Subgroups — C₂×C₆₇×#2619 #30713857

Order 17152.

4342 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#127×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#121×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂²×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2619	C₂	1	16	yes	maximal, direct product factor
5	C₂×#394×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂×#392×C₆₇	C₂	1	4	yes	maximal, complemented
7	C₂×#390×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#382×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
10	C₂³×D₄×C₆₇	C₂²	1	4	yes	—
11	C₂³×D₄×C₆₇	C₂²	1	4	yes	—
12	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×#127×C₆₇	—	2	8	no	—
14	C₂×#127×C₆₇	C₂²	1	8	yes	complemented
15	C₂×#121×C₆₇	—	2	16	no	—
16	C₂×#121×C₆₇	C₂²	1	16	yes	complemented
17	C₂×#117×C₆₇	—	2	8	no	—
18	C₂×#117×C₆₇	C₂²	1	8	yes	complemented
19	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
23	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	8	yes	—
24	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
26	#394×C₆₇	C₂²	1	32	yes	complemented
27	#392×C₆₇	C₂²	1	32	yes	complemented
28	#390×C₆₇	C₂²	1	16	yes	complemented
29	#382×C₆₇	C₂²	1	8	yes	complemented
30	C₂×#95×C₆₇	C₂²	1	4	yes	—
31	C₂⁵×C₆₇	C₂³	1	4	yes	—
32	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
33	C₂²×D₄×C₆₇	—	2	16	no	—
34	C₂²×D₄×C₆₇	—	2	8	no	—
35	C₂²×D₄×C₆₇	—	2	16	no	—
36	C₂²×D₄×C₆₇	—	2	8	no	—
37	C₂²×D₄×C₆₇	—	2	8	no	—
38	C₂²×D₄×C₆₇	—	4	16	no	—
39	C₂²×D₄×C₆₇	—	4	16	no	—
40	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
41	C₂²×D₄×C₆₇	C₂³	1	16	yes	—
42	C₂²×D₄×C₆₇	C₂³	1	16	yes	—
43	C₂³×C₄×C₆₇	—	2	4	no	—
44	C₂³×C₄×C₆₇	—	2	4	no	—
45	C₂³×C₄×C₆₇	D₄	1	8	yes	complemented
46	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
47	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
48	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
49	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
51	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
52	#127×C₆₇	—	2	32	no	—
53	#121×C₆₇	—	2	64	no	—
54	#117×C₆₇	—	2	32	no	—
55	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
56	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
57	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
58	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
59	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
60	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
61	C₂×C₂²⋊C₄×C₆₇	—	4	16	no	—
62	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
63	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
64	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	—
65	C₂×C₄²×C₆₇	—	2	4	no	—
66	C₂×C₄²×C₆₇	D₄	1	8	yes	complemented
67	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
68	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
69	#95×C₆₇	C₂³	1	16	yes	—
70	C₂⁴×C₆₇	—	2	2	no	—
71	C₂⁴×C₆₇	—	2	2	no	—
72	C₂⁴×C₆₇	—	2	8	no	—
73	C₂⁴×C₆₇	—	2	8	no	—
74	C₂⁴×C₆₇	—	2	8	no	—
75	C₂⁴×C₆₇	—	2	8	no	—
76	C₂⁴×C₆₇	—	2	16	no	—
77	C₂⁴×C₆₇	—	2	16	no	—
