Subgroups — #30865224

Order 17152.

1444 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22568842	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#14524002	C₂	1	1	yes	maximal, characteristic, complemented
3	#22561129	C₂	1	4	yes	maximal, complemented
4	#22561038	C₂	1	4	yes	maximal, complemented
5	#22560153	C₂	1	4	yes	maximal, complemented
6	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic
7	C₂×#14524002	—	2	1	no	—
8	#16863453	—	2	1	no	—
9	#16863453	—	2	1	no	—
10	#16863449	—	2	1	no	—
11	#16863449	—	2	1	no	—
12	#16863420	C₂²	1	2	yes	complemented
13	C₂×#14523970	C₂²	1	16	yes	complemented
14	#16863360	C₂²	1	2	yes	—
15	C₄×#11761612	C₂²	1	2	yes	complemented
16	C₄×C₄⋊Dic₆₇	—	2	1	no	—
17	C₄×C₄⋊Dic₆₇	C₂²	1	2	yes	complemented
18	C₄×C₂²⋊Dic₆₇	—	2	1	no	—
19	C₄×C₂²⋊Dic₆₇	C₂²	1	2	yes	—
20	#16863242	—	2	1	no	—
21	C₄²×Dic₆₇	C₂²	1	2	yes	complemented
22	C₂²×#41×C₆₇	C₂²	1	2	yes	—
23	#532×C₆₇	—	2	1	no	—
24	#532×C₆₇	—	2	1	no	—
25	#532×C₆₇	—	2	1	no	—
26	#532×C₆₇	—	2	1	no	—
27	#532×C₆₇	C₄	1	2	yes	complemented
28	#532×C₆₇	C₄	1	2	yes	complemented
29	#532×C₆₇	C₂²	1	2	yes	—
30	#532×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄⋊Q₈×C₆₇	C₄	1	1	yes	characteristic, complemented
32	C₂×#127×C₆₇	C₄	1	1	yes	characteristic, complemented
33	C₂×#124×C₆₇	C₄	1	2	yes	complemented
34	C₂×#121×C₆₇	—	2	1	no	—
35	C₂×#121×C₆₇	—	2	1	no	—
36	C₂×C₄×D₄×C₆₇	—	2	1	no	—
37	C₂×C₄×D₄×C₆₇	—	2	1	no	—
38	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#11761612	C₂³	1	4	yes	—
40	#14524002	—	2	8	no	—
41	C₂×C₄⋊Dic₆₇	—	2	2	no	—
42	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
43	C₂×C₄×Dic₆₇	—	2	2	no	—
44	C₂×C₄×Dic₆₇	—	2	2	no	—
45	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
46	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
47	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
48	#14523970	—	4	16	no	—
49	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
50	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
51	#14523954	—	2	2	no	—
52	C₄×C₆₇⋊C₈	—	2	2	no	—
53	C₆₇⋊#95	—	2	2	no	—
54	C₆₇⋊#95	—	2	2	no	—
55	C₂×#41×C₆₇	—	2	2	no	—
56	C₂×#41×C₆₇	—	2	2	no	—
57	C₂×#41×C₆₇	—	4	8	no	—
58	C₂×#41×C₆₇	C₂×C₄	1	4	yes	—
59	C₂×#41×C₆₇	C₂³	1	4	yes	—
60	C₂²×Q₈×C₆₇	C₂×C₄	1	2	yes	—
61	C₂²×D₄×C₆₇	—	2	2	no	—
62	C₂²×D₄×C₆₇	—	2	1	no	—
63	C₂²×D₄×C₆₇	—	2	1	no	—
64	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
65	C₂³×C₄×C₆₇	—	2	2	no	—
66	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
69	C₄⋊Q₈×C₆₇	—	2	1	no	—
70	C₄⋊Q₈×C₆₇	—	2	1	no	—
71	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
72	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
73	#127×C₆₇	—	2	1	no	—
74	#127×C₆₇	—	2	1	no	—
75	#127×C₆₇	C₂×C₄	1	2	yes	—
76	#127×C₆₇	C₂×C₄	1	2	yes	—
77	#124×C₆₇	—	2	2	no	—
78	#124×C₆₇	—	2	2	no	—
79	#124×C₆₇	C₂×C₄	1	4	yes	—
80	#124×C₆₇	C₂×C₄	1	4	yes	—
81	#121×C₆₇	—	2	2	no	—
82	#121×C₆₇	—	2	2	no	—
83	#121×C₆₇	—	2	2	no	—
84	#121×C₆₇	—	2	2	no	—
85	#121×C₆₇	—	2	2	no	—
86	#121×C₆₇	—	2	2	no	—
87	#121×C₆₇	—	2	2	no	—
88	#121×C₆₇	—	2	2	no	—
89	C₄×D₄×C₆₇	—	2	2	no	—
90	C₄×D₄×C₆₇	—	2	2	no	—
91	C₄×D₄×C₆₇	—	2	2	no	—
92	C₄×D₄×C₆₇	—	2	2	no	—
93	C₄×D₄×C₆₇	—	2	2	no	—
94	C₄×D₄×C₆₇	—	2	2	no	—
95	C₄×D₄×C₆₇	—	2	2	no	—
96	C₄×D₄×C₆₇	—	2	2	no	—
97	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
