Subgroups — #30863666

Order 17152.

738 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569991	C₂	1	1	yes	maximal, characteristic
2	C₄×#14524049	C₂	1	1	yes	maximal, characteristic
3	#22561154	C₂	1	1	yes	maximal, characteristic, complemented
4	#22560982	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560805	C₂	1	2	yes	maximal, complemented
6	#22560483	C₂	1	2	yes	maximal
7	#22560226	C₂	1	1	yes	maximal, characteristic
8	#22560094	C₂	1	2	yes	maximal, complemented
9	#22560076	C₂	1	1	yes	maximal, characteristic, complemented
10	#22560055	C₂	1	2	yes	maximal
11	C₆₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524049	C₂²	1	1	yes	characteristic
13	C₂×#14524049	C₂²	1	1	yes	characteristic
14	C₄×#11761628	C₂²	1	1	yes	characteristic
15	#16863700	C₄	1	2	yes	complemented
16	#16863693	C₄	1	2	yes	complemented
17	#16863688	C₄	1	1	yes	characteristic, complemented
18	#16863683	C₄	1	1	yes	characteristic, complemented
19	#16863678	C₄	1	1	yes	characteristic, complemented
20	#16863673	C₄	1	1	yes	characteristic, complemented
21	C₂×#14523978	C₂²	1	2	yes	—
22	#16863432	C₂²	1	2	yes	—
23	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×#14523969	C₂²	1	2	yes	—
25	#16863390	C₂²	1	2	yes	—
26	#16863351	C₂²	1	1	yes	characteristic
27	#16863351	C₂²	1	1	yes	characteristic
28	#16863350	—	2	1	no	—
29	#16863350	—	2	1	no	—
30	C₄×#11761612	C₂²	1	1	yes	characteristic
31	C₄×#11761611	—	2	1	no	—
32	C₂×#14523953	C₂²	1	2	yes	—
33	C₄×C₈×D₆₇	—	2	1	no	—
34	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
35	#16863160	C₂²	1	2	yes	—
36	#16863157	C₂²	1	2	yes	—
37	#16863155	C₂²	1	2	yes	—
38	#16863155	C₂²	1	2	yes	—
39	#16863150	C₂²	1	2	yes	—
40	#533×C₆₇	C₂²	1	1	yes	characteristic
41	#446×C₆₇	—	2	1	no	—
42	#446×C₆₇	—	2	1	no	—
43	C₈×Q₈×C₆₇	—	2	1	no	—
44	C₈×Q₈×C₆₇	—	2	1	no	—
45	#424×C₆₇	C₂²	1	2	yes	—
46	#423×C₆₇	C₂²	1	1	yes	characteristic
47	#405×C₆₇	C₂²	1	2	yes	—
48	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×#11761628	C₂³	1	1	yes	characteristic
50	#14524049	—	2	2	no	—
51	#14524049	—	2	2	no	—
52	#14524049	—	2	2	no	—
53	#14524049	Q₈	1	4	yes	complemented
54	C₂×#11761612	C₂³	1	1	yes	characteristic
55	C₂×#11761612	C₂³	1	1	yes	characteristic
56	C₂×#11761611	—	2	1	no	—
57	C₂×#11761611	—	2	1	no	—
58	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
59	C₂×C₈×D₆₇	—	2	1	no	—
60	C₂×C₈×D₆₇	—	2	1	no	—
61	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
63	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
64	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
65	C₄×C₂²⋊D₆₇	—	2	1	no	—
66	C₄×C₂²⋊D₆₇	—	2	1	no	—
67	#14524002	C₂³	1	1	yes	characteristic
68	#14524000	—	2	1	no	—
69	C₂×C₄⋊Dic₆₇	—	2	1	no	—
70	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
71	C₄²×D₆₇	—	2	1	no	—
72	#14523978	—	2	4	no	—
73	#14523976	C₂×C₄	1	2	yes	—
74	#14523976	C₂×C₄	1	2	yes	—
75	#14523974	C₂×C₄	1	2	yes	—
76	#14523974	C₂×C₄	1	2	yes	—
77	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
78	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
79	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
80	#14523969	—	2	4	no	—
