Finite Group Databasebeta

← #29577780

Subgroups — #29577780

Order 15616.

578 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 131 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#21454843C211yesmaximal, characteristic
2#21450136C211yesmaximal, characteristic
3#21445907C212yesmaximal, complemented
4#21443686C212yesmaximal, complemented
5C61×#1799C211yesmaximal, characteristic
6C22×C4⋊Dic61C2211yescharacteristic
7D4×#92418—24no—
8#16839815—21no—
9C2×C22⋊#92418—21no—
10C2×C22⋊#92418C2212yes—
11#16839701C412yescomplemented
12#16839698C412yescomplemented
13#16839660—21no—
14#16839642—21no—
15#16839634—21no—
16#16839622—21no—
17#16839622C2211yescharacteristic
18#16839524—24no—
19C2×C4×D4×C61C2211yescharacteristic
20C2×#99×C61—21no—
21C61×#380C2212yes—
22C61×#342—21no—
23C23×Dic61—21no—
24C22×#92418—22no—
25C22×#92418D414yes—
26C2×C4⋊Dic61—22no—
27C2×C4⋊Dic61—22no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61C2×C412yes—
31C2×#11758196—22no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—22no—
34C4⋊#92418—22no—
35C22⋊#92418—22no—
36C22⋊#92418—22no—
37C22⋊#92418—22no—
38C4×#92418—22no—
39#14519684—22no—
40#14519684—22no—
41#14519684C2×C412yes—
42C22×D4×C61D411yescharacteristic
43C23×C4×C61D411yescharacteristic
44C23×C4×C61C2311yescharacteristic
45C4×D4×C61—22no—
46C4×D4×C61—22no—
47C2×C4⋊C4×C61—22no—
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C22⋊C4×C61—22no—
50C2×C22⋊C4×C61C2×C411yescharacteristic
51C2×C22⋊C4×C61D411yescharacteristic
52C2×C42×C61D411yescharacteristic
53#99×C61—42no—
54#95×C61—22no—
55C24×C61C22⋊C411yescharacteristic
56C24×C61C2×D411yescharacteristic
57C2×D4×C61—22no—
58C2×D4×C61—22no—
59C2×D4×C61SD1612yes—
60C2×D4×C61Q1612yes—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—42no—
64C22×C4×C61—42no—
65C22×C4×C61—42no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D412yes—
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61#4112yes—
73C22×Dic61—22no—
74C22×Dic61—22no—
75C22×Dic61—42no—
76C22×Dic61—82no—
77C4⋊C4×C61—22no—
78C4⋊C4×C61—44no—
79C22⋊C4×C61—22no—
80C22⋊C4×C61—22no—
81C22⋊C4×C61—42no—
82C22⋊C4×C61—42no—
83C42×C61—21no—
84C42×C61—21no—
85C22⋊Dic61—42no—
86C22⋊Dic61—82no—
87C4⋊Dic61—24no—
88C4⋊Dic61—42no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91#11758196—82no—
92C2×#92418—24no—
93C2×#92418—44no—
94C2×#92418—82no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—41no—
98C23×C61—41no—
99C23×C61—41no—
100C23×C61—41no—
101C23×C61#10312yes—
102C23×C61C2×C22⋊C411yescharacteristic
103C23×C61#12112yes—
104C23×C61C2×SD1611yescharacteristic
105C23×C61C2×Q1611yescharacteristic
106C23×C61#13512yes—
107D4×C61—24no—
108D4×C61—24no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—24no—
112C2×C4×C61—22no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—41no—
116C2×C4×C61—42no—
117C2×C4×C61—42no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—81no—
121C2×C4×C61—82no—
122C2×C4×C61—82no—
123C2×C4×C61—82no—
124C2×C4×C61#10312yes—
125C2×C4×C61C4×D412yes—
126C2×C4×C61#12011yescharacteristic
127C2×C4×C61#12311yescharacteristic
128C2×Dic61—42no—
129C2×Dic61—42no—
130C2×Dic61—42no—
131C2×Dic61—42no—
132C2×Dic61—42no—
133C2×Dic61—42no—
134C2×Dic61—84no—
135#92418—44no—
136#9469—611nomaximal, Sylow
137C22×C61—21no—
138C22×C61—22no—
139C22×C61—21no—
140C22×C61—22no—
141C22×C61—22no—
142C22×C61—41no—
143C22×C61—41no—
144C22×C61—42no—
145C22×C61—42no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61—81no—
149C22×C61#38611yescharacteristic
150C22×C61C2×#10311yescharacteristic
151C22×C61#41611yescharacteristic
152C22×C61#46512yes—
153C22×C61#46712yes—
154C4×C61—21no—
155C4×C61—22no—
156C4×C61—22no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—162no—
160C4×C61#45812yes—
161Dic61—82no—
162Dic61—82no—
163#2972—611no—
164#2487—611no—
165#1824—612no—
166#1799D6111yescharacteristic
