Finite Group Databasebeta

← #29572777

Subgroups — #29572777

Order 15616.

456 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519769C211yesmaximal, characteristic
2#21445672C211yesmaximal, characteristic
3C2×#16839503C212yesmaximal
4#21443701C212yesmaximal
5C61×#1767C211yesmaximal, characteristic
6C2×#14519769C2211yescharacteristic
7C2×C4⋊#92418—21no—
8C2×#14519688C2212yes—
9#16839660C411yescharacteristic
10#16839660C411yescharacteristic
11#16839646—21no—
12#16839646—21no—
13#16839628C2211yescharacteristic
14C4×#11758196—21no—
15C4×#11758196—21no—
16C4×C4⋊Dic61C411yescharacteristic
17C4×C4⋊Dic61C411yescharacteristic
18#16839517—21no—
19#16839503—24no—
20C2×C4⋊C8×C61—21no—
21C2×#97×C61C2212yes—
22C43×C61C2211yescharacteristic
23C61×#336—21no—
24C22×#92418—22no—
25#14519769—21no—
26#14519769—21no—
27#14519769D412yes—
28#14519769Q812yes—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61—21no—
39C4⋊#92418—24no—
40#14519688—22no—
41#14519688—22no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48C22×C8×C61—22no—
49C2×C42×C61C2×C411yescharacteristic
50C2×C42×C61C2×C411yescharacteristic
51C2×C42×C61D411yescharacteristic
52C2×C42×C61D411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C2×C42×C61D411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56C4⋊C8×C61—24no—
57#97×C61—22no—
58#97×C61—22no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C2×C8×C61—24no—
71C2×C8×C61—42no—
72C2×C8×C61—42no—
73C42×C61—22no—
74C42×C61—22no—
75C42×C61—22no—
76C42×C61—41no—
77C42×C61—41no—
78C42×C61—41no—
79C42×C61C2×D411yescharacteristic
80C42×C61C2×Q811yescharacteristic
81C42×C61#4111yescharacteristic
82C42×C61#4111yescharacteristic
83C4⋊Dic61—21no—
84C4⋊Dic61—21no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87C4⋊Dic61C4⋊C412yes—
88C4⋊Dic61C4⋊C412yes—
89#11758196—22no—
90#11758196—22no—
91#11758196—22no—
92#11758196—22no—
93#11758196—42no—
94#11758196—42no—
95C4×Dic61—42no—
96C4×Dic61—42no—
97C2×#92418—24no—
98C2×#92418—42no—
99C2×#92418—42no—
100C23×C61C2×C22⋊C411yescharacteristic
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—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61#10112yes—
117C2×C4×C61#10412yes—
118C2×C4×C61#10412yes—
119C2×C4×C61C2×C4⋊C411yescharacteristic
120C2×C4×C61#11711yescharacteristic
121C2×C4×C61#12111yescharacteristic
122C2×C4×C61#12111yescharacteristic
123C2×C4×C61C22⋊Q811yescharacteristic
124C2×C4×C61C22⋊Q811yescharacteristic
125C2×Dic61—22no—
126C2×Dic61—22no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C8×C61—44no—
138#92418—44no—
139#8580—611nomaximal, Sylow
140C22×C61#38011yescharacteristic
141C22×C61C2×#10111yescharacteristic
142C22×C61#41311yescharacteristic
143C22×C61C2×#10411yescharacteristic
144C22×C61C2×#10411yescharacteristic
145C22×C61#42111yescharacteristic
146C22×C61#42111yescharacteristic
147C4×C61—21no—
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61#33014yescomplemented
157Dic61—42no—
158Dic61—42no—
159Dic61—81no—
160Dic61—81no—
161C4×#125—611no—
162#1767—611no—
163#1767D6111yescharacteristic
164C2×#330—612no—
165#1295—612no—
166C2×C61C2×#33011yescharacteristic
167C2×C61#152911yescharacteristic
168C2×C61#152911yescharacteristic
169C2×C61#153711yescharacteristic
170C2×C61#180111yescharacteristic
171C2×C61#180611yescharacteristic
172C2×C61#180611yescharacteristic
173C2×#125—611no—
