Subgroups — C₆₇×#21405 #30700656

Order 17152.

1422 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1993	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1961	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1895	C₂	1	4	yes	maximal, complemented
7	C₄×#102×C₆₇	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₆₇	—	2	1	no	—
9	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
10	#532×C₆₇	—	2	4	no	—
11	#532×C₆₇	C₄	1	8	yes	complemented
12	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×#124×C₆₇	—	2	1	no	—
15	C₂×#121×C₆₇	—	2	1	no	—
16	C₂×#121×C₆₇	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₆₇	—	2	1	no	—
18	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×#102×C₆₇	C₂²	1	8	yes	—
21	C₄×M₁₆×C₆₇	—	2	4	no	—
22	C₂×#97×C₆₇	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
24	#383×C₆₇	—	2	1	no	—
25	#382×C₆₇	C₂²	1	2	yes	—
26	#381×C₆₇	—	2	1	no	—
27	#380×C₆₇	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
30	#376×C₆₇	—	2	1	no	—
31	#340×C₆₇	C₂²	1	8	yes	—
32	C₂×#41×C₆₇	—	2	8	no	—
33	C₂×#41×C₆₇	—	4	8	no	—
34	C₂²×Q₈×C₆₇	—	2	1	no	—
35	C₂²×D₄×C₆₇	—	2	2	no	—
36	C₂²×D₄×C₆₇	—	2	1	no	—
37	C₂²×D₄×C₆₇	—	2	1	no	—
38	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
39	C₂³×C₄×C₆₇	—	2	2	no	—
40	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₆₇	—	2	4	no	—
44	C₂×M₁₆×C₆₇	—	2	8	no	—
45	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
46	C₄⋊Q₈×C₆₇	—	2	2	no	—
47	C₄⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
48	#127×C₆₇	—	2	2	no	—
49	#127×C₆₇	C₂×C₄	1	4	yes	—
50	#124×C₆₇	—	2	8	no	—
51	#121×C₆₇	—	2	8	no	—
52	#121×C₆₇	—	2	4	no	—
53	#121×C₆₇	C₂×C₄	1	8	yes	—
54	C₄×D₄×C₆₇	—	2	8	no	—
55	C₄×D₄×C₆₇	—	2	4	no	—
56	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	—
57	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
63	C₂×C₄²×C₆₇	—	2	2	no	—
64	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
65	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₆₇	D₄	1	4	yes	—
68	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
70	#102×C₆₇	—	2	16	no	—
71	#97×C₆₇	—	2	4	no	—
72	C₄×C₈×C₆₇	—	2	4	no	—
73	#95×C₆₇	—	2	2	no	—
74	#95×C₆₇	—	2	2	no	—
75	#95×C₆₇	—	2	2	no	—
76	#95×C₆₇	—	2	2	no	—
77	C₂⁴×C₆₇	—	2	2	no	—
78	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
79	#41×C₆₇	—	4	32	no	—
80	C₂×Q₈×C₆₇	—	2	4	no	—
81	C₂×Q₈×C₆₇	—	4	4	no	—
82	C₂×D₄×C₆₇	—	2	8	no	—
83	C₂×D₄×C₆₇	—	2	4	no	—
84	C₂×D₄×C₆₇	—	2	4	no	—
85	C₂×D₄×C₆₇	—	2	2	no	—
86	C₂×D₄×C₆₇	—	2	8	no	—
87	C₂×D₄×C₆₇	—	4	4	no	—
88	C₂×D₄×C₆₇	—	4	4	no	—
89	C₂×D₄×C₆₇	—	4	8	no	—
90	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₆₇	—	2	4	no	—
92	C₂²×C₄×C₆₇	—	2	4	no	—
93	C₂²×C₄×C₆₇	—	2	2	no	—
94	C₂²×C₄×C₆₇	—	2	8	no	—
95	C₂²×C₄×C₆₇	—	2	4	no	—
96	C₂²×C₄×C₆₇	—	4	2	no	—
97	C₂²×C₄×C₆₇	—	4	8	no	—
98	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
100	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
105	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
108	M₁₆×C₆₇	—	2	16	no	—
109	C₂×C₈×C₆₇	—	2	4	no	—
110	C₂×C₈×C₆₇	—	2	4	no	—
111	C₂×C₈×C₆₇	#41	1	8	yes	complemented
112	C₄⋊C₄×C₆₇	—	2	4	no	—
113	C₄⋊C₄×C₆₇	—	2	2	no	—
114	C₄⋊C₄×C₆₇	—	2	8	no	—
115	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
116	C₂²⋊C₄×C₆₇	—	2	8	no	—
117	C₂²⋊C₄×C₆₇	—	2	8	no	—
118	C₂²⋊C₄×C₆₇	—	4	4	no	—
119	C₄²×C₆₇	—	4	4	no	—
120	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
121	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
122	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
123	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
124	C₄²×C₆₇	C₂×D₄	1	2	yes	—
125	C₄²×C₆₇	C₂×D₄	1	2	yes	—
126	C₂³×C₆₇	—	2	2	no	—
127	C₂³×C₆₇	—	2	2	no	—
128	C₂³×C₆₇	—	2	2	no	—
129	C₂³×C₆₇	—	2	4	no	—
130	C₂³×C₆₇	—	4	4	no	—
131	C₂³×C₆₇	—	4	4	no	—
132	C₂³×C₆₇	—	4	4	no	—