78	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
79	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
80	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
81	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
82	C₂×D₄×C₆₇	—	2	32	no	—
83	C₂×D₄×C₆₇	—	2	16	no	—
84	C₂×D₄×C₆₇	—	2	32	no	—
85	C₂×D₄×C₆₇	—	2	16	no	—
86	C₂×D₄×C₆₇	—	2	16	no	—
87	C₂×D₄×C₆₇	—	4	32	no	—
88	C₂×D₄×C₆₇	—	4	32	no	—
89	C₂×D₄×C₆₇	—	4	64	no	—
90	C₂×D₄×C₆₇	—	4	64	no	—
91	C₂×D₄×C₆₇	—	4	32	no	—
92	C₂²×C₄×C₆₇	—	2	2	no	—
93	C₂²×C₄×C₆₇	—	2	2	no	—
94	C₂²×C₄×C₆₇	—	2	8	no	—
95	C₂²×C₄×C₆₇	—	2	32	no	—
96	C₂²×C₄×C₆₇	—	2	8	no	—
97	C₂²×C₄×C₆₇	—	2	8	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	16	no	—
102	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
103	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
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	16	yes	complemented
107	C₂²×C₄×C₆₇	#41	1	4	yes	—
108	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
109	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
110	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
111	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
112	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
113	C₄⋊C₄×C₆₇	—	2	16	no	—
114	C₄⋊C₄×C₆₇	—	2	16	no	—
115	C₂²⋊C₄×C₆₇	—	2	16	no	—
116	C₂²⋊C₄×C₆₇	—	2	32	no	—
117	C₂²⋊C₄×C₆₇	—	4	32	no	—
118	C₄²×C₆₇	—	2	8	no	—
119	C₄²×C₆₇	C₂×D₄	1	16	yes	complemented
120	C₂³×C₆₇	—	2	8	no	—
121	C₂³×C₆₇	—	2	16	no	—
122	C₂³×C₆₇	—	2	2	no	—
123	C₂³×C₆₇	—	2	2	no	—
124	C₂³×C₆₇	—	2	8	no	—
125	C₂³×C₆₇	—	2	8	no	—
126	C₂³×C₆₇	—	2	8	no	—
127	C₂³×C₆₇	—	2	8	no	—
128	C₂³×C₆₇	—	2	16	no	—
129	C₂³×C₆₇	—	2	16	no	—
130	C₂³×C₆₇	—	4	8	no	—
131	C₂³×C₆₇	—	4	8	no	—
132	C₂³×C₆₇	—	4	16	no	—
133	C₂³×C₆₇	—	4	32	no	—
134	C₂³×C₆₇	—	4	16	no	—
135	C₂³×C₆₇	—	4	16	no	—
136	C₂³×C₆₇	—	4	32	no	—
137	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
138	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
139	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
140	C₂³×C₆₇	C₂×#41	1	2	yes	—
141	C₂³×C₆₇	H(5,𝔽₂)	1	8	yes	—
142	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
143	D₄×C₆₇	—	4	64	no	—
144	D₄×C₆₇	—	4	64	no	—
145	D₄×C₆₇	—	4	32	no	—
146	C₂×C₄×C₆₇	—	2	8	no	—
147	C₂×C₄×C₆₇	—	2	16	no	—
148	C₂×C₄×C₆₇	—	2	2	no	—
149	C₂×C₄×C₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	2	8	no	—
151	C₂×C₄×C₆₇	—	2	32	no	—
152	C₂×C₄×C₆₇	—	2	4	no	—
153	C₂×C₄×C₆₇	—	2	8	no	—
154	C₂×C₄×C₆₇	—	2	8	no	—
155	C₂×C₄×C₆₇	—	2	16	no	—
156	C₂×C₄×C₆₇	—	4	8	no	—
157	C₂×C₄×C₆₇	—	4	16	no	—
158	C₂×C₄×C₆₇	#121	1	16	yes	—
159	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
160	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
161	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
162	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
163	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
164	C₂²×C₆₇	—	2	4	no	—
165	C₂²×C₆₇	—	2	8	no	—
166	C₂²×C₆₇	—	4	16	no	—
167	C₂²×C₆₇	—	4	4	no	—
168	C₂²×C₆₇	—	4	4	no	—
169	C₂²×C₆₇	—	4	8	no	—
170	C₂²×C₆₇	—	4	16	no	—
