Finite Group Databasebeta

← #29568305

Subgroups — #29568305

Order 15616.

402 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 105 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#21448290C211yesmaximal, characteristic
2#21445961C211yesmaximal, characteristic
3#21445934C211yesmaximal, characteristic
4#21443644C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic
6#21443642C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C2×#14519742C411yescharacteristic
9C2×#14519706—21no—
10#16839668C2211yescharacteristic
11#16839667C411yescharacteristic
12#16839661C411yescharacteristic
13#16839649—21no—
14#16839643—21no—
15C4⋊C4×Dic61—21no—
16C4⋊C4×Dic61C411yescharacteristic
17#16839607—21no—
18C42×Dic61C2211yescharacteristic
19#16839517C2211yescharacteristic
20#16839517C2211yescharacteristic
21#16839516—21no—
22#16839516—21no—
23#16839516—21no—
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×#92418—21no—
29C22×#92418—21no—
30#14519742—22no—
31#14519742—22no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61C2×C411yescharacteristic
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43#14519706—42no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C22×C8×C61—21no—
51C22×C8×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56#95×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C22×C411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C2×Dic122—21no—
69C2×Dic122—41no—
70C2×Dic122—41no—
71C2×Dic122M1612yes—
72C2×C8×C61—41no—
73C2×C8×C61—41no—
74C2×C8×C61—41no—
75C2×C8×C61—41no—
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61M1612yes—
83C42×C61—41no—
84C4⋊Dic61—42no—
85C4⋊Dic61—41no—
86#11758196—24no—
87C4×Dic61—24no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—41no—
93C4×Dic61—41no—
94C4×Dic61—41no—
95C4×Dic61—42no—
96C4×Dic61SD1612yes—
97C4×Dic61Q1612yes—
98C2×#92418—41no—
99C2×#92418—41no—
100C2×#92418—41no—
101C2×#92418—41no—
102C2×#92418—41no—
103C2×#92418—41no—
104C23×C61C2×C22⋊C411yescharacteristic
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—22no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61C2×M1611yescharacteristic
118C2×C4×C61C2×M1611yescharacteristic
119C2×C4×C61C2×SD1611yescharacteristic
120C2×C4×C61C2×Q1611yescharacteristic
121C2×C4×C61#13511yescharacteristic
122C2×C4×C61#13511yescharacteristic
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
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—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61#10312yes—
140C2×Dic61#10312yes—
141Dic122—42no—
142Dic122—42no—
143C8×C61—81no—
144C8×C61—81no—
145#92418—81no—
146#92418—81no—
147#7644—611nomaximal, Sylow
148C22×C61#40711yescharacteristic
149C22×C61#41011yescharacteristic
150C22×C61#41311yescharacteristic
151C22×C61C2×#10311yescharacteristic
152C22×C61#41611yescharacteristic
153C22×C61#42111yescharacteristic
154C22×C61#42111yescharacteristic
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—42no—
162C4×C61—81no—
163Dic61—22no—
164Dic61—22no—
165Dic61—42no—
166Dic61—41no—
167Dic61—41no—
168Dic61—81no—
169#2295—611no—
170#1839—611no—
171#1831—611no—
172#1272—611no—
173#1272—611no—
174#1271—611no—
175#1271D6111yescharacteristic
176C2×C61#146411yescharacteristic
177C2×C61#148711yescharacteristic
178C2×C61#148811yescharacteristic
179C2×C61#151811yescharacteristic
180C2×C61#152111yescharacteristic
181C2×C61#153511yescharacteristic
182C2×C61#154211yescharacteristic
183C2×C4×Q8—611no—
184C2×C4⋊C8—1221no—
185#391—611no—
186#391—611no—
187#389—611no—
188#389C2×D6111yescharacteristic
189#387—1221no—
190#387—1221no—
191C4×C4⋊C4—611no—
192C4×C4⋊C4—1221no—
193#376—1221no—
194C43—611no—
195#336—611no—
196#336—611no—
197#336—1221no—
198#336—1221no—
199#336—1221no—
200#336C2×D6111yescharacteristic
201#336C2×D6111yescharacteristic
202C61#764411yescharacteristic, complemented, Sylow
203C22×Q8—611no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—1221no—
207C22×C8—1221no—
208C4×Q8—1222no—
209C4×Q8—1222no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4C4×D6111yescharacteristic
215C2×C4⋊C4C4×D6111yescharacteristic
216C2×C42—611no—
217C2×C42—611no—
218C2×C42—611no—
219C2×C42—611no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—1221no—
223C2×C42—1221no—
224C2×C42C22×D6111yescharacteristic
225C4⋊C8—2442no—
226#95—21no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233C2×Q8—612no—
234C2×Q8—1221no—
235C2×Q8—2441no—
236C2×Q8—2441no—
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—41no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—2441no—
255C2×C8—2441no—
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—1224no—
265C4⋊C4—2441no—
266C4⋊C4—2442no—
267C4⋊C4#1175818912yes—
268C42—41no—
269C42—612no—
270C42—612no—
271C42—1224no—
272C42—1221no—
273C42—1221no—
274C42—1221no—
275C42—1221no—
276C42—2441no—
277C42—2441no—
278C42—2441no—
279C42—2442no—
280C23C22⋊C4×D6111yescharacteristic
281Q8—2442no—
282Q8—2442no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—612no—
296C2×C4—612no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
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—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4M16×D6111yescharacteristic
314C2×C4C2×#1175818911yescharacteristic
315C2×C4SD16×D6111yescharacteristic
316C2×C4Q16×D6111yescharacteristic
317C2×C4#1451979611yescharacteristic
318C2×C4#1451979811yescharacteristic
319C8—81no—
320C8—81no—
321C8—4881no—
322C8—4881no—
323C22#1683972411yescharacteristic
324C22#1683973411yescharacteristic
325C22#1683974511yescharacteristic
326C22#103×D6111yescharacteristic
327C22#1683975511yescharacteristic
328C22#1683977711yescharacteristic
329C22#1683977711yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—42no—
337C4—81no—
338C4—1222no—
339C4—1222no—
340C4—4881no—
341C4—2442no—
342C4—2441no—
343C4—2441no—
344C2#2144415211yescharacteristic
345C2#2144424611yescharacteristic
346C2#2144425011yescharacteristic
347C2#2144438111yescharacteristic
348C2#2144439311yescharacteristic
349C2#2144444911yescharacteristic
350C2#2144447511yescharacteristic
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#7644
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
202. C61#7644semidirect

Maximal subgroups

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

subgroupindex
#214482902
#214459612
#214459342
#214436442
#214436422
C61×#12712
#764461