Subgroups — #34030265

Order 18688.

682 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626692	C₂	1	1	yes	maximal, characteristic, complemented
2	#22626690	C₂	1	1	yes	maximal, characteristic
3	#22626327	C₂	1	4	yes	maximal, complemented
4	SD₃₂×#64408	C₂	1	4	yes	maximal, complemented
5	#22626282	C₂	1	1	yes	maximal, characteristic, complemented
6	#22626241	C₂	1	1	yes	maximal, characteristic, complemented
7	#22626240	C₂	1	1	yes	maximal, characteristic
8	#22626139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×SD₃₂×D₇₃	C₂	1	1	yes	maximal, characteristic
10	#17989655	—	2	1	no	—
11	#17989654	—	2	1	no	—
12	#17989643	C₂²	1	1	yes	characteristic
13	#17989628	—	2	2	no	—
14	#17989627	—	2	2	no	—
15	Q₁₆×#64408	C₂²	1	4	yes	complemented
16	D₈×#64408	C₂²	1	4	yes	—
17	#17989597	C₂²	1	1	yes	characteristic
18	#17989597	C₂²	1	1	yes	characteristic
19	#17989580	—	2	1	no	—
20	#17989579	—	2	1	no	—
21	#17989550	C₂²	1	1	yes	characteristic
22	#17989514	C₂²	1	2	yes	complemented
23	#17989513	C₂²	1	2	yes	complemented
24	#17989500	C₂²	1	4	yes	complemented
25	#17989499	C₂²	1	4	yes	—
26	#17989474	C₂²	1	2	yes	complemented
27	C₁₆×#64408	C₂²	1	2	yes	complemented
28	C₂×Q₁₆×D₇₃	C₂²	1	1	yes	characteristic
29	C₂×D₈×D₇₃	C₂²	1	1	yes	characteristic
30	C₂×#14556536	C₄	1	1	yes	characteristic, complemented
31	C₂×#14556535	C₄	1	1	yes	characteristic, complemented
32	C₂×#14556534	C₄	1	1	yes	characteristic, complemented
33	SD₃₂×D₇₃	C₄	1	2	yes	complemented
34	SD₃₂×D₇₃	C₄	1	2	yes	complemented
35	SD₃₂×D₇₃	C₂²	1	2	yes	—
36	SD₃₂×D₇₃	C₂²	1	2	yes	—
37	C₂×C₁₆×D₇₃	C₂²	1	1	yes	characteristic
38	C₂×SD₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
39	D₇₃⋊M₁₆	D₄	1	1	yes	characteristic
40	Q₈×#64408	—	2	4	no	—
41	Q₈×#64408	—	4	2	no	—
42	D₄×#64408	—	2	4	no	—
43	D₄×#64408	—	4	2	no	—
44	#14556670	—	2	1	no	—
45	#14556670	—	2	1	no	—
46	#14556670	—	4	2	no	—
47	#14556670	D₄	1	1	yes	characteristic
48	C₂×C₂²⋊#64408	—	4	2	no	—
49	#14556666	—	2	1	no	—
50	#14556665	—	2	1	no	—
51	#14556664	C₂³	1	2	yes	—
52	#14556660	C₂³	1	2	yes	—
53	#14556660	C₂³	1	2	yes	—
54	#14556659	—	2	1	no	—
55	#14556659	—	2	1	no	—
56	#14556654	—	2	4	no	—
57	#14556653	—	2	4	no	—
58	#14556645	D₄	1	2	yes	—
59	C₈×#64408	C₂³	1	2	yes	—
60	C₂×Q₈×D₇₃	—	2	1	no	—
61	C₂×D₄×D₇₃	—	2	1	no	—
62	C₂×Dic₂₉₂	C₂×C₄	1	1	yes	characteristic, complemented
