Subgroups — #31010100

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×#16863828	C₂	1	2	yes	maximal, complemented
2	#22570637	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14524065	C₂	1	1	yes	maximal, characteristic, complemented
4	#22562272	C₂	1	2	yes	maximal, complemented
5	#22562265	C₂	1	2	yes	maximal, complemented
6	#22562260	C₂	1	1	yes	maximal, characteristic, complemented
7	#22562255	C₂	1	1	yes	maximal, characteristic, complemented
8	#22562250	C₂	1	1	yes	maximal, characteristic, complemented
9	#22562245	C₂	1	1	yes	maximal, characteristic, complemented
10	#22561917	C₂	1	2	yes	maximal, complemented
11	C₂×C₄⋊C₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524065	—	2	1	no	—
13	C₂×#14524065	C₂²	1	2	yes	—
14	C₂×#14524065	C₂²	1	1	yes	characteristic
15	#16863946	—	2	1	no	—
16	C₄×#11761628	—	2	1	no	—
17	#16863828	—	2	8	no	—
18	C₂×Dic₅₃₆	C₂²	1	2	yes	—
19	C₂×#14523988	C₂²	1	2	yes	—
20	C₂×#14523988	C₂²	1	2	yes	—
21	C₂×D₁₀₇₂	C₂²	1	2	yes	—
22	#16863780	—	2	1	no	—
23	#16863780	C₂²	1	2	yes	—
24	#16863776	C₂²	1	1	yes	characteristic
25	#16863773	C₂²	1	1	yes	characteristic
26	#16863769	—	2	1	no	—
27	C₄×Dic₂₆₈	C₂²	1	1	yes	characteristic
28	C₄×Dic₂₆₈	C₂²	1	1	yes	characteristic
29	C₄×#11761617	—	2	1	no	—
30	C₄×#11761617	—	2	1	no	—
31	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
32	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
33	#16863434	C₂²	1	1	yes	characteristic
34	#16863393	—	2	1	no	—
35	#16863201	C₂²	1	2	yes	—
36	#16863201	C₂²	1	2	yes	—
37	#16863198	C₂²	1	2	yes	—
38	#16863198	C₂²	1	2	yes	—
39	C₂²×C₁₆×C₆₇	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₄⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
42	C₄⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
43	C₄⋊C₁₆×C₆₇	C₂²	1	2	yes	—
44	C₂×#11761628	—	2	1	no	—
45	C₂×#11761628	—	2	2	no	—
46	#14524065	—	2	4	no	—
47	#14524065	—	2	2	no	—
48	#14524065	—	2	4	no	—
49	#14524065	—	4	4	no	—
50	#14524065	D₄	1	4	yes	complemented
51	C₂×Dic₂₆₈	—	2	1	no	—
52	C₂×Dic₂₆₈	C₂³	1	2	yes	—
53	C₂×Dic₂₆₈	C₂³	1	1	yes	characteristic
54	C₂×#11761617	—	2	1	no	—
55	C₂×#11761617	—	2	2	no	—
56	C₂×#11761617	—	2	2	no	—
57	C₂×D₅₃₆	—	2	1	no	—
58	C₂×D₅₃₆	C₂³	1	2	yes	—
59	C₂×D₅₃₆	C₂³	1	1	yes	characteristic
60	#14524043	—	2	1	no	—
61	#14524040	—	2	1	no	—
62	#14524031	—	2	2	no	—
63	#14524017	—	4	1	no	—
64	#14524017	—	4	1	no	—
65	C₄×Dic₁₃₄	—	2	1	no	—
66	C₄×Dic₁₃₄	—	2	1	no	—
67	C₄×D₂₆₈	—	2	1	no	—
68	C₄×D₂₆₈	—	2	1	no	—
