Group #23783796 — subgroups

Subgroups — C₄₁×#7595 #23783796

Order 10496.

630 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 166 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×C₄₁×#391	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1817	C₂	1	2	yes	maximal
3	C₄₁×#1272	C₂	1	4	yes	maximal, complemented
4	C₂³×Q₈×C₄₁	C₄	1	1	yes	characteristic
5	C₂²×C₄⋊C₄×C₄₁	C₄	1	1	yes	characteristic
6	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊C₈×C₄₁	—	2	2	no	—
8	C₄₁×#391	—	2	2	no	—
9	C₄₁×#391	C₄	1	2	yes	—
10	C₄₁×#391	C₂²	1	2	yes	—
11	C₂×#95×C₄₁	—	2	2	no	—
12	C₄₁×#336	—	2	2	no	—
13	C₄₁×#336	C₂²	1	4	yes	—
14	C₂²×Q₈×C₄₁	—	2	1	no	—
15	C₂²×Q₈×C₄₁	—	2	2	no	—
16	C₂²×Q₈×C₄₁	—	4	2	no	—
17	C₂²×Q₈×C₄₁	—	4	2	no	—
18	C₂²×Q₈×C₄₁	C₈	1	4	yes	complemented
19	C₂²×Q₈×C₄₁	C₂×C₄	1	2	yes	—
20	C₂³×C₄×C₄₁	—	2	1	no	—
21	C₂³×C₄×C₄₁	—	2	1	no	—
22	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₄₁	D₄	1	2	yes	—
24	C₂²×C₈×C₄₁	—	2	4	no	—
25	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
26	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
27	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₄₁	—	4	2	no	—
29	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₄₁	D₄	1	2	yes	—
31	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
32	C₂²⋊C₈×C₄₁	—	4	4	no	—
33	#95×C₄₁	—	2	4	no	—
34	#95×C₄₁	—	2	4	no	—
35	C₂⁴×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Q₈×C₄₁	—	2	4	no	—
37	C₂×Q₈×C₄₁	—	2	2	no	—
38	C₂×Q₈×C₄₁	—	4	8	no	—
39	C₂×Q₈×C₄₁	—	4	2	no	—
40	C₂×Q₈×C₄₁	—	4	2	no	—
41	C₂×Q₈×C₄₁	—	4	8	no	—
42	C₂×Q₈×C₄₁	—	4	2	no	—
43	C₂×Q₈×C₄₁	—	4	2	no	—
44	C₂×Q₈×C₄₁	C₂×C₈	1	4	yes	—
45	C₂²×C₄×C₄₁	—	2	2	no	—
46	C₂²×C₄×C₄₁	—	2	2	no	—
47	C₂²×C₄×C₄₁	—	2	4	no	—
48	C₂²×C₄×C₄₁	—	2	4	no	—
49	C₂²×C₄×C₄₁	—	2	2	no	—
50	C₂²×C₄×C₄₁	—	2	4	no	—
51	C₂²×C₄×C₄₁	—	2	2	no	—
52	C₂²×C₄×C₄₁	—	4	2	no	—
53	C₂²×C₄×C₄₁	—	4	2	no	—
54	C₂²×C₄×C₄₁	—	4	2	no	—
55	C₂²×C₄×C₄₁	—	4	4	no	—
56	C₂²×C₄×C₄₁	—	4	2	no	—
57	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₄₁	C₂×C₈	1	2	yes	—
60	C₂²×C₄×C₄₁	M₁₆	1	2	yes	—
61	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₄₁	—	4	4	no	—
64	C₂×C₈×C₄₁	—	4	4	no	—
65	C₂×C₈×C₄₁	—	4	4	no	—
66	C₄⋊C₄×C₄₁	—	4	2	no	—
67	C₄⋊C₄×C₄₁	—	4	2	no	—
68	C₄²×C₄₁	—	4	1	no	—
69	C₄²×C₄₁	—	4	2	no	—
70	C₄²×C₄₁	—	4	1	no	—
71	C₂³×C₄₁	—	2	2	no	—
72	C₂³×C₄₁	—	2	2	no	—
73	C₂³×C₄₁	C₂²⋊C₈	1	2	yes	—
74	C₂³×C₄₁	#99	1	2	yes	—
75	C₂³×C₄₁	#100	1	2	yes	—
76	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	Q₈×C₄₁	—	4	4	no	—
