Subgroups — #22574475

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	#16864139	C₂	1	2	yes	maximal, complemented
2	#16864133	C₂	1	2	yes	maximal, complemented
3	#16864132	C₂	1	2	yes	maximal, complemented
4	#16864114	C₂	1	2	yes	maximal, complemented
5	#16864110	C₂	1	2	yes	maximal, complemented
6	#16864077	C₂	1	2	yes	maximal, complemented
7	#16864052	C₂	1	2	yes	maximal, complemented
8	#16864040	C₂	1	2	yes	maximal, complemented
9	#16864013	C₂	1	2	yes	maximal, complemented
10	#16864010	C₂	1	4	yes	maximal, complemented
11	#16863981	C₂	1	4	yes	maximal, complemented
12	#16863967	C₂	1	1	yes	maximal, characteristic, complemented
13	#16863906	C₂	1	2	yes	maximal, complemented
14	#16863903	C₂	1	1	yes	maximal, characteristic, complemented
15	#535×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11761627	C₂²	1	2	yes	—
17	C₂²×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
19	#14524042	C₂²	1	2	yes	complemented
20	#14524041	C₂²	1	2	yes	complemented
21	#14524037	C₂²	1	4	yes	complemented
22	#14524036	C₂²	1	4	yes	complemented
23	#14524036	C₂²	1	4	yes	complemented
24	#14524030	C₂²	1	2	yes	—
25	#14524030	C₂²	1	2	yes	complemented
26	#14524030	C₂²	1	4	yes	complemented
27	#14524030	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	#14524025	C₂²	1	4	yes	complemented
32	#14524024	C₂²	1	1	yes	characteristic
33	#14524024	C₂²	1	4	yes	complemented
34	#14524024	C₂²	1	4	yes	complemented
35	#14524024	C₂²	1	1	yes	characteristic, complemented
36	#14524024	C₂²	1	2	yes	complemented
37	#14524024	C₂²	1	2	yes	complemented
38	#14524023	C₂²	1	2	yes	complemented
39	#14524022	C₂²	1	2	yes	complemented
40	#14524022	C₂²	1	2	yes	complemented
41	#14524020	C₂²	1	4	yes	complemented
42	#14524020	C₂²	1	4	yes	complemented
43	#14524019	C₂²	1	2	yes	complemented
44	#14524015	C₂²	1	4	yes	—
45	#14524015	C₂²	1	4	yes	complemented
46	#14524015	C₂²	1	4	yes	complemented
47	#14524014	C₂²	1	2	yes	—
48	#14524014	C₂²	1	2	yes	—
49	#14524012	C₂²	1	4	yes	—
50	#14524011	C₂²	1	1	yes	characteristic
51	#14524011	C₂²	1	1	yes	characteristic, complemented
52	#14524011	C₂²	1	4	yes	complemented
53	C₄×Dic₁₃₄	C₂²	1	4	yes	complemented
54	#14524008	C₂²	1	2	yes	complemented
55	D₄×Dic₆₇	C₂²	1	2	yes	complemented
56	D₄×Dic₆₇	C₂²	1	4	yes	complemented
57	D₄×Dic₆₇	C₂²	1	4	yes	complemented
58	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
59	C₄×C₂²⋊D₆₇	C₂²	1	2	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	#14523999	C₂²	1	4	yes	complemented
65	C₂×C₂²⋊Dic₆₇	C₂²	1	4	yes	complemented
66	C₂×#41×C₆₇	C₂²	1	1	yes	characteristic
67	C₂²×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#127×C₆₇	C₂²	1	2	yes	—
69	#124×C₆₇	C₂²	1	2	yes	complemented
70	#121×C₆₇	C₂²	1	2	yes	—
71	#121×C₆₇	C₂²	1	2	yes	complemented
72	#120×C₆₇	C₂²	1	2	yes	—
73	#120×C₆₇	C₂²	1	2	yes	complemented
74	#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₆₇	C₂³	1	1	yes	characteristic
76	#11761627	—	4	4	no	—
77	C₂×Dic₁₃₄	—	4	2	no	—
78	C₂×Dic₁₃₄	C₂³	1	2	yes	—
79	C₂×Dic₁₃₄	C₂³	1	4	yes	—
80	C₂×Dic₁₃₄	C₂³	1	2	yes	—
81	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
82	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
83	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
84	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
