Subgroups — #34034070

Order 18688.

586 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989706	C₂	1	1	yes	maximal, characteristic
2	C₂×#17989706	C₂	1	1	yes	maximal, characteristic
3	#22627012	C₂	1	4	yes	maximal, complemented
4	C₂×#17989553	C₂	1	1	yes	maximal, characteristic
5	C₂×#14556688	—	2	1	no	—
6	C₂×#14556688	C₄	1	2	yes	complemented
7	#17989706	—	2	1	no	—
8	#17989706	—	2	1	no	—
9	#17989706	—	2	1	no	—
10	#17989706	—	2	1	no	—
11	#17989706	C₄	1	2	yes	complemented
12	#17989706	C₄	1	2	yes	complemented
13	#17989706	C₄	1	2	yes	complemented
14	#17989706	C₂²	1	2	yes	—
15	C₂×#14556687	—	2	1	no	—
16	C₂×#14556687	—	2	1	no	—
17	C₂×#14556686	—	2	1	no	—
18	C₂×#14556686	C₂²	1	2	yes	—
19	C₂²×#11924036	C₂²	1	1	yes	characteristic
20	C₂×#14556670	C₄	1	1	yes	characteristic
21	#17989553	—	2	1	no	—
22	#17989553	—	2	1	no	—
23	#17989553	C₄	1	2	yes	—
24	#17989553	C₂²	1	2	yes	—
25	C₂×#14556645	—	2	1	no	—
26	C₂×C₈×#64408	—	2	1	no	—
27	C₂×M₁₆×D₇₃	C₄	1	1	yes	characteristic
28	#14556688	—	2	2	no	—
29	#14556688	—	2	2	no	—
30	#14556688	—	2	2	no	—
31	#14556688	C₂×C₄	1	4	yes	complemented
32	#14556687	—	2	2	no	—
33	#14556687	—	2	2	no	—
34	#14556687	—	2	2	no	—
35	#14556687	—	2	2	no	—
36	#14556686	—	2	2	no	—
37	#14556686	—	2	2	no	—
38	#14556686	—	2	2	no	—
39	#14556686	C₂×C₄	1	4	yes	complemented
40	C₂×#11924040	—	2	2	no	—
41	C₂×#11924040	—	2	2	no	—
42	C₂×#11924036	C₂×C₄	1	1	yes	characteristic
43	C₂×#11924036	C₂×C₄	1	1	yes	characteristic
44	C₂×#11924036	C₂×C₄	1	1	yes	characteristic
45	C₂×#11924036	C₂×C₄	1	1	yes	characteristic
46	C₂×#11924036	C₂×C₄	1	1	yes	characteristic
47	C₂×#11924036	D₄	1	1	yes	characteristic
48	C₂×#11924036	D₄	1	1	yes	characteristic
49	C₂×#11924036	D₄	1	1	yes	characteristic
50	C₂×#11924036	D₄	1	1	yes	characteristic
51	C₂×#11924036	D₄	1	1	yes	characteristic
52	C₂×#11924036	Q₈	1	1	yes	characteristic
53	C₂×#11924036	C₂³	1	1	yes	characteristic
54	C₂²×#10596833	D₄	1	1	yes	characteristic
55	C₂²×#10596833	Q₈	1	1	yes	characteristic
56	#14556670	—	2	1	no	—
57	#14556670	—	2	1	no	—
58	#14556670	C₈	1	2	yes	—
59	#14556670	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊#64408	C₈	1	2	yes	—
61	C₂×C₂²⋊#64408	—	2	1	no	—
62	C₂×C₄×#64408	—	2	1	no	—
63	#14556645	—	2	2	no	—
64	#14556645	—	2	2	no	—
65	C₈×#64408	—	2	2	no	—
66	C₈×#64408	—	2	2	no	—
67	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
68	C₂×#11924012	C₈	1	1	yes	characteristic
69	C₂×#11924011	—	2	1	no	—
70	M₁₆×D₇₃	—	2	1	no	—
71	M₁₆×D₇₃	—	2	1	no	—
72	M₁₆×D₇₃	C₈	1	2	yes	—
73	M₁₆×D₇₃	C₂×C₄	1	2	yes	—
74	C₂×C₈×D₇₃	—	2	1	no	—
75	C₂×M₁₆×C₇₃	C₈	1	1	yes	characteristic
76	#11924040	—	2	4	no	—
77	#11924040	—	2	4	no	—
78	C₂²×#64408	—	2	2	no	—
79	#11924036	C₄²	1	1	yes	characteristic
80	#11924036	C₄²	1	1	yes	characteristic
81	#11924036	C₂²⋊C₄	1	1	yes	characteristic
82	#11924036	C₂²⋊C₄	1	1	yes	characteristic
83	#11924036	C₂²⋊C₄	1	1	yes	characteristic
84	#11924036	C₂²⋊C₄	1	1	yes	characteristic
85	#11924036	C₂²⋊C₄	1	1	yes	characteristic
86	#11924036	C₂²⋊C₄	1	1	yes	characteristic
87	#11924036	C₄⋊C₄	1	1	yes	characteristic
88	#11924036	C₄⋊C₄	1	1	yes	characteristic
89	#11924036	C₄⋊C₄	1	1	yes	characteristic
90	#11924036	C₄⋊C₄	1	1	yes	characteristic
91	#11924036	C₂²×C₄	1	1	yes	characteristic
92	#11924036	C₂²×C₄	1	1	yes	characteristic
93	#11924036	C₂×D₄	1	1	yes	characteristic
