Subgroups — Q₈×#41×D₇₃ #33993052

Order 18688.

7522 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#11924029	C₂	1	1	yes	maximal, characteristic, complemented
2	#22623513	C₂	1	3	yes	maximal, complemented
3	Q₈×#11924028	C₂	1	3	yes	maximal, complemented
4	#41×Dic₁₄₆	C₂	1	3	yes	maximal, complemented
5	#22623510	C₂	1	9	yes	maximal, complemented
6	#22623509	C₂	1	9	yes	maximal, complemented
7	Q₈×#11924027	C₂	1	3	yes	maximal, complemented
8	Q₈²×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#557×D₇₃	C₂	1	3	yes	maximal, complemented
10	#554×D₇₃	C₂	1	9	yes	maximal, complemented
11	D₄×Q₈×D₇₃	C₂	1	3	yes	maximal, complemented
12	#533×D₇₃	C₂	1	9	yes	maximal, complemented
13	C₄×#41×D₇₃	C₂	1	3	yes	maximal
14	C₂×C₄×Q₈×D₇₃	C₂	1	3	yes	maximal, complemented
15	Q₈×#41×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×D₇₃	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×D₇₃	C₂²	1	3	yes	—
18	Q₈×Dic₁₄₆	C₂²	1	3	yes	complemented
19	Q₈×Dic₁₄₆	C₂²	1	3	yes	complemented
20	#17989317	C₂²	1	9	yes	complemented
21	#17989316	C₂²	1	3	yes	complemented
22	#17989315	C₂²	1	9	yes	complemented
23	#17989314	C₂²	1	18	yes	complemented
24	#17989313	C₂²	1	6	yes	complemented
25	#17989312	C₂²	1	9	yes	complemented
26	#17989298	C₂²	1	9	yes	complemented
27	#17989297	C₂²	1	9	yes	complemented
28	#17989296	C₂²	1	18	yes	complemented
29	#17989295	C₂²	1	18	yes	complemented
30	#17989294	C₂²	1	9	yes	complemented
31	#17989293	C₂²	1	18	yes	complemented
32	#17989292	C₂²	1	18	yes	complemented
33	#17989291	C₂²	1	36	yes	complemented
34	Q₈×D₂₉₂	C₂²	1	3	yes	complemented
35	D₄×Dic₁₄₆	C₂²	1	9	yes	complemented
36	#17989252	C₂²	1	9	yes	complemented
37	Q₈×C₂²⋊D₇₃	C₂²	1	6	yes	complemented
38	#17989250	C₂²	1	18	yes	complemented
39	#17989144	C₂²	1	9	yes	complemented
40	#17989143	C₂²	1	18	yes	complemented
41	#17989142	C₂²	1	9	yes	complemented
42	#17989142	C₂²	1	9	yes	complemented
43	#17989141	C₂²	1	18	yes	complemented
44	#17989141	C₂²	1	18	yes	complemented
45	#17989140	C₂²	1	18	yes	complemented
46	#17989139	C₂²	1	18	yes	complemented
47	#17989139	C₂²	1	18	yes	complemented
48	C₄⋊Q₈×D₇₃	C₂²	1	9	yes	—
49	C₄⋊Q₈×D₇₃	C₂²	1	9	yes	—
50	#125×D₇₃	C₂²	1	18	yes	—
51	C₂²⋊Q₈×D₇₃	C₂²	1	18	yes	—
52	C₂²⋊Q₈×D₇₃	C₂²	1	18	yes	—
53	#41×Dic₇₃	C₂²	1	3	yes	—
54	C₄×#11924029	C₂²	1	3	yes	—
55	C₄×#11924029	C₂²	1	3	yes	—
56	C₄×#11924028	C₂²	1	9	yes	—
57	#17989055	C₂²	1	9	yes	—
58	C₄×#11924027	C₂²	1	9	yes	—
59	C₄×#11924027	C₂²	1	9	yes	—
60	C₂×Q₈×Dic₇₃	C₂²	1	3	yes	complemented
61	C₂×C₄×Dic₁₄₆	C₂²	1	9	yes	complemented
62	C₂×#14556556	C₂²	1	9	yes	complemented
63	C₄×Q₈×D₇₃	C₂²	1	3	yes	—
64	C₄×Q₈×D₇₃	C₂²	1	3	yes	—
65	C₄×Q₈×D₇₃	C₂²	1	9	yes	—
66	C₄×Q₈×D₇₃	C₂²	1	3	yes	—
67	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
68	C₄×Q₈×D₇₃	C₂²	1	9	yes	—
69	C₄×Q₈×D₇₃	C₂²	1	6	yes	—
70	C₄×Q₈×D₇₃	C₂²	1	3	yes	complemented
71	C₄×Q₈×D₇₃	C₂²	1	9	yes	complemented
72	C₄×Q₈×D₇₃	C₂²	1	9	yes	complemented
73	C₄×Q₈×D₇₃	C₂²	1	3	yes	complemented
74	C₄×D₄×D₇₃	C₂²	1	9	yes	—
75	C₄×D₄×D₇₃	C₂²	1	9	yes	—
76	#117×D₇₃	C₂²	1	9	yes	—
77	C₂×C₄⋊C₄×D₇₃	C₂²	1	9	yes	—
78	C₂×C₄²×D₇₃	C₂²	1	9	yes	—
