Subgroups — #30770794

Order 17152.

736 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	C₂×#16863380	C₂	1	1	yes	maximal, characteristic
2	#22568654	C₂	1	1	yes	maximal, characteristic
3	#22558331	C₂	1	4	yes	maximal, complemented
4	C₂×#413×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11761612	—	2	1	no	—
6	C₂²×#11761612	C₄	1	1	yes	characteristic
7	C₂²×#11761612	C₄	1	1	yes	characteristic
8	#16863380	—	2	1	no	—
9	#16863380	—	2	1	no	—
10	#16863380	C₄	1	2	yes	—
11	#16863380	C₂²	1	2	yes	—
12	C₂×#14523962	—	2	1	no	—
13	C₂×#14523960	C₄	1	2	yes	—
14	#16863363	—	2	1	no	—
15	#16863363	—	2	1	no	—
16	#16863363	C₄	1	2	yes	—
17	#16863363	C₂²	1	2	yes	—
18	#16863360	—	2	1	no	—
19	#16863360	—	2	1	no	—
20	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₆₇	—	2	1	no	—
22	#413×C₆₇	—	2	1	no	—
23	#413×C₆₇	—	2	1	no	—
24	#413×C₆₇	C₄	1	2	yes	—
25	#413×C₆₇	C₂²	1	2	yes	—
26	C₂×#101×C₆₇	—	2	1	no	—
27	C₂×#100×C₆₇	C₄	1	2	yes	—
28	C₂×#11761612	—	2	1	no	—
29	C₂×#11761612	—	2	1	no	—
30	C₂×#11761612	—	2	1	no	—
31	C₂×#11761612	—	2	2	no	—
32	C₂×#11761612	—	2	2	no	—
33	C₂×#11761612	—	2	2	no	—
34	C₂×#11761612	—	4	1	no	—
35	C₂×#11761612	—	4	1	no	—
36	C₂×#11761612	—	4	1	no	—
37	C₂×#11761612	—	4	1	no	—
38	C₂×#11761612	—	4	1	no	—
39	C₂×#11761612	—	4	1	no	—
40	C₂×#11761612	—	4	1	no	—
41	C₂×#11761612	C₂×C₄	1	2	yes	—
42	C₂²×C₆₇⋊C₈	—	2	1	no	—
43	C₂²×C₆₇⋊C₈	—	4	1	no	—
44	C₂²×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
45	#14523962	—	2	2	no	—
46	#14523962	—	2	2	no	—
47	#14523960	—	2	2	no	—
48	#14523960	C₂×C₄	1	4	yes	—
49	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
50	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
51	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
52	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
53	C₂×#41×C₆₇	—	4	1	no	—
54	C₂×#41×C₆₇	—	4	1	no	—
55	C₂×#41×C₆₇	—	4	1	no	—
56	C₂×#41×C₆₇	—	4	1	no	—
57	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
58	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
59	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
60	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
61	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
62	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
63	C₂×#41×C₆₇	Q₈	1	1	yes	characteristic
64	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
66	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
67	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
68	C₂²×D₄×C₆₇	Q₈	1	1	yes	characteristic
69	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
71	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
72	C₂×M₁₆×C₆₇	—	2	2	no	—
73	C₂×M₁₆×C₆₇	—	2	2	no	—
74	C₂×M₁₆×C₆₇	—	2	2	no	—
75	C₂×M₁₆×C₆₇	—	4	1	no	—
76	C₂×M₁₆×C₆₇	—	4	1	no	—
77	C₂×M₁₆×C₆₇	—	4	1	no	—
78	C₂²×C₈×C₆₇	—	4	1	no	—
79	#101×C₆₇	—	2	2	no	—
