Finite Group Databasebeta

← #29589734

Subgroups — #29589734

Order 15616.

414 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 105 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#436×D61C211yesmaximal, characteristic
2#21447573C211yesmaximal, characteristic, complemented
3#21447412C211yesmaximal, characteristic, complemented
4#21443778C211yesmaximal, characteristic, complemented
5#21443777C211yesmaximal, characteristic, complemented
6#21443776C211yesmaximal, characteristic, complemented
7C61×#1330C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C4×D4×D61C411yescharacteristic
10C2×#14519716—21no—
11C2×#14519716—21no—
12#16839841C2211yescharacteristic
13#16839840C411yescharacteristic
14#16839839C411yescharacteristic
15#16839838—21no—
16#16839837—21no—
17C4⋊C8×D61C411yescharacteristic
18C22⋊C8×D61—21no—
19C4×C8×D61C2211yescharacteristic
20C4⋊#11758185C2211yescharacteristic, complemented
21#16839580—21no—
22#16839538C2211yescharacteristic, complemented
23C16×Dic61—21no—
24C61×#436C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic, complemented
26C61×#346C2211yescharacteristic, complemented
27C2×D4×D61C811yescharacteristic
28C22×C4×D61—21no—
29C2×#11758194—21no—
30C2×#11758189—21no—
31C2×#11758189—21no—
32M16×D61—42no—
33M16×D61—42no—
34C2×C8×D61—21no—
35C2×C8×D61D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37C4×D244C2×C411yescharacteristic
38D4×Dic61C811yescharacteristic
39#14519739C811yescharacteristic
40C4×C22⋊D61—21no—
41#14519737—21no—
42C4⋊C4×D61C811yescharacteristic
43C22⋊C4×D61—21no—
44C42×D61C2×C411yescharacteristic
45#14519716—24no—
46#14519716—42no—
47C2×#11758185—21no—
48C2×#11758185—21no—
49C4⋊#92418C2×C411yescharacteristic
50#14519706—21no—
51C22⋊#92418—21no—
52#14519689—21no—
53#14519689—21no—
54C4×#92418C2×C411yescharacteristic
55C8×Dic61D411yescharacteristic
56C8×Dic61D411yescharacteristic
57C2×M16×C61—21no—
58C4×D4×C61C2×C411yescharacteristic
59C2×C16×C61—21no—
60C2×C16×C61—21no—
61C4⋊C8×C61C2×C411yescharacteristic
62C22⋊C8×C61—21no—
63C4×C8×C61C2311yescharacteristic
64C23×D61—21no—
65C2×D4×C61C2×C811yescharacteristic
66C22×C4×C61—21no—
67C2×C22⋊D61—21no—
68C22×Dic61—21no—
69D4×D61—42no—
70C2×D244C2×C811yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—42no—
75C2×C4×D61—42no—
76C2×C4×D61C22⋊C411yescharacteristic
77C2×C4×D61C2×C811yescharacteristic
78C2×C4×D61M1611yescharacteristic
79M16×C61—41no—
80M16×C61—41no—
81C2×C8×C61—21no—
82C2×C8×C61C2×D411yescharacteristic
83C2×C8×C61C2×D411yescharacteristic
84C4⋊C4×C61C2×C811yescharacteristic
85C22⋊C4×C61—21no—
86C42×C61C22×C411yescharacteristic
87C22⋊Dic61—21no—
88#11758198—21no—
89#11758198—21no—
90C4⋊Dic61C2×C811yescharacteristic
91#11758196—21no—
92C4×Dic61C22⋊C411yescharacteristic
93C4×Dic61C2×C811yescharacteristic
94C4×Dic61M1611yescharacteristic
95#11758194—42no—
96C2×#92418—21no—
97C2×#92418C22⋊C411yescharacteristic
98C2×#92418C22⋊C411yescharacteristic
99#11758189—41no—
100#11758189—41no—
101#11758189—42no—
102C8×D61—22no—
103C8×D61—42no—
104C8×D61D812yes—
105C8×D61SD1612yes—
106C16×C61—22no—
107C16×C61—41no—
108#11758185—22no—
109#11758185—41no—
110C23×C61—21no—
111C22×D61—21no—
112C22×D61—42no—
113C22×D61—42no—
114C22×D61—42no—
115C22×D61C22⋊C811yescharacteristic
116D4×C61—41no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61C2×C22⋊C411yescharacteristic
121C2×C4×C61C22×C811yescharacteristic
122C2×C4×C61C2×M1611yescharacteristic
123C22⋊D61—42no—
124C2×Dic61—21no—
125C2×Dic61—42no—
126C2×Dic61C22⋊C811yescharacteristic
127C2×Dic61C22⋊C811yescharacteristic
128C2×Dic61C22⋊C811yescharacteristic
129D244—41no—
130C4×D61—22no—
131C4×D61—41no—
132C4×D61—42no—
133C4×D61—41no—
134C4×D61—41no—
135C4×D61—42no—
136C4×D61#10212yes—
137C4×D61#10412yes—
138C8×C61—21no—
139C8×C61—41no—
140C8×C61C2×D811yescharacteristic
141C8×C61C2×SD1611yescharacteristic
142#92418—21no—
143#92418—41no—
144#92418#10212yes—
145#11587—611nomaximal, Sylow
146C22×C61—41no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61C2×C22⋊C811yescharacteristic
150C2×D61—21no—
151C2×D61—21no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—84no—
156C2×D61D4⋊C812yes—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—41no—
160C4×C61C2×#10211yescharacteristic
