Subgroups — #22626629

Order 9344.

392 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989612	C₂	1	2	yes	maximal, complemented
2	#17989611	C₂	1	2	yes	maximal, complemented
3	#17989610	C₂	1	1	yes	maximal, characteristic, complemented
4	#17989607	C₂	1	1	yes	maximal, characteristic, complemented
5	#17989605	C₂	1	1	yes	maximal, characteristic, complemented
6	#17989604	C₂	1	1	yes	maximal, characteristic, complemented
7	#17989590	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14556658	C₂	1	1	yes	maximal, characteristic, complemented
9	#17989560	C₂	1	2	yes	maximal
10	#17989551	C₂	1	2	yes	maximal, complemented
11	C₄×#11924027	C₂	1	1	yes	maximal, characteristic
12	C₂×#11924037	C₂²	1	2	yes	—
13	C₂²×#10596833	C₂²	1	2	yes	—
14	#14556658	C₂²	1	1	yes	characteristic
15	#14556658	C₂²	1	1	yes	characteristic
16	#14556658	C₂²	1	2	yes	—
17	#14556658	C₂²	1	1	yes	characteristic
18	#14556658	C₂²	1	1	yes	characteristic
19	C₄⋊#10596833	C₂²	1	2	yes	—
20	#14556648	C₂²	1	2	yes	—
21	#14556648	C₂²	1	2	yes	—
22	C₂²⋊#10596833	C₂²	1	2	yes	—
23	C₂²⋊#10596833	C₂²	1	2	yes	—
24	#14556646	C₂²	1	2	yes	—
25	#14556646	C₂²	1	2	yes	—
26	C₄×#10596833	C₂²	1	2	yes	—
27	C₄×#10596833	C₂²	1	2	yes	—
28	C₂×#11924027	C₂²	1	1	yes	characteristic
29	C₄×Dic₁₄₆	C₄	1	1	yes	characteristic
30	#14556556	C₄	1	1	yes	characteristic
31	D₄×Dic₇₃	C₄	1	1	yes	characteristic
32	C₄×C₂²⋊D₇₃	C₄	1	1	yes	characteristic
33	C₄×C₂²⋊D₇₃	C₄	1	1	yes	characteristic
34	#14556551	C₄	1	1	yes	characteristic
35	#14556551	C₄	1	1	yes	characteristic
36	#14556549	C₂²	1	1	yes	characteristic
37	#14556547	C₂²	1	1	yes	characteristic
38	#14556547	C₂²	1	1	yes	characteristic
39	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
41	C₄²×D₇₃	C₂²	1	1	yes	characteristic
42	C₄×D₄×C₇₃	C₄	1	1	yes	characteristic
43	#11924037	—	2	4	no	—
44	C₂×#10596833	—	2	4	no	—
45	C₂×#10596833	C₂³	1	2	yes	—
46	C₂×#10596833	C₂³	1	2	yes	—
47	C₂×#10596833	C₂³	1	2	yes	—
48	C₂×#10596833	C₂³	1	2	yes	—
49	#11924027	—	2	2	no	—
50	#11924027	—	2	2	no	—
51	C₂×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
52	C₂×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
57	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
58	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
61	C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
62	#11924007	C₂×C₄	1	1	yes	characteristic
63	#11924007	C₂×C₄	1	1	yes	characteristic
64	#11924007	C₂×C₄	1	1	yes	characteristic
65	#11924007	C₂×C₄	1	1	yes	characteristic
66	C₂²⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
67	C₂²⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
68	#11924005	C₂×C₄	1	1	yes	characteristic
69	#11924005	C₂×C₄	1	1	yes	characteristic
70	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
71	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
72	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
73	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
74	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
75	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
76	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
