Subgroups — C₂×#22612314 #33244255

Order 18688.

7630 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	C₂²×#14556550	C₂	1	2	yes	maximal, complemented
2	#22612314	C₂	1	16	yes	maximal, direct product factor
3	C₂×#17988450	C₂	1	2	yes	maximal, complemented
4	C₂×#17988447	C₂	1	4	yes	maximal, complemented
5	C₂×#17988443	C₂	1	2	yes	maximal
6	C₂×C₄×C₂²⋊Dic₇₃	C₂	1	4	yes	maximal, complemented
7	C₂⁵×C₄×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#14556550	—	2	16	no	—
9	C₂×#14556550	C₂²	1	16	yes	complemented
10	C₂²×C₄⋊Dic₇₃	C₂²	1	4	yes	complemented
11	C₂²×C₂²⋊Dic₇₃	C₂²	1	8	yes	—
12	C₂²×C₂²⋊Dic₇₃	C₂²	1	4	yes	—
13	C₂²×C₄×Dic₇₃	C₂²	1	4	yes	complemented
14	#17988450	C₂²	1	16	yes	complemented
15	#17988447	C₂²	1	32	yes	complemented
16	#17988443	C₂²	1	16	yes	—
17	C₄×C₂²⋊Dic₇₃	C₂²	1	32	yes	complemented
18	C₂×#14556498	C₂²	1	8	yes	complemented
19	C₂⁶×C₇₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₇₃	—	2	16	no	—
21	C₂⁴×C₄×C₇₃	C₄	1	16	yes	complemented
22	C₂⁴×C₄×C₇₃	C₂²	1	2	yes	—
23	C₂⁴×C₄×C₇₃	C₂²	1	2	yes	—
24	C₂⁴×C₄×C₇₃	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₇₃	C₂²	1	8	yes	—
26	C₂⁴×C₄×C₇₃	C₂²	1	1	yes	characteristic
27	C₂³×Dic₇₃	C₂³	1	8	yes	—
28	#14556550	—	2	64	no	—
29	C₂×C₄⋊Dic₇₃	—	2	16	no	—
30	C₂×C₄⋊Dic₇₃	C₂³	1	16	yes	complemented
31	C₂×C₂²⋊Dic₇₃	—	2	16	no	—
32	C₂×C₂²⋊Dic₇₃	—	2	32	no	—
33	C₂×C₂²⋊Dic₇₃	C₂³	1	32	yes	—
34	C₂×C₂²⋊Dic₇₃	C₂³	1	16	yes	—
35	C₂×C₄×Dic₇₃	—	2	16	no	—
36	C₂×C₄×Dic₇₃	C₂³	1	16	yes	complemented
37	#14556498	C₂³	1	32	yes	complemented
38	C₂⁵×C₇₃	—	2	8	no	—
39	C₂⁵×C₇₃	—	2	16	no	—
40	C₂⁵×C₇₃	C₂×C₄	1	8	yes	—
41	C₂⁵×C₇₃	C₂³	1	4	yes	—
42	C₂⁵×C₇₃	C₂³	1	1	yes	characteristic
43	C₂⁵×C₇₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₇₃	—	2	8	no	—
45	C₂³×C₄×C₇₃	—	2	128	no	—
46	C₂³×C₄×C₇₃	—	2	16	no	—
47	C₂³×C₄×C₇₃	—	2	16	no	—
48	C₂³×C₄×C₇₃	—	2	64	no	—
49	C₂³×C₄×C₇₃	C₂×C₄	1	8	yes	—
50	C₂³×C₄×C₇₃	C₂×C₄	1	16	yes	—
51	C₂³×C₄×C₇₃	C₂×C₄	1	16	yes	—
52	C₂³×C₄×C₇₃	C₂×C₄	1	8	yes	—
53	C₂³×C₄×C₇₃	C₂×C₄	1	64	yes	complemented
54	C₂³×C₄×C₇₃	D₄	1	16	yes	—
