Subgroups — #31732070

Order 17152.

2620 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	#22574978	C₂	1	4	yes	maximal, complemented
2	#22572013	C₂	1	2	yes	maximal, complemented
3	#22572008	C₂	1	2	yes	maximal, complemented
4	#22572002	C₂	1	4	yes	maximal, complemented
5	#22571994	C₂	1	8	yes	maximal, complemented
6	#22569925	C₂	1	4	yes	maximal, complemented
7	#22569557	C₂	1	4	yes	maximal, complemented
8	C₂×#16863514	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864232	C₂²	1	4	yes	complemented
11	#16864210	—	2	4	no	—
12	#16864209	C₂²	1	8	yes	complemented
13	#16864203	—	2	8	no	—
14	#16864202	C₂²	1	16	yes	complemented
15	#16864198	—	2	4	no	—
16	#16864197	C₂²	1	8	yes	complemented
17	#16864194	C₂²	1	8	yes	complemented
18	#16864193	—	2	8	no	—
19	C₂×#14524065	C₂²	1	2	yes	—
20	#135×D₆₇	—	2	8	no	—
21	C₂×#14524049	C₂²	1	4	yes	complemented
22	#16863668	C₂²	1	8	yes	complemented
23	#16863663	C₂²	1	8	yes	complemented
24	#16863656	C₂²	1	16	yes	complemented
25	#16863578	C₂²	1	8	yes	complemented
26	#16863573	C₂²	1	8	yes	complemented
27	#16863568	C₂²	1	8	yes	complemented
28	#16863563	C₂²	1	8	yes	complemented
29	#16863514	C₂²	1	4	yes	complemented
30	#16863514	C₂²	1	4	yes	complemented
31	#16863514	C₂²	1	4	yes	complemented
32	#16863514	C₂²	1	4	yes	complemented
33	C₂×#14523979	C₂²	1	2	yes	complemented
34	C₂×#14523971	C₂²	1	4	yes	complemented
35	#16863380	C₂²	1	4	yes	complemented
36	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
37	#532×C₆₇	C₂²	1	2	yes	complemented
38	#495×C₆₇	C₂²	1	4	yes	complemented
39	#494×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#493×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	#492×C₆₇	C₂²	1	2	yes	complemented
42	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#14524091	C₂³	1	8	yes	—
44	#14524090	—	2	8	no	—
45	#14524089	—	2	8	no	—
46	#14524088	—	4	4	no	—
47	#14524088	C₂³	1	8	yes	—
48	C₂×#11761628	—	4	4	no	—
49	C₂×#11761628	C₂³	1	4	yes	—
50	#41×D₆₇	—	2	16	no	—
51	#14524075	—	2	16	no	—
52	#14524074	C₂³	1	16	yes	—
53	#14524073	—	2	8	no	—
54	#14524072	—	2	16	no	—
55	#14524070	—	2	16	no	—
56	#14524069	C₂³	1	16	yes	—
57	#14524068	—	2	8	no	—
58	#14524067	—	2	16	no	—
59	#14524066	—	2	8	no	—
60	#14524065	D₄	1	4	yes	complemented
61	#14524065	D₄	1	4	yes	complemented
62	#14524065	C₂³	1	4	yes	—
63	#14524065	C₂³	1	4	yes	—
64	#14524064	—	2	16	no	—
65	#14524063	—	2	16	no	—
66	#14524062	—	2	8	no	—
