Subgroups — #36367168

Order 22144.

1242 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012223	C₂	1	1	yes	maximal, characteristic, complemented
2	#26012200	C₂	1	1	yes	maximal, characteristic, complemented
3	#26012199	C₂	1	1	yes	maximal, characteristic, complemented
4	#26012188	C₂	1	1	yes	maximal, characteristic, complemented
5	#26012187	C₂	1	1	yes	maximal, characteristic, complemented
6	#26012184	C₂	1	2	yes	maximal, complemented
7	#26012167	C₂	1	2	yes	maximal, complemented
8	#26012164	C₂	1	2	yes	maximal, complemented
9	#26012129	C₂	1	1	yes	maximal, characteristic, complemented
10	#26012128	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#26012036	C₂	1	1	yes	maximal, characteristic, complemented
13	#26012027	C₂	1	1	yes	maximal, characteristic, complemented
14	#26012020	C₂	1	1	yes	maximal, characteristic, complemented
15	#26012018	C₂	1	2	yes	maximal, complemented
16	#26012001	C₂	1	2	yes	maximal, complemented
17	#26011997	C₂	1	2	yes	maximal, complemented
18	#41×Dic₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#14583825	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×D₄×Dic₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#19149639	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14583825	C₂²	1	1	yes	characteristic
25	C₂×#14583825	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊D₁₇₃	C₂²	1	2	yes	—
27	C₂×D₄×D₁₇₃	C₂²	1	1	yes	characteristic
28	C₂³×Dic₁₇₃	C₂²	1	2	yes	complemented
29	C₂²×C₄×D₁₇₃	C₂²	1	2	yes	complemented
30	#19149678	C₂²	1	1	yes	characteristic, complemented
31	#19149675	C₂²	1	1	yes	characteristic
32	#19149674	C₂²	1	2	yes	complemented
33	#19149674	C₂²	1	2	yes	complemented
34	#19149672	C₂²	1	2	yes	complemented
35	#19149672	C₂²	1	2	yes	complemented
36	#19149671	C₂²	1	1	yes	characteristic, complemented
37	#19149670	C₂²	1	1	yes	characteristic, complemented
38	#19149669	C₂²	1	2	yes	complemented
39	#19149668	C₂²	1	1	yes	characteristic, complemented
40	#19149665	C₂²	1	2	yes	complemented
41	#19149665	C₂²	1	2	yes	complemented
42	#19149663	C₂²	1	2	yes	complemented
43	#19149663	C₂²	1	2	yes	complemented
44	#19149662	C₂²	1	2	yes	complemented
45	#19149661	C₂²	1	2	yes	complemented
46	#19149661	C₂²	1	2	yes	complemented
47	#19149661	C₂²	1	2	yes	complemented
48	#19149660	C₂²	1	2	yes	complemented
49	#19149659	C₂²	1	2	yes	complemented
50	#19149658	C₂²	1	2	yes	complemented
51	#19149656	C₂²	1	2	yes	complemented
52	#19149656	C₂²	1	2	yes	complemented
53	#19149656	C₂²	1	2	yes	complemented
54	#19149655	C₂²	1	1	yes	characteristic, complemented
55	#19149653	C₂²	1	1	yes	characteristic
56	#19149653	C₂²	1	1	yes	characteristic, complemented
57	#19149651	C₂²	1	2	yes	—
58	#19149651	C₂²	1	2	yes	complemented
59	#19149651	C₂²	1	2	yes	complemented
60	#19149651	C₂²	1	2	yes	complemented
61	#19149650	C₂²	1	1	yes	characteristic
62	#19149650	C₂²	1	2	yes	complemented
63	#19149648	C₂²	1	2	yes	—
64	#19149647	C₂²	1	2	yes	—
65	#19149647	C₂²	1	2	yes	complemented
66	Q₈×Dic₁₇₃	C₂²	1	1	yes	characteristic, complemented
67	Q₈×Dic₁₇₃	C₂²	1	1	yes	characteristic, complemented
68	C₄×Dic₃₄₆	C₂²	1	1	yes	characteristic, complemented
