Subgroups — #30745720

Order 17152.

650 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863453	C₂	1	1	yes	maximal, characteristic
2	#22562607	C₂	1	1	yes	maximal, characteristic
3	#22558076	C₂	1	4	yes	maximal
4	C₆₇×#2285	C₂	1	1	yes	maximal, characteristic
5	#16863453	—	2	1	no	—
6	#16863453	—	2	1	no	—
7	#16863453	—	2	1	no	—
8	#16863453	—	2	1	no	—
9	C₂×C₄⋊(C₆₇⋊C₈)	C₄	1	2	yes	complemented
10	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
11	C₂×#14523954	C₄	1	2	yes	complemented
12	#16863264	C₄	1	2	yes	complemented
13	#16863262	—	2	1	no	—
14	#16863259	—	2	1	no	—
15	#16863256	C₂²	1	2	yes	—
16	C₄×C₄⋊Dic₆₇	—	2	1	no	—
17	C₄×C₂²⋊Dic₆₇	—	2	1	no	—
18	#16863242	C₄	1	2	yes	complemented
19	C₂×#117×C₆₇	—	2	1	no	—
20	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
21	#384×C₆₇	—	2	1	no	—
22	#382×C₆₇	C₄	1	2	yes	complemented
23	#380×C₆₇	—	2	1	no	—
24	#380×C₆₇	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₆₇	—	2	1	no	—
26	C₄×C₄⋊C₄×C₆₇	C₄	1	2	yes	complemented
27	C₂²×C₆₇⋊C₈	C₂×C₄	1	4	yes	—
28	C₂×C₄⋊Dic₆₇	—	2	2	no	—
29	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
30	C₂×C₄×Dic₆₇	—	2	2	no	—
31	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
32	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
33	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
34	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
35	#14523954	—	2	2	no	—
36	#14523954	—	2	2	no	—
37	C₆₇⋊#95	—	2	2	no	—
38	C₆₇⋊#95	—	2	2	no	—
39	C₆₇⋊#95	—	2	2	no	—
40	C₆₇⋊#95	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
44	#117×C₆₇	—	4	4	no	—
45	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
49	C₂×C₄²×C₆₇	—	2	2	no	—
50	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
54	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
61	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
62	#95×C₆₇	—	2	2	no	—
63	#95×C₆₇	C₂×C₄	1	4	yes	—
64	C₂²×Dic₆₇	—	2	4	no	—
65	C₂×C₆₇⋊C₈	—	2	4	no	—
66	C₂×C₆₇⋊C₈	—	4	4	no	—
67	C₄⋊Dic₆₇	—	4	4	no	—
68	C₂²⋊Dic₆₇	—	4	2	no	—
69	C₂²⋊Dic₆₇	—	4	2	no	—
70	C₄×Dic₆₇	—	4	4	no	—
71	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₆₇	—	2	2	no	—
73	C₂²×C₄×C₆₇	—	2	2	no	—
74	C₂²×C₄×C₆₇	—	2	4	no	—
75	C₂²×C₄×C₆₇	—	4	2	no	—
76	C₂²×C₄×C₆₇	—	4	2	no	—
77	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
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	1	yes	characteristic
85	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
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	1	yes	characteristic
93	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
95	C₄⋊C₄×C₆₇	—	4	4	no	—
96	C₄⋊C₄×C₆₇	—	4	4	no	—
97	C₄⋊C₄×C₆₇	—	4	4	no	—
98	C₂²⋊C₄×C₆₇	—	4	4	no	—
99	C₄²×C₆₇	—	4	4	no	—
100	C₄²×C₆₇	C₄²	1	1	yes	characteristic
101	C₄²×C₆₇	C₄²	1	1	yes	characteristic
102	C₄²×C₆₇	C₄²	1	1	yes	characteristic
103	C₄²×C₆₇	C₄²	1	1	yes	characteristic
104	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
108	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
116	C₂³×C₆₇	—	4	1	no	—
117	C₂³×C₆₇	—	4	1	no	—
118	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂³×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
122	C₂³×C₆₇	#137	1	2	yes	—
123	C₂×C₄×C₆₇	—	2	2	no	—
124	C₂×C₄×C₆₇	—	2	2	no	—
125	C₂×C₄×C₆₇	—	2	1	no	—
126	C₂×C₄×C₆₇	—	2	1	no	—
127	C₂×C₄×C₆₇	—	2	1	no	—
128	C₂×C₄×C₆₇	—	2	1	no	—
129	C₂×C₄×C₆₇	—	2	2	no	—
130	C₂×C₄×C₆₇	—	2	2	no	—
131	C₂×C₄×C₆₇	—	2	2	no	—
132	C₂×C₄×C₆₇	—	2	2	no	—
133	C₂×C₄×C₆₇	—	2	2	no	—
134	C₂×C₄×C₆₇	—	2	2	no	—
135	C₂×C₄×C₆₇	—	2	2	no	—
136	C₂×C₄×C₆₇	—	2	2	no	—
137	C₂×C₄×C₆₇	—	4	1	no	—
138	C₂×C₄×C₆₇	—	4	1	no	—
139	C₂×C₄×C₆₇	—	4	1	no	—
140	C₂×C₄×C₆₇	—	4	1	no	—
141	C₂×C₄×C₆₇	—	4	1	no	—
142	C₂×C₄×C₆₇	—	4	1	no	—
143	C₂×C₄×C₆₇	—	4	4	no	—
144	C₂×C₄×C₆₇	—	4	4	no	—
145	C₂×C₄×C₆₇	—	4	4	no	—
