Subgroups — #22573963

Order 8576.

1022 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864116	C₂	1	2	yes	maximal, complemented
2	#16864103	C₂	1	2	yes	maximal, complemented
3	#16864086	C₂	1	2	yes	maximal, complemented
4	#16864086	C₂	1	2	yes	maximal, complemented
5	#16864083	C₂	1	4	yes	maximal, complemented
6	#16864077	C₂	1	4	yes	maximal, complemented
7	#16864024	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864013	C₂	1	2	yes	maximal, complemented
9	#16864006	C₂	1	2	yes	maximal, complemented
10	#16863967	C₂	1	1	yes	maximal, characteristic, complemented
11	#16863948	C₂	1	2	yes	maximal, complemented
12	#16863927	C₂	1	2	yes	maximal, complemented
13	C₂×#14524022	C₂	1	1	yes	maximal, characteristic, complemented
14	#16863879	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863873	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14524002	C₂	1	1	yes	maximal, characteristic, complemented
17	#525×C₆₇	C₂	1	1	yes	maximal, characteristic
18	C₂²×Dic₁₃₄	C₂²	1	1	yes	characteristic
19	#14524043	C₂²	1	2	yes	complemented
20	#14524042	C₂²	1	2	yes	complemented
21	#14524041	C₂²	1	2	yes	complemented
22	#14524036	C₂²	1	4	yes	—
23	#14524036	C₂²	1	4	yes	—
24	#14524036	C₂²	1	4	yes	complemented
25	#14524036	C₂²	1	4	yes	complemented
26	#14524035	C₂²	1	2	yes	complemented
27	#14524034	C₂²	1	2	yes	complemented
28	#14524034	C₂²	1	4	yes	complemented
29	#14524033	C₂²	1	4	yes	complemented
30	#14524033	C₂²	1	4	yes	complemented
31	#14524030	C₂²	1	4	yes	—
32	#14524030	C₂²	1	2	yes	complemented
33	#14524024	C₂²	1	4	yes	—
34	#14524024	C₂²	1	4	yes	—
35	#14524024	C₂²	1	4	yes	—
36	#14524022	C₂²	1	2	yes	—
37	#14524022	C₂²	1	2	yes	—
38	#14524022	C₂²	1	2	yes	—
39	#14524022	C₂²	1	2	yes	—
40	#14524022	C₂²	1	2	yes	complemented
41	#14524022	C₂²	1	2	yes	complemented
42	#14524020	C₂²	1	4	yes	—
43	#14524020	C₂²	1	4	yes	—
44	#14524020	C₂²	1	4	yes	complemented
45	Q₈×Dic₆₇	C₂²	1	2	yes	complemented
46	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
47	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
48	#14524008	C₂²	1	2	yes	complemented
49	#14524008	C₂²	1	2	yes	complemented
50	#14524008	C₂²	1	4	yes	complemented
51	D₄×Dic₆₇	C₂²	1	4	yes	—
52	D₄×Dic₆₇	C₂²	1	4	yes	—
53	D₄×Dic₆₇	C₂²	1	2	yes	complemented
54	#14524002	C₂²	1	2	yes	—
55	#14524002	C₂²	1	1	yes	characteristic
56	#14524002	C₂²	1	2	yes	—
57	#14524002	C₂²	1	1	yes	characteristic
58	#14524002	C₂²	1	1	yes	characteristic
59	#14524002	C₂²	1	1	yes	characteristic
60	#14524002	C₂²	1	2	yes	complemented
61	#14523999	C₂²	1	4	yes	—
62	#14523999	C₂²	1	4	yes	—
63	#14523999	C₂²	1	4	yes	complemented
64	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
65	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
66	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
67	C₂×C₄⋊Dic₆₇	C₂²	1	2	yes	complemented
68	C₂×Dic₆₇⋊C₄	C₂²	1	2	yes	—
