Subgroups — #30869745

Order 17152.

772 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	#22570698	C₂	1	1	yes	maximal, characteristic
2	#22569127	C₂	1	1	yes	maximal, characteristic
3	#22561125	C₂	1	1	yes	maximal, characteristic, complemented
4	#22561105	C₂	1	1	yes	maximal, characteristic
5	#22560746	C₂	1	2	yes	maximal, complemented
6	#22560728	C₂	1	2	yes	maximal, complemented
7	#22560703	C₂	1	2	yes	maximal, complemented
8	#22560679	C₂	1	2	yes	maximal, complemented
9	#22560332	C₂	1	1	yes	maximal, characteristic, complemented
10	#22559964	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2950	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524074	C₂²	1	2	yes	—
13	C₂×#14524065	C₂²	1	1	yes	characteristic
14	#16864162	C₂²	1	2	yes	—
15	#16863970	C₂²	1	2	yes	—
16	#16863789	C₄	1	4	yes	complemented
17	#16863781	C₄	1	2	yes	complemented
18	#16863774	C₄	1	2	yes	complemented
19	#16863519	—	2	2	no	—
20	#16863514	—	2	2	no	—
21	C₂×#14523979	C₂²	1	1	yes	characteristic
22	#16863414	C₂²	1	2	yes	—
23	#16863414	C₂²	1	2	yes	—
24	#16863405	C₂²	1	2	yes	—
25	C₂×#14523962	C₂²	1	2	yes	—
26	#16863369	C₂²	1	2	yes	—
27	#16863351	C₂²	1	1	yes	characteristic
28	#16863351	C₂²	1	1	yes	characteristic
29	#16863166	C₂²	1	2	yes	—
30	C₆₇⋊#338	C₂²	1	1	yes	characteristic
31	#16863153	C₂²	1	1	yes	characteristic
32	#16863152	C₂²	1	2	yes	—
33	#16863152	C₂²	1	1	yes	characteristic
34	#16863152	C₂²	1	1	yes	characteristic
35	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
36	#519×C₆₇	C₂²	1	2	yes	—
37	#441×C₆₇	—	2	2	no	—
38	C₄×Q₁₆×C₆₇	—	2	2	no	—
39	#427×C₆₇	C₂²	1	1	yes	characteristic
40	#419×C₆₇	C₂²	1	2	yes	—
41	#405×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#11761628	C₂³	1	2	yes	—
43	#14524074	—	4	2	no	—
44	#14524074	—	4	2	no	—
45	#14524065	—	2	1	no	—
46	#14524065	—	2	1	no	—
47	#14524065	—	2	1	no	—
48	#14524065	—	2	1	no	—
49	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic
50	C₂×#11761618	C₂×C₄	1	4	yes	—
51	C₂×#11761617	C₂×C₄	1	2	yes	—
52	C₂×#11761615	C₂×C₄	1	4	yes	—
53	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic
54	#14524051	—	4	2	no	—
55	#14524049	—	2	4	no	—
56	C₂×#11761612	C₂³	1	1	yes	characteristic
57	C₂×#11761612	C₂³	1	2	yes	—
58	C₂×#11761612	C₂³	1	1	yes	characteristic
59	M₁₆×D₆₇	—	4	2	no	—
60	#14524041	C₂×C₄	1	4	yes	—
61	#14524032	C₂×C₄	1	4	yes	—
62	#14524026	—	4	2	no	—
63	#14524019	—	4	2	no	—
64	#14524002	C₂³	1	1	yes	characteristic
65	#14524002	C₂³	1	1	yes	characteristic
66	#14523979	—	2	1	no	—
67	#14523979	—	2	1	no	—
68	#14523971	—	2	4	no	—
69	#14523971	—	4	2	no	—
70	#14523967	—	4	2	no	—
71	#14523962	—	4	2	no	—