78	Q₈×C₄₁	—	4	8	no	—
79	Q₈×C₄₁	—	4	4	no	—
80	C₂×C₄×C₄₁	—	2	4	no	—
81	C₂×C₄×C₄₁	—	2	4	no	—
82	C₂×C₄×C₄₁	—	2	2	no	—
83	C₂×C₄×C₄₁	—	2	1	no	—
84	C₂×C₄×C₄₁	—	2	1	no	—
85	C₂×C₄×C₄₁	—	2	1	no	—
86	C₂×C₄×C₄₁	—	2	1	no	—
87	C₂×C₄×C₄₁	—	2	2	no	—
88	C₂×C₄×C₄₁	—	2	4	no	—
89	C₂×C₄×C₄₁	—	2	2	no	—
90	C₂×C₄×C₄₁	—	2	2	no	—
91	C₂×C₄×C₄₁	—	2	2	no	—
92	C₂×C₄×C₄₁	—	4	8	no	—
93	C₂×C₄×C₄₁	—	4	8	no	—
94	C₂×C₄×C₄₁	—	4	2	no	—
95	C₂×C₄×C₄₁	—	4	2	no	—
96	C₂×C₄×C₄₁	—	4	2	no	—
97	C₂×C₄×C₄₁	—	4	4	no	—
98	C₂×C₄×C₄₁	—	8	4	no	—
99	C₂×C₄×C₄₁	C₂²⋊C₈	1	2	yes	—
100	C₂×C₄×C₄₁	C₂²×C₈	1	1	yes	characteristic
101	C₂×C₄×C₄₁	C₂×M₁₆	1	1	yes	characteristic
102	C₂×C₄×C₄₁	#137	1	4	yes	—
103	C₈×C₄₁	—	8	4	no	—
104	#7595	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂²×C₄₁	—	2	2	no	—
106	C₂²×C₄₁	—	2	4	no	—
107	C₂²×C₄₁	—	2	4	no	—
108	C₂²×C₄₁	—	2	2	no	—
109	C₂²×C₄₁	#323	1	4	yes	—
110	C₂²×C₄₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
111	C₂²×C₄₁	C₂×#99	1	1	yes	characteristic
112	C₂²×C₄₁	C₂×#100	1	1	yes	characteristic
113	C₂²×C₄₁	#419	1	2	yes	—
114	C₂²×C₄₁	#421	1	2	yes	—
115	C₄×C₄₁	—	2	2	no	—
116	C₄×C₄₁	—	2	1	no	—
117	C₄×C₄₁	—	2	1	no	—
118	C₄×C₄₁	—	2	4	no	—
119	C₄×C₄₁	—	4	4	no	—
120	C₄×C₄₁	—	4	2	no	—
121	C₄×C₄₁	—	8	2	no	—
122	C₂×#391	C₂×C₄₁	1	1	yes	characteristic
123	#1817	C₂×C₄₁	1	2	yes	—
124	#1272	C₂×C₄₁	1	4	yes	complemented
125	C₂×C₄₁	—	2	4	no	—
126	C₂×C₄₁	C₂×#323	1	1	yes	characteristic
127	C₂×C₄₁	#1479	1	2	yes	—
128	C₂×C₄₁	#1511	1	2	yes	—
129	C₂×C₄₁	#1533	1	1	yes	characteristic
130	C₂×C₄₁	#1558	1	1	yes	characteristic
131	C₂³×Q₈	C₄×C₄₁	1	1	yes	characteristic
132	C₂²×C₄⋊C₄	C₄×C₄₁	1	1	yes	characteristic
133	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
134	C₂×C₂²⋊C₈	—	2	2	no	—
135	#391	—	2	2	no	—
136	#391	C₄×C₄₁	1	2	yes	—
137	#391	C₂²×C₄₁	1	2	yes	—
138	C₂×#95	—	2	2	no	—
139	#336	—	2	2	no	—
140	#336	C₂²×C₄₁	1	4	yes	—
141	C₄₁	#7595	1	1	yes	characteristic, direct product factor, Sylow
142	C₂²×Q₈	—	2	1	no	—
143	C₂²×Q₈	—	2	2	no	—
144	C₂²×Q₈	—	4	2	no	—
145	C₂²×Q₈	—	4	2	no	—
146	C₂²×Q₈	C₈×C₄₁	1	4	yes	complemented
147	C₂²×Q₈	C₂×C₄×C₄₁	1	2	yes	—
148	C₂³×C₄	—	2	1	no	—
149	C₂³×C₄	—	2	1	no	—
150	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
151	C₂³×C₄	D₄×C₄₁	1	2	yes	—
152	C₂²×C₈	—	2	4	no	—
153	C₂×C₄⋊C₄	—	2	1	no	—
154	C₂×C₄⋊C₄	—	4	2	no	—
155	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
156	C₂×C₄²	—	4	2	no	—
157	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
