Subgroups — #25250991

Order 11008.

696 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19147731	C₂	1	2	yes	maximal, complemented
2	#19145023	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14583017	C₂	1	1	yes	maximal, characteristic, complemented
4	#19136677	C₂	1	2	yes	maximal, complemented
5	#19136672	C₂	1	2	yes	maximal, complemented
6	#19136665	C₂	1	4	yes	maximal, complemented
7	#19136345	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₃×#364	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13063347	—	2	1	no	—
10	C₂×#13063347	C₂²	1	1	yes	characteristic
11	C₂×#13063347	C₂²	1	2	yes	—
12	C₂×#13063331	—	2	1	no	—
13	#14583449	—	2	1	no	—
14	#14583342	—	2	2	no	—
15	#14583342	C₂²	1	4	yes	—
16	#14583337	—	2	2	no	—
17	#14583337	C₂²	1	4	yes	—
18	#14583331	—	2	4	no	—
19	#14583283	—	2	1	no	—
20	#14583283	C₂²	1	2	yes	complemented
21	#14583279	C₂²	1	1	yes	characteristic, complemented
22	#14583276	C₂²	1	1	yes	characteristic, complemented
23	#14583272	—	2	1	no	—
24	#14583017	—	2	1	no	—
25	#14583017	—	2	1	no	—
26	#14583017	C₂²	1	2	yes	—
27	#14583017	C₂²	1	2	yes	—
28	C₂×#13063261	C₂²	1	1	yes	characteristic
29	C₂×#13063253	—	2	1	no	—
30	#14582716	C₂²	1	4	yes	complemented
31	#14582713	C₂²	1	4	yes	complemented
32	C₂×M₃₂×C₄₃	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
34	C₄₃×#364	C₂²	1	2	yes	complemented
35	C₄₃×#364	C₂²	1	2	yes	complemented
36	C₂×#10621898	—	2	1	no	—
37	C₂×#10621898	—	2	2	no	—
38	#13063347	—	2	1	no	—
39	#13063347	—	2	1	no	—
40	#13063347	—	2	2	no	—
41	#13063347	—	2	2	no	—
42	#13063347	—	2	2	no	—
43	#13063347	—	2	2	no	—
44	#13063347	—	4	1	no	—
45	#13063347	—	4	1	no	—
46	#13063347	—	4	1	no	—
47	#13063347	—	4	1	no	—
48	#13063347	D₄	1	2	yes	complemented
49	#13063347	C₂³	1	2	yes	—
50	C₂×Dic₁₇₂	—	2	1	no	—
51	C₂×Dic₁₇₂	D₄	1	1	yes	characteristic, complemented
52	C₂×Dic₁₇₂	C₂³	1	2	yes	—
53	C₂×#10621873	—	2	1	no	—
54	C₂×#10621873	—	2	2	no	—
55	C₂×#10621873	—	2	2	no	—
56	C₂×D₃₄₄	—	2	1	no	—
57	C₂×D₃₄₄	D₄	1	1	yes	characteristic, complemented
58	C₂×D₃₄₄	C₂³	1	2	yes	—
59	#13063331	—	2	2	no	—
60	#13063331	—	2	2	no	—
61	#13063331	—	4	1	no	—
62	#13063331	—	4	1	no	—
63	C₂×#10621877	—	2	1	no	—
64	C₂×#10621872	—	4	1	no	—
65	C₂×C₈×D₄₃	—	4	1	no	—
66	#13063325	—	2	1	no	—
67	#13063322	—	2	1	no	—
68	#13063313	—	2	2	no	—
69	#13063299	—	4	2	no	—
70	C₄×D₁₇₂	—	4	2	no	—
71	Dic₃₄₄	—	2	4	no	—
72	#13063270	—	2	4	no	—
73	#13063270	—	2	4	no	—
74	D₆₈₈	—	2	4	no	—
75	#13063261	—	2	1	no	—
76	#13063261	C₂³	1	2	yes	—
77	#13063253	—	2	2	no	—
78	#13063253	—	2	2	no	—
79	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
82	M₃₂×C₄₃	—	2	2	no	—
83	M₃₂×C₄₃	C₂³	1	4	yes	—
84	C₂×C₁₆×C₄₃	—	2	2	no	—
