Finite Group Databasebeta

← #29569112

Subgroups — #29569112

Order 15616.

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

normal subgroups only

This group has 478 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#21447346C211yesmaximal, characteristic
3#21447292C211yesmaximal, characteristic, complemented
4#21447290C211yesmaximal, characteristic, complemented
5#21443641C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic, complemented
8C2×#14519757—21no—
9C2×#14519755—21no—
10C2×#14519711—21no—
11C2×#14519711—21no—
12C2×#14519710—21no—
13C2×#14519699—21no—
14#16839684—21no—
15#16839684—21no—
16#16839683—21no—
17#16839664C2211yescharacteristic
18#16839660C2211yescharacteristic
19#16839640—21no—
20#16839632C2211yescharacteristic
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#14519757—42no—
32#14519757—42no—
33#14519755—42no—
34#14519755—42no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49#14519711—42no—
50#14519711—42no—
51#14519710—42no—
52#14519699—42no—
53#14519684—21no—
54#14519684—21no—
55C22×C8×C61—21no—
56C22×C8×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C4⋊C4×C61D411yescharacteristic
60C2×C42×C61C2311yescharacteristic
61#95×C61—21no—
62C23×D61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—41no—
72C2×D244—21no—
73C2×D244—41no—
74C2×D244—41no—
75C2×D244Q1612yes—
76C2×C4×D61—42no—
77C2×C4×D61—42no—
78C2×C4×D61—81no—
79C2×Dic122—42no—
80C2×Dic122—42no—
81C2×Dic122—81no—
82C2×C8×C61—22no—
83C2×C8×C61—22no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61D812yes—
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⋊Dic61—41no—
106C4⋊Dic61—41no—
107C4⋊Dic61—41no—
108C4⋊Dic61—41no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111C4⋊Dic61D812yes—
112#11758196—42no—
113#11758196—41no—
114#11758196—41no—
115C2×#92418—22no—
116C2×#92418—41no—
117C2×#92418—41no—
118C23×C61#12011yescharacteristic
119C22×D61—22no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—22no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61C2×D811yescharacteristic
139C2×C4×C61C2×D811yescharacteristic
140C2×C4×C61C2×Q1611yescharacteristic
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—
153C2×Dic61—81no—
154C2×Dic61—81no—
155C2×Dic61—81no—
156D244—42no—
157D244—81no—
158C4×D61—84no—
159Dic122—84no—
160C8×C61—42no—
161C8×C61—42no—
162#92418—42no—
163#7797—611nomaximal, Sylow
164C22×C61#44711yescharacteristic
165C22×C61#44711yescharacteristic
166C22×C61#45111yescharacteristic
167C22×C61#45311yescharacteristic
168C22×C61#45611yescharacteristic
169C22×C61#45611yescharacteristic
170C22×C61#45811yescharacteristic
171C2×D61—42no—
172C2×D61—42no—
173C2×D61—42no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—42no—
185C4×C61—81no—
186Dic61—42no—
187Dic61—81no—
188Dic61—81no—
189Dic61—161no—
190#2683—611no—
191#2093—611no—
192#2083—611no—
193#2083—611no—
194#1271—611no—
195#1271D6111yescharacteristic, complemented
196#1270—611no—
197C2×C61#161011yescharacteristic
198C2×C61#161011yescharacteristic
199C2×C61#161411yescharacteristic
200C2×C61#161911yescharacteristic
201C2×C61#164911yescharacteristic
202C2×C61#164911yescharacteristic
203C2×C61#166011yescharacteristic
204D61—82no—
205C2×C22⋊Q8—1221no—
206C2×C22⋊Q8—1221no—
207C2×#107—1221no—
208C2×#107—1221no—
209C2×#107—1221no—
210C2×#102—1221no—
211#396—1221no—
212#396—1221no—
213#395—1221no—
214#390—611no—
215#389—611no—
216#389C2×D6111yescharacteristic
217#386—1221no—
218#384—611no—
219#340—1221no—
220#340—1221no—
221#336—611no—
222#336C2×D6111yescharacteristic
223#336C2×D6111yescharacteristic
224C61#779711yescharacteristic, complemented, Sylow
225C22×Q8—1221no—
226C22×D4—611no—
227C23×C4—1221no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—1221no—
231C22⋊Q8—2442no—
232C22⋊Q8—2442no—
233C22⋊Q8—2442no—
234C22⋊Q8—2442no—
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⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4D24411yescharacteristic
246C2×C4⋊C4D24411yescharacteristic
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C42C22×D6111yescharacteristic
253#107—2442no—
254#107—2442no—
255#107—2442no—
256#102—2442no—
257#95—21no—
258#95—1221no—
259#95—1221no—
260C24—1221no—
261C2×Q8—4881no—
262C2×Q8—2442no—
263C2×Q8—2442no—
264C2×D4—612no—
265C2×D4—1221no—
266C2×D4—2441no—
267C2×D4—2441no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—4881no—
274C22×C4—2442no—
275C22×C4—2442no—
276C22×C4—2441no—
277C22×C4C2×D24411yescharacteristic
278C22×C4D4×D6111yescharacteristic
279C22×C4D4×D6111yescharacteristic
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—1222no—
287C2×C8—2441no—
288C2×C8—2441no—
289C4⋊C4—21no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—612no—
294C4⋊C4—1221no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2442no—
300C4⋊C4—2442no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C4⋊C4D48812yes—
308C22⋊C4—4881no—
309C22⋊C4—2442no—
310C22⋊C4—2442no—
311C22⋊C4—2441no—
312C22⋊C4—2441no—
313C22⋊C4—2441no—
314C22⋊C4—2441no—
315C42—41no—
316C23—1222no—
317C23—2441no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23—2441no—
322C23—2441no—
323C23#1451974711yescharacteristic
324Q8—4884no—
325D4—4881no—
326D4—2442no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—1222no—
340C2×C4—4884no—
341C2×C4—4881no—
342C2×C4—4881no—
343C2×C4—4881no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4D8×D6111yescharacteristic
353C2×C4C2×D48811yescharacteristic
354C2×C4Q16×D6111yescharacteristic
355C2×C4#1451980411yescharacteristic
356C2×C4#1451980511yescharacteristic
357C2×C4#1451980611yescharacteristic
358C8—42no—
359C8—42no—
360C8—2442no—
361C22—4881no—
362C22—4881no—
363C22—4881no—
364C22—4881no—
365C22—2442no—
366C22—2442no—
367C22—2442no—
368C22#1683989711yescharacteristic
369C22#1683989811yescharacteristic
370C22#1683991911yescharacteristic
371C22#1683993111yescharacteristic
372C22#1683994611yescharacteristic
373C22#1683994711yescharacteristic
374C22#1683995311yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—81no—
383C4—9761no—
384C4—4881no—
385C4—4881no—
386C4—2442no—
387C2—4882no—
388C2#2144482311yescharacteristic
389C2#2144482411yescharacteristic
390C2#2144484511yescharacteristic
391C2#2144487511yescharacteristic
392C2#2144506911yescharacteristic
393C2#2144507011yescharacteristic
394C2#2144513211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1271D61
hypocenterC61#7797
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
3. #21447292C2semidirect
4. #21447290C2semidirect
5. #21443641C2semidirect
7. C61×#1271C2semidirect
195. #1271D61semidirect
224. C61#7797semidirect

Maximal subgroups

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

subgroupindex
#214521902
#214473462
#214472922
#214472902
#214436412
#214436392
C61×#12712
#779761