Subgroups — #30863654

Order 17152.

750 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569997	C₂	1	1	yes	maximal, characteristic
2	#22569139	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14524050	C₂	1	1	yes	maximal, characteristic
4	#22561152	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560982	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560806	C₂	1	2	yes	maximal, complemented
7	#22560482	C₂	1	2	yes	maximal
8	#22560087	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₄×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#22560047	C₂	1	2	yes	maximal
11	C₆₇×#1806	C₂	1	1	yes	maximal, characteristic
12	C₂×#14524050	C₂²	1	1	yes	characteristic
13	C₂×#14524050	C₂²	1	1	yes	characteristic
14	#16863953	C₂²	1	1	yes	characteristic
15	#16863703	C₄	1	2	yes	complemented
16	#16863696	C₄	1	2	yes	complemented
17	#16863691	C₄	1	1	yes	characteristic, complemented
18	#16863686	C₄	1	1	yes	characteristic, complemented
19	#16863681	C₄	1	1	yes	characteristic, complemented
20	#16863676	C₄	1	1	yes	characteristic, complemented
21	#16863523	—	2	1	no	—
22	#16863523	—	2	1	no	—
23	#16863520	—	2	1	no	—
24	#16863520	—	2	1	no	—
25	C₂×#14523978	C₂²	1	2	yes	—
26	#16863432	C₂²	1	2	yes	—
27	#16863424	C₂²	1	2	yes	—
28	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
29	#16863392	C₂²	1	2	yes	—
30	#16863354	C₂²	1	2	yes	—
31	#16863352	—	2	1	no	—
32	#16863352	—	2	1	no	—
33	#16863352	C₂²	1	1	yes	characteristic
34	#16863352	C₂²	1	1	yes	characteristic
35	C₄×#11761612	—	2	1	no	—
36	C₄×#11761612	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₆₇⋊C₈	—	2	1	no	—
38	C₂×C₄×C₆₇⋊C₈	C₂²	1	2	yes	—
39	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
40	#16863160	C₂²	1	2	yes	—
41	#16863156	C₂²	1	2	yes	—
42	#16863156	C₂²	1	2	yes	—
43	#16863151	C₂²	1	2	yes	—
44	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
45	#423×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×#104×C₆₇	C₂²	1	2	yes	—
47	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
48	#339×C₆₇	C₂²	1	2	yes	—
49	#14524050	—	2	2	no	—
50	#14524050	—	2	2	no	—
51	#14524050	—	2	2	no	—
52	#14524050	Q₈	1	4	yes	complemented
53	C₂×#11761612	—	2	1	no	—
54	C₂×#11761612	—	2	1	no	—
55	C₂×#11761612	C₂³	1	1	yes	characteristic
56	C₂×#11761612	C₂³	1	1	yes	characteristic
57	C₂²×C₆₇⋊C₈	—	2	1	no	—
58	C₂²×C₆₇⋊C₈	—	2	1	no	—
59	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
60	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
62	#14524043	C₂×C₄	1	1	yes	characteristic
63	#14524043	C₂×C₄	1	1	yes	characteristic
64	#14524035	C₂×C₄	1	2	yes	—
65	#14524022	—	2	1	no	—
66	#14524022	—	2	1	no	—
67	C₄×Dic₁₃₄	—	2	1	no	—
68	C₄×Dic₁₃₄	—	2	1	no	—
69	#14524002	C₂³	1	2	yes	—
70	#14523978	—	2	4	no	—
71	#14523976	C₂×C₄	1	2	yes	—
72	#14523976	C₂×C₄	1	2	yes	—
73	#14523974	C₂×C₄	1	2	yes	—
74	#14523974	C₂×C₄	1	2	yes	—
75	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
76	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
77	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
78	Dic₆₇⋊C₈	—	2	2	no	—
79	Dic₆₇⋊C₈	—	2	2	no	—
80	#14523967	C₂×C₄	1	2	yes	—
