Subgroups — C₂×#22618815 #33950148

Order 18688.

2806 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989070	C₂	1	2	yes	maximal, complemented
2	#22618815	C₂	1	16	yes	maximal, direct product factor
3	C₂×#17988699	C₂	1	2	yes	maximal, complemented
4	C₂×#17988694	C₂	1	2	yes	maximal, complemented
5	C₂×SD₁₆×Dic₇₃	C₂	1	4	yes	maximal, complemented
6	C₂²×#14556523	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#17988588	C₂	1	2	yes	maximal, complemented
8	C₂×#17988542	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#135×C₇₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×#11924012	C₂²	1	1	yes	characteristic
11	#17989070	—	2	8	no	—
12	#17989070	C₂²	1	16	yes	complemented
13	C₂×Q₈×Dic₇₃	C₂²	1	4	yes	—
14	C₂×D₄×Dic₇₃	—	2	4	no	—
15	C₂×D₄×Dic₇₃	C₂²	1	4	yes	—
16	C₂×#14556550	—	2	2	no	—
17	C₂×#14556550	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊Dic₇₃	—	2	2	no	—
19	C₂²×C₄⋊Dic₇₃	C₂²	1	2	yes	—
20	#17988699	C₂²	1	16	yes	complemented
21	#17988694	C₂²	1	16	yes	complemented
22	SD₁₆×Dic₇₃	C₂²	1	32	yes	complemented
23	C₂×#14556523	C₂²	1	2	yes	—
24	C₂×#14556523	C₂²	1	2	yes	—
25	C₂×#14556523	C₂²	1	8	yes	complemented
26	#17988588	C₂²	1	16	yes	complemented
27	C₂×#14556515	C₂²	1	4	yes	—
28	C₂×#14556512	C₂²	1	4	yes	—
29	#17988542	C₂²	1	8	yes	complemented
30	C₂×#14556501	C₂²	1	2	yes	—
31	C₂×C₈×Dic₇₃	C₂²	1	2	yes	—
32	C₂²×#41×C₇₃	C₂²	1	2	yes	—
33	C₂×#135×C₇₃	C₄	1	16	yes	complemented
34	C₂×#135×C₇₃	C₂²	1	8	yes	—
35	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
36	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
37	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
38	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
39	C₂³×Dic₇₃	—	2	4	no	—
40	C₂³×Dic₇₃	—	2	2	no	—
41	C₂×#11924012	—	2	4	no	—
42	C₂×#11924012	C₂³	1	4	yes	—
43	C₂²×#10596831	C₂³	1	2	yes	—
44	Q₈×Dic₇₃	—	2	8	no	—
45	Q₈×Dic₇₃	C₂³	1	16	yes	—
46	D₄×Dic₇₃	—	2	32	no	—
47	D₄×Dic₇₃	—	2	8	no	—
48	D₄×Dic₇₃	C₂³	1	16	yes	—
49	#14556550	—	2	16	no	—
50	#14556550	D₄	1	4	yes	—
51	#14556550	C₂³	1	4	yes	—
52	C₂×C₄⋊Dic₇₃	—	2	4	no	—
53	C₂×C₄⋊Dic₇₃	—	2	16	no	—
54	C₂×C₄⋊Dic₇₃	—	2	2	no	—
55	C₂×C₄⋊Dic₇₃	—	2	4	no	—
56	C₂×C₄⋊Dic₇₃	D₄	1	2	yes	—
57	C₂×C₄⋊Dic₇₃	C₂³	1	4	yes	—
58	C₂×C₄⋊Dic₇₃	C₂³	1	8	yes	—
59	C₂×C₂²⋊Dic₇₃	—	2	4	no	—
60	C₂×C₂²⋊Dic₇₃	D₄	1	2	yes	—
61	C₂×C₄×Dic₇₃	—	2	4	no	—
62	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
63	#14556523	C₂³	1	8	yes	—