63	C₂×#11924018	—	2	1	no	—
64	Q₁₆×D₇₃	—	2	1	no	—
65	Q₁₆×D₇₃	—	2	1	no	—
66	Q₁₆×D₇₃	C₂×C₄	1	2	yes	complemented
67	Q₁₆×D₇₃	C₂³	1	2	yes	—
68	C₂×D₅₈₄	C₂×C₄	1	1	yes	characteristic
69	C₂×#11924013	—	2	1	no	—
70	D₈×D₇₃	—	2	1	no	—
71	D₈×D₇₃	—	2	1	no	—
72	D₈×D₇₃	C₂×C₄	1	2	yes	—
73	D₈×D₇₃	C₂³	1	2	yes	—
74	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
75	#14556536	C₂×C₄	1	2	yes	complemented
76	#14556536	C₂×C₄	1	2	yes	complemented
77	#14556535	C₂×C₄	1	2	yes	complemented
78	#14556535	C₂×C₄	1	2	yes	complemented
79	#14556534	C₂×C₄	1	2	yes	complemented
80	#14556534	C₂×C₄	1	2	yes	complemented
81	C₂×#11924003	C₂×C₄	1	1	yes	characteristic, complemented
82	C₁₆×D₇₃	C₂×C₄	1	1	yes	characteristic, complemented
83	C₁₆×D₇₃	C₂×C₄	1	1	yes	characteristic, complemented
84	C₁₆×D₇₃	C₂³	1	1	yes	characteristic
85	C₁₆×D₇₃	C₂³	1	1	yes	characteristic
86	C₂×Q₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
87	C₂×D₈×C₇₃	C₂×C₄	1	1	yes	characteristic
88	SD₃₂×C₇₃	C₂×C₄	1	2	yes	complemented
89	SD₃₂×C₇₃	C₂×C₄	1	2	yes	complemented
90	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
91	C₂²×#64408	—	4	4	no	—
92	#11924038	—	2	1	no	—
93	#11924037	—	2	1	no	—
94	#11924036	C₂×D₄	1	2	yes	—
95	C₄⋊#64408	—	2	2	no	—
96	C₄⋊#64408	—	2	2	no	—
97	C₄⋊#64408	—	4	4	no	—
98	C₄⋊#64408	D₈	1	2	yes	—
99	C₂²⋊#64408	—	4	1	no	—
100	C₂²⋊#64408	—	4	1	no	—
101	C₂²⋊#64408	—	4	4	no	—
102	C₂²⋊#64408	D₈	1	2	yes	—
103	C₄×#64408	—	4	4	no	—
104	C₄×#64408	—	4	1	no	—
105	C₄×#64408	—	4	1	no	—
106	C₄×#64408	C₂×D₄	1	2	yes	—
107	#11924031	—	2	2	no	—
108	C₂³×D₇₃	—	4	1	no	—
109	C₂×Dic₁₄₆	—	2	1	no	—
110	C₂×Dic₁₄₆	—	4	1	no	—
111	Q₈×D₇₃	—	2	2	no	—
112	Q₈×D₇₃	—	2	2	no	—
113	Q₈×D₇₃	—	4	1	no	—
114	Q₈×D₇₃	—	4	1	no	—
115	C₂×D₂₉₂	—	2	1	no	—
116	C₂×C₂²⋊D₇₃	—	4	1	no	—
117	D₄×D₇₃	—	2	2	no	—
118	D₄×D₇₃	—	2	2	no	—
119	D₄×D₇₃	—	4	1	no	—
120	D₄×D₇₃	—	4	1	no	—
121	C₂×C₄×D₇₃	—	4	1	no	—
122	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
123	Dic₂₉₂	—	2	1	no	—
124	Dic₂₉₂	C₂²×C₄	1	2	yes	—
125	#11924018	—	2	2	no	—
126	#11924018	—	2	2	no	—
127	D₅₈₄	—	2	1	no	—
128	D₅₈₄	C₂²×C₄	1	2	yes	—
129	#11924013	—	2	2	no	—
130	#11924013	—	2	2	no	—
131	C₂×#10596831	#41	1	1	yes	characteristic
132	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₇₃	C₂×D₄	1	1	yes	characteristic
134	C₈×D₇₃	#41	1	1	yes	characteristic
