Subgroups — #34082437

Order 19328.

1556 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₅₁	C₂	1	2	yes	maximal, complemented
2	#23752789	C₂	1	4	yes	maximal, complemented
3	#23752787	C₂	1	2	yes	maximal, complemented
4	#23752782	C₂	1	2	yes	maximal, complemented
5	#23752780	C₂	1	2	yes	maximal, complemented
6	#23752775	C₂	1	2	yes	maximal, complemented
7	#23752770	C₂	1	4	yes	maximal, complemented
8	#23752762	C₂	1	1	yes	maximal, characteristic, complemented
9	#23752758	C₂	1	2	yes	maximal, complemented
10	#23752721	C₂	1	8	yes	maximal, complemented
11	C₂×#18012696	C₂	1	1	yes	maximal, characteristic, complemented
12	#532×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#14559005	C₂²	1	2	yes	—
14	C₂×#14559004	C₂²	1	4	yes	—
15	C₂×#14559004	C₂²	1	2	yes	complemented
16	C₂×#14559003	C₂²	1	2	yes	—
17	C₂×#14559003	C₂²	1	4	yes	complemented
18	#41×D₁₅₁	—	2	16	no	—
19	C₂×Q₈×D₁₅₁	C₂²	1	2	yes	complemented
20	C₂×D₄×D₁₅₁	C₂²	1	4	yes	—
21	C₂×D₄×D₁₅₁	C₂²	1	2	yes	complemented
22	C₂²×C₄×D₁₅₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₁₅₁	C₂²	1	4	yes	complemented
24	#18012739	C₂²	1	1	yes	characteristic, complemented
25	#18012737	C₂²	1	2	yes	complemented
26	#18012736	C₂²	1	1	yes	characteristic, complemented
27	#18012735	C₂²	1	2	yes	complemented
28	#18012728	C₂²	1	2	yes	complemented
29	#18012727	C₂²	1	2	yes	complemented
30	#18012726	C₂²	1	2	yes	complemented
31	#18012724	C₂²	1	8	yes	complemented
32	#18012721	C₂²	1	8	yes	complemented
33	#18012717	C₂²	1	8	yes	complemented
34	#18012716	C₂²	1	8	yes	complemented
35	#18012713	C₂²	1	4	yes	complemented
36	#18012712	C₂²	1	8	yes	complemented
37	#18012711	C₂²	1	8	yes	complemented
38	#18012711	C₂²	1	8	yes	complemented
39	#18012709	C₂²	1	8	yes	complemented
40	#18012707	C₂²	1	8	yes	complemented
41	C₄×D₆₀₄	C₂²	1	4	yes	complemented
42	C₄×C₂²⋊D₁₅₁	C₂²	1	8	yes	complemented
43	#18012696	C₂²	1	4	yes	complemented
44	#18012696	C₂²	1	2	yes	complemented
45	#18012696	C₂²	1	2	yes	complemented
46	C₂×Dic₁₅₁⋊C₄	C₂²	1	2	yes	complemented
47	C₂×(C₂×D₁₅₁)⋊C₄	C₂²	1	2	yes	—
48	C₂×C₄×Dic₁₅₁	C₂²	1	1	yes	characteristic, complemented
49	C₂×#41×C₁₅₁	C₂²	1	2	yes	complemented
