Subgroups — #34021341

Order 18688.

1070 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989598	C₂	1	2	yes	maximal
2	C₂×#17989597	C₂	1	1	yes	maximal, characteristic
3	C₂²×#14556660	C₂	1	1	yes	maximal, characteristic
4	#22626412	C₂	1	2	yes	maximal
5	#22625869	C₂	1	4	yes	maximal, complemented
6	#22625868	C₂	1	2	yes	maximal, complemented
7	#22625867	C₂	1	2	yes	maximal, complemented
8	#405×D₇₃	C₂	1	1	yes	maximal, characteristic
9	C₂×#14556670	C₂²	1	2	yes	—
10	C₂²×C₄⋊#64408	C₂²	1	2	yes	—
11	#17989598	—	2	8	no	—
12	#17989597	—	2	4	no	—
13	C₂×#14556660	—	2	4	no	—
14	C₂×#14556660	C₂²	1	2	yes	—
15	C₂×#14556660	C₂²	1	2	yes	—
16	C₂×#14556660	C₂²	1	1	yes	characteristic
17	C₂×#14556660	C₂²	1	1	yes	characteristic
18	C₂×#14556660	C₂²	1	4	yes	—
19	C₂×#14556659	C₂²	1	2	yes	—
20	C₂×#14556659	C₂²	1	4	yes	—
21	#17989538	—	2	4	no	—
22	#17989534	—	2	4	no	—
23	#17989533	C₂²	1	4	yes	—
24	#17989531	C₂²	1	4	yes	—
25	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
26	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
27	#117×D₇₃	C₂²	1	1	yes	characteristic
28	#17988545	C₄	1	1	yes	characteristic, complemented
29	#17988544	C₄	1	2	yes	complemented
30	#17988543	C₄	1	1	yes	characteristic, complemented
31	#17988542	C₄	1	1	yes	characteristic, complemented
32	#17988541	C₄	1	2	yes	complemented
33	#97×D₇₃	C₂²	1	2	yes	—
34	C₄×C₈×D₇₃	C₂²	1	2	yes	—
35	#405×C₇₃	C₄	1	1	yes	characteristic, complemented
36	C₂³×#64408	—	2	2	no	—
37	#14556670	—	2	4	no	—
38	#14556670	—	2	4	no	—
39	C₂×C₄⋊#64408	—	2	4	no	—
40	C₂×C₄⋊#64408	—	2	4	no	—
41	C₂×C₄⋊#64408	—	2	2	no	—
42	C₂×C₄⋊#64408	—	2	8	no	—
43	C₂×C₄⋊#64408	C₂³	1	4	yes	—
44	C₂×C₄⋊#64408	C₂³	1	2	yes	—
45	C₂×C₄⋊#64408	C₂³	1	2	yes	—
46	C₂×C₂²⋊#64408	—	2	2	no	—
47	C₂×C₄×#64408	—	2	2	no	—
48	#14556660	—	2	4	no	—
49	#14556660	—	2	4	no	—
50	#14556660	—	2	2	no	—
51	#14556660	—	2	2	no	—
52	#14556660	—	2	8	no	—
53	#14556659	—	2	4	no	—
54	#14556659	—	2	8	no	—
55	(C₂×#64408)⋊C₄	—	2	8	no	—
56	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
57	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
58	C₂×#11924011	C₂×C₄	1	2	yes	—
59	M₁₆×D₇₃	D₄	1	4	yes	—
60	M₁₆×D₇₃	Q₈	1	4	yes	—
61	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₇₃	D₄	1	4	yes	—
65	C₂×C₈×D₇₃	Q₈	1	4	yes	—
66	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₇₃	C₂³	1	2	yes	—
68	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
69	#14556550	C₂×C₄	1	1	yes	characteristic
70	#14556549	Q₈	1	2	yes	—
71	#14556548	C₂×C₄	1	2	yes	—
72	#14556547	Q₈	1	2	yes	—
73	C₄⋊C₄×D₇₃	D₄	1	2	yes	—
74	C₂²⋊C₄×D₇₃	D₄	1	2	yes	—
75	C₄²×D₇₃	C₂³	1	2	yes	—
76	#14556502	C₂×C₄	1	2	yes	complemented
77	#14556501	C₂×C₄	1	2	yes	complemented
78	#14556501	C₂×C₄	1	2	yes	complemented
79	C₄×#10596831	C₂×C₄	1	2	yes	complemented
80	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
