Subgroups — #1388×D₆₇ #30770760

Order 17152.

554 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#108×D₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#108×D₆₇	C₂	1	1	yes	maximal, characteristic
4	#22558322	C₂	1	1	yes	maximal, characteristic, complemented
5	#22558321	C₂	1	1	yes	maximal, characteristic, complemented
6	#22558320	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1388	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₆₇	—	2	1	no	—
9	C₂×M₁₆×D₆₇	—	2	1	no	—
10	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
11	C₂×#14523983	C₂²	1	1	yes	characteristic
12	C₂×#14523982	—	2	1	no	—
13	M₃₂×D₆₇	—	2	1	no	—
14	M₃₂×D₆₇	—	2	1	no	—
15	M₃₂×D₆₇	C₄	1	2	yes	—
16	M₃₂×D₆₇	C₄	1	2	yes	—
17	C₂×C₁₆×D₆₇	—	2	1	no	—
18	C₂×#14523979	C₂²	1	1	yes	characteristic
19	C₂×#14523979	C₂²	1	1	yes	characteristic
20	C₂×#14523978	—	2	1	no	—
21	C₂×#14523978	—	2	1	no	—
22	#108×D₆₇	—	2	1	no	—
23	#108×D₆₇	—	2	1	no	—
24	#108×D₆₇	—	2	1	no	—
25	#108×D₆₇	—	2	1	no	—
26	#108×D₆₇	C₄	1	2	yes	—
27	#108×D₆₇	C₄	1	2	yes	—
28	#108×D₆₇	C₄	1	2	yes	—
29	#108×D₆₇	C₄	1	2	yes	—
30	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₆₇	D₄	1	1	yes	characteristic
34	C₂×#11761612	—	2	1	no	—
35	C₂×#11761612	—	2	1	no	—
36	C₂×#11761611	—	4	1	no	—
37	C₂×#11761611	—	4	1	no	—
38	M₁₆×D₆₇	—	2	2	no	—
39	M₁₆×D₆₇	—	2	2	no	—
40	M₁₆×D₆₇	—	2	2	no	—
41	M₁₆×D₆₇	—	2	2	no	—
42	M₁₆×D₆₇	—	4	1	no	—
43	M₁₆×D₆₇	—	4	1	no	—
44	M₁₆×D₆₇	—	4	1	no	—
45	M₁₆×D₆₇	—	4	1	no	—
46	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
47	C₂×C₈×D₆₇	—	4	1	no	—
48	C₂×C₈×D₆₇	—	4	1	no	—
49	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
56	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
57	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
58	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
59	C₂×C₈×D₆₇	Q₈	1	1	yes	characteristic
60	C₂×C₈×D₆₇	Q₈	1	1	yes	characteristic
61	#14523983	—	2	1	no	—
62	#14523983	C₂×C₄	1	2	yes	—
63	#14523982	—	2	2	no	—
64	#14523982	—	2	2	no	—
65	C₂×C₆₇⋊C₁₆	—	2	1	no	—
66	C₁₆×D₆₇	—	2	2	no	—
67	C₁₆×D₆₇	—	2	2	no	—
68	#14523979	—	2	1	no	—
69	#14523979	—	2	1	no	—
70	#14523979	C₂×C₄	1	2	yes	—
71	#14523979	C₂×C₄	1	2	yes	—
72	#14523978	—	2	2	no	—
73	#14523978	—	2	2	no	—
74	#14523978	—	2	2	no	—
75	#14523978	—	2	2	no	—
76	C₂×M₁₆×C₆₇	—	2	1	no	—
77	C₂×M₁₆×C₆₇	—	2	1	no	—
78	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
79	M₃₂×C₆₇	—	2	1	no	—
80	M₃₂×C₆₇	C₂×C₄	1	2	yes	—
81	C₂×C₁₆×C₆₇	—	2	1	no	—
82	#108×C₆₇	—	2	1	no	—
83	#108×C₆₇	—	2	1	no	—
84	#108×C₆₇	C₂×C₄	1	2	yes	—
85	#108×C₆₇	C₂×C₄	1	2	yes	—
86	C₂³×D₆₇	Q₁₆	1	1	yes	characteristic
87	C₂²×Dic₆₇	Q₁₆	1	1	yes	characteristic
88	C₂×C₄×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₆₇	C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₆₇	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₆₇	D₈	1	1	yes	characteristic