133	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₆₇	—	4	8	no	—
136	D₄×C₆₇	—	2	8	no	—
137	D₄×C₆₇	—	4	8	no	—
138	D₄×C₆₇	—	4	8	no	—
139	D₄×C₆₇	—	4	16	no	—
140	D₄×C₆₇	—	4	4	no	—
141	C₂×C₄×C₆₇	—	2	2	no	—
142	C₂×C₄×C₆₇	—	2	2	no	—
143	C₂×C₄×C₆₇	—	2	2	no	—
144	C₂×C₄×C₆₇	—	2	2	no	—
145	C₂×C₄×C₆₇	—	2	4	no	—
146	C₂×C₄×C₆₇	—	2	4	no	—
147	C₂×C₄×C₆₇	—	2	8	no	—
148	C₂×C₄×C₆₇	—	2	4	no	—
149	C₂×C₄×C₆₇	—	4	4	no	—
150	C₂×C₄×C₆₇	—	4	4	no	—
151	C₂×C₄×C₆₇	—	4	16	no	—
152	C₂×C₄×C₆₇	—	4	4	no	—
153	C₂×C₄×C₆₇	—	4	4	no	—
154	C₂×C₄×C₆₇	—	4	4	no	—
155	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	4	yes	—
161	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
164	C₈×C₆₇	—	2	8	no	—
165	C₂²×C₆₇	—	2	2	no	—
166	C₂²×C₆₇	—	2	2	no	—
167	C₂²×C₆₇	—	2	2	no	—
168	C₂²×C₆₇	—	4	4	no	—
169	C₂²×C₆₇	—	4	4	no	—
170	C₂²×C₆₇	—	4	4	no	—
171	C₂²×C₆₇	—	4	4	no	—
172	C₂²×C₆₇	—	8	8	no	—
173	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
174	C₂²×C₆₇	#532	1	2	yes	—
175	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
176	C₂²×C₆₇	#575	1	2	yes	—
177	C₄×C₆₇	—	2	2	no	—
178	C₄×C₆₇	—	2	2	no	—
179	C₄×C₆₇	—	2	2	no	—
180	C₄×C₆₇	—	2	2	no	—
181	C₄×C₆₇	—	4	4	no	—
182	C₄×C₆₇	—	8	4	no	—
183	C₄×C₆₇	#418	1	4	yes	—
184	C₄×C₆₇	C₄×#41	1	2	yes	—
185	C₄×C₆₇	#525	1	2	yes	—
186	#21405	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂×C₆₇	—	4	2	no	—
188	C₂×C₆₇	—	8	4	no	—
189	C₂×C₆₇	#2297	1	1	yes	characteristic
190	C₂×C₆₇	C₂×#418	1	1	yes	characteristic
191	C₂×C₆₇	#2896	1	1	yes	characteristic
192	C₂×C₆₇	#3171	1	4	yes	—
193	C₂×#532	C₂×C₆₇	1	1	yes	characteristic
194	C₂×C₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
195	#2283	C₂×C₆₇	1	1	yes	characteristic, complemented
196	#1993	C₂×C₆₇	1	2	yes	complemented
197	#1961	C₂×C₆₇	1	2	yes	complemented
198	#1895	C₂×C₆₇	1	4	yes	complemented
199	C₄×#102	C₂×C₆₇	1	4	yes	complemented
200	C₆₇	#21405	1	1	yes	characteristic, direct product factor, Sylow
201	C₂²×#41	—	2	1	no	—
202	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
203	#532	—	2	4	no	—
204	#532	C₄×C₆₇	1	8	yes	complemented
205	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
206	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
207	C₂×#124	—	2	1	no	—
208	C₂×#121	—	2	1	no	—
209	C₂×#121	C₂²×C₆₇	1	2	yes	—
210	C₂×C₄×D₄	—	2	1	no	—
211	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
212	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
213	C₂×#102	C₂²×C₆₇	1	8	yes	—
214	C₄×M₁₆	—	2	4	no	—
215	C₂×#97	C₂²×C₆₇	1	2	yes	—
216	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
217	#383	—	2	1	no	—
218	#382	C₂²×C₆₇	1	2	yes	—
219	#381	—	2	1	no	—
220	#380	C₂²×C₆₇	1	2	yes	—
221	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
222	C₄×C₂²⋊C₄	—	2	1	no	—
223	#376	—	2	1	no	—
224	#340	C₂²×C₆₇	1	8	yes	—
225	C₂×#41	—	2	8	no	—
226	C₂×#41	—	4	8	no	—
227	C₂²×Q₈	—	2	1	no	—
228	C₂²×D₄	—	2	2	no	—
229	C₂²×D₄	—	2	1	no	—
230	C₂²×D₄	—	2	1	no	—
231	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
234	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
236	C₂×M₁₆	—	2	4	no	—
237	C₂×M₁₆	—	2	8	no	—
238	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
239	C₄⋊Q₈	—	2	2	no	—
240	C₄⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
241	#127	—	2	2	no	—
242	#127	C₂×C₄×C₆₇	1	4	yes	—
243	#124	—	2	8	no	—
244	#121	—	2	8	no	—
245	#121	—	2	4	no	—
246	#121	C₂×C₄×C₆₇	1	8	yes	—
247	C₄×D₄	—	2	8	no	—
248	C₄×D₄	—	2	4	no	—
249	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
252	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
258	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
259	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
260	C₂×C₄²	D₄×C₆₇	1	4	yes	—
261	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
263	#102	—	2	16	no	—
264	#97	—	2	4	no	—
