Subgroups — #3395×D₇₃ #33966908

Order 18688.

1894 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#557×D₇₃	C₂	1	2	yes	maximal
2	#22622937	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622936	C₂	1	3	yes	maximal, complemented
4	#22622935	C₂	1	3	yes	maximal, complemented
5	#22622934	C₂	1	2	yes	maximal, complemented
6	#22622933	C₂	1	6	yes	maximal, complemented
7	#494×D₇₃	C₂	1	3	yes	maximal
8	#462×D₇₃	C₂	1	6	yes	maximal
9	C₈×Q₈×D₇₃	C₂	1	1	yes	maximal, characteristic
10	C₄×Q₁₆×D₇₃	C₂	1	3	yes	maximal
11	C₇₃×#3395	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₇₃	C₂²	1	3	yes	—
13	C₂×Q₁₆×D₇₃	C₂²	1	6	yes	—
14	#17989316	C₂²	1	2	yes	—
15	#17989315	C₂²	1	6	yes	—
16	#17989314	—	2	6	no	—
17	#17989313	—	2	2	no	—
18	#17989312	C₂²	1	6	yes	—
19	C₄⋊Q₈×D₇₃	C₂²	1	6	yes	—
20	#125×D₇₃	—	2	6	no	—
21	C₄×Q₈×D₇₃	—	2	2	no	—
22	C₄×Q₈×D₇₃	C₂²	1	6	yes	—
23	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
24	#17988967	C₂²	1	3	yes	—
25	#17988966	C₂²	1	6	yes	—
26	#17988965	C₂²	1	6	yes	—
27	#17988965	C₂²	1	6	yes	—
28	#17988798	C₂²	1	6	yes	—
29	#17988797	C₂²	1	6	yes	—
30	#17988796	C₂²	1	12	yes	—
31	#17988795	C₂²	1	12	yes	—
32	#17988794	C₂²	1	6	yes	—
33	Q₈×#10596831	C₂²	1	1	yes	characteristic
34	C₈×Dic₁₄₆	C₂²	1	3	yes	—
35	#17988711	C₂²	1	3	yes	—
36	C₄×Dic₂₉₂	C₂²	1	3	yes	—
37	Q₁₆×Dic₇₃	C₂²	1	3	yes	—
38	#17988681	C₂²	1	3	yes	—
39	C₄×#11924018	C₂²	1	6	yes	—
40	#17988679	C₂²	1	6	yes	—
41	#107×D₇₃	C₂²	1	1	yes	characteristic
42	C₄⋊C₈×D₇₃	C₂²	1	3	yes	—
43	#103×D₇₃	C₂²	1	6	yes	—
44	C₄×C₈×D₇₃	C₂²	1	3	yes	—
45	#557×C₇₃	C₂²	1	2	yes	—
46	#494×C₇₃	C₂²	1	3	yes	—
47	#462×C₇₃	C₂²	1	6	yes	—
48	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic
49	C₄×Q₁₆×C₇₃	C₂²	1	3	yes	—
50	C₂×Q₈×D₇₃	D₄	1	1	yes	characteristic
51	C₂×Q₈×D₇₃	C₂³	1	6	yes	—
52	C₂×Dic₂₉₂	C₂³	1	3	yes	—
53	C₂×Dic₂₉₂	C₂³	1	6	yes	—
54	C₂×#11924018	C₂³	1	6	yes	—
55	C₂×#11924018	C₂³	1	12	yes	—
56	Q₁₆×D₇₃	—	2	12	no	—
57	Q₁₆×D₇₃	—	4	12	no	—
58	C₂×C₈×D₇₃	C₂³	1	3	yes	—
59	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
60	#14556591	C₂³	1	6	yes	—
61	#14556590	—	2	6	no	—
62	#14556590	—	2	6	no	—
