Subgroups — #22574161

Order 8576.

1142 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864132	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864116	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864110	C₂	1	2	yes	maximal, complemented
4	#16864077	C₂	1	4	yes	maximal, complemented
5	D₄×Dic₁₃₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864052	C₂	1	2	yes	maximal, complemented
7	#16864040	C₂	1	2	yes	maximal, complemented
8	#16864040	C₂	1	2	yes	maximal, complemented
9	#16864013	C₂	1	2	yes	maximal, complemented
10	#16863981	C₂	1	4	yes	maximal, complemented
11	#16863944	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863928	C₂	1	1	yes	maximal, characteristic, complemented
13	#16863927	C₂	1	2	yes	maximal, complemented
14	C₂×#14524030	C₂	1	2	yes	maximal, complemented
15	#16863871	C₂	1	2	yes	maximal, complemented
16	C₄×#11761627	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11761627	C₂²	1	1	yes	characteristic
19	C₂×#11761627	C₂²	1	2	yes	complemented
20	C₂²×Dic₁₃₄	C₂²	1	2	yes	complemented
21	#14524043	C₂²	1	1	yes	characteristic, complemented
22	#14524042	C₂²	1	2	yes	complemented
23	#14524036	C₂²	1	4	yes	complemented
24	#14524036	C₂²	1	2	yes	complemented
25	#14524036	C₂²	1	4	yes	complemented
26	#14524034	C₂²	1	1	yes	characteristic, complemented
27	#14524030	C₂²	1	2	yes	—
28	#14524030	C₂²	1	1	yes	characteristic
29	#14524030	C₂²	1	2	yes	complemented
30	#14524030	C₂²	1	4	yes	complemented
31	#14524030	C₂²	1	2	yes	complemented
32	#14524030	C₂²	1	4	yes	complemented
33	#14524030	C₂²	1	2	yes	complemented
34	#14524029	C₂²	1	4	yes	complemented
35	#14524025	C₂²	1	2	yes	complemented
36	#14524024	C₂²	1	4	yes	complemented
37	#14524024	C₂²	1	4	yes	complemented
38	#14524024	C₂²	1	4	yes	complemented
39	#14524023	C₂²	1	1	yes	characteristic, complemented
40	#14524022	C₂²	1	2	yes	complemented
41	#14524022	C₂²	1	2	yes	complemented
42	#14524020	C₂²	1	4	yes	complemented
43	#14524020	C₂²	1	4	yes	complemented
44	#14524015	C₂²	1	4	yes	complemented
45	#14524015	C₂²	1	4	yes	complemented
46	#14524014	C₂²	1	1	yes	characteristic
47	#14524014	C₂²	1	2	yes	complemented
48	#14524014	C₂²	1	2	yes	complemented
49	#14524012	C₂²	1	4	yes	complemented
50	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
51	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
52	#14524008	C₂²	1	1	yes	characteristic, complemented
53	#14524008	C₂²	1	2	yes	complemented
54	D₄×Dic₆₇	C₂²	1	2	yes	—
55	D₄×Dic₆₇	C₂²	1	1	yes	characteristic
56	D₄×Dic₆₇	C₂²	1	2	yes	complemented
57	D₄×Dic₆₇	C₂²	1	2	yes	complemented
58	D₄×Dic₆₇	C₂²	1	4	yes	complemented
59	D₄×Dic₆₇	C₂²	1	2	yes	complemented
