Subgroups — D₄×#137×C₆₇ #30740320

Order 17152.

2746 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₆₇	C₂	1	2	yes	maximal, complemented
2	D₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×D₄×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×Q₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
5	D₄×SD₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3278	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3276	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3270	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3266	C₂	1	4	yes	maximal, complemented
10	C₆₇×#3152	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3056	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3039	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3007	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3004	C₂	1	2	yes	maximal, complemented
16	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	2	yes	—
19	C₂³×Q₈×C₆₇	C₂²	1	2	yes	complemented
20	C₂×#137×C₆₇	—	2	16	no	—
21	C₂×#137×C₆₇	C₂²	1	2	yes	—
22	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
24	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
25	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
26	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
27	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
28	C₂²×Q₁₆×C₆₇	C₂²	1	4	yes	complemented
29	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
30	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
31	#550×C₆₇	C₂²	1	1	yes	characteristic
32	D₄×Q₈×C₆₇	—	2	1	no	—
33	D₄×Q₈×C₆₇	—	2	2	no	—
34	D₄×Q₈×C₆₇	—	2	1	no	—
35	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
36	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₆₇	C₂²	1	4	yes	complemented
38	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
39	#548×C₆₇	C₂²	1	2	yes	—
40	#547×C₆₇	—	2	1	no	—
41	#547×C₆₇	C₂²	1	1	yes	characteristic
42	#546×C₆₇	—	2	2	no	—
43	#546×C₆₇	C₂²	1	2	yes	—
44	D₄²×C₆₇	—	2	1	no	—
45	D₄²×C₆₇	C₂²	1	1	yes	characteristic
46	#532×C₆₇	—	2	1	no	—
47	#532×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊Q₈×C₆₇	—	2	1	no	—
49	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#525×C₆₇	—	2	2	no	—
51	#525×C₆₇	C₂²	1	2	yes	—
52	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
53	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
54	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×D₄×C₆₇	—	2	1	no	—
57	C₂×C₄×D₄×C₆₇	—	2	1	no	—
58	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
59	#497×C₆₇	C₂²	1	4	yes	complemented
60	#494×C₆₇	C₂²	1	2	yes	complemented
61	#492×C₆₇	C₂²	1	2	yes	complemented
62	#470×C₆₇	C₂²	1	4	yes	complemented
63	#468×C₆₇	C₂²	1	4	yes	complemented
64	#467×C₆₇	C₂²	1	4	yes	complemented
65	#465×C₆₇	C₂²	1	4	yes	complemented
66	#464×C₆₇	C₂²	1	4	yes	complemented
67	#462×C₆₇	C₂²	1	2	yes	complemented
68	#462×C₆₇	C₂²	1	2	yes	complemented
69	#462×C₆₇	C₂²	1	2	yes	complemented
70	#461×C₆₇	C₂²	1	2	yes	complemented
71	#461×C₆₇	C₂²	1	2	yes	complemented
72	#460×C₆₇	C₂²	1	2	yes	complemented
73	#452×C₆₇	C₂²	1	4	yes	complemented
74	#452×C₆₇	C₂²	1	4	yes	complemented
75	#451×C₆₇	C₂²	1	4	yes	complemented
76	#451×C₆₇	C₂²	1	4	yes	complemented
77	#451×C₆₇	C₂²	1	4	yes	complemented
78	#450×C₆₇	C₂²	1	4	yes	complemented
79	#448×C₆₇	C₂²	1	4	yes	complemented
80	#448×C₆₇	C₂²	1	4	yes	complemented
81	#441×C₆₇	C₂²	1	2	yes	complemented
82	#440×C₆₇	C₂²	1	2	yes	complemented
83	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
84	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
85	#436×C₆₇	C₂²	1	2	yes	complemented
86	#435×C₆₇	C₂²	1	4	yes	complemented
87	C₈×D₄×C₆₇	C₂²	1	2	yes	—
88	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#419×C₆₇	C₂²	1	2	yes	complemented
91	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#417×C₆₇	C₂²	1	1	yes	characteristic
93	#417×C₆₇	C₂²	1	2	yes	complemented
94	#407×C₆₇	C₂²	1	2	yes	complemented
95	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	C₂×#41×C₆₇	—	2	2	no	—
97	C₂×#41×C₆₇	—	2	2	no	—
98	C₂×#41×C₆₇	—	2	8	no	—
99	C₂×#41×C₆₇	—	4	4	no	—
100	C₂×#41×C₆₇	C₂³	1	2	yes	—
101	C₂×#41×C₆₇	C₂³	1	2	yes	—
102	C₂×#41×C₆₇	C₂³	1	2	yes	—
103	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
104	C₂²×Q₈×C₆₇	—	2	2	no	—
105	C₂²×Q₈×C₆₇	—	2	2	no	—
106	C₂²×Q₈×C₆₇	—	2	2	no	—
107	C₂²×Q₈×C₆₇	—	2	8	no	—
108	C₂²×Q₈×C₆₇	—	4	4	no	—
109	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
110	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
111	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
112	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
113	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₆₇	—	2	2	no	—
115	C₂²×D₄×C₆₇	—	2	1	no	—
116	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