80	#101×C₆₇	—	2	2	no	—
81	#100×C₆₇	—	2	2	no	—
82	#100×C₆₇	C₂×C₄	1	4	yes	—
83	#11761612	—	2	4	no	—
84	#11761612	—	4	2	no	—
85	#11761612	—	4	2	no	—
86	#11761612	—	4	2	no	—
87	#11761612	—	4	2	no	—
88	#11761612	—	4	1	no	—
89	#11761612	—	4	1	no	—
90	#11761612	—	4	1	no	—
91	#11761612	—	4	1	no	—
92	#11761612	—	4	2	no	—
93	C₂×C₆₇⋊C₈	—	2	2	no	—
94	C₂×C₆₇⋊C₈	—	2	2	no	—
95	C₂×C₆₇⋊C₈	—	4	2	no	—
96	C₂×C₆₇⋊C₈	—	4	2	no	—
97	C₂×C₆₇⋊C₈	—	4	2	no	—
98	C₂×C₆₇⋊C₈	—	4	2	no	—
99	C₂×C₆₇⋊C₈	—	4	2	no	—
100	C₂⁴×C₆₇	C₄²	1	1	yes	characteristic
101	C₂⁴×C₆₇	C₄⋊C₄	1	1	yes	characteristic
102	C₂⁴×C₆₇	C₄⋊C₄	1	1	yes	characteristic
103	#41×C₆₇	—	4	1	no	—
104	#41×C₆₇	—	4	1	no	—
105	#41×C₆₇	—	4	1	no	—
106	#41×C₆₇	—	4	1	no	—
107	#41×C₆₇	—	4	1	no	—
108	#41×C₆₇	—	4	1	no	—
109	#41×C₆₇	—	4	1	no	—
110	#41×C₆₇	—	4	1	no	—
111	#41×C₆₇	—	4	1	no	—
112	#41×C₆₇	—	4	1	no	—
113	#41×C₆₇	—	4	1	no	—
114	#41×C₆₇	—	4	1	no	—
115	#41×C₆₇	—	4	1	no	—
116	#41×C₆₇	—	4	1	no	—
117	#41×C₆₇	—	4	1	no	—
118	#41×C₆₇	—	4	1	no	—
119	C₂×Q₈×C₆₇	—	4	1	no	—
120	C₂×Q₈×C₆₇	—	4	1	no	—
121	C₂×Q₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
122	C₂×Q₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
123	C₂×Q₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
124	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
125	C₂×D₄×C₆₇	—	4	1	no	—
126	C₂×D₄×C₆₇	—	4	1	no	—
127	C₂×D₄×C₆₇	—	4	1	no	—
128	C₂×D₄×C₆₇	—	4	1	no	—
129	C₂×D₄×C₆₇	—	4	1	no	—
130	C₂×D₄×C₆₇	—	4	1	no	—
131	C₂×D₄×C₆₇	C₄²	1	1	yes	characteristic
132	C₂×D₄×C₆₇	C₄²	1	1	yes	characteristic
133	C₂×D₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
134	C₂×D₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×D₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
136	C₂×D₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
137	C₂×D₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
138	C₂×D₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
139	C₂×D₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
140	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
141	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
142	C₂×D₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
143	C₂²×C₄×C₆₇	—	2	1	no	—
144	C₂²×C₄×C₆₇	—	2	1	no	—
145	C₂²×C₄×C₆₇	—	2	1	no	—
146	C₂²×C₄×C₆₇	—	2	1	no	—
147	C₂²×C₄×C₆₇	—	2	1	no	—
148	C₂²×C₄×C₆₇	—	2	1	no	—
149	C₂²×C₄×C₆₇	—	2	1	no	—
150	C₂²×C₄×C₆₇	—	2	1	no	—
151	C₂²×C₄×C₆₇	—	2	1	no	—
152	C₂²×C₄×C₆₇	—	2	1	no	—
153	C₂²×C₄×C₆₇	—	2	1	no	—
154	C₂²×C₄×C₆₇	—	2	1	no	—
155	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
156	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
167	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
168	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
171	M₁₆×C₆₇	—	2	4	no	—
172	M₁₆×C₆₇	—	4	2	no	—
173	M₁₆×C₆₇	—	4	2	no	—
