Finite Group Databasebeta

← #29589680

Subgroups — #29589680

Order 15616.

374 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 73 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#21451025C211yesmaximal, characteristic
2#21444161C211yesmaximal, characteristic
3#21444141C211yesmaximal, characteristic
4#21443765C211yesmaximal, characteristic
5#21443764C211yesmaximal, characteristic
6#21443764C211yesmaximal, characteristic
7C61×#1325C211yesmaximal, characteristic
8C2×#14519776C411yescharacteristic
9C2×#14519742C2211yescharacteristic
10#16839816—21no—
11#16839812—21no—
12#16839682—21no—
13#16839682—21no—
14#16839668C411yescharacteristic
15#16839667C411yescharacteristic
16#16839657—21no—
17#16839657—21no—
18#16839631C2211yescharacteristic
19C4×#11758196C411yescharacteristic
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22#16839487—21no—
23#16839487—21no—
24C61×#384C2211yescharacteristic
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122C2×C411yescharacteristic
29#14519776—41no—
30#14519776—41no—
31#14519742—41no—
32#14519742—41no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196D411yescharacteristic
39C2×#11758196D411yescharacteristic
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44#14519706—41no—
45#14519706—41no—
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48#14519687—41no—
49C8×Dic61—41no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2311yescharacteristic
59C2×C42×C61C2×C411yescharacteristic
60C22⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22×C411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C2×Dic122—21no—
74C2×Dic122—21no—
75C2×Dic122—22no—
76C2×Dic122—41no—
77C2×Dic122—42no—
78C2×Dic122—81no—
79C2×Dic122—81no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—81no—
85C4⋊C4×C61—81no—
86C42×C61—21no—
87C42×C61—21no—
88C4⋊Dic61—41no—
89#11758196—24no—
90#11758196—41no—
91#11758196—41no—
92#11758196—41no—
93#11758196—41no—
94#11758196—81no—
95#11758196—81no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C2×#92418—41no—
105C2×#92418—41no—
106C23×C61C2×C22⋊C411yescharacteristic
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—22no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61#13111yescharacteristic
120C2×C4×C61#13111yescharacteristic
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—22no—
124C2×Dic61—22no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61#9911yescharacteristic
136C2×Dic61#9911yescharacteristic
137C2×Dic61#10112yes—
138Dic122—42no—
139Dic122—42no—
140Dic122—84no—
141C8×C61—81no—
142C8×C61—81no—
143#92418—81no—
144#92418—81no—
145#11574—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61#40811yescharacteristic
149C22×C61C2×#9911yescharacteristic
150C22×C61C2×#10111yescharacteristic
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—42no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61—81no—
157Dic61—21no—
158Dic61—22no—
159Dic61—42no—
160Dic61—41no—
161Dic61—41no—
162Dic61—81no—
163Dic61#35612yes—
164#2567—611no—
165#1467—611no—
166#1461—611no—
167#1325—611no—
168#1325—611no—
169#1325—611no—
170#1325D6111yescharacteristic
171C2×C61—21no—
172C2×C61—21no—
173C2×C61#147211yescharacteristic
174C2×C61#212811yescharacteristic
175C2×C61C2×#35611yescharacteristic
176C2×C4⋊Q8—611no—
177C2×C4×Q8—611no—
178#432—1221no—
179#431—1221no—
180#395—1221no—
181#395—1221no—
182#391—611no—
183#391—611no—
184#389—1221no—
185#389—1221no—
186#384—611no—
187#384C2×D6111yescharacteristic
188C4×C4⋊C4—611no—
189#324—611no—
190#324—611no—
191#324—1221no—
192#324—1221no—
193#324C2×D6111yescharacteristic
194#324C2×D6111yescharacteristic
195C61#1157411yescharacteristic, complemented, Sylow
196C22×Q8—611no—
197C22×Q8—1221no—
198C4⋊Q8—2441no—
199C4⋊Q8—2441no—
200C4×Q8—2441no—
201C4×Q8—2441no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4C4×D6111yescharacteristic
212C2×C4⋊C4C22×D6111yescharacteristic
213C2×C42—611no—
214C2×C42—611no—
215C2×C42—611no—
216C2×C42—611no—
217C2×C42C4×D6111yescharacteristic
218C4⋊C8—2441no—
219C4⋊C8—2441no—
220C22⋊C8—21no—
221C22⋊C8—21no—
222C22⋊C8—1221no—
223C22⋊C8—1221no—
224#97—2441no—
225C4×C8—2441no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231C2×Q8—1222no—
232C2×Q8—1221no—
233C2×Q8—1221no—
234C2×Q8—4881no—
235C2×Q8—4881no—
236C2×Q8—2441no—
237C2×Q8—2442no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4C2×C4×D6111yescharacteristic
247C22×C4D4×D6111yescharacteristic
248C22×C4D4×D6111yescharacteristic
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—2441no—
252C2×C8—2441no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C4⋊C4—1224no—
258C4⋊C4—4881no—
259C4⋊C4—4881no—
260C4⋊C4—2441no—
261C4⋊C4—2441no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C42—21no—
266C42—21no—
267C42—1221no—
268C42—1221no—
269C42—1221no—
270C42—1221no—
271C42—1221no—
272C42—1221no—
273C42—1221no—
274C42—1221no—
275C23C22⋊C4×D6111yescharacteristic
276Q8—4884no—
277Q8—2442no—
278Q8—2442no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—611no—
292C2×C4—611no—
293C2×C4—612no—
294C2×C4—1222no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1222no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4#1451978311yescharacteristic
309C2×C4#1451978511yescharacteristic
310C8—81no—
311C8—81no—
312C8—4881no—
313C8—4881no—
314C22—21no—
315C22—21no—
316C22#1683972711yescharacteristic
317C22#99×D6111yescharacteristic
318C22#101×D6111yescharacteristic
319C4—21no—
320C4—21no—
321C4—42no—
322C4—41no—
323C4—41no—
324C4—81no—
325C4—612no—
326C4—1221no—
327C4—1222no—
328C4—4881no—
329C4—2442no—
330C4—2441no—
331C4—2441no—
332C2—21no—
333C2—21no—
334C2#2144418111yescharacteristic
335C2#2144748911yescharacteristic
336C2#356×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1325C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1325D61
hypocenterC61#11574
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
195. C61#11574semidirect

Maximal subgroups

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

subgroupindex
#214510252
#214441612
#214441412
#214437652
#214437642
C61×#13252
#1157461