Subgroups — #22623645

Order 9344.

1040 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989309	C₂	1	2	yes	maximal, complemented
2	#17989308	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989303	C₂	1	1	yes	maximal, characteristic, complemented
4	#17989300	C₂	1	1	yes	maximal, characteristic, complemented
5	#17989299	C₂	1	2	yes	maximal, complemented
6	#17989288	C₂	1	2	yes	maximal, complemented
7	#17989283	C₂	1	1	yes	maximal, characteristic, complemented
8	#17989281	C₂	1	1	yes	maximal, characteristic, complemented
9	#17989279	C₂	1	1	yes	maximal, characteristic, complemented
10	#17989278	C₂	1	1	yes	maximal, characteristic, complemented
11	#17989273	C₂	1	2	yes	maximal, complemented
12	#17989214	C₂	1	1	yes	maximal, characteristic, complemented
13	#17989176	C₂	1	2	yes	maximal, complemented
14	#17989171	C₂	1	2	yes	maximal, complemented
15	#17989167	C₂	1	1	yes	maximal, characteristic, complemented
16	#17989124	C₂	1	2	yes	maximal, complemented
17	#17989120	C₂	1	2	yes	maximal, complemented
18	#17989100	C₂	1	1	yes	maximal, characteristic, complemented
19	#17989096	C₂	1	1	yes	maximal, characteristic, complemented
20	#17989069	C₂	1	1	yes	maximal, characteristic, complemented
21	#17989067	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#556×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11924029	C₂²	1	1	yes	characteristic
25	C₂×#11924028	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₇₃	C₂²	1	1	yes	characteristic
27	#14556590	C₂²	1	1	yes	characteristic, complemented
28	#14556589	C₂²	1	2	yes	complemented
29	#14556586	C₂²	1	2	yes	—
30	#14556586	C₂²	1	2	yes	complemented
31	#14556586	C₂²	1	2	yes	complemented
32	#14556585	C₂²	1	2	yes	—
33	#14556585	C₂²	1	2	yes	complemented
34	#14556584	C₂²	1	2	yes	—
35	#14556583	C₂²	1	1	yes	characteristic, complemented
36	#14556582	C₂²	1	2	yes	complemented
37	#14556582	C₂²	1	1	yes	characteristic, complemented
38	#14556581	C₂²	1	2	yes	complemented
39	#14556581	C₂²	1	2	yes	complemented
40	#14556580	C₂²	1	2	yes	—
41	#14556580	C₂²	1	2	yes	complemented
42	#14556579	C₂²	1	2	yes	—
43	#14556577	C₂²	1	2	yes	—
44	#14556577	C₂²	1	2	yes	complemented
45	#14556576	C₂²	1	2	yes	—
46	#14556576	C₂²	1	1	yes	characteristic
47	#14556576	C₂²	1	2	yes	—
48	#14556575	C₂²	1	2	yes	—
49	#14556573	C₂²	1	1	yes	characteristic
50	#14556573	C₂²	1	2	yes	—
51	#14556573	C₂²	1	2	yes	—
52	#14556569	C₂²	1	2	yes	—
53	#14556569	C₂²	1	1	yes	characteristic
54	#14556569	C₂²	1	2	yes	complemented
55	#14556568	C₂²	1	1	yes	characteristic
56	#14556567	C₂²	1	2	yes	—
57	#14556567	C₂²	1	1	yes	characteristic
