Finite Group Databasebeta

← #29590248

Subgroups — #29590248

Order 15616.

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

normal subgroups only

This group has 508 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#466×D61C211yesmaximal, characteristic
2#21447428C211yesmaximal, characteristic, complemented
3#21445534C211yesmaximal, 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×#14519735—21no—
12C2×#14519716—21no—
13#16839999C411yescharacteristic, complemented
14#16839998C2211yescharacteristic
15#16839997—21no—
16#16839996—21no—
17#16839995C411yescharacteristic, complemented
18#107×D61C411yescharacteristic, complemented
19#102×D61—21no—
20C22⋊#11758185C2211yescharacteristic, complemented
21#16839541—21no—
22#16839525C2211yescharacteristic, complemented
23#16839524—21no—
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—
44#14519735—24no—
45#14519735—42no—
46C2×C4⋊Dic61—21no—
47C4⋊C4×D61—21no—
48C2×#11758198—41no—
49C22⋊C4×D61—41no—
50C2×C4×Dic61—41no—
51#14519716—42no—
52C2×#11758185—21no—
53#14519711C2×C411yescharacteristic
54#14519710—21no—
55#14519699—21no—
56#14519698—21no—
57#14519697—21no—
58C2×D8×C61C2×C411yescharacteristic
59C22×C8×C61C2311yescharacteristic
60#121×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C16×C61—21no—
63#107×C61C2×C411yescharacteristic
64#102×C61—21no—
65C23×D61—41no—
66C23×D61D811yescharacteristic
67C2×D4×C61—21no—
68C2×D4×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61C2×D411yescharacteristic
71C2×C22⋊D61—41no—
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C22×Dic61—41no—
75C22×Dic61D811yescharacteristic
76D4×D61—42no—
77D4×D61—42no—
78D4×D61—82no—
79D4×D61—82no—
80C2×D244—21no—
81C2×D244—41no—
82C2×C4×D61—22no—
83C2×C4×D61—22no—
84C2×C4×D61—41no—
85C2×C4×D61C22⋊C411yescharacteristic
86C2×C4×D61C22⋊C411yescharacteristic
87C2×C4×D61SD1611yescharacteristic
88C2×C4×D61SD1611yescharacteristic
89D8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61C22×C411yescharacteristic
92C2×C8×C61C2×D411yescharacteristic
93C4⋊C4×C61—22no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊Dic61—41no—
98#11758199—42no—
99#11758198—44no—
100#11758198—41no—
101#11758198—41no—
102C4⋊Dic61—22no—
103C4⋊Dic61—21no—
104C4⋊Dic61—41no—
105#11758196—41no—
106C4×Dic61—44no—
107C2×#92418—41no—
108C2×#92418C22⋊C411yescharacteristic
109C2×#92418C22⋊C411yescharacteristic
110D488—41no—
111C8×D61—22no—
112C8×D61—22no—
113C8×D61—41no—
114C8×D61—41no—
115C16×C61—41no—
116#11758185—41no—
117C23×C61—41no—
118C23×C61C2×D811yescharacteristic
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—22no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—82no—
125C22×D61—82no—
126C22×D61—82no—
127C22×D61#10211yescharacteristic
128C22×D61#10211yescharacteristic
129D4×C61—41no—
130D4×C61—41no—
131D4×C61—81no—
132D4×C61—81no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—42no—
136C2×C4×C61—41no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61C2×C22⋊C411yescharacteristic
140C2×C4×C61C2×SD1611yescharacteristic
141C22⋊D61—82no—
142C22⋊D61—81no—
143C22⋊D61—81no—
144C22⋊D61—82no—
145C2×Dic61—22no—
146C2×Dic61—42no—
147C2×Dic61—41no—
148C2×Dic61—81no—
149C2×Dic61—81no—
150C2×Dic61#10211yescharacteristic
151C2×Dic61#10211yescharacteristic
152D244—41no—
153D244—41no—
154D244—82no—
155C4×D61—22no—
156C4×D61—21no—
157C4×D61—21no—
158C4×D61—22no—
159C4×D61—82no—
160C4×D61#9912yes—
161C4×D61#10412yes—
162C8×C61—21no—
163C8×C61—21no—
164#92418—21no—
165#92418—21no—
166#11705—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61C2×#10211yescharacteristic
173C22×C61#50911yescharacteristic
174C22×C61#50911yescharacteristic
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—42no—
181C2×D61—42no—
182C2×D61—81no—
183C2×D61—81no—
184C2×D61—81no—
185C2×D61—164no—
186C2×D61#32712yes—
187C4×C61—21no—
188C4×C61—82no—
189C4×C61—81no—
190C4×C61C2×#9911yescharacteristic
191C4×C61C2×#10411yescharacteristic
192Dic61—21no—
193Dic61—82no—
194Dic61—81no—
195Dic61#32712yes—
196C2×#466—611no—
197#2112—611no—
198#1735—611no—
199#1347—611no—
200#1347—611no—
201#1347—611no—
202#1347D6111yescharacteristic, complemented
203C2×C61—21no—
204C2×C61—21no—
205C2×C61—161no—
206C2×C61C2×#32711yescharacteristic
207C2×C61#214011yescharacteristic
