Subgroups — #31010092

Order 17152.

718 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863826	C₂	1	2	yes	maximal, complemented
2	C₄×#14524065	C₂	1	1	yes	maximal, characteristic, complemented
3	#22562268	C₂	1	2	yes	maximal, complemented
4	#22562261	C₂	1	2	yes	maximal, complemented
5	#22562256	C₂	1	1	yes	maximal, characteristic, complemented
6	#22562251	C₂	1	1	yes	maximal, characteristic, complemented
7	#22562246	C₂	1	1	yes	maximal, characteristic, complemented
8	#22562241	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄⋊(C₆₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
10	#22561916	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524065	C₂²	1	1	yes	characteristic
13	C₄×#11761628	—	2	1	no	—
14	#16863826	—	2	8	no	—
15	C₂×#14523989	C₂²	1	2	yes	—
16	C₂×#14523987	C₂²	1	2	yes	—
17	C₂×#14523986	C₂²	1	2	yes	—
18	C₂×#14523984	C₂²	1	2	yes	—
19	C₂²×C₆₇⋊C₁₆	C₂²	1	2	yes	—
20	C₄×Dic₂₆₈	C₂²	1	1	yes	characteristic
21	C₄×Dic₂₆₈	C₂²	1	1	yes	characteristic
22	C₄×#11761617	—	2	1	no	—
23	C₄×#11761617	—	2	1	no	—
24	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
25	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
26	#16863434	C₂²	1	1	yes	characteristic
27	#16863393	—	2	1	no	—
28	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	1	yes	characteristic
29	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	1	yes	characteristic
30	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	2	yes	—
31	#16863200	C₂²	1	2	yes	—
32	#16863200	C₂²	1	2	yes	—
33	#16863197	C₂²	1	2	yes	—
34	#16863197	C₂²	1	2	yes	—
35	C₂×#135×C₆₇	—	2	1	no	—
36	C₂×#135×C₆₇	C₂²	1	2	yes	—
37	#532×C₆₇	—	2	1	no	—
38	#495×C₆₇	—	2	1	no	—
39	#495×C₆₇	C₂²	1	2	yes	—
40	#494×C₆₇	C₂²	1	1	yes	characteristic
41	#493×C₆₇	C₂²	1	1	yes	characteristic
42	#492×C₆₇	—	2	1	no	—
43	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#11761628	—	2	1	no	—
45	#14524065	—	2	2	no	—
46	#14524065	D₄	1	4	yes	complemented
47	C₂×Dic₂₆₈	C₂³	1	1	yes	characteristic
48	C₂×#11761617	—	2	1	no	—
49	C₂×D₅₃₆	C₂³	1	1	yes	characteristic
50	C₄×Dic₁₃₄	—	2	1	no	—
51	C₄×Dic₁₃₄	—	2	1	no	—
52	C₄×D₂₆₈	—	2	1	no	—
53	C₄×D₂₆₈	—	2	1	no	—
54	C₄×C₂²⋊D₆₇	—	4	1	no	—
55	C₄×C₂²⋊D₆₇	—	4	1	no	—
56	#14524002	—	2	1	no	—
57	#14524000	—	4	1	no	—
58	C₄²×D₆₇	—	4	1	no	—
59	#14523989	—	2	4	no	—
60	#14523987	—	2	4	no	—
61	#14523986	—	2	4	no	—
62	#14523984	—	2	4	no	—
63	C₂×C₆₇⋊C₁₆	—	2	4	no	—
64	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
65	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
66	#14523977	C₂³	1	1	yes	characteristic
67	#14523977	C₂³	1	1	yes	characteristic
68	#14523975	—	2	1	no	—
69	#14523968	—	2	1	no	—
70	#14523968	—	2	1	no	—
71	#14523965	—	2	1	no	—
72	#14523965	—	2	1	no	—
73	C₂×#41×C₆₇	—	2	2	no	—