72	#14523957	—	4	2	no	—
73	#14523953	—	2	1	no	—
74	#14523953	C₂×C₄	1	2	yes	—
75	C₈×Dic₆₇	—	2	1	no	—
76	C₈×Dic₆₇	C₂×C₄	1	2	yes	—
77	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
78	C₂×Q₁₆×C₆₇	—	2	1	no	—
79	C₂×Q₁₆×C₆₇	—	2	1	no	—
80	C₂×Q₁₆×C₆₇	—	2	1	no	—
81	C₂×Q₁₆×C₆₇	—	2	1	no	—
82	C₂×Q₁₆×C₆₇	C₂×C₄	1	2	yes	—
83	C₂×Q₁₆×C₆₇	C₂×C₄	1	2	yes	—
84	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
86	C₄×Q₈×C₆₇	—	2	4	no	—
87	C₄×Q₈×C₆₇	—	4	2	no	—
88	#117×C₆₇	—	4	2	no	—
89	#117×C₆₇	C₂³	1	2	yes	—
90	#117×C₆₇	C₂³	1	1	yes	characteristic
91	#107×C₆₇	—	2	1	no	—
92	#106×C₆₇	—	2	1	no	—
93	#103×C₆₇	—	2	4	no	—
94	#97×C₆₇	D₄	1	2	yes	—
95	C₄×C₈×C₆₇	D₄	1	2	yes	—
96	#11761628	—	2	2	no	—
97	#11761628	—	2	2	no	—
98	#11761628	—	2	2	no	—
99	#11761628	—	2	2	no	—
100	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
101	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
102	C₂×C₂²⋊D₆₇	—	2	2	no	—
103	C₂×C₄×D₆₇	—	2	2	no	—
104	Dic₂₆₈	—	2	1	no	—
105	Dic₂₆₈	—	2	1	no	—
106	#11761618	—	4	4	no	—
107	#11761617	—	2	2	no	—
108	#11761617	—	2	2	no	—
109	#11761615	—	4	4	no	—
110	D₅₃₆	—	2	1	no	—
111	D₅₃₆	—	2	1	no	—
112	#11761612	—	2	1	no	—
113	#11761612	—	2	1	no	—
114	#11761612	—	2	2	no	—
115	#11761612	—	2	1	no	—
116	#11761612	—	2	2	no	—
117	#11761612	—	2	1	no	—
118	#11761611	—	4	4	no	—
119	C₂×C₆₇⋊C₈	—	2	1	no	—
120	C₂×C₆₇⋊C₈	—	2	2	no	—
121	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
122	C₈×D₆₇	—	4	4	no	—
123	C₄⋊Dic₆₇	—	2	1	no	—
124	C₄⋊Dic₆₇	—	2	1	no	—
125	Dic₆₇⋊C₄	—	4	4	no	—
126	C₂²⋊Dic₆₇	—	2	1	no	—
127	C₂²⋊Dic₆₇	—	2	1	no	—
128	(C₂×D₆₇)⋊C₄	—	4	4	no	—
129	C₄×Dic₆₇	—	2	1	no	—
130	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
131	C₂×Q₈×C₆₇	—	2	2	no	—
132	C₂×Q₈×C₆₇	—	2	2	no	—
133	C₂×Q₈×C₆₇	—	2	2	no	—
134	C₂×Q₈×C₆₇	—	2	2	no	—
135	C₂×Q₈×C₆₇	—	2	2	no	—
136	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₆₇	—	2	2	no	—
138	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
139	Q₁₆×C₆₇	—	2	2	no	—
140	Q₁₆×C₆₇	—	2	2	no	—
141	Q₁₆×C₆₇	—	2	2	no	—
142	Q₁₆×C₆₇	—	2	2	no	—
143	M₁₆×C₆₇	—	2	1	no	—
144	M₁₆×C₆₇	—	2	1	no	—
145	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
151	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
152	C₄⋊C₄×C₆₇	—	2	1	no	—
153	C₄⋊C₄×C₆₇	—	2	2	no	—
154	C₄⋊C₄×C₆₇	—	4	4	no	—
155	C₂²⋊C₄×C₆₇	—	2	1	no	—
156	C₂²⋊C₄×C₆₇	—	2	2	no	—
157	C₄²×C₆₇	—	2	2	no	—
158	C₄²×C₆₇	—	4	4	no	—
159	C₄²×C₆₇	C₂×D₄	1	2	yes	—
160	C₂³×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₆₇	—	2	2	no	—
162	Q₈×C₆₇	—	2	4	no	—
163	Q₈×C₆₇	—	2	4	no	—
164	Q₈×C₆₇	—	4	2	no	—
165	Q₈×C₆₇	—	4	2	no	—
166	C₂×C₄×C₆₇	—	2	4	no	—
167	C₂×C₄×C₆₇	—	2	2	no	—
168	C₂×C₄×C₆₇	—	4	2	no	—
