Finite Group Databasebeta

← D61⋊#1327 #30603913

Subgroups — D61⋊#1327 #30603913

Order 15616.

410 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 88 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
1D61⋊#349C212yesmaximal
2#21460766C212yesmaximal, complemented
3#21460765C212yesmaximal, complemented
4#423×D61C211yesmaximal, characteristic
5D61⋊M32—22no—
6#16840659—22no—
7#16840658C2214yes—
8C2×M16×D61C411yescharacteristic
9C2×M16×D61C2211yescharacteristic
10C2×C42×D61C411yescharacteristic
11#16839786C2211yescharacteristic
12#16839785C411yescharacteristic
13#16839785C2211yescharacteristic
14#16839784—22no—
15C4⋊C8×D61—22no—
16C61×#423C411yescharacteristic
17#14519852—42no—
18#14519851—24no—
19D61⋊C16—42no—
20C22×C4×D61—21no—
21C22×C4×D61C2×C411yescharacteristic
22C2×#11758194C2×C411yescharacteristic
23C2×#11758194C2311yescharacteristic
24C2×#11758189—21no—
25C2×#11758189D412yes—
26M16×D61—41no—
27M16×D61—41no—
28M16×D61—41no—
29M16×D61—41no—
30C2×C8×D61—21no—
31C2×C8×D61D412yes—
32C2×C4×Dic61—21no—
33C2×C4×Dic61C2×C411yescharacteristic
34C42×D61—21no—
35C42×D61—21no—
36C42×D61C811yescharacteristic
37C42×D61C811yescharacteristic
38C42×D61C811yescharacteristic
39C42×D61C811yescharacteristic
40C4⋊#92418—22no—
41#14519706—22no—
42#14519706—22no—
43C2×M16×C61C2×C411yescharacteristic
44C2×M16×C61C2×C411yescharacteristic
45C2×C42×C61C2×C411yescharacteristic
46C4⋊C8×C61—22no—
47C23×D61M1611yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61C22×C411yescharacteristic
50C22×Dic61—21no—
51C22×Dic61M1611yescharacteristic
52C2×C4×D61—21no—
53C2×C4×D61—21no—
54C2×C4×D61—21no—
55C2×C4×D61—21no—
56C2×C4×D61—21no—
57C2×C4×D61—21no—
58C2×C4×D61—21no—
59C2×C4×D61—21no—
60C2×C4×D61—44no—
61C2×C4×D61C22⋊C411yescharacteristic
62C2×C4×D61C22⋊C411yescharacteristic
63C2×C4×D61C2×C811yescharacteristic
64C2×C4×D61C2×C811yescharacteristic
65M16×C61—41no—
66M16×C61—41no—
67C2×C8×C61—21no—
68C2×C8×C61C22⋊C412yes—
69C42×C61—21no—
70C42×C61C2×C811yescharacteristic
71C42×C61C2×C811yescharacteristic
72C4×Dic61—21no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C4×Dic61—21no—
76C4×Dic61—21no—
77C4×Dic61C2×C811yescharacteristic
78C4×Dic61C2×C811yescharacteristic
79#11758194—41no—
80#11758194—41no—
81C2×#92418—21no—
82C2×#92418C2×D412yes—
83#11758189—42no—
84#11758189—42no—
85C8×D61—22no—
86C8×D61—22no—
87C8×D61—41no—
88C8×D61—41no—
89#11758187—44no—
90C23×C61C2×M1611yescharacteristic
91C22×D61—21no—
92C22×D61—21no—
93C22×D61—42no—
94C22×D61C22⋊C811yescharacteristic
95C22×D61C22⋊C811yescharacteristic
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—42no—
101C2×C4×C61C2×C22⋊C411yescharacteristic
102C2×C4×C61C22×C811yescharacteristic
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—42no—
108C2×Dic61C22⋊C811yescharacteristic
109C2×Dic61C22⋊C811yescharacteristic
110C4×D61—24no—
111C4×D61—21no—
112C4×D61—21no—
113C4×D61—21no—
114C4×D61—21no—
115C4×D61—21no—
116C4×D61—21no—
117C4×D61—42no—
118C4×D61—42no—
119C4×D61—42no—
120C4×D61#9911yescharacteristic
121C4×D61#9911yescharacteristic
122C4×D61#10111yescharacteristic
123C4×D61#10111yescharacteristic
124C8×C61—22no—
125C8×C61—41no—
126#92418—22no—
127#92418—41no—
128C2×#1327—611nomaximal, Sylow
129C22×C61—21no—
130C22×C61—41no—
131C22×C61C2×C22⋊C811yescharacteristic
132C2×D61—22no—
133C2×D61—21no—
134C2×D61—42no—
135C2×D61—42no—
136C2×D61—41no—
137C2×D61#32411yescharacteristic
