Subgroups — C₂×#22624995 #34012180

Order 18688.

614 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989643	C₂	1	1	yes	maximal, characteristic
2	C₂×D₇₃⋊#108	C₂	1	1	yes	maximal, characteristic
3	#22624995	C₂	1	4	yes	maximal, direct product factor
4	C₂×#106×D₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×D₇₃⋊M₁₆	—	2	1	no	—
6	C₂×#14556666	—	2	1	no	—
7	#17989643	—	2	1	no	—
8	#17989643	—	2	1	no	—
9	#17989643	C₄	1	2	yes	complemented
10	#17989643	C₂²	1	2	yes	—
11	C₂×#14556665	—	2	1	no	—
12	C₂×#14556664	C₄	1	2	yes	complemented
13	C₂×#14556662	—	2	1	no	—
14	D₇₃⋊#108	—	2	1	no	—
15	D₇₃⋊#108	—	2	1	no	—
16	D₇₃⋊#108	C₄	1	2	yes	complemented
17	D₇₃⋊#108	C₂²	1	2	yes	—
18	C₂×#14556661	C₄	1	2	yes	complemented
19	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×D₇₃	—	2	1	no	—
21	C₂×#14556523	C₄	1	1	yes	characteristic
22	C₂×#14556522	—	2	1	no	—
23	#106×D₇₃	—	2	1	no	—
24	#106×D₇₃	—	2	1	no	—
25	#106×D₇₃	C₄	1	2	yes	—
26	#106×D₇₃	C₂²	1	2	yes	—
27	C₂×#106×C₇₃	C₄	1	1	yes	characteristic
28	C₂×#11924038	—	2	2	no	—
29	D₇₃⋊M₁₆	—	2	2	no	—
30	D₇₃⋊M₁₆	—	2	2	no	—
31	D₇₃⋊M₁₆	—	4	1	no	—
32	D₇₃⋊M₁₆	—	4	1	no	—
33	C₂×#11924037	—	4	1	no	—
34	C₂×#11924036	—	4	1	no	—
35	#14556666	—	2	2	no	—
36	#14556666	—	2	2	no	—
37	#14556665	—	2	2	no	—
38	#14556665	—	2	2	no	—
39	#14556664	—	2	2	no	—
40	#14556664	C₂×C₄	1	4	yes	complemented
41	C₂×#11924031	—	2	2	no	—
42	#14556662	—	2	2	no	—
43	#14556662	—	2	2	no	—
44	#14556661	—	2	2	no	—
45	#14556661	C₂×C₄	1	4	yes	complemented
46	C₂²×C₄×D₇₃	—	4	1	no	—
47	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
48	C₂²×#10596831	D₄	1	1	yes	characteristic
49	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
55	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
56	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
57	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
58	C₂×C₈×D₇₃	Q₈	1	1	yes	characteristic
59	C₂×C₈×D₇₃	Q₈	1	1	yes	characteristic
60	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊Dic₇₃	—	2	1	no	—
62	C₂×#11924007	—	4	1	no	—
63	C₄⋊C₄×D₇₃	—	2	2	no	—
64	C₄⋊C₄×D₇₃	—	2	2	no	—
65	C₄⋊C₄×D₇₃	—	4	1	no	—
66	C₄⋊C₄×D₇₃	—	4	1	no	—
67	#14556523	—	2	1	no	—
68	#14556523	C₂×C₄	1	2	yes	—
69	#14556522	—	2	2	no	—
70	#14556522	—	2	2	no	—
71	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
73	#106×C₇₃	—	2	1	no	—
74	#106×C₇₃	C₂×C₄	1	2	yes	—
75	#11924038	—	2	4	no	—
76	#11924038	—	4	2	no	—
77	#11924037	—	4	2	no	—
78	#11924037	—	4	2	no	—
79	#11924036	—	4	2	no	—
80	#11924036	—	4	2	no	—
81	C₂×#10596833	—	4	2	no	—
82	#11924031	—	2	4	no	—
83	C₂³×D₇₃	SD₁₆	1	1	yes	characteristic
84	C₂²×Dic₇₃	—	4	1	no	—
85	C₂²×Dic₇₃	D₈	1	1	yes	characteristic
86	C₂×C₄×D₇₃	—	4	2	no	—
87	C₂×C₄×D₇₃	—	4	2	no	—
88	C₂×C₄×D₇₃	—	8	4	no	—
89	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₇₃	D₈	1	1	yes	characteristic
95	C₂×C₄×D₇₃	SD₁₆	1	1	yes	characteristic