79	Q₈²×C₇₃	C₂²	1	1	yes	characteristic, complemented
80	#557×C₇₃	C₂²	1	3	yes	complemented
81	#554×C₇₃	C₂²	1	9	yes	complemented
82	D₄×Q₈×C₇₃	C₂²	1	3	yes	complemented
83	#533×C₇₃	C₂²	1	9	yes	complemented
84	C₄×#41×C₇₃	C₂²	1	3	yes	—
85	C₂×C₄×Q₈×C₇₃	C₂²	1	3	yes	complemented
86	C₂×#11924029	C₂³	1	1	yes	characteristic
87	C₂×#11924028	C₂³	1	3	yes	—
88	C₂×#11924027	C₂³	1	3	yes	—
89	#41×D₇₃	Q₈	1	16	yes	direct product factor
90	C₂²×Dic₁₄₆	C₂³	1	9	yes	—
91	C₂×Q₈×D₇₃	—	2	24	no	—
92	C₂×Q₈×D₇₃	C₂³	1	9	yes	—
93	C₂×Q₈×D₇₃	C₂³	1	9	yes	—
94	C₂×Q₈×D₇₃	C₂³	1	3	yes	—
95	C₂×Q₈×D₇₃	C₂³	1	6	yes	—
96	C₂×Q₈×D₇₃	C₂³	1	1	yes	characteristic
97	C₂×Q₈×D₇₃	C₂³	1	1	yes	characteristic
98	C₂×D₄×D₇₃	C₂³	1	3	yes	—
99	C₂²×C₄×D₇₃	C₂³	1	9	yes	—
100	C₂²×C₄×D₇₃	C₂³	1	9	yes	—
101	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
102	#14556591	C₂³	1	9	yes	—
103	#14556591	C₂³	1	9	yes	—
104	#14556590	C₂³	1	18	yes	—
105	#14556590	C₂³	1	18	yes	—
106	#14556590	C₂³	1	18	yes	—
107	#14556590	C₂³	1	18	yes	—
108	#14556589	C₂³	1	18	yes	—
109	#14556589	C₂³	1	18	yes	—
110	#14556583	C₂³	1	18	yes	—
111	#14556582	C₂³	1	18	yes	—
112	#14556582	C₂³	1	18	yes	—
113	#14556581	C₂³	1	36	yes	—
114	#14556581	C₂³	1	36	yes	—
115	#14556571	C₂³	1	18	yes	—
116	#14556571	C₂³	1	18	yes	—
117	#14556570	C₂³	1	18	yes	—
118	#14556570	C₂³	1	18	yes	—
119	#14556569	C₂³	1	36	yes	—
120	#14556569	C₂³	1	36	yes	—
121	#14556568	C₂³	1	36	yes	—
122	#14556568	C₂³	1	36	yes	—
123	#14556567	C₂³	1	18	yes	—
124	#14556567	C₂³	1	18	yes	—
125	Q₈×Dic₇₃	C₂³	1	6	yes	—
126	Q₈×Dic₇₃	C₂³	1	9	yes	—
127	Q₈×Dic₇₃	C₂³	1	3	yes	—
128	Q₈×Dic₇₃	C₂³	1	9	yes	—
129	Q₈×Dic₇₃	C₂³	1	1	yes	characteristic
130	Q₈×Dic₇₃	C₂³	1	3	yes	—
131	Q₈×Dic₇₃	C₂³	1	3	yes	—
132	C₄×Dic₁₄₆	C₂³	1	18	yes	—
133	C₄×Dic₁₄₆	C₂³	1	18	yes	—
134	C₄×Dic₁₄₆	C₂³	1	9	yes	—
135	C₄×Dic₁₄₆	C₂³	1	9	yes	—
136	C₄×Dic₁₄₆	C₂³	1	18	yes	—
137	C₄×Dic₁₄₆	C₂³	1	9	yes	—
138	C₄×Dic₁₄₆	C₂³	1	3	yes	—
139	C₄×Dic₁₄₆	C₂³	1	9	yes	—
140	C₄×Dic₁₄₆	C₂³	1	9	yes	—
141	#14556556	C₂³	1	18	yes	—
142	#14556556	C₂³	1	9	yes	—
143	#14556556	C₂³	1	18	yes	—
144	#14556556	C₂³	1	9	yes	—
145	#14556556	C₂³	1	18	yes	—
146	#14556556	C₂³	1	9	yes	—
147	#14556556	C₂³	1	3	yes	—
148	#14556556	C₂³	1	9	yes	—
149	#14556556	C₂³	1	9	yes	—
150	C₄×D₂₉₂	C₂³	1	9	yes	—
151	C₄×D₂₉₂	C₂³	1	9	yes	—
152	D₄×Dic₇₃	C₂³	1	9	yes	—
153	D₄×Dic₇₃	C₂³	1	9	yes	—
154	#14556553	C₂³	1	9	yes	—
155	#14556553	C₂³	1	9	yes	—
156	C₄×C₂²⋊D₇₃	C₂³	1	18	yes	—
157	C₄×C₂²⋊D₇₃	C₂³	1	18	yes	—
158	#14556551	C₂³	1	18	yes	—
159	#14556551	C₂³	1	18	yes	—
160	#14556550	C₂³	1	9	yes	—
161	#14556549	C₂³	1	9	yes	—
162	#14556549	C₂³	1	9	yes	—
163	#14556548	C₂³	1	18	yes	—
164	#14556547	C₂³	1	18	yes	—
165	C₂×C₄⋊Dic₇₃	C₂³	1	9	yes	—
166	C₂×#11924007	C₂³	1	18	yes	—
167	C₄⋊C₄×D₇₃	C₂³	1	9	yes	—
168	C₄⋊C₄×D₇₃	C₂³	1	9	yes	—
169	C₄⋊C₄×D₇₃	C₂³	1	9	yes	—
170	C₄⋊C₄×D₇₃	C₂³	1	18	yes	—
171	C₄⋊C₄×D₇₃	C₂³	1	18	yes	—
172	C₄⋊C₄×D₇₃	C₂³	1	3	yes	—
173	C₄⋊C₄×D₇₃	C₂³	1	9	yes	—
174	C₄⋊C₄×D₇₃	C₂³	1	9	yes	—
175	C₄⋊C₄×D₇₃	C₂³	1	18	yes	—
176	C₂²⋊C₄×D₇₃	C₂³	1	18	yes	—
177	C₂×C₄×Dic₇₃	C₂³	1	9	yes	—
178	C₂×C₄×Dic₇₃	C₂³	1	9	yes	—
179	C₂×C₄×Dic₇₃	C₂³	1	9	yes	—
