Subgroups — #30746136

Order 17152.

674 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863449	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863420	C₂	1	1	yes	maximal, characteristic
3	#22558112	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2285	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11761612	—	2	1	no	—
6	#16863449	—	2	1	no	—
7	#16863449	—	2	1	no	—
8	#16863449	C₄	1	2	yes	complemented
9	#16863449	C₂²	1	2	yes	—
10	#16863420	—	2	1	no	—
11	#16863420	—	2	1	no	—
12	#16863420	C₄	1	2	yes	complemented
13	#16863420	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
15	C₂×C₄⋊(C₆₇⋊C₈)	C₄	1	2	yes	complemented
16	C₂×C₄⋊(C₆₇⋊C₈)	C₄	1	2	yes	complemented
17	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
18	C₂×C₄×C₆₇⋊C₈	—	2	1	no	—
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	—
23	#380×C₆₇	—	2	1	no	—
24	#380×C₆₇	C₄	1	2	yes	—
25	C₄×C₄⋊C₄×C₆₇	—	2	1	no	—
26	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
27	C₂×#11761612	—	2	2	no	—
28	C₂×#11761612	—	2	2	no	—
29	C₂×#11761612	—	4	2	no	—
30	C₂×#11761612	—	4	2	no	—
31	C₂²×C₆₇⋊C₈	—	2	2	no	—
32	C₂²×C₆₇⋊C₈	—	2	2	no	—
33	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
34	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
35	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
36	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
37	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
38	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
39	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
40	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
41	C₄×C₆₇⋊C₈	—	2	2	no	—
42	C₄×C₆₇⋊C₈	—	2	2	no	—
43	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
46	#117×C₆₇	—	4	2	no	—
47	#117×C₆₇	—	4	2	no	—
48	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
51	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
52	C₂×C₄²×C₆₇	—	2	2	no	—
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	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₆₇	C₂×C₄	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	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
63	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
64	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
65	#95×C₆₇	—	2	2	no	—
66	#95×C₆₇	C₂×C₄	1	4	yes	—
67	#11761612	—	4	4	no	—
68	#11761612	—	4	2	no	—
69	#11761612	—	4	2	no	—
70	C₂×C₆₇⋊C₈	—	2	4	no	—
71	C₂×C₆₇⋊C₈	—	2	4	no	—
72	C₂×C₆₇⋊C₈	—	4	4	no	—
73	C₂×C₆₇⋊C₈	—	4	4	no	—
74	C₂⁴×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₆₇	—	2	4	no	—
76	C₂²×C₄×C₆₇	—	4	2	no	—
77	C₂²×C₄×C₆₇	—	4	2	no	—
78	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
79	C₂²×C₄×C₆₇	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	D₈	1	2	yes	—
94	C₂²×C₄×C₆₇	SD₁₆	1	2	yes	—
95	C₂²×C₄×C₆₇	SD₁₆	1	2	yes	—
96	C₂²×C₄×C₆₇	Q₁₆	1	2	yes	—
97	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
100	C₄⋊C₄×C₆₇	—	4	4	no	—
101	C₄⋊C₄×C₆₇	—	4	4	no	—
102	C₄⋊C₄×C₆₇	—	4	4	no	—
103	C₂²⋊C₄×C₆₇	—	4	4	no	—
104	C₄²×C₆₇	—	4	2	no	—
105	C₄²×C₆₇	—	4	2	no	—
106	C₄²×C₆₇	C₄²	1	1	yes	characteristic
107	C₄²×C₆₇	C₄²	1	1	yes	characteristic
108	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
109	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
110	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
111	C₄²×C₆₇	C₂²⋊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	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
118	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
122	C₂³×C₆₇	—	4	1	no	—
123	C₂³×C₆₇	—	4	1	no	—
124	C₂³×C₆₇	#95	1	1	yes	characteristic
125	C₂³×C₆₇	#95	1	1	yes	characteristic
126	C₂³×C₆₇	#102	1	2	yes	—
127	C₂³×C₆₇	#103	1	2	yes	—
128	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	—	4	1	no	—
136	C₂×C₄×C₆₇	—	4	1	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	4	no	—
142	C₂×C₄×C₆₇	—	4	4	no	—
143	C₂×C₄×C₆₇	—	4	4	no	—
144	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
145	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
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	#102	1	2	yes	—
151	C₂×C₄×C₆₇	#102	1	2	yes	—
152	C₂×C₄×C₆₇	#102	1	2	yes	—
153	C₂×C₄×C₆₇	#103	1	2	yes	—
154	C₂×C₄×C₆₇	#103	1	2	yes	—
155	C₂×C₄×C₆₇	#103	1	2	yes	—
156	C₂×C₄×C₆₇	#106	1	2	yes	—
157	C₂×C₄×C₆₇	#106	1	2	yes	—
