Subgroups — #25977545

Order 11008.

1958 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148190	C₂	1	2	yes	maximal, complemented
2	#19147608	C₂	1	3	yes	maximal, complemented
3	#19147601	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147593	C₂	1	6	yes	maximal, complemented
5	#19147584	C₂	1	3	yes	maximal, complemented
6	#19147577	C₂	1	2	yes	maximal, complemented
7	#19147570	C₂	1	1	yes	maximal, characteristic, complemented
8	#19145023	C₂	1	3	yes	maximal, complemented
9	#19144052	C₂	1	6	yes	maximal, complemented
10	C₄×#13063347	C₂	1	3	yes	maximal, complemented
11	C₂×C₈×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	C₂²	1	3	yes	—
13	C₂×#13063347	C₂²	1	6	yes	—
14	#14583634	C₂²	1	6	yes	—
15	#14583628	C₂²	1	2	yes	—
16	#14583622	C₂²	1	6	yes	—
17	#14583597	—	2	6	no	—
18	#14583571	C₂²	1	2	yes	—
19	#14583560	—	2	2	no	—
20	#14583449	C₂²	1	6	yes	—
21	#14583436	—	2	6	no	—
22	C₄×#10621902	—	2	2	no	—
23	C₄×#10621898	C₂²	1	6	yes	—
24	#14583283	C₂²	1	6	yes	—
25	#14583283	C₂²	1	6	yes	—
26	#14583279	C₂²	1	3	yes	—
27	#14583276	C₂²	1	3	yes	—
28	#14583272	C₂²	1	6	yes	—
29	#14583122	C₂²	1	12	yes	—
30	#14583115	C₂²	1	12	yes	—
31	#14583110	C₂²	1	6	yes	—
32	#14583105	C₂²	1	6	yes	—
33	#14583100	C₂²	1	6	yes	—
34	#14583095	C₂²	1	6	yes	—
35	C₄×Dic₁₇₂	C₂²	1	3	yes	—
36	C₄×Dic₁₇₂	C₂²	1	3	yes	—
37	C₄×#10621873	C₂²	1	6	yes	—
38	C₄×#10621873	C₂²	1	6	yes	—
39	C₄×D₃₄₄	C₂²	1	3	yes	—
40	C₄×D₃₄₄	C₂²	1	3	yes	—
41	#14582937	C₂²	1	1	yes	characteristic
42	#14582896	C₂²	1	6	yes	—
43	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
44	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic
46	C₈×Q₈×C₄₃	C₂²	1	3	yes	—
47	C₈×Q₈×C₄₃	C₂²	1	3	yes	—
48	C₂×C₄⋊C₈×C₄₃	C₂²	1	3	yes	—
49	C₂×C₄×C₈×C₄₃	C₂²	1	3	yes	—
50	C₂×#10621902	—	2	2	no	—
51	C₂×#10621898	C₂³	1	6	yes	—
52	#13063347	—	2	12	no	—
53	#13063347	—	4	12	no	—
54	C₂×Dic₁₇₂	C₂³	1	3	yes	—
55	C₂×Dic₁₇₂	C₂³	1	6	yes	—
56	C₂×#10621873	C₂³	1	6	yes	—
57	C₂×#10621873	C₂³	1	12	yes	—
58	C₂×D₃₄₄	C₂³	1	3	yes	—
59	C₂×D₃₄₄	C₂³	1	6	yes	—
60	#13063325	C₂³	1	6	yes	—
61	#13063322	C₂³	1	6	yes	—
62	#13063320	—	2	12	no	—
63	#13063316	—	2	6	no	—
64	#13063314	—	2	6	no	—
65	#13063313	C₂³	1	12	yes	—
66	#13063310	—	2	12	no	—
67	#13063301	—	2	6	no	—
68	#13063300	—	2	6	no	—
69	#13063299	—	2	6	no	—
70	#13063299	—	2	6	no	—
71	Q₈×Dic₄₃	—	2	2	no	—
72	C₄×Dic₈₆	C₂³	1	6	yes	—
73	C₄×Dic₈₆	C₂³	1	6	yes	—
74	C₄×D₁₇₂	—	2	6	no	—
75	C₄×D₁₇₂	—	2	6	no	—
76	C₄×D₁₇₂	C₂³	1	6	yes	—
77	C₄×D₁₇₂	C₂³	1	6	yes	—
78	#13063287	—	2	6	no	—
79	C₄×C₂²⋊D₄₃	—	2	6	no	—
80	C₄×C₂²⋊D₄₃	—	2	6	no	—
81	#13063284	C₂³	1	2	yes	—
82	#13063283	—	2	6	no	—
83	#13063282	—	2	6	no	—
84	C₄²×D₄₃	—	2	6	no	—