58	#14556567	C₂²	1	1	yes	characteristic, complemented
59	#14556566	C₂²	1	2	yes	—
60	#14556566	C₂²	1	2	yes	—
61	#14556566	C₂²	1	1	yes	characteristic
62	#14556566	C₂²	1	1	yes	characteristic, complemented
63	#14556565	C₂²	1	1	yes	characteristic
64	#14556565	C₂²	1	1	yes	characteristic, complemented
65	#14556564	C₂²	1	2	yes	—
66	#14556564	C₂²	1	2	yes	—
67	#14556564	C₂²	1	2	yes	—
68	#14556564	C₂²	1	1	yes	characteristic
69	#14556564	C₂²	1	2	yes	complemented
70	#14556563	C₂²	1	2	yes	—
71	#14556563	C₂²	1	1	yes	characteristic
72	#14556561	C₂²	1	2	yes	—
73	#14556561	C₂²	1	1	yes	characteristic
74	#14556559	C₂²	1	1	yes	characteristic
75	Q₈×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
76	C₄×Dic₁₄₆	C₂²	1	2	yes	complemented
77	#14556556	C₂²	1	2	yes	complemented
78	C₄×D₂₉₂	C₂²	1	2	yes	—
79	C₄×D₂₉₂	C₂²	1	2	yes	—
80	C₄×D₂₉₂	C₂²	1	1	yes	characteristic
81	C₄×D₂₉₂	C₂²	1	2	yes	complemented
82	C₄×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
83	#14556553	C₂²	1	2	yes	—
84	#14556553	C₂²	1	2	yes	—
85	#14556553	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
88	#14556551	C₂²	1	2	yes	—
89	#14556551	C₂²	1	2	yes	—
90	#14556551	C₂²	1	2	yes	complemented
91	#14556551	C₂²	1	2	yes	complemented
92	#14556550	C₂²	1	1	yes	characteristic
93	#14556549	C₂²	1	1	yes	characteristic
94	#14556549	C₂²	1	1	yes	characteristic
95	#14556549	C₂²	1	1	yes	characteristic
96	#14556549	C₂²	1	2	yes	complemented
97	#14556549	C₂²	1	1	yes	characteristic, complemented
98	#14556548	C₂²	1	1	yes	characteristic
99	#14556548	C₂²	1	2	yes	—
100	#14556548	C₂²	1	2	yes	complemented
101	#14556548	C₂²	1	2	yes	complemented
102	#14556548	C₂²	1	2	yes	complemented
103	#14556547	C₂²	1	2	yes	—
104	#14556547	C₂²	1	2	yes	complemented
105	C₂×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic, complemented
106	C₄⋊C₄×D₇₃	C₂²	1	1	yes	characteristic
107	C₄⋊C₄×D₇₃	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₇₃	C₂²	1	2	yes	complemented
109	C₄⋊C₄×D₇₃	C₂²	1	1	yes	characteristic, complemented
110	C₂²⋊C₄×D₇₃	C₂²	1	2	yes	—
111	C₄²×D₇₃	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
113	#126×C₇₃	C₂²	1	2	yes	—
114	#126×C₇₃	C₂²	1	2	yes	complemented
115	#124×C₇₃	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₇₃	C₂²	1	2	yes	complemented
119	C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
121	#117×C₇₃	C₂²	1	1	yes	characteristic
122	#117×C₇₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₇₃	C₂³	1	1	yes	characteristic
124	#11924029	—	2	4	no	—
125	#11924028	—	2	4	no	—
126	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₄₆	C₂³	1	2	yes	—