50	C₄⋊Q₈×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
51	#127×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
52	#124×C₁₅₁	C₂²	1	2	yes	complemented
53	#121×C₁₅₁	C₂²	1	4	yes	complemented
54	C₄×D₄×C₁₅₁	C₂²	1	4	yes	complemented
55	C₂×C₄²×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
56	C₂³×D₁₅₁	C₂³	1	4	yes	—
57	C₂³×D₁₅₁	C₂³	1	1	yes	characteristic
58	#14559005	—	2	8	no	—
59	#14559004	—	2	16	no	—
60	#14559004	—	2	8	no	—
61	#14559003	—	2	16	no	—
62	#14559003	—	2	8	no	—
63	C₂×Dic₃₀₂	C₂³	1	4	yes	—
64	C₂×Dic₃₀₂	C₂³	1	2	yes	—
65	Q₈×D₁₅₁	—	2	8	no	—
66	C₂×D₆₀₄	C₂³	1	4	yes	—
67	C₂×D₆₀₄	C₂³	1	2	yes	—
68	C₂×D₆₀₄	C₂³	1	4	yes	—
69	C₂×C₂²⋊D₁₅₁	C₂³	1	4	yes	—
70	C₂×C₂²⋊D₁₅₁	C₂³	1	4	yes	—
71	C₂×C₂²⋊D₁₅₁	C₂³	1	4	yes	—
72	C₂×C₂²⋊D₁₅₁	C₂³	1	8	yes	—
73	D₄×D₁₅₁	—	2	16	no	—
74	D₄×D₁₅₁	—	2	8	no	—
75	C₂²×Dic₁₅₁	C₂³	1	4	yes	—
76	C₂²×Dic₁₅₁	C₂³	1	2	yes	—
77	C₂²×Dic₁₅₁	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₁₅₁	—	2	16	no	—
79	C₂×C₄×D₁₅₁	D₄	1	8	yes	complemented
80	C₂×C₄×D₁₅₁	C₂³	1	4	yes	—
81	C₂×C₄×D₁₅₁	C₂³	1	4	yes	—
82	C₂×C₄×D₁₅₁	C₂³	1	4	yes	—
83	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
84	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
85	C₄⋊Dic₁₅₁	C₂³	1	4	yes	—
86	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
87	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
88	Dic₁₅₁⋊C₄	C₂³	1	8	yes	—
89	C₂²⋊Dic₁₅₁	C₂³	1	8	yes	—
90	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
91	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
92	(C₂×D₁₅₁)⋊C₄	C₂³	1	8	yes	—
93	(C₂×D₁₅₁)⋊C₄	C₂³	1	8	yes	—
94	C₄×Dic₁₅₁	C₂³	1	2	yes	—
95	C₄×Dic₁₅₁	C₂³	1	2	yes	—
96	#41×C₁₅₁	—	2	8	no	—
97	C₂×Q₈×C₁₅₁	C₂³	1	2	yes	—
98	C₂×D₄×C₁₅₁	C₂³	1	4	yes	—
99	C₂×D₄×C₁₅₁	C₂³	1	2	yes	—
100	C₂×D₄×C₁₅₁	C₂³	1	4	yes	—
101	C₂²×C₄×C₁₅₁	C₂³	1	4	yes	—
102	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
103	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
104	C₄⋊C₄×C₁₅₁	C₂³	1	4	yes	—
105	C₂²⋊C₄×C₁₅₁	C₂³	1	8	yes	—
106	C₄²×C₁₅₁	C₂³	1	2	yes	—
107	C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
108	C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
109	C₂²×D₁₅₁	—	2	8	no	—
