Subgroups — #22574261

Order 8576.

1124 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864116	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864101	C₂	1	2	yes	maximal, complemented
3	#16864080	C₂	1	2	yes	maximal, complemented
4	#16864074	C₂	1	4	yes	maximal, complemented
5	#16864061	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864053	C₂	1	2	yes	maximal, complemented
7	#16864051	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864043	C₂	1	2	yes	maximal, complemented
9	#16864013	C₂	1	2	yes	maximal, complemented
10	#16863989	C₂	1	4	yes	maximal, complemented
11	#16863951	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863928	C₂	1	1	yes	maximal, characteristic, complemented
13	#16863903	C₂	1	2	yes	maximal, complemented
14	C₂²⋊Q₈×D₆₇	C₂	1	2	yes	maximal, complemented
15	#16863877	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11761628	C₂²	1	2	yes	—
19	C₂×Q₈×D₆₇	C₂²	1	2	yes	complemented
20	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₆₇	C₂²	1	2	yes	—
22	#14524043	C₂²	1	1	yes	characteristic, complemented
23	#14524042	C₂²	1	2	yes	complemented
24	#14524036	C₂²	1	4	yes	complemented
25	#14524036	C₂²	1	4	yes	complemented
26	#14524036	C₂²	1	2	yes	complemented
27	#14524034	C₂²	1	1	yes	characteristic, complemented
28	#14524034	C₂²	1	2	yes	complemented
29	#14524033	C₂²	1	4	yes	complemented
30	#14524030	C₂²	1	2	yes	—
31	#14524030	C₂²	1	4	yes	complemented
32	#14524030	C₂²	1	1	yes	characteristic, complemented
33	#14524025	C₂²	1	4	yes	—
34	#14524025	C₂²	1	2	yes	—
35	#14524025	C₂²	1	4	yes	complemented
36	#14524024	C₂²	1	4	yes	complemented
37	#14524023	C₂²	1	2	yes	—
38	#14524023	C₂²	1	1	yes	characteristic
39	#14524022	C₂²	1	2	yes	complemented
40	#14524022	C₂²	1	4	yes	complemented
41	#14524022	C₂²	1	2	yes	complemented
42	#14524021	C₂²	1	4	yes	—
43	#14524021	C₂²	1	4	yes	complemented
44	#14524020	C₂²	1	4	yes	complemented
45	#14524019	C₂²	1	2	yes	—
46	#14524019	C₂²	1	2	yes	complemented
47	#14524014	C₂²	1	4	yes	—
48	#14524014	C₂²	1	1	yes	characteristic
49	#14524014	C₂²	1	2	yes	complemented
50	#14524011	C₂²	1	4	yes	—
51	Q₈×Dic₆₇	C₂²	1	2	yes	complemented
52	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
53	#14524008	C₂²	1	2	yes	complemented
54	#14524008	C₂²	1	2	yes	complemented
55	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
56	D₄×Dic₆₇	C₂²	1	1	yes	characteristic
57	#14524005	C₂²	1	2	yes	—
58	#14524005	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₆₇	C₂²	1	4	yes	—
62	C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
63	C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