64	#14556523	C₂³	1	8	yes	—
65	#14556515	C₂³	1	16	yes	—
66	#14556512	C₂³	1	16	yes	—
67	#14556501	C₂³	1	8	yes	—
68	C₈×Dic₇₃	C₂³	1	8	yes	—
69	C₂×#41×C₇₃	—	2	4	no	—
70	C₂×#41×C₇₃	—	2	8	no	—
71	C₂×#41×C₇₃	C₂×C₄	1	16	yes	complemented
72	C₂×#41×C₇₃	C₂³	1	8	yes	—
73	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
74	C₂²×D₄×C₇₃	—	2	2	no	—
75	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₇₃	—	2	2	no	—
77	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
78	#135×C₇₃	C₂×C₄	1	64	yes	complemented
79	C₂×Q₁₆×C₇₃	C₂×C₄	1	8	yes	complemented
80	C₂×Q₁₆×C₇₃	C₂³	1	4	yes	—
81	C₂×SD₁₆×C₇₃	C₂×C₄	1	16	yes	complemented
82	C₂×SD₁₆×C₇₃	C₂³	1	8	yes	—
83	C₂×D₈×C₇₃	C₂×C₄	1	8	yes	complemented
84	C₂×D₈×C₇₃	C₂³	1	4	yes	—
85	C₂²×C₈×C₇₃	C₂×C₄	1	8	yes	complemented
86	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
89	C₂²×Dic₇₃	—	2	4	no	—
90	C₂²×Dic₇₃	—	2	8	no	—
91	C₂²×Dic₇₃	—	2	16	no	—
92	C₂²×Dic₇₃	—	8	8	no	—
93	C₂²×Dic₇₃	—	8	4	no	—
94	C₂²×Dic₇₃	C₂×D₄	1	4	yes	—
95	#11924012	—	2	8	no	—
96	C₂×#10596831	—	2	4	no	—
97	C₂×#10596831	C₂⁴	1	4	yes	—
98	C₄⋊Dic₇₃	—	2	8	no	—
99	C₄⋊Dic₇₃	—	2	4	no	—
100	C₄⋊Dic₇₃	—	2	16	no	—
101	C₄⋊Dic₇₃	C₂×D₄	1	8	yes	—
102	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
103	C₂²⋊Dic₇₃	—	2	16	no	—
104	C₂²⋊Dic₇₃	C₂×D₄	1	8	yes	—
105	C₄×Dic₇₃	—	2	16	no	—
106	C₄×Dic₇₃	C₂×D₄	1	4	yes	—
107	C₄×Dic₇₃	C₂⁴	1	4	yes	—
108	C₂⁴×C₇₃	—	2	2	no	—
109	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
110	#41×C₇₃	—	2	32	no	—
111	#41×C₇₃	—	2	16	no	—
112	#41×C₇₃	C₂²×C₄	1	32	yes	complemented
113	C₂×Q₈×C₇₃	—	2	2	no	—
114	C₂×Q₈×C₇₃	—	2	4	no	—
115	C₂×Q₈×C₇₃	C₂²×C₄	1	8	yes	—
116	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
117	C₂×D₄×C₇₃	—	2	16	no	—
118	C₂×D₄×C₇₃	—	2	8	no	—
119	C₂×D₄×C₇₃	—	2	2	no	—
120	C₂×D₄×C₇₃	—	2	4	no	—
121	C₂×D₄×C₇₃	C₂²×C₄	1	8	yes	—
122	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₇₃	—	2	2	no	—
124	C₂²×C₄×C₇₃	—	2	16	no	—
125	C₂²×C₄×C₇₃	—	2	8	no	—
126	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
127	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₇₃	#41	1	4	yes	—
130	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
132	Q₁₆×C₇₃	C₂²×C₄	1	16	yes	complemented
133	SD₁₆×C₇₃	C₂²×C₄	1	32	yes	complemented
134	D₈×C₇₃	C₂²×C₄	1	16	yes	complemented
135	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
136	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
