Finite Group Databasebeta

← #29591083

Subgroups — #29591083

Order 15616.

470 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 89 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#466×D61C211yesmaximal, characteristic
2C22⋊C16×D61C211yesmaximal, characteristic, complemented
3#21445847C211yesmaximal, characteristic, complemented
4#21443829C211yesmaximal, characteristic, complemented
5#21443828C211yesmaximal, characteristic, complemented
6#21443827C211yesmaximal, characteristic, complemented
7C61×#1347C211yesmaximal, characteristic, complemented
8C2×D8×D61C411yescharacteristic, complemented
9C22×C8×D61C2211yescharacteristic
10#121×D61—21no—
11C2×C16×D61—21no—
12#16839999C411yescharacteristic, complemented
13#16839998C2211yescharacteristic
14#16839997—21no—
15#16839996—21no—
16#16839995C411yescharacteristic, complemented
17C2×#14519710—21no—
18#107×D61C411yescharacteristic, complemented
19#102×D61—21no—
20#16839619—21no—
21C22⋊#11758185C2211yescharacteristic, complemented
22#16839541—21no—
23#16839525C2211yescharacteristic, complemented
24C61×#466C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic, complemented
26C61×#340C2211yescharacteristic, complemented
27C2×D4×D61—21no—
28C2×D4×D61—41no—
29C22×C4×D61D411yescharacteristic
30C2×D488C2×C411yescharacteristic
31C2×#11758199—21no—
32D8×D61—42no—
33C22×#92418D411yescharacteristic
34C2×C8×D61—42no—
35C2×C8×D61C2×C411yescharacteristic
36C2×C8×D61C2×C411yescharacteristic
37C2×C8×D61D411yescharacteristic
38C2×C8×D61D411yescharacteristic
39#14519752—21no—
40#14519751—21no—
41#14519750—41no—
42#14519749—41no—
43#14519748—21no—
44C2×C4⋊Dic61—21no—
45C4⋊C4×D61—21no—
46C2×#11758198—41no—
47C22⋊C4×D61—41no—
48C2×#11758185—21no—
49C16×D61—42no—
50#14519711C2×C411yescharacteristic
51#14519710—21no—
52#14519710—42no—
53#14519699—21no—
54#14519698—21no—
55#14519697—21no—
56#14519684—41no—
57C2×D8×C61C2×C411yescharacteristic
58C22×C8×C61C2311yescharacteristic
59#121×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C16×C61—21no—
62#107×C61C2×C411yescharacteristic
63#102×C61—21no—
64C23×D61—41no—
65C23×D61D811yescharacteristic
66C2×D4×C61—21no—
67C2×D4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61C2×D411yescharacteristic
70C2×C22⋊D61—41no—
71C2×C22⋊D61—41no—
72C2×C22⋊D61—41no—
73C22×Dic61—41no—
74C22×Dic61D811yescharacteristic
75D4×D61—42no—
76D4×D61—42no—
77D4×D61—82no—
78D4×D61—82no—
79C2×D244—21no—
80C2×D244—41no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61C22⋊C411yescharacteristic
85C2×C4×D61C22⋊C411yescharacteristic
86C2×C4×D61SD1611yescharacteristic
87C2×C4×D61SD1611yescharacteristic
88D8×C61—41no—
89C2×C8×C61—41no—
90C2×C8×C61C22×C411yescharacteristic
91C2×C8×C61C2×D411yescharacteristic
92C4⋊C4×C61—21no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C22⋊C4×C61—41no—
96C22⋊Dic61—41no—
97#11758199—42no—
98#11758198—41no—
99#11758198—41no—
100#11758198—82no—
101C4⋊Dic61—21no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104#11758196—41no—
105C2×#92418—22no—
106C2×#92418C22⋊C411yescharacteristic
107C2×#92418C22⋊C411yescharacteristic
108D488—41no—
109C8×D61—22no—
110C8×D61—22no—
111C8×D61—41no—
112C8×D61—41no—
113C16×C61—41no—
114#11758185—41no—
115C23×C61—41no—
116C23×C61C2×D811yescharacteristic
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—82no—
121C22×D61—82no—
122C22×D61—82no—
123C22×D61#10211yescharacteristic
124C22×D61#10211yescharacteristic
125C22×D61D1612yes—
126C22×D61SD3212yes—
127D4×C61—41no—
128D4×C61—41no—
129D4×C61—81no—
130D4×C61—81no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61C2×C22⋊C411yescharacteristic
138C2×C4×C61C2×SD1611yescharacteristic
139C22⋊D61—82no—
140C22⋊D61—81no—
141C22⋊D61—81no—
142C22⋊D61—82no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148C2×Dic61#10211yescharacteristic
149C2×Dic61#10211yescharacteristic
150D244—41no—
151D244—41no—
152D244—82no—
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—41no—
158C4×D61—41no—
159C4×D61—82no—
160C8×C61—21no—
161C8×C61—21no—
162#92418—21no—
163#92418#9912yes—
164#11886—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61C2×#10211yescharacteristic
171C22×C61C2×D1611yescharacteristic
172C22×C61C2×SD3211yescharacteristic
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—42no—
178C2×D61—42no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C2×D61—164no—
183C2×D61#35712yes—
184C2×D61#35712yes—
185C4×C61—21no—
186C4×C61—81no—
187C4×C61—161no—
188C4×C61C2×#9911yescharacteristic
189C4×C61#42111yescharacteristic
190Dic61—21no—
191Dic61—21no—
192Dic61—81no—
193Dic61—161no—
194C2×#466—611no—
