Subgroups — #31720174

Order 17152.

2604 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574980	C₂	1	1	yes	maximal, characteristic
2	#22574920	C₂	1	1	yes	maximal, characteristic, complemented
3	#22569124	C₂	1	6	yes	maximal, complemented
4	#22569116	C₂	1	6	yes	maximal, complemented
5	#22569110	C₂	1	6	yes	maximal, complemented
6	C₂×#16863516	C₂	1	6	yes	maximal, complemented
7	#22568818	C₂	1	1	yes	maximal, characteristic, complemented
8	#22568756	C₂	1	1	yes	maximal, characteristic, complemented
9	#22568754	C₂	1	1	yes	maximal, characteristic, complemented
10	#22568635	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3573	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864232	C₂²	1	1	yes	characteristic
13	#16864211	C₄	1	4	yes	complemented
14	#16864207	C₄	1	4	yes	complemented
15	#16864204	C₄	1	4	yes	complemented
16	#16864199	C₄	1	4	yes	complemented
17	#16864194	C₂²	1	6	yes	—
18	C₂×#14524063	C₂²	1	6	yes	—
19	#16864163	C₂²	1	1	yes	characteristic
20	#16864162	C₂²	1	6	yes	complemented
21	#16864161	—	2	4	no	—
22	C₂×#14524050	C₂²	1	1	yes	characteristic
23	C₂×#14524049	C₂²	1	6	yes	complemented
24	#131×D₆₇	—	2	4	no	—
25	#41×Dic₆₇	C₂²	1	1	yes	characteristic
26	#16863516	C₂²	1	4	yes	complemented
27	#16863516	C₂²	1	12	yes	complemented
28	#16863516	C₂²	1	12	yes	complemented
29	#16863516	C₂²	1	12	yes	complemented
30	#16863511	C₂²	1	24	yes	complemented
31	#16863444	C₂²	1	6	yes	complemented
32	C₂×#14523978	C₂²	1	6	yes	complemented
33	#16863413	C₂²	1	6	yes	complemented
34	#16863412	C₂²	1	6	yes	complemented
35	C₂×#14523970	C₂²	1	6	yes	complemented
36	C₂×#14523969	C₂²	1	6	yes	complemented
37	#16863354	C₂²	1	3	yes	complemented
38	#16863351	C₂²	1	3	yes	complemented
39	M₁₆×Dic₆₇	C₂²	1	3	yes	complemented
40	C₂×#14523953	C₂²	1	3	yes	complemented
41	#585×C₆₇	C₂²	1	1	yes	characteristic
42	#568×C₆₇	—	2	4	no	—
43	#568×C₆₇	C₂²	1	1	yes	characteristic
44	#568×C₆₇	C₂²	1	6	yes	complemented
45	C₂×#131×C₆₇	—	2	4	no	—
46	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#131×C₆₇	C₂²	1	6	yes	complemented
48	#14524091	—	2	1	no	—
49	#14524090	C₂×C₄	1	4	yes	—
50	#14524089	C₂×C₄	1	4	yes	—
51	#14524088	—	2	3	no	—
52	C₂×#11761628	C₂³	1	6	yes	—
53	#41×D₆₇	—	2	4	no	—
54	#14524074	C₂×C₄	1	12	yes	complemented
