Subgroups — #30761687

Order 17152.

986 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	C₄×#14524002	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863157	C₂	1	4	yes	maximal
4	C₂×#423×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#14524002	C₂²	1	2	yes	—
6	C₂²×C₄⋊Dic₆₇	—	2	1	no	—
7	C₂²×C₄×Dic₆₇	C₂²	1	2	yes	—
8	C₄×C₄⋊Dic₆₇	—	2	2	no	—
9	C₄×C₄⋊Dic₆₇	C₄	1	2	yes	complemented
10	C₄×C₄⋊Dic₆₇	C₄	1	2	yes	complemented
11	C₄×C₄⋊Dic₆₇	C₄	1	4	yes	complemented
12	C₄×C₂²⋊Dic₆₇	—	2	1	no	—
13	C₄×C₂²⋊Dic₆₇	—	2	1	no	—
14	#16863242	—	2	1	no	—
15	C₂×C₆₇⋊#95	—	2	1	no	—
16	C₄²×Dic₆₇	—	2	1	no	—
17	#16863157	—	2	8	no	—
18	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
20	#423×C₆₇	—	2	2	no	—
21	#423×C₆₇	C₄	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₆₇	—	2	1	no	—
23	C₂×C₄⋊C₈×C₆₇	—	2	1	no	—
24	C₂³×Dic₆₇	—	2	2	no	—
25	#14524002	—	2	2	no	—
26	#14524002	—	2	2	no	—
27	#14524002	D₄	1	4	yes	—
28	#14524002	Q₈	1	4	yes	—
29	C₂×C₄⋊Dic₆₇	—	2	8	no	—
30	C₂×C₄⋊Dic₆₇	—	2	4	no	—
31	C₂×C₄⋊Dic₆₇	C₂×C₄	1	4	yes	—
32	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
33	C₂×C₄×Dic₆₇	—	2	2	no	—
34	C₂×C₄×Dic₆₇	—	2	2	no	—
35	C₂×C₄×Dic₆₇	—	2	2	no	—
36	C₂×C₄×Dic₆₇	—	2	4	no	—
37	C₂×C₄×Dic₆₇	—	2	2	no	—
38	C₂×C₄×Dic₆₇	—	2	4	no	—
39	C₂×C₄×Dic₆₇	C₂×C₄	1	4	yes	—
40	C₆₇⋊#95	—	2	4	no	—
41	C₆₇⋊#95	—	2	2	no	—
42	C₆₇⋊#95	—	2	2	no	—
43	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₆₇	—	2	2	no	—
47	C₂×M₁₆×C₆₇	—	2	4	no	—
48	C₂×M₁₆×C₆₇	—	2	4	no	—
49	C₂×M₁₆×C₆₇	C₂×C₄	1	4	yes	—
50	C₂²×C₈×C₆₇	—	2	2	no	—
51	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₆₇	D₄	1	2	yes	—
58	C₂×C₄²×C₆₇	Q₈	1	2	yes	—
59	C₄⋊C₈×C₆₇	—	2	4	no	—
60	C₄⋊C₈×C₆₇	—	2	4	no	—
61	C₂²×Dic₆₇	—	2	8	no	—
62	C₂²×Dic₆₇	—	2	4	no	—
63	C₂²×Dic₆₇	—	2	4	no	—
64	C₂²×Dic₆₇	—	4	4	no	—
65	C₂²×Dic₆₇	—	4	4	no	—
66	C₄⋊Dic₆₇	—	2	16	no	—
67	C₄⋊Dic₆₇	—	2	4	no	—
68	C₄⋊Dic₆₇	C₄⋊C₄	1	8	yes	complemented
69	C₂²⋊Dic₆₇	—	2	4	no	—
70	C₂²⋊Dic₆₇	—	2	4	no	—
71	C₄×Dic₆₇	—	2	4	no	—
72	C₄×Dic₆₇	—	2	4	no	—
73	C₄×Dic₆₇	—	2	8	no	—
74	C₄×Dic₆₇	—	4	4	no	—
75	C₄×Dic₆₇	—	4	4	no	—
76	C₄×Dic₆₇	—	4	2	no	—
77	C₄×Dic₆₇	—	4	2	no	—
78	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₇	—	2	4	no	—
80	C₂²×C₄×C₆₇	—	4	2	no	—
81	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
85	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
86	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₇	C₄⋊C₄	1	2	yes	—
88	C₂²×C₄×C₆₇	C₄⋊C₄	1	2	yes	—
89	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
97	C₂²×C₄×C₆₇	#41	1	2	yes	—
98	C₂²×C₄×C₆₇	#41	1	2	yes	—
99	M₁₆×C₆₇	—	2	8	no	—
100	M₁₆×C₆₇	—	4	2	no	—
101	M₁₆×C₆₇	—	4	2	no	—
102	C₂×C₈×C₆₇	—	2	4	no	—
103	C₂×C₈×C₆₇	—	4	4	no	—
104	C₄²×C₆₇	C₄²	1	2	yes	—
105	C₄²×C₆₇	C₄²	1	2	yes	—
106	C₄²×C₆₇	C₂²⋊C₄	1	2	yes	—
107	C₄²×C₆₇	C₂²⋊C₄	1	2	yes	—
108	C₄²×C₆₇	C₄⋊C₄	1	2	yes	—
109	C₄²×C₆₇	C₄⋊C₄	1	2	yes	—