171	C₂²×C₆₇	—	4	8	no	—
172	C₂²×C₆₇	—	4	8	no	—
173	C₂²×C₆₇	—	4	16	no	—
174	C₂²×C₆₇	—	8	32	no	—
175	C₂²×C₆₇	C₂×#121	1	4	yes	—
176	C₂²×C₆₇	#535	1	8	yes	—
177	C₂²×C₆₇	#535	1	8	yes	—
178	C₂²×C₆₇	#540	1	8	yes	—
179	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
180	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
181	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
182	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
183	C₄×C₆₇	—	2	4	no	—
184	C₄×C₆₇	—	2	8	no	—
185	C₄×C₆₇	—	4	4	no	—
186	C₄×C₆₇	—	4	8	no	—
187	C₄×C₆₇	C₂×#121	1	8	yes	—
188	C₂×#2619	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂×C₆₇	—	4	4	no	—
190	C₂×C₆₇	—	8	8	no	—
191	C₂×C₆₇	#2619	1	8	yes	direct product factor
192	C₂×C₆₇	C₂²×#121	1	1	yes	characteristic
193	C₂×C₆₇	C₂×#535	1	2	yes	—
194	C₂×C₆₇	C₂×#535	1	2	yes	—
195	C₂×C₆₇	C₂×#540	1	2	yes	—
196	C₂²×#127	C₂×C₆₇	1	1	yes	characteristic, complemented
197	C₂²×#121	C₂×C₆₇	1	2	yes	complemented
198	C₂²×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
199	#2619	C₂×C₆₇	1	16	yes	direct product factor
200	C₂×#394	C₂×C₆₇	1	4	yes	complemented
201	C₂×#392	C₂×C₆₇	1	4	yes	complemented
202	C₂×#390	C₂×C₆₇	1	2	yes	complemented
203	C₂×#382	C₂×C₆₇	1	1	yes	characteristic, complemented
204	C₆₇	C₂×#2619	1	1	yes	characteristic, direct product factor, Sylow
205	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
206	C₂³×D₄	C₂²×C₆₇	1	4	yes	—
207	C₂³×D₄	C₂²×C₆₇	1	4	yes	—
208	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
209	C₂×#127	—	2	8	no	—
210	C₂×#127	C₂²×C₆₇	1	8	yes	complemented
211	C₂×#121	—	2	16	no	—
212	C₂×#121	C₂²×C₆₇	1	16	yes	complemented
213	C₂×#117	—	2	8	no	—
214	C₂×#117	C₂²×C₆₇	1	8	yes	complemented
215	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
216	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
217	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
218	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
219	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	8	yes	—
220	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
221	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
222	#394	C₂²×C₆₇	1	32	yes	complemented
223	#392	C₂²×C₆₇	1	32	yes	complemented
224	#390	C₂²×C₆₇	1	16	yes	complemented
225	#382	C₂²×C₆₇	1	8	yes	complemented
226	C₂×#95	C₂²×C₆₇	1	4	yes	—
227	C₂⁵	C₂³×C₆₇	1	4	yes	—
228	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
229	C₂²×D₄	—	2	16	no	—
230	C₂²×D₄	—	2	8	no	—
231	C₂²×D₄	—	2	16	no	—
232	C₂²×D₄	—	2	8	no	—
233	C₂²×D₄	—	2	8	no	—
234	C₂²×D₄	—	4	16	no	—
235	C₂²×D₄	—	4	16	no	—
236	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
237	C₂²×D₄	C₂³×C₆₇	1	16	yes	—
238	C₂²×D₄	C₂³×C₆₇	1	16	yes	—
239	C₂³×C₄	—	2	4	no	—
240	C₂³×C₄	—	2	4	no	—
241	C₂³×C₄	D₄×C₆₇	1	8	yes	complemented
242	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
243	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
244	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
246	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