63	#14556589	C₂³	1	12	yes	—
64	#14556583	—	2	6	no	—
65	#14556582	—	2	6	no	—
66	#14556582	—	2	6	no	—
67	#14556581	—	2	12	no	—
68	#14556581	—	2	12	no	—
69	Q₈×Dic₇₃	—	2	2	no	—
70	Q₈×Dic₇₃	D₄	1	1	yes	characteristic
71	Q₈×Dic₇₃	C₂³	1	6	yes	—
72	C₄×Dic₁₄₆	—	2	6	no	—
73	C₄×Dic₁₄₆	—	2	6	no	—
74	C₄×Dic₁₄₆	C₂³	1	6	yes	—
75	C₄×Dic₁₄₆	C₂³	1	3	yes	—
76	#14556556	—	2	6	no	—
77	#14556556	—	2	6	no	—
78	#14556556	D₄	1	3	yes	—
79	#14556556	C₂³	1	6	yes	—
80	C₄⋊C₄×D₇₃	—	2	6	no	—
81	C₄⋊C₄×D₇₃	—	2	6	no	—
82	C₄⋊C₄×D₇₃	—	2	6	no	—
83	C₄⋊C₄×D₇₃	D₄	1	3	yes	—
84	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
85	C₄²×D₇₃	—	2	6	no	—
86	C₄²×D₇₃	C₂³	1	3	yes	—
87	#14556525	C₂³	1	1	yes	characteristic
88	#14556524	C₂³	1	2	yes	—
89	C₄⋊#10596831	C₂³	1	3	yes	—
90	#14556520	C₂³	1	6	yes	—
91	#14556516	C₂³	1	6	yes	—
92	#14556515	C₂³	1	6	yes	—
93	#14556514	C₂³	1	6	yes	—
94	C₄×#10596831	C₂³	1	3	yes	—
95	C₈×Dic₇₃	C₂³	1	3	yes	—
96	C₈×Dic₇₃	C₂³	1	3	yes	—
97	C₂×Q₁₆×C₇₃	C₂³	1	3	yes	—
98	C₂×Q₁₆×C₇₃	C₂³	1	6	yes	—
99	C₄⋊Q₈×C₇₃	C₂³	1	6	yes	—
100	#125×C₇₃	—	2	6	no	—
101	C₄×Q₈×C₇₃	—	2	2	no	—
102	C₄×Q₈×C₇₃	C₂³	1	6	yes	—
103	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
104	#107×C₇₃	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₇₃	C₂³	1	3	yes	—
106	#103×C₇₃	C₂³	1	6	yes	—
107	C₄×C₈×C₇₃	C₂³	1	3	yes	—
108	C₂×Dic₁₄₆	—	2	6	no	—
109	C₂×Dic₁₄₆	C₂×D₄	1	3	yes	—
110	C₂×Dic₁₄₆	C₂⁴	1	6	yes	—
111	Q₈×D₇₃	—	2	12	no	—
112	Q₈×D₇₃	—	2	12	no	—
113	Q₈×D₇₃	Q₁₆	1	8	yes	complemented
114	C₂×C₄×D₇₃	—	2	2	no	—
115	C₂×C₄×D₇₃	—	2	6	no	—
116	C₂×C₄×D₇₃	C₂×D₄	1	3	yes	—
117	C₂×C₄×D₇₃	C₂×D₄	1	3	yes	—
118	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
119	Dic₂₉₂	—	2	6	no	—
120	Dic₂₉₂	—	4	6	no	—
121	#11924018	—	2	12	no	—
122	#11924018	—	4	12	no	—
123	C₂×#10596831	C₂⁴	1	3	yes	—
124	C₂×#10596831	C₂⁴	1	1	yes	characteristic
125	C₈×D₇₃	—	2	6	no	—
126	C₈×D₇₃	#41	1	4	yes	—
127	C₄⋊Dic₇₃	—	2	6	no	—
128	C₄⋊Dic₇₃	—	2	6	no	—
129	C₄⋊Dic₇₃	—	2	6	no	—
130	C₄⋊Dic₇₃	C₂×D₄	1	3	yes	—
131	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
132	#11924007	—	2	6	no	—
133	#11924007	—	2	12	no	—
