Subgroups — #547×D₁₇₃ #36367016

Order 22144.

1632 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₇₃	C₂	1	2	yes	maximal, complemented
2	#26012146	C₂	1	1	yes	maximal, characteristic, complemented
3	#26012145	C₂	1	1	yes	maximal, characteristic, complemented
4	#26012144	C₂	1	1	yes	maximal, characteristic, complemented
5	#26012143	C₂	1	2	yes	maximal, complemented
6	#26012142	C₂	1	2	yes	maximal, complemented
7	#26012141	C₂	1	2	yes	maximal, complemented
8	#26012140	C₂	1	2	yes	maximal, complemented
9	#26012139	C₂	1	4	yes	maximal, complemented
10	C₄⋊Q₈×D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#123×D₁₇₃	C₂	1	4	yes	maximal, complemented
12	C₂²⋊Q₈×D₁₇₃	C₂	1	2	yes	maximal, complemented
13	#121×D₁₇₃	C₂	1	2	yes	maximal, complemented
14	C₄×D₄×D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×D₄×D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄⋊C₄×D₁₇₃	C₂	1	2	yes	maximal, complemented
17	#547×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14583827	C₂²	1	2	yes	complemented
19	C₂×#14583826	C₂²	1	4	yes	complemented
20	C₂×#14583826	C₂²	1	2	yes	complemented
21	C₂×#14583825	C₂²	1	4	yes	complemented
22	C₂×#14583825	C₂²	1	2	yes	complemented
23	#41×D₁₇₃	—	2	16	no	—
24	C₂×Q₈×D₁₇₃	C₂²	1	2	yes	—
25	C₂×D₄×D₁₇₃	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₁₇₃	C₂²	1	4	yes	—
27	C₂×D₄×D₁₇₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₁₇₃	C₂²	1	2	yes	—
29	C₂²×C₄×D₁₇₃	C₂²	1	4	yes	—
30	C₂²×C₄×D₁₇₃	C₂²	1	2	yes	—
31	#19149679	C₂²	1	1	yes	characteristic, complemented
32	#19149678	C₂²	1	2	yes	complemented
33	#19149678	C₂²	1	2	yes	complemented
34	#19149677	C₂²	1	2	yes	complemented
35	#19149664	C₂²	1	4	yes	complemented
36	#19149664	C₂²	1	4	yes	complemented
37	#19149663	C₂²	1	4	yes	complemented
38	#19149662	C₂²	1	4	yes	complemented
39	#19149661	C₂²	1	4	yes	complemented
40	#19149661	C₂²	1	4	yes	complemented
41	#19149660	C₂²	1	4	yes	complemented
42	#19149659	C₂²	1	2	yes	complemented
43	#19149658	C₂²	1	2	yes	complemented
44	#19149657	C₂²	1	4	yes	complemented
45	#19149656	C₂²	1	4	yes	complemented
46	#19149655	C₂²	1	2	yes	complemented
47	#19149654	C₂²	1	2	yes	complemented
48	#19149653	C₂²	1	2	yes	complemented
49	#19149652	C₂²	1	4	yes	complemented
50	#19149651	C₂²	1	4	yes	complemented
51	#19149650	C₂²	1	2	yes	complemented
52	C₄×D₆₉₂	C₂²	1	1	yes	characteristic, complemented
53	C₄×D₆₉₂	C₂²	1	1	yes	characteristic, complemented