158	C₂×C₄²	D₄×C₄₁	1	2	yes	—
159	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
160	C₂²⋊C₈	—	4	4	no	—
161	#95	—	2	4	no	—
162	#95	—	2	4	no	—
163	C₂⁴	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
164	C₂×Q₈	—	2	4	no	—
165	C₂×Q₈	—	2	2	no	—
166	C₂×Q₈	—	4	8	no	—
167	C₂×Q₈	—	4	2	no	—
168	C₂×Q₈	—	4	2	no	—
169	C₂×Q₈	—	4	8	no	—
170	C₂×Q₈	—	4	2	no	—
171	C₂×Q₈	—	4	2	no	—
172	C₂×Q₈	C₂×C₈×C₄₁	1	4	yes	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	—	2	4	no	—
176	C₂²×C₄	—	2	4	no	—
177	C₂²×C₄	—	2	2	no	—
178	C₂²×C₄	—	2	4	no	—
179	C₂²×C₄	—	2	2	no	—
180	C₂²×C₄	—	4	2	no	—
181	C₂²×C₄	—	4	2	no	—
182	C₂²×C₄	—	4	2	no	—
183	C₂²×C₄	—	4	4	no	—
184	C₂²×C₄	—	4	2	no	—
185	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
186	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
187	C₂²×C₄	C₂×C₈×C₄₁	1	2	yes	—
188	C₂²×C₄	M₁₆×C₄₁	1	2	yes	—
189	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
190	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
191	C₂×C₈	—	4	4	no	—
192	C₂×C₈	—	4	4	no	—
193	C₂×C₈	—	4	4	no	—
194	C₄⋊C₄	—	4	2	no	—
195	C₄⋊C₄	—	4	2	no	—
196	C₄²	—	4	1	no	—
197	C₄²	—	4	2	no	—
198	C₄²	—	4	1	no	—
199	C₂³	—	2	2	no	—
200	C₂³	—	2	2	no	—
201	C₂³	C₂²⋊C₈×C₄₁	1	2	yes	—
202	C₂³	#99×C₄₁	1	2	yes	—
203	C₂³	#100×C₄₁	1	2	yes	—
204	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
205	Q₈	—	4	4	no	—
206	Q₈	—	4	8	no	—
207	Q₈	—	4	4	no	—
208	C₂×C₄	—	2	4	no	—
209	C₂×C₄	—	2	4	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	4	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	4	8	no	—
221	C₂×C₄	—	4	8	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	4	no	—
226	C₂×C₄	—	8	4	no	—
227	C₂×C₄	C₂²⋊C₈×C₄₁	1	2	yes	—
228	C₂×C₄	C₂²×C₈×C₄₁	1	1	yes	characteristic
229	C₂×C₄	C₂×M₁₆×C₄₁	1	1	yes	characteristic
230	C₂×C₄	#137×C₄₁	1	4	yes	—
231	C₈	—	8	4	no	—
232	C₂²	—	2	4	no	—
233	C₂²	—	2	2	no	—
234	C₂²	—	2	2	no	—
235	C₂²	—	2	4	no	—
236	C₂²	C₄₁×#323	1	4	yes	—
237	C₂²	C₂×C₂²⋊C₈×C₄₁	1	1	yes	characteristic
238	C₂²	C₂×#99×C₄₁	1	1	yes	characteristic
239	C₂²	C₂×#100×C₄₁	1	1	yes	characteristic
240	C₂²	C₄₁×#419	1	2	yes	—
241	C₂²	C₄₁×#421	1	2	yes	—
242	C₄	—	2	4	no	—
243	C₄	—	2	2	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	4	2	no	—
247	C₄	—	4	4	no	—
248	C₄	—	8	2	no	—
249	C₂	—	2	4	no	—
250	C₂	C₂×C₄₁×#323	1	1	yes	characteristic
251	C₂	C₄₁×#1479	1	2	yes	—
252	C₂	C₄₁×#1511	1	2	yes	—
253	C₂	C₄₁×#1533	1	1	yes	characteristic
254	C₂	C₄₁×#1558	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄₁×#391