98	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
101	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
113	C₂²×Dic₆₇	—	2	4	no	—
114	#11761612	—	2	8	no	—
115	C₂×C₆₇⋊C₈	—	2	4	no	—
116	C₄⋊Dic₆₇	—	2	8	no	—
117	C₂²⋊Dic₆₇	—	2	8	no	—
118	C₄×Dic₆₇	—	2	8	no	—
119	C₄×Dic₆₇	—	2	8	no	—
120	C₄×Dic₆₇	—	4	4	no	—
121	C₂⁴×C₆₇	—	2	2	no	—
122	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
123	#41×C₆₇	—	2	16	no	—
124	#41×C₆₇	—	4	8	no	—
125	#41×C₆₇	—	4	8	no	—
126	#41×C₆₇	—	4	8	no	—
127	C₂×Q₈×C₆₇	—	2	2	no	—
128	C₂×Q₈×C₆₇	—	4	4	no	—
129	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
130	C₂×D₄×C₆₇	—	2	4	no	—
131	C₂×D₄×C₆₇	—	2	4	no	—
132	C₂×D₄×C₆₇	—	2	2	no	—
133	C₂×D₄×C₆₇	—	2	2	no	—
134	C₂×D₄×C₆₇	—	2	2	no	—
135	C₂×D₄×C₆₇	—	2	2	no	—
136	C₂×D₄×C₆₇	—	2	2	no	—
137	C₂×D₄×C₆₇	—	4	4	no	—
138	C₂×D₄×C₆₇	—	4	4	no	—
139	C₂×D₄×C₆₇	—	4	8	no	—
140	C₂×D₄×C₆₇	—	4	4	no	—
141	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₆₇	—	2	4	no	—
143	C₂²×C₄×C₆₇	—	2	4	no	—
144	C₂²×C₄×C₆₇	—	2	2	no	—
145	C₂²×C₄×C₆₇	—	2	4	no	—
146	C₂²×C₄×C₆₇	—	2	4	no	—
147	C₂²×C₄×C₆₇	—	4	2	no	—
148	C₂²×C₄×C₆₇	—	4	8	no	—
149	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
167	C₄⋊C₄×C₆₇	—	2	2	no	—
168	C₄⋊C₄×C₆₇	—	2	2	no	—
169	C₄⋊C₄×C₆₇	—	2	2	no	—
170	C₄⋊C₄×C₆₇	—	2	2	no	—
171	C₂²⋊C₄×C₆₇	—	2	4	no	—
172	C₂²⋊C₄×C₆₇	—	2	4	no	—
173	C₂²⋊C₄×C₆₇	—	2	4	no	—
174	C₂²⋊C₄×C₆₇	—	2	4	no	—
175	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
176	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
177	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
178	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
179	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
180	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
181	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
182	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
183	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
184	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
185	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
186	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
187	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
191	C₂³×C₆₇	—	2	2	no	—
192	C₂³×C₆₇	—	2	2	no	—
193	C₂³×C₆₇	—	2	4	no	—
194	C₂³×C₆₇	—	4	1	no	—
195	C₂³×C₆₇	—	4	4	no	—
196	C₂³×C₆₇	—	4	4	no	—
197	C₂³×C₆₇	—	4	4	no	—
198	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₆₇	—	2	8	no	—
202	Q₈×C₆₇	—	4	4	no	—
203	D₄×C₆₇	—	2	8	no	—
204	D₄×C₆₇	—	4	4	no	—
205	D₄×C₆₇	—	4	4	no	—
206	D₄×C₆₇	—	4	8	no	—
207	D₄×C₆₇	—	4	8	no	—
208	D₄×C₆₇	—	4	4	no	—
209	D₄×C₆₇	—	4	4	no	—
210	D₄×C₆₇	—	4	4	no	—
211	C₂×C₄×C₆₇	—	2	2	no	—
212	C₂×C₄×C₆₇	—	2	2	no	—
213	C₂×C₄×C₆₇	—	2	2	no	—
214	C₂×C₄×C₆₇	—	2	2	no	—
215	C₂×C₄×C₆₇	—	2	2	no	—
216	C₂×C₄×C₆₇	—	2	2	no	—
217	C₂×C₄×C₆₇	—	2	2	no	—
218	C₂×C₄×C₆₇	—	2	2	no	—
219	C₂×C₄×C₆₇	—	2	2	no	—
220	C₂×C₄×C₆₇	—	2	2	no	—
221	C₂×C₄×C₆₇	—	2	2	no	—
222	C₂×C₄×C₆₇	—	2	2	no	—
223	C₂×C₄×C₆₇	—	2	2	no	—
224	C₂×C₄×C₆₇	—	2	4	no	—
225	C₂×C₄×C₆₇	—	4	1	no	—
226	C₂×C₄×C₆₇	—	4	1	no	—
227	C₂×C₄×C₆₇	—	4	1	no	—
228	C₂×C₄×C₆₇	—	4	8	no	—
229	C₂×C₄×C₆₇	—	4	4	no	—
230	C₂×C₄×C₆₇	—	4	8	no	—
231	C₂×C₄×C₆₇	#104	1	4	yes	complemented
232	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
243	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
245	C₂×Dic₆₇	—	2	8	no	—
246	C₂×Dic₆₇	—	4	4	no	—
