Finite Group Databasebeta

← #29568913

Subgroups — #29568913

Order 15616.

416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 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#21452771C211yesmaximal, characteristic
2#21447153C211yesmaximal, characteristic
3#21447152C211yesmaximal, characteristic
4#21447066C211yesmaximal, characteristic
5#21443641C211yesmaximal, characteristic
6#21443641C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9C2×#14519767—21no—
10C2×#14519709—21no—
11C2×#14519708—21no—
12C2×#14519702—21no—
13C2×#14519702—21no—
14#16839694—21no—
15#16839692—21no—
16#16839692—21no—
17#16839661—21no—
18#16839660C2211yescharacteristic
19#16839660C2211yescharacteristic
20#16839647—21no—
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×#92418—21no—
29#14519777—42no—
30#14519767—42no—
31#14519767—42no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×C4×Dic61—21no—
45#14519709—42no—
46#14519708—42no—
47#14519702—42no—
48#14519702—42no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54C22×C8×C61—21no—
55C22×C8×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60#95×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—41no—
71C2×Dic122—22no—
72C2×Dic122—41no—
73C2×Dic122—41no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76C2×Dic122—41no—
77C2×C8×C61—22no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C2×C8×C61—41no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61SD1612yes—
88C42×C61—41no—
89C4⋊Dic61—21no—
90C4⋊Dic61—22no—
91C4⋊Dic61—22no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—42no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61—81no—
100C4⋊Dic61SD1612yes—
101#11758196—42no—
102#11758196—42no—
103#11758196—41no—
104#11758196—41no—
105#11758196—41no—
106#11758196—41no—
107C4×Dic61—42no—
108C2×#92418—22no—
109C2×#92418—41no—
110C2×#92418—41no—
111C23×C61#12011yescharacteristic
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—22no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61C2×SD1611yescharacteristic
125C2×C4×C61C2×SD1611yescharacteristic
126C2×C4×C61#13511yescharacteristic
127C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C61#13711yescharacteristic
129C2×C4×C61#13711yescharacteristic
130C2×Dic61—22no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—42no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145Dic122—42no—
146Dic122—42no—
147Dic122—81no—
148Dic122—81no—
149C8×C61—42no—
150C8×C61—81no—
151#92418—42no—
152#7768—611nomaximal, Sylow
153C22×C61#44811yescharacteristic
154C22×C61#45011yescharacteristic
155C22×C61#45211yescharacteristic
156C22×C61#45411yescharacteristic
157C22×C61#45611yescharacteristic
158C22×C61#45611yescharacteristic
159C22×C61B(4,𝔽2)11yescharacteristic
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—42no—
167C4×C61—81no—
168Dic61—42no—
169Dic61—82no—
170Dic61—81no—
171Dic61—81no—
172Dic61—81no—
173#2726—611no—
174#2058—611no—
175#2058—611no—
176#2043—611no—
177#1271—611no—
178#1271—611no—
179#1271D6111yescharacteristic
180C2×C61#159911yescharacteristic
181C2×C61#160311yescharacteristic
182C2×C61#160411yescharacteristic
183C2×C61#163511yescharacteristic
184C2×C61#165111yescharacteristic
185C2×C61#165311yescharacteristic
186C2×C61#166311yescharacteristic
187C2×C4⋊Q8—611no—
188C2×#125—1221no—
189C2×#106—1221no—
190C2×#106—1221no—
191C2×#103—1221no—
192C2×#103—1221no—
193#398—1221no—
194#398—1221no—
195#398—1221no—
196#389—611no—
197#389—611no—
198#389—1221no—
199#389C2×D6111yescharacteristic
200#387—1221no—
201#340—1221no—
202#340—1221no—
203#336—611no—
204#336C2×D6111yescharacteristic
205#336C2×D6111yescharacteristic
206C61#776811yescharacteristic, complemented, Sylow
207C22×Q8—1221no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—1221no—
211C4⋊Q8—2442no—
212#125—2442no—
213#125—2442no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4D24411yescharacteristic
228C2×C4⋊C4D24411yescharacteristic
229C2×C42—1221no—
230C2×C42C22×D6111yescharacteristic
231#106—2442no—
232#106—2442no—
233#103—2442no—
234#103—2442no—
235#95—21no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241C2×Q8—1222no—
242C2×Q8—2441no—
243C2×Q8—2441no—
244C2×Q8—2441no—
245C2×Q8—2441no—
246C2×Q8—2441no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—2441no—
254C22×C4C2×D24411yescharacteristic
255C22×C4D4×D6111yescharacteristic
256C22×C4D4×D6111yescharacteristic
257C2×C8—22no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—1222no—
264C2×C8—2441no—
265C2×C8—2441no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—612no—
271C4⋊C4—1222no—
272C4⋊C4—1222no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—4881no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2442no—
280C4⋊C4—2442no—
281C4⋊C4—2442no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C4⋊C4#1175819012yes—
289C42—41no—
290C42—2442no—
291C23#1451974711yescharacteristic
292Q8—4881no—
293Q8—4881no—
294Q8—2442no—
295Q8—2442no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—1222no—
309C2×C4—4881no—
310C2×C4—4881no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2442no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4SD16×D6111yescharacteristic
324C2×C4C2×#1175819011yescharacteristic
325C2×C4#1451979611yescharacteristic
326C2×C4#1451980511yescharacteristic
327C2×C4#1451980611yescharacteristic
328C2×C4#1451980911yescharacteristic
329C8—42no—
330C8—81no—
331C8—2442no—
332C22#1683990211yescharacteristic
333C22#1683991511yescharacteristic
334C22#1683992511yescharacteristic
335C22#1683993611yescharacteristic
336C22#1683994611yescharacteristic
337C22#1683994711yescharacteristic
338C22#1683995011yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—42no—
346C4—81no—
347C4—4881no—
348C4—4882no—
349C4—4881no—
350C4—4881no—
351C4—2442no—
352C2#2144476011yescharacteristic
353C2#2144478311yescharacteristic
354C2#2144479011yescharacteristic
355C2#2144497211yescharacteristic
356C2#2144508511yescharacteristic
357C2#2144509711yescharacteristic
358C2#2144514911yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61#120
hypercenter#1271D61
hypocenterC61#7768
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
206. C61#7768semidirect

Maximal subgroups

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

subgroupindex
#214527712
#214471532
#214471522
#214470662
#214436412
C61×#12712
#776861