Finite Group Databasebeta

← D61×#1411 #29600339

Subgroups — D61×#1411 #29600339

Order 15616.

398 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 61 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#494×D61C211yesmaximal, characteristic
2#356×D61C212yesmaximal
3#21443988C211yesmaximal, characteristic, complemented
4#21443987C212yesmaximal, complemented
5C61×#1411C211yesmaximal, characteristic, complemented
6C2×Q16×D61—22no—
7C4⋊Q8×D61C411yescharacteristic
8C4⋊Q8×D61C2211yescharacteristic
9#16840142C411yescharacteristic
10#16840141C411yescharacteristic
11#16840141C2211yescharacteristic
12#16840140—22no—
13#101×D61—22no—
14C4×C8×D61C411yescharacteristic
15#16839561C2212yes—
16#16839560—22no—
17C61×#494C2211yescharacteristic
18C61×#356C2212yes—
19C2×Q8×D61—21no—
20C2×Q8×D61D412yes—
21C2×Dic244—22no—
22C2×#11758202—22no—
23C2×#11758202—22no—
24Q16×D61—44no—
25Q16×D61—44no—
26M16×D61—42no—
27C2×C8×D61—21no—
28#14519777C2×C411yescharacteristic
29#14519777C2×C411yescharacteristic
30#14519776—41no—
31#14519776—41no—
32#14519775—21no—
33#14519775D412yes—
34C4⋊C4×D61—41no—
35C4⋊C4×D61—41no—
36C42×D61C2×C411yescharacteristic
37#14519696—22no—
38#14519695—42no—
39C4×#92418C2×C411yescharacteristic
40C8×Dic61—21no—
41C2×Q16×C61—22no—
42C4⋊Q8×C61C2×C411yescharacteristic
43C4⋊Q8×C61C2311yescharacteristic
44#101×C61—22no—
45C4×C8×C61C2×C411yescharacteristic
46C2×Q8×C61—21no—
47C2×Q8×C61C2×D412yes—
48Q8×D61—42no—
49Q8×D61—42no—
50Q8×D61—42no—
51Q8×D61—42no—
52C2×C4×D61—21no—
53C2×C4×D61—22no—
54C2×C4×D61—41no—
55C2×C4×D61C22⋊C411yescharacteristic
56C2×Dic122—21no—
57C2×Dic122—22no—
58C2×Dic122—41no—
59C2×Dic122C22⋊C412yes—
60Q16×C61—44no—
61M16×C61—42no—
62C2×C8×C61—21no—
63C4⋊C4×C61—41no—
64C4⋊C4×C61—41no—
65C42×C61C22×C411yescharacteristic
66#11758202—44no—
67#11758202—44no—
68C4⋊Dic61—41no—
69C4⋊Dic61—41no—
70#11758196—42no—
71#11758196—42no—
72C4×Dic61—21no—
73C4×Dic61C22⋊C411yescharacteristic
74#11758194—42no—
75C2×#92418—21no—
76Dic244—44no—
77#11758189—82no—
78C8×D61—22no—
79C8×D61—22no—
80C8×D61—82no—
81C22×D61#9911yescharacteristic
82Q8×C61—42no—
83Q8×C61—42no—
84C2×C4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61—41no—
87C2×C4×C61C2×C22⋊C411yescharacteristic
88C2×Dic61—21no—
89C2×Dic61—22no—
90C2×Dic61—41no—
91C2×Dic61#9911yescharacteristic
92C4×D61—24no—
93C4×D61—21no—
94C4×D61—21no—
95C4×D61—42no—
96C4×D61—42no—
97C4×D61—81no—
98C4×D61—81no—
99Dic122—42no—
100Dic122—42no—
101Dic122—82no—
102Dic122—82no—
103C8×C61—22no—
104C8×C61—82no—
105#92418—22no—
106#92418—82no—
107C2×#1411—611nomaximal, Sylow
108C22×C61C2×#9911yescharacteristic
109C2×D61—22no—
110C2×D61#35311yescharacteristic
111C2×D61#35311yescharacteristic
112C4×C61—22no—
113C4×C61—21no—
114C4×C61—42no—
115C4×C61—81no—
116Dic61—22no—
117Dic61—21no—
118Dic61—42no—
119Dic61—81no—
120C2×#494—611no—
121C2×#356—612no—
122#1411—611no—
123#1411—612no—
