Subgroups — #30838542

Order 17152.

704 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570788	C₂	1	1	yes	maximal, characteristic, complemented
2	#22569666	C₂	1	2	yes	maximal, complemented
3	#22569175	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559778	C₂	1	2	yes	maximal, complemented
5	#22559771	C₂	1	2	yes	maximal, complemented
6	#22559728	C₂	1	1	yes	maximal, characteristic, complemented
7	#22559723	C₂	1	1	yes	maximal, characteristic, complemented
8	#22559694	C₂	1	1	yes	maximal, characteristic, complemented
9	#22559689	C₂	1	1	yes	maximal, characteristic, complemented
10	#22558859	C₂	1	2	yes	maximal, complemented
11	C₂×#334×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524065	—	2	2	no	—
13	#16863946	C₂²	1	2	yes	—
14	C₄×#11761628	C₂²	1	1	yes	characteristic
15	#16863801	C₂²	1	1	yes	characteristic
16	#16863773	C₂²	1	1	yes	characteristic
17	#16863743	C₂²	1	2	yes	—
18	#16863632	—	2	1	no	—
19	#16863632	—	2	1	no	—
20	#16863619	—	2	2	no	—
21	#16863612	—	2	2	no	—
22	#16863607	C₂²	1	2	yes	—
23	#16863602	C₂²	1	2	yes	—
24	#16863597	C₂²	1	2	yes	—
25	#16863592	C₂²	1	2	yes	—
26	#16863526	C₂²	1	1	yes	characteristic
27	#16863526	C₂²	1	1	yes	characteristic
28	C₄×D₅₃₆	—	2	1	no	—
29	C₄×D₅₃₆	—	2	1	no	—
30	#16863475	C₂²	1	1	yes	characteristic
31	#16863475	C₂²	1	1	yes	characteristic
32	#16863467	—	2	1	no	—
33	#16863467	—	2	1	no	—
34	#16863449	C₂²	1	1	yes	characteristic
35	#16863447	—	2	1	no	—
36	#16863393	—	2	2	no	—
37	C₄×#11761611	—	2	1	no	—
38	#16863143	C₂²	1	2	yes	—
39	#16863143	C₂²	1	2	yes	—
40	#16863139	C₂²	1	2	yes	—
41	#16863139	C₂²	1	2	yes	—
42	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
44	#334×C₆₇	C₂²	1	2	yes	—
45	#334×C₆₇	C₂²	1	1	yes	characteristic
46	#334×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#11761628	—	2	2	no	—
48	C₂×#11761628	D₄	1	1	yes	characteristic
49	#14524065	—	4	8	no	—
50	C₂×Dic₂₆₈	—	2	2	no	—
51	C₂×#11761617	—	2	2	no	—
52	C₂×#11761617	—	2	2	no	—
53	C₂×D₅₃₆	—	2	2	no	—
54	C₂×D₅₃₆	—	2	1	no	—
55	C₂×D₅₃₆	—	2	1	no	—
56	C₂×#11761611	—	2	1	no	—
57	C₂×#11761611	—	2	1	no	—
58	#14524043	C₂³	1	2	yes	—
59	#14524040	C₂³	1	2	yes	—
60	#14524031	—	2	2	no	—
61	#14524017	—	2	2	no	—
62	#14524017	—	2	2	no	—
63	C₄×Dic₁₃₄	D₄	1	1	yes	characteristic
64	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
65	C₄×D₂₆₈	—	2	2	no	—
66	C₄×D₂₆₈	—	2	2	no	—
67	C₄×D₂₆₈	D₄	1	1	yes	characteristic
68	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
69	C₄×C₂²⋊D₆₇	—	2	1	no	—
70	C₄×C₂²⋊D₆₇	—	2	1	no	—
71	#14524002	D₄	1	1	yes	characteristic
72	#14524000	—	2	1	no	—
73	C₄²×D₆₇	—	2	1	no	—
74	#14523977	—	2	1	no	—
75	#14523977	—	2	1	no	—
76	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
