Subgroups — #22573875

Order 8576.

1658 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14524089	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#11761629	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864068	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864065	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864057	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864039	C₂	1	3	yes	maximal, complemented
7	#16864037	C₂	1	3	yes	maximal, complemented
8	D₄×D₂₆₈	C₂	1	3	yes	maximal, complemented
9	#16864030	C₂	1	3	yes	maximal, complemented
10	#16863976	C₂	1	3	yes	maximal, complemented
11	#16863964	C₂	1	3	yes	maximal, complemented
12	#16863905	C₂	1	3	yes	maximal, complemented
13	#121×D₆₇	C₂	1	3	yes	maximal, complemented
14	#16863878	C₂	1	1	yes	maximal, characteristic, complemented
15	#548×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	#14524089	—	2	8	no	—
17	C₂×#11761629	—	2	8	no	—
18	C₂×#11761629	C₂²	1	1	yes	characteristic
19	C₂×#11761629	C₂²	1	3	yes	complemented
20	C₂×#11761629	C₂²	1	1	yes	characteristic, complemented
21	C₂×#11761629	C₂²	1	1	yes	characteristic, complemented
22	C₂×#11761629	C₂²	1	3	yes	complemented
23	C₂×#11761628	C₂²	1	3	yes	complemented
24	C₂²×D₂₆₈	C₂²	1	3	yes	complemented
25	C₂²×D₂₆₈	C₂²	1	3	yes	complemented
26	C₂×D₄×D₆₇	C₂²	1	3	yes	complemented
27	C₂×D₄×D₆₇	C₂²	1	3	yes	complemented
28	C₂×D₄×D₆₇	C₂²	1	6	yes	complemented
29	C₂²×C₄×D₆₇	C₂²	1	3	yes	complemented
30	#14524040	C₂²	1	3	yes	complemented
31	#14524039	C₂²	1	3	yes	complemented
32	#14524032	C₂²	1	3	yes	complemented
33	#14524028	C₂²	1	3	yes	complemented
34	#14524025	C₂²	1	3	yes	complemented
35	#14524021	C₂²	1	3	yes	complemented
36	#14524020	C₂²	1	1	yes	characteristic, complemented
37	#14524019	C₂²	1	3	yes	complemented
38	#14524018	C₂²	1	3	yes	complemented
39	#14524018	C₂²	1	6	yes	complemented
40	#14524018	C₂²	1	3	yes	complemented
41	#14524017	C₂²	1	3	yes	complemented
42	#14524017	C₂²	1	3	yes	complemented
43	#14524016	C₂²	1	6	yes	complemented
44	#14524016	C₂²	1	6	yes	complemented
45	#14524016	C₂²	1	3	yes	complemented
46	#14524015	C₂²	1	3	yes	complemented
47	#14524014	C₂²	1	3	yes	complemented
48	#14524013	C₂²	1	6	yes	complemented
49	#14524013	C₂²	1	3	yes	complemented
50	#14524013	C₂²	1	6	yes	complemented
51	#14524011	C₂²	1	3	yes	complemented
52	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
53	C₄×D₂₆₈	C₂²	1	3	yes	complemented
54	C₄×D₂₆₈	C₂²	1	3	yes	complemented
55	#14524005	C₂²	1	3	yes	complemented
56	C₄×C₂²⋊D₆₇	C₂²	1	3	yes	complemented
