Subgroups — C₂×C₆₇×#2632 #30713850

Order 17152.

2806 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2632	C₂	1	16	yes	maximal, direct product factor
4	C₂×#399×C₆₇	C₂	1	2	yes	maximal, complemented
5	C₂×#395×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#394×C₆₇	C₂	1	2	yes	maximal
7	C₂×#393×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#388×C₆₇	C₂	1	4	yes	maximal, complemented
9	C₂×#383×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×#124×C₆₇	—	2	8	no	—
14	C₂×#124×C₆₇	C₂²	1	8	yes	—
15	C₂×C₄×Q₈×C₆₇	—	2	8	no	—
16	C₂×C₄×Q₈×C₆₇	C₂²	1	8	yes	complemented
17	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
20	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
22	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
24	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
25	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
26	#399×C₆₇	C₂²	1	16	yes	complemented
27	#395×C₆₇	C₂²	1	16	yes	complemented
28	#394×C₆₇	C₂²	1	16	yes	—
29	#393×C₆₇	C₂²	1	16	yes	complemented
30	#388×C₆₇	C₂²	1	32	yes	complemented
31	#383×C₆₇	C₂²	1	8	yes	complemented
32	C₂×#95×C₆₇	C₂²	1	2	yes	—
33	C₂×#95×C₆₇	C₂²	1	2	yes	—
34	C₂×#95×C₆₇	C₂²	1	2	yes	—
35	C₂×#95×C₆₇	C₂²	1	4	yes	—
36	C₂⁵×C₆₇	C₂³	1	2	yes	—
37	C₂²×Q₈×C₆₇	—	2	4	no	—
38	C₂²×Q₈×C₆₇	—	2	4	no	—
39	C₂²×Q₈×C₆₇	—	2	8	no	—
40	C₂²×Q₈×C₆₇	—	4	4	no	—
41	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
42	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
43	C₂²×D₄×C₆₇	—	2	4	no	—
44	C₂²×D₄×C₆₇	—	4	4	no	—
45	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
46	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
47	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
48	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
49	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
53	#124×C₆₇	—	2	32	no	—
54	C₄×Q₈×C₆₇	—	2	32	no	—
55	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
56	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
57	C₂×C₄⋊C₄×C₆₇	—	4	8	no	—
58	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
59	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	—
61	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
62	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
63	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
64	C₂×C₂²⋊C₄×C₆₇	—	4	8	no	—
65	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
66	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
67	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
68	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
69	C₂×C₄²×C₆₇	—	2	8	no	—
70	C₂×C₄²×C₆₇	D₄	1	8	yes	—
71	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
72	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
73	#95×C₆₇	C₂³	1	8	yes	—
74	#95×C₆₇	C₂³	1	8	yes	—
75	#95×C₆₇	C₂³	1	8	yes	—
76	#95×C₆₇	C₂³	1	16	yes	—
77	C₂⁴×C₆₇	—	2	4	no	—
78	C₂⁴×C₆₇	—	2	8	no	—
79	C₂⁴×C₆₇	—	2	8	no	—
80	C₂⁴×C₆₇	—	2	8	no	—
81	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
82	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
83	C₂×Q₈×C₆₇	—	2	32	no	—
84	C₂×Q₈×C₆₇	—	2	8	no	—
85	C₂×Q₈×C₆₇	—	2	8	no	—
86	C₂×Q₈×C₆₇	—	2	16	no	—
87	C₂×Q₈×C₆₇	—	4	8	no	—
88	C₂×Q₈×C₆₇	—	4	16	no	—
89	C₂×D₄×C₆₇	—	2	8	no	—
90	C₂×D₄×C₆₇	—	4	8	no	—
91	C₂×D₄×C₆₇	—	4	16	no	—
92	C₂²×C₄×C₆₇	—	2	4	no	—
93	C₂²×C₄×C₆₇	—	2	4	no	—
94	C₂²×C₄×C₆₇	—	2	4	no	—
95	C₂²×C₄×C₆₇	—	2	4	no	—
96	C₂²×C₄×C₆₇	—	2	4	no	—
97	C₂²×C₄×C₆₇	—	2	4	no	—
98	C₂²×C₄×C₆₇	—	2	4	no	—
99	C₂²×C₄×C₆₇	—	2	8	no	—
100	C₂²×C₄×C₆₇	—	2	8	no	—