117	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
118	C₂³×C₄×C₆₇	—	2	2	no	—
119	C₂³×C₄×C₆₇	—	2	2	no	—
120	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
121	#137×C₆₇	—	2	8	no	—
122	#137×C₆₇	—	2	8	no	—
123	#137×C₆₇	—	2	16	no	—
124	#137×C₆₇	—	2	16	no	—
125	#137×C₆₇	—	2	8	no	—
126	#137×C₆₇	—	4	4	no	—
127	#137×C₆₇	D₄	1	8	yes	direct product factor
128	C₂×Q₁₆×C₆₇	—	2	16	no	—
129	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
130	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
131	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
132	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
133	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
134	C₂×SD₁₆×C₆₇	—	2	16	no	—
135	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
136	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
137	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
138	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
139	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
140	C₂×M₁₆×C₆₇	—	2	8	no	—
141	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
142	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
143	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
146	C₄⋊Q₈×C₆₇	—	2	2	no	—
147	C₄⋊Q₈×C₆₇	—	2	2	no	—
148	C₄⋊Q₈×C₆₇	—	2	4	no	—
149	C₄⋊Q₈×C₆₇	—	2	1	no	—
150	C₄⋊Q₈×C₆₇	—	2	1	no	—
151	C₄⋊Q₈×C₆₇	—	2	1	no	—
152	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
153	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
155	#127×C₆₇	—	2	1	no	—
156	#127×C₆₇	C₂³	1	1	yes	characteristic
157	#124×C₆₇	—	2	2	no	—
158	#124×C₆₇	C₂³	1	2	yes	—
159	#123×C₆₇	—	2	2	no	—
160	#123×C₆₇	—	2	2	no	—
161	#123×C₆₇	—	2	2	no	—
162	C₂²⋊Q₈×C₆₇	—	2	2	no	—
163	C₂²⋊Q₈×C₆₇	—	2	2	no	—
164	C₂²⋊Q₈×C₆₇	—	2	2	no	—
165	C₂²⋊Q₈×C₆₇	—	2	4	no	—
166	C₂²⋊Q₈×C₆₇	—	2	4	no	—
167	C₂²⋊Q₈×C₆₇	—	2	4	no	—
168	C₂²⋊Q₈×C₆₇	—	2	4	no	—
169	C₂²⋊Q₈×C₆₇	—	2	2	no	—
170	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
171	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
172	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
173	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
174	#121×C₆₇	—	2	2	no	—
175	#121×C₆₇	—	2	1	no	—
176	#121×C₆₇	—	2	1	no	—
177	#121×C₆₇	—	2	1	no	—
178	#121×C₆₇	—	2	1	no	—
179	#121×C₆₇	—	2	2	no	—
180	#121×C₆₇	—	2	2	no	—
181	#121×C₆₇	C₂³	1	2	yes	—
182	#121×C₆₇	C₂³	1	2	yes	—
183	#120×C₆₇	—	2	2	no	—
184	#120×C₆₇	—	2	2	no	—
185	#120×C₆₇	—	2	2	no	—
186	C₄×Q₈×C₆₇	—	2	1	no	—
187	C₄×Q₈×C₆₇	—	2	1	no	—
188	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
189	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
190	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
191	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
192	C₄×D₄×C₆₇	—	2	1	no	—
193	C₄×D₄×C₆₇	—	2	2	no	—
194	C₄×D₄×C₆₇	—	2	4	no	—
195	C₄×D₄×C₆₇	—	2	2	no	—
196	C₄×D₄×C₆₇	—	2	2	no	—
197	C₄×D₄×C₆₇	—	2	1	no	—
198	C₄×D₄×C₆₇	—	2	1	no	—
199	C₄×D₄×C₆₇	—	2	2	no	—
200	C₄×D₄×C₆₇	—	2	1	no	—
201	C₄×D₄×C₆₇	—	2	2	no	—
202	C₄×D₄×C₆₇	—	2	1	no	—
203	C₄×D₄×C₆₇	—	2	1	no	—
204	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
205	C₄×D₄×C₆₇	D₄	1	2	yes	—
206	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
207	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₄×D₄×C₆₇	C₂³	1	2	yes	—
211	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
212	#117×C₆₇	—	2	1	no	—
213	#117×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
215	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
216	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
217	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
218	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
219	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
222	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
223	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
224	C₂×C₄²×C₆₇	—	2	1	no	—
225	C₂×C₄²×C₆₇	—	2	1	no	—
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	#107×C₆₇	C₂³	1	2	yes	—
228	#106×C₆₇	C₂³	1	2	yes	—
229	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
230	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
231	#103×C₆₇	C₂³	1	2	yes	—
232	#103×C₆₇	C₂³	1	2	yes	—
233	#103×C₆₇	C₂³	1	4	yes	—
234	#103×C₆₇	C₂³	1	4	yes	—
235	#103×C₆₇	C₂³	1	2	yes	—
236	#103×C₆₇	C₂³	1	4	yes	—
237	#102×C₆₇	C₂³	1	2	yes	—
238	#102×C₆₇	C₂³	1	4	yes	—
239	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
240	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
241	#97×C₆₇	C₂³	1	2	yes	—
242	C₄×C₈×C₆₇	C₂³	1	2	yes	—
243	C₂⁴×C₆₇	—	2	2	no	—
244	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
245	#41×C₆₇	—	2	2	no	—
246	#41×C₆₇	—	2	4	no	—
247	#41×C₆₇	—	2	4	no	—
248	#41×C₆₇	—	2	4	no	—
249	#41×C₆₇	—	2	4	no	—
250	#41×C₆₇	—	4	8	no	—
251	#41×C₆₇	—	4	2	no	—
252	#41×C₆₇	—	4	2	no	—