57	C₄×C₂²⋊D₆₇	C₂²	1	3	yes	complemented
58	#14524000	C₂²	1	3	yes	complemented
59	C₄⋊C₄×D₆₇	C₂²	1	3	yes	complemented
60	C₂²⋊C₄×D₆₇	C₂²	1	6	yes	complemented
61	C₂×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	C₂²×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#124×C₆₇	C₂²	1	3	yes	complemented
64	C₂²⋊Q₈×C₆₇	C₂²	1	3	yes	complemented
65	#121×C₆₇	C₂²	1	3	yes	complemented
66	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	C₄×D₄×C₆₇	C₂²	1	3	yes	complemented
68	C₂³×D₆₇	C₂³	1	3	yes	—
69	C₂³×D₆₇	C₂³	1	6	yes	—
70	#11761629	—	2	4	no	—
71	#11761629	—	2	4	no	—
72	#11761629	—	2	12	no	—
73	#11761629	—	2	12	no	—
74	#11761629	D₄	1	8	yes	complemented
75	#11761628	—	2	12	no	—
76	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
77	C₂×D₂₆₈	—	2	12	no	—
78	C₂×D₂₆₈	—	2	12	no	—
79	C₂×D₂₆₈	C₂³	1	6	yes	—
80	C₂×D₂₆₈	C₂³	1	3	yes	—
81	C₂×D₂₆₈	C₂³	1	3	yes	—
82	C₂×D₂₆₈	C₂³	1	3	yes	—
83	C₂×D₂₆₈	C₂³	1	3	yes	—
84	C₂×D₂₆₈	C₂³	1	6	yes	—
85	C₂×D₂₆₈	C₂³	1	3	yes	—
86	C₂×C₂²⋊D₆₇	C₂³	1	3	yes	—
87	C₂×C₂²⋊D₆₇	C₂³	1	3	yes	—
88	C₂×C₂²⋊D₆₇	C₂³	1	3	yes	—
89	C₂×C₂²⋊D₆₇	C₂³	1	3	yes	—
90	C₂×C₂²⋊D₆₇	C₂³	1	6	yes	—
91	D₄×D₆₇	—	2	12	no	—
92	D₄×D₆₇	—	2	12	no	—
93	D₄×D₆₇	—	4	12	no	—
94	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
95	C₂×C₄×D₆₇	—	2	12	no	—
96	C₂×C₄×D₆₇	C₂³	1	3	yes	—
97	C₂×C₄×D₆₇	C₂³	1	3	yes	—
98	C₂×C₄×D₆₇	C₂³	1	3	yes	—
99	C₂×C₄×D₆₇	C₂³	1	3	yes	—
100	C₂×C₄×D₆₇	C₂³	1	6	yes	—
101	C₂×C₄×D₆₇	C₂³	1	3	yes	—
102	C₄⋊Dic₆₇	C₂³	1	3	yes	—
103	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
104	Dic₆₇⋊C₄	C₂³	1	3	yes	—
105	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
106	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
107	Dic₆₇⋊C₄	C₂³	1	3	yes	—
108	C₂²⋊Dic₆₇	C₂³	1	3	yes	—
109	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
110	(C₂×D₆₇)⋊C₄	C₂³	1	3	yes	—
111	(C₂×D₆₇)⋊C₄	C₂³	1	6	yes	—
112	(C₂×D₆₇)⋊C₄	C₂³	1	3	yes	—
113	(C₂×D₆₇)⋊C₄	C₂³	1	3	yes	—
114	(C₂×D₆₇)⋊C₄	C₂³	1	3	yes	—
115	(C₂×D₆₇)⋊C₄	C₂³	1	3	yes	—
116	(C₂×D₆₇)⋊C₄	C₂³	1	3	yes	—
117	C₄×Dic₆₇	C₂³	1	3	yes	—
118	#41×C₆₇	—	2	4	no	—
119	C₂×Q₈×C₆₇	—	2	4	no	—
120	C₂×Q₈×C₆₇	C₂³	1	3	yes	—
121	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×D₄×C₆₇	C₂³	1	3	yes	—
123	C₂×D₄×C₆₇	C₂³	1	3	yes	—
124	C₂²×C₄×C₆₇	C₂³	1	3	yes	—
125	C₂²×C₄×C₆₇	C₂³	1	3	yes	—
126	C₄⋊C₄×C₆₇	C₂³	1	3	yes	—
127	C₄⋊C₄×C₆₇	C₂³	1	3	yes	—
128	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂²⋊C₄×C₆₇	C₂³	1	3	yes	—
130	C₂²⋊C₄×C₆₇	C₂³	1	6	yes	—
131	C₄²×C₆₇	C₂³	1	3	yes	—
132	C₂³×C₆₇	C₂⁴	1	3	yes	—
