Subgroups — #22574558

Order 8576.

1060 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864149	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864141	C₂	1	2	yes	maximal, complemented
3	#16864139	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864110	C₂	1	2	yes	maximal, complemented
5	#16864077	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864077	C₂	1	2	yes	maximal, complemented
7	#16864074	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864072	C₂	1	2	yes	maximal, complemented
9	#16864040	C₂	1	2	yes	maximal, complemented
10	#16864033	C₂	1	2	yes	maximal, complemented
11	#16864014	C₂	1	2	yes	maximal, complemented
12	#16864013	C₂	1	2	yes	maximal, complemented
13	#16863981	C₂	1	2	yes	maximal, complemented
14	#16863978	C₂	1	2	yes	maximal, complemented
15	#16863968	C₂	1	2	yes	maximal, complemented
16	#16863955	C₂	1	1	yes	maximal, characteristic, complemented
17	#16863923	C₂	1	2	yes	maximal, complemented
18	C₂×#14524030	C₂	1	1	yes	maximal, characteristic, complemented
19	#534×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#11761627	C₂²	1	2	yes	—
21	C₂²×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
23	#14524042	C₂²	1	2	yes	complemented
24	#14524042	C₂²	1	2	yes	complemented
25	#14524038	C₂²	1	2	yes	complemented
26	#14524036	C₂²	1	2	yes	complemented
27	#14524036	C₂²	1	2	yes	complemented
28	#14524036	C₂²	1	2	yes	complemented
29	#14524036	C₂²	1	2	yes	complemented
30	#14524036	C₂²	1	2	yes	complemented
31	#14524033	C₂²	1	2	yes	complemented
32	#14524030	C₂²	1	1	yes	characteristic
33	#14524030	C₂²	1	1	yes	characteristic
34	#14524030	C₂²	1	2	yes	complemented
35	#14524030	C₂²	1	2	yes	complemented
36	#14524030	C₂²	1	2	yes	complemented
37	#14524030	C₂²	1	2	yes	complemented
38	#14524030	C₂²	1	1	yes	characteristic, complemented
39	#14524030	C₂²	1	1	yes	characteristic, complemented
40	#14524029	C₂²	1	2	yes	complemented
41	#14524029	C₂²	1	2	yes	complemented
42	#14524029	C₂²	1	2	yes	complemented
43	#14524029	C₂²	1	2	yes	complemented
44	#14524029	C₂²	1	2	yes	complemented
45	#14524027	C₂²	1	2	yes	complemented
46	#14524026	C₂²	1	2	yes	complemented
47	#14524026	C₂²	1	2	yes	complemented
48	#14524025	C₂²	1	2	yes	complemented
49	#14524025	C₂²	1	2	yes	complemented
50	#14524024	C₂²	1	1	yes	characteristic
51	#14524024	C₂²	1	1	yes	characteristic, complemented
52	#14524024	C₂²	1	2	yes	complemented
53	#14524024	C₂²	1	2	yes	complemented
54	#14524024	C₂²	1	2	yes	complemented
55	#14524024	C₂²	1	2	yes	complemented
56	#14524022	C₂²	1	2	yes	complemented
57	#14524022	C₂²	1	2	yes	complemented