64	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
65	#14524002	C₂²	1	2	yes	complemented
66	#14524002	C₂²	1	2	yes	complemented
67	#14524001	C₂²	1	2	yes	—
68	#14524001	C₂²	1	4	yes	complemented
69	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
70	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₆₇	C₂²	1	4	yes	complemented
72	C₂²⋊C₄×D₆₇	C₂²	1	4	yes	—
73	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
74	C₄²×D₆₇	C₂²	1	1	yes	characteristic
75	C₂×#41×C₆₇	C₂²	1	2	yes	complemented
76	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#123×C₆₇	C₂²	1	4	yes	complemented
78	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
79	#121×C₆₇	C₂²	1	2	yes	—
80	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
81	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
83	C₂³×D₆₇	C₂³	1	2	yes	—
84	#11761628	—	2	8	no	—
85	C₂×Dic₁₃₄	C₂³	1	2	yes	—
86	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
87	C₂×Dic₁₃₄	C₂³	1	4	yes	—
88	Q₈×D₆₇	—	4	4	no	—
89	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
93	D₄×D₆₇	—	2	4	no	—
94	C₂²×Dic₆₇	C₂³	1	2	yes	—
95	C₂×C₄×D₆₇	—	4	4	no	—
96	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
97	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₆₇	C₂³	1	4	yes	—
100	C₂×C₄×D₆₇	C₂³	1	2	yes	—
101	C₂×C₄×D₆₇	C₂³	1	2	yes	—
102	C₂×C₄×D₆₇	C₂³	1	4	yes	—
103	C₂×C₄×D₆₇	C₂³	1	2	yes	—
104	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
105	C₄⋊Dic₆₇	C₂³	1	2	yes	—
106	C₄⋊Dic₆₇	C₂³	1	2	yes	—
107	C₄⋊Dic₆₇	C₂³	1	2	yes	—
108	C₄⋊Dic₆₇	C₂³	1	2	yes	—
109	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
110	C₄⋊Dic₆₇	C₂³	1	4	yes	—
111	Dic₆₇⋊C₄	C₂³	1	2	yes	—
112	Dic₆₇⋊C₄	C₂³	1	4	yes	—
113	Dic₆₇⋊C₄	C₂³	1	4	yes	—
114	Dic₆₇⋊C₄	C₂³	1	4	yes	—
115	Dic₆₇⋊C₄	C₂³	1	4	yes	—
116	Dic₆₇⋊C₄	C₂³	1	2	yes	—
117	Dic₆₇⋊C₄	C₂³	1	2	yes	—
118	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
119	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
120	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
121	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
122	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
123	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
124	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
125	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
127	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
128	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
129	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
130	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
131	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
132	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
