Subgroups — #30761640

Order 17152.

1110 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863419	C₂	1	1	yes	maximal, characteristic
2	#22562612	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×Dic₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#16863157	C₂	1	1	yes	maximal, characteristic
5	C₂×#16863156	C₂	1	1	yes	maximal, characteristic
6	C₂×#16863155	C₂	1	1	yes	maximal, characteristic
7	C₂×#339×C₆₇	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11761612	C₂²	1	1	yes	characteristic
9	C₂×#14524002	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₆₇	—	2	2	no	—
11	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
13	#16863419	—	2	2	no	—
14	#16863419	C₄	1	4	yes	complemented
15	C₂×Dic₆₇⋊C₈	—	2	2	no	—
16	#16863265	C₄	1	2	yes	complemented
17	#16863261	C₄	1	2	yes	complemented
18	#16863254	—	2	2	no	—
19	C₄×Dic₆₇⋊C₄	—	2	2	no	—
20	C₄²×Dic₆₇	—	2	2	no	—
21	C₄²×Dic₆₇	C₄	1	4	yes	complemented
22	#16863157	—	2	2	no	—
23	#16863156	—	2	2	no	—
24	#16863155	—	2	2	no	—
25	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
28	#339×C₆₇	—	2	2	no	—
29	C₂³×Dic₆₇	—	2	1	no	—
30	C₂³×Dic₆₇	D₄	1	2	yes	—
31	C₂×#11761612	—	2	1	no	—
32	C₂×#11761612	—	2	1	no	—
33	C₂×#11761612	—	2	1	no	—
34	C₂×#11761612	—	2	1	no	—
35	C₂×#11761612	—	2	1	no	—
36	C₂×#11761612	C₂×C₄	1	2	yes	—
37	C₂²×C₆₇⋊C₈	—	2	1	no	—
38	#14524002	—	2	1	no	—
39	#14524002	—	2	1	no	—
40	#14524002	—	2	1	no	—
41	#14524002	—	2	1	no	—
42	C₂×C₄⋊Dic₆₇	C₂×C₄	1	2	yes	—
43	C₂×Dic₆₇⋊C₄	—	2	4	no	—
44	C₂×C₂²⋊Dic₆₇	—	2	1	no	—
45	C₂×C₄×Dic₆₇	—	2	16	no	—
46	C₂×C₄×Dic₆₇	—	2	8	no	—
47	C₂×C₄×Dic₆₇	—	2	1	no	—
48	C₂×C₄×Dic₆₇	—	2	1	no	—
49	C₂×C₄×Dic₆₇	—	2	1	no	—
50	C₂×C₄×Dic₆₇	—	2	1	no	—
51	C₂×C₄×Dic₆₇	C₂×C₄	1	2	yes	—
52	C₂×C₄×Dic₆₇	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₆₇	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₆₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₆₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₆₇	D₄	1	2	yes	—
57	C₂×C₄×Dic₆₇	D₄	1	2	yes	—
58	C₂×C₄×Dic₆₇	D₄	1	2	yes	—
59	C₂×C₄×Dic₆₇	Q₈	1	2	yes	—
60	C₂×C₄×Dic₆₇	Q₈	1	2	yes	—
61	Dic₆₇⋊C₈	—	2	8	no	—
62	C₆₇⋊#95	—	2	4	no	—
63	C₂³×C₄×C₆₇	—	2	1	no	—
64	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₆₇	—	2	1	no	—
66	C₂×M₁₆×C₆₇	—	2	1	no	—
67	C₂×M₁₆×C₆₇	—	2	1	no	—
68	C₂×M₁₆×C₆₇	—	2	1	no	—
69	C₂×M₁₆×C₆₇	—	2	1	no	—
70	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₆₇	—	2	1	no	—
72	#117×C₆₇	—	2	1	no	—
73	#117×C₆₇	—	2	1	no	—
74	#117×C₆₇	—	2	1	no	—
75	#117×C₆₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
77	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
