Finite Group Databasebeta

← D61×#1413 #29600368

Subgroups — D61×#1413 #29600368

Order 15616.

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

normal subgroups only

This group has 314 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#491×D61C211yesmaximal, characteristic
2#356×D61C212yesmaximal
3#21443992C211yesmaximal, characteristic, complemented
4#21443991C212yesmaximal, complemented
5C61×#1413C211yesmaximal, characteristic, complemented
6C4⋊Q8×D61C2211yescharacteristic
7#125×D61C411yescharacteristic
8#16840132C411yescharacteristic
9#16840131C411yescharacteristic
10#16840130C2211yescharacteristic
11#16840129—22no—
12#103×D61—22no—
13#101×D61—22no—
14#97×D61C411yescharacteristic
15#16839561C2212yes—
16#16839560—22no—
17C61×#491C2211yescharacteristic
18C61×#356C2212yes—
19C2×Q8×D61D412yes—
20M16×D61—42no—
21C2×C8×D61—21no—
22#14519777C2×C411yescharacteristic
23#14519776—41no—
24#14519775D412yes—
25#14519769C2×C411yescharacteristic
26#14519768—21no—
27#14519767—41no—
28C4⋊C4×D61—21no—
29C4⋊C4×D61—41no—
30C4⋊C4×D61—41no—
31C42×D61C2×C411yescharacteristic
32#14519702—22no—
33#14519701—22no—
34#14519700—22no—
35#14519696—22no—
36#14519695—42no—
37#14519688C2×C411yescharacteristic
38#14519687—21no—
39C4⋊Q8×C61C2311yescharacteristic
40#125×C61C2×C411yescharacteristic
41#103×C61—22no—
42#101×C61—22no—
43#97×C61C2×C411yescharacteristic
44C2×Q8×C61C2×D412yes—
45Q8×D61—42no—
46Q8×D61—42no—
47C2×C4×D61—22no—
48C2×C4×D61—21no—
49C2×C4×D61—41no—
50C2×C4×D61C22⋊C411yescharacteristic
51C2×Dic122—22no—
52C2×Dic122C22⋊C412yes—
53M16×C61—42no—
54C2×C8×C61—21no—
55C4⋊C4×C61—21no—
56C4⋊C4×C61—41no—
57C4⋊C4×C61—41no—
58C42×C61C22×C411yescharacteristic
59C4⋊Dic61—21no—
60C4⋊Dic61—41no—
61C4⋊Dic61—41no—
62#11758196—42no—
63#11758196—41no—
64#11758196—41no—
65#11758196—41no—
66C4×Dic61—21no—
67C4×Dic61C22⋊C411yescharacteristic
68#11758194—42no—
69C2×#92418—21no—
70#11758189—82no—
71C8×D61—41no—
72C8×D61—41no—
73C8×D61—82no—
74C22×D61#9911yescharacteristic
75Q8×C61—42no—
76C2×C4×C61—22no—
77C2×C4×C61—21no—
78C2×C4×C61—41no—
79C2×C4×C61C2×C22⋊C411yescharacteristic
80C2×Dic61—21no—
81C2×Dic61—22no—
82C2×Dic61—41no—
83C2×Dic61#9911yescharacteristic
84C4×D61—21no—
85C4×D61—21no—
86C4×D61—42no—
87C4×D61—42no—
88C4×D61—42no—
89C4×D61—82no—
90Dic122—42no—
91Dic122—82no—
92C8×C61—41no—
93C8×C61—82no—
94#92418—41no—
95#92418—82no—
96C2×#1413—611nomaximal, Sylow
97C22×C61C2×#9911yescharacteristic
98C2×D61—22no—
99C2×D61#35411yescharacteristic
100C2×D61#35411yescharacteristic
101C4×C61—21no—
102C4×C61—41no—
103C4×C61—42no—
104C4×C61—81no—
105Dic61—21no—
106Dic61—41no—
107Dic61—42no—
108Dic61—81no—
109C2×#491—611no—
110C2×#356—612no—
111#1413—611no—
112#1413—612no—
