Subgroups — #34034535

Order 18688.

714 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22627175	C₂	1	2	yes	maximal, complemented
2	#22627062	C₂	1	2	yes	maximal, complemented
3	#22627061	C₂	1	2	yes	maximal, complemented
4	SD₁₆×#10596842	C₂	1	4	yes	maximal, complemented
5	C₂×#17989676	C₂	1	1	yes	maximal, characteristic, complemented
6	#22627050	C₂	1	2	yes	maximal, complemented
7	#22627040	C₂	1	1	yes	maximal, characteristic, complemented
8	#135×#64408	C₂	1	1	yes	maximal, characteristic
9	Q₈×#10596842	C₂²	1	4	yes	—
10	D₄×#10596842	—	2	4	no	—
11	D₄×#10596842	C₂²	1	4	yes	—
12	#17989700	—	2	2	no	—
13	#17989700	C₂²	1	1	yes	characteristic
14	#17989700	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊#10596842	—	2	2	no	—
16	C₂×C₄⋊#10596842	C₂²	1	2	yes	—
17	#17989676	C₂²	1	2	yes	—
18	#17989676	C₂²	1	2	yes	—
19	Q₈⋊#10596842	C₂²	1	4	yes	—
20	D₄⋊#10596842	C₂²	1	4	yes	—
21	#17989671	C₂²	1	2	yes	—
22	C₈×#10596842	C₂²	1	2	yes	—
23	#41×#64408	C₂²	1	2	yes	—
24	Q₁₆×#64408	C₄	1	1	yes	characteristic
25	Q₁₆×#64408	C₂²	1	1	yes	characteristic
26	SD₁₆×#64408	C₄	1	2	yes	—
27	SD₁₆×#64408	C₂²	1	2	yes	—
28	D₈×#64408	C₄	1	1	yes	characteristic
29	D₈×#64408	C₂²	1	1	yes	characteristic
30	#17989597	C₄	1	1	yes	characteristic
31	#17989577	C₄	1	2	yes	—
32	C₂×C₈×#64408	C₂²	1	1	yes	characteristic
33	#135×D₇₃	C₄	1	1	yes	characteristic
34	C₂²×#10596842	—	2	4	no	—
35	C₂²×#10596842	—	2	2	no	—
36	C₄⋊#10596842	—	2	4	no	—
37	C₄⋊#10596842	—	2	2	no	—
38	C₄⋊#10596842	—	2	1	no	—
39	C₄⋊#10596842	D₄	1	2	yes	—
40	C₄⋊#10596842	C₂³	1	4	yes	—
41	C₂²⋊#10596842	—	2	4	no	—
42	C₂²⋊#10596842	—	2	1	no	—
43	C₂²⋊#10596842	D₄	1	2	yes	—
44	C₄×#10596842	—	2	4	no	—
45	C₄×#10596842	C₂³	1	2	yes	—
46	C₄×#10596842	C₂³	1	2	yes	—
47	C₂×#11924036	C₂×C₄	1	1	yes	characteristic
48	Q₈×#64408	C₂×C₄	1	2	yes	—
49	Q₈×#64408	C₂³	1	2	yes	—
50	D₄×#64408	—	2	2	no	—
51	D₄×#64408	—	2	2	no	—
52	D₄×#64408	C₂×C₄	1	2	yes	—
53	D₄×#64408	C₂³	1	2	yes	—
54	#14556670	—	2	2	no	—
55	#14556670	C₂×C₄	1	2	yes	—
56	C₂×C₄×#64408	—	2	2	no	—
57	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
58	#14556660	C₂×C₄	1	1	yes	characteristic
59	#14556660	C₂×C₄	1	1	yes	characteristic
60	#14556659	C₂×C₄	1	2	yes	—
61	#14556654	C₂×C₄	1	2	yes	—
62	#14556654	C₂×C₄	1	2	yes	—
63	#14556653	C₂×C₄	1	2	yes	—
64	#14556653	C₂×C₄	1	2	yes	—