77	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
78	Dic₆₇⋊C₈	—	2	1	no	—
79	Dic₆₇⋊C₈	—	2	1	no	—
80	#14523968	—	2	2	no	—
81	#14523968	—	2	2	no	—
82	#14523965	—	2	2	no	—
83	#14523965	—	2	2	no	—
84	#14523965	—	2	2	no	—
85	#14523965	—	2	2	no	—
86	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
87	(C₂×D₆₇)⋊C₈	—	2	1	no	—
88	(C₂×D₆₇)⋊C₈	—	2	1	no	—
89	#14523953	—	2	1	no	—
90	#14523953	—	2	1	no	—
91	C₄×C₆₇⋊C₈	—	2	1	no	—
92	C₂²×C₈×C₆₇	—	2	2	no	—
93	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
94	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₆₇	—	2	2	no	—
97	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
98	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
99	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
101	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
103	#11761628	—	2	4	no	—
104	#11761628	—	4	4	no	—
105	#11761628	—	4	4	no	—
106	C₂×Dic₁₃₄	—	2	2	no	—
107	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
108	C₂×D₂₆₈	—	2	2	no	—
109	C₂×D₂₆₈	—	2	2	no	—
110	C₂×D₂₆₈	—	2	2	no	—
111	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
112	C₂×C₂²⋊D₆₇	—	2	1	no	—
113	C₂×C₂²⋊D₆₇	—	4	2	no	—
114	C₂×C₄×D₆₇	—	2	1	no	—
115	C₂×C₄×D₆₇	—	2	1	no	—
116	C₂×C₄×D₆₇	—	2	1	no	—
117	C₂×C₄×D₆₇	—	4	2	no	—
118	Dic₂₆₈	—	4	4	no	—
119	#11761617	—	4	4	no	—
120	#11761617	—	4	4	no	—
121	D₅₃₆	—	4	2	no	—
122	D₅₃₆	—	4	4	no	—
123	D₅₃₆	—	4	2	no	—
124	#11761611	—	4	2	no	—
125	#11761611	—	4	2	no	—
126	C₂×C₆₇⋊C₈	—	2	1	no	—
127	C₂×C₆₇⋊C₈	—	2	1	no	—
128	C₄⋊Dic₆₇	—	2	2	no	—
129	C₄⋊Dic₆₇	—	2	2	no	—
130	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
131	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
132	Dic₆₇⋊C₄	—	2	1	no	—
133	Dic₆₇⋊C₄	—	2	1	no	—
134	C₂²⋊Dic₆₇	—	2	1	no	—
135	(C₂×D₆₇)⋊C₄	—	2	1	no	—
136	(C₂×D₆₇)⋊C₄	—	2	1	no	—
137	(C₂×D₆₇)⋊C₄	—	4	2	no	—
138	(C₂×D₆₇)⋊C₄	—	4	2	no	—
139	C₄×Dic₆₇	—	2	1	no	—
140	C₄×Dic₆₇	—	2	1	no	—
141	C₄×Dic₆₇	—	2	1	no	—
142	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
145	C₂×C₈×C₆₇	—	2	2	no	—
146	C₂×C₈×C₆₇	—	2	2	no	—
147	C₂×C₈×C₆₇	—	2	2	no	—
148	C₂×C₈×C₆₇	—	4	1	no	—
149	C₂×C₈×C₆₇	—	4	4	no	—
150	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₆₇	#41	1	1	yes	characteristic
157	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
158	C₂³×C₆₇	#121	1	1	yes	characteristic
159	C₂²×D₆₇	—	2	1	no	—
160	C₂²×D₆₇	—	4	2	no	—
161	C₂×C₄×C₆₇	—	2	1	no	—
162	C₂×C₄×C₆₇	—	2	1	no	—
163	C₂×C₄×C₆₇	—	4	1	no	—
164	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
165	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
167	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	4	yes	—
168	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
171	C₂²⋊D₆₇	—	4	2	no	—
