Subgroups — #22624375

Order 9344.

1004 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989341	C₂	1	2	yes	maximal, complemented
2	#17989339	C₂	1	2	yes	maximal, complemented
3	#17989315	C₂	1	1	yes	maximal, characteristic, complemented
4	#17989309	C₂	1	1	yes	maximal, characteristic, complemented
5	#17989293	C₂	1	2	yes	maximal, complemented
6	#17989288	C₂	1	2	yes	maximal, complemented
7	Q₈×D₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
8	#17989250	C₂	1	1	yes	maximal, characteristic, complemented
9	#17989250	C₂	1	1	yes	maximal, characteristic, complemented
10	#17989249	C₂	1	1	yes	maximal, characteristic, complemented
11	#17989247	C₂	1	1	yes	maximal, characteristic, complemented
12	#17989239	C₂	1	1	yes	maximal, characteristic, complemented
13	#17989217	C₂	1	2	yes	maximal, complemented
14	#17989203	C₂	1	2	yes	maximal, complemented
15	#17989200	C₂	1	1	yes	maximal, characteristic, complemented
16	#17989185	C₂	1	2	yes	maximal, complemented
17	#17989178	C₂	1	2	yes	maximal, complemented
18	#17989163	C₂	1	1	yes	maximal, characteristic, complemented
19	#17989162	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄⋊Q₈×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#17989122	C₂	1	1	yes	maximal, characteristic, complemented
22	#17989115	C₂	1	1	yes	maximal, characteristic, complemented
23	#541×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×Dic₁₄₆	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₇₃	C₂²	1	1	yes	characteristic
28	C₂×Q₈×D₇₃	C₂²	1	1	yes	characteristic
29	C₂×Q₈×D₇₃	C₂²	1	1	yes	characteristic
30	#14556591	C₂²	1	1	yes	characteristic
31	#14556591	C₂²	1	1	yes	characteristic
32	#14556591	C₂²	1	2	yes	—
33	#14556590	C₂²	1	2	yes	—
34	#14556590	C₂²	1	2	yes	—
35	#14556590	C₂²	1	2	yes	—
36	#14556590	C₂²	1	2	yes	—
37	#14556589	C₂²	1	1	yes	characteristic
38	#14556589	C₂²	1	1	yes	characteristic
39	#14556589	C₂²	1	1	yes	characteristic
40	#14556586	C₂²	1	2	yes	—
41	#14556586	C₂²	1	2	yes	—
42	#14556586	C₂²	1	2	yes	—
43	#14556586	C₂²	1	2	yes	—
44	#14556586	C₂²	1	1	yes	characteristic
45	#14556585	C₂²	1	2	yes	—
46	#14556584	C₂²	1	1	yes	characteristic
47	#14556583	C₂²	1	2	yes	—
48	#14556582	C₂²	1	2	yes	—
49	#14556582	C₂²	1	2	yes	—
50	#14556581	C₂²	1	2	yes	—
51	#14556581	C₂²	1	1	yes	characteristic
52	#14556581	C₂²	1	2	yes	—
53	#14556580	C₂²	1	1	yes	characteristic
54	#14556579	C₂²	1	1	yes	characteristic
55	#14556579	C₂²	1	1	yes	characteristic
56	#14556579	C₂²	1	2	yes	—
57	#14556577	C₂²	1	1	yes	characteristic
58	#14556577	C₂²	1	2	yes	—
59	#14556576	C₂²	1	2	yes	—
60	#14556576	C₂²	1	2	yes	—
61	#14556576	C₂²	1	2	yes	—
62	#14556576	C₂²	1	1	yes	characteristic
