Subgroups — #31764449

Order 17152.

9494 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574364	C₂	1	24	yes	maximal, complemented
2	#22573898	C₂	1	6	yes	maximal, complemented
3	#22573896	C₂	1	12	yes	maximal, complemented
4	#22573844	C₂	1	6	yes	maximal, complemented
5	#22573838	C₂	1	12	yes	maximal, complemented
6	C₂²×#14524012	C₂	1	2	yes	maximal, complemented
7	C₂²×#120×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14524088	C₂²	1	6	yes	complemented
9	C₂³×C₂²⋊D₆₇	C₂²	1	6	yes	complemented
10	#16864139	C₂²	1	8	yes	complemented
11	#16864135	C₂²	1	24	yes	complemented
12	#16864077	C₂²	1	24	yes	complemented
13	#16864072	C₂²	1	48	yes	complemented
14	#16864040	C₂²	1	48	yes	complemented
15	#16864036	C₂²	1	48	yes	complemented
16	#16864033	C₂²	1	48	yes	complemented
17	D₄×C₂²⋊D₆₇	C₂²	1	48	yes	complemented
18	#16864028	C₂²	1	24	yes	complemented
19	#16864022	C₂²	1	6	yes	complemented
20	#16863984	C₂²	1	24	yes	complemented
21	#16863981	C₂²	1	48	yes	complemented
22	#16863963	C₂²	1	12	yes	complemented
23	#16863961	C₂²	1	24	yes	complemented
24	#16863958	C₂²	1	6	yes	complemented
25	#16863956	C₂²	1	24	yes	complemented
26	#16863955	C₂²	1	12	yes	complemented
27	#16863955	C₂²	1	12	yes	complemented
28	#16863907	C₂²	1	12	yes	complemented
29	#16863902	C₂²	1	24	yes	complemented
30	C₂×#14524012	C₂²	1	12	yes	complemented
31	C₂×#14524012	C₂²	1	12	yes	complemented
32	C₂×#14524012	C₂²	1	24	yes	complemented
33	C₂×#14524012	C₂²	1	4	yes	complemented
34	#120×D₆₇	C₂²	1	8	yes	complemented
35	#16863871	C₂²	1	6	yes	complemented
36	#16863869	C₂²	1	12	yes	complemented
37	C₂²×C₂²⋊Dic₆₇	C₂²	1	6	yes	complemented
38	C₂⁶×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂³×D₄×C₆₇	C₂²	1	3	yes	complemented
40	C₂×#120×C₆₇	C₂²	1	12	yes	complemented
41	C₂×#120×C₆₇	C₂²	1	12	yes	complemented
42	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	3	yes	complemented
43	C₂⁴×D₆₇	C₂³	1	2	yes	complemented
44	#14524088	—	4	24	no	—
45	C₂×#11761628	C₂³	1	12	yes	complemented
46	C₂×#11761627	C₂³	1	24	yes	complemented
47	C₂²×C₂²⋊D₆₇	—	4	24	no	—
48	C₂²×C₂²⋊D₆₇	C₂³	1	12	yes	—
49	C₂²×C₂²⋊D₆₇	C₂³	1	24	yes	complemented
50	C₂²×C₂²⋊D₆₇	C₂³	1	24	yes	complemented
51	C₂²×C₂²⋊D₆₇	C₂³	1	12	yes	complemented
52	C₂²×C₂²⋊D₆₇	C₂³	1	12	yes	complemented
53	C₂×D₄×D₆₇	C₂³	1	24	yes	complemented
54	C₂³×Dic₆₇	C₂³	1	6	yes	complemented
