Subgroups — #34002103

Order 18688.

666 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989603	C₂	1	1	yes	maximal, characteristic
2	C₂×#17989603	C₂	1	1	yes	maximal, characteristic
3	#22624764	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
5	#17989603	—	2	1	no	—
6	#17989603	—	2	1	no	—
7	#17989603	—	2	1	no	—
8	#17989603	—	2	1	no	—
9	#17989603	C₄	1	2	yes	—
10	#17989603	C₄	1	2	yes	—
11	#17989603	C₄	1	2	yes	—
12	#17989603	C₂²	1	2	yes	—
13	C₂×C₄⋊#10596833	—	2	1	no	—
14	C₂×C₄⋊#10596833	C₄	1	2	yes	—
15	C₂×C₂²⋊#10596833	—	2	1	no	—
16	C₂×C₂²⋊#10596833	—	2	1	no	—
17	C₂×C₄×#10596833	—	2	1	no	—
18	C₂×C₄×#10596833	C₂²	1	2	yes	—
19	C₂²×#11924012	C₄	1	1	yes	characteristic
20	C₂²×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
21	M₁₆×Dic₇₃	—	2	1	no	—
22	M₁₆×Dic₇₃	—	2	1	no	—
23	M₁₆×Dic₇₃	C₄	1	2	yes	—
24	M₁₆×Dic₇₃	C₂²	1	2	yes	—
25	C₂×#14556501	—	2	1	no	—
26	C₂×C₈×Dic₇₃	—	2	1	no	—
27	C₂²×M₁₆×C₇₃	C₄	1	1	yes	characteristic
28	C₂²×#10596833	—	2	2	no	—
29	C₂²×#10596833	—	2	2	no	—
30	C₄⋊#10596833	—	2	2	no	—
31	C₄⋊#10596833	—	2	2	no	—
32	C₄⋊#10596833	—	2	2	no	—
33	C₄⋊#10596833	C₂×C₄	1	4	yes	—
34	C₂²⋊#10596833	—	2	2	no	—
35	C₂²⋊#10596833	—	2	2	no	—
36	C₂²⋊#10596833	—	2	2	no	—
37	C₂²⋊#10596833	—	2	2	no	—
38	C₄×#10596833	—	2	2	no	—
39	C₄×#10596833	—	2	2	no	—
40	C₄×#10596833	—	2	2	no	—
41	C₄×#10596833	C₂×C₄	1	4	yes	—
42	C₂³×Dic₇₃	D₄	1	1	yes	characteristic
43	C₂³×Dic₇₃	Q₈	1	1	yes	characteristic
44	C₂×#11924012	—	2	1	no	—
45	C₂×#11924012	—	2	2	no	—
46	C₂×#11924012	C₈	1	4	yes	complemented
47	C₂×#11924012	C₂×C₄	1	2	yes	—
48	C₂²×#10596831	—	2	1	no	—
49	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
57	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
58	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
59	C₂×C₄×Dic₇₃	Q₈	1	1	yes	characteristic
60	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
61	#14556501	—	2	2	no	—
62	#14556501	—	2	2	no	—
63	C₈×Dic₇₃	—	2	2	no	—
64	C₈×Dic₇₃	—	2	2	no	—
65	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
66	C₂×M₁₆×C₇₃	—	2	1	no	—
67	C₂×M₁₆×C₇₃	—	2	2	no	—
68	C₂×M₁₆×C₇₃	C₈	1	4	yes	complemented
69	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₇₃	—	2	1	no	—
71	C₂×#10596833	—	2	4	no	—
72	C₂×#10596833	—	2	4	no	—
73	C₂×#10596833	—	4	4	no	—
74	C₂×#10596833	—	4	4	no	—
75	C₂²×Dic₇₃	—	4	2	no	—
76	C₂²×Dic₇₃	—	4	2	no	—
77	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
89	#11924012	—	2	4	no	—
90	#11924012	—	2	2	no	—
91	#11924012	C₂×C₈	1	4	yes	complemented
92	C₂×#10596831	—	2	4	no	—
93	C₂×#10596831	—	2	2	no	—
