Subgroups — #22574486

Order 8576.

1058 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864138	C₂	1	2	yes	maximal, complemented
2	#16864136	C₂	1	2	yes	maximal, complemented
3	#16864130	C₂	1	2	yes	maximal, complemented
4	#16864117	C₂	1	2	yes	maximal, complemented
5	#16864109	C₂	1	2	yes	maximal, complemented
6	#16864076	C₂	1	2	yes	maximal, complemented
7	#16864057	C₂	1	2	yes	maximal, complemented
8	#16864037	C₂	1	2	yes	maximal, complemented
9	#16864020	C₂	1	4	yes	maximal, complemented
10	#16864019	C₂	1	2	yes	maximal, complemented
11	#16863982	C₂	1	4	yes	maximal, complemented
12	#16863960	C₂	1	1	yes	maximal, characteristic, complemented
13	#16863909	C₂	1	2	yes	maximal, complemented
14	#16863903	C₂	1	1	yes	maximal, characteristic, complemented
15	#536×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11761629	C₂²	1	2	yes	—
17	C₂²×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
19	#14524042	C₂²	1	2	yes	complemented
20	#14524039	C₂²	1	2	yes	—
21	#14524038	C₂²	1	4	yes	complemented
22	#14524038	C₂²	1	4	yes	complemented
23	#14524036	C₂²	1	4	yes	complemented
24	#14524032	C₂²	1	2	yes	complemented
25	#14524032	C₂²	1	2	yes	complemented
26	#14524032	C₂²	1	4	yes	complemented
27	#14524031	C₂²	1	4	yes	complemented
28	#14524029	C₂²	1	4	yes	—
29	#14524029	C₂²	1	4	yes	complemented
30	#14524029	C₂²	1	4	yes	complemented
31	#14524028	C₂²	1	4	yes	complemented
32	#14524028	C₂²	1	4	yes	complemented
33	#14524025	C₂²	1	4	yes	complemented
34	#14524024	C₂²	1	1	yes	characteristic
35	#14524024	C₂²	1	1	yes	characteristic, complemented
36	#14524023	C₂²	1	4	yes	complemented
37	#14524019	C₂²	1	2	yes	complemented
38	#14524019	C₂²	1	4	yes	complemented
39	#14524019	C₂²	1	2	yes	complemented
40	#14524018	C₂²	1	4	yes	—
41	#14524018	C₂²	1	2	yes	—
42	#14524017	C₂²	1	2	yes	—
43	#14524017	C₂²	1	2	yes	complemented
44	#14524017	C₂²	1	4	yes	complemented
45	#14524016	C₂²	1	4	yes	complemented
46	#14524014	C₂²	1	2	yes	—
47	#14524013	C₂²	1	4	yes	—
48	#14524013	C₂²	1	4	yes	complemented
49	#14524011	C₂²	1	2	yes	—
50	#14524011	C₂²	1	1	yes	characteristic
51	#14524011	C₂²	1	1	yes	characteristic, complemented
52	#14524011	C₂²	1	2	yes	complemented
53	Q₈×Dic₆₇	C₂²	1	2	yes	complemented
54	#14524008	C₂²	1	4	yes	complemented
55	#14524005	C₂²	1	2	yes	complemented
56	#14524005	C₂²	1	4	yes	complemented
57	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
58	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
60	(C₂²⋊D₆₇)⋊C₄	C₂²	1	4	yes	complemented
61	#14524002	C₂²	1	1	yes	characteristic, complemented
62	#14524002	C₂²	1	1	yes	characteristic, complemented
63	#14524001	C₂²	1	2	yes	complemented
64	#14524000	C₂²	1	4	yes	complemented
65	C₂²⋊C₄×D₆₇	C₂²	1	4	yes	complemented
66	C₂×#41×C₆₇	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	C₄⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
69	#124×C₆₇	C₂²	1	2	yes	—
70	#123×C₆₇	C₂²	1	2	yes	complemented
71	#123×C₆₇	C₂²	1	2	yes	complemented
72	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