158	C₂×C₄×C₆₇	#107	1	2	yes	—
159	C₂×C₄×C₆₇	#107	1	2	yes	—
160	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
168	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
170	C₆₇⋊C₈	—	4	4	no	—
171	C₆₇⋊C₈	—	4	4	no	—
172	C₂²×C₆₇	—	2	1	no	—
173	C₂²×C₆₇	—	2	1	no	—
174	C₂²×C₆₇	—	2	1	no	—
175	C₂²×C₆₇	—	2	1	no	—
176	C₂²×C₆₇	—	2	1	no	—
177	C₂²×C₆₇	—	2	1	no	—
178	C₂²×C₆₇	—	4	2	no	—
179	C₂²×C₆₇	—	4	2	no	—
180	C₂²×C₆₇	#340	1	2	yes	—
181	C₂²×C₆₇	#340	1	2	yes	—
182	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
183	C₂²×C₆₇	C₂×#102	1	1	yes	characteristic
184	C₂²×C₆₇	C₂×#103	1	1	yes	characteristic
185	C₄×C₆₇	—	2	1	no	—
186	C₄×C₆₇	—	2	1	no	—
187	C₄×C₆₇	—	2	1	no	—
188	C₄×C₆₇	—	2	1	no	—
189	C₄×C₆₇	—	2	1	no	—
190	C₄×C₆₇	—	2	1	no	—
191	C₄×C₆₇	—	8	4	no	—
192	C₄×C₆₇	#340	1	2	yes	—
193	C₄×C₆₇	#340	1	2	yes	—
194	C₄×C₆₇	#344	1	2	yes	—
195	C₄×C₆₇	C₂×#102	1	1	yes	characteristic
196	C₄×C₆₇	C₂×#103	1	1	yes	characteristic
197	C₄×C₆₇	#421	1	2	yes	—
198	C₄×C₆₇	C₂×#106	1	1	yes	characteristic
199	C₄×C₆₇	C₂×#107	1	1	yes	characteristic
200	#8095	—	67	1	no	maximal, Sylow
201	C₂×C₆₇	—	2	1	no	—
202	C₂×C₆₇	—	2	2	no	—
203	C₂×C₆₇	—	2	2	no	—
204	C₂×C₆₇	—	2	1	no	—
205	C₂×C₆₇	#1733	1	1	yes	characteristic
206	C₂×C₆₇	C₂×#340	1	1	yes	characteristic
207	C₂×C₆₇	C₂×#344	1	1	yes	characteristic
208	C₂×#431	—	67	1	no	—
209	C₂×#423	—	67	1	no	—
210	#2285	D₆₇	1	1	yes	characteristic
211	#1303	—	67	4	no	—
212	C₆₇	#8095	1	1	yes	characteristic, complemented, Sylow
213	C₂²×M₁₆	—	134	1	no	—
214	C₂×#117	—	2	1	no	—
215	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
216	#431	—	67	2	no	—
217	#431	—	67	2	no	—
218	#431	—	134	1	no	—
219	#431	—	134	1	no	—
220	#423	—	67	2	no	—
221	#423	—	67	2	no	—
222	#423	—	134	1	no	—
223	#423	—	134	1	no	—
224	C₂×C₄⋊C₈	—	67	2	no	—
225	C₂×C₄⋊C₈	—	67	2	no	—
226	C₂×C₄⋊C₈	—	134	1	no	—
227	C₂×C₂²⋊C₈	—	134	1	no	—
228	C₂×C₄×C₈	—	134	1	no	—
229	#384	—	2	1	no	—
230	#382	Dic₆₇	1	2	yes	—
231	#380	—	2	1	no	—
232	#380	Dic₆₇	1	2	yes	—
233	C₄×C₄⋊C₄	—	2	1	no	—
234	C₄×C₄⋊C₄	C₂×D₆₇	1	2	yes	—
235	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
236	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
237	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
238	C₂×M₁₆	—	268	2	no	—
239	C₂×M₁₆	—	268	2	no	—
240	C₂×M₁₆	—	134	2	no	—
241	C₂×M₁₆	—	134	2	no	—
242	C₂²×C₈	—	134	2	no	—
243	C₂²×C₈	—	134	2	no	—
244	#117	—	4	2	no	—
245	#117	—	4	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
252	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
253	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
254	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
255	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
256	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
257	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
258	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
259	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
260	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
261	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
262	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
263	C₄⋊C₈	—	67	4	no	—
264	C₄⋊C₈	—	67	4	no	—
265	C₄⋊C₈	—	134	2	no	—
266	C₄⋊C₈	—	134	2	no	—
267	C₄⋊C₈	—	134	2	no	—
268	C₄⋊C₈	—	134	2	no	—
269	C₂²⋊C₈	—	134	2	no	—
270	C₂²⋊C₈	—	134	2	no	—
271	C₄×C₈	—	134	2	no	—
272	C₄×C₈	—	134	2	no	—
273	#95	—	2	2	no	—
274	#95	C₂×Dic₆₇	1	4	yes	—
275	C₂⁴	C₂²⋊Dic₆₇	1	1	yes	characteristic
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
280	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
281	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
282	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
283	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
284	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
285	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
287	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
288	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
289	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
290	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
291	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
292	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
293	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
