Subgroups — #31009327

Order 17152.

490 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569138	C₂	1	1	yes	maximal, characteristic
2	#22562118	C₂	1	1	yes	maximal, characteristic, complemented
3	#22562117	C₂	1	1	yes	maximal, characteristic, complemented
4	#22562116	C₂	1	1	yes	maximal, characteristic, complemented
5	#22562116	C₂	1	1	yes	maximal, characteristic, complemented
6	#22562115	C₂	1	1	yes	maximal, characteristic, complemented
7	#22562115	C₂	1	1	yes	maximal, characteristic, complemented
8	#22562114	C₂	1	1	yes	maximal, characteristic, complemented
9	#22561966	C₂	1	1	yes	maximal, characteristic
10	#22561966	C₂	1	1	yes	maximal, characteristic
11	#22561963	C₂	1	1	yes	maximal, characteristic
12	#22561807	C₂	1	1	yes	maximal, characteristic
13	#22561804	C₂	1	1	yes	maximal, characteristic
14	#346×D₆₇	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2183	C₂	1	1	yes	maximal, characteristic, complemented
16	#16863950	C₄	1	1	yes	characteristic
17	C₂×#14523982	C₂²	1	1	yes	characteristic
18	C₂×#14523982	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×D₆₇	C₂²	1	1	yes	characteristic
20	C₂×C₁₆×D₆₇	C₂²	1	1	yes	characteristic
21	#16863527	C₄	1	1	yes	characteristic
22	#16863525	C₄	1	1	yes	characteristic
23	#16863525	C₄	1	1	yes	characteristic
24	#16863523	C₄	1	1	yes	characteristic
25	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
26	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
27	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
28	#16863421	C₄	1	1	yes	characteristic
29	#16863421	C₄	1	1	yes	characteristic
30	#16863418	C₄	1	1	yes	characteristic
31	#16863350	C₂²	1	1	yes	characteristic
32	#16863350	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
34	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	1	yes	characteristic
35	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	1	yes	characteristic
36	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	1	yes	characteristic
37	Dic₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
38	Dic₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
39	Dic₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
40	Dic₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
41	Dic₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
42	Dic₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
43	#16863172	C₂²	1	1	yes	characteristic
44	#16863172	C₂²	1	1	yes	characteristic
45	#16863171	C₂²	1	1	yes	characteristic
46	#16863171	C₂²	1	1	yes	characteristic
47	#16863171	C₂²	1	1	yes	characteristic
48	#16863171	C₂²	1	1	yes	characteristic
49	C₄×C₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
50	C₁₆×Dic₆₇	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₆₇	C₂²	1	1	yes	characteristic
52	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
53	C₄⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
54	C₄⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
55	C₄⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
56	#346×C₆₇	C₂²	1	1	yes	characteristic
57	#346×C₆₇	C₂²	1	1	yes	characteristic
58	C₄×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×#11761611	C₂×C₄	1	1	yes	characteristic
60	C₂×#11761611	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
63	#14524042	C₈	1	1	yes	characteristic
64	#14524041	C₈	1	1	yes	characteristic