95	C₂×C₄×D₆₇	D₈	1	1	yes	characteristic
96	C₂×C₄×D₆₇	SD₁₆	1	1	yes	characteristic
97	C₂×C₄×D₆₇	SD₁₆	1	1	yes	characteristic
98	C₂×C₄×D₆₇	SD₁₆	1	1	yes	characteristic
99	C₂×C₄×D₆₇	SD₁₆	1	1	yes	characteristic
100	#11761612	—	2	2	no	—
101	#11761612	—	2	2	no	—
102	#11761612	—	4	1	no	—
103	#11761612	—	4	1	no	—
104	#11761611	—	4	2	no	—
105	#11761611	—	4	2	no	—
106	#11761611	—	4	2	no	—
107	#11761611	—	4	2	no	—
108	C₂×C₆₇⋊C₈	—	4	1	no	—
109	C₂×C₆₇⋊C₈	—	4	1	no	—
110	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×C₆₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₆₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
116	C₈×D₆₇	—	4	2	no	—
117	C₈×D₆₇	—	4	2	no	—
118	C₈×D₆₇	—	4	2	no	—
119	C₈×D₆₇	—	4	2	no	—
120	C₈×D₆₇	C₄²	1	1	yes	characteristic
121	C₈×D₆₇	C₄²	1	1	yes	characteristic
122	C₈×D₆₇	C₄²	1	1	yes	characteristic
123	C₈×D₆₇	C₄²	1	1	yes	characteristic
124	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
125	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
126	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
127	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
128	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
129	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
130	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
131	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
132	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
133	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
134	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
135	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
136	C₆₇⋊C₁₆	—	2	2	no	—
137	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
138	M₁₆×C₆₇	—	2	2	no	—
139	M₁₆×C₆₇	—	2	2	no	—
140	M₁₆×C₆₇	—	4	1	no	—
141	M₁₆×C₆₇	—	4	1	no	—
142	C₂×C₈×C₆₇	—	4	1	no	—
143	C₂×C₈×C₆₇	—	4	1	no	—
144	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₆₇	C₂×Q₈	1	1	yes	characteristic
150	C₁₆×C₆₇	—	2	2	no	—
151	C₂³×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
152	C₂²×D₆₇	—	4	2	no	—
153	C₂²×D₆₇	#103	1	1	yes	characteristic
154	C₂²×D₆₇	#103	1	1	yes	characteristic
155	C₂²×D₆₇	#103	1	1	yes	characteristic
156	C₂²×D₆₇	#103	1	1	yes	characteristic
157	C₂²×D₆₇	#107	1	1	yes	characteristic
158	C₂²×D₆₇	#107	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×Dic₆₇	#103	1	1	yes	characteristic
166	C₂×Dic₆₇	#103	1	1	yes	characteristic
167	C₂×Dic₆₇	#103	1	1	yes	characteristic
168	C₂×Dic₆₇	#103	1	1	yes	characteristic
169	C₂×Dic₆₇	#107	1	1	yes	characteristic
170	C₂×Dic₆₇	#107	1	1	yes	characteristic
171	C₄×D₆₇	#95	1	1	yes	characteristic
172	C₄×D₆₇	#95	1	1	yes	characteristic
173	C₄×D₆₇	#95	1	1	yes	characteristic
174	C₄×D₆₇	#95	1	1	yes	characteristic
175	C₄×D₆₇	#102	1	1	yes	characteristic
176	C₄×D₆₇	#102	1	1	yes	characteristic
177	C₄×D₆₇	#102	1	1	yes	characteristic
178	C₄×D₆₇	#102	1	1	yes	characteristic