253	#41×C₆₇	—	4	8	no	—
254	#41×C₆₇	C₂×D₄	1	4	yes	—
255	C₂×Q₈×C₆₇	—	2	1	no	—
256	C₂×Q₈×C₆₇	—	2	2	no	—
257	C₂×Q₈×C₆₇	—	2	4	no	—
258	C₂×Q₈×C₆₇	—	2	4	no	—
259	C₂×Q₈×C₆₇	—	2	2	no	—
260	C₂×Q₈×C₆₇	—	2	2	no	—
261	C₂×Q₈×C₆₇	—	2	8	no	—
262	C₂×Q₈×C₆₇	—	2	4	no	—
263	C₂×Q₈×C₆₇	—	2	8	no	—
264	C₂×Q₈×C₆₇	—	2	4	no	—
265	C₂×Q₈×C₆₇	—	2	4	no	—
266	C₂×Q₈×C₆₇	—	4	8	no	—
267	C₂×Q₈×C₆₇	—	4	4	no	—
268	C₂×Q₈×C₆₇	—	4	4	no	—
269	C₂×Q₈×C₆₇	—	4	2	no	—
270	C₂×Q₈×C₆₇	—	4	8	no	—
271	C₂×Q₈×C₆₇	—	4	8	no	—
272	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	complemented
273	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
274	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
275	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
276	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
277	C₂×D₄×C₆₇	—	2	1	no	—
278	C₂×D₄×C₆₇	—	2	4	no	—
279	C₂×D₄×C₆₇	—	2	4	no	—
280	C₂×D₄×C₆₇	—	2	2	no	—
281	C₂×D₄×C₆₇	—	2	2	no	—
282	C₂×D₄×C₆₇	—	2	2	no	—
283	C₂×D₄×C₆₇	—	2	2	no	—
284	C₂×D₄×C₆₇	—	2	2	no	—
285	C₂×D₄×C₆₇	—	2	1	no	—
286	C₂×D₄×C₆₇	—	2	2	no	—
287	C₂×D₄×C₆₇	—	2	1	no	—
288	C₂×D₄×C₆₇	—	4	2	no	—
289	C₂×D₄×C₆₇	—	4	8	no	—
290	C₂×D₄×C₆₇	—	4	4	no	—
291	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
292	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
293	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
294	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
295	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₆₇	—	2	1	no	—
297	C₂²×C₄×C₆₇	—	2	1	no	—
298	C₂²×C₄×C₆₇	—	2	4	no	—
299	C₂²×C₄×C₆₇	—	2	4	no	—
300	C₂²×C₄×C₆₇	—	2	1	no	—
301	C₂²×C₄×C₆₇	—	2	2	no	—
302	C₂²×C₄×C₆₇	—	2	2	no	—
303	C₂²×C₄×C₆₇	—	2	4	no	—
304	C₂²×C₄×C₆₇	—	2	4	no	—
305	C₂²×C₄×C₆₇	—	2	1	no	—
306	C₂²×C₄×C₆₇	—	2	2	no	—
307	C₂²×C₄×C₆₇	—	2	2	no	—
308	C₂²×C₄×C₆₇	—	2	2	no	—
309	C₂²×C₄×C₆₇	—	2	1	no	—
310	C₂²×C₄×C₆₇	—	4	8	no	—
311	C₂²×C₄×C₆₇	—	4	8	no	—
312	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
314	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
315	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
316	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
320	Q₁₆×C₆₇	—	2	8	no	—
321	Q₁₆×C₆₇	—	2	8	no	—
322	Q₁₆×C₆₇	—	2	8	no	—
323	Q₁₆×C₆₇	—	4	4	no	—
324	Q₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
325	SD₁₆×C₆₇	—	2	8	no	—
326	SD₁₆×C₆₇	—	2	8	no	—
327	SD₁₆×C₆₇	—	2	8	no	—
328	SD₁₆×C₆₇	—	4	4	no	—
329	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
330	M₁₆×C₆₇	—	2	4	no	—
331	M₁₆×C₆₇	—	2	2	no	—
332	M₁₆×C₆₇	—	2	8	no	—
333	M₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
334	C₂×C₈×C₆₇	—	2	8	no	—
335	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
336	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
337	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₆₇	—	2	1	no	—
339	C₄⋊C₄×C₆₇	—	2	2	no	—
340	C₄⋊C₄×C₆₇	—	2	2	no	—
341	C₄⋊C₄×C₆₇	—	2	2	no	—
342	C₄⋊C₄×C₆₇	—	2	2	no	—
343	C₄⋊C₄×C₆₇	—	2	2	no	—
344	C₄⋊C₄×C₆₇	—	2	2	no	—
345	C₄⋊C₄×C₆₇	—	2	2	no	—
346	C₄⋊C₄×C₆₇	—	2	4	no	—
347	C₄⋊C₄×C₆₇	—	2	4	no	—
348	C₄⋊C₄×C₆₇	—	2	1	no	—
349	C₄⋊C₄×C₆₇	—	2	1	no	—
350	C₄⋊C₄×C₆₇	—	2	1	no	—
351	C₄⋊C₄×C₆₇	—	2	1	no	—
352	C₄⋊C₄×C₆₇	—	2	2	no	—
353	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
354	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
355	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
357	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
359	C₂²⋊C₄×C₆₇	—	2	2	no	—
360	C₂²⋊C₄×C₆₇	—	2	4	no	—
361	C₂²⋊C₄×C₆₇	—	2	4	no	—
362	C₂²⋊C₄×C₆₇	—	2	1	no	—
363	C₂²⋊C₄×C₆₇	—	2	2	no	—
364	C₂²⋊C₄×C₆₇	—	2	2	no	—
365	C₂²⋊C₄×C₆₇	—	2	2	no	—
366	C₂²⋊C₄×C₆₇	—	2	1	no	—
367	C₂²⋊C₄×C₆₇	—	2	1	no	—
368	C₂²⋊C₄×C₆₇	—	2	2	no	—
369	C₂²⋊C₄×C₆₇	—	2	2	no	—
370	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
371	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
372	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
373	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
374	C₄²×C₆₇	—	2	1	no	—
375	C₄²×C₆₇	—	2	1	no	—
376	C₄²×C₆₇	—	2	1	no	—
377	C₄²×C₆₇	—	2	2	no	—
378	C₄²×C₆₇	—	2	2	no	—
379	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
380	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
381	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
382	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
383	C₂³×C₆₇	—	2	4	no	—
384	C₂³×C₆₇	—	2	4	no	—
385	C₂³×C₆₇	—	2	1	no	—
386	C₂³×C₆₇	—	2	2	no	—
387	C₂³×C₆₇	—	4	2	no	—
388	C₂³×C₆₇	—	4	4	no	—
389	C₂³×C₆₇	—	4	4	no	—
390	C₂³×C₆₇	—	8	2	no	—
391	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
392	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
393	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
394	Q₈×C₆₇	—	2	4	no	—
395	Q₈×C₆₇	—	2	2	no	—
396	Q₈×C₆₇	—	2	1	no	—
397	Q₈×C₆₇	—	2	4	no	—
398	Q₈×C₆₇	—	2	2	no	—
399	Q₈×C₆₇	—	2	4	no	—