94	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
95	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
96	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
97	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
103	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
104	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
105	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
106	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
107	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
109	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
110	C₂⁴×C₇₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
112	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
113	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₃	C₂×C₈	1	2	yes	—
117	C₂²×C₄×C₇₃	C₂×C₈	1	2	yes	—
118	C₂²×C₄×C₇₃	M₁₆	1	2	yes	—
119	C₂²×C₄×C₇₃	M₁₆	1	2	yes	—
120	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
121	M₁₆×C₇₃	—	2	4	no	—
122	M₁₆×C₇₃	—	2	2	no	—
123	M₁₆×C₇₃	C₂×C₈	1	4	yes	complemented
124	C₂×C₈×C₇₃	—	2	4	no	—
125	C₂×C₈×C₇₃	—	2	2	no	—
126	C₂³×C₇₃	—	4	1	no	—
127	C₂³×C₇₃	—	4	1	no	—
128	C₂³×C₇₃	#95	1	1	yes	characteristic
129	C₂³×C₇₃	#95	1	1	yes	characteristic
130	C₂³×C₇₃	C₄⋊C₈	1	2	yes	—
131	C₂³×C₇₃	C₄⋊C₈	1	2	yes	—
132	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₇₃	#95	1	1	yes	characteristic
134	C₂×C₄×C₇₃	#95	1	1	yes	characteristic
135	C₂×C₄×C₇₃	C₄×C₈	1	2	yes	—
136	C₂×C₄×C₇₃	C₄×C₈	1	2	yes	—
137	C₂×C₄×C₇₃	#97	1	2	yes	—
138	C₂×C₄×C₇₃	#97	1	2	yes	—
139	C₂×C₄×C₇₃	C₂²⋊C₈	1	2	yes	—
140	C₂×C₄×C₇₃	C₂²⋊C₈	1	2	yes	—
141	C₂×C₄×C₇₃	C₂²⋊C₈	1	2	yes	—
142	C₂×C₄×C₇₃	C₂²⋊C₈	1	2	yes	—
143	C₂×C₄×C₇₃	C₄⋊C₈	1	2	yes	—
144	C₂×C₄×C₇₃	C₄⋊C₈	1	2	yes	—
145	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
146	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
148	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
149	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
150	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
151	C₂×Dic₇₃	—	2	2	no	—
152	C₂×Dic₇₃	—	2	2	no	—
153	C₂×Dic₇₃	—	2	2	no	—
154	C₂×Dic₇₃	—	2	2	no	—
155	C₂×Dic₇₃	—	2	2	no	—
156	C₂×Dic₇₃	—	2	2	no	—
157	C₂×Dic₇₃	—	4	1	no	—
158	C₂×Dic₇₃	—	4	1	no	—
159	C₂×Dic₇₃	—	4	1	no	—
160	C₂×Dic₇₃	—	4	1	no	—
161	C₂×Dic₇₃	—	4	1	no	—
162	C₂×Dic₇₃	—	4	1	no	—
163	C₂×Dic₇₃	#95	1	1	yes	characteristic
164	C₂×Dic₇₃	#95	1	1	yes	characteristic
165	C₂×Dic₇₃	#95	1	1	yes	characteristic
166	C₂×Dic₇₃	#95	1	1	yes	characteristic
167	C₂×Dic₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×Dic₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	#10596833	—	4	4	no	—