265	C₄×C₈	—	2	4	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	C₂⁴	—	2	2	no	—
271	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
272	#41	—	4	32	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	4	4	no	—
275	C₂×D₄	—	2	8	no	—
276	C₂×D₄	—	2	4	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	8	no	—
280	C₂×D₄	—	4	4	no	—
281	C₂×D₄	—	4	4	no	—
282	C₂×D₄	—	4	8	no	—
283	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	8	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	8	no	—
291	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
292	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
293	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
300	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
301	M₁₆	—	2	16	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	#41×C₆₇	1	8	yes	complemented
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	8	no	—
308	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
309	C₂²⋊C₄	—	2	8	no	—
310	C₂²⋊C₄	—	2	8	no	—
311	C₂²⋊C₄	—	4	4	no	—
312	C₄²	—	4	4	no	—
313	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
314	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
315	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
316	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
317	C₄²	C₂×D₄×C₆₇	1	2	yes	—
318	C₄²	C₂×D₄×C₆₇	1	2	yes	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	4	4	no	—
324	C₂³	—	4	4	no	—
325	C₂³	—	4	4	no	—
326	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
327	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
328	Q₈	—	4	8	no	—
329	D₄	—	2	8	no	—
330	D₄	—	4	8	no	—
331	D₄	—	4	8	no	—
332	D₄	—	4	16	no	—
333	D₄	—	4	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	16	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
349	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
350	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
351	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
352	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
353	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	4	yes	—
354	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
356	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
357	C₈	—	2	8	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	4	4	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	8	8	no	—
366	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
367	C₂²	#532×C₆₇	1	2	yes	—
368	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
369	C₂²	#575×C₆₇	1	2	yes	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	4	4	no	—
375	C₄	—	8	4	no	—
376	C₄	#418×C₆₇	1	4	yes	—
377	C₄	C₄×#41×C₆₇	1	2	yes	—
378	C₄	#525×C₆₇	1	2	yes	—
379	C₂	—	4	2	no	—
380	C₂	—	8	4	no	—
381	C₂	C₆₇×#2297	1	1	yes	characteristic
382	C₂	C₂×#418×C₆₇	1	1	yes	characteristic
383	C₂	C₆₇×#2896	1	1	yes	characteristic
384	C₂	C₆₇×#3171	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂³×C₆₇	C₂²×D₄
prime radical	C₂×#532×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×M₁₆×C₆₇	C₂	semidirect
3. C₆₇×#2283	C₂	semidirect
4. C₆₇×#1993	C₂	semidirect
5. C₆₇×#1961	C₂	semidirect
6. C₆₇×#1895	C₂	semidirect
7. C₄×#102×C₆₇	C₂	semidirect
11. #532×C₆₇	C₄	semidirect
111. C₂×C₈×C₆₇	#41	semidirect
186. #21405	C₆₇	direct (N × H)
194. C₂×C₄×M₁₆	C₂×C₆₇	semidirect
195. #2283	C₂×C₆₇	semidirect
196. #1993	C₂×C₆₇	semidirect
197. #1961	C₂×C₆₇	semidirect
198. #1895	C₂×C₆₇	semidirect
199. C₄×#102	C₂×C₆₇	semidirect
200. C₆₇	#21405	direct (N × H)
204. #532	C₄×C₆₇	semidirect
304. C₂×C₈	#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×#532×C₆₇	2
C₂×C₄×M₁₆×C₆₇	2
C₆₇×#2283	2
C₆₇×#1993	2
C₆₇×#1961	2
C₆₇×#1895	2
C₄×#102×C₆₇	2
#21405	67

Subgroups — C67×#21405 #30700656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#21405 #30700656