Finite Group Databasebeta

← #29569069

Subgroups — #29569069

Order 15616.

462 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 87 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#21452190C211yesmaximal, characteristic
2#21447296C211yesmaximal, characteristic, complemented
3#21447223C211yesmaximal, characteristic
4#21443643C211yesmaximal, characteristic, complemented
5#21443642C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#2099C211yesmaximal, characteristic, complemented
8C2×#14519757—21no—
9C2×#14519755—21no—
10C2×#14519708—21no—
11C2×#14519697—21no—
12#16839684—21no—
13#16839684—21no—
14#16839683—21no—
15#16839664C2211yescharacteristic
16#16839660C2211yescharacteristic
17#16839640—21no—
18#16839524—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C61×#389C2211yescharacteristic
23C61×#384C2211yescharacteristic
24C61×#340—21no—
25C61×#340—21no—
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C22×#92418—21no—
31C22×#92418—21no—
32#14519757—42no—
33#14519757—42no—
34#14519755—42no—
35#14519755—42no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47#14519708—42no—
48#14519697—42no—
49#14519684—21no—
50#14519684—21no—
51C22×C8×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C42×C61C2311yescharacteristic
59#95×C61—21no—
60C23×D61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—41no—
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C2×D244—21no—
71C2×D244—41no—
72C2×D244—41no—
73C2×D244SD1612yes—
74C2×C4×D61—42no—
75C2×C4×D61—42no—
76C2×C4×D61—81no—
77C2×Dic122—42no—
78C2×Dic122—42no—
79C2×Dic122—81no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C2×C8×C61—41no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—42no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61SD1612yes—
93C42×C61—41no—
94#11758198—42no—
95#11758198—42no—
96#11758198—41no—
97#11758198—41no—
98#11758198—41no—
99#11758198—41no—
100#11758198—81no—
101C4⋊Dic61—21no—
102C4⋊Dic61—42no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105C4⋊Dic61D812yes—
106#11758196—42no—
107#11758196—41no—
108#11758196—41no—
109C2×#92418—22no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115C23×C61#12011yescharacteristic
116C22×D61—22no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
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—22no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61C2×D811yescharacteristic
139C2×C4×C61C2×SD1611yescharacteristic
140C2×C4×C61C2×SD1611yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C61#13711yescharacteristic
144C2×Dic61—22no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153D244—42no—
154D244—81no—
155C4×D61—84no—
156Dic122—84no—
157C8×C61—81no—
158#92418—42no—
159#92418—81no—
160#7791—611nomaximal, Sylow
161C22×C61#44711yescharacteristic
162C22×C61#44811yescharacteristic
163C22×C61#45011yescharacteristic
164C22×C61#45411yescharacteristic
165C22×C61#45511yescharacteristic
166C22×C61#45611yescharacteristic
167C22×C61#45811yescharacteristic
168C2×D61—42no—
169C2×D61—42no—
170C2×D61—42no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—42no—
182C4×C61—81no—
183C4×C61—161no—
184Dic61—42no—
185Dic61—81no—
186Dic61—81no—
187#2683—611no—
188#2099D6111yescharacteristic, complemented
189#2084—611no—
190#2071—611no—
191#1271—611no—
192#1271—611no—
193#1270—611no—
194C2×C61#160811yescharacteristic
195C2×C61#161011yescharacteristic
196C2×C61#161611yescharacteristic
197C2×C61#162711yescharacteristic
198C2×C61#163911yescharacteristic
199C2×C61#165111yescharacteristic
200C2×C61#166411yescharacteristic
201D61—82no—
202C2×C22⋊Q8—1221no—
203C2×C22⋊Q8—1221no—
204C2×#106—1221no—
205C2×#102—1221no—
206#396—1221no—
207#396—1221no—
208#395—1221no—
209#390—611no—
210#389—611no—
211#389C2×D6111yescharacteristic
212#386—1221no—
213#384C2×D6111yescharacteristic
214#340—21no—
215#340—21no—
216#340—1221no—
217#340—1221no—
218#336—611no—
219#336—611no—
220#336C2×D6111yescharacteristic
221C61#779111yescharacteristic, complemented, Sylow
222C22×Q8—1221no—
223C22×D4—611no—
224C23×C4—1221no—
225C22×C8—21no—
226C22×C8—1221no—
227C22×C8—1221no—
228C22⋊Q8—2442no—
229C22⋊Q8—2442no—
230C22⋊Q8—2442no—
231C22⋊Q8—2442no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4C22⋊D6111yescharacteristic
243C2×C4⋊C4C22⋊D6111yescharacteristic
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C42C22×D6111yescharacteristic
250#106—2442no—
251#102—2442no—
252#95—21no—
253#95—1221no—
254#95—1221no—
255C24—1221no—
256C2×Q8—4881no—
257C2×Q8—2442no—
258C2×Q8—2442no—
259C2×D4—612no—
260C2×D4—1221no—
261C2×D4—2441no—
262C2×D4—2441no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—4881no—
270C22×C4—2442no—
271C22×C4—2442no—
272C22×C4D4×D6111yescharacteristic
273C22×C4D4×D6111yescharacteristic
274C22×C4C2×C22⋊D6111yescharacteristic
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—1222no—
279C2×C8—2441no—
280C2×C8—2441no—
281C2×C8—2441no—
282C2×C8—2441no—
283C2×C8—2441no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—42no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—612no—
294C4⋊C4—1221no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2442no—
298C4⋊C4—2442no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C4⋊C4#1175820112yes—
302C22⋊C4—4881no—
303C22⋊C4—2442no—
304C22⋊C4—2442no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C42—41no—
310C23—1222no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23#1451974511yescharacteristic
318Q8—4884no—
319D4—4881no—
320D4—2442no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—1222no—
337C2×C4—4884no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4D8×D6111yescharacteristic
347C2×C4SD16×D6111yescharacteristic
348C2×C4C2×#1175820111yescharacteristic
349C2×C4#1451980111yescharacteristic
350C2×C4#1451980211yescharacteristic
351C2×C4#1451980611yescharacteristic
352C8—81no—
353C8—4881no—
354C8—2442no—
355C22—4881no—
356C22—4881no—
357C22—4881no—
358C22—4881no—
359C22—2442no—
360C22—2442no—
361C22—2442no—
362C22#1683989411yescharacteristic
363C22#1683989911yescharacteristic
364C22#1683991211yescharacteristic
365C22#1683993411yescharacteristic
366C22#1683993811yescharacteristic
367C22#1683994311yescharacteristic
368C22#1683995111yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—81no—
377C4—161no—
378C4—4881no—
379C4—4881no—
380C4—2442no—
381C2—4882no—
382C2#2144480811yescharacteristic
383C2#2144482011yescharacteristic
384C2#2144485511yescharacteristic
385C2#2144491911yescharacteristic
386C2#2144499711yescharacteristic
387C2#2144508111yescharacteristic
388C2#2144515011yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2099C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#2099D61
hypocenterC61#7791
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
2. #21447296C2semidirect
4. #21443643C2semidirect
5. #21443642C2semidirect
7. C61×#2099C2semidirect
188. #2099D61semidirect
221. C61#7791semidirect

Maximal subgroups

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

subgroupindex
#214521902
#214472962
#214472232
#214436432
#214436422
#214436392
C61×#20992
#779161