169	C₂×C₄×C₆₇	—	4	2	no	—
170	C₂×C₄×C₆₇	—	4	2	no	—
171	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂²⋊D₆₇	—	4	2	no	—
178	C₂²⋊D₆₇	—	4	2	no	—
179	C₂×Dic₆₇	—	2	2	no	—
180	C₂×Dic₆₇	—	2	2	no	—
181	C₂×Dic₆₇	—	4	1	no	—
182	D₂₆₈	—	2	2	no	—
183	D₂₆₈	—	2	2	no	—
184	C₄×D₆₇	—	4	2	no	—
185	C₄×D₆₇	—	4	2	no	—
186	Dic₁₃₄	—	2	2	no	—
187	Dic₁₃₄	—	2	2	no	—
188	C₈×C₆₇	—	2	2	no	—
189	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
190	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
191	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
192	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
193	C₆₇⋊C₈	—	2	2	no	—
194	C₆₇⋊C₈	—	4	2	no	—
195	C₆₇⋊C₈	—	4	1	no	—
196	C₂²×C₆₇	—	4	1	no	—
197	C₂²×C₆₇	#518	1	1	yes	characteristic
198	C₂²×C₆₇	#535	1	1	yes	characteristic
199	C₂²×C₆₇	#540	1	1	yes	characteristic
200	C₂×D₆₇	—	4	2	no	—
201	C₂×D₆₇	—	8	2	no	—
202	C₄×C₆₇	—	4	2	no	—
203	C₄×C₆₇	—	4	4	no	—
204	C₄×C₆₇	—	8	2	no	—
205	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₆₇	#518	1	1	yes	characteristic
207	C₄×C₆₇	#535	1	1	yes	characteristic
208	C₄×C₆₇	#540	1	1	yes	characteristic
209	Dic₆₇	—	4	2	no	—
210	Dic₆₇	—	4	2	no	—
211	Dic₆₇	—	8	1	no	—
212	#22285	—	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	#2328	1	1	yes	characteristic
217	D₆₇	—	8	2	no	—
218	#3156	—	67	1	no	—
219	#2957	—	67	1	no	—
220	#2950	D₆₇	1	1	yes	characteristic, complemented
221	#1979	—	67	1	no	—
222	#1976	—	67	1	no	—
223	#1912	—	67	2	no	—
224	#1909	—	67	2	no	—
225	#1905	—	67	2	no	—
226	#1902	—	67	2	no	—
227	#1833	—	67	1	no	—
228	#1747	—	67	1	no	—
229	C₆₇	#22285	1	1	yes	characteristic, complemented, Sylow
230	C₂×#137	—	67	2	no	—
231	C₂×#135	—	67	1	no	—
232	C₂²×Q₁₆	C₂×D₆₇	1	1	yes	characteristic
233	#568	—	67	2	no	—
234	#536	—	67	2	no	—
235	#519	C₂×D₆₇	1	2	yes	—
236	#497	—	67	4	no	—
237	#495	—	67	2	no	—
238	#494	—	67	2	no	—
239	#444	—	134	2	no	—
240	#443	—	134	2	no	—
241	#441	—	2	2	no	—
242	C₄×Q₁₆	—	2	2	no	—
243	C₂×#108	—	67	1	no	—
244	#427	C₂×D₆₇	1	1	yes	characteristic
245	#421	—	67	2	no	—
246	#421	—	67	2	no	—
247	#419	—	67	2	no	—
248	#419	C₂×D₆₇	1	2	yes	—
249	C₂×#101	—	67	2	no	—
250	#410	—	67	2	no	—
251	#405	—	67	1	no	—
252	#405	—	67	1	no	—
253	#405	C₂×D₆₇	1	1	yes	characteristic
254	#344	—	67	2	no	—
255	#338	—	67	1	no	—
256	H(3,ℤ/4)	—	67	1	no	—
257	H(3,ℤ/4)	—	67	2	no	—
258	H(3,ℤ/4)	—	67	1	no	—
259	H(3,ℤ/4)	—	67	1	no	—
260	C₂×#41	—	67	2	no	—
261	C₂²×Q₈	C₂²×D₆₇	1	2	yes	—
262	#137	—	268	2	no	—
263	#137	—	268	2	no	—
264	#135	—	134	1	no	—
265	#135	—	134	1	no	—
266	#135	—	134	1	no	—
267	#135	—	134	1	no	—
268	C₂×Q₁₆	—	2	1	no	—
269	C₂×Q₁₆	—	2	1	no	—
270	C₂×Q₁₆	—	2	1	no	—