96	C₂×C₄×D₇₃	SD₁₆	1	1	yes	characteristic
97	C₂×C₄×D₇₃	SD₁₆	1	1	yes	characteristic
98	C₂×C₄×D₇₃	Q₁₆	1	1	yes	characteristic
99	C₂×C₄×D₇₃	Q₁₆	1	1	yes	characteristic
100	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
101	C₂×#10596831	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×#10596831	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×#10596831	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×#10596831	C₄⋊C₄	1	1	yes	characteristic
105	C₂×#10596831	C₄⋊C₄	1	1	yes	characteristic
106	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
107	C₈×D₇₃	C₄²	1	1	yes	characteristic
108	C₈×D₇₃	C₄²	1	1	yes	characteristic
109	C₈×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₈×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
111	C₈×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₈×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
114	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
115	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
116	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
117	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
118	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
119	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
120	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
121	C₈×D₇₃	C₂×D₄	1	1	yes	characteristic
122	C₈×D₇₃	C₂×Q₈	1	1	yes	characteristic
123	C₄⋊Dic₇₃	—	2	2	no	—
124	C₄⋊Dic₇₃	—	4	1	no	—
125	#11924007	—	4	2	no	—
126	#11924007	—	4	2	no	—
127	C₂²×C₄×C₇₃	—	4	1	no	—
128	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
130	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
131	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
135	C₄⋊C₄×C₇₃	—	2	2	no	—
136	C₄⋊C₄×C₇₃	—	4	1	no	—
137	C₂³×C₇₃	#102	1	1	yes	characteristic
138	C₂²×D₇₃	—	2	4	no	—
139	C₂²×D₇₃	#102	1	1	yes	characteristic
140	C₂²×D₇₃	#103	1	1	yes	characteristic
141	C₂²×D₇₃	#103	1	1	yes	characteristic
142	C₂²×D₇₃	#106	1	1	yes	characteristic
143	C₂²×D₇₃	#106	1	1	yes	characteristic
144	C₂²×D₇₃	C₂×SD₁₆	1	1	yes	characteristic
145	C₂×C₄×C₇₃	—	4	2	no	—
146	C₂×C₄×C₇₃	—	8	2	no	—
147	C₂×C₄×C₇₃	#95	1	1	yes	characteristic
148	C₂×C₄×C₇₃	#95	1	1	yes	characteristic
149	C₂×C₄×C₇₃	#102	1	1	yes	characteristic
150	C₂×C₄×C₇₃	#103	1	1	yes	characteristic
151	C₂×C₄×C₇₃	#103	1	1	yes	characteristic
152	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×Dic₇₃	—	4	2	no	—
154	C₂×Dic₇₃	—	8	2	no	—
155	C₂×Dic₇₃	#102	1	1	yes	characteristic
156	C₂×Dic₇₃	#102	1	1	yes	characteristic
157	C₂×Dic₇₃	#102	1	1	yes	characteristic
158	C₂×Dic₇₃	#107	1	1	yes	characteristic
159	C₂×Dic₇₃	#107	1	1	yes	characteristic
160	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
161	C₄×D₇₃	—	8	4	no	—
162	C₄×D₇₃	—	8	4	no	—
163	C₄×D₇₃	#95	1	1	yes	characteristic
164	C₄×D₇₃	#95	1	1	yes	characteristic
165	C₄×D₇₃	#102	1	1	yes	characteristic
166	C₄×D₇₃	#102	1	1	yes	characteristic
