Subgroups — #1690×D₆₇ #30838433

Order 17152.

682 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#494×D₆₇	C₂	1	1	yes	maximal, characteristic
2	#475×D₆₇	C₂	1	2	yes	maximal
3	#446×D₆₇	C₂	1	1	yes	maximal, characteristic
4	#22559704	C₂	1	1	yes	maximal, characteristic, complemented
5	#22559703	C₂	1	1	yes	maximal, characteristic, complemented
6	#22559702	C₂	1	2	yes	maximal, complemented
7	#22559701	C₂	1	2	yes	maximal, complemented
8	#22559700	C₂	1	1	yes	maximal, characteristic, complemented
9	#334×D₆₇	C₂	1	1	yes	maximal, characteristic
10	#332×D₆₇	C₂	1	2	yes	maximal
11	C₆₇×#1690	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₆₇	—	2	1	no	—
13	C₂×Q₁₆×D₆₇	—	2	1	no	—
14	C₄⋊Q₈×D₆₇	C₂²	1	2	yes	—
15	C₄×Q₈×D₆₇	C₂²	1	1	yes	characteristic
16	#16863776	C₂²	1	1	yes	characteristic
17	#16863775	C₂²	1	2	yes	—
18	#16863774	—	2	1	no	—
19	#16863774	—	2	1	no	—
20	#16863682	C₂²	1	2	yes	—
21	#16863681	C₂²	1	2	yes	—
22	#16863680	—	2	2	no	—
23	#16863679	—	2	2	no	—
24	#16863678	C₂²	1	2	yes	—
25	#16863527	C₂²	1	1	yes	characteristic
26	#16863526	C₂²	1	1	yes	characteristic
27	#16863525	—	2	1	no	—
28	#16863524	—	2	1	no	—
29	#16863523	C₂²	1	1	yes	characteristic
30	#106×D₆₇	—	2	2	no	—
31	C₄⋊C₈×D₆₇	—	2	1	no	—
32	C₄⋊C₈×D₆₇	C₂²	1	1	yes	characteristic
33	C₄⋊C₈×D₆₇	C₂²	1	2	yes	—
34	#103×D₆₇	—	2	2	no	—
35	#97×D₆₇	—	2	1	no	—
36	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
37	#16863147	C₂²	1	1	yes	characteristic
38	#16863146	C₂²	1	2	yes	—
39	#16863143	C₂²	1	2	yes	—
40	#16863142	C₂²	1	2	yes	—
41	#16863141	C₂²	1	2	yes	—
42	#494×C₆₇	C₂²	1	1	yes	characteristic
43	#475×C₆₇	C₂²	1	2	yes	—
44	#446×C₆₇	C₂²	1	1	yes	characteristic
45	#334×C₆₇	C₂²	1	1	yes	characteristic
46	#332×C₆₇	C₂²	1	2	yes	—
47	C₂×Q₈×D₆₇	—	2	2	no	—
48	C₂×Q₈×D₆₇	D₄	1	1	yes	characteristic
49	C₂×Dic₂₆₈	—	2	1	no	—
50	C₂×Dic₂₆₈	—	2	1	no	—
51	C₂×#11761618	—	2	2	no	—
52	C₂×#11761618	—	2	2	no	—
53	Q₁₆×D₆₇	—	4	4	no	—
54	Q₁₆×D₆₇	—	4	4	no	—
55	C₂×C₈×D₆₇	—	2	1	no	—
56	C₂×C₈×D₆₇	—	2	2	no	—
57	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
58	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
59	#14524043	C₂³	1	2	yes	—
60	#14524042	—	2	2	no	—
61	#14524042	—	2	2	no	—
62	#14524041	—	2	2	no	—
63	Q₈×Dic₆₇	D₄	1	1	yes	characteristic
64	C₄×Dic₁₃₄	—	2	1	no	—
65	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
66	#14524008	—	2	1	no	—
67	#14524008	D₄	1	1	yes	characteristic
68	C₄⋊C₄×D₆₇	—	2	1	no	—
69	C₄⋊C₄×D₆₇	—	2	2	no	—
70	C₄⋊C₄×D₆₇	—	2	2	no	—
71	C₄⋊C₄×D₆₇	D₄	1	1	yes	characteristic
72	C₄²×D₆₇	—	2	1	no	—
73	C₄²×D₆₇	C₂³	1	1	yes	characteristic
74	#14523975	—	2	2	no	—
75	#14523974	—	2	2	no	—
76	#14523974	—	2	2	no	—
