Subgroups — C₂×#22627009 #34034061

Order 18688.

586 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556687	C₂	1	1	yes	maximal, characteristic
2	C₂²×#14556687	C₂	1	1	yes	maximal, characteristic
3	#22627009	C₂	1	4	yes	maximal, direct product factor
4	C₂×#17989551	C₂	1	1	yes	maximal, characteristic
5	C₂×#14556687	—	2	1	no	—
6	C₂×#14556687	—	2	1	no	—
7	C₂×#14556687	—	2	1	no	—
8	C₂×#14556687	—	2	1	no	—
9	C₂×#14556687	—	2	1	no	—
10	C₂×#14556687	—	2	1	no	—
11	C₂×#14556687	—	2	1	no	—
12	C₂×#14556687	C₄	1	2	yes	complemented
13	C₂×#14556687	C₄	1	2	yes	complemented
14	C₂×#14556687	C₄	1	2	yes	complemented
15	C₂×#14556687	C₂²	1	2	yes	—
16	C₂×#14556687	C₂²	1	2	yes	—
17	C₂²×#11924040	—	2	1	no	—
18	C₂²×#11924040	C₄	1	2	yes	complemented
19	C₂²×#11924037	C₄	1	1	yes	characteristic
20	C₂³×#10596833	C₂²	1	1	yes	characteristic
21	#17989551	—	2	1	no	—
22	#17989551	—	2	1	no	—
23	#17989551	C₄	1	2	yes	—
24	#17989551	C₂²	1	2	yes	—
25	C₂×#14556646	—	2	1	no	—
26	C₂×C₄×#10596833	—	2	1	no	—
27	C₂×#14556547	C₄	1	1	yes	characteristic
28	#14556687	—	2	2	no	—
29	#14556687	—	2	2	no	—
30	#14556687	—	2	2	no	—
31	#14556687	—	2	2	no	—
32	#14556687	—	2	2	no	—
33	#14556687	—	2	2	no	—
34	#14556687	—	2	2	no	—
35	#14556687	C₂×C₄	1	4	yes	complemented
36	C₂×#11924040	—	2	2	no	—
37	C₂×#11924040	—	2	2	no	—
38	C₂×#11924040	—	2	2	no	—
39	C₂×#11924040	—	2	2	no	—
40	C₂×#11924040	—	2	2	no	—
41	C₂×#11924040	C₂×C₄	1	4	yes	complemented
42	C₂×#11924037	—	2	1	no	—
43	C₂×#11924037	—	2	1	no	—
44	C₂×#11924037	—	2	1	no	—
45	C₂×#11924037	C₈	1	2	yes	—
46	C₂×#11924037	C₈	1	2	yes	—
47	C₂×#11924037	C₂×C₄	1	2	yes	—
48	C₂²×#10596833	—	2	1	no	—
49	C₂²×#10596833	C₂×C₄	1	1	yes	characteristic
50	C₂²×#10596833	C₂×C₄	1	1	yes	characteristic
51	C₂²×#10596833	C₂×C₄	1	1	yes	characteristic
52	C₂²×#10596833	C₂×C₄	1	1	yes	characteristic
53	C₂²×#10596833	C₂×C₄	1	1	yes	characteristic
54	C₂²×#10596833	D₄	1	1	yes	characteristic
55	C₂²×#10596833	D₄	1	1	yes	characteristic
56	C₂²×#10596833	D₄	1	1	yes	characteristic
57	C₂²×#10596833	D₄	1	1	yes	characteristic
58	C₂²×#10596833	D₄	1	1	yes	characteristic
59	C₂²×#10596833	D₄	1	1	yes	characteristic
60	C₂²×#10596833	Q₈	1	1	yes	characteristic
61	C₂²×#10596833	Q₈	1	1	yes	characteristic
62	C₂²×#10596833	C₂³	1	1	yes	characteristic
63	#14556646	—	2	2	no	—
64	#14556646	—	2	2	no	—
65	C₄×#10596833	—	2	2	no	—
66	C₄×#10596833	—	2	2	no	—
67	C₂³×Dic₇₃	C₂×C₄	1	1	yes	characteristic
68	#14556547	—	2	1	no	—
69	#14556547	—	2	1	no	—
70	#14556547	C₈	1	2	yes	—
71	#14556547	C₂×C₄	1	2	yes	—
72	C₂×#11924007	—	2	1	no	—
73	C₂×C₂²⋊Dic₇₃	C₈	1	1	yes	characteristic
74	C₂×C₄×Dic₇₃	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₇₃	C₈	1	1	yes	characteristic
76	#11924040	—	2	4	no	—
77	#11924040	—	2	4	no	—
78	#11924037	—	2	2	no	—
79	#11924037	—	2	2	no	—
80	#11924037	—	2	2	no	—
81	#11924037	C₂×C₈	1	4	yes	—
82	C₂×#10596833	—	2	2	no	—
83	C₂×#10596833	—	2	2	no	—
84	C₂×#10596833	—	2	2	no	—
85	C₂×#10596833	C₄²	1	1	yes	characteristic
86	C₂×#10596833	C₄²	1	1	yes	characteristic