172	C₂²⋊D₆₇	—	8	4	no	—
173	C₂×Dic₆₇	—	2	1	no	—
174	C₂×Dic₆₇	—	2	1	no	—
175	C₂×Dic₆₇	—	2	1	no	—
176	C₂×Dic₆₇	—	4	2	no	—
177	D₂₆₈	—	2	2	no	—
178	D₂₆₈	—	4	2	no	—
179	D₂₆₈	—	4	2	no	—
180	D₂₆₈	—	4	2	no	—
181	D₂₆₈	—	4	2	no	—
182	D₂₆₈	—	8	2	no	—
183	C₄×D₆₇	—	4	2	no	—
184	C₄×D₆₇	—	4	1	no	—
185	C₄×D₆₇	—	4	1	no	—
186	C₄×D₆₇	—	4	2	no	—
187	C₄×D₆₇	—	8	4	no	—
188	Dic₁₃₄	—	2	2	no	—
189	Dic₁₃₄	—	4	2	no	—
190	Dic₁₃₄	—	4	2	no	—
191	C₈×C₆₇	—	2	1	no	—
192	C₈×C₆₇	—	2	1	no	—
193	C₈×C₆₇	—	2	1	no	—
194	C₈×C₆₇	—	4	2	no	—
195	C₈×C₆₇	—	4	2	no	—
196	C₈×C₆₇	#135	1	2	yes	complemented
197	C₆₇⋊C₈	—	4	1	no	—
198	C₆₇⋊C₈	—	4	1	no	—
199	C₂²×C₆₇	—	2	1	no	—
200	C₂²×C₆₇	—	2	1	no	—
201	C₂²×C₆₇	#469	1	2	yes	—
202	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
203	C₂×D₆₇	—	4	1	no	—
204	C₂×D₆₇	—	4	1	no	—
205	C₂×D₆₇	—	4	1	no	—
206	C₂×D₆₇	—	8	2	no	—
207	C₂×D₆₇	—	8	2	no	—
208	C₂×D₆₇	—	8	2	no	—
209	C₄×C₆₇	—	2	1	no	—
210	C₄×C₆₇	—	2	1	no	—
211	C₄×C₆₇	—	2	1	no	—
212	C₄×C₆₇	#469	1	2	yes	—
213	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
214	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
215	C₄×C₆₇	#575	1	1	yes	characteristic
216	Dic₆₇	—	4	1	no	—
217	Dic₆₇	—	4	1	no	—
218	Dic₆₇	—	4	1	no	—
219	Dic₆₇	—	8	2	no	—
220	#19157	—	67	1	no	maximal, Sylow
221	C₂×C₆₇	—	2	2	no	—
222	C₂×C₆₇	#3035	1	1	yes	characteristic
223	C₂×C₆₇	C₂×#469	1	1	yes	characteristic
224	C₂×C₆₇	#3067	1	1	yes	characteristic
225	D₆₇	—	8	1	no	—
226	D₆₇	—	16	2	no	—
227	#3169	—	67	1	no	—
228	#3035	—	67	2	no	—
229	#2965	—	67	1	no	—
230	#1702	—	67	2	no	—
231	#1701	—	67	2	no	—
232	#1694	—	67	1	no	—
233	#1693	—	67	1	no	—
234	#1688	—	67	1	no	—
235	#1687	—	67	1	no	—
236	C₂×#334	D₆₇	1	1	yes	characteristic, complemented
237	#1540	—	67	2	no	—
238	C₆₇	#19157	1	1	yes	characteristic, complemented, Sylow
239	C₂×#135	—	134	2	no	—
240	#532	—	67	2	no	—
241	C₄×#41	—	67	1	no	—
242	#500	—	67	1	no	—
243	#493	—	67	1	no	—
244	#486	—	67	2	no	—
245	#466	—	134	1	no	—
246	#466	—	134	1	no	—
247	#464	—	134	2	no	—
248	#463	—	134	2	no	—
249	#462	—	67	2	no	—
250	#461	—	67	2	no	—
251	#460	—	67	2	no	—
252	#459	—	67	2	no	—
253	#446	—	67	1	no	—
254	#446	—	67	1	no	—
255	C₄×D₈	—	134	1	no	—
256	C₄×D₈	—	134	1	no	—
257	#436	—	67	1	no	—
258	#436	—	67	1	no	—
259	#435	—	134	1	no	—
260	#435	—	134	1	no	—
261	#431	—	67	1	no	—
262	#431	—	134	1	no	—
263	C₂×C₄⋊C₈	C₂×D₆₇	1	2	yes	—
264	#416	—	134	2	no	—
265	C₄×M₁₆	—	134	1	no	—
266	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
267	#334	C₂×D₆₇	1	1	yes	characteristic
268	#334	C₂×D₆₇	1	1	yes	characteristic
269	#334	C₂×D₆₇	1	2	yes	—
270	#332	—	67	2	no	—
271	#332	—	67	2	no	—
272	#331	—	67	2	no	—
273	#331	—	67	2	no	—
274	C₂×#41	—	67	1	no	—
275	C₂×#41	—	134	2	no	—
276	#135	—	268	8	no	—