94	#11924036	C₂×D₄	1	1	yes	characteristic
95	C₂×#10596833	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×#10596833	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×#10596833	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×#10596833	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×#10596833	C₄⋊C₄	1	1	yes	characteristic
100	C₂×#10596833	C₄⋊C₄	1	1	yes	characteristic
101	C₂×#10596833	C₄⋊C₄	1	1	yes	characteristic
102	C₂×#10596833	C₄⋊C₄	1	1	yes	characteristic
103	C₂×#10596833	C₄⋊C₄	1	1	yes	characteristic
104	C₂×#10596833	C₄⋊C₄	1	1	yes	characteristic
105	C₂×#10596833	C₂×D₄	1	1	yes	characteristic
106	C₂×#10596833	C₂×Q₈	1	1	yes	characteristic
107	C₄⋊#64408	—	2	2	no	—
108	C₄⋊#64408	C₂×C₈	1	4	yes	—
109	C₂²⋊#64408	—	2	2	no	—
110	C₂²⋊#64408	—	2	2	no	—
111	C₄×#64408	—	2	2	no	—
112	C₄×#64408	—	2	2	no	—
113	C₂³×D₇₃	M₁₆	1	1	yes	characteristic
114	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
116	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
117	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
121	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
122	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
123	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
124	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
125	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
126	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
127	#11924012	—	2	1	no	—
128	#11924012	C₂×C₈	1	2	yes	—
129	#11924011	—	2	2	no	—
130	#11924011	—	2	2	no	—
131	C₂×#10596831	—	2	1	no	—
132	C₈×D₇₃	—	2	2	no	—
133	C₈×D₇₃	—	2	2	no	—
134	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
135	M₁₆×C₇₃	—	2	1	no	—
136	M₁₆×C₇₃	C₂×C₈	1	2	yes	—
137	C₂×C₈×C₇₃	—	2	1	no	—
138	C₂³×C₇₃	C₄⋊C₈	1	1	yes	characteristic
139	C₂²×D₇₃	—	4	2	no	—
140	C₂²×D₇₃	#97	1	1	yes	characteristic
141	C₂²×D₇₃	#97	1	1	yes	characteristic
142	C₂²×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
143	C₂²×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
144	C₂²×D₇₃	C₄⋊C₈	1	1	yes	characteristic
145	C₂²×D₇₃	C₂×M₁₆	1	1	yes	characteristic
146	C₂×#64408	—	2	4	no	—
147	C₂×#64408	—	4	4	no	—
148	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
149	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
150	C₂×C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
151	C₂×C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
152	C₂×C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
153	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
154	C₂×Dic₇₃	#95	1	1	yes	characteristic
155	C₂×Dic₇₃	#95	1	1	yes	characteristic
156	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
157	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
158	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
159	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₄×D₇₃	#95	1	1	yes	characteristic
161	C₄×D₇₃	#95	1	1	yes	characteristic
162	C₄×D₇₃	C₄×C₈	1	1	yes	characteristic
163	C₄×D₇₃	C₄×C₈	1	1	yes	characteristic
164	C₄×D₇₃	#97	1	1	yes	characteristic
165	C₄×D₇₃	#97	1	1	yes	characteristic
166	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
167	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
168	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
169	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
170	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