55	#14524073	C₂×C₄	1	12	yes	complemented
56	#14524069	C₂×C₄	1	12	yes	complemented
57	#14524068	C₂×C₄	1	12	yes	complemented
58	#14524063	C₂×C₄	1	12	yes	complemented
59	#14524063	C₂×C₄	1	12	yes	complemented
60	#14524063	C₂³	1	12	yes	—
61	#14524063	C₂³	1	4	yes	—
62	C₂×#11761618	C₂×C₄	1	6	yes	complemented
63	C₂×#11761616	C₂×C₄	1	6	yes	complemented
64	C₂×#11761615	C₂×C₄	1	6	yes	complemented
65	C₂×#11761613	C₂×C₄	1	6	yes	complemented
66	#14524051	—	2	12	no	—
67	#14524050	—	2	4	no	—
68	#14524050	C₂×C₄	1	4	yes	—
69	#14524050	C₂×C₄	1	4	yes	—
70	#14524049	—	2	6	no	—
71	#14524049	—	2	6	no	—
72	#14524049	C₂³	1	12	yes	—
73	#14524049	C₂³	1	4	yes	—
74	C₂×#11761612	C₂³	1	6	yes	—
75	C₂×#11761612	C₂³	1	3	yes	—
76	C₂×#11761611	—	2	6	no	—
77	M₁₆×D₆₇	—	2	12	no	—
78	C₂²×C₆₇⋊C₈	C₂³	1	3	yes	—
79	C₂×C₈×D₆₇	—	2	6	no	—
80	Q₈×Dic₆₇	—	2	1	no	—
81	D₄×Dic₆₇	—	2	3	no	—
82	#14524002	C₂³	1	3	yes	—
83	C₂×C₄×Dic₆₇	C₂³	1	3	yes	—
84	#14523978	C₂³	1	12	yes	—
85	#14523978	C₂³	1	4	yes	—
86	#14523970	C₂³	1	12	yes	—
87	#14523970	C₂³	1	4	yes	—
88	#14523969	C₂³	1	12	yes	—
89	#14523969	C₂³	1	4	yes	—
90	#14523953	C₂³	1	1	yes	characteristic
91	#14523953	C₂³	1	3	yes	—
92	#14523953	C₂³	1	3	yes	—
93	#14523953	C₂³	1	3	yes	—
94	C₈×Dic₆₇	C₂³	1	6	yes	—
95	2₋¹⁺⁴×C₆₇	—	2	1	no	—
96	2₋¹⁺⁴×C₆₇	C₂×C₄	1	4	yes	—
97	H(5,𝔽₂)×C₆₇	—	2	3	no	—
98	H(5,𝔽₂)×C₆₇	C₂×C₄	1	4	yes	—
99	C₂×#41×C₆₇	—	2	4	no	—
100	C₂×#41×C₆₇	C₂³	1	6	yes	—
101	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
102	#131×C₆₇	—	2	4	no	—
103	#131×C₆₇	—	2	12	no	—
104	#131×C₆₇	—	2	6	no	—
105	#131×C₆₇	—	2	6	no	—
106	#131×C₆₇	D₄	1	4	yes	—
107	#131×C₆₇	D₄	1	4	yes	—
108	#131×C₆₇	C₂³	1	12	yes	—
109	#131×C₆₇	C₂³	1	4	yes	—
110	C₂×M₁₆×C₆₇	—	2	12	no	—
111	C₂×M₁₆×C₆₇	—	2	6	no	—
112	C₂×M₁₆×C₆₇	C₂³	1	6	yes	—
113	C₂×M₁₆×C₆₇	C₂³	1	3	yes	—
114	C₂²×C₈×C₆₇	—	2	6	no	—
115	C₂²×C₈×C₆₇	C₂³	1	3	yes	—
116	#11761629	—	2	4	no	—
117	#11761628	—	2	6	no	—
118	#11761628	—	2	6	no	—
119	#11761628	C₂²×C₄	1	12	yes	—
120	#11761628	C₂⁴	1	4	yes	—
121	#11761627	—	2	12	no	—
122	C₂×Dic₁₃₄	C₂²×C₄	1	6	yes	—
123	Q₈×D₆₇	—	2	4	no	—
124	C₂×D₂₆₈	C₂²×C₄	1	6	yes	—
125	C₂×C₂²⋊D₆₇	—	2	6	no	—
126	D₄×D₆₇	—	2	12	no	—
127	C₂²×Dic₆₇	—	2	3	no	—
128	C₂×C₄×D₆₇	—	2	6	no	—
129	#11761618	C₂²×C₄	1	4	yes	—
130	#11761618	C₂²×C₄	1	12	yes	—