179	C₄×D₆₇	#102	1	1	yes	characteristic
180	C₄×D₆₇	#102	1	1	yes	characteristic
181	C₄×D₆₇	#102	1	1	yes	characteristic
182	C₄×D₆₇	#102	1	1	yes	characteristic
183	C₄×D₆₇	#106	1	1	yes	characteristic
184	C₄×D₆₇	#106	1	1	yes	characteristic
185	C₄×D₆₇	#106	1	1	yes	characteristic
186	C₄×D₆₇	#106	1	1	yes	characteristic
187	C₈×C₆₇	—	4	2	no	—
188	C₈×C₆₇	—	4	2	no	—
189	C₈×C₆₇	C₂×C₄²	1	1	yes	characteristic
190	C₈×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₆₇⋊C₈	—	4	2	no	—
194	C₆₇⋊C₈	—	4	2	no	—
195	C₆₇⋊C₈	#95	1	1	yes	characteristic
196	C₆₇⋊C₈	#95	1	1	yes	characteristic
197	C₆₇⋊C₈	#95	1	1	yes	characteristic
198	C₆₇⋊C₈	#95	1	1	yes	characteristic
199	C₂²×C₆₇	—	4	1	no	—
200	C₂²×C₆₇	C₂×#103	1	1	yes	characteristic
201	C₂²×C₆₇	C₂×#103	1	1	yes	characteristic
202	C₂²×C₆₇	C₂×#107	1	1	yes	characteristic
203	C₂×D₆₇	—	2	2	no	—
204	C₂×D₆₇	—	2	2	no	—
205	C₂×D₆₇	—	2	2	no	—
206	C₂×D₆₇	—	4	1	no	—
207	C₂×D₆₇	—	4	1	no	—
208	C₂×D₆₇	—	4	1	no	—
209	C₂×D₆₇	#340	1	1	yes	characteristic
210	C₂×D₆₇	#340	1	1	yes	characteristic
211	C₂×D₆₇	#340	1	1	yes	characteristic
212	C₂×D₆₇	#340	1	1	yes	characteristic
213	C₄×C₆₇	C₂×#95	1	1	yes	characteristic
214	C₄×C₆₇	C₂×#102	1	1	yes	characteristic
215	C₄×C₆₇	C₂×#102	1	1	yes	characteristic
216	C₄×C₆₇	C₂×#106	1	1	yes	characteristic
217	Dic₆₇	#340	1	1	yes	characteristic
218	Dic₆₇	#340	1	1	yes	characteristic
219	Dic₆₇	#340	1	1	yes	characteristic
220	Dic₆₇	#340	1	1	yes	characteristic
221	C₂×#1388	—	67	1	no	maximal, Sylow
222	C₂×C₆₇	—	2	1	no	—
223	C₂×C₆₇	—	2	1	no	—
224	C₂×C₆₇	—	2	1	no	—
225	C₂×C₆₇	C₂×#340	1	1	yes	characteristic
226	D₆₇	—	2	1	no	—
227	D₆₇	—	2	1	no	—
228	D₆₇	—	2	1	no	—
229	D₆₇	#1388	1	2	yes	direct product factor
230	C₂²×M₃₂	—	67	1	no	—
231	C₂²×#108	—	67	1	no	—
232	C₂²×#108	—	67	1	no	—
233	#1388	—	67	1	no	—
234	#1388	—	67	1	no	—
235	#1388	—	67	1	no	—
236	#1388	D₆₇	1	1	yes	characteristic, direct product factor
237	C₆₇	C₂×#1388	1	1	yes	characteristic, complemented, Sylow
238	C₂²×M₁₆	—	134	1	no	—
239	C₂²×M₁₆	—	134	1	no	—
240	C₂³×C₈	—	67	1	no	—
241	C₂×M₃₂	—	67	1	no	—
242	C₂×M₃₂	—	67	2	no	—
243	C₂×M₃₂	—	67	2	no	—
244	C₂×M₃₂	—	134	1	no	—
245	C₂×M₃₂	—	134	1	no	—
246	C₂×M₃₂	—	134	1	no	—
247	C₂×M₃₂	C₂×D₆₇	1	1	yes	characteristic
248	C₂²×C₁₆	—	134	1	no	—
249	C₂×#108	—	67	1	no	—
250	C₂×#108	—	67	1	no	—
251	C₂×#108	—	67	2	no	—
252	C₂×#108	—	67	2	no	—
253	C₂×#108	—	67	2	no	—
254	C₂×#108	—	67	2	no	—
255	C₂×#108	—	134	1	no	—
256	C₂×#108	—	134	1	no	—
257	C₂×#108	—	134	1	no	—
258	C₂×#108	—	134	1	no	—
259	C₂×#108	—	134	1	no	—
260	C₂×#108	—	134	1	no	—
261	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
262	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
263	C₂³×C₄	—	67	1	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	268	1	no	—
267	C₂×M₁₆	—	268	1	no	—
268	C₂×M₁₆	—	268	1	no	—
269	C₂×M₁₆	—	268	1	no	—
270	C₂×M₁₆	—	268	1	no	—
271	C₂×M₁₆	—	268	1	no	—