174	M₁₆×C₆₇	—	4	2	no	—
175	C₂×C₈×C₆₇	—	4	2	no	—
176	C₂×C₈×C₆₇	—	4	2	no	—
177	C₂×C₈×C₆₇	—	4	2	no	—
178	C₂³×C₆₇	—	2	1	no	—
179	C₂³×C₆₇	—	2	1	no	—
180	C₂³×C₆₇	—	2	1	no	—
181	C₂³×C₆₇	—	2	1	no	—
182	C₂³×C₆₇	—	2	1	no	—
183	C₂³×C₆₇	—	2	1	no	—
184	C₂³×C₆₇	—	8	1	no	—
185	C₂³×C₆₇	—	8	1	no	—
186	C₂³×C₆₇	—	8	1	no	—
187	C₂³×C₆₇	#95	1	1	yes	characteristic
188	C₂³×C₆₇	#95	1	1	yes	characteristic
189	C₂³×C₆₇	#95	1	1	yes	characteristic
190	C₂³×C₆₇	#95	1	1	yes	characteristic
191	C₂³×C₆₇	C₂×C₄²	1	1	yes	characteristic
192	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
194	Q₈×C₆₇	—	4	1	no	—
195	Q₈×C₆₇	—	4	1	no	—
196	Q₈×C₆₇	—	4	1	no	—
197	Q₈×C₆₇	—	4	1	no	—
198	D₄×C₆₇	—	4	1	no	—
199	D₄×C₆₇	—	4	1	no	—
200	D₄×C₆₇	—	4	1	no	—
201	D₄×C₆₇	—	4	1	no	—
202	D₄×C₆₇	—	4	1	no	—
203	D₄×C₆₇	—	4	1	no	—
204	D₄×C₆₇	—	4	1	no	—
205	D₄×C₆₇	—	4	1	no	—
206	D₄×C₆₇	—	4	1	no	—
207	D₄×C₆₇	—	4	1	no	—
208	D₄×C₆₇	—	4	1	no	—
209	D₄×C₆₇	—	4	1	no	—
210	C₂×C₄×C₆₇	—	2	1	no	—
211	C₂×C₄×C₆₇	—	2	1	no	—
212	C₂×C₄×C₆₇	—	2	1	no	—
213	C₂×C₄×C₆₇	—	2	1	no	—
214	C₂×C₄×C₆₇	—	2	1	no	—
215	C₂×C₄×C₆₇	—	2	1	no	—
216	C₂×C₄×C₆₇	—	2	1	no	—
217	C₂×C₄×C₆₇	—	2	1	no	—
218	C₂×C₄×C₆₇	—	2	1	no	—
219	C₂×C₄×C₆₇	—	2	1	no	—
220	C₂×C₄×C₆₇	—	2	1	no	—
221	C₂×C₄×C₆₇	—	2	1	no	—
222	C₂×C₄×C₆₇	—	2	1	no	—
223	C₂×C₄×C₆₇	—	2	1	no	—
224	C₂×C₄×C₆₇	—	2	1	no	—
225	C₂×C₄×C₆₇	—	2	1	no	—
226	C₂×C₄×C₆₇	—	2	1	no	—
227	C₂×C₄×C₆₇	—	2	1	no	—
228	C₂×C₄×C₆₇	—	2	1	no	—
229	C₂×C₄×C₆₇	—	2	1	no	—
230	C₂×C₄×C₆₇	—	2	1	no	—
231	C₂×C₄×C₆₇	—	2	1	no	—
232	C₂×C₄×C₆₇	—	2	1	no	—
233	C₂×C₄×C₆₇	—	2	1	no	—
234	C₂×C₄×C₆₇	—	2	1	no	—
235	C₂×C₄×C₆₇	—	2	1	no	—
236	C₂×C₄×C₆₇	—	2	1	no	—
237	C₂×C₄×C₆₇	—	2	1	no	—
238	C₂×C₄×C₆₇	—	2	1	no	—
239	C₂×C₄×C₆₇	—	2	1	no	—
240	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
241	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
242	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
243	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
244	C₂×C₄×C₆₇	#99	1	1	yes	characteristic
245	C₂×C₄×C₆₇	#99	1	1	yes	characteristic
246	C₂×C₄×C₆₇	#99	1	1	yes	characteristic
247	C₂×C₄×C₆₇	#99	1	1	yes	characteristic
248	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
252	C₈×C₆₇	—	4	4	no	—
253	C₆₇⋊C₈	—	4	4	no	—
254	C₆₇⋊C₈	—	4	2	no	—
255	C₆₇⋊C₈	—	4	2	no	—
256	C₂²×C₆₇	—	2	1	no	—
257	C₂²×C₆₇	—	2	1	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	—	4	1	no	—
263	C₂²×C₆₇	—	4	1	no	—
264	C₂²×C₆₇	—	4	1	no	—
265	C₂²×C₆₇	—	4	1	no	—
266	C₂²×C₆₇	—	4	1	no	—
267	C₂²×C₆₇	—	4	1	no	—
268	C₂²×C₆₇	—	4	1	no	—
269	C₂²×C₆₇	—	4	2	no	—
270	C₂²×C₆₇	—	4	2	no	—
271	C₂²×C₆₇	—	8	1	no	—
272	C₂²×C₆₇	—	8	1	no	—
273	C₂²×C₆₇	—	8	1	no	—
274	C₂²×C₆₇	—	8	1	no	—
275	C₂²×C₆₇	#342	1	1	yes	characteristic
276	C₂²×C₆₇	#342	1	1	yes	characteristic
277	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
278	C₄×C₆₇	—	2	1	no	—
