Subgroups — C₂²×#17989387 #33999790

Order 18688.

11294 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11924028	C₂	1	2	yes	maximal, complemented
2	C₂×#17989387	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#14556624	C₂	1	4	yes	maximal, complemented
4	C₂²×#14556619	C₂	1	4	yes	maximal, complemented
5	C₂²×#14556613	C₂	1	4	yes	maximal, complemented
6	C₂³×M₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#11924028	—	2	2	no	—
8	C₂²×#11924028	—	2	2	no	—
9	C₂²×#11924028	—	2	24	no	—
10	C₂²×#11924028	C₂²	1	4	yes	—
11	C₂²×#11924028	C₂²	1	4	yes	complemented
12	C₂²×#11924028	C₂²	1	48	yes	complemented
13	C₂³×Dic₁₄₆	C₂²	1	2	yes	complemented
14	C₂³×D₂₉₂	C₂²	1	2	yes	complemented
15	C₂³×C₂²⋊D₇₃	—	2	2	no	—
16	C₂³×C₄×D₇₃	—	2	2	no	—
17	#17989387	C₂²	1	256	yes	direct product factor
18	C₂×#14556624	C₂²	1	96	yes	complemented
19	C₂×#14556619	C₂²	1	96	yes	complemented
20	C₂×#14556613	C₂²	1	96	yes	complemented
21	C₂²×Dic₂₉₂	C₂²	1	4	yes	complemented
22	C₂²×#11924017	C₂²	1	8	yes	complemented
23	C₂²×D₅₈₄	C₂²	1	4	yes	complemented
24	C₂⁴×C₄×C₇₃	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₇₃	C₂²	1	4	yes	complemented
26	C₂²×M₁₆×C₇₃	C₂²	1	24	yes	complemented
27	C₂³×C₈×C₇₃	C₂²	1	2	yes	complemented
28	C₂⁴×D₇₃	—	2	2	no	—
29	C₂×#11924028	—	2	24	no	—
30	C₂×#11924028	—	2	48	no	—
31	C₂×#11924028	—	2	48	no	—
32	C₂×#11924028	—	2	24	no	—
33	C₂×#11924028	—	2	192	no	—
34	C₂×#11924028	C₂³	1	48	yes	—
35	C₂×#11924028	C₂³	1	48	yes	complemented
36	C₂×#11924028	C₂³	1	128	yes	complemented
37	C₂²×Dic₁₄₆	—	2	2	no	—
38	C₂²×Dic₁₄₆	—	2	12	no	—
39	C₂²×Dic₁₄₆	C₂³	1	4	yes	—
40	C₂²×Dic₁₄₆	C₂³	1	24	yes	complemented
41	C₂²×D₂₉₂	—	2	2	no	—
42	C₂²×D₂₉₂	—	2	12	no	—
43	C₂²×D₂₉₂	C₂³	1	4	yes	—
44	C₂²×D₂₉₂	C₂³	1	24	yes	complemented
45	C₂²×C₂²⋊D₇₃	—	2	4	no	—
46	C₂²×C₂²⋊D₇₃	—	2	4	no	—
47	C₂²×C₂²⋊D₇₃	—	2	48	no	—
48	C₂³×Dic₇₃	—	2	2	no	—
49	C₂²×C₄×D₇₃	—	2	4	no	—
50	C₂²×C₄×D₇₃	—	2	48	no	—
51	C₂²×C₄×D₇₃	—	2	4	no	—
52	#14556624	C₂³	1	256	yes	complemented
53	#14556619	C₂³	1	256	yes	complemented
54	#14556613	C₂³	1	256	yes	complemented
55	C₂×Dic₂₉₂	C₂³	1	48	yes	complemented