81	#14523966	C₂×C₄	1	2	yes	—
82	#14523966	C₂×C₄	1	2	yes	—
83	#14523963	C₂×C₄	1	2	yes	—
84	#14523963	C₂×C₄	1	2	yes	—
85	#14523954	—	2	1	no	—
86	#14523953	—	2	1	no	—
87	#14523953	—	2	1	no	—
88	#14523953	—	2	4	no	—
89	C₄×C₆₇⋊C₈	—	2	1	no	—
90	C₈×Dic₆₇	—	2	1	no	—
91	C₈×Dic₆₇	—	2	1	no	—
92	C₆₇⋊#95	—	2	1	no	—
93	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
94	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
97	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
98	#125×C₆₇	C₂×C₄	1	2	yes	—
99	C₂²⋊Q₈×C₆₇	—	2	1	no	—
100	C₂²⋊Q₈×C₆₇	—	2	1	no	—
101	C₄×Q₈×C₆₇	—	2	1	no	—
102	C₄×Q₈×C₆₇	—	2	1	no	—
103	#117×C₆₇	C₂³	1	2	yes	—
104	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₆₇	—	2	2	no	—
106	C₄⋊C₈×C₆₇	—	2	2	no	—
107	C₄⋊C₈×C₆₇	—	2	1	no	—
108	C₄⋊C₈×C₆₇	—	2	1	no	—
109	#97×C₆₇	—	2	2	no	—
110	C₄×C₈×C₆₇	—	2	2	no	—
111	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
112	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
113	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
114	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
115	#11761628	—	2	1	no	—
116	#11761628	—	2	1	no	—
117	#11761628	C₂×Q₈	1	2	yes	—
118	#11761628	#41	1	2	yes	—
119	C₂×Dic₁₃₄	C₂²×C₄	1	1	yes	characteristic
120	C₂×D₂₆₈	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊D₆₇	—	2	1	no	—
122	C₂²×Dic₆₇	—	2	2	no	—
123	C₂×C₄×D₆₇	—	2	1	no	—
124	C₂×C₄×D₆₇	—	2	1	no	—
125	C₂×C₄×D₆₇	—	2	1	no	—
126	#11761612	—	2	1	no	—
127	#11761612	—	2	1	no	—
128	#11761612	C₂×Q₈	1	2	yes	—
129	#11761612	#41	1	2	yes	—
130	#11761611	—	2	4	no	—
131	#11761611	—	2	4	no	—
132	C₂×C₆₇⋊C₈	—	2	1	no	—
133	C₂×C₆₇⋊C₈	—	2	1	no	—
134	C₂×C₆₇⋊C₈	—	2	2	no	—
135	C₂×C₆₇⋊C₈	—	2	2	no	—
136	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
138	C₈×D₆₇	—	2	4	no	—
139	C₈×D₆₇	—	2	4	no	—
140	C₄⋊Dic₆₇	—	4	2	no	—
141	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
142	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
143	Dic₆₇⋊C₄	—	2	1	no	—
144	Dic₆₇⋊C₄	—	2	1	no	—
145	C₂²⋊Dic₆₇	—	2	1	no	—
146	(C₂×D₆₇)⋊C₄	—	2	1	no	—
147	(C₂×D₆₇)⋊C₄	—	2	1	no	—
148	C₄×Dic₆₇	—	2	1	no	—
149	C₄×Dic₆₇	—	2	1	no	—
150	C₄×Dic₆₇	—	2	1	no	—
151	C₄×Dic₆₇	—	2	2	no	—
152	C₄×Dic₆₇	—	2	2	no	—
153	C₂×Q₈×C₆₇	—	2	1	no	—
154	C₂×Q₈×C₆₇	—	2	1	no	—
155	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
156	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
157	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
158	M₁₆×C₆₇	—	2	2	no	—
159	M₁₆×C₆₇	—	2	2	no	—
160	C₂×C₈×C₆₇	—	2	1	no	—
161	C₂×C₈×C₆₇	—	2	1	no	—
162	C₂×C₈×C₆₇	—	2	2	no	—
163	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₆₇	C₂×Q₈	1	2	yes	—
168	C₂×C₈×C₆₇	#41	1	2	yes	—
169	C₄⋊C₄×C₆₇	—	2	2	no	—
170	C₄⋊C₄×C₆₇	—	2	2	no	—
171	C₄⋊C₄×C₆₇	—	2	1	no	—
172	C₄⋊C₄×C₆₇	—	2	1	no	—
173	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
174	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
175	C₂²⋊C₄×C₆₇	—	2	2	no	—
176	C₄²×C₆₇	—	2	2	no	—
177	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
181	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
182	C₂²×D₆₇	—	2	1	no	—
183	Q₈×C₆₇	—	4	2	no	—
184	Q₈×C₆₇	—	4	2	no	—