77	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
78	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
79	C₂×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
82	C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
83	C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
84	C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
85	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
86	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
87	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×D₇₃	C₂²×C₄	1	1	yes	characteristic
89	D₄×C₇₃	—	2	2	no	—
90	C₂×C₄×C₇₃	—	4	1	no	—
91	C₂×C₄×C₇₃	—	4	1	no	—
92	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²⋊D₇₃	—	2	2	no	—
98	C₂²⋊D₇₃	—	2	2	no	—
99	C₂×Dic₇₃	—	2	2	no	—
100	C₂×Dic₇₃	—	2	2	no	—
101	C₂×Dic₇₃	—	2	1	no	—
102	C₂×Dic₇₃	—	2	1	no	—
103	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×Dic₇₃	#41	1	2	yes	—
110	C₂×Dic₇₃	#41	1	2	yes	—
111	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
112	C₄×D₇₃	—	2	2	no	—
113	C₄×D₇₃	—	2	1	no	—
114	C₄×D₇₃	—	2	1	no	—
115	C₄×D₇₃	—	4	1	no	—
116	Dic₁₄₆	—	2	2	no	—
117	#10596833	—	2	2	no	—
118	#10596833	—	2	2	no	—
119	#10596833	—	2	2	no	—
120	#10596833	—	2	2	no	—
121	C₂²×C₇₃	—	2	1	no	—
122	C₂²×C₇₃	—	2	1	no	—
123	C₂²×C₇₃	—	2	1	no	—
124	C₂²×C₇₃	—	2	1	no	—
125	C₂²×C₇₃	—	2	1	no	—
126	C₂²×C₇₃	#117	1	2	yes	—
127	C₂²×C₇₃	C₂³×C₄	1	1	yes	characteristic
128	C₂×D₇₃	—	2	1	no	—
129	C₂×D₇₃	—	2	1	no	—
130	C₂×D₇₃	—	2	1	no	—
131	C₄×C₇₃	—	2	1	no	—
132	C₄×C₇₃	—	2	1	no	—
133	C₄×C₇₃	—	2	1	no	—
134	C₄×C₇₃	—	2	1	no	—
135	C₄×C₇₃	—	2	1	no	—
136	Dic₇₃	—	2	1	no	—
137	Dic₇₃	—	2	1	no	—
138	Dic₇₃	—	2	1	no	—
139	Dic₇₃	—	2	1	no	—
140	Dic₇₃	#117	1	2	yes	—
141	Dic₇₃	#131	1	2	yes	—
142	Dic₇₃	C₂×#41	1	1	yes	characteristic
143	Dic₇₃	C₂×#41	1	1	yes	characteristic
144	C₂×C₇₃	—	2	2	no	—
145	C₂×C₇₃	—	4	1	no	—
146	C₂×C₇₃	C₂×#117	1	1	yes	characteristic
147	C₂×C₇₃	C₂×#131	1	1	yes	characteristic
148	C₂×C₇₃	#568	1	1	yes	characteristic
149	D₇₃	—	4	1	no	—
150	#2925	—	73	1	no	maximal, Sylow
151	C₇₃	#2925	1	1	yes	characteristic, complemented, Sylow
152	C₄×#41	—	73	1	no	—
153	#433	—	73	2	no	—
154	#433	—	73	2	no	—
155	#432	—	73	1	no	—
156	#432	—	73	1	no	—
157	#431	—	73	1	no	—
158	#431	—	73	1	no	—
159	#423	—	73	1	no	—
160	C₂×C₄⋊C₈	—	73	1	no	—
161	#408	—	73	2	no	—
162	#405	—	73	2	no	—
163	C₂×#41	—	73	1	no	—
164	C₂×M₁₆	—	73	2	no	—
165	C₂²×C₈	—	73	2	no	—
166	C₄×Q₈	—	73	1	no	—
167	C₄×Q₈	—	73	1	no	—
168	C₄×D₄	—	73	1	no	—
169	C₄×D₄	—	73	1	no	—
170	C₄×D₄	—	73	1	no	—
171	C₄×D₄	—	73	1	no	—
172	C₄×D₄	—	73	1	no	—
173	C₄×D₄	#64408	1	1	yes	characteristic
174	#117	—	73	1	no	—
175	#117	—	73	1	no	—
176	#117	—	73	1	no	—
177	C₂×C₄²	—	73	1	no	—
178	C₂×C₄²	—	73	1	no	—
179	C₂×C₄²	—	73	1	no	—
180	C₄⋊C₈	—	73	1	no	—
181	C₄⋊C₈	—	73	1	no	—
182	C₄⋊C₈	—	73	2	no	—
183	C₄⋊C₈	—	73	1	no	—
184	C₄⋊C₈	—	73	1	no	—
185	C₄⋊C₈	—	73	2	no	—
186	C₂²⋊C₈	—	73	2	no	—
187	C₂²⋊C₈	—	73	2	no	—
188	C₂²⋊C₈	—	73	2	no	—
189	C₂²⋊C₈	—	73	2	no	—
190	#97	—	73	2	no	—
191	#97	—	73	2	no	—
192	C₄×C₈	—	73	2	no	—
193	C₄×C₈	—	73	2	no	—
194	#41	—	146	2	no	—
195	#41	—	146	2	no	—
196	C₂×Q₈	—	73	1	no	—
197	C₂×D₄	—	73	1	no	—
198	C₂×D₄	—	73	1	no	—
