Group #29513670 — subgroups

Subgroups — C₆₁×#10237 #29513670

Order 15616.

560 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#477	C₂	1	2	yes	maximal
2	C₆₁×#2582	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#1956	C₂	1	1	yes	maximal, characteristic
4	C₂×C₆₁×Q₈⋊C₈	C₂	1	2	yes	maximal
5	C₆₁×#1296	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
8	C₆₁×#477	—	2	4	no	—
9	C₆₁×#477	—	2	4	no	—
10	C₂×#107×C₆₁	—	2	2	no	—
11	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
12	C₂×#103×C₆₁	—	2	2	no	—
13	C₂×#103×C₆₁	—	2	2	no	—
14	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₆₁×#398	—	2	2	no	—
16	C₆₁×#391	—	2	2	no	—
17	C₆₁×#389	—	2	2	no	—
18	C₆₁×#384	C₂²	1	1	yes	characteristic
19	C₆₁×Q₈⋊C₈	—	2	4	no	—
20	C₂²×Q₈×C₆₁	—	2	1	no	—
21	C₂²×Q₈×C₆₁	D₄	1	2	yes	—
22	C₂²×C₈×C₆₁	—	2	1	no	—
23	C₂²×C₈×C₆₁	—	2	2	no	—
24	C₄⋊Q₈×C₆₁	—	2	2	no	—
25	C₄⋊Q₈×C₆₁	—	2	1	no	—
26	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
27	C₄×Q₈×C₆₁	—	2	2	no	—
28	C₄×Q₈×C₆₁	—	2	2	no	—
29	C₄×Q₈×C₆₁	—	2	2	no	—
30	C₄×Q₈×C₆₁	—	2	2	no	—
31	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
32	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
33	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
34	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
35	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
36	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
37	C₂×C₄²×C₆₁	—	2	2	no	—
38	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
39	#107×C₆₁	—	2	8	no	—
40	C₄⋊C₈×C₆₁	—	2	2	no	—
41	C₄⋊C₈×C₆₁	D₄	1	4	yes	—
42	#103×C₆₁	—	2	8	no	—
43	#103×C₆₁	—	4	4	no	—
44	C₄×C₈×C₆₁	—	2	2	no	—
45	#95×C₆₁	—	2	4	no	—
46	#95×C₆₁	—	2	2	no	—
47	C₂×Q₈×C₆₁	—	2	2	no	—
48	C₂×Q₈×C₆₁	—	2	2	no	—
49	C₂×Q₈×C₆₁	—	2	2	no	—
50	C₂×Q₈×C₆₁	—	2	2	no	—
51	C₂×Q₈×C₆₁	—	2	2	no	—
52	C₂×Q₈×C₆₁	—	2	2	no	—
53	C₂×Q₈×C₆₁	—	4	2	no	—
54	C₂×Q₈×C₆₁	—	4	2	no	—
55	C₂×Q₈×C₆₁	—	4	1	no	—
56	C₂×Q₈×C₆₁	Q₁₆	1	4	yes	—
57	C₂²×C₄×C₆₁	—	2	2	no	—
58	C₂²×C₄×C₆₁	—	2	2	no	—
59	C₂²×C₄×C₆₁	—	2	2	no	—
60	C₂²×C₄×C₆₁	—	4	1	no	—
61	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₆₁	—	2	2	no	—
64	C₂×C₈×C₆₁	—	2	4	no	—
65	C₂×C₈×C₆₁	—	4	1	no	—
66	C₂×C₈×C₆₁	—	4	1	no	—
67	C₂×C₈×C₆₁	—	4	2	no	—
68	C₂×C₈×C₆₁	—	4	2	no	—
69	C₄⋊C₄×C₆₁	—	2	4	no	—
70	C₄⋊C₄×C₆₁	—	2	2	no	—
71	C₄⋊C₄×C₆₁	—	2	2	no	—
72	C₄⋊C₄×C₆₁	—	4	2	no	—
73	C₄⋊C₄×C₆₁	—	4	2	no	—
74	C₄⋊C₄×C₆₁	—	4	2	no	—
75	C₄⋊C₄×C₆₁	—	4	2	no	—
76	C₄⋊C₄×C₆₁	—	4	2	no	—
77	C₄⋊C₄×C₆₁	—	4	2	no	—
78	C₄⋊C₄×C₆₁	—	8	2	no	—
79	C₄²×C₆₁	—	4	2	no	—
80	C₄²×C₆₁	—	4	2	no	—
81	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₆₁	C₂×D₄	1	2	yes	—
83	C₄²×C₆₁	#41	1	1	yes	characteristic