134	#11924007	—	2	6	no	—
135	#11924007	—	2	12	no	—
136	#11924007	—	2	2	no	—
137	#11924007	C₂×D₄	1	6	yes	—
138	C₄×Dic₇₃	—	2	6	no	—
139	C₄×Dic₇₃	—	2	6	no	—
140	C₄×Dic₇₃	—	2	6	no	—
141	C₄×Dic₇₃	C₂×D₄	1	3	yes	—
142	C₄×Dic₇₃	C₂×D₄	1	3	yes	—
143	C₄×Dic₇₃	C₂⁴	1	3	yes	—
144	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
145	C₂×Q₈×C₇₃	C₂⁴	1	6	yes	—
146	Q₁₆×C₇₃	—	2	6	no	—
147	Q₁₆×C₇₃	—	4	6	no	—
148	C₂×C₈×C₇₃	C₂⁴	1	3	yes	—
149	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
150	C₄⋊C₄×C₇₃	—	2	6	no	—
151	C₄⋊C₄×C₇₃	—	2	6	no	—
152	C₄⋊C₄×C₇₃	—	2	6	no	—
153	C₄⋊C₄×C₇₃	C₂×D₄	1	3	yes	—
154	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
155	C₄²×C₇₃	—	2	6	no	—
156	C₄²×C₇₃	C₂⁴	1	3	yes	—
157	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₇₃	—	2	6	no	—
159	Q₈×C₇₃	—	2	6	no	—
160	Q₈×C₇₃	C₂×Q₁₆	1	4	yes	complemented
161	C₂×C₄×C₇₃	—	2	2	no	—
162	C₂×C₄×C₇₃	—	2	6	no	—
163	C₂×C₄×C₇₃	C₂²×D₄	1	3	yes	—
164	C₂×C₄×C₇₃	C₂²×D₄	1	3	yes	—
165	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
166	C₂×Dic₇₃	—	2	2	no	—
167	C₂×Dic₇₃	—	2	6	no	—
168	C₂×Dic₇₃	C₂²×D₄	1	3	yes	—
169	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×Dic₇₃	C₂²×D₄	1	3	yes	—
171	C₄×D₇₃	—	2	6	no	—
172	C₄×D₇₃	—	4	12	no	—
173	C₄×D₇₃	—	4	4	no	—
174	C₄×D₇₃	C₂×Q₁₆	1	12	yes	—
175	C₄×D₇₃	C₂×#41	1	2	yes	—
176	C₄×D₇₃	H(5,𝔽₂)	1	2	yes	—
177	Dic₁₄₆	—	2	6	no	—
178	Dic₁₄₆	—	2	6	no	—
179	Dic₁₄₆	—	4	12	no	—
180	Dic₁₄₆	C₂×Q₁₆	1	12	yes	complemented
181	C₈×C₇₃	—	2	3	no	—
182	C₈×C₇₃	C₂×#41	1	2	yes	—
183	#10596831	—	2	3	no	—
184	#10596831	C₂×#41	1	2	yes	—
185	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
186	C₂×D₇₃	#550	1	2	yes	—
187	C₂×D₇₃	C₂²×Q₁₆	1	2	yes	—
188	C₂×D₇₃	#578	1	2	yes	—
189	C₄×C₇₃	—	2	3	no	—
190	C₄×C₇₃	—	4	6	no	—
191	C₄×C₇₃	—	4	2	no	—
192	C₄×C₇₃	C₂²×Q₁₆	1	6	yes	—
193	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
194	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
195	Dic₇₃	—	2	3	no	—
196	Dic₇₃	—	4	6	no	—
197	Dic₇₃	—	4	2	no	—
198	Dic₇₃	#550	1	2	yes	—
199	Dic₇₃	C₂²×Q₁₆	1	6	yes	—
200	C₂×#3395	—	73	1	no	maximal, Sylow
201	C₂×C₇₃	C₂×#550	1	1	yes	characteristic