146	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
147	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
148	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
149	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
150	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
151	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
152	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
153	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×Dic₆₇	—	4	4	no	—
159	C₂×Dic₆₇	—	4	4	no	—
160	C₂×Dic₆₇	—	4	4	no	—
161	C₆₇⋊C₈	—	4	4	no	—
162	C₂²×C₆₇	—	2	1	no	—
163	C₂²×C₆₇	—	2	1	no	—
164	C₂²×C₆₇	—	2	1	no	—
165	C₂²×C₆₇	—	2	1	no	—
166	C₂²×C₆₇	—	2	1	no	—
167	C₂²×C₆₇	—	2	1	no	—
168	C₂²×C₆₇	—	4	2	no	—
169	C₂²×C₆₇	—	4	2	no	—
170	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
171	C₂²×C₆₇	#417	1	2	yes	—
172	C₂²×C₆₇	#418	1	1	yes	characteristic
173	C₂²×C₆₇	#419	1	1	yes	characteristic
174	C₂²×C₆₇	#428	1	2	yes	—
175	C₄×C₆₇	—	2	1	no	—
176	C₄×C₆₇	—	2	1	no	—
177	C₄×C₆₇	—	2	1	no	—
178	C₄×C₆₇	—	2	1	no	—
179	C₄×C₆₇	—	2	1	no	—
180	C₄×C₆₇	—	2	1	no	—
181	C₄×C₆₇	—	2	1	no	—
182	C₄×C₆₇	—	2	1	no	—
183	C₄×C₆₇	—	2	1	no	—
184	C₄×C₆₇	—	2	1	no	—
185	C₄×C₆₇	—	8	4	no	—
186	C₄×C₆₇	H(3,ℤ/4)	1	2	yes	—
187	C₄×C₆₇	#410	1	2	yes	—
188	Dic₆₇	—	8	4	no	—
189	#7984	—	67	1	no	maximal, Sylow
190	C₂×C₆₇	—	2	2	no	—
191	C₂×C₆₇	—	2	1	no	—
192	C₂×C₆₇	—	2	1	no	—
193	C₂×C₆₇	—	2	2	no	—
194	C₂×C₆₇	C₂×H(3,ℤ/4)	1	1	yes	characteristic
195	C₂×C₆₇	#1736	1	1	yes	characteristic
196	C₂×C₆₇	#1740	1	1	yes	characteristic
197	C₂×#432	—	67	1	no	—
198	#2285	D₆₇	1	1	yes	characteristic
199	#2283	—	67	1	no	—
200	#1289	—	67	4	no	—
201	C₆₇	#7984	1	1	yes	characteristic, complemented, Sylow
202	C₂×#117	—	2	1	no	—
203	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
204	#432	—	134	1	no	—
205	#432	—	134	1	no	—
206	#432	—	134	1	no	—
207	#432	—	134	1	no	—
208	C₂×C₄⋊C₈	—	67	2	no	—
209	C₂×C₂²⋊C₈	—	67	2	no	—
210	C₂×#97	—	67	2	no	—
211	#384	—	2	1	no	—
212	#383	—	67	2	no	—
213	#382	—	134	1	no	—
214	#382	Dic₆₇	1	2	yes	complemented
215	#381	—	134	1	no	—
216	#380	—	2	1	no	—
217	#380	—	67	2	no	—
218	#380	C₂×D₆₇	1	2	yes	—
219	C₄×C₄⋊C₄	—	2	1	no	—
220	C₄×C₄⋊C₄	—	134	1	no	—
221	C₄×C₄⋊C₄	Dic₆₇	1	2	yes	complemented
222	C₄×C₂²⋊C₄	—	134	1	no	—
223	#376	—	67	2	no	—
224	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
225	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
226	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
227	C₂²×C₈	—	67	4	no	—
228	#117	—	4	4	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	134	2	no	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₂²⋊C₄	—	134	2	no	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	—	134	2	no	—
237	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
238	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
239	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
240	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
241	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
242	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
243	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
244	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
245	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
246	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
247	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
248	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
249	C₄⋊C₈	—	134	2	no	—
250	C₄⋊C₈	—	134	2	no	—
251	C₂²⋊C₈	—	134	2	no	—
252	C₂²⋊C₈	—	134	2	no	—
253	#97	—	134	2	no	—
254	#97	—	134	2	no	—
255	#95	—	2	2	no	—
256	#95	—	67	4	no	—
257	#95	—	134	2	no	—
258	#95	—	134	2	no	—
259	#95	—	134	2	no	—
260	#95	C₂×Dic₆₇	1	4	yes	—
261	C₂⁴	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	134	4	no	—