84	C₂³×C₆₁	#120	1	1	yes	characteristic
85	Q₈×C₆₁	—	2	4	no	—
86	Q₈×C₆₁	—	2	4	no	—
87	Q₈×C₆₁	—	4	4	no	—
88	Q₈×C₆₁	—	4	2	no	—
89	Q₈×C₆₁	—	4	2	no	—
90	Q₈×C₆₁	—	8	2	no	—
91	C₂×C₄×C₆₁	—	2	1	no	—
92	C₂×C₄×C₆₁	—	2	1	no	—
93	C₂×C₄×C₆₁	—	2	4	no	—
94	C₂×C₄×C₆₁	—	4	2	no	—
95	C₂×C₄×C₆₁	—	4	2	no	—
96	C₂×C₄×C₆₁	—	4	2	no	—
97	C₂×C₄×C₆₁	—	4	2	no	—
98	C₂×C₄×C₆₁	—	4	4	no	—
99	C₂×C₄×C₆₁	—	4	2	no	—
100	C₂×C₄×C₆₁	—	4	2	no	—
101	C₂×C₄×C₆₁	—	4	2	no	—
102	C₂×C₄×C₆₁	—	8	1	no	—
103	C₂×C₄×C₆₁	—	8	1	no	—
104	C₂×C₄×C₆₁	#120	1	2	yes	—
105	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
106	C₂×C₄×C₆₁	#121	1	2	yes	—
107	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
108	C₂×C₄×C₆₁	C₂×Q₁₆	1	2	yes	—
109	C₂×C₄×C₆₁	#135	1	2	yes	—
110	C₂×C₄×C₆₁	#137	1	2	yes	—
111	C₂×C₄×C₆₁	#137	1	2	yes	—
112	C₈×C₆₁	—	4	2	no	—
113	C₈×C₆₁	—	4	4	no	—
114	#10237	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂²×C₆₁	#392	1	1	yes	characteristic
116	C₂²×C₆₁	#451	1	2	yes	—
117	C₂²×C₆₁	#452	1	2	yes	—
118	C₂²×C₆₁	#453	1	1	yes	characteristic
119	C₂²×C₆₁	#454	1	1	yes	characteristic
120	C₄×C₆₁	—	2	1	no	—
121	C₄×C₆₁	—	2	1	no	—
122	C₄×C₆₁	—	4	4	no	—
123	C₄×C₆₁	—	8	2	no	—
124	C₄×C₆₁	—	8	2	no	—
125	C₄×C₆₁	—	8	2	no	—
126	C₄×C₆₁	#451	1	2	yes	—
127	C₄×C₆₁	#452	1	2	yes	—
128	C₄×C₆₁	#467	1	2	yes	—
129	C₄×C₆₁	#470	1	2	yes	—
130	C₂×#477	C₂×C₆₁	1	2	yes	—
131	#2582	C₂×C₆₁	1	1	yes	characteristic
132	#1956	C₂×C₆₁	1	1	yes	characteristic
133	C₂×Q₈⋊C₈	C₂×C₆₁	1	2	yes	—
134	#1296	C₂×C₆₁	1	1	yes	characteristic
135	C₂×C₆₁	#1630	1	1	yes	characteristic
136	C₂×C₆₁	#1633	1	1	yes	characteristic
137	C₂×C₆₁	#1636	1	2	yes	—
138	C₂×C₆₁	#2001	1	2	yes	—
139	C₂×C₆₁	#2006	1	1	yes	characteristic
140	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
141	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
142	#477	—	2	4	no	—
143	#477	—	2	4	no	—
144	C₂×#107	—	2	2	no	—
145	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
146	C₂×#103	—	2	2	no	—
147	C₂×#103	—	2	2	no	—
148	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
149	#398	—	2	2	no	—
150	#391	—	2	2	no	—
151	#389	—	2	2	no	—
152	#384	C₂²×C₆₁	1	1	yes	characteristic
153	Q₈⋊C₈	—	2	4	no	—
154	C₆₁	#10237	1	1	yes	characteristic, direct product factor, Sylow
155	C₂²×Q₈	—	2	1	no	—
156	C₂²×Q₈	D₄×C₆₁	1	2	yes	—
157	C₂²×C₈	—	2	1	no	—
158	C₂²×C₈	—	2	2	no	—
159	C₄⋊Q₈	—	2	2	no	—
160	C₄⋊Q₈	—	2	1	no	—
161	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
162	C₄×Q₈	—	2	2	no	—
163	C₄×Q₈	—	2	2	no	—
164	C₄×Q₈	—	2	2	no	—
165	C₄×Q₈	—	2	2	no	—
166	C₂×C₄⋊C₄	—	2	2	no	—
167	C₂×C₄⋊C₄	—	2	2	no	—
168	C₂×C₄⋊C₄	—	2	2	no	—
169	C₂×C₄⋊C₄	—	2	2	no	—