56	C₂×#11924017	C₂³	1	96	yes	complemented
57	C₂×D₅₈₄	C₂³	1	48	yes	complemented
58	C₂⁵×C₇₃	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₇₃	D₄	1	2	yes	—
60	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₇₃	D₄	1	12	yes	—
62	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₇₃	C₂³	1	12	yes	—
65	C₂×M₁₆×C₇₃	C₂³	1	48	yes	complemented
66	C₂×M₁₆×C₇₃	C₂³	1	64	yes	complemented
67	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
68	C₂²×C₈×C₇₃	C₂³	1	24	yes	complemented
69	C₂³×D₇₃	—	2	4	no	—
70	C₂³×D₇₃	—	2	24	no	—
71	C₂³×D₇₃	—	4	16	no	—
72	#11924028	—	2	96	no	—
73	#11924028	—	2	96	no	—
74	#11924028	—	2	128	no	—
75	#11924028	—	2	128	no	—
76	#11924028	C₂⁴	1	64	yes	—
77	#11924028	C₂⁴	1	64	yes	complemented
78	C₂×Dic₁₄₆	—	2	12	no	—
79	C₂×Dic₁₄₆	—	2	48	no	—
80	C₂×Dic₁₄₆	—	2	24	no	—
81	C₂×Dic₁₄₆	C₂⁴	1	24	yes	—
82	C₂×Dic₁₄₆	C₂⁴	1	32	yes	complemented
83	C₂×D₂₉₂	—	2	12	no	—
84	C₂×D₂₉₂	—	2	48	no	—
85	C₂×D₂₉₂	—	2	24	no	—
86	C₂×D₂₉₂	C₂⁴	1	24	yes	—
87	C₂×D₂₉₂	C₂⁴	1	32	yes	complemented
88	C₂×C₂²⋊D₇₃	—	2	48	no	—
89	C₂×C₂²⋊D₇₃	—	2	48	no	—
90	C₂×C₂²⋊D₇₃	—	2	128	no	—
91	C₂²×Dic₇₃	—	2	4	no	—
92	C₂²×Dic₇₃	—	2	24	no	—
93	C₂×C₄×D₇₃	—	2	48	no	—
94	C₂×C₄×D₇₃	—	2	128	no	—
95	C₂×C₄×D₇₃	—	2	48	no	—
96	Dic₂₉₂	C₂⁴	1	64	yes	complemented
97	#11924017	C₂⁴	1	128	yes	complemented
98	D₅₈₄	C₂⁴	1	64	yes	complemented
99	C₂⁴×C₇₃	—	4	4	no	—
100	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
101	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
102	C₂⁴×C₇₃	C₂×D₄	1	12	yes	—
103	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₇₃	C₂×D₄	1	24	yes	—
105	C₂²×C₄×C₇₃	C₂×D₄	1	12	yes	—
106	C₂²×C₄×C₇₃	C₂×D₄	1	6	yes	—
107	C₂²×C₄×C₇₃	C₂×D₄	1	12	yes	—
108	C₂²×C₄×C₇₃	C₂×D₄	1	48	yes	—
109	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
111	C₂²×C₄×C₇₃	C₂⁴	1	6	yes	—
112	C₂²×C₄×C₇₃	C₂⁴	1	12	yes	—
113	C₂²×C₄×C₇₃	C₂⁴	1	16	yes	—
114	M₁₆×C₇₃	C₂⁴	1	64	yes	complemented
115	C₂×C₈×C₇₃	C₂⁴	1	24	yes	—
116	C₂×C₈×C₇₃	C₂⁴	1	32	yes	complemented
117	C₂³×C₇₃	—	2	4	no	—
118	C₂³×C₇₃	—	2	8	no	—
119	C₂³×C₇₃	—	4	24	no	—
120	C₂³×C₇₃	C₂²×D₄	1	12	yes	—
121	C₂³×C₇₃	C₂²×D₄	1	6	yes	—
122	C₂³×C₇₃	C₂²×D₄	1	16	yes	—
