Finite Group Databasebeta

← #29589125

Subgroups — #29589125

Order 15616.

686 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 115 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#21448399C211yesmaximal, characteristic
2#21444133C211yesmaximal, characteristic, complemented
3#21443750C214yesmaximal, complemented
4C61×#1458C211yesmaximal, characteristic, complemented
5C23×D244C411yescharacteristic
6C2×#14519736C411yescharacteristic
7#16839815—21no—
8#16839664—21no—
9#16839664—21no—
10#16839663C412yes—
11#16839663C2212yes—
12#16839617—21no—
13#16839617—21no—
14#16839488C2212yescomplemented
15#16839486—21no—
16C2×#117×C61C2211yescharacteristic
17C61×#431—21no—
18C61×#324C2212yescomplemented
19C61×#323—21no—
20C24×D61—21no—
21C22×D244—21no—
22C22×D244—22no—
23C22×D244—41no—
24C22×D244—41no—
25C22×D244—42no—
26C22×D244C814yescomplemented
27C22×D244C2×C412yes—
28#14519736—42no—
29C2×C4⋊Dic61—21no—
30C2×C22⋊Dic61—21no—
31C2×#11758198—22no—
32C2×#11758198—22no—
33C2×#11758198—22no—
34C2×#11758198—22no—
35C2×C4×Dic61C2×C412yes—
36C4⋊#92418—41no—
37C22⋊#92418—22no—
38C4×#92418—41no—
39C23×C4×C61C2×C411yescharacteristic
40#117×C61—41no—
41#117×C61—41no—
42C2×C4⋊C4×C61C2×C411yescharacteristic
43C2×C4⋊C4×C61C2311yescharacteristic
44C2×C22⋊C4×C61D411yescharacteristic
45C2×C22⋊C4×C61D411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48C4⋊C8×C61—41no—
49C22⋊C8×C61—22no—
50C4×C8×C61—41no—
51C24×C61C22⋊C411yescharacteristic
52C23×D61—22no—
53C23×D61—24no—
54C23×D61—42no—
55C23×D61—42no—
56C23×D61—82no—
57C23×D61—82no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—22no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C2×C812yes—
65C22×C4×C61M1612yes—
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—22no—
70C2×D244—24no—
71C2×D244—22no—
72C2×D244—44no—
73C2×D244—44no—
74C2×D244—42no—
75C2×D244—42no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—42no—
79C2×D244—44no—
80C2×D244—44no—
81C2×D244C2×C814yes—
82C2×C8×C61—42no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C42×C61—21no—
88C42×C61—21no—
89C42×C61—21no—
90C42×C61—21no—
91C22⋊Dic61—42no—
92#11758198—82no—
93#11758198—82no—
94#11758198—82no—
95#11758198—82no—
96C4⋊Dic61—42no—
97C4×Dic61—42no—
98C2×#92418—42no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61C22⋊C812yes—
104C23×C61C2×C22⋊C411yescharacteristic
105C22×D61—24no—
106C22×D61—42no—
107C22×D61—42no—
108C22×D61—42no—
109C22×D61—42no—
110C22×D61—48no—
111C22×D61—42no—
112C22×D61—42no—
113C22×D61—88no—
114C22×D61—88no—
115C22×D61—84no—
116C22×D61—84no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—22no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61C22⋊C812yes—
132C2×C4×C61#9911yescharacteristic
133C2×C4×C61#9911yescharacteristic
134C2×C4×C61#10012yes—
135C2×C4×C61C22×C811yescharacteristic
136C2×C4×C61C2×M1611yescharacteristic
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140D244—44no—
141D244—44no—
142D244—44no—
143D244—44no—
144C8×C61—82no—
145#92418—82no—
146#11433—611nomaximal, Sylow
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—22no—
150C22×C61—42no—
151C22×C61—42no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61C2×C22⋊C811yescharacteristic
155C22×C61C2×#9911yescharacteristic
156C22×C61C2×#10011yescharacteristic
157C2×D61—44no—
158C2×D61—44no—
159C2×D61—44no—
160C2×D61—82no—
161C2×D61—82no—
162C2×D61—816no—
163C2×D61—82no—
164C2×D61—82no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61#32312yes—
172C4×C61#32312yes—
173Dic61—82no—
174#2309—611no—
175#1458—611no—
176#1458D6111yescharacteristic, complemented
177#1318—614no—
178C2×C61—21no—
179C2×C61—21no—
180C2×C61—42no—
181C2×C61C2×#32311yescharacteristic
182C2×C61#212811yescharacteristic
183C2×C61#213411yescharacteristic
184D61—84no—
185C23×D4—611no—
186C2×#117—611no—
187C2×#117C2×D6111yescharacteristic