69	C₂×C₂²⋊Dic₆₇	C₂²	1	2	yes	—
70	C₂×C₂²⋊Dic₆₇	C₂²	1	2	yes	—
71	C₂×C₄×Dic₆₇	C₂²	1	2	yes	—
72	C₂×#41×C₆₇	C₂²	1	1	yes	characteristic
73	C₂³×C₄×C₆₇	C₂²	1	1	yes	characteristic
74	#123×C₆₇	C₂²	1	2	yes	—
75	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
76	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
77	#121×C₆₇	C₂²	1	1	yes	characteristic
78	#121×C₆₇	C₂²	1	1	yes	characteristic
79	#120×C₆₇	C₂²	1	2	yes	—
80	C₄×D₄×C₆₇	C₂²	1	2	yes	—
81	C₄×D₄×C₆₇	C₂²	1	2	yes	—
82	#117×C₆₇	C₂²	1	1	yes	characteristic
83	C₂×Dic₁₃₄	—	2	4	no	—
84	C₂×Dic₁₃₄	C₂³	1	2	yes	—
85	C₂×Dic₁₃₄	C₂³	1	2	yes	—
86	C₂×Dic₁₃₄	C₂³	1	4	yes	—
87	C₂²×Dic₆₇	C₂³	1	2	yes	—
88	C₂²×Dic₆₇	C₂³	1	2	yes	—
89	C₂²×Dic₆₇	C₂³	1	2	yes	—
90	C₂²×Dic₆₇	C₂³	1	2	yes	—
91	C₂²×Dic₆₇	C₂³	1	4	yes	—
92	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
93	C₄⋊Dic₆₇	C₂³	1	2	yes	—
94	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
95	C₄⋊Dic₆₇	C₂³	1	2	yes	—
96	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
97	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₆₇	C₂³	1	2	yes	—
99	C₄⋊Dic₆₇	C₂³	1	2	yes	—
100	C₄⋊Dic₆₇	C₂³	1	4	yes	—
101	C₄⋊Dic₆₇	C₂³	1	4	yes	—
102	Dic₆₇⋊C₄	C₂³	1	4	yes	—
103	Dic₆₇⋊C₄	C₂³	1	4	yes	—
104	Dic₆₇⋊C₄	C₂³	1	4	yes	—
105	Dic₆₇⋊C₄	C₂³	1	4	yes	—
106	Dic₆₇⋊C₄	C₂³	1	4	yes	—
107	Dic₆₇⋊C₄	C₂³	1	4	yes	—
108	Dic₆₇⋊C₄	C₂³	1	4	yes	—
109	Dic₆₇⋊C₄	C₂³	1	4	yes	—
110	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
111	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
112	C₂²⋊Dic₆₇	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	4	yes	—
117	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
118	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
119	C₄×Dic₆₇	C₂³	1	2	yes	—
120	C₄×Dic₆₇	C₂³	1	2	yes	—
121	C₄×Dic₆₇	C₂³	1	2	yes	—
122	C₄×Dic₆₇	C₂³	1	2	yes	—
123	C₄×Dic₆₇	C₂³	1	4	yes	—
124	C₄×Dic₆₇	C₂³	1	4	yes	—
125	C₄×Dic₆₇	C₂³	1	4	yes	—
126	C₂⁴×C₆₇	C₂³	1	1	yes	characteristic
127	#41×C₆₇	—	2	4	no	—
128	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₆₇	C₂³	1	2	yes	—
130	C₂×D₄×C₆₇	C₂³	1	2	yes	—
131	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₆₇	C₂³	1	2	yes	—
133	C₂²×C₄×C₆₇	—	2	4	no	—
134	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
137	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₄²×C₆₇	C₂³	1	2	yes	—
151	C₂³×C₆₇	—	2	2	no	—
152	C₂³×C₆₇	—	2	2	no	—
153	C₂³×C₆₇	—	4	1	no	—
154	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
155	C₂³×C₆₇	C₂⁴	1	2	yes	—
156	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
157	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
158	Q₈×C₆₇	—	2	2	no	—
159	D₄×C₆₇	—	2	4	no	—
160	D₄×C₆₇	—	2	4	no	—
161	D₄×C₆₇	—	2	2	no	—
162	D₄×C₆₇	—	4	2	no	—
163	C₂×C₄×C₆₇	—	2	2	no	—
164	C₂×C₄×C₆₇	—	2	2	no	—
165	C₂×C₄×C₆₇	—	2	2	no	—
166	C₂×C₄×C₆₇	—	2	2	no	—
167	C₂×C₄×C₆₇	—	2	2	no	—
168	C₂×C₄×C₆₇	—	2	4	no	—
169	C₂×C₄×C₆₇	#41	1	4	yes	—