63	#14556576	C₂²	1	2	yes	—
64	#14556575	C₂²	1	2	yes	—
65	#14556575	C₂²	1	2	yes	—
66	#14556573	C₂²	1	1	yes	characteristic
67	#14556573	C₂²	1	2	yes	—
68	#14556571	C₂²	1	1	yes	characteristic
69	#14556571	C₂²	1	2	yes	—
70	#14556571	C₂²	1	2	yes	—
71	#14556571	C₂²	1	2	yes	—
72	#14556571	C₂²	1	1	yes	characteristic
73	#14556571	C₂²	1	1	yes	characteristic
74	#14556571	C₂²	1	2	yes	—
75	#14556571	C₂²	1	2	yes	—
76	#14556569	C₂²	1	2	yes	—
77	#14556569	C₂²	1	2	yes	—
78	#14556569	C₂²	1	2	yes	—
79	#14556569	C₂²	1	2	yes	—
80	#14556569	C₂²	1	2	yes	—
81	#14556569	C₂²	1	2	yes	—
82	#14556569	C₂²	1	1	yes	characteristic
83	#14556568	C₂²	1	2	yes	—
84	#14556568	C₂²	1	2	yes	—
85	#14556566	C₂²	1	1	yes	characteristic
86	#14556566	C₂²	1	2	yes	—
87	#14556564	C₂²	1	2	yes	—
88	#14556564	C₂²	1	2	yes	—
89	#14556564	C₂²	1	1	yes	characteristic
90	C₄×Dic₁₄₆	C₂²	1	2	yes	—
91	C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
92	#14556556	C₂²	1	1	yes	characteristic
93	#14556556	C₂²	1	1	yes	characteristic
94	#14556556	C₂²	1	1	yes	characteristic
95	C₄×D₂₉₂	C₂²	1	2	yes	—
96	C₄×D₂₉₂	C₂²	1	2	yes	—
97	C₄×D₂₉₂	C₂²	1	1	yes	characteristic
98	#14556553	C₂²	1	1	yes	characteristic
99	#14556553	C₂²	1	2	yes	—
100	#14556553	C₂²	1	2	yes	—
101	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
103	#14556551	C₂²	1	2	yes	—
104	#14556551	C₂²	1	2	yes	—
105	#14556549	C₂²	1	2	yes	—
106	#14556548	C₂²	1	1	yes	characteristic
107	#14556548	C₂²	1	2	yes	—
108	C₄⋊C₄×D₇₃	C₂²	1	2	yes	—
109	C₄⋊C₄×D₇₃	C₂²	1	2	yes	—
110	C₄⋊C₄×D₇₃	C₂²	1	2	yes	—
111	C₄²×D₇₃	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
113	#126×C₇₃	C₂²	1	2	yes	—
114	#126×C₇₃	C₂²	1	2	yes	—
115	#125×C₇₃	C₂²	1	1	yes	characteristic
116	#125×C₇₃	C₂²	1	2	yes	—
117	#125×C₇₃	C₂²	1	2	yes	—
118	C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
119	C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
121	C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
122	#117×C₇₃	C₂²	1	1	yes	characteristic
123	#11924029	—	4	2	no	—
124	#11924028	—	4	2	no	—
125	C₂×Dic₁₄₆	—	4	2	no	—
126	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₄₆	C₂³	1	2	yes	—
131	C₂×Dic₁₄₆	C₂³	1	2	yes	—
132	C₂×Dic₁₄₆	C₂³	1	2	yes	—
133	C₂×Dic₁₄₆	C₂³	1	2	yes	—
134	Q₈×D₇₃	—	4	2	no	—
135	Q₈×D₇₃	—	4	2	no	—
136	Q₈×D₇₃	—	4	2	no	—
137	C₂×D₂₉₂	C₂³	1	2	yes	—
138	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
139	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
140	C₂×D₂₉₂	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
144	C₂²×Dic₇₃	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	1	yes	characteristic
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	2	yes	—
