Subgroups — C₆₇×#19101 #30698352

Order 17152.

802 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3100	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1669	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1667	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1665	C₂	1	4	yes	maximal, complemented
7	C₆₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1540	C₂	1	2	yes	maximal, complemented
9	C₂×#135×C₆₇	—	2	1	no	—
10	C₂×#135×C₆₇	—	2	1	no	—
11	C₂³×C₈×C₆₇	—	2	1	no	—
12	#532×C₆₇	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
14	#495×C₆₇	—	2	1	no	—
15	#495×C₆₇	—	2	1	no	—
16	#494×C₆₇	C₂²	1	1	yes	characteristic, complemented
17	#493×C₆₇	C₂²	1	1	yes	characteristic, complemented
18	#492×C₆₇	C₂²	1	2	yes	complemented
19	#480×C₆₇	—	2	2	no	—
20	#474×C₆₇	C₂²	1	4	yes	—
21	#459×C₆₇	C₂²	1	4	yes	—
22	#447×C₆₇	—	2	2	no	—
23	C₄×D₈×C₆₇	—	2	4	no	—
24	C₈×D₄×C₆₇	—	2	1	no	—
25	C₈×D₄×C₆₇	—	2	1	no	—
26	C₈×D₄×C₆₇	C₂²	1	2	yes	—
27	C₈×D₄×C₆₇	C₂²	1	2	yes	—
28	#431×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₆₇	—	2	1	no	—
31	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
32	#335×C₆₇	C₂²	1	2	yes	complemented
33	#334×C₆₇	C₂²	1	2	yes	complemented
34	#332×C₆₇	C₂²	1	4	yes	complemented
35	#331×C₆₇	C₂²	1	4	yes	complemented
36	C₂×#41×C₆₇	—	2	2	no	—
37	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₆₇	—	2	1	no	—
39	#135×C₆₇	—	4	4	no	—
40	#135×C₆₇	—	4	4	no	—
41	C₂×Q₁₆×C₆₇	—	2	1	no	—
42	C₂×Q₁₆×C₆₇	—	2	1	no	—
43	C₂×SD₁₆×C₆₇	—	2	2	no	—
44	C₂×SD₁₆×C₆₇	—	2	2	no	—
45	C₂×D₈×C₆₇	—	2	4	no	—
46	C₂×D₈×C₆₇	—	2	1	no	—
47	C₂×D₈×C₆₇	—	2	1	no	—
48	C₂²×C₈×C₆₇	—	2	1	no	—
49	C₂²×C₈×C₆₇	—	2	2	no	—
50	C₂²×C₈×C₆₇	—	2	2	no	—
51	C₂²×C₈×C₆₇	—	4	4	no	—
52	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
54	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
55	#127×C₆₇	C₂³	1	2	yes	—
56	#124×C₆₇	—	2	2	no	—
57	#121×C₆₇	—	2	2	no	—
58	#121×C₆₇	—	2	2	no	—
59	C₄×D₄×C₆₇	—	2	1	no	—
60	C₄×D₄×C₆₇	—	2	2	no	—
61	C₄×D₄×C₆₇	—	2	1	no	—
62	C₄×D₄×C₆₇	—	2	2	no	—
63	C₄×D₄×C₆₇	D₄	1	2	yes	—
64	C₄×D₄×C₆₇	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
67	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
68	#107×C₆₇	—	2	4	no	—
69	C₄⋊C₈×C₆₇	—	2	1	no	—
70	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
71	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
72	#102×C₆₇	—	2	4	no	—
73	#102×C₆₇	—	2	4	no	—
74	C₂²⋊C₈×C₆₇	—	2	2	no	—
75	C₂²⋊C₈×C₆₇	—	2	2	no	—
76	C₂²⋊C₈×C₆₇	—	2	2	no	—
77	C₄×C₈×C₆₇	—	2	2	no	—
78	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
79	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
80	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
82	C₂⁴×C₆₇	—	2	1	no	—
83	#41×C₆₇	—	4	4	no	—
84	#41×C₆₇	—	4	4	no	—
85	C₂×Q₈×C₆₇	—	2	2	no	—
86	C₂×D₄×C₆₇	—	2	4	no	—
87	C₂×D₄×C₆₇	—	2	1	no	—
88	C₂×D₄×C₆₇	—	2	2	no	—
89	C₂×D₄×C₆₇	—	2	2	no	—
90	C₂×D₄×C₆₇	—	2	2	no	—
91	C₂×D₄×C₆₇	—	4	2	no	—
92	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₆₇	—	2	1	no	—
94	C₂²×C₄×C₆₇	—	2	2	no	—
95	C₂²×C₄×C₆₇	—	2	2	no	—