78	C₂×C₄²×C₆₇	—	2	1	no	—
79	C₂×C₄²×C₆₇	—	2	1	no	—
80	C₂×C₄²×C₆₇	—	2	1	no	—
81	C₂×C₄²×C₆₇	—	2	1	no	—
82	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₆₇	D₄	1	2	yes	—
84	C₂×C₄²×C₆₇	Q₈	1	2	yes	—
85	C₂²×Dic₆₇	—	2	8	no	—
86	C₂²×Dic₆₇	—	2	2	no	—
87	C₂²×Dic₆₇	—	2	2	no	—
88	C₂²×Dic₆₇	—	2	2	no	—
89	C₂²×Dic₆₇	—	2	8	no	—
90	C₂²×Dic₆₇	—	2	2	no	—
91	C₂²×Dic₆₇	C₂²⋊C₄	1	2	yes	—
92	C₂²×Dic₆₇	C₂²⋊C₄	1	4	yes	—
93	C₂²×Dic₆₇	C₂²⋊C₄	1	2	yes	—
94	C₂²×Dic₆₇	C₄⋊C₄	1	4	yes	—
95	#11761612	—	2	2	no	—
96	#11761612	—	2	2	no	—
97	#11761612	—	4	1	no	—
98	#11761612	—	4	1	no	—
99	C₂×C₆₇⋊C₈	—	2	2	no	—
100	C₂×C₆₇⋊C₈	—	4	1	no	—
101	C₂×C₆₇⋊C₈	—	4	1	no	—
102	C₄⋊Dic₆₇	—	2	2	no	—
103	C₄⋊Dic₆₇	—	2	2	no	—
104	Dic₆₇⋊C₄	—	4	8	no	—
105	C₂²⋊Dic₆₇	—	4	1	no	—
106	C₂²⋊Dic₆₇	—	4	1	no	—
107	C₄×Dic₆₇	—	2	32	no	—
108	C₄×Dic₆₇	—	2	2	no	—
109	C₄×Dic₆₇	—	2	2	no	—
110	C₄×Dic₆₇	—	2	2	no	—
111	C₄×Dic₆₇	—	4	1	no	—
112	C₄×Dic₆₇	—	4	1	no	—
113	C₄×Dic₆₇	C₄²	1	2	yes	—
114	C₄×Dic₆₇	C₄²	1	2	yes	—
115	C₄×Dic₆₇	C₂²⋊C₄	1	4	yes	—
116	C₄×Dic₆₇	C₄⋊C₄	1	2	yes	—
117	C₄×Dic₆₇	C₄⋊C₄	1	4	yes	—
118	C₄×Dic₆₇	C₄⋊C₄	1	2	yes	—
119	C₄×Dic₆₇	C₄⋊C₄	1	4	yes	complemented
120	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₆₇	—	2	8	no	—
122	C₂²×C₄×C₆₇	—	2	2	no	—
123	C₂²×C₄×C₆₇	—	2	2	no	—
124	C₂²×C₄×C₆₇	—	2	2	no	—
125	C₂²×C₄×C₆₇	—	2	2	no	—
126	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
134	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
135	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
136	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
137	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
138	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
139	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
140	M₁₆×C₆₇	—	2	2	no	—
141	M₁₆×C₆₇	—	2	2	no	—
142	M₁₆×C₆₇	—	4	1	no	—
143	M₁₆×C₆₇	—	4	1	no	—
144	C₂×C₈×C₆₇	—	2	2	no	—
145	C₂×C₈×C₆₇	—	4	1	no	—
146	C₂×C₈×C₆₇	—	4	1	no	—
147	C₄⋊C₄×C₆₇	—	2	2	no	—
148	C₄⋊C₄×C₆₇	—	2	2	no	—
149	C₂²⋊C₄×C₆₇	—	4	1	no	—
150	C₂²⋊C₄×C₆₇	—	4	1	no	—
151	C₄²×C₆₇	—	2	2	no	—
152	C₄²×C₆₇	—	2	2	no	—
153	C₄²×C₆₇	—	2	2	no	—
154	C₄²×C₆₇	—	4	1	no	—
155	C₄²×C₆₇	—	4	1	no	—
156	C₄²×C₆₇	C₄⋊C₄	1	4	yes	complemented
157	C₂³×C₆₇	—	2	4	no	—
158	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂³×C₆₇	#121	1	1	yes	characteristic
162	C₂³×C₆₇	#121	1	1	yes	characteristic
163	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
164	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₆₇	—	2	8	no	—
166	C₂×C₄×C₆₇	—	2	8	no	—
167	C₂×C₄×C₆₇	—	2	8	no	—
168	C₂×C₄×C₆₇	—	2	4	no	—
169	C₂×C₄×C₆₇	—	4	2	no	—
170	C₂×C₄×C₆₇	—	4	4	no	—