85	C₂²×Dic₆₇	C₂³	1	4	yes	—
86	C₂²×Dic₆₇	C₂³	1	4	yes	—
87	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
88	C₂²×Dic₆₇	C₂³	1	2	yes	—
89	C₂×C₄×D₆₇	—	4	2	no	—
90	C₂×C₄×D₆₇	C₂³	1	2	yes	—
91	C₂×C₄×D₆₇	C₂³	1	2	yes	—
92	C₄⋊Dic₆₇	C₂³	1	2	yes	—
93	C₄⋊Dic₆₇	C₂³	1	2	yes	—
94	C₄⋊Dic₆₇	C₂³	1	4	yes	—
95	Dic₆₇⋊C₄	C₂³	1	2	yes	—
96	Dic₆₇⋊C₄	C₂³	1	4	yes	—
97	Dic₆₇⋊C₄	C₂³	1	4	yes	—
98	Dic₆₇⋊C₄	C₂³	1	2	yes	—
99	Dic₆₇⋊C₄	C₂³	1	4	yes	—
100	Dic₆₇⋊C₄	C₂³	1	4	yes	—
101	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
102	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
103	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
104	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
105	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
106	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
107	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
108	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
109	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
110	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
111	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
112	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
113	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
114	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
115	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
116	C₄×Dic₆₇	C₂³	1	2	yes	—
117	C₄×Dic₆₇	C₂³	1	4	yes	—
118	C₄×Dic₆₇	C₂³	1	2	yes	—
119	C₄×Dic₆₇	C₂³	1	4	yes	—
120	C₂⁴×C₆₇	C₂³	1	2	yes	—
121	#41×C₆₇	—	4	2	no	—
122	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
123	C₂×D₄×C₆₇	—	4	2	no	—
124	C₂×D₄×C₆₇	C₂³	1	2	yes	—
125	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₆₇	C₂³	1	4	yes	—
127	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₆₇	C₂³	1	4	yes	—
129	C₂×D₄×C₆₇	C₂³	1	2	yes	—
130	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₄⋊C₄×C₆₇	C₂³	1	2	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	—	4	2	no	—
140	C₂³×C₆₇	—	4	4	no	—
141	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
142	C₂³×C₆₇	C₂⁴	1	4	yes	—
143	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
144	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
145	C₂²×D₆₇	—	4	1	no	—
146	C₂²×D₆₇	—	4	2	no	—
147	C₂²×D₆₇	C₂⁴	1	2	yes	—
148	Q₈×C₆₇	—	4	1	no	—
149	D₄×C₆₇	—	2	4	no	—
150	D₄×C₆₇	—	4	2	no	—
151	D₄×C₆₇	—	4	4	no	—
152	D₄×C₆₇	—	4	4	no	—
153	D₄×C₆₇	—	4	1	no	—
154	D₄×C₆₇	—	4	1	no	—
155	D₄×C₆₇	—	4	1	no	—
156	C₂×C₄×C₆₇	—	2	2	no	—
157	C₂×C₄×C₆₇	—	2	2	no	—
158	C₂×C₄×C₆₇	—	2	2	no	—
159	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	no	—
167	C₂²⋊D₆₇	—	4	4	no	—
168	C₂×Dic₆₇	—	4	1	no	—
169	C₂×Dic₆₇	—	4	4	no	—
170	C₂×Dic₆₇	—	4	2	no	—
171	C₂×Dic₆₇	—	4	4	no	—
172	C₂×Dic₆₇	C₂⁴	1	2	yes	—
173	C₂×Dic₆₇	C₂⁴	1	4	yes	—
174	C₂×Dic₆₇	C₂⁴	1	2	yes	—
175	C₂×Dic₆₇	C₂⁴	1	2	yes	—
176	C₂×Dic₆₇	C₂⁴	1	4	yes	—
177	C₄×D₆₇	—	2	4	no	—
178	C₄×D₆₇	—	4	2	no	—
179	Dic₁₃₄	—	2	4	no	—
180	Dic₁₃₄	—	4	2	no	—
181	Dic₁₃₄	—	4	4	no	—
182	C₂²×C₆₇	—	2	1	no	—
183	C₂²×C₆₇	—	2	4	no	—
184	C₂²×C₆₇	—	2	1	no	—
185	C₂²×C₆₇	—	2	1	no	—
186	C₂²×C₆₇	—	2	4	no	—
187	C₂²×C₆₇	—	2	2	no	—
188	C₂²×C₆₇	—	2	4	no	—
189	C₂²×C₆₇	—	2	2	no	—
190	C₂²×C₆₇	—	2	2	no	—
191	C₂²×C₆₇	—	8	4	no	—
192	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
193	C₂×D₆₇	—	2	2	no	—
194	C₂×D₆₇	—	2	2	no	—