77	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
78	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
79	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
80	Dic₆₇⋊C₈	—	2	1	no	—
81	Dic₆₇⋊C₈	—	2	1	no	—
82	Dic₆₇⋊C₈	—	2	2	no	—
83	Dic₆₇⋊C₈	—	2	1	no	—
84	#14523968	—	2	2	no	—
85	#14523967	—	2	2	no	—
86	#14523966	—	2	2	no	—
87	#14523954	—	2	1	no	—
88	#14523953	—	2	1	no	—
89	#14523953	—	2	1	no	—
90	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
91	C₈×Dic₆₇	D₄	1	1	yes	characteristic
92	C₈×Dic₆₇	D₄	1	1	yes	characteristic
93	C₂×Q₁₆×C₆₇	—	2	1	no	—
94	C₂×Q₁₆×C₆₇	—	2	1	no	—
95	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
96	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
97	#106×C₆₇	—	2	2	no	—
98	C₄⋊C₈×C₆₇	—	2	1	no	—
99	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
100	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
101	#103×C₆₇	—	2	2	no	—
102	#97×C₆₇	—	2	1	no	—
103	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
104	C₂×Dic₁₃₄	—	2	1	no	—
105	C₂×Dic₁₃₄	—	2	2	no	—
106	C₂×Dic₁₃₄	—	4	2	no	—
107	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
108	Q₈×D₆₇	—	2	4	no	—
109	Q₈×D₆₇	—	4	4	no	—
110	Q₈×D₆₇	—	4	4	no	—
111	C₂×C₄×D₆₇	—	2	1	no	—
112	C₂×C₄×D₆₇	—	2	1	no	—
113	C₂×C₄×D₆₇	—	4	2	no	—
114	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
117	Dic₂₆₈	—	4	2	no	—
118	Dic₂₆₈	—	4	2	no	—
119	#11761618	—	4	4	no	—
120	#11761618	—	4	4	no	—
121	C₂×C₆₇⋊C₈	—	2	1	no	—
122	C₂×C₆₇⋊C₈	—	2	2	no	—
123	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
124	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
125	C₈×D₆₇	—	2	2	no	—
126	C₈×D₆₇	—	4	2	no	—
127	C₈×D₆₇	—	4	4	no	—
128	C₈×D₆₇	SD₁₆	1	4	yes	—
129	C₄⋊Dic₆₇	—	2	1	no	—
130	C₄⋊Dic₆₇	—	2	2	no	—
131	C₄⋊Dic₆₇	—	2	2	no	—
132	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
133	Dic₆₇⋊C₄	—	2	1	no	—
134	Dic₆₇⋊C₄	—	2	1	no	—
135	Dic₆₇⋊C₄	—	2	1	no	—
136	Dic₆₇⋊C₄	—	4	2	no	—
137	Dic₆₇⋊C₄	—	4	2	no	—
138	C₄×Dic₆₇	—	2	1	no	—
139	C₄×Dic₆₇	—	2	1	no	—
140	C₄×Dic₆₇	—	2	1	no	—
141	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
142	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
143	C₄×Dic₆₇	#41	1	1	yes	characteristic
144	C₂×Q₈×C₆₇	—	2	2	no	—
145	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
146	Q₁₆×C₆₇	—	4	2	no	—
147	Q₁₆×C₆₇	—	4	2	no	—
148	C₂×C₈×C₆₇	—	2	2	no	—
149	C₂×C₈×C₆₇	—	2	1	no	—
150	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
152	C₄⋊C₄×C₆₇	—	2	1	no	—
153	C₄⋊C₄×C₆₇	—	2	2	no	—
154	C₄⋊C₄×C₆₇	—	2	2	no	—
155	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₆₇	—	2	1	no	—
157	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