C₂

yes

maximal, characteristic

C₄₁×#1817

C₂

yes

maximal

C₄₁×#1272

C₂

yes

maximal, complemented

C₂³×Q₈×C₄₁

C₄

yes

characteristic

C₂²×C₄⋊C₄×C₄₁

C₄

yes

characteristic

C₂²×C₄²×C₄₁

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₄₁

—

C₄₁×#391

—

C₄₁×#391

C₄

yes

—

C₄₁×#391

C₂²

yes

—

C₂×#95×C₄₁

—

C₄₁×#336

—

C₄₁×#336

C₂²

yes

—

C₂²×Q₈×C₄₁

—

C₂²×Q₈×C₄₁

—

C₂²×Q₈×C₄₁

—

C₂²×Q₈×C₄₁

—

C₂²×Q₈×C₄₁

C₈

yes

complemented

C₂²×Q₈×C₄₁

C₂×C₄

yes

—

C₂³×C₄×C₄₁

—

C₂³×C₄×C₄₁

—

C₂³×C₄×C₄₁

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₁

D₄

yes

—

C₂²×C₈×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

C₂×C₄

yes

—

C₂×C₄²×C₄₁

—

C₂×C₄²×C₄₁

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₁

D₄

yes

—

C₂×C₄²×C₄₁

C₂³

yes

characteristic

C₂²⋊C₈×C₄₁

—

#95×C₄₁

—

#95×C₄₁

—

C₂⁴×C₄₁

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

C₂×C₈

yes

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₁

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₁

C₂×C₈

yes

—

C₂²×C₄×C₄₁

M₁₆

yes

—

C₂²×C₄×C₄₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₁

C₂×D₄

yes

—

C₂×C₈×C₄₁

—

C₂×C₈×C₄₁

—

C₂×C₈×C₄₁

—

C₄⋊C₄×C₄₁

—

C₄⋊C₄×C₄₁

—

C₄²×C₄₁

—

C₄²×C₄₁

—

C₄²×C₄₁

—

C₂³×C₄₁

—

C₂³×C₄₁

—

C₂³×C₄₁

C₂²⋊C₈

yes

—

C₂³×C₄₁

#99

yes

—

C₂³×C₄₁

#100

yes

—

C₂³×C₄₁

C₂×C₂²⋊C₄

yes

characteristic

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

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

C₂²⋊C₈

yes

—

100

C₂×C₄×C₄₁

C₂²×C₈

yes

characteristic

101

C₂×C₄×C₄₁

C₂×M₁₆

yes

characteristic

102

C₂×C₄×C₄₁

#137

yes

—

103

C₈×C₄₁

—

104

#7595

C₄₁

yes

maximal, characteristic, direct product factor, Sylow

105

C₂²×C₄₁

—

106

C₂²×C₄₁

—

107

C₂²×C₄₁

—

108

C₂²×C₄₁

—

109

C₂²×C₄₁

#323

yes

—

110

C₂²×C₄₁

C₂×C₂²⋊C₈

yes

characteristic

111

C₂²×C₄₁

C₂×#99

yes

characteristic

112

C₂²×C₄₁

C₂×#100

yes

characteristic

113

C₂²×C₄₁

#419

yes

—

114

C₂²×C₄₁

#421

yes

—

115

C₄×C₄₁

—

116

C₄×C₄₁

—

117

C₄×C₄₁

—

118

C₄×C₄₁

—

119

C₄×C₄₁

—

120

C₄×C₄₁

—

121

C₄×C₄₁

—

122

C₂×#391

C₂×C₄₁

yes

characteristic

123

#1817

C₂×C₄₁

yes

—

124

#1272

C₂×C₄₁

yes

complemented

125

C₂×C₄₁

—

126

C₂×C₄₁

C₂×#323

yes

characteristic

127

C₂×C₄₁

#1479

yes

—

128

C₂×C₄₁

#1511

yes

—

129

C₂×C₄₁

#1533

yes

characteristic

130

C₂×C₄₁

#1558

yes

characteristic

131

C₂³×Q₈

C₄×C₄₁

yes

characteristic

132

C₂²×C₄⋊C₄

C₄×C₄₁

yes

characteristic

133

C₂²×C₄²

C₂²×C₄₁

yes

characteristic

134

C₂×C₂²⋊C₈

—

135

#391

—

136

#391

C₄×C₄₁

yes

—

137

#391

C₂²×C₄₁

yes

—

138

C₂×#95

—

139

#336

—

140

#336

C₂²×C₄₁

yes

—

141

C₄₁

#7595

yes

characteristic, direct product factor, Sylow

142

C₂²×Q₈

—

143

C₂²×Q₈

—

144

C₂²×Q₈

—

145

C₂²×Q₈

—

146

C₂²×Q₈

C₈×C₄₁

yes