73	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
74	#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₆₇	C₂³	1	2	yes	—
76	C₂³×D₆₇	C₂³	1	1	yes	characteristic
77	#11761629	—	4	4	no	—
78	C₂×Dic₁₃₄	C₂³	1	4	yes	—
79	C₂×D₂₆₈	—	4	2	no	—
80	C₂×D₂₆₈	C₂³	1	2	yes	—
81	C₂×D₂₆₈	C₂³	1	4	yes	—
82	C₂×D₂₆₈	C₂³	1	4	yes	—
83	C₂×D₂₆₈	C₂³	1	2	yes	—
84	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
85	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
86	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
87	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
88	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
89	C₂×C₄×D₆₇	—	4	2	no	—
90	C₂×C₄×D₆₇	C₂³	1	2	yes	—
91	C₂×C₄×D₆₇	C₂³	1	4	yes	—
92	C₂×C₄×D₆₇	C₂³	1	4	yes	—
93	C₂×C₄×D₆₇	C₂³	1	2	yes	—
94	C₄⋊Dic₆₇	C₂³	1	2	yes	—
95	C₄⋊Dic₆₇	C₂³	1	2	yes	—
96	C₄⋊Dic₆₇	C₂³	1	4	yes	—
97	Dic₆₇⋊C₄	C₂³	1	2	yes	—
98	Dic₆₇⋊C₄	C₂³	1	4	yes	—
99	Dic₆₇⋊C₄	C₂³	1	4	yes	—
100	Dic₆₇⋊C₄	C₂³	1	2	yes	—
101	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
102	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
103	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
104	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
105	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
106	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
107	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
108	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
109	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
110	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
111	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
112	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
113	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
114	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
115	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
116	C₄×Dic₆₇	C₂³	1	4	yes	—
117	C₄×Dic₆₇	C₂³	1	2	yes	—
118	C₄×Dic₆₇	C₂³	1	2	yes	—
119	C₄×Dic₆₇	C₂³	1	4	yes	—
120	#41×C₆₇	—	4	2	no	—
121	C₂×Q₈×C₆₇	—	4	2	no	—
122	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
123	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
124	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
132	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
134	C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
135	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
137	C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
138	C₄²×C₆₇	C₂³	1	2	yes	—
139	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
140	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
141	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
142	C₂²×D₆₇	—	4	1	no	—
143	C₂²×D₆₇	—	4	2	no	—
144	C₂²×D₆₇	—	4	2	no	—
145	C₂²×D₆₇	—	4	4	no	—
146	C₂²×D₆₇	C₂⁴	1	2	yes	—
147	C₂²×D₆₇	C₂⁴	1	4	yes	—
148	Q₈×C₆₇	—	2	4	no	—
149	Q₈×C₆₇	—	4	2	no	—
150	Q₈×C₆₇	—	4	1	no	—
151	D₄×C₆₇	—	4	1	no	—
152	D₄×C₆₇	—	4	1	no	—
153	D₄×C₆₇	—	4	1	no	—
154	C₂×C₄×C₆₇	—	2	2	no	—
155	C₂×C₄×C₆₇	—	2	2	no	—
156	C₂×C₄×C₆₇	—	2	2	no	—
157	C₂×C₄×C₆₇	—	4	2	no	—
