Subgroups — C₆₇×#34547 #30713798

Order 17152.

2938 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2399	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2398	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2396	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2395	C₂	1	4	yes	maximal, complemented
7	C₆₇×#2392	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2392	C₂	1	4	yes	maximal, complemented
9	C₆₇×#2388	C₂	1	4	yes	maximal, complemented
10	C₄²×D₄×C₆₇	C₂	1	4	yes	maximal, complemented
11	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₆₇	C₂²	1	2	yes	—
13	C₄×#41×C₆₇	—	2	16	no	—
14	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	—
17	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
18	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
20	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
22	C₂×#117×C₆₇	C₂²	1	2	yes	—
23	C₂×#117×C₆₇	C₂²	1	4	yes	—
24	C₂×#117×C₆₇	C₂²	1	2	yes	—
25	C₂²×C₄²×C₆₇	C₂²	1	4	yes	—
26	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
27	#400×C₆₇	C₂²	1	4	yes	—
28	#399×C₆₇	C₂²	1	4	yes	—
29	#398×C₆₇	C₂²	1	4	yes	—
30	#398×C₆₇	C₂²	1	4	yes	—
31	#397×C₆₇	C₂²	1	4	yes	—
32	#397×C₆₇	C₂²	1	4	yes	—
33	#396×C₆₇	C₂²	1	8	yes	—
34	#395×C₆₇	C₂²	1	4	yes	—
35	#394×C₆₇	C₂²	1	8	yes	—
36	#394×C₆₇	C₂²	1	4	yes	—
37	#394×C₆₇	C₂²	1	4	yes	—
38	#393×C₆₇	C₂²	1	4	yes	—
39	#392×C₆₇	C₂²	1	4	yes	—
40	#392×C₆₇	C₂²	1	4	yes	—
41	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
42	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
43	C₄×C₄⋊C₄×C₆₇	C₂²	1	8	yes	—
44	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
45	C₄×C₂²⋊C₄×C₆₇	C₂²	1	8	yes	—
46	C₄×C₂²⋊C₄×C₆₇	C₂²	1	8	yes	—
47	C₄×C₂²⋊C₄×C₆₇	C₂²	1	8	yes	—
48	#376×C₆₇	C₂²	1	1	yes	characteristic
49	#376×C₆₇	C₂²	1	1	yes	characteristic
50	C₄³×C₆₇	C₂²	1	2	yes	—
51	C₂×#41×C₆₇	—	2	8	no	—
52	C₂×#41×C₆₇	—	2	16	no	—
53	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
54	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
55	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
56	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
57	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
58	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
59	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
61	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
62	C₄×Q₈×C₆₇	—	2	8	no	—
63	C₄×Q₈×C₆₇	—	2	8	no	—
64	C₄×D₄×C₆₇	—	2	16	no	—
65	C₄×D₄×C₆₇	—	2	16	no	—
66	C₄×D₄×C₆₇	—	2	32	no	—
67	C₄×D₄×C₆₇	—	2	8	no	—
68	C₄×D₄×C₆₇	—	2	8	no	—
69	C₄×D₄×C₆₇	—	2	16	no	—
70	#117×C₆₇	—	2	8	no	—
71	#117×C₆₇	—	2	16	no	—
72	#117×C₆₇	—	2	8	no	—
73	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
79	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
80	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
81	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
82	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
83	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
84	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
85	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
86	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
87	C₂×C₄²×C₆₇	—	2	16	no	—
