Finite Group Databasebeta

← #29591166

Subgroups — #29591166

Order 15616.

372 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 77 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#21451180C211yesmaximal, characteristic
2#21445814C211yesmaximal, characteristic
3#21444141C211yesmaximal, characteristic
4#21443849C211yesmaximal, characteristic
5#21443847C211yesmaximal, characteristic
6#21443845C211yesmaximal, characteristic
7C61×#1354C211yesmaximal, characteristic
8C2×Q8×Dic61C411yescharacteristic
9C2×#14519742C2211yescharacteristic
10#16839812—21no—
11#16839785—21no—
12C2×#14519695—21no—
13#16839702C411yescharacteristic
14#16839701C2211yescharacteristic
15#16839681C411yescharacteristic
16#16839666—21no—
17#16839657—21no—
18#16839649—21no—
19#16839648—21no—
20#16839626C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#395C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C2×#11758194—21no—
29Q8×Dic61—41no—
30Q8×Dic61—41no—
31#14519742—41no—
32#14519742—41no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196C2×C411yescharacteristic
38C2×#11758196D411yescharacteristic
39C2×C4×Dic61—21no—
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43#14519706—41no—
44#14519706—41no—
45#14519706—41no—
46#14519695—42no—
47C22⋊#92418—21no—
48C8×Dic61—41no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684C2×C411yescharacteristic
56C22×Q8×C61C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C2×Q8×C61—42no—
64C2×Q8×C61—41no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×Dic122SD1612yes—
79C2×Dic122Q1612yes—
80M16×C61—41no—
81M16×C61—41no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—42no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89#11758196—41no—
90#11758196—41no—
91#11758196—42no—
92#11758196—42no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—42no—
100#11758194—41no—
101#11758194—41no—
102C2×#92418—41no—
103C2×#92418—41no—
104C23×C61C2×C22⋊C411yescharacteristic
105Q8×C61—42no—
106Q8×C61—42no—
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×C61C2×SD1611yescharacteristic
120C2×C4×C61C2×Q1611yescharacteristic
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—42no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61#9911yescharacteristic
134C2×Dic61#9911yescharacteristic
135C2×Dic61#10312yes—
136C2×Dic61#10312yes—
137Dic122—42no—
138Dic122—42no—
139C8×C61—81no—
140C8×C61—81no—
141#92418—81no—
142#92418—81no—
143#11905—611nomaximal, Sylow
144C22×C61—21no—
145C22×C61—21no—
146C22×C61C2×#9911yescharacteristic
147C22×C61C2×#10311yescharacteristic
148C22×C61#42111yescharacteristic
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—41no—
152C4×C61—42no—
153C4×C61—41no—
154C4×C61—81no—
155Dic61—21no—
156Dic61—21no—
157Dic61—22no—
158Dic61—22no—
159Dic61—41no—
160Dic61—81no—
161Dic61—81no—
162#2581—611no—
163#1801—611no—
164#1461—611no—
165#1354—611no—
166#1354D6111yescharacteristic
167#1353—611no—
168#1353—611no—
169C2×C61—21no—
170C2×C61—21no—
171C2×C61#152011yescharacteristic
172C2×C61#212011yescharacteristic
173C2×C61#213311yescharacteristic
174C2×C4×Q8—611no—
175C2×C4×Q8—611no—
176#431—1221no—
177#423—1221no—
178C2×#101—1221no—
179#400—611no—
180#400—611no—
181#395—611no—
182#395C2×D6111yescharacteristic
183#391—1221no—
184#389—1221no—
185#387—1221no—
186#387—1221no—
187#382—611no—
188#343—611no—
189#343C2×D6111yescharacteristic
190#324—611no—
191#324—1221no—
192#324C2×D6111yescharacteristic
193C61#1190511yescharacteristic, complemented, Sylow
194C22×Q8—611no—
195C22×Q8C4×D6111yescharacteristic
196C2×M16—21no—
197C2×M16—1221no—
198C4×Q8—2441no—
199C4×Q8—2441no—
200C4×Q8—2441no—
201C4×Q8—2441no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4C22×D6111yescharacteristic
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—611no—
213C2×C42—1221no—
214C4⋊C8—2441no—
215C4⋊C8—2441no—
216C4⋊C8—2441no—
217#101—2442no—
218C22⋊C8—21no—
219C22⋊C8—1221no—
220C4×C8—2441no—
221#95—21no—
222#95—611no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95C4×D6111yescharacteristic
230C2×Q8—42no—
231C2×Q8—41no—
232C2×Q8—612no—
233C2×Q8—612no—
234C2×Q8—2441no—
235C2×Q8—2441no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4C2×C4×D6111yescharacteristic
245C22×C4D4×D6111yescharacteristic
246C22×C4D4×D6111yescharacteristic
247M16—41no—
248M16—41no—
249M16—2441no—
250M16—2441no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—2441no—
254C2×C8—2441no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—2441no—
258C4⋊C4—2441no—
259C4⋊C4—2441no—
260C4⋊C4—2442no—
261C4⋊C4—2441no—
262C4⋊C4—2441no—
263C4⋊C4—2442no—
264C42—1221no—
265C42—1221no—
266C42—1221no—
267C42—1221no—
268C42—1221no—
269C42—1221no—
270C42—2442no—
271C23C22⋊C4×D6111yescharacteristic
272Q8—42no—
273Q8—42no—
274Q8—2442no—
275Q8—2442no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—611no—
289C2×C4—611no—
290C2×C4—612no—
291C2×C4—612no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2442no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4SD16×D6111yescharacteristic
305C2×C4Q16×D6111yescharacteristic
306C8—81no—
307C8—81no—
308C8—4881no—
309C8—4881no—
310C22—21no—
311C22—21no—
312C22#99×D6111yescharacteristic
313C22#103×D6111yescharacteristic
314C22#1683977711yescharacteristic
315C4—21no—
316C4—21no—
317C4—41no—
318C4—42no—
319C4—41no—
320C4—81no—
321C4—1222no—
322C4—1222no—
323C4—1221no—
324C4—1221no—
325C4—4881no—
326C4—4881no—
327C4—2441no—
328C2—21no—
329C2—21no—
330C2#2144438911yescharacteristic
331C2#2144745711yescharacteristic
332C2#2144750711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1354C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1354D61
hypocenterC61#11905
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
193. C61#11905semidirect

Maximal subgroups

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

subgroupindex
#214511802
#214458142
#214441412
#214438492
#214438472
#214438452
C61×#13542
#1190561