Subgroups — #30868151

Order 17152.

636 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569144	C₂	1	1	yes	maximal, characteristic, complemented
2	#22568853	C₂	1	1	yes	maximal, characteristic
3	#22561154	C₂	1	1	yes	maximal, characteristic, complemented
4	#22560985	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560963	C₂	1	2	yes	maximal, complemented
6	#22560922	C₂	1	2	yes	maximal
7	#22560859	C₂	1	2	yes	maximal
8	#22560810	C₂	1	2	yes	maximal, complemented
9	#22560229	C₂	1	1	yes	maximal, characteristic
10	#22560079	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3076	C₂	1	1	yes	maximal, characteristic
12	#16863527	—	2	1	no	—
13	#16863527	—	2	1	no	—
14	Q₈×C₆₇⋊C₈	—	2	1	no	—
15	Q₈×C₆₇⋊C₈	—	2	1	no	—
16	#16863457	—	2	1	no	—
17	#16863457	—	2	1	no	—
18	#16863449	—	2	1	no	—
19	#16863449	—	2	1	no	—
20	C₂×#14523979	C₂²	1	2	yes	—
21	#16863423	C₂²	1	1	yes	characteristic
22	#16863423	C₂²	1	1	yes	characteristic
23	#16863423	C₂²	1	2	yes	—
24	#16863420	C₂²	1	1	yes	characteristic
25	C₂×#14523970	C₂²	1	2	yes	—
26	#16863363	C₂²	1	1	yes	characteristic
27	#16863363	C₂²	1	1	yes	characteristic
28	#16863352	C₂²	1	2	yes	—
29	C₄×#11761612	C₂²	1	1	yes	characteristic
30	C₂×#14523953	C₂²	1	2	yes	—
31	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
33	#16863161	C₂²	1	2	yes	—
34	#16863155	C₂²	1	2	yes	—
35	#16863155	C₂²	1	2	yes	—
36	#16863155	C₂²	1	2	yes	—
37	#16863150	C₂²	1	2	yes	—
38	#533×C₆₇	C₂²	1	1	yes	characteristic
39	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
40	#479×C₆₇	C₄	1	2	yes	complemented
41	#478×C₆₇	C₄	1	2	yes	complemented
42	#477×C₆₇	C₄	1	1	yes	characteristic, complemented
43	#476×C₆₇	C₄	1	1	yes	characteristic, complemented
44	#475×C₆₇	C₄	1	1	yes	characteristic, complemented
45	#474×C₆₇	C₄	1	1	yes	characteristic, complemented
46	#427×C₆₇	C₂²	1	2	yes	—
47	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
48	#416×C₆₇	C₂²	1	2	yes	—
49	C₂×#11761612	C₂³	1	1	yes	characteristic
50	C₂×#11761612	C₂³	1	1	yes	characteristic
51	C₂×#11761612	C₂³	1	2	yes	—
52	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊Dic₆₇	—	2	1	no	—
55	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
56	#14523979	—	4	2	no	—
57	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
58	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
59	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
60	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
61	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
62	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
63	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
64	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
65	#14523970	—	4	2	no	—
66	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
67	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
68	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
69	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
70	#14523954	—	2	2	no	—
71	#14523954	—	2	1	no	—
72	#14523953	—	4	2	no	—
73	C₄×C₆₇⋊C₈	—	2	2	no	—
74	C₄×C₆₇⋊C₈	—	2	1	no	—