138C2×D61#32411yescharacteristic
139C4×C61—22no—
140C4×C61—21no—
141C4×C61—41no—
142C4×C61C2×#9911yescharacteristic
143C4×C61C2×#10111yescharacteristic
144Dic61—22no—
145Dic61—21no—
146Dic61—41no—
147Dic61#32411yescharacteristic
148Dic61#32411yescharacteristic
149C2×#423—611no—
150C2×#349—612no—
151#1327—612no—
152#1327—612no—
153C2×C61—21no—
154C2×C61—41no—
155C2×C61C2×#32411yescharacteristic
156D61—21no—
157D61—41no—
158D61#132712yescomplemented
159C22×M16—611no—
160C22×M16—611no—
161C22×C42—611no—
162C2×M32—1222no—
163#423—611no—
164#423—611no—
165#423—611no—
166#423—1222no—
167#423#692311yescharacteristic
168C2×C4⋊C8—1222no—
169#349—614no—
170#349—1222no—
171C61C2×#132711yescharacteristic, complemented, Sylow
172C23×C4—611no—
173C23×C4—1221no—
174C2×M16—611no—
175C2×M16—612no—
176C2×M16—611no—
177C2×M16—1221no—
178C2×M16—2441no—
179C2×M16—2441no—
180C2×M16—2441no—
181C2×M16—2441no—
182C2×M16C2×#692311yescharacteristic
183C2×M16C2×#692311yescharacteristic
184C22×C8—612no—
185C22×C8—1221no—
186C2×C42—611no—
187C2×C42—611no—
188C2×C42—611no—
189C2×C42—611no—
190C2×C42—611no—
191C2×C42—1221no—
192C2×C42—1221no—
193C2×C42—1221no—
194C2×C42C2×#692311yescharacteristic
195M32—1224no—
196M32—2442no—
197C2×C16—2442no—
198C4⋊C8—22no—
199C4⋊C8—1222no—
200C4⋊C8—1222no—
201C4⋊C8—1222no—
202C24—611no—
203C22×C4—21no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—611no—
209C22×C4—1221no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4—1221no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4—1221no—
217C22×C4—1221no—
218C22×C4—2444no—
219C22×C4C22×#692311yescharacteristic
220M16—41no—
221M16—41no—
222M16—2442no—
223M16—2442no—
224M16—2441no—
225M16—2441no—
226C2×C8—21no—
227C2×C8—612no—
228C2×C8—1222no—
229C2×C8—1222no—
230C2×C8—1221no—
231C2×C8—2441no—
232C2×C8—2441no—
233C2×C8C22⋊#692312yes—
234C42—21no—
235C42—611no—
236C42—611no—
237C42—1221no—
238C42—1221no—
239C42—1221no—
240C42—1221no—
241C42—1221no—
242C42D61⋊C811yescharacteristic
243C42D61⋊C811yescharacteristic
244C16—2444no—
245C23—611no—
246C23—611no—
247C23—1221no—
248C23—1221no—
249C23—2442no—
250C23D61⋊M1611yescharacteristic
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—611no—
257C2×C4—611no—
258C2×C4—611no—
259C2×C4—611no—
260C2×C4—611no—
261C2×C4—611no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1224no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—2442no—
274C2×C4—2442no—
275C2×C4—2442no—
276C2×C4—2442no—
277C2×C4C2×C22⋊#692311yescharacteristic
278C2×C4C2×D61⋊C811yescharacteristic
279C8—22no—
280C8—41no—
281C8—1222no—
282C8—2441no—
283C22—21no—
284C22—41no—
285C22—611no—
286C22—611no—
287C22—1222no—
288C22—1221no—
289C22—2441no—
290C22—2442no—
291C22—2442no—
292C22D61⋊(C22⋊C8)11yescharacteristic
293C4—22no—
294C4—21no—
295C4—41no—
296C4—611no—
297C4—611no—
298C4—1222no—
299C4—1221no—
300C4—2441no—
301C4D61⋊#9911yescharacteristic
302C4D61⋊#10111yescharacteristic
303C2—21no—
304C2—41no—
305C2—612no—
306C2—1221no—
307C2—2441no—
308C2D61⋊#32411yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#423C4
socleC2×C61C2×#324
prime radicalC23×D61M16
cosocleC2×#11758194C23
hypercenter#423#6923
hypocenterC61C2×#1327
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #21460766C2semidirect
3. #21460765C2semidirect
158. D61#1327semidirect
171. C61C2×#1327semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3492
#214607662
#214607652
#423×D612
C2×#132761