171	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
172	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
178	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
179	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₆₇	C₄×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₆₇	C₄×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₆₇	C₄×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₆₇	C₄×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
188	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
189	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
190	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
191	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
192	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
193	C₂×C₄×C₆₇	#125	1	1	yes	characteristic
194	C₂×C₄×C₆₇	#125	1	1	yes	characteristic
195	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
196	C₂×C₄×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
197	C₂×C₄×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
198	C₂×C₄×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
199	C₂×Dic₆₇	—	2	8	no	—
200	C₂×Dic₆₇	—	2	8	no	—
201	C₂×Dic₆₇	—	2	8	no	—
202	C₂×Dic₆₇	—	2	4	no	—
203	C₂×Dic₆₇	—	2	4	no	—
204	C₂×Dic₆₇	—	2	8	no	—
205	C₂×Dic₆₇	—	2	8	no	—
206	C₂×Dic₆₇	—	4	2	no	—
207	C₂×Dic₆₇	—	4	4	no	—
208	C₂×Dic₆₇	#95	1	4	yes	—
209	C₂×Dic₆₇	#95	1	4	yes	—
210	C₂×Dic₆₇	#104	1	8	yes	—
211	C₈×C₆₇	—	4	2	no	—
212	C₆₇⋊C₈	—	4	2	no	—
213	C₂²×C₆₇	—	2	2	no	—
214	C₂²×C₆₇	—	2	2	no	—
215	C₂²×C₆₇	—	2	2	no	—
216	C₂²×C₆₇	—	2	2	no	—
217	C₂²×C₆₇	—	2	2	no	—
218	C₂²×C₆₇	—	2	2	no	—
219	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
220	C₂²×C₆₇	#380	1	1	yes	characteristic
221	C₂²×C₆₇	#380	1	1	yes	characteristic
222	C₂²×C₆₇	#389	1	1	yes	characteristic
223	C₂²×C₆₇	#389	1	1	yes	characteristic
224	C₂²×C₆₇	#390	1	1	yes	characteristic
225	C₂²×C₆₇	#391	1	1	yes	characteristic
226	C₂²×C₆₇	C₂×#104	1	4	yes	—
227	C₄×C₆₇	—	2	8	no	—
228	C₄×C₆₇	—	8	2	no	—
229	C₄×C₆₇	C₄×C₄⋊C₄	1	1	yes	characteristic
230	C₄×C₆₇	C₄×C₄⋊C₄	1	1	yes	characteristic
231	C₄×C₆₇	#382	1	1	yes	characteristic
232	C₄×C₆₇	#384	1	1	yes	characteristic
233	C₄×C₆₇	#389	1	1	yes	characteristic
234	C₄×C₆₇	#389	1	1	yes	characteristic
235	C₄×C₆₇	#390	1	1	yes	characteristic
236	C₄×C₆₇	#391	1	1	yes	characteristic
237	Dic₆₇	—	2	8	no	—
238	Dic₆₇	—	2	4	no	—
239	Dic₆₇	—	8	2	no	—
240	Dic₆₇	#339	1	8	yes	complemented
241	#10839	—	67	1	no	maximal, Sylow
242	C₂×C₆₇	—	2	1	no	—
243	C₂×C₆₇	—	2	1	no	—
244	C₂×C₆₇	—	2	1	no	—
245	C₂×C₆₇	—	2	1	no	—
246	C₂×C₆₇	C₄⋊#95	1	1	yes	characteristic
247	C₂×C₆₇	C₂×#339	1	2	yes	—