279	C₄×C₆₇	—	2	1	no	—
280	C₄×C₆₇	—	2	1	no	—
281	C₄×C₆₇	—	2	1	no	—
282	C₄×C₆₇	—	2	1	no	—
283	C₄×C₆₇	—	2	1	no	—
284	C₄×C₆₇	#342	1	1	yes	characteristic
285	C₄×C₆₇	#342	1	1	yes	characteristic
286	C₄×C₆₇	C₂×#99	1	1	yes	characteristic
287	C₄×C₆₇	C₂×#99	1	1	yes	characteristic
288	#12579	—	67	1	no	maximal, Sylow
289	C₂×C₆₇	—	2	1	no	—
290	C₂×C₆₇	—	2	1	no	—
291	C₂×C₆₇	—	2	1	no	—
292	C₂×C₆₇	—	4	1	no	—
293	C₂×C₆₇	—	4	1	no	—
294	C₂×C₆₇	—	4	1	no	—
295	C₂×C₆₇	—	4	1	no	—
296	C₂×C₆₇	—	4	1	no	—
297	C₂×C₆₇	—	4	1	no	—
298	C₂×C₆₇	C₂×#342	1	1	yes	characteristic
299	C₂×#413	—	67	1	no	—
300	C₂×#413	D₆₇	1	1	yes	characteristic
301	#2879	—	67	1	no	—
302	#1392	—	67	4	no	—
303	C₆₇	#12579	1	1	yes	characteristic, complemented, Sylow
304	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic
305	C₂²×M₁₆	—	2	1	no	—
306	C₂²×M₁₆	—	67	1	no	—
307	C₂²×M₁₆	—	67	1	no	—
308	C₂²×M₁₆	—	134	1	no	—
309	#413	—	2	1	no	—
310	#413	—	2	1	no	—
311	#413	—	67	2	no	—
312	#413	—	67	2	no	—
313	#413	—	134	1	no	—
314	#413	—	134	1	no	—
315	#413	Dic₆₇	1	2	yes	—
316	#413	C₂×D₆₇	1	2	yes	—
317	C₂×#101	—	2	1	no	—
318	C₂×#101	—	134	1	no	—
319	C₂×#100	—	67	2	no	—
320	C₂×#100	Dic₆₇	1	2	yes	—
321	#408	—	67	2	no	—
322	#408	—	67	2	no	—
323	#408	—	134	1	no	—
324	#408	—	134	1	no	—
325	#407	—	134	1	no	—
326	#407	—	134	1	no	—
327	C₂×#41	—	4	1	no	—
328	C₂×#41	—	4	1	no	—
329	C₂×#41	—	4	1	no	—
330	C₂×#41	—	4	1	no	—
331	C₂×#41	Dic₁₃₄	1	1	yes	characteristic
332	C₂×#41	C₄×D₆₇	1	1	yes	characteristic
333	C₂×#41	C₄×D₆₇	1	1	yes	characteristic
334	C₂×#41	D₂₆₈	1	1	yes	characteristic
335	C₂×#41	C₂×Dic₆₇	1	1	yes	characteristic
336	C₂×#41	C₂²⋊D₆₇	1	1	yes	characteristic
337	C₂×#41	C₂²⋊D₆₇	1	1	yes	characteristic
338	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
339	C₂²×Q₈	C₂²⋊D₆₇	1	1	yes	characteristic
340	C₂²×D₄	Dic₁₃₄	1	1	yes	characteristic
341	C₂²×D₄	C₄×D₆₇	1	1	yes	characteristic
342	C₂²×D₄	C₂×Dic₆₇	1	1	yes	characteristic
343	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
344	C₂³×C₄	D₂₆₈	1	1	yes	characteristic
345	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
346	C₂×M₁₆	—	2	2	no	—
347	C₂×M₁₆	—	2	2	no	—
348	C₂×M₁₆	—	2	2	no	—
349	C₂×M₁₆	—	4	1	no	—
350	C₂×M₁₆	—	4	1	no	—
351	C₂×M₁₆	—	4	1	no	—
352	C₂×M₁₆	—	268	1	no	—
353	C₂×M₁₆	—	268	1	no	—
354	C₂×M₁₆	—	268	1	no	—
355	C₂×M₁₆	—	268	1	no	—
356	C₂×M₁₆	—	268	1	no	—
357	C₂×M₁₆	—	268	1	no	—
358	C₂×M₁₆	—	268	1	no	—
359	C₂×M₁₆	—	67	2	no	—
360	C₂×M₁₆	—	134	2	no	—
361	C₂×M₁₆	—	134	2	no	—
362	C₂×M₁₆	—	134	2	no	—
363	C₂×M₁₆	—	134	1	no	—
364	C₂×M₁₆	—	134	1	no	—
365	C₂×M₁₆	—	134	1	no	—
366	C₂²×C₈	—	4	1	no	—
367	C₂²×C₈	—	268	1	no	—
368	C₂²×C₈	—	67	2	no	—
369	C₂²×C₈	—	134	1	no	—
370	#101	—	2	2	no	—
371	#101	—	2	2	no	—
372	#101	—	134	2	no	—
373	#101	—	134	2	no	—
374	#100	—	2	2	no	—
375	#100	—	67	4	no	—
376	#100	—	134	2	no	—
377	#100	C₂×Dic₆₇	1	4	yes	—