128	C₂×D₂₉₂	C₂³	1	2	yes	—
129	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
130	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
131	C₂×D₂₉₂	C₂³	1	2	yes	—
132	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
133	C₂×D₂₉₂	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
140	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
141	C₂²×Dic₇₃	C₂³	1	2	yes	—
142	C₂×C₄×D₇₃	—	2	4	no	—
143	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₇₃	C₂³	1	2	yes	—
145	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₇₃	C₂³	1	2	yes	—
149	C₂×C₄×D₇₃	C₂³	1	2	yes	—
150	C₂×C₄×D₇₃	C₂³	1	2	yes	—
151	C₂×C₄×D₇₃	C₂³	1	2	yes	—
152	C₂×C₄×D₇₃	C₂³	1	2	yes	—
153	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₇₃	C₂³	1	2	yes	—
158	C₄⋊Dic₇₃	C₂³	1	2	yes	—
159	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₇₃	C₂³	1	2	yes	—
161	#11924007	C₂³	1	2	yes	—
162	#11924007	C₂³	1	2	yes	—
163	#11924007	C₂³	1	1	yes	characteristic
164	#11924007	C₂³	1	2	yes	—
165	#11924007	C₂³	1	2	yes	—
166	#11924007	C₂³	1	2	yes	—
167	#11924007	C₂³	1	1	yes	characteristic
168	#11924007	C₂³	1	1	yes	characteristic
169	#11924007	C₂³	1	2	yes	—
170	#11924007	C₂³	1	2	yes	—
171	#11924007	C₂³	1	2	yes	—
172	#11924007	C₂³	1	1	yes	characteristic
173	#11924007	C₂³	1	2	yes	—
174	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
177	#11924005	C₂³	1	2	yes	—
178	#11924005	C₂³	1	2	yes	—
179	#11924005	C₂³	1	1	yes	characteristic
180	#11924005	C₂³	1	1	yes	characteristic
181	#11924005	C₂³	1	1	yes	characteristic
182	#11924005	C₂³	1	2	yes	—
183	#11924005	C₂³	1	2	yes	—
184	#11924005	C₂³	1	2	yes	—
185	#11924005	C₂³	1	2	yes	—
186	#11924005	C₂³	1	2	yes	—
187	#11924005	C₂³	1	2	yes	—
188	#11924005	C₂³	1	2	yes	—
189	#11924005	C₂³	1	2	yes	—
190	#11924005	C₂³	1	2	yes	—
191	#11924005	C₂³	1	1	yes	characteristic
192	#11924005	C₂³	1	1	yes	characteristic
193	#11924005	C₂³	1	2	yes	—
194	#11924005	C₂³	1	1	yes	characteristic
195	C₄×Dic₇₃	C₂³	1	2	yes	—
196	C₄×Dic₇₃	C₂³	1	2	yes	—
197	C₄×Dic₇₃	C₂³	1	2	yes	—
198	C₄×Dic₇₃	C₂³	1	2	yes	—
199	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
200	C₄×Dic₇₃	C₂³	1	2	yes	—
201	C₄×Dic₇₃	C₂³	1	2	yes	—
202	C₂×Q₈×C₇₃	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₇₃	C₂³	1	2	yes	—
204	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
207	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
212	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
213	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
214	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