88	C₂×C₄²×C₆₇	D₄	1	8	yes	complemented
89	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
90	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
91	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
92	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
93	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
94	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
95	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
97	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
98	#95×C₆₇	C₂³	1	4	yes	—
99	#95×C₆₇	C₂³	1	4	yes	—
100	#95×C₆₇	C₂³	1	4	yes	—
101	#95×C₆₇	C₂³	1	8	yes	—
102	#95×C₆₇	C₂³	1	4	yes	—
103	#95×C₆₇	C₂³	1	8	yes	—
104	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
105	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
106	#41×C₆₇	—	2	64	no	—
107	C₂×Q₈×C₆₇	—	2	4	no	—
108	C₂×Q₈×C₆₇	—	2	8	no	—
109	C₂×D₄×C₆₇	—	2	8	no	—
110	C₂×D₄×C₆₇	—	2	16	no	—
111	C₂×D₄×C₆₇	—	2	8	no	—
112	C₂×D₄×C₆₇	—	2	8	no	—
113	C₂×D₄×C₆₇	—	2	4	no	—
114	C₂×D₄×C₆₇	—	2	8	no	—
115	C₂×D₄×C₆₇	—	2	8	no	—
116	C₂²×C₄×C₆₇	—	2	8	no	—
117	C₂²×C₄×C₆₇	—	2	4	no	—
118	C₂²×C₄×C₆₇	—	2	8	no	—
119	C₂²×C₄×C₆₇	—	2	8	no	—
120	C₂²×C₄×C₆₇	—	2	8	no	—
121	C₂²×C₄×C₆₇	—	2	8	no	—
122	C₂²×C₄×C₆₇	—	2	16	no	—
123	C₂²×C₄×C₆₇	—	2	16	no	—
124	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
125	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₆₇	#41	1	16	yes	complemented
127	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
129	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
131	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
136	C₄⋊C₄×C₆₇	—	2	8	no	—
137	C₄⋊C₄×C₆₇	—	2	8	no	—
138	C₄⋊C₄×C₆₇	—	2	4	no	—
139	C₄⋊C₄×C₆₇	—	2	4	no	—
140	C₄⋊C₄×C₆₇	—	2	8	no	—
141	C₄⋊C₄×C₆₇	—	2	16	no	—
142	C₄⋊C₄×C₆₇	—	2	8	no	—
143	C₂²⋊C₄×C₆₇	—	2	8	no	—
144	C₂²⋊C₄×C₆₇	—	2	16	no	—
145	C₂²⋊C₄×C₆₇	—	2	8	no	—
146	C₂²⋊C₄×C₆₇	—	2	8	no	—
147	C₂²⋊C₄×C₆₇	—	2	8	no	—
148	C₂²⋊C₄×C₆₇	—	2	16	no	—
149	C₂²⋊C₄×C₆₇	—	2	16	no	—
150	C₄²×C₆₇	—	2	8	no	—
151	C₄²×C₆₇	—	2	8	no	—
152	C₄²×C₆₇	—	2	8	no	—
153	C₄²×C₆₇	—	2	4	no	—
154	C₄²×C₆₇	—	2	16	no	—
155	C₄²×C₆₇	C₂×D₄	1	4	yes	—
156	C₄²×C₆₇	C₂×D₄	1	8	yes	—
157	C₄²×C₆₇	C₂×D₄	1	4	yes	—
158	C₄²×C₆₇	#41	1	8	yes	complemented
159	C₂³×C₆₇	—	2	4	no	—
160	C₂³×C₆₇	—	2	2	no	—
161	C₂³×C₆₇	—	2	8	no	—
162	C₂³×C₆₇	—	2	8	no	—
163	C₂³×C₆₇	—	2	4	no	—
164	C₂³×C₆₇	—	2	4	no	—
165	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
166	C₂³×C₆₇	C₂×#41	1	8	yes	—
167	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
168	Q₈×C₆₇	—	2	16	no	—
169	D₄×C₆₇	—	2	32	no	—
170	D₄×C₆₇	—	2	16	no	—
171	D₄×C₆₇	—	2	32	no	—
172	C₂×C₄×C₆₇	—	2	4	no	—
173	C₂×C₄×C₆₇	—	2	8	no	—
174	C₂×C₄×C₆₇	—	2	2	no	—
175	C₂×C₄×C₆₇	—	2	4	no	—
176	C₂×C₄×C₆₇	—	2	4	no	—
177	C₂×C₄×C₆₇	—	2	16	no	—
178	C₂×C₄×C₆₇	—	2	32	no	—
179	C₂×C₄×C₆₇	—	2	8	no	—
180	C₂×C₄×C₆₇	—	2	4	no	—
181	C₂×C₄×C₆₇	—	2	4	no	—
182	C₂×C₄×C₆₇	—	2	8	no	—
183	C₂×C₄×C₆₇	—	2	4	no	—
184	C₂×C₄×C₆₇	—	2	8	no	—
185	C₂×C₄×C₆₇	—	2	8	no	—
186	C₂×C₄×C₆₇	—	4	16	no	—
187	C₂×C₄×C₆₇	—	4	16	no	—
188	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
189	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
190	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