65	C₈×#64408	C₂×C₄	1	1	yes	characteristic
66	C₈×#64408	C₂×C₄	1	1	yes	characteristic
67	C₈×#64408	C₂³	1	1	yes	characteristic
68	C₈×#64408	C₂³	1	1	yes	characteristic
69	#41×D₇₃	C₂×C₄	1	2	yes	—
70	#14556614	C₈	1	1	yes	characteristic, complemented
71	#14556613	C₈	1	1	yes	characteristic, complemented
72	#14556612	C₈	1	2	yes	complemented
73	#14556611	C₈	1	2	yes	complemented
74	#14556610	C₈	1	1	yes	characteristic, complemented
75	Q₁₆×D₇₃	C₂×C₄	1	1	yes	characteristic
76	SD₁₆×D₇₃	C₂×C₄	1	2	yes	—
77	D₈×D₇₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
79	#135×C₇₃	C₈	1	1	yes	characteristic, complemented
80	C₂×#10596842	—	2	4	no	—
81	C₂×#10596842	—	2	2	no	—
82	C₂×#10596842	—	8	4	no	—
83	C₂×#10596842	—	8	2	no	—
84	C₂×#10596842	C₂×D₄	1	4	yes	—
85	C₂²×#64408	—	2	2	no	—
86	C₂²×#64408	—	2	2	no	—
87	C₂²×#64408	C₂×D₄	1	1	yes	characteristic
88	C₂²×#64408	#41	1	1	yes	characteristic
89	#11924036	—	2	1	no	—
90	#11924036	C₂²×C₄	1	1	yes	characteristic
91	#11924036	C₂²×C₄	1	1	yes	characteristic
92	C₂×#10596833	—	2	1	no	—
93	C₄⋊#64408	—	2	2	no	—
94	C₄⋊#64408	—	2	2	no	—
95	C₄⋊#64408	C₂²×C₄	1	2	yes	—
96	C₄⋊#64408	C₂²×C₄	1	2	yes	—
97	C₂²⋊#64408	—	2	2	no	—
98	C₂²⋊#64408	—	2	2	no	—
99	C₂²⋊#64408	—	2	2	no	—
100	C₄×#64408	—	2	2	no	—
101	C₄×#64408	—	2	2	no	—
102	C₄×#64408	—	2	2	no	—
103	C₄×#64408	C₂²×C₄	1	1	yes	characteristic
104	C₄×#64408	C₂×D₄	1	1	yes	characteristic
105	C₄×#64408	#41	1	1	yes	characteristic
106	C₄×#64408	C₂⁴	1	1	yes	characteristic
107	#11924029	C₂×C₈	1	2	yes	complemented
108	#11924028	—	2	2	no	—
109	#11924028	C₂×C₈	1	2	yes	complemented
110	#11924027	—	2	2	no	—
111	#11924027	C₂×C₈	1	2	yes	complemented
112	Q₈×D₇₃	C₂²×C₄	1	2	yes	—
113	D₄×D₇₃	—	2	2	no	—
114	D₄×D₇₃	C₂²×C₄	1	2	yes	—
115	C₂×C₄×D₇₃	—	2	2	no	—
116	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
117	Dic₂₉₂	C₂×C₈	1	1	yes	characteristic, complemented
118	#11924018	C₂×C₈	1	2	yes	complemented
119	#11924017	C₂×C₈	1	2	yes	complemented
120	#11924016	C₂×C₈	1	2	yes	complemented
121	#11924015	C₂×C₈	1	2	yes	complemented
122	D₅₈₄	C₂×C₈	1	1	yes	characteristic, complemented
123	#11924013	C₂×C₈	1	2	yes	complemented
124	C₂×#10596831	C₂×C₈	1	1	yes	characteristic, complemented
125	C₈×D₇₃	C₂×C₈	1	1	yes	characteristic, complemented
126	C₈×D₇₃	C₂×C₈	1	1	yes	characteristic, complemented