96	C₂²×C₄×C₆₇	—	4	2	no	—
97	C₂²×C₄×C₆₇	—	4	2	no	—
98	C₂²×C₄×C₆₇	—	4	2	no	—
99	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
102	Q₁₆×C₆₇	—	4	2	no	—
103	Q₁₆×C₆₇	—	4	2	no	—
104	SD₁₆×C₆₇	—	4	4	no	—
105	SD₁₆×C₆₇	—	4	4	no	—
106	D₈×C₆₇	—	4	2	no	—
107	D₈×C₆₇	—	4	8	no	—
108	D₈×C₆₇	—	4	2	no	—
109	C₂×C₈×C₆₇	—	2	2	no	—
110	C₂×C₈×C₆₇	—	2	4	no	—
111	C₂×C₈×C₆₇	—	2	2	no	—
112	C₂×C₈×C₆₇	—	4	2	no	—
113	C₂×C₈×C₆₇	—	4	4	no	—
114	C₂×C₈×C₆₇	—	4	4	no	—
115	C₂×C₈×C₆₇	D₈	1	4	yes	complemented
116	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
120	C₄⋊C₄×C₆₇	—	2	1	no	—
121	C₄⋊C₄×C₆₇	—	2	2	no	—
122	C₄⋊C₄×C₆₇	—	2	2	no	—
123	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
124	C₂²⋊C₄×C₆₇	—	2	2	no	—
125	C₂²⋊C₄×C₆₇	—	2	2	no	—
126	C₂²⋊C₄×C₆₇	—	4	2	no	—
127	C₂²⋊C₄×C₆₇	—	4	2	no	—
128	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₆₇	#41	1	1	yes	characteristic
131	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
132	C₂³×C₆₇	—	2	4	no	—
133	C₂³×C₆₇	—	2	2	no	—
134	C₂³×C₆₇	—	4	2	no	—
135	C₂³×C₆₇	—	4	2	no	—
136	C₂³×C₆₇	—	4	2	no	—
137	C₂³×C₆₇	#121	1	1	yes	characteristic
138	Q₈×C₆₇	—	4	2	no	—
139	Q₈×C₆₇	—	4	2	no	—
140	D₄×C₆₇	—	2	4	no	—
141	D₄×C₆₇	—	2	2	no	—
142	D₄×C₆₇	—	4	2	no	—
143	D₄×C₆₇	—	4	4	no	—
144	D₄×C₆₇	—	4	2	no	—
145	D₄×C₆₇	—	8	2	no	—
146	D₄×C₆₇	—	8	4	no	—
147	D₄×C₆₇	#135	1	4	yes	complemented
148	C₂×C₄×C₆₇	—	2	2	no	—
149	C₂×C₄×C₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	4	1	no	—
151	C₂×C₄×C₆₇	—	4	2	no	—
152	C₂×C₄×C₆₇	—	4	2	no	—
153	C₂×C₄×C₆₇	—	4	2	no	—
154	C₂×C₄×C₆₇	—	4	4	no	—
155	C₂×C₄×C₆₇	—	4	2	no	—
156	C₂×C₄×C₆₇	—	8	4	no	—
157	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
158	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
159	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
161	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
162	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
165	C₈×C₆₇	—	2	1	no	—
166	C₈×C₆₇	—	2	1	no	—
167	C₈×C₆₇	—	4	2	no	—
168	C₈×C₆₇	—	4	4	no	—
169	C₈×C₆₇	C₂×D₈	1	2	yes	—
170	C₈×C₆₇	C₂×D₈	1	2	yes	—
171	C₂²×C₆₇	—	2	1	no	—
172	C₂²×C₆₇	—	2	1	no	—
173	C₂²×C₆₇	—	2	4	no	—
174	C₂²×C₆₇	—	4	8	no	—
175	C₂²×C₆₇	—	4	2	no	—
176	C₂²×C₆₇	—	4	2	no	—
177	C₂²×C₆₇	—	8	2	no	—
178	C₂²×C₆₇	—	8	2	no	—
179	C₂²×C₆₇	—	8	2	no	—
180	C₂²×C₆₇	#459	1	2	yes	—
181	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
182	C₄×C₆₇	—	2	1	no	—
183	C₄×C₆₇	—	2	1	no	—
184	C₄×C₆₇	—	2	1	no	—
185	C₄×C₆₇	—	4	2	no	—
186	C₄×C₆₇	—	8	2	no	—
187	C₄×C₆₇	#459	1	2	yes	—
188	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
189	C₄×C₆₇	C₂×#135	1	2	yes	—
190	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	#19101	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂×C₆₇	—	2	2	no	—
193	C₂×C₆₇	—	4	4	no	—
194	C₂×C₆₇	—	16	2	no	—
195	C₂×C₆₇	C₂×#459	1	1	yes	characteristic
196	C₂×C₆₇	#3050	1	1	yes	characteristic
197	C₂×C₆₇	#3067	1	1	yes	characteristic
198	#3147	C₂×C₆₇	1	1	yes	characteristic, complemented
199	#3100	C₂×C₆₇	1	2	yes	complemented
200	C₂×C₈×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
