Subgroups — #30825307

Order 17152.

714 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569316	C₂	1	2	yes	maximal, complemented
2	C₄×#14524062	C₂	1	1	yes	maximal, characteristic
3	#22559021	C₂	1	2	yes	maximal, complemented
4	#22559018	C₂	1	2	yes	maximal, complemented
5	C₈×Dic₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#22559015	C₂	1	1	yes	maximal, characteristic, complemented
7	D₈×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#335×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558593	C₂	1	2	yes	maximal, complemented
10	#22558491	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524062	C₄	1	1	yes	characteristic
13	C₄×#11761627	C₂²	1	2	yes	—
14	C₈×Dic₁₃₄	C₂²	1	2	yes	—
15	#16863520	C₂²	1	2	yes	—
16	C₄×Dic₂₆₈	C₂²	1	1	yes	characteristic
17	#16863490	C₄	1	1	yes	characteristic
18	#16863487	C₄	1	2	yes	—
19	C₄×#11761616	C₂²	1	2	yes	—
20	D₈×Dic₆₇	C₄	1	1	yes	characteristic
21	D₄×C₆₇⋊C₈	C₂²	1	2	yes	—
22	C₈×C₂²⋊D₆₇	—	2	2	no	—
23	(C₂²⋊D₆₇)⋊C₈	—	2	2	no	—
24	#16863447	C₂²	1	1	yes	characteristic
25	#16863447	C₂²	1	1	yes	characteristic
26	#16863446	—	2	2	no	—
27	#16863433	C₄	1	1	yes	characteristic
28	C₂×Dic₆₇⋊C₈	—	2	2	no	—
29	C₄⋊C₈×D₆₇	C₂²	1	2	yes	—
30	#16863389	C₄	1	2	yes	—
31	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
32	#16863149	C₂²	1	1	yes	characteristic
33	#16863148	C₂²	1	2	yes	—
34	#16863128	C₂²	1	2	yes	—
35	#16863126	C₂²	1	2	yes	—
36	D₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
37	#16863118	C₂²	1	1	yes	characteristic
38	#16863118	C₂²	1	1	yes	characteristic
39	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
40	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₆₇	C₂²	1	2	yes	—
42	#335×C₆₇	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
44	C₈²×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×#11761627	C₂×C₄	1	2	yes	—
46	#14524062	C₈	1	8	yes	complemented
47	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic
48	C₂×#11761616	C₂×C₄	1	2	yes	—
49	C₂²×C₆₇⋊C₈	—	2	2	no	—
50	C₂×C₈×D₆₇	—	2	2	no	—
51	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
53	C₄×Dic₁₃₄	C₂³	1	2	yes	—
54	#14524008	C₂×C₄	1	2	yes	—
55	D₄×Dic₆₇	C₂×C₄	1	2	yes	—
56	C₄×C₂²⋊D₆₇	—	2	2	no	—
57	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
58	#14524001	C₂×C₄	1	2	yes	—
59	#14523999	—	2	2	no	—
60	C₂×C₄×Dic₆₇	—	2	2	no	—
61	C₄²×D₆₇	C₂³	1	1	yes	characteristic
62	#14523977	C₂×C₄	1	1	yes	characteristic
63	#14523974	C₂×C₄	1	2	yes	—
64	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
65	Dic₆₇⋊C₈	—	2	2	no	—
66	Dic₆₇⋊C₈	—	2	2	no	—
