Subgroups — #25250866

Order 11008.

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×#14583331	C₂	1	2	yes	maximal, complemented
2	#19145023	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13063347	C₂	1	1	yes	maximal, characteristic, complemented
4	#19136658	C₂	1	2	yes	maximal, complemented
5	#19136651	C₂	1	2	yes	maximal, complemented
6	#19136646	C₂	1	1	yes	maximal, characteristic, complemented
7	#19136641	C₂	1	1	yes	maximal, characteristic, complemented
8	#19136636	C₂	1	1	yes	maximal, characteristic, complemented
9	#19136631	C₂	1	1	yes	maximal, characteristic, complemented
10	#19136303	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	—	2	1	no	—
13	C₂×#13063347	C₂²	1	2	yes	—
14	C₂×#13063347	C₂²	1	1	yes	characteristic
15	#14583449	—	2	1	no	—
16	C₄×#10621898	—	2	1	no	—
17	#14583331	—	2	8	no	—
18	C₂×Dic₃₄₄	C₂²	1	2	yes	—
19	C₂×#13063270	C₂²	1	2	yes	—
20	C₂×#13063270	C₂²	1	2	yes	—
21	C₂×D₆₈₈	C₂²	1	2	yes	—
22	#14583283	—	2	1	no	—
23	#14583283	C₂²	1	2	yes	—
24	#14583279	C₂²	1	1	yes	characteristic
25	#14583276	C₂²	1	1	yes	characteristic
26	#14583272	—	2	1	no	—
27	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic
28	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic
29	C₄×#10621873	—	2	1	no	—
30	C₄×#10621873	—	2	1	no	—
31	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
32	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
33	#14582937	C₂²	1	1	yes	characteristic
34	#14582896	—	2	1	no	—
35	#14582704	C₂²	1	2	yes	—
36	#14582704	C₂²	1	2	yes	—
37	#14582701	C₂²	1	2	yes	—
38	#14582701	C₂²	1	2	yes	—
39	C₂²×C₁₆×C₄₃	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₄₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
43	C₄₃×C₄⋊C₁₆	C₂²	1	2	yes	—
44	C₂×#10621898	—	2	1	no	—
45	C₂×#10621898	—	2	2	no	—
46	#13063347	—	2	2	no	—
47	#13063347	—	2	4	no	—
48	#13063347	—	2	4	no	—
49	#13063347	—	4	4	no	—
50	#13063347	D₄	1	4	yes	complemented
51	C₂×Dic₁₇₂	—	2	1	no	—
52	C₂×Dic₁₇₂	C₂³	1	2	yes	—
53	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
54	C₂×#10621873	—	2	1	no	—
55	C₂×#10621873	—	2	2	no	—
56	C₂×#10621873	—	2	2	no	—
57	C₂×D₃₄₄	—	2	1	no	—
58	C₂×D₃₄₄	C₂³	1	2	yes	—
59	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
60	#13063325	—	2	1	no	—
61	#13063322	—	2	1	no	—
62	#13063313	—	2	2	no	—
63	#13063299	—	4	1	no	—
64	#13063299	—	4	1	no	—
65	C₄×Dic₈₆	—	2	1	no	—
66	C₄×Dic₈₆	—	2	1	no	—
67	C₄×D₁₇₂	—	2	1	no	—
68	C₄×D₁₇₂	—	2	1	no	—
69	C₄×D₁₇₂	—	4	1	no	—
70	C₄×D₁₇₂	—	4	1	no	—
71	C₄×C₂²⋊D₄₃	—	4	1	no	—
72	C₄×C₂²⋊D₄₃	—	4	1	no	—
73	#13063284	—	2	1	no	—
74	#13063282	—	4	1	no	—
75	C₄²×D₄₃	—	4	1	no	—
76	Dic₃₄₄	—	2	4	no	—
77	#13063270	—	2	4	no	—
