Finite Group Databasebeta

← #29590240

Subgroups — #29590240

Order 15616.

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

normal subgroups only

This group has 466 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#21455402C211yesmaximal, characteristic
2C22⋊C16×D61C211yesmaximal, characteristic, complemented
3#21445534C211yesmaximal, characteristic, complemented
4#21443831C211yesmaximal, characteristic, complemented
5#21443829C211yesmaximal, characteristic, complemented
6#21443827C211yesmaximal, characteristic, complemented
7C61×#1348C211yesmaximal, characteristic, complemented
8C2×#14519800C411yescharacteristic, complemented
9C22×C8×D61C2211yescharacteristic
10#16840275—21no—
11C2×#14519735—21no—
12C2×C16×D61—21no—
13#16840000C411yescharacteristic, complemented
14#16839999C411yescharacteristic, complemented
15#16839998C2211yescharacteristic
16#16839994—21no—
17#16839993—21no—
18#16839799C411yescharacteristic, complemented
19#16839757—21no—
20C22⋊#11758185C2211yescharacteristic
21#16839541—21no—
22#16839525C2211yescharacteristic
23#16839524—21no—
24C61×#467C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×#340C2211yescharacteristic
27C2×#11758226—21no—
28C22×C4×D61D411yescharacteristic
29#14519800—42no—
30C2×#11758201—21no—
31C2×D488C2×C411yescharacteristic
32C22×#92418D411yescharacteristic
33C2×C8×D61—42no—
34C2×C8×D61C2×C411yescharacteristic
35C2×C8×D61C2×C411yescharacteristic
36C2×C8×D61D411yescharacteristic
37C2×C8×D61D411yescharacteristic
38#14519762—41no—
39#14519753—21no—
40#14519752—21no—
41#14519751—21no—
42#14519747—41no—
43#14519739—41no—
44#14519737—41no—
45#14519735—24no—
46#14519735—21no—
47#14519735—42no—
48C2×C4⋊Dic61—21no—
49C2×#11758198—41no—
50C2×C4×Dic61—41no—
51C2×#11758185—21no—
52C16×D61—42no—
53#14519711C2×C411yescharacteristic
54#14519708—21no—
55#14519701—21no—
56#14519699—21no—
57#14519697—21no—
58C2×Q16×C61C2×C411yescharacteristic
59C22×C8×C61C2311yescharacteristic
60C22⋊Q8×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C16×C61—21no—
63#107×C61C2×C411yescharacteristic
64#103×C61—21no—
65C23×D61D811yescharacteristic
66C2×Q8×C61—21no—
67C22×C4×C61—41no—
68C22×C4×C61C2×D411yescharacteristic
69C2×C22⋊D61—41no—
70C22×Dic61—41no—
71C22×Dic61D811yescharacteristic
72#11758226—42no—
73#11758226—42no—
74C2×D244—21no—
75C2×D244—41no—
76C2×D244—41no—
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—41no—
80C2×C4×D61C22⋊C411yescharacteristic
81C2×C4×D61C22⋊C411yescharacteristic
82C2×C4×D61SD1611yescharacteristic
83C2×C4×D61SD1611yescharacteristic
84Q16×C61—41no—
85C2×C8×C61—41no—
86C2×C8×C61C22×C411yescharacteristic
87C2×C8×C61C2×D411yescharacteristic
88C4⋊C4×C61—22no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93#11758201—42no—
94#11758198—44no—
95#11758198—41no—
96#11758198—41no—
97#11758198—41no—
98#11758198—41no—
99C4⋊Dic61—22no—
100C4⋊Dic61—21no—
101C4⋊Dic61—41no—
102#11758196—41no—
103C4×Dic61—44no—
104C4×Dic61—41no—
105C2×#92418—41no—
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×C61C2×D811yescharacteristic
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—22no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61#10211yescharacteristic
122C22×D61#10211yescharacteristic
123Q8×C61—41no—
124Q8×C61—41no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—42no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61C2×C22⋊C411yescharacteristic
133C2×C4×C61C2×SD1611yescharacteristic
134C22⋊D61—81no—
135C22⋊D61—81no—
136C2×Dic61—22no—
137C2×Dic61—42no—
138C2×Dic61—41no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61#10211yescharacteristic
142C2×Dic61#10211yescharacteristic
143D244—41no—
144D244—41no—
145D244—82no—
146D244—82no—
147C4×D61—22no—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—22no—
151C4×D61—82no—
152C4×D61#9912yes—
153C4×D61#10412yes—
154C8×C61—21no—
155C8×C61—21no—
156#92418—21no—
157#92418—21no—
158#11703—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61C2×#10211yescharacteristic
162C22×C61#50811yescharacteristic
163C22×C61#50811yescharacteristic
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—42no—
170C2×D61—42no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61#32712yes—
175C4×C61—21no—
176C4×C61—82no—
177C4×C61—81no—
178C4×C61—81no—
179C4×C61C2×#9911yescharacteristic
180C4×C61C2×#10411yescharacteristic
181Dic61—21no—
182Dic61—82no—
183Dic61—81no—
184Dic61#32712yes—