54	D₄×Dic₁₇₃	C₂²	1	1	yes	characteristic, complemented
55	D₄×Dic₁₇₃	C₂²	1	1	yes	characteristic, complemented
56	#19149641	C₂²	1	1	yes	characteristic, complemented
57	#19149641	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	complemented
60	#19149639	C₂²	1	2	yes	complemented
61	#19149639	C₂²	1	2	yes	complemented
62	C₂×C₄⋊Dic₁₇₃	C₂²	1	2	yes	complemented
63	C₂×#14583805	C₂²	1	4	yes	complemented
64	C₄⋊C₄×D₁₇₃	C₂²	1	1	yes	characteristic
65	C₄⋊C₄×D₁₇₃	C₂²	1	2	yes	—
66	C₄⋊C₄×D₁₇₃	C₂²	1	4	yes	—
67	C₄⋊C₄×D₁₇₃	C₂²	1	1	yes	characteristic
68	C₄⋊C₄×D₁₇₃	C₂²	1	2	yes	—
69	C₄⋊C₄×D₁₇₃	C₂²	1	4	yes	complemented
70	C₄⋊C₄×D₁₇₃	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₁₇₃	C₂²	1	2	yes	complemented
72	C₂²⋊C₄×D₁₇₃	C₂²	1	2	yes	—
73	C₂²⋊C₄×D₁₇₃	C₂²	1	2	yes	—
74	C₂²⋊C₄×D₁₇₃	C₂²	1	4	yes	—
75	C₄²×D₁₇₃	C₂²	1	1	yes	characteristic
76	C₂×#41×C₁₇₃	C₂²	1	2	yes	complemented
77	C₄⋊Q₈×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
78	#123×C₁₇₃	C₂²	1	4	yes	complemented
79	C₂²⋊Q₈×C₁₇₃	C₂²	1	2	yes	complemented
80	#121×C₁₇₃	C₂²	1	2	yes	complemented
81	C₄×D₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄⋊C₄×C₁₇₃	C₂²	1	2	yes	complemented
84	C₂³×D₁₇₃	C₂³	1	2	yes	—
85	C₂³×D₁₇₃	C₂³	1	2	yes	—
86	#14583827	—	2	8	no	—
87	#14583826	—	2	8	no	—
88	#14583826	—	2	16	no	—
89	#14583825	—	2	16	no	—
90	#14583825	—	2	8	no	—
91	C₂×Dic₃₄₆	C₂³	1	4	yes	—
92	C₂×Dic₃₄₆	C₂³	1	2	yes	—
93	Q₈×D₁₇₃	—	2	8	no	—
94	C₂×D₆₉₂	C₂³	1	1	yes	characteristic
95	C₂×D₆₉₂	C₂³	1	4	yes	—
96	C₂×D₆₉₂	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
98	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
101	D₄×D₁₇₃	—	2	16	no	—
102	D₄×D₁₇₃	—	2	4	no	—
103	D₄×D₁₇₃	D₄	1	8	yes	complemented
104	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
105	C₂²×Dic₁₇₃	C₂³	1	4	yes	—
106	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
107	C₂×C₄×D₁₇₃	—	2	16	no	—
108	C₂×C₄×D₁₇₃	—	2	8	no	—
109	C₂×C₄×D₁₇₃	—	2	8	no	—
110	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
112	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
113	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
114	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
115	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
116	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
117	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
118	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
119	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