400	Q₈×C₆₇	—	2	2	no	—
401	Q₈×C₆₇	—	4	8	no	—
402	Q₈×C₆₇	—	4	8	no	—
403	Q₈×C₆₇	—	4	4	no	—
404	Q₈×C₆₇	—	4	4	no	—
405	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
406	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
407	D₄×C₆₇	—	2	4	no	—
408	D₄×C₆₇	—	2	4	no	—
409	D₄×C₆₇	—	2	2	no	—
410	D₄×C₆₇	—	2	2	no	—
411	D₄×C₆₇	—	2	1	no	—
412	D₄×C₆₇	—	2	2	no	—
413	D₄×C₆₇	—	4	4	no	—
414	D₄×C₆₇	—	4	4	no	—
415	D₄×C₆₇	—	4	4	no	—
416	D₄×C₆₇	—	4	4	no	—
417	D₄×C₆₇	—	4	4	no	—
418	D₄×C₆₇	—	4	2	no	—
419	D₄×C₆₇	—	8	1	no	—
420	D₄×C₆₇	—	8	2	no	—
421	D₄×C₆₇	#137	1	4	yes	direct product factor
422	D₄×C₆₇	C₂²×D₄	1	2	yes	—
423	C₂×C₄×C₆₇	—	2	4	no	—
424	C₂×C₄×C₆₇	—	2	4	no	—
425	C₂×C₄×C₆₇	—	2	1	no	—
426	C₂×C₄×C₆₇	—	2	2	no	—
427	C₂×C₄×C₆₇	—	2	4	no	—
428	C₂×C₄×C₆₇	—	2	4	no	—
429	C₂×C₄×C₆₇	—	2	4	no	—
430	C₂×C₄×C₆₇	—	2	2	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	2	no	—
433	C₂×C₄×C₆₇	—	2	2	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	1	no	—
436	C₂×C₄×C₆₇	—	2	1	no	—
437	C₂×C₄×C₆₇	—	2	2	no	—
438	C₂×C₄×C₆₇	—	2	2	no	—
439	C₂×C₄×C₆₇	—	2	4	no	—
440	C₂×C₄×C₆₇	—	4	1	no	—
441	C₂×C₄×C₆₇	—	4	4	no	—
442	C₂×C₄×C₆₇	—	4	4	no	—
443	C₂×C₄×C₆₇	—	4	8	no	—
444	C₂×C₄×C₆₇	—	4	8	no	—
445	C₂×C₄×C₆₇	—	4	4	no	—
446	C₂×C₄×C₆₇	—	4	2	no	—
447	C₂×C₄×C₆₇	—	4	4	no	—
448	C₂×C₄×C₆₇	—	4	4	no	—
449	C₂×C₄×C₆₇	—	4	2	no	—
450	C₂×C₄×C₆₇	—	8	1	no	—
451	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
458	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
460	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
461	C₈×C₆₇	—	2	4	no	—
462	C₈×C₆₇	—	2	2	no	—
463	C₈×C₆₇	C₂²×D₄	1	4	yes	—
464	C₂²×C₆₇	—	2	1	no	—
465	C₂²×C₆₇	—	2	2	no	—
466	C₂²×C₆₇	—	2	2	no	—
467	C₂²×C₆₇	—	2	1	no	—
468	C₂²×C₆₇	—	2	2	no	—
469	C₂²×C₆₇	—	2	2	no	—
470	C₂²×C₆₇	—	2	2	no	—
471	C₂²×C₆₇	—	2	2	no	—
472	C₂²×C₆₇	—	4	8	no	—
473	C₂²×C₆₇	—	4	1	no	—
474	C₂²×C₆₇	—	4	1	no	—
475	C₂²×C₆₇	—	4	2	no	—
476	C₂²×C₆₇	—	4	2	no	—
477	C₂²×C₆₇	—	4	2	no	—
478	C₂²×C₆₇	—	8	8	no	—
479	C₂²×C₆₇	D₄²	1	2	yes	—
480	C₂²×C₆₇	C₂×#137	1	4	yes	complemented
481	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
482	C₄×C₆₇	—	2	1	no	—
483	C₄×C₆₇	—	2	1	no	—
484	C₄×C₆₇	—	2	2	no	—
485	C₄×C₆₇	—	2	2	no	—
486	C₄×C₆₇	—	2	2	no	—
487	C₄×C₆₇	—	2	4	no	—
488	C₄×C₆₇	—	2	1	no	—
489	C₄×C₆₇	—	4	2	no	—
490	C₄×C₆₇	—	4	1	no	—
491	C₄×C₆₇	—	4	2	no	—
492	C₄×C₆₇	—	4	4	no	—
493	C₄×C₆₇	—	4	1	no	—
494	C₄×C₆₇	D₄²	1	2	yes	—
495	C₄×C₆₇	C₂×#137	1	2	yes	complemented
496	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
497	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
498	D₄×#137	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
499	C₂×C₆₇	—	2	2	no	—
500	C₂×C₆₇	—	2	4	no	—
501	C₂×C₆₇	—	4	2	no	—
502	C₂×C₆₇	—	4	2	no	—
503	C₂×C₆₇	—	8	2	no	—
504	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
505	C₂×C₆₇	C₂²×#137	1	1	yes	characteristic
506	C₂×C₆₇	#3586	1	1	yes	characteristic
507	C₂²×#137	C₂×C₆₇	1	2	yes	complemented
508	D₄×#41	C₂×C₆₇	1	1	yes	characteristic
509	C₂×D₄×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
510	D₄×Q₁₆	C₂×C₆₇	1	2	yes	complemented
511	D₄×SD₁₆	C₂×C₆₇	1	2	yes	complemented
512	#3278	C₂×C₆₇	1	2	yes	complemented
513	#3276	C₂×C₆₇	1	2	yes	complemented
514	#3270	C₂×C₆₇	1	4	yes	complemented
515	#3266	C₂×C₆₇	1	4	yes	complemented
516	#3152	C₂×C₆₇	1	1	yes	characteristic, complemented
517	#3056	C₂×C₆₇	1	2	yes	complemented
518	#3039	C₂×C₆₇	1	1	yes	characteristic, complemented
519	#3037	C₂×C₆₇	1	1	yes	characteristic, complemented
520	#3007	C₂×C₆₇	1	2	yes	complemented
521	#3004	C₂×C₆₇	1	2	yes	complemented
522	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
523	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
524	C₆₇	D₄×#137	1	1	yes	characteristic, direct product factor, Sylow
525	C₂²×#41	C₂²×C₆₇	1	2	yes	—
526	C₂³×Q₈	C₂²×C₆₇	1	2	yes	complemented
527	C₂×#137	—	2	16	no	—
528	C₂×#137	C₂²×C₆₇	1	2	yes	—
529	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
530	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
531	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
532	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
533	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
534	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
535	C₂²×Q₁₆	C₂²×C₆₇	1	4	yes	complemented
536	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
537	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
538	#550	C₂²×C₆₇	1	1	yes	characteristic
539	D₄×Q₈	—	2	1	no	—
540	D₄×Q₈	—	2	2	no	—
541	D₄×Q₈	—	2	1	no	—
542	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
543	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
544	D₄×Q₈	C₂²×C₆₇	1	4	yes	complemented
545	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
546	#548	C₂²×C₆₇	1	2	yes	—
547	#547	—	2	1	no	—