137	C₂×C₈×C₇₃	C₂²×C₄	1	16	yes	complemented
138	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
139	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
140	C₂³×C₇₃	—	2	4	no	—
141	C₂³×C₇₃	—	2	8	no	—
142	C₂³×C₇₃	—	2	4	no	—
143	C₂³×C₇₃	—	4	4	no	—
144	C₂³×C₇₃	—	4	4	no	—
145	C₂³×C₇₃	C₄×D₄	1	4	yes	—
146	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
147	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₇₃	—	2	8	no	—
149	Q₈×C₇₃	—	2	4	no	—
150	Q₈×C₇₃	C₂³×C₄	1	8	yes	—
151	D₄×C₇₃	—	2	32	no	—
152	D₄×C₇₃	—	2	8	no	—
153	D₄×C₇₃	—	2	4	no	—
154	D₄×C₇₃	C₂³×C₄	1	8	yes	—
155	C₂×C₄×C₇₃	—	2	8	no	—
156	C₂×C₄×C₇₃	—	2	4	no	—
157	C₂×C₄×C₇₃	—	2	32	no	—
158	C₂×C₄×C₇₃	C₄×D₄	1	4	yes	—
159	C₂×C₄×C₇₃	C₄×D₄	1	8	yes	—
160	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
161	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
162	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
163	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
165	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
166	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
167	C₂×Dic₇₃	—	2	8	no	—
168	C₂×Dic₇₃	—	2	8	no	—
169	C₂×Dic₇₃	—	4	8	no	—
170	C₂×Dic₇₃	—	8	16	no	—
171	C₂×Dic₇₃	—	8	8	no	—
172	C₂×Dic₇₃	C₂²×D₄	1	8	yes	—
173	C₈×C₇₃	C₂³×C₄	1	4	yes	—
174	C₈×C₇₃	C₂³×C₄	1	4	yes	—
175	#10596831	—	2	4	no	—
176	C₂²×C₇₃	—	2	8	no	—
177	C₂²×C₇₃	—	2	4	no	—
178	C₂²×C₇₃	—	2	8	no	—
179	C₂²×C₇₃	—	4	16	no	—
180	C₂²×C₇₃	—	4	4	no	—
181	C₂²×C₇₃	—	4	4	no	—
182	C₂²×C₇₃	C₂×C₄×D₄	1	4	yes	—
183	C₂²×C₇₃	C₂×C₄×D₄	1	2	yes	—
184	C₂²×C₇₃	#577	1	4	yes	—
185	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
186	C₄×C₇₃	—	2	8	no	—
187	C₄×C₇₃	C₂×C₄×D₄	1	4	yes	—
188	C₄×C₇₃	C₂×C₄×D₄	1	2	yes	—
189	C₄×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
190	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
191	Dic₇₃	—	2	8	no	—
192	Dic₇₃	—	4	8	no	—
193	C₂×#2952	—	73	1	no	maximal, Sylow
194	C₂×C₇₃	—	2	4	no	—
195	C₂×C₇₃	—	4	8	no	—
196	C₂×C₇₃	#2952	1	4	yes	complemented
197	C₂×C₇₃	C₂²×C₄×D₄	1	1	yes	characteristic
198	C₂×C₇₃	C₂×#577	1	2	yes	—
199	C₂²×#135	D₇₃	1	1	yes	characteristic
200	C₂×#520	—	73	2	no	—
201	#2952	—	73	16	no	—
202	C₂×#442	—	73	2	no	—
203	C₂×#441	—	73	2	no	—
204	C₂×C₄×SD₁₆	—	73	4	no	—
205	C₂²×#106	—	73	1	no	—
206	C₂×#417	—	73	2	no	—
207	C₂×#405	—	73	1	no	—
208	C₇₃	C₂×#2952	1	1	yes	characteristic, complemented, Sylow
209	C₂²×#41	C₂×D₇₃	1	2	yes	—