67	C₂×Dic₂₆₈	D₄	1	2	yes	complemented
68	Q₁₆×D₆₇	—	2	8	no	—
69	C₂×#11761617	D₄	1	4	yes	complemented
70	SD₁₆×D₆₇	—	2	16	no	—
71	C₂×D₅₃₆	D₄	1	2	yes	complemented
72	D₈×D₆₇	—	2	8	no	—
73	#14524049	—	2	4	no	—
74	#14524049	—	2	4	no	—
75	#14524049	C₂³	1	8	yes	—
76	#14524049	C₂³	1	8	yes	—
77	C₂×#11761612	C₂³	1	4	yes	—
78	C₂×#11761611	—	2	4	no	—
79	C₂×C₈×D₆₇	—	2	4	no	—
80	#14523979	C₂³	1	4	yes	—
81	#14523979	C₂³	1	4	yes	—
82	#14523971	C₂³	1	8	yes	—
83	#14523971	C₂³	1	8	yes	—
84	#14523962	C₂³	1	8	yes	—
85	#14523960	C₂³	1	8	yes	—
86	C₂×#41×C₆₇	C₂³	1	4	yes	—
87	#135×C₆₇	—	2	4	no	—
88	#135×C₆₇	—	2	4	no	—
89	#135×C₆₇	—	2	4	no	—
90	#135×C₆₇	—	2	4	no	—
91	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
92	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	—
93	C₂×D₈×C₆₇	C₂³	1	4	yes	—
94	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
95	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
96	#127×C₆₇	C₂³	1	2	yes	—
97	#124×C₆₇	C₂³	1	4	yes	—
98	#121×C₆₇	—	4	2	no	—
99	C₄×D₄×C₆₇	—	4	2	no	—
100	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₆₇	C₂³	1	2	yes	—
104	#11761629	—	2	16	no	—
105	#11761628	—	2	4	no	—
106	#11761628	—	2	4	no	—
107	#11761628	—	4	8	no	—
108	#11761628	—	4	8	no	—
109	#11761628	—	4	8	no	—
110	#11761628	C₂×D₄	1	8	yes	—
111	#11761628	C₂⁴	1	8	yes	—
112	#11761627	—	2	16	no	—
113	#11761627	—	4	16	no	—
114	C₂×Dic₁₃₄	—	4	4	no	—
115	C₂×Dic₁₃₄	C₂×D₄	1	4	yes	—
116	Q₈×D₆₇	—	2	16	no	—
117	C₂×D₂₆₈	—	4	4	no	—
118	C₂×D₂₆₈	C₂×D₄	1	4	yes	—
119	C₂×C₂²⋊D₆₇	—	2	4	no	—
120	C₂×C₂²⋊D₆₇	—	4	8	no	—
121	D₄×D₆₇	—	2	16	no	—
122	D₄×D₆₇	—	4	16	no	—
123	C₂×C₄×D₆₇	—	2	4	no	—
124	C₂×C₄×D₆₇	—	4	8	no	—
125	Dic₂₆₈	C₂×D₄	1	4	yes	—
126	Dic₂₆₈	C₂×D₄	1	4	yes	—
127	#11761618	—	2	16	no	—
128	#11761617	C₂×D₄	1	8	yes	—
129	#11761617	C₂×D₄	1	8	yes	—
130	#11761616	—	2	16	no	—
131	#11761615	—	2	16	no	—
132	D₅₃₆	C₂×D₄	1	4	yes	—
133	D₅₃₆	C₂×D₄	1	4	yes	—
134	#11761613	—	2	16	no	—
135	#11761612	—	2	4	no	—
136	#11761612	C₂⁴	1	8	yes	—
137	#11761611	—	2	8	no	—
138	#11761611	—	2	8	no	—
139	C₂×C₆₇⋊C₈	—	2	4	no	—
140	C₈×D₆₇	—	2	8	no	—
141	C₈×D₆₇	—	2	8	no	—
142	#41×C₆₇	—	2	8	no	—
143	#41×C₆₇	—	2	8	no	—
144	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
145	C₂×D₄×C₆₇	—	2	4	no	—
146	C₂×D₄×C₆₇	—	4	2	no	—
147	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₆₇	—	2	1	no	—
149	C₂²×C₄×C₆₇	—	2	4	no	—
150	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
151	Q₁₆×C₆₇	—	2	4	no	—
152	Q₁₆×C₆₇	—	2	4	no	—