131	#11761616	C₂²×C₄	1	4	yes	—
132	#11761616	C₂²×C₄	1	12	yes	—
133	#11761615	C₂²×C₄	1	4	yes	—
134	#11761615	C₂²×C₄	1	12	yes	—
135	#11761613	C₂²×C₄	1	4	yes	—
136	#11761613	C₂²×C₄	1	12	yes	—
137	#11761612	—	2	6	no	—
138	#11761612	C₂²×C₄	1	12	yes	—
139	#11761612	C₂⁴	1	4	yes	—
140	#11761611	—	2	12	no	—
141	#11761611	—	2	4	no	—
142	C₂×C₆₇⋊C₈	—	2	6	no	—
143	C₂×C₆₇⋊C₈	C₂²×C₄	1	6	yes	—
144	C₂×C₆₇⋊C₈	C₂²×C₄	1	6	yes	—
145	C₂×C₆₇⋊C₈	C₂⁴	1	3	yes	—
146	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
147	C₈×D₆₇	—	2	4	no	—
148	C₈×D₆₇	—	2	12	no	—
149	C₄⋊Dic₆₇	—	2	3	no	—
150	C₂²⋊Dic₆₇	—	2	3	no	—
151	C₄×Dic₆₇	—	2	3	no	—
152	C₄×Dic₆₇	C₂⁴	1	3	yes	—
153	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
154	#41×C₆₇	—	2	4	no	—
155	#41×C₆₇	—	2	12	no	—
156	#41×C₆₇	—	2	6	no	—
157	#41×C₆₇	—	2	6	no	—
158	#41×C₆₇	C₂²×C₄	1	12	yes	—
159	#41×C₆₇	C₂²×C₄	1	4	yes	—
160	#41×C₆₇	C₂×D₄	1	4	yes	—
161	#41×C₆₇	C₂⁴	1	4	yes	—
162	C₂×Q₈×C₆₇	—	2	4	no	—
163	C₂×Q₈×C₆₇	C₂²×C₄	1	6	yes	—
164	C₂×Q₈×C₆₇	#41	1	1	yes	characteristic
165	C₂×D₄×C₆₇	—	2	6	no	—
166	C₂×D₄×C₆₇	—	2	12	no	—
167	C₂×D₄×C₆₇	C₂²×C₄	1	6	yes	—
168	C₂×D₄×C₆₇	#41	1	3	yes	—
169	C₂²×C₄×C₆₇	—	2	6	no	—
170	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
171	M₁₆×C₆₇	—	2	6	no	—
172	M₁₆×C₆₇	—	2	12	no	—
173	M₁₆×C₆₇	—	2	4	no	—
174	M₁₆×C₆₇	C₂×D₄	1	12	yes	—
175	M₁₆×C₆₇	C₂⁴	1	4	yes	—
176	C₂×C₈×C₆₇	—	2	6	no	—
177	C₂×C₈×C₆₇	—	2	4	no	—
178	C₂×C₈×C₆₇	—	2	12	no	—
179	C₂×C₈×C₆₇	C₂×D₄	1	6	yes	—
180	C₂×C₈×C₆₇	C₂×D₄	1	6	yes	—
181	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
182	C₂×C₈×C₆₇	C₂⁴	1	3	yes	—
183	C₂³×C₆₇	—	2	6	no	—
184	C₂³×C₆₇	C₂×#41	1	3	yes	—
185	C₂²×D₆₇	—	2	6	no	—
186	Q₈×C₆₇	—	2	6	no	—
187	Q₈×C₆₇	C₄×D₄	1	4	yes	—
188	Q₈×C₆₇	C₂³×C₄	1	4	yes	—
189	D₄×C₆₇	—	2	12	no	—
190	D₄×C₆₇	—	2	4	no	—
191	D₄×C₆₇	—	2	6	no	—
192	D₄×C₆₇	C₄×D₄	1	12	yes	—
193	D₄×C₆₇	C₂³×C₄	1	4	yes	—
194	C₂×C₄×C₆₇	—	2	6	no	—
195	C₂×C₄×C₆₇	—	2	12	no	—
196	C₂×C₄×C₆₇	—	2	4	no	—
197	C₂×C₄×C₆₇	C₂³×C₄	1	6	yes	—
198	C₂×C₄×C₆₇	C₂²×D₄	1	6	yes	—
199	C₂×C₄×C₆₇	C₂×#41	1	3	yes	—
200	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
201	C₂²⋊D₆₇	—	2	12	no	—
202	C₂²⋊D₆₇	—	2	4	no	—
203	C₂×Dic₆₇	—	2	6	no	—
204	C₂×Dic₆₇	—	2	1	no	—
205	C₂×Dic₆₇	—	2	3	no	—
206	C₂×Dic₆₇	—	8	3	no	—
207	D₂₆₈	—	2	6	no	—
208	D₂₆₈	C₂³×C₄	1	4	yes	—