221	C₄²×C₇₃	C₂³	1	2	yes	—
222	C₄²×C₇₃	C₂³	1	2	yes	—
223	C₄²×C₇₃	C₂³	1	1	yes	characteristic
224	C₄²×C₇₃	C₂³	1	2	yes	—
225	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
226	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
227	C₂²×D₇₃	—	2	2	no	—
228	C₂²×D₇₃	—	4	1	no	—
229	C₂²×D₇₃	—	4	1	no	—
230	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
231	C₂²×D₇₃	C₂⁴	1	2	yes	—
232	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
233	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
234	Q₈×C₇₃	—	2	2	no	—
235	Q₈×C₇₃	—	4	2	no	—
236	D₄×C₇₃	—	4	1	no	—
237	C₂×C₄×C₇₃	—	2	2	no	—
238	C₂×C₄×C₇₃	—	2	2	no	—
239	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
240	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
245	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
246	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
247	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
248	C₂²⋊D₇₃	—	2	2	no	—
249	C₂²⋊D₇₃	—	2	2	no	—
250	C₂²⋊D₇₃	—	4	1	no	—
251	C₂²⋊D₇₃	—	4	2	no	—
252	C₂²⋊D₇₃	—	4	1	no	—
253	C₂²⋊D₇₃	—	4	2	no	—
254	C₂×Dic₇₃	—	2	2	no	—
255	C₂×Dic₇₃	—	4	2	no	—
256	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₇₃	C₂⁴	1	2	yes	—
258	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₇₃	C₂⁴	1	2	yes	—
261	C₂×Dic₇₃	C₂⁴	1	2	yes	—
262	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
264	D₂₉₂	—	2	2	no	—
265	D₂₉₂	—	2	4	no	—
266	D₂₉₂	—	2	2	no	—
267	D₂₉₂	—	4	2	no	—
268	D₂₉₂	—	4	1	no	—
269	D₂₉₂	—	4	2	no	—
270	C₄×D₇₃	—	2	2	no	—
271	C₄×D₇₃	—	2	2	no	—
272	C₄×D₇₃	—	2	2	no	—
273	C₄×D₇₃	—	2	2	no	—
274	C₄×D₇₃	—	2	4	no	—
275	C₄×D₇₃	—	4	2	no	—
276	C₄×D₇₃	—	4	2	no	—
277	C₄×D₇₃	—	4	2	no	—
278	C₄×D₇₃	—	4	2	no	—
279	C₄×D₇₃	—	4	2	no	—
280	C₄×D₇₃	#41	1	4	yes	—
281	Dic₁₄₆	—	2	2	no	—
282	Dic₁₄₆	—	4	2	no	—
283	C₂²×C₇₃	—	2	1	no	—
284	C₂²×C₇₃	—	2	1	no	—
285	C₂²×C₇₃	—	2	1	no	—
286	C₂²×C₇₃	—	2	1	no	—
287	C₂²×C₇₃	—	2	1	no	—
288	C₂²×C₇₃	—	2	1	no	—
289	C₂²×C₇₃	C₂⁵	1	1	yes	characteristic
290	C₂×D₇₃	—	2	1	no	—
291	C₂×D₇₃	—	2	1	no	—
292	C₂×D₇₃	—	2	1	no	—
293	C₂×D₇₃	—	2	2	no	—
294	C₂×D₇₃	—	2	1	no	—
295	C₂×D₇₃	—	2	1	no	—
296	C₂×D₇₃	—	2	2	no	—
297	C₂×D₇₃	—	2	2	no	—
298	C₂×D₇₃	—	2	1	no	—
299	C₂×D₇₃	—	2	1	no	—
300	C₂×D₇₃	—	2	1	no	—
301	C₂×D₇₃	—	4	4	no	—
302	C₂×D₇₃	C₂×#41	1	2	yes	—
303	C₄×C₇₃	—	2	1	no	—
304	C₄×C₇₃	—	2	1	no	—
305	C₄×C₇₃	—	2	2	no	—
306	C₄×C₇₃	—	2	2	no	—
307	C₄×C₇₃	—	2	2	no	—
308	C₄×C₇₃	—	2	1	no	—
309	C₄×C₇₃	—	2	2	no	—
310	C₄×C₇₃	—	2	1	no	—
311	C₄×C₇₃	C₂×#41	1	2	yes	—
312	Dic₇₃	—	2	1	no	—
313	Dic₇₃	—	2	1	no	—
314	Dic₇₃	—	2	1	no	—
315	Dic₇₃	—	2	2	no	—
316	Dic₇₃	—	2	2	no	—
317	Dic₇₃	—	2	1	no	—
