Finite Group Databasebeta

← C61×#10325 #29513758

Subgroups — C61×#10325 #29513758

Order 15616.

602 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3189C211yesmaximal, characteristic
2C61×#2855C212yesmaximal
3C61×#1817C211yesmaximal, characteristic
4C61×#1520C212yesmaximal
5C61×#1289C211yesmaximal, characteristic
6C2×C22⋊Q8×C61C2212yes—
7C22×C42×C61C2211yescharacteristic
8C61×#484—22no—
9C61×#467—22no—
10C61×#451—22no—
11C2×C22⋊C8×C61C2211yescharacteristic
12C2×C22⋊C8×C61C2211yescharacteristic
13C61×#391—22no—
14C61×#389—22no—
15C61×#387—24no—
16C61×#385—22no—
17C61×#381—22no—
18C61×#380C2212yes—
19C61×#336—22no—
20C61×#328—24no—
21C22×Q8×C61D412yes—
22C23×C4×C61D411yescharacteristic
23C23×C4×C61D411yescharacteristic
24C23×C4×C61C2311yescharacteristic
25C2×Q16×C61—22no—
26C22×C8×C61—21no—
27C22×C8×C61D412yes—
28C22⋊Q8×C61—22no—
29C22⋊Q8×C61—22no—
30C22⋊Q8×C61—22no—
31C22⋊Q8×C61—22no—
32C2×C4⋊C4×C61—24no—
33C2×C4⋊C4×C61—22no—
34C2×C4⋊C4×C61—22no—
35C2×C4⋊C4×C61D412yes—
36C2×C22⋊C4×C61—22no—
37C2×C22⋊C4×C61—22no—
38C2×C42×C61—21no—
39C2×C42×C61—22no—
40C2×C42×C61—22no—
41C2×C42×C61—21no—
42#107×C61—22no—
43#103×C61—24no—
44C22⋊C8×C61—22no—
45C22⋊C8×C61—22no—
46#95×C61—24no—
47#95×C61—24no—
48#95×C61—24no—
49#95×C61D414yes—
50C24×C61C2×D411yescharacteristic
51C2×Q8×C61—22no—
52C2×Q8×C61—22no—
53C2×Q8×C61—44no—
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—22no—
60C22×C4×C61—22no—
61C22×C4×C61—24no—
62C22×C4×C61—22no—
63C22×C4×C61—42no—
64C22×C4×C61—42no—
65C22×C4×C61Q1612yescomplemented
66C22×C4×C61C2×D412yes—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D412yes—
69C22×C4×C61#4111yescharacteristic
70Q16×C61—82no—
71C2×C8×C61—22no—
72C2×C8×C61—42no—
73C2×C8×C61—42no—
74C2×C8×C61—41no—
75C4⋊C4×C61—22no—
76C4⋊C4×C61—22no—
77C4⋊C4×C61—44no—
78C4⋊C4×C61—48no—
79C4⋊C4×C61—42no—
80C4⋊C4×C61—42no—
81C22⋊C4×C61—42no—
82C22⋊C4×C61—42no—
83C22⋊C4×C61—42no—
84C22⋊C4×C61—42no—
85C42×C61—41no—
86C42×C61—42no—
87C42×C61—41no—
88C23×C61—41no—
89C23×C61—41no—
90C23×C61#12012yes—
91C23×C61#12111yescharacteristic
92C23×C61C2×Q1611yescharacteristic
93C23×C61#13511yescharacteristic
94C23×C61#13712yes—
95Q8×C61—44no—
96Q8×C61—82no—
97C2×C4×C61—24no—
98C2×C4×C61—22no—
99C2×C4×C61—24no—
100C2×C4×C61—22no—
101C2×C4×C61—24no—
102C2×C4×C61—22no—
103C2×C4×C61—42no—
104C2×C4×C61—41no—
105C2×C4×C61—42no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—42no—
110C2×C4×C61—41no—
111C2×C4×C61—44no—
112C2×C4×C61—44no—
113C2×C4×C61—44no—
114C2×C4×C61—44no—
115C2×C4×C61—42no—
116C2×C4×C61—42no—
117C2×C4×C61—44no—
118C2×C4×C61#12011yescharacteristic
119C2×C4×C61#12112yes—
120C2×C4×C61#12711yescharacteristic
121C8×C61—42no—
122C8×C61—81no—
123#10325C6111yesmaximal, characteristic, direct product factor, Sylow
124C22×C61—22no—
125C22×C61—21no—
126C22×C61—22no—
127C22×C61—21no—
128C22×C61—41no—
129C22×C61—41no—
130C22×C61—42no—
131C22×C61#39211yescharacteristic
132C22×C61#45112yes—
133C22×C61#45212yes—
134C22×C61#46711yescharacteristic
135C22×C61#47011yescharacteristic
136C4×C61—21no—
137C4×C61—22no—
138C4×C61—42no—
139C4×C61—42no—
140C4×C61—84no—
141C4×C61—82no—
142C4×C61—82no—
143C4×C61#45812yes—