548	#547	C₂²×C₆₇	1	1	yes	characteristic
549	#546	—	2	2	no	—
550	#546	C₂²×C₆₇	1	2	yes	—
551	D₄²	—	2	1	no	—
552	D₄²	C₂²×C₆₇	1	1	yes	characteristic
553	#532	—	2	1	no	—
554	#532	C₂²×C₆₇	1	1	yes	characteristic
555	C₂×C₄⋊Q₈	—	2	1	no	—
556	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
557	#525	—	2	2	no	—
558	#525	C₂²×C₆₇	1	2	yes	—
559	C₂×C₂²⋊Q₈	—	2	2	no	—
560	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
561	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
562	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
563	C₂×C₄×D₄	—	2	1	no	—
564	C₂×C₄×D₄	—	2	1	no	—
565	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
566	#497	C₂²×C₆₇	1	4	yes	complemented
567	#494	C₂²×C₆₇	1	2	yes	complemented
568	#492	C₂²×C₆₇	1	2	yes	complemented
569	#470	C₂²×C₆₇	1	4	yes	complemented
570	#468	C₂²×C₆₇	1	4	yes	complemented
571	#467	C₂²×C₆₇	1	4	yes	complemented
572	#465	C₂²×C₆₇	1	4	yes	complemented
573	#464	C₂²×C₆₇	1	4	yes	complemented
574	#462	C₂²×C₆₇	1	2	yes	complemented
575	#462	C₂²×C₆₇	1	2	yes	complemented
576	#462	C₂²×C₆₇	1	2	yes	complemented
577	#461	C₂²×C₆₇	1	2	yes	complemented
578	#461	C₂²×C₆₇	1	2	yes	complemented
579	#460	C₂²×C₆₇	1	2	yes	complemented
580	#452	C₂²×C₆₇	1	4	yes	complemented
581	#452	C₂²×C₆₇	1	4	yes	complemented
582	#451	C₂²×C₆₇	1	4	yes	complemented
583	#451	C₂²×C₆₇	1	4	yes	complemented
584	#451	C₂²×C₆₇	1	4	yes	complemented
585	#450	C₂²×C₆₇	1	4	yes	complemented
586	#448	C₂²×C₆₇	1	4	yes	complemented
587	#448	C₂²×C₆₇	1	4	yes	complemented
588	#441	C₂²×C₆₇	1	2	yes	complemented
589	#440	C₂²×C₆₇	1	2	yes	complemented
590	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
591	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
592	#436	C₂²×C₆₇	1	2	yes	complemented
593	#435	C₂²×C₆₇	1	4	yes	complemented
594	C₈×D₄	C₂²×C₆₇	1	2	yes	—
595	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
596	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
597	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
598	#419	C₂²×C₆₇	1	2	yes	complemented
599	#417	C₂²×C₆₇	1	1	yes	characteristic
600	#417	C₂²×C₆₇	1	2	yes	complemented
601	#407	C₂²×C₆₇	1	2	yes	complemented
602	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
603	C₂×#41	—	2	2	no	—
604	C₂×#41	—	2	2	no	—
605	C₂×#41	—	2	8	no	—
606	C₂×#41	—	4	4	no	—
607	C₂×#41	C₂³×C₆₇	1	2	yes	—
608	C₂×#41	C₂³×C₆₇	1	2	yes	—
609	C₂×#41	C₂³×C₆₇	1	2	yes	—
610	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
611	C₂²×Q₈	—	2	2	no	—
612	C₂²×Q₈	—	2	2	no	—
613	C₂²×Q₈	—	2	2	no	—
614	C₂²×Q₈	—	2	8	no	—
615	C₂²×Q₈	—	4	4	no	—
616	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
617	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
618	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
619	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
620	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
621	C₂²×D₄	—	2	2	no	—
622	C₂²×D₄	—	2	1	no	—
623	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
624	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
625	C₂³×C₄	—	2	2	no	—
626	C₂³×C₄	—	2	2	no	—
627	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
628	#137	—	2	8	no	—
629	#137	—	2	8	no	—
630	#137	—	2	16	no	—
631	#137	—	2	16	no	—
632	#137	—	2	8	no	—
633	#137	—	4	4	no	—
634	#137	D₄×C₆₇	1	8	yes	direct product factor
635	C₂×Q₁₆	—	2	16	no	—
636	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
637	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
638	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
639	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
640	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
641	C₂×SD₁₆	—	2	16	no	—
642	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
643	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
644	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
645	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
646	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
647	C₂×M₁₆	—	2	8	no	—
648	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
649	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
650	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
651	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
652	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
653	C₄⋊Q₈	—	2	2	no	—
654	C₄⋊Q₈	—	2	2	no	—
655	C₄⋊Q₈	—	2	4	no	—
656	C₄⋊Q₈	—	2	1	no	—
657	C₄⋊Q₈	—	2	1	no	—
658	C₄⋊Q₈	—	2	1	no	—
659	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
660	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
661	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
662	#127	—	2	1	no	—
663	#127	C₂³×C₆₇	1	1	yes	characteristic
664	#124	—	2	2	no	—
665	#124	C₂³×C₆₇	1	2	yes	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	2	no	—
672	C₂²⋊Q₈	—	2	4	no	—
673	C₂²⋊Q₈	—	2	4	no	—
