Subgroups — #30874352

Order 17152.

812 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569127	C₂	1	1	yes	maximal, characteristic
2	#22569125	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863512	C₂	1	1	yes	maximal, characteristic
4	#22568819	C₂	1	2	yes	maximal, complemented
5	#22561000	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560452	C₂	1	2	yes	maximal, complemented
7	#22560446	C₂	1	2	yes	maximal, complemented
8	#22560379	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560262	C₂	1	2	yes	maximal, complemented
10	#22560089	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1953	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524065	C₂²	1	1	yes	characteristic
13	#16864162	C₂²	1	2	yes	—
14	#16864162	C₂²	1	2	yes	—
15	C₂×#14524051	C₂²	1	2	yes	—
16	#16863519	—	2	2	no	—
17	#16863517	—	2	2	no	—
18	#16863514	—	2	2	no	—
19	#16863512	—	2	2	no	—
20	#16863512	C₄	1	2	yes	complemented
21	#16863512	C₄	1	2	yes	complemented
22	#16863512	C₄	1	2	yes	complemented
23	#16863512	C₄	1	2	yes	complemented
24	#16863445	C₂²	1	2	yes	—
25	#16863443	—	2	4	no	—
26	C₂×#14523979	C₂²	1	1	yes	characteristic
27	C₂×#14523978	C₂²	1	2	yes	—
28	C₂×#14523978	C₂²	1	1	yes	characteristic
29	#108×D₆₇	—	2	4	no	—
30	#16863432	C₂²	1	1	yes	characteristic
31	#16863419	C₂²	1	2	yes	—
32	#16863414	C₂²	1	2	yes	—
33	#16863412	C₂²	1	2	yes	—
34	C₂×#14523969	C₂²	1	2	yes	—
35	#16863351	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
37	#16863168	C₂²	1	2	yes	—
38	#16863157	C₂²	1	1	yes	characteristic
39	#16863155	C₂²	1	1	yes	characteristic
40	#430×C₆₇	C₂²	1	2	yes	—
41	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
43	#405×C₆₇	C₂²	1	1	yes	characteristic
44	#344×C₆₇	C₂²	1	2	yes	—
45	C₂×#11761628	C₂³	1	2	yes	—
46	#14524065	C₂×C₄	1	2	yes	—
47	#14524065	C₂×C₄	1	2	yes	—
48	#14524065	D₄	1	2	yes	—
49	#14524065	D₄	1	2	yes	—
50	C₂×Dic₂₆₈	Q₈	1	1	yes	characteristic
51	C₂×#11761617	Q₈	1	2	yes	—
52	C₂×D₅₃₆	Q₈	1	1	yes	characteristic
53	#14524051	—	2	2	no	—
54	#14524051	—	2	2	no	—
55	#14524051	—	2	4	no	—
56	#14524051	—	4	2	no	—
57	#14524051	C₂×C₄	1	4	yes	—
58	#14524051	C₂×C₄	1	4	yes	—
59	#14524049	—	2	4	no	—
60	#14524049	—	4	2	no	—
61	C₂×#11761612	C₂³	1	2	yes	—
62	C₂×#11761612	C₂³	1	1	yes	characteristic
63	C₂×#11761611	—	2	2	no	—
64	M₁₆×D₆₇	—	2	4	no	—
65	M₁₆×D₆₇	—	2	4	no	—
66	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₆₇	—	2	2	no	—
68	#14524002	C₂³	1	1	yes	characteristic
69	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
70	#14523979	—	2	4	no	—
71	#14523979	—	2	1	no	—
72	#14523979	—	2	1	no	—
73	#14523978	—	2	2	no	—
74	#14523978	—	2	2	no	—
75	#14523978	D₄	1	2	yes	—