67	Dic₆₇⋊C₈	—	2	1	no	—
68	Dic₆₇⋊C₈	—	2	2	no	—
69	Dic₆₇⋊C₈	D₄	1	1	yes	characteristic
70	Dic₆₇⋊C₈	D₄	1	1	yes	characteristic
71	#14523968	C₂×C₄	1	2	yes	—
72	#14523966	C₂×C₄	1	2	yes	—
73	#14523964	C₂×C₄	1	2	yes	—
74	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
75	(C₂×D₆₇)⋊C₈	—	2	1	no	—
76	(C₂×D₆₇)⋊C₈	D₄	1	1	yes	characteristic
77	(C₂×D₆₇)⋊C₈	D₄	1	1	yes	characteristic
78	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
81	C₈×Dic₆₇	—	2	2	no	—
82	C₈×Dic₆₇	—	2	2	no	—
83	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
85	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₆₇	—	2	2	no	—
87	C₄×D₄×C₆₇	C₂³	1	2	yes	—
88	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
90	#102×C₆₇	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₆₇	—	2	2	no	—
92	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	#11761627	—	2	4	no	—
96	#11761627	C₂×C₈	1	8	yes	complemented
97	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
98	C₂×C₂²⋊D₆₇	—	2	2	no	—
99	C₂²×Dic₆₇	—	2	2	no	—
100	C₂²×Dic₆₇	—	2	2	no	—
101	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
104	Dic₂₆₈	C₂×C₈	1	4	yes	complemented
105	#11761616	C₂×C₈	1	8	yes	complemented
106	C₂×C₆₇⋊C₈	—	2	2	no	—
107	C₂×C₆₇⋊C₈	—	2	1	no	—
108	C₂×C₆₇⋊C₈	—	8	2	no	—
109	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
112	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
113	C₈×D₆₇	—	2	2	no	—
114	C₈×D₆₇	—	8	2	no	—
115	C₈×D₆₇	C₂×C₈	1	4	yes	complemented
116	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
117	Dic₆₇⋊C₄	—	2	2	no	—
118	Dic₆₇⋊C₄	—	2	2	no	—
119	C₂²⋊Dic₆₇	—	2	2	no	—
120	(C₂×D₆₇)⋊C₄	—	2	2	no	—
121	C₄×Dic₆₇	—	2	2	no	—
122	C₄×Dic₆₇	—	2	2	no	—
123	C₄×Dic₆₇	—	2	2	no	—
124	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
126	C₄×Dic₆₇	#41	1	1	yes	characteristic
127	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₆₇	—	2	2	no	—
129	D₈×C₆₇	C₂×C₈	1	4	yes	complemented
130	C₂×C₈×C₆₇	—	2	2	no	—
131	C₂×C₈×C₆₇	—	2	1	no	—
132	C₂×C₈×C₆₇	—	8	2	no	—
133	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
137	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
138	C₂²⋊C₄×C₆₇	—	2	2	no	—
139	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
140	C₂³×C₆₇	—	2	2	no	—
141	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
142	D₄×C₆₇	—	2	2	no	—
143	D₄×C₆₇	C₂²×C₈	1	4	yes	—
144	C₂×C₄×C₆₇	—	2	2	no	—
145	C₂×C₄×C₆₇	—	4	2	no	—
146	C₂×C₄×C₆₇	—	4	2	no	—
147	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
150	C₂²⋊D₆₇	—	2	8	no	—
151	C₂×Dic₆₇	—	2	2	no	—
152	C₂×Dic₆₇	—	2	8	no	—
153	C₂×Dic₆₇	—	2	2	no	—