185	C₂×C₄×C₆₇	—	2	2	no	—
186	C₂×C₄×C₆₇	—	2	2	no	—
187	C₂×C₄×C₆₇	—	2	2	no	—
188	C₂×C₄×C₆₇	—	4	1	no	—
189	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
199	C₂²⋊D₆₇	—	2	2	no	—
200	C₂²⋊D₆₇	—	2	2	no	—
201	C₂×Dic₆₇	—	2	1	no	—
202	C₂×Dic₆₇	—	2	1	no	—
203	C₂×Dic₆₇	—	2	1	no	—
204	C₂×Dic₆₇	—	4	2	no	—
205	C₂×Dic₆₇	—	4	2	no	—
206	C₂×Dic₆₇	—	4	2	no	—
207	D₂₆₈	—	2	1	no	—
208	D₂₆₈	C₄×Q₈	1	2	yes	—
209	C₄×D₆₇	—	2	2	no	—
210	C₄×D₆₇	—	2	2	no	—
211	C₄×D₆₇	—	4	2	no	—
212	C₄×D₆₇	—	4	2	no	—
213	Dic₁₃₄	—	2	1	no	—
214	Dic₁₃₄	C₄×Q₈	1	2	yes	—
215	C₈×C₆₇	—	2	1	no	—
216	C₈×C₆₇	—	2	1	no	—
217	C₈×C₆₇	—	4	2	no	—
218	C₈×C₆₇	C₂²⋊Q₈	1	2	yes	—
219	C₈×C₆₇	C₂²⋊Q₈	1	2	yes	—
220	C₆₇⋊C₈	—	2	2	no	—
221	C₆₇⋊C₈	—	2	2	no	—
222	C₆₇⋊C₈	—	2	2	no	—
223	C₆₇⋊C₈	—	2	2	no	—
224	C₂²×C₆₇	—	2	1	no	—
225	C₂²×C₆₇	—	2	1	no	—
226	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
227	C₂²×C₆₇	#529	1	1	yes	characteristic
228	C₂²×C₆₇	#533	1	1	yes	characteristic
229	C₂×D₆₇	—	2	2	no	—
230	C₂×D₆₇	—	4	1	no	—
231	C₂×D₆₇	—	4	1	no	—
232	C₄×C₆₇	—	2	1	no	—
233	C₄×C₆₇	—	2	1	no	—
234	C₄×C₆₇	—	2	1	no	—
235	C₄×C₆₇	—	4	2	no	—
236	C₄×C₆₇	—	4	2	no	—
237	C₄×C₆₇	#444	1	2	yes	—
238	C₄×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
239	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
240	C₄×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
241	C₄×C₆₇	#525	1	1	yes	characteristic
242	Dic₆₇	—	2	2	no	—
243	Dic₆₇	—	4	1	no	—
244	Dic₆₇	—	4	1	no	—
245	Dic₆₇	—	8	2	no	—
246	#21628	—	67	1	no	maximal, Sylow
247	C₂×C₆₇	—	2	1	no	—
248	C₂×C₆₇	—	2	1	no	—
249	C₂×C₆₇	C₄×C₂²⋊Q₈	1	1	yes	characteristic
250	C₂×C₆₇	C₂×#444	1	1	yes	characteristic
251	C₂×C₆₇	#2955	1	1	yes	characteristic
252	D₆₇	—	4	2	no	—
253	#3076	—	67	1	no	—
254	#2960	D₆₇	1	1	yes	characteristic, complemented
255	C₄×#131	—	67	1	no	—
256	#1986	—	67	1	no	—
257	#1950	—	67	1	no	—
258	#1922	—	67	2	no	—
259	#1866	—	67	2	no	—
260	#1806	—	67	1	no	—
261	#1773	—	67	2	no	—
262	#1770	—	67	1	no	—
263	#1765	—	67	2	no	—
264	C₆₇	#21628	1	1	yes	characteristic, complemented, Sylow
265	C₂×#131	—	67	1	no	—
266	C₂×#131	—	67	1	no	—
267	#533	C₂×D₆₇	1	1	yes	characteristic
268	C₄×#41	—	67	1	no	—
269	#479	—	67	2	no	—
270	#478	—	67	2	no	—
271	#477	—	67	1	no	—
272	#476	—	67	1	no	—
273	#475	—	67	1	no	—
274	#474	—	67	1	no	—
275	#446	—	2	1	no	—
276	#446	—	2	1	no	—
277	C₈×Q₈	—	2	1	no	—
278	C₈×Q₈	—	2	1	no	—
279	C₂×#108	—	67	2	no	—
280	#427	—	67	2	no	—
281	#424	C₂×D₆₇	1	2	yes	—
282	#423	C₂×D₆₇	1	1	yes	characteristic
283	C₂×C₄⋊C₈	—	67	1	no	—
284	C₂×#104	—	67	2	no	—
285	#416	—	67	2	no	—
286	#405	—	67	1	no	—
287	#405	—	67	1	no	—
288	#405	—	134	1	no	—
289	#405	—	134	1	no	—
290	#405	C₂×D₆₇	1	2	yes	—
291	C₄×M₁₆	—	67	1	no	—
292	C₄×M₁₆	—	134	1	no	—
293	C₂×#97	—	67	2	no	—
294	C₂×C₄×C₈	—	134	1	no	—
295	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
296	C₄×C₄⋊C₄	—	67	1	no	—
297	#341	—	67	2	no	—
298	#339	—	67	2	no	—
299	#339	—	67	2	no	—
300	#339	—	67	2	no	—
301	#336	—	67	2	no	—
302	C₂×#41	—	67	1	no	—
303	#131	—	67	4	no	—
304	#131	—	134	2	no	—
305	#131	—	134	2	no	—
306	#131	—	134	2	no	—
307	C₂×M₁₆	—	67	1	no	—
308	C₂×M₁₆	—	67	1	no	—
309	C₂×M₁₆	—	134	1	no	—