87	C₂×#10596833	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×#10596833	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×#10596833	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×#10596833	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×#10596833	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×#10596833	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×#10596833	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×#10596833	C₂²⋊C₄	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	C₄⋊C₄	1	1	yes	characteristic
98	C₂×#10596833	C₄⋊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	C₄⋊C₄	1	1	yes	characteristic
106	C₂×#10596833	C₄⋊C₄	1	1	yes	characteristic
107	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
108	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
109	C₂×#10596833	C₂×D₄	1	1	yes	characteristic
110	C₂×#10596833	C₂×D₄	1	1	yes	characteristic
111	C₂×#10596833	C₂×D₄	1	1	yes	characteristic
112	C₂×#10596833	C₂×Q₈	1	1	yes	characteristic
113	C₂²×Dic₇₃	—	2	1	no	—
114	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
115	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
116	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
119	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
120	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
121	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
122	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
123	C₂²×Dic₇₃	M₁₆	1	1	yes	characteristic
124	C₂²×Dic₇₃	M₁₆	1	1	yes	characteristic
125	C₂²×Dic₇₃	M₁₆	1	1	yes	characteristic
126	C₂²×Dic₇₃	M₁₆	1	1	yes	characteristic
127	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
128	#11924007	—	2	2	no	—
129	#11924007	—	2	2	no	—
130	C₂²⋊Dic₇₃	—	2	1	no	—
131	C₂²⋊Dic₇₃	C₂×C₈	1	2	yes	—
132	C₄×Dic₇₃	—	2	2	no	—
133	C₄×Dic₇₃	—	2	2	no	—
134	C₂⁴×C₇₃	C₂×C₈	1	1	yes	characteristic
135	C₂²×C₄×C₇₃	—	2	1	no	—
136	C₂²⋊C₄×C₇₃	—	2	1	no	—
137	C₂²⋊C₄×C₇₃	C₂×C₈	1	2	yes	—
138	C₂³×C₇₃	—	4	2	no	—
139	C₂³×C₇₃	C₄×C₈	1	1	yes	characteristic
140	C₂³×C₇₃	C₄×C₈	1	1	yes	characteristic
141	C₂³×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
142	C₂³×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
143	C₂³×C₇₃	C₄⋊C₈	1	1	yes	characteristic
144	C₂³×C₇₃	C₄⋊C₈	1	1	yes	characteristic
145	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
146	C₂×C₄×C₇₃	—	2	2	no	—
147	C₂×C₄×C₇₃	—	4	2	no	—
148	C₂×Dic₇₃	—	2	2	no	—
149	C₂×Dic₇₃	—	4	2	no	—
150	C₂×Dic₇₃	#95	1	1	yes	characteristic
151	C₂×Dic₇₃	#95	1	1	yes	characteristic
152	C₂×Dic₇₃	#95	1	1	yes	characteristic
153	C₂×Dic₇₃	#95	1	1	yes	characteristic
154	C₂×Dic₇₃	C₄×C₈	1	1	yes	characteristic
155	C₂×Dic₇₃	C₄×C₈	1	1	yes	characteristic
156	C₂×Dic₇₃	#97	1	1	yes	characteristic
157	C₂×Dic₇₃	#97	1	1	yes	characteristic
158	C₂×Dic₇₃	#97	1	1	yes	characteristic
159	C₂×Dic₇₃	#97	1	1	yes	characteristic
160	C₂×Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
161	C₂×Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
162	C₂×Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
163	C₂×Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
164	C₂×Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
165	C₂×Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
166	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
