Subgroups — #36367154

Order 22144.

1112 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012225	C₂	1	2	yes	maximal, complemented
2	#26012223	C₂	1	1	yes	maximal, characteristic, complemented
3	#26012218	C₂	1	1	yes	maximal, characteristic, complemented
4	#26012212	C₂	1	1	yes	maximal, characteristic, complemented
5	#26012208	C₂	1	2	yes	maximal, complemented
6	#26012194	C₂	1	1	yes	maximal, characteristic, complemented
7	#26012192	C₂	1	2	yes	maximal, complemented
8	#26012188	C₂	1	1	yes	maximal, characteristic, complemented
9	#26012186	C₂	1	2	yes	maximal, complemented
10	#26012159	C₂	1	1	yes	maximal, characteristic, complemented
11	#26012151	C₂	1	1	yes	maximal, characteristic, complemented
12	#26012149	C₂	1	1	yes	maximal, characteristic, complemented
13	#26012038	C₂	1	2	yes	maximal, complemented
14	#26012038	C₂	1	1	yes	maximal, characteristic, complemented
15	#26012028	C₂	1	1	yes	maximal, characteristic, complemented
16	#26012021	C₂	1	2	yes	maximal, complemented
17	#26012019	C₂	1	2	yes	maximal, complemented
18	C₄×#14583826	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#14583826	C₂	1	1	yes	maximal, characteristic, complemented
20	#26011959	C₂	1	2	yes	maximal, complemented
21	C₄×#14583825	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×Q₈×D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#529×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14583826	C₂²	1	2	yes	—
25	C₂×#14583826	C₂²	1	1	yes	characteristic
26	C₂×#14583826	C₂²	1	1	yes	characteristic
27	C₂×#14583825	C₂²	1	1	yes	characteristic
28	C₂×Q₈×D₁₇₃	C₂²	1	1	yes	characteristic
29	#19149678	C₂²	1	2	yes	—
30	#19149678	C₂²	1	1	yes	characteristic
31	#19149675	C₂²	1	1	yes	characteristic
32	#19149675	C₂²	1	2	yes	—
33	#19149674	C₂²	1	2	yes	—
34	#19149674	C₂²	1	2	yes	—
35	#19149674	C₂²	1	2	yes	—
36	#19149672	C₂²	1	2	yes	—
37	#19149672	C₂²	1	2	yes	—
38	#19149670	C₂²	1	1	yes	characteristic
39	#19149669	C₂²	1	2	yes	—
40	#19149669	C₂²	1	2	yes	—
41	#19149668	C₂²	1	1	yes	characteristic
42	#19149665	C₂²	1	2	yes	—
43	#19149665	C₂²	1	2	yes	—
44	#19149665	C₂²	1	2	yes	—
45	#19149665	C₂²	1	2	yes	—
46	#19149665	C₂²	1	2	yes	—
47	#19149664	C₂²	1	2	yes	—
48	#19149664	C₂²	1	2	yes	—
49	#19149663	C₂²	1	2	yes	—
50	#19149661	C₂²	1	2	yes	—
51	#19149660	C₂²	1	2	yes	—
52	#19149657	C₂²	1	2	yes	—
53	#19149656	C₂²	1	2	yes	—
54	#19149655	C₂²	1	1	yes	characteristic
55	#19149654	C₂²	1	2	yes	—
56	#19149654	C₂²	1	1	yes	characteristic
57	#19149654	C₂²	1	1	yes	characteristic
