Group #23785597 — subgroups

Subgroups — C₄₁×#9396 #23785597

Order 10496.

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

normal subgroups only

This group has 470 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	C₄₁×#2982	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2568	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1801	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1549	C₂	1	2	yes	maximal
5	C₄₁×#1303	C₂	1	2	yes	maximal
6	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
8	C₈×Q₈×C₄₁	—	2	4	no	—
9	C₄₁×#431	—	2	2	no	—
10	C₄₁×#431	C₂²	1	2	yes	—
11	C₄₁×#423	C₂²	1	2	yes	—
12	C₂×#101×C₄₁	—	2	1	no	—
13	C₄₁×#400	C₄	1	4	yes	—
14	C₄₁×#391	—	2	1	no	—
15	C₄₁×#391	—	2	2	no	—
16	C₄₁×#382	—	2	1	no	—
17	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#343	—	2	1	no	—
19	C₄₁×#332	—	2	4	no	—
20	C₂²×Q₈×C₄₁	—	2	1	no	—
21	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
22	C₂×M₁₆×C₄₁	—	2	2	no	—
23	C₄⋊Q₈×C₄₁	—	2	2	no	—
24	C₄⋊Q₈×C₄₁	—	2	2	no	—
25	C₄×Q₈×C₄₁	—	2	2	no	—
26	C₄×Q₈×C₄₁	—	2	2	no	—
27	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
28	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
29	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
30	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
31	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₄₁	—	2	1	no	—
33	C₂×C₄²×C₄₁	D₄	1	2	yes	—
34	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
35	C₄⋊C₈×C₄₁	—	2	4	no	—
36	C₄⋊C₈×C₄₁	—	2	2	no	—
37	C₄⋊C₈×C₄₁	—	2	2	no	—
38	C₄⋊C₈×C₄₁	D₄	1	4	yes	—
39	#101×C₄₁	—	4	2	no	—
40	C₂²⋊C₈×C₄₁	—	2	2	no	—
41	C₄×C₈×C₄₁	—	2	4	no	—
42	C₄×C₈×C₄₁	—	2	2	no	—
43	#95×C₄₁	—	2	4	no	—
44	#95×C₄₁	—	2	4	no	—
45	#95×C₄₁	C₂×C₄	1	2	yes	—
46	C₂×Q₈×C₄₁	—	2	2	no	—
47	C₂×Q₈×C₄₁	—	2	2	no	—
48	C₂×Q₈×C₄₁	—	4	4	no	—
49	C₂×Q₈×C₄₁	—	4	1	no	—
50	C₂×Q₈×C₄₁	—	4	1	no	—
51	C₂×Q₈×C₄₁	SD₁₆	1	2	yes	—
52	C₂×Q₈×C₄₁	Q₁₆	1	2	yes	—
53	C₂²×C₄×C₄₁	—	2	2	no	—
54	C₂²×C₄×C₄₁	—	2	2	no	—
55	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
60	M₁₆×C₄₁	—	4	2	no	—
61	M₁₆×C₄₁	—	4	2	no	—
62	C₂×C₈×C₄₁	—	2	4	no	—
63	C₂×C₈×C₄₁	—	4	2	no	—
64	C₄⋊C₄×C₄₁	—	2	4	no	—
65	C₄⋊C₄×C₄₁	—	2	2	no	—
66	C₄⋊C₄×C₄₁	—	2	4	no	—
67	C₄⋊C₄×C₄₁	—	4	2	no	—
68	C₄⋊C₄×C₄₁	—	4	2	no	—
69	C₄²×C₄₁	—	2	2	no	—
70	C₄²×C₄₁	—	2	2	no	—
71	C₄²×C₄₁	—	4	2	no	—
72	C₄²×C₄₁	C₂×D₄	1	2	yes	—
73	C₄²×C₄₁	#41	1	2	yes	—
74	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	Q₈×C₄₁	—	2	4	no	—