161C4×C61C2×#10411yescharacteristic
162Dic61—21no—
163Dic61—41no—
164Dic61D4⋊C812yes—
165Dic61#34912yes—
166C2×#436—611no—
167#2150—611no—
168C4×M32—611no—
169#1330—611no—
170#1330—611no—
171#1330—611no—
172#1330D6111yescharacteristic, complemented
173C2×C61—81no—
174C2×C61C2×D4⋊C811yescharacteristic
175C2×C61C2×#34911yescharacteristic
176C2×C61#211711yescharacteristic
177D61—22no—
178D61—81no—
179C22×M16—1221no—
180C2×C4×D4—611no—
181C2×M32—1221no—
182C2×M32—1221no—
183#436—611no—
184#436—611no—
185#436—611no—
186#436—1221no—
187#436—1221no—
188#436C2×D6111yescharacteristic
189C2×C4⋊C8—611no—
190C2×C22⋊C8—1221no—
191C2×C4×C8—611no—
192C4⋊C16—611no—
193C4⋊C16—1221no—
194C4⋊C16C2×D6111yescharacteristic, complemented
195#346—611no—
196#346C2×D6111yescharacteristic, complemented
197C4×C16—1221no—
198C61#1158711yescharacteristic, complemented, Sylow
199C22×D4—611no—
200C23×C4—1221no—
201C2×M16—21no—
202C2×M16—1221no—
203C2×M16—1221no—
204C2×M16—1221no—
205C2×M16—2442no—
206C2×M16—2442no—
207C22×C8—611no—
208C22×C8—611no—
209C22×C8—1221no—
210C4×D4—611no—
211C4×D4—611no—
212C4×D4—611no—
213C4×D4—1221no—
214C4×D4—1221no—
215C4×D4C4×D6111yescharacteristic
216C2×C4⋊C4—611no—
217C2×C22⋊C4—1221no—
218C2×C42—611no—
219M32—1224no—
220M32—2442no—
221C2×C16—21no—
222C2×C16—21no—
223C2×C16—1221no—
224C2×C16—1221no—
225C4⋊C8—611no—
226C4⋊C8—1221no—
227C4⋊C8C4×D6111yescharacteristic
228C22⋊C8—21no—
229C22⋊C8—1221no—
230C22⋊C8—1221no—
231C22⋊C8—1221no—
232C4×C8—611no—
233C4×C8—611no—
234C4×C8—611no—
235C4×C8C22×D6111yescharacteristic
236C24—1221no—
237C2×D4—611no—
238C2×D4—1221no—
239C2×D4—2442no—
240C2×D4C8×D6111yescharacteristic
241C22×C4—21no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—2442no—
250C22×C4—2442no—
251M16—41no—
252M16—41no—
253M16—2442no—
254M16—2442no—
255M16—2441no—
256M16—2441no—
257C2×C8—21no—
258C2×C8—611no—
259C2×C8—612no—
260C2×C8—612no—
261C2×C8—611no—
262C2×C8—1222no—
263C2×C8—1221no—
264C2×C8—2442no—
265C2×C8D4×D6111yescharacteristic
266C2×C8D4×D6111yescharacteristic
267C4⋊C4—611no—
268C4⋊C4—1221no—
269C4⋊C4C8×D6111yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—1221no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C42—611no—
275C42—611no—
276C42—611no—
277C42C2×C4×D6111yescharacteristic
278C16—22no—
279C16—41no—
280C16—1222no—
281C16—2441no—
282C23—21no—
283C23—611no—
284C23—1221no—
285C23—2442no—
286C23—2442no—
287C23—2442no—
288D4—41no—
289D4—2441no—
290D4—2442no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—611no—
295C2×C4—611no—
296C2×C4—612no—
297C2×C4—612no—
298C2×C4—611no—
299C2×C4—1222no—
300C2×C4—1221no—
301C2×C4—2441no—
302C2×C4—2442no—
303C2×C4—2442no—
304C2×C4—2442no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4C22⋊C4×D6111yescharacteristic
308C2×C4C2×C8×D6111yescharacteristic
309C2×C4M16×D6111yescharacteristic
310C8—21no—
311C8—41no—
312C8—612no—
313C8—1221no—
314C8—2441no—
315C8D8×D6111yescharacteristic
316C8SD16×D6111yescharacteristic
317C22—41no—
318C22—41no—
319C22—41no—
320C22—612no—
321C22—1221no—
322C22—1221no—
323C22—4884no—
324C22—2441no—
325C22—2441no—
326C22—2441no—
327C22C22⋊C8×D6111yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—612no—
332C4—612no—
333C4—1221no—
334C4—2441no—
335C4#102×D6111yescharacteristic
336C4#104×D6111yescharacteristic
337C2—81no—
338C2—1222no—
339C2—4881no—
340C2D4⋊C8×D6111yescharacteristic
341C2#349×D6111yescharacteristic
342C2#2144744511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC4×C8C22×D61
FittingC61×#1330C2
socleC22×C61C2×C22⋊C8
prime radicalC2×D4×D61C8
cosocleC4×C8×C61C23
hypercenter#1330D61
hypocenterC61#11587
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #21447573C2semidirect
3. #21447412C2semidirect
4. #21443778C2semidirect
5. #21443777C2semidirect
6. #21443776C2semidirect
7. C61×#1330C2semidirect
20. C4⋊#11758185C22semidirect
22. #16839538C22semidirect
25. C61×C4⋊C16C22semidirect
26. C61×#346C22semidirect
172. #1330D61semidirect
194. C4⋊C16C2×D61semidirect
196. #346C2×D61semidirect
198. C61#11587semidirect

Maximal subgroups

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

subgroupindex
#436×D612
#214475732
#214474122
#214437782
#214437772
#214437762
C61×#13302
#1158761