158	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂⁴	1	4	yes	—
160	C₂×C₄×C₆₇	C₂⁴	1	4	yes	—
161	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
164	C₂²⋊D₆₇	—	4	2	no	—
165	C₂²⋊D₆₇	—	4	4	no	—
166	C₂²⋊D₆₇	—	4	4	no	—
167	C₂²⋊D₆₇	—	4	2	no	—
168	C₂×Dic₆₇	—	4	1	no	—
169	C₂×Dic₆₇	C₂⁴	1	2	yes	—
170	C₂×Dic₆₇	C₂⁴	1	4	yes	—
171	C₂×Dic₆₇	C₂⁴	1	2	yes	—
172	C₂×Dic₆₇	C₂⁴	1	2	yes	—
173	D₂₆₈	—	2	4	no	—
174	D₂₆₈	—	4	2	no	—
175	D₂₆₈	—	4	4	no	—
176	D₂₆₈	—	4	4	no	—
177	C₄×D₆₇	—	2	4	no	—
178	C₄×D₆₇	—	4	2	no	—
179	C₄×D₆₇	—	4	4	no	—
180	C₄×D₆₇	—	4	4	no	—
181	Dic₁₃₄	—	4	4	no	—
182	C₂²×C₆₇	—	2	1	no	—
183	C₂²×C₆₇	—	2	1	no	—
184	C₂²×C₆₇	—	2	1	no	—
185	C₂²×C₆₇	—	2	2	no	—
186	C₂²×C₆₇	—	2	2	no	—
187	C₂²×C₆₇	—	2	2	no	—
188	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
189	C₂×D₆₇	—	2	2	no	—
190	C₂×D₆₇	—	2	4	no	—
191	C₂×D₆₇	—	2	4	no	—
192	C₂×D₆₇	—	2	2	no	—
193	C₂×D₆₇	—	2	4	no	—
194	C₂×D₆₇	—	2	2	no	—
195	C₂×D₆₇	—	4	4	no	—
196	C₂×D₆₇	—	8	4	no	—
197	C₄×C₆₇	—	2	1	no	—
198	C₄×C₆₇	—	2	4	no	—
199	C₄×C₆₇	—	2	1	no	—
200	C₄×C₆₇	—	2	1	no	—
201	C₄×C₆₇	—	2	4	no	—
202	C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
203	Dic₆₇	—	2	2	no	—
204	Dic₆₇	—	2	2	no	—
205	Dic₆₇	—	2	4	no	—
206	Dic₆₇	—	2	2	no	—
207	C₂×C₆₇	—	4	1	no	—
208	C₂×C₆₇	—	4	1	no	—
209	C₂×C₆₇	—	4	1	no	—
210	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₆₇	#585	1	2	yes	—
212	D₆₇	—	4	2	no	—
213	D₆₇	—	4	4	no	—
214	#3540	—	67	1	no	maximal, Sylow
215	C₆₇	#3540	1	1	yes	characteristic, complemented, Sylow
216	H(3,𝔽₄)	—	67	2	no	—
217	#560	—	67	2	no	—
218	#559	—	67	2	no	—
219	#556	—	67	2	no	—
220	#555	—	67	2	no	—
221	#551	—	67	2	no	—
222	#548	—	67	2	no	—
223	#546	—	67	2	no	—
224	#542	—	67	4	no	—
225	#542	—	67	2	no	—
226	#538	—	67	4	no	—
227	#536	D₆₇	1	1	yes	characteristic, complemented
228	#535	—	67	1	no	—
229	#525	—	67	1	no	—
230	#525	—	67	2	no	—
231	C₂×#41	—	67	2	no	—
232	C₂×#41	C₂×D₆₇	1	1	yes	characteristic
233	C₂²×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
234	C₂²×D₄	—	67	1	no	—
235	C₂³×C₄	—	67	1	no	—
236	C₄⋊Q₈	—	67	2	no	—
237	C₄⋊Q₈	C₂×D₆₇	1	2	yes	complemented
238	#127	—	67	2	no	—
239	#126	—	67	4	no	—
240	#126	—	67	4	no	—
241	#126	—	67	4	no	—
242	#124	—	67	2	no	—
243	#124	—	67	2	no	—
244	#124	—	67	4	no	—
245	#124	—	67	4	no	—
246	#124	—	67	4	no	—
247	#124	—	67	4	no	—
248	#124	—	67	4	no	—
249	#124	C₂×D₆₇	1	2	yes	—
250	#123	—	67	1	no	—
251	#123	—	67	1	no	—
252	#123	—	67	4	no	—
253	#123	—	67	4	no	—
254	#123	—	67	4	no	—
255	#123	C₂×D₆₇	1	2	yes	complemented
256	#123	C₂×D₆₇	1	2	yes	complemented
257	C₂²⋊Q₈	—	67	2	no	—
258	C₂²⋊Q₈	—	67	2	no	—
259	C₂²⋊Q₈	—	67	4	no	—
260	C₂²⋊Q₈	—	67	4	no	—
261	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
262	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
263	#121	—	67	2	no	—
264	#121	—	67	2	no	—
265	#121	—	67	2	no	—
266	#121	—	67	4	no	—
267	#121	—	67	2	no	—
268	#121	—	67	4	no	—
269	#121	—	67	4	no	—
270	#120	—	67	1	no	—
271	#120	—	67	1	no	—
272	#120	—	67	2	no	—
273	#120	—	67	2	no	—
274	#120	—	67	4	no	—
275	#120	—	67	4	no	—