294	C₂²×C₄	#11761613	1	2	yes	—
295	C₂²×C₄	#11761615	1	2	yes	—
296	C₂²×C₄	#11761616	1	2	yes	—
297	C₂²×C₄	#11761618	1	2	yes	—
298	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
301	M₁₆	—	268	4	no	—
302	M₁₆	—	268	2	no	—
303	M₁₆	—	268	2	no	—
304	C₂×C₈	—	268	4	no	—
305	C₂×C₈	—	268	4	no	—
306	C₂×C₈	—	134	4	no	—
307	C₂×C₈	—	134	4	no	—
308	C₄⋊C₄	—	4	4	no	—
309	C₄⋊C₄	—	4	4	no	—
310	C₄⋊C₄	—	4	4	no	—
311	C₂²⋊C₄	—	4	4	no	—
312	C₄²	—	4	2	no	—
313	C₄²	—	4	2	no	—
314	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
315	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
316	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
317	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
318	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
319	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
320	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
321	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
322	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
323	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
324	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
325	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
326	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
327	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
328	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
329	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
330	C₂³	—	4	1	no	—
331	C₂³	—	4	1	no	—
332	C₂³	C₆₇⋊#95	1	1	yes	characteristic
333	C₂³	C₆₇⋊#95	1	1	yes	characteristic
334	C₂³	#14523964	1	2	yes	—
335	C₂³	#14523967	1	2	yes	—
336	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
353	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
354	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
355	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
356	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
357	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
358	C₂×C₄	#14523963	1	2	yes	—
359	C₂×C₄	#14523963	1	2	yes	—
360	C₂×C₄	#14523964	1	2	yes	—
361	C₂×C₄	#14523966	1	2	yes	—
362	C₂×C₄	#14523966	1	2	yes	—
363	C₂×C₄	#14523967	1	2	yes	—
364	C₂×C₄	#14523974	1	2	yes	—
365	C₂×C₄	#14523974	1	2	yes	—
366	C₂×C₄	#14523976	1	2	yes	—
367	C₂×C₄	#14523976	1	2	yes	—
368	C₂×C₄	C₂×C₄×Dic₆₇	1	1	yes	characteristic
369	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
370	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
371	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
372	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
374	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
375	C₂×C₄	C₂×#11761615	1	1	yes	characteristic
376	C₂×C₄	C₂×#11761616	1	1	yes	characteristic
377	C₂×C₄	C₂×#11761618	1	1	yes	characteristic
378	C₈	—	268	4	no	—
379	C₈	—	268	4	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	#16863158	1	2	yes	—
389	C₂²	#16863158	1	2	yes	—
390	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
391	C₂²	C₂×#14523964	1	1	yes	characteristic
392	C₂²	C₂×#14523967	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	8	4	no	—
400	C₄	#16863158	1	2	yes	—
401	C₄	#16863158	1	2	yes	—
402	C₄	#16863166	1	2	yes	—
403	C₄	C₂×#14523963	1	1	yes	characteristic
404	C₄	C₂×#14523966	1	1	yes	characteristic
405	C₄	#16863414	1	2	yes	—
406	C₄	C₂×#14523974	1	1	yes	characteristic
407	C₄	C₂×#14523976	1	1	yes	characteristic
408	C₂	—	2	1	no	—
409	C₂	—	2	1	no	—
410	C₂	—	2	2	no	—
411	C₂	—	2	2	no	—
412	C₂	#22559919	1	1	yes	characteristic
413	C₂	C₂×#16863158	1	1	yes	characteristic
414	C₂	C₂×#16863166	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄
commutator	C₂×C₄×C₆₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₆₇×#2285	C₂
socle	C₂²×C₆₇	C₂×#95
prime radical	C₂⁴×C₆₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	#2285	D₆₇
hypocenter	C₆₇	#8095
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2285

Complements

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

N	H ≅ G/N	type
3. #22558112	C₂	semidirect
8. #16863449	C₄	semidirect
12. #16863420	C₄	semidirect
15. C₂×C₄⋊(C₆₇⋊C₈)	C₄	semidirect
16. C₂×C₄⋊(C₆₇⋊C₈)	C₄	semidirect
212. C₆₇	#8095	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863449	2
C₂×#16863420	2
#22558112	2
C₆₇×#2285	2
#8095	67