123	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
124	C₂²×D₇₃	—	2	24	no	—
125	C₂²×D₇₃	—	2	32	no	—
126	C₂²×D₇₃	—	4	96	no	—
127	C₂²×D₇₃	—	4	16	no	—
128	C₂×C₄×C₇₃	C₂²×D₄	1	6	yes	—
129	C₂×C₄×C₇₃	C₂²×D₄	1	12	yes	—
130	C₂×C₄×C₇₃	C₂²×D₄	1	32	yes	—
131	C₂×C₄×C₇₃	C₂²×D₄	1	3	yes	—
132	C₂×C₄×C₇₃	C₂²×D₄	1	24	yes	—
133	C₂×C₄×C₇₃	C₂²×D₄	1	12	yes	—
134	C₂×C₄×C₇₃	C₂²×D₄	1	16	yes	—
135	C₂×C₄×C₇₃	C₂⁵	1	3	yes	—
136	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
137	C₂×C₄×C₇₃	C₂⁵	1	8	yes	—
138	C₂²⋊D₇₃	—	2	64	no	—
139	C₂²⋊D₇₃	—	2	64	no	—
140	C₂×Dic₇₃	—	2	24	no	—
141	C₂×Dic₇₃	—	2	32	no	—
142	D₂₉₂	—	2	24	no	—
143	D₂₉₂	—	2	32	no	—
144	D₂₉₂	C₂⁵	1	16	yes	—
145	C₄×D₇₃	—	2	64	no	—
146	C₄×D₇₃	—	2	64	no	—
147	Dic₁₄₆	—	2	24	no	—
148	Dic₁₄₆	—	2	32	no	—
149	Dic₁₄₆	C₂⁵	1	16	yes	—
150	C₈×C₇₃	C₂⁵	1	16	yes	—
151	C₂²×C₇₃	—	2	24	no	—
152	C₂²×C₇₃	—	2	12	no	—
153	C₂²×C₇₃	—	4	16	no	—
154	C₂²×C₇₃	#575	1	4	yes	complemented
155	C₂²×C₇₃	C₂³×D₄	1	8	yes	—
156	C₂²×C₇₃	C₂³×D₄	1	4	yes	—
157	C₂²×C₇₃	C₂³×D₄	1	3	yes	—
158	C₂×D₇₃	—	2	16	no	—
159	C₂×D₇₃	—	4	64	no	—
160	C₂×D₇₃	—	4	48	no	—
161	C₄×C₇₃	C₂³×D₄	1	3	yes	—
162	C₄×C₇₃	C₂³×D₄	1	8	yes	—
163	C₄×C₇₃	C₂³×D₄	1	4	yes	—
164	C₄×C₇₃	C₂⁶	1	1	yes	characteristic
165	Dic₇₃	—	2	16	no	—
166	C₂²×#575	—	73	1	no	maximal, Sylow
167	C₂×C₇₃	—	2	8	no	—
168	C₂×C₇₃	—	2	4	no	—
169	C₂×C₇₃	C₂×#575	1	6	yes	complemented
170	C₂×C₇₃	C₂⁴×D₄	1	1	yes	characteristic
171	D₇₃	—	4	16	no	—
172	C₂³×#41	—	73	2	no	—
173	C₂×#575	—	73	48	no	—
174	C₂²×#137	—	73	4	no	—
175	C₂²×AGL(1,ℤ/8)	—	73	4	no	—
176	C₂²×#135	—	73	4	no	—
177	C₂³×M₁₆	D₇₃	1	1	yes	characteristic, complemented
178	C₇₃	C₂²×#575	1	1	yes	characteristic, complemented, Sylow
179	C₂²×#41	—	73	4	no	—
180	C₂²×#41	—	73	4	no	—
181	C₂²×#41	—	73	48	no	—
182	C₂²×#41	—	146	2	no	—
183	C₂²×#41	—	146	24	no	—
184	C₂²×#41	—	146	2	no	—
185	C₂³×Q₈	—	73	2	no	—
186	C₂³×D₄	—	73	2	no	—
187	C₂³×D₄	—	146	2	no	—
188	C₂⁴×C₄	—	146	2	no	—
189	C₂⁴×C₄	C₂×D₇₃	1	1	yes	characteristic
190	#575	—	73	256	no	—
191	C₂×#137	—	73	96	no	—
192	C₂×AGL(1,ℤ/8)	—	73	96	no	—
193	C₂×#135	—	73	96	no	—
194	C₂²×Q₁₆	—	73	4	no	—