76	Q₈×C₄₁	—	2	4	no	—
77	Q₈×C₄₁	—	8	2	no	—
78	Q₈×C₄₁	—	8	2	no	—
79	C₂×C₄×C₄₁	—	2	2	no	—
80	C₂×C₄×C₄₁	—	2	2	no	—
81	C₂×C₄×C₄₁	—	2	2	no	—
82	C₂×C₄×C₄₁	—	2	2	no	—
83	C₂×C₄×C₄₁	—	4	1	no	—
84	C₂×C₄×C₄₁	—	4	2	no	—
85	C₂×C₄×C₄₁	—	4	2	no	—
86	C₂×C₄×C₄₁	—	4	2	no	—
87	C₂×C₄×C₄₁	—	4	4	no	—
88	C₂×C₄×C₄₁	—	4	2	no	—
89	C₂×C₄×C₄₁	—	4	2	no	—
90	C₂×C₄×C₄₁	#103	1	4	yes	—
91	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
92	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
93	C₂×C₄×C₄₁	#121	1	2	yes	—
94	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
95	C₂×C₄×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
96	C₂×C₄×C₄₁	C₂×Q₁₆	1	1	yes	characteristic
97	C₂×C₄×C₄₁	#135	1	2	yes	—
98	C₈×C₄₁	—	4	4	no	—
99	C₈×C₄₁	—	8	2	no	—
100	#9396	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₂²×C₄₁	—	2	1	no	—
102	C₂²×C₄₁	—	2	1	no	—
103	C₂²×C₄₁	#386	1	1	yes	characteristic
104	C₂²×C₄₁	C₂×#103	1	1	yes	characteristic
105	C₂²×C₄₁	#416	1	1	yes	characteristic
106	C₄×C₄₁	—	2	1	no	—
107	C₄×C₄₁	—	2	4	no	—
108	C₄×C₄₁	—	2	2	no	—
109	C₄×C₄₁	—	4	2	no	—
110	C₄×C₄₁	—	8	2	no	—
111	C₄×C₄₁	—	8	2	no	—
112	C₄×C₄₁	#454	1	2	yes	—
113	C₄×C₄₁	#465	1	2	yes	—
114	C₄×C₄₁	#467	1	2	yes	—
115	#2982	C₂×C₄₁	1	1	yes	characteristic
116	#2568	C₂×C₄₁	1	1	yes	characteristic
117	#1801	C₂×C₄₁	1	1	yes	characteristic
118	#1549	C₂×C₄₁	1	2	yes	—
119	#1303	C₂×C₄₁	1	2	yes	—
120	C₂×C₄₁	—	2	1	no	—
121	C₂×C₄₁	—	2	1	no	—
122	C₂×C₄₁	#1888	1	1	yes	characteristic
123	C₂×C₄₁	#1892	1	1	yes	characteristic
124	C₂×C₄₁	#1915	1	1	yes	characteristic
125	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
126	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
127	C₈×Q₈	—	2	4	no	—
128	#431	—	2	2	no	—
129	#431	C₂²×C₄₁	1	2	yes	—
130	#423	C₂²×C₄₁	1	2	yes	—
131	C₂×#101	—	2	1	no	—
132	#400	C₄×C₄₁	1	4	yes	—
133	#391	—	2	1	no	—
134	#391	—	2	2	no	—
135	#382	—	2	1	no	—
136	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
137	#343	—	2	1	no	—
138	#332	—	2	4	no	—
139	C₄₁	#9396	1	1	yes	characteristic, direct product factor, Sylow
140	C₂²×Q₈	—	2	1	no	—
141	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
142	C₂×M₁₆	—	2	2	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₂×C₄⋊C₄	—	2	1	no	—
148	C₂×C₄⋊C₄	—	2	1	no	—
149	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
150	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
