Subgroups — C₆₇×#18015 #30697266

Order 17152.

640 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3106	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2979	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1590	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1586	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1585	C₂	1	2	yes	maximal, complemented
7	C₈×D₈×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1574	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1492	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1450	C₂	1	1	yes	maximal, characteristic, complemented
12	#532×C₆₇	C₂²	1	1	yes	characteristic
13	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
14	#482×C₆₇	C₄	1	2	yes	—
15	#477×C₆₇	C₄	1	1	yes	characteristic
16	#476×C₆₇	C₄	1	1	yes	characteristic
17	#460×C₆₇	C₄	1	1	yes	characteristic
18	#459×C₆₇	C₄	1	1	yes	characteristic
19	#449×C₆₇	C₄	1	2	yes	—
20	#446×C₆₇	C₂²	1	2	yes	—
21	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
22	C₄×D₈×C₆₇	C₂²	1	2	yes	—
23	#436×C₆₇	—	2	1	no	—
24	#436×C₆₇	C₂²	1	2	yes	—
25	#435×C₆₇	—	2	2	no	—
26	C₈×D₄×C₆₇	—	2	1	no	—
27	C₈×D₄×C₆₇	C₂²	1	2	yes	—
28	C₈×D₄×C₆₇	C₂²	1	2	yes	—
29	#432×C₆₇	—	2	1	no	—
30	#431×C₆₇	C₂²	1	1	yes	characteristic
31	#431×C₆₇	C₂²	1	1	yes	characteristic
32	#431×C₆₇	C₂²	1	1	yes	characteristic
33	#423×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₆₇	—	2	1	no	—
35	#408×C₆₇	—	2	2	no	—
36	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
37	#335×C₆₇	C₂²	1	2	yes	—
38	#334×C₆₇	C₂²	1	2	yes	—
39	Q₈⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
40	Q₈⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
41	D₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
42	D₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
44	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
45	#322×C₆₇	C₂²	1	2	yes	—
46	C₈²×C₆₇	C₂²	1	2	yes	—
47	C₂×#41×C₆₇	—	2	1	no	—
48	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
49	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
50	C₂×D₈×C₆₇	C₂×C₄	1	2	yes	—
51	C₂×M₁₆×C₆₇	—	2	1	no	—
52	C₂×M₁₆×C₆₇	—	2	2	no	—
53	C₂²×C₈×C₆₇	—	2	1	no	—
54	C₂²×C₈×C₆₇	—	2	2	no	—
55	C₂²×C₈×C₆₇	—	2	2	no	—
56	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
57	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
58	#124×C₆₇	—	2	1	no	—
59	#121×C₆₇	—	2	1	no	—
60	#121×C₆₇	C₂×C₄	1	2	yes	—
61	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
62	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₆₇	—	2	1	no	—
64	C₄×D₄×C₆₇	—	2	1	no	—
65	C₄×D₄×C₆₇	—	2	1	no	—
66	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
67	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
68	C₄×D₄×C₆₇	C₂³	1	2	yes	—
69	#117×C₆₇	—	2	1	no	—
70	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₆₇	—	2	1	no	—
72	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
73	#107×C₆₇	C₂×C₄	1	2	yes	—
74	#106×C₆₇	C₂×C₄	1	2	yes	—
75	C₄⋊C₈×C₆₇	—	2	2	no	—
76	C₄⋊C₈×C₆₇	—	2	1	no	—
77	C₄⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
78	C₄⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
79	C₄⋊C₈×C₆₇	D₄	1	1	yes	characteristic
80	C₄⋊C₈×C₆₇	D₄	1	1	yes	characteristic
81	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
82	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
84	#103×C₆₇	C₂×C₄	1	2	yes	—