58	#14524021	C₂²	1	2	yes	complemented
59	#14524021	C₂²	1	2	yes	complemented
60	#14524020	C₂²	1	2	yes	complemented
61	#14524020	C₂²	1	2	yes	complemented
62	#14524020	C₂²	1	2	yes	complemented
63	#14524020	C₂²	1	2	yes	complemented
64	#14524020	C₂²	1	2	yes	complemented
65	#14524015	C₂²	1	2	yes	—
66	#14524015	C₂²	1	2	yes	—
67	#14524015	C₂²	1	2	yes	complemented
68	#14524015	C₂²	1	2	yes	complemented
69	#14524015	C₂²	1	2	yes	complemented
70	#14524014	C₂²	1	2	yes	complemented
71	#14524014	C₂²	1	2	yes	complemented
72	#14524012	C₂²	1	2	yes	—
73	#14524012	C₂²	1	2	yes	complemented
74	#14524011	C₂²	1	1	yes	characteristic
75	#14524011	C₂²	1	2	yes	complemented
76	#14524011	C₂²	1	1	yes	characteristic, complemented
77	#14524008	C₂²	1	2	yes	complemented
78	D₄×Dic₆₇	C₂²	1	2	yes	complemented
79	D₄×Dic₆₇	C₂²	1	2	yes	complemented
80	D₄×Dic₆₇	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
83	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
84	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
85	#14524002	C₂²	1	2	yes	complemented
86	#14524001	C₂²	1	2	yes	complemented
87	#14523999	C₂²	1	2	yes	complemented
88	#14523999	C₂²	1	2	yes	complemented
89	#14523999	C₂²	1	2	yes	complemented
90	C₂×C₂²⋊Dic₆₇	C₂²	1	2	yes	complemented
91	C₂×C₂²⋊Dic₆₇	C₂²	1	2	yes	complemented
92	C₂×C₂²⋊Dic₆₇	C₂²	1	2	yes	complemented
93	C₂×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
94	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
95	C₂×C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
96	C₂²×D₄×C₆₇	C₂²	1	1	yes	characteristic
97	C₂²×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#123×C₆₇	C₂²	1	1	yes	characteristic
99	#123×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#123×C₆₇	C₂²	1	2	yes	complemented
101	#121×C₆₇	C₂²	1	2	yes	—
102	#121×C₆₇	C₂²	1	2	yes	complemented
103	#120×C₆₇	C₂²	1	2	yes	—
104	#120×C₆₇	C₂²	1	1	yes	characteristic
105	#120×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₆₇	C₂³	1	1	yes	characteristic
108	#11761627	—	4	4	no	—
109	C₂×Dic₁₃₄	—	4	2	no	—
110	C₂×Dic₁₃₄	C₂³	1	2	yes	—
111	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
112	C₂×Dic₁₃₄	C₂³	1	2	yes	—
113	C₂×Dic₁₃₄	C₂³	1	2	yes	—
114	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
115	C₂×C₂²⋊D₆₇	—	4	2	no	—
116	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
122	C₂²×Dic₆₇	C₂³	1	2	yes	—
123	C₂²×Dic₆₇	C₂³	1	2	yes	—
124	C₂²×Dic₆₇	C₂³	1	2	yes	—
125	C₂²×Dic₆₇	C₂³	1	2	yes	—
126	C₂²×Dic₆₇	C₂³	1	2	yes	—
127	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
128	C₂×C₄×D₆₇	C₂³	1	2	yes	—
129	C₂×C₄×D₆₇	C₂³	1	2	yes	—