69	#19149644	C₂²	1	1	yes	characteristic, complemented
70	C₄×D₆₉₂	C₂²	1	1	yes	characteristic, complemented
71	D₄×Dic₁₇₃	C₂²	1	1	yes	characteristic
72	D₄×Dic₁₇₃	C₂²	1	1	yes	characteristic
73	D₄×Dic₁₇₃	C₂²	1	1	yes	characteristic
74	D₄×Dic₁₇₃	C₂²	1	2	yes	complemented
75	D₄×Dic₁₇₃	C₂²	1	2	yes	complemented
76	D₄×Dic₁₇₃	C₂²	1	1	yes	characteristic, complemented
77	D₄×Dic₁₇₃	C₂²	1	2	yes	complemented
78	D₄×Dic₁₇₃	C₂²	1	1	yes	characteristic, complemented
79	D₄×Dic₁₇₃	C₂²	1	1	yes	characteristic, complemented
80	D₄×Dic₁₇₃	C₂²	1	2	yes	complemented
81	#19149641	C₂²	1	1	yes	characteristic, complemented
82	C₄×C₂²⋊D₁₇₃	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊D₁₇₃	C₂²	1	1	yes	characteristic, complemented
85	#19149639	C₂²	1	2	yes	—
86	#19149639	C₂²	1	1	yes	characteristic
87	#19149639	C₂²	1	2	yes	complemented
88	#19149639	C₂²	1	2	yes	complemented
89	#19149639	C₂²	1	2	yes	complemented
90	#19149639	C₂²	1	2	yes	complemented
91	#19149639	C₂²	1	2	yes	complemented
92	#19149639	C₂²	1	2	yes	complemented
93	#19149639	C₂²	1	2	yes	complemented
94	#19149639	C₂²	1	1	yes	characteristic, complemented
95	#19149638	C₂²	1	2	yes	complemented
96	#19149638	C₂²	1	1	yes	characteristic, complemented
97	#19149637	C₂²	1	1	yes	characteristic, complemented
98	#19149637	C₂²	1	2	yes	complemented
99	#19149635	C₂²	1	1	yes	characteristic, complemented
100	#19149635	C₂²	1	1	yes	characteristic, complemented
101	#19149635	C₂²	1	2	yes	complemented
102	C₂×C₄⋊Dic₁₇₃	C₂²	1	1	yes	characteristic, complemented
103	C₂×#14583805	C₂²	1	2	yes	complemented
104	C₄⋊C₄×D₁₇₃	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₂²⋊Dic₁₇₃	C₂²	1	2	yes	complemented
106	C₂×#14583803	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₁₇₃	C₂²	1	2	yes	complemented
108	C₂×C₄×Dic₁₇₃	C₂²	1	2	yes	complemented
109	C₂×C₄×Dic₁₇₃	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₄×Dic₁₇₃	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₁₇₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₁₇₃	C₂²	1	1	yes	characteristic
113	C₂²×D₄×C₁₇₃	C₂²	1	1	yes	characteristic
114	#124×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
115	#123×C₁₇₃	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₇₃	C₂²	1	2	yes	complemented
118	#121×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
119	#120×C₁₇₃	C₂²	1	2	yes	complemented
120	C₄×D₄×C₁₇₃	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊C₄×C₁₇₃	C₂²	1	2	yes	complemented
123	C₂³×D₁₇₃	C₂³	1	2	yes	—
124	#14583825	—	2	4	no	—
125	#14583825	—	4	4	no	—
126	C₂×Dic₃₄₆	C₂³	1	1	yes	characteristic
127	C₂×Dic₃₄₆	C₂³	1	2	yes	—
128	C₂×D₆₉₂	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₇₃	—	2	8	no	—
130	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₇₃	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₇₃	C₂³	1	1	yes	characteristic
138	D₄×D₁₇₃	—	2	4	no	—
139	C₂²×Dic₁₇₃	—	4	4	no	—
140	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
141	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
142	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
143	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