120	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
121	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
122	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
123	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
124	C₄⋊Dic₁₇₃	C₂³	1	4	yes	—
125	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
126	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
127	#14583805	C₂³	1	2	yes	—
128	#14583805	C₂³	1	4	yes	—
129	#14583805	C₂³	1	4	yes	—
130	#14583805	C₂³	1	4	yes	—
131	#14583805	C₂³	1	2	yes	—
132	#14583805	C₂³	1	4	yes	—
133	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
134	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
135	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
136	#14583803	C₂³	1	2	yes	—
137	#14583803	C₂³	1	2	yes	—
138	#14583803	C₂³	1	2	yes	—
139	#14583803	C₂³	1	2	yes	—
140	#14583803	C₂³	1	4	yes	—
141	#14583803	C₂³	1	4	yes	—
142	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
143	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
144	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
145	#41×C₁₇₃	—	2	8	no	—
146	C₂×Q₈×C₁₇₃	C₂³	1	2	yes	—
147	C₂×D₄×C₁₇₃	C₂³	1	4	yes	—
148	C₂×D₄×C₁₇₃	C₂³	1	1	yes	characteristic
149	C₂×D₄×C₁₇₃	C₂³	1	1	yes	characteristic
150	C₂²×C₄×C₁₇₃	C₂³	1	4	yes	—
151	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
152	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
153	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
154	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
155	C₄⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₁₇₃	C₂³	1	4	yes	—
157	C₄⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
158	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
160	C₂²⋊C₄×C₁₇₃	C₂³	1	4	yes	—
161	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
162	C₂²×D₁₇₃	—	2	4	no	—
163	C₂²×D₁₇₃	—	2	4	no	—
164	C₂²×D₁₇₃	—	2	4	no	—
165	C₂²×D₁₇₃	—	2	4	no	—
166	C₂²×D₁₇₃	—	2	4	no	—
167	C₂²×D₁₇₃	C₂×D₄	1	8	yes	—
168	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
169	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
170	C₂²×D₁₇₃	C₂⁴	1	1	yes	characteristic
171	Dic₃₄₆	—	2	4	no	—
172	Dic₃₄₆	—	2	8	no	—
173	D₆₉₂	—	2	8	no	—
174	D₆₉₂	—	2	2	no	—
175	D₆₉₂	C₂×D₄	1	4	yes	complemented
176	C₂²⋊D₁₇₃	—	2	8	no	—
177	C₂²⋊D₁₇₃	—	2	8	no	—
178	C₂²⋊D₁₇₃	—	2	4	no	—
179	C₂²⋊D₁₇₃	C₂×D₄	1	8	yes	complemented
180	C₂×Dic₁₇₃	—	2	8	no	—
181	C₂×Dic₁₇₃	—	2	4	no	—
182	C₂×Dic₁₇₃	—	2	4	no	—