674	C₂²⋊Q₈	—	2	4	no	—
675	C₂²⋊Q₈	—	2	4	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
678	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
679	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
680	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
681	#121	—	2	2	no	—
682	#121	—	2	1	no	—
683	#121	—	2	1	no	—
684	#121	—	2	1	no	—
685	#121	—	2	1	no	—
686	#121	—	2	2	no	—
687	#121	—	2	2	no	—
688	#121	C₂³×C₆₇	1	2	yes	—
689	#121	C₂³×C₆₇	1	2	yes	—
690	#120	—	2	2	no	—
691	#120	—	2	2	no	—
692	#120	—	2	2	no	—
693	C₄×Q₈	—	2	1	no	—
694	C₄×Q₈	—	2	1	no	—
695	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
696	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
697	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
698	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
699	C₄×D₄	—	2	1	no	—
700	C₄×D₄	—	2	2	no	—
701	C₄×D₄	—	2	4	no	—
702	C₄×D₄	—	2	2	no	—
703	C₄×D₄	—	2	2	no	—
704	C₄×D₄	—	2	1	no	—
705	C₄×D₄	—	2	1	no	—
706	C₄×D₄	—	2	2	no	—
707	C₄×D₄	—	2	1	no	—
708	C₄×D₄	—	2	2	no	—
709	C₄×D₄	—	2	1	no	—
710	C₄×D₄	—	2	1	no	—
711	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
712	C₄×D₄	D₄×C₆₇	1	2	yes	—
713	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
714	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
715	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
716	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
717	C₄×D₄	C₂³×C₆₇	1	2	yes	—
718	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
719	#117	—	2	1	no	—
720	#117	C₂³×C₆₇	1	1	yes	characteristic
721	C₂×C₄⋊C₄	—	2	1	no	—
722	C₂×C₄⋊C₄	—	2	1	no	—
723	C₂×C₄⋊C₄	—	2	1	no	—
724	C₂×C₄⋊C₄	—	2	2	no	—
725	C₂×C₄⋊C₄	—	2	1	no	—
726	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
727	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
728	C₂×C₂²⋊C₄	—	2	2	no	—
729	C₂×C₂²⋊C₄	—	2	2	no	—
730	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
731	C₂×C₄²	—	2	1	no	—
732	C₂×C₄²	—	2	1	no	—
733	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
734	#107	C₂³×C₆₇	1	2	yes	—
735	#106	C₂³×C₆₇	1	2	yes	—
736	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
737	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
738	#103	C₂³×C₆₇	1	2	yes	—
739	#103	C₂³×C₆₇	1	4	yes	—
740	#103	C₂³×C₆₇	1	2	yes	—
741	#103	C₂³×C₆₇	1	2	yes	—
742	#103	C₂³×C₆₇	1	4	yes	—
743	#103	C₂³×C₆₇	1	4	yes	—
744	#102	C₂³×C₆₇	1	2	yes	—
745	#102	C₂³×C₆₇	1	4	yes	—
746	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
747	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
748	#97	C₂³×C₆₇	1	2	yes	—
749	C₄×C₈	C₂³×C₆₇	1	2	yes	—
750	C₂⁴	—	2	2	no	—
751	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
752	#41	—	2	2	no	—
753	#41	—	2	4	no	—
754	#41	—	2	4	no	—
755	#41	—	2	4	no	—
756	#41	—	2	4	no	—
757	#41	—	4	8	no	—
758	#41	—	4	2	no	—
759	#41	—	4	2	no	—
760	#41	—	4	8	no	—
761	#41	C₂×D₄×C₆₇	1	4	yes	—
762	C₂×Q₈	—	2	1	no	—
763	C₂×Q₈	—	2	2	no	—
764	C₂×Q₈	—	2	4	no	—
765	C₂×Q₈	—	2	4	no	—
766	C₂×Q₈	—	2	2	no	—
767	C₂×Q₈	—	2	2	no	—
768	C₂×Q₈	—	2	8	no	—
769	C₂×Q₈	—	2	4	no	—
770	C₂×Q₈	—	2	8	no	—
771	C₂×Q₈	—	2	4	no	—
772	C₂×Q₈	—	2	4	no	—
773	C₂×Q₈	—	4	8	no	—
774	C₂×Q₈	—	4	4	no	—
775	C₂×Q₈	—	4	4	no	—
776	C₂×Q₈	—	4	2	no	—
777	C₂×Q₈	—	4	8	no	—
778	C₂×Q₈	—	4	8	no	—
779	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	complemented
780	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
781	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
782	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
783	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	4	no	—
786	C₂×D₄	—	2	4	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	1	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	4	2	no	—
796	C₂×D₄	—	4	8	no	—
797	C₂×D₄	—	4	4	no	—
798	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
799	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
800	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
801	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
802	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	4	no	—
811	C₂²×C₄	—	2	4	no	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	4	8	no	—
818	C₂²×C₄	—	4	8	no	—
819	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
820	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
821	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
822	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
823	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
827	Q₁₆	—	2	8	no	—
828	Q₁₆	—	2	8	no	—
829	Q₁₆	—	2	8	no	—
830	Q₁₆	—	4	4	no	—
831	Q₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
832	SD₁₆	—	2	8	no	—
833	SD₁₆	—	2	8	no	—
834	SD₁₆	—	2	8	no	—
835	SD₁₆	—	4	4	no	—
836	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
837	M₁₆	—	2	4	no	—
838	M₁₆	—	2	2	no	—