110	C₄²×C₆₇	C₄⋊C₄	1	2	yes	—
111	C₄²×C₆₇	C₄⋊C₄	1	2	yes	—
112	C₂³×C₆₇	—	2	2	no	—
113	C₂³×C₆₇	—	2	2	no	—
114	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
116	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
117	C₂³×C₆₇	#121	1	2	yes	—
118	C₂³×C₆₇	C₂²⋊Q₈	1	2	yes	—
119	C₂×C₄×C₆₇	—	2	2	no	—
120	C₂×C₄×C₆₇	—	2	2	no	—
121	C₂×C₄×C₆₇	—	2	2	no	—
122	C₂×C₄×C₆₇	—	2	4	no	—
123	C₂×C₄×C₆₇	—	2	4	no	—
124	C₂×C₄×C₆₇	—	4	2	no	—
125	C₂×C₄×C₆₇	—	4	2	no	—
126	C₂×C₄×C₆₇	#95	1	2	yes	—
127	C₂×C₄×C₆₇	#95	1	2	yes	—
128	C₂×C₄×C₆₇	#95	1	2	yes	—
129	C₂×C₄×C₆₇	#95	1	2	yes	—
130	C₂×C₄×C₆₇	#104	1	4	yes	—
131	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
132	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
134	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₆₇	#117	1	2	yes	—
137	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
138	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
139	C₂×C₄×C₆₇	C₄×Q₈	1	2	yes	—
140	C₂×C₄×C₆₇	C₄×Q₈	1	2	yes	—
141	C₂×C₄×C₆₇	#121	1	2	yes	—
142	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
144	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
145	C₂×C₄×C₆₇	#125	1	2	yes	—
146	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₄⋊Q₈	1	2	yes	—
149	C₂×Dic₆₇	—	2	8	no	—
150	C₂×Dic₆₇	—	2	8	no	—
151	C₂×Dic₆₇	—	4	16	no	—
152	C₂×Dic₆₇	—	4	4	no	—
153	C₂×Dic₆₇	—	4	4	no	—
154	C₂×Dic₆₇	—	4	4	no	—
155	C₂×Dic₆₇	—	4	4	no	—
156	C₈×C₆₇	—	4	4	no	—
157	C₂²×C₆₇	—	2	4	no	—
158	C₂²×C₆₇	—	2	4	no	—
159	C₂²×C₆₇	—	2	1	no	—
160	C₂²×C₆₇	—	2	1	no	—
161	C₂²×C₆₇	—	2	1	no	—
162	C₂²×C₆₇	—	2	1	no	—
163	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
164	C₂²×C₆₇	#380	1	2	yes	—
165	C₂²×C₆₇	#389	1	2	yes	—
166	C₂²×C₆₇	#390	1	1	yes	characteristic
167	C₂²×C₆₇	#391	1	1	yes	characteristic
168	C₂²×C₆₇	C₂×#104	1	2	yes	—
169	C₂²×C₆₇	#421	1	2	yes	—
170	C₄×C₆₇	—	2	2	no	—
171	C₄×C₆₇	—	2	2	no	—
172	C₄×C₆₇	—	2	2	no	—
173	C₄×C₆₇	#339	1	4	yes	complemented
174	C₄×C₆₇	C₄×C₄⋊C₄	1	2	yes	—
175	C₄×C₆₇	#382	1	1	yes	characteristic
176	C₄×C₆₇	#384	1	1	yes	characteristic
177	C₄×C₆₇	#389	1	2	yes	—
178	C₄×C₆₇	#390	1	1	yes	characteristic
179	C₄×C₆₇	#391	1	1	yes	characteristic
180	Dic₆₇	—	4	8	no	—
181	Dic₆₇	—	4	8	no	—
182	#10852	—	67	1	no	maximal, Sylow
183	C₂×C₆₇	—	2	1	no	—
184	C₂×C₆₇	—	2	2	no	—
185	C₂×C₆₇	—	2	1	no	—
186	C₂×C₆₇	C₄⋊#95	1	1	yes	characteristic
187	C₂×C₆₇	C₂×#339	1	1	yes	characteristic
188	C₂×C₆₇	#1733	1	1	yes	characteristic
189	C₂×C₆₇	#1806	1	4	yes	—
190	C₂×#423	D₆₇	1	1	yes	characteristic
191	C₄×#117	—	67	1	no	—
192	C₂×C₄×C₄⋊C₄	—	67	1	no	—
193	C₂×#339	—	67	4	no	—
194	C₆₇	#10852	1	1	yes	characteristic, complemented, Sylow
195	C₂²×M₁₆	C₂×D₆₇	1	2	yes	—
196	C₂×#117	—	67	2	no	—
197	C₂²×C₄⋊C₄	—	134	1	no	—
198	C₂²×C₄²	—	67	2	no	—
199	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
200	#423	—	2	2	no	—
201	#423	Dic₆₇	1	4	yes	complemented
202	C₂×C₄⋊C₈	—	2	1	no	—
