Subgroups — #34083387

Order 19328.

1058 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23752954	C₂	1	2	yes	maximal, complemented
2	#23752952	C₂	1	2	yes	maximal, complemented
3	#23752946	C₂	1	2	yes	maximal, complemented
4	#23752933	C₂	1	2	yes	maximal, complemented
5	#23752925	C₂	1	2	yes	maximal, complemented
6	#23752892	C₂	1	2	yes	maximal, complemented
7	#23752873	C₂	1	2	yes	maximal, complemented
8	#23752853	C₂	1	2	yes	maximal, complemented
9	#23752836	C₂	1	4	yes	maximal, complemented
10	#23752835	C₂	1	2	yes	maximal, complemented
11	#23752798	C₂	1	4	yes	maximal, complemented
12	#23752776	C₂	1	1	yes	maximal, characteristic, complemented
13	#23752725	C₂	1	2	yes	maximal, complemented
14	#23752719	C₂	1	1	yes	maximal, characteristic, complemented
15	#536×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14559005	C₂²	1	2	yes	—
17	C₂²×D₆₀₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₄×D₁₅₁	C₂²	1	1	yes	characteristic, complemented
19	#18012738	C₂²	1	2	yes	complemented
20	#18012735	C₂²	1	2	yes	—
21	#18012734	C₂²	1	4	yes	complemented
22	#18012734	C₂²	1	4	yes	complemented
23	#18012732	C₂²	1	4	yes	complemented
24	#18012728	C₂²	1	2	yes	complemented
25	#18012728	C₂²	1	2	yes	complemented
26	#18012728	C₂²	1	4	yes	complemented
27	#18012727	C₂²	1	4	yes	complemented
28	#18012725	C₂²	1	4	yes	—
29	#18012725	C₂²	1	4	yes	complemented
30	#18012725	C₂²	1	4	yes	complemented
31	#18012724	C₂²	1	4	yes	complemented
32	#18012724	C₂²	1	4	yes	complemented
33	#18012721	C₂²	1	4	yes	complemented
34	#18012720	C₂²	1	1	yes	characteristic
35	#18012720	C₂²	1	1	yes	characteristic, complemented
36	#18012719	C₂²	1	4	yes	complemented
37	#18012715	C₂²	1	2	yes	complemented
38	#18012715	C₂²	1	2	yes	complemented
39	#18012715	C₂²	1	4	yes	complemented
40	#18012714	C₂²	1	2	yes	—
41	#18012714	C₂²	1	4	yes	—
42	#18012713	C₂²	1	2	yes	—
43	#18012713	C₂²	1	2	yes	complemented
44	#18012713	C₂²	1	4	yes	complemented
45	#18012712	C₂²	1	4	yes	complemented
46	#18012710	C₂²	1	2	yes	—
47	#18012709	C₂²	1	4	yes	—
48	#18012709	C₂²	1	4	yes	complemented
49	#18012707	C₂²	1	1	yes	characteristic
50	#18012707	C₂²	1	2	yes	—
51	#18012707	C₂²	1	1	yes	characteristic, complemented
52	#18012707	C₂²	1	2	yes	complemented
53	Q₈×Dic₁₅₁	C₂²	1	2	yes	complemented
54	#18012704	C₂²	1	4	yes	complemented
55	#18012701	C₂²	1	4	yes	complemented
56	#18012701	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₁₅₁	C₂²	1	2	yes	—
58	C₄×C₂²⋊D₁₅₁	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₁₅₁	C₂²	1	4	yes	complemented