154	C₂×Dic₆₇	—	8	2	no	—
155	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
156	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
157	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
158	C₄×D₆₇	—	2	1	no	—
159	C₄×D₆₇	—	2	1	no	—
160	C₄×D₆₇	—	4	1	no	—
161	C₄×D₆₇	C₂²×C₈	1	2	yes	—
162	C₄×D₆₇	#131	1	2	yes	—
163	Dic₁₃₄	—	2	2	no	—
164	Dic₁₃₄	C₂²×C₈	1	4	yes	—
165	C₈×C₆₇	—	2	1	no	—
166	C₈×C₆₇	—	2	1	no	—
167	C₈×C₆₇	—	2	1	no	—
168	C₈×C₆₇	—	4	1	no	—
169	C₈×C₆₇	—	4	2	no	—
170	C₈×C₆₇	C₂²×C₈	1	2	yes	—
171	C₆₇⋊C₈	—	2	1	no	—
172	C₆₇⋊C₈	—	2	1	no	—
173	C₆₇⋊C₈	—	2	1	no	—
174	C₆₇⋊C₈	—	4	1	no	—
175	C₆₇⋊C₈	—	4	2	no	—
176	C₆₇⋊C₈	C₂²×C₈	1	2	yes	—
177	C₂²×C₆₇	—	2	4	no	—
178	C₂²×C₆₇	—	4	2	no	—
179	C₂²×C₆₇	—	4	2	no	—
180	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
181	C₂×D₆₇	—	2	1	no	—
182	C₂×D₆₇	—	2	1	no	—
183	C₂×D₆₇	C₈×D₄	1	2	yes	—
184	C₄×C₆₇	—	2	1	no	—
185	C₄×C₆₇	—	4	2	no	—
186	C₄×C₆₇	C₂³×C₈	1	1	yes	characteristic
187	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
188	C₄×C₆₇	#576	1	1	yes	characteristic
189	C₄×C₆₇	#578	1	1	yes	characteristic
190	Dic₆₇	—	2	4	no	—
191	Dic₆₇	—	2	1	no	—
192	Dic₆₇	—	2	1	no	—
193	Dic₆₇	—	4	2	no	—
194	Dic₆₇	C₈×D₄	1	2	yes	—
195	#17857	—	67	1	no	maximal, Sylow
196	C₂×C₆₇	—	4	4	no	—
197	C₂×C₆₇	C₂×C₈×D₄	1	1	yes	characteristic
198	C₂×C₆₇	#2951	1	1	yes	characteristic
199	C₂×C₆₇	#2957	1	1	yes	characteristic
200	D₆₇	—	2	2	no	—
201	#2988	—	67	2	no	—
202	C₄×#135	—	67	1	no	—
203	SD₁₆⋊C₈	—	67	2	no	—
204	SD₁₆⋊C₈	—	67	2	no	—
205	C₈×Q₁₆	—	67	1	no	—
206	C₈×Q₁₆	—	67	1	no	—
207	C₈×D₈	—	67	1	no	—
208	C₈×D₈	D₆₇	1	1	yes	characteristic, complemented
209	C₂×#335	—	67	1	no	—
210	#1477	—	67	2	no	—
211	#1450	—	67	1	no	—
212	C₆₇	#17857	1	1	yes	characteristic, complemented, Sylow
213	C₂×#135	—	67	1	no	—
214	C₄×#41	—	67	2	no	—
215	C₈×Q₈	—	67	2	no	—
216	C₈×Q₈	—	67	2	no	—
217	C₄×Q₁₆	—	67	1	no	—
218	C₄×Q₁₆	—	67	1	no	—
219	C₄×SD₁₆	—	67	2	no	—
220	C₄×SD₁₆	—	67	2	no	—
221	C₄×D₈	—	67	1	no	—
222	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic
223	C₈×D₄	—	67	2	no	—
224	C₈×D₄	—	134	2	no	—
225	C₈×D₄	—	134	2	no	—
226	C₈×D₄	C₂×D₆₇	1	2	yes	—
227	#431	—	67	1	no	—
228	#431	—	67	1	no	—
229	#431	—	134	2	no	—
230	#427	—	67	1	no	—
231	C₂×C₄⋊C₈	—	67	2	no	—
232	C₂×C₄⋊C₈	—	134	2	no	—
233	#416	—	67	2	no	—
234	C₂×C₄×C₈	—	67	1	no	—
235	#335	—	67	2	no	—
236	#335	—	67	1	no	—
237	#335	C₂×D₆₇	1	1	yes	characteristic
238	Q₈⋊C₈	—	67	2	no	—
239	Q₈⋊C₈	—	67	2	no	—
240	D₄⋊C₈	—	67	2	no	—
241	D₄⋊C₈	C₂×D₆₇	1	2	yes	—
242	#322	—	67	1	no	—
243	#322	—	67	1	no	—
244	C₈²	—	67	1	no	—