201	#1669	C₂×C₆₇	1	2	yes	complemented
202	#1667	C₂×C₆₇	1	2	yes	complemented
203	#1665	C₂×C₆₇	1	4	yes	complemented
204	#1564	C₂×C₆₇	1	1	yes	characteristic, complemented
205	#1540	C₂×C₆₇	1	2	yes	complemented
206	C₆₇	#19101	1	1	yes	characteristic, direct product factor, Sylow
207	C₂×#135	—	2	1	no	—
208	C₂×#135	—	2	1	no	—
209	C₂³×C₈	—	2	1	no	—
210	#532	C₂²×C₆₇	1	2	yes	—
211	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
212	#495	—	2	1	no	—
213	#495	—	2	1	no	—
214	#494	C₂²×C₆₇	1	1	yes	characteristic, complemented
215	#493	C₂²×C₆₇	1	1	yes	characteristic, complemented
216	#492	C₂²×C₆₇	1	2	yes	complemented
217	#480	—	2	2	no	—
218	#474	C₂²×C₆₇	1	4	yes	—
219	#459	C₂²×C₆₇	1	4	yes	—
220	#447	—	2	2	no	—
221	C₄×D₈	—	2	4	no	—
222	C₈×D₄	—	2	1	no	—
223	C₈×D₄	—	2	1	no	—
224	C₈×D₄	C₂²×C₆₇	1	2	yes	—
225	C₈×D₄	C₂²×C₆₇	1	2	yes	—
226	#431	C₂²×C₆₇	1	2	yes	—
227	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
228	C₂×C₂²⋊C₈	—	2	1	no	—
229	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
230	#335	C₂²×C₆₇	1	2	yes	complemented
231	#334	C₂²×C₆₇	1	2	yes	complemented
232	#332	C₂²×C₆₇	1	4	yes	complemented
233	#331	C₂²×C₆₇	1	4	yes	complemented
234	C₂×#41	—	2	2	no	—
235	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
236	C₂³×C₄	—	2	1	no	—
237	#135	—	4	4	no	—
238	#135	—	4	4	no	—
239	C₂×Q₁₆	—	2	1	no	—
240	C₂×Q₁₆	—	2	1	no	—
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×D₈	—	2	4	no	—
244	C₂×D₈	—	2	1	no	—
245	C₂×D₈	—	2	1	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	4	4	no	—
250	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
251	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
252	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
253	#127	C₂³×C₆₇	1	2	yes	—
254	#124	—	2	2	no	—
255	#121	—	2	2	no	—
256	#121	—	2	2	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	D₄×C₆₇	1	2	yes	—
262	C₄×D₄	C₂³×C₆₇	1	2	yes	—
263	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
266	#107	—	2	4	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
269	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
270	#102	—	2	4	no	—
271	#102	—	2	4	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	—	2	2	no	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₄×C₈	—	2	2	no	—
276	C₄×C₈	D₄×C₆₇	1	1	yes	characteristic
277	C₄×C₈	D₄×C₆₇	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
280	C₂⁴	—	2	1	no	—
281	#41	—	4	4	no	—
282	#41	—	4	4	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
299	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
300	Q₁₆	—	4	2	no	—
301	Q₁₆	—	4	2	no	—
302	SD₁₆	—	4	4	no	—
303	SD₁₆	—	4	4	no	—
304	D₈	—	4	2	no	—
305	D₈	—	4	8	no	—
306	D₈	—	4	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	4	2	no	—
311	C₂×C₈	—	4	4	no	—
312	C₂×C₈	—	4	4	no	—
313	C₂×C₈	D₈×C₆₇	1	4	yes	complemented
314	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
315	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
316	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