69	C₄×D₂₆₈	—	4	1	no	—
70	C₄×D₂₆₈	—	4	1	no	—
71	C₄×C₂²⋊D₆₇	—	4	1	no	—
72	C₄×C₂²⋊D₆₇	—	4	1	no	—
73	#14524002	—	2	1	no	—
74	#14524000	—	4	1	no	—
75	C₄²×D₆₇	—	4	1	no	—
76	Dic₅₃₆	—	2	4	no	—
77	#14523988	—	2	4	no	—
78	#14523988	—	2	4	no	—
79	D₁₀₇₂	—	2	4	no	—
80	#14523977	C₂³	1	1	yes	characteristic
81	#14523977	C₂³	1	1	yes	characteristic
82	#14523975	—	2	1	no	—
83	#14523968	—	2	1	no	—
84	#14523968	—	2	1	no	—
85	#14523965	—	2	1	no	—
86	#14523965	—	2	1	no	—
87	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
88	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
90	C₂×C₁₆×C₆₇	—	2	4	no	—
91	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
92	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
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	#11761628	—	4	4	no	—
100	#11761628	—	4	4	no	—
101	C₂×Dic₁₃₄	—	2	1	no	—
102	C₂×Dic₁₃₄	—	2	2	no	—
103	C₂×D₂₆₈	—	2	1	no	—
104	C₂×D₂₆₈	—	2	2	no	—
105	C₂×D₂₆₈	—	4	1	no	—
106	C₂×D₂₆₈	—	4	1	no	—
107	C₂×C₂²⋊D₆₇	—	4	1	no	—
108	C₂×C₂²⋊D₆₇	—	4	2	no	—
109	C₂×C₄×D₆₇	—	4	1	no	—
110	C₂×C₄×D₆₇	—	4	1	no	—
111	C₂×C₄×D₆₇	—	4	1	no	—
112	C₂×C₄×D₆₇	—	4	2	no	—
113	Dic₂₆₈	—	2	2	no	—
114	Dic₂₆₈	—	2	1	no	—
115	Dic₂₆₈	—	2	2	no	—
116	Dic₂₆₈	—	4	2	no	—
117	Dic₂₆₈	C₂×D₄	1	2	yes	—
118	#11761617	—	2	4	no	—
119	#11761617	—	4	4	no	—
120	#11761617	—	4	4	no	—
121	D₅₃₆	—	2	2	no	—
122	D₅₃₆	—	2	1	no	—
123	D₅₃₆	—	2	2	no	—
124	D₅₃₆	—	4	2	no	—
125	D₅₃₆	C₂×D₄	1	2	yes	—
126	C₄⋊Dic₆₇	—	2	1	no	—
127	C₄⋊Dic₆₇	—	2	1	no	—
128	C₄⋊Dic₆₇	—	4	1	no	—
129	C₄⋊Dic₆₇	—	4	1	no	—
130	Dic₆₇⋊C₄	—	4	1	no	—
131	Dic₆₇⋊C₄	—	4	1	no	—
132	C₂²⋊Dic₆₇	—	4	1	no	—
133	(C₂×D₆₇)⋊C₄	—	4	1	no	—
134	(C₂×D₆₇)⋊C₄	—	4	1	no	—
135	(C₂×D₆₇)⋊C₄	—	4	2	no	—
136	(C₂×D₆₇)⋊C₄	—	4	2	no	—
137	C₄×Dic₆₇	—	4	1	no	—
138	C₄×Dic₆₇	—	4	1	no	—
139	C₄×Dic₆₇	—	4	1	no	—
140	C₂²×C₄×C₆₇	D₈	1	1	yes	characteristic
141	C₂²×C₄×C₆₇	D₈	1	1	yes	characteristic
142	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₆₇	—	2	2	no	—
144	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₆₇	#41	1	2	yes	—
149	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
150	C₄²×C₆₇	D₈	1	1	yes	characteristic
151	C₄²×C₆₇	D₈	1	1	yes	characteristic
152	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
154	C₁₆×C₆₇	—	2	2	no	—
155	C₁₆×C₆₇	—	2	2	no	—
156	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
157	C₂²×D₆₇	—	4	1	no	—
158	C₂²×D₆₇	—	4	2	no	—
159	C₂×C₄×C₆₇	—	2	2	no	—
160	C₂×C₄×C₆₇	—	4	1	no	—
161	C₂×C₄×C₆₇	#121	1	2	yes	—
