Finite Group Databasebeta

← #29568998

Subgroups — #29568998

Order 15616.

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

normal subgroups only

This group has 478 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#21452779C211yesmaximal, characteristic
2#21447152C211yesmaximal, characteristic, complemented
3#21447148C211yesmaximal, characteristic, complemented
4#21446904C211yesmaximal, characteristic
5#21443643C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic, complemented
8C22×#11758190—21no—
9C2×#14519777C2211yescharacteristic
10C2×#14519772—21no—
11C2×#14519711—21no—
12C2×#14519708—21no—
13C2×#14519702—21no—
14#16839697—21no—
15#16839684—21no—
16#16839680—21no—
17#16839664C2211yescharacteristic
18#16839660C2211yescharacteristic
19#16839659—21no—
20#16839652—21no—
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×D244D411yescharacteristic
29C2×#11758190—42no—
30C2×#11758190—42no—
31C2×#11758190—42no—
32C22×#92418—21no—
33#14519777—42no—
34#14519772—42no—
35#14519772—42no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×C4×Dic61—21no—
51#14519711—42no—
52#14519708—42no—
53#14519702—42no—
54#14519684—21no—
55#14519684—21no—
56C22×C8×C61—21no—
57C22×C8×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61D411yescharacteristic
60C2×C4⋊C4×C61D411yescharacteristic
61C2×C42×C61C2311yescharacteristic
62#95×C61—21no—
63C23×D61—21no—
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—22no—
84C2×C8×C61—22no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C42×C61—41no—
95#11758198—42no—
96#11758198—42no—
97#11758198—41no—
98#11758198—41no—
99#11758198—41no—
100#11758198—41no—
101#11758198—81no—
102#11758198—81no—
103C4⋊Dic61—21no—
104C4⋊Dic61—22no—
105C4⋊Dic61—22no—
106C4⋊Dic61—41no—
107C4⋊Dic61—41no—
108C4⋊Dic61—41no—
109C4⋊Dic61—41no—
110C4⋊Dic61SD1612yescomplemented
111#11758196—42no—
112#11758196—41no—
113#11758196—41no—
114#11758196—81no—
115C4×Dic61—42no—
116C2×#92418—22no—
117C2×#92418—41no—
118C2×#92418—41no—
119#11758190—48no—
120C23×C61#12011yescharacteristic
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61C2×SD1611yescharacteristic
141C2×C4×C61#13511yescharacteristic
142C2×C4×C61#13511yescharacteristic
143C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C61#13711yescharacteristic
146C2×Dic61—22no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—42no—
155C2×Dic61—41no—
156C2×Dic61—81no—
157C2×Dic61—81no—
158D244—42no—
159D244—81no—
160Dic122—42no—
161Dic122—42no—
162Dic122—81no—
163Dic122—81no—
164C8×C61—42no—
165C8×C61—42no—
166#92418—42no—
167#7780—611nomaximal, Sylow
168C22×C61#44911yescharacteristic
169C22×C61#45011yescharacteristic
170C22×C61#45211yescharacteristic
171C22×C61#45311yescharacteristic
172C22×C61#45611yescharacteristic
173C22×C61#45611yescharacteristic
174C22×C61B(4,𝔽2)11yescharacteristic
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—81no—
189C4×C61—81no—
190Dic61—42no—
191Dic61—82no—
192Dic61—81no—
193Dic61—81no—
194#2727—611no—
195#2058—611no—
196#2057—611no—
197#2013—611no—
198#1271—611no—
199#1271D6111yescharacteristic, complemented
200#1270—611no—
201C2×C61#160011yescharacteristic
202C2×C61#160311yescharacteristic
203C2×C61#160411yescharacteristic
204C2×C61#163111yescharacteristic
205C2×C61#165011yescharacteristic
206C2×C61#165411yescharacteristic
207C2×C61#166011yescharacteristic
208D61—161no—
209C22×SD16—1221no—
210C2×C4⋊Q8—611no—
211C2×#126—1221no—
212C2×#107—1221no—
213C2×#106—1221no—
214C2×#103—1221no—
215#399—1221no—
216#396—1221no—
