Finite Group Databasebeta

← #29573561

Subgroups — #29573561

Order 15616.

530 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 123 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#21448729C211yesmaximal, characteristic
2#21444137C211yesmaximal, characteristic
3#21443697C212yesmaximal, complemented
4#21443686C212yesmaximal, complemented
5C61×#1799C211yesmaximal, characteristic
6C2×D4×Dic61—21no—
7C2×C22⋊#92418C2212yes—
8#16839661—21no—
9#16839637—21no—
10#16839637—21no—
11#16839628C411yescharacteristic, complemented
12#16839622C411yescharacteristic, complemented
13#16839622C2211yescharacteristic
14C4×C4⋊Dic61C411yescharacteristic, complemented
15C2×#14519684C411yescharacteristic, complemented
16C2×#14519684C2211yescharacteristic
17#16839488—21no—
18#16839486—21no—
19C2×C4×D4×C61C2211yescharacteristic
20C2×#99×C61—21no—
21C61×#380C2212yes—
22C61×#342—21no—
23C23×Dic61—21no—
24C23×Dic61—21no—
25C22×#92418—22no—
26D4×Dic61—44no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C22⋊Dic61—21no—
32C2×C22⋊Dic61—21no—
33C2×C4×Dic61—21no—
34C22⋊#92418—22no—
35C22⋊#92418—22no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684C2×C411yescharacteristic
40#14519684C2×C411yescharacteristic
41#14519684C2×C411yescharacteristic
42#14519684C2×C411yescharacteristic
43C22×D4×C61D411yescharacteristic
44C23×C4×C61C2×C411yescharacteristic
45C23×C4×C61C2311yescharacteristic
46C4×D4×C61—22no—
47C4×D4×C61—22no—
48C2×C4⋊C4×C61—22no—
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C22⋊C4×C61—22no—
51C2×C22⋊C4×C61D411yescharacteristic
52C2×C22⋊C4×C61D411yescharacteristic
53C2×C42×C61C2×C411yescharacteristic
54#99×C61—42no—
55#95×C61—22no—
56C24×C61C22⋊C411yescharacteristic
57C24×C61C2×D411yescharacteristic
58C2×D4×C61—22no—
59C2×D4×C61—22no—
60C2×D4×C61SD1612yes—
61C2×D4×C61Q1612yes—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—42no—
65C22×C4×C61—81no—
66C22×C4×C61—81no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61#4112yes—
73C22×C4×C61#4112yes—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—42no—
79C22×Dic61—42no—
80C22×Dic61—42no—
81C22×Dic61—42no—
82C22×Dic61—81no—
83C22×Dic61—81no—
84C4⋊C4×C61—22no—
85C4⋊C4×C61—82no—
86C22⋊C4×C61—22no—
87C22⋊C4×C61—22no—
88C22⋊C4×C61—42no—
89C22⋊C4×C61—42no—
90C42×C61—21no—
91C42×C61—21no—
92C22⋊Dic61—42no—
93C22⋊Dic61—42no—
94C4⋊Dic61—42no—
95C4⋊Dic61—42no—
96C4⋊Dic61—81no—
97C4⋊Dic61—81no—
98C4×Dic61—42no—
99C2×#92418—42no—
100C2×#92418—82no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61#10312yes—
108C23×C61C2×C22⋊C411yescharacteristic
109C23×C61#12312yes—
110C23×C61C2×SD1611yescharacteristic
111C23×C61C2×Q1611yescharacteristic
112C23×C61AGL(1,ℤ/8)12yes—
113D4×C61—24no—
114D4×C61—24no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—42no—
120C2×C4×C61—41no—
121C2×C4×C61—42no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—81no—
126C2×C4×C61—81no—
127C2×C4×C61—82no—
128C2×C4×C61—82no—
129C2×C4×C61—82no—
130C2×C4×C61#10312yes—
131C2×C4×C61#11711yescharacteristic
132C2×C4×C61#11711yescharacteristic
133C2×C4×C61#12312yes—
134C2×Dic61—22no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—84no—
147C2×Dic61—84no—
148#92418—82no—
149#8761—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—22no—
152C22×C61—21no—
153C22×C61—22no—
154C22×C61—22no—
155C22×C61—42no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—42no—
159C22×C61—42no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61#38111yescharacteristic
163C22×C61C2×#10311yescharacteristic
164C22×C61#41811yescharacteristic
165C22×C61#48112yes—
166C22×C61#48412yes—
167C4×C61—22no—
168C4×C61—22no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61—162no—
174Dic61—42no—
175Dic61—81no—
176Dic61—81no—
177Dic61—81no—
178#2349—611no—
179#1799D6111yescharacteristic
180#1459—611no—
181#1294—612no—
182#1289—612no—
