Finite Group Databasebeta

← #29577716

Subgroups — #29577716

Order 15616.

432 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 95 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#21454903C211yesmaximal, characteristic
2#21451034C211yesmaximal, characteristic
3#21444537C211yesmaximal, characteristic
4#21444535C211yesmaximal, characteristic
5#21444162C211yesmaximal, characteristic
6#21443675C211yesmaximal, characteristic
7C61×#1285C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10#16839891—22no—
11#16839890—22no—
12#16839819C2211yescharacteristic
13#16839819C2211yescharacteristic
14#16839816—21no—
15#16839812—21no—
16#16839702—21no—
17#16839702—21no—
18#16839668C412yes—
19#16839667—21no—
20#16839667—21no—
21#16839628C412yes—
22#16839509—22no—
23#16839507—22no—
24#16839487—21no—
25#16839487—21no—
26C61×#432C2211yescharacteristic
27C61×#432C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C22×Dic122—21no—
30C22×Dic122C2×C411yescharacteristic
31#14519777—21no—
32#14519777—21no—
33#14519777—21no—
34#14519777—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61C2×C412yes—
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×#11758196D411yescharacteristic
43C2×#11758196D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C4⋊#92418—21no—
47C4⋊#92418D412yes—
48#14519706—22no—
49#14519706—22no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52#14519688—21no—
53#14519688—21no—
54#14519687—22no—
55C8×Dic61—22no—
56#14519684—22no—
57#14519684—22no—
58#14519684—22no—
59#14519684—22no—
60C2×C4⋊C4×C61—21no—
61C2×C42×C61C2×C412yes—
62C2×C42×C61C2311yescharacteristic
63C4⋊C8×C61—21no—
64C4⋊C8×C61D412yes—
65C22⋊C8×C61—21no—
66C22⋊C8×C61—21no—
67#97×C61—21no—
68#97×C61—21no—
69#95×C61—21no—
70C22×C4×C61—22no—
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—22no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C2×Dic122—21no—
80C2×Dic122—21no—
81C2×Dic122—22no—
82C2×Dic122—41no—
83C2×Dic122—44no—
84C2×Dic122—41no—
85C2×Dic122—41no—
86C2×C8×C61—22no—
87C2×C8×C61—41no—
88C4⋊C4×C61—42no—
89C42×C61—42no—
90C42×C61C2×D411yescharacteristic
91C42×C61C2×D411yescharacteristic
92C42×C61#4111yescharacteristic
93C42×C61#4111yescharacteristic
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61—22no—
97C4⋊Dic61—22no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C2×#92418—22no—
109C2×#92418—41no—
110C23×C61C2×C22⋊C411yescharacteristic
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—22no—
114C2×C4×C61—41no—
115C2×C4×C61—42no—
116C2×C4×C61—42no—
117C2×C4×C61—42no—
118C2×C4×C61C4×D411yescharacteristic
119C2×C4×C61C4×D411yescharacteristic
120C2×C4×C61#12011yescharacteristic
121C2×C4×C61#12111yescharacteristic
122C2×C4×C61#12111yescharacteristic
123C2×C4×C61#12311yescharacteristic
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—44no—
134C2×Dic61—42no—
135C2×Dic61#10112yes—
136Dic122—42no—
137Dic122—42no—
138Dic122—82no—
139Dic122—82no—
140C8×C61—42no—
141C8×C61—81no—
142#92418—42no—
143#92418—81no—
144#9456—611nomaximal, Sylow
145C22×C61—21no—
146C22×C61—21no—
147C22×C61#38611yescharacteristic
148C22×C61C2×#10111yescharacteristic
149C22×C61#41311yescharacteristic
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—82no—
156C4×C61#45412yes—
157Dic61—22no—
158Dic61—41no—
159Dic61—41no—
160Dic61—41no—
161Dic61—82no—
162#2983—611no—
163#2568—611no—
164#1556—611no—
165#1556—611no—
