Subgroups — C₄×#17989643 #34029783

Order 18688.

918 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989643	C₂	1	2	yes	maximal
2	#22626138	C₂	1	2	yes	maximal, complemented
3	#22626137	C₂	1	2	yes	maximal, complemented
4	C₄×#14556666	C₂	1	2	yes	maximal, complemented
5	C₄×#14556665	C₂	1	2	yes	maximal, complemented
6	#22626132	C₂	1	2	yes	maximal, complemented
7	C₄×#14556664	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
9	C₂×#14556666	C₂²	1	4	yes	—
10	#17989643	C₄	1	16	yes	direct product factor
11	C₂×#14556665	C₂²	1	4	yes	—
12	C₂×#14556664	C₂²	1	4	yes	—
13	#17989476	C₂²	1	4	yes	complemented
14	#17989475	C₂²	1	4	yes	complemented
15	#17989473	C₂²	1	4	yes	complemented
16	C₄×#11924031	C₂²	1	4	yes	complemented
17	C₂²×C₈×D₇₃	C₄	1	1	yes	characteristic
18	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₄²×D₇₃	C₄	1	1	yes	characteristic
20	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₇₃	C₄	1	1	yes	characteristic
22	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
23	C₄×C₈×D₇₃	C₄	1	1	yes	characteristic
24	C₄×C₈×D₇₃	C₄	1	1	yes	characteristic
25	C₄×C₈×D₇₃	C₄	1	1	yes	characteristic
26	C₄×C₈×D₇₃	C₄	1	1	yes	characteristic
27	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
28	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
29	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
32	#14556666	C₂×C₄	1	16	yes	complemented
33	#14556665	C₂×C₄	1	16	yes	complemented
34	#14556664	C₂×C₄	1	16	yes	complemented
35	C₂×#11924031	C₂³	1	8	yes	—
36	C₂²×C₄×D₇₃	C₈	1	2	yes	—
37	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
39	C₂²×#10596831	C₂³	1	1	yes	characteristic
40	C₂×C₈×D₇₃	C₈	1	8	yes	—
41	C₂×C₈×D₇₃	C₂×C₄	1	8	yes	—
42	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
49	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
50	C₂×C₄×Dic₇₃	C₈	1	2	yes	—
51	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₇₃	C₈	1	2	yes	—
53	C₄²×D₇₃	C₈	1	2	yes	—
54	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
58	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
59	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
60	C₄×#10596831	C₂³	1	1	yes	characteristic
61	C₄×#10596831	C₂³	1	1	yes	characteristic
62	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
63	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
64	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
65	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
66	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