55	#14524039	C₂³	1	24	yes	complemented
56	#14524036	C₂³	1	48	yes	complemented
57	#14524030	C₂³	1	24	yes	complemented
58	#14524029	C₂³	1	48	yes	complemented
59	#14524027	C₂³	1	24	yes	complemented
60	#14524026	C₂³	1	24	yes	complemented
61	#14524025	C₂³	1	48	yes	complemented
62	#14524024	C₂³	1	24	yes	complemented
63	#14524024	C₂³	1	24	yes	complemented
64	#14524022	C₂³	1	24	yes	complemented
65	#14524020	C₂³	1	48	yes	complemented
66	#14524017	C₂³	1	24	yes	complemented
67	#14524016	C₂³	1	48	yes	complemented
68	#14524015	C₂³	1	48	yes	complemented
69	#14524015	C₂³	1	48	yes	complemented
70	#14524014	C₂³	1	48	yes	complemented
71	#14524013	C₂³	1	24	yes	complemented
72	#14524012	C₂³	1	48	yes	—
73	#14524012	C₂³	1	16	yes	complemented
74	#14524012	C₂³	1	8	yes	complemented
75	#14524012	C₂³	1	8	yes	complemented
76	#14524012	C₂³	1	24	yes	complemented
77	#14524012	C₂³	1	24	yes	complemented
78	#14524012	C₂³	1	24	yes	complemented
79	#14524011	C₂³	1	24	yes	complemented
80	#14524011	C₂³	1	24	yes	complemented
81	D₄×Dic₆₇	C₂³	1	48	yes	complemented
82	C₄×C₂²⋊D₆₇	C₂³	1	48	yes	complemented
83	(C₂²⋊D₆₇)⋊C₄	C₂³	1	48	yes	complemented
84	#14524002	C₂³	1	12	yes	complemented
85	#14523999	C₂³	1	24	yes	complemented
86	C₂×C₂²⋊Dic₆₇	C₂³	1	12	yes	—
87	C₂×C₂²⋊Dic₆₇	C₂³	1	24	yes	complemented
88	C₂×C₂²⋊Dic₆₇	C₂³	1	24	yes	complemented
89	C₂×C₂²⋊Dic₆₇	C₂³	1	12	yes	complemented
90	C₂×C₂²⋊Dic₆₇	C₂³	1	12	yes	complemented
91	C₂²⋊C₄×D₆₇	C₂³	1	24	yes	complemented
92	C₂⁵×C₆₇	—	4	12	no	—
93	C₂⁵×C₆₇	C₂³	1	3	yes	—
94	C₂⁵×C₆₇	C₂³	1	6	yes	—
95	C₂⁵×C₆₇	C₂³	1	6	yes	—
96	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic, complemented
97	C₂²×D₄×C₆₇	—	4	12	no	—
98	C₂²×D₄×C₆₇	C₂³	1	6	yes	—
99	C₂²×D₄×C₆₇	C₂³	1	24	yes	complemented
100	C₂²×D₄×C₆₇	C₂³	1	6	yes	complemented
101	C₂³×C₄×C₆₇	C₂³	1	3	yes	complemented
102	#120×C₆₇	C₂³	1	24	yes	—
103	#120×C₆₇	C₂³	1	8	yes	complemented
104	#120×C₆₇	C₂³	1	8	yes	complemented
105	#120×C₆₇	C₂³	1	24	yes	complemented
106	C₂×C₂²⋊C₄×C₆₇	C₂³	1	6	yes	—
107	C₂×C₂²⋊C₄×C₆₇	C₂³	1	24	yes	complemented
108	C₂×C₂²⋊C₄×C₆₇	C₂³	1	6	yes	complemented
109	C₂³×D₆₇	—	4	12	no	—
110	C₂³×D₆₇	C₂⁴	1	12	yes	—
111	C₂³×D₆₇	C₂⁴	1	4	yes	complemented
112	#11761628	—	4	24	no	—
113	#11761627	—	4	48	no	—
114	C₂×Dic₁₃₄	C₂⁴	1	12	yes	complemented
115	C₂×D₂₆₈	C₂⁴	1	12	yes	complemented