85	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
86	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
87	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	—	2	1	no	—
90	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
91	C₂×C₂²⋊D₄₃	—	4	1	no	—
92	C₂×C₂²⋊D₄₃	—	4	2	no	—
93	#10621898	—	2	2	no	—
94	#10621898	—	2	2	no	—
95	#10621898	—	4	1	no	—
96	#10621898	—	4	1	no	—
97	#10621898	—	4	2	no	—
98	#10621898	—	4	2	no	—
99	#10621898	—	4	2	no	—
100	#10621898	—	4	2	no	—
101	C₂×D₁₇₂	—	2	1	no	—
102	C₂×D₁₇₂	—	2	2	no	—
103	C₂×D₁₇₂	—	4	2	no	—
104	C₂×C₄×D₄₃	—	4	1	no	—
105	C₂×C₄×D₄₃	—	4	2	no	—
106	C₂×Dic₈₆	—	2	1	no	—
107	C₂×Dic₈₆	—	2	2	no	—
108	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
109	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
110	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
111	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
112	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
118	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
119	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
120	C₄²×C₄₃	—	2	1	no	—
121	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
123	(C₂×D₄₃)⋊C₄	—	4	4	no	—
124	C₄⋊Dic₄₃	—	4	2	no	—
125	#10621877	—	2	2	no	—
126	#10621877	—	4	1	no	—
127	C₂×C₄₃⋊C₈	—	4	1	no	—
128	Dic₁₇₂	—	2	1	no	—
129	Dic₁₇₂	—	2	2	no	—
130	Dic₁₇₂	—	2	2	no	—
131	Dic₁₇₂	—	4	1	no	—
132	Dic₁₇₂	—	4	1	no	—
133	Dic₁₇₂	C₂×D₄	1	2	yes	—
134	D₃₄₄	—	2	1	no	—
135	D₃₄₄	—	2	2	no	—
136	D₃₄₄	—	2	2	no	—
137	D₃₄₄	—	4	1	no	—
138	D₃₄₄	—	4	1	no	—
139	D₃₄₄	C₂×D₄	1	2	yes	—
140	#10621873	—	2	2	no	—
141	#10621873	—	2	2	no	—
142	#10621873	—	4	2	no	—
143	#10621873	—	4	2	no	—
144	#10621873	—	4	2	no	—
145	#10621873	—	4	2	no	—
146	#10621872	—	4	2	no	—
147	#10621872	—	4	2	no	—
148	C₈×D₄₃	—	4	2	no	—
149	C₈×D₄₃	—	4	2	no	—
150	C₁₆×C₄₃	—	2	4	no	—
151	C₂³×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂²×D₄₃	—	4	1	no	—
153	C₂²×D₄₃	—	4	2	no	—
154	C₂×C₄×C₄₃	—	2	1	no	—
155	C₂×C₄×C₄₃	—	2	1	no	—
156	C₂×C₄×C₄₃	—	4	2	no	—
157	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
158	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
163	C₂²⋊D₄₃	—	4	2	no	—
164	C₂²⋊D₄₃	—	4	2	no	—
165	C₂²⋊D₄₃	—	8	2	no	—
166	C₂²⋊D₄₃	—	8	2	no	—
167	C₂×Dic₄₃	—	4	1	no	—
168	C₂×Dic₄₃	—	4	2	no	—
169	D₁₇₂	—	2	2	no	—
170	D₁₇₂	—	4	2	no	—
171	D₁₇₂	—	4	2	no	—
172	D₁₇₂	—	4	1	no	—
173	D₁₇₂	—	8	4	no	—
174	C₄×D₄₃	—	4	2	no	—
175	C₄×D₄₃	—	4	2	no	—
176	C₄×D₄₃	—	8	2	no	—
177	C₄×D₄₃	—	8	2	no	—
178	Dic₈₆	—	2	2	no	—
179	Dic₈₆	—	4	1	no	—
180	Dic₈₆	—	4	2	no	—
181	Dic₈₆	—	4	2	no	—
182	C₈×C₄₃	#121	1	1	yes	characteristic
183	C₈×C₄₃	#121	1	1	yes	characteristic
184	C₈×C₄₃	C₂×D₈	1	1	yes	characteristic