248	C₂×C₆₇	#1962	1	2	yes	—
249	C₂×C₆₇	#1994	1	2	yes	—
250	C₂×#423	—	67	1	no	—
251	#2285	—	67	1	no	—
252	C₂×C₄³	—	67	1	no	—
253	C₂×#339	—	67	1	no	—
254	C₂×#339	—	67	1	no	—
255	C₂×#339	—	67	1	no	—
256	C₂×#339	D₆₇	1	1	yes	characteristic
257	C₆₇	#10839	1	1	yes	characteristic, complemented, Sylow
258	C₂²×M₁₆	—	67	1	no	—
259	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
260	C₂×#117	—	67	1	no	—
261	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
262	C₂²×C₄²	—	67	1	no	—
263	C₂²×C₄²	—	67	1	no	—
264	C₂²×C₄²	—	134	2	no	—
265	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
266	#423	—	67	4	no	—
267	#423	—	134	2	no	—
268	C₂×C₄⋊C₈	—	134	2	no	—
269	#384	—	67	2	no	—
270	#382	—	67	2	no	—
271	#380	—	134	2	no	—
272	C₄×C₄⋊C₄	—	134	2	no	—
273	C₄³	—	67	4	no	—
274	C₄³	—	134	2	no	—
275	#339	—	2	2	no	—
276	#339	—	134	2	no	—
277	#339	—	134	2	no	—
278	#339	—	134	2	no	—
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	—	67	2	no	—
281	C₂³×C₄	—	134	1	no	—
282	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	2	1	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	—	2	1	no	—
287	C₂×M₁₆	—	2	1	no	—
288	C₂×M₁₆	—	67	2	no	—
289	C₂×M₁₆	—	134	1	no	—
290	C₂×M₁₆	—	134	1	no	—
291	C₂×M₁₆	—	134	1	no	—
292	C₂×M₁₆	—	134	1	no	—
293	C₂×M₁₆	—	134	1	no	—
294	C₂×M₁₆	C₄×D₆₇	1	2	yes	—
295	C₂²×C₈	—	2	1	no	—
296	C₂²×C₈	—	134	1	no	—
297	#117	—	2	1	no	—
298	#117	—	2	1	no	—
299	#117	—	2	1	no	—
300	#117	—	2	1	no	—
301	#117	—	134	1	no	—
302	#117	—	134	1	no	—
303	#117	—	134	1	no	—
304	#117	—	134	1	no	—
305	C₂×C₄⋊C₄	—	67	2	no	—
306	C₂×C₄⋊C₄	—	134	4	no	—
307	C₂×C₄⋊C₄	C₄×D₆₇	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	134	1	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	67	2	no	—
315	C₂×C₄²	—	67	1	no	—
316	C₂×C₄²	—	67	1	no	—
317	C₂×C₄²	—	67	2	no	—
318	C₂×C₄²	—	67	2	no	—
319	C₂×C₄²	—	67	2	no	—
320	C₂×C₄²	—	67	2	no	—
321	C₂×C₄²	—	67	2	no	—
322	C₂×C₄²	—	67	2	no	—
323	C₂×C₄²	—	67	2	no	—
324	C₂×C₄²	—	134	1	no	—
325	C₂×C₄²	—	134	8	no	—
326	C₂×C₄²	—	134	16	no	—
327	C₂×C₄²	—	134	1	no	—
328	C₂×C₄²	—	134	1	no	—
329	C₂×C₄²	—	134	1	no	—
330	C₂×C₄²	Dic₁₃₄	1	2	yes	—
331	C₂×C₄²	C₄×D₆₇	1	2	yes	—
332	C₂×C₄²	C₂²⋊D₆₇	1	2	yes	—
333	C₄⋊C₈	—	134	8	no	—
334	#95	—	134	4	no	—
335	C₂⁴	D₄×D₆₇	1	1	yes	characteristic
336	C₂²×C₄	—	2	8	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	67	2	no	—
342	C₂²×C₄	—	67	2	no	—
343	C₂²×C₄	—	67	4	no	—
344	C₂²×C₄	—	67	4	no	—
345	C₂²×C₄	—	134	2	no	—
346	C₂²×C₄	—	134	8	no	—
347	C₂²×C₄	—	134	8	no	—
348	C₂²×C₄	—	134	2	no	—
349	C₂²×C₄	—	134	2	no	—
350	C₂²×C₄	—	134	2	no	—
351	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