144	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
145	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
146	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
147	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
148	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
149	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
150	C₂×C₄×D₁₇₃	—	4	4	no	—
151	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
155	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
156	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
157	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
160	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
162	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
164	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
165	#14583805	C₂³	1	2	yes	—
166	#14583805	C₂³	1	1	yes	characteristic
167	#14583805	C₂³	1	2	yes	—
168	#14583805	C₂³	1	2	yes	—
169	#14583805	C₂³	1	2	yes	—
170	#14583805	C₂³	1	1	yes	characteristic
171	#14583805	C₂³	1	1	yes	characteristic
172	#14583805	C₂³	1	1	yes	characteristic
173	#14583805	C₂³	1	2	yes	—
174	#14583805	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
184	#14583803	C₂³	1	2	yes	—
185	#14583803	C₂³	1	2	yes	—
186	#14583803	C₂³	1	1	yes	characteristic
187	#14583803	C₂³	1	2	yes	—
188	#14583803	C₂³	1	2	yes	—
189	#14583803	C₂³	1	2	yes	—
190	#14583803	C₂³	1	1	yes	characteristic
191	#14583803	C₂³	1	2	yes	—
192	#14583803	C₂³	1	2	yes	—
193	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₇₃	C₂³	1	2	yes	—
199	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₇₃	C₂³	1	2	yes	—
202	C₄×Dic₁₇₃	C₂³	1	2	yes	—
203	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
205	C₂⁴×C₁₇₃	C₂³	1	2	yes	—
206	#41×C₁₇₃	—	2	4	no	—
207	C₂×Q₈×C₁₇₃	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₇₃	—	2	4	no	—
209	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
210	C₂×D₄×C₁₇₃	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
212	C₂×D₄×C₁₇₃	C₂³	1	1	yes	characteristic
213	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
214	C₂×D₄×C₁₇₃	C₂³	1	1	yes	characteristic
215	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
216	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
217	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
218	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
219	C₄⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
221	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
229	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
230	C₂²×D₁₇₃	—	2	4	no	—
231	C₂²×D₁₇₃	—	2	4	no	—
232	C₂²×D₁₇₃	—	4	2	no	—
233	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
234	C₂²×D₁₇₃	C₂⁴	1	1	yes	characteristic
235	Dic₃₄₆	—	2	2	no	—
236	Dic₃₄₆	—	4	2	no	—
237	D₆₉₂	—	2	2	no	—
238	C₂²⋊D₁₇₃	—	2	4	no	—
239	C₂²⋊D₁₇₃	—	2	4	no	—
240	C₂²⋊D₁₇₃	—	2	4	no	—
241	C₂²⋊D₁₇₃	—	2	2	no	—
242	C₂²⋊D₁₇₃	—	2	4	no	—
243	C₂²⋊D₁₇₃	—	4	2	no	—
244	C₂²⋊D₁₇₃	—	4	2	no	—
245	C₂²⋊D₁₇₃	#41	1	4	yes	complemented
246	C₂×Dic₁₇₃	—	2	2	no	—
247	C₂×Dic₁₇₃	—	2	4	no	—
248	C₂×Dic₁₇₃	—	2	2	no	—
249	C₂×Dic₁₇₃	—	2	4	no	—
