Subgroups — #34083246

Order 19328.

1058 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23752962	C₂	1	1	yes	maximal, characteristic, complemented
2	#23752961	C₂	1	2	yes	maximal, complemented
3	#23752957	C₂	1	4	yes	maximal, complemented
4	#23752956	C₂	1	2	yes	maximal, complemented
5	#23752954	C₂	1	1	yes	maximal, characteristic, complemented
6	#23752950	C₂	1	4	yes	maximal, complemented
7	#23752949	C₂	1	2	yes	maximal, complemented
8	#23752758	C₂	1	2	yes	maximal, complemented
9	#23752746	C₂	1	2	yes	maximal, complemented
10	#23752742	C₂	1	4	yes	maximal, complemented
11	#23752721	C₂	1	4	yes	maximal, complemented
12	#23752719	C₂	1	2	yes	maximal, complemented
13	#532×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14559004	C₂²	1	2	yes	—
15	C₂²×C₄×D₁₅₁	C₂²	1	2	yes	complemented
16	#18012737	C₂²	1	2	yes	complemented
17	#18012735	C₂²	1	2	yes	—
18	#18012734	C₂²	1	4	yes	complemented
19	#18012733	C₂²	1	4	yes	complemented
20	#18012732	C₂²	1	4	yes	complemented
21	#18012731	C₂²	1	2	yes	complemented
22	#18012729	C₂²	1	4	yes	complemented
23	#18012728	C₂²	1	2	yes	—
24	#18012727	C₂²	1	2	yes	—
25	#18012726	C₂²	1	2	yes	complemented
26	#18012725	C₂²	1	4	yes	—
27	#18012724	C₂²	1	4	yes	—
28	#18012723	C₂²	1	4	yes	complemented
29	#18012722	C₂²	1	4	yes	complemented
30	#18012721	C₂²	1	4	yes	complemented
31	#18012720	C₂²	1	2	yes	—
32	#18012720	C₂²	1	2	yes	complemented
33	#18012720	C₂²	1	4	yes	complemented
34	#18012718	C₂²	1	2	yes	complemented
35	#18012717	C₂²	1	4	yes	complemented
36	#18012716	C₂²	1	4	yes	complemented
37	#18012716	C₂²	1	4	yes	complemented
38	#18012715	C₂²	1	4	yes	complemented
39	#18012713	C₂²	1	2	yes	—
40	#18012712	C₂²	1	4	yes	—
41	#18012711	C₂²	1	4	yes	—
42	#18012711	C₂²	1	4	yes	—
43	#18012711	C₂²	1	4	yes	complemented
44	#18012711	C₂²	1	4	yes	complemented
45	#18012710	C₂²	1	4	yes	—
46	#18012709	C₂²	1	4	yes	—
47	#18012707	C₂²	1	2	yes	—
48	#18012707	C₂²	1	2	yes	complemented
49	#18012707	C₂²	1	4	yes	complemented
50	C₄×Dic₃₀₂	C₂²	1	2	yes	complemented
51	C₄×D₆₀₄	C₂²	1	2	yes	—
52	C₄×C₂²⋊D₁₅₁	C₂²	1	4	yes	—
53	C₄×C₂²⋊D₁₅₁	C₂²	1	4	yes	complemented
54	C₄×C₂²⋊D₁₅₁	C₂²	1	4	yes	complemented
55	#18012698	C₂²	1	2	yes	complemented
56	#18012696	C₂²	1	4	yes	complemented
57	C₂×C₄×Dic₁₅₁	C₂²	1	2	yes	complemented
58	C₂×#41×C₁₅₁	C₂²	1	1	yes	characteristic
59	C₂×#41×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
60	C₄⋊Q₈×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
61	#127×C₁₅₁	C₂²	1	1	yes	characteristic
62	#124×C₁₅₁	C₂²	1	1	yes	characteristic
63	#124×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
64	#121×C₁₅₁	C₂²	1	4	yes	complemented
65	C₄×D₄×C₁₅₁	C₂²	1	4	yes	complemented