151	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
152	C₂×C₄²	—	2	1	no	—
153	C₂×C₄²	D₄×C₄₁	1	2	yes	—
154	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
155	C₄⋊C₈	—	2	4	no	—
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	D₄×C₄₁	1	4	yes	—
159	#101	—	4	2	no	—
160	C₂²⋊C₈	—	2	2	no	—
161	C₄×C₈	—	2	4	no	—
162	C₄×C₈	—	2	2	no	—
163	#95	—	2	4	no	—
164	#95	—	2	4	no	—
165	#95	C₂×C₄×C₄₁	1	2	yes	—
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	4	4	no	—
169	C₂×Q₈	—	4	1	no	—
170	C₂×Q₈	—	4	1	no	—
171	C₂×Q₈	SD₁₆×C₄₁	1	2	yes	—
172	C₂×Q₈	Q₁₆×C₄₁	1	2	yes	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
176	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
177	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
178	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
179	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
180	M₁₆	—	4	2	no	—
181	M₁₆	—	4	2	no	—
182	C₂×C₈	—	2	4	no	—
183	C₂×C₈	—	4	2	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	2	4	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	2	2	no	—
191	C₄²	—	4	2	no	—
192	C₄²	C₂×D₄×C₄₁	1	2	yes	—
193	C₄²	#41×C₄₁	1	2	yes	—
194	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
195	Q₈	—	2	4	no	—
196	Q₈	—	2	4	no	—
197	Q₈	—	8	2	no	—
198	Q₈	—	8	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	4	1	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	4	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	#103×C₄₁	1	4	yes	—
211	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
212	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
213	C₂×C₄	#121×C₄₁	1	2	yes	—
214	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
215	C₂×C₄	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
216	C₂×C₄	C₂×Q₁₆×C₄₁	1	1	yes	characteristic
217	C₂×C₄	#135×C₄₁	1	2	yes	—
218	C₈	—	4	4	no	—
219	C₈	—	8	2	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	C₄₁×#386	1	1	yes	characteristic
223	C₂²	C₂×#103×C₄₁	1	1	yes	characteristic
224	C₂²	C₄₁×#416	1	1	yes	characteristic
225	C₄	—	2	1	no	—
226	C₄	—	2	4	no	—
227	C₄	—	2	2	no	—
228	C₄	—	4	2	no	—
229	C₄	—	8	2	no	—
230	C₄	—	8	2	no	—
231	C₄	C₄₁×#454	1	2	yes	—
232	C₄	C₄₁×#465	1	2	yes	—
233	C₄	C₄₁×#467	1	2	yes	—
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	C₄₁×#1888	1	1	yes	characteristic
237	C₂	C₄₁×#1892	1	1	yes	characteristic
238	C₂	C₄₁×#1915	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄₁×#2982

