Subgroups — C₆₇×#32912 #30712163

Order 17152.

1430 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#519×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#460×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×#448×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2619	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#1880	C₂	1	4	yes	maximal, complemented
6	C₆₇×#1875	C₂	1	2	yes	maximal, complemented
7	C₆₇×#1805	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
10	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	—
11	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
12	C₂×#121×C₆₇	C₂²	1	2	yes	—
13	#519×C₆₇	—	2	8	no	—
14	C₂×C₄×Q₈×C₆₇	—	2	2	no	—
15	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
17	C₂×#117×C₆₇	—	2	2	no	—
18	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
20	#460×C₆₇	—	2	8	no	—
21	#448×C₆₇	—	2	8	no	—
22	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
23	C₂×#103×C₆₇	C₂²	1	4	yes	—
24	C₂×#102×C₆₇	C₂²	1	4	yes	—
25	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
26	#394×C₆₇	—	2	2	no	—
27	#392×C₆₇	—	2	2	no	—
28	#390×C₆₇	C₂²	1	2	yes	—
29	#382×C₆₇	C₂²	1	1	yes	characteristic
30	#340×C₆₇	C₂²	1	4	yes	—
31	#336×C₆₇	C₂²	1	2	yes	—
32	C₂²×Q₈×C₆₇	—	2	4	no	—
33	C₂²×Q₈×C₆₇	—	2	4	no	—
34	C₂²×Q₈×C₆₇	—	2	1	no	—
35	C₂²×Q₈×C₆₇	—	2	2	no	—
36	C₂²×Q₈×C₆₇	D₄	1	4	yes	complemented
37	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
38	C₂²×D₄×C₆₇	—	2	2	no	—
39	C₂²×D₄×C₆₇	—	2	2	no	—
40	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₆₇	—	2	1	no	—
42	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
43	C₂×SD₁₆×C₆₇	—	2	8	no	—
44	C₂×SD₁₆×C₆₇	—	2	8	no	—
45	C₂×SD₁₆×C₆₇	—	2	8	no	—
46	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
47	#127×C₆₇	—	2	4	no	—
48	#121×C₆₇	—	2	4	no	—
49	#121×C₆₇	—	2	4	no	—
50	C₄×Q₈×C₆₇	—	2	16	no	—
51	C₄×Q₈×C₆₇	—	2	4	no	—
52	C₄×Q₈×C₆₇	—	2	4	no	—
53	C₄×Q₈×C₆₇	—	2	4	no	—
54	C₄×Q₈×C₆₇	D₄	1	8	yes	complemented
55	#117×C₆₇	—	2	16	no	—
56	#117×C₆₇	—	2	4	no	—
57	#117×C₆₇	—	2	4	no	—
58	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
67	C₂×C₄²×C₆₇	—	2	2	no	—
68	C₂×C₄²×C₆₇	—	2	2	no	—
69	C₂×C₄²×C₆₇	—	2	1	no	—
70	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₆₇	—	2	4	no	—
73	#103×C₆₇	—	2	8	no	—
74	#102×C₆₇	—	2	8	no	—
75	C₂²⋊C₈×C₆₇	—	2	4	no	—
76	#95×C₆₇	—	2	2	no	—
77	C₂⁴×C₆₇	—	2	2	no	—
78	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₆₇	—	2	4	no	—
80	C₂×Q₈×C₆₇	—	2	16	no	—
81	C₂×Q₈×C₆₇	—	2	4	no	—
82	C₂×Q₈×C₆₇	—	2	16	no	—
83	C₂×Q₈×C₆₇	—	2	4	no	—
84	C₂×Q₈×C₆₇	—	2	2	no	—
85	C₂×Q₈×C₆₇	—	2	2	no	—
86	C₂×Q₈×C₆₇	—	2	2	no	—
87	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
88	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
89	C₂×Q₈×C₆₇	#41	1	4	yes	—