116	C₂×C₂²⋊D₆₇	—	2	48	no	—
117	C₂×C₂²⋊D₆₇	—	4	24	no	—
118	C₂×C₂²⋊D₆₇	—	4	48	no	—
119	C₂×C₂²⋊D₆₇	—	4	48	no	—
120	C₂×C₂²⋊D₆₇	—	4	24	no	—
121	C₂×C₂²⋊D₆₇	C₂⁴	1	24	yes	—
122	C₂×C₂²⋊D₆₇	C₂⁴	1	24	yes	—
123	C₂×C₂²⋊D₆₇	C₂⁴	1	48	yes	—
124	C₂×C₂²⋊D₆₇	C₂⁴	1	24	yes	complemented
125	D₄×D₆₇	—	4	48	no	—
126	C₂²×Dic₆₇	—	4	12	no	—
127	C₂²×Dic₆₇	C₂⁴	1	12	yes	—
128	C₂²×Dic₆₇	C₂⁴	1	24	yes	—
129	C₂²×Dic₆₇	C₂⁴	1	12	yes	complemented
130	C₂×C₄×D₆₇	C₂⁴	1	24	yes	complemented
131	C₄⋊Dic₆₇	C₂⁴	1	24	yes	complemented
132	Dic₆₇⋊C₄	C₂⁴	1	48	yes	complemented
133	C₂²⋊Dic₆₇	C₂⁴	1	24	yes	—
134	C₂²⋊Dic₆₇	C₂⁴	1	24	yes	—
135	C₂²⋊Dic₆₇	C₂⁴	1	48	yes	—
136	C₂²⋊Dic₆₇	C₂⁴	1	24	yes	complemented
137	(C₂×D₆₇)⋊C₄	C₂⁴	1	48	yes	complemented
138	C₄×Dic₆₇	C₂⁴	1	24	yes	complemented
139	C₂⁴×C₆₇	—	2	12	no	—
140	C₂⁴×C₆₇	—	2	24	no	—
141	C₂⁴×C₆₇	—	4	12	no	—
142	C₂⁴×C₆₇	—	4	24	no	—
143	C₂⁴×C₆₇	—	4	24	no	—
144	C₂⁴×C₆₇	—	4	12	no	—
145	C₂⁴×C₆₇	—	4	6	no	—
146	C₂⁴×C₆₇	—	4	64	no	—
147	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
148	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
149	C₂⁴×C₆₇	C₂⁴	1	12	yes	—
150	C₂⁴×C₆₇	C₂⁴	1	6	yes	—
151	C₂⁴×C₆₇	C₂⁴	1	3	yes	—
152	C₂⁴×C₆₇	C₂⁴	1	6	yes	—
153	C₂⁴×C₆₇	C₂⁴	1	6	yes	—
154	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
155	C₂⁴×C₆₇	C₂⁴	1	3	yes	—
156	C₂×D₄×C₆₇	—	2	24	no	—
157	C₂×D₄×C₆₇	—	4	12	no	—
158	C₂×D₄×C₆₇	—	4	48	no	—
159	C₂×D₄×C₆₇	C₂⁴	1	24	yes	—
160	C₂×D₄×C₆₇	C₂⁴	1	24	yes	—
161	C₂²×C₄×C₆₇	—	4	6	no	—
162	C₂²×C₄×C₆₇	C₂⁴	1	6	yes	—
163	C₂²×C₄×C₆₇	C₂⁴	1	12	yes	—
164	C₂²⋊C₄×C₆₇	C₂⁴	1	24	yes	—
165	C₂²⋊C₄×C₆₇	C₂⁴	1	24	yes	—
166	C₂³×C₆₇	—	2	6	no	—
167	C₂³×C₆₇	—	2	12	no	—
168	C₂³×C₆₇	—	2	24	no	—
169	C₂³×C₆₇	—	2	6	no	—
170	C₂³×C₆₇	—	2	24	no	—
171	C₂³×C₆₇	—	2	24	no	—
172	C₂³×C₆₇	—	2	12	no	—
173	C₂³×C₆₇	—	2	12	no	—
174	C₂³×C₆₇	—	4	6	no	—
175	C₂³×C₆₇	—	4	6	no	—
176	C₂³×C₆₇	—	4	12	no	—
177	C₂³×C₆₇	—	4	12	no	—
178	C₂³×C₆₇	—	4	6	no	—
179	C₂³×C₆₇	—	4	6	no	—
180	C₂³×C₆₇	—	4	12	no	—
181	C₂³×C₆₇	—	4	96	no	—
182	C₂³×C₆₇	—	4	48	no	—
183	C₂³×C₆₇	—	4	96	no	—
184	C₂³×C₆₇	—	8	8	no	—
185	C₂³×C₆₇	H(5,𝔽₂)	1	12	yes	complemented
186	C₂³×C₆₇	C₂⁵	1	6	yes	—
187	C₂³×C₆₇	C₂⁵	1	4	yes	—
188	C₂³×C₆₇	C₂⁵	1	6	yes	—
189	C₂³×C₆₇	C₂⁵	1	3	yes	—
190	C₂²×D₆₇	—	2	24	no	—
191	C₂²×D₆₇	—	4	24	no	—
192	C₂²×D₆₇	—	4	12	no	—
193	C₂²×D₆₇	—	8	16	no	—
194	C₂²×D₆₇	C₂⁵	1	8	yes	—
195	D₄×C₆₇	—	2	48	no	—