247	C₂×Dic₆₇	—	4	4	no	—
248	C₆₇⋊C₈	—	4	4	no	—
249	C₂²×C₆₇	—	2	1	no	—
250	C₂²×C₆₇	—	2	1	no	—
251	C₂²×C₆₇	—	2	1	no	—
252	C₂²×C₆₇	—	2	1	no	—
253	C₂²×C₆₇	—	2	1	no	—
254	C₂²×C₆₇	—	2	1	no	—
255	C₂²×C₆₇	—	2	1	no	—
256	C₂²×C₆₇	—	4	4	no	—
257	C₂²×C₆₇	—	4	4	no	—
258	C₂²×C₆₇	—	4	4	no	—
259	C₂²×C₆₇	—	4	4	no	—
260	C₂²×C₆₇	—	8	8	no	—
261	C₂²×C₆₇	C₂×#104	1	2	yes	—
262	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
263	C₂²×C₆₇	#535	1	2	yes	—
264	C₄×C₆₇	—	2	1	no	—
265	C₄×C₆₇	—	2	1	no	—
266	C₄×C₆₇	—	2	1	no	—
267	C₄×C₆₇	—	2	1	no	—
268	C₄×C₆₇	—	2	1	no	—
269	C₄×C₆₇	—	2	1	no	—
270	C₄×C₆₇	—	2	1	no	—
271	C₄×C₆₇	—	4	4	no	—
272	C₄×C₆₇	C₂×#104	1	2	yes	—
273	C₄×C₆₇	C₂×#104	1	2	yes	—
274	C₄×C₆₇	#421	1	2	yes	—
275	C₄×C₆₇	#518	1	2	yes	—
276	C₄×C₆₇	#535	1	2	yes	—
277	Dic₆₇	—	4	8	no	—
278	#21815	—	67	1	no	maximal, Sylow
279	C₂×C₆₇	—	2	2	no	—
280	C₂×C₆₇	—	2	2	no	—
281	C₂×C₆₇	—	4	1	no	—
282	C₂×C₆₇	—	8	4	no	—
283	C₂×C₆₇	#2309	1	1	yes	characteristic
284	C₂×C₆₇	C₂²×#104	1	1	yes	characteristic
285	C₂×C₆₇	C₂×#421	1	1	yes	characteristic
286	C₂×#532	D₆₇	1	1	yes	characteristic
287	#2920	—	67	1	no	—
288	C₄×#117	—	67	1	no	—
289	#1980	—	67	4	no	—
290	#1962	—	67	4	no	—
291	#1789	—	67	4	no	—
292	C₆₇	#21815	1	1	yes	characteristic, complemented, Sylow
293	C₂²×#41	C₂×D₆₇	1	2	yes	—
294	#532	—	2	1	no	—
295	#532	—	2	1	no	—
296	#532	—	2	1	no	—
297	#532	—	2	1	no	—
298	#532	Dic₆₇	1	2	yes	complemented
299	#532	Dic₆₇	1	2	yes	complemented
300	#532	C₂×D₆₇	1	2	yes	—
301	#532	C₂×D₆₇	1	2	yes	—
302	C₂×C₄⋊Q₈	Dic₆₇	1	1	yes	characteristic, complemented
303	C₂×#127	Dic₆₇	1	1	yes	characteristic, complemented
304	C₂×#124	Dic₆₇	1	2	yes	complemented
305	C₂×#121	—	2	1	no	—
306	C₂×#121	—	2	1	no	—
307	C₂×C₄×D₄	—	2	1	no	—
308	C₂×C₄×D₄	—	2	1	no	—
309	C₂×#117	—	134	1	no	—
310	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
311	#432	—	134	1	no	—
312	#432	—	134	1	no	—
313	#431	—	134	1	no	—
314	#431	—	134	1	no	—
315	#423	—	67	2	no	—
316	C₂×#104	—	67	16	no	—
317	#407	—	67	2	no	—
318	C₄×M₁₆	—	67	2	no	—
319	C₄×C₄⋊C₄	—	67	2	no	—
320	C₄×C₄⋊C₄	—	134	1	no	—
321	C₄×C₂²⋊C₄	—	67	2	no	—
322	C₄×C₂²⋊C₄	—	134	1	no	—
323	#376	—	134	1	no	—
324	C₄³	—	67	2	no	—
325	C₂×#41	—	2	2	no	—
326	C₂×#41	—	2	2	no	—
327	C₂×#41	—	4	8	no	—
328	C₂×#41	C₂×Dic₆₇	1	4	yes	—
329	C₂×#41	C₂²×D₆₇	1	4	yes	—
330	C₂²×Q₈	C₂×Dic₆₇	1	2	yes	—
331	C₂²×D₄	—	2	2	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	C₂×Dic₆₇	1	2	yes	—
335	C₂³×C₄	—	2	2	no	—
336	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
337	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
338	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
339	C₂×M₁₆	—	67	4	no	—
340	C₄⋊Q₈	—	2	1	no	—
341	C₄⋊Q₈	—	2	1	no	—
342	C₄⋊Q₈	C₂×Dic₆₇	1	2	yes	—
343	C₄⋊Q₈	C₂×Dic₆₇	1	2	yes	—
344	#127	—	2	1	no	—
345	#127	—	2	1	no	—
346	#127	C₂×Dic₆₇	1	2	yes	—
347	#127	C₂×Dic₆₇	1	2	yes	—
348	#124	—	2	2	no	—
349	#124	—	2	2	no	—
350	#124	C₂×Dic₆₇	1	4	yes	—
351	#124	C₂×Dic₆₇	1	4	yes	—
352	#121	—	2	2	no	—
353	#121	—	2	2	no	—
354	#121	—	2	2	no	—
355	#121	—	2	2	no	—
356	#121	—	2	2	no	—
357	#121	—	2	2	no	—
358	#121	—	2	2	no	—
359	#121	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	2	no	—
368	#117	—	134	8	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	134	2	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₂²⋊C₄	—	134	2	no	—