209	C₄×D₆₇	—	2	12	no	—
210	C₄×D₆₇	—	2	4	no	—
211	Dic₁₃₄	—	2	6	no	—
212	Dic₁₃₄	C₂³×C₄	1	4	yes	—
213	C₈×C₆₇	—	2	4	no	—
214	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
215	C₈×C₆₇	C₂²×D₄	1	6	yes	—
216	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
217	C₆₇⋊C₈	—	2	4	no	—
218	C₆₇⋊C₈	C₂³×C₄	1	1	yes	characteristic
219	C₆₇⋊C₈	C₂³×C₄	1	1	yes	characteristic
220	C₆₇⋊C₈	C₂³×C₄	1	6	yes	—
221	C₂²×C₆₇	—	2	4	no	—
222	C₂²×C₆₇	—	4	3	no	—
223	C₂²×C₆₇	—	8	6	no	—
224	C₂²×C₆₇	C₂×C₄×D₄	1	6	yes	—
225	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
226	C₂×D₆₇	—	2	4	no	—
227	C₂×D₆₇	—	8	6	no	—
228	C₄×C₆₇	—	2	4	no	—
229	C₄×C₆₇	C₂×C₄×D₄	1	6	yes	—
230	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
231	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
232	Dic₆₇	—	2	4	no	—
233	Dic₆₇	—	4	3	no	—
234	Dic₆₇	—	4	1	no	—
235	#60184	—	67	1	no	maximal, Sylow
236	C₂×C₆₇	—	2	1	no	—
237	C₂×C₆₇	—	2	6	no	—
238	C₂×C₆₇	—	4	4	no	—
239	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
240	D₆₇	—	4	4	no	—
241	#3584	—	67	1	no	—
242	#3573	—	67	1	no	—
243	#3573	D₆₇	1	1	yes	characteristic, complemented
244	#2957	—	67	6	no	—
245	#2956	—	67	6	no	—
246	#2955	—	67	6	no	—
247	C₂×#444	—	67	6	no	—
248	#2916	—	67	1	no	—
249	#2901	—	67	1	no	—
250	#2901	—	67	1	no	—
251	#2875	—	67	1	no	—
252	C₆₇	#60184	1	1	yes	characteristic, complemented, Sylow
253	#585	—	67	1	no	—
254	#585	C₂×D₆₇	1	1	yes	characteristic
255	#578	—	67	4	no	—
256	#577	—	67	4	no	—
257	#577	—	67	4	no	—
258	#576	—	67	4	no	—
259	#575	—	67	6	no	—
260	C₂×#135	—	67	6	no	—
261	#568	—	2	4	no	—
262	#568	—	67	1	no	—
263	#568	—	67	6	no	—
264	#568	—	134	4	no	—
265	#568	C₂×D₆₇	1	1	yes	characteristic
266	#568	C₂×D₆₇	1	6	yes	complemented
267	C₂×#131	—	2	4	no	—
268	C₂×#131	—	67	1	no	—
269	C₂×#131	—	67	6	no	—
270	C₂×#131	—	134	4	no	—
271	C₂×#131	C₂×D₆₇	1	1	yes	characteristic
272	C₂×#131	C₂×D₆₇	1	6	yes	complemented
273	C₄×#41	—	67	1	no	—
274	#444	—	67	4	no	—
275	#444	—	67	12	no	—
276	#444	—	67	12	no	—
277	#444	—	67	12	no	—
278	#443	—	67	24	no	—
279	#430	—	67	6	no	—
280	C₂×#108	—	67	6	no	—
281	#421	—	67	6	no	—
282	#421	—	67	6	no	—
283	C₂×#104	—	67	6	no	—
284	C₂×#104	—	67	6	no	—
285	#405	—	67	3	no	—
286	#405	—	67	3	no	—
287	C₄×M₁₆	—	67	3	no	—
288	C₂×#97	—	67	3	no	—