196	D₄×C₆₇	—	4	24	no	—
197	C₂×C₄×C₆₇	—	2	12	no	—
198	C₂×C₄×C₆₇	—	4	12	no	—
199	C₂×C₄×C₆₇	C₂⁵	1	12	yes	—
200	C₂²⋊D₆₇	—	2	48	no	—
201	C₂²⋊D₆₇	—	2	48	no	—
202	C₂²⋊D₆₇	—	4	24	no	—
203	C₂²⋊D₆₇	—	4	48	no	—
204	C₂×Dic₆₇	—	2	24	no	—
205	C₂×Dic₆₇	—	4	24	no	—
206	C₂×Dic₆₇	—	4	12	no	—
207	C₂×Dic₆₇	C₂⁵	1	24	yes	—
208	D₂₆₈	—	4	12	no	—
209	C₄×D₆₇	—	4	24	no	—
210	Dic₁₃₄	—	4	12	no	—
211	C₂²×C₆₇	—	2	16	no	—
212	C₂²×C₆₇	—	2	8	no	—
213	C₂²×C₆₇	—	2	12	no	—
214	C₂²×C₆₇	—	2	6	no	—
215	C₂²×C₆₇	—	2	12	no	—
216	C₂²×C₆₇	—	2	12	no	—
217	C₂²×C₆₇	—	2	6	no	—
218	C₂²×C₆₇	—	4	12	no	—
219	C₂²×C₆₇	—	4	24	no	—
220	C₂²×C₆₇	—	4	48	no	—
221	C₂²×C₆₇	—	4	24	no	—
222	C₂²×C₆₇	—	4	12	no	—
223	C₂²×C₆₇	—	4	8	no	—
224	C₂²×C₆₇	—	8	12	no	—
225	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	12	yes	—
226	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	6	yes	—
227	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
228	C₂×D₆₇	—	2	24	no	—
229	C₂×D₆₇	—	8	24	no	—
230	C₂×D₆₇	—	16	4	no	—
231	C₄×C₆₇	—	2	12	no	—
232	Dic₆₇	—	2	24	no	—
233	#62817	—	67	1	no	maximal, Sylow
234	C₂×C₆₇	—	2	12	no	—
235	C₂×C₆₇	—	2	6	no	—
236	C₂×C₆₇	—	4	4	no	—
237	C₂×C₆₇	—	4	6	no	—
238	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	3	yes	—
239	D₆₇	—	4	8	no	—
240	#3532	—	67	24	no	—
241	#3490	—	67	12	no	—
242	#3490	—	67	6	no	—
243	#3484	—	67	6	no	—
244	#3484	—	67	12	no	—
245	C₂²×#120	—	67	2	no	—
246	C₂²×#120	D₆₇	1	1	yes	characteristic, complemented
247	C₆₇	#62817	1	1	yes	characteristic, complemented, Sylow
248	C₂⁶	C₂×D₆₇	1	1	yes	characteristic, complemented
249	C₂×H(5,𝔽₂)	—	67	6	no	—
250	C₂³×D₄	—	67	6	no	—
251	C₂³×D₄	C₂×D₆₇	1	3	yes	complemented
252	H(3,𝔽₄)	—	67	8	no	—
253	#560	—	67	24	no	—
254	#551	—	67	24	no	—
255	#551	—	67	48	no	—
256	#546	—	67	48	no	—
257	#546	—	67	48	no	—
258	#546	—	67	48	no	—
259	D₄²	—	67	48	no	—
260	D₄²	—	67	24	no	—
261	#543	—	67	6	no	—
262	#538	—	67	48	no	—
263	#538	—	67	24	no	—
264	#535	—	67	12	no	—
265	#535	—	67	24	no	—
266	#534	—	67	12	no	—
267	#534	—	67	12	no	—
268	#534	—	67	24	no	—
269	#534	—	67	6	no	—
270	#525	—	67	12	no	—
271	#525	—	67	24	no	—
272	C₂×#120	—	67	12	no	—
273	C₂×#120	—	67	12	no	—
274	C₂×#120	—	67	24	no	—
275	C₂×#120	—	67	4	no	—
276	C₂×#120	—	67	8	no	—
277	C₂×#120	C₂×D₆₇	1	12	yes	complemented
278	C₂×#120	C₂×D₆₇	1	12	yes	complemented
279	#518	—	67	6	no	—
280	#518	—	67	12	no	—