67	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
68	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
69	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
73	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
77	#11924031	C₂²×C₄	1	16	yes	complemented
78	C₂³×D₇₃	C₂×C₈	1	1	yes	characteristic
79	C₂²×Dic₇₃	C₂×C₈	1	2	yes	—
80	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
81	C₂×C₄×D₇₃	—	2	8	no	—
82	C₂×C₄×D₇₃	C₄²	1	4	yes	—
83	C₂×C₄×D₇₃	C₂×C₈	1	2	yes	—
84	C₂×C₄×D₇₃	C₂×C₈	1	2	yes	—
85	C₂×C₄×D₇₃	C₂×C₈	1	2	yes	—
86	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
87	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
88	C₂×C₄×D₇₃	C₂×C₈	1	4	yes	—
89	C₂×C₄×D₇₃	C₂×C₈	1	2	yes	—
90	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×#10596831	C₂×C₈	1	4	yes	—
93	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
94	C₂×#10596831	C₂²×C₄	1	4	yes	—
95	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
96	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
97	C₂×#10596831	C₂⁴	1	1	yes	characteristic
98	C₈×D₇₃	C₄²	1	4	yes	—
99	C₈×D₇₃	C₄²	1	4	yes	—
100	C₈×D₇₃	C₂×C₈	1	4	yes	—
101	C₈×D₇₃	C₂×C₈	1	4	yes	—
102	C₈×D₇₃	C₂×C₈	1	4	yes	—
103	C₈×D₇₃	C₂×C₈	1	4	yes	—
104	C₈×D₇₃	C₂²×C₄	1	4	yes	—
105	C₈×D₇₃	C₂²×C₄	1	4	yes	—
106	C₄×Dic₇₃	C₂×C₈	1	2	yes	—
107	C₄×Dic₇₃	C₂×C₈	1	2	yes	—
108	C₄×Dic₇₃	C₂×C₈	1	2	yes	—
109	C₄×Dic₇₃	C₂×C₈	1	2	yes	—
110	C₄×Dic₇₃	C₂×C₈	1	2	yes	—
111	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
112	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₃	C₂×C₈	1	2	yes	—
114	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₇₃	C₄²	1	4	yes	—
116	C₂×C₈×C₇₃	C₂×C₈	1	4	yes	—
117	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₇₃	C₂×C₈	1	2	yes	—
122	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
124	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
125	C₂²×D₇₃	—	2	4	no	—
126	C₂²×D₇₃	C₄×C₈	1	4	yes	—
127	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
128	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
129	C₂×C₄×C₇₃	—	2	4	no	—
130	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
131	C₂×C₄×C₇₃	C₂²×C₈	1	2	yes	—
132	C₂×C₄×C₇₃	C₂²×C₈	1	2	yes	—
133	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
134	C₂×C₄×C₇₃	C₂²×C₈	1	2	yes	—
135	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
136	C₂×Dic₇₃	—	2	4	no	—
137	C₂×Dic₇₃	C₄×C₈	1	4	yes	—
138	C₂×Dic₇₃	C₂²×C₈	1	2	yes	—
139	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
140	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