271	C₂×Q₁₆	—	2	1	no	—
272	C₂×Q₁₆	—	67	4	no	—
273	C₂×Q₁₆	—	67	1	no	—
274	C₂×Q₁₆	C₄×D₆₇	1	2	yes	—
275	C₂×Q₁₆	C₄×D₆₇	1	2	yes	—
276	C₂×SD₁₆	—	67	4	no	—
277	C₂×SD₁₆	—	67	2	no	—
278	C₂×D₈	—	67	1	no	—
279	#131	—	268	2	no	—
280	#131	—	134	4	no	—
281	C₂×M₁₆	—	268	2	no	—
282	C₂×M₁₆	—	67	1	no	—
283	C₂×M₁₆	—	67	2	no	—
284	C₂×M₁₆	—	67	1	no	—
285	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
286	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
287	C₄⋊Q₈	—	67	4	no	—
288	#124	—	67	4	no	—
289	#123	—	268	2	no	—
290	C₂²⋊Q₈	—	268	2	no	—
291	C₄×Q₈	—	2	4	no	—
292	C₄×Q₈	—	4	2	no	—
293	#117	—	4	2	no	—
294	#117	—	67	1	no	—
295	#117	—	67	1	no	—
296	#117	C₂²×D₆₇	1	2	yes	—
297	#117	C₂²×D₆₇	1	1	yes	characteristic
298	#108	—	134	1	no	—
299	#108	—	134	1	no	—
300	#107	—	2	1	no	—
301	#106	—	2	1	no	—
302	#104	—	268	2	no	—
303	#104	—	134	4	no	—
304	#103	—	2	4	no	—
305	#103	—	268	2	no	—
306	#101	—	268	2	no	—
307	#99	—	268	2	no	—
308	#97	—	67	2	no	—
309	#97	—	134	1	no	—
310	#97	C₂²⋊D₆₇	1	2	yes	—
311	C₄×C₈	—	67	2	no	—
312	C₄×C₈	—	134	1	no	—
313	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
314	#41	—	134	2	no	—
315	#41	—	134	2	no	—
316	#41	—	134	2	no	—
317	#41	—	134	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	67	2	no	—
324	C₂×Q₈	C₂×C₄×D₆₇	1	4	yes	—
325	C₂×D₄	—	67	2	no	—
326	C₂×D₄	—	134	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	134	2	no	—
329	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
330	Q₁₆	—	2	2	no	—
331	Q₁₆	—	2	2	no	—
332	Q₁₆	—	2	2	no	—
333	Q₁₆	—	2	2	no	—
334	Q₁₆	—	268	4	no	—
335	Q₁₆	—	134	1	no	—
336	Q₁₆	—	134	1	no	—
337	SD₁₆	—	268	4	no	—
338	SD₁₆	—	134	2	no	—
339	SD₁₆	—	134	2	no	—
340	D₈	—	134	1	no	—
341	D₈	—	134	1	no	—
342	M₁₆	—	2	1	no	—
343	M₁₆	—	2	1	no	—
344	M₁₆	—	268	4	no	—
345	M₁₆	—	134	2	no	—
346	M₁₆	—	134	1	no	—
347	M₁₆	—	134	1	no	—
348	M₁₆	—	134	2	no	—
349	M₁₆	—	134	1	no	—
350	M₁₆	—	134	1	no	—
351	C₂×C₈	—	268	4	no	—
352	C₂×C₈	—	67	2	no	—
353	C₂×C₈	—	134	1	no	—
354	C₂×C₈	—	134	2	no	—
355	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
356	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
357	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
358	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
359	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
360	C₂×C₈	#11761628	1	1	yes	characteristic
361	C₂×C₈	#11761628	1	1	yes	characteristic
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₄⋊C₄	—	268	4	no	—
366	C₄⋊C₄	—	134	1	no	—
367	C₄⋊C₄	—	134	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	268	4	no	—
371	C₂²⋊C₄	—	134	1	no	—
372	C₂²⋊C₄	—	134	1	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	4	4	no	—