65	#14524033	C₈	1	1	yes	characteristic
66	#14524033	C₈	1	1	yes	characteristic
67	#14524023	C₈	1	1	yes	characteristic
68	#14524021	C₈	1	1	yes	characteristic
69	#14524021	C₈	1	1	yes	characteristic
70	#14524019	C₈	1	1	yes	characteristic
71	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
72	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
73	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
74	#14524000	C₂×C₄	1	1	yes	characteristic
75	#14524000	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₆₇	C₂×C₄	1	1	yes	characteristic
77	#14523982	—	2	2	no	—
78	#14523982	—	2	2	no	—
79	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
83	C₁₆×D₆₇	—	2	2	no	—
84	C₁₆×D₆₇	Q₈	1	4	yes	complemented
85	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
86	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
87	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
88	Dic₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
89	Dic₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
90	Dic₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
91	Dic₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
92	Dic₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
93	Dic₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
94	#14523954	C₂×C₄	1	1	yes	characteristic
95	#14523954	C₂×C₄	1	1	yes	characteristic
96	#14523953	C₂×C₄	1	1	yes	characteristic
97	#14523953	C₂×C₄	1	1	yes	characteristic
98	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
101	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
102	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
103	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
104	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
105	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
106	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
107	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
108	C₄⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
109	C₄⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
110	C₄⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
111	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
113	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×Dic₁₃₄	C₂×C₈	1	1	yes	characteristic
115	C₂×Dic₁₃₄	C₂×C₈	1	1	yes	characteristic
116	C₂×Dic₁₃₄	C₂×C₈	1	1	yes	characteristic
117	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
118	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
119	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
120	#11761611	—	2	2	no	—
121	#11761611	—	2	2	no	—
122	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
126	C₈×D₆₇	—	2	2	no	—
127	C₈×D₆₇	C₂×Q₈	1	2	yes	—
128	C₈×D₆₇	#41	1	2	yes	—
129	C₄⋊Dic₆₇	C₂×C₈	1	1	yes	characteristic
130	C₄⋊Dic₆₇	C₂×C₈	1	1	yes	characteristic
131	C₄⋊Dic₆₇	C₂×C₈	1	1	yes	characteristic
132	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
133	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
134	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
135	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
136	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
137	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
138	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
139	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