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	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
175	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
177	C₂×Dic₆₇	—	2	4	no	—
178	C₂×Dic₆₇	—	2	4	no	—
179	C₂×Dic₆₇	—	4	2	no	—
180	C₂×Dic₆₇	—	4	2	no	—
181	C₂×Dic₆₇	—	4	4	no	—
182	C₂×Dic₆₇	C₂⁴	1	2	yes	—
183	C₂×Dic₆₇	C₂⁴	1	2	yes	—
184	C₂×Dic₆₇	C₂⁴	1	2	yes	—
185	C₂×Dic₆₇	C₂⁴	1	4	yes	—
186	C₂×Dic₆₇	C₂⁴	1	2	yes	—
187	C₂×Dic₆₇	C₂⁴	1	4	yes	—
188	Dic₁₃₄	—	2	4	no	—
189	Dic₁₃₄	—	2	4	no	—
190	Dic₁₃₄	—	4	4	no	—
191	C₂²×C₆₇	—	2	1	no	—
192	C₂²×C₆₇	—	2	1	no	—
193	C₂²×C₆₇	—	2	1	no	—
194	C₂²×C₆₇	—	2	1	no	—
195	C₂²×C₆₇	—	2	1	no	—
196	C₂²×C₆₇	—	2	2	no	—
197	C₂²×C₆₇	—	2	2	no	—
198	C₂²×C₆₇	—	2	1	no	—
199	C₂²×C₆₇	—	2	2	no	—
200	C₂²×C₆₇	—	2	1	no	—
201	C₂²×C₆₇	—	4	4	no	—
202	C₂²×C₆₇	C₂×#41	1	2	yes	—
203	C₂²×C₆₇	2₋¹⁺⁴	1	2	yes	—
204	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
205	C₄×C₆₇	—	2	1	no	—
206	C₄×C₆₇	—	2	1	no	—
207	C₄×C₆₇	—	2	2	no	—
208	C₄×C₆₇	—	2	2	no	—
209	C₄×C₆₇	—	2	2	no	—
210	C₄×C₆₇	C₂×#41	1	2	yes	—
211	C₄×C₆₇	C₂×#41	1	2	yes	—
212	Dic₆₇	—	2	4	no	—
213	Dic₆₇	—	2	2	no	—
214	Dic₆₇	—	2	2	no	—
215	Dic₆₇	—	2	2	no	—
216	Dic₆₇	—	2	4	no	—
217	Dic₆₇	—	2	2	no	—
218	C₂×C₆₇	—	2	2	no	—
219	C₂×C₆₇	—	2	2	no	—
220	C₂×C₆₇	—	4	2	no	—
221	C₂×C₆₇	—	4	1	no	—
222	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
223	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
224	C₂×C₆₇	#585	1	1	yes	characteristic
225	#3495	—	67	1	no	maximal, Sylow
226	C₆₇	#3495	1	1	yes	characteristic, complemented, Sylow
227	#556	—	67	2	no	—
228	#554	—	67	2	no	—
229	#552	—	67	4	no	—
230	#552	—	67	2	no	—
231	#552	—	67	2	no	—
232	#551	—	67	4	no	—
233	#544	—	67	1	no	—
234	#542	—	67	2	no	—
235	#541	—	67	2	no	—
236	#536	—	67	1	no	—
237	#533	—	67	2	no	—
238	#529	—	67	2	no	—
239	#525	D₆₇	1	1	yes	characteristic
240	C₂×C₂²⋊Q₈	—	67	1	no	—
241	#520	—	67	1	no	—
242	#519	—	67	1	no	—
243	C₂×#117	—	67	1	no	—
244	C₂×#41	C₂×D₆₇	1	1	yes	characteristic
245	C₂²×Q₈	—	67	1	no	—
246	C₂³×C₄	C₂×D₆₇	1	1	yes	characteristic
247	C₄⋊Q₈	—	67	2	no	—
248	C₄⋊Q₈	—	67	2	no	—
249	C₄⋊Q₈	—	67	2	no	—
250	#126	—	67	4	no	—
251	#126	—	67	4	no	—
252	#126	—	67	4	no	—
253	#126	—	67	4	no	—
254	#125	—	67	2	no	—
255	#125	—	67	4	no	—
256	#125	—	67	4	no	—
257	#125	—	67	4	no	—
258	#125	—	67	2	no	—
259	#124	—	67	2	no	—
260	#124	—	67	4	no	—
261	#123	—	67	4	no	—
262	#123	—	67	4	no	—
263	#123	—	67	4	no	—
264	#123	C₂×D₆₇	1	2	yes	—
265	C₂²⋊Q₈	—	67	2	no	—
266	C₂²⋊Q₈	—	67	2	no	—
267	C₂²⋊Q₈	—	67	2	no	—
268	C₂²⋊Q₈	—	67	2	no	—
269	C₂²⋊Q₈	—	67	2	no	—
270	C₂²⋊Q₈	—	67	2	no	—
271	C₂²⋊Q₈	—	67	4	no	—
272	C₂²⋊Q₈	—	67	4	no	—
273	C₂²⋊Q₈	—	67	4	no	—
274	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
275	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
276	#121	C₂×D₆₇	1	1	yes	characteristic
277	#121	C₂×D₆₇	1	1	yes	characteristic
278	#120	C₂×D₆₇	1	2	yes	—