101	C₂²×C₄×C₆₇	—	2	8	no	—
102	C₂²×C₄×C₆₇	—	2	8	no	—
103	C₂²×C₄×C₆₇	—	2	8	no	—
104	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₆₇	#41	1	8	yes	—
108	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
109	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
111	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
112	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
113	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
115	C₄⋊C₄×C₆₇	—	2	16	no	—
116	C₄⋊C₄×C₆₇	—	2	8	no	—
117	C₄⋊C₄×C₆₇	—	4	16	no	—
118	C₂²⋊C₄×C₆₇	—	2	16	no	—
119	C₂²⋊C₄×C₆₇	—	2	16	no	—
120	C₂²⋊C₄×C₆₇	—	2	32	no	—
121	C₂²⋊C₄×C₆₇	—	4	16	no	—
122	C₄²×C₆₇	—	2	16	no	—
123	C₄²×C₆₇	C₂×D₄	1	16	yes	—
124	C₂³×C₆₇	—	2	4	no	—
125	C₂³×C₆₇	—	2	8	no	—
126	C₂³×C₆₇	—	2	8	no	—
127	C₂³×C₆₇	—	2	8	no	—
128	C₂³×C₆₇	—	4	8	no	—
129	C₂³×C₆₇	—	4	8	no	—
130	C₂³×C₆₇	—	4	8	no	—
131	C₂³×C₆₇	—	4	32	no	—
132	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
133	C₂³×C₆₇	C₂×#41	1	4	yes	—
134	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
135	C₂³×C₆₇	2₋¹⁺⁴	1	4	yes	—
136	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
137	Q₈×C₆₇	—	2	32	no	—
138	Q₈×C₆₇	—	4	16	no	—
139	D₄×C₆₇	—	4	16	no	—
140	C₂×C₄×C₆₇	—	2	8	no	—
141	C₂×C₄×C₆₇	—	2	16	no	—
142	C₂×C₄×C₆₇	—	2	8	no	—
143	C₂×C₄×C₆₇	—	2	8	no	—
144	C₂×C₄×C₆₇	—	2	4	no	—
145	C₂×C₄×C₆₇	—	2	4	no	—
146	C₂×C₄×C₆₇	—	2	4	no	—
147	C₂×C₄×C₆₇	—	2	4	no	—
148	C₂×C₄×C₆₇	—	2	4	no	—
149	C₂×C₄×C₆₇	—	2	4	no	—
150	C₂×C₄×C₆₇	—	2	4	no	—
151	C₂×C₄×C₆₇	—	2	8	no	—
152	C₂×C₄×C₆₇	—	2	8	no	—
153	C₂×C₄×C₆₇	—	2	8	no	—
154	C₂×C₄×C₆₇	—	2	8	no	—
155	C₂×C₄×C₆₇	—	2	8	no	—
156	C₂×C₄×C₆₇	—	4	8	no	—
157	C₂×C₄×C₆₇	—	4	8	no	—
158	C₂×C₄×C₆₇	—	4	16	no	—
159	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
160	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
161	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
162	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
163	C₂²×C₆₇	—	4	4	no	—
164	C₂²×C₆₇	—	4	4	no	—
165	C₂²×C₆₇	—	4	4	no	—
166	C₂²×C₆₇	—	4	16	no	—
167	C₂²×C₆₇	—	8	16	no	—
168	C₂²×C₆₇	#525	1	4	yes	—
169	C₂²×C₆₇	#535	1	4	yes	—
170	C₂²×C₆₇	#536	1	4	yes	—
171	C₂²×C₆₇	#542	1	16	yes	—
172	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
173	C₂²×C₆₇	C₂²×#41	1	2	yes	—
174	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
175	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
176	C₄×C₆₇	—	2	4	no	—
177	C₄×C₆₇	—	2	8	no	—
178	C₄×C₆₇	—	2	4	no	—
179	C₄×C₆₇	—	2	4	no	—
180	C₄×C₆₇	—	4	4	no	—
181	C₄×C₆₇	—	4	4	no	—
182	C₄×C₆₇	—	4	8	no	—
183	C₂×#2632	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂×C₆₇	—	8	4	no	—
185	C₂×C₆₇	#2632	1	8	yes	direct product factor
186	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
187	C₂×C₆₇	C₂×#535	1	1	yes	characteristic
188	C₂×C₆₇	C₂×#536	1	1	yes	characteristic
189	C₂×C₆₇	C₂×#542	1	4	yes	—
190	C₂²×#124	C₂×C₆₇	1	1	yes	characteristic
191	C₂²×C₄×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
192	#2632	C₂×C₆₇	1	16	yes	direct product factor
193	C₂×#399	C₂×C₆₇	1	2	yes	complemented
194	C₂×#395	C₂×C₆₇	1	2	yes	complemented
195	C₂×#394	C₂×C₆₇	1	2	yes	—
196	C₂×#393	C₂×C₆₇	1	2	yes	complemented
197	C₂×#388	C₂×C₆₇	1	4	yes	complemented
198	C₂×#383	C₂×C₆₇	1	1	yes	characteristic, complemented
199	C₆₇	C₂×#2632	1	1	yes	characteristic, direct product factor, Sylow
200	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
201	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
202	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