203	C₂×C₄⋊C₈	—	2	1	no	—
204	C₄×C₄⋊C₄	—	67	4	no	—
205	C₄×C₄⋊C₄	—	67	2	no	—
206	C₄×C₄⋊C₄	—	67	2	no	—
207	C₄×C₄⋊C₄	—	134	2	no	—
208	C₄×C₂²⋊C₄	—	134	1	no	—
209	C₄×C₂²⋊C₄	—	134	1	no	—
210	#376	—	134	1	no	—
211	C₂×#95	—	134	1	no	—
212	C₄³	—	134	1	no	—
213	#339	—	134	8	no	—
214	C₂³×C₄	—	134	2	no	—
215	C₂³×C₄	D₂₆₈	1	1	yes	characteristic
216	C₂³×C₄	D₂₆₈	1	1	yes	characteristic
217	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	2	4	no	—
220	C₂×M₁₆	—	2	4	no	—
221	C₂×M₁₆	C₂×Dic₆₇	1	4	yes	—
222	C₂²×C₈	—	2	2	no	—
223	#117	—	67	4	no	—
224	#117	—	67	4	no	—
225	#117	—	134	2	no	—
226	#117	—	134	2	no	—
227	C₂×C₄⋊C₄	—	67	4	no	—
228	C₂×C₄⋊C₄	—	134	8	no	—
229	C₂×C₄⋊C₄	—	134	4	no	—
230	C₂×C₂²⋊C₄	—	134	2	no	—
231	C₂×C₄²	—	67	4	no	—
232	C₂×C₄²	—	134	2	no	—
233	C₂×C₄²	—	134	2	no	—
234	C₂×C₄²	—	134	2	no	—
235	C₂×C₄²	—	134	4	no	—
236	C₂×C₄²	—	134	4	no	—
237	C₂×C₄²	—	134	2	no	—
238	C₂×C₄²	Dic₁₃₄	1	2	yes	—
239	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
240	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
241	C₂×C₄²	C₄×D₆₇	1	2	yes	—
242	C₂×C₄²	C₂×Dic₆₇	1	2	yes	—
243	C₂×C₄²	C₂²⋊D₆₇	1	2	yes	—
244	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
245	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
246	C₄⋊C₈	—	2	4	no	—
247	C₄⋊C₈	—	2	4	no	—
248	#95	—	134	4	no	—
249	#95	—	134	2	no	—
250	#95	—	134	2	no	—
251	C₂⁴	C₂×D₂₆₈	1	1	yes	characteristic
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	—	268	4	no	—
255	C₂²×C₄	—	268	4	no	—
256	C₂²×C₄	—	134	8	no	—
257	C₂²×C₄	—	134	4	no	—
258	C₂²×C₄	—	134	4	no	—
259	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	2	yes	—
263	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	2	yes	—
264	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊Dic₆₇	1	2	yes	—
266	C₂²×C₄	C₄⋊Dic₆₇	1	2	yes	—
267	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
269	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
270	C₂²×C₄	D₄×D₆₇	1	2	yes	—
271	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
273	C₂²×C₄	Q₈×D₆₇	1	2	yes	—
274	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
275	C₂²×C₄	#11761627	1	2	yes	—
276	C₂²×C₄	#11761629	1	2	yes	—
277	M₁₆	—	2	8	no	—
278	M₁₆	—	4	2	no	—
279	M₁₆	—	4	2	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	4	4	no	—
282	C₄⋊C₄	—	67	8	no	—
283	C₄⋊C₄	—	134	16	no	—
284	C₄⋊C₄	—	134	4	no	—
285	C₂²⋊C₄	—	134	4	no	—
286	C₂²⋊C₄	—	134	4	no	—
287	C₄²	—	268	4	no	—
288	C₄²	—	268	4	no	—
289	C₄²	—	268	2	no	—
290	C₄²	—	268	2	no	—
291	C₄²	—	134	8	no	—
292	C₄²	—	134	4	no	—
293	C₄²	—	134	4	no	—
294	C₄²	C₄×Dic₆₇	1	2	yes	—
295	C₄²	C₄×Dic₆₇	1	2	yes	—
296	C₄²	C₂²⋊Dic₆₇	1	2	yes	—
297	C₄²	C₂²⋊Dic₆₇	1	2	yes	—
298	C₄²	Dic₆₇⋊C₄	1	2	yes	—
299	C₄²	Dic₆₇⋊C₄	1	2	yes	—
300	C₄²	Dic₆₇⋊C₄	1	2	yes	—
301	C₄²	Dic₆₇⋊C₄	1	2	yes	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