185	C₈×C₄₃	C₂×D₈	1	1	yes	characteristic
186	C₈×C₄₃	C₂×D₈	1	1	yes	characteristic
187	C₈×C₄₃	C₂×D₈	1	1	yes	characteristic
188	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
189	C₈×C₄₃	C₂×#41	1	1	yes	characteristic
190	C₄₃⋊C₈	—	4	2	no	—
191	#33594	—	43	1	no	maximal, Sylow
192	C₂²×C₄₃	—	4	1	no	—
193	C₂²×C₄₃	#459	1	1	yes	characteristic
194	C₂²×C₄₃	#459	1	1	yes	characteristic
195	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
196	C₂×D₄₃	—	4	2	no	—
197	C₂×D₄₃	—	8	2	no	—
198	C₂×D₄₃	—	8	4	no	—
199	C₂×D₄₃	—	8	2	no	—
200	C₄×C₄₃	—	2	2	no	—
201	C₄×C₄₃	—	4	1	no	—
202	C₄×C₄₃	#459	1	1	yes	characteristic
203	C₄×C₄₃	#459	1	1	yes	characteristic
204	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
205	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
206	Dic₄₃	—	4	2	no	—
207	Dic₄₃	—	8	2	no	—
208	#3414	—	43	2	no	—
209	#3147	—	43	1	no	—
210	C₂×#443	—	43	1	no	—
211	#2214	—	43	2	no	—
212	#2213	—	43	2	no	—
213	#2212	—	43	4	no	—
214	C₂×#364	D₄₃	1	1	yes	characteristic, complemented
215	#2148	—	43	2	no	—
216	C₂×C₄₃	—	2	1	no	—
217	C₂×C₄₃	—	2	1	no	—
218	C₂×C₄₃	—	2	1	no	—
219	C₂×C₄₃	C₂×#459	1	1	yes	characteristic
220	D₄₃	—	8	2	no	—
221	D₄₃	—	16	2	no	—
222	C₂×#135	—	43	1	no	—
223	C₂×#135	—	43	2	no	—
224	C₂×#135	—	86	1	no	—
225	C₂×#131	—	86	1	no	—
226	#532	—	86	1	no	—
227	#510	—	43	4	no	—
228	#510	—	86	2	no	—
229	#509	—	43	4	no	—
230	#509	—	86	2	no	—
231	#508	—	86	4	no	—
232	C₂×M₃₂	C₂×D₄₃	1	2	yes	—
233	#495	—	43	2	no	—
234	#495	—	86	1	no	—
235	#494	—	43	1	no	—
236	#493	—	43	1	no	—
237	#492	—	86	1	no	—
238	#443	—	43	2	no	—
239	#443	—	43	2	no	—
240	#443	—	86	1	no	—
241	#443	—	86	1	no	—
242	C₂×#108	—	43	1	no	—
243	C₂×#104	—	86	1	no	—
244	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
245	#364	C₂×D₄₃	1	2	yes	complemented
246	#364	C₂×D₄₃	1	2	yes	complemented
247	#362	—	43	4	no	—
248	#361	—	43	4	no	—
249	C₄₃	#33594	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	—	86	1	no	—
251	C₂×#41	—	86	2	no	—
252	#135	—	43	2	no	—
253	#135	—	43	2	no	—
254	#135	—	86	1	no	—
255	#135	—	86	2	no	—
256	#135	—	86	2	no	—
257	#135	—	86	1	no	—
258	#135	—	86	2	no	—
259	#135	—	86	2	no	—
260	#135	—	172	1	no	—
261	#135	—	172	1	no	—
262	#135	—	172	1	no	—
263	#135	—	172	1	no	—
264	C₂×Q₁₆	—	43	1	no	—
265	C₂×Q₁₆	—	43	2	no	—
266	C₂×Q₁₆	—	86	1	no	—
267	C₂×SD₁₆	—	86	2	no	—
268	C₂×SD₁₆	—	86	2	no	—
269	C₂×SD₁₆	—	86	1	no	—
270	C₂×D₈	—	43	1	no	—
271	C₂×D₈	—	43	2	no	—
272	C₂×D₈	—	86	1	no	—
273	#131	—	86	2	no	—
274	#131	—	86	2	no	—
275	#131	—	172	1	no	—
276	#131	—	172	1	no	—
277	C₂×M₁₆	—	86	1	no	—
278	C₂×M₁₆	—	172	1	no	—
279	C₂²×C₈	—	172	1	no	—
280	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
281	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