180	C₄²×D₇₃	C₂³	1	9	yes	—
181	C₄²×D₇₃	C₂³	1	9	yes	—
182	C₄²×D₇₃	C₂³	1	9	yes	—
183	C₄²×D₇₃	C₂³	1	9	yes	—
184	C₄²×D₇₃	C₂³	1	9	yes	—
185	C₄²×D₇₃	C₂³	1	3	yes	—
186	C₄²×D₇₃	C₂³	1	9	yes	—
187	C₄²×D₇₃	C₂³	1	9	yes	—
188	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
189	C₂²×Q₈×C₇₃	C₂³	1	3	yes	—
190	C₄⋊Q₈×C₇₃	C₂³	1	9	yes	—
191	C₄⋊Q₈×C₇₃	C₂³	1	9	yes	—
192	#125×C₇₃	C₂³	1	18	yes	—
193	C₂²⋊Q₈×C₇₃	C₂³	1	18	yes	—
194	C₂²⋊Q₈×C₇₃	C₂³	1	18	yes	—
195	C₄×Q₈×C₇₃	C₂³	1	6	yes	—
196	C₄×Q₈×C₇₃	C₂³	1	9	yes	—
197	C₄×Q₈×C₇₃	C₂³	1	3	yes	—
198	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
199	C₄×Q₈×C₇₃	C₂³	1	9	yes	—
200	C₄×Q₈×C₇₃	C₂³	1	3	yes	—
201	C₄×Q₈×C₇₃	C₂³	1	3	yes	—
202	C₄×D₄×C₇₃	C₂³	1	9	yes	—
203	C₄×D₄×C₇₃	C₂³	1	9	yes	—
204	#117×C₇₃	C₂³	1	9	yes	—
205	C₂×C₄⋊C₄×C₇₃	C₂³	1	9	yes	—
206	C₂×C₄²×C₇₃	C₂³	1	9	yes	—
207	C₂³×D₇₃	C₂⁴	1	3	yes	—
208	#11924029	C₂×Q₈	1	8	yes	complemented
209	#11924028	C₂×Q₈	1	24	yes	complemented
210	#11924027	C₂×Q₈	1	24	yes	complemented
211	C₂×Dic₁₄₆	—	2	36	no	—
212	C₂×Dic₁₄₆	C₂⁴	1	18	yes	—
213	C₂×Dic₁₄₆	C₂⁴	1	9	yes	—
214	C₂×Dic₁₄₆	C₂⁴	1	18	yes	—
215	C₂×Dic₁₄₆	C₂⁴	1	3	yes	—
216	C₂×Dic₁₄₆	C₂⁴	1	3	yes	—
217	Q₈×D₇₃	—	2	12	no	—
218	Q₈×D₇₃	—	2	36	no	—
219	Q₈×D₇₃	—	2	36	no	—
220	Q₈×D₇₃	—	4	12	no	—
221	Q₈×D₇₃	C₂×Q₈	1	8	yes	complemented
222	Q₈×D₇₃	#41	1	8	yes	direct product factor
223	C₂×D₂₉₂	C₂⁴	1	3	yes	—
224	C₂×C₂²⋊D₇₃	C₂⁴	1	6	yes	—
225	D₄×D₇₃	C₂×Q₈	1	24	yes	complemented
226	C₂²×Dic₇₃	C₂⁴	1	9	yes	—
227	C₂²×Dic₇₃	C₂⁴	1	9	yes	—
228	C₂²×Dic₇₃	C₂⁴	1	3	yes	—
229	C₂×C₄×D₇₃	—	2	36	no	—
230	C₂×C₄×D₇₃	—	4	18	no	—
231	C₂×C₄×D₇₃	C₂×Q₈	1	24	yes	complemented
232	C₂×C₄×D₇₃	C₂⁴	1	3	yes	—
233	C₂×C₄×D₇₃	C₂⁴	1	9	yes	—
234	C₂×C₄×D₇₃	C₂⁴	1	9	yes	—
235	C₂×C₄×D₇₃	C₂⁴	1	9	yes	—
236	C₂×C₄×D₇₃	C₂⁴	1	9	yes	—
237	C₂×C₄×D₇₃	C₂⁴	1	9	yes	—
238	C₂×C₄×D₇₃	C₂⁴	1	9	yes	—
239	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×D₇₃	C₂⁴	1	3	yes	—
241	C₂×C₄×D₇₃	C₂⁴	1	3	yes	—
242	C₂×C₄×D₇₃	C₂⁴	1	3	yes	—
243	C₂×C₄×D₇₃	C₂⁴	1	3	yes	—
244	C₄⋊Dic₇₃	C₂⁴	1	3	yes	—
245	C₄⋊Dic₇₃	C₂⁴	1	9	yes	—
246	C₄⋊Dic₇₃	C₂⁴	1	18	yes	—
247	C₄⋊Dic₇₃	C₂⁴	1	9	yes	—
248	C₄⋊Dic₇₃	C₂⁴	1	9	yes	—
249	C₄⋊Dic₇₃	C₂⁴	1	18	yes	—
250	#11924007	C₂⁴	1	6	yes	—
251	#11924007	C₂⁴	1	18	yes	—
252	#11924007	C₂⁴	1	18	yes	—
253	#11924007	C₂⁴	1	18	yes	—
254	#11924007	C₂⁴	1	18	yes	—
255	#11924007	C₂⁴	1	18	yes	—
256	#11924007	C₂⁴	1	36	yes	—
257	C₂²⋊Dic₇₃	C₂⁴	1	18	yes	—
258	#11924005	C₂⁴	1	18	yes	—
259	#11924005	C₂⁴	1	18	yes	—
260	C₄×Dic₇₃	C₂⁴	1	3	yes	—
261	C₄×Dic₇₃	C₂⁴	1	3	yes	—
262	C₄×Dic₇₃	C₂⁴	1	3	yes	—
263	C₄×Dic₇₃	C₂⁴	1	9	yes	—
264	C₄×Dic₇₃	C₂⁴	1	9	yes	—
265	C₄×Dic₇₃	C₂⁴	1	9	yes	—
266	C₄×Dic₇₃	C₂⁴	1	9	yes	—
267	C₄×Dic₇₃	C₂⁴	1	9	yes	—
268	C₄×Dic₇₃	C₂⁴	1	9	yes	—
269	C₄×Dic₇₃	C₂⁴	1	9	yes	—
270	C₄×Dic₇₃	C₂⁴	1	9	yes	—
271	C₄×Dic₇₃	C₂⁴	1	9	yes	—
272	#41×C₇₃	C₂×Q₈	1	8	yes	complemented
273	C₂×Q₈×C₇₃	—	2	12	no	—
274	C₂×Q₈×C₇₃	C₂⁴	1	9	yes	—
275	C₂×Q₈×C₇₃	C₂⁴	1	6	yes	—
276	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
277	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
278	C₂×D₄×C₇₃	C₂⁴	1	3	yes	—
279	C₂²×C₄×C₇₃	C₂⁴	1	9	yes	—
280	C₂²×C₄×C₇₃	C₂⁴	1	9	yes	—