195	C₂²×SD₁₆	—	73	8	no	—
196	C₂²×D₈	—	73	4	no	—
197	C₂²×M₁₆	C₂×D₇₃	1	4	yes	complemented
198	C₂²×M₁₆	C₂×D₇₃	1	24	yes	complemented
199	C₂³×C₈	C₂×D₇₃	1	2	yes	complemented
200	C₂⁵	—	146	2	no	—
201	C₂⁵	D₂₉₂	1	1	yes	characteristic
202	C₂×#41	—	73	48	no	—
203	C₂×#41	—	73	48	no	—
204	C₂×#41	—	73	128	no	—
205	C₂×#41	—	146	48	no	—
206	C₂×#41	—	146	24	no	—
207	C₂×#41	—	146	24	no	—
208	C₂×#41	—	146	48	no	—
209	C₂×#41	—	146	192	no	—
210	C₂²×Q₈	—	73	4	no	—
211	C₂²×Q₈	—	73	24	no	—
212	C₂²×Q₈	—	146	2	no	—
213	C₂²×Q₈	—	146	12	no	—
214	C₂²×D₄	—	73	4	no	—
215	C₂²×D₄	—	73	24	no	—
216	C₂²×D₄	—	146	4	no	—
217	C₂²×D₄	—	146	4	no	—
218	C₂²×D₄	—	146	48	no	—
219	C₂²×D₄	—	146	2	no	—
220	C₂²×D₄	—	146	12	no	—
221	C₂³×C₄	—	146	2	no	—
222	C₂³×C₄	—	146	4	no	—
223	C₂³×C₄	—	146	48	no	—
224	C₂³×C₄	—	146	4	no	—
225	C₂³×C₄	D₂₉₂	1	1	yes	characteristic
226	C₂³×C₄	D₂₉₂	1	12	yes	—
227	C₂³×C₄	D₂₉₂	1	2	yes	—
228	C₂³×C₄	C₂²×D₇₃	1	2	yes	—
229	C₂³×C₄	C₂²×D₇₃	1	12	yes	—
230	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
231	#137	—	73	256	no	—
232	AGL(1,ℤ/8)	—	73	256	no	—
233	#135	—	73	256	no	—
234	C₂×Q₁₆	—	73	48	no	—
235	C₂×SD₁₆	—	73	96	no	—
236	C₂×D₈	—	73	48	no	—
237	C₂×M₁₆	C₂²×D₇₃	1	48	yes	complemented
238	C₂×M₁₆	C₂²×D₇₃	1	64	yes	complemented
239	C₂²×C₈	C₂²×D₇₃	1	4	yes	—
240	C₂²×C₈	C₂²×D₇₃	1	24	yes	complemented
241	C₂⁴	—	4	4	no	—
242	C₂⁴	—	292	16	no	—
243	C₂⁴	—	146	24	no	—
244	C₂⁴	—	146	4	no	—
245	C₂⁴	C₂×D₂₉₂	1	2	yes	—
246	C₂⁴	C₂×D₂₉₂	1	1	yes	characteristic
247	C₂⁴	C₂×D₂₉₂	1	12	yes	—
248	#41	—	73	64	no	—
249	#41	—	73	64	no	—
250	#41	—	146	128	no	—
251	#41	—	146	96	no	—
252	#41	—	146	96	no	—
253	#41	—	146	128	no	—
254	C₂×Q₈	—	73	24	no	—
255	C₂×Q₈	—	73	32	no	—
256	C₂×Q₈	—	146	24	no	—
257	C₂×Q₈	—	146	12	no	—
258	C₂×Q₈	—	146	48	no	—
259	C₂×D₄	—	73	24	no	—
260	C₂×D₄	—	73	32	no	—
261	C₂×D₄	—	146	48	no	—
262	C₂×D₄	—	146	48	no	—
263	C₂×D₄	—	146	128	no	—
264	C₂×D₄	—	146	24	no	—
265	C₂×D₄	—	146	12	no	—
266	C₂×D₄	—	146	48	no	—
267	C₂²×C₄	—	146	24	no	—
268	C₂²×C₄	—	146	4	no	—
269	C₂²×C₄	—	146	48	no	—
270	C₂²×C₄	—	146	48	no	—
271	C₂²×C₄	—	146	128	no	—
272	C₂²×C₄	C₂×D₂₉₂	1	2	yes	—