305	C₂³	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
306	C₂³	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
307	C₂³	#14524018	1	2	yes	—
308	C₂³	#14524023	1	2	yes	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	268	4	no	—
317	C₂×C₄	—	268	16	no	—
318	C₂×C₄	—	268	4	no	—
319	C₂×C₄	—	268	4	no	—
320	C₂×C₄	—	268	4	no	—
321	C₂×C₄	—	134	8	no	—
322	C₂×C₄	—	134	8	no	—
323	C₂×C₄	C₆₇⋊#95	1	2	yes	—
324	C₂×C₄	C₆₇⋊#95	1	2	yes	—
325	C₂×C₄	C₆₇⋊#95	1	2	yes	—
326	C₂×C₄	C₆₇⋊#95	1	2	yes	—
327	C₂×C₄	#14523969	1	4	yes	—
328	C₂×C₄	C₂×C₄×Dic₆₇	1	1	yes	characteristic
329	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
330	C₂×C₄	C₄⋊C₄×D₆₇	1	2	yes	—
331	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
333	C₂×C₄	#14524001	1	2	yes	—
334	C₂×C₄	#14524005	1	2	yes	—
335	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
336	C₂×C₄	#14524008	1	2	yes	—
337	C₂×C₄	Q₈×Dic₆₇	1	2	yes	—
338	C₂×C₄	#14524014	1	2	yes	—
339	C₂×C₄	#14524019	1	2	yes	—
340	C₂×C₄	#14524030	1	1	yes	characteristic
341	C₂×C₄	#14524032	1	1	yes	characteristic
342	C₂×C₄	#14524034	1	2	yes	—
343	C₂×C₄	#14524039	1	1	yes	characteristic
344	C₂×C₄	#14524041	1	1	yes	characteristic
345	C₂×C₄	#14524042	1	2	yes	—
346	C₈	—	4	4	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	4	no	—
352	C₂²	—	2	4	no	—
353	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
354	C₂²	#16863253	1	2	yes	—
355	C₂²	#16863295	1	2	yes	—
356	C₂²	#16863297	1	1	yes	characteristic
357	C₂²	#16863301	1	1	yes	characteristic
358	C₂²	C₂×#14523969	1	2	yes	—
359	C₂²	#16863412	1	2	yes	—
360	C₄	—	2	2	no	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	268	8	no	—
364	C₄	—	268	8	no	—
365	C₄	#16863157	1	4	yes	complemented
366	C₄	C₄⋊C₄×Dic₆₇	1	2	yes	—
367	C₄	#16863261	1	1	yes	characteristic
368	C₄	#16863265	1	1	yes	characteristic
369	C₄	#16863292	1	2	yes	—
370	C₄	#16863299	1	1	yes	characteristic
371	C₄	#16863303	1	1	yes	characteristic
372	C₂	—	2	1	no	—
373	C₂	—	2	2	no	—
374	C₂	—	2	1	no	—
375	C₂	#22558438	1	1	yes	characteristic
376	C₂	C₂×#16863157	1	1	yes	characteristic
377	C₂	#22559920	1	1	yes	characteristic
378	C₂	#22560226	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₆₇
commutator	C₂×C₄×C₆₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₆₇
Fitting	C₂×#423×C₆₇	C₂
socle	C₂³×C₆₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₆₇	C₂×D₄
cosocle	C₂³×C₄×C₆₇	C₂³
hypercenter	C₂×#423	D₆₇
hypocenter	C₆₇	#10852
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
9. C₄×C₄⋊Dic₆₇	C₄	semidirect
10. C₄×C₄⋊Dic₆₇	C₄	semidirect
11. C₄×C₄⋊Dic₆₇	C₄	semidirect
21. #423×C₆₇	C₄	semidirect
68. C₄⋊Dic₆₇	C₄⋊C₄	semidirect
173. C₄×C₆₇	#339	semidirect
194. C₆₇	#10852	semidirect
201. #423	Dic₆₇	semidirect
365. C₄	#16863157	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14524002	2
C₂×C₄×C₄⋊Dic₆₇	2
C₂×#16863157	2
C₂×#423×C₆₇	2
#10852	67