378	C₂²⋊C₈	—	134	2	no	—
379	C₂²⋊C₈	—	134	2	no	—
380	C₂²⋊C₈	—	134	2	no	—
381	C₂²⋊C₈	—	134	2	no	—
382	C₂⁴	C₄×Dic₆₇	1	1	yes	characteristic
383	C₂⁴	Dic₆₇⋊C₄	1	1	yes	characteristic
384	C₂⁴	C₄⋊Dic₆₇	1	1	yes	characteristic
385	#41	—	4	1	no	—
386	#41	—	4	1	no	—
387	#41	—	4	1	no	—
388	#41	—	4	1	no	—
389	#41	—	4	1	no	—
390	#41	—	4	1	no	—
391	#41	—	4	1	no	—
392	#41	—	4	1	no	—
393	#41	—	4	1	no	—
394	#41	—	4	1	no	—
395	#41	—	4	1	no	—
396	#41	—	4	1	no	—
397	#41	—	4	1	no	—
398	#41	—	4	1	no	—
399	#41	—	4	1	no	—
400	#41	—	4	1	no	—
401	C₂×Q₈	—	4	1	no	—
402	C₂×Q₈	—	4	1	no	—
403	C₂×Q₈	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
404	C₂×Q₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
405	C₂×Q₈	Dic₆₇⋊C₄	1	1	yes	characteristic
406	C₂×Q₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
407	C₂×D₄	—	4	1	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	—	4	1	no	—
410	C₂×D₄	—	4	1	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	—	4	1	no	—
413	C₂×D₄	C₄×Dic₆₇	1	1	yes	characteristic
414	C₂×D₄	C₄×Dic₆₇	1	1	yes	characteristic
415	C₂×D₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
416	C₂×D₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
417	C₂×D₄	Dic₆₇⋊C₄	1	1	yes	characteristic
418	C₂×D₄	Dic₆₇⋊C₄	1	1	yes	characteristic
419	C₂×D₄	Dic₆₇⋊C₄	1	1	yes	characteristic
420	C₂×D₄	C₄⋊Dic₆₇	1	1	yes	characteristic
421	C₂×D₄	C₄⋊Dic₆₇	1	1	yes	characteristic
422	C₂×D₄	C₂×C₄×D₆₇	1	1	yes	characteristic
423	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
424	C₂×D₄	C₂×Dic₁₃₄	1	1	yes	characteristic
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
438	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
439	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
440	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
441	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
442	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
443	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
444	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
445	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
446	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
447	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
448	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
449	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
450	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
453	M₁₆	—	2	4	no	—
454	M₁₆	—	4	2	no	—
455	M₁₆	—	4	2	no	—
456	M₁₆	—	4	2	no	—
457	M₁₆	—	268	2	no	—
458	M₁₆	—	268	2	no	—
459	M₁₆	—	268	2	no	—
460	M₁₆	—	268	2	no	—
461	M₁₆	—	268	1	no	—
462	M₁₆	—	268	1	no	—
463	M₁₆	—	268	1	no	—
464	M₁₆	—	268	1	no	—
465	M₁₆	—	268	2	no	—
466	M₁₆	—	134	4	no	—
467	C₂×C₈	—	4	2	no	—
468	C₂×C₈	—	4	2	no	—
469	C₂×C₈	—	4	2	no	—
470	C₂×C₈	—	268	2	no	—
471	C₂×C₈	—	268	2	no	—