154	C₂×C₄×D₇₃	C₂³	1	2	yes	—
155	C₄⋊Dic₇₃	C₂³	1	2	yes	—
156	C₄⋊Dic₇₃	C₂³	1	2	yes	—
157	C₄⋊Dic₇₃	C₂³	1	2	yes	—
158	C₄⋊Dic₇₃	C₂³	1	2	yes	—
159	C₄⋊Dic₇₃	C₂³	1	2	yes	—
160	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₇₃	C₂³	1	2	yes	—
162	C₄⋊Dic₇₃	C₂³	1	2	yes	—
163	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
164	#11924007	C₂³	1	1	yes	characteristic
165	#11924007	C₂³	1	2	yes	—
166	#11924007	C₂³	1	2	yes	—
167	#11924007	C₂³	1	2	yes	—
168	#11924007	C₂³	1	2	yes	—
169	#11924007	C₂³	1	1	yes	characteristic
170	#11924007	C₂³	1	1	yes	characteristic
171	#11924007	C₂³	1	1	yes	characteristic
172	#11924007	C₂³	1	2	yes	—
173	#11924007	C₂³	1	1	yes	characteristic
174	#11924007	C₂³	1	2	yes	—
175	#11924007	C₂³	1	2	yes	—
176	#11924007	C₂³	1	2	yes	—
177	#11924007	C₂³	1	2	yes	—
178	#11924007	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
181	#11924005	C₂³	1	2	yes	—
182	#11924005	C₂³	1	1	yes	characteristic
183	#11924005	C₂³	1	2	yes	—
184	#11924005	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
190	#11924005	C₂³	1	1	yes	characteristic
191	#11924005	C₂³	1	2	yes	—
192	#11924005	C₂³	1	2	yes	—
193	#11924005	C₂³	1	2	yes	—
194	#11924005	C₂³	1	1	yes	characteristic
195	#11924005	C₂³	1	2	yes	—
196	#11924005	C₂³	1	2	yes	—
197	#11924005	C₂³	1	1	yes	characteristic
198	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
200	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
201	C₄×Dic₇₃	C₂³	1	2	yes	—
202	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
203	C₄×Dic₇₃	C₂³	1	2	yes	—
204	C₄×Dic₇₃	C₂³	1	2	yes	—
205	C₂×Q₈×C₇₃	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₇₃	C₂³	1	1	yes	characteristic
207	C₂²×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	1	yes	characteristic
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	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
216	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
217	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
218	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
219	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
224	C₄²×C₇₃	C₂³	1	1	yes	characteristic
225	C₄²×C₇₃	C₂³	1	1	yes	characteristic
226	C₄²×C₇₃	C₂³	1	2	yes	—
227	C₄²×C₇₃	C₂³	1	2	yes	—
228	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
229	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
230	C₂²×D₇₃	C₂⁴	1	2	yes	—
231	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
232	Q₈×C₇₃	—	2	2	no	—
233	Q₈×C₇₃	—	2	2	no	—
234	C₂×C₄×C₇₃	—	2	2	no	—
235	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
238	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