158	C₂²×D₆₇	#121	1	1	yes	characteristic
159	Q₈×C₆₇	—	2	2	no	—
160	Q₈×C₆₇	—	4	2	no	—
161	Q₈×C₆₇	—	4	2	no	—
162	C₂×C₄×C₆₇	—	2	1	no	—
163	C₂×C₄×C₆₇	—	2	1	no	—
164	C₂×C₄×C₆₇	—	4	2	no	—
165	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
168	C₂×Dic₆₇	—	2	1	no	—
169	C₂×Dic₆₇	—	2	1	no	—
170	C₂×Dic₆₇	—	4	2	no	—
171	C₂×Dic₆₇	#121	1	1	yes	characteristic
172	C₂×Dic₆₇	#121	1	1	yes	characteristic
173	C₂×Dic₆₇	#121	1	1	yes	characteristic
174	C₄×D₆₇	—	2	2	no	—
175	C₄×D₆₇	—	4	2	no	—
176	C₄×D₆₇	—	4	2	no	—
177	C₄×D₆₇	—	8	4	no	—
178	C₄×D₆₇	C₂×SD₁₆	1	2	yes	—
179	C₄×D₆₇	AGL(1,ℤ/8)	1	2	yes	—
180	C₄×D₆₇	#137	1	4	yes	—
181	Dic₁₃₄	—	2	2	no	—
182	Dic₁₃₄	—	4	2	no	—
183	Dic₁₃₄	—	4	2	no	—
184	Dic₁₃₄	—	4	2	no	—
185	Dic₁₃₄	—	8	4	no	—
186	C₈×C₆₇	—	2	1	no	—
187	C₈×C₆₇	—	4	1	no	—
188	C₈×C₆₇	—	4	2	no	—
189	C₈×C₆₇	C₂×SD₁₆	1	2	yes	—
190	C₆₇⋊C₈	—	2	1	no	—
191	C₆₇⋊C₈	—	4	1	no	—
192	C₆₇⋊C₈	—	4	2	no	—
193	C₆₇⋊C₈	C₂×SD₁₆	1	2	yes	—
194	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
195	C₂×D₆₇	#460	1	2	yes	—
196	C₂×D₆₇	#470	1	2	yes	—
197	C₂×D₆₇	#473	1	2	yes	—
198	C₄×C₆₇	—	2	1	no	—
199	C₄×C₆₇	—	4	1	no	—
200	C₄×C₆₇	—	4	1	no	—
201	C₄×C₆₇	—	8	2	no	—
202	C₄×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
203	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₄×C₆₇	C₂×#137	1	2	yes	—
205	Dic₆₇	—	2	1	no	—
206	Dic₆₇	—	4	1	no	—
207	Dic₆₇	—	4	1	no	—
208	Dic₆₇	—	8	2	no	—
209	Dic₆₇	#460	1	2	yes	—
210	Dic₆₇	#470	1	2	yes	—
211	C₂×#1690	—	67	1	no	maximal, Sylow
212	C₂×C₆₇	C₂×#460	1	1	yes	characteristic
213	C₂×C₆₇	C₂×#470	1	1	yes	characteristic
214	C₂×C₆₇	C₂×#473	1	1	yes	characteristic
215	D₆₇	#1690	1	4	yes	direct product factor
216	C₂×#494	—	67	1	no	—
217	C₂×#475	—	67	2	no	—
218	C₂×#446	—	67	1	no	—
219	#1690	—	67	1	no	—
220	#1690	—	67	2	no	—
221	#1690	—	67	1	no	—
222	#1690	—	67	1	no	—
223	#1690	—	67	2	no	—
224	#1690	D₆₇	1	1	yes	characteristic, direct product factor
225	C₂×#334	—	67	1	no	—
226	C₂×#332	—	67	2	no	—
227	C₆₇	C₂×#1690	1	1	yes	characteristic, complemented, Sylow
228	C₂²×Q₁₆	—	134	1	no	—
229	C₂²×Q₁₆	—	134	1	no	—
230	C₂×C₄⋊Q₈	—	67	2	no	—
231	C₂×C₄×Q₈	—	67	1	no	—
232	#494	—	67	2	no	—
233	#494	—	67	1	no	—
234	#494	—	134	1	no	—
235	#494	—	134	1	no	—
236	#494	C₂×D₆₇	1	1	yes	characteristic
237	#475	—	67	2	no	—
238	#475	—	67	2	no	—
239	#475	—	67	2	no	—
240	#475	—	134	2	no	—
241	#475	—	134	2	no	—
242	#475	C₂×D₆₇	1	2	yes	—
243	#446	—	67	1	no	—
244	#446	—	67	1	no	—
245	#446	—	67	1	no	—
246	#446	—	134	1	no	—
247	#446	—	134	1	no	—
248	#446	C₂×D₆₇	1	1	yes	characteristic
249	C₂×#106	—	134	2	no	—
250	C₂×C₄⋊C₈	—	67	2	no	—
251	C₂×C₄⋊C₈	—	67	1	no	—
252	C₂×C₄⋊C₈	—	134	1	no	—