289	2₋¹⁺⁴	—	2	1	no	—
290	2₋¹⁺⁴	—	67	4	no	—
291	2₋¹⁺⁴	—	134	1	no	—
292	2₋¹⁺⁴	C₄×D₆₇	1	4	yes	—
293	H(5,𝔽₂)	—	2	3	no	—
294	H(5,𝔽₂)	—	67	4	no	—
295	H(5,𝔽₂)	—	134	3	no	—
296	H(5,𝔽₂)	C₄×D₆₇	1	4	yes	—
297	C₂×#41	—	2	4	no	—
298	C₂×#41	—	67	6	no	—
299	C₂×#41	—	134	4	no	—
300	C₂×#41	C₂²×D₆₇	1	6	yes	—
301	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
302	#137	—	67	12	no	—
303	#137	—	67	12	no	—
304	AGL(1,ℤ/8)	—	67	12	no	—
305	AGL(1,ℤ/8)	—	67	12	no	—
306	#135	—	67	12	no	—
307	#135	—	67	12	no	—
308	#135	—	67	4	no	—
309	#135	—	67	12	no	—
310	C₂×Q₁₆	—	67	6	no	—
311	C₂×SD₁₆	—	67	6	no	—
312	C₂×SD₁₆	—	67	6	no	—
313	C₂×D₈	—	67	6	no	—
314	#131	—	2	4	no	—
315	#131	—	2	12	no	—
316	#131	—	2	6	no	—
317	#131	—	2	6	no	—
318	#131	—	67	4	no	—
319	#131	—	67	4	no	—
320	#131	—	67	4	no	—
321	#131	—	67	12	no	—
322	#131	—	134	4	no	—
323	#131	—	134	12	no	—
324	#131	—	134	6	no	—
325	#131	—	134	6	no	—
326	#131	C₂²⋊D₆₇	1	4	yes	—
327	#131	C₂²⋊D₆₇	1	4	yes	—
328	#131	C₂²×D₆₇	1	4	yes	—
329	#131	C₂²×D₆₇	1	12	yes	—
330	C₂×M₁₆	—	2	12	no	—
331	C₂×M₁₆	—	2	6	no	—
332	C₂×M₁₆	—	67	3	no	—
333	C₂×M₁₆	—	67	6	no	—
334	C₂×M₁₆	—	134	12	no	—
335	C₂×M₁₆	—	134	6	no	—
336	C₂×M₁₆	C₂²×D₆₇	1	6	yes	—
337	C₂×M₁₆	C₂²×D₆₇	1	3	yes	—
338	C₂²×C₈	—	2	6	no	—
339	C₂²×C₈	—	67	3	no	—
340	C₂²×C₈	—	134	6	no	—
341	C₂²×C₈	C₂²×D₆₇	1	3	yes	—
342	C₄×Q₈	—	134	1	no	—
343	C₄×D₄	—	134	3	no	—
344	#117	—	67	3	no	—
345	C₂×C₄²	—	67	3	no	—
346	#108	—	67	4	no	—
347	#108	—	67	12	no	—
348	#104	—	67	4	no	—
349	#104	—	67	12	no	—
350	#104	—	67	4	no	—
351	#104	—	67	12	no	—
352	#97	—	67	1	no	—
353	#97	—	67	3	no	—
354	#97	—	67	3	no	—
355	#97	—	67	3	no	—
356	C₄×C₈	—	67	6	no	—
357	#41	—	2	4	no	—
358	#41	—	2	12	no	—
359	#41	—	2	6	no	—
360	#41	—	2	6	no	—
361	#41	—	67	12	no	—
362	#41	—	67	4	no	—
363	#41	—	134	4	no	—
364	#41	—	134	12	no	—
365	#41	—	134	6	no	—
366	#41	—	134	6	no	—
367	#41	C₂×C₄×D₆₇	1	12	yes	—
368	#41	C₂×C₄×D₆₇	1	4	yes	—
369	#41	C₂×C₂²⋊D₆₇	1	4	yes	—
370	#41	C₂³×D₆₇	1	4	yes	—
371	C₂×Q₈	—	2	4	no	—
372	C₂×Q₈	—	67	6	no	—
373	C₂×Q₈	—	134	4	no	—
374	C₂×Q₈	C₂×C₄×D₆₇	1	6	yes	—
375	C₂×Q₈	#11761628	1	1	yes	characteristic
376	C₂×D₄	—	2	6	no	—
377	C₂×D₄	—	2	12	no	—
378	C₂×D₄	—	67	6	no	—
379	C₂×D₄	—	134	6	no	—
380	C₂×D₄	—	134	12	no	—
381	C₂×D₄	C₂×C₄×D₆₇	1	6	yes	—