55	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₇₃	C₂³	1	8	yes	—
57	C₂³×C₄×C₇₃	C₂³	1	8	yes	—
58	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
59	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
61	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
62	C₂²×Dic₇₃	—	2	16	no	—
63	C₂²×Dic₇₃	—	2	32	no	—
64	C₂²×Dic₇₃	C₂⁴	1	16	yes	—
65	C₄⋊Dic₇₃	—	2	32	no	—
66	C₂²⋊Dic₇₃	—	2	32	no	—
67	C₂²⋊Dic₇₃	—	2	64	no	—
68	C₄×Dic₇₃	—	2	32	no	—
69	C₂⁴×C₇₃	—	2	128	no	—
70	C₂⁴×C₇₃	—	2	32	no	—
71	C₂⁴×C₇₃	—	2	64	no	—
72	C₂⁴×C₇₃	—	2	16	no	—
73	C₂⁴×C₇₃	—	2	8	no	—
74	C₂⁴×C₇₃	—	2	32	no	—
75	C₂⁴×C₇₃	—	2	8	no	—
76	C₂⁴×C₇₃	—	2	8	no	—
77	C₂⁴×C₇₃	C₂²×C₄	1	16	yes	—
78	C₂⁴×C₇₃	C₂²×C₄	1	4	yes	—
79	C₂⁴×C₇₃	C₂²×C₄	1	8	yes	—
80	C₂⁴×C₇₃	C₂×D₄	1	8	yes	—
81	C₂⁴×C₇₃	#41	1	16	yes	—
82	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
83	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
84	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
85	C₂²×C₄×C₇₃	—	2	32	no	—
86	C₂²×C₄×C₇₃	—	2	16	no	—
87	C₂²×C₄×C₇₃	—	2	8	no	—
88	C₂²×C₄×C₇₃	—	2	64	no	—
89	C₂²×C₄×C₇₃	—	2	64	no	—
90	C₂²×C₄×C₇₃	—	2	256	no	—
91	C₂²×C₄×C₇₃	—	2	32	no	—
92	C₂²×C₄×C₇₃	—	2	32	no	—
93	C₂²×C₄×C₇₃	C₂²⋊C₄	1	64	yes	complemented
94	C₂²×C₄×C₇₃	C₂²×C₄	1	8	yes	—
95	C₂²×C₄×C₇₃	C₂²×C₄	1	16	yes	—
96	C₂²×C₄×C₇₃	C₂²×C₄	1	32	yes	—
97	C₂²×C₄×C₇₃	C₂²×C₄	1	32	yes	—
98	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₇₃	C₂²×C₄	1	16	yes	—
101	C₂²×C₄×C₇₃	C₂×D₄	1	8	yes	—
102	C₂²×C₄×C₇₃	C₂×D₄	1	8	yes	—
103	C₂²×C₄×C₇₃	C₂×D₄	1	32	yes	—
104	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
106	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
107	C₂³×C₇₃	—	2	128	no	—
108	C₂³×C₇₃	—	2	256	no	—
109	C₂³×C₇₃	—	2	32	no	—
110	C₂³×C₇₃	—	2	16	no	—
111	C₂³×C₇₃	—	2	16	no	—
112	C₂³×C₇₃	—	2	16	no	—
113	C₂³×C₇₃	—	2	64	no	—
114	C₂³×C₇₃	—	2	32	no	—
115	C₂³×C₇₃	—	2	64	no	—
116	C₂³×C₇₃	—	2	8	no	—
117	C₂³×C₇₃	—	2	8	no	—
118	C₂³×C₇₃	—	2	8	no	—
119	C₂³×C₇₃	C₂×C₂²⋊C₄	1	16	yes	—
120	C₂³×C₇₃	#117	1	32	yes	complemented
121	C₂³×C₇₃	C₂³×C₄	1	4	yes	—
122	C₂³×C₇₃	C₂³×C₄	1	8	yes	—
123	C₂³×C₇₃	C₂³×C₄	1	2	yes	—