183	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
184	C₂×Dic₁₇₃	C₂⁴	1	4	yes	—
185	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
186	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
187	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
188	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
189	C₄×D₁₇₃	—	2	4	no	—
190	C₄×D₁₇₃	—	2	8	no	—
191	C₄×D₁₇₃	—	2	8	no	—
192	C₄×D₁₇₃	—	2	8	no	—
193	C₄×D₁₇₃	—	2	4	no	—
194	C₄×D₁₇₃	—	2	2	no	—
195	C₄×D₁₇₃	—	2	4	no	—
196	C₄×D₁₇₃	—	2	4	no	—
197	C₄×D₁₇₃	—	2	4	no	—
198	C₄×D₁₇₃	—	2	4	no	—
199	C₄×D₁₇₃	C₂×D₄	1	4	yes	—
200	C₄×D₁₇₃	#41	1	4	yes	complemented
201	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
202	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
203	Q₈×C₁₇₃	—	2	4	no	—
204	D₄×C₁₇₃	—	2	8	no	—
205	D₄×C₁₇₃	—	2	2	no	—
206	D₄×C₁₇₃	C₂×D₄	1	4	yes	complemented
207	C₂×C₄×C₁₇₃	—	2	8	no	—
208	C₂×C₄×C₁₇₃	—	2	4	no	—
209	C₂×C₄×C₁₇₃	—	2	4	no	—
210	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
211	C₂×C₄×C₁₇₃	C₂⁴	1	4	yes	—
212	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
213	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
214	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
215	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
216	C₂²×C₁₇₃	—	2	2	no	—
217	C₂²×C₁₇₃	—	2	2	no	—
218	C₂²×C₁₇₃	—	2	2	no	—
219	C₂²×C₁₇₃	—	2	2	no	—
220	C₂²×C₁₇₃	—	2	2	no	—
221	C₂²×C₁₇₃	C₂²×D₄	1	4	yes	—
222	C₂²×C₁₇₃	C₂⁵	1	1	yes	characteristic
223	C₂×D₁₇₃	—	2	2	no	—
224	C₂×D₁₇₃	—	2	2	no	—
225	C₂×D₁₇₃	—	2	16	no	—
226	C₂×D₁₇₃	—	2	2	no	—
227	C₂×D₁₇₃	—	2	2	no	—
228	C₂×D₁₇₃	—	2	2	no	—
229	C₂×D₁₇₃	—	4	8	no	—
230	C₂×D₁₇₃	C₂²×D₄	1	4	yes	—
231	C₂×D₁₇₃	C₂²×D₄	1	2	yes	—
232	C₂×D₁₇₃	C₂×#41	1	2	yes	—
233	C₂×D₁₇₃	2₋¹⁺⁴	1	2	yes	—
234	C₄×C₁₇₃	—	2	2	no	—
235	C₄×C₁₇₃	—	2	4	no	—
236	C₄×C₁₇₃	—	2	2	no	—
237	C₄×C₁₇₃	—	2	1	no	—
238	C₄×C₁₇₃	C₂²×D₄	1	2	yes	—
239	C₄×C₁₇₃	C₂×#41	1	2	yes	complemented
240	Dic₁₇₃	—	2	2	no	—
241	Dic₁₇₃	—	2	4	no	—
242	Dic₁₇₃	—	2	2	no	—
243	Dic₁₇₃	—	2	1	no	—
244	Dic₁₇₃	C₂²×D₄	1	2	yes	—
245	Dic₁₇₃	C₂×#41	1	2	yes	complemented
246	C₂×C₁₇₃	—	2	4	no	—
247	C₂×C₁₇₃	—	4	2	no	—
248	C₂×C₁₇₃	C₂³×D₄	1	1	yes	characteristic
249	C₂×C₁₇₃	C₂²×#41	1	1	yes	characteristic
250	C₂×C₁₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
251	D₁₇₃	—	2	4	no	—
252	D₁₇₃	—	4	2	no	—
253	D₁₇₃	#547	1	4	yes	direct product factor
254	C₁₇₃	C₂×#547	1	1	yes	characteristic, complemented, Sylow
255	C₂×#547	—	173	1	no	maximal, Sylow
256	C₂²×#41	—	173	2	no	—