281	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
282	C₄⋊C₄×C₇₃	C₂⁴	1	3	yes	—
283	C₄⋊C₄×C₇₃	C₂⁴	1	18	yes	—
284	C₄⋊C₄×C₇₃	C₂⁴	1	9	yes	—
285	C₄⋊C₄×C₇₃	C₂⁴	1	9	yes	—
286	C₄⋊C₄×C₇₃	C₂⁴	1	9	yes	—
287	C₄⋊C₄×C₇₃	C₂⁴	1	18	yes	—
288	C₂²⋊C₄×C₇₃	C₂⁴	1	18	yes	—
289	C₄²×C₇₃	C₂⁴	1	3	yes	—
290	C₄²×C₇₃	C₂⁴	1	9	yes	—
291	C₄²×C₇₃	C₂⁴	1	9	yes	—
292	C₄²×C₇₃	C₂⁴	1	9	yes	—
293	C₂³×C₇₃	C₂⁵	1	3	yes	—
294	C₂²×D₇₃	—	2	6	no	—
295	C₂²×D₇₃	—	2	6	no	—
296	C₂²×D₇₃	C₂²×Q₈	1	12	yes	—
297	C₂²×D₇₃	C₂⁵	1	3	yes	—
298	C₂²×D₇₃	C₂⁵	1	1	yes	characteristic
299	Q₈×C₇₃	—	2	18	no	—
300	Q₈×C₇₃	—	4	6	no	—
301	Q₈×C₇₃	C₂²×Q₈	1	4	yes	complemented
302	Q₈×C₇₃	C₂×#41	1	4	yes	complemented
303	D₄×C₇₃	C₂²×Q₈	1	12	yes	complemented
304	C₂×C₄×C₇₃	—	2	18	no	—
305	C₂×C₄×C₇₃	—	4	9	no	—
306	C₂×C₄×C₇₃	C₂²×Q₈	1	12	yes	complemented
307	C₂×C₄×C₇₃	C₂⁵	1	3	yes	—
308	C₂×C₄×C₇₃	C₂⁵	1	9	yes	—
309	C₂×C₄×C₇₃	C₂⁵	1	9	yes	—
310	C₂×C₄×C₇₃	C₂⁵	1	3	yes	—
311	C₂×C₄×C₇₃	C₂⁵	1	3	yes	—
312	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
313	C₂²⋊D₇₃	C₂²×Q₈	1	24	yes	complemented
314	C₂×Dic₇₃	—	2	18	no	—
315	C₂×Dic₇₃	—	4	9	no	—
316	C₂×Dic₇₃	C₂²×Q₈	1	12	yes	complemented
317	C₂×Dic₇₃	C₂⁵	1	3	yes	—
318	C₂×Dic₇₃	C₂⁵	1	9	yes	—
319	C₂×Dic₇₃	C₂⁵	1	9	yes	—
320	C₂×Dic₇₃	C₂⁵	1	1	yes	characteristic
321	C₂×Dic₇₃	C₂⁵	1	3	yes	—
322	C₂×Dic₇₃	C₂⁵	1	3	yes	—
323	D₂₉₂	C₂²×Q₈	1	12	yes	complemented
324	C₄×D₇₃	—	2	18	no	—
325	C₄×D₇₃	—	2	6	no	—
326	C₄×D₇₃	—	2	18	no	—
327	C₄×D₇₃	—	2	18	no	—
328	C₄×D₇₃	—	2	18	no	—
329	C₄×D₇₃	—	4	9	no	—
330	C₄×D₇₃	—	4	9	no	—
331	C₄×D₇₃	C₂²×Q₈	1	4	yes	—
332	C₄×D₇₃	C₂²×Q₈	1	12	yes	—
333	C₄×D₇₃	C₂²×Q₈	1	12	yes	complemented
334	C₄×D₇₃	C₂²×Q₈	1	12	yes	complemented
335	C₄×D₇₃	C₂×#41	1	12	yes	—
336	Dic₁₄₆	—	2	18	no	—
337	Dic₁₄₆	—	2	36	no	—
338	Dic₁₄₆	—	4	18	no	—
339	Dic₁₄₆	C₂²×Q₈	1	12	yes	complemented
340	Dic₁₄₆	C₂×#41	1	12	yes	complemented
341	C₂²×C₇₃	—	2	3	no	—
342	C₂²×C₇₃	—	2	3	no	—
343	C₂²×C₇₃	C₂³×Q₈	1	6	yes	—
344	C₂²×C₇₃	C₂⁶	1	1	yes	characteristic
345	C₂×D₇₃	—	2	3	no	—
346	C₂×D₇₃	—	2	3	no	—
347	C₂×D₇₃	—	2	24	no	—
348	C₂×D₇₃	C₂³×Q₈	1	6	yes	—
349	C₂×D₇₃	C₂³×Q₈	1	2	yes	—
350	C₂×D₇₃	C₂²×#41	1	2	yes	—
351	C₂×D₇₃	#585	1	2	yes	—
352	C₄×C₇₃	—	2	9	no	—
353	C₄×C₇₃	—	2	9	no	—
354	C₄×C₇₃	—	2	3	no	—
355	C₄×C₇₃	C₂³×Q₈	1	6	yes	—
356	C₄×C₇₃	C₂³×Q₈	1	2	yes	—
357	C₄×C₇₃	C₂²×#41	1	6	yes	—
358	Dic₇₃	—	2	9	no	—
359	Dic₇₃	—	2	9	no	—
360	Dic₇₃	—	2	3	no	—
361	Dic₇₃	C₂³×Q₈	1	6	yes	—
362	Dic₇₃	C₂³×Q₈	1	2	yes	—
363	Dic₇₃	C₂²×#41	1	6	yes	—
364	C₂×Q₈×#41	—	73	1	no	maximal, Sylow
365	C₂×C₇₃	—	2	6	no	—
366	C₂×C₇₃	C₂⁴×Q₈	1	1	yes	characteristic
367	C₂×C₇₃	C₂³×#41	1	1	yes	characteristic
368	C₂×C₇₃	C₂×#585	1	1	yes	characteristic
369	D₇₃	—	2	6	no	—
370	D₇₃	Q₈×#41	1	4	yes	direct product factor
371	Q₈×#41	—	73	1	no	—
372	Q₈×#41	—	73	3	no	—
373	Q₈×#41	—	73	9	no	—
374	Q₈×#41	—	73	3	no	—
375	Q₈×#41	—	73	9	no	—
376	Q₈×#41	—	73	3	no	—
377	Q₈×#41	—	73	3	no	—
378	Q₈×#41	D₇₃	1	1	yes	characteristic, direct product factor
379	C₂×Q₈²	—	73	1	no	—
380	C₂×#557	—	73	3	no	—
381	C₂×#554	—	73	9	no	—
382	C₂×D₄×Q₈	—	73	3	no	—
383	C₂×#533	—	73	9	no	—
384	C₂×C₄×#41	—	73	3	no	—
385	C₂²×C₄×Q₈	—	73	3	no	—