76	#14523978	D₄	1	2	yes	—
77	#14523976	—	2	1	no	—
78	#14523974	—	2	1	no	—
79	Dic₆₇⋊C₈	—	4	2	no	—
80	#14523971	—	2	4	no	—
81	#14523969	—	2	4	no	—
82	#14523969	C₂×C₄	1	4	yes	—
83	#14523969	C₂×C₄	1	4	yes	—
84	#14523953	—	2	1	no	—
85	C₈×Dic₆₇	—	2	1	no	—
86	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
90	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
91	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
92	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	#117×C₆₇	C₂³	1	1	yes	characteristic
95	#108×C₆₇	—	2	4	no	—
96	#108×C₆₇	—	2	1	no	—
97	#108×C₆₇	—	2	1	no	—
98	#108×C₆₇	C₂×C₄	1	2	yes	—
99	#108×C₆₇	C₂×C₄	1	2	yes	—
100	#97×C₆₇	—	2	1	no	—
101	C₄×C₈×C₆₇	—	2	1	no	—
102	#11761628	—	2	2	no	—
103	#11761628	—	2	2	no	—
104	#11761628	C₂²×C₄	1	4	yes	—
105	#11761628	C₂×D₄	1	4	yes	—
106	C₂×Dic₁₃₄	C₂×Q₈	1	2	yes	—
107	C₂×D₂₆₈	C₂×Q₈	1	2	yes	—
108	C₂×C₂²⋊D₆₇	—	2	2	no	—
109	C₂²×Dic₆₇	—	2	1	no	—
110	C₂×C₄×D₆₇	—	2	2	no	—
111	Dic₂₆₈	C₄⋊C₄	1	2	yes	—
112	Dic₂₆₈	C₄⋊C₄	1	2	yes	—
113	#11761617	C₄⋊C₄	1	4	yes	—
114	#11761617	C₄⋊C₄	1	4	yes	—
115	D₅₃₆	C₄⋊C₄	1	2	yes	—
116	D₅₃₆	C₄⋊C₄	1	2	yes	—
117	#11761612	—	2	1	no	—
118	#11761612	—	2	2	no	—
119	#11761612	—	2	2	no	—
120	#11761612	C₂×D₄	1	2	yes	—
121	#11761611	—	2	4	no	—
122	#11761611	—	2	4	no	—
123	#11761611	—	4	4	no	—
124	#11761611	—	4	4	no	—
125	C₂×C₆₇⋊C₈	—	2	1	no	—
126	C₂×C₆₇⋊C₈	—	2	2	no	—
127	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
130	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
131	C₂×C₆₇⋊C₈	#41	1	1	yes	characteristic
132	C₂×C₆₇⋊C₈	#41	1	1	yes	characteristic
133	C₈×D₆₇	—	2	4	no	—
134	C₈×D₆₇	—	2	4	no	—
135	C₈×D₆₇	—	4	4	no	—
136	C₈×D₆₇	—	4	4	no	—
137	C₄⋊Dic₆₇	—	2	1	no	—
138	C₂²⋊Dic₆₇	—	2	1	no	—
139	C₄×Dic₆₇	—	2	1	no	—
140	C₄×Dic₆₇	—	2	1	no	—
141	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
144	M₁₆×C₆₇	—	2	2	no	—
145	M₁₆×C₆₇	—	2	1	no	—
146	M₁₆×C₆₇	—	2	2	no	—
147	M₁₆×C₆₇	—	2	2	no	—
148	M₁₆×C₆₇	C₂²×C₄	1	4	yes	—
149	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₆₇	—	2	2	no	—
151	C₂×C₈×C₆₇	—	2	1	no	—
152	C₂×C₈×C₆₇	—	2	2	no	—
153	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₆₇	C₂×Q₈	1	1	yes	characteristic
158	C₂×C₈×C₆₇	C₂×Q₈	1	1	yes	characteristic
159	C₄⋊C₄×C₆₇	—	2	1	no	—
160	C₂²⋊C₄×C₆₇	—	2	1	no	—
161	C₄²×C₆₇	—	2	1	no	—
162	C₂³×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
163	C₂²×D₆₇	—	2	2	no	—
164	C₂×C₄×C₆₇	—	4	1	no	—
165	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂²⋊D₆₇	—	2	4	no	—
172	C₂²⋊D₆₇	—	2	4	no	—
173	C₂×Dic₆₇	—	2	1	no	—
174	C₂×Dic₆₇	—	2	2	no	—
175	C₂×Dic₆₇	—	2	1	no	—
176	C₂×Dic₆₇	—	4	2	no	—
177	C₂×Dic₆₇	—	4	1	no	—
178	D₂₆₈	—	2	2	no	—