85	#102×C₆₇	C₂×C₄	1	2	yes	—
86	#102×C₆₇	C₂×C₄	1	2	yes	—
87	#102×C₆₇	C₂×C₄	1	2	yes	—
88	C₂²⋊C₈×C₆₇	—	2	1	no	—
89	C₂²⋊C₈×C₆₇	—	2	2	no	—
90	C₂²⋊C₈×C₆₇	—	2	2	no	—
91	C₂²⋊C₈×C₆₇	—	2	2	no	—
92	C₂²⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
93	C₂²⋊C₈×C₆₇	D₄	1	2	yes	—
94	#97×C₆₇	—	2	2	no	—
95	C₄×C₈×C₆₇	—	2	1	no	—
96	C₄×C₈×C₆₇	—	2	1	no	—
97	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₆₇	C₂³	1	2	yes	—
100	C₄×C₈×C₆₇	C₂³	1	2	yes	—
101	#41×C₆₇	—	2	2	no	—
102	#41×C₆₇	—	4	1	no	—
103	#41×C₆₇	—	8	1	no	—
104	#41×C₆₇	—	8	1	no	—
105	C₂×Q₈×C₆₇	—	2	1	no	—
106	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×D₄×C₆₇	—	2	1	no	—
108	C₂×D₄×C₆₇	—	2	2	no	—
109	C₂×D₄×C₆₇	—	2	1	no	—
110	C₂×D₄×C₆₇	—	2	1	no	—
111	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₇	—	2	1	no	—
114	C₂²×C₄×C₆₇	—	2	1	no	—
115	C₂²×C₄×C₆₇	—	2	1	no	—
116	C₂²×C₄×C₆₇	—	2	2	no	—
117	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
120	SD₁₆×C₆₇	—	4	2	no	—
121	D₈×C₆₇	—	2	4	no	—
122	M₁₆×C₆₇	—	8	2	no	—
123	M₁₆×C₆₇	—	8	1	no	—
124	C₂×C₈×C₆₇	—	2	4	no	—
125	C₂×C₈×C₆₇	—	2	1	no	—
126	C₂×C₈×C₆₇	—	2	1	no	—
127	C₂×C₈×C₆₇	—	2	2	no	—
128	C₂×C₈×C₆₇	—	2	1	no	—
129	C₂×C₈×C₆₇	—	2	1	no	—
130	C₂×C₈×C₆₇	—	8	2	no	—
131	C₂×C₈×C₆₇	—	8	2	no	—
132	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₆₇	—	2	1	no	—
137	C₄⋊C₄×C₆₇	—	2	1	no	—
138	C₄⋊C₄×C₆₇	—	2	1	no	—
139	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
141	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
142	C₂²⋊C₄×C₆₇	—	2	1	no	—
143	C₂²⋊C₄×C₆₇	—	2	1	no	—
144	C₂²⋊C₄×C₆₇	—	2	2	no	—
145	C₂²⋊C₄×C₆₇	—	2	1	no	—
146	C₂²⋊C₄×C₆₇	—	2	2	no	—
147	C₄²×C₆₇	—	2	1	no	—
148	C₄²×C₆₇	—	2	1	no	—
149	C₄²×C₆₇	—	2	1	no	—
150	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₆₇	#41	1	1	yes	characteristic
153	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
154	C₂³×C₆₇	—	2	1	no	—
155	C₂³×C₆₇	—	2	2	no	—
156	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
157	Q₈×C₆₇	—	2	1	no	—
158	Q₈×C₆₇	—	2	1	no	—
159	Q₈×C₆₇	—	8	1	no	—
160	D₄×C₆₇	—	2	2	no	—
161	D₄×C₆₇	—	2	1	no	—
162	D₄×C₆₇	—	2	2	no	—
163	D₄×C₆₇	—	4	2	no	—
164	D₄×C₆₇	—	4	2	no	—
165	D₄×C₆₇	—	8	1	no	—
166	D₄×C₆₇	—	8	2	no	—
167	D₄×C₆₇	#131	1	2	yes	—
168	C₂×C₄×C₆₇	—	2	1	no	—
169	C₂×C₄×C₆₇	—	2	1	no	—
170	C₂×C₄×C₆₇	—	2	1	no	—
171	C₂×C₄×C₆₇	—	2	1	no	—
172	C₂×C₄×C₆₇	—	2	2	no	—
173	C₂×C₄×C₆₇	—	2	1	no	—
174	C₂×C₄×C₆₇	—	2	1	no	—
175	C₂×C₄×C₆₇	—	2	1	no	—
176	C₂×C₄×C₆₇	—	2	2	no	—
177	C₂×C₄×C₆₇	—	4	2	no	—
178	C₂×C₄×C₆₇	—	4	1	no	—
179	C₂×C₄×C₆₇	—	4	2	no	—
180	C₂×C₄×C₆₇	—	4	2	no	—
181	C₂×C₄×C₆₇	—	4	1	no	—
182	C₂×C₄×C₆₇	—	4	2	no	—
183	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
189	C₈×C₆₇	—	2	2	no	—
190	C₈×C₆₇	—	2	2	no	—
191	C₈×C₆₇	—	2	2	no	—
192	C₈×C₆₇	—	2	2	no	—
193	C₈×C₆₇	—	2	2	no	—
194	C₈×C₆₇	—	2	2	no	—
195	C₈×C₆₇	—	4	1	no	—
196	C₈×C₆₇	—	4	2	no	—
197	C₈×C₆₇	—	4	1	no	—
198	C₂²×C₆₇	—	2	1	no	—
199	C₂²×C₆₇	—	2	2	no	—
200	C₂²×C₆₇	—	2	1	no	—
201	C₂²×C₆₇	—	2	1	no	—
202	C₂²×C₆₇	—	4	1	no	—
203	C₂²×C₆₇	—	4	1	no	—
204	C₂²×C₆₇	—	4	2	no	—
205	C₂²×C₆₇	—	4	2	no	—
206	C₂²×C₆₇	—	4	2	no	—
207	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
208	C₄×C₆₇	—	2	1	no	—
209	C₄×C₆₇	—	2	1	no	—
210	C₄×C₆₇	—	2	1	no	—
211	C₄×C₆₇	—	4	1	no	—
212	C₄×C₆₇	—	4	1	no	—
213	C₄×C₆₇	—	4	2	no	—
214	C₄×C₆₇	—	4	1	no	—
215	C₄×C₆₇	#443	1	2	yes	—
216	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