90	C₂×D₄×C₆₇	—	2	4	no	—
91	C₂×D₄×C₆₇	—	2	2	no	—
92	C₂×D₄×C₆₇	—	2	2	no	—
93	C₂×D₄×C₆₇	—	2	4	no	—
94	C₂×D₄×C₆₇	—	4	4	no	—
95	C₂×D₄×C₆₇	—	4	4	no	—
96	C₂×D₄×C₆₇	—	8	4	no	—
97	C₂×D₄×C₆₇	—	8	4	no	—
98	C₂²×C₄×C₆₇	—	2	4	no	—
99	C₂²×C₄×C₆₇	—	2	4	no	—
100	C₂²×C₄×C₆₇	—	2	4	no	—
101	C₂²×C₄×C₆₇	—	2	2	no	—
102	C₂²×C₄×C₆₇	—	2	2	no	—
103	C₂²×C₄×C₆₇	—	2	2	no	—
104	C₂²×C₄×C₆₇	—	2	2	no	—
105	C₂²×C₄×C₆₇	—	2	2	no	—
106	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₆₇	#41	1	2	yes	—
111	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
112	SD₁₆×C₆₇	—	4	16	no	—
113	C₂×C₈×C₆₇	—	2	4	no	—
114	C₂×C₈×C₆₇	—	2	4	no	—
115	C₂×C₈×C₆₇	—	2	4	no	—
116	C₄⋊C₄×C₆₇	—	2	8	no	—
117	C₄⋊C₄×C₆₇	—	2	8	no	—
118	C₄⋊C₄×C₆₇	—	2	4	no	—
119	C₄⋊C₄×C₆₇	—	2	2	no	—
120	C₄⋊C₄×C₆₇	—	2	2	no	—
121	C₄⋊C₄×C₆₇	—	2	2	no	—
122	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
123	C₂²⋊C₄×C₆₇	—	2	4	no	—
124	C₂²⋊C₄×C₆₇	—	2	4	no	—
125	C₂²⋊C₄×C₆₇	—	4	4	no	—
126	C₂²⋊C₄×C₆₇	—	8	4	no	—
127	C₄²×C₆₇	—	2	8	no	—
128	C₄²×C₆₇	—	2	4	no	—
129	C₄²×C₆₇	—	2	8	no	—
130	C₄²×C₆₇	—	2	2	no	—
131	C₄²×C₆₇	C₂×D₄	1	4	yes	—
132	C₂³×C₆₇	—	2	1	no	—
133	C₂³×C₆₇	—	2	1	no	—
134	C₂³×C₆₇	—	2	4	no	—
135	C₂³×C₆₇	—	4	2	no	—
136	C₂³×C₆₇	—	4	2	no	—
137	C₂³×C₆₇	—	4	2	no	—
138	C₂³×C₆₇	—	4	4	no	—
139	C₂³×C₆₇	—	4	4	no	—
140	C₂³×C₆₇	#121	1	2	yes	—
141	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
142	Q₈×C₆₇	—	2	16	no	—
143	Q₈×C₆₇	—	2	4	no	—
144	Q₈×C₆₇	—	2	4	no	—
145	Q₈×C₆₇	—	2	4	no	—
146	Q₈×C₆₇	#121	1	8	yes	—
147	D₄×C₆₇	—	4	4	no	—
148	D₄×C₆₇	—	4	4	no	—
149	D₄×C₆₇	—	8	8	no	—
150	D₄×C₆₇	—	8	8	no	—
151	C₂×C₄×C₆₇	—	2	16	no	—
152	C₂×C₄×C₆₇	—	2	4	no	—
153	C₂×C₄×C₆₇	—	2	1	no	—
154	C₂×C₄×C₆₇	—	2	4	no	—
155	C₂×C₄×C₆₇	—	2	4	no	—
156	C₂×C₄×C₆₇	—	2	1	no	—
157	C₂×C₄×C₆₇	—	2	4	no	—
158	C₂×C₄×C₆₇	—	2	4	no	—
159	C₂×C₄×C₆₇	—	2	4	no	—
160	C₂×C₄×C₆₇	—	2	2	no	—
161	C₂×C₄×C₆₇	—	2	4	no	—
162	C₂×C₄×C₆₇	—	2	4	no	—
163	C₂×C₄×C₆₇	—	4	4	no	—
164	C₂×C₄×C₆₇	—	4	2	no	—
165	C₂×C₄×C₆₇	—	4	4	no	—
166	C₂×C₄×C₆₇	#120	1	4	yes	—
167	C₂×C₄×C₆₇	#121	1	2	yes	—
168	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
171	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
172	C₈×C₆₇	—	4	4	no	—
173	C₂²×C₆₇	—	2	2	no	—
174	C₂²×C₆₇	—	2	4	no	—
175	C₂²×C₆₇	—	4	2	no	—
176	C₂²×C₆₇	—	4	2	no	—
177	C₂²×C₆₇	—	8	2	no	—
178	C₂²×C₆₇	—	8	4	no	—
179	C₂²×C₆₇	—	8	4	no	—
180	C₂²×C₆₇	—	8	2	no	—
181	C₂²×C₆₇	—	8	2	no	—
182	C₂²×C₆₇	C₂×#120	1	1	yes	characteristic
183	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
184	C₂²×C₆₇	#525	1	1	yes	characteristic
185	C₂²×C₆₇	#577	1	4	yes	—
186	C₄×C₆₇	—	2	8	no	—
187	C₄×C₆₇	—	2	2	no	—
188	C₄×C₆₇	—	2	4	no	—
189	C₄×C₆₇	—	4	2	no	—
190	C₄×C₆₇	—	4	4	no	—
191	C₄×C₆₇	—	8	2	no	—
192	C₄×C₆₇	C₂×#121	1	2	yes	—
193	C₄×C₆₇	#525	1	2	yes	—