78	#13063270	—	2	4	no	—
79	D₆₈₈	—	2	4	no	—
80	#13063259	C₂³	1	1	yes	characteristic
81	#13063259	C₂³	1	1	yes	characteristic
82	#13063257	—	2	1	no	—
83	#13063250	—	2	1	no	—
84	#13063250	—	2	1	no	—
85	#13063247	—	2	1	no	—
86	#13063247	—	2	1	no	—
87	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
88	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
90	C₂×C₁₆×C₄₃	—	2	4	no	—
91	C₂×C₁₆×C₄₃	C₂³	1	2	yes	—
92	C₂×C₁₆×C₄₃	C₂³	1	2	yes	—
93	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
94	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
95	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
100	C₂×C₂²⋊D₄₃	—	4	1	no	—
101	C₂×C₂²⋊D₄₃	—	4	2	no	—
102	#10621898	—	2	4	no	—
103	#10621898	—	4	2	no	—
104	#10621898	—	4	4	no	—
105	#10621898	—	4	4	no	—
106	C₂×D₁₇₂	—	2	1	no	—
107	C₂×D₁₇₂	—	2	2	no	—
108	C₂×D₁₇₂	—	4	1	no	—
109	C₂×D₁₇₂	—	4	1	no	—
110	C₂×C₄×D₄₃	—	4	1	no	—
111	C₂×C₄×D₄₃	—	4	1	no	—
112	C₂×C₄×D₄₃	—	4	1	no	—
113	C₂×C₄×D₄₃	—	4	2	no	—
114	C₂×Dic₈₆	—	2	1	no	—
115	C₂×Dic₈₆	—	2	2	no	—
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₄₃	#41	1	2	yes	—
122	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
123	C₄²×C₄₃	D₈	1	1	yes	characteristic
124	C₄²×C₄₃	D₈	1	1	yes	characteristic
125	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂²⋊Dic₄₃	—	4	1	no	—
128	(C₂×D₄₃)⋊C₄	—	4	1	no	—
129	(C₂×D₄₃)⋊C₄	—	4	1	no	—
130	(C₂×D₄₃)⋊C₄	—	4	2	no	—
131	(C₂×D₄₃)⋊C₄	—	4	2	no	—
132	C₄⋊Dic₄₃	—	2	1	no	—
133	C₄⋊Dic₄₃	—	2	1	no	—
134	C₄⋊Dic₄₃	—	4	1	no	—
135	C₄⋊Dic₄₃	—	4	1	no	—
136	Dic₄₃⋊C₄	—	4	1	no	—
137	Dic₄₃⋊C₄	—	4	1	no	—
138	C₄×Dic₄₃	—	4	1	no	—
139	C₄×Dic₄₃	—	4	1	no	—
140	C₄×Dic₄₃	—	4	1	no	—
141	Dic₁₇₂	—	2	2	no	—
142	Dic₁₇₂	—	2	1	no	—
143	Dic₁₇₂	—	2	2	no	—
144	Dic₁₇₂	—	4	2	no	—
145	Dic₁₇₂	C₂×D₄	1	2	yes	—
146	D₃₄₄	—	2	2	no	—
147	D₃₄₄	—	2	1	no	—
148	D₃₄₄	—	2	2	no	—
149	D₃₄₄	—	4	2	no	—
150	D₃₄₄	C₂×D₄	1	2	yes	—
151	#10621873	—	2	4	no	—
152	#10621873	—	4	4	no	—
153	#10621873	—	4	4	no	—
154	C₁₆×C₄₃	—	2	2	no	—
155	C₁₆×C₄₃	—	2	2	no	—
156	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
157	C₂²×D₄₃	—	4	1	no	—
158	C₂²×D₄₃	—	4	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	4	1	no	—
161	C₂×C₄×C₄₃	#121	1	2	yes	—
162	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
168	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
169	C₂²⋊D₄₃	—	4	4	no	—
170	C₂²⋊D₄₃	—	8	4	no	—
171	C₂×Dic₄₃	—	4	1	no	—
172	C₂×Dic₄₃	—	4	1	no	—
173	C₂×Dic₄₃	—	4	1	no	—
174	C₂×Dic₄₃	—	4	2	no	—
175	D₁₇₂	—	2	2	no	—
176	D₁₇₂	—	4	2	no	—
177	D₁₇₂	—	4	1	no	—
178	D₁₇₂	—	4	2	no	—
179	D₁₇₂	—	8	2	no	—
180	D₁₇₂	—	8	2	no	—
181	C₄×D₄₃	—	4	4	no	—
182	C₄×D₄₃	—	8	2	no	—
183	C₄×D₄₃	—	8	4	no	—
184	C₄×D₄₃	—	8	2	no	—