60	(C₂²⋊D₁₅₁)⋊C₄	C₂²	1	4	yes	complemented
61	#18012698	C₂²	1	1	yes	characteristic, complemented
62	#18012698	C₂²	1	1	yes	characteristic, complemented
63	#18012697	C₂²	1	2	yes	complemented
64	#18012696	C₂²	1	4	yes	complemented
65	C₂²⋊C₄×D₁₅₁	C₂²	1	4	yes	complemented
66	C₂×#41×C₁₅₁	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
68	C₄⋊Q₈×C₁₅₁	C₂²	1	2	yes	complemented
69	#124×C₁₅₁	C₂²	1	2	yes	—
70	#123×C₁₅₁	C₂²	1	2	yes	complemented
71	#123×C₁₅₁	C₂²	1	2	yes	complemented
72	C₂²⋊Q₈×C₁₅₁	C₂²	1	2	yes	complemented
73	C₂²⋊Q₈×C₁₅₁	C₂²	1	2	yes	complemented
74	#117×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₁₅₁	C₂³	1	2	yes	—
76	C₂³×D₁₅₁	C₂³	1	1	yes	characteristic
77	#14559005	—	4	4	no	—
78	C₂×Dic₃₀₂	C₂³	1	4	yes	—
79	C₂×D₆₀₄	—	4	2	no	—
80	C₂×D₆₀₄	C₂³	1	2	yes	—
81	C₂×D₆₀₄	C₂³	1	4	yes	—
82	C₂×D₆₀₄	C₂³	1	4	yes	—
83	C₂×D₆₀₄	C₂³	1	2	yes	—
84	C₂×C₂²⋊D₁₅₁	C₂³	1	4	yes	—
85	C₂×C₂²⋊D₁₅₁	C₂³	1	2	yes	—
86	C₂×C₂²⋊D₁₅₁	C₂³	1	2	yes	—
87	C₂×C₂²⋊D₁₅₁	C₂³	1	4	yes	—
88	C₂²×Dic₁₅₁	C₂³	1	1	yes	characteristic
89	C₂×C₄×D₁₅₁	—	4	2	no	—
90	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
91	C₂×C₄×D₁₅₁	C₂³	1	4	yes	—
92	C₂×C₄×D₁₅₁	C₂³	1	4	yes	—
93	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
94	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
95	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
96	C₄⋊Dic₁₅₁	C₂³	1	4	yes	—
97	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
98	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
99	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
100	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
101	C₂²⋊Dic₁₅₁	C₂³	1	2	yes	—
102	C₂²⋊Dic₁₅₁	C₂³	1	2	yes	—
103	C₂²⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
104	C₂²⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
105	C₂²⋊Dic₁₅₁	C₂³	1	2	yes	—
106	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
107	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
108	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
109	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
110	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
111	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
112	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
113	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
114	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
115	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
116	C₄×Dic₁₅₁	C₂³	1	4	yes	—
117	C₄×Dic₁₅₁	C₂³	1	2	yes	—
118	C₄×Dic₁₅₁	C₂³	1	2	yes	—
119	C₄×Dic₁₅₁	C₂³	1	4	yes	—
120	#41×C₁₅₁	—	4	2	no	—
121	C₂×Q₈×C₁₅₁	—	4	2	no	—