133	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
134	C₂²×D₆₇	—	2	6	no	—
135	C₂²×D₆₇	—	2	6	no	—
136	C₂²×D₆₇	—	2	12	no	—
137	C₂²×D₆₇	—	4	3	no	—
138	C₂²×D₆₇	—	4	6	no	—
139	C₂²×D₆₇	—	4	6	no	—
140	C₂²×D₆₇	C₂⁴	1	3	yes	—
141	C₂²×D₆₇	C₂⁴	1	3	yes	—
142	C₂²×D₆₇	C₂⁴	1	3	yes	—
143	Q₈×C₆₇	—	2	6	no	—
144	Q₈×C₆₇	C₂×D₄	1	4	yes	complemented
145	D₄×C₆₇	—	2	6	no	—
146	D₄×C₆₇	—	2	6	no	—
147	C₂×C₄×C₆₇	—	2	6	no	—
148	C₂×C₄×C₆₇	—	2	6	no	—
149	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂⁴	1	3	yes	—
151	C₂×C₄×C₆₇	C₂⁴	1	3	yes	—
152	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂⁴	1	3	yes	—
154	C₂²⋊D₆₇	—	2	6	no	—
155	C₂²⋊D₆₇	—	2	6	no	—
156	C₂²⋊D₆₇	—	2	6	no	—
157	C₂²⋊D₆₇	—	4	6	no	—
158	C₂²⋊D₆₇	—	4	3	no	—
159	C₂×Dic₆₇	—	2	2	no	—
160	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
161	C₂×Dic₆₇	C₂⁴	1	3	yes	—
162	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
163	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
164	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
165	D₂₆₈	—	2	6	no	—
166	D₂₆₈	—	2	12	no	—
167	D₂₆₈	—	2	6	no	—
168	D₂₆₈	—	2	6	no	—
169	D₂₆₈	—	4	6	no	—
170	D₂₆₈	—	4	3	no	—
171	D₂₆₈	C₂×D₄	1	12	yes	complemented
172	C₄×D₆₇	—	2	6	no	—
173	C₄×D₆₇	—	2	6	no	—
174	C₄×D₆₇	—	2	6	no	—
175	C₄×D₆₇	—	2	6	no	—
176	C₄×D₆₇	—	4	6	no	—
177	C₄×D₆₇	C₂×D₄	1	12	yes	complemented
178	Dic₁₃₄	—	2	2	no	—
179	C₂²×C₆₇	—	2	1	no	—
180	C₂²×C₆₇	—	2	1	no	—
181	C₂²×C₆₇	—	2	3	no	—
182	C₂²×C₆₇	—	2	3	no	—
183	C₂²×C₆₇	—	2	3	no	—
184	C₂²×C₆₇	H(5,𝔽₂)	1	2	yes	complemented
185	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
186	C₂×D₆₇	—	2	3	no	—
187	C₂×D₆₇	—	2	3	no	—
188	C₂×D₆₇	—	2	3	no	—
189	C₂×D₆₇	—	2	3	no	—
190	C₂×D₆₇	—	2	3	no	—
191	C₂×D₆₇	—	2	3	no	—
192	C₂×D₆₇	—	2	3	no	—
193	C₂×D₆₇	—	2	3	no	—
194	C₂×D₆₇	—	4	12	no	—
195	C₂×D₆₇	—	8	12	no	—
196	C₂×D₆₇	C₂²×D₄	1	6	yes	—
197	C₄×C₆₇	—	2	1	no	—
198	C₄×C₆₇	—	2	3	no	—
199	C₄×C₆₇	—	2	3	no	—
200	C₄×C₆₇	—	2	1	no	—
201	C₄×C₆₇	C₂²×D₄	1	6	yes	—
202	Dic₆₇	—	2	1	no	—
203	Dic₆₇	—	2	1	no	—
204	Dic₆₇	—	2	3	no	—
205	Dic₆₇	—	2	1	no	—
206	Dic₆₇	C₂²×D₄	1	2	yes	—
207	C₂×C₆₇	—	2	2	no	—
208	C₂×C₆₇	—	4	3	no	—
209	C₂×C₆₇	C₂³×D₄	1	1	yes	characteristic
210	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₆₇	#585	1	1	yes	characteristic
212	D₆₇	—	2	6	no	—
213	D₆₇	—	4	3	no	—
214	D₆₇	—	4	3	no	—
215	#3488	—	67	1	no	maximal, Sylow
216	C₆₇	#3488	1	1	yes	characteristic, complemented, Sylow
217	C₂×H(5,𝔽₂)	—	67	1	no	—
218	C₂²×#41	—	67	1	no	—
219	#550	—	67	1	no	—
220	#550	—	67	1	no	—
221	#548	—	67	1	no	—
222	#548	D₆₇	1	1	yes	characteristic, complemented