210	C₂×#135	Dic₇₃	1	16	yes	complemented
211	C₂×#135	C₂×D₇₃	1	8	yes	—
212	C₂²×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
213	C₂²×SD₁₆	C₂×D₇₃	1	2	yes	—
214	C₂²×D₈	C₂×D₇₃	1	1	yes	characteristic
215	C₂²×M₁₆	—	73	1	no	—
216	C₂³×C₈	C₂×D₇₃	1	1	yes	characteristic
217	#520	—	73	16	no	—
218	#520	—	146	8	no	—
219	C₂×C₄×Q₈	—	73	4	no	—
220	C₂×C₄×D₄	—	73	4	no	—
221	C₂×C₄×D₄	—	146	4	no	—
222	C₂×#117	—	73	1	no	—
223	C₂×#117	—	146	2	no	—
224	C₂²×C₄⋊C₄	—	73	2	no	—
225	C₂²×C₄⋊C₄	—	146	2	no	—
226	#442	—	73	16	no	—
227	#441	—	73	16	no	—
228	C₄×SD₁₆	—	73	32	no	—
229	C₂×#106	—	73	2	no	—
230	C₂×#106	—	73	2	no	—
231	C₂×#106	—	73	8	no	—
232	#417	—	73	16	no	—
233	C₂×#103	—	73	4	no	—
234	C₂×#102	—	73	4	no	—
235	#405	—	73	8	no	—
236	C₂×#97	—	73	2	no	—
237	C₂×C₄×C₈	—	73	2	no	—
238	C₂×#41	—	2	4	no	—
239	C₂×#41	—	2	8	no	—
240	C₂×#41	C₂×Dic₇₃	1	16	yes	complemented
241	C₂×#41	C₂²×D₇₃	1	8	yes	—
242	C₂²×Q₈	C₂²×D₇₃	1	2	yes	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	—	146	4	no	—
247	C₂³×C₄	—	146	2	no	—
248	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
249	#135	C₂×Dic₇₃	1	64	yes	complemented
250	C₂×Q₁₆	C₂×Dic₇₃	1	8	yes	complemented
251	C₂×Q₁₆	C₂²×D₇₃	1	4	yes	—
252	C₂×SD₁₆	C₂×Dic₇₃	1	16	yes	complemented
253	C₂×SD₁₆	C₂²×D₇₃	1	8	yes	—
254	C₂×D₈	C₂×Dic₇₃	1	8	yes	complemented
255	C₂×D₈	C₂²×D₇₃	1	4	yes	—
256	C₂×M₁₆	—	73	4	no	—
257	C₂×M₁₆	—	146	4	no	—
258	C₂²×C₈	—	73	2	no	—
259	C₂²×C₈	C₂×Dic₇₃	1	8	yes	complemented
260	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
261	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
262	C₂²×C₈	C₂²×D₇₃	1	4	yes	—
263	C₄×Q₈	—	73	16	no	—
264	C₄×Q₈	—	146	8	no	—
265	C₄×D₄	—	73	16	no	—
266	C₄×D₄	—	146	8	no	—
267	C₄×D₄	—	146	32	no	—
268	#117	—	73	4	no	—
269	#117	—	73	4	no	—
270	#117	—	146	16	no	—
271	C₂×C₄⋊C₄	—	73	2	no	—
272	C₂×C₄⋊C₄	—	73	4	no	—
273	C₂×C₄⋊C₄	—	73	8	no	—
274	C₂×C₄⋊C₄	—	146	16	no	—
275	C₂×C₄⋊C₄	—	146	4	no	—
276	C₂×C₄⋊C₄	—	146	2	no	—
277	C₂×C₄⋊C₄	—	146	4	no	—
278	C₂×C₂²⋊C₄	—	73	2	no	—
279	C₂×C₂²⋊C₄	—	146	4	no	—
280	C₂×C₄²	—	73	2	no	—
281	C₂×C₄²	—	146	4	no	—
282	#106	—	73	8	no	—
283	#106	—	73	8	no	—
284	#103	—	73	16	no	—
285	#102	—	73	16	no	—
286	#97	—	73	8	no	—
287	C₄×C₈	—	73	8	no	—
288	C₂⁴	—	2	2	no	—
289	C₂⁴	D₄×D₇₃	1	1	yes	characteristic
290	#41	—	2	32	no	—
291	#41	—	2	16	no	—
292	#41	C₂²×Dic₇₃	1	32	yes	complemented
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	C₂²×Dic₇₃	1	8	yes	—
