Finite Group Databasebeta

← D61×#1327 #29589196

Subgroups — D61×#1327 #29589196

Order 15616.

410 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 91 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#423×D61C211yesmaximal, characteristic
2#349×D61C212yesmaximal
3#21443770C211yesmaximal, characteristic, complemented
4#21443769C212yesmaximal, complemented
5C61×#1327C211yesmaximal, characteristic, complemented
6C2×M16×D61C411yescharacteristic
7C2×M16×D61C2211yescharacteristic
8C2×C42×D61C411yescharacteristic
9M32×D61—22no—
10#16839786C411yescharacteristic
11#16839785C411yescharacteristic
12#16839785C2211yescharacteristic
13#16839784—22no—
14C4⋊C8×D61—22no—
15#16839544C2212yes—
16#16839543—22no—
17C61×#423C2211yescharacteristic
18C61×#349C2212yes—
19C22×C4×D61—21no—
20C22×C4×D61C2×C411yescharacteristic
21C2×#11758194C2×C411yescharacteristic
22C2×#11758194C2×C411yescharacteristic
23C2×#11758189—21no—
24C2×#11758189D412yes—
25M16×D61—41no—
26M16×D61—41no—
27M16×D61—41no—
28M16×D61—41no—
29C2×C8×D61—21no—
30C2×C8×D61D412yes—
31C2×C4×Dic61—21no—
32C2×C4×Dic61C2×C411yescharacteristic
33C42×D61—21no—
34C42×D61—21no—
35C42×D61C811yescharacteristic
36C42×D61C811yescharacteristic
37C42×D61C811yescharacteristic
38C42×D61C811yescharacteristic
39#14519717—22no—
40#14519716—42no—
41C16×D61—42no—
42C4⋊#92418—22no—
43#14519706—22no—
44#14519706—22no—
45C2×M16×C61C2×C411yescharacteristic
46C2×M16×C61C2311yescharacteristic
47C2×C42×C61C2×C411yescharacteristic
48M32×C61—22no—
49C4⋊C8×C61—22no—
50C23×D61M1611yescharacteristic
51C22×C4×C61—21no—
52C22×C4×C61C22×C411yescharacteristic
53C22×Dic61—21no—
54C22×Dic61M1611yescharacteristic
55C2×C4×D61—21no—
56C2×C4×D61—21no—
57C2×C4×D61—21no—
58C2×C4×D61—21no—
59C2×C4×D61—21no—
60C2×C4×D61—21no—
61C2×C4×D61—21no—
62C2×C4×D61—21no—
63C2×C4×D61—44no—
64C2×C4×D61C22⋊C411yescharacteristic
65C2×C4×D61C22⋊C411yescharacteristic
66C2×C4×D61C2×C811yescharacteristic
67C2×C4×D61C2×C811yescharacteristic
68M16×C61—41no—
69M16×C61—41no—
70C2×C8×C61—21no—
71C2×C8×C61C2×D412yes—
72C42×C61—21no—
73C42×C61C2×C811yescharacteristic
74C42×C61C2×C811yescharacteristic
75C4×Dic61—21no—
76C4×Dic61—21no—
77C4×Dic61—21no—
78C4×Dic61—21no—
79C4×Dic61—21no—
80C4×Dic61C2×C811yescharacteristic
81C4×Dic61C2×C811yescharacteristic
82#11758194—41no—
83#11758194—41no—
84C2×#92418—21no—
85C2×#92418C22⋊C412yes—
86#11758189—42no—
87#11758189—42no—
88C8×D61—22no—
89C8×D61—22no—
90C8×D61—41no—
91C8×D61—41no—
92C16×C61—42no—
93#11758185—42no—
94C23×C61C2×M1611yescharacteristic
95C22×D61—21no—
96C22×D61—21no—
97C22×D61—42no—
98C22×D61C22⋊C811yescharacteristic
99C22×D61C22⋊C811yescharacteristic
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—42no—
105C2×C4×C61C2×C22⋊C411yescharacteristic
106C2×C4×C61C22×C811yescharacteristic
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—42no—
112C2×Dic61C22⋊C811yescharacteristic
113C2×Dic61C22⋊C811yescharacteristic
114C4×D61—24no—
115C4×D61—21no—
116C4×D61—21no—
117C4×D61—21no—
118C4×D61—21no—
119C4×D61—21no—
120C4×D61—21no—
121C4×D61—42no—
122C4×D61—42no—
123C4×D61—42no—
124C4×D61#9911yescharacteristic
125C4×D61#9911yescharacteristic
126C4×D61#10111yescharacteristic
127C4×D61#10111yescharacteristic
128C8×C61—22no—
129C8×C61—41no—
130#92418—22no—
131#92418—41no—
132C2×#1327—611nomaximal, Sylow
133C22×C61—21no—
134C22×C61—41no—
135C22×C61C2×C22⋊C811yescharacteristic
136C2×D61—22no—
137C2×D61—21no—
138C2×D61—42no—
139C2×D61—42no—
140C2×D61—41no—
141C2×D61#32411yescharacteristic
142C2×D61#32411yescharacteristic
143C4×C61—22no—
144C4×C61—21no—