268	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
274	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
276	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
279	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
282	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
285	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
286	C₂×C₈	—	268	4	no	—
287	C₂×C₈	—	134	4	no	—
288	C₄⋊C₄	—	4	4	no	—
289	C₄⋊C₄	—	4	4	no	—
290	C₄⋊C₄	—	4	4	no	—
291	C₄⋊C₄	—	268	4	no	—
292	C₂²⋊C₄	—	4	4	no	—
293	C₂²⋊C₄	—	268	2	no	—
294	C₂²⋊C₄	—	268	2	no	—
295	C₄²	—	4	4	no	—
296	C₄²	—	268	4	no	—
297	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
298	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
299	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
300	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
301	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
302	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
303	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
304	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
305	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
306	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
307	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
308	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
309	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
310	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
311	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
312	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
316	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
317	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
318	C₂³	#14524069	1	2	yes	—
319	C₂³	#14524074	1	2	yes	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	268	4	no	—
344	C₂×C₄	—	268	4	no	—
345	C₂×C₄	—	268	4	no	—
346	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
347	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
348	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
349	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
350	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
351	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
352	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
353	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
354	C₂×C₄	C₂×C₄×Dic₆₇	1	1	yes	characteristic
355	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
358	C₈	—	268	4	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
368	C₂²	#16863395	1	2	yes	—
369	C₂²	#16863401	1	1	yes	characteristic
370	C₂²	#16863405	1	1	yes	characteristic
371	C₂²	#16863436	1	2	yes	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	8	4	no	—
383	C₄	—	536	4	no	—
384	C₄	#16863152	1	2	yes	—
385	C₄	#16863369	1	2	yes	—
386	C₂	—	2	1	no	—
387	C₂	—	2	2	no	—
388	C₂	—	2	1	no	—
389	C₂	—	2	2	no	—
390	C₂	C₂×#16863152	1	1	yes	characteristic
391	C₂	#22559928	1	1	yes	characteristic
392	C₂	#22559941	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₆₇⋊#95
commutator	C₂×C₄×C₆₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₆₇
Fitting	C₆₇×#2285	C₂
socle	C₂²×C₆₇	C₂×#95
prime radical	C₂⁴×C₆₇	C₂×D₄
cosocle	C₂³×C₄×C₆₇	C₂³
hypercenter	#2285	D₆₇
hypocenter	C₆₇	#7984
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ #2285

Complements

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

N	H ≅ G/N	type
9. C₂×C₄⋊(C₆₇⋊C₈)	C₄	semidirect
11. C₂×#14523954	C₄	semidirect
12. #16863264	C₄	semidirect
18. #16863242	C₄	semidirect
22. #382×C₆₇	C₄	semidirect
26. C₄×C₄⋊C₄×C₆₇	C₄	semidirect
201. C₆₇	#7984	semidirect
214. #382	Dic₆₇	semidirect
221. C₄×C₄⋊C₄	Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863453	2
#22562607	2
#22558076	2
C₆₇×#2285	2
#7984	67