74	#135×C₆₇	—	2	4	no	—
75	#135×C₆₇	—	2	4	no	—
76	#135×C₆₇	—	4	4	no	—
77	C₂×Q₁₆×C₆₇	—	2	1	no	—
78	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
79	C₂×SD₁₆×C₆₇	—	2	2	no	—
80	C₂×SD₁₆×C₆₇	—	2	2	no	—
81	C₂×D₈×C₆₇	—	2	1	no	—
82	C₂×D₈×C₆₇	C₂³	1	2	yes	—
83	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
84	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
85	C₄⋊Q₈×C₆₇	—	2	1	no	—
86	#127×C₆₇	—	2	1	no	—
87	#124×C₆₇	—	2	2	no	—
88	#121×C₆₇	—	4	1	no	—
89	#121×C₆₇	—	4	1	no	—
90	C₄×D₄×C₆₇	—	4	1	no	—
91	C₄×D₄×C₆₇	—	4	1	no	—
92	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
93	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
94	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
95	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
97	#11761628	—	2	4	no	—
98	#11761628	—	4	2	no	—
99	C₂×Dic₁₃₄	—	2	1	no	—
100	C₂×D₂₆₈	—	2	1	no	—
101	C₂×C₂²⋊D₆₇	—	4	1	no	—
102	C₂×C₄×D₆₇	—	4	1	no	—
103	C₂×C₄×D₆₇	—	4	1	no	—
104	C₂×C₄×D₆₇	—	4	1	no	—
105	Dic₂₆₈	—	2	1	no	—
106	Dic₂₆₈	C₂×D₄	1	2	yes	—
107	#11761617	—	2	4	no	—
108	D₅₃₆	—	2	1	no	—
109	D₅₃₆	C₂×D₄	1	2	yes	—
110	C₄⋊Dic₆₇	—	2	1	no	—
111	C₄⋊Dic₆₇	—	2	1	no	—
112	Dic₆₇⋊C₄	—	4	1	no	—
113	Dic₆₇⋊C₄	—	4	1	no	—
114	C₂²⋊Dic₆₇	—	4	1	no	—
115	(C₂×D₆₇)⋊C₄	—	4	1	no	—
116	(C₂×D₆₇)⋊C₄	—	4	1	no	—
117	C₄×Dic₆₇	—	4	1	no	—
118	C₄×Dic₆₇	—	4	1	no	—
119	C₄×Dic₆₇	—	4	1	no	—
120	C₆₇⋊C₁₆	—	2	2	no	—
121	C₆₇⋊C₁₆	—	2	2	no	—
122	#41×C₆₇	—	4	4	no	—
123	#41×C₆₇	—	4	4	no	—
124	C₂×Q₈×C₆₇	—	2	2	no	—
125	C₂×D₄×C₆₇	—	2	2	no	—
126	C₂×D₄×C₆₇	—	4	2	no	—
127	C₂×D₄×C₆₇	—	4	1	no	—
128	C₂×D₄×C₆₇	—	4	1	no	—
129	C₂²×C₄×C₆₇	—	4	2	no	—
130	C₂²×C₄×C₆₇	D₈	1	1	yes	characteristic
131	C₂²×C₄×C₆₇	D₈	1	1	yes	characteristic
132	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
133	Q₁₆×C₆₇	—	2	2	no	—
134	Q₁₆×C₆₇	—	2	2	no	—
135	Q₁₆×C₆₇	—	4	2	no	—
136	SD₁₆×C₆₇	—	4	4	no	—
137	SD₁₆×C₆₇	—	4	4	no	—
138	D₈×C₆₇	—	2	2	no	—
139	D₈×C₆₇	—	2	2	no	—
140	D₈×C₆₇	—	4	2	no	—
141	C₂×C₈×C₆₇	—	2	2	no	—
142	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₆₇	#41	1	2	yes	—
147	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
148	C₄⋊C₄×C₆₇	—	4	1	no	—
149	C₄⋊C₄×C₆₇	—	4	1	no	—
150	C₂²⋊C₄×C₆₇	—	4	2	no	—
151	C₂²⋊C₄×C₆₇	—	4	2	no	—
152	C₄²×C₆₇	D₈	1	1	yes	characteristic
153	C₄²×C₆₇	D₈	1	1	yes	characteristic
154	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
156	C₂³×C₆₇	—	4	2	no	—
157	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
158	C₂²×D₆₇	—	4	1	no	—
159	Q₈×C₆₇	—	4	2	no	—
160	Q₈×C₆₇	—	4	2	no	—
161	D₄×C₆₇	—	4	2	no	—
162	D₄×C₆₇	—	4	2	no	—
163	D₄×C₆₇	—	8	2	no	—
164	D₄×C₆₇	—	8	4	no	—
165	D₄×C₆₇	—	8	2	no	—
166	C₂×C₄×C₆₇	—	2	2	no	—
167	C₂×C₄×C₆₇	—	4	1	no	—
168	C₂×C₄×C₆₇	—	4	2	no	—
169	C₂×C₄×C₆₇	—	8	4	no	—
170	C₂×C₄×C₆₇	#121	1	2	yes	—