241	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
242	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
243	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
245	C₂²⋊D₇₃	—	2	2	no	—
246	C₂²⋊D₇₃	—	2	2	no	—
247	C₂²⋊D₇₃	—	4	2	no	—
248	C₂×Dic₇₃	—	4	2	no	—
249	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₇₃	C₂⁴	1	2	yes	—
254	C₂×Dic₇₃	C₂⁴	1	2	yes	—
255	C₂×Dic₇₃	C₂⁴	1	2	yes	—
256	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
258	D₂₉₂	—	2	4	no	—
259	D₂₉₂	—	2	2	no	—
260	D₂₉₂	—	2	2	no	—
261	D₂₉₂	—	4	2	no	—
262	C₄×D₇₃	—	2	2	no	—
263	C₄×D₇₃	—	2	2	no	—
264	C₄×D₇₃	—	2	2	no	—
265	C₄×D₇₃	—	2	2	no	—
266	C₄×D₇₃	—	2	4	no	—
267	C₄×D₇₃	—	4	2	no	—
268	C₄×D₇₃	—	4	2	no	—
269	C₄×D₇₃	—	4	2	no	—
270	C₄×D₇₃	—	4	2	no	—
271	C₄×D₇₃	—	4	2	no	—
272	Dic₁₄₆	—	2	2	no	—
273	Dic₁₄₆	—	2	2	no	—
274	Dic₁₄₆	—	2	2	no	—
275	Dic₁₄₆	—	2	2	no	—
276	Dic₁₄₆	—	4	2	no	—
277	Dic₁₄₆	—	4	2	no	—
278	Dic₁₄₆	—	4	2	no	—
279	Dic₁₄₆	—	4	2	no	—
280	C₂²×C₇₃	—	2	1	no	—
281	C₂²×C₇₃	—	2	1	no	—
282	C₂²×C₇₃	—	2	1	no	—
283	C₂²×C₇₃	C₂⁵	1	1	yes	characteristic
284	C₂×D₇₃	—	2	1	no	—
285	C₂×D₇₃	—	2	1	no	—
286	C₂×D₇₃	—	2	1	no	—
287	C₂×D₇₃	—	2	2	no	—
288	C₂×D₇₃	—	2	2	no	—
289	C₂×D₇₃	—	2	1	no	—
290	C₂×D₇₃	—	2	2	no	—
291	C₂×D₇₃	—	2	1	no	—
292	C₂×D₇₃	2₋¹⁺⁴	1	2	yes	—
293	C₄×C₇₃	—	2	1	no	—
294	C₄×C₇₃	—	2	2	no	—
295	C₄×C₇₃	—	2	2	no	—
296	C₄×C₇₃	—	2	1	no	—
297	C₄×C₇₃	—	2	1	no	—
298	C₄×C₇₃	—	2	1	no	—
299	C₄×C₇₃	—	2	2	no	—
300	C₄×C₇₃	—	2	1	no	—
301	C₄×C₇₃	—	2	2	no	—
302	C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
303	Dic₇₃	—	2	2	no	—
304	Dic₇₃	—	2	2	no	—
305	Dic₇₃	—	2	2	no	—
306	Dic₇₃	—	2	1	no	—
307	Dic₇₃	—	2	1	no	—
308	Dic₇₃	—	2	1	no	—
309	Dic₇₃	—	2	1	no	—
310	Dic₇₃	—	2	1	no	—
311	Dic₇₃	2₋¹⁺⁴	1	2	yes	—
312	C₂×C₇₃	—	4	1	no	—
313	C₂×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
315	C₂×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
316	D₇₃	—	2	2	no	—
317	D₇₃	—	4	1	no	—
318	D₇₃	—	4	2	no	—
319	#3552	—	73	1	no	maximal, Sylow
320	C₇₃	#3552	1	1	yes	characteristic, complemented, Sylow
321	#563	—	73	2	no	—
322	#563	—	73	2	no	—
323	#557	—	73	1	no	—
324	#556	—	73	1	no	—
325	#554	—	73	2	no	—
326	#553	—	73	2	no	—
327	D₄×Q₈	—	73	1	no	—
328	D₄×Q₈	—	73	1	no	—
329	D₄×Q₈	—	73	1	no	—
330	#548	—	73	1	no	—
331	#548	—	73	1	no	—
332	#547	—	73	1	no	—
333	#544	—	73	2	no	—
334	#542	—	73	2	no	—
335	#541	—	73	1	no	—
336	#541	D₇₃	1	1	yes	characteristic, complemented
337	#539	—	73	2	no	—
338	#539	—	73	2	no	—
339	#536	—	73	1	no	—
340	#536	—	73	1	no	—
341	C₂×C₄⋊Q₈	—	73	1	no	—
342	#529	—	73	1	no	—
343	#529	—	73	1	no	—
344	C₂×#41	—	73	1	no	—
345	C₂×#41	—	73	1	no	—
346	C₂²×Q₈	—	73	1	no	—
347	C₂²×Q₈	—	73	1	no	—
348	C₂²×Q₈	—	73	1	no	—