191	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
193	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
194	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
195	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
196	C₂²×C₆₇	—	2	4	no	—
197	C₂²×C₆₇	—	2	8	no	—
198	C₂²×C₆₇	—	2	2	no	—
199	C₂²×C₆₇	—	2	16	no	—
200	C₂²×C₆₇	—	4	4	no	—
201	C₂²×C₆₇	—	4	4	no	—
202	C₂²×C₆₇	—	4	4	no	—
203	C₂²×C₆₇	—	4	8	no	—
204	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
205	C₂²×C₆₇	C₂²×#41	1	4	yes	—
206	C₂²×C₆₇	C₂²×#41	1	2	yes	—
207	C₄×C₆₇	—	2	4	no	—
208	C₄×C₆₇	—	2	8	no	—
209	C₄×C₆₇	—	2	2	no	—
210	C₄×C₆₇	—	2	8	no	—
211	C₄×C₆₇	—	4	4	no	—
212	C₄×C₆₇	—	4	4	no	—
213	C₄×C₆₇	—	4	4	no	—
214	C₄×C₆₇	#525	1	8	yes	—
215	C₄×C₆₇	#532	1	4	yes	—
216	#34547	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂×C₆₇	—	4	2	no	—
218	C₂×C₆₇	—	4	8	no	—
219	C₂×C₆₇	C₂×#525	1	2	yes	—
220	C₂×C₆₇	C₂×#532	1	1	yes	characteristic
221	C₂×C₆₇	#3444	1	4	yes	—
222	C₂×C₄×#41	C₂×C₆₇	1	2	yes	complemented
223	#2399	C₂×C₆₇	1	1	yes	characteristic, complemented
224	#2398	C₂×C₆₇	1	2	yes	complemented
225	#2397	C₂×C₆₇	1	1	yes	characteristic, complemented
226	#2396	C₂×C₆₇	1	4	yes	complemented
227	#2395	C₂×C₆₇	1	4	yes	complemented
228	#2392	C₂×C₆₇	1	4	yes	complemented
229	#2392	C₂×C₆₇	1	4	yes	complemented
230	#2388	C₂×C₆₇	1	4	yes	complemented
231	C₄²×D₄	C₂×C₆₇	1	4	yes	complemented
232	C₄×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
233	C₆₇	#34547	1	1	yes	characteristic, direct product factor, Sylow
234	C₂²×#41	C₂²×C₆₇	1	2	yes	—
235	C₄×#41	—	2	16	no	—
236	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
237	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
238	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	—
239	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
240	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
241	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
242	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
243	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
244	C₂×#117	C₂²×C₆₇	1	2	yes	—
245	C₂×#117	C₂²×C₆₇	1	4	yes	—
246	C₂×#117	C₂²×C₆₇	1	2	yes	—
247	C₂²×C₄²	C₂²×C₆₇	1	4	yes	—
248	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
249	#400	C₂²×C₆₇	1	4	yes	—
250	#399	C₂²×C₆₇	1	4	yes	—
251	#398	C₂²×C₆₇	1	4	yes	—
252	#398	C₂²×C₆₇	1	4	yes	—
253	#397	C₂²×C₆₇	1	4	yes	—
254	#397	C₂²×C₆₇	1	4	yes	—
255	#396	C₂²×C₆₇	1	8	yes	—
256	#395	C₂²×C₆₇	1	4	yes	—
257	#394	C₂²×C₆₇	1	8	yes	—
258	#394	C₂²×C₆₇	1	4	yes	—
259	#394	C₂²×C₆₇	1	4	yes	—
260	#393	C₂²×C₆₇	1	4	yes	—
261	#392	C₂²×C₆₇	1	4	yes	—
262	#392	C₂²×C₆₇	1	4	yes	—
263	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
264	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
265	C₄×C₄⋊C₄	C₂²×C₆₇	1	8	yes	—
266	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
267	C₄×C₂²⋊C₄	C₂²×C₆₇	1	8	yes	—
268	C₄×C₂²⋊C₄	C₂²×C₆₇	1	8	yes	—
269	C₄×C₂²⋊C₄	C₂²×C₆₇	1	8	yes	—
270	#376	C₂²×C₆₇	1	1	yes	characteristic
271	#376	C₂²×C₆₇	1	1	yes	characteristic
272	C₄³	C₂²×C₆₇	1	2	yes	—
273	C₂×#41	—	2	8	no	—
274	C₂×#41	—	2	16	no	—
275	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
