Finite Group Databasebeta

← #29596811

Subgroups — #29596811

Order 15616.

536 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 95 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#21448931C211yesmaximal, characteristic
2C2×#16839557C211yesmaximal, characteristic
3#21446100C212yesmaximal
4#21443938C212yesmaximal
5C61×#1885C211yesmaximal, characteristic
6C2×#14519692C2212yes—
7#16839669—21no—
8#16839655—22no—
9#16839642C2212yes—
10#16839634—22no—
11C22⋊C4×Dic61—22no—
12#16839608—21no—
13#16839557C414yescomplemented
14#16839529—22no—
15C2×#124×C61C2211yescharacteristic
16C61×#518C2211yescharacteristic
17C61×#419—21no—
18C2×#100×C61C2211yescharacteristic
19C61×#339—21no—
20C23×Dic61D412yes—
21C2×C4⋊Dic61—21no—
22C2×#11758196—42no—
23C2×C22⋊Dic61—22no—
24C2×C22⋊Dic61—22no—
25C2×C22⋊Dic61D412yes—
26C2×C4×Dic61—22no—
27C2×C4×Dic61—21no—
28#14519692—22no—
29#14519692C2×C414yes—
30#14519684—21no—
31#14519684—21no—
32#14519684—22no—
33#14519684—22no—
34#14519684—42no—
35C22×Q8×C61D411yescharacteristic
36C22×D4×C61C2311yescharacteristic
37C2×M16×C61—21no—
38#124×C61—22no—
39#124×C61C2×C412yes—
40#124×C61Q812yes—
41C4×D4×C61—42no—
42#117×C61—21no—
43C2×C22⋊C4×C61—22no—
44C2×C22⋊C4×C61—22no—
45C2×C42×C61D411yescharacteristic
46#103×C61—42no—
47#100×C61—22no—
48C24×C61C2×D412yes—
49C2×Q8×C61—21no—
50C2×Q8×C61—41no—
51C2×Q8×C61—41no—
52C2×Q8×C61C4⋊C412yescomplemented
53C2×D4×C61—41no—
54C2×D4×C61—41no—
55C2×D4×C61C22×C411yescharacteristic
56C2×D4×C61C2×Q811yescharacteristic
57C2×D4×C61#4112yes—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61C2×D411yescharacteristic
63C22×Dic61—22no—
64C22×Dic61—22no—
65C22×Dic61—44no—
66C22×Dic61—42no—
67C22×Dic61—42no—
68M16×C61—41no—
69M16×C61—41no—
70C2×C8×C61—41no—
71C4⋊C4×C61—22no—
72C22⋊C4×C61—24no—
73C22⋊C4×C61—24no—
74C22⋊C4×C61—42no—
75C22⋊C4×C61—41no—
76C42×C61—21no—
77C42×C61—41no—
78C42×C61C4⋊C412yescomplemented
79C22⋊Dic61—24no—
80C22⋊Dic61—44no—
81C22⋊Dic61—42no—
82C22⋊Dic61—42no—
83C4⋊Dic61—81no—
84#11758196—84no—
85C4×Dic61—44no—
86C4×Dic61—81no—
87C23×C61—22no—
88C23×C61—22no—
89C23×C61—42no—
90C23×C61—42no—
91C23×C61C4×D412yes—
92C23×C61#12011yescharacteristic
93C23×C61C22⋊Q812yes—
94Q8×C61—42no—
95Q8×C61—81no—
96D4×C61—41no—
97D4×C61—41no—
98D4×C61—42no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—42no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—42no—
107C2×C4×C61—82no—
108C2×C4×C61—82no—
109C2×C4×C61C2×C4⋊C411yescharacteristic
110C2×C4×C61#12311yescharacteristic
111C2×Dic61—24no—
112C2×Dic61—42no—
113C2×Dic61—42no—
114C2×Dic61—44no—
115C2×Dic61—42no—
116C2×Dic61—44no—
117C2×Dic61—42no—
118C2×Dic61—42no—
119C2×Dic61—82no—
120C2×Dic61—82no—
121C2×Dic61—82no—
122C8×C61—81no—
123#12965—611nomaximal, Sylow
124C22×C61—22no—
125C22×C61—22no—
126C22×C61—22no—
127C22×C61—42no—
128C22×C61—42no—
129C22×C61—42no—
130C22×C61—42no—
131C22×C61—82no—
132C22×C61#38511yescharacteristic
133C22×C61B(4,𝔽2)11yescharacteristic
134C22×C61#45811yescharacteristic
135C4×C61—21no—
136C4×C61—21no—
137C4×C61—42no—
138C4×C61—42no—
139C4×C61—82no—
140Dic61—44no—
141Dic61—82no—
142Dic61—84no—
143#2372—611no—
144C2×#354—611no—
145#1885D6111yescharacteristic
146#1867—612no—
147#1390—612no—
148C2×C61—21no—
149C2×C61—21no—