250	C₂×Dic₁₇₃	—	2	2	no	—
251	C₂×Dic₁₇₃	—	2	4	no	—
252	C₂×Dic₁₇₃	—	2	2	no	—
253	C₂×Dic₁₇₃	—	4	2	no	—
254	C₂×Dic₁₇₃	—	4	2	no	—
255	C₂×Dic₁₇₃	—	4	2	no	—
256	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
257	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
261	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
263	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
266	C₄×D₁₇₃	—	2	2	no	—
267	C₄×D₁₇₃	—	2	2	no	—
268	C₄×D₁₇₃	—	2	2	no	—
269	C₄×D₁₇₃	—	2	4	no	—
270	C₄×D₁₇₃	—	4	2	no	—
271	C₄×D₁₇₃	—	4	2	no	—
272	C₂³×C₁₇₃	—	2	4	no	—
273	C₂³×C₁₇₃	—	2	4	no	—
274	C₂³×C₁₇₃	—	4	2	no	—
275	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
276	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
277	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
278	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
279	Q₈×C₁₇₃	—	2	2	no	—
280	D₄×C₁₇₃	—	2	2	no	—
281	D₄×C₁₇₃	—	2	4	no	—
282	D₄×C₁₇₃	—	2	4	no	—
283	D₄×C₁₇₃	—	2	2	no	—
284	D₄×C₁₇₃	—	4	2	no	—
285	D₄×C₁₇₃	#41	1	4	yes	complemented
286	C₂×C₄×C₁₇₃	—	2	4	no	—
287	C₂×C₄×C₁₇₃	—	2	2	no	—
288	C₂×C₄×C₁₇₃	—	2	2	no	—
289	C₂×C₄×C₁₇₃	—	4	2	no	—
290	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
291	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
292	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
293	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
294	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
295	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
296	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₁₇₃	—	2	1	no	—
298	C₂²×C₁₇₃	—	2	2	no	—
299	C₂²×C₁₇₃	—	2	2	no	—
300	C₂²×C₁₇₃	—	2	1	no	—
301	C₂²×C₁₇₃	—	2	1	no	—
302	C₂²×C₁₇₃	—	2	2	no	—
303	C₂²×C₁₇₃	—	2	1	no	—
304	C₂²×C₁₇₃	—	2	2	no	—
305	C₂²×C₁₇₃	—	2	1	no	—
306	C₂²×C₁₇₃	—	2	2	no	—
307	C₂²×C₁₇₃	—	4	8	no	—
308	C₂²×C₁₇₃	C₂×#41	1	2	yes	—
309	C₂²×C₁₇₃	C₂×#41	1	4	yes	—
310	C₂²×C₁₇₃	C₂⁵	1	1	yes	characteristic
311	C₂×D₁₇₃	—	2	1	no	—
312	C₂×D₁₇₃	—	2	1	no	—
313	C₂×D₁₇₃	—	2	2	no	—
314	C₂×D₁₇₃	—	2	2	no	—
315	C₂×D₁₇₃	—	2	2	no	—
316	C₂×D₁₇₃	—	4	8	no	—
317	C₂×D₁₇₃	C₂×#41	1	2	yes	—
318	C₄×C₁₇₃	—	2	1	no	—
319	C₄×C₁₇₃	—	2	1	no	—
320	C₄×C₁₇₃	—	2	2	no	—
321	C₄×C₁₇₃	—	2	1	no	—
322	C₄×C₁₇₃	—	2	1	no	—
323	C₄×C₁₇₃	—	2	2	no	—
324	C₄×C₁₇₃	C₂×#41	1	2	yes	—
325	Dic₁₇₃	—	2	1	no	—
326	Dic₁₇₃	—	2	1	no	—
327	Dic₁₇₃	—	2	2	no	—
328	Dic₁₇₃	—	2	1	no	—
329	Dic₁₇₃	—	2	2	no	—
330	Dic₁₇₃	—	2	1	no	—
331	Dic₁₇₃	—	2	2	no	—
332	Dic₁₇₃	—	2	1	no	—
333	Dic₁₇₃	C₂×#41	1	2	yes	—
334	Dic₁₇₃	H(5,𝔽₂)	1	2	yes	—
335	C₂×C₁₇₃	—	2	4	no	—
336	C₂×C₁₇₃	—	2	2	no	—
337	C₂×C₁₇₃	—	4	1	no	—
338	C₂×C₁₇₃	—	4	2	no	—
339	C₂×C₁₇₃	C₂²×#41	1	1	yes	characteristic
340	C₂×C₁₇₃	C₂²×#41	1	1	yes	characteristic
341	C₂×C₁₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
342	D₁₇₃	—	2	2	no	—
343	D₁₇₃	—	4	2	no	—
344	C₁₇₃	#3481	1	1	yes	characteristic, complemented, Sylow
345	#3481	—	173	1	no	maximal, Sylow
346	#559	—	173	1	no	—
347	#554	—	173	1	no	—
348	#554	—	173	1	no	—
349	#553	—	173	2	no	—
350	#553	—	173	1	no	—
351	#553	—	173	1	no	—
352	#551	—	173	2	no	—
353	#551	—	173	2	no	—
354	#546	—	173	1	no	—
355	#546	—	173	2	no	—