276	C₄×Q₈	—	67	2	no	—
277	C₄×Q₈	—	67	4	no	—
278	C₄×D₄	—	67	2	no	—
279	C₄×D₄	—	67	2	no	—
280	C₄×D₄	—	67	4	no	—
281	C₄×D₄	—	67	4	no	—
282	C₄×D₄	—	67	2	no	—
283	C₄×D₄	—	67	4	no	—
284	#117	—	67	1	no	—
285	#117	—	67	1	no	—
286	#117	—	67	2	no	—
287	#117	—	67	4	no	—
288	#117	C₂×D₆₇	1	1	yes	characteristic, complemented
289	C₂×C₂²⋊C₄	—	67	4	no	—
290	C₂⁴	—	67	2	no	—
291	C₂⁴	—	67	1	no	—
292	#41	—	4	2	no	—
293	#41	—	268	4	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	67	4	no	—
296	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
297	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
298	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
299	C₂×D₄	—	268	2	no	—
300	C₂×D₄	—	67	2	no	—
301	C₂×D₄	—	67	4	no	—
302	C₂×D₄	—	67	2	no	—
303	C₂×D₄	—	67	4	no	—
304	C₂×D₄	—	67	4	no	—
305	C₂×D₄	—	67	4	no	—
306	C₂×D₄	—	67	2	no	—
307	C₂×D₄	—	67	2	no	—
308	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
309	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
310	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
311	C₂²×C₄	—	268	2	no	—
312	C₂²×C₄	—	67	1	no	—
313	C₂²×C₄	—	67	4	no	—
314	C₂²×C₄	—	67	4	no	—
315	C₂²×C₄	—	67	2	no	—
316	C₂²×C₄	—	67	2	no	—
317	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
318	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
321	C₄⋊C₄	—	67	2	no	—
322	C₄⋊C₄	—	67	2	no	—
323	C₄⋊C₄	—	67	2	no	—
324	C₄⋊C₄	—	67	4	no	—
325	C₄⋊C₄	—	67	4	no	—
326	C₄⋊C₄	—	67	2	no	—
327	C₄⋊C₄	—	67	4	no	—
328	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
329	C₄⋊C₄	C₂²×D₆₇	1	4	yes	—
330	C₄⋊C₄	C₂²×D₆₇	1	4	yes	—
331	C₂²⋊C₄	—	67	2	no	—
332	C₂²⋊C₄	—	67	2	no	—
333	C₂²⋊C₄	—	67	1	no	—
334	C₂²⋊C₄	—	67	1	no	—
335	C₂²⋊C₄	—	67	2	no	—
336	C₂²⋊C₄	—	67	4	no	—
337	C₂²⋊C₄	—	67	4	no	—
338	C₂²⋊C₄	—	67	4	no	—
339	C₂²⋊C₄	—	67	4	no	—
340	C₂²⋊C₄	—	67	2	no	—
341	C₂²⋊C₄	—	67	4	no	—
342	C₂²⋊C₄	—	67	4	no	—
343	C₂²⋊C₄	—	67	4	no	—
344	C₂²⋊C₄	—	67	2	no	—
345	C₂²⋊C₄	—	67	4	no	—
346	C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
347	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
348	C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
349	C₄²	—	67	4	no	—
350	C₄²	—	67	2	no	—
351	C₄²	—	67	2	no	—
352	C₄²	—	67	4	no	—
353	C₄²	C₂²×D₆₇	1	2	yes	—
354	C₂³	—	268	1	no	—
355	C₂³	—	268	2	no	—
356	C₂³	—	268	2	no	—
357	C₂³	—	268	4	no	—
358	C₂³	—	67	2	no	—
359	C₂³	—	67	4	no	—
360	C₂³	C₂³×D₆₇	1	1	yes	characteristic
361	C₂³	C₂³×D₆₇	1	1	yes	characteristic
362	C₂³	C₂³×D₆₇	1	1	yes	characteristic
363	Q₈	—	2	4	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	4	1	no	—
366	Q₈	—	268	4	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	1	no	—
370	D₄	—	268	2	no	—
371	D₄	—	268	4	no	—
372	D₄	—	268	4	no	—
373	D₄	—	268	2	no	—
374	D₄	—	268	4	no	—
375	D₄	—	268	4	no	—
376	D₄	—	268	2	no	—
377	D₄	—	134	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	268	2	no	—
383	C₂×C₄	—	268	4	no	—
384	C₂×C₄	—	268	4	no	—
385	C₂×C₄	—	268	1	no	—
386	C₂×C₄	—	67	2	no	—
387	C₂×C₄	—	67	4	no	—
388	C₂×C₄	—	67	2	no	—
389	C₂×C₄	—	67	2	no	—
