Subgroups — C₂×#22607914 #32995800

Order 18688.

346 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988717	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#11924003	C₂	1	1	yes	maximal, characteristic
3	#22607914	C₂	1	4	yes	maximal, direct product factor
4	C₂×#346×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×Dic₁₄₆	C₄	1	1	yes	characteristic
6	C₂²×#11924003	—	2	1	no	—
7	#17988717	—	2	1	no	—
8	#17988717	—	2	1	no	—
9	#17988717	C₄	1	2	yes	—
10	#17988717	C₂²	1	2	yes	—
11	C₂×C₄⋊#10596831	C₄	1	1	yes	characteristic
12	C₂×#14556520	—	2	1	no	—
13	C₂×#14556501	—	2	1	no	—
14	C₄⋊#11924003	—	2	1	no	—
15	C₄⋊#11924003	C₂²	1	2	yes	—
16	C₂²×C₁₆×C₇₃	—	2	1	no	—
17	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
18	#346×C₇₃	—	2	1	no	—
19	#346×C₇₃	C₂²	1	2	yes	—
20	C₂²×Dic₁₄₆	C₈	1	1	yes	characteristic
21	C₂²×#10596831	—	2	1	no	—
22	C₄×Dic₁₄₆	—	2	1	no	—
23	C₄×Dic₁₄₆	—	2	1	no	—
24	C₄×Dic₁₄₆	C₈	1	2	yes	—
25	C₄×Dic₁₄₆	C₂×C₄	1	2	yes	—
26	C₂×C₄⋊Dic₇₃	C₈	1	1	yes	characteristic
27	C₂×#11924007	—	2	1	no	—
28	C₂×C₄×Dic₇₃	—	2	1	no	—
29	C₂×#11924003	—	2	2	no	—
30	C₂×#11924003	—	4	2	no	—
31	C₄⋊#10596831	—	2	1	no	—
32	C₄⋊#10596831	C₂×C₄	1	2	yes	—
33	#14556520	—	2	2	no	—
34	#14556520	—	2	2	no	—
35	#14556501	—	2	2	no	—
36	#14556501	—	2	2	no	—
37	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₁₆×C₇₃	—	2	4	no	—
41	C₂×C₁₆×C₇₃	—	2	2	no	—
42	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
44	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
45	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
46	C₂×Dic₁₄₆	—	2	1	no	—
47	C₂×Dic₁₄₆	—	4	2	no	—
48	C₂×Dic₁₄₆	C₂×C₈	1	2	yes	—
49	C₂²×Dic₇₃	—	2	1	no	—
50	C₂²×Dic₇₃	—	2	1	no	—
51	C₂×#10596831	—	2	2	no	—
52	C₂×#10596831	—	4	2	no	—
53	C₄⋊Dic₇₃	—	2	1	no	—
54	C₄⋊Dic₇₃	C₂×C₈	1	2	yes	—
55	#11924007	—	2	2	no	—
56	#11924007	—	2	2	no	—
57	C₄×Dic₇₃	—	2	2	no	—
58	C₄×Dic₇₃	—	2	2	no	—
59	#11924003	—	4	2	no	—
60	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
62	C₂²×C₄×C₇₃	M₁₆	1	1	yes	characteristic
63	C₂×C₈×C₇₃	—	2	2	no	—
64	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₇₃	SD₁₆	1	2	yes	—
67	C₂×C₈×C₇₃	Q₁₆	1	2	yes	—
68	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₄²×C₇₃	C₂×C₈	1	1	yes	characteristic
72	C₄²×C₇₃	M₁₆	1	1	yes	characteristic
73	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
74	C₁₆×C₇₃	—	2	4	no	—
75	C₂³×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
76	C₂×C₄×C₇₃	—	2	2	no	—
77	C₂×C₄×C₇₃	—	2	2	no	—
78	C₂×C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
79	C₂×C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
80	C₂×C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
81	C₂×C₄×C₇₃	#103	1	2	yes	—
82	C₂×C₄×C₇₃	#104	1	2	yes	—