162	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
168	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
169	C₂²⋊D₆₇	—	4	4	no	—
170	C₂²⋊D₆₇	—	8	4	no	—
171	C₂×Dic₆₇	—	4	1	no	—
172	C₂×Dic₆₇	—	4	1	no	—
173	C₂×Dic₆₇	—	4	1	no	—
174	C₂×Dic₆₇	—	4	2	no	—
175	D₂₆₈	—	2	2	no	—
176	D₂₆₈	—	4	2	no	—
177	D₂₆₈	—	4	1	no	—
178	D₂₆₈	—	4	2	no	—
179	D₂₆₈	—	8	2	no	—
180	D₂₆₈	—	8	2	no	—
181	C₄×D₆₇	—	4	4	no	—
182	C₄×D₆₇	—	8	2	no	—
183	C₄×D₆₇	—	8	4	no	—
184	C₄×D₆₇	—	8	2	no	—
185	Dic₁₃₄	—	2	2	no	—
186	Dic₁₃₄	—	4	1	no	—
187	Dic₁₃₄	—	4	2	no	—
188	Dic₁₃₄	—	4	2	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	#459	1	2	yes	—
197	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
198	C₂×D₆₇	—	4	2	no	—
199	C₂×D₆₇	—	8	1	no	—
200	C₂×D₆₇	—	8	1	no	—
201	C₂×D₆₇	—	8	2	no	—
202	C₂×D₆₇	—	8	2	no	—
203	C₂×D₆₇	—	8	2	no	—
204	C₄×C₆₇	—	2	1	no	—
205	C₄×C₆₇	—	2	1	no	—
206	C₄×C₆₇	—	2	1	no	—
207	C₄×C₆₇	#459	1	2	yes	—
208	C₄×C₆₇	#508	1	2	yes	complemented
209	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
210	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
211	Dic₆₇	—	4	2	no	—
212	Dic₆₇	—	8	1	no	—
213	Dic₆₇	—	8	1	no	—
214	Dic₆₇	—	8	2	no	—
215	#33579	—	67	1	no	maximal, Sylow
216	C₂×C₆₇	—	2	2	no	—
217	C₂×C₆₇	C₂×#459	1	1	yes	characteristic
218	C₂×C₆₇	C₂×#508	1	1	yes	characteristic
219	C₂×C₆₇	#3414	1	1	yes	characteristic
220	D₆₇	—	8	2	no	—
221	D₆₇	—	16	2	no	—
222	C₂×#508	—	67	2	no	—
223	#3147	—	67	1	no	—
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	D₆₇	1	1	yes	characteristic, complemented
232	#2138	—	67	2	no	—
233	C₆₇	#33579	1	1	yes	characteristic, complemented, Sylow
234	C₂×#135	—	67	1	no	—
235	C₂×#135	—	67	2	no	—
236	C₂×#135	—	134	1	no	—
237	#532	—	134	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	C₂×D₆₇	1	2	yes	—
245	#495	—	67	2	no	—
246	#495	—	134	1	no	—
247	#494	—	67	1	no	—
248	#493	—	67	1	no	—
249	#492	—	134	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	C₂×D₆₇	1	1	yes	characteristic
260	C₄⋊C₁₆	C₂×D₆₇	1	1	yes	characteristic
261	C₄⋊C₁₆	C₂×D₆₇	1	2	yes	—
262	#358	—	67	2	no	—
263	#358	—	67	2	no	—
264	#357	—	67	2	no	—
265	#357	—	67	2	no	—
266	C₂×#41	—	134	2	no	—
267	C₂×#41	—	134	1	no	—
268	#135	—	268	4	no	—
269	#135	—	67	4	no	—
270	#135	—	134	4	no	—
271	#135	—	134	4	no	—
272	#135	—	134	2	no	—
273	C₂×Q₁₆	—	67	1	no	—
274	C₂×Q₁₆	—	67	2	no	—
275	C₂×Q₁₆	—	134	1	no	—
276	C₂×SD₁₆	—	134	2	no	—
277	C₂×SD₁₆	—	134	2	no	—
278	C₂×SD₁₆	—	134	1	no	—
279	C₂×D₈	—	67	1	no	—
280	C₂×D₈	—	67	2	no	—