281	C₂²×C₂²⋊C₄	—	67	6	no	—
282	C₂²×C₂²⋊C₄	C₂×D₆₇	1	3	yes	complemented
283	C₂⁵	—	4	12	no	—
284	C₂⁵	—	67	2	no	—
285	C₂⁵	C₂²×D₆₇	1	6	yes	—
286	C₂⁵	C₂²×D₆₇	1	3	yes	—
287	C₂⁵	C₂²×D₆₇	1	6	yes	—
288	C₂⁵	C₂²×D₆₇	1	1	yes	characteristic, complemented
289	H(5,𝔽₂)	—	268	24	no	—
290	C₂×#41	—	67	24	no	—
291	C₂×#41	—	67	12	no	—
292	C₂²×D₄	—	4	12	no	—
293	C₂²×D₄	—	268	24	no	—
294	C₂²×D₄	—	67	12	no	—
295	C₂²×D₄	—	67	24	no	—
296	C₂²×D₄	—	67	24	no	—
297	C₂²×D₄	—	67	12	no	—
298	C₂²×D₄	—	67	24	no	—
299	C₂²×D₄	—	67	12	no	—
300	C₂²×D₄	C₂²×D₆₇	1	6	yes	—
301	C₂²×D₄	C₂²×D₆₇	1	6	yes	complemented
302	C₂²×D₄	C₂²×D₆₇	1	24	yes	complemented
303	C₂³×C₄	—	67	6	no	—
304	C₂³×C₄	C₂²×D₆₇	1	3	yes	complemented
305	#127	—	67	24	no	—
306	#126	—	67	48	no	—
307	#124	—	67	24	no	—
308	#124	—	67	48	no	—
309	#123	—	67	24	no	—
310	#123	—	67	24	no	—
311	#123	—	67	24	no	—
312	#123	—	67	24	no	—
313	#123	—	67	48	no	—
314	C₂²⋊Q₈	—	67	24	no	—
315	C₂²⋊Q₈	—	67	48	no	—
316	#121	—	67	48	no	—
317	#121	—	67	48	no	—
318	#121	—	67	48	no	—
319	#121	—	67	24	no	—
320	#121	—	67	48	no	—
321	#120	—	67	8	no	—
322	#120	—	67	8	no	—
323	#120	—	67	24	no	—
324	#120	—	67	24	no	—
325	#120	—	67	48	no	—
326	#120	—	67	16	no	—
327	#120	—	67	24	no	—
328	#120	—	67	24	no	—
329	#120	—	67	24	no	—
330	#120	—	67	24	no	—
331	#120	C₂²×D₆₇	1	24	yes	—
332	#120	C₂²×D₆₇	1	8	yes	complemented
333	#120	C₂²×D₆₇	1	24	yes	complemented
334	#120	C₂²×D₆₇	1	8	yes	complemented
335	C₄×D₄	—	67	48	no	—
336	C₄×D₄	—	67	48	no	—
337	C₄×D₄	—	67	48	no	—
338	#117	—	67	12	no	—
339	#117	—	67	24	no	—
340	C₂×C₂²⋊C₄	—	67	12	no	—
341	C₂×C₂²⋊C₄	—	67	12	no	—
342	C₂×C₂²⋊C₄	—	67	24	no	—
343	C₂×C₂²⋊C₄	—	67	24	no	—
344	C₂×C₂²⋊C₄	—	67	12	no	—
345	C₂×C₂²⋊C₄	—	67	24	no	—
346	C₂×C₂²⋊C₄	C₂²×D₆₇	1	6	yes	—
347	C₂×C₂²⋊C₄	C₂²×D₆₇	1	6	yes	complemented
348	C₂×C₂²⋊C₄	C₂²×D₆₇	1	24	yes	complemented
349	C₂⁴	—	2	12	no	—
350	C₂⁴	—	2	24	no	—
351	C₂⁴	—	4	12	no	—
352	C₂⁴	—	4	24	no	—
353	C₂⁴	—	4	24	no	—
354	C₂⁴	—	4	12	no	—
355	C₂⁴	—	4	6	no	—
356	C₂⁴	—	4	64	no	—
357	C₂⁴	—	268	12	no	—
358	C₂⁴	—	67	4	no	—
359	C₂⁴	—	67	12	no	—
360	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
361	C₂⁴	C₂³×D₆₇	1	2	yes	—
362	C₂⁴	C₂³×D₆₇	1	6	yes	—
363	C₂⁴	C₂³×D₆₇	1	12	yes	—
364	C₂⁴	C₂³×D₆₇	1	6	yes	—
365	C₂⁴	C₂³×D₆₇	1	6	yes	—
366	C₂⁴	C₂³×D₆₇	1	3	yes	—
367	C₂⁴	C₂³×D₆₇	1	2	yes	—
368	C₂⁴	C₂³×D₆₇	1	3	yes	—