282	C₄⋊Q₈	—	86	1	no	—
283	#127	—	86	1	no	—
284	#124	—	86	2	no	—
285	#121	—	172	2	no	—
286	C₄×D₄	—	172	2	no	—
287	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
288	Q₃₂	—	86	4	no	—
289	SD₃₂	—	86	4	no	—
290	SD₃₂	—	86	4	no	—
291	D₁₆	—	86	4	no	—
292	M₃₂	—	2	2	no	—
293	M₃₂	C₂²×D₄₃	1	4	yes	—
294	C₂×C₁₆	—	2	2	no	—
295	#108	—	43	2	no	—
296	#108	—	86	1	no	—
297	#104	—	86	2	no	—
298	#104	—	86	2	no	—
299	C₄×C₈	D₁₇₂	1	1	yes	characteristic
300	C₄×C₈	D₁₇₂	1	1	yes	characteristic
301	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
302	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
303	#41	—	86	2	no	—
304	#41	—	86	2	no	—
305	#41	—	172	2	no	—
306	#41	—	172	2	no	—
307	#41	—	172	2	no	—
308	#41	—	172	2	no	—
309	#41	—	172	1	no	—
310	#41	—	172	1	no	—
311	C₂×Q₈	—	86	1	no	—
312	C₂×Q₈	—	86	2	no	—
313	C₂×D₄	—	86	1	no	—
314	C₂×D₄	—	86	2	no	—
315	C₂×D₄	—	172	2	no	—
316	C₂×D₄	—	172	2	no	—
317	C₂×D₄	—	172	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	172	2	no	—
320	C₂²×C₄	—	172	1	no	—
321	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
322	Q₁₆	—	43	2	no	—
323	Q₁₆	—	86	1	no	—
324	Q₁₆	—	86	2	no	—
325	Q₁₆	—	86	2	no	—
326	Q₁₆	—	172	1	no	—
327	Q₁₆	—	172	1	no	—
328	SD₁₆	—	86	2	no	—
329	SD₁₆	—	86	2	no	—
330	SD₁₆	—	172	2	no	—
331	SD₁₆	—	172	2	no	—
332	SD₁₆	—	172	2	no	—
333	SD₁₆	—	172	2	no	—
334	D₈	—	43	2	no	—
335	D₈	—	86	1	no	—
336	D₈	—	86	2	no	—
337	D₈	—	86	2	no	—
338	D₈	—	172	1	no	—
339	D₈	—	172	1	no	—
340	M₁₆	—	86	2	no	—
341	M₁₆	—	172	1	no	—
342	M₁₆	—	172	2	no	—
343	M₁₆	—	172	2	no	—
344	C₂×C₈	—	172	1	no	—
345	C₂×C₈	—	172	2	no	—
346	C₂×C₈	—	172	2	no	—
347	C₂×C₈	D₃₄₄	1	1	yes	characteristic
348	C₂×C₈	D₃₄₄	1	1	yes	characteristic
349	C₂×C₈	D₃₄₄	1	1	yes	characteristic
350	C₂×C₈	D₃₄₄	1	1	yes	characteristic
351	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
352	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
353	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
354	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
355	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
356	C₂×C₈	#10621902	1	1	yes	characteristic
357	C₂×C₈	#10621902	1	1	yes	characteristic
358	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
359	C₄⋊C₄	—	172	2	no	—
360	C₂²⋊C₄	—	172	4	no	—
361	C₄²	—	2	1	no	—
362	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
363	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
364	C₁₆	—	2	4	no	—
365	C₂³	—	172	2	no	—
366	C₂³	—	172	1	no	—
367	C₂³	#13063353	1	1	yes	characteristic
368	Q₈	—	86	2	no	—
369	Q₈	—	172	2	no	—
370	Q₈	—	172	2	no	—
371	Q₈	—	172	1	no	—
372	D₄	—	86	2	no	—
373	D₄	—	344	4	no	—
374	D₄	—	344	2	no	—
375	D₄	—	344	2	no	—