58	#19149652	C₂²	1	2	yes	—
59	#19149652	C₂²	1	2	yes	—
60	#19149652	C₂²	1	2	yes	—
61	#19149652	C₂²	1	2	yes	—
62	#19149651	C₂²	1	2	yes	—
63	#19149650	C₂²	1	2	yes	—
64	#19149650	C₂²	1	1	yes	characteristic
65	Q₈×Dic₁₇₃	C₂²	1	1	yes	characteristic
66	C₄×Dic₃₄₆	C₂²	1	1	yes	characteristic
67	C₄×Dic₃₄₆	C₂²	1	1	yes	characteristic
68	C₄×Dic₃₄₆	C₂²	1	2	yes	—
69	C₄×Dic₃₄₆	C₂²	1	1	yes	characteristic
70	C₄×Dic₃₄₆	C₂²	1	1	yes	characteristic
71	#19149644	C₂²	1	2	yes	—
72	#19149644	C₂²	1	2	yes	—
73	#19149644	C₂²	1	1	yes	characteristic
74	#19149644	C₂²	1	1	yes	characteristic
75	#19149644	C₂²	1	2	yes	—
76	C₄×D₆₉₂	C₂²	1	1	yes	characteristic
77	C₄×D₆₉₂	C₂²	1	1	yes	characteristic
78	C₄×D₆₉₂	C₂²	1	1	yes	characteristic
79	C₄×D₆₉₂	C₂²	1	1	yes	characteristic
80	C₄×D₆₉₂	C₂²	1	2	yes	—
81	D₄×Dic₁₇₃	C₂²	1	1	yes	characteristic
82	#19149641	C₂²	1	2	yes	—
83	#19149641	C₂²	1	2	yes	—
84	C₄×C₂²⋊D₁₇₃	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	—
86	C₄×C₂²⋊D₁₇₃	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₁₇₃	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	—
89	C₄×C₂²⋊D₁₇₃	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	—
92	#19149639	C₂²	1	2	yes	—
93	#19149639	C₂²	1	2	yes	—
94	#19149639	C₂²	1	2	yes	—
95	#19149639	C₂²	1	2	yes	—
96	#19149639	C₂²	1	2	yes	—
97	#19149638	C₂²	1	1	yes	characteristic
98	#19149638	C₂²	1	1	yes	characteristic
99	#19149637	C₂²	1	1	yes	characteristic
100	#19149636	C₂²	1	2	yes	—
101	#19149636	C₂²	1	1	yes	characteristic
102	#19149636	C₂²	1	2	yes	—
103	#19149636	C₂²	1	1	yes	characteristic
104	#19149635	C₂²	1	2	yes	—
105	C₄⋊C₄×D₁₇₃	C₂²	1	2	yes	—
106	C₄⋊C₄×D₁₇₃	C₂²	1	1	yes	characteristic
107	C₂×C₄×Dic₁₇₃	C₂²	1	2	yes	—
108	C₄²×D₁₇₃	C₂²	1	2	yes	—
109	C₄²×D₁₇₃	C₂²	1	1	yes	characteristic
110	C₄²×D₁₇₃	C₂²	1	1	yes	characteristic
111	C₄²×D₁₇₃	C₂²	1	2	yes	—
112	#126×C₁₇₃	C₂²	1	2	yes	—
113	#125×C₁₇₃	C₂²	1	1	yes	characteristic
114	#124×C₁₇₃	C₂²	1	1	yes	characteristic
115	#123×C₁₇₃	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₇₃	C₂²	1	1	yes	characteristic
117	#121×C₁₇₃	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₁₇₃	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₁₇₃	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₁₇₃	C₂²	1	2	yes	—
121	#117×C₁₇₃	C₂²	1	2	yes	—
122	C₂×C₄²×C₁₇₃	C₂²	1	1	yes	characteristic
123	#14583826	—	2	4	no	—
124	#14583826	—	2	8	no	—
125	#14583826	—	2	4	no	—
126	#14583825	—	2	4	no	—
127	C₂×Dic₃₄₆	C₂³	1	2	yes	—
128	C₂×Dic₃₄₆	C₂³	1	2	yes	—
129	C₂×Dic₃₄₆	C₂³	1	1	yes	characteristic