172	#10596833	—	4	4	no	—
173	C₈×C₇₃	—	2	4	no	—
174	#10596831	—	2	4	no	—
175	C₂²×C₇₃	—	2	1	no	—
176	C₂²×C₇₃	—	2	1	no	—
177	C₂²×C₇₃	—	2	1	no	—
178	C₂²×C₇₃	—	2	1	no	—
179	C₂²×C₇₃	—	2	1	no	—
180	C₂²×C₇₃	—	2	1	no	—
181	C₂²×C₇₃	—	4	2	no	—
182	C₂²×C₇₃	—	4	2	no	—
183	C₂²×C₇₃	#336	1	2	yes	—
184	C₂²×C₇₃	#336	1	2	yes	—
185	C₂²×C₇₃	C₂×#95	1	1	yes	characteristic
186	C₂²×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
187	C₂²×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
188	C₄×C₇₃	#336	1	2	yes	—
189	C₄×C₇₃	#336	1	2	yes	—
190	C₄×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
191	C₄×C₇₃	C₂×#97	1	1	yes	characteristic
192	C₄×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
193	C₄×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
194	Dic₇₃	—	2	1	no	—
195	Dic₇₃	—	2	1	no	—
196	Dic₇₃	—	2	1	no	—
197	Dic₇₃	—	2	1	no	—
198	Dic₇₃	—	2	1	no	—
199	Dic₇₃	—	2	1	no	—
200	Dic₇₃	#421	1	2	yes	—
201	Dic₇₃	#430	1	2	yes	—
202	#7882	—	73	1	no	maximal, Sylow
203	C₂×C₇₃	—	2	2	no	—
204	C₂×C₇₃	—	2	2	no	—
205	C₂×C₇₃	—	2	1	no	—
206	C₂×C₇₃	—	2	1	no	—
207	C₂×C₇₃	C₂×#336	1	1	yes	characteristic
208	C₂×C₇₃	#1733	1	1	yes	characteristic
209	C₂×C₇₃	#1738	1	1	yes	characteristic
210	C₂×#431	—	73	1	no	—
211	C₂×#431	—	73	1	no	—
212	C₂×C₄×M₁₆	—	73	1	no	—
213	#1278	—	73	4	no	—
214	C₇₃	#7882	1	1	yes	characteristic, complemented, Sylow
215	C₂²×M₁₆	—	73	1	no	—
216	C₂²×M₁₆	#64408	1	1	yes	characteristic
217	C₂²×C₄²	—	73	1	no	—
218	#431	—	73	2	no	—
219	#431	—	73	2	no	—
220	#431	—	73	2	no	—
221	#431	—	73	2	no	—
222	#431	—	146	1	no	—
223	#431	—	146	1	no	—
224	#431	—	146	1	no	—
225	#431	—	146	1	no	—
226	C₂×C₄⋊C₈	—	73	2	no	—
227	C₂×C₄⋊C₈	—	146	1	no	—
228	C₂×C₂²⋊C₈	—	146	1	no	—
229	C₂×C₂²⋊C₈	—	146	1	no	—
230	C₄×M₁₆	—	73	2	no	—
231	C₄×M₁₆	—	73	2	no	—
232	C₄×M₁₆	—	146	1	no	—
233	C₄×M₁₆	—	146	1	no	—
234	C₂×#97	—	146	1	no	—
235	C₂×C₄×C₈	—	73	2	no	—
236	C₂×C₄×C₈	—	146	1	no	—
237	C₂×C₄×C₈	—	146	1	no	—
238	C₂³×C₄	—	73	1	no	—
239	C₂³×C₄	—	73	1	no	—
240	C₂³×C₄	C₂×#64408	1	1	yes	characteristic
241	C₂×M₁₆	—	2	1	no	—
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	73	4	no	—
244	C₂×M₁₆	—	73	2	no	—
245	C₂×M₁₆	—	146	1	no	—
246	C₂×M₁₆	—	146	2	no	—
247	C₂×M₁₆	#10596833	1	4	yes	complemented
248	C₂×M₁₆	C₂×#64408	1	2	yes	—
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	—	146	2	no	—
251	C₂²×C₈	—	146	2	no	—
252	C₂²×C₈	—	146	1	no	—
253	C₂×C₄²	—	73	1	no	—
254	C₂×C₄²	—	73	1	no	—
255	C₂×C₄²	—	73	1	no	—
256	C₂×C₄²	—	73	1	no	—
257	C₂×C₄²	—	73	1	no	—
258	C₂×C₄²	—	73	1	no	—