318	Dic₇₃	—	2	2	no	—
319	Dic₇₃	C₂×#41	1	2	yes	—
320	C₂×C₇₃	—	4	1	no	—
321	C₂×C₇₃	—	4	1	no	—
322	C₂×C₇₃	C₂²×#41	1	1	yes	characteristic
323	C₂×C₇₃	#585	1	1	yes	characteristic
324	C₂×C₇₃	#585	1	1	yes	characteristic
325	D₇₃	—	2	2	no	—
326	D₇₃	—	4	2	no	—
327	D₇₃	—	4	1	no	—
328	D₇₃	—	4	1	no	—
329	#3493	—	73	1	no	maximal, Sylow
330	C₇₃	#3493	1	1	yes	characteristic, complemented, Sylow
331	#556	—	73	1	no	—
332	#556	—	73	2	no	—
333	#556	D₇₃	1	1	yes	characteristic, complemented
334	#555	—	73	1	no	—
335	#555	—	73	2	no	—
336	#555	—	73	1	no	—
337	#553	—	73	2	no	—
338	#553	—	73	1	no	—
339	#553	—	73	1	no	—
340	#552	—	73	2	no	—
341	#552	—	73	1	no	—
342	#552	—	73	1	no	—
343	#544	—	73	1	no	—
344	#538	—	73	2	no	—
345	#538	—	73	2	no	—
346	#537	—	73	1	no	—
347	#529	—	73	2	no	—
348	#529	—	73	2	no	—
349	#525	—	73	1	no	—
350	#525	—	73	1	no	—
351	#520	—	73	1	no	—
352	#520	—	73	1	no	—
353	C₂×#117	—	73	1	no	—
354	C₂×#41	—	73	1	no	—
355	C₂×#41	—	73	1	no	—
356	C₂³×C₄	—	73	1	no	—
357	C₄⋊Q₈	—	73	2	no	—
358	C₄⋊Q₈	—	73	1	no	—
359	C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
360	#126	—	73	2	no	—
361	#126	—	73	2	no	—
362	#126	—	73	2	no	—
363	#126	—	73	2	no	—
364	#126	—	73	2	no	—
365	#126	—	73	2	no	—
366	#126	C₂×D₇₃	1	2	yes	—
367	#126	C₂×D₇₃	1	2	yes	complemented
368	#125	—	73	2	no	—
369	#125	—	73	2	no	—
370	#125	—	73	2	no	—
371	#125	—	73	1	no	—
372	#125	—	73	1	no	—
373	#124	—	73	2	no	—
374	#124	—	73	2	no	—
375	#124	—	73	2	no	—
376	#124	—	73	2	no	—
377	#124	—	73	2	no	—
378	#124	C₂×D₇₃	1	2	yes	—
379	#123	—	73	2	no	—
380	#123	—	73	1	no	—
381	#123	—	73	2	no	—
382	#123	—	73	1	no	—
383	#123	—	73	2	no	—
384	#123	—	73	2	no	—
385	#123	—	73	2	no	—
386	C₂²⋊Q₈	—	73	1	no	—
387	C₂²⋊Q₈	—	73	2	no	—
388	C₂²⋊Q₈	—	73	1	no	—
389	C₂²⋊Q₈	—	73	1	no	—
390	C₂²⋊Q₈	—	73	2	no	—
391	C₂²⋊Q₈	—	73	2	no	—
392	C₂²⋊Q₈	—	73	1	no	—
393	C₂²⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
394	C₂²⋊Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
395	#121	—	73	1	no	—
396	#121	—	73	2	no	—
397	#121	—	73	1	no	—
398	#121	—	73	1	no	—
399	#121	—	73	1	no	—
400	#121	—	73	2	no	—
401	#121	—	73	1	no	—
402	#121	—	73	2	no	—
403	#121	—	73	1	no	—
404	#121	—	73	2	no	—
405	#121	—	73	2	no	—
406	#121	—	73	2	no	—
407	#121	—	73	2	no	—
408	#120	—	73	1	no	—
409	#120	—	73	2	no	—
410	#120	—	73	1	no	—
411	C₄×Q₈	—	73	1	no	—
412	C₄×Q₈	—	73	2	no	—
413	C₄×Q₈	—	73	2	no	—
414	C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
415	C₄×Q₈	C₂×D₇₃	1	2	yes	complemented
416	C₄×D₄	—	73	1	no	—
417	C₄×D₄	—	73	1	no	—
418	C₄×D₄	—	73	2	no	—
419	C₄×D₄	—	73	1	no	—