245	C₈²	C₂×D₆₇	1	1	yes	characteristic
246	C₂×#41	—	67	2	no	—
247	#135	—	67	8	no	—
248	C₂×Q₁₆	—	67	1	no	—
249	C₂×SD₁₆	—	67	2	no	—
250	C₂×D₈	C₄×D₆₇	1	1	yes	characteristic
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	67	1	no	—
253	C₂²×C₈	—	67	1	no	—
254	C₂²×C₈	—	134	2	no	—
255	C₂²×C₈	—	134	2	no	—
256	C₄×Q₈	—	67	2	no	—
257	C₄×Q₈	—	67	2	no	—
258	C₄×D₄	—	67	2	no	—
259	C₄×D₄	—	134	2	no	—
260	C₄×D₄	—	134	2	no	—
261	C₄×D₄	C₂²×D₆₇	1	2	yes	—
262	#117	—	67	2	no	—
263	#117	—	134	2	no	—
264	C₂×C₄²	—	67	1	no	—
265	C₂×C₄²	—	134	2	no	—
266	#107	—	67	1	no	—
267	#107	C₄×D₆₇	1	1	yes	characteristic
268	#106	—	67	2	no	—
269	C₄⋊C₈	—	67	1	no	—
270	C₄⋊C₈	—	67	1	no	—
271	C₄⋊C₈	—	67	2	no	—
272	C₄⋊C₈	—	134	2	no	—
273	C₄⋊C₈	—	134	1	no	—
274	C₄⋊C₈	—	134	2	no	—
275	C₄⋊C₈	—	134	2	no	—
276	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
277	#103	—	67	2	no	—
278	#103	—	67	2	no	—
279	#102	—	67	2	no	—
280	#102	C₄×D₆₇	1	2	yes	—
281	C₂²⋊C₈	—	2	2	no	—
282	C₂²⋊C₈	—	67	1	no	—
283	C₂²⋊C₈	—	67	1	no	—
284	C₂²⋊C₈	—	134	1	no	—
285	C₂²⋊C₈	—	134	2	no	—
286	C₄×C₈	—	67	1	no	—
287	C₄×C₈	—	67	1	no	—
288	C₄×C₈	—	67	1	no	—
289	C₄×C₈	—	67	1	no	—
290	C₄×C₈	—	67	1	no	—
291	C₄×C₈	—	134	2	no	—
292	C₄×C₈	—	134	2	no	—
293	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
294	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
295	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
296	#41	—	67	8	no	—
297	#41	—	134	4	no	—
298	C₂×Q₈	—	67	2	no	—
299	C₂×D₄	—	134	2	no	—
300	C₂×D₄	C₂×C₄×D₆₇	1	2	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	67	1	no	—
303	C₂²×C₄	—	67	1	no	—
304	C₂²×C₄	—	67	1	no	—
305	C₂²×C₄	—	134	2	no	—
306	C₂²×C₄	—	134	2	no	—
307	Q₁₆	—	67	4	no	—
308	SD₁₆	—	67	8	no	—
309	D₈	C₈×D₆₇	1	4	yes	complemented
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	8	2	no	—
313	C₂×C₈	—	536	2	no	—
314	C₂×C₈	—	536	2	no	—
315	C₂×C₈	—	67	1	no	—
316	C₂×C₈	—	67	4	no	—
317	C₂×C₈	—	67	1	no	—
318	C₂×C₈	—	67	1	no	—
319	C₂×C₈	—	67	1	no	—
320	C₂×C₈	—	134	2	no	—
321	C₂×C₈	—	134	2	no	—
322	C₂×C₈	—	134	1	no	—
323	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
324	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
325	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
326	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
327	C₄⋊C₄	—	67	2	no	—
328	C₄⋊C₄	—	134	2	no	—
329	C₄⋊C₄	—	134	2	no	—
330	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	134	2	no	—
333	C₂²⋊C₄	—	134	2	no	—
334	C₄²	—	67	1	no	—
335	C₄²	—	67	1	no	—
336	C₄²	—	67	1	no	—
337	C₄²	—	134	2	no	—
338	C₄²	—	134	2	no	—
339	C₄²	—	134	2	no	—