130	C₂×Dic₃₄₆	C₂³	1	1	yes	characteristic
131	Q₈×D₁₇₃	—	2	4	no	—
132	C₂×D₆₉₂	C₂³	1	2	yes	—
133	C₂×D₆₉₂	C₂³	1	1	yes	characteristic
134	C₂×D₆₉₂	C₂³	1	1	yes	characteristic
135	C₂×D₆₉₂	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₇₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₇₃	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
143	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
144	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
145	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
146	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
148	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
150	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
156	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
158	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
162	#14583805	C₂³	1	2	yes	—
163	#14583805	C₂³	1	2	yes	—
164	#14583805	C₂³	1	2	yes	—
165	#14583805	C₂³	1	2	yes	—
166	#14583805	C₂³	1	1	yes	characteristic
167	#14583805	C₂³	1	1	yes	characteristic
168	#14583805	C₂³	1	2	yes	—
169	#14583805	C₂³	1	2	yes	—
170	#14583805	C₂³	1	2	yes	—
171	#14583805	C₂³	1	1	yes	characteristic
172	#14583805	C₂³	1	1	yes	characteristic
173	#14583805	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
179	#14583803	C₂³	1	1	yes	characteristic
180	#14583803	C₂³	1	1	yes	characteristic
181	#14583803	C₂³	1	2	yes	—
182	#14583803	C₂³	1	2	yes	—
183	#14583803	C₂³	1	1	yes	characteristic
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	2	yes	—
191	C₄×Dic₁₇₃	C₂³	1	2	yes	—
192	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
193	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₇₃	C₂³	1	2	yes	—
195	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₇₃	C₂³	1	2	yes	—
197	C₄×Dic₁₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
202	C₄×Dic₁₇₃	C₂³	1	2	yes	—
203	C₄×Dic₁₇₃	C₂³	1	2	yes	—
204	C₂×Q₈×C₁₇₃	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₁₇₃	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
207	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
208	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
222	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
223	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
224	C₄²×C₁₇₃	C₂³	1	2	yes	—
225	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
226	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
227	C₂²×D₁₇₃	C₂⁴	1	1	yes	characteristic
228	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