83	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
85	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
86	C₂×Dic₇₃	—	2	2	no	—
87	C₂×Dic₇₃	—	2	2	no	—
88	C₂×Dic₇₃	—	4	2	no	—
89	C₂×Dic₇₃	—	4	2	no	—
90	Dic₁₄₆	—	4	2	no	—
91	Dic₁₄₆	—	4	2	no	—
92	C₈×C₇₃	—	2	1	no	—
93	C₈×C₇₃	—	2	1	no	—
94	C₈×C₇₃	#103	1	2	yes	—
95	C₈×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
96	C₈×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
97	#10596831	—	4	2	no	—
98	C₂²×C₇₃	Q₈⋊C₈	1	2	yes	—
99	C₂²×C₇₃	#349	1	2	yes	—
100	C₂²×C₇₃	#350	1	2	yes	—
101	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
102	C₄×C₇₃	—	2	1	no	—
103	C₄×C₇₃	—	2	1	no	—
104	C₄×C₇₃	—	2	1	no	—
105	C₄×C₇₃	—	2	1	no	—
106	C₄×C₇₃	Q₈⋊C₈	1	2	yes	—
107	C₄×C₇₃	C₂×#103	1	1	yes	characteristic
108	C₄×C₇₃	C₂×#104	1	1	yes	characteristic
109	Dic₇₃	—	4	2	no	—
110	Dic₇₃	—	4	2	no	—
111	C₂×#1338	—	73	1	no	maximal, Sylow
112	C₂×C₇₃	#1338	1	4	yes	complemented
113	C₂×C₇₃	C₂×Q₈⋊C₈	1	1	yes	characteristic
114	C₂×C₇₃	C₂×#349	1	1	yes	characteristic
115	C₂×C₇₃	C₂×#350	1	1	yes	characteristic
116	C₂×#446	—	73	1	no	—
117	C₂×C₄⋊C₁₆	—	73	1	no	—
118	C₂×#346	D₇₃	1	1	yes	characteristic
119	#1338	—	73	4	no	—
120	C₇₃	C₂×#1338	1	1	yes	characteristic, complemented, Sylow
121	C₂×C₄×Q₈	—	73	1	no	—
122	C₂²×C₁₆	—	2	1	no	—
123	C₂²×C₁₆	—	146	1	no	—
124	#446	—	73	2	no	—
125	#446	—	73	2	no	—
126	#446	—	146	1	no	—
127	#446	—	146	1	no	—
128	C₂×C₄⋊C₈	—	73	1	no	—
129	C₂×C₄⋊C₈	—	146	1	no	—
130	C₂×#97	—	146	1	no	—
131	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
132	C₄⋊C₁₆	—	73	2	no	—
133	C₄⋊C₁₆	—	146	1	no	—
134	#346	—	2	1	no	—
135	#346	C₂×D₇₃	1	2	yes	—
136	C₂²×Q₈	—	73	1	no	—
137	C₂²×C₈	—	146	1	no	—
138	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
139	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
140	C₄×Q₈	—	73	2	no	—
141	C₄×Q₈	—	73	2	no	—
142	C₄×Q₈	—	146	1	no	—
143	C₄×Q₈	—	146	1	no	—
144	C₂×C₄⋊C₄	—	73	1	no	—
145	C₂×C₄⋊C₄	—	146	1	no	—
146	C₂×C₄²	—	146	1	no	—
147	C₂×C₄²	C₄×D₇₃	1	1	yes	characteristic
148	C₂×C₁₆	—	2	4	no	—
149	C₂×C₁₆	—	2	2	no	—
150	C₂×C₁₆	—	292	2	no	—
151	C₂×C₁₆	—	146	2	no	—
152	C₄⋊C₈	—	73	2	no	—
153	C₄⋊C₈	—	146	2	no	—
154	C₄⋊C₈	—	146	2	no	—
155	C₄⋊C₈	—	146	1	no	—
156	#97	—	146	2	no	—
157	#97	—	146	2	no	—
158	C₄×C₈	C₄×D₇₃	1	1	yes	characteristic
159	C₄×C₈	D₂₉₂	1	1	yes	characteristic
160	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
161	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
162	C₂×Q₈	—	292	2	no	—
163	C₂×Q₈	—	73	2	no	—
164	C₂×Q₈	—	146	1	no	—
165	C₂²×C₄	—	146	1	no	—
166	C₂²×C₄	—	146	1	no	—
167	C₂²×C₄	#11924005	1	1	yes	characteristic
168	C₂²×C₄	C₈×D₇₃	1	1	yes	characteristic
169	C₂²×C₄	#11924011	1	1	yes	characteristic
