Subgroups — C₂×C₆₇×#1965 #30700466

Order 17152.

2206 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×#127×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#423×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#100×C₆₇	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1965	C₂	1	8	yes	maximal, direct product factor
6	C₂³×D₄×C₆₇	C₄	1	4	yes	—
7	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
8	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
9	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
10	C₂×#127×C₆₇	—	2	1	no	—
11	C₂×#127×C₆₇	—	2	1	no	—
12	C₂×#127×C₆₇	—	2	2	no	—
13	C₂×#127×C₆₇	—	2	2	no	—
14	C₂×#127×C₆₇	—	2	2	no	—
15	C₂×#127×C₆₇	C₄	1	4	yes	—
16	C₂×#127×C₆₇	C₂²	1	4	yes	—
17	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
18	#423×C₆₇	—	2	2	no	—
19	#423×C₆₇	C₂²	1	4	yes	complemented
20	C₂×C₄⋊C₈×C₆₇	—	2	2	no	—
21	C₂×#100×C₆₇	—	2	16	no	—
22	C₂×#100×C₆₇	C₂²	1	16	yes	complemented
23	C₄×M₁₆×C₆₇	—	2	2	no	—
24	C₄×M₁₆×C₆₇	C₂²	1	4	yes	complemented
25	C₂×#97×C₆₇	—	2	1	no	—
26	C₂×C₄×C₈×C₆₇	—	2	1	no	—
27	C₂⁵×C₆₇	C₂×C₄	1	4	yes	—
28	C₂²×D₄×C₆₇	—	2	8	no	—
29	C₂²×D₄×C₆₇	—	2	4	no	—
30	C₂²×D₄×C₆₇	—	2	4	no	—
31	C₂²×D₄×C₆₇	—	2	2	no	—
32	C₂²×D₄×C₆₇	—	2	2	no	—
33	C₂²×D₄×C₆₇	—	2	2	no	—
34	C₂²×D₄×C₆₇	—	2	2	no	—
35	C₂²×D₄×C₆₇	—	2	8	no	—
36	C₂²×D₄×C₆₇	—	2	8	no	—
37	C₂²×D₄×C₆₇	—	4	16	no	—
38	C₂²×D₄×C₆₇	C₂×C₄	1	4	yes	—
39	C₂²×D₄×C₆₇	C₂×C₄	1	16	yes	—
40	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
41	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₆₇	—	2	2	no	—
44	C₂×M₁₆×C₆₇	—	2	4	no	—
45	C₂×M₁₆×C₆₇	—	2	2	no	—
46	C₂×M₁₆×C₆₇	—	2	8	no	—
47	C₂×M₁₆×C₆₇	D₄	1	8	yes	complemented
48	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
49	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
50	C₂²×C₈×C₆₇	—	2	2	no	—
51	C₂²×C₈×C₆₇	—	2	2	no	—
52	#127×C₆₇	—	2	4	no	—
53	#127×C₆₇	—	2	8	no	—
54	#127×C₆₇	—	2	4	no	—
55	#127×C₆₇	—	2	8	no	—
56	#127×C₆₇	—	2	4	no	—
57	#127×C₆₇	—	2	4	no	—
58	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₆₇	D₄	1	2	yes	—
62	C₂×C₄²×C₆₇	D₄	1	2	yes	—
63	C₂×C₄²×C₆₇	D₄	1	2	yes	—
64	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
65	C₄⋊C₈×C₆₇	—	2	8	no	—
66	#100×C₆₇	—	2	32	no	—
67	#97×C₆₇	—	2	4	no	—
68	C₄×C₈×C₆₇	—	2	4	no	—
69	C₂⁴×C₆₇	—	2	4	no	—
70	C₂⁴×C₆₇	—	2	4	no	—
71	C₂⁴×C₆₇	—	2	16	no	—
72	C₂⁴×C₆₇	—	4	16	no	—
73	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
74	C₂⁴×C₆₇	C₂²×C₄	1	8	yes	—
75	C₂×D₄×C₆₇	—	2	16	no	—
76	C₂×D₄×C₆₇	—	2	4	no	—
77	C₂×D₄×C₆₇	—	2	4	no	—
78	C₂×D₄×C₆₇	—	2	16	no	—
79	C₂×D₄×C₆₇	—	2	16	no	—
80	C₂×D₄×C₆₇	—	2	8	no	—
81	C₂×D₄×C₆₇	—	2	4	no	—
82	C₂×D₄×C₆₇	—	2	4	no	—
83	C₂×D₄×C₆₇	—	2	8	no	—
84	C₂×D₄×C₆₇	—	4	16	no	—
85	C₂×D₄×C₆₇	—	4	32	no	—
86	C₂×D₄×C₆₇	—	4	32	no	—
87	C₂×D₄×C₆₇	—	4	16	no	—
88	C₂×D₄×C₆₇	—	4	8	no	—
89	C₂×D₄×C₆₇	—	4	8	no	—
90	C₂×D₄×C₆₇	—	4	4	no	—
91	C₂×D₄×C₆₇	—	4	4	no	—
92	C₂×D₄×C₆₇	—	4	4	no	—
93	C₂×D₄×C₆₇	—	4	4	no	—
94	C₂²×C₄×C₆₇	—	2	8	no	—
95	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
96	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
98	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₆₇	#41	1	4	yes	—