122	C₂×Q₈×C₁₅₁	C₂³	1	2	yes	—
123	C₂×Q₈×C₁₅₁	C₂³	1	2	yes	—
124	C₂×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
132	C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
133	C₄⋊C₄×C₁₅₁	C₂³	1	4	yes	—
134	C₄⋊C₄×C₁₅₁	C₂³	1	4	yes	—
135	C₂²⋊C₄×C₁₅₁	C₂³	1	4	yes	—
136	C₂²⋊C₄×C₁₅₁	C₂³	1	4	yes	—
137	C₂²⋊C₄×C₁₅₁	C₂³	1	2	yes	—
138	C₄²×C₁₅₁	C₂³	1	2	yes	—
139	C₂²×D₁₅₁	—	4	1	no	—
140	C₂²×D₁₅₁	—	4	2	no	—
141	C₂²×D₁₅₁	—	4	2	no	—
142	C₂²×D₁₅₁	—	4	4	no	—
143	C₂²×D₁₅₁	C₂⁴	1	2	yes	—
144	C₂²×D₁₅₁	C₂⁴	1	4	yes	—
145	Dic₃₀₂	—	4	4	no	—
146	D₆₀₄	—	2	4	no	—
147	D₆₀₄	—	4	2	no	—
148	D₆₀₄	—	4	4	no	—
149	D₆₀₄	—	4	4	no	—
150	C₂²⋊D₁₅₁	—	4	2	no	—
151	C₂²⋊D₁₅₁	—	4	4	no	—
152	C₂²⋊D₁₅₁	—	4	4	no	—
153	C₂²⋊D₁₅₁	—	4	2	no	—
154	C₂×Dic₁₅₁	—	4	1	no	—
155	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
156	C₂×Dic₁₅₁	C₂⁴	1	4	yes	—
157	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
158	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
159	C₄×D₁₅₁	—	2	4	no	—
160	C₄×D₁₅₁	—	4	2	no	—
161	C₄×D₁₅₁	—	4	4	no	—
162	C₄×D₁₅₁	—	4	4	no	—
163	C₂³×C₁₅₁	C₂⁴	1	1	yes	characteristic
164	C₂³×C₁₅₁	C₂⁴	1	1	yes	characteristic
165	C₂³×C₁₅₁	C₂⁴	1	1	yes	characteristic
166	Q₈×C₁₅₁	—	2	4	no	—
167	Q₈×C₁₅₁	—	4	2	no	—
168	Q₈×C₁₅₁	—	4	1	no	—
169	D₄×C₁₅₁	—	4	1	no	—
170	D₄×C₁₅₁	—	4	1	no	—
171	D₄×C₁₅₁	—	4	1	no	—
172	C₂×C₄×C₁₅₁	—	2	2	no	—
173	C₂×C₄×C₁₅₁	—	2	2	no	—
174	C₂×C₄×C₁₅₁	—	2	2	no	—
175	C₂×C₄×C₁₅₁	—	4	2	no	—
176	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₅₁	C₂⁴	1	4	yes	—
178	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
180	C₂×C₄×C₁₅₁	C₂⁴	1	4	yes	—
181	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
182	C₂²×C₁₅₁	—	2	1	no	—
183	C₂²×C₁₅₁	—	2	1	no	—
184	C₂²×C₁₅₁	—	2	1	no	—
185	C₂²×C₁₅₁	—	2	2	no	—
186	C₂²×C₁₅₁	—	2	2	no	—
187	C₂²×C₁₅₁	—	2	2	no	—
188	C₂²×C₁₅₁	C₂⁵	1	1	yes	characteristic
189	C₂×D₁₅₁	—	2	2	no	—
190	C₂×D₁₅₁	—	2	4	no	—
191	C₂×D₁₅₁	—	2	4	no	—
192	C₂×D₁₅₁	—	2	2	no	—
193	C₂×D₁₅₁	—	2	4	no	—
194	C₂×D₁₅₁	—	2	2	no	—
195	C₂×D₁₅₁	—	4	4	no	—
196	C₂×D₁₅₁	—	8	4	no	—
197	C₄×C₁₅₁	—	2	1	no	—
198	C₄×C₁₅₁	—	2	1	no	—
199	C₄×C₁₅₁	—	2	1	no	—
200	C₄×C₁₅₁	—	2	4	no	—
201	C₄×C₁₅₁	—	2	4	no	—
202	C₄×C₁₅₁	H(5,𝔽₂)	1	2	yes	—
203	Dic₁₅₁	—	2	2	no	—
204	Dic₁₅₁	—	2	2	no	—
205	Dic₁₅₁	—	2	4	no	—
206	Dic₁₅₁	—	2	2	no	—
207	C₂×C₁₅₁	—	4	1	no	—
208	C₂×C₁₅₁	—	4	1	no	—
209	C₂×C₁₅₁	—	4	1	no	—
210	C₂×C₁₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₁₅₁	#585	1	2	yes	—
212	D₁₅₁	—	4	2	no	—
213	D₁₅₁	—	4	4	no	—
214	C₁₅₁	#3540	1	1	yes	characteristic, complemented, Sylow
215	#3540	—	151	1	no	maximal, Sylow
216	H(3,𝔽₄)	—	151	2	no	—