296	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
297	C₂×D₄	—	2	16	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	C₂²×Dic₇₃	1	8	yes	—
302	C₂×D₄	C₂³×D₇₃	1	4	yes	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	16	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	584	4	no	—
307	C₂²×C₄	—	584	8	no	—
308	C₂²×C₄	—	73	4	no	—
309	C₂²×C₄	—	146	4	no	—
310	C₂²×C₄	—	146	16	no	—
311	C₂²×C₄	—	146	8	no	—
312	C₂²×C₄	C₂²×Dic₇₃	1	4	yes	—
313	C₂²×C₄	D₄×D₇₃	1	2	yes	—
314	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
315	C₂²×C₄	#11924027	1	4	yes	—
316	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
317	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
318	Q₁₆	C₂²×Dic₇₃	1	16	yes	complemented
319	SD₁₆	C₂²×Dic₇₃	1	32	yes	complemented
320	D₈	C₂²×Dic₇₃	1	16	yes	complemented
321	M₁₆	—	146	8	no	—
322	C₂×C₈	—	73	4	no	—
323	C₂×C₈	—	146	4	no	—
324	C₂×C₈	C₂²×Dic₇₃	1	4	yes	—
325	C₂×C₈	C₂²×Dic₇₃	1	4	yes	—
326	C₂×C₈	C₂²×Dic₇₃	1	16	yes	complemented
327	C₂×C₈	C₂³×D₇₃	1	2	yes	—
328	C₂×C₈	C₂³×D₇₃	1	2	yes	—
329	C₄⋊C₄	—	73	8	no	—
330	C₄⋊C₄	—	73	8	no	—
331	C₄⋊C₄	—	146	16	no	—
332	C₄⋊C₄	—	146	8	no	—
333	C₄⋊C₄	—	146	4	no	—
334	C₂²⋊C₄	—	73	8	no	—
335	C₂²⋊C₄	—	146	16	no	—
336	C₄²	—	73	4	no	—
337	C₄²	—	73	4	no	—
338	C₄²	—	146	16	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	2	8	no	—
342	C₂³	—	4	4	no	—
343	C₂³	—	4	4	no	—
344	C₂³	D₄×Dic₇₃	1	4	yes	—
345	C₂³	C₂×D₄×D₇₃	1	2	yes	—
346	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
347	Q₈	—	2	4	no	—
348	Q₈	—	2	8	no	—
349	Q₈	C₂³×Dic₇₃	1	8	yes	—
350	D₄	—	2	32	no	—
351	D₄	—	2	4	no	—
352	D₄	—	2	8	no	—
353	D₄	C₂³×Dic₇₃	1	8	yes	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	32	no	—
357	C₂×C₄	—	292	8	no	—
358	C₂×C₄	—	584	8	no	—
359	C₂×C₄	—	584	16	no	—
360	C₂×C₄	—	73	8	no	—
361	C₂×C₄	—	146	8	no	—
362	C₂×C₄	—	146	8	no	—
363	C₂×C₄	D₄×Dic₇₃	1	4	yes	—
364	C₂×C₄	D₄×Dic₇₃	1	8	yes	—
365	C₂×C₄	C₂³×Dic₇₃	1	2	yes	—
366	C₂×C₄	C₂³×Dic₇₃	1	4	yes	—
367	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
369	C₂×C₄	C₂×#11924027	1	2	yes	—
370	C₂×C₄	C₂×#11924027	1	4	yes	—
371	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
372	C₈	—	146	4	no	—
373	C₈	C₂³×Dic₇₃	1	4	yes	—
374	C₈	C₂³×Dic₇₃	1	4	yes	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	8	no	—
377	C₂²	—	2	8	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	16	no	—
381	C₂²	C₂×D₄×Dic₇₃	1	4	yes	—