349	C₂²×Q₈	—	73	1	no	—
350	C₄⋊Q₈	—	73	1	no	—
351	C₄⋊Q₈	—	73	1	no	—
352	C₄⋊Q₈	—	73	1	no	—
353	C₄⋊Q₈	—	73	2	no	—
354	C₄⋊Q₈	—	73	2	no	—
355	C₄⋊Q₈	—	73	2	no	—
356	C₄⋊Q₈	—	73	2	no	—
357	C₄⋊Q₈	—	73	1	no	—
358	C₄⋊Q₈	—	73	1	no	—
359	C₄⋊Q₈	—	73	2	no	—
360	C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
361	#126	—	73	2	no	—
362	#126	—	73	1	no	—
363	#126	—	73	2	no	—
364	#126	—	73	2	no	—
365	#126	—	73	2	no	—
366	#126	—	73	1	no	—
367	#126	—	73	2	no	—
368	#126	C₂×D₇₃	1	2	yes	—
369	#126	C₂×D₇₃	1	2	yes	—
370	#125	—	73	1	no	—
371	#125	—	73	2	no	—
372	#125	—	73	2	no	—
373	#125	—	73	2	no	—
374	#125	—	73	2	no	—
375	#125	—	73	2	no	—
376	#125	C₂×D₇₃	1	1	yes	characteristic
377	#125	C₂×D₇₃	1	2	yes	—
378	#125	C₂×D₇₃	1	2	yes	—
379	#124	—	73	1	no	—
380	#124	—	73	1	no	—
381	#124	—	73	2	no	—
382	#124	—	73	1	no	—
383	#124	—	73	1	no	—
384	#124	—	73	2	no	—
385	#123	—	73	2	no	—
386	#123	—	73	1	no	—
387	#123	—	73	2	no	—
388	#123	—	73	2	no	—
389	#123	—	73	2	no	—
390	#123	—	73	1	no	—
391	#123	—	73	2	no	—
392	#123	—	73	2	no	—
393	#123	—	73	2	no	—
394	C₂²⋊Q₈	—	73	1	no	—
395	C₂²⋊Q₈	—	73	1	no	—
396	C₂²⋊Q₈	—	73	2	no	—
397	C₂²⋊Q₈	—	73	2	no	—
398	C₂²⋊Q₈	—	73	2	no	—
399	C₂²⋊Q₈	—	73	2	no	—
400	C₂²⋊Q₈	—	73	2	no	—
401	C₂²⋊Q₈	—	73	2	no	—
402	C₂²⋊Q₈	—	73	2	no	—
403	C₂²⋊Q₈	—	73	1	no	—
404	C₂²⋊Q₈	—	73	1	no	—
405	C₂²⋊Q₈	—	73	2	no	—
406	C₂²⋊Q₈	—	73	2	no	—
407	C₂²⋊Q₈	—	73	2	no	—
408	C₂²⋊Q₈	—	73	2	no	—
409	C₂²⋊Q₈	—	73	2	no	—
410	C₂²⋊Q₈	—	73	2	no	—
411	C₂²⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
412	C₂²⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
413	#121	—	73	1	no	—
414	#121	—	73	2	no	—
415	#121	—	73	1	no	—
416	#121	—	73	2	no	—
417	#121	—	73	2	no	—
418	C₄×Q₈	—	73	1	no	—
419	C₄×Q₈	—	73	1	no	—
420	C₄×Q₈	—	73	1	no	—
421	C₄×Q₈	—	73	1	no	—
422	C₄×Q₈	—	73	2	no	—
423	C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
424	C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
425	C₄×D₄	—	73	1	no	—
426	C₄×D₄	—	73	1	no	—
427	C₄×D₄	—	73	1	no	—
428	C₄×D₄	—	73	2	no	—
429	C₄×D₄	—	73	2	no	—
430	C₄×D₄	—	73	2	no	—
431	C₄×D₄	—	73	2	no	—
432	C₄×D₄	—	73	1	no	—
433	C₄×D₄	—	73	2	no	—
434	C₄×D₄	—	73	2	no	—
435	#117	—	73	2	no	—
436	#117	—	73	1	no	—
437	#117	—	73	2	no	—
438	#117	C₂×D₇₃	1	1	yes	characteristic
439	C₂×C₄⋊C₄	—	73	2	no	—
440	C₂×C₄⋊C₄	—	73	2	no	—
441	C₂×C₄⋊C₄	—	73	2	no	—
442	C₂×C₄²	—	73	1	no	—
443	#41	—	292	2	no	—
444	#41	—	292	2	no	—
445	C₂×Q₈	—	292	2	no	—
446	C₂×Q₈	—	292	2	no	—
447	C₂×Q₈	—	292	2	no	—
448	C₂×Q₈	—	292	2	no	—
449	C₂×Q₈	—	73	2	no	—
450	C₂×Q₈	—	73	2	no	—
451	C₂×Q₈	—	73	2	no	—
452	C₂×Q₈	—	73	2	no	—
453	C₂×Q₈	—	73	1	no	—
454	C₂×Q₈	—	73	1	no	—
455	C₂×Q₈	—	73	1	no	—
456	C₂×Q₈	—	73	1	no	—