110	C₂²×D₁₅₁	—	4	2	no	—
111	C₂²×D₁₅₁	—	4	8	no	—
112	C₂²×D₁₅₁	C₂×D₄	1	4	yes	—
113	C₂²×D₁₅₁	C₂⁴	1	4	yes	—
114	C₂²×D₁₅₁	C₂⁴	1	2	yes	—
115	Dic₃₀₂	—	2	4	no	—
116	Dic₃₀₂	—	2	8	no	—
117	D₆₀₄	—	2	8	no	—
118	D₆₀₄	—	2	4	no	—
119	D₆₀₄	—	4	4	no	—
120	C₂²⋊D₁₅₁	—	2	8	no	—
121	C₂²⋊D₁₅₁	—	2	8	no	—
122	C₂²⋊D₁₅₁	—	2	8	no	—
123	C₂²⋊D₁₅₁	—	4	8	no	—
124	C₂×Dic₁₅₁	—	2	8	no	—
125	C₂×Dic₁₅₁	—	4	2	no	—
126	C₂×Dic₁₅₁	C₂×D₄	1	4	yes	—
127	C₂×Dic₁₅₁	C₂⁴	1	4	yes	—
128	C₂×Dic₁₅₁	C₂⁴	1	4	yes	—
129	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
130	C₄×D₁₅₁	—	2	8	no	—
131	C₄×D₁₅₁	—	2	8	no	—
132	C₄×D₁₅₁	—	2	8	no	—
133	C₄×D₁₅₁	C₂×D₄	1	8	yes	—
134	C₄×D₁₅₁	C₂×D₄	1	8	yes	—
135	C₂³×C₁₅₁	C₂⁴	1	4	yes	—
136	C₂³×C₁₅₁	C₂⁴	1	1	yes	characteristic
137	Q₈×C₁₅₁	—	2	4	no	—
138	D₄×C₁₅₁	—	2	8	no	—
139	D₄×C₁₅₁	—	2	4	no	—
140	D₄×C₁₅₁	—	4	4	no	—
141	C₂×C₄×C₁₅₁	—	2	8	no	—
142	C₂×C₄×C₁₅₁	—	4	2	no	—
143	C₂×C₄×C₁₅₁	C₂×D₄	1	4	yes	—
144	C₂×C₄×C₁₅₁	C₂⁴	1	4	yes	—
145	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
146	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
147	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
148	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
149	C₂²×C₁₅₁	—	2	2	no	—
150	C₂²×C₁₅₁	—	2	4	no	—
151	C₂²×C₁₅₁	—	2	8	no	—
152	C₂²×C₁₅₁	C₂²×D₄	1	2	yes	—
153	C₂²×C₁₅₁	C₂⁵	1	1	yes	characteristic
154	C₂×D₁₅₁	—	2	4	no	—
155	C₂×D₁₅₁	—	2	4	no	—
156	C₂×D₁₅₁	—	2	8	no	—
157	C₂×D₁₅₁	—	4	4	no	—
158	C₂×D₁₅₁	—	4	16	no	—
159	C₂×D₁₅₁	C₂²×D₄	1	4	yes	—
160	C₄×C₁₅₁	—	2	4	no	—
161	C₄×C₁₅₁	—	2	2	no	—
162	C₄×C₁₅₁	—	2	2	no	—
163	C₄×C₁₅₁	C₂²×D₄	1	2	yes	—
164	C₄×C₁₅₁	C₂²×D₄	1	2	yes	—
165	Dic₁₅₁	—	2	4	no	—
166	Dic₁₅₁	—	2	4	no	—
167	Dic₁₅₁	C₂²×D₄	1	4	yes	—
168	C₂×C₁₅₁	—	2	2	no	—
169	C₂×C₁₅₁	—	4	4	no	—
170	C₂×C₁₅₁	C₂³×D₄	1	1	yes	characteristic
171	C₂×C₁₅₁	#585	1	2	yes	—
172	D₁₅₁	—	2	4	no	—
173	D₁₅₁	—	4	4	no	—
174	C₁₅₁	#3449	1	1	yes	characteristic, complemented, Sylow
175	#3449	—	151	1	no	maximal, Sylow
176	C₂²×#41	—	151	2	no	—
177	#537	—	151	4	no	—
178	#536	—	151	2	no	—
179	#536	—	151	2	no	—
180	#535	—	151	2	no	—
181	#535	—	151	2	no	—
182	#534	—	151	4	no	—
183	#532	—	151	2	no	—
184	#532	—	151	1	no	—