194	#32912	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂×C₆₇	—	4	2	no	—
196	C₂×C₆₇	—	16	2	no	—
197	C₂×C₆₇	#2847	1	1	yes	characteristic
198	C₂×C₆₇	#3010	1	2	yes	—
199	C₂×C₆₇	#3043	1	2	yes	—
200	C₂×C₆₇	#3126	1	2	yes	—
201	C₂×#519	C₂×C₆₇	1	1	yes	characteristic, complemented
202	C₂×#460	C₂×C₆₇	1	2	yes	complemented
203	C₂×#448	C₂×C₆₇	1	2	yes	complemented
204	#2619	C₂×C₆₇	1	1	yes	characteristic
205	#1880	C₂×C₆₇	1	4	yes	complemented
206	#1875	C₂×C₆₇	1	2	yes	complemented
207	#1805	C₂×C₆₇	1	2	yes	complemented
208	#1798	C₂×C₆₇	1	1	yes	characteristic, complemented
209	C₆₇	#32912	1	1	yes	characteristic, direct product factor, Sylow
210	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
211	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	—
212	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
213	C₂×#121	C₂²×C₆₇	1	2	yes	—
214	#519	—	2	8	no	—
215	C₂×C₄×Q₈	—	2	2	no	—
216	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
217	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
218	C₂×#117	—	2	2	no	—
219	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
220	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
221	#460	—	2	8	no	—
222	#448	—	2	8	no	—
223	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
224	C₂×#103	C₂²×C₆₇	1	4	yes	—
225	C₂×#102	C₂²×C₆₇	1	4	yes	—
226	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
227	#394	—	2	2	no	—
228	#392	—	2	2	no	—
229	#390	C₂²×C₆₇	1	2	yes	—
230	#382	C₂²×C₆₇	1	1	yes	characteristic
231	#340	C₂²×C₆₇	1	4	yes	—
232	#336	C₂²×C₆₇	1	2	yes	—
233	C₂²×Q₈	—	2	4	no	—
234	C₂²×Q₈	—	2	4	no	—
235	C₂²×Q₈	—	2	1	no	—
236	C₂²×Q₈	—	2	2	no	—
237	C₂²×Q₈	D₄×C₆₇	1	4	yes	complemented
238	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
242	C₂³×C₄	—	2	1	no	—
243	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
244	C₂×SD₁₆	—	2	8	no	—
245	C₂×SD₁₆	—	2	8	no	—
246	C₂×SD₁₆	—	2	8	no	—
247	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
248	#127	—	2	4	no	—
249	#121	—	2	4	no	—
250	#121	—	2	4	no	—
251	C₄×Q₈	—	2	16	no	—
252	C₄×Q₈	—	2	4	no	—
253	C₄×Q₈	—	2	4	no	—
254	C₄×Q₈	—	2	4	no	—
255	C₄×Q₈	D₄×C₆₇	1	8	yes	complemented
256	#117	—	2	16	no	—
257	#117	—	2	4	no	—
258	#117	—	2	4	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	4	no	—
267	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
273	C₄⋊C₈	—	2	4	no	—
274	#103	—	2	8	no	—
275	#102	—	2	8	no	—
276	C₂²⋊C₈	—	2	4	no	—
277	#95	—	2	2	no	—
278	C₂⁴	—	2	2	no	—
279	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
280	C₂×Q₈	—	2	4	no	—
281	C₂×Q₈	—	2	16	no	—
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	2	16	no	—
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
289	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