133	C₄×Dic₆₇	C₂³	1	4	yes	—
134	C₄×Dic₆₇	C₂³	1	4	yes	—
135	C₄×Dic₆₇	C₂³	1	2	yes	—
136	#41×C₆₇	—	4	4	no	—
137	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
138	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×D₄×C₆₇	C₂³	1	4	yes	—
141	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
142	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
143	C₂²×C₄×C₆₇	C₂³	1	4	yes	—
144	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
147	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
152	C₄²×C₆₇	C₂³	1	1	yes	characteristic
153	C₂³×C₆₇	C₂⁴	1	2	yes	—
154	C₂³×C₆₇	C₂⁴	1	2	yes	—
155	C₂²×D₆₇	—	2	4	no	—
156	C₂²×D₆₇	—	2	4	no	—
157	C₂²×D₆₇	—	4	2	no	—
158	C₂²×D₆₇	C₂⁴	1	2	yes	—
159	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
160	Q₈×C₆₇	—	2	4	no	—
161	D₄×C₆₇	—	2	2	no	—
162	D₄×C₆₇	—	2	2	no	—
163	D₄×C₆₇	—	4	4	no	—
164	C₂×C₄×C₆₇	—	2	4	no	—
165	C₂×C₄×C₆₇	—	2	4	no	—
166	C₂×C₄×C₆₇	—	4	4	no	—
167	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
169	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
170	C₂×C₄×C₆₇	C₂⁴	1	4	yes	—
171	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₆₇	—	2	4	no	—
174	C₂²⋊D₆₇	—	2	8	no	—
175	C₂²⋊D₆₇	—	2	4	no	—
176	C₂×Dic₆₇	—	4	2	no	—
177	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₆₇	C₂⁴	1	2	yes	—
179	C₂×Dic₆₇	C₂⁴	1	4	yes	—
180	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
181	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
182	C₂×Dic₆₇	C₂⁴	1	2	yes	—
183	C₂×Dic₆₇	C₂⁴	1	2	yes	—
184	D₂₆₈	#41	1	4	yes	complemented
185	C₄×D₆₇	—	2	8	no	—
186	C₄×D₆₇	—	2	2	no	—
187	C₄×D₆₇	—	2	2	no	—
188	C₄×D₆₇	—	2	2	no	—
189	C₄×D₆₇	—	2	4	no	—
190	C₄×D₆₇	—	4	2	no	—
191	C₄×D₆₇	—	4	2	no	—
192	C₄×D₆₇	—	4	4	no	—
193	Dic₁₃₄	—	2	4	no	—
194	Dic₁₃₄	—	2	2	no	—
195	Dic₁₃₄	—	4	4	no	—
196	C₂²×C₆₇	—	2	2	no	—
197	C₂²×C₆₇	—	2	2	no	—
198	C₂²×C₆₇	—	2	2	no	—
199	C₂²×C₆₇	—	2	2	no	—
200	C₂²×C₆₇	—	2	2	no	—
201	C₂²×C₆₇	—	2	2	no	—
202	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
203	C₂×D₆₇	—	2	1	no	—
204	C₂×D₆₇	—	2	2	no	—
205	C₂×D₆₇	—	2	1	no	—
206	C₂×D₆₇	—	2	2	no	—
207	C₂×D₆₇	—	4	8	no	—
208	C₂×D₆₇	C₂×#41	1	4	yes	—
209	C₂×D₆₇	2₋¹⁺⁴	1	2	yes	—
210	C₄×C₆₇	—	2	2	no	—
211	C₄×C₆₇	—	2	4	no	—
212	C₄×C₆₇	—	2	2	no	—
213	C₄×C₆₇	—	2	1	no	—
214	C₄×C₆₇	C₂×#41	1	2	yes	—
215	C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
216	Dic₆₇	—	2	4	no	—
217	Dic₆₇	—	2	1	no	—
218	Dic₆₇	—	2	2	no	—
219	Dic₆₇	—	2	2	no	—
220	Dic₆₇	—	2	1	no	—
221	Dic₆₇	—	2	1	no	—
222	Dic₆₇	—	2	2	no	—
223	C₂×C₆₇	—	4	2	no	—
224	C₂×C₆₇	—	4	2	no	—
225	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
226	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