195C2×C22⋊C16—611no—
196#1808—611no—
197#1347—611no—
198#1347—611no—
199#1347—611no—
200#1347D6111yescharacteristic, complemented
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—161no—
204C2×C61#151911yescharacteristic
205C2×C61C2×#35711yescharacteristic
206C2×C61#214511yescharacteristic
207D61—22no—
208D61—22no—
209D61—161no—
210C22×D8—611no—
211C23×C8—611no—
212C2×#121—1221no—
213C22×C16—1221no—
214#466—611no—
215#466—611no—
216#466—611no—
217#466—1221no—
218#466—1221no—
219#466C2×D6111yescharacteristic
220C2×#107—611no—
221C2×#107—1221no—
222C2×#102—1221no—
223#380—1221no—
224C22⋊C16—611no—
225C22⋊C16—1221no—
226C22⋊C16C2×D6111yescharacteristic, complemented
227#340—611no—
228#340C2×D6111yescharacteristic, complemented
229C61#1188611yescharacteristic, complemented, Sylow
230C22×D4—1221no—
231C22×D4—2441no—
232C23×C4—611no—
233C2×D8—611no—
234C2×D8—1221no—
235C2×D8—2442no—
236C2×D8C4×D6111yescharacteristic
237C22×C8—611no—
238C22×C8—611no—
239C22×C8—611no—
240C22×C8—611no—
241C22×C8—611no—
242C22×C8—2442no—
243C22×C8C22×D6111yescharacteristic
244#121—21no—
245#121—1221no—
246#121—1221no—
247#121—1221no—
248#121—2441no—
249#121—2441no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4—1221no—
253C2×C22⋊C4—2441no—
254C2×C22⋊C4—2441no—
255C2×C16—21no—
256C2×C16—1221no—
257C2×C16—2442no—
258#107—611no—
259#107—1221no—
260#107—2442no—
261#107C4×D6111yescharacteristic
262#102—21no—
263#102—1221no—
264#102—1221no—
265#102—1221no—
266#95—2441no—
267C24—611no—
268C24—2441no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—1221no—
272C2×D4—4882no—
273C2×D4—4882no—
274C2×D4—2441no—
275C2×D4—2441no—
276C2×D4—2442no—
277C2×D4—2442no—
278C2×D4—2441no—
279C2×D4—2441no—
280C22×C4—41no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—2441no—
287C22×C4—2441no—
288C22×C4—2441no—
289C22×C4—2441no—
290C22×C4D4×D6111yescharacteristic
291D8—41no—
292D8—2441no—
293D8—2442no—
294C2×C8—41no—
295C2×C8—611no—
296C2×C8—611no—
297C2×C8—1222no—
298C2×C8—1222no—
299C2×C8—1222no—
300C2×C8—2441no—
301C2×C8—2441no—
302C2×C8C2×C4×D6111yescharacteristic
303C2×C8D4×D6111yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—1221no—
308C4⋊C4—2441no—
309C4⋊C4—2441no—
310C4⋊C4—2441no—
311C22⋊C4—41no—
312C22⋊C4—4882no—
313C22⋊C4—2441no—
314C22⋊C4—2441no—
315C22⋊C4—2441no—
316C16—41no—
317C16—2441no—
318C23—41no—
319C23—611no—
320C23—611no—
321C23—612no—
322C23—612no—
323C23—4882no—
324C23—4882no—
325C23—4882no—
326C23—2441no—
327C23—2441no—
328C23—2441no—
329C23D8×D6111yescharacteristic
330D4—41no—
331D4—41no—
332D4—81no—
333D4—81no—
334D4—4882no—
335D4—4882no—
336D4—4882no—
337D4—4881no—
338D4—4881no—
339D4—2441no—
340D4—2441no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—4882no—
354C2×C4—4881no—
355C2×C4—4881no—
356C2×C4—4881no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4C22⋊C4×D6111yescharacteristic
362C2×C4SD16×D6111yescharacteristic
363C8—21no—
364C8—21no—
365C8—612no—
366C8—1221no—
367C22—21no—
368C22—21no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—612no—
373C22—612no—
374C22—1221no—
375C22—1221no—
376C22—1221no—
377C22—1221no—
378C22—9764no—
379C22—4881no—
380C22—4881no—
381C22—4881no—
382C22—2442no—
383C22—2442no—
384C22#102×D6111yescharacteristic
385C22D16×D6111yescharacteristic
386C22SD32×D6111yescharacteristic
387C4—21no—
388C4—81no—
389C4—161no—
390C4—1221no—
391C4—1221no—
392C4—9761no—
393C4—4881no—
394C4#99×D6111yescharacteristic
395C4#1683977711yescharacteristic
396C2—21no—
397C2—21no—
398C2—161no—
399C2—1222no—
400C2—1222no—
401C2—9761no—
402C2#2144438511yescharacteristic
403C2#357×D6111yescharacteristic
404C2#2144755311yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1347C2
socleC22×C61C2×#102
prime radical#466×D61C2
cosocleC22×C8×C61C23
hypercenter#1347D61
hypocenterC61#11886
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1347

Complements

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

NH ≅ G/Ntype
2. C22⋊C16×D61C2semidirect
3. #21445847C2semidirect
4. #21443829C2semidirect
5. #21443828C2semidirect
6. #21443827C2semidirect
7. C61×#1347C2semidirect
8. C2×D8×D61C4semidirect
12. #16839999C4semidirect
16. #16839995C4semidirect
18. #107×D61C4semidirect
21. C22⋊#11758185C22semidirect
23. #16839525C22semidirect
25. C61×C22⋊C16C22semidirect
26. C61×#340C22semidirect
200. #1347D61semidirect
226. C22⋊C16C2×D61semidirect
228. #340C2×D61semidirect
229. C61#11886semidirect

Maximal subgroups

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

subgroupindex
#466×D612
C22⋊C16×D612
#214458472
#214438292
#214438282
#214438272
C61×#13472
#1188661