124	C₂³×C₇₃	C₂²×D₄	1	8	yes	—
125	C₂³×C₇₃	C₂²×D₄	1	4	yes	—
126	C₂³×C₇₃	C₂×#41	1	16	yes	—
127	C₂³×C₇₃	C₂×#41	1	8	yes	—
128	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
129	C₂×C₄×C₇₃	—	2	32	no	—
130	C₂×C₄×C₇₃	—	2	16	no	—
131	C₂×C₄×C₇₃	—	2	8	no	—
132	C₂×C₄×C₇₃	—	2	64	no	—
133	C₂×C₄×C₇₃	—	2	64	no	—
134	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	16	yes	—
135	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	16	yes	—
136	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	64	yes	complemented
137	C₂×C₄×C₇₃	C₂³×C₄	1	8	yes	—
138	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
139	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
140	C₂×C₄×C₇₃	C₂²×D₄	1	8	yes	—
141	C₂×C₄×C₇₃	C₂²×D₄	1	8	yes	—
142	C₂×Dic₇₃	—	2	16	no	—
143	C₂×Dic₇₃	—	2	32	no	—
144	C₂×Dic₇₃	—	4	32	no	—
145	C₂²×C₇₃	—	2	128	no	—
146	C₂²×C₇₃	—	2	8	no	—
147	C₂²×C₇₃	—	2	8	no	—
148	C₂²×C₇₃	—	2	8	no	—
149	C₂²×C₇₃	—	2	16	no	—
150	C₂²×C₇₃	—	2	32	no	—
151	C₂²×C₇₃	—	2	32	no	—
152	C₂²×C₇₃	—	2	64	no	—
153	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	8	yes	—
154	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	4	yes	—
155	C₂²×C₇₃	C₂×#117	1	8	yes	—
156	C₂²×C₇₃	C₂×#117	1	16	yes	complemented
157	C₂²×C₇₃	#525	1	16	yes	—
158	C₂²×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
159	C₂²×C₇₃	C₂³×D₄	1	2	yes	—
160	C₂²×C₇₃	C₂²×#41	1	4	yes	—
161	C₄×C₇₃	—	2	8	no	—
162	C₄×C₇₃	C₂²×C₂²⋊C₄	1	8	yes	—
163	C₄×C₇₃	C₂²×C₂²⋊C₄	1	8	yes	—
164	Dic₇₃	—	4	16	no	—
165	C₂×#2280	—	73	1	no	maximal, Sylow
166	C₂×C₇₃	—	2	8	no	—
167	C₂×C₇₃	—	2	16	no	—
168	C₂×C₇₃	#2280	1	8	yes	complemented
169	C₂×C₇₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₇₃	C₂²×#117	1	2	yes	—
171	C₂×C₇₃	C₂×#525	1	4	yes	—
172	C₂⁵×C₄	D₇₃	1	1	yes	characteristic
173	C₂²×#117	—	73	2	no	—
174	#2280	—	73	16	no	—
175	C₂×#381	—	73	2	no	—
176	C₂×#380	—	73	4	no	—
177	C₂×#379	—	73	2	no	—
178	C₂×C₄×C₂²⋊C₄	—	73	4	no	—
179	C₇₃	C₂×#2280	1	1	yes	characteristic, complemented, Sylow
180	C₂⁶	C₂×D₇₃	1	1	yes	characteristic
181	C₂⁴×C₄	—	2	16	no	—
182	C₂⁴×C₄	Dic₇₃	1	16	yes	complemented