106	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
107	M₁₆×C₆₇	—	2	8	no	—
108	M₁₆×C₆₇	—	2	4	no	—
109	M₁₆×C₆₇	—	2	8	no	—
110	M₁₆×C₆₇	—	4	4	no	—
111	M₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
112	C₂×C₈×C₆₇	—	2	8	no	—
113	C₂×C₈×C₆₇	—	2	4	no	—
114	C₂×C₈×C₆₇	—	2	4	no	—
115	C₂×C₈×C₆₇	—	4	4	no	—
116	C₄²×C₆₇	C₂²⋊C₄	1	2	yes	—
117	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
118	C₄²×C₆₇	C₂²⋊C₄	1	2	yes	—
119	C₄²×C₆₇	C₂×D₄	1	4	yes	—
120	C₄²×C₆₇	C₂×D₄	1	2	yes	—
121	C₄²×C₆₇	C₂×D₄	1	2	yes	—
122	C₂³×C₆₇	—	2	4	no	—
123	C₂³×C₆₇	—	2	8	no	—
124	C₂³×C₆₇	—	2	16	no	—
125	C₂³×C₆₇	—	4	16	no	—
126	C₂³×C₆₇	—	4	16	no	—
127	C₂³×C₆₇	—	4	8	no	—
128	C₂³×C₆₇	—	4	8	no	—
129	C₂³×C₆₇	—	4	16	no	—
130	C₂³×C₆₇	—	8	32	no	—
131	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₆₇	C₄×D₄	1	4	yes	—
134	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
135	D₄×C₆₇	—	4	32	no	—
136	D₄×C₆₇	—	4	8	no	—
137	D₄×C₆₇	—	4	4	no	—
138	D₄×C₆₇	—	4	4	no	—
139	D₄×C₆₇	—	4	8	no	—
140	D₄×C₆₇	—	4	8	no	—
141	D₄×C₆₇	—	4	32	no	—
142	C₂×C₄×C₆₇	—	2	4	no	—
143	C₂×C₄×C₆₇	—	2	8	no	—
144	C₂×C₄×C₆₇	—	2	8	no	—
145	C₂×C₄×C₆₇	#100	1	8	yes	complemented
146	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
147	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
150	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
151	C₂×C₄×C₆₇	#121	1	4	yes	—
152	C₂×C₄×C₆₇	#121	1	4	yes	—
153	C₂×C₄×C₆₇	#124	1	2	yes	—
154	C₂×C₄×C₆₇	#124	1	2	yes	—
155	C₂×C₄×C₆₇	#127	1	2	yes	—
156	C₂×C₄×C₆₇	#127	1	2	yes	—
157	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
159	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
161	C₈×C₆₇	—	2	8	no	—
162	C₈×C₆₇	—	4	4	no	—
163	C₂²×C₆₇	—	2	2	no	—
164	C₂²×C₆₇	—	2	2	no	—
165	C₂²×C₆₇	—	2	8	no	—
166	C₂²×C₆₇	—	4	16	no	—
167	C₂²×C₆₇	—	4	8	no	—
168	C₂²×C₆₇	—	8	16	no	—
169	C₂²×C₆₇	—	8	16	no	—
170	C₂²×C₆₇	—	8	16	no	—
171	C₂²×C₆₇	#390	1	2	yes	—
172	C₂²×C₆₇	#390	1	2	yes	—
173	C₂²×C₆₇	C₂×#100	1	4	yes	—
174	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
175	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
176	C₄×C₆₇	—	2	4	no	—
177	C₄×C₆₇	#390	1	2	yes	—
178	C₄×C₆₇	#390	1	2	yes	—
179	C₄×C₆₇	C₂×#100	1	8	yes	complemented
180	C₄×C₆₇	C₂×#121	1	2	yes	—
181	C₄×C₆₇	C₂×#124	1	1	yes	characteristic
182	C₄×C₆₇	C₂×#127	1	1	yes	characteristic
183	C₂×#1965	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂×C₆₇	—	2	2	no	—
185	C₂×C₆₇	—	2	2	no	—
186	C₂×C₆₇	—	8	8	no	—
187	C₂×C₆₇	#1965	1	4	yes	direct product factor
188	C₂×C₆₇	C₂×#390	1	1	yes	characteristic
189	C₂×C₆₇	C₂²×#100	1	2	yes	—
190	C₂²×#127	C₂×C₆₇	1	1	yes	characteristic
191	C₂×#423	C₂×C₆₇	1	1	yes	characteristic, complemented
192	C₂²×#100	C₂×C₆₇	1	4	yes	complemented
193	C₂×C₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
194	#1965	C₂×C₆₇	1	8	yes	direct product factor
195	C₆₇	C₂×#1965	1	1	yes	characteristic, direct product factor, Sylow
196	C₂³×D₄	C₄×C₆₇	1	4	yes	—
197	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
198	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
199	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
200	C₂×#127	—	2	1	no	—