217	#560	—	151	2	no	—
218	#559	—	151	2	no	—
219	#556	—	151	2	no	—
220	#555	—	151	2	no	—
221	#551	—	151	2	no	—
222	#548	—	151	2	no	—
223	#546	—	151	2	no	—
224	#542	—	151	4	no	—
225	#542	—	151	2	no	—
226	#538	—	151	4	no	—
227	#536	D₁₅₁	1	1	yes	characteristic, complemented
228	#535	—	151	1	no	—
229	#525	—	151	1	no	—
230	#525	—	151	2	no	—
231	C₂×#41	—	151	2	no	—
232	C₂×#41	C₂×D₁₅₁	1	1	yes	characteristic
233	C₂²×Q₈	C₂×D₁₅₁	1	1	yes	characteristic, complemented
234	C₂²×D₄	—	151	1	no	—
235	C₂³×C₄	—	151	1	no	—
236	C₄⋊Q₈	—	151	2	no	—
237	C₄⋊Q₈	C₂×D₁₅₁	1	2	yes	complemented
238	#127	—	151	2	no	—
239	#126	—	151	4	no	—
240	#126	—	151	4	no	—
241	#126	—	151	4	no	—
242	#124	—	151	2	no	—
243	#124	—	151	2	no	—
244	#124	—	151	4	no	—
245	#124	—	151	4	no	—
246	#124	—	151	4	no	—
247	#124	—	151	4	no	—
248	#124	—	151	4	no	—
249	#124	C₂×D₁₅₁	1	2	yes	—
250	#123	—	151	1	no	—
251	#123	—	151	1	no	—
252	#123	—	151	4	no	—
253	#123	—	151	4	no	—
254	#123	—	151	4	no	—
255	#123	C₂×D₁₅₁	1	2	yes	complemented
256	#123	C₂×D₁₅₁	1	2	yes	complemented
257	C₂²⋊Q₈	—	151	2	no	—
258	C₂²⋊Q₈	—	151	2	no	—
259	C₂²⋊Q₈	—	151	4	no	—
260	C₂²⋊Q₈	—	151	4	no	—
261	C₂²⋊Q₈	C₂×D₁₅₁	1	2	yes	complemented
262	C₂²⋊Q₈	C₂×D₁₅₁	1	2	yes	complemented
263	#121	—	151	2	no	—
264	#121	—	151	2	no	—
265	#121	—	151	2	no	—
266	#121	—	151	4	no	—
267	#121	—	151	2	no	—
268	#121	—	151	4	no	—
269	#121	—	151	4	no	—
270	#120	—	151	1	no	—
271	#120	—	151	1	no	—
272	#120	—	151	2	no	—
273	#120	—	151	2	no	—
274	#120	—	151	4	no	—
275	#120	—	151	4	no	—
276	C₄×Q₈	—	151	2	no	—
277	C₄×Q₈	—	151	4	no	—
278	C₄×D₄	—	151	2	no	—
279	C₄×D₄	—	151	2	no	—
280	C₄×D₄	—	151	4	no	—
281	C₄×D₄	—	151	4	no	—
282	C₄×D₄	—	151	2	no	—
283	C₄×D₄	—	151	4	no	—
284	#117	—	151	1	no	—
285	#117	—	151	1	no	—
286	#117	—	151	2	no	—
287	#117	—	151	4	no	—
288	#117	C₂×D₁₅₁	1	1	yes	characteristic, complemented
289	C₂×C₂²⋊C₄	—	151	4	no	—
290	C₂⁴	—	151	2	no	—
291	C₂⁴	—	151	1	no	—
292	#41	—	4	2	no	—
293	#41	—	604	4	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	151	4	no	—
296	C₂×Q₈	C₂²×D₁₅₁	1	2	yes	—
297	C₂×Q₈	C₂²×D₁₅₁	1	2	yes	—
298	C₂×Q₈	C₂²×D₁₅₁	1	1	yes	characteristic
299	C₂×D₄	—	604	2	no	—
300	C₂×D₄	—	151	2	no	—
301	C₂×D₄	—	151	4	no	—
302	C₂×D₄	—	151	2	no	—
303	C₂×D₄	—	151	4	no	—
304	C₂×D₄	—	151	2	no	—
305	C₂×D₄	—	151	4	no	—
306	C₂×D₄	—	151	4	no	—
307	C₂×D₄	—	151	2	no	—
308	C₂×D₄	C₂²×D₁₅₁	1	1	yes	characteristic
309	C₂×D₄	C₂²×D₁₅₁	1	1	yes	characteristic
310	C₂×D₄	C₂²×D₁₅₁	1	1	yes	characteristic
311	C₂²×C₄	—	604	2	no	—
312	C₂²×C₄	—	151	2	no	—
313	C₂²×C₄	—	151	1	no	—
314	C₂²×C₄	—	151	4	no	—