217#394—1221no—
218#390—611no—
219#389—611no—
220#389—1221no—
221#389C2×D6111yescharacteristic
222#388—1221no—
223#340—1221no—
224#340—1221no—
225#336—611no—
226#336C2×D6111yescharacteristic
227#336C2×D6111yescharacteristic
228C61#778011yescharacteristic, complemented, Sylow
229C22×Q8—1221no—
230C22×D4—611no—
231C2×SD16—2442no—
232C2×SD16—2442no—
233C2×SD16—2442no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—1221no—
237C4⋊Q8—2442no—
238#126—2442no—
239#126—2442no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4D24411yescharacteristic
250C2×C4⋊C4D24411yescharacteristic
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C42—1221no—
258C2×C42C22×D6111yescharacteristic
259#107—2442no—
260#106—2442no—
261#103—2442no—
262#95—21no—
263#95—1221no—
264#95—1221no—
265C24—1221no—
266C2×Q8—1222no—
267C2×Q8—2441no—
268C2×Q8—2441no—
269C2×Q8—2441no—
270C2×Q8—2441no—
271C2×Q8—2441no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—2441no—
275C2×D4—2441no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—2441no—
282C22×C4C2×D24411yescharacteristic
283C22×C4D4×D6111yescharacteristic
284C22×C4D4×D6111yescharacteristic
285SD16—2448no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—1222no—
293C2×C8—2441no—
294C2×C8—2441no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—612no—
301C4⋊C4—1222no—
302C4⋊C4—1222no—
303C4⋊C4—1221no—
304C4⋊C4—4881no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C4⋊C4—2441no—
308C4⋊C4—2441no—
309C4⋊C4—2442no—
310C4⋊C4—2441no—
311C4⋊C4—2441no—
312C22⋊C4—4881no—
313C22⋊C4—4881no—
314C22⋊C4—2442no—
315C22⋊C4—2442no—
316C22⋊C4—2441no—
317C22⋊C4—2441no—
318C22⋊C4—2441no—
319C22⋊C4—2441no—
320C42—41no—
321C42—2442no—
322C23—2441no—
323C23—2441no—
324C23—2441no—
325C23—2441no—
326C23—2441no—
327C23—2441no—
328C23—2441no—
329C23#1451974711yescharacteristic
330Q8—4881no—
331Q8—4881no—
332Q8—2442no—
333Q8—2442no—
334D4—4881no—
335D4—2442no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—1222no—
349C2×C4—4881no—
350C2×C4—4881no—
351C2×C4—2441no—
352C2×C4—2442no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4SD16×D6111yescharacteristic
361C2×C4#1451979911yescharacteristic
362C2×C4#1451980011yescharacteristic
363C2×C4#1451980111yescharacteristic
364C2×C4#1451980411yescharacteristic
365C2×C4#1451981011yescharacteristic
366C8—42no—
367C8—42no—
368C8—2442no—
369C22—4881no—
370C22—4881no—
371C22—4881no—
372C22—4881no—
373C22—4881no—
374C22—4881no—
375C22—4881no—
376C22#1683991011yescharacteristic
377C22#1683991411yescharacteristic
378C22#1683992611yescharacteristic
379C22#1683993111yescharacteristic
380C22#1683994611yescharacteristic
381C22#1683994711yescharacteristic
382C22#1683995011yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—81no—
390C4—81no—
391C4—4881no—
392C4—4882no—
393C4—4881no—
394C4—2442no—
395C2—9761no—
396C2#2144476811yescharacteristic
397C2#2144478411yescharacteristic
398C2#2144478911yescharacteristic
399C2#2144494911yescharacteristic
400C2#2144507811yescharacteristic
401C2#2144510411yescharacteristic
402C2#2144513211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1271D61
hypocenterC61#7780
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. #21447148C2semidirect
5. #21443643C2semidirect
7. C61×#1271C2semidirect
110. C4⋊Dic61SD16semidirect
199. #1271D61semidirect
228. C61#7780semidirect

Maximal subgroups

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

subgroupindex
#214527792
#214471522
#214471482
#214469042
#214436432
#214436392
C61×#12712
#778061