203	C₂×#124	—	2	8	no	—
204	C₂×#124	C₂²×C₆₇	1	8	yes	—
205	C₂×C₄×Q₈	—	2	8	no	—
206	C₂×C₄×Q₈	C₂²×C₆₇	1	8	yes	complemented
207	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
208	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
209	C₂²×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
210	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
211	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
212	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
213	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
214	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
215	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
216	#399	C₂²×C₆₇	1	16	yes	complemented
217	#395	C₂²×C₆₇	1	16	yes	complemented
218	#394	C₂²×C₆₇	1	16	yes	—
219	#393	C₂²×C₆₇	1	16	yes	complemented
220	#388	C₂²×C₆₇	1	32	yes	complemented
221	#383	C₂²×C₆₇	1	8	yes	complemented
222	C₂×#95	C₂²×C₆₇	1	4	yes	—
223	C₂×#95	C₂²×C₆₇	1	2	yes	—
224	C₂×#95	C₂²×C₆₇	1	2	yes	—
225	C₂×#95	C₂²×C₆₇	1	2	yes	—
226	C₂⁵	C₂³×C₆₇	1	2	yes	—
227	C₂²×Q₈	—	2	4	no	—
228	C₂²×Q₈	—	2	4	no	—
229	C₂²×Q₈	—	2	8	no	—
230	C₂²×Q₈	—	4	4	no	—
231	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
232	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
233	C₂²×D₄	—	2	4	no	—
234	C₂²×D₄	—	4	4	no	—
235	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
236	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
237	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
238	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
239	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
241	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
242	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
243	#124	—	2	32	no	—
244	C₄×Q₈	—	2	32	no	—
245	C₂×C₄⋊C₄	—	2	8	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	4	8	no	—
248	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
249	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
250	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	—
251	C₂×C₂²⋊C₄	—	2	8	no	—
252	C₂×C₂²⋊C₄	—	2	8	no	—
253	C₂×C₂²⋊C₄	—	2	16	no	—
254	C₂×C₂²⋊C₄	—	4	8	no	—
255	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
256	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
257	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
258	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
259	C₂×C₄²	—	2	8	no	—
260	C₂×C₄²	D₄×C₆₇	1	8	yes	—
261	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
262	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
263	#95	C₂³×C₆₇	1	8	yes	—
264	#95	C₂³×C₆₇	1	8	yes	—
265	#95	C₂³×C₆₇	1	8	yes	—
266	#95	C₂³×C₆₇	1	16	yes	—
267	C₂⁴	—	2	4	no	—
268	C₂⁴	—	2	8	no	—
269	C₂⁴	—	2	8	no	—
270	C₂⁴	—	2	8	no	—
271	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
272	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
273	C₂×Q₈	—	2	32	no	—
274	C₂×Q₈	—	2	8	no	—
275	C₂×Q₈	—	2	8	no	—
276	C₂×Q₈	—	2	16	no	—
277	C₂×Q₈	—	4	8	no	—
278	C₂×Q₈	—	4	16	no	—
279	C₂×D₄	—	2	8	no	—
280	C₂×D₄	—	4	8	no	—
281	C₂×D₄	—	4	16	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	8	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
295	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
296	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
297	C₂²×C₄	#41×C₆₇	1	8	yes	—
298	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
299	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
300	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