257	#547	—	173	2	no	—
258	#547	—	173	1	no	—
259	#547	—	173	4	no	—
260	#547	—	173	2	no	—
261	#547	—	173	2	no	—
262	#547	—	173	1	no	—
263	#547	—	173	1	no	—
264	#547	—	173	2	no	—
265	#547	D₁₇₃	1	1	yes	characteristic, direct product factor
266	C₂×C₄⋊Q₈	—	173	1	no	—
267	C₂×#123	—	173	4	no	—
268	C₂×C₂²⋊Q₈	—	173	2	no	—
269	C₂×#121	—	173	2	no	—
270	C₂×C₄×D₄	—	173	1	no	—
271	C₂×C₄×D₄	—	173	1	no	—
272	C₂²×C₄⋊C₄	—	173	2	no	—
273	C₂×#41	—	346	16	no	—
274	C₂×#41	—	173	2	no	—
275	C₂×#41	—	173	2	no	—
276	C₂×#41	—	173	4	no	—
277	C₂×#41	—	173	2	no	—
278	C₂×#41	—	173	4	no	—
279	C₂×#41	C₂×D₁₇₃	1	2	yes	complemented
280	C₂²×Q₈	—	173	2	no	—
281	C₂²×D₄	—	173	1	no	—
282	C₂²×D₄	—	173	4	no	—
283	C₂²×D₄	—	173	1	no	—
284	C₂³×C₄	—	173	2	no	—
285	C₂³×C₄	—	173	4	no	—
286	C₂³×C₄	—	173	2	no	—
287	C₄⋊Q₈	—	173	2	no	—
288	C₄⋊Q₈	—	173	2	no	—
289	C₄⋊Q₈	—	173	2	no	—
290	C₄⋊Q₈	—	173	1	no	—
291	C₄⋊Q₈	C₂×D₁₇₃	1	1	yes	characteristic, complemented
292	#123	—	173	4	no	—
293	#123	—	173	4	no	—
294	#123	—	173	4	no	—
295	#123	—	173	4	no	—
296	#123	—	173	4	no	—
297	#123	—	173	4	no	—
298	#123	—	173	4	no	—
299	#123	C₂×D₁₇₃	1	4	yes	complemented
300	C₂²⋊Q₈	—	173	2	no	—
301	C₂²⋊Q₈	—	173	2	no	—
302	C₂²⋊Q₈	—	173	4	no	—
303	C₂²⋊Q₈	—	173	2	no	—
304	C₂²⋊Q₈	—	173	4	no	—
305	C₂²⋊Q₈	C₂×D₁₇₃	1	2	yes	complemented
306	#121	—	173	2	no	—
307	#121	—	173	4	no	—
308	#121	—	173	2	no	—
309	#121	—	173	2	no	—
310	#121	—	173	4	no	—
311	#121	C₂×D₁₇₃	1	2	yes	complemented
312	C₄×D₄	—	173	1	no	—
313	C₄×D₄	—	173	1	no	—
314	C₄×D₄	—	173	2	no	—
315	C₄×D₄	—	173	2	no	—
316	C₄×D₄	—	173	1	no	—
317	C₄×D₄	—	173	1	no	—
318	C₄×D₄	—	173	2	no	—
319	C₄×D₄	—	173	2	no	—
320	C₄×D₄	—	173	1	no	—
321	C₄×D₄	—	173	1	no	—
322	C₄×D₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
323	C₄×D₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
324	C₂×C₄⋊C₄	—	173	4	no	—
325	C₂×C₄⋊C₄	—	173	2	no	—
326	C₂×C₄⋊C₄	—	173	1	no	—
327	C₂×C₄⋊C₄	—	173	2	no	—
328	C₂×C₄⋊C₄	—	173	4	no	—
329	C₂×C₄⋊C₄	—	173	4	no	—
330	C₂×C₄⋊C₄	—	173	2	no	—
331	C₂×C₄⋊C₄	—	173	2	no	—
332	C₂×C₄⋊C₄	—	173	1	no	—
333	C₂×C₄⋊C₄	—	173	2	no	—
334	C₂×C₄⋊C₄	C₂×D₁₇₃	1	2	yes	complemented
335	C₂×C₂²⋊C₄	—	173	2	no	—
336	C₂×C₂²⋊C₄	—	173	2	no	—
337	C₂×C₂²⋊C₄	—	173	4	no	—
338	C₂×C₄²	—	173	1	no	—
339	C₂⁴	—	173	2	no	—
340	C₂⁴	—	173	2	no	—
341	#41	—	2	8	no	—
342	#41	—	346	16	no	—
343	#41	—	346	8	no	—
344	#41	—	346	16	no	—
345	#41	—	346	8	no	—
346	#41	—	346	8	no	—
347	C₂×Q₈	—	346	8	no	—
348	C₂×Q₈	—	173	2	no	—