75	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
76	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
77	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
78	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
79	C₆₇⋊#95	—	2	1	no	—
80	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
82	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
83	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
84	#125×C₆₇	C₂×C₄	1	2	yes	—
85	C₂²⋊Q₈×C₆₇	—	2	1	no	—
86	C₂²⋊Q₈×C₆₇	—	2	1	no	—
87	C₄×Q₈×C₆₇	—	2	1	no	—
88	C₄×Q₈×C₆₇	—	2	1	no	—
89	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
90	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₆₇	—	2	1	no	—
92	C₄×D₄×C₆₇	—	2	1	no	—
93	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
94	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
95	#117×C₆₇	—	2	1	no	—
96	#117×C₆₇	C₂³	1	1	yes	characteristic
97	#117×C₆₇	C₂³	1	2	yes	—
98	C₂×C₄²×C₆₇	—	2	1	no	—
99	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
100	#107×C₆₇	C₂×C₄	1	2	yes	—
101	#107×C₆₇	C₂×C₄	1	2	yes	—
102	#106×C₆₇	C₂×C₄	1	2	yes	—
103	#106×C₆₇	C₂×C₄	1	2	yes	—
104	C₄⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
105	C₄⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
106	C₄⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
107	#103×C₆₇	C₂×C₄	1	2	yes	—
108	#103×C₆₇	C₂×C₄	1	2	yes	—
109	#102×C₆₇	C₂×C₄	1	2	yes	—
110	#102×C₆₇	C₂×C₄	1	2	yes	—
111	C₂²×Dic₆₇	—	2	2	no	—
112	#11761612	—	2	2	no	—
113	#11761612	—	2	1	no	—
114	#11761612	—	2	1	no	—
115	#11761612	—	2	1	no	—
116	#11761612	—	2	1	no	—
117	#11761612	—	2	2	no	—
118	C₂×C₆₇⋊C₈	—	2	1	no	—
119	C₂×C₆₇⋊C₈	—	2	1	no	—
120	C₂×C₆₇⋊C₈	—	2	1	no	—
121	C₂×C₆₇⋊C₈	—	2	1	no	—
122	C₂×C₆₇⋊C₈	—	2	1	no	—
123	C₂×C₆₇⋊C₈	—	2	1	no	—
124	C₂×C₆₇⋊C₈	—	2	2	no	—
125	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
126	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
127	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
128	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
129	C₄⋊Dic₆₇	—	4	2	no	—
130	C₄×Dic₆₇	—	2	2	no	—
131	C₄×Dic₆₇	—	2	2	no	—
132	#41×C₆₇	—	2	1	no	—
133	#41×C₆₇	—	2	1	no	—
134	#41×C₆₇	—	2	1	no	—
135	#41×C₆₇	—	2	1	no	—
136	C₂×Q₈×C₆₇	—	2	1	no	—
137	C₂×Q₈×C₆₇	—	2	1	no	—
138	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×D₄×C₆₇	—	2	1	no	—
140	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₇	—	2	1	no	—
142	C₂²×C₄×C₆₇	—	2	1	no	—
143	C₂²×C₄×C₆₇	—	2	1	no	—
144	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
145	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
146	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
147	C₂×C₈×C₆₇	—	2	2	no	—
148	C₂×C₈×C₆₇	—	2	2	no	—
149	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
151	C₄⋊C₄×C₆₇	—	2	1	no	—
152	C₄⋊C₄×C₆₇	—	2	1	no	—
153	C₄⋊C₄×C₆₇	—	2	2	no	—
154	C₄⋊C₄×C₆₇	—	2	2	no	—
155	C₄⋊C₄×C₆₇	—	2	1	no	—
156	C₄⋊C₄×C₆₇	—	2	1	no	—
157	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
158	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
159	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
160	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