141	C₂×Dic₇₃	C₂²×C₈	1	2	yes	—
142	C₄×D₇₃	—	2	4	no	—
143	C₄×D₇₃	—	2	4	no	—
144	C₄×D₇₃	—	2	4	no	—
145	C₄×D₇₃	C₄×C₈	1	4	yes	—
146	C₄×D₇₃	C₄×C₈	1	4	yes	—
147	C₄×D₇₃	M₃₂	1	8	yes	complemented
148	C₄×D₇₃	C₂×C₄²	1	2	yes	—
149	C₄×D₇₃	C₂×C₄²	1	2	yes	—
150	C₄×D₇₃	C₂²×C₈	1	2	yes	—
151	C₄×D₇₃	C₂²×C₈	1	2	yes	—
152	C₈×C₇₃	C₂×C₄²	1	2	yes	—
153	C₈×C₇₃	C₂×C₄²	1	2	yes	—
154	C₈×C₇₃	C₂²×C₈	1	2	yes	—
155	C₈×C₇₃	C₂²×C₈	1	2	yes	—
156	#10596831	C₂×C₄²	1	2	yes	—
157	#10596831	C₂²×C₈	1	2	yes	—
158	#10596831	C₂²×C₈	1	2	yes	—
159	#10596831	C₂³×C₄	1	2	yes	—
160	C₂²×C₇₃	—	2	2	no	—
161	C₂²×C₇₃	C₂×C₄×C₈	1	2	yes	—
162	C₂²×C₇₃	C₂³×C₈	1	1	yes	characteristic
163	C₂×D₇₃	—	2	2	no	—
164	C₂×D₇₃	—	2	8	no	—
165	C₂×D₇₃	C₂×C₄×C₈	1	2	yes	—
166	C₂×D₇₃	C₂×C₄×C₈	1	2	yes	—
167	C₂×D₇₃	C₂×M₃₂	1	4	yes	—
168	C₄×C₇₃	—	2	2	no	—
169	C₄×C₇₃	C₂×C₄×C₈	1	2	yes	—
170	C₄×C₇₃	C₂×M₃₂	1	4	yes	complemented
171	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
172	C₄×C₇₃	C₂³×C₈	1	1	yes	characteristic
173	Dic₇₃	—	2	2	no	—
174	Dic₇₃	C₂×C₄×C₈	1	2	yes	—
175	Dic₇₃	C₂×C₄×C₈	1	2	yes	—
176	Dic₇₃	C₂×M₃₂	1	4	yes	complemented
177	C₂×C₄×M₃₂	—	73	1	no	maximal, Sylow
178	C₂×C₇₃	—	2	2	no	—
179	C₂×C₇₃	C₂²×C₄×C₈	1	1	yes	characteristic
180	C₂×C₇₃	C₂²×M₃₂	1	2	yes	—
181	D₇₃	—	2	2	no	—
182	D₇₃	C₄×M₃₂	1	4	yes	complemented
183	C₂²×M₃₂	—	73	2	no	—
184	C₂²×C₄×C₈	—	73	1	no	—
185	C₄×M₃₂	—	73	2	no	—
186	C₄×M₃₂	—	73	2	no	—
187	C₄×M₃₂	—	73	2	no	—
188	C₄×M₃₂	—	73	2	no	—
189	C₂×#346	—	73	2	no	—
190	C₂×C₄×C₁₆	—	73	2	no	—
191	C₇₃	C₂×C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
192	C₂³×C₈	—	73	1	no	—
193	C₂³×C₈	—	73	1	no	—
194	C₂²×C₄²	—	73	1	no	—
195	C₂×M₃₂	—	73	4	no	—
196	C₂×M₃₂	—	73	16	no	—
197	C₂×M₃₂	—	73	4	no	—
198	C₂²×C₁₆	—	73	4	no	—
199	C₂×C₄×C₈	—	73	1	no	—
200	C₂×C₄×C₈	—	73	1	no	—
201	C₂×C₄×C₈	—	73	1	no	—
202	C₂×C₄×C₈	—	73	1	no	—
203	C₂×C₄×C₈	—	73	1	no	—
204	C₂×C₄×C₈	—	73	1	no	—
205	C₂×C₄×C₈	—	73	1	no	—
206	C₂×C₄×C₈	—	73	1	no	—
207	C₂×C₄×C₈	—	73	1	no	—
208	C₂×C₄×C₈	—	73	1	no	—
209	C₂×C₄×C₈	—	73	1	no	—
210	C₂×C₄×C₈	#64408	1	1	yes	characteristic
211	#346	—	73	4	no	—
212	#346	—	73	4	no	—
213	C₄×C₁₆	—	73	4	no	—
214	C₄×C₁₆	—	73	4	no	—
215	C₂³×C₄	—	73	1	no	—
216	C₂³×C₄	—	73	2	no	—
217	C₂²×C₈	—	73	1	no	—
218	C₂²×C₈	—	73	1	no	—
219	C₂²×C₈	—	73	8	no	—
220	C₂²×C₈	—	73	8	no	—
221	C₂²×C₈	—	73	1	no	—
222	C₂²×C₈	—	73	1	no	—
223	C₂²×C₈	—	73	1	no	—
224	C₂²×C₈	—	73	1	no	—
225	C₂²×C₈	—	73	1	no	—
226	C₂²×C₈	—	73	1	no	—
227	C₂²×C₈	—	73	1	no	—
228	C₂²×C₈	—	73	1	no	—
229	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
