Finite Group Databasebeta

← C61×#11819 #29515252

Subgroups — C61×#11819 #29515252

Order 15616.

368 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2628C211yesmaximal, characteristic
2C61×#1822C211yesmaximal, characteristic
3C61×#1464C211yesmaximal, characteristic
4C61×#1354C214yesmaximal, complemented
5C2×C4⋊Q8×C61C411yescharacteristic
6C2×#117×C61C2211yescharacteristic
7C61×#432—21no—
8C61×#407—21no—
9C61×#400—21no—
10C61×#399—21no—
11C61×#395C2212yes—
12C61×#393C412yes—
13C61×#389—21no—
14C61×#382C411yescharacteristic
15C61×#380—21no—
16C61×#343—21no—
17C61×#343C2212yes—
18C61×#324C2212yes—
19C61×#323—21no—
20C22×Q8×C61C2×C412yes—
21C23×C4×C61D411yescharacteristic
22C2×M16×C61—22no—
23C4⋊Q8×C61—41no—
24C4⋊Q8×C61—41no—
25#117×C61—41no—
26#117×C61—41no—
27C2×C4⋊C4×C61—21no—
28C2×C4⋊C4×C61—21no—
29C2×C4⋊C4×C61—21no—
30C2×C4⋊C4×C61—22no—
31C2×C4⋊C4×C61D411yescharacteristic
32C2×C4⋊C4×C61C2311yescharacteristic
33C2×C22⋊C4×C61—22no—
34C2×C22⋊C4×C61C2×C411yescharacteristic
35C2×C22⋊C4×C61D411yescharacteristic
36C2×C42×C61C2×C411yescharacteristic
37C2×C42×C61D411yescharacteristic
38C4⋊C8×C61—41no—
39C22⋊C8×C61—22no—
40C22⋊C8×C61—41no—
41C22⋊C8×C61—41no—
42#97×C61—41no—
43#95×C61—21no—
44#95×C61—22no—
45#95×C61—22no—
46#95×C61C2×C412yes—
47C24×C61C22⋊C411yescharacteristic
48C2×Q8×C61—42no—
49C2×Q8×C61—82no—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—22no—
55C22×C4×C61—41no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62M16×C61—42no—
63M16×C61—42no—
64C2×C8×C61—42no—
65C2×C8×C61—42no—
66C4⋊C4×C61—41no—
67C4⋊C4×C61—41no—
68C4⋊C4×C61—42no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—82no—
73C22⋊C4×C61—41no—
74C22⋊C4×C61—41no—
75C22⋊C4×C61—82no—
76C42×C61—21no—
77C42×C61—21no—
78C42×C61—21no—
79C42×C61—21no—
80C23×C61—21no—
81C23×C61—21no—
82C23×C61—21no—
83C23×C61—41no—
84C23×C61—41no—
85C23×C61C2×C22⋊C411yescharacteristic
86Q8×C61—84no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—42no—
102C2×C4×C61—42no—
103C2×C4×C61—42no—
104C2×C4×C61—42no—
105C2×C4×C61—42no—
106C2×C4×C61—42no—
107C2×C4×C61#9911yescharacteristic
108C2×C4×C61#9911yescharacteristic
109C2×C4×C61#13712yes—
110C8×C61—82no—
111C8×C61—82no—
112#11819C6111yesmaximal, characteristic, direct product factor, Sylow
113C22×C61—21no—
114C22×C61—21no—
115C22×C61—42no—
116C22×C61—41no—
117C22×C61—41no—
118C22×C61—41no—
119C22×C61—81no—
120C22×C61C2×#9911yescharacteristic
121C22×C61#41911yescharacteristic
122C22×C61#42111yescharacteristic
123C4×C61—22no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—41no—
127C4×C61—41no—
128C4×C61—41no—
129C4×C61—41no—
130C4×C61—82no—
131C4×C61—82no—
132#2628C2×C6111yescharacteristic
133#1822C2×C6111yescharacteristic
134#1464C2×C6111yescharacteristic
135#1354C2×C6114yescomplemented
136C2×C61—21no—
137C2×C61—21no—
138C2×C61—81no—
139C2×C61#151111yescharacteristic
140C2×C61#212211yescharacteristic
141C2×C61#213511yescharacteristic
142C2×C4⋊Q8C4×C6111yescharacteristic
143C2×#117C22×C6111yescharacteristic
144#432—21no—
145#407—21no—
146#400—21no—
147#399—21no—
148#395C22×C6112yes—
149#393C4×C6112yes—
150#389—21no—
151#382C4×C6111yescharacteristic
152#380—21no—
153#343—21no—
154#343C22×C6112yes—
155#324C22×C6112yes—
156#323—21no—
157C61#1181911yescharacteristic, direct product factor, Sylow
158C22×Q8C2×C4×C6112yes—
159C23×C4D4×C6111yescharacteristic
160C2×M16—22no—
161C4⋊Q8—41no—
162C4⋊Q8—41no—
163#117—41no—
164#117—41no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4D4×C6111yescharacteristic
170C2×C4⋊C4C23×C6111yescharacteristic
171C2×C22⋊C4—22no—
172C2×C22⋊C4C2×C4×C6111yescharacteristic
173C2×C22⋊C4D4×C6111yescharacteristic
174C2×C42C2×C4×C6111yescharacteristic
175C2×C42D4×C6111yescharacteristic
176C4⋊C8—41no—
177C22⋊C8—22no—
178C22⋊C8—41no—
179C22⋊C8—41no—
180#97—41no—
181#95—21no—
182#95—22no—
183#95—22no—
184#95C2×C4×C6112yes—
185C24C22⋊C4×C6111yescharacteristic
186C2×Q8—42no—
187C2×Q8—82no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—41no—
194C22×C4C22⋊C4×C6111yescharacteristic
195C22×C4C22⋊C4×C6111yescharacteristic
196C22×C4C22⋊C4×C6111yescharacteristic
197C22×C4C22×C4×C6111yescharacteristic
198C22×C4C2×D4×C6111yescharacteristic
199C22×C4C2×D4×C6111yescharacteristic
200M16—42no—
201M16—42no—
202C2×C8—42no—
203C2×C8—42no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—82no—
211C22⋊C4—41no—
212C22⋊C4—41no—
213C22⋊C4—82no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C23—21no—
219C23—21no—
220C23—21no—
221C23—41no—
222C23—41no—
223C23C2×C22⋊C4×C6111yescharacteristic
224Q8—84no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4#99×C6111yescharacteristic
246C2×C4#99×C6111yescharacteristic
247C2×C4#137×C6112yes—
248C8—82no—
249C8—82no—
250C22—21no—
251C22—21no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22C2×#99×C6111yescharacteristic
258C22C61×#41911yescharacteristic
259C22C61×#42111yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—82no—
268C4—82no—
269C2—21no—
270C2—21no—
271C2—81no—
272C2C61×#151111yescharacteristic
273C2C61×#212211yescharacteristic
274C2C61×#213511yescharacteristic
subgroupG/H
center, socleC22×C61C2×#99
commutatorC22×C4C22×C4×C61
Frattini, cosocleC2×C4⋊C4C23×C61
prime radicalC24×C61C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C2×#117×C61 ◁ G

Complements

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

NH ≅ G/Ntype
4. C61×#1354C2semidirect
112. #11819C61direct (N × H)
135. #1354C2×C61semidirect
157. C61#11819direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#26282
C61×#18222
C61×#14642
C61×#13542
#1181961