170	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
171	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
172	C₂×C₄²	—	2	2	no	—
173	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
174	#107	—	2	8	no	—
175	C₄⋊C₈	—	2	2	no	—
176	C₄⋊C₈	D₄×C₆₁	1	4	yes	—
177	#103	—	2	8	no	—
178	#103	—	4	4	no	—
179	C₄×C₈	—	2	2	no	—
180	#95	—	2	4	no	—
181	#95	—	2	2	no	—
182	C₂×Q₈	—	2	2	no	—
183	C₂×Q₈	—	2	2	no	—
184	C₂×Q₈	—	2	2	no	—
185	C₂×Q₈	—	2	2	no	—
186	C₂×Q₈	—	2	2	no	—
187	C₂×Q₈	—	2	2	no	—
188	C₂×Q₈	—	4	2	no	—
189	C₂×Q₈	—	4	2	no	—
190	C₂×Q₈	—	4	1	no	—
191	C₂×Q₈	Q₁₆×C₆₁	1	4	yes	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	2	2	no	—
195	C₂²×C₄	—	4	1	no	—
196	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
197	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
198	C₂×C₈	—	2	2	no	—
199	C₂×C₈	—	2	4	no	—
200	C₂×C₈	—	4	1	no	—
201	C₂×C₈	—	4	1	no	—
202	C₂×C₈	—	4	2	no	—
203	C₂×C₈	—	4	2	no	—
204	C₄⋊C₄	—	2	4	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₄⋊C₄	—	2	2	no	—
207	C₄⋊C₄	—	4	2	no	—
208	C₄⋊C₄	—	4	2	no	—
209	C₄⋊C₄	—	4	2	no	—
210	C₄⋊C₄	—	4	2	no	—
211	C₄⋊C₄	—	4	2	no	—
212	C₄⋊C₄	—	4	2	no	—
213	C₄⋊C₄	—	8	2	no	—
214	C₄²	—	4	2	no	—
215	C₄²	—	4	2	no	—
216	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
217	C₄²	C₂×D₄×C₆₁	1	2	yes	—
218	C₄²	#41×C₆₁	1	1	yes	characteristic
219	C₂³	#120×C₆₁	1	1	yes	characteristic
220	Q₈	—	2	4	no	—
221	Q₈	—	2	4	no	—
222	Q₈	—	4	4	no	—
223	Q₈	—	4	2	no	—
224	Q₈	—	4	2	no	—
225	Q₈	—	8	2	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	4	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	4	4	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	8	1	no	—
238	C₂×C₄	—	8	1	no	—
239	C₂×C₄	#120×C₆₁	1	2	yes	—
240	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
241	C₂×C₄	#121×C₆₁	1	2	yes	—
242	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
243	C₂×C₄	C₂×Q₁₆×C₆₁	1	2	yes	—
244	C₂×C₄	#135×C₆₁	1	2	yes	—
245	C₂×C₄	#137×C₆₁	1	2	yes	—
246	C₂×C₄	#137×C₆₁	1	2	yes	—
247	C₈	—	4	2	no	—
248	C₈	—	4	4	no	—
249	C₂²	C₆₁×#392	1	1	yes	characteristic
250	C₂²	C₆₁×#451	1	2	yes	—
251	C₂²	C₆₁×#452	1	2	yes	—
252	C₂²	C₆₁×#453	1	1	yes	characteristic
253	C₂²	C₆₁×#454	1	1	yes	characteristic
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	4	4	no	—
257	C₄	—	8	2	no	—
258	C₄	—	8	2	no	—
259	C₄	—	8	2	no	—
260	C₄	C₆₁×#451	1	2	yes	—
261	C₄	C₆₁×#452	1	2	yes	—
262	C₄	C₆₁×#467	1	2	yes	—
263	C₄	C₆₁×#470	1	2	yes	—
264	C₂	C₆₁×#1630	1	1	yes	characteristic
265	C₂	C₆₁×#1633	1	1	yes	characteristic
266	C₂	C₆₁×#1636	1	2	yes	—
267	C₂	C₆₁×#2001	1	2	yes	—
268	C₂	C₆₁×#2006	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₆₁×#477