81	#14523967	C₂×C₄	1	2	yes	—
82	#14523964	C₂×C₄	1	2	yes	—
83	#14523964	C₂×C₄	1	2	yes	—
84	#14523954	—	2	1	no	—
85	#14523954	—	2	1	no	—
86	#14523954	—	2	1	no	—
87	#14523953	—	2	2	no	—
88	C₄×C₆₇⋊C₈	—	2	1	no	—
89	C₄×C₆₇⋊C₈	—	2	1	no	—
90	C₄×C₆₇⋊C₈	—	2	4	no	—
91	C₄×C₆₇⋊C₈	—	2	1	no	—
92	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
93	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
94	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
95	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
96	C₈×Dic₆₇	—	2	2	no	—
97	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
98	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
99	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
100	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
101	C₄×D₄×C₆₇	—	2	1	no	—
102	C₄×D₄×C₆₇	—	2	1	no	—
103	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
104	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
105	#117×C₆₇	—	2	1	no	—
106	#117×C₆₇	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
108	C₂×C₄²×C₆₇	—	2	1	no	—
109	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
110	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
111	C₄⋊C₈×C₆₇	—	2	1	no	—
112	C₄⋊C₈×C₆₇	—	2	1	no	—
113	#104×C₆₇	—	2	4	no	—
114	#95×C₆₇	—	2	1	no	—
115	C₂×Dic₁₃₄	—	2	1	no	—
116	C₂×Dic₁₃₄	—	2	1	no	—
117	#11761612	—	2	4	no	—
118	#11761612	—	2	1	no	—
119	#11761612	—	2	1	no	—
120	#11761612	—	2	4	no	—
121	#11761612	C₂×Q₈	1	2	yes	—
122	#11761612	#41	1	2	yes	—
123	C₂×C₆₇⋊C₈	—	2	4	no	—
124	C₂×C₆₇⋊C₈	—	2	1	no	—
125	C₂×C₆₇⋊C₈	—	2	1	no	—
126	C₂×C₆₇⋊C₈	—	2	2	no	—
127	C₂×C₆₇⋊C₈	—	2	2	no	—
128	C₂×C₆₇⋊C₈	—	2	1	no	—
129	C₂×C₆₇⋊C₈	—	2	1	no	—
130	C₂×C₆₇⋊C₈	—	2	4	no	—
131	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
132	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
133	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
134	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
136	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₆₇⋊C₈	C₂×Q₈	1	2	yes	—
138	C₂×C₆₇⋊C₈	#41	1	2	yes	—
139	C₄⋊Dic₆₇	—	2	1	no	—
140	C₄⋊Dic₆₇	—	2	1	no	—
141	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
142	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
143	Dic₆₇⋊C₄	—	2	2	no	—
144	Dic₆₇⋊C₄	—	2	2	no	—
145	C₂²⋊Dic₆₇	—	2	2	no	—
146	C₄×Dic₆₇	—	2	2	no	—
147	#41×C₆₇	—	2	1	no	—
148	#41×C₆₇	—	2	1	no	—
149	#41×C₆₇	C₂×Q₈	1	2	yes	—
150	#41×C₆₇	#41	1	2	yes	—
151	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₄×C₆₇	—	2	1	no	—
153	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₆₇	—	2	1	no	—
155	C₂²×C₄×C₆₇	—	2	2	no	—
156	C₂²×C₄×C₆₇	—	2	1	no	—
157	C₂²×C₄×C₆₇	—	2	1	no	—
158	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
159	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
160	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
161	M₁₆×C₆₇	—	2	2	no	—
162	M₁₆×C₆₇	—	2	2	no	—
163	C₂×C₈×C₆₇	—	2	2	no	—
164	C₄⋊C₄×C₆₇	—	2	4	no	—
165	C₄⋊C₄×C₆₇	—	2	1	no	—
166	C₄⋊C₄×C₆₇	—	2	1	no	—
167	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
168	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²⋊C₄×C₆₇	—	2	1	no	—