201	C₂×#127	—	2	1	no	—
202	C₂×#127	—	2	2	no	—
203	C₂×#127	—	2	2	no	—
204	C₂×#127	—	2	2	no	—
205	C₂×#127	C₄×C₆₇	1	4	yes	—
206	C₂×#127	C₂²×C₆₇	1	4	yes	—
207	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
208	#423	—	2	2	no	—
209	#423	C₂²×C₆₇	1	4	yes	complemented
210	C₂×C₄⋊C₈	—	2	2	no	—
211	C₂×#100	—	2	16	no	—
212	C₂×#100	C₂²×C₆₇	1	16	yes	complemented
213	C₄×M₁₆	—	2	2	no	—
214	C₄×M₁₆	C₂²×C₆₇	1	4	yes	complemented
215	C₂×#97	—	2	1	no	—
216	C₂×C₄×C₈	—	2	1	no	—
217	C₂⁵	C₂×C₄×C₆₇	1	4	yes	—
218	C₂²×D₄	—	2	4	no	—
219	C₂²×D₄	—	2	8	no	—
220	C₂²×D₄	—	2	4	no	—
221	C₂²×D₄	—	2	2	no	—
222	C₂²×D₄	—	2	2	no	—
223	C₂²×D₄	—	2	2	no	—
224	C₂²×D₄	—	2	2	no	—
225	C₂²×D₄	—	2	8	no	—
226	C₂²×D₄	—	2	8	no	—
227	C₂²×D₄	—	4	16	no	—
228	C₂²×D₄	C₂×C₄×C₆₇	1	4	yes	—
229	C₂²×D₄	C₂×C₄×C₆₇	1	16	yes	—
230	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
231	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
232	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	4	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	8	no	—
237	C₂×M₁₆	D₄×C₆₇	1	8	yes	complemented
238	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
239	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	#127	—	2	4	no	—
243	#127	—	2	8	no	—
244	#127	—	2	4	no	—
245	#127	—	2	4	no	—
246	#127	—	2	4	no	—
247	#127	—	2	8	no	—
248	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
249	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
250	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
251	C₂×C₄²	D₄×C₆₇	1	2	yes	—
252	C₂×C₄²	D₄×C₆₇	1	2	yes	—
253	C₂×C₄²	D₄×C₆₇	1	2	yes	—
254	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
255	C₄⋊C₈	—	2	8	no	—
256	#100	—	2	32	no	—
257	#97	—	2	4	no	—
258	C₄×C₈	—	2	4	no	—
259	C₂⁴	—	2	4	no	—
260	C₂⁴	—	2	4	no	—
261	C₂⁴	—	2	16	no	—
262	C₂⁴	—	4	16	no	—
263	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
264	C₂⁴	C₂²×C₄×C₆₇	1	8	yes	—
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	—	2	4	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	16	no	—
269	C₂×D₄	—	2	16	no	—
270	C₂×D₄	—	2	8	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	8	no	—
274	C₂×D₄	—	4	16	no	—
275	C₂×D₄	—	4	32	no	—
276	C₂×D₄	—	4	32	no	—
277	C₂×D₄	—	4	16	no	—
278	C₂×D₄	—	4	8	no	—
279	C₂×D₄	—	4	8	no	—
280	C₂×D₄	—	4	4	no	—
281	C₂×D₄	—	4	4	no	—
282	C₂×D₄	—	4	4	no	—
283	C₂×D₄	—	4	4	no	—
284	C₂²×C₄	—	2	8	no	—
285	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
286	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
287	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
289	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
295	C₂²×C₄	#41×C₆₇	1	4	yes	—
296	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
297	M₁₆	—	2	8	no	—
298	M₁₆	—	2	4	no	—
299	M₁₆	—	2	8	no	—
300	M₁₆	—	4	4	no	—
301	M₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
302	C₂×C₈	—	2	8	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	4	4	no	—
306	C₄²	C₂²⋊C₄×C₆₇	1	2	yes	—
307	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
308	C₄²	C₂²⋊C₄×C₆₇	1	2	yes	—
309	C₄²	C₂×D₄×C₆₇	1	2	yes	—
310	C₄²	C₂×D₄×C₆₇	1	2	yes	—
311	C₄²	C₂×D₄×C₆₇	1	4	yes	—
312	C₂³	—	2	4	no	—