140	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
141	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
142	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
143	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
144	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
145	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
146	C₄×Dic₆₇	C₂×C₈	1	1	yes	characteristic
147	C₄×Dic₆₇	C₂×C₈	1	1	yes	characteristic
148	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
151	C₆₇⋊C₁₆	—	2	1	no	—
152	C₆₇⋊C₁₆	—	2	1	no	—
153	C₆₇⋊C₁₆	—	2	1	no	—
154	C₆₇⋊C₁₆	C₂×Q₈	1	2	yes	—
155	C₂×Q₈×C₆₇	C₂×C₈	1	1	yes	characteristic
156	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
160	C₄⋊C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
161	C₄⋊C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
162	C₄⋊C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
163	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
166	C₁₆×C₆₇	—	2	1	no	—
167	C₁₆×C₆₇	—	2	1	no	—
168	C₁₆×C₆₇	—	2	1	no	—
169	C₁₆×C₆₇	C₂×Q₈	1	2	yes	—
170	C₂²×D₆₇	C₂²×C₈	1	1	yes	characteristic
171	Q₈×C₆₇	—	4	1	no	—
172	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
174	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
175	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
176	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
177	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
178	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
179	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
180	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
181	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
182	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
183	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
184	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
185	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
186	C₄×D₆₇	—	4	1	no	—
187	C₄×D₆₇	—	4	1	no	—
188	C₄×D₆₇	C₄×Q₈	1	2	yes	—
189	C₄×D₆₇	#131	1	2	yes	—
190	Dic₁₃₄	—	4	1	no	—
191	Dic₁₃₄	—	4	1	no	—
192	Dic₁₃₄	—	4	1	no	—
193	C₈×C₆₇	—	2	1	no	—
194	C₈×C₆₇	—	2	1	no	—
195	C₈×C₆₇	—	2	1	no	—
196	C₈×C₆₇	C₂²×Q₈	1	1	yes	characteristic
197	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
198	C₆₇⋊C₈	—	2	1	no	—
199	C₆₇⋊C₈	—	2	1	no	—
200	C₆₇⋊C₈	—	2	1	no	—
201	C₆₇⋊C₈	C₄×Q₈	1	2	yes	—
202	C₂²×C₆₇	C₂³×C₈	1	1	yes	characteristic
203	C₂×D₆₇	—	2	1	no	—
204	C₂×D₆₇	—	2	1	no	—
205	C₂×D₆₇	C₈×Q₈	1	2	yes	—
206	C₄×C₆₇	—	2	1	no	—
207	C₄×C₆₇	—	2	1	no	—
208	C₄×C₆₇	—	2	1	no	—
209	C₄×C₆₇	—	2	1	no	—
210	C₄×C₆₇	—	2	1	no	—
211	C₄×C₆₇	—	2	1	no	—
212	C₄×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
213	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
214	Dic₆₇	—	2	1	no	—
215	Dic₆₇	—	2	1	no	—
216	Dic₆₇	—	2	1	no	—
217	Dic₆₇	—	2	1	no	—
218	Dic₆₇	—	2	1	no	—
219	Dic₆₇	—	2	1	no	—
220	Dic₆₇	C₈×Q₈	1	2	yes	—
221	#33475	—	67	1	no	maximal, Sylow
222	C₂×C₆₇	C₂×C₈×Q₈	1	1	yes	characteristic
223	C₂×C₆₇	#3407	1	1	yes	characteristic
224	C₂×C₆₇	#3407	1	1	yes	characteristic
225	D₆₇	—	2	2	no	—
226	#2960	—	67	1	no	—
227	#2183	—	67	1	no	—
228	#2183	—	67	1	no	—
229	#2183	—	67	1	no	—
230	#2183	—	67	1	no	—
231	#2183	—	67	1	no	—
232	#2183	—	67	1	no	—
233	#2183	—	67	1	no	—
234	#2183	D₆₇	1	1	yes	characteristic, complemented
235	#2151	—	67	1	no	—
236	#2151	—	67	1	no	—
237	#2150	—	67	1	no	—
238	#2108	—	67	1	no	—