60	D₄×Dic₆₇	C₂²	1	2	yes	complemented
61	D₄×Dic₆₇	C₂²	1	4	yes	complemented
62	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
64	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
65	#14524002	C₂²	1	2	yes	complemented
66	#14524002	C₂²	1	2	yes	complemented
67	#14524001	C₂²	1	1	yes	characteristic, complemented
68	#14523999	C₂²	1	2	yes	complemented
69	#14523999	C₂²	1	4	yes	complemented
70	C₂×C₂²⋊Dic₆₇	C₂²	1	4	yes	complemented
71	C₂×C₂²⋊Dic₆₇	C₂²	1	4	yes	complemented
72	C₂×C₂²⋊Dic₆₇	C₂²	1	4	yes	complemented
73	C₂×C₄×Dic₆₇	C₂²	1	2	yes	complemented
74	C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
75	C₂²×D₄×C₆₇	C₂²	1	2	yes	—
76	C₂²×D₄×C₆₇	C₂²	1	2	yes	—
77	#127×C₆₇	C₂²	1	1	yes	characteristic
78	#121×C₆₇	C₂²	1	2	yes	—
79	#121×C₆₇	C₂²	1	2	yes	—
80	#120×C₆₇	C₂²	1	4	yes	—
81	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
82	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
83	#11761627	—	2	4	no	—
84	#11761627	—	4	4	no	—
85	C₂×Dic₁₃₄	—	4	4	no	—
86	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
87	C₂×Dic₁₃₄	C₂³	1	2	yes	—
88	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
89	C₂×Dic₁₃₄	C₂³	1	4	yes	—
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	C₂²×Dic₆₇	C₂³	1	2	yes	—
94	C₂²×Dic₆₇	C₂³	1	2	yes	—
95	C₂²×Dic₆₇	C₂³	1	4	yes	—
96	C₂²×Dic₆₇	C₂³	1	4	yes	—
97	C₂²×Dic₆₇	C₂³	1	4	yes	—
98	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
101	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
102	C₄⋊Dic₆₇	C₂³	1	2	yes	—
103	C₄⋊Dic₆₇	C₂³	1	2	yes	—
104	C₄⋊Dic₆₇	C₂³	1	2	yes	—
105	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
106	C₄⋊Dic₆₇	C₂³	1	2	yes	—
107	Dic₆₇⋊C₄	C₂³	1	2	yes	—
108	Dic₆₇⋊C₄	C₂³	1	2	yes	—
109	Dic₆₇⋊C₄	C₂³	1	2	yes	—
110	Dic₆₇⋊C₄	C₂³	1	4	yes	—
111	Dic₆₇⋊C₄	C₂³	1	4	yes	—
112	Dic₆₇⋊C₄	C₂³	1	2	yes	—
113	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
114	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
115	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
116	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
117	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
118	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
119	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
120	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
121	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
122	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
123	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
124	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
125	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
127	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
128	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