183C2×C61—21no—
184C2×C61—22no—
185C2×C61—21no—
186C2×C61—22no—
187C2×C61—42no—
188C2×C61#182411yescharacteristic
189C2×C61#182711yescharacteristic
190C2×C61#182811yescharacteristic
191C2×C4×D4—1221no—
192C2×C4×D4C2×D6111yescharacteristic
193C2×#99—21no—
194C2×C22⋊C8—612no—
195#389—1221no—
196#385—1221no—
197#385—1221no—
198#382—611no—
199#380—611no—
200#380—611no—
201#380C2×D6112yes—
202C4×C4⋊C4—611no—
203C2×#95—611no—
204C2×#95—611no—
205#342—21no—
206#324—1221no—
207#323—1221no—
208C61#876111yescharacteristic, complemented, Sylow
209C22×D4C22⋊D6111yescharacteristic
210C23×C4—1221no—
211C23×C4—1221no—
212C23×C4C4×D6111yescharacteristic
213C23×C4C22×D6111yescharacteristic
214C22×C8—1222no—
215C4×D4—22no—
216C4×D4—22no—
217C4×D4—2444no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4D24411yescharacteristic
224C2×C22⋊C4—22no—
225C2×C22⋊C4—1221no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4D24411yescharacteristic
228C2×C22⋊C4C22⋊D6111yescharacteristic
229C2×C42—1221no—
230C2×C42C4×D6111yescharacteristic
231#99—42no—
232C22⋊C8—1222no—
233C22⋊C8—1222no—
234#95—22no—
235#95—611no—
236#95—611no—
237#95—611no—
238#95—611no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242C24#1175819811yescharacteristic
243C24C2×C22⋊D6111yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4#1175820012yes—
247C2×D4#1175820212yes—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—42no—
251C22×C4—81no—
252C22×C4—81no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—4881no—
258C22×C4—4881no—
259C22×C4—2442no—
260C22×C4—2442no—
261C22×C4—2442no—
262C22×C4—2442no—
263C22×C4#1175819811yescharacteristic
264C22×C4#1175819811yescharacteristic
265C22×C4#1175819811yescharacteristic
266C22×C4C2×C4×D6111yescharacteristic
267C22×C4C2×D24411yescharacteristic
268C22×C4#1175822412yes—
269C22×C4#1175822412yes—
270C2×C8—4882no—
271C2×C8—2442no—
272C4⋊C4—22no—
273C4⋊C4—82no—
274C4⋊C4—4881no—
275C4⋊C4—4881no—
276C4⋊C4—2442no—
277C4⋊C4—2442no—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—2442no—
283C22⋊C4—2442no—
284C42—21no—
285C42—21no—
286C42—2442no—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23#1451970012yes—
294C23C2×#1175819811yescharacteristic
295C23#1451975812yes—
296C23C2×#1175820011yescharacteristic
297C23C2×#1175820211yescharacteristic
298C23#1451980212yes—
299D4—24no—
300D4—24no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—82no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4—1222no—
317C2×C4—4884no—
318C2×C4—4884no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4#1451970012yes—
331C2×C4#1451973311yescharacteristic
332C2×C4#1451973311yescharacteristic
333C2×C4#1451976112yes—
334C8—4882no—
335C22—21no—
336C22—22no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22—42no—
344C22—42no—
345C22—41no—
346C22—41no—
347C22#1683962311yescharacteristic
348C22C2×#1451970011yescharacteristic
349C22#1683976611yescharacteristic
350C22#1684007812yes—
351C22#1684009512yes—
352C4—22no—
353C4—22no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—162no—
359C4—4881no—
360C4—4881no—
361C4—4881no—
362C4—2442no—
363C2—22no—
364C2—21no—
365C2—21no—
366C2—22no—
367C2—42no—
368C2#2144590711yescharacteristic
369C2#2144592011yescharacteristic
370C2#2144592511yescharacteristic
subgroupG/H
centerC22#16839623
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1799C2
socleC22×C61#381
prime radicalC22×D4×C61D4
cosocleC23×C4×C61C23
hypercenter#1799D61
hypocenterC61#8761
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. #21443697C2semidirect
4. #21443686C2semidirect
11. #16839628C4semidirect
12. #16839622C4semidirect
14. C4×C4⋊Dic61C4semidirect
15. C2×#14519684C4semidirect
208. C61#8761semidirect

Maximal subgroups

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

subgroupindex
#214487292
#214441372
#214436972
#214436862
C61×#17992
#876161