153	SD₁₆×C₆₇	—	2	8	no	—
154	SD₁₆×C₆₇	—	2	8	no	—
155	D₈×C₆₇	—	2	4	no	—
156	D₈×C₆₇	—	2	4	no	—
157	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
158	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
161	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
162	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
163	C₄⋊C₄×C₆₇	—	4	2	no	—
164	C₂²⋊C₄×C₆₇	—	4	4	no	—
165	C₄²×C₆₇	—	2	1	no	—
166	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
167	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
168	C₂³×C₆₇	—	2	4	no	—
169	C₂³×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂²×D₆₇	—	2	4	no	—
171	C₂²×D₆₇	—	4	8	no	—
172	Q₈×C₆₇	—	2	8	no	—
173	D₄×C₆₇	—	2	8	no	—
174	D₄×C₆₇	—	4	8	no	—
175	D₄×C₆₇	—	8	4	no	—
176	C₂×C₄×C₆₇	—	2	1	no	—
177	C₂×C₄×C₆₇	—	2	1	no	—
178	C₂×C₄×C₆₇	—	2	4	no	—
179	C₂×C₄×C₆₇	—	4	2	no	—
180	C₂×C₄×C₆₇	—	4	4	no	—
181	C₂×C₄×C₆₇	—	4	4	no	—
182	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
183	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
184	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
186	C₂²⋊D₆₇	—	2	8	no	—
187	C₂²⋊D₆₇	—	2	8	no	—
188	C₂²⋊D₆₇	—	4	16	no	—
189	C₂×Dic₆₇	—	2	4	no	—
190	C₂×Dic₆₇	—	4	8	no	—
191	D₂₆₈	—	2	4	no	—
192	D₂₆₈	—	4	8	no	—
193	D₂₆₈	C₂²×D₄	1	8	yes	—
194	C₄×D₆₇	—	2	8	no	—
195	C₄×D₆₇	—	2	8	no	—
196	C₄×D₆₇	—	4	16	no	—
197	Dic₁₃₄	—	2	4	no	—
198	Dic₁₃₄	—	4	8	no	—
199	Dic₁₃₄	C₂²×D₄	1	8	yes	—
200	C₈×C₆₇	C₂²×D₄	1	2	yes	—
201	C₈×C₆₇	C₂²×D₄	1	2	yes	—
202	C₈×C₆₇	C₂²×D₄	1	2	yes	—
203	C₈×C₆₇	C₂²×D₄	1	2	yes	—
204	C₆₇⋊C₈	—	2	8	no	—
205	C₂²×C₆₇	—	4	1	no	—
206	C₂²×C₆₇	—	4	4	no	—
207	C₂²×C₆₇	—	8	4	no	—
208	C₂²×C₆₇	D₄²	1	2	yes	—
209	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
210	C₂×D₆₇	—	2	8	no	—
211	C₂×D₆₇	—	8	4	no	—
212	C₂×D₆₇	—	16	8	no	—
213	C₄×C₆₇	—	2	2	no	—
214	C₄×C₆₇	—	4	1	no	—
215	C₄×C₆₇	—	4	4	no	—
216	C₄×C₆₇	D₄²	1	1	yes	characteristic
217	C₄×C₆₇	D₄²	1	1	yes	characteristic
218	C₄×C₆₇	C₂³×D₄	1	2	yes	—
219	Dic₆₇	—	2	8	no	—
220	#61105	—	67	1	no	maximal, Sylow
221	C₂×C₆₇	—	2	1	no	—
222	C₂×C₆₇	—	2	2	no	—
223	C₂×C₆₇	—	8	4	no	—
224	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
225	D₆₇	—	4	8	no	—
226	#3584	—	67	4	no	—
227	#3293	—	67	2	no	—
228	#3292	—	67	2	no	—
229	#3291	—	67	4	no	—
230	#3290	—	67	8	no	—
231	#3147	D₆₇	1	1	yes	characteristic, complemented
232	#3067	—	67	4	no	—
233	#3018	—	67	4	no	—
234	C₂×#443	—	67	2	no	—
235	C₆₇	#61105	1	1	yes	characteristic, complemented, Sylow