217	C₄×C₆₇	#568	1	1	yes	characteristic
218	C₄×C₆₇	#576	1	1	yes	characteristic
219	C₄×C₆₇	#577	1	1	yes	characteristic
220	#18015	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂×C₆₇	—	4	1	no	—
222	C₂×C₆₇	—	4	2	no	—
223	C₂×C₆₇	—	8	2	no	—
224	C₂×C₆₇	#2933	1	1	yes	characteristic
225	C₂×C₆₇	#2946	1	1	yes	characteristic
226	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
227	#3106	C₂×C₆₇	1	1	yes	characteristic
228	#2990	C₂×C₆₇	1	1	yes	characteristic, complemented
229	#2979	C₂×C₆₇	1	1	yes	characteristic, complemented
230	#1590	C₂×C₆₇	1	2	yes	complemented
231	#1586	C₂×C₆₇	1	2	yes	complemented
232	#1585	C₂×C₆₇	1	2	yes	complemented
233	C₈×D₈	C₂×C₆₇	1	2	yes	complemented
234	#1574	C₂×C₆₇	1	1	yes	characteristic, complemented
235	#1492	C₂×C₆₇	1	1	yes	characteristic, complemented
236	#1476	C₂×C₆₇	1	1	yes	characteristic, complemented
237	#1450	C₂×C₆₇	1	1	yes	characteristic, complemented
238	C₆₇	#18015	1	1	yes	characteristic, direct product factor, Sylow
239	#532	C₂²×C₆₇	1	1	yes	characteristic
240	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
241	#482	C₄×C₆₇	1	2	yes	—
242	#477	C₄×C₆₇	1	1	yes	characteristic
243	#476	C₄×C₆₇	1	1	yes	characteristic
244	#460	C₄×C₆₇	1	1	yes	characteristic
245	#459	C₄×C₆₇	1	1	yes	characteristic
246	#449	C₄×C₆₇	1	2	yes	—
247	#446	C₂²×C₆₇	1	2	yes	—
248	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
249	C₄×D₈	C₂²×C₆₇	1	2	yes	—
250	#436	—	2	1	no	—
251	#436	C₂²×C₆₇	1	2	yes	—
252	#435	—	2	2	no	—
253	C₈×D₄	—	2	1	no	—
254	C₈×D₄	C₂²×C₆₇	1	2	yes	—
255	C₈×D₄	C₂²×C₆₇	1	2	yes	—
256	#432	—	2	1	no	—
257	#431	C₂²×C₆₇	1	1	yes	characteristic
258	#431	C₂²×C₆₇	1	1	yes	characteristic
259	#431	C₂²×C₆₇	1	1	yes	characteristic
260	#423	C₂²×C₆₇	1	1	yes	characteristic
261	C₂×C₄⋊C₈	—	2	1	no	—
262	#408	—	2	2	no	—
263	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
264	#335	C₂²×C₆₇	1	2	yes	—
265	#334	C₂²×C₆₇	1	2	yes	—
266	Q₈⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
267	Q₈⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
268	D₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
269	D₄⋊C₈	C₂²×C₆₇	1	2	yes	—
270	D₄⋊C₈	C₂²×C₆₇	1	2	yes	—
271	D₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
272	#322	C₂²×C₆₇	1	2	yes	—
273	C₈²	C₂²×C₆₇	1	2	yes	—
274	C₂×#41	—	2	1	no	—
275	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
276	C₂×SD₁₆	C₂×C₄×C₆₇	1	2	yes	—
277	C₂×D₈	C₂×C₄×C₆₇	1	2	yes	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
284	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
285	#124	—	2	1	no	—
286	#121	—	2	1	no	—
287	#121	C₂×C₄×C₆₇	1	2	yes	—
288	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
289	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
294	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
295	C₄×D₄	C₂³×C₆₇	1	2	yes	—
296	#117	—	2	1	no	—
297	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
300	#107	C₂×C₄×C₆₇	1	2	yes	—
301	#106	C₂×C₄×C₆₇	1	2	yes	—
302	C₄⋊C₈	—	2	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
305	C₄⋊C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
306	C₄⋊C₈	D₄×C₆₇	1	1	yes	characteristic
307	C₄⋊C₈	D₄×C₆₇	1	1	yes	characteristic
308	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
309	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
310	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