202	C₂×C₇₃	C₂³×Q₁₆	1	1	yes	characteristic
203	C₂×C₇₃	C₂×#578	1	1	yes	characteristic
204	D₇₃	#3395	1	4	yes	direct product factor
205	C₂×#557	—	73	2	no	—
206	#3395	—	73	3	no	—
207	#3395	—	73	6	no	—
208	#3395	—	73	1	no	—
209	#3395	—	73	3	no	—
210	#3395	—	73	2	no	—
211	#3395	D₇₃	1	1	yes	characteristic, direct product factor
212	C₂×#494	—	73	3	no	—
213	C₂×#462	—	73	6	no	—
214	C₂×C₈×Q₈	—	73	1	no	—
215	C₂×C₄×Q₁₆	—	73	3	no	—
216	C₇₃	C₂×#3395	1	1	yes	characteristic, complemented, Sylow
217	C₂²×Q₁₆	—	73	6	no	—
218	C₂²×Q₁₆	—	73	3	no	—
219	#557	—	73	6	no	—
220	#557	—	73	6	no	—
221	#557	—	73	2	no	—
222	#557	—	146	2	no	—
223	#557	—	146	6	no	—
224	#557	C₂×D₇₃	1	2	yes	—
225	C₂×C₄⋊Q₈	—	73	6	no	—
226	C₂×#125	—	146	6	no	—
227	C₂×C₄×Q₈	—	73	1	no	—
228	C₂×C₄×Q₈	—	73	6	no	—
229	C₂×C₄×Q₈	—	146	2	no	—
230	#494	—	73	6	no	—
231	#494	—	73	6	no	—
232	#494	—	73	6	no	—
233	#494	—	73	3	no	—
234	#494	C₂×D₇₃	1	3	yes	—
235	#462	—	73	12	no	—
236	#462	—	73	6	no	—
237	#462	—	73	6	no	—
238	#462	—	73	6	no	—
239	#462	—	73	12	no	—
240	#462	C₂×D₇₃	1	6	yes	—
241	C₈×Q₈	—	73	1	no	—
242	C₈×Q₈	—	73	3	no	—
243	C₈×Q₈	—	73	3	no	—
244	C₈×Q₈	C₂×D₇₃	1	1	yes	characteristic
245	C₄×Q₁₆	—	73	3	no	—
246	C₄×Q₁₆	—	73	6	no	—
247	C₄×Q₁₆	—	73	3	no	—
248	C₄×Q₁₆	—	73	6	no	—
249	C₄×Q₁₆	—	73	3	no	—
250	C₄×Q₁₆	C₂×D₇₃	1	3	yes	—
251	C₂×#107	—	73	1	no	—
252	C₂×C₄⋊C₈	—	73	3	no	—
253	C₂×#103	—	73	6	no	—
254	C₂×C₄×C₈	—	73	3	no	—
255	C₂²×Q₈	—	73	1	no	—
256	C₂²×Q₈	—	73	6	no	—
257	C₂×Q₁₆	—	292	12	no	—
258	C₂×Q₁₆	—	73	12	no	—
259	C₂×Q₁₆	—	73	6	no	—
260	C₂×Q₁₆	—	73	6	no	—
261	C₂×Q₁₆	—	73	3	no	—
262	C₂×Q₁₆	—	146	12	no	—
263	C₂×Q₁₆	C₂²×D₇₃	1	3	yes	—
264	C₂×Q₁₆	C₂²×D₇₃	1	6	yes	—
265	C₂²×C₈	—	73	1	no	—
266	C₂²×C₈	—	73	3	no	—
267	C₄⋊Q₈	—	73	12	no	—
268	C₄⋊Q₈	—	73	6	no	—
269	C₄⋊Q₈	—	146	6	no	—
270	C₄⋊Q₈	—	146	6	no	—
271	C₄⋊Q₈	C₂²×D₇₃	1	6	yes	—
272	#125	—	2	6	no	—
273	#125	—	146	6	no	—
274	#125	—	146	12	no	—
275	#125	—	146	12	no	—
276	#125	—	146	6	no	—
277	#125	—	146	6	no	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	73	1	no	—
280	C₄×Q₈	—	73	3	no	—
281	C₄×Q₈	—	73	3	no	—