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	2	yes	—
134	Dic₆₇⋊C₄	C₂³	1	2	yes	—
135	Dic₆₇⋊C₄	C₂³	1	2	yes	—
136	Dic₆₇⋊C₄	C₂³	1	2	yes	—
137	Dic₆₇⋊C₄	C₂³	1	2	yes	—
138	Dic₆₇⋊C₄	C₂³	1	2	yes	—
139	Dic₆₇⋊C₄	C₂³	1	2	yes	—
140	Dic₆₇⋊C₄	C₂³	1	2	yes	—
141	Dic₆₇⋊C₄	C₂³	1	2	yes	—
142	Dic₆₇⋊C₄	C₂³	1	2	yes	—
143	Dic₆₇⋊C₄	C₂³	1	2	yes	—
144	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
145	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
146	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
147	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
148	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
149	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
150	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
151	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
152	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
153	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
154	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
155	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
156	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
157	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
158	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
159	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
160	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
161	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
167	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
168	C₄×Dic₆₇	C₂³	1	2	yes	—
169	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
170	C₄×Dic₆₇	C₂³	1	2	yes	—
171	C₄×Dic₆₇	C₂³	1	2	yes	—
172	C₄×Dic₆₇	C₂³	1	2	yes	—
173	C₄×Dic₆₇	C₂³	1	2	yes	—
174	C₂⁴×C₆₇	C₂³	1	1	yes	characteristic
175	C₂⁴×C₆₇	C₂³	1	1	yes	characteristic
176	C₂⁴×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×D₄×C₆₇	—	4	2	no	—
178	C₂×D₄×C₆₇	—	4	2	no	—
179	C₂×D₄×C₆₇	C₂³	1	2	yes	—
180	C₂×D₄×C₆₇	C₂³	1	2	yes	—
181	C₂×D₄×C₆₇	C₂³	1	2	yes	—
182	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×D₄×C₆₇	C₂³	1	2	yes	—
186	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
189	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
190	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
194	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂³×C₆₇	—	2	2	no	—
200	C₂³×C₆₇	—	2	2	no	—
201	C₂³×C₆₇	—	4	1	no	—
202	C₂³×C₆₇	—	4	2	no	—
203	C₂³×C₆₇	—	4	2	no	—
204	C₂³×C₆₇	—	4	2	no	—
205	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
206	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
207	C₂³×C₆₇	C₂⁴	1	2	yes	—
208	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
