Finite Group Databasebeta

← #29577844

Subgroups — #29577844

Order 15616.

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

normal subgroups only

This group has 518 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#21450102C211yesmaximal, characteristic
2#21448419C211yesmaximal, characteristic
3#21445918C211yesmaximal, characteristic
4#21444148C211yesmaximal, characteristic
5#21443673C211yesmaximal, characteristic
6#21443672C211yesmaximal, characteristic
7C61×#1826C211yesmaximal, characteristic
8C22×#11758196C2211yescharacteristic
9#16839726C2211yescharacteristic
10#16839700C412yescomplemented
11#16839693C412yescomplemented
12#16839646—22no—
13#16839646—22no—
14#16839644—22no—
15#16839634—21no—
16#16839625C2211yescharacteristic
17#16839623—21no—
18#16839623—21no—
19#16839620—21no—
20C4×C22⋊Dic61C2211yescharacteristic
21#16839521—22no—
22#16839487—22no—
23C2×#117×C61C2211yescharacteristic
24C61×#407C2211yescharacteristic
25C4×C22⋊C4×C61C2211yescharacteristic
26C61×#339—22no—
27C23×Dic61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C2×#11758194—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—22no—
35C2×#11758196—22no—
36C2×#11758196C2×C412yes—
37C2×#11758196D412yes—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C4×Dic61D412yes—
41C22⋊#92418—21no—
42C22⋊#92418—21no—
43#14519684—22no—
44#14519684—24no—
45#14519684—21no—
46#14519684—21no—
47#14519684—22no—
48#14519684—22no—
49#14519684—22no—
50#14519684C2×C412yes—
51C23×C4×C61C2311yescharacteristic
52C2×M16×C61—21no—
53#117×C61—21no—
54#117×C61—21no—
55#117×C61—21no—
56#117×C61—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C42×C61—21no—
62C2×C42×C61D412yes—
63C22⋊C8×C61—21no—
64C22⋊C8×C61—21no—
65#95×C61—21no—
66C24×C61C2×D411yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—22no—
70C22×C4×C61—42no—
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61#4111yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—22no—
82C22×Dic61—22no—
83C22×Dic61—42no—
84C22×Dic61—42no—
85C22×Dic61C22⋊C412yes—
86C22×Dic61C22⋊C412yes—
87M16×C61—42no—
88C2×C8×C61—41no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—21no—
93C22⋊C4×C61—42no—
94C22⋊C4×C61—41no—
95C22⋊C4×C61—41no—
96C42×C61—42no—
97C42×C61—41no—
98C42×C61—41no—
99C22⋊Dic61—42no—
100C22⋊Dic61—42no—
101#11758196—22no—
102#11758196—22no—
103#11758196—22no—
104#11758196—22no—
105#11758196—44no—
106#11758196—82no—
107C4×Dic61—42no—
108#11758194—42no—
109C2×#92418—41no—
110C23×C61—22no—
111C23×C61—22no—
112C23×C61—41no—
113C23×C61C2×C22⋊C411yescharacteristic
114C23×C61#12011yescharacteristic
115C23×C61#12311yescharacteristic
116C2×C4×C61—22no—
117C2×C4×C61—22no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—42no—
123C2×C4×C61—42no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61C4×D411yescharacteristic
130C2×C4×C61C4×D411yescharacteristic
131C2×C4×C61#12111yescharacteristic
132C2×C4×C61#12111yescharacteristic
133C2×Dic61—22no—
134C2×Dic61—22no—
135C2×Dic61—22no—
136C2×Dic61—22no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—42no—
147C2×Dic61—81no—
148C8×C61—81no—
149#92418—81no—
150#9482—611nomaximal, Sylow
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—44no—
159C22×C61#38611yescharacteristic
160C22×C61#42112yes—
161C22×C61#45812yes—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—82no—
167C4×C61—81no—
168C4×C61—81no—
169Dic61—42no—
170Dic61—42no—
171Dic61—82no—
172Dic61—82no—
173#2484—611no—
174#2313—611no—
175#1826—611no—
176#1826D6111yescharacteristic
177#1463—611no—
178#1284—611no—