C₂

yes

maximal, characteristic

C₄₁×#2568

C₂

yes

maximal, characteristic

C₄₁×#1801

C₂

yes

maximal, characteristic

C₄₁×#1549

C₂

yes

maximal

C₄₁×#1303

C₂

yes

maximal

C₂×C₄⋊Q₈×C₄₁

C₂²

yes

characteristic

C₂×C₄×Q₈×C₄₁

C₂²

yes

characteristic

C₈×Q₈×C₄₁

—

C₄₁×#431

—

C₄₁×#431

C₂²

yes

—

C₄₁×#423

C₂²

yes

—

C₂×#101×C₄₁

—

C₄₁×#400

C₄

yes

—

C₄₁×#391

—

C₄₁×#391

—

C₄₁×#382

—

C₄×C₄⋊C₄×C₄₁

C₂²

yes

characteristic

C₄₁×#343

—

C₄₁×#332

—

C₂²×Q₈×C₄₁

—

C₂²×Q₈×C₄₁

D₄

yes

characteristic

C₂×M₁₆×C₄₁

—

C₄⋊Q₈×C₄₁

—

C₄⋊Q₈×C₄₁

—

C₄×Q₈×C₄₁

—

C₄×Q₈×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₄₁

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₄₁

D₄

yes

characteristic

C₂×C₄²×C₄₁

—

C₂×C₄²×C₄₁

D₄

yes

—

C₂×C₄²×C₄₁

C₂³

yes

characteristic

C₄⋊C₈×C₄₁

—

C₄⋊C₈×C₄₁

—

C₄⋊C₈×C₄₁

—

C₄⋊C₈×C₄₁

D₄

yes

—

#101×C₄₁

—

C₂²⋊C₈×C₄₁

—

C₄×C₈×C₄₁

—

C₄×C₈×C₄₁

—

#95×C₄₁

—

#95×C₄₁

—

#95×C₄₁

C₂×C₄

yes

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

SD₁₆

yes

—

C₂×Q₈×C₄₁

Q₁₆

yes

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₁

C₂×D₄

yes

characteristic

M₁₆×C₄₁

—

M₁₆×C₄₁

—

C₂×C₈×C₄₁

—

C₂×C₈×C₄₁

—

C₄⋊C₄×C₄₁

—

C₄⋊C₄×C₄₁

—

C₄⋊C₄×C₄₁

—

C₄⋊C₄×C₄₁

—

C₄⋊C₄×C₄₁

—

C₄²×C₄₁

—

C₄²×C₄₁

—

C₄²×C₄₁

—

C₄²×C₄₁

C₂×D₄

yes

—

C₄²×C₄₁

#41

yes

—

C₂³×C₄₁

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₄₁

—

Q₈×C₄₁

—

Q₈×C₄₁

—

Q₈×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

#103

yes

—

C₂×C₄×C₄₁

C₄×D₄

yes

—

C₂×C₄×C₄₁

#120

yes

characteristic

C₂×C₄×C₄₁

#121

yes

—

C₂×C₄×C₄₁

#123

yes

characteristic

C₂×C₄×C₄₁

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₁

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₄₁

#135

yes

—

C₈×C₄₁

—

C₈×C₄₁

—

100

#9396

C₄₁

yes

maximal, characteristic, direct product factor, Sylow

101

C₂²×C₄₁

—

102

C₂²×C₄₁

—

103

C₂²×C₄₁

#386

yes

characteristic

104

C₂²×C₄₁

C₂×#103

yes

characteristic

105

C₂²×C₄₁

#416

yes

characteristic

106

C₄×C₄₁

—

107

C₄×C₄₁

—

108

C₄×C₄₁

—

109

C₄×C₄₁

—

110

C₄×C₄₁

—

111

C₄×C₄₁

—

112

C₄×C₄₁

#454

yes

—

113

C₄×C₄₁

#465

yes

—

114

C₄×C₄₁

#467

yes

—

115

#2982

C₂×C₄₁

yes

characteristic

116

#2568

C₂×C₄₁

yes

characteristic

117

#1801

C₂×C₄₁

yes

characteristic

118

#1549

C₂×C₄₁

yes

—

119

#1303

C₂×C₄₁

yes

—

120

C₂×C₄₁

—

121

C₂×C₄₁

—

122

C₂×C₄₁

#1888

yes

characteristic

123

C₂×C₄₁

#1892

yes

characteristic

124

C₂×C₄₁

#1915

yes

characteristic

125

C₂×C₄⋊Q₈

C₂²×C₄₁

yes

characteristic

126

C₂×C₄×Q₈

C₂²×C₄₁

yes

characteristic

127

C₈×Q₈

—

128

#431

—

129

#431

C₂²×C₄₁

yes

—

130

#423

C₂²×C₄₁

yes

—

131

C₂×#101

—

132

#400

C₄×C₄₁

yes

—

133

#391

—

134

#391

—

135

#382

—

136

C₄×C₄⋊C₄

C₂²×C₄₁

yes