129	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
130	C₄×Dic₆₇	C₂³	1	2	yes	—
131	C₄×Dic₆₇	C₂³	1	2	yes	—
132	C₄×Dic₆₇	C₂³	1	2	yes	—
133	C₄×Dic₆₇	C₂³	1	4	yes	—
134	C₄×Dic₆₇	C₂³	1	2	yes	—
135	C₂⁴×C₆₇	C₂³	1	4	yes	—
136	C₂×D₄×C₆₇	—	2	8	no	—
137	C₂×D₄×C₆₇	—	4	4	no	—
138	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×D₄×C₆₇	C₂³	1	4	yes	—
140	C₂×D₄×C₆₇	C₂³	1	2	yes	—
141	C₂×D₄×C₆₇	C₂³	1	2	yes	—
142	C₂×D₄×C₆₇	C₂³	1	2	yes	—
143	C₂×D₄×C₆₇	C₂³	1	4	yes	—
144	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
146	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
147	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	—	2	8	no	—
154	C₂³×C₆₇	—	4	4	no	—
155	C₂³×C₆₇	—	4	4	no	—
156	C₂³×C₆₇	C₂⁴	1	2	yes	—
157	C₂³×C₆₇	C₂⁴	1	4	yes	—
158	C₂³×C₆₇	C₂⁴	1	2	yes	—
159	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
160	D₄×C₆₇	—	2	8	no	—
161	D₄×C₆₇	—	2	4	no	—
162	D₄×C₆₇	—	2	2	no	—
163	D₄×C₆₇	—	2	4	no	—
164	D₄×C₆₇	—	4	4	no	—
165	D₄×C₆₇	—	4	2	no	—
166	D₄×C₆₇	#41	1	4	yes	complemented
167	C₂×C₄×C₆₇	—	2	4	no	—
168	C₂×C₄×C₆₇	—	2	4	no	—
169	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
171	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
172	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
174	C₂²⋊D₆₇	—	2	4	no	—
175	C₂²⋊D₆₇	—	4	2	no	—
176	C₂²⋊D₆₇	—	4	4	no	—
177	C₂×Dic₆₇	—	2	4	no	—
178	C₂×Dic₆₇	—	4	2	no	—
179	C₂×Dic₆₇	—	4	4	no	—
180	C₂×Dic₆₇	—	4	4	no	—
181	C₂×Dic₆₇	—	4	4	no	—
182	C₂×Dic₆₇	C₂⁴	1	2	yes	—
183	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
184	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
185	C₂×Dic₆₇	C₂⁴	1	2	yes	—
186	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
187	C₂×Dic₆₇	C₂⁴	1	2	yes	—
188	C₂×Dic₆₇	C₂⁴	1	2	yes	—
189	C₂×Dic₆₇	C₂⁴	1	4	yes	—
190	C₄×D₆₇	—	2	2	no	—
191	C₄×D₆₇	—	2	2	no	—
192	C₄×D₆₇	—	4	1	no	—
193	Dic₁₃₄	—	2	2	no	—
194	Dic₁₃₄	—	2	2	no	—
195	Dic₁₃₄	—	2	4	no	—
196	Dic₁₃₄	—	4	4	no	—
197	C₂²×C₆₇	—	2	2	no	—
198	C₂²×C₆₇	—	2	2	no	—
199	C₂²×C₆₇	—	2	2	no	—
200	C₂²×C₆₇	—	2	4	no	—
201	C₂²×C₆₇	—	2	4	no	—
202	C₂²×C₆₇	—	2	2	no	—
203	C₂²×C₆₇	—	2	4	no	—
204	C₂²×C₆₇	—	2	2	no	—
205	C₂²×C₆₇	—	8	8	no	—
206	C₂²×C₆₇	C₂×#41	1	4	yes	—
207	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
208	C₂×D₆₇	—	2	1	no	—
209	C₂×D₆₇	—	2	1	no	—
210	C₂×D₆₇	—	2	1	no	—
211	C₄×C₆₇	—	2	2	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	2	no	—
217	Dic₆₇	—	2	1	no	—
218	Dic₆₇	—	2	2	no	—
219	Dic₆₇	—	2	4	no	—
220	Dic₆₇	—	2	1	no	—
221	Dic₆₇	—	2	1	no	—
222	Dic₆₇	—	2	2	no	—
223	Dic₆₇	—	2	2	no	—
224	C₂×C₆₇	—	2	4	no	—
225	C₂×C₆₇	—	4	4	no	—
226	C₂×C₆₇	—	4	2	no	—
227	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