171	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
172	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
173	C₄×D₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
175	C₄×D₇₃	C₂×M₁₆	1	1	yes	characteristic
176	#10596833	#95	1	1	yes	characteristic
177	#10596833	#95	1	1	yes	characteristic
178	#10596833	#95	1	1	yes	characteristic
179	#10596833	#95	1	1	yes	characteristic
180	#10596833	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	#10596833	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	#10596833	C₂×C₄⋊C₄	1	1	yes	characteristic
183	#10596833	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₈×C₇₃	—	2	2	no	—
185	#10596831	—	2	2	no	—
186	C₂²×C₇₃	—	4	1	no	—
187	C₂²×C₇₃	#336	1	1	yes	characteristic
188	C₂²×C₇₃	#336	1	1	yes	characteristic
189	C₂²×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
190	C₂×D₇₃	—	2	2	no	—
191	C₂×D₇₃	—	2	2	no	—
192	C₂×D₇₃	—	2	2	no	—
193	C₂×D₇₃	—	4	1	no	—
194	C₂×D₇₃	—	4	1	no	—
195	C₂×D₇₃	—	4	1	no	—
196	C₂×D₇₃	#336	1	1	yes	characteristic
197	C₂×D₇₃	#336	1	1	yes	characteristic
198	C₂×D₇₃	C₂×#97	1	1	yes	characteristic
199	C₂×D₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
200	#64408	—	4	4	no	—
201	C₄×C₇₃	#336	1	1	yes	characteristic
202	C₄×C₇₃	#336	1	1	yes	characteristic
203	C₄×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
204	C₄×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
205	Dic₇₃	#336	1	1	yes	characteristic
206	Dic₇₃	#336	1	1	yes	characteristic
207	Dic₇₃	C₂×#95	1	1	yes	characteristic
208	Dic₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
209	#12554	—	73	1	no	maximal, Sylow
210	C₂×C₇₃	—	2	1	no	—
211	C₂×C₇₃	—	2	1	no	—
212	C₂×C₇₃	—	2	1	no	—
213	C₂×C₇₃	C₂×#336	1	1	yes	characteristic
214	D₇₃	—	2	1	no	—
215	D₇₃	—	2	1	no	—
216	D₇₃	—	2	1	no	—
217	D₇₃	#2117	1	2	yes	—
218	C₂²×M₃₂	—	73	1	no	—
219	C₂²×M₃₂	—	73	1	no	—
220	C₂×#405	—	73	1	no	—
221	#1379	—	73	4	no	—
222	C₇₃	#12554	1	1	yes	characteristic, complemented, Sylow
223	C₂²×M₁₆	—	73	1	no	—
224	C₂³×C₈	—	73	1	no	—
225	C₂×#117	—	73	1	no	—
226	C₂×M₃₂	—	73	2	no	—
227	C₂×M₃₂	—	73	2	no	—
228	C₂×M₃₂	—	73	2	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	C₂×M₃₂	—	146	1	no	—
236	C₂×M₃₂	—	146	1	no	—
237	C₂×M₃₂	—	146	1	no	—
238	C₂²×C₁₆	—	73	2	no	—
239	C₂²×C₁₆	—	146	1	no	—
240	#405	—	73	2	no	—
241	#405	—	73	2	no	—
242	#405	—	146	1	no	—
243	#405	—	146	1	no	—
244	C₂×#97	—	146	1	no	—
245	C₂×C₄×C₈	—	146	1	no	—
246	C₂³×C₄	—	73	1	no	—
247	C₂×M₁₆	—	73	1	no	—
248	C₂×M₁₆	—	73	2	no	—
249	C₂×M₁₆	—	73	2	no	—
250	C₂×M₁₆	—	146	1	no	—
251	C₂×M₁₆	—	146	1	no	—
252	C₂×M₁₆	—	146	1	no	—
253	C₂×M₁₆	#10596842	1	1	yes	characteristic
254	C₂²×C₈	—	73	1	no	—
255	C₂²×C₈	—	73	1	no	—
256	C₂²×C₈	—	73	1	no	—
257	C₂²×C₈	—	73	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	—	146	1	no	—
269	#117	—	73	2	no	—
270	#117	—	73	2	no	—
271	#117	—	146	1	no	—
272	#117	—	146	1	no	—
273	C₂×C₄⋊C₄	—	73	2	no	—
274	C₂×C₂²⋊C₄	—	146	1	no	—
275	C₂×C₄²	—	146	1	no	—
276	M₃₂	—	73	4	no	—
277	M₃₂	—	146	2	no	—
278	M₃₂	—	146	2	no	—
279	M₃₂	—	146	2	no	—
280	M₃₂	—	146	2	no	—
281	M₃₂	—	146	2	no	—
282	M₃₂	—	146	2	no	—
283	M₃₂	—	146	2	no	—
284	C₂×C₁₆	—	73	4	no	—
285	C₂×C₁₆	—	146	2	no	—
286	C₂×C₁₆	—	146	2	no	—
287	C₂×C₁₆	—	146	2	no	—
288	C₂×C₁₆	—	146	2	no	—
289	C₂×C₁₆	—	146	2	no	—
290	#97	—	146	2	no	—
291	#97	—	146	2	no	—
292	C₄×C₈	—	146	2	no	—