349	C₂×Q₈	—	173	4	no	—
350	C₂×Q₈	C₂²×D₁₇₃	1	2	yes	—
351	C₂×D₄	—	346	16	no	—
352	C₂×D₄	—	346	4	no	—
353	C₂×D₄	—	173	2	no	—
354	C₂×D₄	—	173	4	no	—
355	C₂×D₄	—	173	4	no	—
356	C₂×D₄	—	173	2	no	—
357	C₂×D₄	—	173	8	no	—
358	C₂×D₄	—	173	1	no	—
359	C₂×D₄	—	173	4	no	—
360	C₂×D₄	—	173	1	no	—
361	C₂×D₄	C₂²×D₁₇₃	1	1	yes	characteristic
362	C₂×D₄	C₂²×D₁₇₃	1	4	yes	—
363	C₂×D₄	C₂²×D₁₇₃	1	1	yes	characteristic
364	C₂²×C₄	—	346	16	no	—
365	C₂²×C₄	—	346	8	no	—
366	C₂²×C₄	—	346	8	no	—
367	C₂²×C₄	—	173	2	no	—
368	C₂²×C₄	—	173	4	no	—
369	C₂²×C₄	—	173	2	no	—
370	C₂²×C₄	—	173	1	no	—
371	C₂²×C₄	—	173	2	no	—
372	C₂²×C₄	—	173	2	no	—
373	C₂²×C₄	—	173	4	no	—
374	C₂²×C₄	—	173	2	no	—
375	C₂²×C₄	—	173	2	no	—
376	C₂²×C₄	—	173	4	no	—
377	C₂²×C₄	—	173	4	no	—
378	C₂²×C₄	—	173	2	no	—
379	C₂²×C₄	—	173	2	no	—
380	C₂²×C₄	—	173	1	no	—
381	C₂²×C₄	—	173	1	no	—
382	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
383	C₂²×C₄	C₂²×D₁₇₃	1	4	yes	—
384	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
385	C₄⋊C₄	—	173	2	no	—
386	C₄⋊C₄	—	173	1	no	—
387	C₄⋊C₄	—	173	4	no	—
388	C₄⋊C₄	—	173	2	no	—
389	C₄⋊C₄	—	173	4	no	—
390	C₄⋊C₄	—	173	4	no	—
391	C₄⋊C₄	—	173	4	no	—
392	C₄⋊C₄	—	173	2	no	—
393	C₄⋊C₄	—	173	1	no	—
394	C₄⋊C₄	—	173	4	no	—
395	C₄⋊C₄	—	173	2	no	—
396	C₄⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
398	C₄⋊C₄	C₂²×D₁₇₃	1	4	yes	—
399	C₄⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
400	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
401	C₂²⋊C₄	—	173	2	no	—
402	C₂²⋊C₄	—	173	2	no	—
403	C₂²⋊C₄	—	173	4	no	—
404	C₂²⋊C₄	—	173	2	no	—
405	C₂²⋊C₄	—	173	2	no	—
406	C₂²⋊C₄	—	173	2	no	—
407	C₂²⋊C₄	—	173	2	no	—
408	C₂²⋊C₄	—	173	4	no	—
409	C₂²⋊C₄	—	173	4	no	—
410	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
411	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
412	C₂²⋊C₄	C₂²×D₁₇₃	1	4	yes	—
413	C₄²	—	173	1	no	—
414	C₄²	—	173	1	no	—
415	C₄²	—	173	1	no	—
416	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
417	C₂³	—	346	4	no	—
418	C₂³	—	346	4	no	—
419	C₂³	—	346	4	no	—
420	C₂³	—	346	4	no	—
421	C₂³	—	346	4	no	—
422	C₂³	—	173	2	no	—
423	C₂³	—	173	8	no	—
424	C₂³	—	173	2	no	—
425	C₂³	—	173	1	no	—
426	C₂³	C₂³×D₁₇₃	1	2	yes	—
427	C₂³	C₂³×D₁₇₃	1	2	yes	—
428	Q₈	—	2	4	no	—
429	Q₈	—	346	8	no	—
430	Q₈	—	346	4	no	—
431	D₄	—	2	8	no	—
432	D₄	—	2	2	no	—
433	D₄	—	346	8	no	—
434	D₄	—	346	8	no	—
435	D₄	—	346	8	no	—
436	D₄	—	346	4	no	—
437	D₄	—	346	2	no	—
438	D₄	—	173	8	no	—