85	#13063259	C₂³	1	1	yes	characteristic
86	#13063259	C₂³	1	1	yes	characteristic
87	#13063257	C₂³	1	2	yes	—
88	#13063250	C₂³	1	6	yes	—
89	#13063250	C₂³	1	6	yes	—
90	#13063247	C₂³	1	6	yes	—
91	#13063247	C₂³	1	6	yes	—
92	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
93	C₂²×C₈×C₄₃	C₂³	1	3	yes	—
94	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
96	C₄×Q₈×C₄₃	D₄	1	3	yes	—
97	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₄×Q₈×C₄₃	C₂³	1	3	yes	—
99	C₂×C₄⋊C₄×C₄₃	D₄	1	3	yes	—
100	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
101	C₄⋊C₈×C₄₃	C₂³	1	3	yes	—
102	C₄⋊C₈×C₄₃	C₂³	1	3	yes	—
103	C₄⋊C₈×C₄₃	C₂³	1	6	yes	—
104	C₄×C₈×C₄₃	C₂³	1	3	yes	—
105	C₄×C₈×C₄₃	C₂³	1	3	yes	—
106	C₄×C₈×C₄₃	C₂³	1	3	yes	—
107	C₄×C₈×C₄₃	C₂³	1	3	yes	—
108	C₂×Q₈×C₄₃	—	2	4	no	—
109	C₂×Q₈×C₄₃	C₂×D₄	1	3	yes	—
110	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
112	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
113	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
114	C₂×C₂²⋊D₄₃	—	2	6	no	—
115	#10621902	—	4	8	no	—
116	#10621898	—	2	12	no	—
117	#10621898	—	2	12	no	—
118	C₂×D₁₇₂	—	2	6	no	—
119	C₂×D₁₇₂	—	2	6	no	—
120	C₂×D₁₇₂	C₂⁴	1	6	yes	—
121	C₂×C₄×D₄₃	—	2	6	no	—
122	C₂×C₄×D₄₃	—	2	6	no	—
123	C₂×C₄×D₄₃	—	2	6	no	—
124	C₂×Dic₈₆	C₂⁴	1	6	yes	—
125	C₂×C₈×C₄₃	—	2	6	no	—
126	C₂×C₈×C₄₃	#41	1	4	yes	complemented
127	C₂×C₈×C₄₃	C₂⁴	1	3	yes	—
128	C₂×C₈×C₄₃	C₂⁴	1	3	yes	—
129	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
130	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
131	C₄⋊C₄×C₄₃	C₂×D₄	1	3	yes	—
132	C₄⋊C₄×C₄₃	C₂×D₄	1	3	yes	—
133	C₄⋊C₄×C₄₃	C₂×D₄	1	6	yes	—
134	C₄²×C₄₃	C₂×D₄	1	3	yes	—
135	C₄²×C₄₃	C₂×D₄	1	3	yes	—
136	C₄²×C₄₃	C₂⁴	1	3	yes	—
137	C₄²×C₄₃	C₂⁴	1	3	yes	—
138	C₂²⋊Dic₄₃	—	2	2	no	—
139	(C₂×D₄₃)⋊C₄	—	2	6	no	—
140	(C₂×D₄₃)⋊C₄	—	2	6	no	—
141	(C₂×D₄₃)⋊C₄	—	2	12	no	—
142	(C₂×D₄₃)⋊C₄	—	2	12	no	—
143	C₄⋊Dic₄₃	—	2	6	no	—
144	C₄⋊Dic₄₃	—	2	6	no	—
145	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
146	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
147	Dic₄₃⋊C₄	—	2	6	no	—
148	Dic₄₃⋊C₄	—	2	6	no	—
149	C₄×Dic₄₃	—	2	2	no	—
150	C₄×Dic₄₃	—	2	6	no	—
151	C₄×Dic₄₃	—	2	6	no	—
152	Dic₁₇₂	—	2	6	no	—
153	Dic₁₇₂	—	4	6	no	—
154	D₃₄₄	—	2	6	no	—
155	D₃₄₄	—	4	6	no	—
156	#10621873	—	2	12	no	—
157	#10621873	—	4	12	no	—
158	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
159	C₂²×D₄₃	—	2	6	no	—
160	Q₈×C₄₃	—	2	6	no	—
161	Q₈×C₄₃	#135	1	4	yes	complemented
162	C₂×C₄×C₄₃	—	2	6	no	—
163	C₂×C₄×C₄₃	—	4	3	no	—
164	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
165	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
166	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