253	C₂×#103	—	134	2	no	—
254	C₂×#97	—	134	1	no	—
255	C₂×C₄×C₈	—	67	1	no	—
256	#334	—	67	2	no	—
257	#334	—	67	1	no	—
258	#334	C₂×D₆₇	1	1	yes	characteristic
259	#332	—	67	2	no	—
260	#332	—	67	2	no	—
261	#332	—	67	2	no	—
262	#332	C₂×D₆₇	1	2	yes	—
263	C₂²×Q₈	—	67	1	no	—
264	C₂²×Q₈	—	134	2	no	—
265	C₂×Q₁₆	—	2	1	no	—
266	C₂×Q₁₆	—	2	1	no	—
267	C₂×Q₁₆	—	268	4	no	—
268	C₂×Q₁₆	—	268	4	no	—
269	C₂×Q₁₆	—	134	2	no	—
270	C₂×Q₁₆	—	134	2	no	—
271	C₂×Q₁₆	—	134	1	no	—
272	C₂×Q₁₆	—	134	1	no	—
273	C₂²×C₈	—	67	1	no	—
274	C₂²×C₈	—	67	1	no	—
275	C₂²×C₈	—	134	1	no	—
276	C₂²×C₈	—	134	2	no	—
277	C₄⋊Q₈	—	67	2	no	—
278	C₄⋊Q₈	—	134	2	no	—
279	C₄⋊Q₈	—	134	2	no	—
280	C₄⋊Q₈	—	134	2	no	—
281	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	—
282	C₄×Q₈	—	67	1	no	—
283	C₄×Q₈	—	67	1	no	—
284	C₄×Q₈	—	67	1	no	—
285	C₄×Q₈	—	134	1	no	—
286	C₄×Q₈	—	134	1	no	—
287	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
288	C₂×C₄⋊C₄	—	67	1	no	—
289	C₂×C₄⋊C₄	—	134	2	no	—
290	C₂×C₄⋊C₄	—	134	2	no	—
291	C₂×C₄⋊C₄	—	134	1	no	—
292	C₂×C₄²	—	67	1	no	—
293	C₂×C₄²	—	134	1	no	—
294	#106	—	2	2	no	—
295	#106	—	134	2	no	—
296	#106	—	134	2	no	—
297	#106	—	134	2	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	67	1	no	—
300	C₄⋊C₈	—	67	2	no	—
301	C₄⋊C₈	—	134	1	no	—
302	C₄⋊C₈	—	134	1	no	—
303	C₄⋊C₈	—	134	2	no	—
304	C₄⋊C₈	—	134	1	no	—
305	C₄⋊C₈	—	134	1	no	—
306	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
307	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
308	#103	—	2	2	no	—
309	#103	—	134	2	no	—
310	#103	—	134	2	no	—
311	#103	—	134	2	no	—
312	#97	—	2	1	no	—
313	#97	—	134	1	no	—
314	#97	—	134	1	no	—
315	#97	—	134	1	no	—
316	C₄×C₈	—	67	1	no	—
317	C₄×C₈	—	67	1	no	—
318	C₄×C₈	—	67	1	no	—
319	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	268	2	no	—
322	C₂×Q₈	—	268	4	no	—
323	C₂×Q₈	—	268	4	no	—
324	C₂×Q₈	—	67	1	no	—
325	C₂×Q₈	—	134	1	no	—
326	C₂×Q₈	—	134	4	no	—
327	C₂×Q₈	—	134	2	no	—
328	C₂×Q₈	D₄×D₆₇	1	1	yes	characteristic
329	C₂²×C₄	—	268	2	no	—
330	C₂²×C₄	—	67	1	no	—
331	C₂²×C₄	—	67	1	no	—
332	C₂²×C₄	—	67	1	no	—
333	C₂²×C₄	—	134	1	no	—
334	C₂²×C₄	—	134	1	no	—
335	Q₁₆	—	4	2	no	—
336	Q₁₆	—	4	2	no	—
337	Q₁₆	—	268	2	no	—
338	Q₁₆	—	268	4	no	—
339	Q₁₆	—	268	4	no	—
340	Q₁₆	—	268	2	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	268	2	no	—
344	C₂×C₈	—	268	4	no	—
345	C₂×C₈	—	67	1	no	—
346	C₂×C₈	—	67	4	no	—
347	C₂×C₈	—	67	1	no	—
348	C₂×C₈	—	134	2	no	—
349	C₂×C₈	—	134	1	no	—
350	C₂×C₈	—	134	2	no	—
351	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
352	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	268	2	no	—
357	C₄⋊C₄	—	268	2	no	—
358	C₄⋊C₄	—	67	1	no	—