209	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
210	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
211	C₂²×D₆₇	—	4	1	no	—
212	C₂²×D₆₇	—	4	2	no	—
213	C₂²×D₆₇	C₂⁴	1	2	yes	—
214	D₄×C₆₇	—	2	4	no	—
215	D₄×C₆₇	—	4	1	no	—
216	D₄×C₆₇	—	4	1	no	—
217	D₄×C₆₇	—	4	1	no	—
218	D₄×C₆₇	—	4	1	no	—
219	D₄×C₆₇	—	4	2	no	—
220	D₄×C₆₇	—	4	2	no	—
221	D₄×C₆₇	—	4	2	no	—
222	C₂×C₄×C₆₇	—	2	2	no	—
223	C₂×C₄×C₆₇	—	4	2	no	—
224	C₂×C₄×C₆₇	—	4	1	no	—
225	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
226	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
227	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
228	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
230	C₂²⋊D₆₇	—	2	4	no	—
231	C₂²⋊D₆₇	—	4	2	no	—
232	C₂²⋊D₆₇	—	4	2	no	—
233	C₂²⋊D₆₇	—	4	2	no	—
234	C₂²⋊D₆₇	—	4	2	no	—
235	C₂²⋊D₆₇	—	4	2	no	—
236	C₂×Dic₆₇	—	2	4	no	—
237	C₂×Dic₆₇	—	4	2	no	—
238	C₂×Dic₆₇	—	4	2	no	—
239	C₂×Dic₆₇	—	4	2	no	—
240	C₂×Dic₆₇	—	4	1	no	—
241	C₂×Dic₆₇	—	4	2	no	—
242	C₂×Dic₆₇	C₂⁴	1	2	yes	—
243	C₂×Dic₆₇	C₂⁴	1	2	yes	—
244	C₂×Dic₆₇	C₂⁴	1	2	yes	—
245	C₂×Dic₆₇	C₂⁴	1	2	yes	—
246	C₂×Dic₆₇	C₂⁴	1	2	yes	—
247	C₂×Dic₆₇	C₂⁴	1	2	yes	—
248	C₂×Dic₆₇	C₂⁴	1	2	yes	—
249	C₄×D₆₇	—	4	2	no	—
250	C₄×D₆₇	—	4	2	no	—
251	Dic₁₃₄	—	4	1	no	—
252	Dic₁₃₄	—	4	2	no	—
253	Dic₁₃₄	—	4	1	no	—
254	Dic₁₃₄	—	4	2	no	—
255	Dic₁₃₄	—	4	2	no	—
256	C₂²×C₆₇	—	2	2	no	—
257	C₂²×C₆₇	—	2	2	no	—
258	C₂²×C₆₇	—	2	1	no	—
259	C₂²×C₆₇	—	2	1	no	—
260	C₂²×C₆₇	—	2	1	no	—
261	C₂²×C₆₇	—	2	1	no	—
262	C₂²×C₆₇	—	2	2	no	—
263	C₂²×C₆₇	—	2	2	no	—
264	C₂²×C₆₇	—	2	2	no	—
265	C₂²×C₆₇	—	2	2	no	—
266	C₂²×C₆₇	—	2	2	no	—
267	C₂²×C₆₇	—	2	2	no	—
268	C₂²×C₆₇	—	8	2	no	—
269	C₂²×C₆₇	—	8	2	no	—
270	C₂²×C₆₇	—	8	2	no	—
271	C₂²×C₆₇	H(5,𝔽₂)	1	2	yes	—
272	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
273	C₂×D₆₇	—	2	2	no	—
274	C₂×D₆₇	—	2	2	no	—
275	C₂×D₆₇	—	2	2	no	—
276	C₂×D₆₇	—	8	2	no	—
277	C₄×C₆₇	—	2	1	no	—
278	C₄×C₆₇	—	2	1	no	—
279	C₄×C₆₇	—	2	2	no	—
280	C₄×C₆₇	—	2	2	no	—
281	C₄×C₆₇	—	2	2	no	—
282	Dic₆₇	—	2	2	no	—
283	Dic₆₇	—	2	2	no	—
284	Dic₆₇	—	2	2	no	—
285	Dic₆₇	—	2	2	no	—
286	Dic₆₇	—	2	2	no	—
287	Dic₆₇	—	2	2	no	—
288	Dic₆₇	—	2	2	no	—
289	C₂×C₆₇	—	2	2	no	—
290	C₂×C₆₇	—	4	1	no	—
291	C₂×C₆₇	—	4	2	no	—
292	C₂×C₆₇	—	4	1	no	—
293	C₂×C₆₇	—	4	1	no	—
294	C₂×C₆₇	—	4	1	no	—
295	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
296	C₂×C₆₇	#585	1	2	yes	—
297	D₆₇	—	4	2	no	—
298	#3545	—	67	1	no	maximal, Sylow
299	C₆₇	#3545	1	1	yes	characteristic, complemented, Sylow
300	#563	—	67	1	no	—
301	#562	—	67	2	no	—
302	H(3,𝔽₄)	—	67	1	no	—
303	#555	—	67	2	no	—
304	#551	—	67	1	no	—
305	#551	—	67	2	no	—