375	C₂×C₄²	—	67	4	no	—
376	C₂×C₄²	—	134	2	no	—
377	C₂×C₄²	—	134	2	no	—
378	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
379	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
380	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
381	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
382	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
383	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
384	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
385	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
386	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
387	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
388	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
389	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
390	C₄⋊C₈	—	134	2	no	—
391	C₄⋊C₈	—	134	2	no	—
392	#104	—	268	16	no	—
393	C₂²⋊C₈	—	134	2	no	—
394	C₂²⋊C₈	—	134	2	no	—
395	#97	—	134	2	no	—
396	C₄×C₈	—	134	2	no	—
397	#95	—	134	2	no	—
398	#95	—	134	2	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
401	#41	—	2	16	no	—
402	#41	—	4	8	no	—
403	#41	—	4	8	no	—
404	#41	—	4	8	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	4	4	no	—
407	C₂×Q₈	C₂²×Dic₆₇	1	4	yes	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	4	4	no	—
417	C₂×D₄	—	4	8	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	C₂²×Dic₆₇	1	4	yes	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	4	2	no	—
426	C₂²×C₄	—	4	8	no	—
427	C₂²×C₄	—	134	4	no	—
428	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
429	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
430	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
431	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
432	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
433	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
434	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
435	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
436	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
437	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
440	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
441	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
443	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
445	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
446	M₁₆	—	134	8	no	—
447	C₂×C₈	—	134	4	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	134	8	no	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	134	8	no	—
458	C₄²	—	268	4	no	—
459	C₄²	—	134	8	no	—
460	C₄²	—	134	8	no	—
461	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
462	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
463	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
464	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
465	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
466	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
467	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
468	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
469	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
470	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
471	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
472	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
473	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
