Finite Group Databasebeta

← #29577696

Subgroups — #29577696

Order 15616.

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

normal subgroups only

This group has 468 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#21450807C211yesmaximal, characteristic
3#21444544C211yesmaximal, characteristic
4#21444544C211yesmaximal, characteristic
5#21444162C211yesmaximal, characteristic
6#21443675C211yesmaximal, characteristic
7C61×#1285C211yesmaximal, characteristic
8C2×#14519777C412yes—
9C2×#14519777C2211yescharacteristic
10C2×C4×Dic122C2211yescharacteristic
11#16839891—22no—
12#16839890—22no—
13#16839819C2211yescharacteristic
14#16839819C2211yescharacteristic
15#16839816—21no—
16#16839812—21no—
17#16839694—21no—
18#16839694—21no—
19#16839668C412yes—
20#16839661—21no—
21#16839661—21no—
22#16839510—22no—
23#16839510—22no—
24#16839487—21no—
25#16839487—21no—
26C61×#432C2211yescharacteristic
27C61×#432C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C22×Dic122C2×C411yescharacteristic
30C22×Dic122C2×C412yes—
31#14519777—21no—
32#14519777—21no—
33#14519777—21no—
34#14519777—21no—
35#14519777—44no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—22no—
43C2×C4⋊Dic61—22no—
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×#11758196D411yescharacteristic
46C2×#11758196D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C4⋊#92418—21no—
50C4⋊#92418D412yes—
51#14519706—22no—
52#14519706—22no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55#14519688—21no—
56#14519688—21no—
57#14519687—22no—
58C8×Dic61—22no—
59#14519684—22no—
60#14519684—22no—
61C2×C4⋊C4×C61—21no—
62C2×C42×C61C2×C412yes—
63C2×C42×C61C2311yescharacteristic
64C4⋊C8×C61—21no—
65C4⋊C8×C61D412yes—
66C22⋊C8×C61—21no—
67C22⋊C8×C61—21no—
68#97×C61—21no—
69#97×C61—21no—
70#95×C61—21no—
71C22×C4×C61—22no—
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—22no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C2×Dic122—21no—
81C2×Dic122—21no—
82C2×Dic122—22no—
83C2×Dic122—22no—
84C2×Dic122—22no—
85C2×Dic122—41no—
86C2×Dic122—42no—
87C2×Dic122—42no—
88C2×C8×C61—22no—
89C2×C8×C61—41no—
90C4⋊C4×C61—24no—
91C42×C61—42no—
92C42×C61C2×D411yescharacteristic
93C42×C61C2×D411yescharacteristic
94C42×C61#4111yescharacteristic
95C42×C61#4111yescharacteristic
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61—44no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103C4⋊Dic61—44no—
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C2×#92418—22no—
113C2×#92418—41no—
114C23×C61C2×C22⋊C411yescharacteristic
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—22no—
118C2×C4×C61—24no—
119C2×C4×C61—41no—
120C2×C4×C61—42no—
121C2×C4×C61—42no—
122C2×C4×C61C4×D411yescharacteristic
123C2×C4×C61C4×D411yescharacteristic
124C2×C4×C61#12011yescharacteristic
125C2×C4×C61#12111yescharacteristic
126C2×C4×C61#12111yescharacteristic
127C2×C4×C61#12311yescharacteristic
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61#10012yes—
141Dic122—42no—
142Dic122—42no—
143Dic122—82no—
144Dic122—82no—
145C8×C61—42no—
146C8×C61—81no—
147#92418—42no—
148#92418—81no—
149#9452—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61#38611yescharacteristic
153C22×C61C2×#10011yescharacteristic
154C22×C61#41311yescharacteristic
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—44no—
161C4×C61#45612yes—
162Dic61—22no—
163Dic61—41no—
164Dic61—41no—
165Dic61—41no—
