Finite Group Databasebeta

← #29568898

Subgroups — #29568898

Order 15616.

436 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 87 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#21452850C211yesmaximal, characteristic
2#21447153C211yesmaximal, characteristic
3#21447065C211yesmaximal, characteristic
4#21446961C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic
6#21443643C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9C2×#14519776—21no—
10C2×#14519709—21no—
11C2×#14519702—21no—
12C2×#14519700—21no—
13C2×#14519700—21no—
14#16839695—21no—
15#16839683—21no—
16#16839682—21no—
17#16839668C2211yescharacteristic
18#16839660C2211yescharacteristic
19#16839648—21no—
20#16839645—21no—
21#16839525—21no—
22#16839525—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122—21no—
29C22×Dic122D411yescharacteristic
30C22×#92418—21no—
31#14519777—42no—
32#14519776—42no—
33#14519776—42no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×C4×Dic61—21no—
44#14519709—42no—
45#14519702—42no—
46#14519700—42no—
47#14519700—42no—
48#14519684—21no—
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—21no—
73C2×Dic122—41no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122—42no—
80C2×Dic122—41no—
81C2×Dic122—81no—
82C2×Dic122—81no—
83C2×Dic122SD1612yes—
84C2×C8×C61—22no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61SD1612yes—
95C42×C61—41no—
96C4⋊Dic61—21no—
97C4⋊Dic61—22no—
98C4⋊Dic61—22no—
99C4⋊Dic61—42no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104C4⋊Dic61Q1612yes—
105#11758196—42no—
106#11758196—41no—
107#11758196—41no—
108#11758196—81no—
109C4×Dic61—42no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C23×C61#12011yescharacteristic
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—22no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61C2×SD1611yescharacteristic
127C2×C4×C61C2×SD1611yescharacteristic
128C2×C4×C61C2×Q1611yescharacteristic
129C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C61#13711yescharacteristic
131C2×C4×C61#13711yescharacteristic
132C2×Dic61—22no—
133C2×Dic61—22no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—42no—
144C2×Dic61—41no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147Dic122—42no—
148Dic122—42no—
149Dic122—42no—
150Dic122—81no—
151Dic122—84no—
152Dic122—81no—
153Dic122—81no—
154C8×C61—42no—
155C8×C61—81no—
156#92418—81no—
157#7766—611nomaximal, Sylow
158C22×C61#44811yescharacteristic
159C22×C61#45011yescharacteristic
160C22×C61#45111yescharacteristic
161C22×C61#45411yescharacteristic
162C22×C61#45511yescharacteristic
163C22×C61#45611yescharacteristic
164C22×C61B(4,𝔽2)11yescharacteristic
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—42no—
172C4×C61—81no—
173Dic61—42no—
174Dic61—42no—
175Dic61—82no—
176Dic61—81no—
177Dic61—81no—
178#2734—611no—
179#2058—611no—
180#2043—611no—
181#2024—611no—
182#1272—611no—
183#1271—611no—
184#1271D6111yescharacteristic
185C2×C61#159911yescharacteristic
186C2×C61#160111yescharacteristic
187C2×C61#160511yescharacteristic
188C2×C61#163711yescharacteristic
189C2×C61#164511yescharacteristic
190C2×C61#165111yescharacteristic
191C2×C61#166411yescharacteristic
192C2×C4⋊Q8—611no—
193C2×C4⋊Q8—1221no—
194C2×#106—1221no—
195C2×#103—1221no—
196C2×#103—1221no—
197C2×#103—1221no—
198#398—1221no—
199#395—1221no—
200#395—1221no—
201#391—611no—
202#389—611no—
203#389C2×D6111yescharacteristic
204#387—1221no—
205#387—1221no—
206#340—1221no—
207#340—1221no—
208#336—611no—
209#336C2×D6111yescharacteristic
210#336C2×D6111yescharacteristic
211C61#776611yescharacteristic, complemented, Sylow
212C22×Q8—611no—
213C22×Q8—1221no—
214C22×Q8—1221no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—1221no—
218C4⋊Q8—2442no—
219C4⋊Q8—2442no—
220C4⋊Q8—2442no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4D24411yescharacteristic
232C2×C4⋊C4D24411yescharacteristic
233C2×C42—1221no—
234C2×C42C22×D6111yescharacteristic
235#106—2442no—
236#103—2442no—
237#103—2442no—
238#103—2442no—
239#95—21no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246C2×Q8—612no—
247C2×Q8—1222no—
248C2×Q8—1221no—
249C2×Q8—4881no—
250C2×Q8—4881no—
251C2×Q8—2441no—
252C2×Q8—2441no—
253C2×Q8—2441no—
254C2×Q8—2441no—
255C2×Q8—2441no—
256C2×Q8—2442no—
257C2×Q8—2441no—
258C2×Q8—2441no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—2441no—
266C22×C4C2×D24411yescharacteristic
267C22×C4D4×D6111yescharacteristic
268C22×C4D4×D6111yescharacteristic
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—2441no—
276C2×C8—2441no—
277C2×C8—2441no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—612no—
283C4⋊C4—1222no—
284C4⋊C4—1222no—
285C4⋊C4—1221no—
286C4⋊C4—4881no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4—2441no—
290C4⋊C4—2441no—
291C4⋊C4—2442no—
292C4⋊C4—2442no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C4⋊C4#1175819012yes—
296C42—41no—
297C42—2442no—
298C23#1451974711yescharacteristic
299Q8—4881no—
300Q8—4881no—
301Q8—4881no—
302Q8—4884no—
303Q8—2442no—
304Q8—2442no—
305Q8—2442no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—1222no—
319C2×C4—1222no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2442no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4SD16×D6111yescharacteristic
334C2×C4C2×#1175819011yescharacteristic
335C2×C4Q16×D6111yescharacteristic
336C2×C4#1451980111yescharacteristic
337C2×C4#1451980611yescharacteristic
338C2×C4#1451981011yescharacteristic
339C8—42no—
340C8—81no—
341C8—4881no—
342C22#1683990311yescharacteristic
343C22#1683991411yescharacteristic
344C22#1683991911yescharacteristic
345C22#1683993711yescharacteristic
346C22#1683994111yescharacteristic
347C22#1683994611yescharacteristic
348C22#1683995011yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—42no—
356C4—81no—
357C4—4881no—
358C4—4882no—
359C4—4881no—
360C4—2442no—
361C4—2442no—
362C2#2144476111yescharacteristic
363C2#2144477211yescharacteristic
364C2#2144479411yescharacteristic
365C2#2144498511yescharacteristic
366C2#2144504211yescharacteristic
367C2#2144508411yescharacteristic
368C2#2144515411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61#120
hypercenter#1271D61
hypocenterC61#7766
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
211. C61#7766semidirect

Maximal subgroups

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

subgroupindex
#214528502
#214471532
#214470652
#214469612
#214436442
#214436432
C61×#12712
#776661