167	C₄×D₇₃	#103	1	1	yes	characteristic
168	C₄×D₇₃	#103	1	1	yes	characteristic
169	C₄×D₇₃	#103	1	1	yes	characteristic
170	C₄×D₇₃	#103	1	1	yes	characteristic
171	C₄×D₇₃	#106	1	1	yes	characteristic
172	C₄×D₇₃	#106	1	1	yes	characteristic
173	C₄×D₇₃	#107	1	1	yes	characteristic
174	C₄×D₇₃	#107	1	1	yes	characteristic
175	C₄×D₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₄×D₇₃	C₂×SD₁₆	1	1	yes	characteristic
178	C₄×D₇₃	C₂×Q₁₆	1	1	yes	characteristic
179	#10596833	—	4	4	no	—
180	C₈×C₇₃	#95	1	1	yes	characteristic
181	C₈×C₇₃	#95	1	1	yes	characteristic
182	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
183	C₈×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	#10596831	#95	1	1	yes	characteristic
185	#10596831	#95	1	1	yes	characteristic
186	#10596831	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	#10596831	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂²×C₇₃	—	2	2	no	—
189	C₂²×C₇₃	#340	1	1	yes	characteristic
190	C₂²×C₇₃	#340	1	1	yes	characteristic
191	C₂²×C₇₃	C₂×#102	1	1	yes	characteristic
192	C₂×D₇₃	—	2	2	no	—
193	C₂×D₇₃	—	2	2	no	—
194	C₂×D₇₃	—	2	2	no	—
195	C₂×D₇₃	—	2	2	no	—
196	C₂×D₇₃	—	2	2	no	—
197	C₂×D₇₃	#340	1	1	yes	characteristic
198	C₂×D₇₃	#340	1	1	yes	characteristic
199	C₂×D₇₃	#365	1	4	yes	—
200	C₂×D₇₃	C₂×#103	1	1	yes	characteristic
201	C₂×D₇₃	C₂×#106	1	1	yes	characteristic
202	C₄×C₇₃	—	8	2	no	—
203	C₄×C₇₃	#340	1	1	yes	characteristic
204	C₄×C₇₃	#340	1	1	yes	characteristic
205	C₄×C₇₃	C₂×#95	1	1	yes	characteristic
206	C₄×C₇₃	C₂×#103	1	1	yes	characteristic
207	Dic₇₃	—	8	2	no	—
208	Dic₇₃	#340	1	1	yes	characteristic
209	Dic₇₃	#340	1	1	yes	characteristic
210	Dic₇₃	C₂×#102	1	1	yes	characteristic
211	Dic₇₃	C₂×#107	1	1	yes	characteristic
212	C₂×#1383	—	73	1	no	maximal, Sylow
213	C₂×C₇₃	—	2	1	no	—
214	C₂×C₇₃	—	2	1	no	—
215	C₂×C₇₃	#1383	1	2	yes	complemented
216	C₂×C₇₃	C₂×#340	1	1	yes	characteristic
217	D₇₃	—	2	1	no	—
218	D₇₃	—	2	1	no	—
219	D₇₃	#1383	1	2	yes	complemented
220	D₇₃	C₂×#365	1	2	yes	—
221	C₂²×M₃₂	—	73	1	no	—
222	C₂²×#108	—	73	1	no	—
223	C₂²×#106	—	73	1	no	—
224	#1383	—	73	4	no	—
225	C₇₃	C₂×#1383	1	1	yes	characteristic, complemented, Sylow
226	C₂²×M₁₆	—	146	1	no	—
227	C₂³×C₈	—	73	1	no	—
228	C₂²×C₄⋊C₄	—	146	1	no	—
229	C₂×M₃₂	—	73	2	no	—
230	C₂×M₃₂	—	73	2	no	—
231	C₂×M₃₂	—	146	1	no	—
232	C₂×M₃₂	—	146	1	no	—
233	C₂×M₃₂	—	146	1	no	—
234	C₂×M₃₂	—	146	1	no	—
235	C₂²×C₁₆	—	73	2	no	—
236	C₂×#108	—	73	2	no	—
237	C₂×#108	—	73	2	no	—
238	C₂×#108	—	73	2	no	—
239	C₂×#108	—	146	1	no	—
240	C₂×#108	—	146	1	no	—
241	C₂×#108	—	146	1	no	—
242	C₂×#106	—	73	1	no	—
243	C₂×#106	—	73	2	no	—
244	C₂×#106	—	73	2	no	—
245	C₂×#106	—	146	1	no	—
246	C₂×#106	—	146	1	no	—
247	C₂×#106	—	146	1	no	—
248	C₂×#106	#64408	1	1	yes	characteristic
249	C₂³×C₄	—	292	1	no	—
250	C₂³×C₄	—	73	1	no	—
251	C₂×M₁₆	—	292	1	no	—
252	C₂×M₁₆	—	292	1	no	—
253	C₂×M₁₆	—	292	1	no	—
254	C₂×M₁₆	—	146	2	no	—