474	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
475	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
476	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	4	1	no	—
481	C₂³	—	4	4	no	—
482	C₂³	—	4	4	no	—
483	C₂³	—	4	4	no	—
484	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
485	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
486	C₂³	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
487	Q₈	—	2	8	no	—
488	Q₈	—	4	4	no	—
489	D₄	—	2	8	no	—
490	D₄	—	4	4	no	—
491	D₄	—	4	4	no	—
492	D₄	—	4	8	no	—
493	D₄	—	4	8	no	—
494	D₄	—	4	4	no	—
495	D₄	—	4	4	no	—
496	D₄	—	4	4	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	8	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	8	no	—
517	C₂×C₄	—	268	4	no	—
518	C₂×C₄	—	268	4	no	—
519	C₂×C₄	—	134	8	no	—
520	C₂×C₄	#14523970	1	4	yes	complemented
521	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
522	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
523	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
524	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
525	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
526	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
527	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
528	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
529	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
530	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
531	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
532	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
533	C₂×C₄	#14524088	1	4	yes	—
534	C₈	—	268	4	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	8	8	no	—
547	C₂²	C₂×#14523970	1	2	yes	—
548	C₂²	C₂²×C₂²⋊Dic₆₇	1	1	yes	characteristic
549	C₂²	#16863963	1	2	yes	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	4	4	no	—
558	C₄	—	268	8	no	—
559	C₄	C₂×#14523970	1	2	yes	—
560	C₄	C₂×#14523970	1	2	yes	—
561	C₄	#16863413	1	2	yes	—
562	C₄	#16863871	1	2	yes	—
563	C₄	#16863963	1	2	yes	—
564	C₂	—	2	2	no	—
565	C₂	—	2	2	no	—
566	C₂	—	4	1	no	—
567	C₂	—	8	4	no	—
568	C₂	#22562791	1	1	yes	characteristic
569	C₂	C₂²×#14523970	1	1	yes	characteristic
570	C₂	C₂×#16863413	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting, prime radical	C₂×#532×C₆₇	C₂
socle	C₂²×C₆₇	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₂×#532	D₆₇
hypocenter	C₆₇	#21815
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #22568842	C₂	semidirect
2. C₄×#14524002	C₂	semidirect
3. #22561129	C₂	semidirect
4. #22561038	C₂	semidirect
5. #22560153	C₂	semidirect
12. #16863420	C₂²	semidirect
13. C₂×#14523970	C₂²	semidirect
15. C₄×#11761612	C₂²	semidirect
17. C₄×C₄⋊Dic₆₇	C₂²	semidirect
21. C₄²×Dic₆₇	C₂²	semidirect
27. #532×C₆₇	C₄	semidirect
28. #532×C₆₇	C₄	semidirect
31. C₂×C₄⋊Q₈×C₆₇	C₄	semidirect
32. C₂×#127×C₆₇	C₄	semidirect
33. C₂×#124×C₆₇	C₄	semidirect
231. C₂×C₄×C₆₇	#104	semidirect
292. C₆₇	#21815	semidirect
298. #532	Dic₆₇	semidirect
299. #532	Dic₆₇	semidirect
302. C₂×C₄⋊Q₈	Dic₆₇	semidirect
303. C₂×#127	Dic₆₇	semidirect
304. C₂×#124	Dic₆₇	semidirect
520. C₂×C₄	#14523970	semidirect

Maximal subgroups

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

subgroup	index
#22568842	2
C₄×#14524002	2
#22561129	2
#22561038	2
#22560153	2
C₂×#532×C₆₇	2
#21815	67