839	M₁₆	—	2	8	no	—
840	M₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
841	C₂×C₈	—	2	8	no	—
842	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
843	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
844	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	4	no	—
854	C₄⋊C₄	—	2	4	no	—
855	C₄⋊C₄	—	2	1	no	—
856	C₄⋊C₄	—	2	1	no	—
857	C₄⋊C₄	—	2	1	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
861	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
862	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
863	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
864	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
865	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	1	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	1	no	—
874	C₂²⋊C₄	—	2	1	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
878	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
879	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
880	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
881	C₄²	—	2	1	no	—
882	C₄²	—	2	1	no	—
883	C₄²	—	2	1	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
887	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
888	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
889	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
890	C₂³	—	2	4	no	—
891	C₂³	—	2	4	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	2	no	—
894	C₂³	—	4	2	no	—
895	C₂³	—	4	4	no	—
896	C₂³	—	4	4	no	—
897	C₂³	—	8	2	no	—
898	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
899	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
900	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
901	Q₈	—	2	4	no	—
902	Q₈	—	2	2	no	—
903	Q₈	—	2	1	no	—
904	Q₈	—	2	4	no	—
905	Q₈	—	2	2	no	—
906	Q₈	—	2	4	no	—
907	Q₈	—	2	2	no	—
908	Q₈	—	4	8	no	—
909	Q₈	—	4	8	no	—
910	Q₈	—	4	4	no	—
911	Q₈	—	4	4	no	—
912	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
913	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
914	D₄	—	2	4	no	—
915	D₄	—	2	4	no	—
916	D₄	—	2	2	no	—
917	D₄	—	2	2	no	—
918	D₄	—	2	1	no	—
919	D₄	—	2	2	no	—
920	D₄	—	4	4	no	—
921	D₄	—	4	4	no	—
922	D₄	—	4	4	no	—
923	D₄	—	4	4	no	—
924	D₄	—	4	4	no	—
925	D₄	—	4	2	no	—
926	D₄	—	8	1	no	—
927	D₄	—	8	2	no	—
928	D₄	#137×C₆₇	1	4	yes	direct product factor
929	D₄	C₂²×D₄×C₆₇	1	2	yes	—
930	C₂×C₄	—	2	4	no	—
931	C₂×C₄	—	2	4	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	4	no	—
935	C₂×C₄	—	2	4	no	—
936	C₂×C₄	—	2	4	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	4	no	—
947	C₂×C₄	—	4	1	no	—
948	C₂×C₄	—	4	4	no	—
949	C₂×C₄	—	4	4	no	—
950	C₂×C₄	—	4	8	no	—
951	C₂×C₄	—	4	8	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	2	no	—
954	C₂×C₄	—	4	4	no	—
955	C₂×C₄	—	4	4	no	—
956	C₂×C₄	—	4	2	no	—
957	C₂×C₄	—	8	1	no	—
958	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
960	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
961	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
962	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
963	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
964	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
965	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
966	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
967	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
968	C₈	—	2	4	no	—
969	C₈	—	2	2	no	—
970	C₈	C₂²×D₄×C₆₇	1	4	yes	—
971	C₂²	—	2	1	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	2	no	—
974	C₂²	—	2	2	no	—
975	C₂²	—	2	2	no	—
976	C₂²	—	2	2	no	—
977	C₂²	—	2	2	no	—
978	C₂²	—	2	2	no	—
979	C₂²	—	4	8	no	—
980	C₂²	—	4	1	no	—
981	C₂²	—	4	1	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	8	8	no	—
986	C₂²	D₄²×C₆₇	1	2	yes	—
987	C₂²	C₂×#137×C₆₇	1	4	yes	complemented
988	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	2	2	no	—
993	C₄	—	2	2	no	—
994	C₄	—	2	2	no	—
995	C₄	—	2	4	no	—
996	C₄	—	4	1	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	1	no	—
999	C₄	—	4	2	no	—
1000	C₄	—	4	4	no	—
1001	C₄	D₄²×C₆₇	1	2	yes	—
1002	C₄	C₂×#137×C₆₇	1	2	yes	complemented
1003	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1004	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1005	C₂	—	2	2	no	—
1006	C₂	—	2	4	no	—
1007	C₂	—	4	2	no	—
1008	C₂	—	4	2	no	—
1009	C₂	—	8	2	no	—
1010	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1011	C₂	C₂²×#137×C₆₇	1	1	yes	characteristic
1012	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	D₄×#41×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#137×C₆₇	C₂	semidirect
3. C₂×D₄×Q₈×C₆₇	C₂	semidirect
4. D₄×Q₁₆×C₆₇	C₂	semidirect
5. D₄×SD₁₆×C₆₇	C₂	semidirect
6. C₆₇×#3278	C₂	semidirect
7. C₆₇×#3276	C₂	semidirect
8. C₆₇×#3270	C₂	semidirect
9. C₆₇×#3266	C₂	semidirect
10. C₆₇×#3152	C₂	semidirect