66	C₂×C₄²×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
67	C₂³×D₁₅₁	C₂³	1	2	yes	—
68	#14559004	—	4	4	no	—
69	C₂×Dic₃₀₂	C₂³	1	2	yes	—
70	C₂×Dic₃₀₂	C₂³	1	2	yes	—
71	C₂×D₆₀₄	C₂³	1	2	yes	—
72	C₂×D₆₀₄	C₂³	1	2	yes	—
73	C₂×C₂²⋊D₁₅₁	C₂³	1	4	yes	—
74	C₂×C₂²⋊D₁₅₁	C₂³	1	4	yes	—
75	C₂×C₂²⋊D₁₅₁	C₂³	1	4	yes	—
76	C₂×C₂²⋊D₁₅₁	C₂³	1	4	yes	—
77	C₂²×Dic₁₅₁	C₂³	1	4	yes	—
78	C₂²×Dic₁₅₁	C₂³	1	2	yes	—
79	C₂×C₄×D₁₅₁	—	4	4	no	—
80	C₂×C₄×D₁₅₁	C₂³	1	4	yes	—
81	C₂×C₄×D₁₅₁	C₂³	1	4	yes	—
82	C₄⋊Dic₁₅₁	C₂³	1	4	yes	—
83	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
84	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
85	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
86	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
87	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
88	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
89	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
90	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
91	C₂²⋊Dic₁₅₁	C₂³	1	2	yes	—
92	C₂²⋊Dic₁₅₁	C₂³	1	2	yes	—
93	C₂²⋊Dic₁₅₁	C₂³	1	4	yes	—
94	C₂²⋊Dic₁₅₁	C₂³	1	4	yes	—
95	C₂²⋊Dic₁₅₁	C₂³	1	4	yes	—
96	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
97	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
98	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
99	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
100	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
101	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
102	C₄×Dic₁₅₁	C₂³	1	4	yes	—
103	C₄×Dic₁₅₁	C₂³	1	2	yes	—
104	C₄×Dic₁₅₁	C₂³	1	2	yes	—
105	#41×C₁₅₁	—	4	2	no	—
106	#41×C₁₅₁	—	4	2	no	—
107	C₂×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₁₅₁	C₂³	1	2	yes	—
111	C₂×D₄×C₁₅₁	C₂³	1	4	yes	—
112	C₂×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
113	C₂×D₄×C₁₅₁	C₂³	1	2	yes	—
114	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
115	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
116	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
118	C₄⋊C₄×C₁₅₁	C₂³	1	4	yes	—
119	C₂²⋊C₄×C₁₅₁	C₂³	1	4	yes	—
120	C₂²⋊C₄×C₁₅₁	C₂³	1	4	yes	—
121	C₄²×C₁₅₁	C₂³	1	2	yes	—
122	C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
123	C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
124	C₂²×D₁₅₁	—	4	2	no	—
125	C₂²×D₁₅₁	—	4	4	no	—
126	C₂²×D₁₅₁	C₂⁴	1	4	yes	—
127	Dic₃₀₂	—	4	2	no	—
128	Dic₃₀₂	—	4	2	no	—
129	D₆₀₄	—	4	2	no	—
130	D₆₀₄	—	4	2	no	—
131	C₂²⋊D₁₅₁	—	4	4	no	—
132	C₂²⋊D₁₅₁	—	4	4	no	—
133	C₂²⋊D₁₅₁	—	4	4	no	—
134	C₂²⋊D₁₅₁	—	4	4	no	—
135	C₂×Dic₁₅₁	—	4	2	no	—
136	C₂×Dic₁₅₁	—	4	4	no	—
137	C₂×Dic₁₅₁	C₂⁴	1	4	yes	—
138	C₂×Dic₁₅₁	C₂⁴	1	4	yes	—
139	C₂×Dic₁₅₁	C₂⁴	1	4	yes	—
140	C₄×D₁₅₁	—	2	8	no	—
141	C₄×D₁₅₁	—	4	4	no	—
142	C₂³×C₁₅₁	C₂⁴	1	2	yes	—
143	C₂³×C₁₅₁	C₂⁴	1	1	yes	characteristic