C₂

yes

maximal

C₆₁×#2582

C₂

yes

maximal, characteristic

C₆₁×#1956

C₂

yes

maximal, characteristic

C₂×C₆₁×Q₈⋊C₈

C₂

yes

maximal

C₆₁×#1296

C₂

yes

maximal, characteristic

C₂×C₄⋊Q₈×C₆₁

C₂²

yes

characteristic

C₂×C₄×Q₈×C₆₁

C₂²

yes

—

C₆₁×#477

—

C₆₁×#477

—

C₂×#107×C₆₁

—

C₂×C₄⋊C₈×C₆₁

C₂²

yes

—

C₂×#103×C₆₁

—

C₂×#103×C₆₁

—

C₂×C₄×C₈×C₆₁

C₂²

yes

characteristic

C₆₁×#398

—

C₆₁×#391

—

C₆₁×#389

—

C₆₁×#384

C₂²

yes

characteristic

C₆₁×Q₈⋊C₈

—

C₂²×Q₈×C₆₁

—

C₂²×Q₈×C₆₁

D₄

yes

—

C₂²×C₈×C₆₁

—

C₂²×C₈×C₆₁

—

C₄⋊Q₈×C₆₁

—

C₄⋊Q₈×C₆₁

—

C₄⋊Q₈×C₆₁

D₄

yes

—

C₄×Q₈×C₆₁

—

C₄×Q₈×C₆₁

—

C₄×Q₈×C₆₁

—

C₄×Q₈×C₆₁

—

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

D₄

yes

—

C₂×C₄⋊C₄×C₆₁

D₄

yes

—

C₂×C₄²×C₆₁

—

C₂×C₄²×C₆₁

C₂³

yes

characteristic

#107×C₆₁

—

C₄⋊C₈×C₆₁

—

C₄⋊C₈×C₆₁

D₄

yes

—

#103×C₆₁

—

#103×C₆₁

—

C₄×C₈×C₆₁

—

#95×C₆₁

—

#95×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

Q₁₆

yes

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×D₄

yes

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

C₂×D₄

yes

characteristic

C₄²×C₆₁

C₂×D₄

yes

—

C₄²×C₆₁

yes

C₂³×C₆₁

yes

Q₈×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

100

C₂×C₄×C₆₁

—

101

C₂×C₄×C₆₁

—

102

C₂×C₄×C₆₁

—

103

C₂×C₄×C₆₁

—

104

C₂×C₄×C₆₁

#120

yes

—

105

C₂×C₄×C₆₁

#121

yes

characteristic

106

C₂×C₄×C₆₁

#121

yes

—

107

C₂×C₄×C₆₁

#127

yes

characteristic

108

C₂×C₄×C₆₁

C₂×Q₁₆

yes

—

109

C₂×C₄×C₆₁

#135

yes

—

110

C₂×C₄×C₆₁

#137

yes

—

111

C₂×C₄×C₆₁

#137

yes

—

112

C₈×C₆₁

—

113

C₈×C₆₁

—

114

#10237

C₆₁

yes

maximal, characteristic, direct product factor, Sylow

115

C₂²×C₆₁

#392

yes

characteristic

116

C₂²×C₆₁

#451

yes

—

117

C₂²×C₆₁

#452

yes

—

118

C₂²×C₆₁

#453

yes

characteristic

119

C₂²×C₆₁

#454

yes

characteristic

120

C₄×C₆₁

—

121

C₄×C₆₁

—

122

C₄×C₆₁

—

123

C₄×C₆₁

—

124

C₄×C₆₁

—

125

C₄×C₆₁

—

126

C₄×C₆₁

#451

yes

—

127

C₄×C₆₁

#452

yes

—

128

C₄×C₆₁

#467

yes

—

129

C₄×C₆₁

#470

yes

—

130

C₂×#477

C₂×C₆₁

yes

—

131

#2582

C₂×C₆₁

yes

characteristic

132

#1956

C₂×C₆₁

yes

characteristic

133

C₂×Q₈⋊C₈

C₂×C₆₁

yes

—

134

#1296

C₂×C₆₁

yes

characteristic

135

C₂×C₆₁

#1630

yes

characteristic

136

C₂×C₆₁

#1633

yes

characteristic

137

C₂×C₆₁

#1636

yes

—

138

C₂×C₆₁

#2001

yes

—

139

C₂×C₆₁

#2006

yes

characteristic

140

C₂×C₄⋊Q₈

C₂²×C₆₁

yes

characteristic

141

C₂×C₄×Q₈

C₂²×C₆₁

yes

—

142

#477

—

143

#477

—

144

C₂×#107

—

145

C₂×C₄⋊C₈

C₂²×C₆₁

yes

—

146

C₂×#103

—

147

C₂×#103

—

148

C₂×C₄×C₈

C₂²×C₆₁

yes

characteristic

149

#398

—

150

#391

—

151

#389

—

152

#384

C₂²×C₆₁

yes

characteristic