223	#546	—	67	3	no	—
224	#546	—	67	3	no	—
225	D₄²	—	67	3	no	—
226	D₄²	—	67	3	no	—
227	#537	—	67	3	no	—
228	#535	—	67	3	no	—
229	#525	—	67	3	no	—
230	C₂×#121	—	67	3	no	—
231	#520	—	67	1	no	—
232	H(5,𝔽₂)	—	134	8	no	—
233	C₂×#41	—	67	1	no	—
234	C₂×#41	—	67	3	no	—
235	C₂×#41	—	67	3	no	—
236	C₂×#41	—	67	1	no	—
237	C₂×#41	—	67	1	no	—
238	C₂×#41	—	67	3	no	—
239	C₂×#41	—	134	8	no	—
240	C₂×#41	C₂×D₆₇	1	1	yes	characteristic, complemented
241	C₂²×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
242	C₂²×D₄	—	67	6	no	—
243	C₂²×D₄	—	67	3	no	—
244	C₂²×D₄	—	67	3	no	—
245	C₂²×D₄	—	67	3	no	—
246	C₂²×D₄	—	67	3	no	—
247	C₂³×C₄	—	67	3	no	—
248	#127	—	67	3	no	—
249	#127	—	67	3	no	—
250	#124	—	67	3	no	—
251	#124	C₂×D₆₇	1	3	yes	complemented
252	#123	—	67	3	no	—
253	#123	—	67	3	no	—
254	C₂²⋊Q₈	—	67	3	no	—
255	C₂²⋊Q₈	—	67	3	no	—
256	C₂²⋊Q₈	—	67	1	no	—
257	C₂²⋊Q₈	C₂×D₆₇	1	3	yes	complemented
258	#121	—	67	3	no	—
259	#121	—	67	3	no	—
260	#121	—	67	3	no	—
261	#121	—	67	3	no	—
262	#121	—	67	3	no	—
263	#121	—	67	6	no	—
264	#121	—	67	3	no	—
265	#121	—	67	6	no	—
266	#121	—	67	3	no	—
267	#121	—	67	6	no	—
268	#121	C₂×D₆₇	1	3	yes	complemented
269	#120	—	67	3	no	—
270	#120	—	67	3	no	—
271	#120	—	67	6	no	—
272	#120	—	67	6	no	—
273	C₄×Q₈	—	67	1	no	—
274	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
275	C₄×D₄	—	67	3	no	—
276	C₄×D₄	—	67	3	no	—
277	C₄×D₄	—	67	3	no	—
278	C₄×D₄	—	67	3	no	—
279	C₄×D₄	—	67	3	no	—
280	C₄×D₄	C₂×D₆₇	1	3	yes	complemented
281	#117	—	67	3	no	—
282	C₂×C₄⋊C₄	—	67	3	no	—
283	C₂×C₂²⋊C₄	—	67	6	no	—
284	C₂⁴	—	67	6	no	—
285	C₂⁴	—	67	3	no	—
286	#41	—	2	4	no	—
287	#41	—	67	8	no	—
288	#41	—	134	12	no	—
289	#41	—	134	12	no	—
290	#41	—	134	12	no	—
291	#41	—	134	4	no	—
292	#41	—	134	4	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	67	1	no	—
295	C₂×Q₈	C₂²×D₆₇	1	3	yes	—
296	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
297	C₂×D₄	—	268	12	no	—
298	C₂×D₄	—	67	3	no	—
299	C₂×D₄	—	67	6	no	—
300	C₂×D₄	—	67	3	no	—
301	C₂×D₄	—	67	3	no	—
302	C₂×D₄	—	67	3	no	—
303	C₂×D₄	—	67	3	no	—
304	C₂×D₄	—	67	6	no	—
305	C₂×D₄	—	67	3	no	—
306	C₂×D₄	—	67	6	no	—
307	C₂×D₄	—	67	3	no	—
308	C₂×D₄	—	67	3	no	—
309	C₂×D₄	—	67	3	no	—
310	C₂×D₄	—	134	12	no	—
311	C₂×D₄	—	134	12	no	—
312	C₂×D₄	—	134	12	no	—
313	C₂×D₄	—	134	12	no	—
314	C₂×D₄	C₂²×D₆₇	1	3	yes	—
315	C₂×D₄	C₂²×D₆₇	1	3	yes	—
316	C₂²×C₄	—	67	6	no	—
317	C₂²×C₄	—	67	3	no	—
318	C₂²×C₄	—	67	1	no	—
319	C₂²×C₄	—	67	3	no	—
320	C₂²×C₄	—	67	3	no	—
321	C₂²×C₄	—	67	3	no	—
322	C₂²×C₄	—	67	3	no	—
323	C₂²×C₄	—	134	12	no	—