386	C₇₃	C₂×Q₈×#41	1	1	yes	characteristic, complemented, Sylow
387	C₂²×#41	—	73	1	no	—
388	C₂³×Q₈	—	73	3	no	—
389	Q₈²	—	73	9	no	—
390	Q₈²	—	73	3	no	—
391	Q₈²	—	73	3	no	—
392	Q₈²	C₂×D₇₃	1	1	yes	characteristic, complemented
393	#557	—	73	9	no	—
394	#557	—	73	18	no	—
395	#557	—	73	6	no	—
396	#557	—	73	9	no	—
397	#557	—	73	3	no	—
398	#557	C₂×D₇₃	1	3	yes	complemented
399	#554	—	73	9	no	—
400	#554	—	73	18	no	—
401	#554	—	73	36	no	—
402	#554	—	73	18	no	—
403	#554	—	73	9	no	—
404	#554	—	73	9	no	—
405	#554	—	73	18	no	—
406	#554	—	73	18	no	—
407	#554	C₂×D₇₃	1	9	yes	complemented
408	D₄×Q₈	—	73	6	no	—
409	D₄×Q₈	—	73	9	no	—
410	D₄×Q₈	—	73	18	no	—
411	D₄×Q₈	—	73	3	no	—
412	D₄×Q₈	—	73	9	no	—
413	D₄×Q₈	C₂×D₇₃	1	3	yes	complemented
414	#533	—	73	9	no	—
415	#533	—	73	9	no	—
416	#533	—	73	18	no	—
417	#533	—	73	18	no	—
418	#533	—	73	18	no	—
419	#533	—	73	18	no	—
420	#533	—	73	18	no	—
421	#533	—	73	18	no	—
422	#533	—	73	9	no	—
423	#533	C₂×D₇₃	1	9	yes	complemented
424	C₂×C₄⋊Q₈	—	73	9	no	—
425	C₂×C₄⋊Q₈	—	73	9	no	—
426	C₂×#125	—	73	18	no	—
427	C₂×C₂²⋊Q₈	—	73	18	no	—
428	C₂×C₂²⋊Q₈	—	73	18	no	—
429	C₄×#41	—	73	3	no	—
430	C₄×#41	—	73	3	no	—
431	C₄×#41	—	73	3	no	—
432	C₄×#41	—	73	9	no	—
433	C₄×#41	—	73	9	no	—
434	C₄×#41	—	73	9	no	—
435	C₄×#41	—	73	9	no	—
436	C₄×#41	C₂×D₇₃	1	3	yes	—
437	C₂×C₄×Q₈	—	73	3	no	—
438	C₂×C₄×Q₈	—	73	1	no	—
439	C₂×C₄×Q₈	—	73	9	no	—
440	C₂×C₄×Q₈	—	73	3	no	—
441	C₂×C₄×Q₈	—	73	9	no	—
442	C₂×C₄×Q₈	—	73	3	no	—
443	C₂×C₄×Q₈	—	73	9	no	—
444	C₂×C₄×Q₈	—	73	3	no	—
445	C₂×C₄×Q₈	—	73	9	no	—
446	C₂×C₄×Q₈	—	73	3	no	—
447	C₂×C₄×Q₈	—	73	3	no	—
448	C₂×C₄×Q₈	—	73	6	no	—
449	C₂×C₄×Q₈	—	73	9	no	—
450	C₂×C₄×Q₈	—	73	9	no	—
451	C₂×C₄×Q₈	C₂×D₇₃	1	3	yes	complemented
452	C₂×C₄×D₄	—	73	9	no	—
453	C₂×C₄×D₄	—	73	9	no	—
454	C₂×#117	—	73	9	no	—
455	C₂²×C₄⋊C₄	—	73	9	no	—
456	C₂²×C₄²	—	73	9	no	—
457	C₂×#41	—	73	16	no	—
458	C₂×#41	—	73	1	no	—
459	C₂×#41	—	73	3	no	—
460	C₂×#41	—	73	3	no	—
461	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
462	C₂²×Q₈	—	73	6	no	—
463	C₂²×Q₈	—	73	1	no	—
464	C₂²×Q₈	—	73	1	no	—
465	C₂²×Q₈	—	73	9	no	—
466	C₂²×Q₈	—	73	9	no	—
467	C₂²×Q₈	—	73	3	no	—
468	C₂²×Q₈	—	73	9	no	—
469	C₂²×Q₈	—	146	24	no	—
470	C₂²×Q₈	C₂²×D₇₃	1	3	yes	—
471	C₂²×D₄	—	73	3	no	—
472	C₂³×C₄	—	73	9	no	—
473	C₂³×C₄	—	73	3	no	—
474	C₂³×C₄	—	73	9	no	—
475	C₄⋊Q₈	—	73	18	no	—
476	C₄⋊Q₈	—	73	18	no	—
477	C₄⋊Q₈	—	73	18	no	—
478	C₄⋊Q₈	—	73	18	no	—
479	C₄⋊Q₈	—	73	18	no	—
480	C₄⋊Q₈	—	73	18	no	—
481	C₄⋊Q₈	—	73	9	no	—
482	C₄⋊Q₈	—	73	9	no	—
483	C₄⋊Q₈	C₂²×D₇₃	1	9	yes	—
484	C₄⋊Q₈	C₂²×D₇₃	1	9	yes	—
485	#125	—	73	36	no	—
486	#125	—	73	36	no	—
487	#125	—	73	18	no	—
488	#125	—	73	18	no	—
489	#125	—	73	18	no	—
490	#125	C₂²×D₇₃	1	18	yes	—
491	C₂²⋊Q₈	—	73	18	no	—
492	C₂²⋊Q₈	—	73	18	no	—
493	C₂²⋊Q₈	—	73	18	no	—
494	C₂²⋊Q₈	—	73	18	no	—
495	C₂²⋊Q₈	—	73	36	no	—
496	C₂²⋊Q₈	—	73	18	no	—
497	C₂²⋊Q₈	—	73	36	no	—
498	C₂²⋊Q₈	—	73	18	no	—
499	C₂²⋊Q₈	—	73	36	no	—
500	C₂²⋊Q₈	—	73	36	no	—
501	C₂²⋊Q₈	C₂²×D₇₃	1	18	yes	—
502	C₂²⋊Q₈	C₂²×D₇₃	1	18	yes	—
503	C₄×Q₈	—	73	1	no	—
504	C₄×Q₈	—	73	9	no	—
505	C₄×Q₈	—	73	3	no	—
506	C₄×Q₈	—	73	9	no	—
507	C₄×Q₈	—	73	3	no	—