311	#103	C₂×C₄×C₆₇	1	2	yes	—
312	#102	C₂×C₄×C₆₇	1	2	yes	—
313	#102	C₂×C₄×C₆₇	1	2	yes	—
314	#102	C₂×C₄×C₆₇	1	2	yes	—
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	C₂×C₄×C₆₇	1	2	yes	—
320	C₂²⋊C₈	D₄×C₆₇	1	2	yes	—
321	#97	—	2	2	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
325	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
326	C₄×C₈	C₂³×C₆₇	1	2	yes	—
327	C₄×C₈	C₂³×C₆₇	1	2	yes	—
328	#41	—	2	2	no	—
329	#41	—	4	1	no	—
330	#41	—	8	1	no	—
331	#41	—	8	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
339	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
346	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
347	SD₁₆	—	4	2	no	—
348	D₈	—	2	4	no	—
349	M₁₆	—	8	2	no	—
350	M₁₆	—	8	1	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	8	2	no	—
358	C₂×C₈	—	8	2	no	—
359	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
360	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
361	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
362	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
367	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
368	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
378	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
379	C₄²	#41×C₆₇	1	1	yes	characteristic
380	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	8	1	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	1	no	—
389	D₄	—	2	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	1	no	—
393	D₄	—	8	2	no	—
394	D₄	#131×C₆₇	1	2	yes	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
411	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
412	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
413	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	2	2	no	—
421	C₈	—	2	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	#443×C₆₇	1	2	yes	—
443	C₄	C₂×#131×C₆₇	1	1	yes	characteristic
444	C₄	#568×C₆₇	1	1	yes	characteristic
445	C₄	#576×C₆₇	1	1	yes	characteristic
446	C₄	#577×C₆₇	1	1	yes	characteristic
447	C₂	—	4	1	no	—
448	C₂	—	4	2	no	—
449	C₂	—	8	2	no	—
450	C₂	C₆₇×#2933	1	1	yes	characteristic
451	C₂	C₆₇×#2946	1	1	yes	characteristic
452	C₂	C₂×#443×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₄²	C₂⁴×C₆₇
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₆₇×#3106	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ #431×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2990	C₂	semidirect
3. C₆₇×#2979	C₂	semidirect
4. C₆₇×#1590	C₂	semidirect
5. C₆₇×#1586	C₂	semidirect
6. C₆₇×#1585	C₂	semidirect
7. C₈×D₈×C₆₇	C₂	semidirect
8. C₆₇×#1574	C₂	semidirect
9. C₆₇×#1492	C₂	semidirect
10. C₆₇×#1476	C₂	semidirect
11. C₆₇×#1450	C₂	semidirect
220. #18015	C₆₇	direct (N × H)
228. #2990	C₂×C₆₇	semidirect
229. #2979	C₂×C₆₇	semidirect
230. #1590	C₂×C₆₇	semidirect
231. #1586	C₂×C₆₇	semidirect
232. #1585	C₂×C₆₇	semidirect
233. C₈×D₈	C₂×C₆₇	semidirect
234. #1574	C₂×C₆₇	semidirect
235. #1492	C₂×C₆₇	semidirect
236. #1476	C₂×C₆₇	semidirect
237. #1450	C₂×C₆₇	semidirect
238. C₆₇	#18015	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3106	2
C₆₇×#2990	2
C₆₇×#2979	2
C₆₇×#1590	2
C₆₇×#1586	2
C₆₇×#1585	2
C₈×D₈×C₆₇	2
C₆₇×#1574	2
C₆₇×#1492	2
C₆₇×#1476	2
C₆₇×#1450	2
#18015	67

Subgroups — C67×#18015 #30697266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#18015 #30697266