Finite Group Databasebeta

← #29598297

Subgroups — #29598297

Order 15616.

536 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×#16839552C214yesmaximal
2#21445807C211yesmaximal, characteristic
3C4×#14519694C211yesmaximal, characteristic
4C61×#2486C211yesmaximal, characteristic
5C2×#14519694C2212yes—
6C2×#14519692C2212yes—
7C4×#11758194—21no—
8#16839622—21no—
9#16839552—28no—
10#16839531—21no—
11#16839529—21no—
12C2×#123×C61C2212yes—
13C2×C4×D4×C61C2211yescharacteristic
14C22×C4⋊C4×C61C411yescharacteristic, complemented
15C61×#398—21no—
16C61×#397—21no—
17C61×#389—21no—
18C61×#381C412yescomplemented
19C61×#380—21no—
20C61×#380C411yescharacteristic, complemented
21C2×#11758194—22no—
22C2×C4⋊Dic61—41no—
23C2×C22⋊Dic61—22no—
24#14519694—22no—
25#14519694D414yes—
26#14519692—24no—
27#14519688—41no—
28C4×#92418—41no—
29#14519684—41no—
30C22×D4×C61C2311yescharacteristic
31C23×C4×C61C2×C412yes—
32C23×C4×C61C2×C411yescharacteristic
33C23×C4×C61D411yescharacteristic
34#123×C61—24no—
35#123×C61—24no—
36C4×D4×C61—41no—
37C4×D4×C61—41no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61—21no—
41C2×C4⋊C4×C61—22no—
42C2×C4⋊C4×C61—41no—
43C2×C4⋊C4×C61—41no—
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C22⋊C4×C61—22no—
46C2×C22⋊C4×C61C2×C412yes—
47C2×C22⋊C4×C61C2×C411yescharacteristic
48C2×C22⋊C4×C61D411yescharacteristic
49C2×C42×C61D411yescharacteristic
50#95×C61—22no—
51#95×C61—21no—
52#95×C61—22no—
53C24×C61C22×C411yescharacteristic
54C24×C61C2×D411yescharacteristic
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C2×D4×C61C2×D412yes—
58C2×D4×C61#4112yes—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—22no—
64C22×C4×C61—22no—
65C22×C4×C61—24no—
66C22×C4×C61—42no—
67C22×C4×C61—42no—
68C22×C4×C61—42no—
69C22×C4×C61—42no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—42no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—42no—
78C4⋊C4×C61—42no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—44no—
82C22⋊C4×C61—24no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61—42no—
86C22⋊C4×C61—42no—
87C42×C61—21no—
88C42×C61—21no—
89C22⋊Dic61—42no—
90C22⋊Dic61—42no—
91C4⋊Dic61—82no—
92#11758194—24no—
93#11758194—42no—
94C2×#92418—42no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—41no—
100C23×C61—41no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61C2×C22⋊C411yescharacteristic
104C23×C61C4×D412yes—
105C23×C61#12411yescharacteristic
106C23×C61#12711yescharacteristic
107D4×C61—42no—
108D4×C61—42no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—22no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—42no—
116C2×C4×C61—42no—
117C2×C4×C61—42no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—42no—
122C2×C4×C61—42no—
123C2×C4×C61—42no—
124C2×C4×C61—42no—
125C2×C4×C61—42no—
126C2×C4×C61—42no—
127C2×C4×C61—81no—
128C2×C4×C61—84no—
129C2×C4×C61#9911yescharacteristic
130C2×C4×C61#9911yescharacteristic
131C2×C4×C61#12112yes—
132C2×Dic61—82no—
133C2×Dic61—82no—
134C2×Dic61—82no—
135#92418—44no—
136#13217—611nomaximal, Sylow
137C22×C61—21no—
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—22no—
141C22×C61—21no—
142C22×C61—42no—
143C22×C61—41no—
144C22×C61—41no—
145C22×C61—42no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—81no—
151C22×C61#39011yescharacteristic
152C22×C61C2×#9911yescharacteristic
153C22×C61#41011yescharacteristic
154C4×C61—21no—
155C4×C61—22no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—82no—
160C4×C61—82no—
161C4×C61#35212yescomplemented
162Dic61—162no—
163#2486D6111yescharacteristic
164C2×#352—614no—
165#1799—611no—
166C4×#100—611no—
167C2×C61—21no—
168C2×C61—21no—
169C2×C61—41no—