135	C₈×D₇₃	C₂⁴	1	1	yes	characteristic
136	#11924003	C₂²×C₄	1	1	yes	characteristic
137	#11924003	C₂²×C₄	1	1	yes	characteristic
138	C₂×Q₈×C₇₃	—	2	1	no	—
139	C₂×D₄×C₇₃	—	2	1	no	—
140	Q₁₆×C₇₃	—	2	1	no	—
141	Q₁₆×C₇₃	C₂²×C₄	1	2	yes	—
142	D₈×C₇₃	—	2	1	no	—
143	D₈×C₇₃	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
145	C₁₆×C₇₃	C₂²×C₄	1	1	yes	characteristic
146	C₁₆×C₇₃	C₂²×C₄	1	1	yes	characteristic
147	C₂³×C₇₃	—	4	1	no	—
148	C₂²×D₇₃	—	4	1	no	—
149	C₂²×D₇₃	—	4	2	no	—
150	C₂²×D₇₃	—	4	2	no	—
151	C₂²×D₇₃	—	16	2	no	—
152	C₂²×D₇₃	C₂×D₈	1	1	yes	characteristic
153	C₂×#64408	—	4	2	no	—
154	C₂×#64408	—	4	2	no	—
155	C₂×#64408	—	16	4	no	—
156	C₂×#64408	C₂×D₈	1	4	yes	—
157	Q₈×C₇₃	—	2	2	no	—
158	Q₈×C₇₃	—	4	1	no	—
159	D₄×C₇₃	—	2	2	no	—
160	D₄×C₇₃	—	4	1	no	—
161	C₂×C₄×C₇₃	—	4	1	no	—
162	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
163	C₂²⋊D₇₃	—	4	2	no	—
164	C₂²⋊D₇₃	—	4	2	no	—
165	C₂×Dic₇₃	—	4	1	no	—
166	C₂×Dic₇₃	#135	1	1	yes	characteristic
167	D₂₉₂	—	2	2	no	—
168	D₂₉₂	—	4	1	no	—
169	C₄×D₇₃	—	4	2	no	—
170	C₄×D₇₃	—	4	2	no	—
171	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
172	C₄×D₇₃	C₂×D₈	1	1	yes	characteristic
173	C₄×D₇₃	#135	1	1	yes	characteristic
174	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
175	Dic₁₄₆	—	2	2	no	—
176	Dic₁₄₆	—	4	1	no	—
177	Dic₁₄₆	—	4	2	no	—
178	Dic₁₄₆	—	4	2	no	—
179	#10596833	—	2	2	no	—
180	C₈×C₇₃	C₄×D₄	1	1	yes	characteristic
181	C₈×C₇₃	C₂³×C₄	1	1	yes	characteristic
182	#10596831	C₄×D₄	1	1	yes	characteristic
183	#10596831	C₂×#41	1	1	yes	characteristic
184	C₂²×C₇₃	—	4	2	no	—
185	C₂²×C₇₃	—	16	1	no	—
186	C₂²×C₇₃	C₄×D₈	1	1	yes	characteristic
187	C₂×D₇₃	—	2	2	no	—
188	C₂×D₇₃	—	4	2	no	—
189	C₂×D₇₃	—	8	4	no	—
190	C₂×D₇₃	—	16	2	no	—
191	C₂×D₇₃	—	16	1	no	—
192	C₂×D₇₃	C₄×D₈	1	1	yes	characteristic
193	C₂×D₇₃	C₂²×D₈	1	1	yes	characteristic
194	#64408	—	2	4	no	—
195	#64408	—	8	2	no	—
196	#64408	—	8	2	no	—
197	C₄×C₇₃	—	4	2	no	—
198	C₄×C₇₃	C₄×D₈	1	1	yes	characteristic
199	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
200	Dic₇₃	—	4	2	no	—
201	Dic₇₃	C₄×D₈	1	1	yes	characteristic
202	Dic₇₃	C₂×#135	1	1	yes	characteristic
203	#33457	—	73	1	no	maximal, Sylow
204	C₂×C₇₃	—	2	1	no	—
205	C₂×C₇₃	—	8	2	no	—
206	C₂×C₇₃	C₂×C₄×D₈	1	1	yes	characteristic
207	D₇₃	—	2	1	no	—
208	D₇₃	—	8	2	no	—
209	D₇₃	#3416	1	2	yes	—