508	C₄×Q₈	—	73	3	no	—
509	C₄×Q₈	—	73	6	no	—
510	C₄×Q₈	—	73	3	no	—
511	C₄×Q₈	—	73	9	no	—
512	C₄×Q₈	—	73	18	no	—
513	C₄×Q₈	—	73	9	no	—
514	C₄×Q₈	—	73	18	no	—
515	C₄×Q₈	—	73	9	no	—
516	C₄×Q₈	—	73	9	no	—
517	C₄×Q₈	—	73	9	no	—
518	C₄×Q₈	—	73	18	no	—
519	C₄×Q₈	—	73	3	no	—
520	C₄×Q₈	—	73	18	no	—
521	C₄×Q₈	—	73	9	no	—
522	C₄×Q₈	—	73	9	no	—
523	C₄×Q₈	—	73	9	no	—
524	C₄×Q₈	—	73	18	no	—
525	C₄×Q₈	—	73	9	no	—
526	C₄×Q₈	—	73	9	no	—
527	C₄×Q₈	—	73	18	no	—
528	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
529	C₄×Q₈	C₂²×D₇₃	1	9	yes	—
530	C₄×Q₈	C₂²×D₇₃	1	3	yes	—
531	C₄×Q₈	C₂²×D₇₃	1	9	yes	—
532	C₄×Q₈	C₂²×D₇₃	1	3	yes	—
533	C₄×Q₈	C₂²×D₇₃	1	3	yes	—
534	C₄×Q₈	C₂²×D₇₃	1	6	yes	—
535	C₄×D₄	—	73	9	no	—
536	C₄×D₄	—	73	9	no	—
537	C₄×D₄	—	73	18	no	—
538	C₄×D₄	—	73	18	no	—
539	C₄×D₄	—	73	9	no	—
540	C₄×D₄	—	73	9	no	—
541	C₄×D₄	—	73	18	no	—
542	C₄×D₄	—	73	18	no	—
543	C₄×D₄	—	73	9	no	—
544	C₄×D₄	—	73	9	no	—
545	C₄×D₄	C₂²×D₇₃	1	9	yes	—
546	C₄×D₄	C₂²×D₇₃	1	9	yes	—
547	#117	—	73	9	no	—
548	#117	—	73	9	no	—
549	#117	—	73	9	no	—
550	#117	—	73	18	no	—
551	#117	—	73	18	no	—
552	#117	C₂²×D₇₃	1	9	yes	—
553	C₂×C₄⋊C₄	—	73	18	no	—
554	C₂×C₄⋊C₄	—	73	9	no	—
555	C₂×C₄⋊C₄	—	73	3	no	—
556	C₂×C₄⋊C₄	—	73	18	no	—
557	C₂×C₄⋊C₄	—	73	9	no	—
558	C₂×C₄⋊C₄	—	73	18	no	—
559	C₂×C₄⋊C₄	—	73	9	no	—
560	C₂×C₄⋊C₄	—	73	9	no	—
561	C₂×C₄⋊C₄	—	73	9	no	—
562	C₂×C₄⋊C₄	—	73	9	no	—
563	C₂×C₄⋊C₄	—	73	18	no	—
564	C₂×C₄⋊C₄	C₂²×D₇₃	1	9	yes	—
565	C₂×C₂²⋊C₄	—	73	18	no	—
566	C₂×C₄²	—	73	9	no	—
567	C₂×C₄²	—	73	9	no	—
568	C₂×C₄²	—	73	9	no	—
569	C₂×C₄²	—	73	9	no	—
570	C₂×C₄²	—	73	9	no	—
571	C₂×C₄²	—	73	9	no	—
572	C₂×C₄²	—	73	3	no	—
573	C₂×C₄²	—	73	9	no	—
574	C₂×C₄²	—	73	9	no	—
575	C₂×C₄²	—	73	9	no	—
576	C₂×C₄²	—	73	9	no	—
577	C₂×C₄²	C₂²×D₇₃	1	9	yes	—
578	C₂⁴	—	73	3	no	—
579	#41	—	73	8	no	—
580	#41	—	73	24	no	—
581	#41	—	73	24	no	—
582	#41	Q₈×D₇₃	1	8	yes	direct product factor
583	C₂×Q₈	—	2	12	no	—
584	C₂×Q₈	—	292	12	no	—
585	C₂×Q₈	—	73	8	no	—
586	C₂×Q₈	—	73	8	no	—
587	C₂×Q₈	—	73	18	no	—
588	C₂×Q₈	—	73	3	no	—
589	C₂×Q₈	—	73	3	no	—
590	C₂×Q₈	—	73	18	no	—
591	C₂×Q₈	—	73	9	no	—
592	C₂×Q₈	—	146	36	no	—
593	C₂×Q₈	—	146	36	no	—
594	C₂×Q₈	—	146	36	no	—
595	C₂×Q₈	—	146	12	no	—
596	C₂×Q₈	C₂³×D₇₃	1	9	yes	—
597	C₂×Q₈	C₂³×D₇₃	1	6	yes	—
598	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
599	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
600	C₂×D₄	—	73	6	no	—
601	C₂×D₄	—	73	24	no	—
602	C₂×D₄	—	73	3	no	—
603	C₂×D₄	C₂³×D₇₃	1	3	yes	—
604	C₂²×C₄	—	292	18	no	—
605	C₂²×C₄	—	73	9	no	—
606	C₂²×C₄	—	73	9	no	—
607	C₂²×C₄	—	73	9	no	—
608	C₂²×C₄	—	73	3	no	—
609	C₂²×C₄	—	73	24	no	—
610	C₂²×C₄	—	73	3	no	—
611	C₂²×C₄	—	73	3	no	—
612	C₂²×C₄	—	73	3	no	—
613	C₂²×C₄	—	73	1	no	—
614	C₂²×C₄	—	73	3	no	—
615	C₂²×C₄	—	73	9	no	—
616	C₂²×C₄	—	73	3	no	—
617	C₂²×C₄	—	73	9	no	—
618	C₂²×C₄	—	73	9	no	—
619	C₂²×C₄	—	73	9	no	—
620	C₂²×C₄	—	73	9	no	—
621	C₂²×C₄	—	146	36	no	—
622	C₂²×C₄	C₂³×D₇₃	1	9	yes	—
623	C₂²×C₄	C₂³×D₇₃	1	9	yes	—
624	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
625	C₄⋊C₄	—	73	6	no	—
626	C₄⋊C₄	—	73	18	no	—
627	C₄⋊C₄	—	73	18	no	—
628	C₄⋊C₄	—	73	18	no	—