179#1284—611no—
180C2×C61—22no—
181C2×C61—22no—
182C2×C61—41no—
183C2×C61#189011yescharacteristic
184C2×C61#189711yescharacteristic
185C2×C61#191211yescharacteristic
186C2×#117C2×D6111yescharacteristic
187C22×C4⋊C4—611no—
188#407—611no—
189#407C2×D6111yescharacteristic
190#400—612no—
191#398—612no—
192#387—1222no—
193#387—1222no—
194#387—1222no—
195#385—1221no—
196#381—611no—
197#381—1221no—
198#381—1221no—
199#380—1221no—
200C4×C22⋊C4—611no—
201C4×C22⋊C4C2×D6111yescharacteristic
202#339—22no—
203#339—1222no—
204#324—1222no—
205C61#948211yescharacteristic, complemented, Sylow
206C23×C4—611no—
207C23×C4—611no—
208C23×C4C22×D6111yescharacteristic
209C2×M16—21no—
210C2×M16—1221no—
211#117—21no—
212#117—21no—
213#117—21no—
214#117—21no—
215C2×C4⋊C4—612no—
216C2×C4⋊C4—612no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1222no—
222C2×C4⋊C4—1222no—
223C2×C4⋊C4C4×D6111yescharacteristic
224C2×C4⋊C4C4×D6111yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229C2×C42—21no—
230C2×C42—612no—
231C2×C42C22⋊D6112yes—
232C22⋊C8—21no—
233C22⋊C8—21no—
234C22⋊C8—1221no—
235C22⋊C8—1221no—
236#95—21no—
237#95—612no—
238#95—1222no—
239#95—1222no—
240#95—1222no—
241#95—1222no—
242#95—1224no—
243#95—1221no—
244#95—1221no—
245C24D4×D6111yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—42no—
250C22×C4—612no—
251C22×C4—612no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1222no—
257C22×C4—1222no—
258C22×C4—2442no—
259C22×C4—2442no—
260C22×C4C2×C4×D6111yescharacteristic
261C22×C4#1175822211yescharacteristic
262C22×C4D4×D6111yescharacteristic
263C22×C4D4×D6111yescharacteristic
264C22×C4#1175822411yescharacteristic
265C22×C4C2×C22⋊D6111yescharacteristic
266M16—42no—
267M16—2442no—
268C2×C8—41no—
269C2×C8—2441no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—1222no—
275C4⋊C4—1222no—
276C4⋊C4—1222no—
277C4⋊C4—1222no—
278C4⋊C4—4882no—
279C4⋊C4—2444no—
280C22⋊C4—42no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—2442no—
284C22⋊C4—2442no—
285C42—42no—
286C42—41no—
287C42—41no—
288C42—2442no—
289C23—22no—
290C23—22no—
291C23—41no—
292C23C22⋊C4×D6111yescharacteristic
293C23#1451974511yescharacteristic
294C23#1451975911yescharacteristic
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—1222no—
309C2×C4—1222no—
310C2×C4—1222no—
311C2×C4—1222no—
312C2×C4—4881no—
313C2×C4—2442no—
314C2×C4—2442no—
315C2×C4—2442no—
316C2×C4—2442no—
317C2×C4—2442no—
318C2×C4—2442no—
319C2×C4—2442no—
320C2×C4—2442no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4#1451973711yescharacteristic
324C2×C4C4×C22⋊D6111yescharacteristic
325C2×C4#1451974811yescharacteristic
326C2×C4#1451975011yescharacteristic
327C8—81no—
328C8—4881no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—44no—
337C22#1683963811yescharacteristic
338C22#1683977712yes—
339C22#1683995112yes—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—82no—
345C4—81no—
346C4—81no—
347C4—4882no—
348C4—4882no—
349C4—2442no—
350C4—2442no—
351C2—22no—
352C2—22no—
353C2—41no—
354C2#2144622911yescharacteristic
355C2#2144626411yescharacteristic
356C2#2144635311yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1826C2
socleC22×C61#386
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1826D61
hypocenterC61#9482
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
10. #16839700C4semidirect
11. #16839693C4semidirect
205. C61#9482semidirect

Maximal subgroups

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

subgroupindex
#214501022
#214484192
#214459182
#214441482
#214436732
#214436722
C61×#18262
#948261