369	#41	—	268	24	no	—
370	#41	—	268	48	no	—
371	C₂×Q₈	—	67	12	no	—
372	C₂×D₄	—	2	24	no	—
373	C₂×D₄	—	4	12	no	—
374	C₂×D₄	—	4	48	no	—
375	C₂×D₄	—	268	48	no	—
376	C₂×D₄	—	268	48	no	—
377	C₂×D₄	—	268	48	no	—
378	C₂×D₄	—	268	24	no	—
379	C₂×D₄	—	268	24	no	—
380	C₂×D₄	—	67	48	no	—
381	C₂×D₄	—	67	24	no	—
382	C₂×D₄	—	67	24	no	—
383	C₂×D₄	—	67	24	no	—
384	C₂×D₄	—	67	12	no	—
385	C₂×D₄	—	134	48	no	—
386	C₂×D₄	C₂³×D₆₇	1	24	yes	—
387	C₂×D₄	C₂³×D₆₇	1	24	yes	—
388	C₂²×C₄	—	4	6	no	—
389	C₂²×C₄	—	268	12	no	—
390	C₂²×C₄	—	67	24	no	—
391	C₂²×C₄	—	67	12	no	—
392	C₂²×C₄	—	67	24	no	—
393	C₂²×C₄	—	67	12	no	—
394	C₂²×C₄	C₂³×D₆₇	1	6	yes	—
395	C₂²×C₄	C₂³×D₆₇	1	12	yes	—
396	C₄⋊C₄	—	67	48	no	—
397	C₄⋊C₄	—	67	24	no	—
398	C₂²⋊C₄	—	67	24	no	—
399	C₂²⋊C₄	—	67	24	no	—
400	C₂²⋊C₄	—	67	48	no	—
401	C₂²⋊C₄	—	67	24	no	—
402	C₂²⋊C₄	—	67	48	no	—
403	C₂²⋊C₄	C₂³×D₆₇	1	24	yes	—
404	C₂²⋊C₄	C₂³×D₆₇	1	24	yes	—
405	C₄²	—	67	24	no	—
406	C₂³	—	2	6	no	—
407	C₂³	—	2	12	no	—
408	C₂³	—	2	24	no	—
409	C₂³	—	2	6	no	—
410	C₂³	—	2	24	no	—
411	C₂³	—	2	24	no	—
412	C₂³	—	2	12	no	—
413	C₂³	—	2	12	no	—
414	C₂³	—	4	6	no	—
415	C₂³	—	4	12	no	—
416	C₂³	—	4	6	no	—
417	C₂³	—	4	6	no	—
418	C₂³	—	4	12	no	—
419	C₂³	—	4	6	no	—
420	C₂³	—	4	12	no	—
421	C₂³	—	4	48	no	—
422	C₂³	—	4	96	no	—
423	C₂³	—	4	96	no	—
424	C₂³	—	8	8	no	—
425	C₂³	—	268	24	no	—
426	C₂³	—	268	12	no	—
427	C₂³	—	536	16	no	—
428	C₂³	—	67	8	no	—
429	C₂³	—	134	24	no	—
430	C₂³	#14524088	1	12	yes	complemented
431	C₂³	C₂⁴×D₆₇	1	6	yes	—
432	C₂³	C₂⁴×D₆₇	1	4	yes	—
433	C₂³	C₂⁴×D₆₇	1	3	yes	—
434	C₂³	C₂⁴×D₆₇	1	6	yes	—
435	Q₈	—	268	12	no	—
436	D₄	—	2	48	no	—
437	D₄	—	4	24	no	—
438	D₄	—	268	12	no	—
439	D₄	—	268	48	no	—
440	D₄	—	268	24	no	—
441	D₄	—	134	48	no	—
442	D₄	—	134	48	no	—
443	C₂×C₄	—	2	12	no	—
444	C₂×C₄	—	4	12	no	—
445	C₂×C₄	—	268	24	no	—
446	C₂×C₄	—	268	24	no	—
447	C₂×C₄	—	268	12	no	—
448	C₂×C₄	—	67	24	no	—
449	C₂×C₄	—	134	24	no	—
450	C₂×C₄	C₂⁴×D₆₇	1	12	yes	—
451	C₂²	—	2	8	no	—
452	C₂²	—	2	16	no	—
453	C₂²	—	2	6	no	—
454	C₂²	—	2	12	no	—
455	C₂²	—	2	12	no	—
456	C₂²	—	2	6	no	—
457	C₂²	—	2	12	no	—
458	C₂²	—	4	12	no	—
459	C₂²	—	4	48	no	—
460	C₂²	—	4	24	no	—
461	C₂²	—	4	12	no	—
462	C₂²	—	4	24	no	—
463	C₂²	—	4	8	no	—
464	C₂²	—	8	12	no	—
465	C₂²	—	536	24	no	—
466	C₂²	—	1072	4	no	—
467	C₂²	—	134	24	no	—
468	C₂²	C₂×#14524088	1	6	yes	—
469	C₂²	C₂×#14524088	1	12	yes	—