382	C₂×D₄	#11761628	1	3	yes	—
383	C₂²×C₄	—	2	6	no	—
384	C₂²×C₄	—	134	3	no	—
385	C₂²×C₄	—	134	6	no	—
386	C₂²×C₄	C₂³×D₆₇	1	3	yes	—
387	Q₁₆	—	67	4	no	—
388	Q₁₆	—	67	12	no	—
389	SD₁₆	—	67	4	no	—
390	SD₁₆	—	67	12	no	—
391	SD₁₆	—	67	4	no	—
392	SD₁₆	—	67	12	no	—
393	D₈	—	67	4	no	—
394	D₈	—	67	12	no	—
395	M₁₆	—	2	6	no	—
396	M₁₆	—	2	12	no	—
397	M₁₆	—	2	4	no	—
398	M₁₆	—	67	12	no	—
399	M₁₆	—	67	4	no	—
400	M₁₆	—	134	6	no	—
401	M₁₆	—	134	4	no	—
402	M₁₆	—	134	12	no	—
403	M₁₆	C₂×C₂²⋊D₆₇	1	12	yes	—
404	M₁₆	C₂³×D₆₇	1	4	yes	—
405	C₂×C₈	—	2	6	no	—
406	C₂×C₈	—	2	4	no	—
407	C₂×C₈	—	2	12	no	—
408	C₂×C₈	—	67	6	no	—
409	C₂×C₈	—	67	6	no	—
410	C₂×C₈	—	67	3	no	—
411	C₂×C₈	—	67	1	no	—
412	C₂×C₈	—	134	6	no	—
413	C₂×C₈	—	134	4	no	—
414	C₂×C₈	—	134	12	no	—
415	C₂×C₈	C₂×C₂²⋊D₆₇	1	6	yes	—
416	C₂×C₈	C₂×C₂²⋊D₆₇	1	6	yes	—
417	C₂×C₈	C₂³×D₆₇	1	3	yes	—
418	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
419	C₄⋊C₄	—	134	3	no	—
420	C₂²⋊C₄	—	134	3	no	—
421	C₄²	—	67	3	no	—
422	C₄²	—	67	1	no	—
423	C₄²	—	134	3	no	—
424	C₂³	—	2	6	no	—
425	C₂³	—	134	6	no	—
426	C₂³	C₂×#11761628	1	3	yes	—
427	Q₈	—	2	6	no	—
428	Q₈	—	67	4	no	—
429	Q₈	—	134	6	no	—
430	Q₈	C₄×C₂²⋊D₆₇	1	4	yes	—
431	Q₈	C₂²×C₄×D₆₇	1	4	yes	—
432	D₄	—	2	12	no	—
433	D₄	—	2	4	no	—
434	D₄	—	2	6	no	—
435	D₄	—	67	4	no	—
436	D₄	—	134	12	no	—
437	D₄	—	134	4	no	—
438	D₄	—	134	6	no	—
439	D₄	C₄×C₂²⋊D₆₇	1	12	yes	—
440	D₄	C₂²×C₄×D₆₇	1	4	yes	—
441	C₂×C₄	—	2	6	no	—
442	C₂×C₄	—	2	12	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	536	3	no	—
445	C₂×C₄	—	134	1	no	—
446	C₂×C₄	—	134	3	no	—
447	C₂×C₄	—	134	6	no	—
448	C₂×C₄	—	134	12	no	—
449	C₂×C₄	—	134	4	no	—
450	C₂×C₄	C₂²×C₄×D₆₇	1	6	yes	—
451	C₂×C₄	C₂²×C₂²⋊D₆₇	1	6	yes	—
452	C₂×C₄	C₂×#11761628	1	3	yes	—
453	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
454	C₈	—	2	4	no	—
455	C₈	—	67	1	no	—
456	C₈	—	67	1	no	—
457	C₈	—	67	6	no	—
458	C₈	—	134	4	no	—
459	C₈	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
460	C₈	C₂²×C₂²⋊D₆₇	1	6	yes	—
461	C₈	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
462	C₂²	—	2	4	no	—
463	C₂²	—	4	3	no	—
464	C₂²	—	8	6	no	—
465	C₂²	—	536	6	no	—
466	C₂²	—	134	4	no	—
467	C₂²	C₂×C₄×C₂²⋊D₆₇	1	6	yes	—
468	C₂²	C₂²×#11761628	1	1	yes	characteristic
469	C₄	—	2	4	no	—
470	C₄	—	268	1	no	—
471	C₄	—	268	3	no	—
472	C₄	—	134	4	no	—