457	C₂×Q₈	C₂²×D₇₃	1	1	yes	characteristic
458	C₂×Q₈	C₂²×D₇₃	1	1	yes	characteristic
459	C₂×D₄	—	73	2	no	—
460	C₂×D₄	—	73	1	no	—
461	C₂×D₄	—	73	1	no	—
462	C₂×D₄	—	73	2	no	—
463	C₂×D₄	—	73	2	no	—
464	C₂×D₄	—	73	1	no	—
465	C₂×D₄	—	73	1	no	—
466	C₂²×C₄	—	73	2	no	—
467	C₂²×C₄	—	73	2	no	—
468	C₂²×C₄	—	73	2	no	—
469	C₂²×C₄	—	73	2	no	—
470	C₂²×C₄	—	73	2	no	—
471	C₂²×C₄	—	73	2	no	—
472	C₂²×C₄	—	73	1	no	—
473	C₂²×C₄	—	73	1	no	—
474	C₂²×C₄	—	73	1	no	—
475	C₂²×C₄	—	73	2	no	—
476	C₂²×C₄	—	73	1	no	—
477	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
478	C₄⋊C₄	—	73	1	no	—
479	C₄⋊C₄	—	73	2	no	—
480	C₄⋊C₄	—	73	2	no	—
481	C₄⋊C₄	—	73	2	no	—
482	C₄⋊C₄	—	73	2	no	—
483	C₄⋊C₄	—	73	1	no	—
484	C₄⋊C₄	—	73	1	no	—
485	C₄⋊C₄	—	73	1	no	—
486	C₄⋊C₄	—	73	1	no	—
487	C₄⋊C₄	—	73	2	no	—
488	C₄⋊C₄	—	73	2	no	—
489	C₄⋊C₄	—	73	2	no	—
490	C₄⋊C₄	—	73	2	no	—
491	C₄⋊C₄	—	73	2	no	—
492	C₄⋊C₄	—	73	1	no	—
493	C₄⋊C₄	—	73	2	no	—
494	C₄⋊C₄	—	73	2	no	—
495	C₄⋊C₄	—	73	2	no	—
496	C₄⋊C₄	—	73	2	no	—
497	C₄⋊C₄	—	73	2	no	—
498	C₄⋊C₄	—	73	1	no	—
499	C₄⋊C₄	—	73	2	no	—
500	C₄⋊C₄	—	73	2	no	—
501	C₄⋊C₄	—	73	1	no	—
502	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
503	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
504	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
505	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
506	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
510	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
511	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
513	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
514	C₂²⋊C₄	—	73	1	no	—
515	C₂²⋊C₄	—	73	1	no	—
516	C₂²⋊C₄	—	73	2	no	—
517	C₂²⋊C₄	—	73	2	no	—
518	C₂²⋊C₄	—	73	2	no	—
519	C₂²⋊C₄	—	73	1	no	—
520	C₂²⋊C₄	—	73	2	no	—
521	C₂²⋊C₄	—	73	1	no	—
522	C₂²⋊C₄	—	73	1	no	—
523	C₂²⋊C₄	—	73	2	no	—
524	C₂²⋊C₄	—	73	1	no	—
525	C₂²⋊C₄	—	73	2	no	—
526	C₂²⋊C₄	—	73	2	no	—
527	C₂²⋊C₄	—	73	1	no	—
528	C₂²⋊C₄	—	73	2	no	—
529	C₂²⋊C₄	—	73	2	no	—
530	C₂²⋊C₄	—	73	2	no	—
531	C₂²⋊C₄	—	73	1	no	—
532	C₂²⋊C₄	—	73	2	no	—
533	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
534	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
535	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
537	C₄²	—	73	1	no	—
538	C₄²	—	73	1	no	—
539	C₄²	—	73	1	no	—
540	C₄²	—	73	2	no	—
541	C₄²	—	73	1	no	—
542	C₄²	—	73	2	no	—
543	C₄²	—	73	2	no	—
544	C₄²	C₂²×D₇₃	1	1	yes	characteristic
545	C₄²	C₂²×D₇₃	1	2	yes	—
546	C₄²	C₂²×D₇₃	1	1	yes	characteristic
547	C₄²	C₂²×D₇₃	1	2	yes	—
548	C₂³	—	73	1	no	—
549	C₂³	—	73	1	no	—
550	C₂³	—	73	2	no	—
551	C₂³	C₂³×D₇₃	1	1	yes	characteristic
552	Q₈	—	2	2	no	—
553	Q₈	—	2	2	no	—
554	Q₈	—	292	2	no	—
555	Q₈	—	292	2	no	—