273	C₂²×C₄	C₂×D₂₉₂	1	24	yes	—
274	C₂²×C₄	C₂×D₂₉₂	1	12	yes	—
275	C₂²×C₄	C₂×D₂₉₂	1	6	yes	—
276	C₂²×C₄	C₂×D₂₉₂	1	12	yes	—
277	C₂²×C₄	C₂×D₂₉₂	1	48	yes	—
278	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
279	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
280	C₂²×C₄	C₂³×D₇₃	1	6	yes	—
281	C₂²×C₄	C₂³×D₇₃	1	12	yes	—
282	C₂²×C₄	C₂³×D₇₃	1	16	yes	—
283	Q₁₆	—	73	64	no	—
284	SD₁₆	—	73	128	no	—
285	D₈	—	73	64	no	—
286	M₁₆	C₂³×D₇₃	1	64	yes	complemented
287	C₂×C₈	C₂³×D₇₃	1	24	yes	—
288	C₂×C₈	C₂³×D₇₃	1	32	yes	complemented
289	C₂³	—	2	8	no	—
290	C₂³	—	2	4	no	—
291	C₂³	—	4	24	no	—
292	C₂³	—	292	96	no	—
293	C₂³	—	292	16	no	—
294	C₂³	—	146	32	no	—
295	C₂³	—	146	24	no	—
296	C₂³	C₂²×D₂₉₂	1	12	yes	—
297	C₂³	C₂²×D₂₉₂	1	6	yes	—
298	C₂³	C₂²×D₂₉₂	1	16	yes	—
299	C₂³	C₂²×D₂₉₂	1	1	yes	characteristic
300	Q₈	—	73	16	no	—
301	Q₈	—	146	32	no	—
302	Q₈	—	146	24	no	—
303	D₄	—	73	16	no	—
304	D₄	—	146	64	no	—
305	D₄	—	146	64	no	—
306	D₄	—	146	32	no	—
307	D₄	—	146	24	no	—
308	C₂×C₄	—	146	32	no	—
309	C₂×C₄	—	146	24	no	—
310	C₂×C₄	—	146	64	no	—
311	C₂×C₄	—	146	64	no	—
312	C₂×C₄	C₂²×D₂₉₂	1	6	yes	—
313	C₂×C₄	C₂²×D₂₉₂	1	12	yes	—
314	C₂×C₄	C₂²×D₂₉₂	1	32	yes	—
315	C₂×C₄	C₂²×D₂₉₂	1	3	yes	—
316	C₂×C₄	C₂²×D₂₉₂	1	24	yes	—
317	C₂×C₄	C₂²×D₂₉₂	1	12	yes	—
318	C₂×C₄	C₂²×D₂₉₂	1	16	yes	—
319	C₂×C₄	C₂⁴×D₇₃	1	3	yes	—
320	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
321	C₂×C₄	C₂⁴×D₇₃	1	8	yes	—
322	C₈	C₂⁴×D₇₃	1	16	yes	—
323	C₂²	—	2	24	no	—
324	C₂²	—	2	12	no	—
325	C₂²	—	4	16	no	—
326	C₂²	—	292	64	no	—
327	C₂²	—	292	48	no	—
328	C₂²	—	146	16	no	—
329	C₂²	#17989387	1	4	yes	direct product factor
330	C₂²	C₂³×D₂₉₂	1	8	yes	—
331	C₂²	C₂³×D₂₉₂	1	4	yes	—
332	C₂²	C₂³×D₂₉₂	1	3	yes	—
333	C₄	—	146	16	no	—
334	C₄	C₂³×D₂₉₂	1	4	yes	—
335	C₄	C₂³×D₂₉₂	1	8	yes	—
336	C₄	C₂³×D₂₉₂	1	3	yes	—
337	C₄	C₂⁵×D₇₃	1	1	yes	characteristic
338	C₂	—	2	8	no	—
339	C₂	—	2	4	no	—
340	C₂	—	292	16	no	—
341	C₂	C₂×#17989387	1	6	yes	direct product factor
342	C₂	C₂⁴×D₂₉₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₂₉₂
commutator, cosocle	C₄×C₇₃	C₂⁶
Frattini	C₄	C₂⁵×D₇₃
Fitting	C₂³×M₁₆×C₇₃	C₂
socle	C₂³×C₇₃	C₂²×D₄