239	#2108	—	67	1	no	—
240	C₂×#346	—	67	1	no	—
241	C₆₇	#33475	1	1	yes	characteristic, complemented, Sylow
242	#533	—	67	1	no	—
243	C₂×M₃₂	—	67	1	no	—
244	C₂×M₃₂	—	67	1	no	—
245	C₂²×C₁₆	—	67	1	no	—
246	C₂²×C₁₆	—	67	1	no	—
247	#446	—	67	1	no	—
248	#446	—	67	1	no	—
249	#446	—	67	1	no	—
250	#446	—	67	1	no	—
251	C₈×Q₈	—	67	1	no	—
252	C₈×Q₈	—	67	1	no	—
253	C₈×Q₈	—	67	1	no	—
254	C₈×Q₈	C₂×D₆₇	1	1	yes	characteristic
255	#424	—	67	1	no	—
256	#424	—	67	1	no	—
257	#423	—	67	1	no	—
258	#405	—	67	1	no	—
259	#405	—	67	1	no	—
260	C₂×C₄×C₈	—	67	1	no	—
261	C₄⋊C₁₆	—	67	1	no	—
262	C₄⋊C₁₆	—	67	1	no	—
263	C₄⋊C₁₆	—	67	1	no	—
264	C₄⋊C₁₆	—	67	1	no	—
265	C₄⋊C₁₆	—	67	1	no	—
266	C₄⋊C₁₆	—	67	1	no	—
267	C₄⋊C₁₆	—	67	1	no	—
268	C₄⋊C₁₆	—	67	1	no	—
269	C₄⋊C₁₆	—	67	1	no	—
270	C₄⋊C₁₆	C₂×D₆₇	1	1	yes	characteristic
271	C₄⋊C₁₆	C₂×D₆₇	1	1	yes	characteristic
272	C₄⋊C₁₆	C₂×D₆₇	1	1	yes	characteristic
273	#346	—	67	1	no	—
274	#346	—	67	1	no	—
275	#346	—	67	1	no	—
276	#346	—	67	1	no	—
277	#346	—	67	1	no	—
278	#346	—	67	1	no	—
279	#346	C₂×D₆₇	1	1	yes	characteristic
280	#346	C₂×D₆₇	1	1	yes	characteristic
281	C₄×C₁₆	—	67	1	no	—
282	C₄×C₁₆	—	67	1	no	—
283	C₄×C₁₆	—	67	1	no	—
284	C₄×C₁₆	C₂×D₆₇	1	1	yes	characteristic
285	C₂×M₁₆	—	67	1	no	—
286	C₂×M₁₆	—	67	1	no	—
287	C₂²×C₈	—	67	1	no	—
288	C₂²×C₈	—	67	1	no	—
289	C₄⋊Q₈	—	67	1	no	—
290	C₄⋊Q₈	—	67	1	no	—
291	#125	—	67	1	no	—
292	#125	—	67	1	no	—
293	C₂²⋊Q₈	—	67	1	no	—
294	C₂²⋊Q₈	—	67	1	no	—
295	C₂²⋊Q₈	—	67	1	no	—
296	C₂²⋊Q₈	—	67	1	no	—
297	C₄×Q₈	—	67	1	no	—
298	C₄×Q₈	—	67	1	no	—
299	C₄×Q₈	—	67	1	no	—
300	C₄×Q₈	C₄×D₆₇	1	1	yes	characteristic
301	#117	—	67	1	no	—
302	#117	—	67	1	no	—
303	C₂×C₄²	—	67	1	no	—
304	M₃₂	—	134	2	no	—
305	M₃₂	—	134	2	no	—
306	C₂×C₁₆	—	67	1	no	—
307	C₂×C₁₆	—	67	4	no	—
308	C₂×C₁₆	—	67	1	no	—
309	C₂×C₁₆	—	67	1	no	—
310	C₂×C₁₆	—	67	1	no	—
311	C₂×C₁₆	—	134	2	no	—
312	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
313	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
314	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
315	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
316	C₄⋊C₈	—	67	1	no	—
317	C₄⋊C₈	—	67	1	no	—
318	C₄⋊C₈	—	67	1	no	—
319	C₄⋊C₈	—	67	1	no	—
320	C₄⋊C₈	—	67	1	no	—
321	C₄⋊C₈	—	67	1	no	—
322	C₄⋊C₈	—	67	1	no	—
323	C₄⋊C₈	—	67	1	no	—
324	C₄⋊C₈	—	67	1	no	—
325	C₄⋊C₈	C₄×D₆₇	1	1	yes	characteristic
326	C₄⋊C₈	C₄×D₆₇	1	1	yes	characteristic
327	C₄⋊C₈	C₄×D₆₇	1	1	yes	characteristic
328	#97	—	67	1	no	—
329	#97	—	67	1	no	—
330	#97	—	67	1	no	—
331	#97	—	67	1	no	—
332	C₄×C₈	—	67	1	no	—
333	C₄×C₈	—	67	1	no	—
334	C₄×C₈	—	67	1	no	—
335	C₄×C₈	—	67	1	no	—
336	C₄×C₈	—	67	1	no	—
337	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
338	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
339	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
340	C₂×Q₈	—	67	1	no	—
341	C₂×Q₈	—	67	1	no	—
342	C₂×Q₈	—	67	1	no	—
343	C₂×Q₈	C₈×D₆₇	1	1	yes	characteristic
344	C₂²×C₄	—	67	1	no	—
345	C₂²×C₄	—	67	1	no	—
346	C₂²×C₄	—	67	1	no	—
347	M₁₆	—	134	2	no	—
348	M₁₆	—	134	2	no	—
349	C₂×C₈	—	67	1	no	—
350	C₂×C₈	—	67	2	no	—
351	C₂×C₈	—	67	2	no	—
352	C₂×C₈	—	67	1	no	—
353	C₂×C₈	—	67	1	no	—
354	C₂×C₈	—	67	1	no	—
355	C₂×C₈	—	134	2	no	—
356	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
357	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
358	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