356	#546	D₁₇₃	1	1	yes	characteristic, complemented
357	D₄²	—	173	1	no	—
358	#532	—	173	1	no	—
359	#529	—	173	1	no	—
360	#529	—	173	2	no	—
361	#529	—	173	1	no	—
362	#525	—	173	2	no	—
363	#525	—	173	2	no	—
364	C₄×#41	—	173	1	no	—
365	C₄×#41	—	173	1	no	—
366	C₂×C₄×D₄	—	173	1	no	—
367	C₂×C₄×D₄	—	173	1	no	—
368	C₂×C₄×D₄	—	173	2	no	—
369	C₂×#41	—	173	1	no	—
370	C₂×#41	—	173	2	no	—
371	C₂×#41	C₂×D₁₇₃	1	1	yes	characteristic
372	C₂²×D₄	—	173	2	no	—
373	C₂²×D₄	—	173	1	no	—
374	C₂²×D₄	C₂×D₁₇₃	1	1	yes	characteristic
375	C₂³×C₄	—	173	2	no	—
376	C₂³×C₄	—	173	2	no	—
377	C₄⋊Q₈	—	173	1	no	—
378	#127	—	173	1	no	—
379	#126	—	173	2	no	—
380	#126	—	173	2	no	—
381	#126	—	173	2	no	—
382	#126	—	173	2	no	—
383	#125	—	173	2	no	—
384	#125	—	173	1	no	—
385	#125	—	173	1	no	—
386	#124	—	173	1	no	—
387	#124	—	173	2	no	—
388	#124	—	173	2	no	—
389	#124	C₂×D₁₇₃	1	1	yes	characteristic, complemented
390	#123	—	173	2	no	—
391	#123	—	173	2	no	—
392	#123	—	173	2	no	—
393	#123	—	173	2	no	—
394	#123	—	173	2	no	—
395	#123	—	173	2	no	—
396	#123	—	173	2	no	—
397	#123	C₂×D₁₇₃	1	2	yes	complemented
398	C₂²⋊Q₈	—	173	1	no	—
399	C₂²⋊Q₈	—	173	2	no	—
400	C₂²⋊Q₈	—	173	2	no	—
401	C₂²⋊Q₈	—	173	2	no	—
402	C₂²⋊Q₈	—	173	2	no	—
403	C₂²⋊Q₈	—	173	2	no	—
404	C₂²⋊Q₈	C₂×D₁₇₃	1	1	yes	characteristic, complemented
405	#121	—	173	2	no	—
406	#121	—	173	2	no	—
407	#121	—	173	2	no	—
408	#121	—	173	1	no	—
409	#121	—	173	2	no	—
410	#121	—	173	2	no	—
411	#121	—	173	1	no	—
412	#121	—	173	1	no	—
413	#121	C₂×D₁₇₃	1	2	yes	complemented
414	#121	C₂×D₁₇₃	1	1	yes	characteristic, complemented
415	#120	—	173	2	no	—
416	#120	—	173	2	no	—
417	#120	—	173	2	no	—
418	#120	C₂×D₁₇₃	1	2	yes	complemented
419	C₄×Q₈	—	173	1	no	—
420	C₄×Q₈	—	173	1	no	—
421	C₄×Q₈	—	173	1	no	—
422	C₄×Q₈	—	173	1	no	—
423	C₄×D₄	—	173	1	no	—
424	C₄×D₄	—	173	2	no	—
425	C₄×D₄	—	173	1	no	—
426	C₄×D₄	—	173	1	no	—
427	C₄×D₄	—	173	2	no	—
428	C₄×D₄	—	173	1	no	—
429	C₄×D₄	—	173	2	no	—
430	C₄×D₄	—	173	1	no	—
431	C₄×D₄	—	173	1	no	—
432	C₄×D₄	—	173	2	no	—
433	C₄×D₄	—	173	2	no	—
434	C₄×D₄	—	173	1	no	—
435	C₄×D₄	—	173	1	no	—
436	C₄×D₄	—	173	1	no	—
437	C₄×D₄	—	173	1	no	—
438	C₄×D₄	—	173	2	no	—
439	C₄×D₄	—	173	2	no	—
440	C₄×D₄	—	173	2	no	—
441	C₄×D₄	—	173	2	no	—
442	C₄×D₄	—	173	2	no	—
443	C₄×D₄	—	173	2	no	—
444	C₄×D₄	—	173	2	no	—
445	C₄×D₄	—	173	2	no	—
446	C₄×D₄	—	173	1	no	—
447	C₄×D₄	—	173	1	no	—
448	C₄×D₄	C₂×D₁₇₃	1	1	yes	characteristic
449	C₄×D₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
450	#117	—	173	2	no	—
451	#117	—	173	1	no	—
452	#117	—	173	1	no	—
453	#117	—	173	2	no	—
454	#117	—	173	1	no	—
455	#117	—	173	1	no	—
456	#117	—	173	2	no	—
457	C₂×C₄⋊C₄	—	173	2	no	—
458	C₂×C₄⋊C₄	—	173	1	no	—
459	C₂×C₄⋊C₄	—	173	1	no	—
460	C₂×C₂²⋊C₄	—	173	2	no	—
461	C₂×C₂²⋊C₄	—	173	2	no	—
462	C₂×C₂²⋊C₄	—	173	2	no	—
463	C₂×C₂²⋊C₄	C₂×D₁₇₃	1	2	yes	complemented
464	C₂×C₄²	—	173	1	no	—
465	C₂×C₄²	—	173	2	no	—
466	C₂×C₄²	—	173	1	no	—
467	C₂×C₄²	—	173	1	no	—
468	C₂⁴	—	173	2	no	—
469	C₂⁴	C₂²×D₁₇₃	1	2	yes	—
470	#41	—	2	4	no	—
471	#41	—	346	4	no	—
472	#41	—	692	4	no	—
473	C₂×Q₈	—	173	1	no	—
474	C₂×Q₈	—	173	2	no	—
475	C₂×Q₈	C₂²×D₁₇₃	1	1	yes	characteristic