144	C₂³×C₁₅₁	C₂⁴	1	2	yes	—
145	Q₈×C₁₅₁	—	4	1	no	—
146	Q₈×C₁₅₁	—	4	1	no	—
147	D₄×C₁₅₁	—	4	1	no	—
148	D₄×C₁₅₁	—	4	1	no	—
149	D₄×C₁₅₁	—	4	2	no	—
150	D₄×C₁₅₁	—	4	2	no	—
151	D₄×C₁₅₁	—	4	4	no	—
152	C₂×C₄×C₁₅₁	—	2	2	no	—
153	C₂×C₄×C₁₅₁	—	2	4	no	—
154	C₂×C₄×C₁₅₁	—	2	4	no	—
155	C₂×C₄×C₁₅₁	—	4	2	no	—
156	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
157	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
158	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
159	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
160	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
161	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
162	C₂²×C₁₅₁	—	2	1	no	—
163	C₂²×C₁₅₁	—	2	2	no	—
164	C₂²×C₁₅₁	—	2	2	no	—
165	C₂²×C₁₅₁	—	2	2	no	—
166	C₂²×C₁₅₁	—	2	4	no	—
167	C₂²×C₁₅₁	—	2	4	no	—
168	C₂²×C₁₅₁	C₂⁵	1	1	yes	characteristic
169	C₂×D₁₅₁	—	2	4	no	—
170	C₂×D₁₅₁	—	2	4	no	—
171	C₂×D₁₅₁	—	2	4	no	—
172	C₂×D₁₅₁	—	4	8	no	—
173	C₄×C₁₅₁	—	2	1	no	—
174	C₄×C₁₅₁	—	2	2	no	—
175	C₄×C₁₅₁	—	2	2	no	—
176	C₄×C₁₅₁	—	2	2	no	—
177	C₄×C₁₅₁	—	2	2	no	—
178	C₄×C₁₅₁	H(5,𝔽₂)	1	2	yes	—
179	Dic₁₅₁	—	2	4	no	—
180	Dic₁₅₁	—	2	4	no	—
181	Dic₁₅₁	—	2	4	no	—
182	C₂×C₁₅₁	—	4	2	no	—
183	C₂×C₁₅₁	—	4	1	no	—
184	C₂×C₁₅₁	—	4	2	no	—
185	C₂×C₁₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₁₅₁	#585	1	2	yes	—
187	D₁₅₁	—	4	4	no	—
188	C₁₅₁	#3529	1	1	yes	characteristic, complemented, Sylow
189	#3529	—	151	1	no	maximal, Sylow
190	#563	—	151	2	no	—
191	#563	—	151	1	no	—
192	#562	—	151	2	no	—
193	#562	—	151	4	no	—
194	H(3,𝔽₄)	—	151	1	no	—
195	#560	—	151	2	no	—
196	#560	—	151	4	no	—
197	#532	—	151	2	no	—
198	#532	D₁₅₁	1	1	yes	characteristic, complemented
199	#529	—	151	4	no	—
200	#529	—	151	2	no	—
201	#525	—	151	2	no	—
202	#525	—	151	4	no	—
203	C₂×#41	—	151	2	no	—
204	C₂×#41	C₂×D₁₅₁	1	1	yes	characteristic
205	C₂×#41	C₂×D₁₅₁	1	1	yes	characteristic, complemented
206	C₂³×C₄	—	151	2	no	—
207	C₄⋊Q₈	—	151	2	no	—
208	C₄⋊Q₈	C₂×D₁₅₁	1	1	yes	characteristic, complemented
209	#127	—	151	2	no	—
210	#127	C₂×D₁₅₁	1	1	yes	characteristic
211	#126	—	151	4	no	—
212	#126	—	151	4	no	—
213	#126	—	151	4	no	—
214	#125	—	151	4	no	—
215	#125	—	151	2	no	—
216	#124	—	151	2	no	—
217	#124	—	151	2	no	—
218	#124	—	151	4	no	—
219	#124	—	151	2	no	—
220	#124	C₂×D₁₅₁	1	1	yes	characteristic
221	#124	C₂×D₁₅₁	1	1	yes	characteristic, complemented
222	#123	—	151	2	no	—
223	#123	—	151	2	no	—
224	#123	—	151	4	no	—
225	#123	—	151	4	no	—
226	#123	—	151	4	no	—
227	#123	—	151	4	no	—
228	#123	—	151	4	no	—
229	C₂²⋊Q₈	—	151	4	no	—
230	C₂²⋊Q₈	—	151	2	no	—
231	C₂²⋊Q₈	—	151	4	no	—
232	C₂²⋊Q₈	—	151	4	no	—
233	C₂²⋊Q₈	—	151	4	no	—
234	#121	—	151	4	no	—
235	#121	—	151	4	no	—
236	#121	—	151	4	no	—
237	#121	—	151	4	no	—