420	C₄×D₄	—	73	2	no	—
421	C₄×D₄	—	73	2	no	—
422	C₄×D₄	—	73	2	no	—
423	C₄×D₄	—	73	2	no	—
424	C₄×D₄	—	73	2	no	—
425	C₄×D₄	—	73	2	no	—
426	C₄×D₄	—	73	2	no	—
427	C₄×D₄	—	73	1	no	—
428	C₄×D₄	—	73	1	no	—
429	C₄×D₄	—	73	2	no	—
430	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
431	#117	—	73	1	no	—
432	#117	—	73	1	no	—
433	#117	—	73	1	no	—
434	#117	—	73	1	no	—
435	#117	—	73	1	no	—
436	#117	—	73	2	no	—
437	#117	—	73	2	no	—
438	#117	—	73	2	no	—
439	#117	—	73	2	no	—
440	#117	—	73	1	no	—
441	#117	—	73	2	no	—
442	#117	—	73	2	no	—
443	#117	—	73	2	no	—
444	#117	C₂×D₇₃	1	1	yes	characteristic
445	#117	C₂×D₇₃	1	1	yes	characteristic, complemented
446	C₂×C₄⋊C₄	—	73	1	no	—
447	C₂×C₄⋊C₄	—	73	1	no	—
448	C₂×C₄⋊C₄	—	73	1	no	—
449	C₂×C₄⋊C₄	—	73	2	no	—
450	C₂×C₄⋊C₄	—	73	1	no	—
451	C₂×C₂²⋊C₄	—	73	2	no	—
452	C₂×C₄²	—	73	2	no	—
453	C₂⁴	—	73	1	no	—
454	#41	—	146	4	no	—
455	#41	—	146	4	no	—
456	C₂×Q₈	—	73	2	no	—
457	C₂×Q₈	—	73	1	no	—
458	C₂×Q₈	C₂²×D₇₃	1	1	yes	characteristic
459	C₂×Q₈	C₂²×D₇₃	1	2	yes	—
460	C₂×D₄	—	73	1	no	—
461	C₂×D₄	—	73	2	no	—
462	C₂×D₄	—	73	1	no	—
463	C₂×D₄	—	73	2	no	—
464	C₂×D₄	—	73	1	no	—
465	C₂×D₄	—	73	1	no	—
466	C₂×D₄	—	73	1	no	—
467	C₂×D₄	—	73	2	no	—
468	C₂×D₄	—	73	2	no	—
469	C₂×D₄	—	73	2	no	—
470	C₂×D₄	—	73	1	no	—
471	C₂×D₄	—	73	1	no	—
472	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
473	C₂²×C₄	—	73	2	no	—
474	C₂²×C₄	—	73	2	no	—
475	C₂²×C₄	—	73	2	no	—
476	C₂²×C₄	—	73	2	no	—
477	C₂²×C₄	—	73	2	no	—
478	C₂²×C₄	—	73	2	no	—
479	C₂²×C₄	—	73	1	no	—
480	C₂²×C₄	—	73	1	no	—
481	C₂²×C₄	—	73	1	no	—
482	C₂²×C₄	—	73	2	no	—
483	C₂²×C₄	—	73	1	no	—
484	C₂²×C₄	—	73	1	no	—
485	C₂²×C₄	—	73	1	no	—
486	C₂²×C₄	—	146	4	no	—
487	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
489	C₄⋊C₄	—	73	2	no	—
490	C₄⋊C₄	—	73	1	no	—
491	C₄⋊C₄	—	73	2	no	—
492	C₄⋊C₄	—	73	2	no	—
493	C₄⋊C₄	—	73	1	no	—
494	C₄⋊C₄	—	73	2	no	—
495	C₄⋊C₄	—	73	1	no	—
496	C₄⋊C₄	—	73	2	no	—
497	C₄⋊C₄	—	73	2	no	—
498	C₄⋊C₄	—	73	2	no	—
499	C₄⋊C₄	—	73	1	no	—
500	C₄⋊C₄	—	73	2	no	—
501	C₄⋊C₄	—	73	2	no	—
502	C₄⋊C₄	—	73	1	no	—
503	C₄⋊C₄	—	73	1	no	—
504	C₄⋊C₄	—	73	1	no	—
505	C₄⋊C₄	—	73	2	no	—
506	C₄⋊C₄	—	73	2	no	—
507	C₄⋊C₄	—	73	1	no	—
508	C₄⋊C₄	—	73	2	no	—
509	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
512	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
514	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
515	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
517	C₂²⋊C₄	—	73	2	no	—
518	C₂²⋊C₄	—	73	1	no	—
519	C₂²⋊C₄	—	73	1	no	—
520	C₂²⋊C₄	—	73	2	no	—
521	C₂²⋊C₄	—	73	2	no	—
522	C₂²⋊C₄	—	73	2	no	—
523	C₂²⋊C₄	—	73	1	no	—