hypercenter	C₂³×M₁₆	D₇₃
hypocenter	C₇₃	C₂²×#575
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂⁴×C₄ ◁ C₂³×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂³×#11924028	C₂	semidirect
2. C₂×#17989387	C₂	direct (N × H)
3. C₂²×#14556624	C₂	semidirect
4. C₂²×#14556619	C₂	semidirect
5. C₂²×#14556613	C₂	semidirect
6. C₂³×M₁₆×C₇₃	C₂	semidirect
11. C₂²×#11924028	C₂²	semidirect
12. C₂²×#11924028	C₂²	semidirect
13. C₂³×Dic₁₄₆	C₂²	semidirect
14. C₂³×D₂₉₂	C₂²	semidirect
17. #17989387	C₂²	direct (N × H)
18. C₂×#14556624	C₂²	semidirect
19. C₂×#14556619	C₂²	semidirect
20. C₂×#14556613	C₂²	semidirect
21. C₂²×Dic₂₉₂	C₂²	semidirect
22. C₂²×#11924017	C₂²	semidirect
23. C₂²×D₅₈₄	C₂²	semidirect
25. C₂²×M₁₆×C₇₃	C₂²	semidirect
26. C₂²×M₁₆×C₇₃	C₂²	semidirect
27. C₂³×C₈×C₇₃	C₂²	semidirect
35. C₂×#11924028	C₂³	semidirect
36. C₂×#11924028	C₂³	semidirect
40. C₂²×Dic₁₄₆	C₂³	semidirect
44. C₂²×D₂₉₂	C₂³	semidirect
52. #14556624	C₂³	semidirect
53. #14556619	C₂³	semidirect
54. #14556613	C₂³	semidirect
55. C₂×Dic₂₉₂	C₂³	semidirect
56. C₂×#11924017	C₂³	semidirect
57. C₂×D₅₈₄	C₂³	semidirect
65. C₂×M₁₆×C₇₃	C₂³	semidirect
66. C₂×M₁₆×C₇₃	C₂³	semidirect
68. C₂²×C₈×C₇₃	C₂³	semidirect
77. #11924028	C₂⁴	semidirect
82. C₂×Dic₁₄₆	C₂⁴	semidirect
87. C₂×D₂₉₂	C₂⁴	semidirect
96. Dic₂₉₂	C₂⁴	semidirect
97. #11924017	C₂⁴	semidirect
98. D₅₈₄	C₂⁴	semidirect
114. M₁₆×C₇₃	C₂⁴	semidirect
116. C₂×C₈×C₇₃	C₂⁴	semidirect
154. C₂²×C₇₃	#575	semidirect
169. C₂×C₇₃	C₂×#575	semidirect
177. C₂³×M₁₆	D₇₃	semidirect
178. C₇₃	C₂²×#575	semidirect
197. C₂²×M₁₆	C₂×D₇₃	semidirect
198. C₂²×M₁₆	C₂×D₇₃	semidirect
199. C₂³×C₈	C₂×D₇₃	semidirect
237. C₂×M₁₆	C₂²×D₇₃	semidirect
238. C₂×M₁₆	C₂²×D₇₃	semidirect
240. C₂²×C₈	C₂²×D₇₃	semidirect
286. M₁₆	C₂³×D₇₃	semidirect
288. C₂×C₈	C₂³×D₇₃	semidirect
329. C₂²	#17989387	direct (N × H)
341. C₂	C₂×#17989387	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#11924028	2
C₂×#17989387	2
C₂²×#14556624	2
C₂²×#14556619	2
C₂²×#14556613	2
C₂³×M₁₆×C₇₃	2
C₂²×#575	73

Subgroups — C22×#17989387 #33999790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#17989387 #33999790