238	#121	—	151	4	no	—
239	#121	—	151	2	no	—
240	#121	—	151	4	no	—
241	#121	C₂×D₁₅₁	1	4	yes	complemented
242	#120	—	151	2	no	—
243	#120	—	151	2	no	—
244	#120	—	151	4	no	—
245	#120	—	151	4	no	—
246	C₄×Q₈	—	151	2	no	—
247	C₄×D₄	—	151	4	no	—
248	C₄×D₄	—	151	4	no	—
249	C₄×D₄	—	151	4	no	—
250	C₄×D₄	—	151	2	no	—
251	C₄×D₄	C₂×D₁₅₁	1	4	yes	complemented
252	#117	—	151	2	no	—
253	#117	—	151	4	no	—
254	C₂×C₄²	—	151	2	no	—
255	C₂×C₄²	C₂×D₁₅₁	1	1	yes	characteristic, complemented
256	C₂⁴	—	151	2	no	—
257	#41	—	4	2	no	—
258	#41	—	4	2	no	—
259	#41	—	604	4	no	—
260	C₂×Q₈	—	151	2	no	—
261	C₂×Q₈	—	151	2	no	—
262	C₂×Q₈	C₂²×D₁₅₁	1	1	yes	characteristic
263	C₂×Q₈	C₂²×D₁₅₁	1	1	yes	characteristic
264	C₂×D₄	—	151	4	no	—
265	C₂×D₄	—	151	4	no	—
266	C₂×D₄	—	151	4	no	—
267	C₂×D₄	—	151	4	no	—
268	C₂×D₄	—	151	2	no	—
269	C₂×D₄	—	151	2	no	—
270	C₂×D₄	C₂²×D₁₅₁	1	4	yes	—
271	C₂×D₄	C₂²×D₁₅₁	1	1	yes	characteristic
272	C₂×D₄	C₂²×D₁₅₁	1	2	yes	—
273	C₂×D₄	C₂²×D₁₅₁	1	1	yes	characteristic
274	C₂×D₄	C₂²×D₁₅₁	1	2	yes	—
275	C₂²×C₄	—	604	4	no	—
276	C₂²×C₄	—	151	4	no	—
277	C₂²×C₄	—	151	4	no	—
278	C₂²×C₄	—	151	2	no	—
279	C₂²×C₄	—	151	4	no	—
280	C₂²×C₄	C₂²×D₁₅₁	1	2	yes	—
281	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
282	C₂²×C₄	C₂²×D₁₅₁	1	2	yes	—
283	C₂²×C₄	C₂²×D₁₅₁	1	2	yes	—
284	C₄⋊C₄	—	151	4	no	—
285	C₄⋊C₄	—	151	4	no	—
286	C₄⋊C₄	—	151	4	no	—
287	C₄⋊C₄	—	151	4	no	—
288	C₄⋊C₄	—	151	4	no	—
289	C₄⋊C₄	—	151	4	no	—
290	C₄⋊C₄	—	151	4	no	—
291	C₄⋊C₄	—	151	2	no	—
292	C₄⋊C₄	—	151	2	no	—
293	C₄⋊C₄	C₂²×D₁₅₁	1	4	yes	—
294	C₂²⋊C₄	—	151	2	no	—
295	C₂²⋊C₄	—	151	2	no	—
296	C₂²⋊C₄	—	151	4	no	—
297	C₂²⋊C₄	—	151	4	no	—
298	C₂²⋊C₄	—	151	4	no	—
299	C₂²⋊C₄	—	151	4	no	—
300	C₂²⋊C₄	—	151	4	no	—
301	C₂²⋊C₄	—	151	4	no	—
302	C₂²⋊C₄	—	151	4	no	—
303	C₂²⋊C₄	—	151	4	no	—
304	C₂²⋊C₄	—	151	4	no	—
305	C₂²⋊C₄	C₂²×D₁₅₁	1	4	yes	—
306	C₂²⋊C₄	C₂²×D₁₅₁	1	4	yes	—
307	C₄²	—	151	2	no	—
308	C₄²	—	151	2	no	—
309	C₄²	—	151	4	no	—
310	C₄²	C₂²×D₁₅₁	1	1	yes	characteristic
311	C₄²	C₂²×D₁₅₁	1	1	yes	characteristic
312	C₄²	C₂²×D₁₅₁	1	2	yes	—
313	C₂³	—	604	2	no	—
314	C₂³	—	604	4	no	—
315	C₂³	—	151	4	no	—
316	C₂³	C₂³×D₁₅₁	1	2	yes	—
317	C₂³	C₂³×D₁₅₁	1	1	yes	characteristic
318	C₂³	C₂³×D₁₅₁	1	2	yes	—
319	Q₈	—	4	1	no	—
320	Q₈	—	4	1	no	—
321	Q₈	—	604	2	no	—
322	Q₈	—	604	2	no	—
323	D₄	—	4	2	no	—
324	D₄	—	4	1	no	—
325	D₄	—	4	1	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	4	no	—
328	D₄	—	604	2	no	—
329	D₄	—	604	2	no	—
330	D₄	—	604	4	no	—
331	D₄	—	604	4	no	—
332	D₄	—	604	4	no	—
333	D₄	—	604	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	302	8	no	—
339	C₂×C₄	—	604	4	no	—
340	C₂×C₄	—	604	2	no	—
341	C₂×C₄	—	604	4	no	—
342	C₂×C₄	—	151	4	no	—
343	C₂×C₄	—	151	4	no	—
344	C₂×C₄	—	151	4	no	—