208C2×C61#214511yescharacteristic
209D61—22no—
210D61—41no—
211D61—161no—
212C22×D8—611no—
213C23×C8—611no—
214C2×#121—1221no—
215C2×#117—1221no—
216C2×M32—1221no—
217#466—611no—
218#466—611no—
219#466—611no—
220#466—1221no—
221#466—1221no—
222#466C2×D6111yescharacteristic
223C2×#107—611no—
224C2×#102—1221no—
225C22⋊C16—611no—
226C22⋊C16—1221no—
227C22⋊C16C2×D6111yescharacteristic, complemented
228#340—611no—
229#340—1221no—
230#340C2×D6111yescharacteristic, complemented
231C61#1170511yescharacteristic, complemented, Sylow
232C22×D4—1221no—
233C22×D4—2441no—
234C23×C4—611no—
235C2×D8—611no—
236C2×D8—1221no—
237C2×D8—2442no—
238C2×D8C4×D6111yescharacteristic
239C22×C8—611no—
240C22×C8—611no—
241C22×C8—611no—
242C22×C8—611no—
243C22×C8—611no—
244C22×C8—2442no—
245C22×C8C22×D6111yescharacteristic
246#121—21no—
247#121—1221no—
248#121—1221no—
249#121—1221no—
250#121—2441no—
251#121—2441no—
252#117—1224no—
253#117—2442no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C22⋊C4—2441no—
258C2×C22⋊C4—2441no—
259C2×C42—2441no—
260M32—2442no—
261C2×C16—21no—
262C2×C16—1221no—
263#107—611no—
264#107—1221no—
265#107C4×D6111yescharacteristic
266#102—21no—
267#102—1221no—
268#102—1221no—
269#102—1221no—
270C24—611no—
271C24—2441no—
272C2×D4—21no—
273C2×D4—41no—
274C2×D4—1221no—
275C2×D4—4882no—
276C2×D4—4882no—
277C2×D4—2441no—
278C2×D4—2442no—
279C2×D4—2442no—
280C2×D4—2441no—
281C2×D4—2441no—
282C2×D4—2441no—
283C22×C4—41no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—1222no—
290C22×C4—1222no—
291C22×C4—2441no—
292C22×C4—2441no—
293C22×C4D4×D6111yescharacteristic
294D8—41no—
295D8—2441no—
296D8—2442no—
297C2×C8—41no—
298C2×C8—611no—
299C2×C8—611no—
300C2×C8—1222no—
301C2×C8—1222no—
302C2×C8—2441no—
303C2×C8—2441no—
304C2×C8—2441no—
305C2×C8C2×C4×D6111yescharacteristic
306C2×C8D4×D6111yescharacteristic
307C4⋊C4—22no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—1222no—
311C4⋊C4—1221no—
312C4⋊C4—2441no—
313C4⋊C4—2441no—
314C22⋊C4—41no—
315C22⋊C4—2441no—
316C22⋊C4—2444no—
317C22⋊C4—2441no—
318C22⋊C4—2441no—
319C42—2444no—
320C16—41no—
321C16—2441no—
322C23—41no—
323C23—611no—
324C23—611no—
325C23—1222no—
326C23—1221no—
327C23—1221no—
328C23—4882no—
329C23—4882no—
330C23—4882no—
331C23—2441no—
332C23—2441no—
333C23D8×D6111yescharacteristic
334D4—41no—
335D4—41no—
336D4—81no—
337D4—81no—
338D4—4882no—
339D4—4882no—
340D4—4882no—
341D4—4881no—
342D4—4881no—
343D4—2441no—
344D4—2441no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—611no—
352C2×C4—612no—
353C2×C4—612no—
354C2×C4—611no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—4882no—
361C2×C4—4881no—
362C2×C4—4881no—
363C2×C4—2442no—
364C2×C4—2441no—
365C2×C4C22⋊C4×D6111yescharacteristic
366C2×C4SD16×D6111yescharacteristic
367C8—21no—
368C8—21no—
369C8—1221no—
370C8—1221no—
371C22—21no—
372C22—21no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—612no—
377C22—1221no—
378C22—1221no—
379C22—1221no—
380C22—1221no—
381C22—1221no—
382C22—9764no—
383C22—4881no—
384C22—4881no—
385C22—4881no—
386C22—2442no—
387C22—2442no—
388C22#102×D6111yescharacteristic
389C22#1684019611yescharacteristic
390C22#1684019911yescharacteristic
391C4—21no—
392C4—82no—
393C4—81no—
394C4—612no—
395C4—1221no—
396C4—4882no—
397C4—4881no—
398C4#99×D6111yescharacteristic
399C4#104×D6111yescharacteristic
400C2—21no—
401C2—21no—
402C2—161no—
403C2—1222no—
404C2—9761no—
405C2—2441no—
406C2#327×D6111yescharacteristic
407C2#2144753311yescharacteristic
408C2#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#11705
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. #21447428C2semidirect
3. #21445534C2semidirect
4. #21443829C2semidirect
5. #21443828C2semidirect
6. #21443827C2semidirect
7. C61×#1347C2semidirect
8. C2×D8×D61C4semidirect
13. #16839999C4semidirect
17. #16839995C4semidirect
18. #107×D61C4semidirect
20. C22⋊#11758185C22semidirect
22. #16839525C22semidirect
25. C61×C22⋊C16C22semidirect
26. C61×#340C22semidirect
202. #1347D61semidirect
227. C22⋊C16C2×D61semidirect
230. #340C2×D61semidirect
231. C61#11705semidirect

Maximal subgroups

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

subgroupindex
#466×D612
#214474282
#214455342
#214438292
#214438282
#214438272
C61×#13472
#1170561