228	D₆₇	—	2	2	no	—
229	D₆₇	—	2	4	no	—
230	#3520	—	67	1	no	maximal, Sylow
231	C₆₇	#3520	1	1	yes	characteristic, complemented, Sylow
232	#556	—	67	1	no	—
233	#554	—	67	2	no	—
234	#552	—	67	2	no	—
235	#551	—	67	4	no	—
236	D₄×Q₈	—	67	1	no	—
237	#548	—	67	2	no	—
238	#547	—	67	1	no	—
239	#547	D₆₇	1	1	yes	characteristic, complemented
240	#546	—	67	2	no	—
241	#542	—	67	2	no	—
242	#539	—	67	4	no	—
243	#533	—	67	1	no	—
244	#529	—	67	1	no	—
245	#525	—	67	2	no	—
246	C₂×C₂²⋊Q₈	—	67	2	no	—
247	#520	—	67	2	no	—
248	C₂×C₄×D₄	—	67	1	no	—
249	C₂×#41	—	67	2	no	—
250	C₂×#41	C₂×D₆₇	1	2	yes	complemented
251	C₂²×Q₈	—	67	2	no	—
252	C₂²×D₄	—	67	1	no	—
253	C₂³×C₄	—	67	2	no	—
254	C₄⋊Q₈	—	67	2	no	—
255	C₄⋊Q₈	—	67	1	no	—
256	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
257	#126	—	67	2	no	—
258	#126	—	67	4	no	—
259	#126	—	67	4	no	—
260	#125	—	67	1	no	—
261	#125	—	67	2	no	—
262	#125	—	67	4	no	—
263	#124	—	67	1	no	—
264	#124	—	67	2	no	—
265	#124	—	67	4	no	—
266	#123	—	67	4	no	—
267	#123	—	67	2	no	—
268	#123	—	67	4	no	—
269	#123	—	67	4	no	—
270	#123	C₂×D₆₇	1	4	yes	complemented
271	C₂²⋊Q₈	—	67	2	no	—
272	C₂²⋊Q₈	—	67	2	no	—
273	C₂²⋊Q₈	—	67	2	no	—
274	C₂²⋊Q₈	—	67	4	no	—
275	C₂²⋊Q₈	—	67	2	no	—
276	C₂²⋊Q₈	—	67	1	no	—
277	C₂²⋊Q₈	—	67	4	no	—
278	C₂²⋊Q₈	—	67	2	no	—
279	C₂²⋊Q₈	—	67	4	no	—
280	C₂²⋊Q₈	—	67	4	no	—
281	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
282	#121	—	67	1	no	—
283	#121	—	67	2	no	—
284	#121	—	67	4	no	—
285	#121	C₂×D₆₇	1	2	yes	—
286	#120	—	67	4	no	—
287	C₄×Q₈	—	67	2	no	—
288	C₄×Q₈	—	67	2	no	—
289	C₄×Q₈	—	67	2	no	—
290	C₄×Q₈	—	67	1	no	—
291	C₄×D₄	—	67	1	no	—
292	C₄×D₄	—	67	2	no	—
293	C₄×D₄	—	67	4	no	—
294	C₄×D₄	—	67	4	no	—
295	C₄×D₄	—	67	4	no	—
296	C₄×D₄	—	67	2	no	—
297	C₄×D₄	—	67	1	no	—
298	C₄×D₄	—	67	2	no	—
299	C₄×D₄	—	67	2	no	—
300	C₄×D₄	—	67	1	no	—
301	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
302	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
303	#117	—	67	2	no	—
304	#117	—	67	2	no	—
305	#117	—	67	4	no	—
306	#117	—	67	2	no	—
307	C₂×C₄⋊C₄	—	67	1	no	—
308	C₂×C₄⋊C₄	—	67	4	no	—
309	C₂×C₄⋊C₄	—	67	2	no	—
310	C₂×C₄⋊C₄	C₂×D₆₇	1	2	yes	complemented
311	C₂×C₂²⋊C₄	—	67	2	no	—
312	C₂×C₂²⋊C₄	—	67	4	no	—
313	C₂×C₄²	—	67	1	no	—
314	C₂⁴	—	67	2	no	—
315	#41	—	4	4	no	—
316	#41	—	134	8	no	—
317	C₂×Q₈	—	268	4	no	—
318	C₂×Q₈	—	67	4	no	—
319	C₂×Q₈	—	67	2	no	—
320	C₂×Q₈	—	67	1	no	—
321	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
322	C₂×D₄	—	67	2	no	—
323	C₂×D₄	—	67	4	no	—
324	C₂×D₄	—	67	2	no	—
325	C₂×D₄	—	67	1	no	—
326	C₂×D₄	—	134	4	no	—
327	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