124#1411D6111yescharacteristic, direct product factor
125C2×C61—21no—
126C2×C61C2×#35311yescharacteristic
127D61—21no—
128D61#141112yesdirect product factor
129C22×Q16—1222no—
130C2×C4⋊Q8—611no—
131C2×C4⋊Q8—611no—
132#494—611no—
133#494—611no—
134#494—611no—
135#494—1222no—
136#494C2×D6111yescharacteristic
137C2×#101—1222no—
138C2×C4×C8—611no—
139#356—612no—
140#356—1222no—
141#356C2×D6112yes—
142C61C2×#141111yescharacteristic, complemented, Sylow
143C22×Q8—612no—
144C22×Q8—1221no—
145C2×Q16—22no—
146C2×Q16—1222no—
147C2×Q16—1222no—
148C2×Q16—1222no—
149C2×Q16—2444no—
150C2×Q16—2444no—
151C2×M16—2442no—
152C22×C8—1221no—
153C4⋊Q8—612no—
154C4⋊Q8—611no—
155C4⋊Q8—611no—
156C4⋊Q8—1221no—
157C4⋊Q8—2441no—
158C4⋊Q8—2441no—
159C4⋊Q8C4×D6111yescharacteristic
160C4⋊Q8C22×D6111yescharacteristic
161C2×C4⋊C4—2441no—
162C2×C4⋊C4—2441no—
163C2×C42—611no—
164#101—22no—
165#101—1222no—
166#101—2442no—
167C4×C8—611no—
168C4×C8—1221no—
169C4×C8C4×D6111yescharacteristic
170C2×Q8—21no—
171C2×Q8—612no—
172C2×Q8—1222no—
173C2×Q8—1221no—
174C2×Q8—2441no—
175C2×Q8—2442no—
176C2×Q8—2442no—
177C2×Q8—2442no—
178C2×Q8—2442no—
179C2×Q8D4×D6112yes—
180C22×C4—611no—
181C22×C4—1221no—
182C22×C4—1222no—
183C22×C4—2441no—
184Q16—44no—
185Q16—2444no—
186Q16—2444no—
187Q16—2444no—
188M16—42no—
189M16—4882no—
190M16—2442no—
191C2×C8—21no—
192C2×C8—1222no—
193C2×C8—1222no—
194C2×C8—1221no—
195C2×C8—4882no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—2442no—
199C4⋊C4—2441no—
200C4⋊C4—2441no—
201C4⋊C4—2442no—
202C42—611no—
203C42—1221no—
204C42C2×C4×D6111yescharacteristic
205C23—611no—
206Q8—42no—
207Q8—42no—
208Q8—4882no—
209Q8—4882no—
210Q8—2442no—
211Q8—2442no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—611no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1224no—
219C2×C4—1221no—
220C2×C4—1222no—
221C2×C4—4881no—
222C2×C4—4881no—
223C2×C4—2442no—
224C2×C4—2442no—
225C2×C4—2441no—
226C2×C4C22⋊C4×D6111yescharacteristic
227C8—22no—
228C8—82no—
229C8—1222no—
230C8—4882no—
231C22—611no—
232C22—611no—
233C22—1222no—
234C22#99×D6111yescharacteristic
235C4—22no—
236C4—21no—
237C4—42no—
238C4—81no—
239C4—1222no—
240C4—1221no—
241C4—4881no—
242C4—2442no—
243C2—21no—
244C2—612no—
245C2—1221no—
246C2#353×D6111yescharacteristic
subgroupG/H
centerC2#353×D61
commutatorC42×C61C22×C4
FrattiniC4⋊Q8C22×D61
FittingC61×#1411C2
socleC2×C61C2×#353
prime radicalC22×D61#99
cosocleC4⋊Q8×C61C23
hypercenter#1411D61
hypocenterC61C2×#1411
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #1411

Complements

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

NH ≅ G/Ntype
3. #21443988C2semidirect
4. #21443987C2semidirect
5. C61×#1411C2semidirect
124. #1411D61direct (N × H)
128. D61#1411direct (N × H)
142. C61C2×#1411semidirect

Maximal subgroups

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

subgroupindex
#494×D612
#356×D612
#214439882
#214439872
C61×#14112
C2×#141161