Finite Group Databasebeta

← #29577694

Subgroups — #29577694

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#21450808C211yesmaximal, characteristic
3#21444545C211yesmaximal, characteristic
4#21444162C211yesmaximal, characteristic
5#21443676C211yesmaximal, characteristic
6#21443674C211yesmaximal, characteristic
7C61×#1558C211yesmaximal, characteristic
8C2×#14519775C412yes—
9C2×C4×Dic122C2211yescharacteristic
10#16839891—22no—
11#16839890—22no—
12#16839819C2211yescharacteristic
13#16839819C2211yescharacteristic
14#16839816—21no—
15#16839812—21no—
16#16839693—21no—
17#16839693—21no—
18#16839669C412yes—
19#16839658—21no—
20#16839658—21no—
21C4×C4⋊Dic61C2211yescharacteristic
22#16839511—22no—
23#16839487—21no—
24#16839487—21no—
25C2×C4⋊Q8×C61C2211yescharacteristic
26C61×#432C2211yescharacteristic
27C61×#432C2211yescharacteristic
28C61×#333—22no—
29C22×Dic122C2×C411yescharacteristic
30#14519775—44no—
31C4×Dic122—21no—
32C4×Dic122—21no—
33C4×Dic122—21no—
34C4×Dic122—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—22no—
38C2×#11758196—22no—
39C2×#11758196D411yescharacteristic
40C2×#11758196D411yescharacteristic
41C2×C4×Dic61C2×C412yes—
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C4⋊#92418—21no—
45C4⋊#92418D412yes—
46#14519706—22no—
47#14519706—22no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50#14519688—21no—
51#14519688—21no—
52#14519687—22no—
53C8×Dic61—22no—
54#14519684—21no—
55#14519684—22no—
56#14519684—22no—
57C22×Q8×C61C2×C412yes—
58C4⋊Q8×C61—21no—
59C4⋊Q8×C61—21no—
60C4⋊Q8×C61—21no—
61C4⋊Q8×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C4⋊C8×C61D412yes—
67C22⋊C8×C61—21no—
68C22⋊C8×C61—21no—
69#97×C61—21no—
70#97×C61—21no—
71C2×Q8×C61—22no—
72C2×Q8×C61—22no—
73C2×Q8×C61—42no—
74C2×Q8×C61—42no—
75C22×C4×C61—22no—
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×Dic61—22no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C2×Dic122—21no—
85C2×Dic122—21no—
86C2×Dic122—22no—
87C2×Dic122—41no—
88C2×C8×C61—22no—
89C2×C8×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C42×C61C2×D411yescharacteristic
95C42×C61C2×D411yescharacteristic
96C42×C61#4111yescharacteristic
97C42×C61#4111yescharacteristic
98C4⋊Dic61—24no—
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—44no—
106#11758196—44no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—42no—
112C2×#92418—22no—
113C2×#92418—41no—
114C23×C61C2×C22⋊C411yescharacteristic
115Q8×C61—82no—
116Q8×C61—82no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—22no—
120C2×C4×C61—41no—
121C2×C4×C61—42no—
122C2×C4×C61—42no—
123C2×C4×C61—42no—
124C2×C4×C61C4×D411yescharacteristic
125C2×C4×C61C4×D411yescharacteristic
126C2×C4×C61#12011yescharacteristic
127C2×C4×C61#12111yescharacteristic
128C2×C4×C61#12111yescharacteristic
129C2×C4×C61#12311yescharacteristic
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—24no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61#10012yes—
143Dic122—42no—
144Dic122—42no—
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—82no—
161C4×C61#45612yes—
162Dic61—22no—
163Dic61—44no—
164Dic61—41no—
165Dic61—41no—
166Dic61—41no—
167#2983—611no—
168#2546—611no—
169#1558—611no—
170#1558D6111yescharacteristic
171#1467—611no—
172#1285—611no—
173#1285—611no—
174C2×C61—21no—
175C2×C61—21no—
176C2×C61#188611yescharacteristic
177C2×C61#190011yescharacteristic
178C2×C61#190911yescharacteristic
179C2×C4⋊Q8—612no—
180C2×C4⋊Q8C2×D6111yescharacteristic
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⋊C4—611no—
196#333—22no—
197#333—1222no—
198#324—1221no—
199#324—1221no—
200C61#945211yescharacteristic, complemented, Sylow
201C22×Q8—611no—
202C22×Q8C4×D6112yes—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—2444no—
208C4×Q8—1221no—
209C4×Q8—1221no—
210C4×Q8—1221no—
211C4×Q8—1221no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1222no—
219C2×C4⋊C4—1222no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—612no—
223C2×C42C22×D6111yescharacteristic
224C4⋊C8—21no—
225C4⋊C8—612no—
226C4⋊C8—1222no—
227C4⋊C8—1222no—
228C4⋊C8—1221no—
229C4⋊C8C22⋊D6112yes—
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—1222no—
241#95—1222no—
242#95—1221no—
243C2×Q8—22no—
244C2×Q8—22no—
245C2×Q8—42no—
246C2×Q8—42no—
247C2×Q8—1222no—
248C2×Q8—1221no—
249C2×Q8—1221no—
250C2×Q8—2441no—
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—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—1224no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—2444no—
276C4⋊C4—2444no—
277C42—1221no—
278C42—1221no—
279C42—1221no—
280C42—1221no—
281C42—2442no—
282C42#1175822211yescharacteristic
283C42D4×D6111yescharacteristic
284C42#1175822411yescharacteristic
285C42C2×C22⋊D6111yescharacteristic
286C23C22⋊C4×D6111yescharacteristic
287Q8—82no—
288Q8—82no—
289Q8—2442no—
290Q8—2442no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—612no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1224no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—2442no—
308C2×C4—2442no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4#1451973711yescharacteristic
312C2×C4C4×C22⋊D6111yescharacteristic
313C2×C4#1451974511yescharacteristic
314C2×C4#1451974811yescharacteristic
315C2×C4#1451975011yescharacteristic
316C2×C4#1451975911yescharacteristic
317C8—42no—
318C8—81no—
319C8—4881no—
320C8—2442no—
321C22—21no—
322C22—21no—
323C22#1683963811yescharacteristic
324C22#100×D6111yescharacteristic
325C22#1683974311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—82no—
332C4—1222no—
333C4—2444no—
334C4—2441no—
335C4—2441no—
336C4—2441no—
337C4#1683994312yes—
338C2—21no—
339C2—21no—
340C2#2144620911yescharacteristic
341C2#2144627911yescharacteristic
342C2#2144633811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1558C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1558D61
hypocenterC61#9452
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1558

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
#214508082
#214445452
#214441622
#214436762
#214436742
C61×#15582
#945261