556	Q₈	—	292	2	no	—
557	Q₈	—	292	2	no	—
558	Q₈	—	146	2	no	—
559	Q₈	—	146	2	no	—
560	Q₈	—	146	2	no	—
561	Q₈	—	146	2	no	—
562	D₄	—	292	2	no	—
563	D₄	—	292	2	no	—
564	D₄	—	146	4	no	—
565	D₄	—	146	2	no	—
566	D₄	—	146	2	no	—
567	D₄	—	146	2	no	—
568	D₄	—	146	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	292	2	no	—
571	C₂×C₄	—	292	2	no	—
572	C₂×C₄	—	292	2	no	—
573	C₂×C₄	—	292	2	no	—
574	C₂×C₄	—	292	2	no	—
575	C₂×C₄	—	292	2	no	—
576	C₂×C₄	—	73	1	no	—
577	C₂×C₄	—	73	1	no	—
578	C₂×C₄	—	73	1	no	—
579	C₂×C₄	—	73	1	no	—
580	C₂×C₄	—	73	1	no	—
581	C₂×C₄	—	73	2	no	—
582	C₂×C₄	—	73	2	no	—
583	C₂×C₄	—	73	2	no	—
584	C₂×C₄	—	73	1	no	—
585	C₂×C₄	—	146	4	no	—
586	C₂×C₄	—	146	2	no	—
587	C₂×C₄	—	146	2	no	—
588	C₂×C₄	—	146	2	no	—
589	C₂×C₄	—	146	2	no	—
590	C₂×C₄	C₂³×D₇₃	1	2	yes	—
591	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₇₃	1	2	yes	—
594	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₇₃	1	2	yes	—
597	C₂×C₄	C₂³×D₇₃	1	2	yes	—
598	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	73	2	no	—
604	C₂²	—	146	1	no	—
605	C₂²	—	146	2	no	—
606	C₂²	—	146	2	no	—
607	C₂²	—	146	1	no	—
608	C₂²	—	146	1	no	—
609	C₂²	—	146	2	no	—
610	C₂²	—	146	1	no	—
611	C₂²	—	146	1	no	—
612	C₂²	C₂⁴×D₇₃	1	1	yes	characteristic
613	C₄	—	2	1	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	2	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	73	2	no	—
623	C₄	—	146	1	no	—
624	C₄	—	146	2	no	—
625	C₄	—	146	2	no	—
626	C₄	—	146	2	no	—
627	C₄	—	146	1	no	—
628	C₄	—	146	1	no	—
629	C₄	—	146	1	no	—
630	C₄	—	146	1	no	—
631	C₄	#14556637	1	2	yes	—
632	C₂	—	4	1	no	—
633	C₂	—	292	1	no	—
634	C₂	—	292	2	no	—
635	C₂	—	146	2	no	—
636	C₂	C₂×#14556637	1	1	yes	characteristic
637	C₂	2₋¹⁺⁴×D₇₃	1	1	yes	characteristic
638	C₂	2₋¹⁺⁴×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₃
commutator, socle	C₂²×C₇₃	C₂⁵
Fitting	#541×C₇₃	C₂
hypercenter	#541	D₇₃
hypocenter	C₇₃	#3552
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. #17989341	C₂	semidirect
2. #17989339	C₂	semidirect
3. #17989315	C₂	semidirect
4. #17989309	C₂	semidirect
5. #17989293	C₂	semidirect
6. #17989288	C₂	semidirect
7. Q₈×D₂₉₂	C₂	semidirect
8. #17989250	C₂	semidirect
9. #17989250	C₂	semidirect
10. #17989249	C₂	semidirect
11. #17989247	C₂	semidirect
12. #17989239	C₂	semidirect
13. #17989217	C₂	semidirect
14. #17989203	C₂	semidirect
15. #17989200	C₂	semidirect
16. #17989185	C₂	semidirect
17. #17989178	C₂	semidirect
18. #17989163	C₂	semidirect
19. #17989162	C₂	semidirect
20. C₄⋊Q₈×D₇₃	C₂	semidirect
21. #17989122	C₂	semidirect
22. #17989115	C₂	semidirect
23. #541×C₇₃	C₂	semidirect
320. C₇₃	#3552	semidirect
336. #541	D₇₃	semidirect