167	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
168	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
170	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
171	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
172	C₂²⋊D₄₃	—	4	12	no	—
173	C₂×Dic₄₃	—	2	2	no	—
174	C₂×Dic₄₃	—	2	2	no	—
175	C₂×Dic₄₃	—	2	6	no	—
176	D₁₇₂	—	2	6	no	—
177	D₁₇₂	—	2	6	no	—
178	D₁₇₂	—	4	12	no	—
179	D₁₇₂	—	8	6	no	—
180	C₄×D₄₃	—	4	12	no	—
181	C₄×D₄₃	—	4	12	no	—
182	C₄×D₄₃	—	8	6	no	—
183	Dic₈₆	—	2	6	no	—
184	Dic₈₆	—	2	6	no	—
185	C₈×C₄₃	—	2	3	no	—
186	C₈×C₄₃	—	2	3	no	—
187	C₈×C₄₃	C₂×#41	1	2	yes	—
188	C₈×C₄₃	C₂×#41	1	2	yes	—
189	#61393	—	43	1	no	maximal, Sylow
190	C₂²×C₄₃	—	2	1	no	—
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	#550	1	2	yes	—
193	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
194	C₂×D₄₃	—	4	6	no	—
195	C₂×D₄₃	—	4	6	no	—
196	C₂×D₄₃	—	4	6	no	—
197	C₄×C₄₃	—	2	3	no	—
198	C₄×C₄₃	—	2	3	no	—
199	C₄×C₄₃	—	2	3	no	—
200	C₄×C₄₃	#550	1	2	yes	—
201	C₄×C₄₃	C₂×#135	1	6	yes	—
202	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
203	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
204	Dic₄₃	—	4	2	no	—
205	Dic₄₃	—	4	6	no	—
206	Dic₄₃	—	4	2	no	—
207	#3480	—	43	2	no	—
208	#3396	—	43	3	no	—
209	#3395	—	43	1	no	—
210	#3394	—	43	6	no	—
211	#3393	—	43	3	no	—
212	#3392	—	43	2	no	—
213	#3391	—	43	1	no	—
214	#3147	—	43	3	no	—
215	#3035	—	43	6	no	—
216	C₂×C₈×Q₈	D₄₃	1	1	yes	characteristic, complemented
217	C₄×#135	—	43	3	no	—
218	C₂×C₄₃	—	2	2	no	—
219	C₂×C₄₃	C₂×#550	1	1	yes	characteristic
220	C₂×C₄₃	C₂²×#135	1	1	yes	characteristic
221	C₂×C₄₃	#3584	1	1	yes	characteristic
222	D₄₃	—	8	6	no	—
223	C₂×#135	—	43	3	no	—
224	C₂×#135	—	43	6	no	—
225	#559	—	43	6	no	—
226	#557	—	43	2	no	—
227	#556	—	43	6	no	—
228	#553	—	86	6	no	—
229	#550	—	43	2	no	—
230	#548	—	86	2	no	—
231	#532	—	43	6	no	—
232	#529	—	86	6	no	—
233	C₄×#41	—	43	6	no	—
234	C₄×#41	—	86	2	no	—
235	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
236	#495	—	43	6	no	—
237	#495	—	43	6	no	—
238	#494	—	43	3	no	—
239	#493	—	43	3	no	—
240	#492	—	43	6	no	—
241	#464	—	43	12	no	—
242	#463	—	43	12	no	—
243	#462	—	43	6	no	—
244	#461	—	43	6	no	—
245	#460	—	43	6	no	—
246	#459	—	43	6	no	—
247	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic
248	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic
249	C₈×Q₈	C₂×D₄₃	1	3	yes	—
250	C₈×Q₈	C₂×D₄₃	1	3	yes	—
251	C₄×Q₁₆	—	43	3	no	—
252	C₄×Q₁₆	—	43	3	no	—
253	C₄×SD₁₆	—	43	6	no	—
254	C₄×SD₁₆	—	43	6	no	—
255	C₄×D₈	—	43	3	no	—
256	C₄×D₈	—	43	3	no	—
257	#427	—	43	1	no	—
258	C₂×C₄⋊C₈	C₂×D₄₃	1	3	yes	—
259	#416	—	43	6	no	—
260	C₂×C₄×C₈	C₂×D₄₃	1	3	yes	—