290	C₂×Q₈	#41×C₆₇	1	4	yes	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	4	4	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	8	4	no	—
298	C₂×D₄	—	8	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
311	C₂²×C₄	#41×C₆₇	1	2	yes	—
312	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
313	SD₁₆	—	4	16	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	2	4	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	4	4	no	—
327	C₂²⋊C₄	—	8	4	no	—
328	C₄²	—	2	8	no	—
329	C₄²	—	2	4	no	—
330	C₄²	—	2	8	no	—
331	C₄²	—	2	2	no	—
332	C₄²	C₂×D₄×C₆₇	1	4	yes	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	4	no	—
341	C₂³	#121×C₆₇	1	2	yes	—
342	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
343	Q₈	—	2	16	no	—
344	Q₈	—	2	4	no	—
345	Q₈	—	2	4	no	—
346	Q₈	—	2	4	no	—
347	Q₈	#121×C₆₇	1	8	yes	—
348	D₄	—	4	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	8	8	no	—
351	D₄	—	8	8	no	—
352	C₂×C₄	—	2	16	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	#120×C₆₇	1	4	yes	—
368	C₂×C₄	#121×C₆₇	1	2	yes	—
369	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
371	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
372	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
373	C₈	—	4	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	8	4	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	4	no	—
383	C₂²	C₂×#120×C₆₇	1	1	yes	characteristic
384	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
385	C₂²	#525×C₆₇	1	1	yes	characteristic
386	C₂²	#577×C₆₇	1	4	yes	—
387	C₄	—	2	4	no	—
388	C₄	—	2	8	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	4	no	—
392	C₄	—	8	2	no	—
393	C₄	C₂×#121×C₆₇	1	2	yes	—
394	C₄	#525×C₆₇	1	2	yes	—
395	C₂	—	4	2	no	—
396	C₂	—	16	2	no	—
397	C₂	C₆₇×#2847	1	1	yes	characteristic
398	C₂	C₆₇×#3010	1	2	yes	—
399	C₂	C₆₇×#3043	1	2	yes	—
400	C₂	C₆₇×#3126	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₆₇×#2619	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#519×C₆₇	C₂	semidirect
2. C₂×#460×C₆₇	C₂	semidirect
3. C₂×#448×C₆₇	C₂	semidirect
5. C₆₇×#1880	C₂	semidirect
6. C₆₇×#1875	C₂	semidirect
7. C₆₇×#1805	C₂	semidirect
8. C₆₇×#1798	C₂	semidirect
36. C₂²×Q₈×C₆₇	D₄	semidirect
54. C₄×Q₈×C₆₇	D₄	semidirect
194. #32912	C₆₇	direct (N × H)
201. C₂×#519	C₂×C₆₇	semidirect
202. C₂×#460	C₂×C₆₇	semidirect
203. C₂×#448	C₂×C₆₇	semidirect
205. #1880	C₂×C₆₇	semidirect
206. #1875	C₂×C₆₇	semidirect
207. #1805	C₂×C₆₇	semidirect
208. #1798	C₂×C₆₇	semidirect
209. C₆₇	#32912	direct (N × H)
237. C₂²×Q₈	D₄×C₆₇	semidirect
255. C₄×Q₈	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#519×C₆₇	2
C₂×#460×C₆₇	2
C₂×#448×C₆₇	2
C₆₇×#2619	2
C₆₇×#1880	2
C₆₇×#1875	2
C₆₇×#1805	2
C₆₇×#1798	2
#32912	67

Subgroups — C67×#32912 #30712163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#32912 #30712163