317	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
327	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
328	C₄²	#41×C₆₇	1	1	yes	characteristic
329	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
330	C₂³	—	2	4	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	#121×C₆₇	1	1	yes	characteristic
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	D₄	—	2	4	no	—
339	D₄	—	2	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	4	no	—
342	D₄	—	4	2	no	—
343	D₄	—	8	2	no	—
344	D₄	—	8	4	no	—
345	D₄	#135×C₆₇	1	4	yes	complemented
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	8	4	no	—
355	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
356	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
357	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
358	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
359	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	2	yes	—
360	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
361	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
362	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	4	no	—
367	C₈	C₂×D₈×C₆₇	1	2	yes	—
368	C₈	C₂×D₈×C₆₇	1	2	yes	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	#459×C₆₇	1	2	yes	—
379	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	8	2	no	—
385	C₄	#459×C₆₇	1	2	yes	—
386	C₄	C₂²×D₈×C₆₇	1	1	yes	characteristic
387	C₄	C₂×#135×C₆₇	1	2	yes	—
388	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	4	4	no	—
391	C₂	—	16	2	no	—
392	C₂	C₂×#459×C₆₇	1	1	yes	characteristic
393	C₂	C₆₇×#3050	1	1	yes	characteristic
394	C₂	C₆₇×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₇
socle	C₂²×C₆₇	C₂×#121
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3147	C₂	semidirect
2. C₆₇×#3100	C₂	semidirect
3. C₂×C₈×D₄×C₆₇	C₂	semidirect
4. C₆₇×#1669	C₂	semidirect
5. C₆₇×#1667	C₂	semidirect
6. C₆₇×#1665	C₂	semidirect
7. C₆₇×#1564	C₂	semidirect
8. C₆₇×#1540	C₂	semidirect
16. #494×C₆₇	C₂²	semidirect
17. #493×C₆₇	C₂²	semidirect
18. #492×C₆₇	C₂²	semidirect
32. #335×C₆₇	C₂²	semidirect
33. #334×C₆₇	C₂²	semidirect
34. #332×C₆₇	C₂²	semidirect
35. #331×C₆₇	C₂²	semidirect
115. C₂×C₈×C₆₇	D₈	semidirect
147. D₄×C₆₇	#135	semidirect
191. #19101	C₆₇	direct (N × H)
198. #3147	C₂×C₆₇	semidirect
199. #3100	C₂×C₆₇	semidirect
200. C₂×C₈×D₄	C₂×C₆₇	semidirect
201. #1669	C₂×C₆₇	semidirect
202. #1667	C₂×C₆₇	semidirect
203. #1665	C₂×C₆₇	semidirect
204. #1564	C₂×C₆₇	semidirect
205. #1540	C₂×C₆₇	semidirect
206. C₆₇	#19101	direct (N × H)
214. #494	C₂²×C₆₇	semidirect
215. #493	C₂²×C₆₇	semidirect
216. #492	C₂²×C₆₇	semidirect
230. #335	C₂²×C₆₇	semidirect
231. #334	C₂²×C₆₇	semidirect
232. #332	C₂²×C₆₇	semidirect
233. #331	C₂²×C₆₇	semidirect
313. C₂×C₈	D₈×C₆₇	semidirect
345. D₄	#135×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3147	2
C₆₇×#3100	2
C₂×C₈×D₄×C₆₇	2
C₆₇×#1669	2
C₆₇×#1667	2
C₆₇×#1665	2
C₆₇×#1564	2
C₆₇×#1540	2
#19101	67

Subgroups — C67×#19101 #30698352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#19101 #30698352