281	C₂×D₈	—	134	1	no	—
282	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
283	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
284	C₄⋊Q₈	—	134	1	no	—
285	#127	—	134	1	no	—
286	#124	—	134	2	no	—
287	#121	—	268	1	no	—
288	#121	—	268	1	no	—
289	C₄×Q₈	—	134	1	no	—
290	C₄×Q₈	—	134	1	no	—
291	C₄×D₄	—	268	1	no	—
292	C₄×D₄	—	268	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	D₂₆₈	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	—	2	4	no	—
306	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
307	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
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	D₂₆₈	1	1	yes	characteristic
316	C₄×C₈	D₂₆₈	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
318	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
319	#41	—	268	2	no	—
320	#41	—	268	4	no	—
321	#41	—	268	4	no	—
322	#41	—	134	4	no	—
323	C₂×Q₈	—	134	2	no	—
324	C₂×Q₈	—	134	1	no	—
325	C₂×D₄	—	268	1	no	—
326	C₂×D₄	—	268	2	no	—
327	C₂×D₄	—	268	1	no	—
328	C₂×D₄	—	268	1	no	—
329	C₂×D₄	—	134	2	no	—
330	C₂×D₄	—	134	1	no	—
331	C₂²×C₄	—	268	1	no	—
332	C₂²×C₄	—	268	1	no	—
333	C₂²×C₄	—	268	1	no	—
334	C₂²×C₄	—	268	2	no	—
335	C₂²×C₄	D₅₃₆	1	1	yes	characteristic
336	C₂²×C₄	D₅₃₆	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
338	Q₁₆	—	268	2	no	—
339	Q₁₆	—	67	2	no	—
340	Q₁₆	—	134	2	no	—
341	Q₁₆	—	134	2	no	—
342	Q₁₆	—	134	1	no	—
343	SD₁₆	—	268	4	no	—
344	SD₁₆	—	268	4	no	—
345	SD₁₆	—	134	4	no	—
346	D₈	—	268	2	no	—
347	D₈	—	67	2	no	—
348	D₈	—	134	2	no	—
349	D₈	—	134	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×D₂₆₈	1	1	yes	characteristic
354	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
355	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
356	C₂×C₈	#11761629	1	2	yes	—
357	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
358	C₄⋊C₄	—	268	1	no	—
359	C₄⋊C₄	—	268	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	—	268	1	no	—
365	C₂²⋊C₄	—	268	1	no	—
366	C₂²⋊C₄	—	268	1	no	—
367	C₂²⋊C₄	—	268	2	no	—
368	C₂²⋊C₄	—	268	2	no	—
369	C₄²	—	268	1	no	—
370	C₄²	—	268	1	no	—
371	C₄²	—	268	1	no	—
372	C₄²	D₅₃₆	1	1	yes	characteristic
373	C₄²	D₅₃₆	1	1	yes	characteristic
374	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
375	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
376	C₁₆	—	2	2	no	—
377	C₁₆	—	2	2	no	—
378	C₂³	—	268	1	no	—
379	C₂³	—	268	2	no	—
380	C₂³	C₂×D₅₃₆	1	1	yes	characteristic
381	Q₈	—	268	1	no	—
382	Q₈	—	268	2	no	—
