Finite Group Databasebeta

← #29589102

Subgroups — #29589102

Order 15616.

734 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 93 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#21448396C211yesmaximal, characteristic
2#323×D61C212yesmaximal, complemented
3#21443749C211yesmaximal, characteristic, complemented
4#21443746C212yesmaximal, complemented
5C61×#1317C211yesmaximal, characteristic, complemented
6C23×D244C411yescharacteristic
7C2×C22⋊C4×D61C411yescharacteristic
8C2×C22⋊C4×D61C2211yescharacteristic
9C22⋊C8×D61—22no—
10#16839640—22no—
11#16839640—22no—
12#16839625C411yescharacteristic
13#16839617C411yescharacteristic
14#16839617C2211yescharacteristic
15#16839486C2212yes—
16#16839485—22no—
17C61×#381C2211yescharacteristic
18C61×#323C2212yes—
19C24×D61C2×C411yescharacteristic
20C24×D61C2×C411yescharacteristic
21C22×D244—21no—
22C22×D244—21no—
23C22×D244—22no—
24C22×D244—42no—
25C22×D244—42no—
26C22×D244C814yescomplemented
27C22×C4×D61—21no—
28C22×C4×D61D412yes—
29C2×C8×D61—42no—
30C2×C22⋊Dic61C2×C411yescharacteristic
31C2×C22⋊Dic61C2×C411yescharacteristic
32C2×#11758198—21no—
33C2×#11758198—22no—
34C2×#11758198—22no—
35C2×#11758198D412yes—
36C22⋊C4×D61—42no—
37C22⋊C4×D61—42no—
38C22⋊#92418—22no—
39#14519689—42no—
40#14519684—22no—
41C23×C4×C61C2×C411yescharacteristic
42C2×C22⋊C4×C61C2×C411yescharacteristic
43C2×C22⋊C4×C61C2311yescharacteristic
44C22⋊C8×C61—22no—
45#95×C61—22no—
46C24×C61C22×C411yescharacteristic
47C23×D61—22no—
48C23×D61—22no—
49C23×D61—21no—
50C23×D61—21no—
51C23×D61—41no—
52C23×D61—41no—
53C23×D61—82no—
54C23×D61—82no—
55C23×D61C22⋊C411yescharacteristic
56C23×D61C22⋊C411yescharacteristic
57C23×D61C2×C812yes—
58C23×D61C2×C812yescomplemented
59C23×D61M1612yes—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61C2×C812yescomplemented
66C22×C4×C61C2×D412yes—
67C22×Dic61—21no—
68C22×Dic61C22⋊C412yes—
69C2×D244—24no—
70C2×D244—24no—
71C2×D244—42no—
72C2×D244—42no—
73C2×D244—48no—
74C2×D244—42no—
75C2×D244—42no—
76C2×D244—48no—
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—42no—
80C2×C4×D61—82no—
81C2×C4×D61—82no—
82C2×C8×C61—42no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊Dic61—41no—
86C22⋊Dic61—41no—
87#11758198—42no—
88#11758198—42no—
89#11758198—82no—
90#11758198—82no—
91C2×#92418—42no—
92C8×D61—84no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—42no—
96C23×C61C2×C22⋊C411yescharacteristic
97C23×C61C22×C811yescharacteristic
98C23×C61C2×M1611yescharacteristic
99C22×D61—21no—
100C22×D61—21no—
101C22×D61—24no—
102C22×D61—24no—
103C22×D61—22no—
104C22×D61—42no—
105C22×D61—42no—
106C22×D61—42no—
107C22×D61—42no—
108C22×D61—42no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—42no—
112C22×D61—82no—
113C22×D61—82no—
114C22×D61—84no—
115C22×D61—82no—
116C22×D61—82no—
117C22×D61—82no—
118C22×D61—82no—
119C22×D61—84no—
120C22×D61—84no—
121C22×D61C22⋊C812yes—
122C22×D61C22⋊C812yes—
123C22×D61#9912yes—
124C22×D61#10012yes—
125C2×C4×C61—22no—
126C2×C4×C61—22no—
127C2×C4×C61—42no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—42no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—41no—
134C2×Dic61—22no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137C2×Dic61—41no—
138D244—48no—
139D244—48no—
140C4×D61—44no—
141C4×D61—82no—
142C4×D61—84no—
143C8×C61—82no—
144#92418—82no—
145#11426—611nomaximal, Sylow
146C22×C61—22no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—42no—
152C22×C61—42no—
153C22×C61C2×C22⋊C811yescharacteristic
154C22×C61C2×#9911yescharacteristic
155C22×C61C2×#10011yescharacteristic
156C2×D61—22no—
157C2×D61—22no—
158C2×D61—22no—
159C2×D61—42no—
160C2×D61—42no—
161C2×D61—42no—
162C2×D61—42no—
163C2×D61—42no—
164C2×D61—42no—
165C2×D61—42no—
166C2×D61—42no—
167C2×D61—84no—
168C2×D61—84no—
169C2×D61—82no—
170C2×D61—84no—
171C2×D61—82no—
172C2×D61—84no—
173C2×D61#32314yes—
174C4×C61—42no—
175C4×C61—42no—
176C4×C61—81no—
177Dic61—42no—
178Dic61—81no—
179#2308—611no—