247	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
248	#127	—	2	32	no	—
249	#121	—	2	64	no	—
250	#117	—	2	32	no	—
251	C₂×C₄⋊C₄	—	2	8	no	—
252	C₂×C₄⋊C₄	—	2	8	no	—
253	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
254	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
255	C₂×C₂²⋊C₄	—	2	8	no	—
256	C₂×C₂²⋊C₄	—	2	16	no	—
257	C₂×C₂²⋊C₄	—	4	16	no	—
258	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
259	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
260	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	—
261	C₂×C₄²	—	2	4	no	—
262	C₂×C₄²	D₄×C₆₇	1	8	yes	complemented
263	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
264	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
265	#95	C₂³×C₆₇	1	16	yes	—
266	C₂⁴	—	2	2	no	—
267	C₂⁴	—	2	2	no	—
268	C₂⁴	—	2	8	no	—
269	C₂⁴	—	2	8	no	—
270	C₂⁴	—	2	8	no	—
271	C₂⁴	—	2	8	no	—
272	C₂⁴	—	2	16	no	—
273	C₂⁴	—	2	16	no	—
274	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
275	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
276	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
277	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
278	C₂×D₄	—	2	32	no	—
279	C₂×D₄	—	2	16	no	—
280	C₂×D₄	—	2	32	no	—
281	C₂×D₄	—	2	16	no	—
282	C₂×D₄	—	2	16	no	—
283	C₂×D₄	—	4	32	no	—
284	C₂×D₄	—	4	32	no	—
285	C₂×D₄	—	4	64	no	—
286	C₂×D₄	—	4	64	no	—
287	C₂×D₄	—	4	32	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	32	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	2	8	no	—
297	C₂²×C₄	—	2	16	no	—
298	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
299	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
300	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
301	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
302	C₂²×C₄	C₂×D₄×C₆₇	1	16	yes	complemented
303	C₂²×C₄	#41×C₆₇	1	4	yes	—
304	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
305	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
306	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
307	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
309	C₄⋊C₄	—	2	16	no	—
310	C₄⋊C₄	—	2	16	no	—
311	C₂²⋊C₄	—	2	16	no	—
312	C₂²⋊C₄	—	2	32	no	—
313	C₂²⋊C₄	—	4	32	no	—
314	C₄²	—	2	8	no	—
315	C₄²	C₂×D₄×C₆₇	1	16	yes	complemented
316	C₂³	—	2	8	no	—
317	C₂³	—	2	16	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	8	no	—
321	C₂³	—	2	8	no	—
322	C₂³	—	2	8	no	—
323	C₂³	—	2	8	no	—
324	C₂³	—	2	16	no	—
325	C₂³	—	2	16	no	—
326	C₂³	—	4	8	no	—
327	C₂³	—	4	8	no	—
328	C₂³	—	4	16	no	—
329	C₂³	—	4	32	no	—
330	C₂³	—	4	16	no	—
331	C₂³	—	4	16	no	—
332	C₂³	—	4	32	no	—
333	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
334	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
335	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
336	C₂³	C₂×#41×C₆₇	1	2	yes	—
337	C₂³	H(5,𝔽₂)×C₆₇	1	8	yes	—
338	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
339	D₄	—	4	64	no	—
340	D₄	—	4	64	no	—
341	D₄	—	4	32	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	2	16	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	32	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	2	16	no	—