259	C₂×C₄²	—	73	1	no	—
260	C₂×C₄²	—	73	1	no	—
261	C₂×C₄²	—	73	1	no	—
262	C₂×C₄²	—	73	1	no	—
263	C₂×C₄²	—	73	1	no	—
264	C₂×C₄²	—	73	1	no	—
265	C₄⋊C₈	—	73	4	no	—
266	C₄⋊C₈	—	146	2	no	—
267	C₄⋊C₈	—	146	2	no	—
268	C₄⋊C₈	—	146	2	no	—
269	C₂²⋊C₈	—	146	2	no	—
270	C₂²⋊C₈	—	146	2	no	—
271	C₂²⋊C₈	—	146	2	no	—
272	C₂²⋊C₈	—	146	2	no	—
273	#97	—	146	2	no	—
274	#97	—	146	2	no	—
275	C₄×C₈	—	73	4	no	—
276	C₄×C₈	—	146	2	no	—
277	C₄×C₈	—	146	2	no	—
278	C₄×C₈	—	146	2	no	—
279	C₄×C₈	—	146	2	no	—
280	C₄×C₈	—	146	2	no	—
281	C₂⁴	C₄⋊#64408	1	1	yes	characteristic
282	C₂²×C₄	—	292	2	no	—
283	C₂²×C₄	—	292	2	no	—
284	C₂²×C₄	—	73	1	no	—
285	C₂²×C₄	—	73	1	no	—
286	C₂²×C₄	—	73	1	no	—
287	C₂²×C₄	—	73	1	no	—
288	C₂²×C₄	—	73	1	no	—
289	C₂²×C₄	—	73	1	no	—
290	C₂²×C₄	—	73	1	no	—
291	C₂²×C₄	—	73	1	no	—
292	C₂²×C₄	—	73	1	no	—
293	C₂²×C₄	—	73	1	no	—
294	C₂²×C₄	—	73	1	no	—
295	C₂²×C₄	—	73	1	no	—
296	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
297	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
298	C₂²×C₄	C₂²⋊#64408	1	1	yes	characteristic
299	C₂²×C₄	C₂²⋊#64408	1	1	yes	characteristic
300	C₂²×C₄	C₄⋊#64408	1	1	yes	characteristic
301	C₂²×C₄	C₂×#10596833	1	2	yes	—
302	C₂²×C₄	#11924036	1	2	yes	—
303	C₂²×C₄	#11924037	1	2	yes	—
304	C₂²×C₄	#11924038	1	2	yes	—
305	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
306	M₁₆	—	2	2	no	—
307	M₁₆	—	2	4	no	—
308	M₁₆	—	73	4	no	—
309	M₁₆	—	146	2	no	—
310	M₁₆	—	146	4	no	—
311	M₁₆	C₂×#10596833	1	4	yes	complemented
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	292	4	no	—
315	C₂×C₈	—	292	4	no	—
316	C₂×C₈	—	146	4	no	—
317	C₂×C₈	—	146	4	no	—
318	C₂×C₈	—	146	4	no	—
319	C₂×C₈	—	146	2	no	—
320	C₄²	—	73	1	no	—
321	C₄²	—	73	1	no	—
322	C₄²	—	73	1	no	—
323	C₄²	—	73	1	no	—
324	C₄²	—	73	1	no	—
325	C₄²	—	73	1	no	—
326	C₄²	—	73	1	no	—
327	C₄²	—	73	1	no	—
328	C₄²	—	73	1	no	—
329	C₄²	—	73	1	no	—
330	C₄²	—	73	1	no	—
331	C₄²	—	73	1	no	—
332	C₄²	—	73	1	no	—
333	C₄²	—	73	1	no	—
334	C₄²	—	73	1	no	—
335	C₄²	—	73	1	no	—
336	C₂³	—	4	1	no	—
337	C₂³	—	4	1	no	—
338	C₂³	(C₂×#64408)⋊C₄	1	1	yes	characteristic
339	C₂³	(C₂×#64408)⋊C₄	1	1	yes	characteristic
340	C₂³	C₄⋊#10596833	1	2	yes	—
341	C₂³	#14556658	1	2	yes	—
342	C₂³	C₂×C₄⋊#64408	1	1	yes	characteristic
343	C₂×C₄	—	292	1	no	—
344	C₂×C₄	—	292	1	no	—
345	C₂×C₄	—	292	1	no	—
346	C₂×C₄	—	292	1	no	—
347	C₂×C₄	—	292	1	no	—
348	C₂×C₄	—	292	1	no	—
349	C₂×C₄	—	73	1	no	—
350	C₂×C₄	—	73	1	no	—
351	C₂×C₄	—	73	1	no	—
352	C₂×C₄	—	73	1	no	—
353	C₂×C₄	—	73	1	no	—
354	C₂×C₄	—	73	1	no	—
355	C₂×C₄	—	73	1	no	—
356	C₂×C₄	—	73	1	no	—
357	C₂×C₄	—	146	2	no	—