185	#532	D₁₅₁	1	1	yes	characteristic, complemented
186	#525	—	151	8	no	—
187	C₂×#117	—	151	1	no	—
188	C₂×#41	—	302	16	no	—
189	C₂×#41	—	151	2	no	—
190	C₂×#41	—	151	2	no	—
191	C₂×#41	—	151	4	no	—
192	C₂×#41	—	151	4	no	—
193	C₂×#41	—	151	2	no	—
194	C₂×#41	C₂×D₁₅₁	1	2	yes	complemented
195	C₂²×Q₈	—	151	2	no	—
196	C₂²×D₄	—	151	4	no	—
197	C₂²×D₄	—	151	2	no	—
198	C₂³×C₄	—	151	4	no	—
199	C₂³×C₄	—	151	1	no	—
200	C₄⋊Q₈	—	151	2	no	—
201	C₄⋊Q₈	—	151	1	no	—
202	C₄⋊Q₈	C₂×D₁₅₁	1	1	yes	characteristic, complemented
203	#127	—	151	2	no	—
204	#127	—	151	1	no	—
205	#127	C₂×D₁₅₁	1	1	yes	characteristic, complemented
206	#124	—	151	2	no	—
207	#124	—	151	2	no	—
208	#124	—	151	2	no	—
209	#124	C₂×D₁₅₁	1	2	yes	complemented
210	#123	—	151	8	no	—
211	#123	—	151	8	no	—
212	C₂²⋊Q₈	—	151	8	no	—
213	C₂²⋊Q₈	—	151	8	no	—
214	#121	—	151	8	no	—
215	#121	—	151	8	no	—
216	#121	—	151	4	no	—
217	#121	—	151	8	no	—
218	#121	C₂×D₁₅₁	1	4	yes	complemented
219	#120	—	151	8	no	—
220	#120	—	151	8	no	—
221	C₄×D₄	—	151	8	no	—
222	C₄×D₄	—	151	4	no	—
223	C₄×D₄	C₂×D₁₅₁	1	4	yes	complemented
224	#117	—	151	4	no	—
225	#117	—	151	2	no	—
226	#117	—	151	2	no	—
227	C₂×C₄⋊C₄	—	151	2	no	—
228	C₂×C₂²⋊C₄	—	151	2	no	—
229	C₂×C₄²	—	151	1	no	—
230	C₂×C₄²	C₂×D₁₅₁	1	1	yes	characteristic, complemented
231	C₂⁴	—	151	4	no	—
232	C₂⁴	—	151	1	no	—
233	#41	—	2	8	no	—
234	#41	—	302	16	no	—
235	#41	—	302	16	no	—
236	#41	—	302	8	no	—
237	#41	—	302	8	no	—
238	#41	—	302	8	no	—
239	C₂×Q₈	—	302	8	no	—
240	C₂×Q₈	—	151	4	no	—
241	C₂×Q₈	—	151	2	no	—
242	C₂×Q₈	C₂²×D₁₅₁	1	2	yes	—
243	C₂×D₄	—	302	16	no	—
244	C₂×D₄	—	302	8	no	—
245	C₂×D₄	—	151	4	no	—
246	C₂×D₄	—	151	4	no	—
247	C₂×D₄	—	151	4	no	—
248	C₂×D₄	—	151	8	no	—
249	C₂×D₄	—	151	4	no	—
250	C₂×D₄	—	151	2	no	—
251	C₂×D₄	—	151	4	no	—
252	C₂×D₄	C₂²×D₁₅₁	1	4	yes	—
253	C₂×D₄	C₂²×D₁₅₁	1	2	yes	—
254	C₂×D₄	C₂²×D₁₅₁	1	4	yes	—
255	C₂²×C₄	—	302	16	no	—
256	C₂²×C₄	—	151	4	no	—
257	C₂²×C₄	—	151	4	no	—
258	C₂²×C₄	—	151	4	no	—
259	C₂²×C₄	—	151	4	no	—
260	C₂²×C₄	—	151	2	no	—
261	C₂²×C₄	—	151	1	no	—
262	C₂²×C₄	—	151	8	no	—
263	C₂²×C₄	—	151	2	no	—
264	C₂²×C₄	—	151	2	no	—
265	C₂²×C₄	C₂²×D₁₅₁	1	4	yes	—
266	C₂²×C₄	C₂²×D₁₅₁	1	2	yes	—