229	C₂²×D₁₇₃	C₂⁴	1	1	yes	characteristic
230	Dic₃₄₆	—	2	4	no	—
231	Dic₃₄₆	—	2	4	no	—
232	Dic₃₄₆	—	2	2	no	—
233	Dic₃₄₆	#41	1	4	yes	complemented
234	D₆₉₂	—	2	4	no	—
235	D₆₉₂	—	2	2	no	—
236	D₆₉₂	—	2	2	no	—
237	D₆₉₂	—	4	2	no	—
238	C₂²⋊D₁₇₃	—	2	4	no	—
239	C₂²⋊D₁₇₃	—	2	2	no	—
240	C₂²⋊D₁₇₃	—	2	4	no	—
241	C₂²⋊D₁₇₃	—	2	4	no	—
242	C₂²⋊D₁₇₃	—	2	4	no	—
243	C₂²⋊D₁₇₃	—	2	2	no	—
244	C₂²⋊D₁₇₃	—	4	2	no	—
245	C₂×Dic₁₇₃	—	2	4	no	—
246	C₂×Dic₁₇₃	—	4	2	no	—
247	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
248	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
252	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
255	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
256	C₄×D₁₇₃	—	2	2	no	—
257	C₄×D₁₇₃	—	2	2	no	—
258	C₄×D₁₇₃	—	2	2	no	—
259	C₄×D₁₇₃	—	2	4	no	—
260	C₄×D₁₇₃	—	2	4	no	—
261	C₄×D₁₇₃	—	2	4	no	—
262	C₄×D₁₇₃	—	4	2	no	—
263	C₄×D₁₇₃	—	4	2	no	—
264	C₄×D₁₇₃	—	4	1	no	—
265	C₄×D₁₇₃	—	4	1	no	—
266	C₄×D₁₇₃	#41	1	4	yes	complemented
267	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
268	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
269	Q₈×C₁₇₃	—	2	2	no	—
270	D₄×C₁₇₃	—	2	2	no	—
271	D₄×C₁₇₃	—	4	2	no	—
272	C₂×C₄×C₁₇₃	—	2	2	no	—
273	C₂×C₄×C₁₇₃	—	2	4	no	—
274	C₂×C₄×C₁₇₃	—	2	2	no	—
275	C₂×C₄×C₁₇₃	—	4	1	no	—
276	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
280	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
281	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
283	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₁₇₃	—	2	2	no	—
286	C₂²×C₁₇₃	—	2	1	no	—
287	C₂²×C₁₇₃	—	2	1	no	—
288	C₂²×C₁₇₃	—	2	2	no	—
289	C₂²×C₁₇₃	—	2	1	no	—
290	C₂²×C₁₇₃	—	2	2	no	—
291	C₂²×C₁₇₃	C₂⁵	1	1	yes	characteristic
292	C₂×D₁₇₃	—	2	1	no	—
293	C₂×D₁₇₃	—	2	1	no	—
294	C₂×D₁₇₃	—	2	1	no	—
295	C₂×D₁₇₃	—	2	1	no	—
296	C₂×D₁₇₃	—	2	2	no	—
297	C₂×D₁₇₃	—	2	2	no	—
298	C₂×D₁₇₃	—	2	2	no	—
299	C₂×D₁₇₃	—	2	1	no	—
300	C₂×D₁₇₃	C₂×#41	1	2	yes	—
301	C₄×C₁₇₃	—	2	1	no	—
302	C₄×C₁₇₃	—	2	1	no	—
303	C₄×C₁₇₃	—	2	2	no	—
304	C₄×C₁₇₃	—	2	2	no	—
305	C₄×C₁₇₃	—	2	1	no	—
306	C₄×C₁₇₃	—	2	1	no	—
307	C₄×C₁₇₃	—	2	2	no	—
308	C₄×C₁₇₃	C₂×#41	1	2	yes	—
309	C₄×C₁₇₃	C₂×#41	1	2	yes	—
310	Dic₁₇₃	—	2	1	no	—
311	Dic₁₇₃	—	2	2	no	—
312	Dic₁₇₃	—	2	1	no	—
313	Dic₁₇₃	—	2	1	no	—
314	Dic₁₇₃	—	2	2	no	—
315	Dic₁₇₃	—	2	1	no	—
316	Dic₁₇₃	—	2	1	no	—
317	Dic₁₇₃	C₂×#41	1	4	yes	—
318	Dic₁₇₃	C₂×#41	1	2	yes	—
319	C₂×C₁₇₃	—	4	1	no	—
320	C₂×C₁₇₃	—	4	2	no	—
321	C₂×C₁₇₃	C₂²×#41	1	1	yes	characteristic
322	C₂×C₁₇₃	C₂²×#41	1	1	yes	characteristic
323	C₂×C₁₇₃	#585	1	1	yes	characteristic
324	D₁₇₃	—	2	2	no	—