470	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
471	C₄	—	2	12	no	—
472	C₄	—	134	24	no	—
473	C₂	—	2	6	no	—
474	C₂	—	2	12	no	—
475	C₂	—	4	6	no	—
476	C₂	—	4	4	no	—
477	C₂	—	268	8	no	—
478	C₂	C₂²×#14524088	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₆₇
commutator, socle, cosocle	C₂²×C₆₇	C₂⁶
Fitting	C₂²×#120×C₆₇	C₂
hypercenter	C₂²×#120	D₆₇
hypocenter	C₆₇	#62817
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×#120

Complements

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

N	H ≅ G/N	type
1. #22574364	C₂	semidirect
2. #22573898	C₂	semidirect
3. #22573896	C₂	semidirect
4. #22573844	C₂	semidirect
5. #22573838	C₂	semidirect
6. C₂²×#14524012	C₂	semidirect
7. C₂²×#120×C₆₇	C₂	semidirect
8. C₂×#14524088	C₂²	semidirect
9. C₂³×C₂²⋊D₆₇	C₂²	semidirect
10. #16864139	C₂²	semidirect
11. #16864135	C₂²	semidirect
12. #16864077	C₂²	semidirect
13. #16864072	C₂²	semidirect
14. #16864040	C₂²	semidirect
15. #16864036	C₂²	semidirect
16. #16864033	C₂²	semidirect
17. D₄×C₂²⋊D₆₇	C₂²	semidirect
18. #16864028	C₂²	semidirect
19. #16864022	C₂²	semidirect
20. #16863984	C₂²	semidirect
21. #16863981	C₂²	semidirect
22. #16863963	C₂²	semidirect
23. #16863961	C₂²	semidirect
24. #16863958	C₂²	semidirect
25. #16863956	C₂²	semidirect
26. #16863955	C₂²	semidirect
27. #16863955	C₂²	semidirect
28. #16863907	C₂²	semidirect
29. #16863902	C₂²	semidirect
30. C₂×#14524012	C₂²	semidirect
31. C₂×#14524012	C₂²	semidirect
32. C₂×#14524012	C₂²	semidirect
33. C₂×#14524012	C₂²	semidirect
34. #120×D₆₇	C₂²	semidirect
35. #16863871	C₂²	semidirect
36. #16863869	C₂²	semidirect
37. C₂²×C₂²⋊Dic₆₇	C₂²	semidirect
38. C₂⁶×C₆₇	C₂²	semidirect
39. C₂³×D₄×C₆₇	C₂²	semidirect
40. C₂×#120×C₆₇	C₂²	semidirect
41. C₂×#120×C₆₇	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
43. C₂⁴×D₆₇	C₂³	semidirect
45. C₂×#11761628	C₂³	semidirect
46. C₂×#11761627	C₂³	semidirect
49. C₂²×C₂²⋊D₆₇	C₂³	semidirect
50. C₂²×C₂²⋊D₆₇	C₂³	semidirect
51. C₂²×C₂²⋊D₆₇	C₂³	semidirect
52. C₂²×C₂²⋊D₆₇	C₂³	semidirect
53. C₂×D₄×D₆₇	C₂³	semidirect
54. C₂³×Dic₆₇	C₂³	semidirect
55. #14524039	C₂³	semidirect
56. #14524036	C₂³	semidirect
57. #14524030	C₂³	semidirect
58. #14524029	C₂³	semidirect
59. #14524027	C₂³	semidirect
60. #14524026	C₂³	semidirect
61. #14524025	C₂³	semidirect
62. #14524024	C₂³	semidirect
63. #14524024	C₂³	semidirect