276	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
277	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
278	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
279	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
280	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
281	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
282	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
283	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
284	C₄×Q₈	—	2	8	no	—
285	C₄×Q₈	—	2	8	no	—
286	C₄×D₄	—	2	16	no	—
287	C₄×D₄	—	2	16	no	—
288	C₄×D₄	—	2	32	no	—
289	C₄×D₄	—	2	8	no	—
290	C₄×D₄	—	2	8	no	—
291	C₄×D₄	—	2	16	no	—
292	#117	—	2	8	no	—
293	#117	—	2	16	no	—
294	#117	—	2	8	no	—
295	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
296	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
297	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
300	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
301	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
307	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
308	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
309	C₂×C₄²	—	2	16	no	—
310	C₂×C₄²	D₄×C₆₇	1	8	yes	complemented
311	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
312	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
313	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
314	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
315	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
316	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
317	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
320	#95	C₂³×C₆₇	1	4	yes	—
321	#95	C₂³×C₆₇	1	4	yes	—
322	#95	C₂³×C₆₇	1	4	yes	—
323	#95	C₂³×C₆₇	1	8	yes	—
324	#95	C₂³×C₆₇	1	4	yes	—
325	#95	C₂³×C₆₇	1	8	yes	—
326	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
327	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
328	#41	—	2	64	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	—	2	8	no	—
331	C₂×D₄	—	2	8	no	—
332	C₂×D₄	—	2	16	no	—
333	C₂×D₄	—	2	8	no	—
334	C₂×D₄	—	2	8	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	8	no	—
337	C₂×D₄	—	2	8	no	—
338	C₂²×C₄	—	2	8	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	8	no	—
341	C₂²×C₄	—	2	8	no	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	2	8	no	—
344	C₂²×C₄	—	2	16	no	—
345	C₂²×C₄	—	2	16	no	—
346	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
347	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
348	C₂²×C₄	#41×C₆₇	1	16	yes	complemented
349	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
350	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
351	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
352	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
353	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
354	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
355	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
356	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	—	2	8	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	16	no	—
364	C₄⋊C₄	—	2	8	no	—
365	C₂²⋊C₄	—	2	8	no	—
366	C₂²⋊C₄	—	2	16	no	—
