C2×D244—41no—
71C2×D244—82no—
72C2×D244—82no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C22⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C22⋊C4×C61—42no—
78C22⋊C4×C61—42no—
79C42×C61—21no—
80C42×C61—21no—
81C42×C61—21no—
82C42×C61—21no—
83#11758198—44no—
84#11758198—82no—
85#11758198—82no—
86C4⋊Dic61—42no—
87C2×#92418—42no—
88C23×C61—21no—
89C23×C61—21no—
90C23×C61—41no—
91C23×C61—41no—
92C23×C61C2×C22⋊C411yescharacteristic
93C23×C61AGL(1,ℤ/8)12yes—
94C22×D61—42no—
95C22×D61—42no—
96C22×D61—42no—
97C22×D61—42no—
98C22×D61—42no—
99C22×D61—42no—
100C22×D61—42no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—42no—
111C2×C4×C61—42no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—82no—
117C2×C4×C61—82no—
118C2×C4×C61—82no—
119C2×C4×C61#9911yescharacteristic
120C2×C4×C61#9911yescharacteristic
121C22⋊D61—88no—
122C2×Dic61—42no—
123C2×Dic61—42no—
124C2×Dic61—42no—
125D244—82no—
126D244—82no—
127D244—84no—
128D244—84no—
129#92418—82no—
130#11800—611nomaximal, Sylow
131C22×C61—21no—
132C22×C61—21no—
133C22×C61—22no—
134C22×C61—42no—
135C22×C61—41no—
136C22×C61—41no—
137C22×C61—81no—
138C22×C61C2×#9911yescharacteristic
139C22×C61#41811yescharacteristic
140C22×C61#42111yescharacteristic
141C2×D61—82no—
142C2×D61—82no—
143C2×D61—82no—
144C2×D61—82no—
145C2×D61—82no—
146C2×D61—82no—
147C2×D61—82no—
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61—162no—
156Dic61—82no—
157#2619—611no—
158#1820D6111yescharacteristic, complemented
159#1464—611no—
160#1343—614no—
161C2×C61—21no—
162C2×C61—21no—
163C2×C61—42no—
164C2×C61#151011yescharacteristic
165C2×C61#212211yescharacteristic
166C2×C61#212811yescharacteristic
167D61—162no—
168C2×#127—611no—
169C2×#121—1221no—
170C2×#117C2×D6111yescharacteristic
171#432—1221no—
172#394—612no—
173#394—1221no—
174#392—612no—
175#392—1221no—
176#390—1221no—
177#382—611no—
178#381—21no—
179#342—21no—
180#342C2×D6112yes—
181#324—1221no—
182#323—612no—
183C61#1180011yescharacteristic, complemented, Sylow
184C22×D4—612no—
185C22×D4—1222no—
186C22×D4—1221no—
187C22×D4—1221no—
188C23×C4C22⋊D6111yescharacteristic
189#127—2441no—
190#127—2441no—
191#121—2444no—
192#117—41no—
193#117—41no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4C4×D6111yescharacteristic
196C2×C4⋊C4D24411yescharacteristic
197C2×C22⋊C4—22no—
198C2×C22⋊C4—1222no—
199C2×C22⋊C4—1222no—
200C2×C22⋊C4—1222no—
201C2×C22⋊C4C22⋊D6111yescharacteristic
202C2×C22⋊C4C22×D6111yescharacteristic
203C2×C42C4×D6111yescharacteristic
204C2×C42D24411yescharacteristic
205C4⋊C8—2441no—
206C22⋊C8—1222no—
207#97—2441no—
208#95—41no—
209#95—41no—
210#95—612no—
211#95—1221no—
212C24—1222no—
213C24C2×C22⋊D6111yescharacteristic
214C2×D4—4882no—
215C2×D4—4882no—
216C2×D4—4882no—
217C2×D4—4882no—
218C2×D4—2442no—
219C2×D4—2442no—
220C2×D4—2442no—
221C2×D4—2442no—
222C2×D4—2444no—
223C2×D4—2441no—
224C2×D4—2441no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—42no—
230C22×C4—1222no—
231C22×C4#1175819811yescharacteristic
232C22×C4#1175819811yescharacteristic
233C22×C4#1175819811yescharacteristic
234C22×C4#1175819811yescharacteristic
235C22×C4C2×C4×D6111yescharacteristic
236C22×C4C2×D24411yescharacteristic
237C2×C8—2442no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—2442no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—4882no—
246C22⋊C4—4882no—
247C22⋊C4—2444no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23—2442no—
257C23—2442no—
258C23—2442no—
259C23—2442no—
260C23—2442no—
261C23—2442no—
262C23—2442no—
263C23C2×#1175819811yescharacteristic
264C23#1451980212yes—
265D4—4882no—
266D4—4882no—
267D4—4884no—
268D4—4884no—
269D4—4888no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—82no—
286C2×C4—82no—
287C2×C4—82no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4—2442no—
291C2×C4#1451969111yescharacteristic
292C2×C4#1451969111yescharacteristic
293C8—4882no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—41no—
299C22—41no—
300C22—81no—
301C22—4882no—
302C22—4882no—
303C22—4882no—
304C22—4882no—
305C22—4882no—
306C22—4882no—
307C22—4882no—
308C22C2×#1451969111yescharacteristic
309C22#1683976611yescharacteristic
310C22#1683978011yescharacteristic
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—162no—
319C4—4882no—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—9762no—
324C2#2144434711yescharacteristic
325C2#2144746811yescharacteristic
326C2#2144749011yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1820C2
socleC22×C61C2×#99
prime radical#21451569C2
cosocleC2×C22⋊C4×C61C23
hypercenter#1820D61
hypocenterC61#11800
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1820

Complements

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

NH ≅ G/Ntype
2. #21444153C2semidirect
3. #21443815C2semidirect
4. C61×#1820C2semidirect
5. C2×#14519774C4semidirect
9. #16839679C4semidirect
13. #16839628C4semidirect
158. #1820D61semidirect
183. C61#11800semidirect

Maximal subgroups

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

subgroupindex
#214515692
#214441532
#214438152
C61×#18202
#1180061