166Dic61—82no—
167#2983—611no—
168#2546—611no—
169#1558—611no—
170#1558—611no—
171#1467—611no—
172#1285—611no—
173#1285D6111yescharacteristic
174C2×C61—21no—
175C2×C61—21no—
176C2×C61#188611yescharacteristic
177C2×C61#190011yescharacteristic
178C2×C61#190911yescharacteristic
179C2×C4⋊Q8—612no—
180C2×C4⋊Q8—611no—
181C2×C4×Q8—611no—
182#446—1222no—
183#446—1222no—
184#432—611no—
185#432—611no—
186#432—1221no—
187#432C2×D6111yescharacteristic
188#432C2×D6111yescharacteristic
189#431—1221no—
190#398—1221no—
191#398—1221no—
192#391—612no—
193#389—1221no—
194#389—1221no—
195C4×C4⋊C4C2×D6111yescharacteristic
196#333—1222no—
197#333—1222no—
198#324—1221no—
199#324—1221no—
200C61#945211yescharacteristic, complemented, Sylow
201C22×Q8—611no—
202C22×Q8—612no—
203C4⋊Q8—1221no—
204C4⋊Q8—1221no—
205C4⋊Q8—1221no—
206C4⋊Q8—1221no—
207C4⋊Q8—2444no—
208C4×Q8—1221no—
209C4×Q8—1221no—
210C4×Q8—1221no—
211C4×Q8—1221no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—1222no—
217C2×C4⋊C4—1222no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42C4×D6112yes—
223C2×C42C22×D6111yescharacteristic
224C4⋊C8—21no—
225C4⋊C8—612no—
226C4⋊C8—1222no—
227C4⋊C8—1222no—
228C4⋊C8—1221no—
229C4⋊C8D24412yes—
230C22⋊C8—21no—
231C22⋊C8—21no—
232C22⋊C8—1221no—
233C22⋊C8—1221no—
234#97—21no—
235#97—21no—
236#97—1222no—
237#97—1221no—
238#97—1221no—
239C4×C8—1222no—
240#95—21no—
241#95—1222no—
242#95—1222no—
243C2×Q8—1222no—
244C2×Q8—1221no—
245C2×Q8—1221no—
246C2×Q8—1222no—
247C2×Q8—1222no—
248C2×Q8—2441no—
249C2×Q8—2442no—
250C2×Q8—2442no—
251C22×C4—22no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—1222no—
257C22×C4C2×C4×D6111yescharacteristic
258C22×C4D4×D6111yescharacteristic
259C22×C4D4×D6111yescharacteristic
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—1222no—
263C2×C8—2441no—
264C4⋊C4—24no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—2444no—
272C4⋊C4—2444no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C42—42no—
278C42—1221no—
279C42—1221no—
280C42—1221no—
281C42—1221no—
282C42C2×D24411yescharacteristic
283C42#1175822211yescharacteristic
284C42D4×D6111yescharacteristic
285C42#1175822611yescharacteristic
286C23C22⋊C4×D6111yescharacteristic
287Q8—4882no—
288Q8—4882no—
289Q8—2442no—
290Q8—2442no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—612no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—2442no—
307C2×C4—2442no—
308C2×C4—2442no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4#1451973911yescharacteristic
312C2×C4C4×D24411yescharacteristic
313C2×C4#1451974711yescharacteristic
314C2×C4#1451975011yescharacteristic
315C2×C4#1451975211yescharacteristic
316C2×C4#1451976211yescharacteristic
317C8—42no—
318C8—81no—
319C8—4881no—
320C8—2442no—
321C22—21no—
322C22—21no—
323C22#1683964011yescharacteristic
324C22#100×D6111yescharacteristic
325C22#1683974511yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—44no—
332C4—1222no—
333C4—4882no—
334C4—2441no—
335C4—2441no—
336C4—2441no—
337C4#1683994612yes—
338C2—21no—
339C2—21no—
340C2#2144621111yescharacteristic
341C2#2144628111yescharacteristic
342C2#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#9452
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
200. C61#9452semidirect

Maximal subgroups

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

subgroupindex
#214549032
#214508072
#214445442
#214441622
#214436752
C61×#12852
#945261