228	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
229	C₂×C₆₇	#585	1	1	yes	characteristic
230	D₆₇	—	4	1	no	—
231	#3514	—	67	1	no	maximal, Sylow
232	C₆₇	#3514	1	1	yes	characteristic, complemented, Sylow
233	#559	—	67	1	no	—
234	#556	—	67	1	no	—
235	#555	—	67	2	no	—
236	#551	—	67	4	no	—
237	D₄×Q₈	—	67	1	no	—
238	#548	—	67	2	no	—
239	#546	—	67	2	no	—
240	#546	—	67	2	no	—
241	D₄²	D₆₇	1	1	yes	characteristic, complemented
242	#542	—	67	2	no	—
243	#538	—	67	4	no	—
244	#532	—	67	1	no	—
245	#529	—	67	2	no	—
246	#529	—	67	1	no	—
247	C₂×#124	—	67	2	no	—
248	#518	—	67	2	no	—
249	C₄×#41	—	67	1	no	—
250	C₂×#41	—	67	2	no	—
251	C₂×#41	—	67	1	no	—
252	C₂²×Q₈	—	67	2	no	—
253	C₂²×D₄	C₂×D₆₇	1	2	yes	—
254	C₂²×D₄	C₂×D₆₇	1	2	yes	—
255	C₄⋊Q₈	—	67	2	no	—
256	C₄⋊Q₈	—	67	1	no	—
257	#127	C₂×D₆₇	1	1	yes	characteristic
258	#126	—	67	4	no	—
259	#126	—	67	2	no	—
260	#126	—	67	4	no	—
261	#125	—	67	1	no	—
262	#124	—	67	1	no	—
263	#124	—	67	2	no	—
264	#124	—	67	4	no	—
265	#124	—	67	2	no	—
266	#124	—	67	2	no	—
267	#124	—	67	4	no	—
268	#124	—	67	2	no	—
269	#124	—	67	4	no	—
270	#123	—	67	4	no	—
271	#123	—	67	4	no	—
272	#123	—	67	4	no	—
273	#123	—	67	2	no	—
274	C₂²⋊Q₈	—	67	2	no	—
275	C₂²⋊Q₈	—	67	2	no	—
276	C₂²⋊Q₈	—	67	1	no	—
277	C₂²⋊Q₈	—	67	4	no	—
278	C₂²⋊Q₈	—	67	4	no	—
279	#121	—	67	1	no	—
280	#121	—	67	2	no	—
281	#121	—	67	2	no	—
282	#121	—	67	4	no	—
283	#121	—	67	4	no	—
284	#121	C₂×D₆₇	1	2	yes	—
285	#121	C₂×D₆₇	1	2	yes	—
286	#120	—	67	4	no	—
287	#120	C₂×D₆₇	1	4	yes	—
288	C₄×Q₈	—	67	1	no	—
289	C₄×Q₈	—	67	2	no	—
290	C₄×Q₈	—	67	1	no	—
291	C₄×Q₈	—	67	1	no	—
292	C₄×D₄	—	67	1	no	—
293	C₄×D₄	—	67	4	no	—
294	C₄×D₄	—	67	2	no	—
295	C₄×D₄	—	67	2	no	—
296	C₄×D₄	—	67	4	no	—
297	C₄×D₄	—	67	2	no	—
298	C₄×D₄	—	67	2	no	—
299	C₄×D₄	—	67	2	no	—
300	C₄×D₄	—	67	2	no	—
301	C₄×D₄	—	67	2	no	—
302	C₄×D₄	—	67	2	no	—
303	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
304	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
305	#117	—	67	2	no	—
306	#117	—	67	2	no	—
307	#117	—	67	1	no	—
308	#117	—	67	2	no	—
309	#117	—	67	4	no	—
310	C₂×C₂²⋊C₄	—	67	4	no	—
311	C₂×C₂²⋊C₄	—	67	4	no	—
312	C₂×C₂²⋊C₄	—	67	4	no	—
313	C₂×C₄²	—	67	2	no	—
314	C₂×C₄²	—	67	1	no	—
315	C₂⁴	C₂²×D₆₇	1	4	yes	—
316	#41	—	268	4	no	—
317	#41	—	134	4	no	—
318	C₂×Q₈	—	268	4	no	—
319	C₂×Q₈	—	67	4	no	—
320	C₂×Q₈	—	67	1	no	—
321	C₂×Q₈	—	67	1	no	—
322	C₂×Q₈	—	67	2	no	—
323	C₂×D₄	—	2	8	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	—	67	2	no	—
326	C₂×D₄	—	67	4	no	—
327	C₂×D₄	—	67	2	no	—
328	C₂×D₄	C₂²×D₆₇	1	4	yes	—
329	C₂×D₄	C₂²×D₆₇	1	2	yes	—
330	C₂×D₄	C₂²×D₆₇	1	2	yes	—
331	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
332	C₂×D₄	C₂²×D₆₇	1	2	yes	—