524	C₂²⋊C₄	—	73	1	no	—
525	C₂²⋊C₄	—	73	2	no	—
526	C₂²⋊C₄	—	73	1	no	—
527	C₂²⋊C₄	—	73	2	no	—
528	C₂²⋊C₄	—	73	2	no	—
529	C₂²⋊C₄	—	73	2	no	—
530	C₂²⋊C₄	—	73	2	no	—
531	C₂²⋊C₄	—	73	2	no	—
532	C₂²⋊C₄	—	73	2	no	—
533	C₂²⋊C₄	—	73	2	no	—
534	C₂²⋊C₄	—	73	1	no	—
535	C₂²⋊C₄	—	73	2	no	—
536	C₂²⋊C₄	—	73	1	no	—
537	C₂²⋊C₄	—	73	1	no	—
538	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
539	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
540	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
542	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
544	C₄²	—	73	2	no	—
545	C₄²	—	73	2	no	—
546	C₄²	—	73	2	no	—
547	C₄²	—	73	2	no	—
548	C₄²	—	73	2	no	—
549	C₄²	—	73	2	no	—
550	C₄²	—	73	1	no	—
551	C₄²	C₂²×D₇₃	1	2	yes	—
552	C₄²	C₂²×D₇₃	1	2	yes	—
553	C₄²	C₂²×D₇₃	1	2	yes	—
554	C₄²	C₂²×D₇₃	1	1	yes	characteristic
555	C₂³	—	292	1	no	—
556	C₂³	—	292	1	no	—
557	C₂³	—	73	1	no	—
558	C₂³	—	73	1	no	—
559	C₂³	—	73	2	no	—
560	C₂³	—	73	1	no	—
561	C₂³	—	146	2	no	—
562	C₂³	C₂³×D₇₃	1	1	yes	characteristic
563	C₂³	C₂³×D₇₃	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	4	2	no	—
566	Q₈	—	292	2	no	—
567	Q₈	—	146	2	no	—
568	D₄	—	4	1	no	—
569	D₄	—	292	2	no	—
570	D₄	—	292	2	no	—
571	D₄	—	292	1	no	—
572	D₄	—	292	2	no	—
573	D₄	—	292	1	no	—
574	D₄	—	292	1	no	—
575	D₄	—	292	2	no	—
576	D₄	—	146	2	no	—
577	D₄	—	146	4	no	—
578	D₄	—	146	2	no	—
579	D₄	—	146	2	no	—
580	D₄	—	146	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	292	2	no	—
584	C₂×C₄	—	292	2	no	—
585	C₂×C₄	—	292	2	no	—
586	C₂×C₄	—	292	2	no	—
587	C₂×C₄	—	292	2	no	—
588	C₂×C₄	—	292	2	no	—
589	C₂×C₄	—	73	1	no	—
590	C₂×C₄	—	73	4	no	—
591	C₂×C₄	—	73	1	no	—
592	C₂×C₄	—	73	2	no	—
593	C₂×C₄	—	73	1	no	—
594	C₂×C₄	—	73	1	no	—
595	C₂×C₄	—	73	2	no	—
596	C₂×C₄	—	73	1	no	—
597	C₂×C₄	—	73	2	no	—
598	C₂×C₄	—	146	2	no	—
599	C₂×C₄	—	146	4	no	—
600	C₂×C₄	—	146	2	no	—
601	C₂×C₄	—	146	2	no	—
602	C₂×C₄	—	146	2	no	—
603	C₂×C₄	—	146	2	no	—
604	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₇₃	1	2	yes	—
606	C₂×C₄	C₂³×D₇₃	1	2	yes	—
607	C₂×C₄	C₂³×D₇₃	1	2	yes	—
608	C₂×C₄	C₂³×D₇₃	1	2	yes	—
609	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	292	4	no	—
620	C₂²	—	73	2	no	—
621	C₂²	—	146	1	no	—
622	C₂²	—	146	2	no	—
623	C₂²	—	146	1	no	—
624	C₂²	—	146	1	no	—
625	C₂²	—	146	2	no	—
626	C₂²	—	146	1	no	—
627	C₂²	—	146	1	no	—
628	C₂²	—	146	2	no	—
629	C₂²	—	146	1	no	—
630	C₂²	—	146	1	no	—
631	C₂²	—	146	1	no	—
632	C₂²	C₂⁴×D₇₃	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	1	no	—
641	C₄	—	73	2	no	—
642	C₄	—	146	1	no	—
643	C₄	—	146	1	no	—
644	C₄	—	146	2	no	—
645	C₄	—	146	1	no	—