306	#551	—	67	1	no	—
307	#551	—	67	2	no	—
308	#546	—	67	2	no	—
309	#546	—	67	2	no	—
310	#542	—	67	2	no	—
311	#542	—	67	2	no	—
312	#538	—	67	2	no	—
313	#538	—	67	2	no	—
314	#536	—	67	2	no	—
315	#534	—	67	1	no	—
316	#534	D₆₇	1	1	yes	characteristic, complemented
317	#529	—	67	2	no	—
318	C₂×#124	—	67	1	no	—
319	C₂×#41	—	67	2	no	—
320	C₂²×Q₈	—	67	1	no	—
321	C₂²×D₄	—	67	1	no	—
322	C₂²×D₄	C₂×D₆₇	1	1	yes	characteristic
323	C₂²×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
324	C₄⋊Q₈	—	67	2	no	—
325	C₄⋊Q₈	—	67	2	no	—
326	#126	—	67	2	no	—
327	#126	—	67	2	no	—
328	#126	—	67	2	no	—
329	#126	—	67	2	no	—
330	#126	—	67	2	no	—
331	#126	—	67	2	no	—
332	#125	—	67	2	no	—
333	#124	—	67	2	no	—
334	#124	—	67	2	no	—
335	#124	—	67	1	no	—
336	#124	—	67	1	no	—
337	#124	—	67	1	no	—
338	#124	—	67	1	no	—
339	#124	—	67	2	no	—
340	#124	—	67	2	no	—
341	#124	—	67	2	no	—
342	#124	—	67	2	no	—
343	#124	—	67	2	no	—
344	#124	—	67	2	no	—
345	#124	—	67	2	no	—
346	#123	—	67	1	no	—
347	#123	—	67	1	no	—
348	#123	—	67	2	no	—
349	#123	—	67	2	no	—
350	#123	—	67	2	no	—
351	#123	—	67	2	no	—
352	#123	—	67	2	no	—
353	#123	—	67	2	no	—
354	#123	—	67	2	no	—
355	#123	—	67	2	no	—
356	#123	—	67	2	no	—
357	#123	C₂×D₆₇	1	1	yes	characteristic
358	#123	C₂×D₆₇	1	2	yes	complemented
359	#123	C₂×D₆₇	1	1	yes	characteristic, complemented
360	C₂²⋊Q₈	—	67	2	no	—
361	C₂²⋊Q₈	—	67	2	no	—
362	C₂²⋊Q₈	—	67	2	no	—
363	C₂²⋊Q₈	—	67	2	no	—
364	C₂²⋊Q₈	—	67	2	no	—
365	C₂²⋊Q₈	—	67	2	no	—
366	C₂²⋊Q₈	—	67	2	no	—
367	C₂²⋊Q₈	—	67	2	no	—
368	C₂²⋊Q₈	—	67	2	no	—
369	#121	—	67	2	no	—
370	#121	—	67	2	no	—
371	#121	—	67	2	no	—
372	#121	—	67	2	no	—
373	#121	—	67	2	no	—
374	#121	—	67	2	no	—
375	#121	—	67	2	no	—
376	#121	C₂×D₆₇	1	2	yes	—
377	#121	C₂×D₆₇	1	2	yes	complemented
378	#120	—	67	2	no	—
379	#120	—	67	2	no	—
380	#120	—	67	1	no	—
381	#120	—	67	1	no	—
382	#120	—	67	2	no	—
383	#120	C₂×D₆₇	1	2	yes	—
384	#120	C₂×D₆₇	1	1	yes	characteristic
385	#120	C₂×D₆₇	1	1	yes	characteristic, complemented
386	C₄×Q₈	—	67	2	no	—
387	C₄×D₄	—	67	2	no	—
388	C₄×D₄	—	67	2	no	—
389	C₄×D₄	—	67	2	no	—
390	C₄×D₄	—	67	2	no	—
391	C₄×D₄	—	67	2	no	—
392	C₄×D₄	—	67	2	no	—
393	C₄×D₄	—	67	2	no	—
394	#117	—	67	2	no	—
395	#117	—	67	2	no	—
396	#117	—	67	2	no	—
397	#117	—	67	2	no	—
398	#117	—	67	2	no	—
399	C₂×C₂²⋊C₄	—	67	2	no	—
400	C₂×C₂²⋊C₄	—	67	2	no	—
401	C₂×C₂²⋊C₄	—	67	1	no	—
402	C₂×C₂²⋊C₄	—	67	2	no	—
403	C₂×C₂²⋊C₄	—	67	2	no	—
404	C₂×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
405	C₂×C₄²	—	67	1	no	—
406	C₂⁴	—	67	1	no	—
407	C₂⁴	C₂²×D₆₇	1	1	yes	characteristic
408	C₂⁴	C₂²×D₆₇	1	1	yes	characteristic