179	D₂₆₈	C₂×C₄⋊C₄	1	4	yes	—
180	C₄×D₆₇	—	2	4	no	—
181	C₄×D₆₇	—	2	4	no	—
182	Dic₁₃₄	—	2	2	no	—
183	Dic₁₃₄	C₂×C₄⋊C₄	1	4	yes	—
184	C₈×C₆₇	—	2	4	no	—
185	C₈×C₆₇	—	2	2	no	—
186	C₈×C₆₇	—	4	2	no	—
187	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₆₇⋊C₈	—	2	2	no	—
192	C₆₇⋊C₈	—	4	2	no	—
193	C₆₇⋊C₈	C₄×D₄	1	1	yes	characteristic
194	C₆₇⋊C₈	C₄×D₄	1	1	yes	characteristic
195	C₆₇⋊C₈	C₄×D₄	1	1	yes	characteristic
196	C₆₇⋊C₈	C₄×D₄	1	1	yes	characteristic
197	C₂²×C₆₇	—	4	1	no	—
198	C₂²×C₆₇	#520	1	1	yes	characteristic
199	C₂²×C₆₇	#547	1	1	yes	characteristic
200	C₂²×C₆₇	D₄×Q₈	1	1	yes	characteristic
201	C₂×D₆₇	—	2	4	no	—
202	C₂×D₆₇	—	8	2	no	—
203	C₄×C₆₇	—	8	1	no	—
204	C₄×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
205	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₆₇	D₄²	1	1	yes	characteristic
207	C₄×C₆₇	#554	1	1	yes	characteristic
208	Dic₆₇	—	2	2	no	—
209	Dic₆₇	—	2	4	no	—
210	Dic₆₇	—	4	1	no	—
211	Dic₆₇	—	8	1	no	—
212	#22694	—	67	1	no	maximal, Sylow
213	C₂×C₆₇	—	2	1	no	—
214	C₂×C₆₇	—	2	1	no	—
215	C₂×C₆₇	—	2	1	no	—
216	C₂×C₆₇	D₄×C₄⋊C₄	1	1	yes	characteristic
217	D₆₇	—	4	4	no	—
218	#2957	—	67	1	no	—
219	#2957	—	67	1	no	—
220	C₂×#443	—	67	1	no	—
221	#2916	—	67	2	no	—
222	#1953	—	67	1	no	—
223	#1953	D₆₇	1	1	yes	characteristic, complemented
224	#1861	—	67	2	no	—
225	#1861	—	67	2	no	—
226	#1848	—	67	1	no	—
227	#1814	—	67	2	no	—
228	#1772	—	67	1	no	—
229	C₆₇	#22694	1	1	yes	characteristic, complemented, Sylow
230	C₂×#135	—	67	1	no	—
231	#568	—	67	2	no	—
232	#568	—	67	2	no	—
233	C₂×#131	—	67	2	no	—
234	#444	—	134	2	no	—
235	#444	—	134	2	no	—
236	#443	—	67	2	no	—
237	#443	—	67	2	no	—
238	#443	—	67	2	no	—
239	#443	—	67	2	no	—
240	#443	—	134	2	no	—
241	#443	—	134	2	no	—
242	#430	—	67	2	no	—
243	#430	—	134	4	no	—
244	#430	C₂×D₆₇	1	2	yes	—
245	C₂×#108	—	67	1	no	—
246	C₂×#108	—	67	2	no	—
247	C₂×#108	—	67	1	no	—
248	C₂×#108	—	134	4	no	—
249	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
250	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
251	#427	—	67	1	no	—
252	#423	—	67	2	no	—
253	#421	—	67	2	no	—
254	#421	—	67	2	no	—
255	C₂×#104	—	67	2	no	—
256	#405	—	67	1	no	—
257	#405	C₂×D₆₇	1	1	yes	characteristic
258	C₂×C₄×C₈	—	67	1	no	—
259	#344	—	67	2	no	—
260	#344	C₂×D₆₇	1	2	yes	—
261	#339	—	67	1	no	—
262	#339	—	67	1	no	—
263	C₂×#41	—	67	2	no	—
264	#135	—	67	2	no	—
265	#135	—	67	2	no	—
266	#135	—	67	2	no	—
267	#135	—	67	2	no	—
268	C₂×Q₁₆	—	67	1	no	—
269	C₂×SD₁₆	—	67	2	no	—
270	C₂×D₈	—	67	1	no	—
271	#131	—	268	2	no	—
272	#131	—	268	2	no	—
273	#131	—	67	4	no	—
274	#131	—	67	4	no	—
275	#131	—	134	4	no	—
276	#131	—	134	4	no	—
277	#131	—	134	2	no	—