170	C₂²⋊C₄×C₆₇	—	2	1	no	—
171	C₂²⋊C₄×C₆₇	—	2	1	no	—
172	C₄²×C₆₇	—	2	1	no	—
173	C₄²×C₆₇	—	2	1	no	—
174	C₄²×C₆₇	—	2	1	no	—
175	C₄²×C₆₇	—	2	2	no	—
176	C₄²×C₆₇	—	2	2	no	—
177	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
181	C₂³×C₆₇	—	2	1	no	—
182	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
183	Q₈×C₆₇	—	2	1	no	—
184	Q₈×C₆₇	C₄×Q₈	1	2	yes	—
185	D₄×C₆₇	—	2	2	no	—
186	D₄×C₆₇	—	2	2	no	—
187	D₄×C₆₇	—	2	1	no	—
188	D₄×C₆₇	C₄×Q₈	1	2	yes	—
189	C₂×C₄×C₆₇	—	2	1	no	—
190	C₂×C₄×C₆₇	—	2	2	no	—
191	C₂×C₄×C₆₇	—	2	2	no	—
192	C₂×C₄×C₆₇	—	2	2	no	—
193	C₂×C₄×C₆₇	—	2	4	no	—
194	C₂×C₄×C₆₇	—	2	1	no	—
195	C₂×C₄×C₆₇	—	2	1	no	—
196	C₂×C₄×C₆₇	—	4	1	no	—
197	C₂×C₄×C₆₇	—	4	2	no	—
198	C₂×C₄×C₆₇	—	4	2	no	—
199	C₂×C₄×C₆₇	—	4	2	no	—
200	C₂×C₄×C₆₇	—	4	2	no	—
201	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
208	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
211	C₂×Dic₆₇	—	2	2	no	—
212	C₂×Dic₆₇	—	2	2	no	—
213	Dic₁₃₄	—	4	2	no	—
214	Dic₁₃₄	—	4	2	no	—
215	C₈×C₆₇	—	4	2	no	—
216	C₆₇⋊C₈	—	2	2	no	—
217	C₆₇⋊C₈	—	2	2	no	—
218	C₆₇⋊C₈	—	2	2	no	—
219	C₆₇⋊C₈	—	2	1	no	—
220	C₆₇⋊C₈	—	2	2	no	—
221	C₆₇⋊C₈	—	2	1	no	—
222	C₆₇⋊C₈	C₂²⋊Q₈	1	2	yes	—
223	C₆₇⋊C₈	C₂²⋊Q₈	1	2	yes	—
224	C₂²×C₆₇	—	2	1	no	—
225	C₂²×C₆₇	—	2	1	no	—
226	C₂²×C₆₇	—	2	2	no	—
227	C₂²×C₆₇	—	4	1	no	—
228	C₂²×C₆₇	—	4	1	no	—
229	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
230	C₂²×C₆₇	#529	1	1	yes	characteristic
231	C₂²×C₆₇	#533	1	1	yes	characteristic
232	C₄×C₆₇	—	2	1	no	—
233	C₄×C₆₇	—	2	1	no	—
234	C₄×C₆₇	—	2	1	no	—
235	C₄×C₆₇	—	2	2	no	—
236	C₄×C₆₇	—	4	4	no	—
237	C₄×C₆₇	—	4	1	no	—
238	C₄×C₆₇	—	4	1	no	—
239	C₄×C₆₇	#443	1	2	yes	—
240	C₄×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
241	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
242	C₄×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
243	C₄×C₆₇	#525	1	1	yes	characteristic
244	Dic₆₇	—	4	2	no	—
245	Dic₆₇	—	4	2	no	—
246	#21627	—	67	1	no	maximal, Sylow
247	C₂×C₆₇	—	2	1	no	—
248	C₂×C₆₇	—	2	1	no	—
249	C₂×C₆₇	—	4	2	no	—
250	C₂×C₆₇	C₄×C₂²⋊Q₈	1	1	yes	characteristic
251	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
252	C₂×C₆₇	#2955	1	1	yes	characteristic
253	#3076	—	67	1	no	—
254	#2960	—	67	1	no	—
255	C₄×#131	—	67	1	no	—
256	#1986	—	67	1	no	—
257	#1950	—	67	1	no	—
258	#1922	—	67	2	no	—
259	#1866	—	67	2	no	—
260	#1806	D₆₇	1	1	yes	characteristic
261	#1772	—	67	2	no	—
262	C₈×C₄⋊C₄	—	67	1	no	—
263	#1764	—	67	2	no	—
264	C₆₇	#21627	1	1	yes	characteristic, complemented, Sylow
265	C₂×#131	—	67	1	no	—
266	C₂×#131	—	67	1	no	—
267	#533	—	67	1	no	—
268	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
269	#479	—	67	2	no	—
270	#478	—	67	2	no	—
271	#477	—	67	1	no	—
272	#476	—	67	1	no	—
273	#475	—	67	1	no	—
274	#474	—	67	1	no	—
275	#446	—	134	1	no	—
276	#446	—	134	1	no	—
277	C₈×Q₈	—	134	1	no	—
278	C₈×Q₈	—	134	1	no	—
279	C₂×#108	—	67	2	no	—
280	#427	—	67	2	no	—
281	#424	—	67	2	no	—
282	#423	C₂×D₆₇	1	1	yes	characteristic
283	C₂×C₄⋊C₈	—	67	1	no	—
284	C₂×#104	C₂×D₆₇	1	2	yes	—
285	#416	—	67	2	no	—
286	#405	—	67	2	no	—
287	#405	—	67	1	no	—
288	#405	—	67	1	no	—
289	#405	—	134	1	no	—
290	#405	—	134	1	no	—