261	C₄₃	#61393	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	43	6	no	—
263	C₂×#41	—	86	2	no	—
264	C₂²×Q₈	D₁₇₂	1	1	yes	characteristic
265	#135	—	86	12	no	—
266	#135	—	172	12	no	—
267	C₂×Q₁₆	—	43	3	no	—
268	C₂×Q₁₆	—	43	6	no	—
269	C₂×SD₁₆	—	43	6	no	—
270	C₂×SD₁₆	—	43	12	no	—
271	C₂×D₈	—	43	3	no	—
272	C₂×D₈	—	43	6	no	—
273	C₂²×C₈	C₂²×D₄₃	1	3	yes	—
274	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
275	C₄⋊Q₈	—	43	6	no	—
276	#127	—	43	6	no	—
277	#126	—	86	12	no	—
278	#125	—	86	6	no	—
279	#124	—	43	12	no	—
280	#124	—	86	6	no	—
281	#123	—	86	12	no	—
282	C₂²⋊Q₈	—	86	6	no	—
283	#121	—	86	6	no	—
284	#121	—	86	6	no	—
285	#121	—	86	6	no	—
286	C₄×Q₈	—	43	6	no	—
287	C₄×Q₈	—	43	6	no	—
288	C₄×Q₈	—	86	2	no	—
289	C₄×Q₈	D₁₇₂	1	1	yes	characteristic
290	C₄×Q₈	D₁₇₂	1	3	yes	—
291	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
292	C₄×Q₈	C₂²×D₄₃	1	3	yes	—
293	C₄×D₄	—	43	6	no	—
294	C₄×D₄	—	43	6	no	—
295	C₄×D₄	—	86	6	no	—
296	C₄×D₄	—	86	6	no	—
297	C₄×D₄	—	86	6	no	—
298	C₄×D₄	—	86	6	no	—
299	C₄×D₄	—	86	6	no	—
300	#117	—	43	2	no	—
301	#117	—	86	6	no	—
302	#117	—	86	6	no	—
303	C₂×C₄⋊C₄	D₁₇₂	1	3	yes	—
304	C₂×C₄²	—	86	6	no	—
305	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
306	#107	—	43	1	no	—
307	#107	—	43	1	no	—
308	#106	—	43	2	no	—
309	C₄⋊C₈	C₂²×D₄₃	1	3	yes	—
310	C₄⋊C₈	C₂²×D₄₃	1	3	yes	—
311	C₄⋊C₈	C₂²×D₄₃	1	6	yes	—
312	#103	—	43	6	no	—
313	#103	—	43	6	no	—
314	#102	—	43	6	no	—
315	#102	—	43	6	no	—
316	C₄×C₈	C₂²×D₄₃	1	3	yes	—
317	C₄×C₈	C₂²×D₄₃	1	3	yes	—
318	C₄×C₈	C₂²×D₄₃	1	3	yes	—
319	C₄×C₈	C₂²×D₄₃	1	3	yes	—
320	#41	—	86	12	no	—
321	#41	—	86	12	no	—
322	#41	—	172	8	no	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	43	6	no	—
325	C₂×Q₈	C₂×D₁₇₂	1	3	yes	—
326	C₂×Q₈	C₂×D₁₇₂	1	1	yes	characteristic
327	C₂×D₄	—	43	6	no	—
328	C₂×D₄	—	86	6	no	—
329	C₂×D₄	—	86	6	no	—
330	C₂×D₄	—	86	6	no	—
331	C₂²×C₄	—	86	6	no	—
332	C₂²×C₄	—	86	6	no	—
333	C₂²×C₄	—	86	6	no	—
334	C₂²×C₄	C₂×D₁₇₂	1	3	yes	—
335	C₂²×C₄	C₂×D₁₇₂	1	3	yes	—
336	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
337	Q₁₆	—	86	6	no	—
338	Q₁₆	—	172	6	no	—
339	SD₁₆	—	86	12	no	—
340	SD₁₆	—	172	12	no	—
341	D₈	—	86	6	no	—
342	D₈	—	172	6	no	—
343	C₂×C₈	—	2	6	no	—
344	C₂×C₈	#10621902	1	4	yes	complemented
345	C₂×C₈	C₂³×D₄₃	1	3	yes	—
346	C₂×C₈	C₂³×D₄₃	1	3	yes	—
347	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
348	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
349	C₄⋊C₄	—	43	2	no	—
350	C₄⋊C₄	—	43	2	no	—
351	C₄⋊C₄	—	86	6	no	—
352	C₄⋊C₄	—	86	6	no	—
353	C₄⋊C₄	—	86	6	no	—
354	C₄⋊C₄	—	86	6	no	—
355	C₄⋊C₄	C₂×D₁₇₂	1	3	yes	—
356	C₄⋊C₄	C₂×D₁₇₂	1	3	yes	—
357	C₄⋊C₄	C₂×D₁₇₂	1	6	yes	—
358	C₂²⋊C₄	—	86	2	no	—
359	C₂²⋊C₄	—	86	6	no	—
360	C₂²⋊C₄	—	86	6	no	—