150C2×C61—42no—
151C2×C61—42no—
152C2×C61#186711yescharacteristic
153C2×C61#219712yes—
154C2×#124C2×D6111yescharacteristic
155#518C2×D6111yescharacteristic
156#419—21no—
157C2×#100C2×D6111yescharacteristic
158C2×#99—612no—
159#391—1221no—
160#388—1222no—
161#386—612no—
162#385—1222no—
163C4×C22⋊C4—1222no—
164#376—1221no—
165#354—614no—
166#342—1222no—
167#339—21no—
168C61#1296511yescharacteristic, complemented, Sylow
169C22×Q8C22⋊D6111yescharacteristic
170C22×D4C22×D6111yescharacteristic
171C23×C4—612no—
172C2×M16—21no—
173#124—22no—
174#124Dic12212yes—
175#124C4×D6112yes—
176C4×D4—42no—
177#117—21no—
178C2×C4⋊C4—1221no—
179C2×C4⋊C4—2442no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—612no—
183C2×C22⋊C4—1222no—
184C2×C22⋊C4—1222no—
185C2×C42—1221no—
186C2×C42—1222no—
187C2×C42C22⋊D6111yescharacteristic
188#103—42no—
189#100—22no—
190#99—614no—
191#99—1222no—
192#95—1221no—
193#95—1221no—
194#95—1222no—
195#95—1222no—
196#95—2442no—
197C24D4×D6112yes—
198C2×Q8—21no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8#1175819612yescomplemented
202C2×D4—41no—
203C2×D4—41no—
204C2×D4C2×Dic12211yescharacteristic
205C2×D4C2×C4×D6111yescharacteristic
206C2×D4#1175822412yes—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—1222no—
212C22×C4—1222no—
213C22×C4—2444no—
214C22×C4—2442no—
215C22×C4—2442no—
216C22×C4C2×C22⋊D6111yescharacteristic
217M16—41no—
218M16—41no—
219C2×C8—41no—
220C4⋊C4—22no—
221C4⋊C4—4881no—
222C4⋊C4—4884no—
223C22⋊C4—24no—
224C22⋊C4—24no—
225C22⋊C4—42no—
226C22⋊C4—41no—
227C22⋊C4—1224no—
228C22⋊C4—2444no—
229C22⋊C4—2442no—
230C22⋊C4—2442no—
231C42—21no—
232C42—41no—
233C42—4881no—
234C42—2444no—
235C42#1175819612yescomplemented
236C23—22no—
237C23—22no—
238C23—42no—
239C23—42no—
240C23#1451973712yes—
241C23#1451974511yescharacteristic
242C23#1451975412yes—
243Q8—42no—
244Q8—81no—
245D4—41no—
246D4—41no—
247D4—42no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—1224no—
259C2×C4—4882no—
260C2×C4—4882no—
261C2×C4—4882no—
262C2×C4—2442no—
263C2×C4—2444no—
264C2×C4—2442no—
265C2×C4—2442no—
266C2×C4—2442no—
267C2×C4—2442no—
268C2×C4—2444no—
269C2×C4C2×#1175819611yescharacteristic
270C2×C4#1451975811yescharacteristic
271C8—81no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—82no—
280C22#1683963411yescharacteristic
281C22#1683994811yescharacteristic
282C22#1683995111yescharacteristic
283C4—21no—
284C4—21no—
285C4—42no—
286C4—42no—
287C4—82no—
288C4—4882no—
289C4—4884no—
290C4—2444no—
291C2—21no—
292C2—21no—
293C2—42no—
294C2—42no—
295C2#2144609911yescharacteristic
296C2#2144780812yes—
subgroupG/H
centerC22#16839948
commutatorC2×D4×C61C22×C4
FrattiniC22×D4C22×D61
FittingC61×#1885C2
socleC22×C61B(4,𝔽2)
prime radical, cosocleC22×D4×C61C23
hypercenter#1885D61
hypocenterC61#12965
LCSG ▷ C2×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1885

Complements

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

NH ≅ G/Ntype
13. #16839557C4semidirect
52. C2×Q8×C61C4⋊C4semidirect
78. C42×C61C4⋊C4semidirect
168. C61#12965semidirect
201. C2×Q8#11758196semidirect
235. C42#11758196semidirect

Maximal subgroups

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

subgroupindex
#214489312
C2×#168395572
#214461002
#214439382
C61×#18852
#1296561