Finite Group Databasebeta

← #29569194

Subgroups — #29569194

Order 15616.

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

normal subgroups only

This group has 378 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#21453781C211yesmaximal, characteristic
2#21447361C211yesmaximal, characteristic
3#21447290C211yesmaximal, characteristic
4#21447229C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic
6#21443644C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C2×#14519710—21no—
9C2×#14519709—21no—
10C2×#14519702—21no—
11C2×#14519702—21no—
12#16839695—21no—
13#16839694—21no—
14#16839682—21no—
15#16839668C2211yescharacteristic
16#16839668C2211yescharacteristic
17#16839666—21no—
18#16839661—21no—
19#16839648—21no—
20#16839632C2211yescharacteristic
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×Dic122D411yescharacteristic
29C22×#92418—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×C4×Dic61—21no—
40#14519710—42no—
41#14519709—42no—
42#14519702—42no—
43#14519702—42no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×C8×C61—21no—
52C22×C8×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C42×C61C2311yescharacteristic
57#95×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—41no—
68C2×Dic122—21no—
69C2×Dic122—21no—
70C2×Dic122—21no—
71C2×Dic122—41no—
72C2×Dic122—41no—
73C2×Dic122—41no—
74C2×Dic122—41no—
75C2×Dic122Q1612yes—
76C2×C8×C61—22no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61SD1612yes—
87C42×C61—41no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96C4⋊Dic61—81no—
97C4⋊Dic61—81no—
98#11758196—81no—
99#11758196—81no—
100C4×Dic61—81no—
101C2×#92418—22no—
102C2×#92418—41no—
103C2×#92418—41no—
104C23×C61#12011yescharacteristic
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×SD1611yescharacteristic
118C2×C4×C61C2×Q1611yescharacteristic
119C2×C4×C61#13511yescharacteristic
120C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C61#13711yescharacteristic
122C2×C4×C61#13711yescharacteristic
123C2×Dic61—22no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—81no—
136C2×Dic61—81no—
137C2×Dic61—81no—
138Dic122—42no—
139Dic122—42no—
140Dic122—81no—
141Dic122—81no—
142C8×C61—42no—
143C8×C61—81no—
144#92418—42no—
145#7809—611nomaximal, Sylow
146C22×C61#44811yescharacteristic
147C22×C61#44911yescharacteristic
148C22×C61#45111yescharacteristic
149C22×C61#45311yescharacteristic
150C22×C61#45511yescharacteristic
151C22×C61#45611yescharacteristic
152C22×C61#45811yescharacteristic
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—42no—
160C4×C61—81no—
161Dic61—42no—
162Dic61—81no—
163Dic61—81no—
164Dic61—81no—
165Dic61—161no—
166#2806—611no—
167#2096—611no—
168#2083—611no—
169#2072—611no—
170#1272—611no—
171#1272—611no—
172#1271D6111yescharacteristic
173C2×C61#161111yescharacteristic
174C2×C61#161211yescharacteristic
175C2×C61#161411yescharacteristic
176C2×C61#162211yescharacteristic
177C2×C61#164511yescharacteristic
178C2×C61#164811yescharacteristic
179C2×C61#166111yescharacteristic
180C2×#107—1221no—
181C2×#106—1221no—
182C2×#103—1221no—
183C2×#103—1221no—
184#398—1221no—
185#398—1221no—
186#395—1221no—
187#391—611no—
188#391—611no—
189#391—1221no—
190#389—1221no—
191#389C2×D6111yescharacteristic
192#387—1221no—
193#384—611no—
194#340—1221no—
195#340—1221no—
196#336—611no—
197#336C2×D6111yescharacteristic
198#336C2×D6111yescharacteristic
199C61#780911yescharacteristic, complemented, Sylow
200C22×Q8—611no—
201C22×Q8—611no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—1221no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4D24411yescharacteristic
216C2×C4⋊C4D24411yescharacteristic
217C2×C42—1221no—
218C2×C42C22×D6111yescharacteristic
219#107—2442no—
220#106—2442no—
221#103—2442no—
222#103—2442no—
223#95—21no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231C2×Q8—612no—
232C2×Q8—1221no—
233C2×Q8—1221no—
234C2×Q8—1221no—
235C2×Q8—2441no—
236C2×Q8—2441no—
237C2×Q8—2441no—
238C2×Q8—2441no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—2441no—
246C22×C4C2×D24411yescharacteristic
247C22×C4D4×D6111yescharacteristic
248C22×C4D4×D6111yescharacteristic
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—1222no—
256C2×C8—2441no—
257C2×C8—2441no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—4881no—
263C4⋊C4—4881no—
264C4⋊C4—4881no—
265C4⋊C4—4881no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4#1175819012yes—
275C42—41no—
276C42—4881no—
277C23#1451974711yescharacteristic
278Q8—4881no—
279Q8—4881no—
280Q8—2442no—
281Q8—2442no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—1222no—
295C2×C4—4881no—
296C2×C4—4881no—
297C2×C4—4881no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4C2×#1175819011yescharacteristic
310C2×C4Q16×D6111yescharacteristic
311C2×C4#1451979811yescharacteristic
312C2×C4#1451980111yescharacteristic
313C2×C4#1451980611yescharacteristic
314C2×C4#1451981011yescharacteristic
315C8—42no—
316C8—81no—
317C8—2442no—
318C22#1683990311yescharacteristic
319C22#1683990811yescharacteristic
320C22#1683991911yescharacteristic
321C22#1683993111yescharacteristic
322C22#1683994111yescharacteristic
323C22#1683994711yescharacteristic
324C22#1683995311yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—81no—
333C4—9761no—
334C4—4881no—
335C4—4881no—
336C4—4881no—
337C4—2442no—
338C2#2144482911yescharacteristic
339C2#2144483411yescharacteristic
340C2#2144484511yescharacteristic
341C2#2144489311yescharacteristic
342C2#2144504211yescharacteristic
343C2#2144506211yescharacteristic
344C2#2144513811yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61#120
hypercenter#1271D61
hypocenterC61#7809
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
199. C61#7809semidirect

Maximal subgroups

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

subgroupindex
#214537812
#214473612
#214472902
#214472292
#214436442
C61×#12712
#780961