170	C₂×C₈	—	2	2	no	—
171	C₂×C₈	—	292	2	no	—
172	C₂×C₈	—	146	2	no	—
173	C₂×C₈	#11924005	1	1	yes	characteristic
174	C₂×C₈	#11924005	1	1	yes	characteristic
175	C₂×C₈	#11924017	1	2	yes	—
176	C₂×C₈	Dic₂₉₂	1	2	yes	—
177	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
178	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
179	C₄⋊C₄	—	73	2	no	—
180	C₄⋊C₄	—	146	2	no	—
181	C₄⋊C₄	—	146	1	no	—
182	C₄⋊C₄	—	146	2	no	—
183	C₄²	—	146	2	no	—
184	C₄²	—	146	2	no	—
185	C₄²	#11924005	1	1	yes	characteristic
186	C₄²	C₈×D₇₃	1	1	yes	characteristic
187	C₄²	#11924011	1	1	yes	characteristic
188	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
189	C₁₆	—	2	4	no	—
190	C₁₆	—	292	2	no	—
191	C₂³	#14556503	1	1	yes	characteristic
192	Q₈	—	292	2	no	—
193	Q₈	—	292	2	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	292	2	no	—
197	C₂×C₄	—	292	2	no	—
198	C₂×C₄	—	146	2	no	—
199	C₂×C₄	—	146	2	no	—
200	C₂×C₄	#14556503	1	1	yes	characteristic
201	C₂×C₄	#14556503	1	1	yes	characteristic
202	C₂×C₄	#14556503	1	1	yes	characteristic
203	C₂×C₄	#14556516	1	2	yes	—
204	C₂×C₄	#14556519	1	2	yes	—
205	C₂×C₄	C₂×#11924005	1	1	yes	characteristic
206	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
207	C₂×C₄	C₂×#11924011	1	1	yes	characteristic
208	C₈	—	2	1	no	—
209	C₈	—	2	1	no	—
210	C₈	—	292	2	no	—
211	C₈	#14556516	1	2	yes	—
212	C₈	C₂×#11924017	1	1	yes	characteristic
213	C₈	C₂×Dic₂₉₂	1	1	yes	characteristic
214	C₂²	#17988319	1	2	yes	—
215	C₂²	#17988368	1	2	yes	—
216	C₂²	#17988372	1	2	yes	—
217	C₂²	C₂×#14556503	1	1	yes	characteristic
218	C₄	—	2	1	no	—
219	C₄	—	2	1	no	—
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	292	2	no	—
223	C₄	—	292	2	no	—
224	C₄	#17988319	1	2	yes	—
225	C₄	C₂×#14556516	1	1	yes	characteristic
226	C₄	C₂×#14556519	1	1	yes	characteristic
227	C₂	#22607914	1	4	yes	direct product factor
228	C₂	C₂×#17988319	1	1	yes	characteristic
229	C₂	C₂×#17988368	1	1	yes	characteristic
230	C₂	C₂×#17988372	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#11924005
commutator	C₂×C₄×C₇₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₇₃
Fitting	C₂×#346×C₇₃	C₂
socle, prime radical	C₂³×C₇₃	C₂²⋊C₈
cosocle	C₄×C₈×C₇₃	C₂³
hypercenter	C₂×#346	D₇₃
hypocenter	C₇₃	C₂×#1338
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#346

Complements

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

N	H ≅ G/N	type
3. #22607914	C₂	direct (N × H)
112. C₂×C₇₃	#1338	semidirect
120. C₇₃	C₂×#1338	semidirect
227. C₂	#22607914	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×#17988717	2
C₂×C₄⋊#11924003	2
#22607914	2
C₂×#346×C₇₃	2
C₂×#1338	73

Subgroups — C2×#22607914 #32995800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22607914 #32995800