333	C₂×D₄	C₂²×D₆₇	1	4	yes	—
334	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
335	C₂²×C₄	—	67	2	no	—
336	C₂²×C₄	—	67	4	no	—
337	C₂²×C₄	—	67	4	no	—
338	C₂²×C₄	—	67	4	no	—
339	C₂²×C₄	—	67	1	no	—
340	C₂²×C₄	—	67	2	no	—
341	C₂²×C₄	—	67	1	no	—
342	C₂²×C₄	—	67	1	no	—
343	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
344	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
345	C₄⋊C₄	—	67	1	no	—
346	C₄⋊C₄	—	67	2	no	—
347	C₄⋊C₄	—	67	2	no	—
348	C₄⋊C₄	—	67	2	no	—
349	C₄⋊C₄	—	67	2	no	—
350	C₄⋊C₄	—	67	2	no	—
351	C₄⋊C₄	—	67	2	no	—
352	C₄⋊C₄	—	67	4	no	—
353	C₄⋊C₄	—	67	1	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	C₂²⋊C₄	—	67	2	no	—
360	C₂²⋊C₄	—	67	2	no	—
361	C₂²⋊C₄	—	67	4	no	—
362	C₂²⋊C₄	—	67	2	no	—
363	C₂²⋊C₄	—	67	2	no	—
364	C₂²⋊C₄	—	67	4	no	—
365	C₂²⋊C₄	—	67	4	no	—
366	C₂²⋊C₄	—	67	4	no	—
367	C₂²⋊C₄	—	67	4	no	—
368	C₂²⋊C₄	—	67	4	no	—
369	C₂²⋊C₄	—	67	4	no	—
370	C₂²⋊C₄	—	67	4	no	—
371	C₂²⋊C₄	—	67	2	no	—
372	C₂²⋊C₄	—	67	2	no	—
373	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
374	C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
375	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
376	C₄²	—	67	1	no	—
377	C₄²	—	67	2	no	—
378	C₄²	—	67	1	no	—
379	C₄²	—	67	1	no	—
380	C₄²	—	67	2	no	—
381	C₄²	—	67	2	no	—
382	C₄²	—	67	4	no	—
383	C₄²	—	67	2	no	—
384	C₄²	C₂²×D₆₇	1	1	yes	characteristic
385	C₂³	—	2	8	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	4	no	—
388	C₂³	—	67	1	no	—
389	C₂³	C₂³×D₆₇	1	2	yes	—
390	C₂³	C₂³×D₆₇	1	4	yes	—
391	C₂³	C₂³×D₆₇	1	2	yes	—
392	Q₈	—	268	4	no	—
393	Q₈	—	134	2	no	—
394	Q₈	—	134	2	no	—
395	Q₈	—	134	4	no	—
396	D₄	—	2	8	no	—
397	D₄	—	2	4	no	—
398	D₄	—	2	2	no	—
399	D₄	—	2	4	no	—
400	D₄	—	4	4	no	—
401	D₄	—	4	2	no	—
402	D₄	—	268	4	no	—
403	D₄	—	268	2	no	—
404	D₄	—	134	4	no	—
405	D₄	#11761627	1	4	yes	complemented
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	268	1	no	—
409	C₂×C₄	—	268	4	no	—
410	C₂×C₄	—	268	4	no	—
411	C₂×C₄	—	268	2	no	—
412	C₂×C₄	—	268	4	no	—
413	C₂×C₄	—	67	1	no	—
414	C₂×C₄	—	67	1	no	—
415	C₂×C₄	—	67	2	no	—
416	C₂×C₄	—	67	2	no	—
417	C₂×C₄	—	67	1	no	—
418	C₂×C₄	—	67	2	no	—
419	C₂×C₄	—	67	2	no	—
420	C₂×C₄	—	67	4	no	—
421	C₂×C₄	—	134	4	no	—
422	C₂×C₄	—	134	2	no	—
423	C₂×C₄	—	134	2	no	—
424	C₂×C₄	C₂³×D₆₇	1	2	yes	—
425	C₂×C₄	C₂³×D₆₇	1	2	yes	—
426	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
427	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
428	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	8	8	no	—
438	C₂²	—	134	1	no	—
439	C₂²	—	134	1	no	—
440	C₂²	—	134	1	no	—
441	C₂²	C₂×#11761627	1	4	yes	—
442	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	134	1	no	—
447	C₄	—	134	2	no	—