161	C₂²⋊C₄×C₆₇	—	2	1	no	—
162	C₂²⋊C₄×C₆₇	—	2	2	no	—
163	C₂²⋊C₄×C₆₇	—	2	1	no	—
164	C₂²⋊C₄×C₆₇	—	2	1	no	—
165	C₄²×C₆₇	—	2	1	no	—
166	C₄²×C₆₇	—	2	1	no	—
167	C₄²×C₆₇	—	2	1	no	—
168	C₄²×C₆₇	—	2	2	no	—
169	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
173	C₂³×C₆₇	—	2	1	no	—
174	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
175	Q₈×C₆₇	—	2	1	no	—
176	Q₈×C₆₇	—	2	1	no	—
177	Q₈×C₆₇	—	4	2	no	—
178	Q₈×C₆₇	—	4	2	no	—
179	D₄×C₆₇	—	2	1	no	—
180	D₄×C₆₇	—	2	1	no	—
181	D₄×C₆₇	—	4	1	no	—
182	D₄×C₆₇	—	4	1	no	—
183	C₂×C₄×C₆₇	—	2	2	no	—
184	C₂×C₄×C₆₇	—	2	1	no	—
185	C₂×C₄×C₆₇	—	2	1	no	—
186	C₂×C₄×C₆₇	—	2	1	no	—
187	C₂×C₄×C₆₇	—	2	2	no	—
188	C₂×C₄×C₆₇	—	2	2	no	—
189	C₂×C₄×C₆₇	—	4	1	no	—
190	C₂×C₄×C₆₇	—	4	2	no	—
191	C₂×C₄×C₆₇	—	4	1	no	—
192	C₂×C₄×C₆₇	—	4	1	no	—
193	C₂×C₄×C₆₇	—	4	2	no	—
194	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
202	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
204	C₂×Dic₆₇	—	4	2	no	—
205	C₂×Dic₆₇	—	4	2	no	—
206	C₂×Dic₆₇	—	4	2	no	—
207	C₈×C₆₇	—	2	2	no	—
208	C₈×C₆₇	—	2	2	no	—
209	C₆₇⋊C₈	—	2	1	no	—
210	C₆₇⋊C₈	—	2	1	no	—
211	C₆₇⋊C₈	—	2	1	no	—
212	C₆₇⋊C₈	—	2	1	no	—
213	C₆₇⋊C₈	—	4	1	no	—
214	C₆₇⋊C₈	—	4	1	no	—
215	C₆₇⋊C₈	—	4	2	no	—
216	C₂²×C₆₇	—	2	1	no	—
217	C₂²×C₆₇	—	2	1	no	—
218	C₂²×C₆₇	—	4	1	no	—
219	C₂²×C₆₇	—	4	1	no	—
220	C₂²×C₆₇	—	4	1	no	—
221	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
222	C₂²×C₆₇	#541	1	1	yes	characteristic
223	C₂²×C₆₇	#542	1	1	yes	characteristic
224	C₄×C₆₇	—	2	1	no	—
225	C₄×C₆₇	—	2	1	no	—
226	C₄×C₆₇	—	2	1	no	—
227	C₄×C₆₇	—	4	1	no	—
228	C₄×C₆₇	—	4	1	no	—
229	C₄×C₆₇	—	4	2	no	—
230	C₄×C₆₇	—	4	1	no	—
231	C₄×C₆₇	—	4	2	no	—
232	C₄×C₆₇	#444	1	2	yes	—
233	C₄×C₆₇	#519	1	1	yes	characteristic
234	C₄×C₆₇	#520	1	1	yes	characteristic
235	C₄×C₆₇	#536	1	1	yes	characteristic
236	C₄×C₆₇	#537	1	1	yes	characteristic
237	Dic₆₇	—	8	2	no	—
238	#22131	—	67	1	no	maximal, Sylow
239	C₂×C₆₇	—	2	1	no	—
240	C₂×C₆₇	—	2	1	no	—
241	C₂×C₆₇	—	8	1	no	—
242	C₂×C₆₇	#2323	1	1	yes	characteristic
243	C₂×C₆₇	C₂×#444	1	1	yes	characteristic
244	C₂×C₆₇	#2955	1	1	yes	characteristic
245	#3076	D₆₇	1	1	yes	characteristic
246	#2960	—	67	1	no	—
247	#2922	—	67	1	no	—
248	#1986	—	67	1	no	—
249	#1950	—	67	1	no	—
250	#1946	—	67	2	no	—
251	#1938	—	67	2	no	—
252	#1929	—	67	2	no	—
253	#1922	—	67	2	no	—
254	#1806	—	67	1	no	—
255	#1770	—	67	1	no	—
256	C₆₇	#22131	1	1	yes	characteristic, complemented, Sylow
257	#533	C₂×D₆₇	1	1	yes	characteristic
258	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
259	#479	Dic₆₇	1	2	yes	complemented
260	#478	Dic₆₇	1	2	yes	complemented
261	#477	Dic₆₇	1	1	yes	characteristic, complemented
262	#476	Dic₆₇	1	1	yes	characteristic, complemented
263	#475	Dic₆₇	1	1	yes	characteristic, complemented
264	#474	Dic₆₇	1	1	yes	characteristic, complemented
265	#446	—	134	1	no	—
266	#446	—	134	1	no	—
267	C₈×Q₈	—	134	1	no	—
268	C₈×Q₈	—	134	1	no	—
269	#433	—	134	1	no	—
270	#433	—	134	1	no	—
271	#431	—	134	1	no	—
272	#431	—	134	1	no	—
273	C₂×#108	—	67	2	no	—
274	#427	C₂×D₆₇	1	2	yes	—
275	#424	—	67	1	no	—
276	#424	—	67	1	no	—