127	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
128	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
129	#41×C₇₃	C₂×C₈	1	2	yes	complemented
130	Q₁₆×C₇₃	C₂×C₈	1	1	yes	characteristic, complemented
131	SD₁₆×C₇₃	C₂×C₈	1	2	yes	complemented
132	D₈×C₇₃	C₂×C₈	1	1	yes	characteristic, complemented
133	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic, complemented
134	C₂²×D₇₃	—	2	2	no	—
135	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
136	C₂×#64408	—	2	2	no	—
137	C₂×#64408	—	2	2	no	—
138	C₂×#64408	—	2	2	no	—
139	C₂×#64408	—	4	1	no	—
140	C₂×#64408	—	4	2	no	—
141	C₂×#64408	—	4	2	no	—
142	C₂×#64408	—	8	2	no	—
143	C₂×#64408	C₄×D₄	1	1	yes	characteristic
144	C₂×#64408	C₄×D₄	1	1	yes	characteristic
145	C₂×#64408	C₂²×D₄	1	1	yes	characteristic
146	C₂×#64408	C₂×#41	1	1	yes	characteristic
147	#10596842	—	2	4	no	—
148	#10596842	—	4	2	no	—
149	#10596842	—	4	4	no	—
150	Q₈×C₇₃	C₂²×C₈	1	2	yes	—
151	D₄×C₇₃	—	2	2	no	—
152	D₄×C₇₃	C₂²×C₈	1	2	yes	—
153	C₂×C₄×C₇₃	—	2	2	no	—
154	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
155	C₂²⋊D₇₃	—	2	2	no	—
156	C₂²⋊D₇₃	—	2	2	no	—
157	C₂²⋊D₇₃	—	2	2	no	—
158	C₂×Dic₇₃	—	2	2	no	—
159	C₂×Dic₇₃	#131	1	1	yes	characteristic
160	D₂₉₂	—	2	2	no	—
161	D₂₉₂	C₂²×C₈	1	2	yes	—
162	C₄×D₇₃	—	2	2	no	—
163	C₄×D₇₃	—	2	2	no	—
164	C₄×D₇₃	—	2	2	no	—
165	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
166	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
167	C₄×D₇₃	#131	1	1	yes	characteristic
168	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
169	Dic₁₄₆	—	2	2	no	—
170	Dic₁₄₆	C₂²×C₈	1	2	yes	—
171	#10596833	—	2	1	no	—
172	#10596833	—	2	1	no	—
173	C₈×C₇₃	C₂²×C₈	1	1	yes	characteristic
174	C₈×C₇₃	C₂²×C₈	1	1	yes	characteristic
175	#10596831	C₂²×C₈	1	1	yes	characteristic
176	#10596831	C₂²×C₈	1	1	yes	characteristic
177	C₂²×C₇₃	—	2	2	no	—
178	C₂²×C₇₃	C₈×D₄	1	1	yes	characteristic
179	C₂×D₇₃	—	2	1	no	—
180	C₂×D₇₃	—	2	1	no	—
181	C₂×D₇₃	—	2	2	no	—
182	C₂×D₇₃	—	4	2	no	—
183	C₂×D₇₃	—	4	2	no	—
184	C₂×D₇₃	C₈×D₄	1	1	yes	characteristic
185	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
186	#64408	—	2	1	no	—
187	#64408	—	2	1	no	—
188	#64408	—	2	1	no	—
189	#64408	—	4	2	no	—
190	#64408	—	4	2	no	—
191	#64408	#577	1	2	yes	—
192	C₄×C₇₃	—	2	2	no	—
193	C₄×C₇₃	C₈×D₄	1	1	yes	characteristic
194	C₄×C₇₃	C₂³×C₈	1	1	yes	characteristic
195	Dic₇₃	—	2	2	no	—
