Finite Group Databasebeta

← C61×#13590 #29517023

Subgroups — C61×#13590 #29517023

Order 15616.

398 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C61×#3152C211yesmaximal, characteristic
2C2×C61×#356C212yesmaximal, complemented
3C61×#1411C212yesmaximal, complemented
4C61×#1410C212yesmaximal, complemented
5C2×#137×C61—22no—
6C61×#532C411yescharacteristic
7C2×C4⋊Q8×C61C2211yescharacteristic
8C61×#497—22no—
9C61×#494C411yescharacteristic
10C61×#494C2211yescharacteristic
11C61×#492C411yescharacteristic
12C61×#492C2211yescharacteristic
13C2×#101×C61—22no—
14C4×M16×C61C411yescharacteristic
15C61×#356—22no—
16C61×#356C2214yes—
17C2×#41×C61—21no—
18C22×Q8×C61D412yes—
19#137×C61—44no—
20#137×C61—44no—
21C2×Q16×C61—22no—
22C2×Q16×C61—22no—
23C2×SD16×C61—22no—
24C2×SD16×C61—22no—
25C2×M16×C61—21no—
26C2×M16×C61—42no—
27C4⋊Q8×C61—41no—
28C4⋊Q8×C61C2×C411yescharacteristic
29C4⋊Q8×C61C2×C411yescharacteristic
30C4⋊Q8×C61D412yes—
31C4⋊Q8×C61C2311yescharacteristic
32#127×C61C2×C411yescharacteristic
33#124×C61—21no—
34#121×C61—41no—
35C4×D4×C61—41no—
36C2×C4⋊C4×C61—41no—
37C2×C42×C61C2×C411yescharacteristic
38#101×C61—24no—
39#101×C61—42no—
40#97×C61—21no—
41C4×C8×C61C2×C411yescharacteristic
42C4×C8×C61C2×C411yescharacteristic
43#41×C61—42no—
44#41×C61—42no—
45C2×Q8×C61—22no—
46C2×Q8×C61—21no—
47C2×Q8×C61—42no—
48C2×Q8×C61—42no—
49C2×Q8×C61C22⋊C412yes—
50C2×Q8×C61C2×D412yes—
51C2×D4×C61—21no—
52C2×D4×C61—41no—
53C2×D4×C61—41no—
54C22×C4×C61—21no—
55C22×C4×C61—22no—
56C22×C4×C61—41no—
57C22×C4×C61C22⋊C411yescharacteristic
58Q16×C61—44no—
59Q16×C61—44no—
60SD16×C61—44no—
61SD16×C61—44no—
62M16×C61—24no—
63M16×C61—44no—
64M16×C61—82no—
65C2×C8×C61—21no—
66C2×C8×C61—21no—
67C2×C8×C61—82no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C22⋊C4×C61—42no—
73C42×C61—21no—
74C42×C61C22⋊C411yescharacteristic
75C42×C61C22×C411yescharacteristic
76C23×C61—41no—
77C23×C61#9911yescharacteristic
78Q8×C61—42no—
79Q8×C61—42no—
80Q8×C61—42no—
81Q8×C61—82no—
82D4×C61—42no—
83D4×C61—82no—
84D4×C61—82no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—42no—
91C2×C4×C61—42no—
92C2×C4×C61—42no—
93C2×C4×C61—41no—
94C2×C4×C61—81no—
95C2×C4×C61—81no—
96C2×C4×C61#9911yescharacteristic
97C2×C4×C61C2×C22⋊C411yescharacteristic
98C8×C61—22no—
99C8×C61—22no—
100C8×C61—84no—
101#13590C6111yesmaximal, characteristic, direct product factor, Sylow
102C22×C61—41no—
103C22×C61—82no—
104C22×C61—81no—
105C22×C61#35312yes—
106C22×C61C2×#9911yescharacteristic
107C4×C61—22no—
108C4×C61—21no—
109C4×C61—21no—
110C4×C61—41no—
111C4×C61—42no—
112C4×C61—42no—
113C4×C61—81no—
114#3152C2×C6111yescharacteristic
115C2×#356C2×C6112yescomplemented
116#1411C2×C6112yescomplemented
117#1410C2×C6112yescomplemented
118C2×C61—21no—
119C2×C61—22no—