282	C₄×Q₈	—	73	6	no	—
283	C₄×Q₈	—	73	6	no	—
284	C₄×Q₈	—	73	6	no	—
285	C₄×Q₈	—	146	6	no	—
286	C₄×Q₈	—	146	6	no	—
287	C₄×Q₈	—	146	6	no	—
288	C₄×Q₈	—	146	6	no	—
289	C₄×Q₈	—	146	2	no	—
290	C₄×Q₈	C₂²×D₇₃	1	6	yes	—
291	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
292	C₂×C₄⋊C₄	—	73	3	no	—
293	C₂×C₄⋊C₄	—	73	2	no	—
294	C₂×C₄⋊C₄	—	146	6	no	—
295	C₂×C₄⋊C₄	—	146	6	no	—
296	C₂×C₄⋊C₄	—	146	6	no	—
297	C₂×C₄²	—	73	3	no	—
298	C₂×C₄²	—	146	6	no	—
299	#107	—	73	1	no	—
300	#107	—	73	2	no	—
301	#107	C₂²×D₇₃	1	1	yes	characteristic
302	C₄⋊C₈	—	73	6	no	—
303	C₄⋊C₈	—	73	3	no	—
304	C₄⋊C₈	C₂²×D₇₃	1	3	yes	—
305	#103	—	73	6	no	—
306	#103	—	73	6	no	—
307	#103	—	73	6	no	—
308	#103	C₂²×D₇₃	1	6	yes	—
309	C₄×C₈	—	73	3	no	—
310	C₄×C₈	—	73	3	no	—
311	C₄×C₈	—	73	3	no	—
312	C₄×C₈	C₂²×D₇₃	1	3	yes	—
313	C₂×Q₈	—	73	8	no	—
314	C₂×Q₈	—	73	3	no	—
315	C₂×Q₈	—	73	6	no	—
316	C₂×Q₈	—	146	6	no	—
317	C₂×Q₈	—	146	12	no	—
318	C₂×Q₈	—	146	12	no	—
319	C₂×Q₈	D₄×D₇₃	1	1	yes	characteristic
320	C₂×Q₈	C₂³×D₇₃	1	6	yes	—
321	C₂²×C₄	—	73	3	no	—
322	C₂²×C₄	—	73	1	no	—
323	C₂²×C₄	—	73	3	no	—
324	C₂²×C₄	—	146	2	no	—
325	C₂²×C₄	—	146	6	no	—
326	Q₁₆	—	2	6	no	—
327	Q₁₆	—	4	6	no	—
328	Q₁₆	—	292	6	no	—
329	Q₁₆	—	292	12	no	—
330	Q₁₆	—	146	12	no	—
331	Q₁₆	—	146	6	no	—
332	C₂×C₈	—	73	1	no	—
333	C₂×C₈	—	73	4	no	—
334	C₂×C₈	—	73	3	no	—
335	C₂×C₈	—	146	6	no	—
336	C₂×C₈	C₂³×D₇₃	1	3	yes	—
337	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
338	C₄⋊C₄	—	2	6	no	—
339	C₄⋊C₄	—	2	6	no	—
340	C₄⋊C₄	—	2	6	no	—
341	C₄⋊C₄	—	73	6	no	—
342	C₄⋊C₄	—	73	3	no	—
343	C₄⋊C₄	—	73	2	no	—
344	C₄⋊C₄	—	146	2	no	—
345	C₄⋊C₄	—	146	6	no	—
346	C₄⋊C₄	—	146	12	no	—
347	C₄⋊C₄	—	146	12	no	—
348	C₄⋊C₄	—	146	6	no	—
349	C₄⋊C₄	—	146	6	no	—
350	C₄⋊C₄	—	146	6	no	—
351	C₄⋊C₄	—	146	6	no	—
352	C₄⋊C₄	D₄×D₇₃	1	3	yes	—
353	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
354	C₄²	—	2	6	no	—
355	C₄²	—	73	3	no	—
356	C₄²	—	73	3	no	—
357	C₄²	—	73	3	no	—
358	C₄²	—	146	6	no	—
359	C₄²	—	146	6	no	—
360	C₄²	—	146	6	no	—
361	C₄²	C₂³×D₇₃	1	3	yes	—
362	C₂³	—	73	1	no	—
363	Q₈	—	2	6	no	—
364	Q₈	—	2	6	no	—
365	Q₈	—	292	12	no	—