210	C₂²×SD₃₂	—	73	1	no	—
211	#2950	—	73	1	no	—
212	#2948	—	73	1	no	—
213	#2175	—	73	4	no	—
214	C₄×SD₃₂	—	73	4	no	—
215	#2158	—	73	1	no	—
216	#2141	—	73	1	no	—
217	#2140	—	73	1	no	—
218	#2108	—	73	1	no	—
219	C₇₃	#33457	1	1	yes	characteristic, complemented, Sylow
220	C₂²×Q₁₆	—	73	1	no	—
221	C₂²×D₈	—	73	1	no	—
222	#519	—	146	1	no	—
223	#518	—	146	1	no	—
224	C₂×SD₃₂	—	73	1	no	—
225	C₂×SD₃₂	—	73	1	no	—
226	C₂×SD₃₂	—	73	2	no	—
227	C₂×SD₃₂	—	73	2	no	—
228	C₂×SD₃₂	—	73	2	no	—
229	C₂×SD₃₂	—	73	2	no	—
230	C₂×SD₃₂	—	73	1	no	—
231	C₂×SD₃₂	#64408	1	1	yes	characteristic, complemented
232	C₂×M₃₂	—	73	1	no	—
233	C₂²×C₁₆	—	73	1	no	—
234	#442	—	146	2	no	—
235	#441	—	146	2	no	—
236	C₄×Q₁₆	—	73	4	no	—
237	C₄×D₈	—	73	4	no	—
238	#427	—	73	1	no	—
239	#427	—	73	1	no	—
240	#419	—	146	1	no	—
241	#418	—	146	1	no	—
242	#405	—	73	1	no	—
243	#367	—	73	2	no	—
244	#366	—	73	2	no	—
245	#358	—	73	4	no	—
246	#357	—	73	4	no	—
247	#346	—	73	2	no	—
248	C₄×C₁₆	—	73	2	no	—
249	C₂²×Q₈	—	146	1	no	—
250	C₂²×D₄	—	146	1	no	—
251	C₂×Q₁₆	—	73	2	no	—
252	C₂×Q₁₆	—	73	2	no	—
253	C₂×Q₁₆	—	73	1	no	—
254	C₂×Q₁₆	—	146	1	no	—
255	C₂×Q₁₆	—	146	1	no	—
256	C₂×Q₁₆	—	146	1	no	—
257	C₂×Q₁₆	C₂×#64408	1	1	yes	characteristic, complemented
258	C₂×D₈	—	73	2	no	—
259	C₂×D₈	—	73	2	no	—
260	C₂×D₈	—	73	1	no	—
261	C₂×D₈	—	146	1	no	—
262	C₂×D₈	—	146	1	no	—
263	C₂×D₈	—	146	1	no	—
264	C₂×D₈	C₂×#64408	1	1	yes	characteristic
265	C₂×M₁₆	—	73	1	no	—
266	C₂²×C₈	—	73	1	no	—
267	C₄×Q₈	—	292	2	no	—
268	C₄×Q₈	—	146	4	no	—
269	C₄×D₄	—	292	2	no	—
270	C₄×D₄	—	146	4	no	—
271	#117	—	292	2	no	—
272	#117	—	73	1	no	—
273	#117	—	146	1	no	—
274	#117	—	146	1	no	—
275	C₂×C₂²⋊C₄	—	292	2	no	—
276	SD₃₂	—	73	2	no	—
277	SD₃₂	—	73	2	no	—
278	SD₃₂	—	73	2	no	—
279	SD₃₂	—	73	2	no	—
280	SD₃₂	—	73	2	no	—
281	SD₃₂	—	73	2	no	—
282	SD₃₂	C₂×#64408	1	2	yes	complemented
283	SD₃₂	C₂×#64408	1	2	yes	complemented
284	M₃₂	—	146	1	no	—
285	M₃₂	—	146	1	no	—
286	C₂×C₁₆	—	73	1	no	—
287	C₂×C₁₆	—	73	1	no	—
288	C₂×C₁₆	—	73	1	no	—
289	C₂×C₁₆	—	73	1	no	—
290	C₂×C₁₆	—	73	1	no	—
291	C₂×C₁₆	—	73	2	no	—
292	C₂×C₁₆	C₂×#64408	1	1	yes	characteristic, complemented
293	#107	—	73	2	no	—
294	#107	—	73	2	no	—
295	#106	—	146	1	no	—
296	#106	—	146	1	no	—
297	#103	—	146	4	no	—
298	#102	—	146	4	no	—
299	#97	—	73	2	no	—
300	C₄×C₈	—	73	2	no	—