313	C₂³	—	2	8	no	—
314	C₂³	—	2	16	no	—
315	C₂³	—	4	16	no	—
316	C₂³	—	4	16	no	—
317	C₂³	—	4	8	no	—
318	C₂³	—	4	8	no	—
319	C₂³	—	4	16	no	—
320	C₂³	—	8	32	no	—
321	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
322	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
323	C₂³	C₄×D₄×C₆₇	1	4	yes	—
324	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
325	D₄	—	4	32	no	—
326	D₄	—	4	8	no	—
327	D₄	—	4	4	no	—
328	D₄	—	4	4	no	—
329	D₄	—	4	8	no	—
330	D₄	—	4	8	no	—
331	D₄	—	4	32	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	#100×C₆₇	1	8	yes	complemented
336	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
338	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
339	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
340	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
341	C₂×C₄	#121×C₆₇	1	4	yes	—
342	C₂×C₄	#121×C₆₇	1	4	yes	—
343	C₂×C₄	#124×C₆₇	1	2	yes	—
344	C₂×C₄	#124×C₆₇	1	2	yes	—
345	C₂×C₄	#127×C₆₇	1	2	yes	—
346	C₂×C₄	#127×C₆₇	1	2	yes	—
347	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
349	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
350	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
351	C₈	—	2	8	no	—
352	C₈	—	4	4	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	8	no	—
356	C₂²	—	4	8	no	—
357	C₂²	—	4	16	no	—
358	C₂²	—	8	16	no	—
359	C₂²	—	8	16	no	—
360	C₂²	—	8	16	no	—
361	C₂²	#390×C₆₇	1	2	yes	—
362	C₂²	#390×C₆₇	1	2	yes	—
363	C₂²	C₂×#100×C₆₇	1	4	yes	—
364	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
365	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
366	C₄	—	2	4	no	—
367	C₄	#390×C₆₇	1	2	yes	—
368	C₄	#390×C₆₇	1	2	yes	—
369	C₄	C₂×#100×C₆₇	1	8	yes	complemented
370	C₄	C₂×#121×C₆₇	1	2	yes	—
371	C₄	C₂×#124×C₆₇	1	1	yes	characteristic
372	C₄	C₂×#127×C₆₇	1	1	yes	characteristic
373	C₂	—	2	2	no	—
374	C₂	—	2	2	no	—
375	C₂	—	8	8	no	—
376	C₂	C₆₇×#1965	1	4	yes	direct product factor
377	C₂	C₂×#390×C₆₇	1	1	yes	characteristic
378	C₂	C₂²×#100×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂²×#127×C₆₇	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#423×C₆₇	C₂	semidirect
3. C₂²×#100×C₆₇	C₂	semidirect
4. C₂×C₄×M₁₆×C₆₇	C₂	semidirect
5. C₆₇×#1965	C₂	direct (N × H)
19. #423×C₆₇	C₂²	semidirect
22. C₂×#100×C₆₇	C₂²	semidirect
24. C₄×M₁₆×C₆₇	C₂²	semidirect
47. C₂×M₁₆×C₆₇	D₄	semidirect
111. M₁₆×C₆₇	C₂×D₄	semidirect
145. C₂×C₄×C₆₇	#100	semidirect
179. C₄×C₆₇	C₂×#100	semidirect
183. C₂×#1965	C₆₇	direct (N × H)
187. C₂×C₆₇	#1965	direct (N × H)
191. C₂×#423	C₂×C₆₇	semidirect
192. C₂²×#100	C₂×C₆₇	semidirect
193. C₂×C₄×M₁₆	C₂×C₆₇	semidirect
194. #1965	C₂×C₆₇	direct (N × H)
195. C₆₇	C₂×#1965	direct (N × H)
209. #423	C₂²×C₆₇	semidirect
212. C₂×#100	C₂²×C₆₇	semidirect
214. C₄×M₁₆	C₂²×C₆₇	semidirect
237. C₂×M₁₆	D₄×C₆₇	semidirect
301. M₁₆	C₂×D₄×C₆₇	semidirect
335. C₂×C₄	#100×C₆₇	semidirect
369. C₄	C₂×#100×C₆₇	semidirect
376. C₂	C₆₇×#1965	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
C₂×#423×C₆₇	2
C₂²×#100×C₆₇	2
C₂×C₄×M₁₆×C₆₇	2
C₆₇×#1965	2
C₂×#1965	67

Subgroups — C2×C67×#1965 #30700466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1965 #30700466