352	C₂×C₄	—	4	16	no	—
353	C₂×C₄	—	4	8	no	—
354	C₂×C₄	#121×C₆₇	1	16	yes	—
355	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
356	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
357	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
358	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
359	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
360	C₂²	—	2	4	no	—
361	C₂²	—	2	8	no	—
362	C₂²	—	4	16	no	—
363	C₂²	—	4	4	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	4	8	no	—
366	C₂²	—	4	16	no	—
367	C₂²	—	4	8	no	—
368	C₂²	—	4	8	no	—
369	C₂²	—	4	16	no	—
370	C₂²	—	8	32	no	—
371	C₂²	C₂×#121×C₆₇	1	4	yes	—
372	C₂²	#535×C₆₇	1	8	yes	—
373	C₂²	#535×C₆₇	1	8	yes	—
374	C₂²	#540×C₆₇	1	8	yes	—
375	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
376	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
377	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
378	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
379	C₄	—	2	4	no	—
380	C₄	—	2	8	no	—
381	C₄	—	4	8	no	—
382	C₄	—	4	4	no	—
383	C₄	C₂×#121×C₆₇	1	8	yes	—
384	C₂	—	4	4	no	—
385	C₂	—	8	8	no	—
386	C₂	C₆₇×#2619	1	8	yes	direct product factor
387	C₂	C₂²×#121×C₆₇	1	1	yes	characteristic
388	C₂	C₂×#535×C₆₇	1	2	yes	—
389	C₂	C₂×#535×C₆₇	1	2	yes	—
390	C₂	C₂×#540×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
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
1. C₂²×#127×C₆₇	C₂	semidirect
2. C₂²×#121×C₆₇	C₂	semidirect
3. C₂²×#117×C₆₇	C₂	semidirect
4. C₆₇×#2619	C₂	direct (N × H)
5. C₂×#394×C₆₇	C₂	semidirect
6. C₂×#392×C₆₇	C₂	semidirect
7. C₂×#390×C₆₇	C₂	semidirect
8. C₂×#382×C₆₇	C₂	semidirect
14. C₂×#127×C₆₇	C₂²	semidirect
16. C₂×#121×C₆₇	C₂²	semidirect
18. C₂×#117×C₆₇	C₂²	semidirect
26. #394×C₆₇	C₂²	semidirect
27. #392×C₆₇	C₂²	semidirect
28. #390×C₆₇	C₂²	semidirect
29. #382×C₆₇	C₂²	semidirect
45. C₂³×C₄×C₆₇	D₄	semidirect
66. C₂×C₄²×C₆₇	D₄	semidirect
106. C₂²×C₄×C₆₇	C₂×D₄	semidirect
119. C₄²×C₆₇	C₂×D₄	semidirect
188. C₂×#2619	C₆₇	direct (N × H)
191. C₂×C₆₇	#2619	direct (N × H)
196. C₂²×#127	C₂×C₆₇	semidirect
197. C₂²×#121	C₂×C₆₇	semidirect
198. C₂²×#117	C₂×C₆₇	semidirect
199. #2619	C₂×C₆₇	direct (N × H)
200. C₂×#394	C₂×C₆₇	semidirect
201. C₂×#392	C₂×C₆₇	semidirect
202. C₂×#390	C₂×C₆₇	semidirect
203. C₂×#382	C₂×C₆₇	semidirect
204. C₆₇	C₂×#2619	direct (N × H)
210. C₂×#127	C₂²×C₆₇	semidirect
212. C₂×#121	C₂²×C₆₇	semidirect
214. C₂×#117	C₂²×C₆₇	semidirect
222. #394	C₂²×C₆₇	semidirect
223. #392	C₂²×C₆₇	semidirect
224. #390	C₂²×C₆₇	semidirect
225. #382	C₂²×C₆₇	semidirect
241. C₂³×C₄	D₄×C₆₇	semidirect
262. C₂×C₄²	D₄×C₆₇	semidirect
302. C₂²×C₄	C₂×D₄×C₆₇	semidirect
315. C₄²	C₂×D₄×C₆₇	semidirect
386. C₂	C₆₇×#2619	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×#127×C₆₇	2
C₂²×#121×C₆₇	2
C₂²×#117×C₆₇	2
C₆₇×#2619	2
C₂×#394×C₆₇	2
C₂×#392×C₆₇	2
C₂×#390×C₆₇	2
C₂×#382×C₆₇	2
C₂×#2619	67

Subgroups — C2×C67×#2619 #30713857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2619 #30713857