120C2×C61—161no—
121C2×C61C2×#35311yescharacteristic
122C2×#137—22no—
123#532C4×C6111yescharacteristic
124C2×C4⋊Q8C22×C6111yescharacteristic
125#497—22no—
126#494C4×C6111yescharacteristic
127#494C22×C6111yescharacteristic
128#492C4×C6111yescharacteristic
129#492C22×C6111yescharacteristic
130C2×#101—22no—
131C4×M16C4×C6111yescharacteristic
132#356—22no—
133#356C22×C6114yes—
134C61#1359011yescharacteristic, direct product factor, Sylow
135C2×#41—21no—
136C22×Q8D4×C6112yes—
137#137—44no—
138#137—44no—
139C2×Q16—22no—
140C2×Q16—22no—
141C2×SD16—22no—
142C2×SD16—22no—
143C2×M16—21no—
144C2×M16—42no—
145C4⋊Q8—41no—
146C4⋊Q8C2×C4×C6111yescharacteristic
147C4⋊Q8C2×C4×C6111yescharacteristic
148C4⋊Q8D4×C6112yes—
149C4⋊Q8C23×C6111yescharacteristic
150#127C2×C4×C6111yescharacteristic
151#124—21no—
152#121—41no—
153C4×D4—41no—
154C2×C4⋊C4—41no—
155C2×C42C2×C4×C6111yescharacteristic
156#101—24no—
157#101—42no—
158#97—21no—
159C4×C8C2×C4×C6111yescharacteristic
160C4×C8C2×C4×C6111yescharacteristic
161#41—42no—
162#41—42no—
163C2×Q8—22no—
164C2×Q8—21no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8C22⋊C4×C6112yes—
168C2×Q8C2×D4×C6112yes—
169C2×D4—21no—
170C2×D4—41no—
171C2×D4—41no—
172C22×C4—21no—
173C22×C4—22no—
174C22×C4—41no—
175C22×C4C22⋊C4×C6111yescharacteristic
176Q16—44no—
177Q16—44no—
178SD16—44no—
179SD16—44no—
180M16—24no—
181M16—44no—
182M16—82no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—82no—
186C4⋊C4—41no—
187C4⋊C4—42no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C22⋊C4—42no—
191C42—21no—
192C42C22⋊C4×C6111yescharacteristic
193C42C22×C4×C6111yescharacteristic
194C23—41no—
195C23#99×C6111yescharacteristic
196Q8—42no—
197Q8—42no—
198Q8—42no—
199Q8—82no—
200D4—42no—
201D4—82no—
202D4—82no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—81no—
213C2×C4—81no—
214C2×C4#99×C6111yescharacteristic
215C2×C4C2×C22⋊C4×C6111yescharacteristic
216C8—22no—
217C8—22no—
218C8—84no—
219C22—41no—
220C22—82no—
221C22—81no—
222C22C61×#35312yes—
223C22C2×#99×C6111yescharacteristic
224C4—22no—
225C4—21no—
226C4—21no—
227C4—41no—
228C4—42no—
229C4—42no—
230C4—81no—
231C2—21no—
232C2—22no—
233C2—161no—
234C2C2×C61×#35311yescharacteristic
subgroupG/H
center, socleC2×C61C2×#353
commutatorC42C22×C4×C61
Frattini, cosocleC4⋊Q8C23×C61
prime radicalC61×#532C4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C61 ◁ C23×C61 ◁ C22×C4×C61 ◁ C2×C4⋊Q8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#356C2semidirect
3. C61×#1411C2semidirect
4. C61×#1410C2semidirect
101. #13590C61direct (N × H)
115. C2×#356C2×C61semidirect
116. #1411C2×C61semidirect
117. #1410C2×C61semidirect
134. C61#13590direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31522
C2×C61×#3562
C61×#14112
C61×#14102
#1359061