315	C₂²×C₄	—	151	4	no	—
316	C₂²×C₄	—	151	2	no	—
317	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
318	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₁₅₁	1	2	yes	—
321	C₄⋊C₄	—	151	2	no	—
322	C₄⋊C₄	—	151	4	no	—
323	C₄⋊C₄	—	151	4	no	—
324	C₄⋊C₄	—	151	2	no	—
325	C₄⋊C₄	—	151	2	no	—
326	C₄⋊C₄	—	151	2	no	—
327	C₄⋊C₄	—	151	4	no	—
328	C₄⋊C₄	C₂²×D₁₅₁	1	2	yes	—
329	C₄⋊C₄	C₂²×D₁₅₁	1	4	yes	—
330	C₄⋊C₄	C₂²×D₁₅₁	1	4	yes	—
331	C₂²⋊C₄	—	151	2	no	—
332	C₂²⋊C₄	—	151	2	no	—
333	C₂²⋊C₄	—	151	1	no	—
334	C₂²⋊C₄	—	151	1	no	—
335	C₂²⋊C₄	—	151	2	no	—
336	C₂²⋊C₄	—	151	4	no	—
337	C₂²⋊C₄	—	151	4	no	—
338	C₂²⋊C₄	—	151	4	no	—
339	C₂²⋊C₄	—	151	4	no	—
340	C₂²⋊C₄	—	151	2	no	—
341	C₂²⋊C₄	—	151	4	no	—
342	C₂²⋊C₄	—	151	4	no	—
343	C₂²⋊C₄	—	151	4	no	—
344	C₂²⋊C₄	—	151	2	no	—
345	C₂²⋊C₄	—	151	4	no	—
346	C₂²⋊C₄	C₂²×D₁₅₁	1	4	yes	—
347	C₂²⋊C₄	C₂²×D₁₅₁	1	2	yes	—
348	C₂²⋊C₄	C₂²×D₁₅₁	1	4	yes	—
349	C₄²	—	151	4	no	—
350	C₄²	—	151	2	no	—
351	C₄²	—	151	2	no	—
352	C₄²	—	151	4	no	—
353	C₄²	C₂²×D₁₅₁	1	2	yes	—
354	C₂³	—	604	1	no	—
355	C₂³	—	604	2	no	—
356	C₂³	—	604	2	no	—
357	C₂³	—	604	4	no	—
358	C₂³	—	151	2	no	—
359	C₂³	—	151	4	no	—
360	C₂³	C₂³×D₁₅₁	1	1	yes	characteristic
361	C₂³	C₂³×D₁₅₁	1	1	yes	characteristic
362	C₂³	C₂³×D₁₅₁	1	1	yes	characteristic
363	Q₈	—	2	4	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	4	1	no	—
366	Q₈	—	604	4	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	1	no	—
370	D₄	—	302	4	no	—
371	D₄	—	604	2	no	—
372	D₄	—	604	4	no	—
373	D₄	—	604	4	no	—
374	D₄	—	604	2	no	—
375	D₄	—	604	4	no	—
376	D₄	—	604	4	no	—
377	D₄	—	604	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	302	4	no	—
383	C₂×C₄	—	604	2	no	—
384	C₂×C₄	—	604	4	no	—
385	C₂×C₄	—	604	4	no	—
386	C₂×C₄	—	604	1	no	—
387	C₂×C₄	—	151	2	no	—
388	C₂×C₄	—	151	4	no	—
389	C₂×C₄	—	151	2	no	—
390	C₂×C₄	—	151	2	no	—
391	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₁₅₁	1	4	yes	—
393	C₂×C₄	C₂³×D₁₅₁	1	4	yes	—
394	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
395	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
396	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	302	2	no	—
404	C₂²	—	302	4	no	—
405	C₂²	—	302	4	no	—
406	C₂²	—	302	2	no	—
407	C₂²	—	302	2	no	—
408	C₂²	—	302	4	no	—
409	C₂²	—	604	4	no	—
410	C₂²	—	1208	4	no	—
411	C₂²	C₂⁴×D₁₅₁	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	4	no	—
416	C₄	—	2	4	no	—
417	C₄	—	302	2	no	—
418	C₄	—	302	2	no	—
419	C₄	—	302	4	no	—
420	C₄	—	302	2	no	—
421	C₄	#18012784	1	2	yes	—
422	C₂	—	4	1	no	—
423	C₂	—	4	1	no	—
424	C₂	—	4	1	no	—
425	C₂	—	604	2	no	—
426	C₂	—	604	4	no	—