81	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
82	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
84	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
85	#97×C₇₃	C₂×C₄	1	2	yes	complemented
86	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
87	C₂²×#64408	—	2	4	no	—
88	C₂²×#64408	—	2	2	no	—
89	C₂²×#64408	—	2	2	no	—
90	C₂²×#64408	—	4	4	no	—
91	C₂²×#64408	—	8	4	no	—
92	C₄⋊#64408	—	2	2	no	—
93	C₄⋊#64408	—	2	4	no	—
94	C₄⋊#64408	—	2	2	no	—
95	C₄⋊#64408	—	2	2	no	—
96	C₄⋊#64408	—	2	4	no	—
97	C₄⋊#64408	—	2	2	no	—
98	C₄⋊#64408	—	4	4	no	—
99	C₄⋊#64408	—	8	8	no	—
100	C₂²⋊#64408	—	4	4	no	—
101	C₄×#64408	—	4	4	no	—
102	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₇₃	C₂×D₄	1	4	yes	—
106	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
107	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
108	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
110	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
111	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
112	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
113	#11924012	C₄⋊C₄	1	4	yes	complemented
114	#11924011	C₄⋊C₄	1	8	yes	complemented
115	C₂×#10596831	C₄⋊C₄	1	4	yes	complemented
116	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
117	C₂×#10596831	C₂²×C₄	1	2	yes	—
118	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
119	C₈×D₇₃	C₄⋊C₄	1	4	yes	complemented
120	C₈×D₇₃	C₄⋊C₄	1	4	yes	complemented
121	C₈×D₇₃	C₂×D₄	1	2	yes	—
122	C₈×D₇₃	C₂×D₄	1	2	yes	—
123	C₈×D₇₃	C₂×D₄	1	4	yes	—
124	C₈×D₇₃	C₂×Q₈	1	2	yes	—
125	C₈×D₇₃	C₂×Q₈	1	2	yes	—
126	C₈×D₇₃	C₂×Q₈	1	4	yes	—
127	C₄⋊Dic₇₃	C₄⋊C₄	1	2	yes	—
128	#11924007	C₄⋊C₄	1	4	yes	—
129	C₂²⋊Dic₇₃	C₄⋊C₄	1	2	yes	—
130	#11924005	C₄⋊C₄	1	4	yes	—
131	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
132	C₄×Dic₇₃	C₂×Q₈	1	4	yes	—
133	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
134	M₁₆×C₇₃	C₄⋊C₄	1	4	yes	complemented
135	C₂×C₈×C₇₃	C₄⋊C₄	1	4	yes	complemented
136	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
139	C₄⋊C₄×C₇₃	C₄⋊C₄	1	2	yes	—
140	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	2	yes	—
141	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
142	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂²×D₇₃	—	2	2	no	—
144	C₂²×D₇₃	—	2	2	no	—
145	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂²×D₇₃	#127	1	2	yes	—
147	C₂²×D₇₃	C₄⋊Q₈	1	2	yes	—
148	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
149	C₂×#64408	—	4	2	no	—
150	C₂×#64408	—	4	2	no	—
151	C₂×#64408	—	4	4	no	—
152	C₂×#64408	—	4	4	no	—
153	C₂×#64408	—	4	8	no	—
154	C₂×#64408	—	4	4	no	—
155	C₂×#64408	—	8	8	no	—
156	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	4	yes	—
157	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×Dic₇₃	C₂×C₄⋊C₄	1	4	yes	—
162	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×Dic₇₃	C₄⋊Q₈	1	2	yes	—
164	C₂×Dic₇₃	C₄⋊Q₈	1	2	yes	—