255	C₂×M₁₆	—	146	2	no	—
256	C₂×M₁₆	—	146	2	no	—
257	C₂²×C₈	—	292	1	no	—
258	C₂²×C₈	—	73	1	no	—
259	C₂²×C₈	—	73	1	no	—
260	C₂²×C₈	—	73	1	no	—
261	C₂²×C₈	—	73	1	no	—
262	C₂²×C₈	—	73	1	no	—
263	C₂²×C₈	—	73	1	no	—
264	C₂²×C₈	—	73	1	no	—
265	C₂²×C₈	—	73	1	no	—
266	C₂²×C₈	—	73	1	no	—
267	C₂²×C₈	—	73	1	no	—
268	C₂²×C₈	—	73	1	no	—
269	C₂²×C₈	—	73	1	no	—
270	C₂²×C₈	—	73	1	no	—
271	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	292	1	no	—
274	C₂×C₄⋊C₄	—	292	1	no	—
275	C₂×C₄⋊C₄	—	292	1	no	—
276	C₂×C₄⋊C₄	—	146	2	no	—
277	C₂×C₄⋊C₄	—	146	2	no	—
278	C₂×C₄⋊C₄	—	146	1	no	—
279	M₃₂	—	146	2	no	—
280	M₃₂	—	146	2	no	—
281	M₃₂	—	146	2	no	—
282	M₃₂	—	146	2	no	—
283	C₂×C₁₆	—	73	4	no	—
284	C₂×C₁₆	—	146	2	no	—
285	C₂×C₁₆	—	146	2	no	—
286	#108	—	73	4	no	—
287	#108	—	146	2	no	—
288	#108	—	146	2	no	—
289	#108	—	146	2	no	—
290	#106	—	2	1	no	—
291	#106	—	73	2	no	—
292	#106	—	146	2	no	—
293	#106	—	146	2	no	—
294	#106	—	146	1	no	—
295	#106	C₂×#64408	1	2	yes	—
296	C₂⁴	—	73	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	292	2	no	—
299	C₂²×C₄	—	292	2	no	—
300	C₂²×C₄	—	292	1	no	—
301	C₂²×C₄	—	584	4	no	—
302	C₂²×C₄	—	73	1	no	—
303	C₂²×C₄	—	73	1	no	—
304	C₂²×C₄	—	73	1	no	—
305	C₂²×C₄	—	73	1	no	—
306	C₂²×C₄	—	73	1	no	—
307	C₂²×C₄	—	73	1	no	—
308	C₂²×C₄	—	73	1	no	—
309	C₂²×C₄	—	73	1	no	—
310	C₂²×C₄	—	73	1	no	—
311	C₂²×C₄	—	73	1	no	—
312	C₂²×C₄	—	73	1	no	—
313	C₂²×C₄	—	73	1	no	—
314	C₂²×C₄	—	73	1	no	—
315	C₂²×C₄	C₂²⋊#64408	1	1	yes	characteristic
316	M₁₆	—	292	2	no	—
317	M₁₆	—	292	2	no	—
318	M₁₆	—	292	2	no	—
319	M₁₆	—	146	4	no	—
320	C₂×C₈	—	292	2	no	—
321	C₂×C₈	—	292	2	no	—
322	C₂×C₈	—	292	2	no	—
323	C₂×C₈	—	73	1	no	—
324	C₂×C₈	—	73	1	no	—
325	C₂×C₈	—	73	1	no	—
326	C₂×C₈	—	73	1	no	—
327	C₂×C₈	—	73	1	no	—
328	C₂×C₈	—	73	1	no	—
329	C₂×C₈	—	73	1	no	—
330	C₂×C₈	—	73	1	no	—
331	C₂×C₈	—	73	1	no	—
332	C₂×C₈	—	73	1	no	—
333	C₂×C₈	—	73	1	no	—
334	C₂×C₈	—	73	1	no	—
335	C₂×C₈	—	73	1	no	—
336	C₂×C₈	—	73	1	no	—
337	C₂×C₈	—	73	1	no	—
338	C₂×C₈	—	73	1	no	—
339	C₂×C₈	—	73	1	no	—
340	C₂×C₈	—	73	1	no	—
341	C₂×C₈	—	73	1	no	—
342	C₂×C₈	—	73	1	no	—
343	C₂×C₈	—	73	1	no	—
344	C₂×C₈	—	73	1	no	—
345	C₂×C₈	C₄×#64408	1	1	yes	characteristic
346	C₂×C₈	C₄×#64408	1	1	yes	characteristic
347	C₂×C₈	C₂²⋊#64408	1	1	yes	characteristic
348	C₂×C₈	C₄⋊#64408	1	1	yes	characteristic
349	C₂×C₈	C₄⋊#64408	1	1	yes	characteristic
350	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	292	2	no	—
354	C₄⋊C₄	—	292	2	no	—
355	C₄⋊C₄	—	292	1	no	—
356	C₄⋊C₄	—	146	2	no	—
357	C₁₆	—	146	4	no	—
358	C₂³	—	73	1	no	—
359	C₂³	—	73	1	no	—
360	C₂³	—	73	1	no	—
361	C₂³	—	73	1	no	—
362	C₂³	—	73	1	no	—
363	C₂³	—	73	1	no	—
364	C₂³	—	146	4	no	—
365	C₂³	#14556653	1	1	yes	characteristic
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	8	2	no	—
368	C₂×C₄	—	292	2	no	—
369	C₂×C₄	—	584	4	no	—
370	C₂×C₄	—	584	4	no	—
371	C₂×C₄	—	584	2	no	—
372	C₂×C₄	—	73	1	no	—