278	#131	—	134	2	no	—
279	C₂×M₁₆	—	67	1	no	—
280	C₂×M₁₆	—	67	2	no	—
281	C₂×M₁₆	—	134	2	no	—
282	C₂×M₁₆	—	134	4	no	—
283	C₂×M₁₆	—	134	4	no	—
284	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
285	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
286	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
287	C₂²×C₈	—	67	1	no	—
288	C₂²×C₈	—	134	2	no	—
289	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
290	#117	—	67	1	no	—
291	#117	C₂²×D₆₇	1	1	yes	characteristic
292	C₂×C₄²	—	67	1	no	—
293	#108	—	2	4	no	—
294	#108	—	2	1	no	—
295	#108	—	2	1	no	—
296	#108	—	67	2	no	—
297	#108	—	67	2	no	—
298	#108	—	134	4	no	—
299	#108	—	134	2	no	—
300	#108	—	134	2	no	—
301	#108	—	134	1	no	—
302	#108	—	134	1	no	—
303	#108	C₄×D₆₇	1	2	yes	—
304	#108	C₄×D₆₇	1	2	yes	—
305	#107	—	134	1	no	—
306	#106	—	134	1	no	—
307	C₄⋊C₈	—	268	2	no	—
308	#104	—	67	4	no	—
309	#104	—	67	4	no	—
310	#104	—	134	4	no	—
311	#104	—	134	4	no	—
312	#97	—	2	1	no	—
313	#97	—	134	1	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	—	67	1	no	—
316	C₄×C₈	—	67	1	no	—
317	C₄×C₈	—	67	1	no	—
318	C₄×C₈	—	67	1	no	—
319	C₄×C₈	—	134	1	no	—
320	#41	—	67	4	no	—
321	#41	—	67	4	no	—
322	#41	—	134	2	no	—
323	#41	—	134	2	no	—
324	C₂×Q₈	—	67	2	no	—
325	C₂×D₄	—	67	2	no	—
326	C₂×D₄	—	134	2	no	—
327	C₂²×C₄	—	134	1	no	—
328	C₂²×C₄	—	134	2	no	—
329	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
330	Q₁₆	—	67	2	no	—
331	Q₁₆	—	67	2	no	—
332	SD₁₆	—	67	4	no	—
333	SD₁₆	—	67	4	no	—
334	D₈	—	67	2	no	—
335	D₈	—	67	2	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	1	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	268	4	no	—
341	M₁₆	—	268	4	no	—
342	M₁₆	—	67	2	no	—
343	M₁₆	—	134	4	no	—
344	M₁₆	—	134	4	no	—
345	M₁₆	—	134	2	no	—
346	M₁₆	—	134	2	no	—
347	M₁₆	—	134	1	no	—
348	M₁₆	C₂×C₄×D₆₇	1	4	yes	—
349	M₁₆	D₄×D₆₇	1	2	yes	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	268	4	no	—
354	C₂×C₈	—	268	4	no	—
355	C₂×C₈	—	67	1	no	—
356	C₂×C₈	—	67	1	no	—
357	C₂×C₈	—	67	1	no	—
358	C₂×C₈	—	67	1	no	—
359	C₂×C₈	—	67	1	no	—
360	C₂×C₈	—	67	1	no	—
361	C₂×C₈	—	134	4	no	—
362	C₂×C₈	—	134	4	no	—
363	C₂×C₈	—	134	2	no	—
364	C₂×C₈	—	134	1	no	—
365	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
367	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
368	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
369	C₂×C₈	Q₈×D₆₇	1	1	yes	characteristic
370	C₂×C₈	Q₈×D₆₇	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	134	1	no	—
373	C₂²⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	134	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	67	1	no	—
377	C₄²	—	67	1	no	—
378	C₄²	—	134	1	no	—
379	C₄²	—	134	1	no	—