174C2×C4⋊C8—21no—
175C2×C4⋊C8—1221no—
176C2×#97—612no—
177C2×#97C2×D6112yes—
178#389—611no—
179#389—611no—
180#387—1221no—
181#387—1221no—
182#382—611no—
183C4×C4⋊C4—611no—
184C4×C4⋊C4—611no—
185C4×C4⋊C4—1221no—
186C4×C4⋊C4—1221no—
187C43C2×D6111yescharacteristic
188#336—21no—
189#336—1221no—
190#330—1224no—
191C61#858011yescharacteristic, complemented, Sylow
192C22×C8—22no—
193C22×C8—1222no—
194#125—612no—
195#125—612no—
196#125—1221no—
197#125—1221no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4—1221no—
206C2×C42—1221no—
207C2×C42—1221no—
208C2×C42C4×D6111yescharacteristic
209C2×C42C4×D6111yescharacteristic
210C2×C42D24411yescharacteristic
211C2×C42D24411yescharacteristic
212C2×C42C22⋊D6111yescharacteristic
213C2×C42C22⋊D6111yescharacteristic
214C2×C42C22×D6111yescharacteristic
215C4⋊C8—24no—
216C4⋊C8—1224no—
217#97—22no—
218#97—22no—
219#97—1222no—
220#97—1222no—
221#95—1221no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4#1175819811yescharacteristic
232C22×C4#1175819811yescharacteristic
233C22×C4#1175819811yescharacteristic
234C22×C4#1175819811yescharacteristic
235C22×C4C2×C4×D6111yescharacteristic
236C22×C4C2×D24411yescharacteristic
237C22×C4C2×C22⋊D6111yescharacteristic
238C2×C8—24no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—1224no—
242C2×C8—2442no—
243C2×C8—2442no—
244C4⋊C4—612no—
245C4⋊C4—612no—
246C4⋊C4—1221no—
247C4⋊C4—1221no—
248C4⋊C4—1222no—
249C4⋊C4—1222no—
250C4⋊C4—1222no—
251C4⋊C4—1222no—
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C4⋊C4—2442no—
255C4⋊C4—2442no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42—2442no—
263C42—2442no—
264C42D4×D6111yescharacteristic
265C42#1175822411yescharacteristic
266C42Q8×D6111yescharacteristic
267C42#1175822611yescharacteristic
268C23C2×#1175819811yescharacteristic
269C2×C4—21no—
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—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—1222no—
285C2×C4—1222no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4#1451969512yes—
297C2×C4#1451970312yes—
298C2×C4#1451970512yes—
299C2×C4C4⋊C4×D6111yescharacteristic
300C2×C4#1451973511yescharacteristic
301C2×C4#1451974811yescharacteristic
302C2×C4#1451975211yescharacteristic
303C2×C4#1451975311yescharacteristic
304C2×C4#1451975711yescharacteristic
305C8—44no—
306C8—2444no—
307C22#1683961911yescharacteristic
308C22C2×#1451969511yescharacteristic
309C22#1683974411yescharacteristic
310C22C2×#1451970311yescharacteristic
311C22C2×#1451970511yescharacteristic
312C22#1683977811yescharacteristic
313C22#1683978011yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—4881no—
324C4—4881no—
325C4—2442no—
326C4—2442no—
327C4#1683950314yescomplemented
328C2C2×#1683950311yescharacteristic
329C2#2144442411yescharacteristic
330C2#2144442711yescharacteristic
331C2#2144445611yescharacteristic
332C2#2144581211yescharacteristic
333C2#2144583611yescharacteristic
334C2#2144584011yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1767C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1767D61
hypocenterC61#8580
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
156. C4×C61#330semidirect
191. C61#8580semidirect
327. C4#16839503semidirect

Maximal subgroups

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

subgroupindex
C4×#145197692
#214456722
C2×#168395032
#214437012
C61×#17672
#858061