345	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
346	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
347	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
348	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
349	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
350	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
351	C₂²	—	2	2	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	302	4	no	—
358	C₂²	—	302	4	no	—
359	C₂²	—	302	4	no	—
360	C₂²	—	604	8	no	—
361	C₂²	C₂⁴×D₁₅₁	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	302	4	no	—
368	C₄	—	302	4	no	—
369	C₄	—	302	4	no	—
370	C₄	#18012784	1	2	yes	—
371	C₂	—	4	2	no	—
372	C₂	—	4	1	no	—
373	C₂	—	4	2	no	—
374	C₂	—	604	4	no	—
375	C₂	C₂×#18012784	1	1	yes	characteristic
376	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	#3529
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. #23752962	C₂	semidirect
2. #23752961	C₂	semidirect
3. #23752957	C₂	semidirect
4. #23752956	C₂	semidirect
5. #23752954	C₂	semidirect
6. #23752950	C₂	semidirect
7. #23752949	C₂	semidirect
8. #23752758	C₂	semidirect
9. #23752746	C₂	semidirect
10. #23752742	C₂	semidirect
11. #23752721	C₂	semidirect
12. #23752719	C₂	semidirect
13. #532×C₁₅₁	C₂	semidirect
15. C₂²×C₄×D₁₅₁	C₂²	semidirect
16. #18012737	C₂²	semidirect
18. #18012734	C₂²	semidirect
19. #18012733	C₂²	semidirect
20. #18012732	C₂²	semidirect
21. #18012731	C₂²	semidirect
22. #18012729	C₂²	semidirect
25. #18012726	C₂²	semidirect
28. #18012723	C₂²	semidirect
29. #18012722	C₂²	semidirect
30. #18012721	C₂²	semidirect
32. #18012720	C₂²	semidirect
33. #18012720	C₂²	semidirect
34. #18012718	C₂²	semidirect
35. #18012717	C₂²	semidirect
36. #18012716	C₂²	semidirect
37. #18012716	C₂²	semidirect
38. #18012715	C₂²	semidirect
43. #18012711	C₂²	semidirect
44. #18012711	C₂²	semidirect
48. #18012707	C₂²	semidirect
49. #18012707	C₂²	semidirect
50. C₄×Dic₃₀₂	C₂²	semidirect
53. C₄×C₂²⋊D₁₅₁	C₂²	semidirect
54. C₄×C₂²⋊D₁₅₁	C₂²	semidirect
55. #18012698	C₂²	semidirect
56. #18012696	C₂²	semidirect
57. C₂×C₄×Dic₁₅₁	C₂²	semidirect
59. C₂×#41×C₁₅₁	C₂²	semidirect
60. C₄⋊Q₈×C₁₅₁	C₂²	semidirect
63. #124×C₁₅₁	C₂²	semidirect
64. #121×C₁₅₁	C₂²	semidirect
65. C₄×D₄×C₁₅₁	C₂²	semidirect
66. C₂×C₄²×C₁₅₁	C₂²	semidirect
188. C₁₅₁	#3529	semidirect
198. #532	D₁₅₁	semidirect
205. C₂×#41	C₂×D₁₅₁	semidirect
208. C₄⋊Q₈	C₂×D₁₅₁	semidirect
221. #124	C₂×D₁₅₁	semidirect
241. #121	C₂×D₁₅₁	semidirect
251. C₄×D₄	C₂×D₁₅₁	semidirect
255. 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
#23752962	2
#23752961	2
#23752957	2
#23752956	2
#23752954	2
#23752950	2
#23752949	2
#23752758	2
#23752746	2
#23752742	2
#23752721	2
#23752719	2
#532×C₁₅₁	2
#3529	151