409	C₂⁴	C₂²×D₆₇	1	1	yes	characteristic
410	#41	—	268	4	no	—
411	C₂×Q₈	—	268	2	no	—
412	C₂×Q₈	—	67	2	no	—
413	C₂×Q₈	—	67	1	no	—
414	C₂×Q₈	—	67	2	no	—
415	C₂×Q₈	—	67	2	no	—
416	C₂×Q₈	—	67	1	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	—	4	2	no	—
419	C₂×D₄	—	268	2	no	—
420	C₂×D₄	—	67	2	no	—
421	C₂×D₄	—	67	2	no	—
422	C₂×D₄	—	67	2	no	—
423	C₂×D₄	—	67	2	no	—
424	C₂×D₄	—	67	2	no	—
425	C₂×D₄	—	67	2	no	—
426	C₂×D₄	C₂²×D₆₇	1	2	yes	—
427	C₂×D₄	C₂²×D₆₇	1	2	yes	—
428	C₂×D₄	C₂²×D₆₇	1	2	yes	—
429	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
430	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
431	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
432	C₂×D₄	C₂²×D₆₇	1	2	yes	—
433	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
434	C₂²×C₄	—	67	2	no	—
435	C₂²×C₄	—	67	2	no	—
436	C₂²×C₄	—	67	2	no	—
437	C₂²×C₄	—	67	2	no	—
438	C₂²×C₄	—	67	1	no	—
439	C₂²×C₄	—	67	2	no	—
440	C₂²×C₄	—	67	2	no	—
441	C₂²×C₄	—	67	2	no	—
442	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
443	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
444	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
445	C₄⋊C₄	—	67	2	no	—
446	C₄⋊C₄	—	67	2	no	—
447	C₄⋊C₄	—	67	2	no	—
448	C₄⋊C₄	—	67	2	no	—
449	C₄⋊C₄	—	67	2	no	—
450	C₄⋊C₄	—	67	2	no	—
451	C₄⋊C₄	—	67	2	no	—
452	C₄⋊C₄	—	67	2	no	—
453	C₄⋊C₄	—	67	2	no	—
454	C₄⋊C₄	—	67	2	no	—
455	C₄⋊C₄	—	67	2	no	—
456	C₄⋊C₄	—	67	2	no	—
457	C₄⋊C₄	—	67	2	no	—
458	C₄⋊C₄	—	67	2	no	—
459	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
460	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
461	C₂²⋊C₄	—	67	2	no	—
462	C₂²⋊C₄	—	67	2	no	—
463	C₂²⋊C₄	—	67	2	no	—
464	C₂²⋊C₄	—	67	2	no	—
465	C₂²⋊C₄	—	67	2	no	—
466	C₂²⋊C₄	—	67	2	no	—
467	C₂²⋊C₄	—	67	2	no	—
468	C₂²⋊C₄	—	67	2	no	—
469	C₂²⋊C₄	—	67	2	no	—
470	C₂²⋊C₄	—	67	1	no	—
471	C₂²⋊C₄	—	67	1	no	—
472	C₂²⋊C₄	—	67	2	no	—
473	C₂²⋊C₄	—	67	2	no	—
474	C₂²⋊C₄	—	67	2	no	—
475	C₂²⋊C₄	—	67	2	no	—
476	C₂²⋊C₄	—	67	2	no	—
477	C₂²⋊C₄	—	67	2	no	—
478	C₂²⋊C₄	—	67	2	no	—
479	C₂²⋊C₄	—	67	2	no	—
480	C₂²⋊C₄	—	67	2	no	—
481	C₂²⋊C₄	—	67	2	no	—
482	C₂²⋊C₄	—	67	2	no	—
483	C₂²⋊C₄	—	67	2	no	—
484	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
485	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
486	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
487	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
488	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
489	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
490	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
491	C₄²	—	67	1	no	—
492	C₄²	—	67	2	no	—
493	C₄²	—	67	1	no	—
494	C₄²	—	67	2	no	—