183	C₂⁴×C₄	C₂×D₇₃	1	2	yes	—
184	C₂⁴×C₄	C₂×D₇₃	1	1	yes	characteristic
185	C₂⁴×C₄	C₂×D₇₃	1	2	yes	—
186	C₂⁴×C₄	C₂×D₇₃	1	8	yes	—
187	C₂⁴×C₄	C₂×D₇₃	1	1	yes	characteristic
188	C₂×#117	—	73	16	no	—
189	C₂×#117	—	146	16	no	—
190	C₂²×C₄⋊C₄	—	73	4	no	—
191	C₂²×C₂²⋊C₄	—	73	4	no	—
192	C₂²×C₂²⋊C₄	—	73	8	no	—
193	C₂²×C₄²	—	73	4	no	—
194	#381	—	73	16	no	—
195	#380	—	73	32	no	—
196	#379	—	73	16	no	—
197	C₄×C₂²⋊C₄	—	73	32	no	—
198	C₂×#95	—	73	8	no	—
199	C₂⁵	—	2	8	no	—
200	C₂⁵	—	2	16	no	—
201	C₂⁵	C₂×Dic₇₃	1	8	yes	—
202	C₂⁵	C₂²×D₇₃	1	4	yes	—
203	C₂⁵	C₂²×D₇₃	1	1	yes	characteristic
204	C₂⁵	C₂²×D₇₃	1	2	yes	—
205	C₂³×C₄	—	2	8	no	—
206	C₂³×C₄	—	2	128	no	—
207	C₂³×C₄	—	2	16	no	—
208	C₂³×C₄	—	2	16	no	—
209	C₂³×C₄	—	2	64	no	—
210	C₂³×C₄	—	73	8	no	—
211	C₂³×C₄	C₂×Dic₇₃	1	8	yes	—
212	C₂³×C₄	C₂×Dic₇₃	1	16	yes	—
213	C₂³×C₄	C₂×Dic₇₃	1	16	yes	—
214	C₂³×C₄	C₂×Dic₇₃	1	8	yes	—
215	C₂³×C₄	C₂×Dic₇₃	1	64	yes	complemented
216	C₂³×C₄	C₂²⋊D₇₃	1	16	yes	—
217	C₂³×C₄	C₂²×D₇₃	1	2	yes	—
218	C₂³×C₄	C₂²×D₇₃	1	8	yes	—
219	C₂³×C₄	C₂²×D₇₃	1	8	yes	—
220	C₂³×C₄	C₂²×D₇₃	1	4	yes	—
221	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
222	C₂³×C₄	C₂²×D₇₃	1	4	yes	—
223	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
224	#117	—	146	64	no	—
225	C₂×C₄⋊C₄	—	73	16	no	—
226	C₂×C₄⋊C₄	—	146	16	no	—
227	C₂×C₂²⋊C₄	—	73	16	no	—
228	C₂×C₂²⋊C₄	—	73	32	no	—
229	C₂×C₂²⋊C₄	—	146	16	no	—
230	C₂×C₂²⋊C₄	—	146	32	no	—
231	C₂×C₄²	—	73	16	no	—
232	C₂×C₄²	—	146	16	no	—
233	#95	—	73	32	no	—
234	C₂⁴	—	2	128	no	—
235	C₂⁴	—	2	32	no	—
236	C₂⁴	—	2	64	no	—
237	C₂⁴	—	2	16	no	—
238	C₂⁴	—	2	8	no	—
239	C₂⁴	—	2	32	no	—
240	C₂⁴	—	2	8	no	—
241	C₂⁴	—	2	8	no	—
242	C₂⁴	C₂²×Dic₇₃	1	16	yes	—
243	C₂⁴	C₂²×Dic₇₃	1	4	yes	—
244	C₂⁴	C₂²×Dic₇₃	1	8	yes	—
245	C₂⁴	C₂×C₂²⋊D₇₃	1	8	yes	—
246	C₂⁴	#11924028	1	16	yes	—
247	C₂⁴	C₂³×D₇₃	1	2	yes	—
248	C₂⁴	C₂³×D₇₃	1	4	yes	—
249	C₂⁴	C₂³×D₇₃	1	1	yes	characteristic
250	C₂²×C₄	—	2	32	no	—
251	C₂²×C₄	—	2	16	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	64	no	—
254	C₂²×C₄	—	2	64	no	—
255	C₂²×C₄	—	2	256	no	—
256	C₂²×C₄	—	2	32	no	—
257	C₂²×C₄	—	2	32	no	—