291	C₄×M₁₆	—	67	1	no	—
292	C₄×M₁₆	—	134	1	no	—
293	C₂×C₄×C₈	—	67	1	no	—
294	C₂×C₄×C₈	—	67	2	no	—
295	C₂×C₄×C₈	—	134	1	no	—
296	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
297	#341	—	67	2	no	—
298	#339	—	67	2	no	—
299	#339	—	67	2	no	—
300	#339	C₂×D₆₇	1	2	yes	—
301	#336	—	67	2	no	—
302	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
303	#131	—	67	4	no	—
304	#131	—	134	2	no	—
305	#131	—	134	2	no	—
306	#131	—	134	2	no	—
307	C₂×M₁₆	—	67	1	no	—
308	C₂×M₁₆	—	67	1	no	—
309	C₂×M₁₆	—	134	1	no	—
310	C₂×M₁₆	—	134	1	no	—
311	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
312	C₂²×C₈	—	67	1	no	—
313	C₂²×C₈	—	67	1	no	—
314	C₂²×C₈	—	67	2	no	—
315	C₂²×C₈	—	134	1	no	—
316	C₂²×C₈	—	134	1	no	—
317	C₄⋊Q₈	—	67	1	no	—
318	C₄⋊Q₈	—	67	1	no	—
319	#125	—	67	2	no	—
320	C₂²⋊Q₈	—	134	1	no	—
321	C₂²⋊Q₈	—	134	1	no	—
322	C₄×Q₈	—	134	1	no	—
323	C₄×Q₈	—	134	1	no	—
324	C₄×Q₈	C₄×D₆₇	1	1	yes	characteristic
325	C₄×Q₈	C₄×D₆₇	1	1	yes	characteristic
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	C₄×D₆₇	1	1	yes	characteristic
329	C₄×D₄	C₄×D₆₇	1	1	yes	characteristic
330	#117	—	2	1	no	—
331	#117	—	67	2	no	—
332	#117	C₂²×D₆₇	1	1	yes	characteristic
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
336	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
337	#108	—	134	4	no	—
338	#107	—	67	2	no	—
339	#107	—	67	2	no	—
340	#106	—	67	2	no	—
341	#106	—	67	2	no	—
342	C₄⋊C₈	—	2	1	no	—
343	C₄⋊C₈	—	2	1	no	—
344	C₄⋊C₈	—	67	1	no	—
345	C₄⋊C₈	—	67	1	no	—
346	C₄⋊C₈	—	67	2	no	—
347	C₄⋊C₈	—	134	2	no	—
348	C₄⋊C₈	—	134	2	no	—
349	#104	—	2	4	no	—
350	#103	—	67	2	no	—
351	#103	—	67	2	no	—
352	#102	—	67	2	no	—
353	#102	—	67	2	no	—
354	#97	—	134	1	no	—
355	#97	—	134	1	no	—
356	#97	—	134	2	no	—
357	#97	—	134	1	no	—
358	C₄×C₈	—	67	1	no	—
359	C₄×C₈	—	67	1	no	—
360	C₄×C₈	—	67	1	no	—
361	C₄×C₈	—	67	1	no	—
362	C₄×C₈	—	134	4	no	—
363	C₄×C₈	—	134	1	no	—
364	C₄×C₈	—	134	1	no	—
365	C₄×C₈	—	134	2	no	—
366	C₄×C₈	—	134	1	no	—
367	#95	—	2	1	no	—
368	#41	—	2	1	no	—
369	#41	—	2	1	no	—
370	#41	Q₈×D₆₇	1	2	yes	—
371	#41	#11761627	1	2	yes	—
372	C₂×Q₈	—	134	1	no	—
373	C₂×Q₈	—	134	1	no	—
374	C₂×Q₈	C₂×C₄×D₆₇	1	1	yes	characteristic
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	C₂×C₄×D₆₇	1	1	yes	characteristic
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	#11761627	1	1	yes	characteristic
382	C₂²×C₄	#11761627	1	1	yes	characteristic
383	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
384	M₁₆	—	2	2	no	—
385	M₁₆	—	2	2	no	—
386	M₁₆	—	67	2	no	—
387	M₁₆	—	67	2	no	—
388	M₁₆	—	134	4	no	—
389	M₁₆	—	134	4	no	—
390	M₁₆	—	134	1	no	—
391	M₁₆	—	134	1	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	67	1	no	—
394	C₂×C₈	—	67	1	no	—
395	C₂×C₈	—	67	2	no	—
396	C₂×C₈	—	67	2	no	—
397	C₂×C₈	—	67	2	no	—
398	C₂×C₈	—	67	2	no	—
399	C₂×C₈	—	67	1	no	—
400	C₂×C₈	—	67	1	no	—
401	C₂×C₈	—	134	4	no	—
402	C₂×C₈	—	134	4	no	—
403	C₂×C₈	—	134	1	no	—
404	C₂×C₈	—	134	1	no	—
405	C₂×C₈	—	134	2	no	—
406	C₂×C₈	—	134	2	no	—
407	C₂×C₈	—	134	1	no	—
408	C₂×C₈	—	134	1	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	67	2	no	—
413	C₄⋊C₄	—	67	2	no	—
414	C₄⋊C₄	—	134	2	no	—