185	Dic₈₆	—	2	2	no	—
186	Dic₈₆	—	4	1	no	—
187	Dic₈₆	—	4	2	no	—
188	Dic₈₆	—	4	2	no	—
189	C₈×C₄₃	—	2	1	no	—
190	C₈×C₄₃	—	2	1	no	—
191	C₈×C₄₃	#121	1	2	yes	—
192	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₄₃	C₂×#41	1	1	yes	characteristic
194	#33579	—	43	1	no	maximal, Sylow
195	C₂²×C₄₃	—	2	1	no	—
196	C₂²×C₄₃	—	2	1	no	—
197	C₂²×C₄₃	#459	1	2	yes	—
198	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
199	C₂×D₄₃	—	4	2	no	—
200	C₂×D₄₃	—	8	1	no	—
201	C₂×D₄₃	—	8	1	no	—
202	C₂×D₄₃	—	8	2	no	—
203	C₂×D₄₃	—	8	2	no	—
204	C₂×D₄₃	—	8	2	no	—
205	C₄×C₄₃	—	2	1	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	2	1	no	—
208	C₄×C₄₃	#459	1	2	yes	—
209	C₄×C₄₃	#508	1	2	yes	complemented
210	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
211	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	Dic₄₃	—	4	2	no	—
213	Dic₄₃	—	8	1	no	—
214	Dic₄₃	—	8	1	no	—
215	Dic₄₃	—	8	2	no	—
216	C₂×#508	—	43	2	no	—
217	#3147	—	43	1	no	—
218	C₄×#135	—	43	1	no	—
219	#2211	—	43	2	no	—
220	#2210	—	43	2	no	—
221	#2209	—	43	1	no	—
222	#2208	—	43	1	no	—
223	#2207	—	43	1	no	—
224	#2206	—	43	1	no	—
225	C₂×C₄⋊C₁₆	D₄₃	1	1	yes	characteristic, complemented
226	#2138	—	43	2	no	—
227	C₂×C₄₃	—	2	2	no	—
228	C₂×C₄₃	C₂×#459	1	1	yes	characteristic
229	C₂×C₄₃	C₂×#508	1	1	yes	characteristic
230	C₂×C₄₃	#3414	1	1	yes	characteristic
231	D₄₃	—	8	2	no	—
232	D₄₃	—	16	2	no	—
233	C₂×#135	—	43	1	no	—
234	C₂×#135	—	43	2	no	—
235	C₂×#135	—	86	1	no	—
236	#532	—	86	1	no	—
237	C₄×#41	—	86	1	no	—
238	#508	—	86	8	no	—
239	C₂×Q₃₂	—	43	2	no	—
240	C₂×SD₃₂	—	43	2	no	—
241	C₂×SD₃₂	—	43	2	no	—
242	C₂×D₁₆	—	43	2	no	—
243	C₂²×C₁₆	C₂×D₄₃	1	2	yes	—
244	#495	—	43	2	no	—
245	#495	—	86	1	no	—
246	#494	—	43	1	no	—
247	#493	—	43	1	no	—
248	#492	—	86	1	no	—
249	C₄×Q₁₆	—	43	1	no	—
250	C₄×Q₁₆	—	43	1	no	—
251	C₄×SD₁₆	—	86	1	no	—
252	C₄×SD₁₆	—	86	1	no	—
253	C₄×D₈	—	43	1	no	—
254	C₄×D₈	—	43	1	no	—
255	#427	—	43	1	no	—
256	#416	—	86	1	no	—
257	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
258	C₄⋊C₁₆	C₂×D₄₃	1	1	yes	characteristic
259	C₄⋊C₁₆	C₂×D₄₃	1	1	yes	characteristic
260	C₄⋊C₁₆	C₂×D₄₃	1	2	yes	—
261	#358	—	43	2	no	—
262	#358	—	43	2	no	—
263	#357	—	43	2	no	—
264	#357	—	43	2	no	—
265	C₄₃	#33579	1	1	yes	characteristic, complemented, Sylow
266	C₂×#41	—	86	1	no	—
267	C₂×#41	—	86	2	no	—
268	#135	—	43	4	no	—
269	#135	—	86	4	no	—
270	#135	—	86	2	no	—
271	#135	—	86	4	no	—
272	#135	—	172	4	no	—
273	C₂×Q₁₆	—	43	1	no	—
274	C₂×Q₁₆	—	43	2	no	—
275	C₂×Q₁₆	—	86	1	no	—
276	C₂×SD₁₆	—	86	1	no	—
277	C₂×SD₁₆	—	86	2	no	—
278	C₂×SD₁₆	—	86	2	no	—
279	C₂×D₈	—	43	1	no	—
280	C₂×D₈	—	43	2	no	—
281	C₂×D₈	—	86	1	no	—
282	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