375	C₄²	—	67	2	no	—
376	C₄²	—	134	1	no	—
377	C₄²	C₂×C₂²⋊D₆₇	1	2	yes	—
378	C₂³	—	134	2	no	—
379	C₂³	#14524088	1	1	yes	characteristic
380	Q₈	—	2	4	no	—
381	Q₈	—	2	4	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	134	2	no	—
385	Q₈	—	134	2	no	—
386	D₄	—	268	2	no	—
387	D₄	—	268	2	no	—
388	D₄	—	134	2	no	—
389	D₄	—	134	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	268	2	no	—
396	C₂×C₄	—	268	2	no	—
397	C₂×C₄	—	268	1	no	—
398	C₂×C₄	—	134	2	no	—
399	C₂×C₄	—	134	2	no	—
400	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
402	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
403	C₂×C₄	#14524088	1	1	yes	characteristic
404	C₂×C₄	#14524089	1	1	yes	characteristic
405	C₂×C₄	#14524089	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	268	2	no	—
408	C₈	—	268	1	no	—
409	C₈	—	134	2	no	—
410	C₈	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
411	C₈	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
412	C₈	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
413	C₈	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
414	C₂²	—	4	1	no	—
415	C₂²	—	268	2	no	—
416	C₂²	—	536	2	no	—
417	C₂²	#16863868	1	1	yes	characteristic
418	C₂²	#16863963	1	1	yes	characteristic
419	C₂²	#16863997	1	1	yes	characteristic
420	C₄	—	4	2	no	—
421	C₄	—	4	4	no	—
422	C₄	—	8	2	no	—
423	C₄	—	268	2	no	—
424	C₄	—	268	2	no	—
425	C₄	—	536	1	no	—
426	C₄	C₂×C₄×C₂²⋊D₆₇	1	1	yes	characteristic
427	C₄	#16863868	1	1	yes	characteristic
428	C₄	#16863960	1	1	yes	characteristic
429	C₄	#16863997	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	536	2	no	—
434	C₂	#22562931	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22562931
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#2950	C₂
socle	C₂×C₆₇	#2328
prime radical	C₂×#14524065	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#2950	D₆₇
hypocenter	C₆₇	#22285
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2950

Complements

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

N	H ≅ G/N	type
3. #22561125	C₂	semidirect
5. #22560746	C₂	semidirect
6. #22560728	C₂	semidirect
7. #22560703	C₂	semidirect
8. #22560679	C₂	semidirect
9. #22560332	C₂	semidirect
10. #22559964	C₂	semidirect
11. C₆₇×#2950	C₂	semidirect
16. #16863789	C₄	semidirect
17. #16863781	C₄	semidirect
18. #16863774	C₄	semidirect
220. #2950	D₆₇	semidirect
229. C₆₇	#22285	semidirect

Maximal subgroups

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

subgroup	index
#22570698	2
#22569127	2
#22561125	2
#22561105	2
#22560746	2
#22560728	2
#22560703	2
#22560679	2
#22560332	2
#22559964	2
C₆₇×#2950	2
#22285	67