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	346	8	no	—
478	C₂×D₄	—	346	4	no	—
479	C₂×D₄	—	173	1	no	—
480	C₂×D₄	—	173	2	no	—
481	C₂×D₄	—	173	2	no	—
482	C₂×D₄	—	173	2	no	—
483	C₂×D₄	—	173	2	no	—
484	C₂×D₄	—	173	1	no	—
485	C₂×D₄	—	173	2	no	—
486	C₂×D₄	—	173	2	no	—
487	C₂×D₄	—	173	1	no	—
488	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
489	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
490	C₂×D₄	C₂²×D₁₇₃	1	1	yes	characteristic
491	C₂×D₄	C₂²×D₁₇₃	1	1	yes	characteristic
492	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
493	C₂×D₄	C₂²×D₁₇₃	1	1	yes	characteristic
494	C₂²×C₄	—	173	1	no	—
495	C₂²×C₄	—	173	2	no	—
496	C₂²×C₄	—	173	1	no	—
497	C₂²×C₄	—	173	1	no	—
498	C₂²×C₄	—	173	2	no	—
499	C₂²×C₄	—	173	1	no	—
500	C₂²×C₄	—	173	2	no	—
501	C₂²×C₄	—	173	1	no	—
502	C₂²×C₄	—	173	1	no	—
503	C₂²×C₄	—	173	1	no	—
504	C₂²×C₄	—	173	2	no	—
505	C₂²×C₄	—	173	2	no	—
506	C₂²×C₄	—	173	2	no	—
507	C₂²×C₄	—	173	2	no	—
508	C₂²×C₄	—	173	2	no	—
509	C₂²×C₄	—	173	2	no	—
510	C₂²×C₄	—	692	4	no	—
511	C₂²×C₄	—	692	4	no	—
512	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
513	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
514	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
515	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
516	C₄⋊C₄	—	173	1	no	—
517	C₄⋊C₄	—	173	1	no	—
518	C₄⋊C₄	—	173	2	no	—
519	C₄⋊C₄	—	173	1	no	—
520	C₄⋊C₄	—	173	2	no	—
521	C₄⋊C₄	—	173	2	no	—
522	C₄⋊C₄	—	173	2	no	—
523	C₄⋊C₄	—	173	2	no	—
524	C₄⋊C₄	—	173	1	no	—
525	C₄⋊C₄	—	173	1	no	—
526	C₄⋊C₄	—	173	1	no	—
527	C₄⋊C₄	—	173	2	no	—
528	C₄⋊C₄	—	173	1	no	—
529	C₄⋊C₄	—	173	1	no	—
530	C₄⋊C₄	—	173	2	no	—
531	C₄⋊C₄	—	173	2	no	—
532	C₄⋊C₄	—	173	2	no	—
533	C₄⋊C₄	—	173	2	no	—
534	C₄⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
537	C₂²⋊C₄	—	173	2	no	—
538	C₂²⋊C₄	—	173	2	no	—
539	C₂²⋊C₄	—	173	2	no	—
540	C₂²⋊C₄	—	173	2	no	—
541	C₂²⋊C₄	—	173	1	no	—
542	C₂²⋊C₄	—	173	2	no	—
543	C₂²⋊C₄	—	173	2	no	—
544	C₂²⋊C₄	—	173	1	no	—
545	C₂²⋊C₄	—	173	2	no	—
546	C₂²⋊C₄	—	173	1	no	—
547	C₂²⋊C₄	—	173	2	no	—
548	C₂²⋊C₄	—	173	2	no	—
549	C₂²⋊C₄	—	173	2	no	—
550	C₂²⋊C₄	—	173	2	no	—
551	C₂²⋊C₄	—	173	2	no	—
552	C₂²⋊C₄	—	173	1	no	—
553	C₂²⋊C₄	—	173	2	no	—
554	C₂²⋊C₄	—	173	2	no	—
555	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
557	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
558	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
561	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
562	C₄²	—	173	1	no	—
563	C₄²	—	173	1	no	—
564	C₄²	—	173	1	no	—
565	C₄²	—	173	1	no	—
566	C₄²	—	173	2	no	—
567	C₄²	—	173	1	no	—
568	C₄²	—	173	1	no	—
569	C₄²	—	173	1	no	—
570	C₄²	—	173	2	no	—
571	C₄²	—	173	1	no	—
572	C₄²	—	173	2	no	—
573	C₄²	—	173	1	no	—
574	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
575	C₂³	—	2	4	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	4	2	no	—
578	C₂³	—	346	4	no	—
579	C₂³	—	346	4	no	—
580	C₂³	—	173	2	no	—
581	C₂³	—	173	1	no	—
582	C₂³	—	692	2	no	—
583	C₂³	C₂³×D₁₇₃	1	2	yes	—
584	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
585	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
586	C₂³	C₂³×D₁₇₃	1	2	yes	—