258	C₂²×C₄	—	73	16	no	—
259	C₂²×C₄	—	146	16	no	—
260	C₂²×C₄	—	146	32	no	—
261	C₂²×C₄	C₂²⋊Dic₇₃	1	64	yes	complemented
262	C₂²×C₄	C₂²×Dic₇₃	1	8	yes	—
263	C₂²×C₄	C₂²×Dic₇₃	1	16	yes	—
264	C₂²×C₄	C₂²×Dic₇₃	1	32	yes	—
265	C₂²×C₄	C₂²×Dic₇₃	1	32	yes	—
266	C₂²×C₄	C₂²×Dic₇₃	1	4	yes	—
267	C₂²×C₄	C₂²×Dic₇₃	1	4	yes	—
268	C₂²×C₄	C₂²×Dic₇₃	1	16	yes	—
269	C₂²×C₄	C₂×C₂²⋊D₇₃	1	8	yes	—
270	C₂²×C₄	C₂×C₂²⋊D₇₃	1	8	yes	—
271	C₂²×C₄	C₂×C₂²⋊D₇₃	1	32	yes	—
272	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
273	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
274	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
275	C₄⋊C₄	—	146	32	no	—
276	C₂²⋊C₄	—	146	32	no	—
277	C₂²⋊C₄	—	146	64	no	—
278	C₄²	—	146	32	no	—
279	C₂³	—	2	256	no	—
280	C₂³	—	2	128	no	—
281	C₂³	—	2	8	no	—
282	C₂³	—	2	8	no	—
283	C₂³	—	2	8	no	—
284	C₂³	—	2	32	no	—
285	C₂³	—	2	16	no	—
286	C₂³	—	2	16	no	—
287	C₂³	—	2	16	no	—
288	C₂³	—	2	64	no	—
289	C₂³	—	2	32	no	—
290	C₂³	—	2	64	no	—
291	C₂³	C₂×C₂²⋊Dic₇₃	1	16	yes	—
292	C₂³	#14556550	1	32	yes	complemented
293	C₂³	C₂³×Dic₇₃	1	4	yes	—
294	C₂³	C₂³×Dic₇₃	1	8	yes	—
295	C₂³	C₂³×Dic₇₃	1	2	yes	—
296	C₂³	C₂²×C₂²⋊D₇₃	1	8	yes	—
297	C₂³	C₂²×C₂²⋊D₇₃	1	4	yes	—
298	C₂³	C₂×#11924028	1	16	yes	—
299	C₂³	C₂×#11924028	1	8	yes	—
300	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	32	no	—
303	C₂×C₄	—	2	16	no	—
304	C₂×C₄	—	2	64	no	—
305	C₂×C₄	—	2	64	no	—
306	C₂×C₄	—	292	32	no	—
307	C₂×C₄	—	146	16	no	—
308	C₂×C₄	—	146	32	no	—
309	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	16	yes	—
310	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	16	yes	—
311	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	64	yes	complemented
312	C₂×C₄	C₂³×Dic₇₃	1	8	yes	—
313	C₂×C₄	C₂³×Dic₇₃	1	4	yes	—
314	C₂×C₄	C₂³×Dic₇₃	1	4	yes	—
315	C₂×C₄	C₂²×C₂²⋊D₇₃	1	8	yes	—
316	C₂×C₄	C₂²×C₂²⋊D₇₃	1	8	yes	—
317	C₂²	—	2	128	no	—
318	C₂²	—	2	32	no	—
319	C₂²	—	2	64	no	—
320	C₂²	—	2	8	no	—
321	C₂²	—	2	8	no	—
322	C₂²	—	2	8	no	—
323	C₂²	—	2	16	no	—
324	C₂²	—	2	32	no	—
325	C₂²	C₂²×C₂²⋊Dic₇₃	1	8	yes	—
326	C₂²	C₂²×C₂²⋊Dic₇₃	1	4	yes	—