165	C₂×Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
166	C₄×D₇₃	—	2	4	no	—
167	C₄×D₇₃	—	2	4	no	—
168	C₄×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
169	C₄×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
170	C₄×D₇₃	#127	1	2	yes	—
171	C₄×D₇₃	C₄⋊Q₈	1	2	yes	—
172	C₄×D₇₃	C₄⋊Q₈	1	2	yes	—
173	C₄×D₇₃	C₄⋊Q₈	1	2	yes	—
174	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
175	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
176	C₄×D₇₃	C₂²×Q₈	1	1	yes	characteristic
177	C₄×D₇₃	C₂²×Q₈	1	1	yes	characteristic
178	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
179	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
180	C₈×C₇₃	C₂×C₄⋊C₄	1	4	yes	—
181	#10596831	C₂×C₄⋊C₄	1	2	yes	—
182	#10596831	C₂×C₄⋊C₄	1	2	yes	—
183	#10596831	C₂×C₄⋊C₄	1	4	yes	—
184	C₂²×C₇₃	—	2	2	no	—
185	C₂²×C₇₃	#384	1	2	yes	—
186	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
187	C₂×D₇₃	—	2	2	no	—
188	C₂×D₇₃	—	2	2	no	—
189	C₂×D₇₃	—	2	2	no	—
190	C₂×D₇₃	—	2	4	no	—
191	C₂×D₇₃	#384	1	2	yes	—
192	C₂×D₇₃	C₂×#127	1	1	yes	characteristic
193	C₂×D₇₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
194	C₂×D₇₃	#576	1	2	yes	—
195	C₂×D₇₃	#578	1	2	yes	—
196	#64408	—	8	2	no	—
197	#64408	—	8	4	no	—
198	#64408	—	8	2	no	—
199	C₄×C₇₃	—	2	4	no	—
200	C₄×C₇₃	#384	1	2	yes	—
201	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
202	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
203	Dic₇₃	—	2	4	no	—
204	Dic₇₃	#384	1	2	yes	—
205	Dic₇₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
206	Dic₇₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
207	#20803	—	73	1	no	maximal, Sylow
208	C₂×C₇₃	—	2	2	no	—
209	C₂×C₇₃	C₂×#384	1	1	yes	characteristic
210	C₂×C₇₃	#2913	1	2	yes	—
211	D₇₃	—	2	2	no	—
212	D₇₃	#3155	1	1	yes	characteristic
213	D₇₃	#3156	1	1	yes	characteristic
214	D₇₃	#3164	1	2	yes	—
215	C₂×#428	—	73	2	no	—
216	C₂×#427	—	73	1	no	—
217	C₂²×#107	—	73	1	no	—
218	C₂×#405	—	73	1	no	—
219	#2317	—	73	2	no	—
220	#1847	—	73	4	no	—
221	#1846	—	73	2	no	—
222	#1845	—	73	2	no	—
223	C₇₃	#20803	1	1	yes	characteristic, complemented, Sylow
224	C₂²×M₁₆	—	73	1	no	—
225	C₂³×C₈	—	73	1	no	—
226	C₂×#117	—	73	1	no	—
227	C₂×#117	—	73	2	no	—
228	C₂²×C₄⋊C₄	—	73	2	no	—
229	#428	—	146	8	no	—
230	#427	—	146	4	no	—
231	C₂×#107	—	73	1	no	—
232	C₂×#107	—	73	2	no	—
233	C₂×#107	—	73	4	no	—
234	C₂×#107	—	73	1	no	—
235	C₂×#107	—	73	2	no	—
236	C₂×#107	—	146	4	no	—
237	C₂×#106	—	73	4	no	—
238	C₂×#106	—	73	2	no	—
239	#405	—	73	1	no	—
240	#405	—	73	1	no	—
241	#405	—	73	1	no	—
242	#405	—	73	2	no	—
243	#405	—	73	2	no	—
244	#405	#64408	1	1	yes	characteristic, complemented
245	C₂×#97	—	73	2	no	—
246	C₂×C₄×C₈	—	73	2	no	—
247	#389	—	146	4	no	—
248	#385	—	146	4	no	—
249	#384	—	73	4	no	—
250	#382	—	73	4	no	—
251	C₂³×C₄	—	73	1	no	—
252	C₂³×C₄	—	146	2	no	—
253	C₂×M₁₆	—	73	1	no	—
254	C₂×M₁₆	—	73	4	no	—