495	C₄²	—	67	2	no	—
496	C₄²	—	67	2	no	—
497	C₄²	—	67	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	268	1	no	—
505	C₂³	—	268	2	no	—
506	C₂³	—	67	2	no	—
507	C₂³	C₂³×D₆₇	1	1	yes	characteristic
508	C₂³	C₂³×D₆₇	1	1	yes	characteristic
509	C₂³	C₂³×D₆₇	1	1	yes	characteristic
510	C₂³	C₂³×D₆₇	1	2	yes	—
511	C₂³	C₂³×D₆₇	1	1	yes	characteristic
512	C₂³	C₂³×D₆₇	1	1	yes	characteristic
513	Q₈	—	268	1	no	—
514	Q₈	—	268	2	no	—
515	Q₈	—	268	1	no	—
516	Q₈	—	268	2	no	—
517	Q₈	—	268	2	no	—
518	D₄	—	2	4	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	268	2	no	—
527	D₄	—	268	2	no	—
528	D₄	—	268	2	no	—
529	D₄	—	268	2	no	—
530	D₄	—	268	2	no	—
531	D₄	—	134	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	268	2	no	—
536	C₂×C₄	—	268	2	no	—
537	C₂×C₄	—	268	1	no	—
538	C₂×C₄	—	268	2	no	—
539	C₂×C₄	—	268	2	no	—
540	C₂×C₄	—	268	2	no	—
541	C₂×C₄	—	268	2	no	—
542	C₂×C₄	—	67	2	no	—
543	C₂×C₄	—	67	2	no	—
544	C₂×C₄	—	67	2	no	—
545	C₂×C₄	—	67	2	no	—
546	C₂×C₄	—	67	2	no	—
547	C₂×C₄	—	67	2	no	—
548	C₂×C₄	—	67	2	no	—
549	C₂×C₄	—	134	4	no	—
550	C₂×C₄	C₂³×D₆₇	1	2	yes	—
551	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
552	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
553	C₂×C₄	C₂³×D₆₇	1	2	yes	—
554	C₂×C₄	C₂³×D₆₇	1	2	yes	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	8	2	no	—
568	C₂²	—	8	2	no	—
569	C₂²	—	8	2	no	—
570	C₂²	—	536	2	no	—
571	C₂²	—	134	2	no	—
572	C₂²	—	134	2	no	—
573	C₂²	—	134	2	no	—
574	C₂²	#14524088	1	2	yes	—
575	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₄	—	134	2	no	—
582	C₄	—	134	2	no	—
583	C₄	—	134	2	no	—
584	C₄	—	134	2	no	—
585	C₄	—	134	2	no	—
586	C₄	—	134	2	no	—
587	C₄	—	134	2	no	—
588	C₂	—	2	2	no	—
589	C₂	—	4	1	no	—
590	C₂	—	4	1	no	—
591	C₂	—	4	2	no	—
592	C₂	—	4	1	no	—
593	C₂	—	4	1	no	—
594	C₂	—	268	2	no	—
595	C₂	C₂×#14524088	1	1	yes	characteristic
596	C₂	#16864231	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#534×C₆₇	C₂
hypercenter	#534	D₆₇
hypocenter	C₆₇	#3545
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #534

Complements

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

N	H ≅ G/N	type
1. #16864149	C₂	semidirect
2. #16864141	C₂	semidirect
3. #16864139	C₂	semidirect
4. #16864110	C₂	semidirect
5. #16864077	C₂	semidirect
6. #16864077	C₂	semidirect
7. #16864074	C₂	semidirect
8. #16864072	C₂	semidirect
9. #16864040	C₂	semidirect
10. #16864033	C₂	semidirect
11. #16864014	C₂	semidirect
12. #16864013	C₂	semidirect
13. #16863981	C₂	semidirect
14. #16863978	C₂	semidirect
15. #16863968	C₂	semidirect
16. #16863955	C₂	semidirect
17. #16863923	C₂	semidirect