327	C₂²	C₂×#14556550	1	8	yes	—
328	C₂²	C₂×#14556550	1	16	yes	complemented
329	C₂²	#17989098	1	16	yes	—
330	C₂²	C₂⁴×Dic₇₃	1	1	yes	characteristic
331	C₂²	C₂³×C₂²⋊D₇₃	1	2	yes	—
332	C₂²	C₂²×#11924028	1	4	yes	—
333	C₄	—	2	8	no	—
334	C₄	—	292	16	no	—
335	C₄	C₂²×C₂²⋊Dic₇₃	1	8	yes	—
336	C₄	C₂²×C₂²⋊Dic₇₃	1	8	yes	—
337	C₂	—	2	8	no	—
338	C₂	—	2	16	no	—
339	C₂	#22612314	1	8	yes	direct product factor
340	C₂	C₂³×C₂²⋊Dic₇₃	1	1	yes	characteristic
341	C₂	C₂²×#14556550	1	2	yes	—
342	C₂	C₂×#17989098	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₇₃
commutator	C₂²×C₇₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₇₃
Fitting	C₂⁵×C₄×C₇₃	C₂
socle	C₂⁴×C₇₃	C₂⁴
prime radical	C₂⁶×C₇₃	C₂²
cosocle	C₂³×C₇₃	C₂⁵
hypercenter	C₂⁵×C₄	D₇₃
hypocenter	C₇₃	C₂×#2280
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂⁵×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#14556550	C₂	semidirect
2. #22612314	C₂	direct (N × H)
3. C₂×#17988450	C₂	semidirect
4. C₂×#17988447	C₂	semidirect
6. C₂×C₄×C₂²⋊Dic₇₃	C₂	semidirect
9. C₂×#14556550	C₂²	semidirect
10. C₂²×C₄⋊Dic₇₃	C₂²	semidirect
13. C₂²×C₄×Dic₇₃	C₂²	semidirect
14. #17988450	C₂²	semidirect
15. #17988447	C₂²	semidirect
17. C₄×C₂²⋊Dic₇₃	C₂²	semidirect
18. C₂×#14556498	C₂²	semidirect
21. C₂⁴×C₄×C₇₃	C₄	semidirect
30. C₂×C₄⋊Dic₇₃	C₂³	semidirect
36. C₂×C₄×Dic₇₃	C₂³	semidirect
37. #14556498	C₂³	semidirect
53. C₂³×C₄×C₇₃	C₂×C₄	semidirect
93. C₂²×C₄×C₇₃	C₂²⋊C₄	semidirect
120. C₂³×C₇₃	#117	semidirect
136. C₂×C₄×C₇₃	C₂×C₂²⋊C₄	semidirect
156. C₂²×C₇₃	C₂×#117	semidirect
168. C₂×C₇₃	#2280	semidirect
179. C₇₃	C₂×#2280	semidirect
182. C₂⁴×C₄	Dic₇₃	semidirect
215. C₂³×C₄	C₂×Dic₇₃	semidirect
261. C₂²×C₄	C₂²⋊Dic₇₃	semidirect
292. C₂³	#14556550	semidirect
311. C₂×C₄	C₂×C₂²⋊Dic₇₃	semidirect
328. C₂²	C₂×#14556550	semidirect
339. C₂	#22612314	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14556550	2
#22612314	2
C₂×#17988450	2
C₂×#17988447	2
C₂×#17988443	2
C₂×C₄×C₂²⋊Dic₇₃	2
C₂⁵×C₄×C₇₃	2
C₂×#2280	73

Subgroups — C2×#22612314 #33244255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22612314 #33244255