Finite Group Databasebeta

← #29577646

Subgroups — #29577646

Order 15616.

456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 89 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#21456220C211yesmaximal, characteristic
2#21448924C211yesmaximal, characteristic, complemented
3#21444445C211yesmaximal, characteristic, complemented
4#21444328C211yesmaximal, characteristic
5#21444326C211yesmaximal, characteristic
6#21443713C211yesmaximal, characteristic, complemented
7C61×#1300C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9C2×#14519769C2211yescharacteristic
10#16840131C412yescomplemented
11#16840127C412yescomplemented
12#16840117—22no—
13#16839819C2211yescharacteristic
14#16839764—21no—
15#16839764—21no—
16#16839647—21no—
17#16839646—21no—
18#16839645—21no—
19#16839644—21no—
20C4×#11758196—21no—
21#16839613—21no—
22#16839608C2211yescharacteristic
23#16839503—22no—
24#16839497—21no—
25#16839497—21no—
26#16839495—21no—
27#16839495—21no—
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×#376C2211yescharacteristic
31C2×#11758222—21no—
32#14519777C2×C411yescharacteristic
33#14519774C2×C411yescharacteristic
34#14519769—21no—
35#14519769—21no—
36#14519769C2×C412yes—
37#14519769D412yes—
38#14519765—21no—
39#14519751—21no—
40#14519751—21no—
41C4×D244—21no—
42C4×D244—21no—
43C2×C4⋊Dic61D411yescharacteristic
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—21no—
51C2×C4×Dic61—21no—
52C4⋊#92418—21no—
53#14519702—22no—
54#14519702—22no—
55#14519699—22no—
56#14519699—22no—
57C22⋊#92418—21no—
58#14519688—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63#14519684—21no—
64#14519684D411yescharacteristic
65#14519684D411yescharacteristic
66C2×M16×C61—21no—
67C2×C42×C61—21no—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C22⋊C8×C61—21no—
71#97×C61—21no—
72#97×C61C2×C412yes—
73C4×C8×C61—21no—
74#95×C61—21no—
75#95×C61D411yescharacteristic
76#95×C61D411yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C2×C22⋊D61—41no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87#11758222—42no—
88#11758222—42no—
89C2×D244—21no—
90C2×D244—21no—
91C2×D244—21no—
92C2×C4×D61—41no—
93C2×Dic122—21no—
94M16×C61—41no—
95M16×C61—41no—
96C2×C8×C61—22no—
97C2×C8×C61—41no—
98C42×C61—42no—
99C42×C61C22×C411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61#4111yescharacteristic
102C42×C61#4111yescharacteristic
103#11758198—41no—
104#11758198—41no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61C22⋊C412yes—
110C4⋊Dic61C22⋊C412yes—
111#11758196—22no—
112#11758196—22no—
113#11758196—22no—
114#11758196—22no—
115#11758196—42no—
116#11758196—42no—
117C4×Dic61—42no—
118C4×Dic61—42no—
119C4×Dic61—42no—
120C2×#92418—41no—
121C23×C61#12011yescharacteristic
122C22×D61—41no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—22no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×C4×C61C4×D411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12311yescharacteristic
139C22⋊D61—81no—
140C22⋊D61—81no—
141C2×Dic61—22no—
142C2×Dic61—22no—
143C2×Dic61—22no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154D244—42no—
155D244—81no—
156D244—81no—
157C4×D61—82no—
158Dic122—42no—
159C8×C61—42no—
160C8×C61—81no—
161#92418—81no—
162#9442—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61#38611yescharacteristic
166C22×C61#45411yescharacteristic
167C22×C61#45411yescharacteristic
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—42no—
178C4×C61—81no—
179Dic61—42no—
180Dic61—42no—
181Dic61—42no—
182Dic61—81no—
183Dic61—81no—
184#3142—611no—
185#2371—611no—
186#1534—611no—
187#1505—611no—
188#1505—611no—
189#1300—611no—
190#1300D6111yescharacteristic, complemented