255	C₂×M₁₆	—	73	4	no	—
256	C₂×M₁₆	—	73	2	no	—
257	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
258	C₂²×C₈	—	73	1	no	—
259	C₂²×C₈	—	73	4	no	—
260	C₂²×C₈	—	73	4	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	2	no	—
266	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
267	#117	—	73	1	no	—
268	#117	—	73	2	no	—
269	#117	—	73	2	no	—
270	#117	—	73	2	no	—
271	#117	—	146	4	no	—
272	#117	—	146	4	no	—
273	#117	C₂×#64408	1	1	yes	characteristic
274	C₂×C₄⋊C₄	—	73	2	no	—
275	C₂×C₄⋊C₄	—	73	4	no	—
276	C₂×C₄⋊C₄	—	73	2	no	—
277	C₂×C₄⋊C₄	—	73	2	no	—
278	C₂×C₄⋊C₄	—	146	2	no	—
279	C₂×C₄⋊C₄	—	146	4	no	—
280	C₂×C₄⋊C₄	—	146	4	no	—
281	C₂×C₄⋊C₄	—	146	8	no	—
282	C₂×C₂²⋊C₄	—	73	2	no	—
283	C₂×C₂²⋊C₄	—	146	2	no	—
284	C₂×C₄²	—	73	2	no	—
285	C₂×C₄²	—	146	2	no	—
286	#107	—	146	4	no	—
287	#107	—	146	4	no	—
288	#107	—	146	2	no	—
289	#107	—	146	2	no	—
290	#107	—	146	8	no	—
291	#106	—	146	4	no	—
292	#106	—	146	8	no	—
293	#97	—	73	2	no	—
294	#97	—	73	2	no	—
295	#97	—	73	2	no	—
296	#97	C₂×#64408	1	2	yes	complemented
297	C₄×C₈	—	73	2	no	—
298	C₄×C₈	—	73	2	no	—
299	C₄×C₈	—	73	2	no	—
300	C₄×C₈	C₂×#64408	1	2	yes	complemented
301	#95	—	146	8	no	—
302	C₂⁴	—	73	1	no	—
303	C₂²×C₄	—	292	4	no	—
304	C₂²×C₄	—	584	4	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	2	no	—
310	C₂²×C₄	—	73	2	no	—
311	C₂²×C₄	—	73	1	no	—
312	C₂²×C₄	—	73	2	no	—
313	C₂²×C₄	—	73	2	no	—
314	C₂²×C₄	—	73	4	no	—
315	C₂²×C₄	—	146	2	no	—
316	C₂²×C₄	—	146	4	no	—
317	C₂²×C₄	—	146	2	no	—
318	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
319	M₁₆	—	73	4	no	—
320	M₁₆	—	73	8	no	—
321	M₁₆	C₄⋊#64408	1	4	yes	complemented
322	C₂×C₈	—	73	1	no	—
323	C₂×C₈	—	73	2	no	—
324	C₂×C₈	—	73	1	no	—
325	C₂×C₈	—	73	4	no	—
326	C₂×C₈	—	73	4	no	—
327	C₂×C₈	—	73	4	no	—
328	C₂×C₈	—	73	2	no	—
329	C₂×C₈	—	73	4	no	—
330	C₂×C₈	—	73	2	no	—
331	C₂×C₈	—	73	2	no	—
332	C₂×C₈	—	73	2	no	—
333	C₂×C₈	—	73	4	no	—
334	C₂×C₈	C₄⋊#64408	1	4	yes	complemented
335	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
336	C₂×C₈	C₂²×#64408	1	2	yes	—
337	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
338	C₄⋊C₄	—	292	4	no	—
339	C₄⋊C₄	—	584	8	no	—
340	C₄⋊C₄	—	73	4	no	—
341	C₄⋊C₄	—	73	2	no	—
342	C₄⋊C₄	—	146	2	no	—
343	C₄⋊C₄	—	146	4	no	—
344	C₄⋊C₄	—	146	2	no	—
345	C₄⋊C₄	—	146	2	no	—
346	C₄⋊C₄	—	146	4	no	—
347	C₄⋊C₄	—	146	2	no	—
348	C₄⋊C₄	C₄⋊#64408	1	2	yes	—
349	C₂²⋊C₄	—	292	4	no	—
350	C₂²⋊C₄	—	73	2	no	—
351	C₂²⋊C₄	—	73	4	no	—
352	C₂²⋊C₄	C₄⋊#64408	1	2	yes	—
353	C₄²	—	292	4	no	—
354	C₄²	—	73	2	no	—
355	C₄²	—	73	4	no	—
356	C₄²	C₂²×#64408	1	2	yes	—
357	C₂³	—	73	1	no	—
358	C₂³	—	73	1	no	—
359	C₂³	—	73	2	no	—
360	C₂³	—	73	2	no	—
361	C₂³	—	146	2	no	—
362	C₂³	—	146	2	no	—
363	C₂³	C₂×C₄⋊#64408	1	1	yes	characteristic
364	C₂×C₄	—	292	2	no	—
365	C₂×C₄	—	292	2	no	—
366	C₂×C₄	—	292	4	no	—
367	C₂×C₄	—	292	4	no	—
368	C₂×C₄	—	292	8	no	—
369	C₂×C₄	—	292	4	no	—