328	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
329	C₂×D₄	C₂²×D₆₇	1	4	yes	—
330	C₂²×C₄	—	268	4	no	—
331	C₂²×C₄	—	67	2	no	—
332	C₂²×C₄	—	67	4	no	—
333	C₂²×C₄	—	67	2	no	—
334	C₂²×C₄	—	67	2	no	—
335	C₂²×C₄	—	67	1	no	—
336	C₂²×C₄	—	67	1	no	—
337	C₂²×C₄	—	67	1	no	—
338	C₂²×C₄	—	67	4	no	—
339	C₂²×C₄	—	67	2	no	—
340	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
341	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
342	C₂²×C₄	C₂²×D₆₇	1	4	yes	—
343	C₄⋊C₄	—	67	2	no	—
344	C₄⋊C₄	—	67	2	no	—
345	C₄⋊C₄	—	67	2	no	—
346	C₄⋊C₄	—	67	1	no	—
347	C₄⋊C₄	—	67	4	no	—
348	C₄⋊C₄	—	67	4	no	—
349	C₄⋊C₄	—	67	4	no	—
350	C₄⋊C₄	—	67	2	no	—
351	C₄⋊C₄	—	67	1	no	—
352	C₄⋊C₄	—	67	2	no	—
353	C₄⋊C₄	—	67	4	no	—
354	C₄⋊C₄	—	67	2	no	—
355	C₄⋊C₄	—	67	4	no	—
356	C₄⋊C₄	—	67	2	no	—
357	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
358	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
359	C₄⋊C₄	C₂²×D₆₇	1	4	yes	—
360	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
361	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
362	C₂²⋊C₄	—	67	2	no	—
363	C₂²⋊C₄	—	67	4	no	—
364	C₂²⋊C₄	—	67	2	no	—
365	C₂²⋊C₄	—	67	2	no	—
366	C₂²⋊C₄	—	67	4	no	—
367	C₂²⋊C₄	—	67	2	no	—
368	C₂²⋊C₄	—	67	4	no	—
369	C₂²⋊C₄	—	67	2	no	—
370	C₂²⋊C₄	—	67	2	no	—
371	C₂²⋊C₄	—	67	4	no	—
372	C₂²⋊C₄	—	67	2	no	—
373	C₂²⋊C₄	—	67	4	no	—
374	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
375	C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
376	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
377	C₄²	—	67	1	no	—
378	C₄²	—	67	1	no	—
379	C₄²	—	67	1	no	—
380	C₄²	—	67	4	no	—
381	C₄²	—	67	4	no	—
382	C₄²	—	67	2	no	—
383	C₄²	C₂²×D₆₇	1	1	yes	characteristic
384	C₂³	—	268	2	no	—
385	C₂³	—	67	1	no	—
386	C₂³	—	67	2	no	—
387	C₂³	—	134	4	no	—
388	C₂³	—	134	4	no	—
389	C₂³	C₂³×D₆₇	1	2	yes	—
390	C₂³	C₂³×D₆₇	1	2	yes	—
391	Q₈	—	2	4	no	—
392	Q₈	—	268	4	no	—
393	Q₈	—	134	4	no	—
394	Q₈	—	134	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	2	no	—
397	D₄	—	4	4	no	—
398	D₄	—	67	4	no	—
399	D₄	—	134	4	no	—
400	D₄	—	134	8	no	—
401	D₄	—	134	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	268	2	no	—
406	C₂×C₄	—	268	2	no	—
407	C₂×C₄	—	268	4	no	—
408	C₂×C₄	—	268	2	no	—
409	C₂×C₄	—	67	1	no	—
410	C₂×C₄	—	67	2	no	—
411	C₂×C₄	—	67	4	no	—
412	C₂×C₄	—	67	1	no	—
413	C₂×C₄	—	67	1	no	—
414	C₂×C₄	—	67	2	no	—
415	C₂×C₄	—	67	2	no	—
416	C₂×C₄	—	134	8	no	—
417	C₂×C₄	—	134	2	no	—
418	C₂×C₄	—	134	2	no	—
419	C₂×C₄	—	134	2	no	—
420	C₂×C₄	—	134	4	no	—
421	C₂×C₄	C₂³×D₆₇	1	2	yes	—
422	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₆₇	1	4	yes	—
424	C₂×C₄	C₂³×D₆₇	1	2	yes	—