277	C₂×Q₁₆	—	134	2	no	—
278	C₂×SD₁₆	—	134	2	no	—
279	C₂×SD₁₆	—	134	2	no	—
280	C₂×D₈	—	134	2	no	—
281	C₂×D₈	—	134	1	no	—
282	C₂×D₈	—	134	1	no	—
283	C₂×M₁₆	—	134	1	no	—
284	C₂×M₁₆	—	134	1	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
287	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
288	C₄⋊Q₈	—	67	2	no	—
289	#127	—	67	2	no	—
290	#124	—	134	2	no	—
291	#121	—	134	2	no	—
292	#121	—	134	2	no	—
293	C₄×Q₈	—	67	1	no	—
294	C₄×Q₈	—	67	1	no	—
295	C₄×D₄	—	67	1	no	—
296	C₄×D₄	—	67	1	no	—
297	C₄×D₄	—	134	1	no	—
298	C₄×D₄	—	134	1	no	—
299	C₄×D₄	—	134	2	no	—
300	C₄×D₄	—	134	2	no	—
301	#117	—	67	1	no	—
302	#117	—	134	1	no	—
303	C₂×C₄²	—	134	1	no	—
304	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
305	#107	—	134	1	no	—
306	#107	—	134	1	no	—
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	—	67	1	no	—
309	C₄⋊C₈	—	67	1	no	—
310	C₄⋊C₈	—	134	1	no	—
311	C₄⋊C₈	—	134	1	no	—
312	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
313	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
314	#103	—	134	2	no	—
315	#103	—	134	2	no	—
316	#102	—	134	2	no	—
317	#102	—	134	2	no	—
318	#102	—	134	2	no	—
319	#102	—	134	2	no	—
320	C₂²⋊C₈	—	134	1	no	—
321	C₂²⋊C₈	—	134	1	no	—
322	C₂²⋊C₈	—	134	1	no	—
323	#97	—	134	1	no	—
324	#97	—	134	1	no	—
325	C₄×C₈	—	134	1	no	—
326	C₄×C₈	D₂₆₈	1	1	yes	characteristic
327	C₄×C₈	D₂₆₈	1	1	yes	characteristic
328	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
330	#41	—	268	4	no	—
331	#41	—	268	4	no	—
332	#41	—	134	4	no	—
333	C₂×Q₈	—	67	1	no	—
334	C₂×Q₈	—	134	2	no	—
335	C₂×D₄	—	268	2	no	—
336	C₂×D₄	—	67	1	no	—
337	C₂×D₄	—	134	1	no	—
338	C₂×D₄	—	134	2	no	—
339	C₂×D₄	—	134	2	no	—
340	C₂×D₄	—	134	2	no	—
341	C₂²×C₄	—	268	2	no	—
342	C₂²×C₄	—	134	1	no	—
343	C₂²×C₄	—	134	1	no	—
344	C₂²×C₄	—	134	1	no	—
345	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
347	C₂²×C₄	#11761629	1	1	yes	characteristic
348	Q₁₆	—	268	4	no	—
349	SD₁₆	—	268	4	no	—
350	SD₁₆	—	268	4	no	—
351	D₈	—	268	2	no	—
352	D₈	—	268	4	no	—
353	D₈	—	268	2	no	—
354	M₁₆	—	268	2	no	—
355	M₁₆	—	268	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	4	4	no	—
361	C₂×C₈	—	134	1	no	—
362	C₂×C₈	—	134	1	no	—
363	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
364	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
365	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
366	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
367	C₄⋊C₄	—	67	1	no	—
368	C₄⋊C₄	—	67	1	no	—
369	C₄⋊C₄	—	134	2	no	—
370	C₄⋊C₄	—	134	2	no	—
371	C₄⋊C₄	—	134	1	no	—
372	C₄⋊C₄	—	134	1	no	—
373	C₂²⋊C₄	—	268	2	no	—
374	C₂²⋊C₄	—	268	2	no	—
375	C₂²⋊C₄	—	134	1	no	—
376	C₂²⋊C₄	—	134	1	no	—
377	C₂²⋊C₄	—	134	1	no	—
378	C₄²	—	134	1	no	—
379	C₄²	—	134	1	no	—