301	C₂⁴	—	292	1	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	292	1	no	—
304	C₂×Q₈	—	292	1	no	—
305	C₂×Q₈	—	292	1	no	—
306	C₂×Q₈	—	146	2	no	—
307	C₂×Q₈	—	146	2	no	—
308	C₂×Q₈	—	146	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	292	1	no	—
311	C₂×D₄	—	292	1	no	—
312	C₂×D₄	—	292	1	no	—
313	C₂×D₄	—	146	2	no	—
314	C₂×D₄	—	146	2	no	—
315	C₂×D₄	—	146	1	no	—
316	C₂²×C₄	—	292	1	no	—
317	C₂²×C₄	—	292	4	no	—
318	C₂²×C₄	—	73	1	no	—
319	Q₁₆	—	2	1	no	—
320	Q₁₆	—	73	2	no	—
321	Q₁₆	—	146	2	no	—
322	Q₁₆	—	146	2	no	—
323	Q₁₆	—	146	1	no	—
324	Q₁₆	C₂²×#64408	1	2	yes	—
325	D₈	—	2	1	no	—
326	D₈	—	73	2	no	—
327	D₈	—	146	2	no	—
328	D₈	—	146	2	no	—
329	D₈	—	146	1	no	—
330	D₈	C₂²×#64408	1	2	yes	—
331	M₁₆	—	146	1	no	—
332	M₁₆	—	146	1	no	—
333	C₂×C₈	—	73	1	no	—
334	C₂×C₈	—	73	1	no	—
335	C₂×C₈	—	73	1	no	—
336	C₂×C₈	—	73	1	no	—
337	C₂×C₈	—	73	1	no	—
338	C₂×C₈	—	73	2	no	—
339	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
340	C₄⋊C₄	—	292	4	no	—
341	C₄⋊C₄	—	73	2	no	—
342	C₄⋊C₄	—	146	2	no	—
343	C₄⋊C₄	—	146	2	no	—
344	C₂²⋊C₄	—	292	1	no	—
345	C₂²⋊C₄	—	292	1	no	—
346	C₂²⋊C₄	—	292	4	no	—
347	C₂²⋊C₄	—	73	2	no	—
348	C₄²	—	292	4	no	—
349	C₄²	—	292	1	no	—
350	C₄²	—	292	1	no	—
351	C₄²	—	73	2	no	—
352	C₁₆	—	73	1	no	—
353	C₁₆	—	73	1	no	—
354	C₁₆	—	146	2	no	—
355	C₁₆	C₂²×#64408	1	1	yes	characteristic
356	C₁₆	C₂²×#64408	1	1	yes	characteristic
357	C₂³	—	4	1	no	—
358	C₂³	—	292	2	no	—
359	C₂³	—	292	2	no	—
360	C₂³	—	292	1	no	—
361	C₂³	—	73	1	no	—
362	C₂³	—	1168	2	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	4	1	no	—
365	Q₈	—	292	2	no	—
366	Q₈	—	292	2	no	—
367	Q₈	—	292	1	no	—
368	Q₈	—	146	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	4	1	no	—
371	D₄	—	292	2	no	—
372	D₄	—	292	2	no	—
373	D₄	—	292	1	no	—
374	D₄	—	146	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	292	2	no	—
377	C₂×C₄	—	292	2	no	—
378	C₂×C₄	—	292	1	no	—
379	C₂×C₄	—	292	2	no	—
380	C₂×C₄	—	292	2	no	—
381	C₂×C₄	—	73	1	no	—
382	C₂×C₄	—	73	1	no	—
383	C₂×C₄	—	73	1	no	—
384	C₂×C₄	—	73	1	no	—
385	C₂×C₄	—	73	1	no	—
386	C₂×C₄	—	73	4	no	—
387	C₂×C₄	—	1168	4	no	—
388	C₂×C₄	D₄×#64408	1	1	yes	characteristic
389	C₈	—	73	1	no	—
390	C₈	—	73	1	no	—
391	C₈	—	146	2	no	—
392	C₈	D₄×#64408	1	1	yes	characteristic
393	C₈	C₂³×#64408	1	1	yes	characteristic
394	C₂²	—	4	2	no	—
395	C₂²	—	16	1	no	—
396	C₂²	—	292	2	no	—