230	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
231	C₂×C₄²	—	73	2	no	—
232	C₂×C₄²	—	73	1	no	—
233	C₂×C₄²	—	73	2	no	—
234	C₂×C₄²	—	73	2	no	—
235	C₂×C₄²	—	73	1	no	—
236	C₂×C₄²	—	73	1	no	—
237	C₂×C₄²	—	73	1	no	—
238	C₂×C₄²	—	73	1	no	—
239	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
240	M₃₂	—	73	16	no	—
241	M₃₂	—	73	16	no	—
242	C₂×C₁₆	—	73	8	no	—
243	C₂×C₁₆	—	73	16	no	—
244	C₄×C₈	—	73	1	no	—
245	C₄×C₈	—	73	1	no	—
246	C₄×C₈	—	73	1	no	—
247	C₄×C₈	—	73	1	no	—
248	C₄×C₈	—	73	1	no	—
249	C₄×C₈	—	73	1	no	—
250	C₄×C₈	—	73	1	no	—
251	C₄×C₈	—	73	1	no	—
252	C₄×C₈	—	73	1	no	—
253	C₄×C₈	—	73	1	no	—
254	C₄×C₈	—	73	1	no	—
255	C₄×C₈	—	73	1	no	—
256	C₄×C₈	C₂×#64408	1	1	yes	characteristic
257	C₄×C₈	C₂×#64408	1	1	yes	characteristic
258	C₄×C₈	C₂×#64408	1	1	yes	characteristic
259	C₄×C₈	C₂×#64408	1	1	yes	characteristic
260	C₂⁴	—	73	1	no	—
261	C₂²×C₄	—	73	1	no	—
262	C₂²×C₄	—	73	2	no	—
263	C₂²×C₄	—	73	1	no	—
264	C₂²×C₄	—	73	1	no	—
265	C₂²×C₄	—	73	4	no	—
266	C₂²×C₄	—	73	1	no	—
267	C₂²×C₄	—	73	1	no	—
268	C₂²×C₄	—	73	4	no	—
269	C₂²×C₄	—	73	2	no	—
270	C₂²×C₄	—	73	2	no	—
271	C₂²×C₄	—	73	2	no	—
272	C₂²×C₄	—	73	2	no	—
273	C₂²×C₄	—	146	8	no	—
274	C₂²×C₄	#11924036	1	2	yes	—
275	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
276	C₂×C₈	—	73	4	no	—
277	C₂×C₈	—	73	1	no	—
278	C₂×C₈	—	73	1	no	—
279	C₂×C₈	—	73	1	no	—
280	C₂×C₈	—	73	1	no	—
281	C₂×C₈	—	73	4	no	—
282	C₂×C₈	—	73	4	no	—
283	C₂×C₈	—	73	4	no	—
284	C₂×C₈	—	73	4	no	—
285	C₂×C₈	—	73	4	no	—
286	C₂×C₈	—	73	4	no	—
287	C₂×C₈	—	73	4	no	—
288	C₂×C₈	—	73	4	no	—
289	C₂×C₈	—	73	4	no	—
290	C₂×C₈	C₄×#64408	1	4	yes	—
291	C₂×C₈	#11924036	1	4	yes	—
292	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
293	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
294	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
295	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
296	C₄²	—	73	2	no	—
297	C₄²	—	73	2	no	—
298	C₄²	—	73	2	no	—
299	C₄²	—	73	2	no	—
300	C₄²	—	73	2	no	—
301	C₄²	—	73	1	no	—
302	C₄²	—	73	1	no	—
303	C₄²	#11924036	1	2	yes	—
304	C₄²	C₂²×#64408	1	1	yes	characteristic
305	C₄²	C₂²×#64408	1	1	yes	characteristic
306	C₁₆	—	73	16	no	—
307	C₂³	—	73	1	no	—
308	C₂³	—	73	1	no	—
309	C₂³	—	73	4	no	—
310	C₂³	—	146	4	no	—
311	C₂³	C₂×#11924036	1	1	yes	characteristic
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	73	2	no	—
314	C₂×C₄	—	73	1	no	—
315	C₂×C₄	—	73	1	no	—
316	C₂×C₄	—	73	4	no	—
317	C₂×C₄	—	73	8	no	—
318	C₂×C₄	—	73	2	no	—
319	C₂×C₄	—	73	2	no	—
320	C₂×C₄	—	73	2	no	—