267	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
268	C₄⋊C₄	—	151	4	no	—
269	C₄⋊C₄	—	151	4	no	—
270	C₄⋊C₄	—	151	8	no	—
271	C₄⋊C₄	—	151	4	no	—
272	C₄⋊C₄	C₂²×D₁₅₁	1	4	yes	—
273	C₂²⋊C₄	—	151	8	no	—
274	C₂²⋊C₄	—	151	4	no	—
275	C₂²⋊C₄	—	151	4	no	—
276	C₂²⋊C₄	—	151	8	no	—
277	C₂²⋊C₄	—	151	8	no	—
278	C₂²⋊C₄	C₂²×D₁₅₁	1	8	yes	—
279	C₄²	—	151	2	no	—
280	C₄²	—	151	2	no	—
281	C₄²	C₂²×D₁₅₁	1	1	yes	characteristic
282	C₄²	C₂²×D₁₅₁	1	1	yes	characteristic
283	C₄²	C₂²×D₁₅₁	1	2	yes	—
284	C₂³	—	302	8	no	—
285	C₂³	—	604	2	no	—
286	C₂³	—	604	8	no	—
287	C₂³	—	151	4	no	—
288	C₂³	—	151	2	no	—
289	C₂³	—	151	4	no	—
290	C₂³	C₂³×D₁₅₁	1	4	yes	—
291	C₂³	C₂³×D₁₅₁	1	1	yes	characteristic
292	Q₈	—	2	4	no	—
293	Q₈	—	302	8	no	—
294	Q₈	—	302	4	no	—
295	D₄	—	2	8	no	—
296	D₄	—	2	4	no	—
297	D₄	—	4	4	no	—
298	D₄	—	302	8	no	—
299	D₄	—	302	8	no	—
300	D₄	—	302	8	no	—
301	D₄	—	302	8	no	—
302	D₄	—	302	4	no	—
303	D₄	—	604	4	no	—
304	D₄	—	604	8	no	—
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	302	8	no	—
308	C₂×C₄	—	302	8	no	—
309	C₂×C₄	—	302	8	no	—
310	C₂×C₄	—	302	8	no	—
311	C₂×C₄	—	604	2	no	—
312	C₂×C₄	—	151	4	no	—
313	C₂×C₄	—	151	4	no	—
314	C₂×C₄	—	151	4	no	—
315	C₂×C₄	—	151	2	no	—
316	C₂×C₄	—	151	8	no	—
317	C₂×C₄	—	151	8	no	—
318	C₂×C₄	D₄×D₁₅₁	1	4	yes	—
319	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
320	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
321	C₂×C₄	C₂³×D₁₅₁	1	4	yes	—
322	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
323	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
324	C₂²	—	2	2	no	—
325	C₂²	—	2	4	no	—
326	C₂²	—	2	8	no	—
327	C₂²	—	302	4	no	—
328	C₂²	—	302	4	no	—
329	C₂²	—	302	8	no	—
330	C₂²	—	604	4	no	—
331	C₂²	—	604	16	no	—
332	C₂²	—	151	4	no	—
333	C₂²	C₂×D₄×D₁₅₁	1	2	yes	—
334	C₂²	C₂⁴×D₁₅₁	1	1	yes	characteristic
335	C₄	—	2	4	no	—
336	C₄	—	2	2	no	—
337	C₄	—	2	2	no	—
338	C₄	—	302	4	no	—
339	C₄	—	302	4	no	—
340	C₄	—	151	4	no	—
341	C₄	C₂×D₄×D₁₅₁	1	2	yes	—
342	C₄	C₂×D₄×D₁₅₁	1	2	yes	—
343	C₂	—	2	2	no	—
344	C₂	—	4	4	no	—
345	C₂	—	302	4	no	—
346	C₂	—	604	4	no	—
347	C₂	C₂²×D₄×D₁₅₁	1	1	yes	characteristic
348	C₂	#23753048	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₅₁