167#1289—612no—
168C2×C61—21no—
169C2×C61—22no—
170C2×C61—21no—
171C2×C61—22no—
172C2×C61—42no—
173C2×C61#189011yescharacteristic
174C2×C61#189211yescharacteristic
175C2×C61#191011yescharacteristic
176C2×C4×D4C2×D6111yescharacteristic
177C22×C4⋊C4—611no—
178C8×D4—1224no—
179#431—1221no—
180C2×#99—21no—
181C2×C22⋊C8—612no—
182C2×C22⋊C8—1221no—
183#400—612no—
184#399—612no—
185#389—1221no—
186#386—1221no—
187#385—1221no—
188#380—611no—
189#380—1221no—
190#380C2×D6112yes—
191#342—21no—
192#340—1224no—
193C61#946911yescharacteristic, complemented, Sylow
194C22×D4C22⋊D6111yescharacteristic
195C23×C4—1221no—
196C23×C4D24411yescharacteristic
197C23×C4C22×D6111yescharacteristic
198C22×C8—614no—
199C22×C8—1222no—
200C4×D4—22no—
201C4×D4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—612no—
204C2×C4⋊C4—1222no—
205C2×C4⋊C4—1222no—
206C2×C4⋊C4—1222no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4C4×D6111yescharacteristic
210C2×C22⋊C4—22no—
211C2×C22⋊C4—1222no—
212C2×C22⋊C4—1221no—
213C2×C22⋊C4C4×D6111yescharacteristic
214C2×C22⋊C4C22⋊D6111yescharacteristic
215C2×C42D24411yescharacteristic
216C4⋊C8—1222no—
217#99—42no—
218C22⋊C8—1222no—
219C22⋊C8—1222no—
220C22⋊C8—1222no—
221C4×C8—1222no—
222#95—22no—
223#95—612no—
224#95—1222no—
225#95—1222no—
226C24#1175819811yescharacteristic
227C24C2×C22⋊D6111yescharacteristic
228C2×D4—22no—
229C2×D4—22no—
230C2×D4#1175820012yes—
231C2×D4#1175820212yes—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—1222no—
238C22×C4—1222no—
239C22×C4—4882no—
240C22×C4—2442no—
241C22×C4#1175819811yescharacteristic
242C22×C4#1175819811yescharacteristic
243C22×C4#1175819811yescharacteristic
244C22×C4C2×C4×D6111yescharacteristic
245C22×C4C2×D24411yescharacteristic
246C22×C4D4×D6112yes—
247C22×C4#1175822412yes—
248C2×C8—1224no—
249C2×C8—4882no—
250C2×C8—2444no—
251C4⋊C4—22no—
252C4⋊C4—44no—
253C4⋊C4—1224no—
254C4⋊C4—4882no—
255C4⋊C4—2442no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C22⋊C4—22no—
259C22⋊C4—22no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—4882no—
263C22⋊C4—2442no—
264C42—21no—
265C42—21no—
266C23—21no—
267C23—21no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23#1451970012yes—
273C23C2×#1175819811yescharacteristic
274C23#1451974912yes—
275C23C2×#1175820011yescharacteristic
276C23C2×#1175820211yescharacteristic
277C23#1451979712yes—
278D4—24no—
279D4—24no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—82no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4—4884no—
296C2×C4—2442no—
297C2×C4—2442no—
298C2×C4—2442no—
299C2×C4—2442no—
300C2×C4—2442no—
301C2×C4—2442no—
302C2×C4#1451970012yes—
303C2×C4#1451973712yes—
304C2×C4#1451974711yescharacteristic
305C2×C4#1451976111yescharacteristic
306C8—2444no—
307C22—21no—
308C22—22no—
309C22—21no—
310C22—22no—
311C22—22no—
312C22—41no—
313C22—41no—
314C22—42no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—81no—
319C22#1683963911yescharacteristic
320C22C2×#1451970011yescharacteristic
321C22#1683975611yescharacteristic
322C22#1683998912yes—
323C22#1684000112yes—
324C4—21no—
325C4—22no—
326C4—22no—
327C4—41no—
328C4—41no—
329C4—162no—
330C4—4882no—
331C4—4882no—
332C4#1683995312yes—
333C2—22no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—42no—
338C2#2144623011yescharacteristic
339C2#2144624011yescharacteristic
340C2#2144634411yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1799C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC23×C4×C61C23
hypercenter#1799D61
hypocenterC61#9469
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #21445907C2semidirect
4. #21443686C2semidirect
11. #16839701C4semidirect
12. #16839698C4semidirect
193. C61#9469semidirect

Maximal subgroups

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

subgroupindex
#214548432
#214501362
#214459072
#214436862
C61×#17992
#946961