166#1467—611no—
167#1285—611no—
168#1285D6111yescharacteristic
169C2×C61—21no—
170C2×C61—21no—
171C2×C61#188811yescharacteristic
172C2×C61#190111yescharacteristic
173C2×C61#190911yescharacteristic
174C2×C4⋊Q8—611no—
175C2×C4×Q8—611no—
176#446—1222no—
177#446—1222no—
178#432—611no—
179#432—611no—
180#432—1221no—
181#432C2×D6111yescharacteristic
182#432C2×D6111yescharacteristic
183#431—1221no—
184#400—1221no—
185#400—1221no—
186#391—612no—
187#391—1221no—
188#391—1221no—
189#382—612no—
190C4×C4⋊C4C2×D6111yescharacteristic
191#332—1222no—
192#332—1222no—
193#324—1221no—
194#324—1221no—
195C61#945611yescharacteristic, complemented, Sylow
196C22×Q8—611no—
197C22×Q8—1221no—
198C4⋊Q8—1221no—
199C4⋊Q8—1221no—
200C4⋊Q8—1221no—
201C4⋊Q8—1221no—
202C4×Q8—1221no—
203C4×Q8—1221no—
204C4×Q8—1221no—
205C4×Q8—1221no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—612no—
211C2×C4⋊C4—1221no—
212C2×C42—611no—
213C2×C42—611no—
214C2×C42C4×D6112yes—
215C2×C42C22×D6111yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—612no—
218C4⋊C8—1222no—
219C4⋊C8—1222no—
220C4⋊C8—1221no—
221C4⋊C8D24412yes—
222C22⋊C8—21no—
223C22⋊C8—21no—
224C22⋊C8—1221no—
225C22⋊C8—1221no—
226#97—21no—
227#97—21no—
228#97—1222no—
229#97—1221no—
230#97—1221no—
231C4×C8—1222no—
232#95—21no—
233#95—1222no—
234#95—1222no—
235#95—1222no—
236#95—1222no—
237C2×Q8—1222no—
238C2×Q8—1221no—
239C2×Q8—1221no—
240C2×Q8—2441no—
241C2×Q8—2444no—
242C2×Q8—2441no—
243C2×Q8—2441no—
244C22×C4—22no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1222no—
250C22×C4C2×C4×D6111yescharacteristic
251C22×C4D4×D6111yescharacteristic
252C22×C4D4×D6111yescharacteristic
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—1222no—
256C2×C8—2441no—
257C4⋊C4—42no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1222no—
265C4⋊C4—1222no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C42—42no—
269C42—1221no—
270C42—1221no—
271C42—1221no—
272C42—1221no—
273C42C2×D24411yescharacteristic
274C42#1175822211yescharacteristic
275C42D4×D6111yescharacteristic
276C42#1175822611yescharacteristic
277C23C22⋊C4×D6111yescharacteristic
278Q8—4882no—
279Q8—4882no—
280Q8—2442no—
281Q8—2442no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—612no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—2444no—
298C2×C4—2442no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4#1451973911yescharacteristic
302C2×C4C4×D24411yescharacteristic
303C2×C4#1451974711yescharacteristic
304C2×C4#1451975011yescharacteristic
305C2×C4#1451975211yescharacteristic
306C2×C4#1451976211yescharacteristic
307C8—42no—
308C8—81no—
309C8—4881no—
310C8—2442no—
311C22—21no—
312C22—21no—
313C22#1683964011yescharacteristic
314C22#101×D6111yescharacteristic
315C22#1683974311yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—82no—
322C4—1222no—
323C4—4882no—
324C4—2441no—
325C4—2441no—
326C4—2441no—
327C4#1683993612yes—
328C2—21no—
329C2—21no—
330C2#2144622111yescharacteristic
331C2#2144628611yescharacteristic
332C2#2144634011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1285C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1285D61
hypocenterC61#9456
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
195. C61#9456semidirect

Maximal subgroups

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

subgroupindex
#214549032
#214510342
#214445372
#214445352
#214441622
#214436752
C61×#12852
#945661