380	C₄²	—	134	1	no	—
381	C₄²	D₄×D₆₇	1	1	yes	characteristic
382	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
383	C₄²	#11761629	1	1	yes	characteristic
384	C₄²	C₂³×D₆₇	1	1	yes	characteristic
385	C₂³	—	268	2	no	—
386	C₂³	—	134	1	no	—
387	C₂³	#14524018	1	1	yes	characteristic
388	Q₈	—	268	2	no	—
389	Q₈	—	268	2	no	—
390	Q₈	—	134	2	no	—
391	D₄	—	268	2	no	—
392	D₄	—	268	2	no	—
393	D₄	—	268	2	no	—
394	D₄	—	268	2	no	—
395	D₄	—	268	2	no	—
396	D₄	—	536	2	no	—
397	D₄	—	536	4	no	—
398	D₄	—	134	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	268	2	no	—
403	C₂×C₄	—	268	2	no	—
404	C₂×C₄	—	268	1	no	—
405	C₂×C₄	—	268	1	no	—
406	C₂×C₄	—	268	2	no	—
407	C₂×C₄	—	536	4	no	—
408	C₂×C₄	—	134	1	no	—
409	C₂×C₄	—	134	1	no	—
410	C₂×C₄	—	134	1	no	—
411	C₂×C₄	#14524018	1	1	yes	characteristic
412	C₂×C₄	#14524018	1	1	yes	characteristic
413	C₂×C₄	#14524018	1	1	yes	characteristic
414	C₂×C₄	#14524070	1	4	yes	—
415	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
417	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	2	no	—
423	C₈	—	268	1	no	—
424	C₈	—	268	1	no	—
425	C₈	#14524065	1	2	yes	complemented
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	268	1	no	—
429	C₂²	—	268	1	no	—
430	C₂²	—	268	1	no	—
431	C₂²	—	536	2	no	—
432	C₂²	—	536	2	no	—
433	C₂²	—	536	2	no	—
434	C₂²	#16863650	1	2	yes	—
435	C₂²	C₂×#14524018	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	268	1	no	—
440	C₄	—	268	1	no	—
441	C₄	—	268	1	no	—
442	C₄	—	536	2	no	—
443	C₄	#16863650	1	2	yes	—
444	C₄	C₂×#14524065	1	1	yes	characteristic
445	C₄	C₂×#14524070	1	2	yes	—
446	C₄	#16864196	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	536	1	no	—
449	C₂	—	1072	2	no	—
450	C₂	#22569666	1	1	yes	characteristic
451	C₂	C₂×#16863650	1	1	yes	characteristic
452	C₂	#22569930	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14524018
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₂×#334×C₆₇	C₂
socle	C₂²×C₆₇	C₂×#121
hypercenter	C₂×#334	D₆₇
hypocenter	C₆₇	#19157
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
1. #22570788	C₂	semidirect
2. #22569666	C₂	semidirect
3. #22569175	C₂	semidirect
4. #22559778	C₂	semidirect
5. #22559771	C₂	semidirect
6. #22559728	C₂	semidirect
7. #22559723	C₂	semidirect
8. #22559694	C₂	semidirect
9. #22559689	C₂	semidirect
10. #22558859	C₂	semidirect
11. C₂×#334×C₆₇	C₂	semidirect
196. C₈×C₆₇	#135	semidirect
236. C₂×#334	D₆₇	semidirect
238. C₆₇	#19157	semidirect
425. C₈	#14524065	semidirect

Maximal subgroups

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

subgroup	index
#22570788	2
#22569666	2
#22569175	2
#22559778	2
#22559771	2
#22559728	2
#22559723	2
#22559694	2
#22559689	2
#22558859	2
C₂×#334×C₆₇	2
#19157	67