196	Dic₇₃	C₈×D₄	1	1	yes	characteristic
197	Dic₇₃	C₂×#131	1	1	yes	characteristic
198	#17858	—	73	1	no	maximal, Sylow
199	C₂×C₇₃	—	2	1	no	—
200	C₂×C₇₃	—	4	2	no	—
201	C₂×C₇₃	C₂×C₈×D₄	1	1	yes	characteristic
202	D₇₃	—	2	1	no	—
203	D₇₃	—	4	2	no	—
204	D₇₃	#2952	1	1	yes	characteristic
205	D₇₃	#2957	1	1	yes	characteristic
206	#2988	—	73	2	no	—
207	C₄×#135	—	73	1	no	—
208	#1580	—	73	2	no	—
209	#1579	—	73	2	no	—
210	C₈×SD₁₆	—	73	4	no	—
211	C₂×#334	—	73	1	no	—
212	#1477	—	73	2	no	—
213	#1450	—	73	1	no	—
214	C₇₃	#17858	1	1	yes	characteristic, complemented, Sylow
215	C₂×#135	—	73	1	no	—
216	C₄×#41	—	73	2	no	—
217	C₈×Q₈	—	73	4	no	—
218	C₄×Q₁₆	—	73	1	no	—
219	C₄×Q₁₆	—	73	1	no	—
220	C₄×SD₁₆	—	73	2	no	—
221	C₄×SD₁₆	—	73	2	no	—
222	C₄×D₈	—	73	1	no	—
223	C₄×D₈	—	73	1	no	—
224	C₈×D₄	—	73	4	no	—
225	C₈×D₄	—	146	4	no	—
226	#431	—	73	1	no	—
227	#431	—	73	1	no	—
228	#431	—	146	2	no	—
229	#427	—	73	1	no	—
230	C₂×C₄⋊C₈	—	73	2	no	—
231	C₂×C₄⋊C₈	—	146	2	no	—
232	#416	—	73	2	no	—
233	C₂×C₄×C₈	—	73	1	no	—
234	#334	—	73	2	no	—
235	#334	—	73	2	no	—
236	Q₈⋊C₈	—	73	4	no	—
237	D₄⋊C₈	—	73	4	no	—
238	#322	—	73	2	no	—
239	C₈²	—	73	2	no	—
240	C₂×#41	—	73	2	no	—
241	#135	—	73	2	no	—
242	#135	—	73	1	no	—
243	#135	—	73	2	no	—
244	#135	—	73	1	no	—
245	#135	—	73	1	no	—
246	#135	#10596842	1	1	yes	characteristic, complemented
247	C₂×Q₁₆	—	73	1	no	—
248	C₂×SD₁₆	—	73	2	no	—
249	C₂×D₈	—	73	1	no	—
250	C₂²×C₈	—	73	1	no	—
251	C₂²×C₈	—	73	1	no	—
252	C₂²×C₈	—	146	4	no	—
253	C₂²×C₈	—	146	2	no	—
254	C₄×Q₈	—	73	2	no	—
255	C₄×Q₈	—	73	2	no	—
256	C₄×D₄	—	73	2	no	—
257	C₄×D₄	—	73	2	no	—
258	C₄×D₄	—	146	2	no	—
259	C₄×D₄	—	146	2	no	—
260	#117	—	73	2	no	—
261	#117	—	146	2	no	—
262	C₂×C₄²	—	73	1	no	—
263	C₂×C₄²	—	146	2	no	—
264	#107	—	73	1	no	—
265	#107	—	73	1	no	—
266	#106	—	73	2	no	—
267	C₄⋊C₈	—	73	2	no	—
268	C₄⋊C₈	—	73	4	no	—
269	C₄⋊C₈	—	146	2	no	—
270	C₄⋊C₈	—	146	1	no	—
271	C₄⋊C₈	—	146	4	no	—
272	#103	—	73	2	no	—
273	#103	—	73	2	no	—
274	#102	—	73	2	no	—
275	#102	—	73	2	no	—
276	C₂²⋊C₈	—	73	2	no	—
277	C₂²⋊C₈	—	146	4	no	—
278	C₂²⋊C₈	—	146	1	no	—
279	C₄×C₈	—	73	2	no	—
280	C₄×C₈	—	73	1	no	—
281	C₄×C₈	—	73	1	no	—
282	C₄×C₈	—	73	1	no	—
283	C₄×C₈	—	73	1	no	—
284	C₄×C₈	—	73	2	no	—
285	C₄×C₈	—	146	4	no	—
286	#41	—	73	2	no	—
287	#41	—	73	2	no	—
288	#41	—	73	2	no	—
289	#41	—	146	2	no	—
290	#41	—	146	2	no	—