293	C₄×C₈	—	146	2	no	—
294	C₂⁴	—	73	1	no	—
295	C₂²×C₄	—	73	1	no	—
296	C₂²×C₄	—	73	1	no	—
297	C₂²×C₄	—	73	1	no	—
298	C₂²×C₄	—	73	1	no	—
299	C₂²×C₄	—	73	1	no	—
300	C₂²×C₄	—	73	1	no	—
301	C₂²×C₄	—	73	1	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	—	146	2	no	—
309	C₂²×C₄	C₂×#10596842	1	1	yes	characteristic
310	M₁₆	—	2	1	no	—
311	M₁₆	—	73	2	no	—
312	M₁₆	—	146	2	no	—
313	M₁₆	—	146	2	no	—
314	M₁₆	—	146	1	no	—
315	M₁₆	C₂×#10596842	1	2	yes	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	73	1	no	—
318	C₂×C₈	—	73	1	no	—
319	C₂×C₈	—	73	1	no	—
320	C₂×C₈	—	73	1	no	—
321	C₂×C₈	—	73	1	no	—
322	C₂×C₈	—	73	1	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	—	146	2	no	—
346	C₂×C₈	—	146	2	no	—
347	C₂×C₈	—	146	1	no	—
348	C₄⋊C₄	—	73	4	no	—
349	C₄⋊C₄	—	146	2	no	—
350	C₂²⋊C₄	—	146	2	no	—
351	C₂²⋊C₄	—	146	2	no	—
352	C₄²	—	146	2	no	—
353	C₄²	—	146	2	no	—
354	C₁₆	—	146	4	no	—
355	C₁₆	—	146	4	no	—
356	C₂³	—	292	2	no	—
357	C₂³	—	73	1	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	C₄⋊#10596842	1	1	yes	characteristic
364	C₂×C₄	—	292	4	no	—
365	C₂×C₄	—	73	1	no	—
366	C₂×C₄	—	73	1	no	—
367	C₂×C₄	—	73	1	no	—
368	C₂×C₄	—	73	1	no	—
369	C₂×C₄	—	73	1	no	—
370	C₂×C₄	—	73	1	no	—
371	C₂×C₄	—	73	1	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	—	146	4	no	—
388	C₂×C₄	C₄×#10596842	1	1	yes	characteristic
389	C₂×C₄	C₄×#10596842	1	1	yes	characteristic
390	C₂×C₄	C₂²⋊#10596842	1	1	yes	characteristic
391	C₂×C₄	C₂²⋊#10596842	1	1	yes	characteristic
392	C₂×C₄	C₄⋊#10596842	1	1	yes	characteristic
393	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	73	1	no	—
396	C₈	—	73	1	no	—
397	C₈	—	73	1	no	—
398	C₈	—	73	1	no	—
399	C₈	—	73	1	no	—
400	C₈	—	73	1	no	—
401	C₈	—	73	1	no	—
402	C₈	—	73	1	no	—
403	C₈	—	146	2	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	292	1	no	—
406	C₂²	—	292	1	no	—
407	C₂²	—	292	1	no	—
408	C₂²	—	73	1	no	—
409	C₂²	—	73	1	no	—
410	C₂²	—	73	1	no	—
411	C₂²	—	73	1	no	—
412	C₂²	—	146	2	no	—
413	C₂²	—	146	2	no	—
414	C₂²	—	146	2	no	—
415	C₂²	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
416	C₂²	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
417	C₂²	C₂×C₄⋊#10596842	1	1	yes	characteristic
418	C₄	—	292	4	no	—
419	C₄	—	73	1	no	—
420	C₄	—	73	1	no	—
421	C₄	—	73	1	no	—
422	C₄	—	73	1	no	—
423	C₄	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
424	C₄	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
425	C₄	C₂×C₄×#10596842	1	1	yes	characteristic
426	C₄	C₂×C₂²⋊#10596842	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	2	1	no	—
430	C₂	—	73	2	no	—
431	C₂	—	146	1	no	—
432	C₂	—	146	1	no	—
433	C₂	—	146	1	no	—
434	C₂	C₂×(C₂×#10596842)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₂²⋊#10596842
commutator	C₄×C₇₃	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#10596842
Fitting	C₂×M₁₆×C₇₃	C₈
socle	C₂×C₇₃	C₂×#336
prime radical	C₂³×D₇₃	M₁₆
cosocle	C₂×#11924036	C₂³
hypercenter	C₂×M₁₆	#10596842
hypocenter	C₇₃	#12554
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. #22627012	C₂	semidirect
6. C₂×#14556688	C₄	semidirect
11. #17989706	C₄	semidirect
12. #17989706	C₄	semidirect
13. #17989706	C₄	semidirect
31. #14556688	C₂×C₄	semidirect
39. #14556686	C₂×C₄	semidirect
222. C₇₃	#12554	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989706	2
#22627012	2
C₂×#17989553	2
#12554	73