354	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
355	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
356	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
358	C₂²×C₄	Q₈×D₆₇	1	1	yes	characteristic
359	C₂²×C₄	Q₈×D₆₇	1	1	yes	characteristic
360	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
361	C₂²×C₄	#11761627	1	1	yes	characteristic
362	C₂²×C₄	#11761627	1	1	yes	characteristic
363	C₂²×C₄	#11761628	1	1	yes	characteristic
364	C₂²×C₄	#11761628	1	1	yes	characteristic
365	M₁₆	—	2	2	no	—
366	M₁₆	—	2	2	no	—
367	M₁₆	—	4	1	no	—
368	M₁₆	—	4	1	no	—
369	M₁₆	—	268	1	no	—
370	M₁₆	—	268	1	no	—
371	M₁₆	—	134	2	no	—
372	M₁₆	—	134	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	4	1	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	—	268	1	no	—
377	C₂×C₈	—	268	1	no	—
378	C₂×C₈	—	134	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	268	8	no	—
382	C₄⋊C₄	—	134	2	no	—
383	C₄⋊C₄	—	134	2	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₂²⋊C₄	—	268	1	no	—
387	C₂²⋊C₄	—	268	1	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	4	1	no	—
392	C₄²	—	4	1	no	—
393	C₄²	—	268	1	no	—
394	C₄²	—	268	1	no	—
395	C₄²	—	67	2	no	—
396	C₄²	—	67	2	no	—
397	C₄²	—	67	4	no	—
398	C₄²	—	67	2	no	—
399	C₄²	—	67	4	no	—
400	C₄²	—	67	2	no	—
401	C₄²	—	67	4	no	—
402	C₄²	—	134	32	no	—
403	C₄²	—	134	2	no	—
404	C₄²	—	134	2	no	—
405	C₄²	—	134	2	no	—
406	C₄²	Dic₆₇⋊C₄	1	4	yes	complemented
407	C₂³	—	2	4	no	—
408	C₂³	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
409	C₂³	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
410	C₂³	C₄⋊C₄×D₆₇	1	1	yes	characteristic
411	C₂³	#14524015	1	1	yes	characteristic
412	C₂³	#14524016	1	1	yes	characteristic
413	C₂³	#14524020	1	1	yes	characteristic
414	C₂³	#14524021	1	1	yes	characteristic
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	268	2	no	—
422	C₂×C₄	—	268	4	no	—
423	C₂×C₄	—	67	4	no	—
424	C₂×C₄	—	67	8	no	—
425	C₂×C₄	—	67	4	no	—
426	C₂×C₄	—	134	8	no	—
427	C₂×C₄	—	134	8	no	—
428	C₂×C₄	—	134	8	no	—
429	C₂×C₄	—	134	8	no	—
430	C₂×C₄	—	134	8	no	—
431	C₂×C₄	—	134	4	no	—
432	C₂×C₄	—	134	4	no	—
433	C₂×C₄	C₄²×D₆₇	1	1	yes	characteristic
434	C₂×C₄	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
435	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
436	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
437	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
438	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
439	C₂×C₄	#14523999	1	1	yes	characteristic
440	C₂×C₄	#14524000	1	1	yes	characteristic
441	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