310	C₂×M₁₆	—	134	1	no	—
311	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
312	C₂²×C₈	—	67	2	no	—
313	C₂²×C₈	—	134	1	no	—
314	C₂²×C₈	—	134	1	no	—
315	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
316	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
317	C₄⋊Q₈	C₄×D₆₇	1	1	yes	characteristic
318	C₄⋊Q₈	C₄×D₆₇	1	1	yes	characteristic
319	#125	C₄×D₆₇	1	2	yes	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	—	67	1	no	—
325	C₄×Q₈	—	67	1	no	—
326	C₄×D₄	—	67	1	no	—
327	C₄×D₄	—	67	1	no	—
328	C₄×D₄	—	134	1	no	—
329	C₄×D₄	—	134	1	no	—
330	#117	—	67	1	no	—
331	#117	—	134	1	no	—
332	#117	C₂²×D₆₇	1	2	yes	—
333	C₂×C₄⋊C₄	—	134	1	no	—
334	C₂×C₄²	—	67	2	no	—
335	C₂×C₄²	—	134	1	no	—
336	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
337	#108	—	134	4	no	—
338	#107	—	67	2	no	—
339	#107	—	67	2	no	—
340	#106	—	67	2	no	—
341	#106	—	67	2	no	—
342	C₄⋊C₈	—	2	2	no	—
343	C₄⋊C₈	—	2	2	no	—
344	C₄⋊C₈	—	2	1	no	—
345	C₄⋊C₈	—	2	1	no	—
346	C₄⋊C₈	—	67	1	no	—
347	C₄⋊C₈	—	67	1	no	—
348	C₄⋊C₈	—	67	2	no	—
349	#104	—	134	4	no	—
350	#103	—	67	2	no	—
351	#103	—	67	2	no	—
352	#102	—	67	2	no	—
353	#102	—	67	2	no	—
354	#97	—	2	2	no	—
355	#97	—	134	1	no	—
356	#97	—	134	1	no	—
357	#97	—	134	4	no	—
358	#97	—	134	1	no	—
359	C₄×C₈	—	2	2	no	—
360	C₄×C₈	—	134	1	no	—
361	C₄×C₈	—	134	1	no	—
362	C₄×C₈	—	134	1	no	—
363	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
364	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
365	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
366	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
367	#95	—	134	1	no	—
368	#41	—	67	2	no	—
369	#41	—	67	2	no	—
370	#41	—	134	1	no	—
371	#41	—	134	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	67	1	no	—
375	C₂×D₄	—	67	1	no	—
376	C₂×D₄	—	134	1	no	—
377	C₂²×C₄	—	134	2	no	—
378	C₂²×C₄	—	134	1	no	—
379	C₂²×C₄	—	134	1	no	—
380	C₂²×C₄	—	134	1	no	—
381	C₂²×C₄	#11761628	1	1	yes	characteristic
382	C₂²×C₄	#11761628	1	1	yes	characteristic
383	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
384	M₁₆	—	2	2	no	—
385	M₁₆	—	2	2	no	—
386	M₁₆	—	67	2	no	—
387	M₁₆	—	67	2	no	—
388	M₁₆	—	134	4	no	—
389	M₁₆	—	134	1	no	—
390	M₁₆	—	134	1	no	—
391	M₁₆	—	134	4	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	67	2	no	—
396	C₂×C₈	—	67	2	no	—
397	C₂×C₈	—	134	4	no	—
398	C₂×C₈	—	134	1	no	—
399	C₂×C₈	—	134	1	no	—
400	C₂×C₈	—	134	2	no	—
401	C₂×C₈	—	134	2	no	—
402	C₂×C₈	—	134	4	no	—
403	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
404	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
405	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
406	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
407	C₂×C₈	Q₈×D₆₇	1	2	yes	—
408	C₂×C₈	#11761629	1	2	yes	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	268	2	no	—
414	C₄⋊C₄	—	67	1	no	—
415	C₄⋊C₄	—	67	1	no	—
416	C₄⋊C₄	—	134	1	no	—
417	C₄⋊C₄	—	134	1	no	—
418	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
419	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	134	1	no	—
422	C₂²⋊C₄	—	134	1	no	—
423	C₂²⋊C₄	—	134	1	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	134	2	no	—
