Finite Group Databasebeta

← #29568949

Subgroups — #29568949

Order 15616.

422 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 79 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#21453801C211yesmaximal, characteristic
2#21447066C211yesmaximal, characteristic, complemented
3#21446960C211yesmaximal, characteristic, complemented
4#21446956C211yesmaximal, characteristic
5#21443643C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#1272C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×#14519702—21no—
10C2×#14519702—21no—
11C2×#14519701—21no—
12C2×#14519699—21no—
13#16839689—21no—
14#16839680—21no—
15#16839673—21no—
16#16839664C2211yescharacteristic
17#16839660C2211yescharacteristic
18#16839654—21no—
19#16839652—21no—
20#16839649—21no—
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#391C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×D244D411yescharacteristic
29C22×#92418—21no—
30#14519777—42no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61D411yescharacteristic
34C2×C4⋊Dic61D411yescharacteristic
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×C4×Dic61—21no—
44#14519702—42no—
45#14519702—42no—
46#14519701—42no—
47#14519699—42no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C22×Q8×C61D411yescharacteristic
53C22×C8×C61—21no—
54C22×C8×C61—21no—
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C42×C61C2311yescharacteristic
57#95×C61—21no—
58#95×C61—21no—
59C23×D61—21no—
60C2×Q8×C61—21no—
61C2×Q8×C61—21no—
62C2×Q8×C61—41no—
63C2×Q8×C61—41no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—41no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—41no—
76C2×D244—41no—
77C2×Dic122—22no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82C2×Dic122—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C4⋊C4×C61—41no—
90C42×C61—41no—
91#11758198—41no—
92#11758198—41no—
93#11758198—41no—
94#11758198—41no—
95#11758198—81no—
96#11758198—81no—
97#11758198—81no—
98#11758198—81no—
99C4⋊Dic61—22no—
100C4⋊Dic61—22no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105C4⋊Dic61—41no—
106C4⋊Dic61—41no—
107#11758196—41no—
108#11758196—41no—
109C4×Dic61—81no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C23×C61#12011yescharacteristic
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121Q8×C61—42no—
122Q8×C61—81no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61#13511yescharacteristic
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61#13511yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C61#13711yescharacteristic
140C2×C4×C61#13711yescharacteristic
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—42no—
150C2×Dic61—41no—
151C2×Dic61—81no—
152C2×Dic61—81no—
153D244—42no—
154D244—81no—
155Dic122—42no—
156Dic122—42no—
157Dic122—81no—
158Dic122—81no—
159C8×C61—81no—
160C8×C61—81no—
161#92418—81no—
162#7773—611nomaximal, Sylow
163C22×C61#44911yescharacteristic
164C22×C61#45211yescharacteristic
165C22×C61#45211yescharacteristic
166C22×C61#45411yescharacteristic
167C22×C61#45511yescharacteristic
168C22×C61#45511yescharacteristic
169C22×C61B(4,𝔽2)11yescharacteristic
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—81no—
184C4×C61—81no—
185Dic61—82no—
186Dic61—81no—
187Dic61—81no—
188Dic61—81no—
189#2808—611no—
190#2043—611no—
191#2024—611no—
192#2023—611no—
193#1272D6111yescharacteristic, complemented
194#1271—611no—
195#1270—611no—
196C2×C61#159711yescharacteristic
197C2×C61#160611yescharacteristic
198C2×C61#160611yescharacteristic
199C2×C61#163811yescharacteristic
200C2×C61#164011yescharacteristic
201C2×C61#164611yescharacteristic
202C2×C61#166211yescharacteristic
203D61—161no—
204C2×C4⋊Q8—611no—
205C2×#103—1221no—
206C2×#103—1221no—
207C2×#103—1221no—
208C2×#102—1221no—
209#397—1221no—
210#394—1221no—
211#393—1221no—
212#391C2×D6111yescharacteristic
213#390—611no—
214#389—611no—
215#388—1221no—
216#388—1221no—
217#387—1221no—
218#340—1221no—
219#340—1221no—
220#336—611no—
221#336C2×D6111yescharacteristic
222#336C2×D6111yescharacteristic
223C61#777311yescharacteristic, complemented, Sylow
224C22×Q8—1221no—
225C22×Q8D24411yescharacteristic
226C22×D4—611no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—1221no—
230C4⋊Q8—2442no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4D24411yescharacteristic
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C42—1221no—
245C2×C42C22×D6111yescharacteristic
246#103—2442no—
247#103—2442no—
248#103—2442no—
249#102—2442no—
250#95—21no—
251#95—21no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255#95—1221no—
256C24—1221no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—1222no—
262C2×Q8—2441no—
263C2×Q8—2441no—
264C2×Q8—2441no—
265C2×Q8—2441no—
266C2×Q8—2441no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—2441no—
270C2×D4—2441no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—2441no—
277C22×C4C2×D24411yescharacteristic
278C22×C4D4×D6111yescharacteristic
279C22×C4D4×D6111yescharacteristic
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—2441no—
287C2×C8—2441no—
288C2×C8—2441no—
289C4⋊C4—41no—
290C4⋊C4—1222no—
291C4⋊C4—1222no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C22⋊C4—4881no—
301C22⋊C4—4881no—
302C22⋊C4—4881no—
303C22⋊C4—4881no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C42—41no—
309C42—4881no—
310C23—2441no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23#1451974711yescharacteristic
318Q8—42no—
319Q8—81no—
320Q8—4881no—
321Q8—4881no—
322Q8—2442no—
323Q8—2442no—
324D4—4881no—
325D4—2442no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—4881no—
339C2×C4—4881no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2442no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4#1451979811yescharacteristic
351C2×C4#1451979911yescharacteristic
352C2×C4#1451980011yescharacteristic
353C2×C4#1451980411yescharacteristic
354C2×C4#1451980911yescharacteristic
355C2×C4#1451981011yescharacteristic
356C8—81no—
357C8—81no—
358C8—4881no—
359C22—4881no—
360C22—4881no—
361C22—4881no—
362C22—4881no—
363C22—4881no—
364C22—4881no—
365C22—4881no—
366C22#1683991011yescharacteristic
367C22#1683992611yescharacteristic
368C22#1683992711yescharacteristic
369C22#1683993611yescharacteristic
370C22#1683994111yescharacteristic
371C22#1683994211yescharacteristic
372C22#1683995011yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—81no—
380C4—81no—
381C4—4882no—
382C4—4881no—
383C4—4881no—
384C4—4881no—
385C2—9761no—
386C2#2144475111yescharacteristic
387C2#2144480111yescharacteristic
388C2#2144480211yescharacteristic
389C2#2144499411yescharacteristic
390C2#2144500811yescharacteristic
391C2#2144504811yescharacteristic
392C2#2144514411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1272D61
hypocenterC61#7773
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #21447066C2semidirect
3. #21446960C2semidirect
5. #21443643C2semidirect
7. C61×#1272C2semidirect
193. #1272D61semidirect
223. C61#7773semidirect

Maximal subgroups

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

subgroupindex
#214538012
#214470662
#214469602
#214469562
#214436432
#214436392
C61×#12722
#777361