145C4×C61—41no—
146C4×C61C2×#9911yescharacteristic
147C4×C61C2×#10111yescharacteristic
148Dic61—22no—
149Dic61—21no—
150Dic61—41no—
151Dic61#32411yescharacteristic
152Dic61#32411yescharacteristic
153C2×#423—611no—
154C2×#349—612no—
155#1327—611no—
156#1327—612no—
157#1327D6111yescharacteristic, direct product factor
158C2×C61—21no—
159C2×C61—41no—
160C2×C61C2×#32411yescharacteristic
161D61—21no—
162D61—41no—
163D61#132712yesdirect product factor
164C22×M16—611no—
165C22×M16—611no—
166C22×C42—611no—
167C2×M32—1222no—
168#423—611no—
169#423—611no—
170#423—611no—
171#423—1222no—
172#423C2×D6111yescharacteristic
173C2×C4⋊C8—1222no—
174#349—612no—
175#349—1222no—
176#349C2×D6112yes—
177C61C2×#132711yescharacteristic, complemented, Sylow
178C23×C4—611no—
179C23×C4—1221no—
180C2×M16—611no—
181C2×M16—612no—
182C2×M16—611no—
183C2×M16—1221no—
184C2×M16—2441no—
185C2×M16—2441no—
186C2×M16—2441no—
187C2×M16—2441no—
188C2×M16C4×D6111yescharacteristic
189C2×M16C22×D6111yescharacteristic
190C22×C8—612no—
191C22×C8—1221no—
192C2×C42—611no—
193C2×C42—611no—
194C2×C42—611no—
195C2×C42—611no—
196C2×C42—611no—
197C2×C42—1221no—
198C2×C42—1221no—
199C2×C42—1221no—
200C2×C42C4×D6111yescharacteristic
201M32—22no—
202M32—1222no—
203M32—2442no—
204C2×C16—2442no—
205C4⋊C8—22no—
206C4⋊C8—1222no—
207C4⋊C8—1222no—
208C4⋊C8—1222no—
209C24—611no—
210C22×C4—21no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—1221no—
217C22×C4—1221no—
218C22×C4—1221no—
219C22×C4—1221no—
220C22×C4—1221no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4—2444no—
226C22×C4C2×C4×D6111yescharacteristic
227M16—41no—
228M16—41no—
229M16—2442no—
230M16—2442no—
231M16—2441no—
232M16—2441no—
233C2×C8—21no—
234C2×C8—612no—
235C2×C8—1222no—
236C2×C8—1222no—
237C2×C8—1221no—
238C2×C8—2441no—
239C2×C8—2441no—
240C2×C8D4×D6112yes—
241C42—21no—
242C42—611no—
243C42—611no—
244C42—1221no—
245C42—1221no—
246C42—1221no—
247C42—1221no—
248C42—1221no—
249C42C8×D6111yescharacteristic
250C42C8×D6111yescharacteristic
251C16—42no—
252C16—2442no—
253C23—611no—
254C23—611no—
255C23—1221no—
256C23—1221no—
257C23—2442no—
258C23M16×D6111yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—611no—
265C2×C4—611no—
266C2×C4—611no—
267C2×C4—611no—
268C2×C4—611no—
269C2×C4—611no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—1224no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—2442no—
282C2×C4—2442no—
283C2×C4—2442no—
284C2×C4—2442no—
285C2×C4C22⋊C4×D6111yescharacteristic
286C2×C4C2×C8×D6111yescharacteristic
287C8—22no—
288C8—41no—
289C8—1222no—
290C8—2441no—
291C22—21no—
292C22—41no—
293C22—611no—
294C22—611no—
295C22—1222no—
296C22—1221no—
297C22—2441no—
298C22—2442no—
299C22—2442no—
300C22C22⋊C8×D6111yescharacteristic
301C4—22no—
302C4—21no—
303C4—41no—
304C4—611no—
305C4—611no—
306C4—1222no—
307C4—1221no—
308C4—2441no—
309C4#99×D6111yescharacteristic
310C4#101×D6111yescharacteristic
311C2—21no—
312C2—41no—
313C2—612no—
314C2—1221no—
315C2—2441no—
316C2#324×D6111yescharacteristic
subgroupG/H
centerC4#99×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×M16C22×D61
FittingC61×#1327C2
socleC2×C61C2×#324
prime radicalC23×D61M16
cosocleC2×M16×C61C23
hypercenter#1327D61
hypocenterC61C2×#1327
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
3. #21443770C2semidirect
4. #21443769C2semidirect
5. C61×#1327C2semidirect
157. #1327D61direct (N × H)
163. D61#1327direct (N × H)
177. C61C2×#1327semidirect

Maximal subgroups

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

subgroupindex
#423×D612
#349×D612
#214437702
#214437692
C61×#13272
C2×#132761