191C2×C61—21no—
192C2×C61—21no—
193C2×C61#188811yescharacteristic
194C2×C61#190611yescharacteristic
195C2×C61#190611yescharacteristic
196D61—161no—
197#532—611no—
198C2×#125—611no—
199#491—612no—
200#490—612no—
201#488—1222no—
202#432—611no—
203#432C2×D6111yescharacteristic
204#417—1221no—
205#417—1221no—
206C4×M16C2×D6111yescharacteristic
207#387—1221no—
208#387—1221no—
209#387—1221no—
210#387—1221no—
211C4×C4⋊C4—1221no—
212C4×C4⋊C4—1221no—
213#376—611no—
214#376C2×D6111yescharacteristic
215#330—1222no—
216#327—1221no—
217#327—1221no—
218#327—1221no—
219#327—1221no—
220C61#944211yescharacteristic, complemented, Sylow
221C2×#41—1221no—
222C2×M16—21no—
223C4⋊Q8—611no—
224#127—611no—
225#125—612no—
226#125—612no—
227#125—1221no—
228#125—1221no—
229#124—1221no—
230#121—1221no—
231#121—1221no—
232C4×D4—1221no—
233C4×D4—1221no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C42—21no—
241C2×C42—1221no—
242C2×C42—1221no—
243C2×C42—1221no—
244C2×C42C22×D6111yescharacteristic
245C4⋊C8—21no—
246C4⋊C8—1221no—
247#103—1222no—
248#103—1222no—
249#102—1222no—
250#102—1222no—
251C22⋊C8—21no—
252C22⋊C8—1221no—
253#97—21no—
254#97—1221no—
255#97C4×D6112yes—
256C4×C8—21no—
257#95—21no—
258#95—611no—
259#95—611no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265#95D24411yescharacteristic
266#95D24411yescharacteristic
267#41—2442no—
268#41—2442no—
269C2×Q8—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—2441no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—2441no—
281C22×C4C2×D24411yescharacteristic
282C22×C4D4×D6111yescharacteristic
283C22×C4D4×D6111yescharacteristic
284M16—41no—
285M16—41no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—2441no—
289C4⋊C4—612no—
290C4⋊C4—612no—
291C4⋊C4—1222no—
292C4⋊C4—1222no—
293C4⋊C4—1222no—
294C4⋊C4—1222no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—2442no—
300C4⋊C4—2442no—
301C22⋊C4—2441no—
302C22⋊C4—2441no—
303C42—42no—
304C42—2442no—
305C42—2442no—
306C42—2442no—
307C42C2×C4×D6111yescharacteristic
308C42#1175822211yescharacteristic
309C42D4×D6111yescharacteristic
310C42#1175822611yescharacteristic
311C23—2441no—
312C23#1451974711yescharacteristic
313Q8—2442no—
314D4—4881no—
315D4—4881no—
316D4—4881no—
317D4—4881no—
318D4—2442no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—1222no—
330C2×C4—1222no—
331C2×C4—1222no—
332C2×C4—4882no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4C22⋊C4×D6111yescharacteristic
344C2×C4#1451973911yescharacteristic
345C2×C4C4×D24411yescharacteristic
346C2×C4#1451975011yescharacteristic
347C2×C4#1451975211yescharacteristic
348C2×C4#1451976211yescharacteristic
349C8—42no—
350C8—81no—
351C8—4881no—
352C22—21no—
353C22—21no—
354C22—4881no—
355C22—4881no—
356C22—4881no—
357C22#1683964011yescharacteristic
358C22#1683993611yescharacteristic
359C22#1683993611yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—42no—
367C4—81no—
368C4—4881no—
369C4—4881no—
370C4—2442no—
371C4—2442no—
372C4—2442no—
373C2—21no—
374C2—21no—
375C2—9761no—
376C2#2144622111yescharacteristic
377C2#2144631911yescharacteristic
378C2#2144632111yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1300C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1300D61
hypocenterC61#9442
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
2. #21448924C2semidirect
3. #21444445C2semidirect
6. #21443713C2semidirect
7. C61×#1300C2semidirect
10. #16840131C4semidirect
11. #16840127C4semidirect
190. #1300D61semidirect
220. C61#9442semidirect

Maximal subgroups

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

subgroupindex
#214562202
#214489242
#214444452
#214443282
#214443262
#214437132
C61×#13002
#944261