279	C₄×Q₈	—	67	2	no	—
280	C₄×Q₈	—	67	2	no	—
281	C₄×Q₈	—	67	2	no	—
282	C₄×Q₈	—	67	4	no	—
283	C₄×Q₈	—	67	2	no	—
284	C₄×Q₈	—	67	2	no	—
285	C₄×D₄	—	67	2	no	—
286	C₄×D₄	—	67	4	no	—
287	C₄×D₄	—	67	4	no	—
288	C₄×D₄	C₂×D₆₇	1	2	yes	—
289	C₄×D₄	C₂×D₆₇	1	2	yes	—
290	#117	—	67	1	no	—
291	#117	—	67	1	no	—
292	#117	—	67	2	no	—
293	#117	—	67	1	no	—
294	#117	—	67	2	no	—
295	#117	—	67	1	no	—
296	#117	—	67	2	no	—
297	#117	—	67	4	no	—
298	#117	—	67	4	no	—
299	#117	—	67	4	no	—
300	#117	C₂×D₆₇	1	1	yes	characteristic
301	C₂×C₄⋊C₄	—	67	1	no	—
302	C₂×C₄⋊C₄	—	67	1	no	—
303	C₂×C₄⋊C₄	—	67	1	no	—
304	C₂×C₄⋊C₄	—	67	2	no	—
305	C₂×C₄⋊C₄	—	67	2	no	—
306	C₂×C₂²⋊C₄	—	67	2	no	—
307	C₂×C₂²⋊C₄	—	67	2	no	—
308	C₂×C₄²	—	67	2	no	—
309	C₂⁴	C₂²×D₆₇	1	1	yes	characteristic
310	#41	—	2	4	no	—
311	C₂×Q₈	—	67	4	no	—
312	C₂×Q₈	—	67	2	no	—
313	C₂×Q₈	—	67	2	no	—
314	C₂×Q₈	—	134	4	no	—
315	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
316	C₂×D₄	C₂²×D₆₇	1	2	yes	—
317	C₂×D₄	C₂²×D₆₇	1	2	yes	—
318	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
319	C₂×D₄	C₂²×D₆₇	1	2	yes	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	67	2	no	—
322	C₂²×C₄	—	67	2	no	—
323	C₂²×C₄	—	67	4	no	—
324	C₂²×C₄	—	67	2	no	—
325	C₂²×C₄	—	67	2	no	—
326	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
327	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
328	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
329	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
330	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
331	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
332	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
333	C₄⋊C₄	—	67	1	no	—
334	C₄⋊C₄	—	67	2	no	—
335	C₄⋊C₄	—	67	1	no	—
336	C₄⋊C₄	—	67	2	no	—
337	C₄⋊C₄	—	67	1	no	—
338	C₄⋊C₄	—	67	1	no	—
339	C₄⋊C₄	—	67	2	no	—
340	C₄⋊C₄	—	67	4	no	—
341	C₄⋊C₄	—	67	2	no	—
342	C₄⋊C₄	—	67	4	no	—
343	C₄⋊C₄	—	67	4	no	—
344	C₄⋊C₄	—	67	4	no	—
345	C₄⋊C₄	—	67	4	no	—
346	C₄⋊C₄	—	67	4	no	—
347	C₄⋊C₄	—	67	4	no	—
348	C₄⋊C₄	—	67	4	no	—
349	C₄⋊C₄	—	67	4	no	—
350	C₄⋊C₄	—	67	4	no	—
351	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
352	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
353	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
354	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
355	C₂²⋊C₄	—	67	2	no	—
356	C₂²⋊C₄	—	67	2	no	—
357	C₂²⋊C₄	—	67	2	no	—
358	C₂²⋊C₄	—	67	2	no	—
359	C₂²⋊C₄	—	67	4	no	—
360	C₂²⋊C₄	—	67	4	no	—
361	C₂²⋊C₄	—	67	4	no	—
362	C₂²⋊C₄	—	67	4	no	—
363	C₂²⋊C₄	—	67	4	no	—
364	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
365	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
366	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
367	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
368	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
369	C₄²	—	67	2	no	—
370	C₄²	—	67	2	no	—
371	C₄²	—	67	2	no	—
372	C₄²	—	67	2	no	—