167	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
168	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
169	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
170	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
171	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
172	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
173	C₂×Dic₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
176	C₂×Dic₇₃	C₂×M₁₆	1	1	yes	characteristic
177	C₂×Dic₇₃	C₂×M₁₆	1	1	yes	characteristic
178	#10596833	—	2	4	no	—
179	#10596833	#95	1	1	yes	characteristic
180	#10596833	#95	1	1	yes	characteristic
181	#10596833	#95	1	1	yes	characteristic
182	#10596833	#95	1	1	yes	characteristic
183	#10596833	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	#10596833	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	#10596833	C₂×C₄⋊C₄	1	1	yes	characteristic
186	#10596833	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂²×C₇₃	—	2	2	no	—
188	C₂²×C₇₃	—	2	2	no	—
189	C₂²×C₇₃	—	2	2	no	—
190	C₂²×C₇₃	—	4	1	no	—
191	C₂²×C₇₃	—	4	1	no	—
192	C₂²×C₇₃	—	4	1	no	—
193	C₂²×C₇₃	—	4	1	no	—
194	C₂²×C₇₃	#336	1	1	yes	characteristic
195	C₂²×C₇₃	#336	1	1	yes	characteristic
196	C₂²×C₇₃	#336	1	1	yes	characteristic
197	C₂²×C₇₃	#336	1	1	yes	characteristic
198	C₂²×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
199	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
200	C₂²×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
201	C₄×C₇₃	—	4	2	no	—
202	Dic₇₃	—	4	2	no	—
203	Dic₇₃	#336	1	1	yes	characteristic
204	Dic₇₃	#336	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×#97	1	1	yes	characteristic
209	Dic₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
210	Dic₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
211	C₂×#1378	—	73	1	no	maximal, Sylow
212	C₂×C₇₃	—	2	1	no	—
213	C₂×C₇₃	—	2	1	no	—
214	C₂×C₇₃	—	2	1	no	—
215	C₂×C₇₃	—	2	1	no	—
216	C₂×C₇₃	—	2	1	no	—
217	C₂×C₇₃	—	2	1	no	—
218	C₂×C₇₃	#1378	1	2	yes	complemented
219	C₂×C₇₃	C₂×#336	1	1	yes	characteristic
220	C₂²×M₃₂	—	73	1	no	—
221	C₂²×M₃₂	—	73	1	no	—
222	C₂×#405	—	73	1	no	—
223	#1378	—	73	4	no	—
224	C₇₃	C₂×#1378	1	1	yes	characteristic, complemented, Sylow
225	C₂²×M₁₆	—	73	1	no	—
226	C₂³×C₈	—	73	1	no	—
227	C₂×#117	—	73	1	no	—
228	C₂×M₃₂	—	73	2	no	—
229	C₂×M₃₂	—	73	2	no	—
230	C₂×M₃₂	—	73	2	no	—
231	C₂×M₃₂	—	73	2	no	—
232	C₂×M₃₂	—	73	2	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	C₂×M₃₂	—	146	1	no	—
239	C₂×M₃₂	—	146	1	no	—
240	C₂²×C₁₆	—	73	2	no	—
241	C₂²×C₁₆	—	146	1	no	—
242	#405	—	73	2	no	—
243	#405	—	73	2	no	—
244	#405	—	146	1	no	—
245	#405	—	146	1	no	—
246	C₂×#97	—	146	1	no	—
247	C₂×C₄×C₈	—	146	1	no	—
248	C₂³×C₄	—	73	1	no	—
249	C₂×M₁₆	—	73	2	no	—
250	C₂×M₁₆	—	73	2	no	—
251	C₂×M₁₆	—	73	2	no	—
252	C₂×M₁₆	—	146	1	no	—
253	C₂×M₁₆	—	146	1	no	—
254	C₂×M₁₆	—	146	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	—	73	1	no	—
269	C₂²×C₈	—	146	1	no	—
270	#117	—	73	2	no	—
271	#117	—	73	2	no	—
272	#117	—	146	1	no	—
273	#117	—	146	1	no	—
274	C₂×C₄⋊C₄	—	146	1	no	—
275	C₂×C₂²⋊C₄	—	73	1	no	—
276	C₂×C₂²⋊C₄	#10596842	1	1	yes	characteristic
277	C₂×C₄²	—	146	1	no	—
278	M₃₂	—	73	4	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	M₃₂	—	146	2	no	—