366	Q₈	—	73	12	no	—
367	Q₈	—	146	6	no	—
368	Q₈	—	146	6	no	—
369	Q₈	Q₁₆×D₇₃	1	4	yes	complemented
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	292	12	no	—
373	C₂×C₄	—	292	4	no	—
374	C₂×C₄	—	73	1	no	—
375	C₂×C₄	—	73	3	no	—
376	C₂×C₄	—	73	2	no	—
377	C₂×C₄	—	73	2	no	—
378	C₂×C₄	—	73	12	no	—
379	C₂×C₄	—	73	3	no	—
380	C₂×C₄	—	146	6	no	—
381	C₂×C₄	—	146	2	no	—
382	C₂×C₄	—	146	6	no	—
383	C₂×C₄	C₂×D₄×D₇₃	1	3	yes	—
384	C₂×C₄	C₂×D₄×D₇₃	1	3	yes	—
385	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
386	C₈	—	2	3	no	—
387	C₈	—	73	2	no	—
388	C₈	—	146	3	no	—
389	C₈	#41×D₇₃	1	2	yes	—
390	C₂²	—	73	2	no	—
391	C₂²	—	73	2	no	—
392	C₂²	—	73	2	no	—
393	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
394	C₄	—	2	3	no	—
395	C₄	—	4	6	no	—
396	C₄	—	4	2	no	—
397	C₄	—	292	6	no	—
398	C₄	—	292	2	no	—
399	C₄	—	73	6	no	—
400	C₄	—	73	2	no	—
401	C₄	—	146	3	no	—
402	C₄	C₂×Q₁₆×D₇₃	1	6	yes	—
403	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
404	C₄	H(5,𝔽₂)×D₇₃	1	1	yes	characteristic
405	C₂	—	73	4	no	—
406	C₂	#550×D₇₃	1	1	yes	characteristic
407	C₂	C₂²×Q₁₆×D₇₃	1	1	yes	characteristic
408	C₂	#578×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3395	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	C₂²×D₇₃	C₂²×D₄
hypercenter	#3395	D₇₃
hypocenter	C₇₃	C₂×#3395
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3395

Complements

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

N	H ≅ G/N	type
2. #22622937	C₂	semidirect
3. #22622936	C₂	semidirect
4. #22622935	C₂	semidirect
5. #22622934	C₂	semidirect
6. #22622933	C₂	semidirect
11. C₇₃×#3395	C₂	semidirect
113. Q₈×D₇₃	Q₁₆	semidirect
160. Q₈×C₇₃	C₂×Q₁₆	semidirect
180. Dic₁₄₆	C₂×Q₁₆	semidirect
204. D₇₃	#3395	direct (N × H)
211. #3395	D₇₃	direct (N × H)
216. C₇₃	C₂×#3395	semidirect
369. Q₈	Q₁₆×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#557×D₇₃	2
#22622937	2
#22622936	2
#22622935	2
#22622934	2
#22622933	2
#494×D₇₃	2
#462×D₇₃	2
C₈×Q₈×D₇₃	2
C₄×Q₁₆×D₇₃	2
C₇₃×#3395	2
C₂×#3395	73

Subgroups — #3395×D73 #33966908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3395×D₇₃ #33966908