144#3189C2×C6111yescharacteristic
145#2855C2×C6112yes—
146#1817C2×C6111yescharacteristic
147#1520C2×C6112yes—
148#1289C2×C6111yescharacteristic
149C2×C61—22no—
150C2×C61—22no—
151C2×C61—21no—
152C2×C61—21no—
153C2×C61#200111yescharacteristic
154C2×C61#201011yescharacteristic
155C2×C61#202211yescharacteristic
156C2×C22⋊Q8C22×C6112yes—
157C22×C42C22×C6111yescharacteristic
158#484—22no—
159#467—22no—
160#451—22no—
161C2×C22⋊C8C22×C6111yescharacteristic
162C2×C22⋊C8C22×C6111yescharacteristic
163#391—22no—
164#389—22no—
165#387—24no—
166#385—22no—
167#381—22no—
168#380C22×C6112yes—
169#336—22no—
170#328—24no—
171C61#1032511yescharacteristic, direct product factor, Sylow
172C22×Q8D4×C6112yes—
173C23×C4D4×C6111yescharacteristic
174C23×C4D4×C6111yescharacteristic
175C23×C4C23×C6111yescharacteristic
176C2×Q16—22no—
177C22×C8—21no—
178C22×C8D4×C6112yes—
179C22⋊Q8—22no—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4D4×C6112yes—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C42—21no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42—21no—
193#107—22no—
194#103—24no—
195C22⋊C8—22no—
196C22⋊C8—22no—
197#95—24no—
198#95—24no—
199#95—24no—
200#95D4×C6114yes—
201C24C2×D4×C6111yescharacteristic
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—44no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—24no—
213C22×C4—22no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4Q16×C6112yescomplemented
217C22×C4C2×D4×C6112yes—
218C22×C4C2×D4×C6111yescharacteristic
219C22×C4C2×D4×C6112yes—
220C22×C4#41×C6111yescharacteristic
221Q16—82no—
222C2×C8—22no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—41no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—44no—
229C4⋊C4—48no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C22⋊C4—42no—
233C22⋊C4—42no—
234C22⋊C4—42no—
235C22⋊C4—42no—
236C42—41no—
237C42—42no—
238C42—41no—
239C23—41no—
240C23—41no—
241C23#120×C6112yes—
242C23#121×C6111yescharacteristic
243C23C2×Q16×C6111yescharacteristic
244C23#135×C6111yescharacteristic
245C23#137×C6112yes—
246Q8—44no—
247Q8—82no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—44no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—44no—
269C2×C4#120×C6111yescharacteristic
270C2×C4#121×C6112yes—
271C2×C4#127×C6111yescharacteristic
272C8—42no—
273C8—81no—
274C22—22no—
275C22—21no—
276C22—22no—
277C22—21no—
278C22—41no—
279C22—41no—
280C22—42no—
281C22C61×#39211yescharacteristic
282C22C61×#45112yes—
283C22C61×#45212yes—
284C22C61×#46711yescharacteristic
285C22C61×#47011yescharacteristic
286C4—21no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—84no—
291C4—82no—
292C4—82no—
293C4C61×#45812yes—
294C2—22no—
295C2—22no—
296C2—21no—
297C2—21no—
298C2C61×#200111yescharacteristic
299C2C61×#201011yescharacteristic
300C2C61×#202211yescharacteristic
subgroupG/H
center, socleC22×C61#392
commutator, Frattini, cosocleC23×C4C23×C61
prime radicalC24×C61C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
65. C22×C4×C61Q16semidirect
123. #10325C61direct (N × H)
171. C61#10325direct (N × H)
216. C22×C4Q16×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#31892
C61×#28552
C61×#18172
C61×#15202
C61×#12892
#1032561