439	D₄	—	173	4	no	—
440	D₄	D₄×D₁₇₃	1	4	yes	complemented
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	346	4	no	—
445	C₂×C₄	—	346	4	no	—
446	C₂×C₄	—	346	8	no	—
447	C₂×C₄	—	346	8	no	—
448	C₂×C₄	—	346	8	no	—
449	C₂×C₄	—	346	2	no	—
450	C₂×C₄	—	346	4	no	—
451	C₂×C₄	—	346	4	no	—
452	C₂×C₄	—	346	8	no	—
453	C₂×C₄	—	346	4	no	—
454	C₂×C₄	—	346	4	no	—
455	C₂×C₄	—	346	4	no	—
456	C₂×C₄	—	346	4	no	—
457	C₂×C₄	—	173	1	no	—
458	C₂×C₄	—	173	2	no	—
459	C₂×C₄	—	173	2	no	—
460	C₂×C₄	—	173	4	no	—
461	C₂×C₄	—	173	1	no	—
462	C₂×C₄	—	173	1	no	—
463	C₂×C₄	—	173	4	no	—
464	C₂×C₄	—	173	4	no	—
465	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
466	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
467	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
468	C₂×C₄	C₂³×D₁₇₃	1	4	yes	—
469	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
470	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	346	16	no	—
477	C₂²	—	346	2	no	—
478	C₂²	—	346	2	no	—
479	C₂²	—	346	2	no	—
480	C₂²	—	346	2	no	—
481	C₂²	—	346	2	no	—
482	C₂²	—	173	4	no	—
483	C₂²	—	173	2	no	—
484	C₂²	—	173	2	no	—
485	C₂²	—	173	2	no	—
486	C₂²	—	692	8	no	—
487	C₂²	C₂×D₄×D₁₇₃	1	4	yes	—
488	C₂²	C₂⁴×D₁₇₃	1	1	yes	characteristic
489	C₄	—	2	2	no	—
490	C₄	—	2	4	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	1	no	—
493	C₄	—	346	2	no	—
494	C₄	—	346	4	no	—
495	C₄	—	346	2	no	—
496	C₄	—	346	1	no	—
497	C₄	—	173	2	no	—
498	C₄	—	173	2	no	—
499	C₄	C₂×D₄×D₁₇₃	1	2	yes	—
500	C₄	#41×D₁₇₃	1	2	yes	complemented
501	C₂	—	2	4	no	—
502	C₂	—	4	2	no	—
503	C₂	—	346	4	no	—
504	C₂	—	173	4	no	—
505	C₂	—	692	2	no	—
506	C₂	C₂²×D₄×D₁₇₃	1	1	yes	characteristic
507	C₂	C₂×#41×D₁₇₃	1	1	yes	characteristic
508	C₂	2₋¹⁺⁴×D₁₇₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇₃
commutator, socle, cosocle	C₂²×C₁₇₃	C₂⁵
Fitting	#547×C₁₇₃	C₂
hypercenter	#547	D₁₇₃
hypocenter	C₁₇₃	C₂×#547
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₇₃	C₂	semidirect
2. #26012146	C₂	semidirect
3. #26012145	C₂	semidirect
4. #26012144	C₂	semidirect
5. #26012143	C₂	semidirect
6. #26012142	C₂	semidirect
7. #26012141	C₂	semidirect
8. #26012140	C₂	semidirect
9. #26012139	C₂	semidirect
10. C₄⋊Q₈×D₁₇₃	C₂	semidirect
11. #123×D₁₇₃	C₂	semidirect
12. C₂²⋊Q₈×D₁₇₃	C₂	semidirect
13. #121×D₁₇₃	C₂	semidirect
14. C₄×D₄×D₁₇₃	C₂	semidirect
15. C₄×D₄×D₁₇₃	C₂	semidirect
16. C₂×C₄⋊C₄×D₁₇₃	C₂	semidirect
17. #547×C₁₇₃	C₂	semidirect
18. C₂×#14583827	C₂²	semidirect
19. C₂×#14583826	C₂²	semidirect