18. C₂×#14524030	C₂	semidirect
19. #534×C₆₇	C₂	semidirect
21. C₂²×Dic₁₃₄	C₂²	semidirect
22. C₂²×C₂²⋊D₆₇	C₂²	semidirect
23. #14524042	C₂²	semidirect
24. #14524042	C₂²	semidirect
25. #14524038	C₂²	semidirect
26. #14524036	C₂²	semidirect
27. #14524036	C₂²	semidirect
28. #14524036	C₂²	semidirect
29. #14524036	C₂²	semidirect
30. #14524036	C₂²	semidirect
31. #14524033	C₂²	semidirect
34. #14524030	C₂²	semidirect
35. #14524030	C₂²	semidirect
36. #14524030	C₂²	semidirect
37. #14524030	C₂²	semidirect
38. #14524030	C₂²	semidirect
39. #14524030	C₂²	semidirect
40. #14524029	C₂²	semidirect
41. #14524029	C₂²	semidirect
42. #14524029	C₂²	semidirect
43. #14524029	C₂²	semidirect
44. #14524029	C₂²	semidirect
45. #14524027	C₂²	semidirect
46. #14524026	C₂²	semidirect
47. #14524026	C₂²	semidirect
48. #14524025	C₂²	semidirect
49. #14524025	C₂²	semidirect
51. #14524024	C₂²	semidirect
52. #14524024	C₂²	semidirect
53. #14524024	C₂²	semidirect
54. #14524024	C₂²	semidirect
55. #14524024	C₂²	semidirect
56. #14524022	C₂²	semidirect
57. #14524022	C₂²	semidirect
58. #14524021	C₂²	semidirect
59. #14524021	C₂²	semidirect
60. #14524020	C₂²	semidirect
61. #14524020	C₂²	semidirect
62. #14524020	C₂²	semidirect
63. #14524020	C₂²	semidirect
64. #14524020	C₂²	semidirect
67. #14524015	C₂²	semidirect
68. #14524015	C₂²	semidirect
69. #14524015	C₂²	semidirect
70. #14524014	C₂²	semidirect
71. #14524014	C₂²	semidirect
73. #14524012	C₂²	semidirect
75. #14524011	C₂²	semidirect
76. #14524011	C₂²	semidirect
77. #14524008	C₂²	semidirect
78. D₄×Dic₆₇	C₂²	semidirect
79. D₄×Dic₆₇	C₂²	semidirect
80. D₄×Dic₆₇	C₂²	semidirect
81. C₄×C₂²⋊D₆₇	C₂²	semidirect
82. C₄×C₂²⋊D₆₇	C₂²	semidirect
83. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
84. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
85. #14524002	C₂²	semidirect
86. #14524001	C₂²	semidirect
87. #14523999	C₂²	semidirect
88. #14523999	C₂²	semidirect
89. #14523999	C₂²	semidirect
90. C₂×C₂²⋊Dic₆₇	C₂²	semidirect
91. C₂×C₂²⋊Dic₆₇	C₂²	semidirect
92. C₂×C₂²⋊Dic₆₇	C₂²	semidirect
93. C₂×C₂²⋊Dic₆₇	C₂²	semidirect
94. C₂²⋊C₄×D₆₇	C₂²	semidirect
95. C₂×C₄×Dic₆₇	C₂²	semidirect
97. C₂²×D₄×C₆₇	C₂²	semidirect
99. #123×C₆₇	C₂²	semidirect
100. #123×C₆₇	C₂²	semidirect
102. #121×C₆₇	C₂²	semidirect
105. #120×C₆₇	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₆₇	C₂²	semidirect
299. C₆₇	#3545	semidirect
316. #534	D₆₇	semidirect
323. C₂²×D₄	C₂×D₆₇	semidirect
358. #123	C₂×D₆₇	semidirect
359. #123	C₂×D₆₇	semidirect
377. #121	C₂×D₆₇	semidirect
385. #120	C₂×D₆₇	semidirect
404. C₂×C₂²⋊C₄	C₂×D₆₇	semidirect