64. #14524022	C₂³	semidirect
65. #14524020	C₂³	semidirect
66. #14524017	C₂³	semidirect
67. #14524016	C₂³	semidirect
68. #14524015	C₂³	semidirect
69. #14524015	C₂³	semidirect
70. #14524014	C₂³	semidirect
71. #14524013	C₂³	semidirect
73. #14524012	C₂³	semidirect
74. #14524012	C₂³	semidirect
75. #14524012	C₂³	semidirect
76. #14524012	C₂³	semidirect
77. #14524012	C₂³	semidirect
78. #14524012	C₂³	semidirect
79. #14524011	C₂³	semidirect
80. #14524011	C₂³	semidirect
81. D₄×Dic₆₇	C₂³	semidirect
82. C₄×C₂²⋊D₆₇	C₂³	semidirect
83. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
84. #14524002	C₂³	semidirect
85. #14523999	C₂³	semidirect
87. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
88. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
89. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
90. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
91. C₂²⋊C₄×D₆₇	C₂³	semidirect
96. C₂⁵×C₆₇	C₂³	semidirect
99. C₂²×D₄×C₆₇	C₂³	semidirect
100. C₂²×D₄×C₆₇	C₂³	semidirect
101. C₂³×C₄×C₆₇	C₂³	semidirect
103. #120×C₆₇	C₂³	semidirect
104. #120×C₆₇	C₂³	semidirect
105. #120×C₆₇	C₂³	semidirect
107. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
108. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
111. C₂³×D₆₇	C₂⁴	semidirect
114. C₂×Dic₁₃₄	C₂⁴	semidirect
115. C₂×D₂₆₈	C₂⁴	semidirect
124. C₂×C₂²⋊D₆₇	C₂⁴	semidirect
129. C₂²×Dic₆₇	C₂⁴	semidirect
130. C₂×C₄×D₆₇	C₂⁴	semidirect
131. C₄⋊Dic₆₇	C₂⁴	semidirect
132. Dic₆₇⋊C₄	C₂⁴	semidirect
136. C₂²⋊Dic₆₇	C₂⁴	semidirect
137. (C₂×D₆₇)⋊C₄	C₂⁴	semidirect
138. C₄×Dic₆₇	C₂⁴	semidirect
185. C₂³×C₆₇	H(5,𝔽₂)	semidirect
246. C₂²×#120	D₆₇	semidirect
247. C₆₇	#62817	semidirect
248. C₂⁶	C₂×D₆₇	semidirect
251. C₂³×D₄	C₂×D₆₇	semidirect
277. C₂×#120	C₂×D₆₇	semidirect
278. C₂×#120	C₂×D₆₇	semidirect
282. C₂²×C₂²⋊C₄	C₂×D₆₇	semidirect
288. C₂⁵	C₂²×D₆₇	semidirect
301. C₂²×D₄	C₂²×D₆₇	semidirect
302. C₂²×D₄	C₂²×D₆₇	semidirect
304. C₂³×C₄	C₂²×D₆₇	semidirect
332. #120	C₂²×D₆₇	semidirect
333. #120	C₂²×D₆₇	semidirect
334. #120	C₂²×D₆₇	semidirect
347. C₂×C₂²⋊C₄	C₂²×D₆₇	semidirect
348. C₂×C₂²⋊C₄	C₂²×D₆₇	semidirect
430. C₂³	#14524088	semidirect

Maximal subgroups

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

subgroup	index
#22574364	2
#22573898	2
#22573896	2
#22573844	2
#22573838	2
C₂²×#14524012	2
C₂²×#120×C₆₇	2
#62817	67