180C2×#323—612no—
181#1317—611no—
182#1317D6111yescharacteristic, complemented
183#1316—612no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—41no—
187C2×C61—41no—
188C2×C61C2×#32311yescharacteristic
189C2×C61#212112yes—
190D61—24no—
191D61—42no—
192D61—82no—
193C23×D4—611no—
194C22×C22⋊C4—611no—
195C22×C22⋊C4—611no—
196C2×C22⋊C8—1222no—
197#386—1222no—
198#386—1222no—
199#381—611no—
200#381C2×D6111yescharacteristic
201#379—611no—
202#379—611no—
203#323—612no—
204#323—1222no—
205#323C2×D6112yes—
206C61#1142611yescharacteristic, complemented, Sylow
207C25—611no—
208C25—611no—
209C22×D4—614no—
210C22×D4—1222no—
211C22×D4—1221no—
212C22×D4—1221no—
213C22×D4—2442no—
214C22×D4—2442no—
215C23×C4—612no—
216C23×C4—1221no—
217C23×C4C4×D6111yescharacteristic
218C22×C8—2442no—
219C2×C22⋊C4—611no—
220C2×C22⋊C4—612no—
221C2×C22⋊C4—611no—
222C2×C22⋊C4—1222no—
223C2×C22⋊C4—1222no—
224C2×C22⋊C4—1221no—
225C2×C22⋊C4—2442no—
226C2×C22⋊C4—2442no—
227C2×C22⋊C4C4×D6111yescharacteristic
228C2×C22⋊C4C22×D6111yescharacteristic
229C22⋊C8—22no—
230C22⋊C8—1222no—
231C22⋊C8—2442no—
232#95—22no—
233#95—1222no—
234C24—611no—
235C24—612no—
236C24—612no—
237C24—611no—
238C24—612no—
239C24—1222no—
240C24—1222no—
241C24—1221no—
242C24—1221no—
243C24—4882no—
244C24—4882no—
245C24—2441no—
246C24—2441no—
247C24C2×C4×D6111yescharacteristic
248C2×D4—1224no—
249C2×D4—1224no—
250C2×D4—2442no—
251C2×D4—2442no—
252C2×D4—2448no—
253C2×D4—2442no—
254C2×D4—2442no—
255C2×D4—2448no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—612no—
262C22×C4—1222no—
263C22×C4—1222no—
264C22×C4—1221no—
265C22×C4—4882no—
266C22×C4—4882no—
267C22×C4—2442no—
268C22×C4C8×D6112yescomplemented
269C22×C4D4×D6112yes—
270C2×C8—42no—
271C2×C8—4884no—
272C2×C8—2442no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—4882no—
276C22⋊C4—4882no—
277C22⋊C4—2442no—
278C22⋊C4—2442no—
279C22⋊C4—2441no—
280C22⋊C4—2441no—
281C23—21no—
282C23—21no—
283C23—42no—
284C23—612no—
285C23—612no—
286C23—612no—
287C23—612no—
288C23—1224no—
289C23—1224no—
290C23—1221no—
291C23—1221no—
292C23—1222no—
293C23—4882no—
294C23—4882no—
295C23—4884no—
296C23—4884no—
297C23—4882no—
298C23—4884no—
299C23—4882no—
300C23—4882no—
301C23—4882no—
302C23—2442no—
303C23—2442no—
304C23—2442no—
305C23—2442no—
306C23—2442no—
307C23—2442no—
308C23—2441no—
309C23—2441no—
310C23C22⋊C4×D6111yescharacteristic
311C23C2×C8×D6111yescharacteristic
312C23M16×D6111yescharacteristic
313D4—2448no—
314D4—2448no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—1222no—
325C2×C4—4882no—
326C2×C4—4884no—
327C2×C4—2444no—
328C2×C4—2442no—
329C2×C4—2441no—
330C2×C4—2442no—
331C8—82no—
332C8—4882no—
333C22—22no—
334C22—21no—
335C22—21no—
336C22—41no—
337C22—41no—
338C22—42no—
339C22—42no—
340C22—614no—
341C22—1222no—
342C22—1222no—
343C22—1222no—
344C22—4882no—
345C22—4884no—
346C22—4884no—
347C22—4884no—
348C22—4884no—
349C22—4882no—
350C22—2442no—
351C22—2442no—
352C22—2442no—
353C22—2442no—
354C22—2442no—
355C22—2442no—
356C22—2442no—
357C22—2442no—
358C22C22⋊C8×D6111yescharacteristic
359C22#99×D6111yescharacteristic
360C22#100×D6111yescharacteristic
361C4—42no—
362C4—42no—
363C4—81no—
364C4—4881no—
365C4—2442no—
366C2—21no—
367C2—21no—
368C2—41no—
369C2—41no—
370C2—1224no—
371C2—4882no—
372C2—2442no—
373C2#323×D6111yescharacteristic
374C2#2144746412yes—
subgroupG/H
centerC22#99×D61
commutatorC23×C61C22×C8
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1317C2
socleC22×C61C2×#99
prime radicalC23×D244C4
cosocleC2×C22⋊C4×C61C23
hypercenter#1317D61
hypocenterC61#11426
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
2. #323×D61C2semidirect
3. #21443749C2semidirect
4. #21443746C2semidirect
5. C61×#1317C2semidirect
26. C22×D244C8semidirect
58. C23×D61C2×C8semidirect
65. C22×C4×C61C2×C8semidirect
182. #1317D61semidirect
206. C61#11426semidirect
268. C22×C4C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214483962
#323×D612
#214437492
#214437462
C61×#13172
#1142661