195	C₂×D₆₇	—	2	2	no	—
196	C₂×D₆₇	—	4	4	no	—
197	C₄×C₆₇	—	2	1	no	—
198	C₄×C₆₇	—	2	1	no	—
199	C₄×C₆₇	—	2	1	no	—
200	C₄×C₆₇	—	2	4	no	—
201	C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
202	Dic₆₇	—	2	4	no	—
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	4	no	—
210	C₂×C₆₇	—	4	1	no	—
211	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₆₇	#585	1	2	yes	—
213	D₆₇	—	4	2	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	—	67	1	no	—
228	#535	D₆₇	1	1	yes	characteristic, complemented
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	—	67	1	no	—
234	C₂²×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
235	C₂³×C₄	—	67	1	no	—
236	C₄⋊Q₈	—	67	2	no	—
237	C₄⋊Q₈	—	67	2	no	—
238	#127	C₂×D₆₇	1	2	yes	—
239	#126	—	67	4	no	—
240	#126	—	67	4	no	—
241	#126	—	67	4	no	—
242	#124	—	67	2	no	—
243	#124	—	67	4	no	—
244	#124	—	67	2	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	complemented
250	#123	—	67	1	no	—
251	#123	—	67	1	no	—
252	#123	—	67	2	no	—
253	#123	—	67	2	no	—
254	#123	—	67	4	no	—
255	#123	—	67	4	no	—
256	#123	—	67	4	no	—
257	C₂²⋊Q₈	—	67	2	no	—
258	C₂²⋊Q₈	—	67	2	no	—
259	C₂²⋊Q₈	—	67	2	no	—
260	C₂²⋊Q₈	—	67	2	no	—
261	C₂²⋊Q₈	—	67	4	no	—
262	C₂²⋊Q₈	—	67	4	no	—
263	#121	—	67	2	no	—
264	#121	—	67	2	no	—
265	#121	—	67	4	no	—
266	#121	—	67	4	no	—
267	#121	—	67	4	no	—
268	#121	C₂×D₆₇	1	2	yes	—
269	#121	C₂×D₆₇	1	2	yes	complemented
270	#120	—	67	4	no	—
271	#120	—	67	1	no	—
272	#120	—	67	4	no	—
273	#120	—	67	1	no	—
274	#120	C₂×D₆₇	1	2	yes	—
275	#120	C₂×D₆₇	1	2	yes	complemented
276	C₄×Q₈	—	67	2	no	—
277	C₄×Q₈	—	67	4	no	—
278	C₄×D₄	—	67	4	no	—
279	C₄×D₄	—	67	4	no	—
280	C₄×D₄	—	67	2	no	—
281	C₄×D₄	—	67	2	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	1	no	—
291	C₂⁴	C₂²×D₆₇	1	2	yes	—
292	#41	—	4	2	no	—
293	#41	—	268	4	no	—
294	C₂×Q₈	—	268	2	no	—
295	C₂×Q₈	—	67	4	no	—
296	C₂×Q₈	—	67	2	no	—
297	C₂×Q₈	—	67	2	no	—
298	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
299	C₂×D₄	—	4	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	C₂²×D₆₇	1	2	yes	—
305	C₂×D₄	C₂²×D₆₇	1	4	yes	—
306	C₂×D₄	C₂²×D₆₇	1	4	yes	—
307	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
308	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
309	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
310	C₂×D₄	C₂²×D₆₇	1	2	yes	—
311	C₂²×C₄	—	268	2	no	—
312	C₂²×C₄	—	67	4	no	—
313	C₂²×C₄	—	67	4	no	—
314	C₂²×C₄	—	67	1	no	—
315	C₂²×C₄	—	67	2	no	—
316	C₂²×C₄	—	67	2	no	—
317	C₂²×C₄	—	67	2	no	—
318	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
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	—	67	4	no	—
329	C₄⋊C₄	—	67	4	no	—
330	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
331	C₂²⋊C₄	—	67	2	no	—
332	C₂²⋊C₄	—	67	4	no	—
333	C₂²⋊C₄	—	67	4	no	—
334	C₂²⋊C₄	—	67	4	no	—
335	C₂²⋊C₄	—	67	1	no	—
336	C₂²⋊C₄	—	67	1	no	—
337	C₂²⋊C₄	—	67	2	no	—
338	C₂²⋊C₄	—	67	2	no	—
339	C₂²⋊C₄	—	67	4	no	—
340	C₂²⋊C₄	—	67	4	no	—
341	C₂²⋊C₄	—	67	4	no	—
342	C₂²⋊C₄	—	67	4	no	—
343	C₂²⋊C₄	—	67	2	no	—
344	C₂²⋊C₄	—	67	4	no	—
345	C₂²⋊C₄	—	67	2	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	2	no	—
350	C₄²	—	67	4	no	—
351	C₄²	—	67	2	no	—
352	C₄²	—	67	4	no	—
353	C₄²	C₂²×D₆₇	1	2	yes	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	4	no	—
356	C₂³	—	268	1	no	—