complemented

147

C₂²×Q₈

C₂×C₄×C₄₁

yes

—

148

C₂³×C₄

—

149

C₂³×C₄

—

150

C₂³×C₄

C₂×C₄×C₄₁

yes

characteristic

151

C₂³×C₄

D₄×C₄₁

yes

—

152

C₂²×C₈

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

C₂×C₄×C₄₁

yes

—

156

C₂×C₄²

—

157

C₂×C₄²

C₂×C₄×C₄₁

yes

characteristic

158

C₂×C₄²

D₄×C₄₁

yes

—

159

C₂×C₄²

C₂³×C₄₁

yes

characteristic

160

C₂²⋊C₈

—

161

#95

—

162

#95

—

163

C₂⁴

C₂²⋊C₄×C₄₁

yes

characteristic

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

C₂×C₈×C₄₁

yes

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

C₂²⋊C₄×C₄₁

yes

—

186

C₂²×C₄

C₂²⋊C₄×C₄₁

yes

characteristic

187

C₂²×C₄

C₂×C₈×C₄₁

yes

—

188

C₂²×C₄

M₁₆×C₄₁

yes

—

189

C₂²×C₄

C₂²×C₄×C₄₁

yes

characteristic

190

C₂²×C₄

C₂×D₄×C₄₁

yes

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄²

—

197

C₄²

—

198

C₄²

—

199

C₂³

—

200

C₂³

—

201

C₂³

C₂²⋊C₈×C₄₁

yes

—

202

C₂³

#99×C₄₁

yes

—

203

C₂³

#100×C₄₁

yes

—

204

C₂³

C₂×C₂²⋊C₄×C₄₁

yes

characteristic

205

Q₈

—

206

Q₈

—

207

Q₈

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

C₂²⋊C₈×C₄₁

yes

—

228

C₂×C₄

C₂²×C₈×C₄₁

yes

characteristic

229

C₂×C₄

C₂×M₁₆×C₄₁

yes

characteristic

230

C₂×C₄

#137×C₄₁

yes

—

231

C₈

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

C₄₁×#323

yes

—

237

C₂²

C₂×C₂²⋊C₈×C₄₁

yes

characteristic

238

C₂²

C₂×#99×C₄₁

yes

characteristic

239

C₂²

C₂×#100×C₄₁

yes

characteristic

240

C₂²

C₄₁×#419

yes

—

241

C₂²

C₄₁×#421

yes

—

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₂

—

250

C₂

C₂×C₄₁×#323

yes

characteristic

251

C₂

C₄₁×#1479

yes

—

252

C₂

C₄₁×#1511

yes

—

253

C₂

C₄₁×#1533

yes

characteristic

254

C₂

C₄₁×#1558

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₄₁
Frattini, cosocle	C₂×C₄²	C₂³×C₄₁
prime radical	C₂⁴×C₄₁	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

subgroup

G/H

center, socle

C₂³×C₄₁

C₂×C₂²⋊C₄

commutator

C₂×C₄

C₂²×C₈×C₄₁

Frattini, cosocle

C₂×C₄²

C₂³×C₄₁

prime radical

C₂⁴×C₄₁

C₂²⋊C₄

LCS

G ▷ C₂×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

N	H ≅ G/N	type
3. C₄₁×#1272	C₂	semidirect
18. C₂²×Q₈×C₄₁	C₈	semidirect
104. #7595	C₄₁	direct (N × H)
124. #1272	C₂×C₄₁	semidirect
141. C₄₁	#7595	direct (N × H)
146. C₂²×Q₈	C₈×C₄₁	semidirect

H ≅ G/N

type

3. C₄₁×#1272

C₂

semidirect

18. C₂²×Q₈×C₄₁

C₈

semidirect

104. #7595

C₄₁

direct (N × H)

124. #1272

C₂×C₄₁

semidirect

141. C₄₁

#7595

direct (N × H)

146. C₂²×Q₈

C₈×C₄₁

semidirect

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

subgroup	index
C₂×C₄₁×#391	2
C₄₁×#1817	2
C₄₁×#1272	2
#7595	41

subgroup

index

C₂×C₄₁×#391

C₄₁×#1817

C₄₁×#1272

#7595

Subgroups — C₄₁×#7595 #23783796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C41×#7595 #23783796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#7595 #23783796