171	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
176	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
178	C₂²⋊D₆₇	—	4	4	no	—
179	C₂×Dic₆₇	—	4	1	no	—
180	C₂×Dic₆₇	—	4	1	no	—
181	C₂×Dic₆₇	—	4	1	no	—
182	D₂₆₈	—	2	2	no	—
183	D₂₆₈	—	4	1	no	—
184	C₄×D₆₇	—	4	4	no	—
185	C₄×D₆₇	—	8	2	no	—
186	C₄×D₆₇	—	8	2	no	—
187	Dic₁₃₄	—	2	2	no	—
188	Dic₁₃₄	—	4	1	no	—
189	C₈×C₆₇	—	2	1	no	—
190	C₈×C₆₇	—	2	1	no	—
191	C₈×C₆₇	#121	1	2	yes	—
192	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
194	C₂²×C₆₇	—	2	1	no	—
195	C₂²×C₆₇	—	2	1	no	—
196	C₂²×C₆₇	—	8	2	no	—
197	C₂²×C₆₇	—	8	2	no	—
198	C₂²×C₆₇	—	8	2	no	—
199	C₂²×C₆₇	#459	1	2	yes	—
200	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
201	C₂×D₆₇	—	4	2	no	—
202	C₂×D₆₇	—	8	1	no	—
203	C₂×D₆₇	—	8	1	no	—
204	C₄×C₆₇	—	2	1	no	—
205	C₄×C₆₇	—	2	1	no	—
206	C₄×C₆₇	—	2	1	no	—
207	C₄×C₆₇	—	8	2	no	—
208	C₄×C₆₇	#459	1	2	yes	—
209	C₄×C₆₇	#508	1	2	yes	complemented
210	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
211	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	Dic₆₇	—	4	2	no	—
213	Dic₆₇	—	8	1	no	—
214	Dic₆₇	—	8	1	no	—
215	#33579	—	67	1	no	maximal, Sylow
216	C₂×C₆₇	—	2	2	no	—
217	C₂×C₆₇	—	16	2	no	—
218	C₂×C₆₇	C₂×#459	1	1	yes	characteristic
219	C₂×C₆₇	C₂×#508	1	1	yes	characteristic
220	C₂×C₆₇	#3414	1	1	yes	characteristic
221	D₆₇	—	8	2	no	—
222	C₂×#508	—	67	2	no	—
223	#3147	D₆₇	1	1	yes	characteristic, complemented
224	C₄×#135	—	67	1	no	—
225	#2211	—	67	2	no	—
226	#2210	—	67	2	no	—
227	#2209	—	67	1	no	—
228	#2208	—	67	1	no	—
229	#2207	—	67	1	no	—
230	#2206	—	67	1	no	—
231	C₂×C₄⋊C₁₆	—	67	1	no	—
232	#2138	—	67	2	no	—
233	C₆₇	#33579	1	1	yes	characteristic, complemented, Sylow
234	C₂×#135	—	2	1	no	—
235	C₂×#135	—	67	1	no	—
236	C₂×#135	C₂×D₆₇	1	2	yes	—
237	#532	—	2	1	no	—
238	C₄×#41	—	134	1	no	—
239	#508	—	134	8	no	—
240	C₂×Q₃₂	—	67	2	no	—
241	C₂×SD₃₂	—	67	2	no	—
242	C₂×SD₃₂	—	67	2	no	—
243	C₂×D₁₆	—	67	2	no	—
244	C₂²×C₁₆	—	67	2	no	—
245	#495	—	2	1	no	—
246	#495	C₂×D₆₇	1	2	yes	—
247	#494	C₂×D₆₇	1	1	yes	characteristic
248	#493	C₂×D₆₇	1	1	yes	characteristic
249	#492	—	2	1	no	—
250	C₄×Q₁₆	—	67	1	no	—
251	C₄×Q₁₆	—	67	1	no	—
252	C₄×SD₁₆	—	134	1	no	—
253	C₄×SD₁₆	—	134	1	no	—
254	C₄×D₈	—	67	1	no	—
255	C₄×D₈	—	67	1	no	—
256	#427	—	67	1	no	—
257	#416	—	134	1	no	—
258	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
259	C₄⋊C₁₆	—	67	1	no	—
260	C₄⋊C₁₆	—	67	1	no	—
261	C₄⋊C₁₆	—	67	2	no	—
262	#358	—	67	2	no	—
263	#358	—	67	2	no	—
264	#357	—	67	2	no	—
265	#357	—	67	2	no	—
266	C₂×#41	—	2	2	no	—
267	C₂×#41	—	134	1	no	—
268	#135	—	2	4	no	—
269	#135	—	2	4	no	—
270	#135	—	4	4	no	—
271	#135	—	67	4	no	—
272	#135	—	134	2	no	—
273	C₂×Q₁₆	—	2	1	no	—
274	C₂×Q₁₆	—	67	1	no	—