472	C₂×C₈	—	268	2	no	—
473	C₂×C₈	—	268	2	no	—
474	C₂×C₈	—	268	2	no	—
475	C₂×C₈	—	134	2	no	—
476	C₂×C₈	—	134	2	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	1	no	—
481	C₂³	—	2	1	no	—
482	C₂³	—	2	1	no	—
483	C₂³	—	8	1	no	—
484	C₂³	—	8	1	no	—
485	C₂³	—	8	1	no	—
486	C₂³	C₆₇⋊#95	1	1	yes	characteristic
487	C₂³	C₆₇⋊#95	1	1	yes	characteristic
488	C₂³	C₆₇⋊#95	1	1	yes	characteristic
489	C₂³	C₆₇⋊#95	1	1	yes	characteristic
490	C₂³	C₂×C₄×Dic₆₇	1	1	yes	characteristic
491	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
492	C₂³	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
493	Q₈	—	4	1	no	—
494	Q₈	—	4	1	no	—
495	Q₈	—	4	1	no	—
496	Q₈	—	4	1	no	—
497	D₄	—	4	1	no	—
498	D₄	—	4	1	no	—
499	D₄	—	4	1	no	—
500	D₄	—	4	1	no	—
501	D₄	—	4	1	no	—
502	D₄	—	4	1	no	—
503	D₄	—	4	1	no	—
504	D₄	—	4	1	no	—
505	D₄	—	4	1	no	—
506	D₄	—	4	1	no	—
507	D₄	—	4	1	no	—
508	D₄	—	4	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
540	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
541	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
542	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
543	C₂×C₄	#14523957	1	1	yes	characteristic
544	C₂×C₄	#14523957	1	1	yes	characteristic
545	C₂×C₄	#14523957	1	1	yes	characteristic
546	C₂×C₄	#14523957	1	1	yes	characteristic
547	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
548	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
549	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
550	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
551	C₈	—	4	4	no	—
552	C₈	—	268	4	no	—
553	C₈	—	268	2	no	—
554	C₈	—	268	2	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	8	1	no	—
571	C₂²	—	8	1	no	—
572	C₂²	—	8	1	no	—
573	C₂²	—	8	1	no	—
574	C₂²	#16863162	1	1	yes	characteristic
575	C₂²	#16863162	1	1	yes	characteristic
576	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	#16863162	1	1	yes	characteristic
584	C₄	#16863162	1	1	yes	characteristic
585	C₄	C₂×#14523957	1	1	yes	characteristic
586	C₄	C₂×#14523957	1	1	yes	characteristic
587	C₂	—	2	1	no	—
588	C₂	—	2	1	no	—
589	C₂	—	2	1	no	—
590	C₂	—	4	1	no	—
591	C₂	—	4	1	no	—
592	C₂	—	4	1	no	—
593	C₂	—	4	1	no	—
594	C₂	—	4	1	no	—
595	C₂	—	4	1	no	—
596	C₂	C₂×#16863162	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#14523957
commutator	C₂³×C₆₇	C₂×C₄²
Frattini	C₂×#41	C₂²×D₆₇
Fitting	C₂×#413×C₆₇	C₂
socle	C₂×C₆₇	C₂×#342
prime radical	C₂²×#41×C₆₇	C₂²
cosocle	C₂×#41×C₆₇	C₂³
hypercenter	C₂×#413	D₆₇
hypocenter	C₆₇	#12579
LCS	G ▷ C₂³×C₆₇ ▷ C₂²×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×#41 ◁ C₂×#413

Complements

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

N	H ≅ G/N	type
3. #22558331	C₂	semidirect
303. C₆₇	#12579	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863380	2
#22568654	2
#22558331	2
C₂×#413×C₆₇	2
#12579	67