473	C₄	C₂×C₄×C₂²⋊D₆₇	1	6	yes	—
474	C₄	C₂³×C₄×D₆₇	1	1	yes	characteristic
475	C₄	C₂³×C₂²⋊D₆₇	1	1	yes	characteristic
476	C₂	—	2	1	no	—
477	C₂	—	2	6	no	—
478	C₂	—	4	4	no	—
479	C₂	—	268	4	no	—
480	C₂	C₂²×C₄×C₂²⋊D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂³×C₂²⋊D₆₇
commutator	C₄×C₆₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₆₇×#3573	C₂
socle	C₂×C₆₇	C₂²×C₄×D₄
prime radical	#22574980	C₂
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	#3573	D₆₇
hypocenter	C₆₇	#60184
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄ ◁ C₂×#131 ◁ #3573

Complements

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

N	H ≅ G/N	type
2. #22574920	C₂	semidirect
3. #22569124	C₂	semidirect
4. #22569116	C₂	semidirect
5. #22569110	C₂	semidirect
6. C₂×#16863516	C₂	semidirect
7. #22568818	C₂	semidirect
8. #22568756	C₂	semidirect
9. #22568754	C₂	semidirect
10. #22568635	C₂	semidirect
11. C₆₇×#3573	C₂	semidirect
13. #16864211	C₄	semidirect
14. #16864207	C₄	semidirect
15. #16864204	C₄	semidirect
16. #16864199	C₄	semidirect
20. #16864162	C₂²	semidirect
23. C₂×#14524049	C₂²	semidirect
26. #16863516	C₂²	semidirect
27. #16863516	C₂²	semidirect
28. #16863516	C₂²	semidirect
29. #16863516	C₂²	semidirect
30. #16863511	C₂²	semidirect
31. #16863444	C₂²	semidirect
32. C₂×#14523978	C₂²	semidirect
33. #16863413	C₂²	semidirect
34. #16863412	C₂²	semidirect
35. C₂×#14523970	C₂²	semidirect
36. C₂×#14523969	C₂²	semidirect
37. #16863354	C₂²	semidirect
38. #16863351	C₂²	semidirect
39. M₁₆×Dic₆₇	C₂²	semidirect
40. C₂×#14523953	C₂²	semidirect
44. #568×C₆₇	C₂²	semidirect
47. C₂×#131×C₆₇	C₂²	semidirect
54. #14524074	C₂×C₄	semidirect
55. #14524073	C₂×C₄	semidirect
56. #14524069	C₂×C₄	semidirect
57. #14524068	C₂×C₄	semidirect
58. #14524063	C₂×C₄	semidirect
59. #14524063	C₂×C₄	semidirect
62. C₂×#11761618	C₂×C₄	semidirect
63. C₂×#11761616	C₂×C₄	semidirect
64. C₂×#11761615	C₂×C₄	semidirect
65. C₂×#11761613	C₂×C₄	semidirect
243. #3573	D₆₇	semidirect
252. C₆₇	#60184	semidirect
266. #568	C₂×D₆₇	semidirect
272. C₂×#131	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22574980	2
#22574920	2
#22569124	2
#22569116	2
#22569110	2
C₂×#16863516	2
#22568818	2
#22568756	2
#22568754	2
#22568635	2
C₆₇×#3573	2
#60184	67