272	C₂×M₁₆	—	134	2	no	—
273	C₂×M₁₆	—	134	2	no	—
274	C₂×M₁₆	—	134	2	no	—
275	C₂×M₁₆	—	134	2	no	—
276	C₂×M₁₆	—	134	1	no	—
277	C₂×M₁₆	—	134	1	no	—
278	C₂²×C₈	—	268	1	no	—
279	C₂²×C₈	—	268	1	no	—
280	C₂²×C₈	—	67	1	no	—
281	C₂²×C₈	—	67	1	no	—
282	C₂²×C₈	—	67	1	no	—
283	C₂²×C₈	—	67	1	no	—
284	C₂²×C₈	—	67	1	no	—
285	C₂²×C₈	—	67	1	no	—
286	C₂²×C₈	—	67	1	no	—
287	C₂²×C₈	—	67	1	no	—
288	C₂²×C₈	—	67	1	no	—
289	C₂²×C₈	—	67	1	no	—
290	C₂²×C₈	—	67	1	no	—
291	C₂²×C₈	—	67	1	no	—
292	C₂²×C₈	—	67	1	no	—
293	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
294	M₃₂	—	2	1	no	—
295	M₃₂	—	67	2	no	—
296	M₃₂	—	134	2	no	—
297	M₃₂	—	134	2	no	—
298	M₃₂	—	134	1	no	—
299	M₃₂	C₄×D₆₇	1	2	yes	—
300	C₂×C₁₆	—	2	1	no	—
301	C₂×C₁₆	—	134	2	no	—
302	C₂×C₁₆	—	134	2	no	—
303	C₂×C₁₆	—	134	1	no	—
304	#108	—	2	1	no	—
305	#108	—	2	1	no	—
306	#108	—	67	2	no	—
307	#108	—	67	2	no	—
308	#108	—	134	2	no	—
309	#108	—	134	2	no	—
310	#108	—	134	2	no	—
311	#108	—	134	2	no	—
312	#108	—	134	1	no	—
313	#108	—	134	1	no	—
314	#108	C₄×D₆₇	1	2	yes	—
315	#108	C₄×D₆₇	1	2	yes	—
316	C₂⁴	—	67	1	no	—
317	C₂²×C₄	—	67	1	no	—
318	C₂²×C₄	—	67	1	no	—
319	C₂²×C₄	—	67	1	no	—
320	C₂²×C₄	—	67	1	no	—
321	C₂²×C₄	—	67	1	no	—
322	C₂²×C₄	—	67	1	no	—
323	C₂²×C₄	—	67	1	no	—
324	C₂²×C₄	—	67	1	no	—
325	C₂²×C₄	—	67	1	no	—
326	C₂²×C₄	—	67	1	no	—
327	C₂²×C₄	—	67	1	no	—
328	C₂²×C₄	—	67	1	no	—
329	C₂²×C₄	—	67	1	no	—
330	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
331	M₁₆	—	2	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	4	1	no	—
334	M₁₆	—	4	1	no	—
335	M₁₆	—	268	2	no	—
336	M₁₆	—	268	2	no	—
337	M₁₆	—	268	2	no	—
338	M₁₆	—	268	2	no	—
339	M₁₆	—	268	1	no	—
340	M₁₆	—	268	1	no	—
341	M₁₆	—	134	2	no	—
342	M₁₆	—	134	2	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	268	2	no	—
346	C₂×C₈	—	268	2	no	—
347	C₂×C₈	—	268	2	no	—
348	C₂×C₈	—	268	2	no	—
349	C₂×C₈	—	268	1	no	—
350	C₂×C₈	—	268	1	no	—
351	C₂×C₈	—	67	1	no	—
352	C₂×C₈	—	67	1	no	—
353	C₂×C₈	—	67	1	no	—
354	C₂×C₈	—	67	1	no	—
355	C₂×C₈	—	67	1	no	—
356	C₂×C₈	—	67	1	no	—
357	C₂×C₈	—	67	1	no	—
358	C₂×C₈	—	67	1	no	—
359	C₂×C₈	—	67	1	no	—
360	C₂×C₈	—	67	1	no	—
361	C₂×C₈	—	67	1	no	—
362	C₂×C₈	—	67	1	no	—
363	C₂×C₈	—	67	1	no	—
364	C₂×C₈	—	67	1	no	—
365	C₂×C₈	—	67	1	no	—
366	C₂×C₈	—	67	1	no	—
367	C₂×C₈	—	67	1	no	—
368	C₂×C₈	—	67	1	no	—
369	C₂×C₈	—	67	1	no	—
370	C₂×C₈	—	67	1	no	—
371	C₂×C₈	—	67	1	no	—
372	C₂×C₈	—	67	1	no	—
373	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
374	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
375	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
376	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
377	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
378	C₂×C₈	Q₈×D₆₇	1	1	yes	characteristic
379	C₁₆	—	2	2	no	—
380	C₁₆	—	134	2	no	—
381	C₂³	—	268	2	no	—
382	C₂³	—	67	1	no	—
383	C₂³	—	67	1	no	—
384	C₂³	—	67	1	no	—