275	C₂×Q₁₆	C₂²×D₆₇	1	2	yes	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂×SD₁₆	—	134	1	no	—
279	C₂×D₈	—	2	1	no	—
280	C₂×D₈	—	67	1	no	—
281	C₂×D₈	C₂²×D₆₇	1	2	yes	—
282	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
283	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
284	C₄⋊Q₈	—	2	1	no	—
285	#127	—	2	1	no	—
286	#124	—	2	2	no	—
287	#121	—	4	1	no	—
288	#121	—	4	1	no	—
289	C₄×Q₈	—	134	1	no	—
290	C₄×Q₈	—	134	1	no	—
291	C₄×D₄	—	4	1	no	—
292	C₄×D₄	—	4	1	no	—
293	C₄×D₄	—	268	1	no	—
294	C₄×D₄	—	268	1	no	—
295	C₄×D₄	—	134	1	no	—
296	C₄×D₄	—	134	1	no	—
297	#117	—	268	1	no	—
298	#117	—	134	1	no	—
299	C₂×C₄²	—	268	1	no	—
300	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
301	Q₃₂	—	134	4	no	—
302	SD₃₂	—	134	4	no	—
303	SD₃₂	—	134	4	no	—
304	D₁₆	—	134	4	no	—
305	C₂×C₁₆	—	67	2	no	—
306	C₂×C₁₆	—	67	2	no	—
307	C₂×C₁₆	—	134	4	no	—
308	#107	—	67	1	no	—
309	#107	—	67	1	no	—
310	#106	—	134	1	no	—
311	#103	—	134	1	no	—
312	#103	—	134	1	no	—
313	#102	—	134	1	no	—
314	#102	—	134	1	no	—
315	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
316	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
318	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
319	#41	—	4	4	no	—
320	#41	—	4	4	no	—
321	#41	—	268	2	no	—
322	#41	—	134	4	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	134	1	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	4	2	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	268	1	no	—
330	C₂×D₄	—	134	1	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	268	1	no	—
333	C₂²×C₄	—	268	1	no	—
334	C₂²×C₄	—	268	1	no	—
335	C₂²×C₄	#11761613	1	1	yes	characteristic
336	C₂²×C₄	#11761613	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
338	Q₁₆	—	2	2	no	—
339	Q₁₆	—	2	2	no	—
340	Q₁₆	—	4	2	no	—
341	Q₁₆	—	67	2	no	—
342	Q₁₆	—	134	1	no	—
343	SD₁₆	—	4	4	no	—
344	SD₁₆	—	4	4	no	—
345	SD₁₆	—	134	4	no	—
346	D₈	—	2	2	no	—
347	D₈	—	2	2	no	—
348	D₈	—	4	2	no	—
349	D₈	—	67	2	no	—
350	D₈	—	134	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	D₄×D₆₇	1	2	yes	—
353	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
354	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
355	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
356	C₂×C₈	#11761627	1	2	yes	—
357	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	268	1	no	—
361	C₄⋊C₄	—	268	1	no	—
362	C₄⋊C₄	—	134	1	no	—
363	C₄⋊C₄	—	134	1	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	268	1	no	—
367	C₂²⋊C₄	—	268	1	no	—
368	C₂²⋊C₄	—	268	1	no	—
369	C₄²	—	268	1	no	—
370	C₄²	—	268	1	no	—
371	C₄²	—	268	1	no	—
372	C₄²	#11761613	1	1	yes	characteristic
373	C₄²	#11761613	1	1	yes	characteristic
374	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
375	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