340	C₄²	C₂³×D₆₇	1	1	yes	characteristic
341	C₂³	—	2	2	no	—
342	C₂³	—	67	1	no	—
343	Q₈	—	67	4	no	—
344	Q₈	—	134	2	no	—
345	D₄	—	2	2	no	—
346	D₄	—	134	8	no	—
347	D₄	C₂×C₈×D₆₇	1	4	yes	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	268	1	no	—
352	C₂×C₄	—	536	2	no	—
353	C₂×C₄	—	67	1	no	—
354	C₂×C₄	—	67	2	no	—
355	C₂×C₄	—	67	2	no	—
356	C₂×C₄	—	67	1	no	—
357	C₂×C₄	—	67	1	no	—
358	C₂×C₄	—	134	2	no	—
359	C₂×C₄	—	134	8	no	—
360	C₂×C₄	—	134	2	no	—
361	C₂×C₄	—	134	1	no	—
362	C₂×C₄	—	134	1	no	—
363	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
364	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
365	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	—	4	1	no	—
370	C₈	—	4	2	no	—
371	C₈	—	268	1	no	—
372	C₈	—	268	2	no	—
373	C₈	—	67	2	no	—
374	C₈	—	134	1	no	—
375	C₈	—	134	1	no	—
376	C₈	—	134	1	no	—
377	C₈	C₂×C₈×D₆₇	1	2	yes	—
378	C₂²	—	2	4	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	67	2	no	—
382	C₂²	—	134	1	no	—
383	C₂²	—	134	1	no	—
384	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	268	2	no	—
388	C₄	—	67	2	no	—
389	C₄	—	134	1	no	—
390	C₄	—	134	1	no	—
391	C₄	—	134	4	no	—
392	C₄	C₂²×C₈×D₆₇	1	1	yes	characteristic
393	C₄	#131×D₆₇	1	1	yes	characteristic
394	C₄	#16864197	1	1	yes	characteristic
395	C₄	#16864210	1	1	yes	characteristic
396	C₂	—	4	4	no	—
397	C₂	—	134	2	no	—
398	C₂	C₈×D₄×D₆₇	1	1	yes	characteristic
399	C₂	#22569079	1	1	yes	characteristic
400	C₂	#22569121	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₄×C₆₇	C₂³×C₈
Frattini	C₄²	C₂³×D₆₇
Fitting	C₈×D₈×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#14524062	C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	C₈×D₈	D₆₇
hypocenter	C₆₇	#17857
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×D₈

Complements

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

N	H ≅ G/N	type
1. #22569316	C₂	semidirect
3. #22559021	C₂	semidirect
4. #22559018	C₂	semidirect
5. C₈×Dic₂₆₈	C₂	semidirect
6. #22559015	C₂	semidirect
7. D₈×C₆₇⋊C₈	C₂	semidirect
8. #335×D₆₇	C₂	semidirect
9. #22558593	C₂	semidirect
10. #22558491	C₂	semidirect
11. C₈×D₈×C₆₇	C₂	semidirect
46. #14524062	C₈	semidirect
96. #11761627	C₂×C₈	semidirect
104. Dic₂₆₈	C₂×C₈	semidirect
105. #11761616	C₂×C₈	semidirect
115. C₈×D₆₇	C₂×C₈	semidirect
129. D₈×C₆₇	C₂×C₈	semidirect
208. C₈×D₈	D₆₇	semidirect
212. C₆₇	#17857	semidirect
309. D₈	C₈×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22569316	2
C₄×#14524062	2
#22559021	2
#22559018	2
C₈×Dic₂₆₈	2
#22559015	2
D₈×C₆₇⋊C₈	2
#335×D₆₇	2
#22558593	2
#22558491	2
C₈×D₈×C₆₇	2
#17857	67