325	D₁₇₃	—	4	1	no	—
326	D₁₇₃	—	4	2	no	—
327	C₁₇₃	#3480	1	1	yes	characteristic, complemented, Sylow
328	#3480	—	173	1	no	maximal, Sylow
329	#559	—	173	1	no	—
330	#559	—	173	2	no	—
331	#557	—	173	1	no	—
332	#556	—	173	2	no	—
333	#556	—	173	1	no	—
334	#553	—	173	2	no	—
335	#553	—	173	1	no	—
336	#553	—	173	2	no	—
337	#553	—	173	1	no	—
338	#550	—	173	1	no	—
339	#548	—	173	1	no	—
340	#548	—	173	1	no	—
341	#532	—	173	2	no	—
342	#532	—	173	1	no	—
343	#529	—	173	1	no	—
344	#529	—	173	2	no	—
345	#529	—	173	2	no	—
346	#529	D₁₇₃	1	1	yes	characteristic, complemented
347	C₄×#41	—	173	1	no	—
348	C₄×#41	—	173	2	no	—
349	C₄×#41	—	173	1	no	—
350	C₄×#41	—	173	1	no	—
351	C₂×C₄×Q₈	—	173	1	no	—
352	C₂×#41	—	173	1	no	—
353	C₂×#41	—	173	2	no	—
354	C₂×#41	—	173	1	no	—
355	C₂×#41	—	173	1	no	—
356	C₂²×Q₈	—	173	1	no	—
357	C₄⋊Q₈	—	173	2	no	—
358	C₄⋊Q₈	—	173	1	no	—
359	#127	—	173	2	no	—
360	#127	—	173	1	no	—
361	#126	—	173	2	no	—
362	#126	—	173	2	no	—
363	#126	—	173	2	no	—
364	#126	—	173	2	no	—
365	#126	—	173	2	no	—
366	#126	C₂×D₁₇₃	1	2	yes	—
367	#125	—	173	2	no	—
368	#125	—	173	2	no	—
369	#125	—	173	1	no	—
370	#125	C₂×D₁₇₃	1	1	yes	characteristic
371	#124	—	173	1	no	—
372	#124	—	173	2	no	—
373	#124	—	173	2	no	—
374	#124	—	173	2	no	—
375	#124	—	173	2	no	—
376	#124	—	173	2	no	—
377	#124	C₂×D₁₇₃	1	1	yes	characteristic
378	#123	—	173	2	no	—
379	#123	—	173	2	no	—
380	#123	—	173	2	no	—
381	#123	—	173	2	no	—
382	#123	—	173	2	no	—
383	#123	C₂×D₁₇₃	1	2	yes	—
384	C₂²⋊Q₈	—	173	1	no	—
385	C₂²⋊Q₈	—	173	2	no	—
386	C₂²⋊Q₈	—	173	2	no	—
387	C₂²⋊Q₈	C₂×D₁₇₃	1	1	yes	characteristic
388	#121	—	173	2	no	—
389	#121	—	173	1	no	—
390	#121	—	173	2	no	—
391	#121	—	173	1	no	—
392	#121	—	173	1	no	—
393	#121	—	173	2	no	—
394	#121	—	173	2	no	—
395	#121	—	173	2	no	—
396	#121	—	173	2	no	—
397	#121	—	173	2	no	—
398	#121	C₂×D₁₇₃	1	1	yes	characteristic
399	C₄×Q₈	—	173	1	no	—
400	C₄×Q₈	—	173	1	no	—
401	C₄×Q₈	—	173	2	no	—
402	C₄×Q₈	—	173	1	no	—
403	C₄×Q₈	—	173	2	no	—
404	C₄×Q₈	—	173	2	no	—
405	C₄×Q₈	—	173	1	no	—
406	C₄×Q₈	—	173	2	no	—
407	C₄×Q₈	—	173	1	no	—
408	C₄×Q₈	—	173	1	no	—
409	C₄×Q₈	—	173	1	no	—
410	C₄×Q₈	C₂×D₁₇₃	1	1	yes	characteristic
411	C₄×D₄	—	173	1	no	—
412	C₄×D₄	—	173	2	no	—
413	C₄×D₄	—	173	2	no	—
414	C₄×D₄	—	173	1	no	—
415	C₄×D₄	—	173	1	no	—
416	C₄×D₄	—	173	1	no	—
417	C₄×D₄	—	173	2	no	—
418	C₄×D₄	—	173	1	no	—
419	C₄×D₄	—	173	2	no	—
420	C₄×D₄	—	173	2	no	—
421	C₄×D₄	—	173	2	no	—
422	C₄×D₄	—	173	2	no	—
423	C₄×D₄	—	173	2	no	—
424	C₄×D₄	—	173	2	no	—
425	C₄×D₄	—	173	2	no	—