373	C₄²	—	67	4	no	—
374	C₄²	—	67	4	no	—
375	C₄²	—	67	4	no	—
376	C₄²	C₂²×D₆₇	1	2	yes	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	C₂³×D₆₇	1	1	yes	characteristic
381	C₂³	C₂³×D₆₇	1	2	yes	—
382	C₂³	C₂³×D₆₇	1	1	yes	characteristic
383	C₂³	C₂³×D₆₇	1	1	yes	characteristic
384	Q₈	—	2	2	no	—
385	Q₈	—	268	4	no	—
386	Q₈	—	134	4	no	—
387	Q₈	—	134	4	no	—
388	D₄	—	2	4	no	—
389	D₄	—	2	4	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	268	4	no	—
399	C₂×C₄	—	268	2	no	—
400	C₂×C₄	—	268	2	no	—
401	C₂×C₄	—	67	2	no	—
402	C₂×C₄	—	67	2	no	—
403	C₂×C₄	—	67	2	no	—
404	C₂×C₄	—	67	4	no	—
405	C₂×C₄	—	67	2	no	—
406	C₂×C₄	—	67	4	no	—
407	C₂×C₄	—	134	4	no	—
408	C₂×C₄	—	134	4	no	—
409	C₂×C₄	#11761627	1	4	yes	—
410	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
411	C₂×C₄	C₂³×D₆₇	1	2	yes	—
412	C₂×C₄	C₂³×D₆₇	1	2	yes	—
413	C₂×C₄	C₂³×D₆₇	1	2	yes	—
414	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
415	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
416	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	4	4	no	—
428	C₂²	C₂×#11761627	1	2	yes	—
429	C₂²	#14524090	1	2	yes	—
430	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	134	4	no	—
437	C₄	—	134	2	no	—
438	C₄	—	134	2	no	—
439	C₄	—	134	2	no	—
440	C₄	—	134	4	no	—
441	C₄	—	134	2	no	—
442	C₄	C₂×#11761627	1	2	yes	—
443	C₄	C₂×#11761627	1	2	yes	—
444	C₂	—	2	2	no	—
445	C₂	—	2	2	no	—
446	C₂	—	4	1	no	—
447	C₂	—	4	2	no	—
448	C₂	C₂²×#11761627	1	1	yes	characteristic
449	C₂	C₂×#14524090	1	1	yes	characteristic
450	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#525×C₆₇	C₂
hypercenter	#525	D₆₇
hypocenter	C₆₇	#3495
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #16864116	C₂	semidirect
2. #16864103	C₂	semidirect
3. #16864086	C₂	semidirect
4. #16864086	C₂	semidirect
5. #16864083	C₂	semidirect
6. #16864077	C₂	semidirect
7. #16864024	C₂	semidirect
8. #16864013	C₂	semidirect
9. #16864006	C₂	semidirect
10. #16863967	C₂	semidirect
11. #16863948	C₂	semidirect
12. #16863927	C₂	semidirect
13. C₂×#14524022	C₂	semidirect
14. #16863879	C₂	semidirect
15. #16863873	C₂	semidirect
16. C₂×#14524002	C₂	semidirect
19. #14524043	C₂²	semidirect
20. #14524042	C₂²	semidirect
21. #14524041	C₂²	semidirect
24. #14524036	C₂²	semidirect
25. #14524036	C₂²	semidirect
26. #14524035	C₂²	semidirect
27. #14524034	C₂²	semidirect
28. #14524034	C₂²	semidirect
29. #14524033	C₂²	semidirect
30. #14524033	C₂²	semidirect
32. #14524030	C₂²	semidirect
40. #14524022	C₂²	semidirect
41. #14524022	C₂²	semidirect
44. #14524020	C₂²	semidirect
45. Q₈×Dic₆₇	C₂²	semidirect
46. C₄×Dic₁₃₄	C₂²	semidirect
47. C₄×Dic₁₃₄	C₂²	semidirect
48. #14524008	C₂²	semidirect
49. #14524008	C₂²	semidirect
50. #14524008	C₂²	semidirect
53. D₄×Dic₆₇	C₂²	semidirect
60. #14524002	C₂²	semidirect
63. #14523999	C₂²	semidirect
67. C₂×C₄⋊Dic₆₇	C₂²	semidirect
226. C₆₇	#3495	semidirect