390	C₂×C₄	—	134	4	no	—
391	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₆₇	1	4	yes	—
393	C₂×C₄	C₂³×D₆₇	1	4	yes	—
394	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
395	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
396	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	268	4	no	—
404	C₂²	—	536	4	no	—
405	C₂²	—	134	2	no	—
406	C₂²	—	134	4	no	—
407	C₂²	—	134	4	no	—
408	C₂²	—	134	2	no	—
409	C₂²	—	134	2	no	—
410	C₂²	—	134	4	no	—
411	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	4	no	—
416	C₄	—	2	4	no	—
417	C₄	—	134	2	no	—
418	C₄	—	134	2	no	—
419	C₄	—	134	4	no	—
420	C₄	—	134	2	no	—
421	C₄	#14524088	1	2	yes	—
422	C₂	—	4	1	no	—
423	C₂	—	4	1	no	—
424	C₂	—	4	1	no	—
425	C₂	—	268	2	no	—
426	C₂	—	268	4	no	—
427	C₂	C₂×#14524088	1	1	yes	characteristic
428	C₂	#16864233	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#536×C₆₇	C₂
hypercenter	#536	D₆₇
hypocenter	C₆₇	#3540
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. #16864138	C₂	semidirect
2. #16864136	C₂	semidirect
3. #16864130	C₂	semidirect
4. #16864117	C₂	semidirect
5. #16864109	C₂	semidirect
6. #16864076	C₂	semidirect
7. #16864057	C₂	semidirect
8. #16864037	C₂	semidirect
9. #16864020	C₂	semidirect
10. #16864019	C₂	semidirect
11. #16863982	C₂	semidirect
12. #16863960	C₂	semidirect
13. #16863909	C₂	semidirect
14. #16863903	C₂	semidirect
15. #536×C₆₇	C₂	semidirect
17. C₂²×D₂₆₈	C₂²	semidirect
18. C₂²×C₄×D₆₇	C₂²	semidirect
19. #14524042	C₂²	semidirect
21. #14524038	C₂²	semidirect
22. #14524038	C₂²	semidirect
23. #14524036	C₂²	semidirect
24. #14524032	C₂²	semidirect
25. #14524032	C₂²	semidirect
26. #14524032	C₂²	semidirect
27. #14524031	C₂²	semidirect
29. #14524029	C₂²	semidirect
30. #14524029	C₂²	semidirect
31. #14524028	C₂²	semidirect
32. #14524028	C₂²	semidirect
33. #14524025	C₂²	semidirect
35. #14524024	C₂²	semidirect
36. #14524023	C₂²	semidirect
37. #14524019	C₂²	semidirect
38. #14524019	C₂²	semidirect
39. #14524019	C₂²	semidirect
43. #14524017	C₂²	semidirect
44. #14524017	C₂²	semidirect
45. #14524016	C₂²	semidirect
48. #14524013	C₂²	semidirect
51. #14524011	C₂²	semidirect
52. #14524011	C₂²	semidirect
53. Q₈×Dic₆₇	C₂²	semidirect
54. #14524008	C₂²	semidirect
55. #14524005	C₂²	semidirect
56. #14524005	C₂²	semidirect
58. C₄×C₂²⋊D₆₇	C₂²	semidirect
59. C₄×C₂²⋊D₆₇	C₂²	semidirect
60. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
61. #14524002	C₂²	semidirect
62. #14524002	C₂²	semidirect
63. #14524001	C₂²	semidirect
64. #14524000	C₂²	semidirect
65. C₂²⋊C₄×D₆₇	C₂²	semidirect
67. C₂²×Q₈×C₆₇	C₂²	semidirect
68. C₄⋊Q₈×C₆₇	C₂²	semidirect
70. #123×C₆₇	C₂²	semidirect
71. #123×C₆₇	C₂²	semidirect
72. C₂²⋊Q₈×C₆₇	C₂²	semidirect
73. C₂²⋊Q₈×C₆₇	C₂²	semidirect
74. #117×C₆₇	C₂²	semidirect
215. C₆₇	#3540	semidirect
227. #536	D₆₇	semidirect
233. C₂²×Q₈	C₂×D₆₇	semidirect
237. C₄⋊Q₈	C₂×D₆₇	semidirect
255. #123	C₂×D₆₇	semidirect
256. #123	C₂×D₆₇	semidirect
261. C₂²⋊Q₈	C₂×D₆₇	semidirect
262. C₂²⋊Q₈	C₂×D₆₇	semidirect
288. #117	C₂×D₆₇	semidirect