113#1413D6111yescharacteristic, direct product factor
114C2×C61—21no—
115C2×C61C2×#35411yescharacteristic
116D61—21no—
117D61#141312yesdirect product factor
118C2×C4⋊Q8—611no—
119C2×#125—611no—
120#491—611no—
121#491—611no—
122#491—611no—
123#491—1222no—
124#491C2×D6111yescharacteristic
125C2×#103—1222no—
126C2×#101—1222no—
127C2×#97—611no—
128#356—612no—
129#356—1222no—
130#356C2×D6112yes—
131C61C2×#141311yescharacteristic, complemented, Sylow
132C22×Q8—612no—
133C2×M16—2442no—
134C22×C8—1221no—
135C4⋊Q8—612no—
136C4⋊Q8—611no—
137C4⋊Q8—2441no—
138C4⋊Q8C22×D6111yescharacteristic
139#125—611no—
140#125—1221no—
141#125—2441no—
142#125C4×D6111yescharacteristic
143C2×C4⋊C4—1221no—
144C2×C4⋊C4—2441no—
145C2×C4⋊C4—2441no—
146C2×C42—611no—
147#103—22no—
148#103—1222no—
149#103—1222no—
150#103—1222no—
151#101—22no—
152#101—1222no—
153#101—2442no—
154#97—611no—
155#97—1221no—
156#97C4×D6111yescharacteristic
157C2×Q8—612no—
158C2×Q8—1222no—
159C2×Q8—2442no—
160C2×Q8—2442no—
161C2×Q8D4×D6112yes—
162C22×C4—611no—
163C22×C4—1221no—
164C22×C4—1222no—
165C22×C4—2441no—
166M16—42no—
167M16—4882no—
168M16—2442no—
169C2×C8—21no—
170C2×C8—1221no—
171C2×C8—4882no—
172C2×C8—2441no—
173C2×C8—2441no—
174C4⋊C4—21no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—1221no—
178C4⋊C4—2442no—
179C4⋊C4—2441no—
180C4⋊C4—2441no—
181C4⋊C4—2441no—
182C4⋊C4—2441no—
183C4⋊C4—2441no—
184C42—611no—
185C42—1221no—
186C42C2×C4×D6111yescharacteristic
187C23—611no—
188Q8—42no—
189Q8—4882no—
190Q8—2442no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—611no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1222no—
199C2×C4—4882no—
200C2×C4—2442no—
201C2×C4—2442no—
202C2×C4—2442no—
203C2×C4—2441no—
204C2×C4C22⋊C4×D6111yescharacteristic
205C8—41no—
206C8—82no—
207C8—4882no—
208C8—2441no—
209C22—611no—
210C22—611no—
211C22—1222no—
212C22#99×D6111yescharacteristic
213C4—21no—
214C4—41no—
215C4—42no—
216C4—81no—
217C4—1221no—
218C4—4881no—
219C4—2441no—
220C4—2442no—
221C2—21no—
222C2—612no—
223C2—1221no—
224C2#354×D6111yescharacteristic
subgroupG/H
centerC2#354×D61
commutatorC42×C61C22×C4
FrattiniC4⋊Q8C22×D61
FittingC61×#1413C2
socleC2×C61C2×#354
prime radicalC22×D61#99
cosocleC4⋊Q8×C61C23
hypercenter#1413D61
hypocenterC61C2×#1413
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #1413

Complements

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

NH ≅ G/Ntype
3. #21443992C2semidirect
4. #21443991C2semidirect
5. C61×#1413C2semidirect
113. #1413D61direct (N × H)
117. D61#1413direct (N × H)
131. C61C2×#1413semidirect

Maximal subgroups

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

subgroupindex
#491×D612
#356×D612
#214439922
#214439912
C61×#14132
C2×#141361