11. C₆₇×#3056	C₂	semidirect
12. C₆₇×#3039	C₂	semidirect
13. C₆₇×#3037	C₂	semidirect
14. C₆₇×#3007	C₂	semidirect
15. C₆₇×#3004	C₂	semidirect
16. C₄×#137×C₆₇	C₂	semidirect
17. D₄×M₁₆×C₆₇	C₂	semidirect
19. C₂³×Q₈×C₆₇	C₂²	semidirect
23. C₂×#137×C₆₇	C₂²	semidirect
24. C₂×#137×C₆₇	C₂²	semidirect
25. C₂×#137×C₆₇	C₂²	semidirect
26. C₂×#137×C₆₇	C₂²	semidirect
27. C₂×#137×C₆₇	C₂²	semidirect
28. C₂²×Q₁₆×C₆₇	C₂²	semidirect
29. C₂²×SD₁₆×C₆₇	C₂²	semidirect
30. C₂²×M₁₆×C₆₇	C₂²	semidirect
37. D₄×Q₈×C₆₇	C₂²	semidirect
38. D₄×Q₈×C₆₇	C₂²	semidirect
49. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
53. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
55. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
59. #497×C₆₇	C₂²	semidirect
60. #494×C₆₇	C₂²	semidirect
61. #492×C₆₇	C₂²	semidirect
62. #470×C₆₇	C₂²	semidirect
63. #468×C₆₇	C₂²	semidirect
64. #467×C₆₇	C₂²	semidirect
65. #465×C₆₇	C₂²	semidirect
66. #464×C₆₇	C₂²	semidirect
67. #462×C₆₇	C₂²	semidirect
68. #462×C₆₇	C₂²	semidirect
69. #462×C₆₇	C₂²	semidirect
70. #461×C₆₇	C₂²	semidirect
71. #461×C₆₇	C₂²	semidirect
72. #460×C₆₇	C₂²	semidirect
73. #452×C₆₇	C₂²	semidirect
74. #452×C₆₇	C₂²	semidirect
75. #451×C₆₇	C₂²	semidirect
76. #451×C₆₇	C₂²	semidirect
77. #451×C₆₇	C₂²	semidirect
78. #450×C₆₇	C₂²	semidirect
79. #448×C₆₇	C₂²	semidirect
80. #448×C₆₇	C₂²	semidirect
81. #441×C₆₇	C₂²	semidirect
82. #440×C₆₇	C₂²	semidirect
83. C₄×Q₁₆×C₆₇	C₂²	semidirect
84. C₄×SD₁₆×C₆₇	C₂²	semidirect
85. #436×C₆₇	C₂²	semidirect
86. #435×C₆₇	C₂²	semidirect
88. #428×C₆₇	C₂²	semidirect
89. #423×C₆₇	C₂²	semidirect
90. #419×C₆₇	C₂²	semidirect
91. #419×C₆₇	C₂²	semidirect
93. #417×C₆₇	C₂²	semidirect
94. #407×C₆₇	C₂²	semidirect
95. C₄×M₁₆×C₆₇	C₂²	semidirect
127. #137×C₆₇	D₄	direct (N × H)
272. C₂×Q₈×C₆₇	C₂×D₄	semidirect
324. Q₁₆×C₆₇	C₂×D₄	semidirect
329. SD₁₆×C₆₇	C₂×D₄	semidirect
333. M₁₆×C₆₇	C₂×D₄	semidirect
421. D₄×C₆₇	#137	direct (N × H)
480. C₂²×C₆₇	C₂×#137	semidirect
495. C₄×C₆₇	C₂×#137	semidirect
498. D₄×#137	C₆₇	direct (N × H)
507. C₂²×#137	C₂×C₆₇	semidirect
509. C₂×D₄×Q₈	C₂×C₆₇	semidirect
510. D₄×Q₁₆	C₂×C₆₇	semidirect
511. D₄×SD₁₆	C₂×C₆₇	semidirect
512. #3278	C₂×C₆₇	semidirect
513. #3276	C₂×C₆₇	semidirect
514. #3270	C₂×C₆₇	semidirect
515. #3266	C₂×C₆₇	semidirect
516. #3152	C₂×C₆₇	semidirect
517. #3056	C₂×C₆₇	semidirect
518. #3039	C₂×C₆₇	semidirect
519. #3037	C₂×C₆₇	semidirect
520. #3007	C₂×C₆₇	semidirect
521. #3004	C₂×C₆₇	semidirect
522. C₄×#137	C₂×C₆₇	semidirect
523. D₄×M₁₆	C₂×C₆₇	semidirect
524. C₆₇	D₄×#137	direct (N × H)
526. C₂³×Q₈	C₂²×C₆₇	semidirect
530. C₂×#137	C₂²×C₆₇	semidirect
531. C₂×#137	C₂²×C₆₇	semidirect
532. C₂×#137	C₂²×C₆₇	semidirect
533. C₂×#137	C₂²×C₆₇	semidirect
534. C₂×#137	C₂²×C₆₇	semidirect
535. C₂²×Q₁₆	C₂²×C₆₇	semidirect
536. C₂²×SD₁₆	C₂²×C₆₇	semidirect
537. C₂²×M₁₆	C₂²×C₆₇	semidirect
544. D₄×Q₈	C₂²×C₆₇	semidirect
545. D₄×Q₈	C₂²×C₆₇	semidirect
556. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
560. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
562. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
566. #497	C₂²×C₆₇	semidirect
567. #494	C₂²×C₆₇	semidirect
568. #492	C₂²×C₆₇	semidirect
569. #470	C₂²×C₆₇	semidirect
570. #468	C₂²×C₆₇	semidirect
571. #467	C₂²×C₆₇	semidirect
572. #465	C₂²×C₆₇	semidirect
573. #464	C₂²×C₆₇	semidirect
574. #462	C₂²×C₆₇	semidirect
575. #462	C₂²×C₆₇	semidirect
576. #462	C₂²×C₆₇	semidirect
577. #461	C₂²×C₆₇	semidirect
578. #461	C₂²×C₆₇	semidirect
579. #460	C₂²×C₆₇	semidirect
580. #452	C₂²×C₆₇	semidirect
581. #452	C₂²×C₆₇	semidirect
582. #451	C₂²×C₆₇	semidirect
583. #451	C₂²×C₆₇	semidirect
584. #451	C₂²×C₆₇	semidirect
585. #450	C₂²×C₆₇	semidirect
586. #448	C₂²×C₆₇	semidirect
587. #448	C₂²×C₆₇	semidirect
588. #441	C₂²×C₆₇	semidirect
589. #440	C₂²×C₆₇	semidirect
590. C₄×Q₁₆	C₂²×C₆₇	semidirect
591. C₄×SD₁₆	C₂²×C₆₇	semidirect
592. #436	C₂²×C₆₇	semidirect
593. #435	C₂²×C₆₇	semidirect
595. #428	C₂²×C₆₇	semidirect
596. #423	C₂²×C₆₇	semidirect
597. #419	C₂²×C₆₇	semidirect
598. #419	C₂²×C₆₇	semidirect
600. #417	C₂²×C₆₇	semidirect
601. #407	C₂²×C₆₇	semidirect
602. C₄×M₁₆	C₂²×C₆₇	semidirect
634. #137	D₄×C₆₇	direct (N × H)
779. C₂×Q₈	C₂×D₄×C₆₇	semidirect
831. Q₁₆	C₂×D₄×C₆₇	semidirect
836. SD₁₆	C₂×D₄×C₆₇	semidirect
840. M₁₆	C₂×D₄×C₆₇	semidirect
928. D₄	#137×C₆₇	direct (N × H)
987. C₂²	C₂×#137×C₆₇	semidirect
1002. C₄	C₂×#137×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#137×C₆₇	2
D₄×#41×C₆₇	2
C₂×D₄×Q₈×C₆₇	2
D₄×Q₁₆×C₆₇	2
D₄×SD₁₆×C₆₇	2
C₆₇×#3278	2
C₆₇×#3276	2
C₆₇×#3270	2
C₆₇×#3266	2
C₆₇×#3152	2
C₆₇×#3056	2
C₆₇×#3039	2
C₆₇×#3037	2
C₆₇×#3007	2
C₆₇×#3004	2
C₄×#137×C₆₇	2
D₄×M₁₆×C₆₇	2
D₄×#137	67

Subgroups — D4×#137×C67 #30740320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#137×C₆₇ #30740320