commutator, socle, cosocle	C₂²×C₁₅₁	C₂⁵
Frattini	C₂²	C₂⁴×D₁₅₁
Fitting	#532×C₁₅₁	C₂
hypercenter	#532	D₁₅₁
hypocenter	C₁₅₁	#3449
LCS	G ▷ C₂²×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂×C₄ ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₅₁	C₂	semidirect
2. #23752789	C₂	semidirect
3. #23752787	C₂	semidirect
4. #23752782	C₂	semidirect
5. #23752780	C₂	semidirect
6. #23752775	C₂	semidirect
7. #23752770	C₂	semidirect
8. #23752762	C₂	semidirect
9. #23752758	C₂	semidirect
10. #23752721	C₂	semidirect
11. C₂×#18012696	C₂	semidirect
12. #532×C₁₅₁	C₂	semidirect
15. C₂×#14559004	C₂²	semidirect
17. C₂×#14559003	C₂²	semidirect
19. C₂×Q₈×D₁₅₁	C₂²	semidirect
21. C₂×D₄×D₁₅₁	C₂²	semidirect
23. C₂²×C₄×D₁₅₁	C₂²	semidirect
24. #18012739	C₂²	semidirect
25. #18012737	C₂²	semidirect
26. #18012736	C₂²	semidirect
27. #18012735	C₂²	semidirect
28. #18012728	C₂²	semidirect
29. #18012727	C₂²	semidirect
30. #18012726	C₂²	semidirect
31. #18012724	C₂²	semidirect
32. #18012721	C₂²	semidirect
33. #18012717	C₂²	semidirect
34. #18012716	C₂²	semidirect
35. #18012713	C₂²	semidirect
36. #18012712	C₂²	semidirect
37. #18012711	C₂²	semidirect
38. #18012711	C₂²	semidirect
39. #18012709	C₂²	semidirect
40. #18012707	C₂²	semidirect
41. C₄×D₆₀₄	C₂²	semidirect
42. C₄×C₂²⋊D₁₅₁	C₂²	semidirect
43. #18012696	C₂²	semidirect
44. #18012696	C₂²	semidirect
45. #18012696	C₂²	semidirect
46. C₂×Dic₁₅₁⋊C₄	C₂²	semidirect
48. C₂×C₄×Dic₁₅₁	C₂²	semidirect
49. C₂×#41×C₁₅₁	C₂²	semidirect
50. C₄⋊Q₈×C₁₅₁	C₂²	semidirect
51. #127×C₁₅₁	C₂²	semidirect
52. #124×C₁₅₁	C₂²	semidirect
53. #121×C₁₅₁	C₂²	semidirect
54. C₄×D₄×C₁₅₁	C₂²	semidirect
55. C₂×C₄²×C₁₅₁	C₂²	semidirect
79. C₂×C₄×D₁₅₁	D₄	semidirect
174. C₁₅₁	#3449	semidirect
185. #532	D₁₅₁	semidirect
194. C₂×#41	C₂×D₁₅₁	semidirect
202. C₄⋊Q₈	C₂×D₁₅₁	semidirect
205. #127	C₂×D₁₅₁	semidirect
209. #124	C₂×D₁₅₁	semidirect
218. #121	C₂×D₁₅₁	semidirect
223. C₄×D₄	C₂×D₁₅₁	semidirect
230. C₂×C₄²	C₂×D₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₅₁	2
#23752789	2
#23752787	2
#23752782	2
#23752780	2
#23752775	2
#23752770	2
#23752762	2
#23752758	2
#23752721	2
C₂×#18012696	2
#532×C₁₅₁	2
#3449	151