383	Q₈	—	268	2	no	—
384	Q₈	—	134	2	no	—
385	D₄	—	268	4	no	—
386	D₄	—	268	2	no	—
387	D₄	—	268	1	no	—
388	D₄	—	268	2	no	—
389	D₄	—	536	2	no	—
390	D₄	—	536	4	no	—
391	D₄	—	536	2	no	—
392	D₄	—	134	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	268	1	no	—
396	C₂×C₄	—	268	4	no	—
397	C₂×C₄	—	268	1	no	—
398	C₂×C₄	—	268	1	no	—
399	C₂×C₄	—	268	2	no	—
400	C₂×C₄	—	536	2	no	—
401	C₂×C₄	—	536	2	no	—
402	C₂×C₄	—	536	4	no	—
403	C₂×C₄	#14524018	1	2	yes	—
404	C₂×C₄	C₂×D₅₃₆	1	1	yes	characteristic
405	C₂×C₄	C₂×D₅₃₆	1	1	yes	characteristic
406	C₂×C₄	C₂×D₅₃₆	1	1	yes	characteristic
407	C₂×C₄	C₂×D₅₃₆	1	1	yes	characteristic
408	C₂×C₄	C₂×D₅₃₆	1	1	yes	characteristic
409	C₂×C₄	#14524071	1	2	yes	—
410	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	#14524018	1	2	yes	—
414	C₈	C₂×D₄×D₆₇	1	1	yes	characteristic
415	C₈	C₂×#11761629	1	1	yes	characteristic
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	268	2	no	—
419	C₂²	—	536	1	no	—
420	C₂²	—	536	1	no	—
421	C₂²	—	536	2	no	—
422	C₂²	—	536	2	no	—
423	C₂²	—	536	2	no	—
424	C₂²	#16863592	1	2	yes	—
425	C₂²	C₂²×D₅₃₆	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	268	2	no	—
430	C₄	—	536	1	no	—
431	C₄	—	536	1	no	—
432	C₄	—	536	2	no	—
433	C₄	#16863592	1	2	yes	—
434	C₄	#16863828	1	2	yes	complemented
435	C₄	C₂×#14524018	1	1	yes	characteristic
436	C₄	C₂×#14524071	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	536	2	no	—
439	C₂	—	1072	2	no	—
440	C₂	C₂×#16863592	1	1	yes	characteristic
441	C₂	C₂×#16863828	1	1	yes	characteristic
442	C₂	#22573345	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₅₃₆
commutator, cosocle	C₂×C₈×C₆₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₂×C₄⋊C₁₆×C₆₇	C₂
socle	C₂²×C₆₇	C₂²×D₈
hypercenter	C₂×C₄⋊C₁₆	D₆₇
hypocenter	C₆₇	#33579
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#16863828	C₂	semidirect
2. #22570637	C₂	semidirect
3. C₄×#14524065	C₂	semidirect
4. #22562272	C₂	semidirect
5. #22562265	C₂	semidirect
6. #22562260	C₂	semidirect
7. #22562255	C₂	semidirect
8. #22562250	C₂	semidirect
9. #22562245	C₂	semidirect
10. #22561917	C₂	semidirect
11. C₂×C₄⋊C₁₆×C₆₇	C₂	semidirect
50. #14524065	D₄	semidirect
208. C₄×C₆₇	#508	semidirect
231. C₂×C₄⋊C₁₆	D₆₇	semidirect
233. C₆₇	#33579	semidirect
434. C₄	#16863828	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863828	2
#22570637	2
C₄×#14524065	2
#22562272	2
#22562265	2
#22562260	2
#22562255	2
#22562250	2
#22562245	2
#22561917	2
C₂×C₄⋊C₁₆×C₆₇	2
#33579	67