646	C₄	—	146	2	no	—
647	C₄	—	146	1	no	—
648	C₄	—	146	2	no	—
649	C₄	#41×D₇₃	1	2	yes	—
650	C₂	—	4	1	no	—
651	C₂	—	4	1	no	—
652	C₂	—	292	1	no	—
653	C₂	—	292	2	no	—
654	C₂	—	292	1	no	—
655	C₂	—	146	2	no	—
656	C₂	C₂×#41×D₇₃	1	1	yes	characteristic
657	C₂	#17989423	1	1	yes	characteristic
658	C₂	#17989424	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₃
commutator, socle	C₂²×C₇₃	C₂⁵
Fitting	#556×C₇₃	C₂
hypercenter	#556	D₇₃
hypocenter	C₇₃	#3493
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #17989309	C₂	semidirect
2. #17989308	C₂	semidirect
3. #17989303	C₂	semidirect
4. #17989300	C₂	semidirect
5. #17989299	C₂	semidirect
6. #17989288	C₂	semidirect
7. #17989283	C₂	semidirect
8. #17989281	C₂	semidirect
9. #17989279	C₂	semidirect
10. #17989278	C₂	semidirect
11. #17989273	C₂	semidirect
12. #17989214	C₂	semidirect
13. #17989176	C₂	semidirect
14. #17989171	C₂	semidirect
15. #17989167	C₂	semidirect
16. #17989124	C₂	semidirect
17. #17989120	C₂	semidirect
18. #17989100	C₂	semidirect
19. #17989096	C₂	semidirect
20. #17989069	C₂	semidirect
21. #17989067	C₂	semidirect
22. #117×D₇₃	C₂	semidirect
23. #556×C₇₃	C₂	semidirect
27. #14556590	C₂²	semidirect
28. #14556589	C₂²	semidirect
30. #14556586	C₂²	semidirect
31. #14556586	C₂²	semidirect
33. #14556585	C₂²	semidirect
35. #14556583	C₂²	semidirect
36. #14556582	C₂²	semidirect
37. #14556582	C₂²	semidirect
38. #14556581	C₂²	semidirect
39. #14556581	C₂²	semidirect
41. #14556580	C₂²	semidirect
44. #14556577	C₂²	semidirect
54. #14556569	C₂²	semidirect
58. #14556567	C₂²	semidirect
62. #14556566	C₂²	semidirect
64. #14556565	C₂²	semidirect
69. #14556564	C₂²	semidirect
75. Q₈×Dic₇₃	C₂²	semidirect
76. C₄×Dic₁₄₆	C₂²	semidirect
77. #14556556	C₂²	semidirect
81. C₄×D₂₉₂	C₂²	semidirect
82. C₄×D₂₉₂	C₂²	semidirect
85. #14556553	C₂²	semidirect
90. #14556551	C₂²	semidirect
91. #14556551	C₂²	semidirect
96. #14556549	C₂²	semidirect
97. #14556549	C₂²	semidirect
100. #14556548	C₂²	semidirect
101. #14556548	C₂²	semidirect
102. #14556548	C₂²	semidirect
104. #14556547	C₂²	semidirect
105. C₂×C₄⋊Dic₇₃	C₂²	semidirect
108. C₄⋊C₄×D₇₃	C₂²	semidirect
109. C₄⋊C₄×D₇₃	C₂²	semidirect
112. C₄⋊Q₈×C₇₃	C₂²	semidirect
114. #126×C₇₃	C₂²	semidirect
117. C₂²⋊Q₈×C₇₃	C₂²	semidirect
118. C₄×Q₈×C₇₃	C₂²	semidirect
119. C₄×Q₈×C₇₃	C₂²	semidirect
122. #117×C₇₃	C₂²	semidirect
330. C₇₃	#3493	semidirect
333. #556	D₇₃	semidirect
359. C₄⋊Q₈	C₂×D₇₃	semidirect
367. #126	C₂×D₇₃	semidirect
394. C₂²⋊Q₈	C₂×D₇₃	semidirect
414. C₄×Q₈	C₂×D₇₃	semidirect
415. C₄×Q₈	C₂×D₇₃	semidirect
445. #117	C₂×D₇₃	semidirect