277	#424	—	67	2	no	—
278	#423	—	67	1	no	—
279	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
280	C₂×#104	—	67	2	no	—
281	#416	C₂×D₆₇	1	2	yes	—
282	#408	—	67	1	no	—
283	#408	—	67	1	no	—
284	#405	—	67	2	no	—
285	C₄×M₁₆	—	67	1	no	—
286	C₂×#97	—	67	2	no	—
287	C₂×C₄×C₈	—	67	1	no	—
288	C₄×C₄⋊C₄	—	67	1	no	—
289	#341	—	67	2	no	—
290	#339	—	67	2	no	—
291	#339	—	67	2	no	—
292	#339	—	67	2	no	—
293	#336	—	67	2	no	—
294	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
295	C₂×M₁₆	—	67	1	no	—
296	C₂×M₁₆	—	67	1	no	—
297	C₂×M₁₆	—	67	2	no	—
298	C₂²×C₈	—	67	1	no	—
299	C₂²×C₈	—	67	1	no	—
300	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
301	C₄⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
302	C₄⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
303	#125	C₂×Dic₆₇	1	2	yes	—
304	C₂²⋊Q₈	—	2	1	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
309	C₄×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
313	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
314	#117	—	2	1	no	—
315	#117	C₂²×D₆₇	1	1	yes	characteristic
316	#117	C₂²×D₆₇	1	2	yes	—
317	C₂×C₄⋊C₄	—	134	1	no	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	—	67	2	no	—
320	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
321	#108	—	268	2	no	—
322	#107	C₂×Dic₆₇	1	2	yes	—
323	#107	C₂×Dic₆₇	1	2	yes	—
324	#106	C₂×Dic₆₇	1	2	yes	—
325	#106	C₂×Dic₆₇	1	2	yes	—
326	C₄⋊C₈	—	134	1	no	—
327	C₄⋊C₈	—	134	1	no	—
328	C₄⋊C₈	—	134	1	no	—
329	C₄⋊C₈	—	134	1	no	—
330	C₄⋊C₈	—	134	2	no	—
331	C₄⋊C₈	—	134	2	no	—
332	C₄⋊C₈	—	134	1	no	—
333	C₄⋊C₈	—	134	1	no	—
334	C₄⋊C₈	C₂×Dic₆₇	1	1	yes	characteristic
335	C₄⋊C₈	C₂×Dic₆₇	1	1	yes	characteristic
336	C₄⋊C₈	C₂×Dic₆₇	1	2	yes	—
337	#104	—	268	2	no	—
338	#103	C₂×Dic₆₇	1	2	yes	—
339	#103	C₂×Dic₆₇	1	2	yes	—
340	#102	C₂×Dic₆₇	1	2	yes	—
341	#102	C₂×Dic₆₇	1	2	yes	—
342	C₂²⋊C₈	—	134	1	no	—
343	C₂²⋊C₈	—	134	1	no	—
344	C₂²⋊C₈	—	134	1	no	—
345	C₂²⋊C₈	—	134	1	no	—
346	#97	—	268	2	no	—
347	#97	—	134	2	no	—
348	#97	—	134	1	no	—
349	C₄×C₈	—	67	1	no	—
350	C₄×C₈	—	67	1	no	—
351	C₄×C₈	—	67	1	no	—
352	C₄×C₈	—	67	1	no	—
353	C₄×C₈	—	134	2	no	—
354	C₄×C₈	—	134	1	no	—
355	#95	—	134	1	no	—
356	#41	—	2	1	no	—
357	#41	—	2	1	no	—
358	#41	—	2	1	no	—
359	#41	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	C₂²×Dic₆₇	1	1	yes	characteristic
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	134	2	no	—
369	C₂²×C₄	#11761627	1	1	yes	characteristic
370	C₂²×C₄	#11761627	1	1	yes	characteristic
371	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
372	M₁₆	—	134	2	no	—
373	M₁₆	—	134	1	no	—
374	M₁₆	—	134	1	no	—
375	M₁₆	—	134	1	no	—
376	M₁₆	—	134	1	no	—
377	M₁₆	—	134	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	67	1	no	—
381	C₂×C₈	—	67	1	no	—
382	C₂×C₈	—	67	1	no	—
383	C₂×C₈	—	67	1	no	—
384	C₂×C₈	—	134	1	no	—
385	C₂×C₈	—	134	1	no	—
386	C₂×C₈	—	134	2	no	—
387	C₂×C₈	—	134	1	no	—
388	C₂×C₈	—	134	1	no	—
389	C₂×C₈	—	134	1	no	—
390	C₂×C₈	—	134	1	no	—
391	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
392	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	268	2	no	—