426	C₄²	—	134	2	no	—
427	C₄²	—	134	1	no	—
428	C₄²	—	134	1	no	—
429	C₄²	—	134	1	no	—
430	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
432	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
433	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
434	C₂³	—	134	1	no	—
435	C₂³	C₂×#11761628	1	1	yes	characteristic
436	Q₈	—	4	2	no	—
437	Q₈	—	4	2	no	—
438	Q₈	—	67	2	no	—
439	Q₈	—	134	1	no	—
440	D₄	—	67	2	no	—
441	D₄	—	134	2	no	—
442	D₄	—	134	2	no	—
443	D₄	—	134	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	268	2	no	—
449	C₂×C₄	—	268	2	no	—
450	C₂×C₄	—	268	2	no	—
451	C₂×C₄	—	268	2	no	—
452	C₂×C₄	—	268	2	no	—
453	C₂×C₄	—	134	1	no	—
454	C₂×C₄	—	134	1	no	—
455	C₂×C₄	—	134	1	no	—
456	C₂×C₄	—	134	2	no	—
457	C₂×C₄	—	134	2	no	—
458	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
459	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
460	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
461	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
463	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
464	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
465	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
466	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
467	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
468	C₈	—	2	1	no	—
469	C₈	—	2	1	no	—
470	C₈	—	4	2	no	—
471	C₈	—	134	2	no	—
472	C₈	—	134	2	no	—
473	C₈	—	134	2	no	—
474	C₈	—	134	2	no	—
475	C₈	#14524019	1	2	yes	—
476	C₈	#14524019	1	2	yes	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	268	1	no	—
480	C₂²	—	268	1	no	—
481	C₂²	—	134	2	no	—
482	C₂²	C₂×C₄×C₂²⋊D₆₇	1	1	yes	characteristic
483	C₂²	#16863933	1	1	yes	characteristic
484	C₂²	#16863950	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	268	1	no	—
491	C₄	—	268	1	no	—
492	C₄	—	536	2	no	—
493	C₄	—	134	2	no	—
494	C₄	#16863516	1	2	yes	—
495	C₄	C₄×Q₈×D₆₇	1	1	yes	characteristic
496	C₄	C₄×#11761629	1	1	yes	characteristic
497	C₄	C₂×#14524019	1	1	yes	characteristic
498	C₄	#16863903	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	268	2	no	—
502	C₂	C₄×#14524019	1	1	yes	characteristic
503	C₂	C₂×#16863516	1	1	yes	characteristic
504	C₂	#22569110	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#2960	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#11761628	C₂³
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#2960	D₆₇
hypocenter	C₆₇	#21628
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
3. #22561154	C₂	semidirect
4. #22560982	C₂	semidirect
5. #22560805	C₂	semidirect
8. #22560094	C₂	semidirect
9. #22560076	C₂	semidirect
11. C₆₇×#2960	C₂	semidirect
15. #16863700	C₄	semidirect
16. #16863693	C₄	semidirect
17. #16863688	C₄	semidirect
18. #16863683	C₄	semidirect
19. #16863678	C₄	semidirect
20. #16863673	C₄	semidirect
53. #14524049	Q₈	semidirect
254. #2960	D₆₇	semidirect
264. C₆₇	#21628	semidirect

Maximal subgroups

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

subgroup	index
#22569991	2
C₄×#14524049	2
#22561154	2
#22560982	2
#22560805	2
#22560483	2
#22560226	2
#22560094	2
#22560076	2
#22560055	2
C₆₇×#2960	2
#21628	67