380	C₂³	—	134	2	no	—
381	C₂³	#14524091	1	1	yes	characteristic
382	Q₈	—	67	4	no	—
383	Q₈	—	134	2	no	—
384	D₄	—	67	4	no	—
385	D₄	—	134	4	no	—
386	D₄	—	134	4	no	—
387	D₄	—	134	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	268	2	no	—
390	C₂×C₄	—	268	1	no	—
391	C₂×C₄	—	134	1	no	—
392	C₂×C₄	—	134	2	no	—
393	C₂×C₄	—	134	1	no	—
394	C₂×C₄	—	134	4	no	—
395	C₂×C₄	—	134	4	no	—
396	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
397	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
398	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
399	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
400	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
401	C₂×C₄	#14524089	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	2	4	no	—
404	C₈	—	4	2	no	—
405	C₈	—	268	2	no	—
406	C₈	—	67	1	no	—
407	C₈	—	67	1	no	—
408	C₈	—	67	1	no	—
409	C₈	—	67	1	no	—
410	C₈	—	134	2	no	—
411	C₈	C₄⋊C₄×D₆₇	1	1	yes	characteristic
412	C₈	C₄⋊C₄×D₆₇	1	1	yes	characteristic
413	C₈	C₄⋊C₄×D₆₇	1	1	yes	characteristic
414	C₈	C₄⋊C₄×D₆₇	1	1	yes	characteristic
415	C₂²	—	4	1	no	—
416	C₂²	—	536	2	no	—
417	C₂²	—	134	4	no	—
418	C₂²	#16863878	1	1	yes	characteristic
419	C₂²	#16864048	1	1	yes	characteristic
420	C₂²	#16864061	1	1	yes	characteristic
421	C₄	—	8	1	no	—
422	C₄	—	268	1	no	—
423	C₄	—	536	1	no	—
424	C₄	—	134	2	no	—
425	C₄	—	134	4	no	—
426	C₄	C₂×C₄⋊C₄×D₆₇	1	1	yes	characteristic
427	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
428	C₄	#16864030	1	1	yes	characteristic
429	C₄	#16864102	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	268	4	no	—
434	C₂	#22563110	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16864030
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1953	C₂
socle	C₂×C₆₇	D₄×C₄⋊C₄
prime radical	C₂×#14524065	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1953	D₆₇
hypocenter	C₆₇	#22694
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1953

Complements

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

N	H ≅ G/N	type
4. #22568819	C₂	semidirect
5. #22561000	C₂	semidirect
6. #22560452	C₂	semidirect
7. #22560446	C₂	semidirect
8. #22560379	C₂	semidirect
9. #22560262	C₂	semidirect
10. #22560089	C₂	semidirect
11. C₆₇×#1953	C₂	semidirect
20. #16863512	C₄	semidirect
21. #16863512	C₄	semidirect
22. #16863512	C₄	semidirect
23. #16863512	C₄	semidirect
223. #1953	D₆₇	semidirect
229. C₆₇	#22694	semidirect

Maximal subgroups

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

subgroup	index
#22569127	2
#22569125	2
C₂×#16863512	2
#22568819	2
#22561000	2
#22560452	2
#22560446	2
#22560379	2
#22560262	2
#22560089	2
C₆₇×#1953	2
#22694	67