361	C₂²⋊C₄	—	86	12	no	—
362	C₂²⋊C₄	—	86	12	no	—
363	C₄²	—	86	6	no	—
364	C₄²	—	86	6	no	—
365	C₄²	—	86	2	no	—
366	C₄²	C₂×D₁₇₂	1	3	yes	—
367	C₄²	C₂×D₁₇₂	1	3	yes	—
368	C₄²	C₂³×D₄₃	1	3	yes	—
369	C₄²	C₂³×D₄₃	1	3	yes	—
370	C₂³	—	86	6	no	—
371	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
372	Q₈	—	2	6	no	—
373	Q₈	—	86	6	no	—
374	Q₈	—	86	6	no	—
375	Q₈	#13063347	1	4	yes	complemented
376	D₄	—	86	6	no	—
377	D₄	—	86	6	no	—
378	D₄	—	344	6	no	—
379	D₄	—	172	12	no	—
380	D₄	—	172	12	no	—
381	C₂×C₄	—	2	6	no	—
382	C₂×C₄	—	4	3	no	—
383	C₂×C₄	—	86	2	no	—
384	C₂×C₄	—	86	2	no	—
385	C₂×C₄	—	86	6	no	—
386	C₂×C₄	—	344	6	no	—
387	C₂×C₄	—	172	12	no	—
388	C₂×C₄	—	172	12	no	—
389	C₂×C₄	C₂²×D₁₇₂	1	3	yes	—
390	C₂×C₄	C₂²×D₁₇₂	1	3	yes	—
391	C₂×C₄	C₂²×D₁₇₂	1	3	yes	—
392	C₂×C₄	C₂²×D₁₇₂	1	3	yes	—
393	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
394	C₂×C₄	C₂×#10621902	1	2	yes	—
395	C₂×C₄	#13063371	1	2	yes	—
396	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
397	C₈	—	2	3	no	—
398	C₈	—	2	3	no	—
399	C₈	C₂×#10621902	1	2	yes	—
400	C₈	C₂×#10621902	1	2	yes	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	172	6	no	—
404	C₂²	—	172	6	no	—
405	C₂²	—	172	6	no	—
406	C₂²	#14583571	1	2	yes	—
407	C₂²	C₂³×D₁₇₂	1	1	yes	characteristic
408	C₄	—	2	3	no	—
409	C₄	—	2	3	no	—
410	C₄	—	2	3	no	—
411	C₄	—	172	2	no	—
412	C₄	—	172	6	no	—
413	C₄	—	172	2	no	—
414	C₄	#14583571	1	2	yes	—
415	C₄	C₂×#13063347	1	6	yes	—
416	C₄	C₂²×#10621902	1	1	yes	characteristic
417	C₄	C₂×#13063371	1	1	yes	characteristic
418	C₂	—	2	2	no	—
419	C₂	—	344	6	no	—
420	C₂	C₂×#14583571	1	1	yes	characteristic
421	C₂	C₂²×#13063347	1	1	yes	characteristic
422	C₂	#19149369	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₈×Q₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₂×C₈×Q₈	D₄₃
hypocenter	C₄₃	#61393
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×Q₈ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
1. #19148190	C₂	semidirect
2. #19147608	C₂	semidirect
3. #19147601	C₂	semidirect
4. #19147593	C₂	semidirect
5. #19147584	C₂	semidirect
6. #19147577	C₂	semidirect
7. #19147570	C₂	semidirect
8. #19145023	C₂	semidirect
9. #19144052	C₂	semidirect
10. C₄×#13063347	C₂	semidirect
11. C₂×C₈×Q₈×C₄₃	C₂	semidirect
126. C₂×C₈×C₄₃	#41	semidirect
161. Q₈×C₄₃	#135	semidirect
216. C₂×C₈×Q₈	D₄₃	semidirect
261. C₄₃	#61393	semidirect
344. C₂×C₈	#10621902	semidirect
375. Q₈	#13063347	semidirect

Maximal subgroups

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

subgroup	index
#19148190	2
#19147608	2
#19147601	2
#19147593	2
#19147584	2
#19147577	2
#19147570	2
#19145023	2
#19144052	2
C₄×#13063347	2
C₂×C₈×Q₈×C₄₃	2
#61393	43