415	C₄⋊C₄	—	134	2	no	—
416	C₄⋊C₄	—	134	1	no	—
417	C₄⋊C₄	—	134	1	no	—
418	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
419	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	134	2	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	134	2	no	—
430	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
432	C₄²	D₄×D₆₇	1	1	yes	characteristic
433	C₄²	D₄×D₆₇	1	1	yes	characteristic
434	C₂³	—	2	1	no	—
435	C₂³	C₂×#11761627	1	1	yes	characteristic
436	Q₈	—	2	1	no	—
437	Q₈	—	268	2	no	—
438	Q₈	—	268	2	no	—
439	Q₈	#14524008	1	2	yes	—
440	D₄	—	2	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	1	no	—
443	D₄	#14524008	1	2	yes	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	134	2	no	—
457	C₂×C₄	—	134	2	no	—
458	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
459	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
460	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
461	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
463	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
464	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
465	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
466	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
467	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
468	C₈	—	4	2	no	—
469	C₈	—	67	2	no	—
470	C₈	—	67	2	no	—
471	C₈	—	134	2	no	—
472	C₈	—	134	2	no	—
473	C₈	—	134	2	no	—
474	C₈	—	134	1	no	—
475	C₈	—	134	1	no	—
476	C₈	—	134	2	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	C₂×(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
483	C₂²	#16863927	1	1	yes	characteristic
484	C₂²	#16863948	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	2	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	268	2	no	—
493	C₄	—	268	2	no	—
494	C₄	#16863510	1	2	yes	—
495	C₄	C₂×#14524008	1	1	yes	characteristic
496	C₄	#16863864	1	1	yes	characteristic
497	C₄	C₂²⋊Q₈×D₆₇	1	1	yes	characteristic
498	C₄	#16863906	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	4	2	no	—
502	C₂	#22562737	1	1	yes	characteristic
503	C₂	C₂×#16863510	1	1	yes	characteristic
504	C₂	#22569108	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×#1806	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#41×C₆₇	C₂³
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1806	D₆₇
hypocenter	C₆₇	#21627
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1806

Complements

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

N	H ≅ G/N	type
2. #22569139	C₂	semidirect
4. #22561152	C₂	semidirect
5. #22560982	C₂	semidirect
6. #22560806	C₂	semidirect
8. #22560087	C₂	semidirect
9. C₄⋊C₄×C₆₇⋊C₈	C₂	semidirect
15. #16863703	C₄	semidirect
16. #16863696	C₄	semidirect
17. #16863691	C₄	semidirect
18. #16863686	C₄	semidirect
19. #16863681	C₄	semidirect
20. #16863676	C₄	semidirect
52. #14524050	Q₈	semidirect
264. C₆₇	#21627	semidirect

Maximal subgroups

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

subgroup	index
#22569997	2
#22569139	2
C₄×#14524050	2
#22561152	2
#22560982	2
#22560806	2
#22560482	2
#22560087	2
C₄⋊C₄×C₆₇⋊C₈	2
#22560047	2
C₆₇×#1806	2
#21627	67