283	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
284	C₄⋊Q₈	—	86	1	no	—
285	#127	—	86	1	no	—
286	#124	—	86	2	no	—
287	#121	—	172	1	no	—
288	#121	—	172	1	no	—
289	C₄×Q₈	—	86	1	no	—
290	C₄×Q₈	—	86	1	no	—
291	C₄×D₄	—	86	1	no	—
292	C₄×D₄	—	86	1	no	—
293	C₄×D₄	—	172	1	no	—
294	C₄×D₄	—	172	1	no	—
295	C₄×D₄	—	172	1	no	—
296	C₄×D₄	—	172	1	no	—
297	#117	—	86	1	no	—
298	#117	—	172	1	no	—
299	C₂×C₄²	—	172	1	no	—
300	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
301	Q₃₂	—	86	4	no	—
302	SD₃₂	—	86	4	no	—
303	SD₃₂	—	86	4	no	—
304	D₁₆	—	86	4	no	—
305	C₂×C₁₆	—	2	4	no	—
306	C₂×C₁₆	C₂²×D₄₃	1	2	yes	—
307	C₂×C₁₆	C₂²×D₄₃	1	2	yes	—
308	#107	—	43	1	no	—
309	#107	—	43	1	no	—
310	#106	—	86	1	no	—
311	#103	—	86	1	no	—
312	#103	—	86	1	no	—
313	#102	—	86	1	no	—
314	#102	—	86	1	no	—
315	C₄×C₈	D₁₇₂	1	1	yes	characteristic
316	C₄×C₈	D₁₇₂	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
318	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
319	#41	—	86	4	no	—
320	#41	—	172	4	no	—
321	#41	—	172	4	no	—
322	#41	—	172	2	no	—
323	C₂×Q₈	—	86	1	no	—
324	C₂×Q₈	—	86	2	no	—
325	C₂×D₄	—	86	1	no	—
326	C₂×D₄	—	86	2	no	—
327	C₂×D₄	—	172	2	no	—
328	C₂×D₄	—	172	1	no	—
329	C₂×D₄	—	172	1	no	—
330	C₂×D₄	—	172	1	no	—
331	C₂²×C₄	—	172	1	no	—
332	C₂²×C₄	—	172	1	no	—
333	C₂²×C₄	—	172	2	no	—
334	C₂²×C₄	—	172	1	no	—
335	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
336	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
338	Q₁₆	—	43	2	no	—
339	Q₁₆	—	86	2	no	—
340	Q₁₆	—	86	1	no	—
341	Q₁₆	—	86	2	no	—
342	Q₁₆	—	172	2	no	—
343	SD₁₆	—	86	4	no	—
344	SD₁₆	—	172	4	no	—
345	SD₁₆	—	172	4	no	—
346	D₈	—	43	2	no	—
347	D₈	—	86	2	no	—
348	D₈	—	86	1	no	—
349	D₈	—	86	2	no	—
350	D₈	—	172	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
353	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
354	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
355	C₂×C₈	D₄×D₄₃	1	2	yes	—
356	C₂×C₈	#10621902	1	2	yes	—
357	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
358	C₄⋊C₄	—	86	1	no	—
359	C₄⋊C₄	—	86	1	no	—
360	C₄⋊C₄	—	172	1	no	—
361	C₄⋊C₄	—	172	1	no	—
362	C₄⋊C₄	—	172	1	no	—
363	C₄⋊C₄	—	172	1	no	—
364	C₂²⋊C₄	—	172	1	no	—
365	C₂²⋊C₄	—	172	1	no	—
366	C₂²⋊C₄	—	172	1	no	—
367	C₂²⋊C₄	—	172	2	no	—
368	C₂²⋊C₄	—	172	2	no	—
369	C₄²	—	172	1	no	—
370	C₄²	—	172	1	no	—
371	C₄²	—	172	1	no	—
372	C₄²	D₃₄₄	1	1	yes	characteristic
373	C₄²	D₃₄₄	1	1	yes	characteristic
374	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
375	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
376	C₁₆	—	2	2	no	—
377	C₁₆	—	2	2	no	—
378	C₂³	—	172	2	no	—
379	C₂³	—	172	1	no	—
380	C₂³	C₂×D₃₄₄	1	1	yes	characteristic