400	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
401	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
402	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
403	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	1	no	—
408	C₄²	—	2	1	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	134	2	no	—
413	C₄²	—	134	2	no	—
414	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
415	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
416	C₄²	D₄×D₆₇	1	1	yes	characteristic
417	C₄²	D₄×D₆₇	1	1	yes	characteristic
418	C₂³	—	2	1	no	—
419	C₂³	C₂×#11761627	1	1	yes	characteristic
420	Q₈	—	2	1	no	—
421	Q₈	—	2	1	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	2	no	—
424	D₄	—	2	1	no	—
425	D₄	—	2	1	no	—
426	D₄	—	4	1	no	—
427	D₄	—	4	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	268	2	no	—
440	C₂×C₄	—	268	2	no	—
441	C₂×C₄	—	268	2	no	—
442	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
443	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
444	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
445	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
446	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
447	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
448	C₂×C₄	#14524089	1	1	yes	characteristic
449	C₂×C₄	#14524090	1	1	yes	characteristic
450	C₂×C₄	#14524091	1	1	yes	characteristic
451	C₂×C₄	#14524091	1	1	yes	characteristic
452	C₈	—	2	2	no	—
453	C₈	—	2	2	no	—
454	C₈	—	268	1	no	—
455	C₈	—	268	1	no	—
456	C₈	—	268	2	no	—
457	C₈	—	134	1	no	—
458	C₈	—	134	1	no	—
459	C₈	—	134	1	no	—
460	C₈	—	134	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
467	C₂²	#16864006	1	1	yes	characteristic
468	C₂²	#16864019	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	536	2	no	—
478	C₄	#16863518	1	2	yes	—
479	C₄	#16863874	1	1	yes	characteristic
480	C₄	#16863879	1	1	yes	characteristic
481	C₄	#16863969	1	1	yes	characteristic
482	C₄	#16863976	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	8	1	no	—
486	C₂	#22562893	1	1	yes	characteristic
487	C₂	C₂×#16863518	1	1	yes	characteristic
488	C₂	#22569112	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#3076	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#41×C₆₇	C₂³
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#3076	D₆₇
hypocenter	C₆₇	#22131
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #22569144	C₂	semidirect
3. #22561154	C₂	semidirect
4. #22560985	C₂	semidirect
5. #22560963	C₂	semidirect
8. #22560810	C₂	semidirect
10. #22560079	C₂	semidirect
40. #479×C₆₇	C₄	semidirect
41. #478×C₆₇	C₄	semidirect
42. #477×C₆₇	C₄	semidirect
43. #476×C₆₇	C₄	semidirect
44. #475×C₆₇	C₄	semidirect
45. #474×C₆₇	C₄	semidirect
256. C₆₇	#22131	semidirect
259. #479	Dic₆₇	semidirect
260. #478	Dic₆₇	semidirect
261. #477	Dic₆₇	semidirect
262. #476	Dic₆₇	semidirect
263. #475	Dic₆₇	semidirect
264. #474	Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22569144	2
#22568853	2
#22561154	2
#22560985	2
#22560963	2
#22560922	2
#22560859	2
#22560810	2
#22560229	2
#22560079	2
C₆₇×#3076	2
#22131	67