373	C₂×C₄	—	73	1	no	—
374	C₂×C₄	—	73	1	no	—
375	C₂×C₄	—	73	1	no	—
376	C₂×C₄	—	73	1	no	—
377	C₂×C₄	—	73	1	no	—
378	C₂×C₄	—	73	1	no	—
379	C₂×C₄	—	73	1	no	—
380	C₂×C₄	—	73	1	no	—
381	C₂×C₄	—	73	1	no	—
382	C₂×C₄	—	73	1	no	—
383	C₂×C₄	—	73	1	no	—
384	C₂×C₄	—	73	1	no	—
385	C₂×C₄	—	73	1	no	—
386	C₂×C₄	—	73	1	no	—
387	C₂×C₄	—	73	1	no	—
388	C₂×C₄	—	73	1	no	—
389	C₂×C₄	—	73	1	no	—
390	C₂×C₄	—	73	1	no	—
391	C₂×C₄	—	73	1	no	—
392	C₂×C₄	—	73	1	no	—
393	C₂×C₄	—	73	1	no	—
394	C₂×C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
395	C₂×C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
396	C₂×C₄	#14556653	1	1	yes	characteristic
397	C₂×C₄	#14556654	1	1	yes	characteristic
398	C₂×C₄	#14556654	1	1	yes	characteristic
399	C₂×C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
400	C₈	—	292	4	no	—
401	C₈	—	73	1	no	—
402	C₈	—	73	1	no	—
403	C₈	—	73	1	no	—
404	C₈	—	73	1	no	—
405	C₈	(C₂×#64408)⋊C₄	1	1	yes	characteristic
406	C₈	(C₂×#64408)⋊C₄	1	1	yes	characteristic
407	C₈	C₂×C₄×#64408	1	1	yes	characteristic
408	C₈	C₂×C₄⋊#64408	1	1	yes	characteristic
409	C₂²	—	2	2	no	—
410	C₂²	—	73	1	no	—
411	C₂²	—	73	1	no	—
412	C₂²	—	73	4	no	—
413	C₂²	—	73	1	no	—
414	C₂²	—	73	1	no	—
415	C₂²	—	146	2	no	—
416	C₂²	—	146	2	no	—
417	C₂²	—	146	2	no	—
418	C₂²	—	146	2	no	—
419	C₂²	—	146	2	no	—
420	C₂²	#17989460	1	1	yes	characteristic
421	C₂²	#17989460	1	1	yes	characteristic
422	C₂²	C₂×#14556653	1	1	yes	characteristic
423	C₄	—	8	2	no	—
424	C₄	—	584	2	no	—
425	C₄	—	73	1	no	—
426	C₄	—	73	1	no	—
427	C₄	—	73	1	no	—
428	C₄	—	73	1	no	—
429	C₄	#17989460	1	1	yes	characteristic
430	C₄	#17989460	1	1	yes	characteristic
431	C₄	C₂×(C₂×#64408)⋊C₄	1	1	yes	characteristic
432	C₄	C₂×#14556654	1	1	yes	characteristic
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	73	2	no	—
436	C₂	—	73	2	no	—
437	C₂	—	146	1	no	—
438	C₂	—	146	1	no	—
439	C₂	#22624995	1	2	yes	direct product factor
440	C₂	C₂×#17989460	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#17989460
commutator	C₈×C₇₃	C₂×C₄²
Frattini	C₂×C₈	C₂²×#64408
Fitting	C₂×#106×C₇₃	C₄
socle	C₂²×C₇₃	#340
prime radical	C₂³×D₇₃	SD₁₆
cosocle	C₂×C₈×D₇₃	C₂³
hypercenter	C₂×#106	#64408
hypocenter	C₇₃	C₂×#1383
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#106

Complements

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

N	H ≅ G/N	type
3. #22624995	C₂	direct (N × H)
9. #17989643	C₄	semidirect
12. C₂×#14556664	C₄	semidirect
16. D₇₃⋊#108	C₄	semidirect
18. C₂×#14556661	C₄	semidirect
40. #14556664	C₂×C₄	semidirect
45. #14556661	C₂×C₄	semidirect
215. C₂×C₇₃	#1383	semidirect
219. D₇₃	#1383	semidirect
225. C₇₃	C₂×#1383	semidirect
439. C₂	#22624995	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#17989643	2
C₂×D₇₃⋊#108	2
#22624995	2
C₂×#106×D₇₃	2
C₂×#1383	73

Subgroups — C2×#22624995 #34012180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22624995 #34012180