301	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
302	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
303	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
304	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
305	C₄⋊C₄	—	2	16	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	4	16	no	—
308	C₂²⋊C₄	—	2	16	no	—
309	C₂²⋊C₄	—	2	16	no	—
310	C₂²⋊C₄	—	2	32	no	—
311	C₂²⋊C₄	—	4	16	no	—
312	C₄²	—	2	16	no	—
313	C₄²	C₂×D₄×C₆₇	1	16	yes	—
314	C₂³	—	2	4	no	—
315	C₂³	—	2	8	no	—
316	C₂³	—	2	8	no	—
317	C₂³	—	2	8	no	—
318	C₂³	—	4	8	no	—
319	C₂³	—	4	8	no	—
320	C₂³	—	4	8	no	—
321	C₂³	—	4	32	no	—
322	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
323	C₂³	C₂×#41×C₆₇	1	4	yes	—
324	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
325	C₂³	2₋¹⁺⁴×C₆₇	1	4	yes	—
326	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
327	Q₈	—	2	32	no	—
328	Q₈	—	4	16	no	—
329	D₄	—	4	16	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	16	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	4	8	no	—
347	C₂×C₄	—	4	8	no	—
348	C₂×C₄	—	4	16	no	—
349	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
350	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
351	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
352	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
353	C₂²	—	4	4	no	—
354	C₂²	—	4	4	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	4	16	no	—
357	C₂²	—	8	16	no	—
358	C₂²	#525×C₆₇	1	4	yes	—
359	C₂²	#535×C₆₇	1	4	yes	—
360	C₂²	#536×C₆₇	1	4	yes	—
361	C₂²	#542×C₆₇	1	16	yes	—
362	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
363	C₂²	C₂²×#41×C₆₇	1	2	yes	—
364	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
365	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	2	yes	—
366	C₄	—	2	4	no	—
367	C₄	—	2	8	no	—
368	C₄	—	2	4	no	—
369	C₄	—	2	4	no	—
370	C₄	—	4	4	no	—
371	C₄	—	4	4	no	—
372	C₄	—	4	8	no	—
373	C₂	—	8	4	no	—
374	C₂	C₆₇×#2632	1	8	yes	direct product factor
375	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
376	C₂	C₂×#535×C₆₇	1	1	yes	characteristic
377	C₂	C₂×#536×C₆₇	1	1	yes	characteristic
378	C₂	C₂×#542×C₆₇	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂³×D₄×C₆₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Q₈×C₆₇	C₂	semidirect
3. C₆₇×#2632	C₂	direct (N × H)
4. C₂×#399×C₆₇	C₂	semidirect
5. C₂×#395×C₆₇	C₂	semidirect
7. C₂×#393×C₆₇	C₂	semidirect
8. C₂×#388×C₆₇	C₂	semidirect
9. C₂×#383×C₆₇	C₂	semidirect
16. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
26. #399×C₆₇	C₂²	semidirect
27. #395×C₆₇	C₂²	semidirect
29. #393×C₆₇	C₂²	semidirect
30. #388×C₆₇	C₂²	semidirect
31. #383×C₆₇	C₂²	semidirect
183. C₂×#2632	C₆₇	direct (N × H)
185. C₂×C₆₇	#2632	direct (N × H)
191. C₂²×C₄×Q₈	C₂×C₆₇	semidirect
192. #2632	C₂×C₆₇	direct (N × H)
193. C₂×#399	C₂×C₆₇	semidirect
194. C₂×#395	C₂×C₆₇	semidirect
196. C₂×#393	C₂×C₆₇	semidirect
197. C₂×#388	C₂×C₆₇	semidirect
198. C₂×#383	C₂×C₆₇	semidirect
199. C₆₇	C₂×#2632	direct (N × H)
206. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
216. #399	C₂²×C₆₇	semidirect
217. #395	C₂²×C₆₇	semidirect
219. #393	C₂²×C₆₇	semidirect
220. #388	C₂²×C₆₇	semidirect
221. #383	C₂²×C₆₇	semidirect
374. C₂	C₆₇×#2632	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#124×C₆₇	2
C₂²×C₄×Q₈×C₆₇	2
C₆₇×#2632	2
C₂×#399×C₆₇	2
C₂×#395×C₆₇	2
C₂×#394×C₆₇	2
C₂×#393×C₆₇	2
C₂×#388×C₆₇	2
C₂×#383×C₆₇	2
C₂×#2632	67

Subgroups — C2×C67×#2632 #30713850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2632 #30713850