199	C₂×D₄	C₂×#64408	1	1	yes	characteristic
200	C₂²×C₄	—	73	1	no	—
201	C₂²×C₄	—	73	1	no	—
202	C₂²×C₄	—	73	1	no	—
203	C₂²×C₄	—	73	1	no	—
204	C₂²×C₄	—	73	1	no	—
205	C₂²×C₄	—	73	1	no	—
206	C₂²×C₄	—	73	1	no	—
207	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
208	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
209	M₁₆	—	146	4	no	—
210	C₂×C₈	—	73	2	no	—
211	C₂×C₈	—	73	2	no	—
212	C₂×C₈	—	73	2	no	—
213	C₂×C₈	—	73	2	no	—
214	C₂×C₈	—	146	4	no	—
215	C₄⋊C₄	—	73	1	no	—
216	C₄⋊C₄	—	73	1	no	—
217	C₄⋊C₄	—	73	1	no	—
218	C₄⋊C₄	—	73	1	no	—
219	C₄⋊C₄	—	73	1	no	—
220	C₄⋊C₄	C₂×#64408	1	1	yes	characteristic
221	C₂²⋊C₄	—	73	1	no	—
222	C₂²⋊C₄	—	73	1	no	—
223	C₂²⋊C₄	—	73	1	no	—
224	C₂²⋊C₄	—	73	1	no	—
225	C₂²⋊C₄	C₂×#64408	1	1	yes	characteristic
226	C₂²⋊C₄	C₂×#64408	1	1	yes	characteristic
227	C₄²	—	73	1	no	—
228	C₄²	—	73	1	no	—
229	C₄²	—	73	1	no	—
230	C₄²	—	73	1	no	—
231	C₄²	—	73	1	no	—
232	C₄²	—	73	1	no	—
233	C₄²	—	73	1	no	—
234	C₄²	—	73	1	no	—
235	C₄²	—	73	1	no	—
236	C₄²	C₂×#64408	1	1	yes	characteristic
237	C₂³	—	73	1	no	—
238	C₂³	C₂²×#64408	1	1	yes	characteristic
239	C₂³	C₂²×#64408	1	1	yes	characteristic
240	Q₈	—	146	2	no	—
241	D₄	—	2	2	no	—
242	D₄	—	146	2	no	—
243	D₄	—	146	2	no	—
244	C₂×C₄	—	4	1	no	—
245	C₂×C₄	—	4	1	no	—
246	C₂×C₄	—	292	1	no	—
247	C₂×C₄	—	73	1	no	—
248	C₂×C₄	—	73	1	no	—
249	C₂×C₄	—	73	1	no	—
250	C₂×C₄	—	73	2	no	—
251	C₂×C₄	—	73	2	no	—
252	C₂×C₄	—	73	1	no	—
253	C₂×C₄	—	73	1	no	—
254	C₂×C₄	—	73	1	no	—
255	C₂×C₄	—	73	1	no	—
256	C₂×C₄	—	146	1	no	—
257	C₂×C₄	—	146	1	no	—
258	C₂×C₄	—	146	2	no	—
259	C₂×C₄	—	146	1	no	—
260	C₂×C₄	—	146	1	no	—
261	C₂×C₄	—	146	2	no	—
262	C₂×C₄	—	146	2	no	—
263	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
264	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
265	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
266	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
267	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
268	C₈	—	146	2	no	—
269	C₈	—	146	2	no	—
270	C₈	—	146	2	no	—
271	C₈	—	146	2	no	—
272	C₂²	—	2	1	no	—
273	C₂²	—	2	1	no	—
274	C₂²	—	2	1	no	—
275	C₂²	—	2	1	no	—
276	C₂²	—	2	1	no	—
277	C₂²	—	146	1	no	—
278	C₂²	—	146	1	no	—
279	C₂²	—	146	1	no	—
280	C₂²	#14556670	1	2	yes	—
281	C₂²	C₂³×#64408	1	1	yes	characteristic
282	C₄	—	2	1	no	—
283	C₄	—	2	1	no	—
284	C₄	—	2	1	no	—
285	C₄	—	2	1	no	—
286	C₄	—	2	1	no	—
287	C₄	—	73	1	no	—
288	C₄	—	73	1	no	—
289	C₄	—	73	2	no	—
290	C₄	—	73	2	no	—
291	C₄	—	146	1	no	—
292	C₄	—	146	1	no	—
293	C₄	—	146	1	no	—
294	C₄	—	146	1	no	—
295	C₂	—	2	2	no	—
296	C₂	—	4	1	no	—
297	C₂	—	292	1	no	—
298	C₂	C₂×#14556670	1	1	yes	characteristic
299	C₂	D₇₃⋊#131	1	1	yes	characteristic
300	C₂	#17989665	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂³×C₄
Fitting	C₄×D₄×C₇₃	C₄
hypercenter	C₄×D₄	#64408
hypocenter	C₇₃	#2925
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #17989612	C₂	semidirect
2. #17989611	C₂	semidirect
3. #17989610	C₂	semidirect
4. #17989607	C₂	semidirect
5. #17989605	C₂	semidirect
6. #17989604	C₂	semidirect
7. #17989590	C₂	semidirect
8. C₂×#14556658	C₂	semidirect
10. #17989551	C₂	semidirect
151. C₇₃	#2925	semidirect