587	Q₈	—	2	2	no	—
588	Q₈	—	346	2	no	—
589	Q₈	—	692	2	no	—
590	D₄	—	2	2	no	—
591	D₄	—	2	4	no	—
592	D₄	—	2	4	no	—
593	D₄	—	2	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	346	4	no	—
596	D₄	—	346	2	no	—
597	D₄	—	346	4	no	—
598	D₄	—	346	4	no	—
599	D₄	—	346	4	no	—
600	D₄	—	346	2	no	—
601	D₄	—	173	4	no	—
602	D₄	—	692	2	no	—
603	D₄	—	692	2	no	—
604	D₄	#14583825	1	4	yes	complemented
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	346	2	no	—
610	C₂×C₄	—	346	2	no	—
611	C₂×C₄	—	346	4	no	—
612	C₂×C₄	—	346	2	no	—
613	C₂×C₄	—	346	4	no	—
614	C₂×C₄	—	346	2	no	—
615	C₂×C₄	—	346	4	no	—
616	C₂×C₄	—	346	4	no	—
617	C₂×C₄	—	346	2	no	—
618	C₂×C₄	—	346	2	no	—
619	C₂×C₄	—	346	2	no	—
620	C₂×C₄	—	173	1	no	—
621	C₂×C₄	—	173	1	no	—
622	C₂×C₄	—	173	2	no	—
623	C₂×C₄	—	173	1	no	—
624	C₂×C₄	—	173	2	no	—
625	C₂×C₄	—	173	1	no	—
626	C₂×C₄	—	173	1	no	—
627	C₂×C₄	—	173	2	no	—
628	C₂×C₄	—	173	1	no	—
629	C₂×C₄	—	173	1	no	—
630	C₂×C₄	—	692	2	no	—
631	C₂×C₄	—	692	2	no	—
632	C₂×C₄	—	692	2	no	—
633	C₂×C₄	—	692	2	no	—
634	C₂×C₄	—	692	2	no	—
635	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
637	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
640	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
641	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	4	8	no	—
653	C₂²	—	346	1	no	—
654	C₂²	—	346	1	no	—
655	C₂²	—	346	2	no	—
656	C₂²	—	346	2	no	—
657	C₂²	—	346	2	no	—
658	C₂²	—	173	2	no	—
659	C₂²	—	692	8	no	—
660	C₂²	#41×D₁₇₃	1	2	yes	—
661	C₂²	C₂×#14583825	1	4	yes	—
662	C₂²	C₂⁴×D₁₇₃	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	346	1	no	—
670	C₄	—	346	2	no	—
671	C₄	—	346	1	no	—
672	C₄	—	346	1	no	—
673	C₄	—	346	2	no	—
674	C₄	—	346	1	no	—
675	C₄	—	346	2	no	—
676	C₄	—	346	1	no	—
677	C₄	—	173	2	no	—
678	C₄	—	173	2	no	—
679	C₄	C₂×#14583825	1	2	yes	—
680	C₂	—	2	2	no	—
681	C₂	—	2	4	no	—
682	C₂	—	4	1	no	—
683	C₂	—	4	2	no	—
684	C₂	—	346	2	no	—
685	C₂	—	692	2	no	—
686	C₂	C₂×#41×D₁₇₃	1	1	yes	characteristic
687	C₂	C₂²×#14583825	1	1	yes	characteristic
688	C₂	H(5,𝔽₂)×D₁₇₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇₃
commutator, socle, cosocle	C₂²×C₁₇₃	C₂⁵
Fitting	#546×C₁₇₃	C₂
hypercenter	#546	D₁₇₃
hypocenter	C₁₇₃	#3481
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #26012223	C₂	semidirect
2. #26012200	C₂	semidirect
3. #26012199	C₂	semidirect
4. #26012188	C₂	semidirect
5. #26012187	C₂	semidirect
6. #26012184	C₂	semidirect
7. #26012167	C₂	semidirect
8. #26012164	C₂	semidirect
9. #26012129	C₂	semidirect
10. #26012128	C₂	semidirect
11. D₄×C₂²⋊D₁₇₃	C₂	semidirect
12. #26012036	C₂	semidirect
13. #26012027	C₂	semidirect
14. #26012020	C₂	semidirect
15. #26012018	C₂	semidirect
16. #26012001	C₂	semidirect
17. #26011997	C₂	semidirect
18. #41×Dic₁₇₃	C₂	semidirect
19. C₄×#14583825	C₂	semidirect
20. C₂×D₄×Dic₁₇₃	C₂	semidirect
21. C₂×#19149639	C₂	semidirect
22. C₄×D₄×D₁₇₃	C₂	semidirect
23. #546×C₁₇₃	C₂	semidirect
25. C₂×#14583825	C₂²	semidirect
28. C₂³×Dic₁₇₃	C₂²	semidirect
29. C₂²×C₄×D₁₇₃	C₂²	semidirect
30. #19149678	C₂²	semidirect
32. #19149674	C₂²	semidirect
33. #19149674	C₂²	semidirect
34. #19149672	C₂²	semidirect