170C2×C61—42no—
171C2×C61—41no—
172C2×C61#196411yescharacteristic
173C2×C61C2×#35211yescharacteristic
174C2×C61#212311yescharacteristic
175C2×#123C2×D6112yes—
176C2×C4×D4C2×D6111yescharacteristic
177C22×C4⋊C4Dic6111yescharacteristic, complemented
178C2×#100—612no—
179C2×#99—612no—
180C4×M16—1221no—
181#398—21no—
182#397—21no—
183#389—21no—
184#381Dic6112yescomplemented
185#380—21no—
186#380—1221no—
187#380Dic6111yescharacteristic, complemented
188#352—1228no—
189#343—1221no—
190#342—1221no—
191C61#1321711yescharacteristic, complemented, Sylow
192C22×D4C22×D6111yescharacteristic
193C23×C4C2×Dic6112yes—
194C23×C4C2×Dic6111yescharacteristic
195C23×C4C22⋊D6111yescharacteristic
196C2×M16—1222no—
197#123—24no—
198#123—24no—
199C4×D4—41no—
200C4×D4—41no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—41no—
206C2×C4⋊C4—41no—
207C2×C4⋊C4—2441no—
208C2×C4⋊C4C22⋊D6111yescharacteristic
209C2×C22⋊C4—22no—
210C2×C22⋊C4—1222no—
211C2×C22⋊C4C2×Dic6112yes—
212C2×C22⋊C4C2×Dic6111yescharacteristic
213C2×C22⋊C4C22⋊D6111yescharacteristic
214C2×C42C22⋊D6111yescharacteristic
215#100—614no—
216#100—1222no—
217#99—1224no—
218#97—2441no—
219C4×C8—2441no—
220#95—22no—
221#95—21no—
222#95—22no—
223#95—2441no—
224C24C22×Dic6111yescharacteristic
225C24C2×C22⋊D6111yescharacteristic
226C2×D4—41no—
227C2×D4—41no—
228C2×D4D4×D6112yes—
229C2×D4#1175822412yes—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—24no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—2442no—
242C22×C4C22⋊Dic6111yescharacteristic
243C22×C4C22⋊Dic6111yescharacteristic
244C22×C4C22⋊Dic6111yescharacteristic
245C22×C4C22⋊Dic6111yescharacteristic
246C22×C4C2×C22⋊D6111yescharacteristic
247M16—1224no—
248M16—2442no—
249C2×C8—2442no—
250C4⋊C4—41no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—44no—
256C4⋊C4—4882no—
257C22⋊C4—24no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—2442no—
263C22⋊C4—2442no—
264C42—21no—
265C42—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23C2×C22⋊Dic6111yescharacteristic
275C23D4×Dic6112yes—
276C23#1451976411yescharacteristic
277C23#1451977311yescharacteristic
278D4—42no—
279D4—42no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—81no—
299C2×C4—84no—
300C2×C4—4882no—
301C2×C4—4882no—
302C2×C4—4882no—
303C2×C4#1451969211yescharacteristic
304C2×C4#1451969211yescharacteristic
305C2×C4#1451974812yes—
306C8—2444no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22—21no—
311C22—21no—
312C22—42no—
313C22—41no—
314C22—41no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22#1683966511yescharacteristic
322C22C2×#1451969211yescharacteristic
323C22#1683973611yescharacteristic
324C4—22no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—82no—
330C4—82no—
331C4—9762no—
332C4#1683955212yescomplemented
333C2—21no—
334C2—21no—
335C2—41no—
336C2—42no—
337C2—41no—
338C2#2144665611yescharacteristic
339C2C2×#1683955211yescharacteristic
340C2#2144747311yescharacteristic
subgroupG/H
centerC22C2×#14519692
commutatorC24×C61C22×C4
FrattiniC22×D4C22×D61
FittingC61×#2486C2
socleC22×C61C2×#99
prime radical, cosocleC22×D4×C61C23
hypercenter#2486D61
hypocenterC61#13217
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2486

Complements

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

NH ≅ G/Ntype
14. C22×C4⋊C4×C61C4semidirect
18. C61×#381C4semidirect
20. C61×#380C4semidirect
161. C4×C61#352semidirect
177. C22×C4⋊C4Dic61semidirect
184. #381Dic61semidirect
187. #380Dic61semidirect
191. C61#13217semidirect
332. C4#16839552semidirect

Maximal subgroups

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

subgroupindex
C2×#168395522
#214458072
C4×#145196942
C61×#24862
#1321761