376	D₄	—	172	2	no	—
377	D₄	—	172	2	no	—
378	D₄	—	172	1	no	—
379	D₄	—	172	2	no	—
380	D₄	—	172	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	344	2	no	—
385	C₂×C₄	—	344	2	no	—
386	C₂×C₄	—	172	2	no	—
387	C₂×C₄	—	172	1	no	—
388	C₂×C₄	—	172	2	no	—
389	C₂×C₄	—	172	2	no	—
390	C₂×C₄	#13063300	1	1	yes	characteristic
391	C₂×C₄	#13063300	1	1	yes	characteristic
392	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
393	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
394	C₂×C₄	#13063353	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
396	C₈	—	172	2	no	—
397	C₈	#13063300	1	1	yes	characteristic
398	C₈	#13063300	1	1	yes	characteristic
399	C₈	C₂×D₃₄₄	1	1	yes	characteristic
400	C₈	C₂×D₃₄₄	1	1	yes	characteristic
401	C₈	C₂×D₃₄₄	1	1	yes	characteristic
402	C₈	C₂×D₃₄₄	1	1	yes	characteristic
403	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
404	C₈	C₂×#10621902	1	1	yes	characteristic
405	C₂²	—	4	1	no	—
406	C₂²	—	344	2	no	—
407	C₂²	—	344	4	no	—
408	C₂²	—	344	2	no	—
409	C₂²	—	172	2	no	—
410	C₂²	#14583095	1	1	yes	characteristic
411	C₂²	#14583095	1	1	yes	characteristic
412	C₂²	C₂×#13063353	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	344	2	no	—
416	C₄	—	172	2	no	—
417	C₄	#14583095	1	1	yes	characteristic
418	C₄	#14583095	1	1	yes	characteristic
419	C₄	C₂×#13063300	1	1	yes	characteristic
420	C₄	C₂²×D₃₄₄	1	1	yes	characteristic
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	344	2	no	—
425	C₂	—	688	2	no	—
426	C₂	C₂×#14583095	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14583095
commutator, cosocle	C₂×C₈×C₄₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₂×C₄₃×#364	C₂
socle	C₂×C₄₃	C₂×#459
hypercenter	C₂×#364	D₄₃
hypocenter	C₄₃	#33594
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

Complements

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

N	H ≅ G/N	type
1. #19147731	C₂	semidirect
2. #19145023	C₂	semidirect
3. C₂×#14583017	C₂	semidirect
4. #19136677	C₂	semidirect
5. #19136672	C₂	semidirect
6. #19136665	C₂	semidirect
7. #19136345	C₂	semidirect
8. C₂×C₄₃×#364	C₂	semidirect
20. #14583283	C₂²	semidirect
21. #14583279	C₂²	semidirect
22. #14583276	C₂²	semidirect
30. #14582716	C₂²	semidirect
31. #14582713	C₂²	semidirect
34. C₄₃×#364	C₂²	semidirect
35. C₄₃×#364	C₂²	semidirect
48. #13063347	D₄	semidirect
51. C₂×Dic₁₇₂	D₄	semidirect
57. C₂×D₃₄₄	D₄	semidirect
214. C₂×#364	D₄₃	semidirect
245. #364	C₂×D₄₃	semidirect
246. #364	C₂×D₄₃	semidirect
249. C₄₃	#33594	semidirect

Maximal subgroups

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

subgroup	index
#19147731	2
#19145023	2
C₂×#14583017	2
#19136677	2
#19136672	2
#19136665	2
#19136345	2
C₂×C₄₃×#364	2
#33594	43