185#3050—611no—
186C2×C22⋊C16—611no—
187#1735—611no—
188#1348—611no—
189#1348D6111yescharacteristic, complemented
190#1347—611no—
191#1347—611no—
192C2×C61—21no—
193C2×C61—21no—
194C2×C61C2×#32711yescharacteristic
195C2×C61#213811yescharacteristic
196C2×C61#214511yescharacteristic
197D61—22no—
198D61—41no—
199D61—161no—
200C2×#135—611no—
201C23×C8—611no—
202#525—1221no—
203C2×#117—1221no—
204C22×C16—1221no—
205#467—611no—
206#467C2×D6111yescharacteristic
207#466—611no—
208#466—611no—
209#465—1221no—
210#465—1221no—
211#427—611no—
212#416—1221no—
213C22⋊C16—611no—
214C22⋊C16—1221no—
215C22⋊C16C2×D6111yescharacteristic
216#340—611no—
217#340—1221no—
218#340C2×D6111yescharacteristic
219C61#1170311yescharacteristic, complemented, Sylow
220C2×#41—1221no—
221C23×C4—611no—
222#135—2442no—
223C2×Q16C4×D6111yescharacteristic
224C2×SD16—1221no—
225C2×D8—611no—
226C22×C8—611no—
227C22×C8—611no—
228C22×C8—611no—
229C22×C8—611no—
230C22×C8—611no—
231C22×C8—2442no—
232C22×C8C22×D6111yescharacteristic
233#123—2441no—
234C22⋊Q8—21no—
235C22⋊Q8—1221no—
236#121—1221no—
237#121—1221no—
238#120—2441no—
239C4×D4—2441no—
240C4×D4—2441no—
241#117—1221no—
242#117—1224no—
243#117—2442no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—1221no—
246C2×C22⋊C4—2441no—
247C2×C42—2441no—
248C2×C16—21no—
249C2×C16—1221no—
250C2×C16—2442no—
251#107—611no—
252#107C4×D6111yescharacteristic
253#106—1221no—
254#103—21no—
255#103—1221no—
256#102—1221no—
257#102—1221no—
258C24—611no—
259#41—2442no—
260#41—2442no—
261C2×Q8—21no—
262C2×D4—1221no—
263C2×D4—2441no—
264C2×D4—2441no—
265C2×D4—2441no—
266C22×C4—41no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—1222no—
273C22×C4—1222no—
274C22×C4—2441no—
275C22×C4—2441no—
276C22×C4D4×D6111yescharacteristic
277Q16—41no—
278SD16—2442no—
279D8—2441no—
280C2×C8—41no—
281C2×C8—611no—
282C2×C8—611no—
283C2×C8—1222no—
284C2×C8—1222no—
285C2×C8—2441no—
286C2×C8—2441no—
287C2×C8—2441no—
288C2×C8C2×C4×D6111yescharacteristic
289C2×C8D4×D6111yescharacteristic
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—1222no—
295C4⋊C4—1221no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C22⋊C4—41no—
299C22⋊C4—2441no—
300C22⋊C4—2441no—
301C22⋊C4—2441no—
302C22⋊C4—2444no—
303C22⋊C4—2441no—
304C42—2441no—
305C42—2444no—
306C16—41no—
307C16—2441no—
308C23—611no—
309C23—611no—
310C23—1222no—
311C23—1221no—
312C23—1221no—
313C23—2441no—
314C23—2441no—
315C23D8×D6111yescharacteristic
316Q8—41no—
317Q8—41no—
318D4—4882no—
319D4—4882no—
320D4—4881no—
321D4—4881no—
322D4—2441no—
323D4—2441no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—611no—
332C2×C4—612no—
333C2×C4—612no—
334C2×C4—611no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—1222no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—4882no—
341C2×C4—4881no—
342C2×C4—4881no—
343C2×C4—2442no—
344C2×C4—2441no—
345C2×C4C22⋊C4×D6111yescharacteristic
346C2×C4SD16×D6111yescharacteristic
347C8—21no—
348C8—21no—
349C8—1221no—
350C8—1221no—
351C22—21no—
352C22—21no—
353C22—612no—
354C22—1221no—
355C22—1221no—
356C22—1221no—
357C22—1221no—
358C22—1221no—
359C22—4881no—
360C22—4881no—
361C22—4881no—
362C22—2442no—
363C22—2442no—
364C22#102×D6111yescharacteristic
365C22#1684019311yescharacteristic
366C22#1684019511yescharacteristic
367C4—21no—
368C4—82no—
369C4—81no—
370C4—81no—
371C4—612no—
372C4—1221no—
373C4—4882no—
374C4—4881no—
375C4#99×D6111yescharacteristic
376C4#104×D6111yescharacteristic
377C2—21no—
378C2—21no—
379C2—1222no—
380C2—9761no—
381C2—2441no—
382C2#327×D6111yescharacteristic
383C2#2144752511yescharacteristic
384C2#2144755311yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1348C2
socleC22×C61C2×#102
prime radical#21455402C2
cosocleC22×C8×C61C23
hypercenter#1348D61
hypocenterC61#11703
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1348

Complements

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

NH ≅ G/Ntype
2. C22⋊C16×D61C2semidirect
3. #21445534C2semidirect
4. #21443831C2semidirect
5. #21443829C2semidirect
6. #21443827C2semidirect
7. C61×#1348C2semidirect
8. C2×#14519800C4semidirect
13. #16840000C4semidirect
14. #16839999C4semidirect
18. #16839799C4semidirect
189. #1348D61semidirect
219. C61#11703semidirect

Maximal subgroups

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

subgroupindex
#214554022
C22⋊C16×D612
#214455342
#214438312
#214438292
#214438272
C61×#13482
#1170361