Finite Group Databasebeta

← #29568275

Subgroups — #29568275

Order 15616.

436 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 107 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#21448378C211yesmaximal, characteristic
2#21445671C211yesmaximal, characteristic
3#21445671C211yesmaximal, characteristic
4#21443643C211yesmaximal, characteristic
5#21443642C211yesmaximal, characteristic
6#21443641C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C2×#14519768C411yescharacteristic
9C2×#14519706—21no—
10C2×#14519706—21no—
11C2×#14519687—21no—
12C2×#14519687—21no—
13#16839660C2211yescharacteristic
14#16839647—21no—
15#16839643—21no—
16#16839627C411yescharacteristic
17C4⋊C4×Dic61—21no—
18C4⋊C4×Dic61C411yescharacteristic
19C4⋊C4×Dic61C411yescharacteristic
20#16839613—21no—
21C42×Dic61C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×#92418—21no—
28C22×#92418—21no—
29#14519768—22no—
30#14519768—22no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44#14519706—24no—
45#14519706—24no—
46#14519687—42no—
47#14519687—42no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C22×C8×C61—21no—
54C22×C8×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C42×C61C2311yescharacteristic
59#95×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61C22×C411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C2×C8×C61—22no—
72C2×C8×C61—22no—
73C2×C8×C61—41no—
74C2×C8×C61—41no—
75C2×C8×C61—41no—
76C2×C8×C61—41no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61M1612yes—
82C42×C61—41no—
83C4⋊Dic61—24no—
84C4⋊Dic61—21no—
85C4⋊Dic61—41no—
86C4⋊Dic61M1612yes—
87#11758196—24no—
88#11758196—41no—
89#11758196—41no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—22no—
97C4×Dic61—22no—
98C4×Dic61—22no—
99C4×Dic61—42no—
100C4×Dic61—42no—
101C2×#92418—22no—
102C2×#92418—22no—
103C2×#92418—41no—
104C2×#92418—41no—
105C2×#92418—41no—
106C2×#92418—41no—
107C23×C61C2×C22⋊C411yescharacteristic
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—22no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61C2×M1611yescharacteristic
121C2×C4×C61C2×M1611yescharacteristic
122C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C61#13711yescharacteristic
125C2×C4×C61#13711yescharacteristic
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—22no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61#10112yes—
142C2×Dic61#10412yes—
143C2×Dic61#10412yes—
144C8×C61—42no—
145C8×C61—42no—
146#92418—42no—
147#92418—42no—
148#7636—611nomaximal, Sylow
149C22×C61#40711yescharacteristic
150C22×C61#41011yescharacteristic
151C22×C61C2×#10111yescharacteristic
152C22×C61#41711yescharacteristic
153C22×C61#41711yescharacteristic
154C22×C61C2×#10411yescharacteristic
155C22×C61C2×#10411yescharacteristic
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—42no—
163C4×C61—81no—
164Dic61—41no—
165Dic61—41no—
166Dic61—41no—
167Dic61—42no—
168Dic61—81no—
169Dic61#33014yes—
170C4×#125—611no—
171#1767—611no—
172#1767—611no—
173#1271—611no—
174#1271—611no—
175#1271—611no—
176#1271D6111yescharacteristic
177C2×C61#146711yescharacteristic
178C2×C61#148911yescharacteristic
179C2×C61#148911yescharacteristic
180C2×C61#150911yescharacteristic
181C2×C61#150911yescharacteristic
182C2×C61C2×#33011yescharacteristic
183C2×C61#156111yescharacteristic
184C2×#125—611no—
185C2×C4⋊C8—1221no—
186C2×C4⋊C8—1221no—
187C2×#97—1221no—
188C2×#97—1221no—
189#389—611no—
190#389C2×D6111yescharacteristic
191#387—1221no—
192#387—1221no—
193#382—611no—
194C4×C4⋊C4—611no—
195C4×C4⋊C4—611no—
196C4×C4⋊C4—1221no—
197C4×C4⋊C4—1221no—
198C43—611no—
199#336—611no—
200#336—611no—
201#336C2×D6111yescharacteristic
202#336C2×D6111yescharacteristic
203C61#763611yescharacteristic, complemented, Sylow
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—1221no—
207C22×C8—1221no—
208#125—1222no—
209#125—1222no—
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⋊C4C4×D6111yescharacteristic
218C2×C42—611no—
219C2×C42—611no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—1221no—
225C2×C42—1221no—
226C2×C42C22×D6111yescharacteristic
227C4⋊C8—1224no—
228C4⋊C8—1224no—
229#97—2442no—
230#97—2442no—
231#95—21no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4C2×C4×D6111yescharacteristic
246C22×C4D4×D6111yescharacteristic
247C22×C4D4×D6111yescharacteristic
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—1222no—
255C2×C8—1222no—
256C2×C8—2441no—
257C2×C8—2441no—
258C2×C8—2441no—
259C2×C8—2441no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—612no—
265C4⋊C4—1224no—
266C4⋊C4—1224no—
267C4⋊C4—1221no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4#1175818912yes—
272C42—41no—
273C42—1222no—
274C42—1222no—
275C42—1222no—
276C42—1221no—
277C42—1221no—
278C42—1221no—
279C42—1221no—
280C42—1221no—
281C42—1221no—
282C42—2442no—
283C42—2442no—
284C23C22⋊C4×D6111yescharacteristic
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—612no—
298C2×C4—612no—
299C2×C4—612no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1222no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4M16×D6111yescharacteristic
316C2×C4C2×#1175818911yescharacteristic
317C2×C4#1451980111yescharacteristic
318C2×C4#1451980411yescharacteristic
319C2×C4#1451980611yescharacteristic
320C2×C4#1451980911yescharacteristic
321C8—42no—
322C8—42no—
323C8—2442no—
324C8—2442no—
325C22#1683972411yescharacteristic
326C22#1683973411yescharacteristic
327C22#101×D6111yescharacteristic
328C22#1683976011yescharacteristic
329C22#1683976211yescharacteristic
330C22#104×D6111yescharacteristic
331C22#104×D6111yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—42no—
339C4—81no—
340C4—614no—
341C4—4881no—
342C4—2441no—
343C4—2441no—
344C4—2442no—
345C4—2441no—
346C2#2144416111yescharacteristic
347C2#2144425511yescharacteristic
348C2#2144425711yescharacteristic
349C2#2144434111yescharacteristic
350C2#2144434311yescharacteristic
351C2#330×D6111yescharacteristic
352C2#2144455511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1271D61
hypocenterC61#7636
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
203. C61#7636semidirect

Maximal subgroups

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

subgroupindex
#214483782
#214456712
#214436432
#214436422
#214436412
C61×#12712
#763661