Finite Group Databasebeta

← #29568928

Subgroups — #29568928

Order 15616.

460 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 81 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#21452748C211yesmaximal, characteristic
2#21447152C211yesmaximal, characteristic, complemented
3#21447066C211yesmaximal, characteristic, complemented
4#21446956C211yesmaximal, characteristic
5#21443643C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×#14519762—21no—
10C2×#14519708—21no—
11C2×#14519702—21no—
12C2×#14519702—21no—
13C2×#14519699—21no—
14#16839695—21no—
15#16839689—21no—
16#16839688—21no—
17#16839664C2211yescharacteristic
18#16839660C2211yescharacteristic
19#16839636—21no—
20#16839633—21no—
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C22×#92418—21no—
31#14519777—42no—
32#14519762—42no—
33#14519762—42no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46#14519708—42no—
47#14519702—42no—
48#14519702—42no—
49#14519699—42no—
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—
61C23×D61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—41no—
71C2×D244—21no—
72C2×D244—41no—
73C2×D244—41no—
74C2×D244SD1612yes—
75C2×C4×D61—42no—
76C2×C4×D61—81no—
77C2×C4×D61—81no—
78C2×Dic122—22no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82C2×Dic122—41no—
83C2×Dic122—41no—
84C2×C8×C61—41no—
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—21no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C42×C61—41no—
96#11758198—42no—
97#11758198—42no—
98#11758198—42no—
99#11758198—41no—
100#11758198—41no—
101#11758198—41no—
102#11758198—41no—
103C4⋊Dic61—22no—
104C4⋊Dic61—22no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—41no—
108C4⋊Dic61—41no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111#11758196—41no—
112#11758196—41no—
113#11758196—81no—
114C2×#92418—22no—
115C2×#92418—41no—
116C2×#92418—41no—
117C23×C61#12011yescharacteristic
118C22×D61—22no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61C2×SD1611yescharacteristic
138C2×C4×C61#13511yescharacteristic
139C2×C4×C61#13511yescharacteristic
140C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C61#13711yescharacteristic
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—42no—
152C2×Dic61—41no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155D244—42no—
156D244—81no—
157C4×D61—84no—
158Dic122—42no—
159Dic122—42no—
160Dic122—81no—
161Dic122—81no—
162C8×C61—81no—
163C8×C61—81no—
164#92418—42no—
165#7770—611nomaximal, Sylow
166C22×C61#44911yescharacteristic
167C22×C61#45011yescharacteristic
168C22×C61#45211yescharacteristic
169C22×C61#45411yescharacteristic
170C22×C61#45511yescharacteristic
171C22×C61#45611yescharacteristic
172C22×C61B(4,𝔽2)11yescharacteristic
173C2×D61—42no—
174C2×D61—42no—
175C2×D61—42no—
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C2×D61—81no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—81no—
187C4×C61—81no—
188Dic61—82no—
189Dic61—81no—
190Dic61—81no—
191Dic61—81no—
192#2724—611no—
193#2058—611no—
194#2043—611no—
195#2023—611no—
196#1271—611no—
197#1271D6111yescharacteristic, complemented
198#1270—611no—
199C2×C61#159711yescharacteristic
200C2×C61#160111yescharacteristic
201C2×C61#160311yescharacteristic
202C2×C61#163511yescharacteristic
203C2×C61#164011yescharacteristic
204C2×C61#165411yescharacteristic
205C2×C61#166411yescharacteristic
206D61—82no—
207C2×C4⋊Q8—611no—
208C2×#123—1221no—
209C2×#106—1221no—
210C2×#103—1221no—
211C2×#103—1221no—
212C2×#102—1221no—
213#398—1221no—
214#397—1221no—
215#397—1221no—
216#390—611no—
217#389—611no—
218#389C2×D6111yescharacteristic
219#385—1221no—
220#385—1221no—
221#340—1221no—
222#340—1221no—
223#336—611no—
224#336C2×D6111yescharacteristic
225#336C2×D6111yescharacteristic
226C61#777011yescharacteristic, complemented, Sylow
227C22×Q8—1221no—
228C22×D4—611no—
229C23×C4—1221no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—1221no—
233C4⋊Q8—2442no—
234#123—2442no—
235#123—2442no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4D24411yescharacteristic
245C2×C4⋊C4D24411yescharacteristic
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C42C22×D6111yescharacteristic
252#106—2442no—
253#103—2442no—
254#103—2442no—
255#102—2442no—
256#95—21no—
257#95—1221no—
258#95—1221no—
259#95—1221no—
260#95—1221no—
261C24—1221no—
262C2×Q8—1222no—
263C2×Q8—2441no—
264C2×Q8—2441no—
265C2×Q8—2441no—
266C2×Q8—2441no—
267C2×Q8—2441no—
268C2×D4—612no—
269C2×D4—1221no—
270C2×D4—2441no—
271C2×D4—2441no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—4881no—
278C22×C4—4881no—
279C22×C4—2442no—
280C22×C4—2441no—
281C22×C4C2×D24411yescharacteristic
282C22×C4D4×D6111yescharacteristic
283C22×C4D4×D6111yescharacteristic
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—1222no—
291C2×C8—2441no—
292C2×C8—2441no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—1222no—
299C4⋊C4—1222no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—4881no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C4⋊C4—2441no—
308C4⋊C4—2441no—
309C22⋊C4—2442no—
310C22⋊C4—2442no—
311C22⋊C4—2442no—
312C22⋊C4—2441no—
313C22⋊C4—2441no—
314C22⋊C4—2441no—
315C22⋊C4—2441no—
316C42—41no—
317C23—1222no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23—2441no—
322C23—2441no—
323C23—2441no—
324C23#1451974711yescharacteristic
325Q8—4881no—
326Q8—4881no—
327Q8—2442no—
328Q8—2442no—
329D4—4881no—
330D4—2442no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—4884no—
344C2×C4—4881no—
345C2×C4—4881no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2442no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4SD16×D6111yescharacteristic
357C2×C4#1451979911yescharacteristic
358C2×C4#1451980011yescharacteristic
359C2×C4#1451980111yescharacteristic
360C2×C4#1451980411yescharacteristic
361C2×C4#1451981011yescharacteristic
362C8—81no—
363C8—81no—
364C8—2442no—
365C22—4881no—
366C22—4881no—
367C22—4881no—
368C22—4881no—
369C22—2442no—
370C22—2442no—
371C22—2442no—
372C22#1683991011yescharacteristic
373C22#1683991411yescharacteristic
374C22#1683992611yescharacteristic
375C22#1683993611yescharacteristic
376C22#1683994111yescharacteristic
377C22#1683994711yescharacteristic
378C22#1683995011yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—81no—
386C4—81no—
387C4—4882no—
388C4—4881no—
389C4—4881no—
390C4—4881no—
391C2—4882no—
392C2#2144475111yescharacteristic
393C2#2144477211yescharacteristic
394C2#2144478411yescharacteristic
395C2#2144497311yescharacteristic
396C2#2144500811yescharacteristic
397C2#2144510411yescharacteristic
398C2#2144515511yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1271D61
hypocenterC61#7770
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
2. #21447152C2semidirect
3. #21447066C2semidirect
5. #21443643C2semidirect
7. C61×#1271C2semidirect
197. #1271D61semidirect
226. C61#7770semidirect

Maximal subgroups

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

subgroupindex
#214527482
#214471522
#214470662
#214469562
#214436432
#214436392
C61×#12712
#777061