Finite Group Databasebeta

← #29568313

Subgroups — #29568313

Order 15616.

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

normal subgroups only

This group has 490 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
1#21448302C211yesmaximal, characteristic
2#21445887C211yesmaximal, characteristic
3#21443643C212yesmaximal, complemented
4#21443641C212yesmaximal, complemented
5C61×#1817C211yesmaximal, characteristic
6C2×#14519736C411yescharacteristic
7C2×#14519736C411yescharacteristic
8C2×C22⋊#92418—21no—
9#16839660C411yescharacteristic
10#16839660C411yescharacteristic
11#16839660C2211yescharacteristic
12#16839660C2211yescharacteristic
13#16839635—21no—
14#16839635—21no—
15C4×#11758196—21no—
16C4×#11758196—21no—
17#16839517—21no—
18#16839517C2212yes—
19C22×C42×C61C2211yescharacteristic
20C2×C22⋊C8×C61—21no—
21C61×#336—21no—
22C61×#336C2212yes—
23C22×#92418—22no—
24#14519736—22no—
25#14519736—22no—
26#14519736—42no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61—21no—
39C22⋊#92418—42no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44C23×C4×C61C2×C411yescharacteristic
45C23×C4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C22×C8×C61—22no—
48C2×C42×C61—42no—
49C2×C42×C61C2×C411yescharacteristic
50C2×C42×C61D411yescharacteristic
51C2×C42×C61D411yescharacteristic
52C2×C42×C61C2311yescharacteristic
53C22⋊C8×C61—42no—
54C24×C61C22⋊C411yescharacteristic
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—22no—
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C2×C8×C61—42no—
76C2×C8×C61—42no—
77C2×C8×C61—42no—
78C42×C61—41no—
79C42×C61—41no—
80C42×C61—41no—
81C42×C61—41no—
82C22⋊Dic61—24no—
83C22⋊Dic61—42no—
84C4⋊Dic61—21no—
85C4⋊Dic61—21no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88C4⋊Dic61M1612yes—
89C4⋊Dic61M1612yes—
90#11758196—42no—
91#11758196—42no—
92#11758196—42no—
93#11758196—42no—
94C4×Dic61—24no—
95C4×Dic61—42no—
96C2×#92418—42no—
97C2×#92418—42no—
98C2×#92418—42no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61#9912yes—
106C23×C61C2×C22⋊C411yescharacteristic
107C2×C4×C61—24no—
108C2×C4×C61—24no—
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—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—44no—
124C2×C4×C61—44no—
125C2×C4×C61#10112yes—
126C2×C4×C61C2×M1611yescharacteristic
127C2×C4×C61C2×M1611yescharacteristic
128C2×C4×C61#13512yes—
129C2×C4×C61#13512yes—
130C2×Dic61—22no—
131C2×Dic61—22no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C8×C61—82no—
143#92418—82no—
144#7646—611nomaximal, Sylow
145C22×C61—22no—
146C22×C61—22no—
147C22×C61—22no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61#40711yescharacteristic
153C22×C61C2×#9911yescharacteristic
154C22×C61C2×#10111yescharacteristic
155C22×C61#41611yescharacteristic
156C22×C61#41611yescharacteristic
157C22×C61#42111yescharacteristic
158C22×C61#42111yescharacteristic
159C4×C61—22no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—22no—
163C4×C61—22no—
164C4×C61—41no—
165C4×C61—41no—
166Dic61—42no—
167Dic61—42no—
168Dic61—81no—
169Dic61—81no—
170#2296—611no—
171#1817—611no—
172#1817D6111yescharacteristic
173#1271—612no—
174#1271—612no—
175C2×C61—42no—
176C2×C61#146311yescharacteristic
177C2×C61#148811yescharacteristic
178C2×C61#148811yescharacteristic
179C2×C61#151611yescharacteristic
180C2×C61#151611yescharacteristic
181C2×C61#153711yescharacteristic
182C2×C61#154411yescharacteristic
183C2×#117—611no—
184C2×#117—611no—
185C22×C42C2×D6111yescharacteristic
186C2×C22⋊C8—21no—
187C2×C22⋊C8—1221no—
188#389—611no—
189#389—611no—
190#389—611no—
191#389—611no—
192#385—1221no—
193#385—1221no—
194C4×C4⋊C4—1221no—
195C4×C4⋊C4—1221no—
196#336—21no—
197#336—612no—
198#336—1221no—
199#336C2×D6112yes—
200C61#764611yescharacteristic, complemented, Sylow
201C23×C4C4×D6111yescharacteristic
202C23×C4D24411yescharacteristic
203C23×C4C22⋊D6111yescharacteristic
204C22×C8—22no—
205C22×C8—1222no—
206#117—1222no—
207#117—1222no—
208#117—2442no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C42—42no—
220C2×C42—1221no—
221C2×C42—1221no—
222C2×C42C4×D6111yescharacteristic
223C2×C42D24411yescharacteristic
224C2×C42C22⋊D6111yescharacteristic
225C2×C42C22×D6111yescharacteristic
226C22⋊C8—42no—
227C22⋊C8—2442no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232C24#1175819811yescharacteristic
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4#1175819811yescharacteristic
248C22×C4#1175819811yescharacteristic
249C22×C4#1175819811yescharacteristic
250C22×C4C2×C4×D6111yescharacteristic
251C22×C4C2×D24411yescharacteristic
252C22×C4C2×C22⋊D6111yescharacteristic
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—2442no—
257C2×C8—2442no—
258C2×C8—2442no—
259C4⋊C4—612no—
260C4⋊C4—612no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2442no—
266C4⋊C4—2442no—
267C4⋊C4—2442no—
268C4⋊C4—2442no—
269C22⋊C4—1224no—
270C22⋊C4—2442no—
271C42—41no—
272C42—41no—
273C42—41no—
274C42—41no—
275C42—1224no—
276C42—2442no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23#1451969112yes—
284C23C2×#1175819811yescharacteristic
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—1222no—
304C2×C4—1222no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4#1451969512yes—
316C2×C4M16×D6111yescharacteristic
317C2×C4M16×D6111yescharacteristic
318C2×C4#1451979712yes—
319C2×C4#1451979912yes—
320C8—82no—
321C8—4882no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22#1683972511yescharacteristic
330C22C2×#1451969111yescharacteristic
331C22C2×#1451969511yescharacteristic
332C22#1683975611yescharacteristic
333C22#1683975911yescharacteristic
334C22#1683977811yescharacteristic
335C22#1683978011yescharacteristic
336C4—22no—
337C4—22no—
338C4—22no—
339C4—21no—
340C4—21no—
341C4—41no—
342C4—41no—
343C4—4881no—
344C4—4881no—
345C4—2442no—
346C4—2442no—
347C2—42no—
348C2#2144414811yescharacteristic
349C2#2144425111yescharacteristic
350C2#2144425411yescharacteristic
351C2#2144437311yescharacteristic
352C2#2144437611yescharacteristic
353C2#2144445611yescharacteristic
354C2#2144448311yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1817C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1817D61
hypocenterC61#7646
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
3. #21443643C2semidirect
4. #21443641C2semidirect
200. C61#7646semidirect

Maximal subgroups

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

subgroupindex
#214483022
#214458872
#214436432
#214436412
C61×#18172
#764661