397	C₂²	—	584	4	no	—
398	C₂²	—	73	1	no	—
399	C₂²	—	73	1	no	—
400	C₂²	—	1168	1	no	—
401	C₂²	—	1168	2	no	—
402	C₂²	—	146	2	no	—
403	C₂²	D₈×#64408	1	1	yes	characteristic
404	C₄	—	4	2	no	—
405	C₄	—	292	2	no	—
406	C₄	—	584	2	no	—
407	C₄	—	584	2	no	—
408	C₄	—	73	1	no	—
409	C₄	—	73	1	no	—
410	C₄	—	146	4	no	—
411	C₄	D₈×#64408	1	1	yes	characteristic
412	C₄	C₂×D₄×#64408	1	1	yes	characteristic
413	C₂	—	2	1	no	—
414	C₂	—	8	2	no	—
415	C₂	—	584	2	no	—
416	C₂	—	73	2	no	—
417	C₂	—	146	1	no	—
418	C₂	C₂×D₈×#64408	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₈×#64408
commutator	C₈×C₇₃	C₂³×C₄
Frattini	C₈	C₂³×#64408
Fitting	C₂×SD₃₂×C₇₃	C₄
socle	C₂×C₇₃	C₂×C₄×D₈
prime radical	C₂×D₈×D₇₃	C₂²
cosocle	C₈×D₇₃	C₂⁴
hypercenter	C₂×SD₃₂	#64408
hypocenter	C₇₃	#33457
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×SD₃₂

Complements

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

N	H ≅ G/N	type
1. #22626692	C₂	semidirect
3. #22626327	C₂	semidirect
4. SD₃₂×#64408	C₂	semidirect
5. #22626282	C₂	semidirect
6. #22626241	C₂	semidirect
8. #22626139	C₂	semidirect
15. Q₁₆×#64408	C₂²	semidirect
22. #17989514	C₂²	semidirect
23. #17989513	C₂²	semidirect
24. #17989500	C₂²	semidirect
26. #17989474	C₂²	semidirect
27. C₁₆×#64408	C₂²	semidirect
30. C₂×#14556536	C₄	semidirect
31. C₂×#14556535	C₄	semidirect
32. C₂×#14556534	C₄	semidirect
33. SD₃₂×D₇₃	C₄	semidirect
34. SD₃₂×D₇₃	C₄	semidirect
38. C₂×SD₃₂×C₇₃	C₄	semidirect
62. C₂×Dic₂₉₂	C₂×C₄	semidirect
66. Q₁₆×D₇₃	C₂×C₄	semidirect
75. #14556536	C₂×C₄	semidirect
76. #14556536	C₂×C₄	semidirect
77. #14556535	C₂×C₄	semidirect
78. #14556535	C₂×C₄	semidirect
79. #14556534	C₂×C₄	semidirect
80. #14556534	C₂×C₄	semidirect
81. C₂×#11924003	C₂×C₄	semidirect
82. C₁₆×D₇₃	C₂×C₄	semidirect
83. C₁₆×D₇₃	C₂×C₄	semidirect
86. C₂×Q₁₆×C₇₃	C₂×C₄	semidirect
88. SD₃₂×C₇₃	C₂×C₄	semidirect
89. SD₃₂×C₇₃	C₂×C₄	semidirect
90. C₂×C₁₆×C₇₃	C₂×C₄	semidirect
219. C₇₃	#33457	semidirect
231. C₂×SD₃₂	#64408	semidirect
257. C₂×Q₁₆	C₂×#64408	semidirect
282. SD₃₂	C₂×#64408	semidirect
283. SD₃₂	C₂×#64408	semidirect
292. C₂×C₁₆	C₂×#64408	semidirect

Maximal subgroups

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

subgroup	index
#22626692	2
#22626690	2
#22626327	2
SD₃₂×#64408	2
#22626282	2
#22626241	2
#22626240	2
#22626139	2
C₂×SD₃₂×D₇₃	2
#33457	73