291	#41	C₂×#10596842	1	2	yes	complemented
292	C₂×Q₈	—	73	2	no	—
293	C₂×D₄	—	73	2	no	—
294	C₂×D₄	—	146	2	no	—
295	C₂²×C₄	—	73	1	no	—
296	C₂²×C₄	—	73	1	no	—
297	C₂²×C₄	—	73	1	no	—
298	C₂²×C₄	—	146	2	no	—
299	C₂²×C₄	—	146	2	no	—
300	C₂²×C₄	—	146	2	no	—
301	Q₁₆	—	73	2	no	—
302	Q₁₆	—	73	1	no	—
303	Q₁₆	C₂×#10596842	1	1	yes	characteristic, complemented
304	SD₁₆	—	73	2	no	—
305	SD₁₆	—	73	2	no	—
306	SD₁₆	—	73	2	no	—
307	SD₁₆	C₂×#10596842	1	2	yes	complemented
308	D₈	—	73	2	no	—
309	D₈	—	73	1	no	—
310	D₈	C₂×#10596842	1	1	yes	characteristic, complemented
311	C₂×C₈	—	584	2	no	—
312	C₂×C₈	—	584	4	no	—
313	C₂×C₈	—	73	1	no	—
314	C₂×C₈	—	73	1	no	—
315	C₂×C₈	—	73	1	no	—
316	C₂×C₈	—	73	1	no	—
317	C₂×C₈	—	73	1	no	—
318	C₂×C₈	—	73	1	no	—
319	C₂×C₈	—	73	1	no	—
320	C₂×C₈	—	73	4	no	—
321	C₂×C₈	—	146	2	no	—
322	C₂×C₈	—	146	4	no	—
323	C₂×C₈	—	146	1	no	—
324	C₂×C₈	—	146	1	no	—
325	C₂×C₈	C₂×#10596842	1	1	yes	characteristic, complemented
326	C₄⋊C₄	—	73	2	no	—
327	C₄⋊C₄	—	73	2	no	—
328	C₄⋊C₄	—	146	2	no	—
329	C₄⋊C₄	—	146	2	no	—
330	C₂²⋊C₄	—	146	2	no	—
331	C₂²⋊C₄	—	146	2	no	—
332	C₂²⋊C₄	—	146	2	no	—
333	C₄²	—	73	1	no	—
334	C₄²	—	73	1	no	—
335	C₄²	—	73	1	no	—
336	C₄²	—	73	1	no	—
337	C₄²	—	146	2	no	—
338	C₄²	—	146	2	no	—
339	C₄²	—	146	2	no	—
340	C₂³	—	73	1	no	—
341	C₂³	—	146	2	no	—
342	Q₈	—	73	2	no	—
343	Q₈	—	146	2	no	—
344	Q₈	C₂²×#10596842	1	2	yes	—
345	D₄	—	2	2	no	—
346	D₄	—	73	2	no	—
347	D₄	—	146	2	no	—
348	D₄	—	146	2	no	—
349	D₄	—	146	2	no	—
350	D₄	—	146	2	no	—
351	D₄	C₂²×#10596842	1	2	yes	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	292	2	no	—
354	C₂×C₄	—	292	2	no	—
355	C₂×C₄	—	292	1	no	—
356	C₂×C₄	—	584	2	no	—
357	C₂×C₄	—	73	1	no	—
358	C₂×C₄	—	73	1	no	—
359	C₂×C₄	—	73	1	no	—
360	C₂×C₄	—	73	1	no	—
361	C₂×C₄	—	73	1	no	—
362	C₂×C₄	—	73	1	no	—
363	C₂×C₄	—	73	1	no	—
364	C₂×C₄	—	73	1	no	—
365	C₂×C₄	—	73	1	no	—
366	C₂×C₄	—	146	2	no	—
367	C₂×C₄	—	146	2	no	—
368	C₂×C₄	—	146	2	no	—
369	C₂×C₄	—	146	2	no	—
370	C₂×C₄	—	146	2	no	—
371	C₂×C₄	—	146	2	no	—
372	C₂×C₄	—	146	2	no	—
373	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
374	C₈	—	292	4	no	—
375	C₈	—	292	2	no	—
376	C₈	—	73	1	no	—
377	C₈	—	73	1	no	—
378	C₈	—	146	4	no	—
379	C₈	—	146	1	no	—
380	C₈	—	146	1	no	—
381	C₈	C₂²×#10596842	1	1	yes	characteristic
382	C₈	C₂²×#10596842	1	1	yes	characteristic
383	C₂²	—	2	2	no	—