385	C₂³	—	67	1	no	—
386	C₂³	—	67	1	no	—
387	C₂³	—	67	1	no	—
388	C₂³	Q₁₆×D₆₇	1	1	yes	characteristic
389	C₂×C₄	—	67	1	no	—
390	C₂×C₄	—	67	1	no	—
391	C₂×C₄	—	67	1	no	—
392	C₂×C₄	—	67	1	no	—
393	C₂×C₄	—	67	1	no	—
394	C₂×C₄	—	67	1	no	—
395	C₂×C₄	—	67	1	no	—
396	C₂×C₄	—	67	1	no	—
397	C₂×C₄	—	67	1	no	—
398	C₂×C₄	—	67	1	no	—
399	C₂×C₄	—	67	1	no	—
400	C₂×C₄	—	67	1	no	—
401	C₂×C₄	—	67	1	no	—
402	C₂×C₄	—	67	1	no	—
403	C₂×C₄	—	67	1	no	—
404	C₂×C₄	—	67	1	no	—
405	C₂×C₄	—	67	1	no	—
406	C₂×C₄	—	67	1	no	—
407	C₂×C₄	—	67	1	no	—
408	C₂×C₄	—	67	1	no	—
409	C₂×C₄	—	67	1	no	—
410	C₂×C₄	—	67	1	no	—
411	C₂×C₄	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
412	C₂×C₄	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
413	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
414	C₂×C₄	D₈×D₆₇	1	1	yes	characteristic
415	C₂×C₄	SD₁₆×D₆₇	1	1	yes	characteristic
416	C₂×C₄	SD₁₆×D₆₇	1	1	yes	characteristic
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₈	—	268	2	no	—
420	C₈	—	268	2	no	—
421	C₈	—	67	1	no	—
422	C₈	—	67	1	no	—
423	C₈	—	67	1	no	—
424	C₈	—	67	1	no	—
425	C₈	C₄²×D₆₇	1	1	yes	characteristic
426	C₈	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
427	C₈	C₄⋊C₄×D₆₇	1	1	yes	characteristic
428	C₈	C₄⋊C₄×D₆₇	1	1	yes	characteristic
429	C₂²	—	4	1	no	—
430	C₂²	—	268	1	no	—
431	C₂²	—	268	1	no	—
432	C₂²	—	268	1	no	—
433	C₂²	—	67	1	no	—
434	C₂²	—	67	1	no	—
435	C₂²	—	67	1	no	—
436	C₂²	—	67	1	no	—
437	C₂²	—	134	2	no	—
438	C₂²	—	134	2	no	—
439	C₂²	—	134	2	no	—
440	C₂²	#103×D₆₇	1	1	yes	characteristic
441	C₂²	#103×D₆₇	1	1	yes	characteristic
442	C₂²	#107×D₆₇	1	1	yes	characteristic
443	C₄	—	67	1	no	—
444	C₄	—	67	1	no	—
445	C₄	—	67	1	no	—
446	C₄	—	67	1	no	—
447	C₄	#95×D₆₇	1	1	yes	characteristic
448	C₄	#102×D₆₇	1	1	yes	characteristic
449	C₄	#102×D₆₇	1	1	yes	characteristic
450	C₄	#106×D₆₇	1	1	yes	characteristic
451	C₂	—	2	1	no	—
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	—	67	2	no	—
455	C₂	—	134	1	no	—
456	C₂	—	134	1	no	—
457	C₂	—	134	1	no	—
458	C₂	#340×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#102×D₆₇
commutator	C₈×C₆₇	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₆₇×#1388	C₂
socle	C₂×C₆₇	C₂×#340
prime radical	C₂³×D₆₇	Q₁₆
cosocle	C₂²×C₈×C₆₇	C₂³
hypercenter	#1388	D₆₇
hypocenter	C₆₇	C₂×#1388
LCS	G ▷ C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1388

Complements

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

N	H ≅ G/N	type
4. #22558322	C₂	semidirect
5. #22558321	C₂	semidirect
6. #22558320	C₂	semidirect
7. C₆₇×#1388	C₂	semidirect
229. D₆₇	#1388	direct (N × H)
236. #1388	D₆₇	direct (N × H)
237. C₆₇	C₂×#1388	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₆₇	2
C₂×#108×D₆₇	2
#22558322	2
#22558321	2
#22558320	2
C₆₇×#1388	2
C₂×#1388	67

Subgroups — #1388×D67 #30770760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1388×D₆₇ #30770760