359	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
360	C₄⋊C₄	—	67	1	no	—
361	C₄⋊C₄	—	67	1	no	—
362	C₄⋊C₄	—	67	1	no	—
363	C₄⋊C₄	—	67	1	no	—
364	C₄⋊C₄	—	67	1	no	—
365	C₄⋊C₄	—	67	1	no	—
366	C₄⋊C₄	—	67	1	no	—
367	C₄⋊C₄	—	67	1	no	—
368	C₄⋊C₄	—	67	1	no	—
369	C₄⋊C₄	—	67	1	no	—
370	C₄⋊C₄	—	67	1	no	—
371	C₄⋊C₄	—	67	1	no	—
372	C₄⋊C₄	—	67	1	no	—
373	C₄⋊C₄	C₈×D₆₇	1	1	yes	characteristic
374	C₄⋊C₄	C₈×D₆₇	1	1	yes	characteristic
375	C₄⋊C₄	C₈×D₆₇	1	1	yes	characteristic
376	C₂²⋊C₄	—	67	1	no	—
377	C₂²⋊C₄	—	67	1	no	—
378	C₂²⋊C₄	—	67	1	no	—
379	C₂²⋊C₄	—	67	1	no	—
380	C₄²	—	67	1	no	—
381	C₄²	—	67	1	no	—
382	C₄²	—	67	1	no	—
383	C₄²	—	67	1	no	—
384	C₄²	—	67	1	no	—
385	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
386	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
387	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
388	C₁₆	—	2	1	no	—
389	C₁₆	—	2	1	no	—
390	C₁₆	—	2	1	no	—
391	C₁₆	—	67	2	no	—
392	C₁₆	—	134	1	no	—
393	C₁₆	—	134	1	no	—
394	C₁₆	—	134	1	no	—
395	C₁₆	Q₈×D₆₇	1	2	yes	—
396	C₂³	—	67	1	no	—
397	Q₈	—	4	1	no	—
398	Q₈	—	268	1	no	—
399	Q₈	—	268	1	no	—
400	Q₈	—	268	1	no	—
401	C₂×C₄	—	268	1	no	—
402	C₂×C₄	—	268	1	no	—
403	C₂×C₄	—	67	1	no	—
404	C₂×C₄	—	67	2	no	—
405	C₂×C₄	—	67	2	no	—
406	C₂×C₄	—	67	1	no	—
407	C₂×C₄	—	67	1	no	—
408	C₂×C₄	—	67	1	no	—
409	C₂×C₄	—	67	1	no	—
410	C₂×C₄	—	67	1	no	—
411	C₂×C₄	—	67	1	no	—
412	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
413	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
414	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
415	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
416	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
417	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
418	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	67	2	no	—
423	C₈	—	134	1	no	—
424	C₈	—	134	1	no	—
425	C₈	—	134	1	no	—
426	C₈	C₂×Q₈×D₆₇	1	1	yes	characteristic
427	C₈	#41×D₆₇	1	1	yes	characteristic
428	C₂²	—	67	2	no	—
429	C₂²	—	134	1	no	—
430	C₂²	—	134	1	no	—
431	C₂²	C₂²×C₈×D₆₇	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	67	2	no	—
439	C₄	—	134	1	no	—
440	C₄	—	134	1	no	—
441	C₄	—	134	1	no	—
442	C₄	—	134	1	no	—
443	C₄	—	134	1	no	—
444	C₄	—	134	1	no	—
445	C₄	C₄×Q₈×D₆₇	1	1	yes	characteristic
446	C₄	#131×D₆₇	1	1	yes	characteristic
447	C₂	—	134	2	no	—
448	C₂	C₈×Q₈×D₆₇	1	1	yes	characteristic
449	C₂	#22573310	1	1	yes	characteristic
450	C₂	#22573311	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₆₇
commutator, socle	C₂²×C₆₇	C₂³×C₈
Fitting	C₆₇×#2183	C₂
prime radical	C₂²×D₆₇	C₂²×C₈
cosocle	C₂×C₈×C₆₇	C₂⁴
hypercenter	#2183	D₆₇
hypocenter	C₆₇	#33475
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ #2183

Complements

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

N	H ≅ G/N	type
2. #22562118	C₂	semidirect
3. #22562117	C₂	semidirect
4. #22562116	C₂	semidirect
5. #22562116	C₂	semidirect
6. #22562115	C₂	semidirect
7. #22562115	C₂	semidirect
8. #22562114	C₂	semidirect
15. C₆₇×#2183	C₂	semidirect
84. C₁₆×D₆₇	Q₈	semidirect
234. #2183	D₆₇	semidirect
241. C₆₇	#33475	semidirect

Maximal subgroups

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

subgroup	index
#22569138	2
#22562118	2
#22562117	2
#22562116	2
#22562115	2
#22562114	2
#22561966	2
#22561963	2
#22561807	2
#22561804	2
#346×D₆₇	2
C₆₇×#2183	2
#33475	67