382	C₂²	C₂×D₄×Dic₇₃	1	2	yes	—
383	C₂²	#17989394	1	4	yes	—
384	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
385	C₄	—	2	8	no	—
386	C₄	—	292	8	no	—
387	C₄	—	146	8	no	—
388	C₄	C₂×D₄×Dic₇₃	1	4	yes	—
389	C₄	C₂×D₄×Dic₇₃	1	2	yes	—
390	C₄	C₂⁴×Dic₇₃	1	1	yes	characteristic
391	C₄	C₂²×#11924027	1	1	yes	characteristic
392	C₂	—	2	4	no	—
393	C₂	—	4	8	no	—
394	C₂	#22618815	1	4	yes	direct product factor
395	C₂	C₂²×D₄×Dic₇₃	1	1	yes	characteristic
396	C₂	C₂×#17989394	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₇₃
commutator	C₄×C₇₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting, prime radical	C₂²×#135×C₇₃	C₂
socle	C₂³×C₇₃	C₂²×D₄
cosocle	C₂×C₄×C₇₃	C₂⁵
hypercenter	C₂²×#135	D₇₃
hypocenter	C₇₃	C₂×#2952
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#17989070	C₂	semidirect
2. #22618815	C₂	direct (N × H)
3. C₂×#17988699	C₂	semidirect
4. C₂×#17988694	C₂	semidirect
5. C₂×SD₁₆×Dic₇₃	C₂	semidirect
6. C₂²×#14556523	C₂	semidirect
7. C₂×#17988588	C₂	semidirect
8. C₂×#17988542	C₂	semidirect
12. #17989070	C₂²	semidirect
20. #17988699	C₂²	semidirect
21. #17988694	C₂²	semidirect
22. SD₁₆×Dic₇₃	C₂²	semidirect
25. C₂×#14556523	C₂²	semidirect
26. #17988588	C₂²	semidirect
29. #17988542	C₂²	semidirect
33. C₂×#135×C₇₃	C₄	semidirect
71. C₂×#41×C₇₃	C₂×C₄	semidirect
78. #135×C₇₃	C₂×C₄	semidirect
79. C₂×Q₁₆×C₇₃	C₂×C₄	semidirect
81. C₂×SD₁₆×C₇₃	C₂×C₄	semidirect
83. C₂×D₈×C₇₃	C₂×C₄	semidirect
85. C₂²×C₈×C₇₃	C₂×C₄	semidirect
112. #41×C₇₃	C₂²×C₄	semidirect
132. Q₁₆×C₇₃	C₂²×C₄	semidirect
133. SD₁₆×C₇₃	C₂²×C₄	semidirect
134. D₈×C₇₃	C₂²×C₄	semidirect
137. C₂×C₈×C₇₃	C₂²×C₄	semidirect
196. C₂×C₇₃	#2952	semidirect
208. C₇₃	C₂×#2952	semidirect
210. C₂×#135	Dic₇₃	semidirect
240. C₂×#41	C₂×Dic₇₃	semidirect
249. #135	C₂×Dic₇₃	semidirect
250. C₂×Q₁₆	C₂×Dic₇₃	semidirect
252. C₂×SD₁₆	C₂×Dic₇₃	semidirect
254. C₂×D₈	C₂×Dic₇₃	semidirect
259. C₂²×C₈	C₂×Dic₇₃	semidirect
292. #41	C₂²×Dic₇₃	semidirect
318. Q₁₆	C₂²×Dic₇₃	semidirect
319. SD₁₆	C₂²×Dic₇₃	semidirect
320. D₈	C₂²×Dic₇₃	semidirect
326. C₂×C₈	C₂²×Dic₇₃	semidirect
394. C₂	#22618815	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×#17989070	2
#22618815	2
C₂×#17988699	2
C₂×#17988694	2
C₂×SD₁₆×Dic₇₃	2
C₂²×#14556523	2
C₂×#17988588	2
C₂×#17988542	2
C₂²×#135×C₇₃	2
C₂×#2952	73

Subgroups — C2×#22618815 #33950148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22618815 #33950148