448	C₄	—	134	1	no	—
449	C₄	—	134	4	no	—
450	C₄	—	134	2	no	—
451	C₄	—	134	1	no	—
452	C₄	—	134	2	no	—
453	C₄	—	134	2	no	—
454	C₄	C₂×#11761627	1	2	yes	—
455	C₄	#14524088	1	2	yes	—
456	C₂	—	2	4	no	—
457	C₂	—	4	2	no	—
458	C₂	—	4	4	no	—
459	C₂	—	268	1	no	—
460	C₂	C₂²×#11761627	1	1	yes	characteristic
461	C₂	C₂×#14524088	1	1	yes	characteristic
462	C₂	#16864231	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	D₄²×C₆₇	C₂
hypercenter	D₄²	D₆₇
hypocenter	C₆₇	#3514
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. #16864132	C₂	semidirect
2. #16864116	C₂	semidirect
3. #16864110	C₂	semidirect
4. #16864077	C₂	semidirect
5. D₄×Dic₁₃₄	C₂	semidirect
6. #16864052	C₂	semidirect
7. #16864040	C₂	semidirect
8. #16864040	C₂	semidirect
9. #16864013	C₂	semidirect
10. #16863981	C₂	semidirect
11. #16863944	C₂	semidirect
12. #16863928	C₂	semidirect
13. #16863927	C₂	semidirect
14. C₂×#14524030	C₂	semidirect
15. #16863871	C₂	semidirect
16. C₄×#11761627	C₂	semidirect
17. D₄²×C₆₇	C₂	semidirect
19. C₂×#11761627	C₂²	semidirect
20. C₂²×Dic₁₃₄	C₂²	semidirect
21. #14524043	C₂²	semidirect
22. #14524042	C₂²	semidirect
23. #14524036	C₂²	semidirect
24. #14524036	C₂²	semidirect
25. #14524036	C₂²	semidirect
26. #14524034	C₂²	semidirect
29. #14524030	C₂²	semidirect
30. #14524030	C₂²	semidirect
31. #14524030	C₂²	semidirect
32. #14524030	C₂²	semidirect
33. #14524030	C₂²	semidirect
34. #14524029	C₂²	semidirect
35. #14524025	C₂²	semidirect
36. #14524024	C₂²	semidirect
37. #14524024	C₂²	semidirect
38. #14524024	C₂²	semidirect
39. #14524023	C₂²	semidirect
40. #14524022	C₂²	semidirect
41. #14524022	C₂²	semidirect
42. #14524020	C₂²	semidirect
43. #14524020	C₂²	semidirect
44. #14524015	C₂²	semidirect
45. #14524015	C₂²	semidirect
47. #14524014	C₂²	semidirect
48. #14524014	C₂²	semidirect
49. #14524012	C₂²	semidirect
50. C₄×Dic₁₃₄	C₂²	semidirect
51. C₄×Dic₁₃₄	C₂²	semidirect
52. #14524008	C₂²	semidirect
53. #14524008	C₂²	semidirect
56. D₄×Dic₆₇	C₂²	semidirect
57. D₄×Dic₆₇	C₂²	semidirect
58. D₄×Dic₆₇	C₂²	semidirect
59. D₄×Dic₆₇	C₂²	semidirect
60. D₄×Dic₆₇	C₂²	semidirect
61. D₄×Dic₆₇	C₂²	semidirect
62. C₄×C₂²⋊D₆₇	C₂²	semidirect
63. C₄×C₂²⋊D₆₇	C₂²	semidirect
64. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
65. #14524002	C₂²	semidirect
66. #14524002	C₂²	semidirect
67. #14524001	C₂²	semidirect
68. #14523999	C₂²	semidirect
69. #14523999	C₂²	semidirect
70. C₂×C₂²⋊Dic₆₇	C₂²	semidirect
71. C₂×C₂²⋊Dic₆₇	C₂²	semidirect
72. C₂×C₂²⋊Dic₆₇	C₂²	semidirect
73. C₂×C₄×Dic₆₇	C₂²	semidirect
74. C₄²×D₆₇	C₂²	semidirect
166. D₄×C₆₇	#41	semidirect
232. C₆₇	#3514	semidirect
241. D₄²	D₆₇	semidirect
405. D₄	#11761627	semidirect