324	C₂²×C₄	C₂²×D₆₇	1	3	yes	—
325	C₂²×C₄	C₂²×D₆₇	1	3	yes	—
326	C₄⋊C₄	—	67	3	no	—
327	C₄⋊C₄	—	67	3	no	—
328	C₄⋊C₄	—	67	1	no	—
329	C₄⋊C₄	—	67	1	no	—
330	C₄⋊C₄	—	67	1	no	—
331	C₄⋊C₄	—	67	3	no	—
332	C₄⋊C₄	C₂²×D₆₇	1	3	yes	—
333	C₄⋊C₄	C₂²×D₆₇	1	3	yes	—
334	C₂²⋊C₄	—	67	3	no	—
335	C₂²⋊C₄	—	67	1	no	—
336	C₂²⋊C₄	—	67	3	no	—
337	C₂²⋊C₄	—	67	6	no	—
338	C₂²⋊C₄	—	67	3	no	—
339	C₂²⋊C₄	—	67	3	no	—
340	C₂²⋊C₄	—	67	3	no	—
341	C₂²⋊C₄	—	67	3	no	—
342	C₂²⋊C₄	—	67	3	no	—
343	C₂²⋊C₄	C₂²×D₆₇	1	6	yes	—
344	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
345	C₂²⋊C₄	C₂²×D₆₇	1	3	yes	—
346	C₄²	—	67	3	no	—
347	C₄²	C₂²×D₆₇	1	3	yes	—
348	C₂³	—	268	3	no	—
349	C₂³	—	268	6	no	—
350	C₂³	—	268	6	no	—
351	C₂³	—	67	3	no	—
352	C₂³	—	67	3	no	—
353	C₂³	—	67	3	no	—
354	C₂³	—	134	6	no	—
355	C₂³	—	134	12	no	—
356	C₂³	—	134	6	no	—
357	C₂³	C₂³×D₆₇	1	3	yes	—
358	C₂³	C₂³×D₆₇	1	1	yes	characteristic
359	Q₈	—	2	6	no	—
360	Q₈	—	134	2	no	—
361	Q₈	D₄×D₆₇	1	4	yes	complemented
362	D₄	—	2	6	no	—
363	D₄	—	2	6	no	—
364	D₄	—	268	6	no	—
365	D₄	—	268	3	no	—
366	D₄	—	268	6	no	—
367	D₄	—	268	3	no	—
368	D₄	—	67	12	no	—
369	D₄	—	134	6	no	—
370	D₄	—	134	12	no	—
371	D₄	—	134	6	no	—
372	D₄	—	134	6	no	—
373	D₄	—	134	6	no	—
374	D₄	—	134	6	no	—
375	D₄	—	134	6	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	2	6	no	—
378	C₂×C₄	—	268	6	no	—
379	C₂×C₄	—	67	1	no	—
380	C₂×C₄	—	67	12	no	—
381	C₂×C₄	—	67	1	no	—
382	C₂×C₄	—	67	3	no	—
383	C₂×C₄	—	67	1	no	—
384	C₂×C₄	—	67	1	no	—
385	C₂×C₄	—	134	6	no	—
386	C₂×C₄	—	134	6	no	—
387	C₂×C₄	—	134	2	no	—
388	C₂×C₄	—	134	6	no	—
389	C₂×C₄	—	134	6	no	—
390	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₆₇	1	3	yes	—
392	C₂×C₄	C₂³×D₆₇	1	3	yes	—
393	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₆₇	1	3	yes	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	3	no	—
398	C₂²	—	2	3	no	—
399	C₂²	—	2	3	no	—
400	C₂²	—	268	12	no	—
401	C₂²	—	536	12	no	—
402	C₂²	—	67	6	no	—
403	C₂²	—	134	3	no	—
404	C₂²	—	134	3	no	—
405	C₂²	—	134	3	no	—
406	C₂²	—	134	3	no	—
407	C₂²	—	134	3	no	—
408	C₂²	—	134	3	no	—
409	C₂²	—	134	3	no	—
410	C₂²	—	134	3	no	—
411	C₂²	#14524089	1	2	yes	complemented
412	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	3	no	—
415	C₄	—	2	3	no	—
416	C₄	—	2	1	no	—
417	C₄	—	67	2	no	—
418	C₄	—	134	1	no	—
419	C₄	—	134	1	no	—
420	C₄	—	134	3	no	—
421	C₄	—	134	1	no	—
422	C₄	C₂×D₄×D₆₇	1	6	yes	—
423	C₂	—	2	2	no	—
424	C₂	—	4	3	no	—
425	C₂	—	268	3	no	—
426	C₂	—	268	3	no	—
427	C₂	—	134	6	no	—
428	C₂	C₂²×D₄×D₆₇	1	1	yes	characteristic
429	C₂	C₂×#14524089	1	1	yes	characteristic