384	C₂²	—	292	2	no	—
385	C₂²	—	292	2	no	—
386	C₂²	—	73	1	no	—
387	C₂²	—	73	1	no	—
388	C₂²	—	146	1	no	—
389	C₂²	—	146	1	no	—
390	C₂²	—	146	2	no	—
391	C₂²	D₄×#10596842	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	292	2	no	—
394	C₄	—	292	2	no	—
395	C₄	—	73	2	no	—
396	C₄	—	73	1	no	—
397	C₄	—	73	1	no	—
398	C₄	—	146	1	no	—
399	C₄	—	146	1	no	—
400	C₄	—	146	1	no	—
401	C₄	—	146	2	no	—
402	C₄	D₄×#10596842	1	1	yes	characteristic
403	C₄	C₂³×#10596842	1	1	yes	characteristic
404	C₂	—	2	1	no	—
405	C₂	—	4	2	no	—
406	C₂	—	292	2	no	—
407	C₂	—	73	1	no	—
408	C₂	—	73	1	no	—
409	C₂	—	146	1	no	—
410	C₂	C₂×D₄×#10596842	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄×#10596842
commutator	C₄×C₇₃	C₂³×C₈
Frattini	C₄	C₂³×#10596842
Fitting	#135×C₇₃	C₈
socle	C₂×C₇₃	C₂×C₈×D₄
prime radical	#135×D₇₃	C₄
cosocle	C₄×#64408	C₂⁴
hypercenter	#135	#10596842
hypocenter	C₇₃	#17858
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #22627175	C₂	semidirect
2. #22627062	C₂	semidirect
3. #22627061	C₂	semidirect
4. SD₁₆×#10596842	C₂	semidirect
5. C₂×#17989676	C₂	semidirect
6. #22627050	C₂	semidirect
7. #22627040	C₂	semidirect
70. #14556614	C₈	semidirect
71. #14556613	C₈	semidirect
72. #14556612	C₈	semidirect
73. #14556611	C₈	semidirect
74. #14556610	C₈	semidirect
79. #135×C₇₃	C₈	semidirect
107. #11924029	C₂×C₈	semidirect
109. #11924028	C₂×C₈	semidirect
111. #11924027	C₂×C₈	semidirect
117. Dic₂₉₂	C₂×C₈	semidirect
118. #11924018	C₂×C₈	semidirect
119. #11924017	C₂×C₈	semidirect
120. #11924016	C₂×C₈	semidirect
121. #11924015	C₂×C₈	semidirect
122. D₅₈₄	C₂×C₈	semidirect
123. #11924013	C₂×C₈	semidirect
124. C₂×#10596831	C₂×C₈	semidirect
125. C₈×D₇₃	C₂×C₈	semidirect
126. C₈×D₇₃	C₂×C₈	semidirect
129. #41×C₇₃	C₂×C₈	semidirect
130. Q₁₆×C₇₃	C₂×C₈	semidirect
131. SD₁₆×C₇₃	C₂×C₈	semidirect
132. D₈×C₇₃	C₂×C₈	semidirect
133. C₂×C₈×C₇₃	C₂×C₈	semidirect
214. C₇₃	#17858	semidirect
246. #135	#10596842	semidirect
291. #41	C₂×#10596842	semidirect
303. Q₁₆	C₂×#10596842	semidirect
307. SD₁₆	C₂×#10596842	semidirect
310. D₈	C₂×#10596842	semidirect
325. C₂×C₈	C₂×#10596842	semidirect

Maximal subgroups

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

subgroup	index
#22627175	2
#22627062	2
#22627061	2
SD₁₆×#10596842	2
C₂×#17989676	2
#22627050	2
#22627040	2
#135×#64408	2
#17858	73