425	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	268	8	no	—
434	C₂²	—	67	4	no	—
435	C₂²	—	67	2	no	—
436	C₂²	—	134	1	no	—
437	C₂²	—	134	2	no	—
438	C₂²	—	134	1	no	—
439	C₂²	—	134	2	no	—
440	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	1	no	—
445	C₄	—	134	1	no	—
446	C₄	—	134	4	no	—
447	C₄	—	134	1	no	—
448	C₄	—	134	2	no	—
449	C₄	—	134	2	no	—
450	C₄	—	134	1	no	—
451	C₄	—	134	2	no	—
452	C₄	#41×D₆₇	1	2	yes	—
453	C₄	#14524088	1	2	yes	—
454	C₂	—	4	2	no	—
455	C₂	—	4	2	no	—
456	C₂	—	134	2	no	—
457	C₂	—	134	4	no	—
458	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
459	C₂	C₂×#14524088	1	1	yes	characteristic
460	C₂	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#547×C₆₇	C₂
hypercenter	#547	D₆₇
hypocenter	C₆₇	#3520
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. #16864116	C₂	semidirect
2. #16864101	C₂	semidirect
3. #16864080	C₂	semidirect
4. #16864074	C₂	semidirect
5. #16864061	C₂	semidirect
6. #16864053	C₂	semidirect
7. #16864051	C₂	semidirect
8. #16864043	C₂	semidirect
9. #16864013	C₂	semidirect
10. #16863989	C₂	semidirect
11. #16863951	C₂	semidirect
12. #16863928	C₂	semidirect
13. #16863903	C₂	semidirect
14. C₂²⋊Q₈×D₆₇	C₂	semidirect
15. #16863877	C₂	semidirect
16. C₄×D₄×D₆₇	C₂	semidirect
17. #547×C₆₇	C₂	semidirect
19. C₂×Q₈×D₆₇	C₂²	semidirect
22. #14524043	C₂²	semidirect
23. #14524042	C₂²	semidirect
24. #14524036	C₂²	semidirect
25. #14524036	C₂²	semidirect
26. #14524036	C₂²	semidirect
27. #14524034	C₂²	semidirect
28. #14524034	C₂²	semidirect
29. #14524033	C₂²	semidirect
31. #14524030	C₂²	semidirect
32. #14524030	C₂²	semidirect
35. #14524025	C₂²	semidirect
36. #14524024	C₂²	semidirect
39. #14524022	C₂²	semidirect
40. #14524022	C₂²	semidirect
41. #14524022	C₂²	semidirect
43. #14524021	C₂²	semidirect
44. #14524020	C₂²	semidirect
46. #14524019	C₂²	semidirect
49. #14524014	C₂²	semidirect
51. Q₈×Dic₆₇	C₂²	semidirect
52. C₄×Dic₁₃₄	C₂²	semidirect
53. #14524008	C₂²	semidirect
54. #14524008	C₂²	semidirect
62. C₄×C₂²⋊D₆₇	C₂²	semidirect
63. C₄×C₂²⋊D₆₇	C₂²	semidirect
65. #14524002	C₂²	semidirect
66. #14524002	C₂²	semidirect
68. #14524001	C₂²	semidirect
70. C₄⋊C₄×D₆₇	C₂²	semidirect
71. C₄⋊C₄×D₆₇	C₂²	semidirect
75. C₂×#41×C₆₇	C₂²	semidirect
76. C₄⋊Q₈×C₆₇	C₂²	semidirect
77. #123×C₆₇	C₂²	semidirect
78. C₂²⋊Q₈×C₆₇	C₂²	semidirect
81. C₄×D₄×C₆₇	C₂²	semidirect
82. C₂×C₄⋊C₄×C₆₇	C₂²	semidirect
184. D₂₆₈	#41	semidirect
231. C₆₇	#3520	semidirect
239. #547	D₆₇	semidirect
250. C₂×#41	C₂×D₆₇	semidirect
256. C₄⋊Q₈	C₂×D₆₇	semidirect
270. #123	C₂×D₆₇	semidirect
281. C₂²⋊Q₈	C₂×D₆₇	semidirect
302. C₄×D₄	C₂×D₆₇	semidirect
310. C₂×C₄⋊C₄	C₂×D₆₇	semidirect