357	C₂³	—	268	2	no	—
358	C₂³	—	67	2	no	—
359	C₂³	C₂³×D₆₇	1	1	yes	characteristic
360	C₂³	C₂³×D₆₇	1	1	yes	characteristic
361	C₂³	C₂³×D₆₇	1	4	yes	—
362	C₂³	C₂³×D₆₇	1	1	yes	characteristic
363	Q₈	—	4	1	no	—
364	Q₈	—	268	2	no	—
365	Q₈	—	268	4	no	—
366	Q₈	—	134	4	no	—
367	D₄	—	2	4	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	1	no	—
371	D₄	—	4	1	no	—
372	D₄	—	4	4	no	—
373	D₄	—	4	4	no	—
374	D₄	—	268	4	no	—
375	D₄	—	268	2	no	—
376	D₄	—	268	4	no	—
377	D₄	—	268	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	268	2	no	—
382	C₂×C₄	—	268	1	no	—
383	C₂×C₄	—	268	2	no	—
384	C₂×C₄	—	268	4	no	—
385	C₂×C₄	—	268	4	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	—	67	4	no	—
391	C₂×C₄	—	134	4	no	—
392	C₂×C₄	C₂³×D₆₇	1	4	yes	—
393	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
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	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	8	4	no	—
407	C₂²	—	268	4	no	—
408	C₂²	—	134	2	no	—
409	C₂²	—	134	2	no	—
410	C₂²	—	134	2	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	—	134	2	no	—
417	C₄	—	134	4	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	4	no	—
424	C₂	—	4	1	no	—
425	C₂	—	4	1	no	—
426	C₂	—	268	2	no	—
427	C₂	C₂×#14524088	1	1	yes	characteristic
428	C₂	#16864231	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#535×C₆₇	C₂
hypercenter	#535	D₆₇
hypocenter	C₆₇	#3540
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. #16864139	C₂	semidirect
2. #16864133	C₂	semidirect
3. #16864132	C₂	semidirect
4. #16864114	C₂	semidirect
5. #16864110	C₂	semidirect
6. #16864077	C₂	semidirect
7. #16864052	C₂	semidirect
8. #16864040	C₂	semidirect
9. #16864013	C₂	semidirect
10. #16864010	C₂	semidirect
11. #16863981	C₂	semidirect
12. #16863967	C₂	semidirect
13. #16863906	C₂	semidirect
14. #16863903	C₂	semidirect
15. #535×C₆₇	C₂	semidirect
17. C₂²×Dic₁₃₄	C₂²	semidirect
18. C₂²×C₄×D₆₇	C₂²	semidirect
19. #14524042	C₂²	semidirect
20. #14524041	C₂²	semidirect
21. #14524037	C₂²	semidirect
22. #14524036	C₂²	semidirect
23. #14524036	C₂²	semidirect
25. #14524030	C₂²	semidirect
26. #14524030	C₂²	semidirect
27. #14524030	C₂²	semidirect
29. #14524029	C₂²	semidirect
30. #14524029	C₂²	semidirect
31. #14524025	C₂²	semidirect
33. #14524024	C₂²	semidirect
34. #14524024	C₂²	semidirect
35. #14524024	C₂²	semidirect
36. #14524024	C₂²	semidirect
37. #14524024	C₂²	semidirect
38. #14524023	C₂²	semidirect
39. #14524022	C₂²	semidirect
40. #14524022	C₂²	semidirect
41. #14524020	C₂²	semidirect
42. #14524020	C₂²	semidirect
43. #14524019	C₂²	semidirect
45. #14524015	C₂²	semidirect
46. #14524015	C₂²	semidirect
51. #14524011	C₂²	semidirect
52. #14524011	C₂²	semidirect
53. C₄×Dic₁₃₄	C₂²	semidirect
54. #14524008	C₂²	semidirect
55. D₄×Dic₆₇	C₂²	semidirect
56. D₄×Dic₆₇	C₂²	semidirect
57. D₄×Dic₆₇	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. #14523999	C₂²	semidirect
65. C₂×C₂²⋊Dic₆₇	C₂²	semidirect
67. C₂²×D₄×C₆₇	C₂²	semidirect
69. #124×C₆₇	C₂²	semidirect
71. #121×C₆₇	C₂²	semidirect
73. #120×C₆₇	C₂²	semidirect
74. #117×C₆₇	C₂²	semidirect
215. C₆₇	#3540	semidirect
228. #535	D₆₇	semidirect
234. C₂²×D₄	C₂×D₆₇	semidirect
249. #124	C₂×D₆₇	semidirect
269. #121	C₂×D₆₇	semidirect
275. #120	C₂×D₆₇	semidirect
288. #117	C₂×D₆₇	semidirect