370	C₂×C₄	—	584	8	no	—
371	C₂×C₄	—	73	1	no	—
372	C₂×C₄	—	73	1	no	—
373	C₂×C₄	—	73	2	no	—
374	C₂×C₄	—	73	2	no	—
375	C₂×C₄	—	73	1	no	—
376	C₂×C₄	—	73	1	no	—
377	C₂×C₄	—	73	2	no	—
378	C₂×C₄	—	73	1	no	—
379	C₂×C₄	—	73	1	no	—
380	C₂×C₄	—	73	2	no	—
381	C₂×C₄	—	73	2	no	—
382	C₂×C₄	—	73	2	no	—
383	C₂×C₄	—	73	2	no	—
384	C₂×C₄	—	73	2	no	—
385	C₂×C₄	—	73	4	no	—
386	C₂×C₄	—	146	4	no	—
387	C₂×C₄	—	146	4	no	—
388	C₂×C₄	C₂×C₄⋊#64408	1	4	yes	—
389	C₂×C₄	C₂×C₄⋊#64408	1	2	yes	—
390	C₂×C₄	C₂×C₄⋊#64408	1	2	yes	—
391	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
392	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
393	C₈	—	73	2	no	—
394	C₈	—	73	2	no	—
395	C₈	—	73	4	no	—
396	C₈	C₂×C₄⋊#64408	1	2	yes	—
397	C₈	C₂×C₄⋊#64408	1	2	yes	—
398	C₈	C₂×C₄⋊#64408	1	4	yes	—
399	C₂²	—	2	2	no	—
400	C₂²	—	73	2	no	—
401	C₂²	—	73	2	no	—
402	C₂²	—	73	1	no	—
403	C₂²	—	73	1	no	—
404	C₂²	—	73	2	no	—
405	C₂²	—	146	2	no	—
406	C₂²	—	146	2	no	—
407	C₂²	—	146	4	no	—
408	C₂²	—	146	2	no	—
409	C₂²	#17989533	1	2	yes	—
410	C₂²	C₂²×C₄⋊#64408	1	1	yes	characteristic
411	C₄	—	2	4	no	—
412	C₄	—	584	4	no	—
413	C₄	—	584	2	no	—
414	C₄	—	584	2	no	—
415	C₄	—	73	1	no	—
416	C₄	—	73	1	no	—
417	C₄	—	73	2	no	—
418	C₄	—	146	4	no	—
419	C₄	#17989533	1	2	yes	—
420	C₄	C₂²×C₄⋊#64408	1	1	yes	characteristic
421	C₄	C₂²×C₄⋊#64408	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	73	1	no	—
424	C₂	—	73	1	no	—
425	C₂	—	73	2	no	—
426	C₂	—	146	2	no	—
427	C₂	C₂×#17989533	1	1	yes	characteristic
428	C₂	#22626586	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#64408
Fitting	#405×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₇₃	C₂×D₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#405	#64408
hypocenter	C₇₃	#20803
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
5. #22625869	C₂	semidirect
6. #22625868	C₂	semidirect
7. #22625867	C₂	semidirect
28. #17988545	C₄	semidirect
29. #17988544	C₄	semidirect
30. #17988543	C₄	semidirect
31. #17988542	C₄	semidirect
32. #17988541	C₄	semidirect
35. #405×C₇₃	C₄	semidirect
76. #14556502	C₂×C₄	semidirect
77. #14556501	C₂×C₄	semidirect
78. #14556501	C₂×C₄	semidirect
79. C₄×#10596831	C₂×C₄	semidirect
80. C₈×Dic₇₃	C₂×C₄	semidirect
81. C₈×Dic₇₃	C₂×C₄	semidirect
85. #97×C₇₃	C₂×C₄	semidirect
86. C₄×C₈×C₇₃	C₂×C₄	semidirect
113. #11924012	C₄⋊C₄	semidirect
114. #11924011	C₄⋊C₄	semidirect
115. C₂×#10596831	C₄⋊C₄	semidirect
119. C₈×D₇₃	C₄⋊C₄	semidirect
120. C₈×D₇₃	C₄⋊C₄	semidirect
134. M₁₆×C₇₃	C₄⋊C₄	semidirect
135. C₂×C₈×C₇₃	C₄⋊C₄	semidirect
223. C₇₃	#20803	semidirect
244. #405	#64408	semidirect
296. #97	C₂×#64408	semidirect
300. C₄×C₈	C₂×#64408	semidirect
321. M₁₆	C₄⋊#64408	semidirect
334. C₂×C₈	C₄⋊#64408	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989598	2
C₂×#17989597	2
C₂²×#14556660	2
#22626412	2
#22625869	2
#22625868	2
#22625867	2
#405×D₇₃	2
#20803	73