characteristic

137

#343

—

138

#332

—

139

C₄₁

#9396

yes

characteristic, direct product factor, Sylow

140

C₂²×Q₈

—

141

C₂²×Q₈

D₄×C₄₁

yes

characteristic

142

C₂×M₁₆

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

C₂×C₄×C₄₁

yes

—

150

C₂×C₄⋊C₄

C₂×C₄×C₄₁

yes

—

151

C₂×C₄⋊C₄

D₄×C₄₁

yes

characteristic

152

C₂×C₄²

—

153

C₂×C₄²

D₄×C₄₁

yes

—

154

C₂×C₄²

C₂³×C₄₁

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

D₄×C₄₁

yes

—

159

#101

—

160

C₂²⋊C₈

—

161

C₄×C₈

—

162

C₄×C₈

—

163

#95

—

164

#95

—

165

#95

C₂×C₄×C₄₁

yes

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

SD₁₆×C₄₁

yes

—

172

C₂×Q₈

Q₁₆×C₄₁

yes

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂²⋊C₄×C₄₁

yes

—

176

C₂²×C₄

C₂²⋊C₄×C₄₁

yes

—

177

C₂²×C₄

C₂²×C₄×C₄₁

yes

characteristic

178

C₂²×C₄

C₂×D₄×C₄₁

yes

characteristic

179

C₂²×C₄

C₂×D₄×C₄₁

yes

characteristic

180

M₁₆

—

181

M₁₆

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

C₂×D₄×C₄₁

yes

—

193

C₄²

#41×C₄₁

yes

—

194

C₂³

C₂×C₂²⋊C₄×C₄₁

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

198

Q₈

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

#103×C₄₁

yes

—

211

C₂×C₄

C₄×D₄×C₄₁

yes

—

212

C₂×C₄

#120×C₄₁

yes

characteristic

213

C₂×C₄

#121×C₄₁

yes

—

214

C₂×C₄

#123×C₄₁

yes

characteristic

215

C₂×C₄

C₂×SD₁₆×C₄₁

yes

characteristic

216

C₂×C₄

C₂×Q₁₆×C₄₁

yes

characteristic

217

C₂×C₄

#135×C₄₁

yes

—

218

C₈

—

219

C₈

—

220

C₂²

—

221

C₂²

—

222

C₂²

C₄₁×#386

yes

characteristic

223

C₂²

C₂×#103×C₄₁

yes

characteristic

224

C₂²

C₄₁×#416

yes

characteristic

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

C₄₁×#454

yes

—

232

C₄

C₄₁×#465

yes

—

233

C₄

C₄₁×#467

yes

—

234

C₂

—

235

C₂

—

236

C₂

C₄₁×#1888

yes

characteristic

237

C₂

C₄₁×#1892

yes

characteristic

238

C₂

C₄₁×#1915

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	#386
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂×C₄²	C₂³×C₄₁
prime radical	C₂³×C₄₁	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

subgroup

G/H

center, socle

C₂²×C₄₁

#386

commutator

C₂²×C₄

C₂²×C₄×C₄₁

Frattini, cosocle

C₂×C₄²

C₂³×C₄₁

prime radical

C₂³×C₄₁

C₂×C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

N	H ≅ G/N	type
100. #9396	C₄₁	direct (N × H)
139. C₄₁	#9396	direct (N × H)

H ≅ G/N

type

100. #9396

C₄₁

direct (N × H)

139. C₄₁

#9396

direct (N × H)

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

subgroup	index
C₄₁×#2982	2
C₄₁×#2568	2
C₄₁×#1801	2
C₄₁×#1549	2
C₄₁×#1303	2
#9396	41

subgroup

index

C₄₁×#2982

C₄₁×#2568

C₄₁×#1801

C₄₁×#1549

C₄₁×#1303

#9396

Subgroups — C₄₁×#9396 #23785597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C41×#9396 #23785597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#9396 #23785597