35. #19149672	C₂²	semidirect
36. #19149671	C₂²	semidirect
37. #19149670	C₂²	semidirect
38. #19149669	C₂²	semidirect
39. #19149668	C₂²	semidirect
40. #19149665	C₂²	semidirect
41. #19149665	C₂²	semidirect
42. #19149663	C₂²	semidirect
43. #19149663	C₂²	semidirect
44. #19149662	C₂²	semidirect
45. #19149661	C₂²	semidirect
46. #19149661	C₂²	semidirect
47. #19149661	C₂²	semidirect
48. #19149660	C₂²	semidirect
49. #19149659	C₂²	semidirect
50. #19149658	C₂²	semidirect
51. #19149656	C₂²	semidirect
52. #19149656	C₂²	semidirect
53. #19149656	C₂²	semidirect
54. #19149655	C₂²	semidirect
56. #19149653	C₂²	semidirect
58. #19149651	C₂²	semidirect
59. #19149651	C₂²	semidirect
60. #19149651	C₂²	semidirect
62. #19149650	C₂²	semidirect
65. #19149647	C₂²	semidirect
66. Q₈×Dic₁₇₃	C₂²	semidirect
67. Q₈×Dic₁₇₃	C₂²	semidirect
68. C₄×Dic₃₄₆	C₂²	semidirect
69. #19149644	C₂²	semidirect
70. C₄×D₆₉₂	C₂²	semidirect
74. D₄×Dic₁₇₃	C₂²	semidirect
75. D₄×Dic₁₇₃	C₂²	semidirect
76. D₄×Dic₁₇₃	C₂²	semidirect
77. D₄×Dic₁₇₃	C₂²	semidirect
78. D₄×Dic₁₇₃	C₂²	semidirect
79. D₄×Dic₁₇₃	C₂²	semidirect
80. D₄×Dic₁₇₃	C₂²	semidirect
81. #19149641	C₂²	semidirect
83. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
84. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
87. #19149639	C₂²	semidirect
88. #19149639	C₂²	semidirect
89. #19149639	C₂²	semidirect
90. #19149639	C₂²	semidirect
91. #19149639	C₂²	semidirect
92. #19149639	C₂²	semidirect
93. #19149639	C₂²	semidirect
94. #19149639	C₂²	semidirect
95. #19149638	C₂²	semidirect
96. #19149638	C₂²	semidirect
97. #19149637	C₂²	semidirect
98. #19149637	C₂²	semidirect
99. #19149635	C₂²	semidirect
100. #19149635	C₂²	semidirect
101. #19149635	C₂²	semidirect
102. C₂×C₄⋊Dic₁₇₃	C₂²	semidirect
103. C₂×#14583805	C₂²	semidirect
104. C₄⋊C₄×D₁₇₃	C₂²	semidirect
105. C₂×C₂²⋊Dic₁₇₃	C₂²	semidirect
106. C₂×#14583803	C₂²	semidirect
107. C₂²⋊C₄×D₁₇₃	C₂²	semidirect
108. C₂×C₄×Dic₁₇₃	C₂²	semidirect
109. C₂×C₄×Dic₁₇₃	C₂²	semidirect
110. C₂×C₄×Dic₁₇₃	C₂²	semidirect
111. C₄²×D₁₇₃	C₂²	semidirect
114. #124×C₁₇₃	C₂²	semidirect
115. #123×C₁₇₃	C₂²	semidirect
116. C₂²⋊Q₈×C₁₇₃	C₂²	semidirect
117. #121×C₁₇₃	C₂²	semidirect
118. #121×C₁₇₃	C₂²	semidirect
119. #120×C₁₇₃	C₂²	semidirect
121. C₄×D₄×C₁₇₃	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₁₇₃	C₂²	semidirect
245. C₂²⋊D₁₇₃	#41	semidirect
285. D₄×C₁₇₃	#41	semidirect
344. C₁₇₃	#3481	semidirect
356. #546	D₁₇₃	semidirect
389. #124	C₂×D₁₇₃	semidirect
397. #123	C₂×D₁₇₃	semidirect
404. C₂²⋊Q₈	C₂×D₁₇₃	semidirect
413. #121	C₂×D₁₇₃	semidirect
414. #121	C₂×D₁₇₃	semidirect
418. #120	C₂×D₁₇₃	semidirect
449. C₄×D₄	C₂×D₁₇₃	semidirect
463. C₂×C₂²⋊C₄	C₂×D₁₇₃	semidirect
604. D₄	#14583825	semidirect

Maximal subgroups

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

subgroup	index
#26012223	2
#26012200	2
#26012199	2
#26012188	2
#26012187	2
#26012184	2
#26012167	2
#26012164	2
#26012129	2
#26012128	2
D₄×C₂²⋊D₁₇₃	2
#26012036	2
#26012027	2
#26012020	2
#26012018	2
#26012001	2
#26011997	2
#41×Dic₁₇₃	2
C₄×#14583825	2
C₂×D₄×Dic₁₇₃	2
C₂×#19149639	2
C₄×D₄×D₁₇₃	2
#546×C₁₇₃	2
#3481	173