427	C₂	C₂×#18012784	1	1	yes	characteristic
428	C₂	#23753049	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₅₁
commutator, socle, cosocle	C₂²×C₁₅₁	C₂⁵
Fitting	#536×C₁₅₁	C₂
hypercenter	#536	D₁₅₁
hypocenter	C₁₅₁	#3540
LCS	G ▷ C₂²×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. #23752954	C₂	semidirect
2. #23752952	C₂	semidirect
3. #23752946	C₂	semidirect
4. #23752933	C₂	semidirect
5. #23752925	C₂	semidirect
6. #23752892	C₂	semidirect
7. #23752873	C₂	semidirect
8. #23752853	C₂	semidirect
9. #23752836	C₂	semidirect
10. #23752835	C₂	semidirect
11. #23752798	C₂	semidirect
12. #23752776	C₂	semidirect
13. #23752725	C₂	semidirect
14. #23752719	C₂	semidirect
15. #536×C₁₅₁	C₂	semidirect
17. C₂²×D₆₀₄	C₂²	semidirect
18. C₂²×C₄×D₁₅₁	C₂²	semidirect
19. #18012738	C₂²	semidirect
21. #18012734	C₂²	semidirect
22. #18012734	C₂²	semidirect
23. #18012732	C₂²	semidirect
24. #18012728	C₂²	semidirect
25. #18012728	C₂²	semidirect
26. #18012728	C₂²	semidirect
27. #18012727	C₂²	semidirect
29. #18012725	C₂²	semidirect
30. #18012725	C₂²	semidirect
31. #18012724	C₂²	semidirect
32. #18012724	C₂²	semidirect
33. #18012721	C₂²	semidirect
35. #18012720	C₂²	semidirect
36. #18012719	C₂²	semidirect
37. #18012715	C₂²	semidirect
38. #18012715	C₂²	semidirect
39. #18012715	C₂²	semidirect
43. #18012713	C₂²	semidirect
44. #18012713	C₂²	semidirect
45. #18012712	C₂²	semidirect
48. #18012709	C₂²	semidirect
51. #18012707	C₂²	semidirect
52. #18012707	C₂²	semidirect
53. Q₈×Dic₁₅₁	C₂²	semidirect
54. #18012704	C₂²	semidirect
55. #18012701	C₂²	semidirect
56. #18012701	C₂²	semidirect
58. C₄×C₂²⋊D₁₅₁	C₂²	semidirect
59. C₄×C₂²⋊D₁₅₁	C₂²	semidirect
60. (C₂²⋊D₁₅₁)⋊C₄	C₂²	semidirect
61. #18012698	C₂²	semidirect
62. #18012698	C₂²	semidirect
63. #18012697	C₂²	semidirect
64. #18012696	C₂²	semidirect
65. C₂²⋊C₄×D₁₅₁	C₂²	semidirect
67. C₂²×Q₈×C₁₅₁	C₂²	semidirect
68. C₄⋊Q₈×C₁₅₁	C₂²	semidirect
70. #123×C₁₅₁	C₂²	semidirect
71. #123×C₁₅₁	C₂²	semidirect
72. C₂²⋊Q₈×C₁₅₁	C₂²	semidirect
73. C₂²⋊Q₈×C₁₅₁	C₂²	semidirect
74. #117×C₁₅₁	C₂²	semidirect
214. C₁₅₁	#3540	semidirect
227. #536	D₁₅₁	semidirect
233. C₂²×Q₈	C₂×D₁₅₁	semidirect
237. C₄⋊Q₈	C₂×D₁₅₁	semidirect
255. #123	C₂×D₁₅₁	semidirect
256. #123	C₂×D₁₅₁	semidirect
261. C₂²⋊Q₈	C₂×D₁₅₁	semidirect
262. C₂²⋊Q₈	C₂×D₁₅₁	semidirect
288. #117	C₂×D₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#23752954	2
#23752952	2
#23752946	2
#23752933	2
#23752925	2
#23752892	2
#23752873	2
#23752853	2
#23752836	2
#23752835	2
#23752798	2
#23752776	2
#23752725	2
#23752719	2
#536×C₁₅₁	2
#3540	151