236	#585	—	67	4	no	—
237	#578	—	67	8	no	—
238	#578	—	134	4	no	—
239	#577	—	67	16	no	—
240	#577	—	134	8	no	—
241	#576	—	67	8	no	—
242	#576	—	134	4	no	—
243	#575	—	67	8	no	—
244	#575	—	134	8	no	—
245	C₂×#135	—	67	2	no	—
246	C₂×#135	—	134	8	no	—
247	C₂×#135	C₂×D₆₇	1	4	yes	complemented
248	C₂×#131	—	67	4	no	—
249	#532	C₂×D₆₇	1	2	yes	complemented
250	#495	C₂×D₆₇	1	4	yes	complemented
251	#494	C₂×D₆₇	1	1	yes	characteristic, complemented
252	#493	C₂×D₆₇	1	1	yes	characteristic, complemented
253	#492	C₂×D₆₇	1	2	yes	complemented
254	#473	—	67	8	no	—
255	#472	—	67	8	no	—
256	#471	—	67	16	no	—
257	#456	—	67	8	no	—
258	#455	—	67	8	no	—
259	#454	—	67	8	no	—
260	#453	—	67	8	no	—
261	#443	—	67	4	no	—
262	#443	—	67	4	no	—
263	#443	—	67	4	no	—
264	#443	—	67	4	no	—
265	C₂×#108	—	67	2	no	—
266	C₂×#104	—	67	4	no	—
267	#413	—	67	4	no	—
268	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
269	2₋¹⁺⁴	—	67	8	no	—
270	2₋¹⁺⁴	—	134	8	no	—
271	H(5,𝔽₂)	—	268	4	no	—
272	H(5,𝔽₂)	—	67	8	no	—
273	H(5,𝔽₂)	—	134	8	no	—
274	C₂×#41	—	268	4	no	—
275	C₂×#41	—	67	4	no	—
276	C₂×#41	—	134	16	no	—
277	C₂×#41	C₂²×D₆₇	1	4	yes	—
278	#137	—	67	16	no	—
279	#137	—	134	16	no	—
280	#137	—	134	16	no	—
281	#137	—	134	8	no	—
282	AGL(1,ℤ/8)	—	67	16	no	—
283	AGL(1,ℤ/8)	—	134	16	no	—
284	AGL(1,ℤ/8)	—	134	16	no	—
285	AGL(1,ℤ/8)	—	134	8	no	—
286	#135	—	2	4	no	—
287	#135	—	2	4	no	—
288	#135	—	2	4	no	—
289	#135	—	2	4	no	—
290	#135	—	67	4	no	—
291	#135	—	67	4	no	—
292	#135	—	67	4	no	—
293	#135	—	67	4	no	—
294	#135	—	134	8	no	—
295	#135	—	134	8	no	—
296	#135	—	134	16	no	—
297	#135	—	134	16	no	—
298	C₂×Q₁₆	—	67	2	no	—
299	C₂×Q₁₆	—	134	8	no	—
300	C₂×Q₁₆	C₂²×D₆₇	1	4	yes	—
301	C₂×SD₁₆	—	67	4	no	—
302	C₂×SD₁₆	—	134	16	no	—
303	C₂×SD₁₆	C₂²×D₆₇	1	8	yes	—
304	C₂×D₈	—	67	2	no	—
305	C₂×D₈	—	134	8	no	—
306	C₂×D₈	C₂²×D₆₇	1	4	yes	—
307	#131	—	67	8	no	—
308	#131	—	67	8	no	—
309	#131	—	134	4	no	—
310	#131	—	134	4	no	—
311	C₂×M₁₆	—	67	4	no	—
312	C₂×M₁₆	—	134	4	no	—
313	C₂²×C₈	—	134	4	no	—
314	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
315	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	—
316	#127	C₂²×D₆₇	1	2	yes	—
317	#124	C₂²×D₆₇	1	4	yes	—
318	#121	—	4	2	no	—
319	C₄×D₄	—	4	2	no	—
320	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
321	#108	—	67	4	no	—
322	#108	—	67	4	no	—
323	#104	—	67	8	no	—
324	#104	—	67	8	no	—
325	#101	—	67	8	no	—
326	#100	—	67	8	no	—
327	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