153

Q₈⋊C₈

—

154

C₆₁

#10237

yes

characteristic, direct product factor, Sylow

155

C₂²×Q₈

—

156

C₂²×Q₈

D₄×C₆₁

yes

—

157

C₂²×C₈

—

158

C₂²×C₈

—

159

C₄⋊Q₈

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

D₄×C₆₁

yes

—

162

C₄×Q₈

—

163

C₄×Q₈

—

164

C₄×Q₈

—

165

C₄×Q₈

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₄⋊C₄

D₄×C₆₁

yes

—

171

C₂×C₄⋊C₄

D₄×C₆₁

yes

—

172

C₂×C₄²

—

173

C₂×C₄²

C₂³×C₆₁

yes

characteristic

174

#107

—

175

C₄⋊C₈

—

176

C₄⋊C₈

D₄×C₆₁

yes

—

177

#103

—

178

#103

—

179

C₄×C₈

—

180

#95

—

181

#95

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

Q₁₆×C₆₁

yes

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

C₂×D₄×C₆₁

yes

characteristic

197

C₂²×C₄

C₂×D₄×C₆₁

yes

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄²

—

215

C₄²

—

216

C₄²

C₂×D₄×C₆₁

yes

characteristic

217

C₄²

C₂×D₄×C₆₁

yes

—

218

C₄²

#41×C₆₁

yes

characteristic

219

C₂³

#120×C₆₁

yes

characteristic

220

Q₈

—

221

Q₈

—

222

Q₈

—

223

Q₈

—

224

Q₈

—

225

Q₈

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

#120×C₆₁

yes

—

240

C₂×C₄

#121×C₆₁

yes

characteristic

241

C₂×C₄

#121×C₆₁

yes

—

242

C₂×C₄

#127×C₆₁

yes

characteristic

243

C₂×C₄

C₂×Q₁₆×C₆₁

yes

—

244

C₂×C₄

#135×C₆₁

yes

—

245

C₂×C₄

#137×C₆₁

yes

—

246

C₂×C₄

#137×C₆₁

yes

—

247

C₈

—

248

C₈

—

249

C₂²

C₆₁×#392

yes

characteristic

250

C₂²

C₆₁×#451

yes

—

251

C₂²

C₆₁×#452

yes

—

252

C₂²

C₆₁×#453

yes

characteristic

253

C₂²

C₆₁×#454

yes

characteristic

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

C₆₁×#451

yes

—

261

C₄

C₆₁×#452

yes

—

262

C₄

C₆₁×#467

yes

—

263

C₄

C₆₁×#470

yes

—

264

C₂

C₆₁×#1630

yes

characteristic

265

C₂

C₆₁×#1633

yes

characteristic

266

C₂

C₆₁×#1636

yes

—

267

C₂

C₆₁×#2001

yes

—

268

C₂

C₆₁×#2006

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₆₁	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₆₁
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₆₁

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₆₁

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

N	H ≅ G/N	type
114. #10237	C₆₁	direct (N × H)
154. C₆₁	#10237	direct (N × H)

H ≅ G/N

type

114. #10237

C₆₁

direct (N × H)

154. C₆₁

#10237

direct (N × H)

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

subgroup	index
C₂×C₆₁×#477	2
C₆₁×#2582	2
C₆₁×#1956	2
C₂×C₆₁×Q₈⋊C₈	2
C₆₁×#1296	2
#10237	61

subgroup

index

C₂×C₆₁×#477

C₆₁×#2582

C₆₁×#1956

C₂×C₆₁×Q₈⋊C₈

C₆₁×#1296

#10237

Subgroups — C₆₁×#10237 #29513670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C61×#10237 #29513670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#10237 #29513670