188#431—21no—
189#431—1221no—
190#390—612no—
191#390—612no—
192#390—1221no—
193#390—1221no—
194#379—1221no—
195#379—1221no—
196#324—612no—
197#324C2×D6112yescomplemented
198#323—21no—
199#323—1221no—
200C61#1143311yescharacteristic, complemented, Sylow
201C25—1221no—
202C22×D4—614no—
203C22×D4—612no—
204C22×D4—1222no—
205C22×D4—1221no—
206C22×D4—2441no—
207C22×D4—2441no—
208C22×D4—2442no—
209C23×C4C4×D6111yescharacteristic
210#117—41no—
211#117—41no—
212#117—2442no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4C4×D6111yescharacteristic
215C2×C4⋊C4C22×D6111yescharacteristic
216C2×C22⋊C4—1222no—
217C2×C22⋊C4—1222no—
218C2×C22⋊C4—1222no—
219C2×C22⋊C4—1222no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4D24411yescharacteristic
222C2×C22⋊C4C22⋊D6111yescharacteristic
223C2×C42—612no—
224C2×C42D24411yescharacteristic
225C2×C42C22⋊D6111yescharacteristic
226C4⋊C8—41no—
227C4⋊C8—2441no—
228C22⋊C8—22no—
229C22⋊C8—1222no—
230C4×C8—41no—
231C4×C8—2441no—
232C24—1224no—
233C24—1222no—
234C24—4882no—
235C24—4882no—
236C24—2442no—
237C24—2442no—
238C24#1175819811yescharacteristic
239C2×D4—614no—
240C2×D4—1224no—
241C2×D4—1222no—
242C2×D4—2442no—
243C2×D4—2442no—
244C2×D4—2444no—
245C2×D4—2444no—
246C2×D4—2444no—
247C2×D4—2444no—
248C2×D4—2441no—
249C2×D4—2441no—
250C2×D4—2442no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—1222no—
255C22×C4C8×D6112yes—
256C22×C4#1175818912yes—
257C22×C4#1175819811yescharacteristic
258C22×C4#1175819811yescharacteristic
259C22×C4#1175819811yescharacteristic
260C22×C4C2×C4×D6111yescharacteristic
261C22×C4C2×D24411yescharacteristic
262C22×C4C2×C22⋊D6111yescharacteristic
263C2×C8—42no—
264C2×C8—2442no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—2442no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—4882no—
271C22⋊C4—4882no—
272C22⋊C4—4882no—
273C22⋊C4—4882no—
274C22⋊C4—2442no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—2442no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—1224no—
285C23—4888no—
286C23—4884no—
287C23—4884no—
288C23—4888no—
289C23—2442no—
290C23—2442no—
291C23—2442no—
292C23—2442no—
293C23—2448no—
294C23—2442no—
295C23—2442no—
296C23#1451968912yes—
297C23C2×#1175819811yescharacteristic
298D4—2444no—
299D4—2444no—
300D4—2444no—
301D4—2444no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—2442no—
317C2×C4—2442no—
318C2×C4—2442no—
319C2×C4#1451968912yes—
320C2×C4#1451969111yescharacteristic
321C2×C4#1451969111yescharacteristic
322C2×C4#1451969312yes—
323C2×C4C2×C8×D6111yescharacteristic
324C2×C4C2×#1175818911yescharacteristic
325C8—82no—
326C8—4882no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—4882no—
335C22—4882no—
336C22—48816no—
337C22—4882no—
338C22—4882no—
339C22—2444no—
340C22—2444no—
341C22—2444no—
342C22C2×#1451968911yescharacteristic
343C22C2×#1451969111yescharacteristic
344C22C2×#1451969311yescharacteristic
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—4882no—
352C4#1683948512yes—
353C4#1683948512yes—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—4884no—
358C2C2×#1683948511yescharacteristic
359C2#2144749011yescharacteristic
360C2#2144751011yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC2×C4×C61C22×C8
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1458C2
socleC22×C61C2×#99
prime radicalC23×D244C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1458D61
hypocenterC61#11433
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #21444133C2semidirect
3. #21443750C2semidirect
4. C61×#1458C2semidirect
14. #16839488C22semidirect
18. C61×#324C22semidirect
26. C22×D244C8semidirect
176. #1458D61semidirect
197. #324C2×D61semidirect
200. C61#11433semidirect

Maximal subgroups

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

subgroupindex
#214483992
#214441332
#214437502
C61×#14582
#1143361