328	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₆₇	1	2	yes	—
330	#41	—	2	8	no	—
331	#41	—	2	8	no	—
332	#41	—	268	8	no	—
333	#41	—	268	8	no	—
334	#41	—	268	8	no	—
335	#41	—	268	16	no	—
336	#41	—	67	8	no	—
337	#41	—	67	8	no	—
338	#41	—	134	16	no	—
339	#41	—	134	16	no	—
340	#41	—	134	4	no	—
341	#41	—	134	4	no	—
342	C₂×Q₈	—	268	4	no	—
343	C₂×Q₈	—	67	4	no	—
344	C₂×Q₈	—	134	16	no	—
345	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	268	4	no	—
349	C₂×D₄	—	268	16	no	—
350	C₂×D₄	—	268	8	no	—
351	C₂×D₄	—	67	4	no	—
352	C₂×D₄	—	134	16	no	—
353	C₂×D₄	—	134	4	no	—
354	C₂×D₄	C₂³×D₆₇	1	4	yes	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	268	8	no	—
358	C₂²×C₄	—	134	4	no	—
359	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
360	Q₁₆	—	2	4	no	—
361	Q₁₆	—	2	4	no	—
362	Q₁₆	—	67	4	no	—
363	Q₁₆	—	67	4	no	—
364	Q₁₆	—	134	16	no	—
365	SD₁₆	—	2	8	no	—
366	SD₁₆	—	2	8	no	—
367	SD₁₆	—	67	8	no	—
368	SD₁₆	—	67	8	no	—
369	SD₁₆	—	134	16	no	—
370	SD₁₆	—	134	16	no	—
371	D₈	—	2	4	no	—
372	D₈	—	2	4	no	—
373	D₈	—	67	4	no	—
374	D₈	—	67	4	no	—
375	D₈	—	134	16	no	—
376	M₁₆	—	67	8	no	—
377	M₁₆	—	134	4	no	—
378	M₁₆	—	134	8	no	—
379	M₁₆	—	134	8	no	—
380	C₂×C₈	—	134	4	no	—
381	C₂×C₈	—	134	8	no	—
382	C₂×C₈	—	134	8	no	—
383	C₂×C₈	D₄×D₆₇	1	2	yes	—
384	C₂×C₈	D₄×D₆₇	1	2	yes	—
385	C₂×C₈	D₄×D₆₇	1	2	yes	—
386	C₂×C₈	D₄×D₆₇	1	2	yes	—
387	C₂×C₈	C₂³×D₆₇	1	2	yes	—
388	C₂×C₈	C₂³×D₆₇	1	2	yes	—
389	C₄⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₄²	—	2	1	no	—
392	C₄²	C₂³×D₆₇	1	1	yes	characteristic
393	C₄²	C₂³×D₆₇	1	1	yes	characteristic
394	C₂³	—	2	4	no	—
395	C₂³	—	268	8	no	—
396	C₂³	—	134	4	no	—
397	C₂³	#14524088	1	1	yes	characteristic
398	Q₈	—	2	8	no	—
399	Q₈	—	268	8	no	—
400	Q₈	—	67	8	no	—
401	Q₈	—	134	4	no	—
402	D₄	—	2	8	no	—
403	D₄	—	4	8	no	—
404	D₄	—	8	4	no	—
405	D₄	—	268	8	no	—
406	D₄	—	268	16	no	—
407	D₄	—	67	8	no	—
408	D₄	—	134	8	no	—
409	D₄	—	134	8	no	—
410	D₄	—	134	4	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	268	16	no	—
418	C₂×C₄	—	268	8	no	—
419	C₂×C₄	—	134	4	no	—
420	C₂×C₄	—	134	8	no	—
421	C₂×C₄	—	134	8	no	—
422	C₂×C₄	C₂×D₄×D₆₇	1	2	yes	—
423	C₂×C₄	C₂×D₄×D₆₇	1	2	yes	—
424	C₂×C₄	#14524088	1	1	yes	characteristic
425	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
426	C₈	—	134	8	no	—
427	C₈	C₂×D₄×D₆₇	1	2	yes	—
428	C₈	C₂×D₄×D₆₇	1	2	yes	—
429	C₈	C₂×D₄×D₆₇	1	2	yes	—
430	C₈	C₂×D₄×D₆₇	1	2	yes	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	8	4	no	—