629	C₄⋊C₄	—	73	18	no	—
630	C₄⋊C₄	—	73	18	no	—
631	C₄⋊C₄	—	73	36	no	—
632	C₄⋊C₄	—	73	3	no	—
633	C₄⋊C₄	—	73	18	no	—
634	C₄⋊C₄	—	73	9	no	—
635	C₄⋊C₄	—	73	9	no	—
636	C₄⋊C₄	—	73	9	no	—
637	C₄⋊C₄	—	73	18	no	—
638	C₄⋊C₄	C₂³×D₇₃	1	3	yes	—
639	C₄⋊C₄	C₂³×D₇₃	1	18	yes	—
640	C₄⋊C₄	C₂³×D₇₃	1	9	yes	—
641	C₄⋊C₄	C₂³×D₇₃	1	9	yes	—
642	C₄⋊C₄	C₂³×D₇₃	1	9	yes	—
643	C₄⋊C₄	C₂³×D₇₃	1	18	yes	—
644	C₂²⋊C₄	—	73	18	no	—
645	C₂²⋊C₄	—	73	18	no	—
646	C₂²⋊C₄	—	73	18	no	—
647	C₂²⋊C₄	C₂³×D₇₃	1	18	yes	—
648	C₄²	—	73	3	no	—
649	C₄²	—	73	3	no	—
650	C₄²	—	73	9	no	—
651	C₄²	—	73	9	no	—
652	C₄²	—	73	9	no	—
653	C₄²	—	73	9	no	—
654	C₄²	—	73	9	no	—
655	C₄²	—	73	9	no	—
656	C₄²	—	73	9	no	—
657	C₄²	—	73	9	no	—
658	C₄²	—	73	3	no	—
659	C₄²	—	73	9	no	—
660	C₄²	C₂³×D₇₃	1	9	yes	—
661	C₄²	C₂³×D₇₃	1	9	yes	—
662	C₄²	C₂³×D₇₃	1	3	yes	—
663	C₄²	C₂³×D₇₃	1	9	yes	—
664	C₂³	—	73	1	no	—
665	C₂³	—	73	12	no	—
666	C₂³	—	73	3	no	—
667	C₂³	—	146	6	no	—
668	C₂³	—	146	6	no	—
669	C₂³	C₂⁴×D₇₃	1	3	yes	—
670	Q₈	—	2	18	no	—
671	Q₈	—	4	6	no	—
672	Q₈	—	292	18	no	—
673	Q₈	—	73	12	no	—
674	Q₈	—	73	12	no	—
675	Q₈	—	146	36	no	—
676	Q₈	—	146	18	no	—
677	Q₈	C₂×Q₈×D₇₃	1	4	yes	complemented
678	Q₈	#41×D₇₃	1	4	yes	direct product factor
679	D₄	—	73	24	no	—
680	D₄	—	73	12	no	—
681	D₄	C₂×Q₈×D₇₃	1	12	yes	complemented
682	C₂×C₄	—	2	18	no	—
683	C₂×C₄	—	4	9	no	—
684	C₂×C₄	—	292	9	no	—
685	C₂×C₄	—	292	9	no	—
686	C₂×C₄	—	292	9	no	—
687	C₂×C₄	—	73	12	no	—
688	C₂×C₄	—	73	1	no	—
689	C₂×C₄	—	73	3	no	—
690	C₂×C₄	—	73	3	no	—
691	C₂×C₄	—	73	4	no	—
692	C₂×C₄	—	73	12	no	—
693	C₂×C₄	—	73	12	no	—
694	C₂×C₄	—	73	12	no	—
695	C₂×C₄	—	73	12	no	—
696	C₂×C₄	—	73	3	no	—
697	C₂×C₄	—	73	9	no	—
698	C₂×C₄	—	73	9	no	—
699	C₂×C₄	—	146	18	no	—
700	C₂×C₄	—	146	6	no	—
701	C₂×C₄	—	146	18	no	—
702	C₂×C₄	—	146	18	no	—
703	C₂×C₄	—	146	18	no	—
704	C₂×C₄	—	146	18	no	—
705	C₂×C₄	C₂×Q₈×D₇₃	1	12	yes	complemented
706	C₂×C₄	C₂⁴×D₇₃	1	3	yes	—
707	C₂×C₄	C₂⁴×D₇₃	1	9	yes	—
708	C₂×C₄	C₂⁴×D₇₃	1	9	yes	—
709	C₂×C₄	C₂⁴×D₇₃	1	3	yes	—
710	C₂×C₄	C₂⁴×D₇₃	1	3	yes	—
711	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
712	C₂²	—	2	3	no	—
713	C₂²	—	2	3	no	—
714	C₂²	—	73	2	no	—
715	C₂²	—	73	2	no	—
716	C₂²	—	73	2	no	—
717	C₂²	—	73	6	no	—
718	C₂²	—	146	24	no	—
719	C₂²	—	146	3	no	—
720	C₂²	—	146	3	no	—
721	C₂²	C₂²×Q₈×D₇₃	1	6	yes	—
722	C₂²	C₂⁵×D₇₃	1	1	yes	characteristic
723	C₄	—	2	9	no	—
724	C₄	—	2	3	no	—
725	C₄	—	2	9	no	—
726	C₄	—	73	2	no	—
727	C₄	—	73	6	no	—
728	C₄	—	73	6	no	—
729	C₄	—	146	9	no	—
730	C₄	—	146	3	no	—
731	C₄	—	146	9	no	—
732	C₄	C₂²×Q₈×D₇₃	1	2	yes	—
733	C₄	C₂²×Q₈×D₇₃	1	6	yes	—
734	C₄	C₂×#41×D₇₃	1	6	yes	—
735	C₂	—	2	6	no	—
736	C₂	—	73	4	no	—
737	C₂	—	146	6	no	—
738	C₂	C₂³×Q₈×D₇₃	1	1	yes	characteristic
739	C₂	C₂²×#41×D₇₃	1	1	yes	characteristic
740	C₂	#585×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₇₃
commutator, socle, cosocle	C₂²×C₇₃	C₂⁶
Frattini	C₂²	C₂⁵×D₇₃
Fitting	Q₈×#41×C₇₃	C₂
prime radical	C₂×#41×D₇₃	C₂²
hypercenter	Q₈×#41	D₇₃
hypocenter	C₇₃	C₂×Q₈×#41
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ Q₈×#41

Complements

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

N	H ≅ G/N	type