20. C₂×#14583826	C₂²	semidirect
21. C₂×#14583825	C₂²	semidirect
22. C₂×#14583825	C₂²	semidirect
31. #19149679	C₂²	semidirect
32. #19149678	C₂²	semidirect
33. #19149678	C₂²	semidirect
34. #19149677	C₂²	semidirect
35. #19149664	C₂²	semidirect
36. #19149664	C₂²	semidirect
37. #19149663	C₂²	semidirect
38. #19149662	C₂²	semidirect
39. #19149661	C₂²	semidirect
40. #19149661	C₂²	semidirect
41. #19149660	C₂²	semidirect
42. #19149659	C₂²	semidirect
43. #19149658	C₂²	semidirect
44. #19149657	C₂²	semidirect
45. #19149656	C₂²	semidirect
46. #19149655	C₂²	semidirect
47. #19149654	C₂²	semidirect
48. #19149653	C₂²	semidirect
49. #19149652	C₂²	semidirect
50. #19149651	C₂²	semidirect
51. #19149650	C₂²	semidirect
52. C₄×D₆₉₂	C₂²	semidirect
53. C₄×D₆₉₂	C₂²	semidirect
54. D₄×Dic₁₇₃	C₂²	semidirect
55. D₄×Dic₁₇₃	C₂²	semidirect
56. #19149641	C₂²	semidirect
57. #19149641	C₂²	semidirect
58. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
59. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
60. #19149639	C₂²	semidirect
61. #19149639	C₂²	semidirect
62. C₂×C₄⋊Dic₁₇₃	C₂²	semidirect
63. C₂×#14583805	C₂²	semidirect
69. C₄⋊C₄×D₁₇₃	C₂²	semidirect
70. C₄⋊C₄×D₁₇₃	C₂²	semidirect
71. C₄⋊C₄×D₁₇₃	C₂²	semidirect
76. C₂×#41×C₁₇₃	C₂²	semidirect
77. C₄⋊Q₈×C₁₇₃	C₂²	semidirect
78. #123×C₁₇₃	C₂²	semidirect
79. C₂²⋊Q₈×C₁₇₃	C₂²	semidirect
80. #121×C₁₇₃	C₂²	semidirect
81. C₄×D₄×C₁₇₃	C₂²	semidirect
82. C₄×D₄×C₁₇₃	C₂²	semidirect
83. C₂×C₄⋊C₄×C₁₇₃	C₂²	semidirect
103. D₄×D₁₇₃	D₄	semidirect
175. D₆₉₂	C₂×D₄	semidirect
179. C₂²⋊D₁₇₃	C₂×D₄	semidirect
200. C₄×D₁₇₃	#41	semidirect
206. D₄×C₁₇₃	C₂×D₄	semidirect
239. C₄×C₁₇₃	C₂×#41	semidirect
245. Dic₁₇₃	C₂×#41	semidirect
253. D₁₇₃	#547	direct (N × H)
254. C₁₇₃	C₂×#547	semidirect
265. #547	D₁₇₃	direct (N × H)
279. C₂×#41	C₂×D₁₇₃	semidirect
291. C₄⋊Q₈	C₂×D₁₇₃	semidirect
299. #123	C₂×D₁₇₃	semidirect
305. C₂²⋊Q₈	C₂×D₁₇₃	semidirect
311. #121	C₂×D₁₇₃	semidirect
322. C₄×D₄	C₂×D₁₇₃	semidirect
323. C₄×D₄	C₂×D₁₇₃	semidirect
334. C₂×C₄⋊C₄	C₂×D₁₇₃	semidirect
440. D₄	D₄×D₁₇₃	semidirect
500. C₄	#41×D₁₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₇₃	2
#26012146	2
#26012145	2
#26012144	2
#26012143	2
#26012142	2
#26012141	2
#26012140	2
#26012139	2
C₄⋊Q₈×D₁₇₃	2
#123×D₁₇₃	2
C₂²⋊Q₈×D₁₇₃	2
#121×D₁₇₃	2
C₄×D₄×D₁₇₃	2
C₂×C₄⋊C₄×D₁₇₃	2
#547×C₁₇₃	2
C₂×#547	173

Subgroups — #547×D173 #36367016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #547×D₁₇₃ #36367016