434	C₂²	—	536	4	no	—
435	C₂²	—	1072	8	no	—
436	C₂²	—	134	8	no	—
437	C₂²	#16864031	1	2	yes	—
438	C₂²	C₂×#14524088	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	4	no	—
442	C₄	—	134	8	no	—
443	C₄	#16864031	1	1	yes	characteristic
444	C₄	#16864031	1	1	yes	characteristic
445	C₄	C₂²×D₄×D₆₇	1	2	yes	—
446	C₂	—	2	1	no	—
447	C₂	—	2	2	no	—
448	C₂	—	8	4	no	—
449	C₂	—	268	8	no	—
450	C₂	C₂×#16864031	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16864031
commutator, cosocle	C₂×C₄×C₆₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₆₇×#3147	C₂
socle	C₂×C₆₇	C₂×D₄²
hypercenter	#3147	D₆₇
hypocenter	C₆₇	#61105
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #3147

Complements

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

N	H ≅ G/N	type
1. #22574978	C₂	semidirect
2. #22572013	C₂	semidirect
3. #22572008	C₂	semidirect
4. #22572002	C₂	semidirect
5. #22571994	C₂	semidirect
6. #22569925	C₂	semidirect
7. #22569557	C₂	semidirect
8. C₂×#16863514	C₂	semidirect
9. C₆₇×#3147	C₂	semidirect
10. #16864232	C₂²	semidirect
12. #16864209	C₂²	semidirect
14. #16864202	C₂²	semidirect
16. #16864197	C₂²	semidirect
17. #16864194	C₂²	semidirect
21. C₂×#14524049	C₂²	semidirect
22. #16863668	C₂²	semidirect
23. #16863663	C₂²	semidirect
24. #16863656	C₂²	semidirect
25. #16863578	C₂²	semidirect
26. #16863573	C₂²	semidirect
27. #16863568	C₂²	semidirect
28. #16863563	C₂²	semidirect
29. #16863514	C₂²	semidirect
30. #16863514	C₂²	semidirect
31. #16863514	C₂²	semidirect
32. #16863514	C₂²	semidirect
33. C₂×#14523979	C₂²	semidirect
34. C₂×#14523971	C₂²	semidirect
35. #16863380	C₂²	semidirect
36. C₂×#135×C₆₇	C₂²	semidirect
37. #532×C₆₇	C₂²	semidirect
38. #495×C₆₇	C₂²	semidirect
39. #494×C₆₇	C₂²	semidirect
40. #493×C₆₇	C₂²	semidirect
41. #492×C₆₇	C₂²	semidirect
42. C₂×C₄×C₈×C₆₇	C₂²	semidirect
60. #14524065	D₄	semidirect
61. #14524065	D₄	semidirect
67. C₂×Dic₂₆₈	D₄	semidirect
69. C₂×#11761617	D₄	semidirect
71. C₂×D₅₃₆	D₄	semidirect
231. #3147	D₆₇	semidirect
235. C₆₇	#61105	semidirect
247. C₂×#135	C₂×D₆₇	semidirect
249. #532	C₂×D₆₇	semidirect
250. #495	C₂×D₆₇	semidirect
251. #494	C₂×D₆₇	semidirect
252. #493	C₂×D₆₇	semidirect
253. #492	C₂×D₆₇	semidirect
268. C₂×C₄×C₈	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22574978	2
#22572013	2
#22572008	2
#22572002	2
#22571994	2
#22569925	2
#22569557	2
C₂×#16863514	2
C₆₇×#3147	2
#61105	67