358	C₂×C₄	—	146	2	no	—
359	C₂×C₄	—	146	2	no	—
360	C₂×C₄	—	146	2	no	—
361	C₂×C₄	—	146	2	no	—
362	C₂×C₄	—	146	2	no	—
363	C₂×C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
364	C₂×C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
365	C₂×C₄	C₄×#10596833	1	2	yes	—
366	C₂×C₄	C₄×#10596833	1	2	yes	—
367	C₂×C₄	#14556646	1	2	yes	—
368	C₂×C₄	#14556646	1	2	yes	—
369	C₂×C₄	C₂²⋊#10596833	1	2	yes	—
370	C₂×C₄	C₂²⋊#10596833	1	2	yes	—
371	C₂×C₄	#14556648	1	2	yes	—
372	C₂×C₄	#14556648	1	2	yes	—
373	C₂×C₄	C₄⋊#10596833	1	2	yes	—
374	C₂×C₄	#14556658	1	2	yes	—
375	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
376	C₂×C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
377	C₂×C₄	C₂²×#10596833	1	1	yes	characteristic
378	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
379	C₂×C₄	C₂×#11924037	1	1	yes	characteristic
380	C₂×C₄	C₂×#11924038	1	1	yes	characteristic
381	C₈	—	2	4	no	—
382	C₈	—	292	4	no	—
383	C₈	—	292	4	no	—
384	C₈	—	146	4	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	#17989453	1	2	yes	—
394	C₂²	#17989453	1	2	yes	—
395	C₂²	C₂×(C₂×#64408)⋊C₄	1	1	yes	characteristic
396	C₂²	C₂×C₄⋊#10596833	1	1	yes	characteristic
397	C₂²	C₂×#14556658	1	1	yes	characteristic
398	C₄	—	73	2	no	—
399	C₄	—	73	2	no	—
400	C₄	—	146	1	no	—
401	C₄	—	146	1	no	—
402	C₄	—	146	1	no	—
403	C₄	—	146	1	no	—
404	C₄	—	146	1	no	—
405	C₄	—	146	1	no	—
406	C₄	#17989453	1	2	yes	—
407	C₄	#17989453	1	2	yes	—
408	C₄	C₂×C₄×#10596833	1	1	yes	characteristic
409	C₄	C₂×#14556646	1	1	yes	characteristic
410	C₄	C₂×C₂²⋊#10596833	1	1	yes	characteristic
411	C₄	C₂×#14556648	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	—	2	1	no	—
415	C₂	—	2	1	no	—
416	C₂	C₂×#17989453	1	1	yes	characteristic
417	C₂	#22625613	1	1	yes	characteristic
418	C₂	#22625624	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊#64408
commutator	C₄×C₇₃	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×#64408
Fitting	C₂²×M₁₆×C₇₃	C₄
socle	C₂²×C₇₃	C₂×#95
prime radical	C₂⁴×C₇₃	C₄⋊C₄
cosocle	C₂×C₄×Dic₇₃	C₂³
hypercenter	C₂²×M₁₆	#64408
hypocenter	C₇₃	#7882
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×M₁₆

Complements

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

N	H ≅ G/N	type
3. #22624764	C₂	semidirect
46. C₂×#11924012	C₈	semidirect
68. C₂×M₁₆×C₇₃	C₈	semidirect
91. #11924012	C₂×C₈	semidirect
123. M₁₆×C₇₃	C₂×C₈	semidirect
214. C₇₃	#7882	semidirect
247. C₂×M₁₆	#10596833	semidirect
311. M₁₆	C₂×#10596833	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989603	2
#22624764	2
C₂×M₁₆×Dic₇₃	2
#7882	73