376	C₁₆	—	134	2	no	—
377	C₁₆	—	134	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	268	1	no	—
380	C₂³	C₂×#11761613	1	1	yes	characteristic
381	Q₈	—	4	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	268	1	no	—
384	Q₈	—	134	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	4	no	—
389	D₄	—	8	2	no	—
390	D₄	—	268	4	no	—
391	D₄	—	268	1	no	—
392	D₄	—	134	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	8	4	no	—
397	C₂×C₄	—	268	1	no	—
398	C₂×C₄	—	268	4	no	—
399	C₂×C₄	—	268	1	no	—
400	C₂×C₄	—	268	1	no	—
401	C₂×C₄	—	536	2	no	—
402	C₂×C₄	—	536	2	no	—
403	C₂×C₄	#14524014	1	2	yes	—
404	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
405	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
406	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
407	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
408	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
409	C₂×C₄	#14524069	1	2	yes	—
410	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	#14524014	1	2	yes	—
414	C₈	C₂×D₄×D₆₇	1	1	yes	characteristic
415	C₈	C₂×#11761627	1	1	yes	characteristic
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	268	2	no	—
422	C₂²	—	536	1	no	—
423	C₂²	—	536	1	no	—
424	C₂²	#16863588	1	2	yes	—
425	C₂²	C₂²×#11761613	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	268	2	no	—
431	C₄	—	536	1	no	—
432	C₄	—	536	1	no	—
433	C₄	#16863588	1	2	yes	—
434	C₄	#16863826	1	2	yes	complemented
435	C₄	C₂×#14524014	1	1	yes	characteristic
436	C₄	C₂×#14524069	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	16	2	no	—
439	C₂	—	536	2	no	—
440	C₂	C₂×#16863588	1	1	yes	characteristic
441	C₂	C₂×#16863826	1	1	yes	characteristic
442	C₂	#22573343	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#11761613
commutator, cosocle	C₂×C₈×C₆₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₆₇×#3147	C₂
socle	C₂²×C₆₇	C₂²×D₈
hypercenter	#3147	D₆₇
hypocenter	C₆₇	#33579
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #3147

Complements

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

N	H ≅ G/N	type
1. C₂×#16863826	C₂	semidirect
2. C₄×#14524065	C₂	semidirect
3. #22562268	C₂	semidirect
4. #22562261	C₂	semidirect
5. #22562256	C₂	semidirect
6. #22562251	C₂	semidirect
7. #22562246	C₂	semidirect
8. #22562241	C₂	semidirect
9. C₂×C₄⋊(C₆₇⋊C₁₆)	C₂	semidirect
10. #22561916	C₂	semidirect
11. C₆₇×#3147	C₂	semidirect
46. #14524065	D₄	semidirect
209. C₄×C₆₇	#508	semidirect
223. #3147	D₆₇	semidirect
233. C₆₇	#33579	semidirect
434. C₄	#16863826	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863826	2
C₄×#14524065	2
#22562268	2
#22562261	2
#22562256	2
#22562251	2
#22562246	2
#22562241	2
C₂×C₄⋊(C₆₇⋊C₁₆)	2
#22561916	2
C₆₇×#3147	2
#33579	67