381	Q₈	—	86	2	no	—
382	Q₈	—	172	2	no	—
383	Q₈	—	172	2	no	—
384	Q₈	—	172	1	no	—
385	D₄	—	86	2	no	—
386	D₄	—	344	2	no	—
387	D₄	—	344	4	no	—
388	D₄	—	344	2	no	—
389	D₄	—	172	4	no	—
390	D₄	—	172	2	no	—
391	D₄	—	172	2	no	—
392	D₄	—	172	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	344	2	no	—
396	C₂×C₄	—	344	2	no	—
397	C₂×C₄	—	344	4	no	—
398	C₂×C₄	—	172	1	no	—
399	C₂×C₄	—	172	1	no	—
400	C₂×C₄	—	172	2	no	—
401	C₂×C₄	—	172	1	no	—
402	C₂×C₄	—	172	4	no	—
403	C₂×C₄	#13063300	1	2	yes	—
404	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
405	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
406	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
407	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
408	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
409	C₂×C₄	#13063353	1	2	yes	—
410	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	#13063300	1	2	yes	—
414	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
415	C₈	C₂×#10621902	1	1	yes	characteristic
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	344	1	no	—
419	C₂²	—	344	1	no	—
420	C₂²	—	344	2	no	—
421	C₂²	—	344	2	no	—
422	C₂²	—	344	2	no	—
423	C₂²	—	172	2	no	—
424	C₂²	#14583095	1	2	yes	—
425	C₂²	C₂²×D₃₄₄	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	344	2	no	—
430	C₄	—	344	1	no	—
431	C₄	—	344	1	no	—
432	C₄	—	172	2	no	—
433	C₄	#14583095	1	2	yes	—
434	C₄	#14583331	1	2	yes	complemented
435	C₄	C₂×#13063300	1	1	yes	characteristic
436	C₄	C₂×#13063353	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	344	2	no	—
439	C₂	—	688	2	no	—
440	C₂	C₂×#14583095	1	1	yes	characteristic
441	C₂	C₂×#14583331	1	1	yes	characteristic
442	C₂	#19147731	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃₄₄
commutator, cosocle	C₂×C₈×C₄₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₂×C₄₃×C₄⋊C₁₆	C₂
socle	C₂²×C₄₃	C₂²×D₈
hypercenter	C₂×C₄⋊C₁₆	D₄₃
hypocenter	C₄₃	#33579
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
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×#14583331	C₂	semidirect
2. #19145023	C₂	semidirect
3. C₄×#13063347	C₂	semidirect
4. #19136658	C₂	semidirect
5. #19136651	C₂	semidirect
6. #19136646	C₂	semidirect
7. #19136641	C₂	semidirect
8. #19136636	C₂	semidirect
9. #19136631	C₂	semidirect
10. #19136303	C₂	semidirect
11. C₂×C₄₃×C₄⋊C₁₆	C₂	semidirect
50. #13063347	D₄	semidirect
209. C₄×C₄₃	#508	semidirect
225. C₂×C₄⋊C₁₆	D₄₃	semidirect
265. C₄₃	#33579	semidirect
434. C₄	#14583331	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583331	2
#19145023	2
C₄×#13063347	2
#19136658	2
#19136651	2
#19136646	2
#19136641	2
#19136636	2
#19136631	2
#19136303	2
C₂×C₄₃×C₄⋊C₁₆	2
#33579	43