430	C₂	#16864233	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#548×C₆₇	C₂
hypercenter	#548	D₆₇
hypocenter	C₆₇	#3488
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. C₂×#14524089	C₂	semidirect
2. C₂²×#11761629	C₂	semidirect
3. #16864068	C₂	semidirect
4. #16864065	C₂	semidirect
5. #16864057	C₂	semidirect
6. #16864039	C₂	semidirect
7. #16864037	C₂	semidirect
8. D₄×D₂₆₈	C₂	semidirect
9. #16864030	C₂	semidirect
10. #16863976	C₂	semidirect
11. #16863964	C₂	semidirect
12. #16863905	C₂	semidirect
13. #121×D₆₇	C₂	semidirect
14. #16863878	C₂	semidirect
15. #548×C₆₇	C₂	semidirect
19. C₂×#11761629	C₂²	semidirect
20. C₂×#11761629	C₂²	semidirect
21. C₂×#11761629	C₂²	semidirect
22. C₂×#11761629	C₂²	semidirect
23. C₂×#11761628	C₂²	semidirect
24. C₂²×D₂₆₈	C₂²	semidirect
25. C₂²×D₂₆₈	C₂²	semidirect
26. C₂×D₄×D₆₇	C₂²	semidirect
27. C₂×D₄×D₆₇	C₂²	semidirect
28. C₂×D₄×D₆₇	C₂²	semidirect
29. C₂²×C₄×D₆₇	C₂²	semidirect
30. #14524040	C₂²	semidirect
31. #14524039	C₂²	semidirect
32. #14524032	C₂²	semidirect
33. #14524028	C₂²	semidirect
34. #14524025	C₂²	semidirect
35. #14524021	C₂²	semidirect
36. #14524020	C₂²	semidirect
37. #14524019	C₂²	semidirect
38. #14524018	C₂²	semidirect
39. #14524018	C₂²	semidirect
40. #14524018	C₂²	semidirect
41. #14524017	C₂²	semidirect
42. #14524017	C₂²	semidirect
43. #14524016	C₂²	semidirect
44. #14524016	C₂²	semidirect
45. #14524016	C₂²	semidirect
46. #14524015	C₂²	semidirect
47. #14524014	C₂²	semidirect
48. #14524013	C₂²	semidirect
49. #14524013	C₂²	semidirect
50. #14524013	C₂²	semidirect
51. #14524011	C₂²	semidirect
52. Q₈×Dic₆₇	C₂²	semidirect
53. C₄×D₂₆₈	C₂²	semidirect
54. C₄×D₂₆₈	C₂²	semidirect
55. #14524005	C₂²	semidirect
56. C₄×C₂²⋊D₆₇	C₂²	semidirect
57. C₄×C₂²⋊D₆₇	C₂²	semidirect
58. #14524000	C₂²	semidirect
59. C₄⋊C₄×D₆₇	C₂²	semidirect
60. C₂²⋊C₄×D₆₇	C₂²	semidirect
61. C₂×#41×C₆₇	C₂²	semidirect
62. C₂²×Q₈×C₆₇	C₂²	semidirect
63. #124×C₆₇	C₂²	semidirect
64. C₂²⋊Q₈×C₆₇	C₂²	semidirect
65. #121×C₆₇	C₂²	semidirect
66. C₄×Q₈×C₆₇	C₂²	semidirect
67. C₄×D₄×C₆₇	C₂²	semidirect
74. #11761629	D₄	semidirect
144. Q₈×C₆₇	C₂×D₄	semidirect
171. D₂₆₈	C₂×D₄	semidirect
177. C₄×D₆₇	C₂×D₄	semidirect
184. C₂²×C₆₇	H(5,𝔽₂)	semidirect
216. C₆₇	#3488	semidirect
222. #548	D₆₇	semidirect
240. C₂×#41	C₂×D₆₇	semidirect
241. C₂²×Q₈	C₂×D₆₇	semidirect
251. #124	C₂×D₆₇	semidirect
257. C₂²⋊Q₈	C₂×D₆₇	semidirect
268. #121	C₂×D₆₇	semidirect
274. C₄×Q₈	C₂×D₆₇	semidirect
280. C₄×D₄	C₂×D₆₇	semidirect
361. Q₈	D₄×D₆₇	semidirect
411. C₂²	#14524089	semidirect