367	C₂²⋊C₄	—	2	8	no	—
368	C₂²⋊C₄	—	2	8	no	—
369	C₂²⋊C₄	—	2	8	no	—
370	C₂²⋊C₄	—	2	16	no	—
371	C₂²⋊C₄	—	2	16	no	—
372	C₄²	—	2	8	no	—
373	C₄²	—	2	8	no	—
374	C₄²	—	2	8	no	—
375	C₄²	—	2	4	no	—
376	C₄²	—	2	16	no	—
377	C₄²	C₂×D₄×C₆₇	1	4	yes	—
378	C₄²	C₂×D₄×C₆₇	1	8	yes	—
379	C₄²	C₂×D₄×C₆₇	1	4	yes	—
380	C₄²	#41×C₆₇	1	8	yes	complemented
381	C₂³	—	2	4	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	8	no	—
384	C₂³	—	2	8	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	4	no	—
387	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
388	C₂³	C₂×#41×C₆₇	1	8	yes	—
389	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
390	Q₈	—	2	16	no	—
391	D₄	—	2	16	no	—
392	D₄	—	2	32	no	—
393	D₄	—	2	32	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	16	no	—
400	C₂×C₄	—	2	32	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	4	16	no	—
409	C₂×C₄	—	4	16	no	—
410	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
411	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
412	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
413	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
414	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
415	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
416	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
417	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	8	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	16	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	4	8	no	—
426	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
427	C₂²	C₂²×#41×C₆₇	1	4	yes	—
428	C₂²	C₂²×#41×C₆₇	1	2	yes	—
429	C₄	—	2	4	no	—
430	C₄	—	2	8	no	—
431	C₄	—	2	2	no	—
432	C₄	—	2	8	no	—
433	C₄	—	4	4	no	—
434	C₄	—	4	4	no	—
435	C₄	—	4	4	no	—
436	C₄	#525×C₆₇	1	8	yes	—
437	C₄	#532×C₆₇	1	4	yes	—
438	C₂	—	4	2	no	—
439	C₂	—	4	8	no	—
440	C₂	C₂×#525×C₆₇	1	2	yes	—
441	C₂	C₂×#532×C₆₇	1	1	yes	characteristic
442	C₂	C₆₇×#3444	1	4	yes	—

	subgroup	G/H
center	C₂×C₄²×C₆₇	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×#41×C₆₇	C₂	semidirect
2. C₆₇×#2399	C₂	semidirect
3. C₆₇×#2398	C₂	semidirect
4. C₆₇×#2397	C₂	semidirect
5. C₆₇×#2396	C₂	semidirect
6. C₆₇×#2395	C₂	semidirect
7. C₆₇×#2392	C₂	semidirect
8. C₆₇×#2392	C₂	semidirect
9. C₆₇×#2388	C₂	semidirect
10. C₄²×D₄×C₆₇	C₂	semidirect
11. C₄×#117×C₆₇	C₂	semidirect
88. C₂×C₄²×C₆₇	D₄	semidirect
126. C₂²×C₄×C₆₇	#41	semidirect
158. C₄²×C₆₇	#41	semidirect
216. #34547	C₆₇	direct (N × H)
222. C₂×C₄×#41	C₂×C₆₇	semidirect
223. #2399	C₂×C₆₇	semidirect
224. #2398	C₂×C₆₇	semidirect
225. #2397	C₂×C₆₇	semidirect
226. #2396	C₂×C₆₇	semidirect
227. #2395	C₂×C₆₇	semidirect
228. #2392	C₂×C₆₇	semidirect
229. #2392	C₂×C₆₇	semidirect
230. #2388	C₂×C₆₇	semidirect
231. C₄²×D₄	C₂×C₆₇	semidirect
232. C₄×#117	C₂×C₆₇	semidirect
233. C₆₇	#34547	direct (N × H)
310. C₂×C₄²	D₄×C₆₇	semidirect
348. C₂²×C₄	#41×C₆₇	semidirect
380. C₄²	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₆₇	2
C₆₇×#2399	2
C₆₇×#2398	2
C₆₇×#2397	2
C₆₇×#2396	2
C₆₇×#2395	2
C₆₇×#2392	2
C₆₇×#2388	2
C₄²×D₄×C₆₇	2
C₄×#117×C₆₇	2
#34547	67

Subgroups — C67×#34547 #30713798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34547 #30713798