285	M₃₂	—	146	2	no	—
286	C₂×C₁₆	—	73	4	no	—
287	C₂×C₁₆	—	146	2	no	—
288	C₂×C₁₆	—	146	2	no	—
289	C₂×C₁₆	—	146	2	no	—
290	C₂×C₁₆	—	146	2	no	—
291	C₂×C₁₆	—	146	2	no	—
292	#97	—	146	2	no	—
293	#97	—	146	2	no	—
294	C₄×C₈	—	146	2	no	—
295	C₄×C₈	—	146	2	no	—
296	C₂⁴	C₂×#10596842	1	1	yes	characteristic
297	C₂²×C₄	—	2	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	—	73	1	no	—
309	C₂²×C₄	—	73	1	no	—
310	C₂²×C₄	—	73	1	no	—
311	C₂²×C₄	—	73	1	no	—
312	C₂²×C₄	—	146	1	no	—
313	M₁₆	—	73	4	no	—
314	M₁₆	—	146	2	no	—
315	M₁₆	—	146	2	no	—
316	M₁₆	—	146	2	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	2	no	—
348	C₄⋊C₄	—	146	2	no	—
349	C₄⋊C₄	—	146	2	no	—
350	C₂²⋊C₄	—	2	1	no	—
351	C₂²⋊C₄	—	73	2	no	—
352	C₂²⋊C₄	—	146	1	no	—
353	C₂²⋊C₄	C₂×#10596842	1	2	yes	—
354	C₄²	—	146	2	no	—
355	C₄²	—	146	2	no	—
356	C₁₆	—	146	4	no	—
357	C₁₆	—	146	4	no	—
358	C₂³	—	4	2	no	—
359	C₂³	C₄×#10596842	1	1	yes	characteristic
360	C₂³	C₄×#10596842	1	1	yes	characteristic
361	C₂³	C₂²⋊#10596842	1	1	yes	characteristic
362	C₂³	C₂²⋊#10596842	1	1	yes	characteristic
363	C₂³	C₄⋊#10596842	1	1	yes	characteristic
364	C₂³	C₄⋊#10596842	1	1	yes	characteristic
365	C₂³	C₂²×#10596842	1	1	yes	characteristic
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	292	2	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	—	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	—	73	1	no	—
395	C₂×C₄	—	73	1	no	—
396	C₂×C₄	—	73	1	no	—
397	C₂×C₄	—	146	2	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	—	73	1	no	—
404	C₈	—	73	1	no	—
405	C₈	—	73	1	no	—
406	C₈	—	146	4	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
415	C₂²	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
416	C₂²	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
417	C₂²	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
418	C₂²	C₂×C₄×#10596842	1	1	yes	characteristic
419	C₂²	C₂×C₂²⋊#10596842	1	1	yes	characteristic
420	C₂²	C₂×C₄⋊#10596842	1	1	yes	characteristic
421	C₄	—	4	2	no	—
422	C₄	—	292	2	no	—
423	C₄	—	73	1	no	—
424	C₄	—	73	1	no	—
425	C₄	—	73	1	no	—
426	C₄	—	73	1	no	—
427	C₄	—	73	1	no	—
428	C₄	—	73	1	no	—
429	C₄	—	73	1	no	—
430	C₄	—	73	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	#22627009	1	2	yes	direct product factor
438	C₂	C₂×(C₂×#10596842)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×#10596842)⋊C₄
commutator	C₂²×C₇₃	C₂×C₄×C₈
Frattini	C₂³	C₂²×#10596842
Fitting	C₂×C₂²⋊C₄×C₇₃	C₈
socle	C₂²×C₇₃	#336
prime radical	C₂⁴×C₇₃	C₂×C₈
cosocle	C₂²×#10596833	C₂³
hypercenter	C₂×C₂²⋊C₄	#10596842
hypocenter	C₇₃	C₂×#1378
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
3. #22627009	C₂	direct (N × H)
12. C₂×#14556687	C₄	semidirect
13. C₂×#14556687	C₄	semidirect
14. C₂×#14556687	C₄	semidirect
18. C₂²×#11924040	C₄	semidirect
35. #14556687	C₂×C₄	semidirect
41. C₂×#11924040	C₂×C₄	semidirect
218. C₂×C₇₃	#1378	semidirect
224. C₇₃	C₂×#1378	semidirect
437. C₂	#22627009	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14556687	2
#22627009	2
C₂×#17989551	2
C₂×#1378	73

Subgroups — C2×#22627009 #34034061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22627009 #34034061