321	C₂×C₄	—	73	2	no	—
322	C₂×C₄	—	73	4	no	—
323	C₂×C₄	—	73	4	no	—
324	C₂×C₄	—	73	2	no	—
325	C₂×C₄	—	146	4	no	—
326	C₂×C₄	—	146	4	no	—
327	C₂×C₄	—	146	4	no	—
328	C₂×C₄	—	146	4	no	—
329	C₂×C₄	C₂×C₄×#64408	1	2	yes	—
330	C₂×C₄	C₂×#11924036	1	2	yes	—
331	C₂×C₄	C₂×#11924036	1	2	yes	—
332	C₂×C₄	C₂×#11924036	1	2	yes	—
333	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
334	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
335	C₈	—	73	2	no	—
336	C₈	—	73	2	no	—
337	C₈	—	73	2	no	—
338	C₈	—	73	2	no	—
339	C₈	C₂×C₄×#64408	1	2	yes	—
340	C₈	C₂×C₄×#64408	1	2	yes	—
341	C₈	C₂×#11924036	1	2	yes	—
342	C₈	C₂×#11924036	1	2	yes	—
343	C₂²	—	2	2	no	—
344	C₂²	—	73	4	no	—
345	C₂²	—	73	2	no	—
346	C₂²	—	73	2	no	—
347	C₂²	—	146	8	no	—
348	C₂²	—	146	2	no	—
349	C₂²	C₄×#11924036	1	2	yes	—
350	C₂²	C₂²×#11924036	1	1	yes	characteristic
351	C₄	—	2	2	no	—
352	C₄	—	73	4	no	—
353	C₄	—	73	2	no	—
354	C₄	—	73	2	no	—
355	C₄	—	146	2	no	—
356	C₄	C₄×#11924036	1	2	yes	—
357	C₄	#17989643	1	4	yes	direct product factor
358	C₄	C₂²×C₄×#64408	1	1	yes	characteristic
359	C₄	C₂²×#11924036	1	1	yes	characteristic
360	C₂	—	2	2	no	—
361	C₂	—	73	4	no	—
362	C₂	—	146	2	no	—
363	C₂	C₂×C₄×#11924036	1	1	yes	characteristic
364	C₂	C₂×#17989643	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×#64408
commutator	C₂×C₇₃	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₂×C₄×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂³×C₈
prime radical	C₂³×D₇₃	C₂×C₈
cosocle	C₂×#10596831	C₂⁴
hypercenter	C₂×C₄×C₈	#64408
hypocenter	C₇₃	C₂×C₄×M₃₂
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #22626138	C₂	semidirect
3. #22626137	C₂	semidirect
4. C₄×#14556666	C₂	semidirect
5. C₄×#14556665	C₂	semidirect
6. #22626132	C₂	semidirect
7. C₄×#14556664	C₂	semidirect
10. #17989643	C₄	direct (N × H)
13. #17989476	C₂²	semidirect
14. #17989475	C₂²	semidirect
15. #17989473	C₂²	semidirect
16. C₄×#11924031	C₂²	semidirect
32. #14556666	C₂×C₄	semidirect
33. #14556665	C₂×C₄	semidirect
34. #14556664	C₂×C₄	semidirect
77. #11924031	C₂²×C₄	semidirect
147. C₄×D₇₃	M₃₂	semidirect
170. C₄×C₇₃	C₂×M₃₂	semidirect
176. Dic₇₃	C₂×M₃₂	semidirect
182. D₇₃	C₄×M₃₂	semidirect
191. C₇₃	C₂×C₄×M₃₂	semidirect
357. C₄	#17989643	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#17989643	2
#22626138	2
#22626137	2
C₄×#14556666	2
C₄×#14556665	2
#22626132	2
C₄×#14556664	2
C₂×C₄×C₈×D₇₃	2
C₂×C₄×M₃₂	73

Subgroups — C4×#17989643 #34029783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#17989643 #34029783