359	C₄⋊C₄	—	134	1	no	—
360	C₄⋊C₄	—	134	1	no	—
361	C₄⋊C₄	—	134	1	no	—
362	C₄⋊C₄	—	134	2	no	—
363	C₄⋊C₄	—	134	2	no	—
364	C₄⋊C₄	—	134	1	no	—
365	C₄⋊C₄	D₄×D₆₇	1	1	yes	characteristic
366	C₄²	—	2	1	no	—
367	C₄²	—	67	1	no	—
368	C₄²	—	67	1	no	—
369	C₄²	—	67	1	no	—
370	C₄²	—	134	1	no	—
371	C₄²	—	134	1	no	—
372	C₄²	—	134	1	no	—
373	C₄²	C₂³×D₆₇	1	1	yes	characteristic
374	C₂³	—	67	1	no	—
375	Q₈	—	2	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	268	2	no	—
379	Q₈	—	268	2	no	—
380	Q₈	—	268	2	no	—
381	Q₈	—	536	4	no	—
382	Q₈	—	134	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	268	2	no	—
387	C₂×C₄	—	268	2	no	—
388	C₂×C₄	—	268	2	no	—
389	C₂×C₄	—	536	4	no	—
390	C₂×C₄	—	67	1	no	—
391	C₂×C₄	—	67	1	no	—
392	C₂×C₄	—	67	2	no	—
393	C₂×C₄	—	67	2	no	—
394	C₂×C₄	—	67	4	no	—
395	C₂×C₄	—	67	1	no	—
396	C₂×C₄	—	134	2	no	—
397	C₂×C₄	—	134	1	no	—
398	C₂×C₄	—	134	1	no	—
399	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
400	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
401	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	4	1	no	—
404	C₈	—	4	2	no	—
405	C₈	—	268	1	no	—
406	C₈	—	268	2	no	—
407	C₈	—	67	2	no	—
408	C₈	—	134	1	no	—
409	C₈	SD₁₆×D₆₇	1	2	yes	—
410	C₂²	—	67	2	no	—
411	C₂²	—	67	2	no	—
412	C₂²	—	67	2	no	—
413	C₂²	#121×D₆₇	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	8	2	no	—
418	C₄	—	268	1	no	—
419	C₄	—	268	1	no	—
420	C₄	—	536	2	no	—
421	C₄	—	67	2	no	—
422	C₄	—	67	2	no	—
423	C₄	—	134	1	no	—
424	C₄	C₂×SD₁₆×D₆₇	1	1	yes	characteristic
425	C₄	AGL(1,ℤ/8)×D₆₇	1	1	yes	characteristic
426	C₄	#137×D₆₇	1	2	yes	—
427	C₂	—	67	4	no	—
428	C₂	#460×D₆₇	1	1	yes	characteristic
429	C₂	#470×D₆₇	1	1	yes	characteristic
430	C₂	#473×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₆₇
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#1690	C₂
socle	C₂²×C₆₇	C₂×#121
prime radical	C₂²×D₆₇	#121
hypercenter	#1690	D₆₇
hypocenter	C₆₇	C₂×#1690
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1690

Complements

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

N	H ≅ G/N	type
4. #22559704	C₂	semidirect
5. #22559703	C₂	semidirect
6. #22559702	C₂	semidirect
7. #22559701	C₂	semidirect
8. #22559700	C₂	semidirect
11. C₆₇×#1690	C₂	semidirect
215. D₆₇	#1690	direct (N × H)
224. #1690	D₆₇	direct (N × H)
227. C₆₇	C₂×#1690	semidirect

Maximal subgroups

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

subgroup	index
#494×D₆₇	2
#475×D₆₇	2
#446×D₆₇	2
#22559704	2
#22559703	2
#22559702	2
#22559701	2
#22559700	2
#334×D₆₇	2
#332×D₆₇	2
C₆₇×#1690	2
C₂×#1690	67

Subgroups — #1690×D67 #30838433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1690×D₆₇ #30838433