1. Q₈×#11924029	C₂	semidirect
2. #22623513	C₂	semidirect
3. Q₈×#11924028	C₂	semidirect
4. #41×Dic₁₄₆	C₂	semidirect
5. #22623510	C₂	semidirect
6. #22623509	C₂	semidirect
7. Q₈×#11924027	C₂	semidirect
8. Q₈²×D₇₃	C₂	semidirect
9. #557×D₇₃	C₂	semidirect
10. #554×D₇₃	C₂	semidirect
11. D₄×Q₈×D₇₃	C₂	semidirect
12. #533×D₇₃	C₂	semidirect
14. C₂×C₄×Q₈×D₇₃	C₂	semidirect
15. Q₈×#41×C₇₃	C₂	semidirect
18. Q₈×Dic₁₄₆	C₂²	semidirect
19. Q₈×Dic₁₄₆	C₂²	semidirect
20. #17989317	C₂²	semidirect
21. #17989316	C₂²	semidirect
22. #17989315	C₂²	semidirect
23. #17989314	C₂²	semidirect
24. #17989313	C₂²	semidirect
25. #17989312	C₂²	semidirect
26. #17989298	C₂²	semidirect
27. #17989297	C₂²	semidirect
28. #17989296	C₂²	semidirect
29. #17989295	C₂²	semidirect
30. #17989294	C₂²	semidirect
31. #17989293	C₂²	semidirect
32. #17989292	C₂²	semidirect
33. #17989291	C₂²	semidirect
34. Q₈×D₂₉₂	C₂²	semidirect
35. D₄×Dic₁₄₆	C₂²	semidirect
36. #17989252	C₂²	semidirect
37. Q₈×C₂²⋊D₇₃	C₂²	semidirect
38. #17989250	C₂²	semidirect
39. #17989144	C₂²	semidirect
40. #17989143	C₂²	semidirect
41. #17989142	C₂²	semidirect
42. #17989142	C₂²	semidirect
43. #17989141	C₂²	semidirect
44. #17989141	C₂²	semidirect
45. #17989140	C₂²	semidirect
46. #17989139	C₂²	semidirect
47. #17989139	C₂²	semidirect
60. C₂×Q₈×Dic₇₃	C₂²	semidirect
61. C₂×C₄×Dic₁₄₆	C₂²	semidirect
62. C₂×#14556556	C₂²	semidirect
70. C₄×Q₈×D₇₃	C₂²	semidirect
71. C₄×Q₈×D₇₃	C₂²	semidirect
72. C₄×Q₈×D₇₃	C₂²	semidirect
73. C₄×Q₈×D₇₃	C₂²	semidirect
79. Q₈²×C₇₃	C₂²	semidirect
80. #557×C₇₃	C₂²	semidirect
81. #554×C₇₃	C₂²	semidirect
82. D₄×Q₈×C₇₃	C₂²	semidirect
83. #533×C₇₃	C₂²	semidirect
85. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
89. #41×D₇₃	Q₈	direct (N × H)
208. #11924029	C₂×Q₈	semidirect
209. #11924028	C₂×Q₈	semidirect
210. #11924027	C₂×Q₈	semidirect
221. Q₈×D₇₃	C₂×Q₈	semidirect
222. Q₈×D₇₃	#41	direct (N × H)
225. D₄×D₇₃	C₂×Q₈	semidirect
231. C₂×C₄×D₇₃	C₂×Q₈	semidirect
272. #41×C₇₃	C₂×Q₈	semidirect
301. Q₈×C₇₃	C₂²×Q₈	semidirect
302. Q₈×C₇₃	C₂×#41	semidirect
303. D₄×C₇₃	C₂²×Q₈	semidirect
306. C₂×C₄×C₇₃	C₂²×Q₈	semidirect
313. C₂²⋊D₇₃	C₂²×Q₈	semidirect
316. C₂×Dic₇₃	C₂²×Q₈	semidirect
323. D₂₉₂	C₂²×Q₈	semidirect
333. C₄×D₇₃	C₂²×Q₈	semidirect
334. C₄×D₇₃	C₂²×Q₈	semidirect
339. Dic₁₄₆	C₂²×Q₈	semidirect
340. Dic₁₄₆	C₂×#41	semidirect
370. D₇₃	Q₈×#41	direct (N × H)
378. Q₈×#41	D₇₃	direct (N × H)
386. C₇₃	C₂×Q₈×#41	semidirect
392. Q₈²	C₂×D₇₃	semidirect
398. #557	C₂×D₇₃	semidirect
407. #554	C₂×D₇₃	semidirect
413. D₄×Q₈	C₂×D₇₃	semidirect
423. #533	C₂×D₇₃	semidirect
451. C₂×C₄×Q₈	C₂×D₇₃	semidirect
582. #41	Q₈×D₇₃	direct (N × H)
677. Q₈	C₂×Q₈×D₇₃	semidirect
678. Q₈	#41×D₇₃	direct (N × H)
681. D₄	C₂×Q₈×D₇₃	semidirect
705. C₂×C₄	C₂×Q₈×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#11924029	2
#22623513	2
Q₈×#11924028	2
#41×Dic₁₄₆	2
#22623510	2
#22623509	2
Q₈×#11924027	2
Q₈²×D₇₃	2
#557×D₇₃	2
#554×D₇₃	2
D₄×Q₈×D₇₃	2
#533×D₇₃	2
C₄×#41×D₇₃	2
C₂×C₄×Q₈×D₇₃	2
Q₈×#41×C₇₃	2
C₂×Q₈×#41	73

Subgroups — Q8×#41×D73 #33993052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#41×D₇₃ #33993052