442	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
443	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
444	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
445	C₂×C₄	#14524008	1	1	yes	characteristic
446	C₂×C₄	#14524008	1	1	yes	characteristic
447	C₂×C₄	C₄×Dic₁₃₄	1	1	yes	characteristic
448	C₂×C₄	C₄×Dic₁₃₄	1	1	yes	characteristic
449	C₂×C₄	#14524015	1	1	yes	characteristic
450	C₂×C₄	#14524016	1	1	yes	characteristic
451	C₂×C₄	#14524020	1	1	yes	characteristic
452	C₂×C₄	#14524021	1	1	yes	characteristic
453	C₂×C₄	#14524029	1	1	yes	characteristic
454	C₂×C₄	#14524029	1	1	yes	characteristic
455	C₂×C₄	#14524033	1	1	yes	characteristic
456	C₂×C₄	#14524033	1	1	yes	characteristic
457	C₂×C₄	#14524039	1	1	yes	characteristic
458	C₂×C₄	#14524041	1	1	yes	characteristic
459	C₂×C₄	#14524042	1	1	yes	characteristic
460	C₂×C₄	#14524042	1	1	yes	characteristic
461	C₈	—	4	2	no	—
462	C₈	—	268	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	#95×D₆₇	1	1	yes	characteristic
470	C₂²	#16863254	1	1	yes	characteristic
471	C₂²	#16863255	1	1	yes	characteristic
472	C₂²	#16863291	1	1	yes	characteristic
473	C₂²	#16863293	1	1	yes	characteristic
474	C₂²	#16863296	1	1	yes	characteristic
475	C₂²	#16863300	1	1	yes	characteristic
476	C₂²	#104×D₆₇	1	4	yes	—
477	C₄	—	2	8	no	—
478	C₄	—	8	2	no	—
479	C₄	—	536	2	no	—
480	C₄	—	67	8	no	—
481	C₄	—	134	8	no	—
482	C₄	—	134	4	no	—
483	C₄	#16863247	1	1	yes	characteristic
484	C₄	C₄×Dic₆₇⋊C₄	1	1	yes	characteristic
485	C₄	#16863260	1	1	yes	characteristic
486	C₄	#16863265	1	1	yes	characteristic
487	C₄	#16863291	1	1	yes	characteristic
488	C₄	#16863293	1	1	yes	characteristic
489	C₄	#16863296	1	1	yes	characteristic
490	C₄	#16863300	1	1	yes	characteristic
491	C₂	—	2	1	no	—
492	C₂	—	2	1	no	—
493	C₂	—	2	1	no	—
494	C₂	—	2	1	no	—
495	C₂	Dic₆₇⋊#95	1	1	yes	characteristic
496	C₂	#339×D₆₇	1	2	yes	—
497	C₂	#22561035	1	2	yes	—
498	C₂	#22561184	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₆₇
Fitting	C₂×#339×C₆₇	C₂
socle	C₂³×C₆₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₆₇	C₂×D₄
cosocle	C₂³×C₄×C₆₇	C₂³
hypercenter	C₂×#339	D₆₇
hypocenter	C₆₇	#10839
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
14. #16863419	C₄	semidirect
16. #16863265	C₄	semidirect
17. #16863261	C₄	semidirect
21. C₄²×Dic₆₇	C₄	semidirect
119. C₄×Dic₆₇	C₄⋊C₄	semidirect
156. C₄²×C₆₇	C₄⋊C₄	semidirect
240. Dic₆₇	#339	semidirect
257. C₆₇	#10839	semidirect
406. C₄²	Dic₆₇⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863419	2
#22562612	2
C₂×C₄²×Dic₆₇	2
C₂×#16863157	2
C₂×#16863156	2
C₂×#16863155	2
C₂×#339×C₆₇	2
#10839	67