Finite Group Databasebeta

← #29590938

Subgroups — #29590938

Order 15616.

368 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 69 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#21451512C211yesmaximal, characteristic
2#21445901C211yesmaximal, characteristic
3#21444132C211yesmaximal, characteristic
4#21443847C211yesmaximal, characteristic, complemented
5#21443845C211yesmaximal, characteristic, complemented
6#21443825C211yesmaximal, characteristic, complemented
7C61×#1346C211yesmaximal, characteristic, complemented
8C2×#14519768C411yescharacteristic
9C2×#14519735C2211yescharacteristic
10#16839812—21no—
11#16839725—21no—
12#16839701C2211yescharacteristic
13#16839699C411yescharacteristic
14#16839688C411yescharacteristic
15#16839661—21no—
16#16839654—21no—
17#16839645—21no—
18#16839633—21no—
19#16839607C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#398C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×C4×D61D411yescharacteristic
28C2×#11758194—21no—
29#14519768—41no—
30#14519768—41no—
31#14519735—41no—
32#14519735—41no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758196—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198C2×C411yescharacteristic
41C2×#11758198D411yescharacteristic
42C2×C4×Dic61—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45#14519706—41no—
46C22⋊#92418—21no—
47#14519689—41no—
48#14519689—41no—
49C8×Dic61—41no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55C2×M16×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2311yescharacteristic
59C22⋊C8×C61—21no—
60#95×C61—21no—
61#95×C61C2×C411yescharacteristic
62C23×D61C22⋊C411yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—41no—
78M16×C61—41no—
79M16×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86#11758198—41no—
87#11758198—41no—
88#11758198—42no—
89#11758198—42no—
90C4⋊Dic61—41no—
91C4⋊Dic61—42no—
92C4⋊Dic61—42no—
93C4⋊Dic61—41no—
94#11758196—41no—
95#11758196—41no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—42no—
101#11758194—41no—
102#11758194—41no—
103C2×#92418—41no—
104C2×#92418—41no—
105C23×C61C2×C22⋊C411yescharacteristic
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—41no—
110C22×D61—41no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—22no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61#13511yescharacteristic
124C2×C4×C61#13511yescharacteristic
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—41no—
136C2×Dic61—41no—
137C2×Dic61#9911yescharacteristic
138C2×Dic61#9911yescharacteristic
139C4×D61—41no—
140C4×D61—41no—
141C4×D61—41no—
142C4×D61—41no—
143C8×C61—81no—
144C8×C61—81no—
145#92418—81no—
146#92418—81no—
147#11853—611nomaximal, Sylow
148C22×C61—21no—
149C22×C61—21no—
150C22×C61C2×#9911yescharacteristic
151C22×C61#41611yescharacteristic
152C22×C61#42111yescharacteristic
153C2×D61—42no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—81no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—42no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—81no—
164Dic61—21no—
165Dic61—21no—
166Dic61—41no—
167Dic61—41no—
168Dic61—81no—
169Dic61—81no—
170#2611—611no—
171#1822—611no—
172#1458—611no—
173#1353—611no—
174#1353—611no—
175#1346—611no—
176#1346D6111yescharacteristic, complemented
177C2×C61—21no—
178C2×C61—21no—
179C2×C61#151611yescharacteristic
180C2×C61#212311yescharacteristic
181C2×C61#213211yescharacteristic
182D61—81no—
183C2×#125—611no—
184C2×#117—611no—
185#431—1221no—
186#407—1221no—
187#400—611no—
188#399—611no—
189#398C2×D6111yescharacteristic
190#397—611no—
191#389—1221no—
192#388—1221no—
193#387—1221no—
194#385—1221no—
195#376—611no—
196#343—611no—
197#343—1221no—
198#343C2×D6111yescharacteristic
199#324—611no—
200#324C2×D6111yescharacteristic
201#323—1221no—
202C61#1185311yescharacteristic, complemented, Sylow
203C23×C4—611no—
204C2×M16—21no—
205C2×M16—1221no—
206#125—2441no—
207#125—2441no—
208#117—2441no—
209#117—2441no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4C4×D6111yescharacteristic
217C2×C4⋊C4C22×D6111yescharacteristic
218C2×C22⋊C4—611no—
219C2×C22⋊C4—611no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4—1221no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—1221no—
225C4⋊C8—2441no—
226C22⋊C8—21no—
227C22⋊C8—1221no—
228C22⋊C8—2441no—
229C22⋊C8—2441no—
230C4×C8—2441no—
231#95—21no—
232#95—611no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237#95C4×D6111yescharacteristic
238C24—611no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—2441no—
251C22×C4C2×C4×D6111yescharacteristic
252C22×C4D4×D6111yescharacteristic
253C22×C4D4×D6111yescharacteristic
254M16—41no—
255M16—41no—
256M16—2441no—
257M16—2441no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—2441no—
261C2×C8—2441no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C4⋊C4—2442no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2442no—
272C22⋊C4—2441no—
273C22⋊C4—2441no—
274C22⋊C4—2442no—
275C22⋊C4—2442no—
276C42—1221no—
277C42—1221no—
278C42—1221no—
279C42—1221no—
280C42—2442no—
281C23—1221no—
282C23—1221no—
283C23—1221no—
284C23—2441no—
285C23—2441no—
286C23C22⋊C4×D6111yescharacteristic
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—611no—
300C2×C4—611no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4#1451979611yescharacteristic
318C2×C4#1451979811yescharacteristic
319C8—81no—
320C8—81no—
321C8—4881no—
322C8—4881no—
323C22—21no—
324C22—21no—
325C22—4881no—
326C22—2442no—
327C22—2441no—
328C22—2441no—
329C22—2441no—
330C22#99×D6111yescharacteristic
331C22#1683975511yescharacteristic
332C22#1683977711yescharacteristic
333C4—21no—
334C4—21no—
335C4—42no—
336C4—41no—
337C4—41no—
338C4—81no—
339C4—1221no—
340C4—1221no—
341C4—4881no—
342C4—4881no—
343C4—2441no—
344C4—2441no—
345C2—21no—
346C2—21no—
347C2—4881no—
348C2#2144437211yescharacteristic
349C2#2144747111yescharacteristic
350C2#2144750311yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1346C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1346D61
hypocenterC61#11853
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
4. #21443847C2semidirect
5. #21443845C2semidirect
6. #21443825C2semidirect
7. C61×#1346C2semidirect
176. #1346D61semidirect
202. C61#11853semidirect

Maximal subgroups

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

subgroupindex
#214515122
#214459012
#214441322
#214438472
#214438452
#214438252
C61×#13462
#1185361