426	C₄×D₄	—	173	2	no	—
427	C₄×D₄	—	173	1	no	—
428	C₄×D₄	—	173	1	no	—
429	C₄×D₄	—	173	1	no	—
430	C₄×D₄	—	173	1	no	—
431	C₄×D₄	—	173	2	no	—
432	C₄×D₄	C₂×D₁₇₃	1	1	yes	characteristic
433	C₄×D₄	C₂×D₁₇₃	1	2	yes	—
434	#117	—	173	1	no	—
435	#117	—	173	1	no	—
436	#117	—	173	1	no	—
437	#117	—	173	2	no	—
438	#117	—	173	1	no	—
439	#117	—	173	2	no	—
440	#117	—	173	1	no	—
441	#117	—	173	2	no	—
442	#117	C₂×D₁₇₃	1	2	yes	—
443	C₂×C₄⋊C₄	—	173	2	no	—
444	C₂×C₄⋊C₄	—	173	1	no	—
445	C₂×C₄²	—	173	2	no	—
446	C₂×C₄²	—	173	2	no	—
447	C₂×C₄²	—	173	1	no	—
448	C₂×C₄²	—	173	1	no	—
449	C₂×C₄²	—	173	2	no	—
450	C₂×C₄²	C₂×D₁₇₃	1	1	yes	characteristic
451	#41	—	346	4	no	—
452	#41	—	346	8	no	—
453	#41	—	346	4	no	—
454	#41	—	346	4	no	—
455	C₂×Q₈	—	346	4	no	—
456	C₂×Q₈	—	173	2	no	—
457	C₂×Q₈	—	173	2	no	—
458	C₂×Q₈	—	173	1	no	—
459	C₂×Q₈	—	173	1	no	—
460	C₂×Q₈	C₂²×D₁₇₃	1	1	yes	characteristic
461	C₂×D₄	—	173	1	no	—
462	C₂×D₄	—	173	2	no	—
463	C₂×D₄	—	173	2	no	—
464	C₂×D₄	—	173	2	no	—
465	C₂×D₄	—	173	1	no	—
466	C₂×D₄	—	173	2	no	—
467	C₂×D₄	—	173	2	no	—
468	C₂×D₄	—	173	2	no	—
469	C₂×D₄	—	173	1	no	—
470	C₂×D₄	—	173	1	no	—
471	C₂×D₄	—	173	2	no	—
472	C₂×D₄	C₂²×D₁₇₃	1	1	yes	characteristic
473	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
474	C₂²×C₄	—	173	2	no	—
475	C₂²×C₄	—	173	2	no	—
476	C₂²×C₄	—	173	1	no	—
477	C₂²×C₄	—	173	2	no	—
478	C₂²×C₄	—	173	1	no	—
479	C₂²×C₄	—	173	1	no	—
480	C₂²×C₄	—	173	2	no	—
481	C₂²×C₄	—	173	1	no	—
482	C₂²×C₄	—	173	2	no	—
483	C₂²×C₄	—	173	2	no	—
484	C₂²×C₄	—	173	1	no	—
485	C₂²×C₄	—	173	1	no	—
486	C₂²×C₄	—	173	2	no	—
487	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
489	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
490	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
491	C₄⋊C₄	—	173	2	no	—
492	C₄⋊C₄	—	173	1	no	—
493	C₄⋊C₄	—	173	2	no	—
494	C₄⋊C₄	—	173	2	no	—
495	C₄⋊C₄	—	173	2	no	—
496	C₄⋊C₄	—	173	1	no	—
497	C₄⋊C₄	—	173	1	no	—
498	C₄⋊C₄	—	173	2	no	—
499	C₄⋊C₄	—	173	2	no	—
500	C₄⋊C₄	—	173	1	no	—
501	C₄⋊C₄	—	173	2	no	—
502	C₄⋊C₄	—	173	1	no	—
503	C₄⋊C₄	—	173	1	no	—
504	C₄⋊C₄	—	173	2	no	—
505	C₄⋊C₄	—	173	1	no	—
506	C₄⋊C₄	—	173	1	no	—
507	C₄⋊C₄	—	173	2	no	—
508	C₄⋊C₄	—	173	2	no	—
509	C₄⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
511	C₄⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
513	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
514	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
515	C₂²⋊C₄	—	173	1	no	—
516	C₂²⋊C₄	—	173	2	no	—
517	C₂²⋊C₄	—	173	2	no	—
518	C₂²⋊C₄	—	173	1	no	—
519	C₂²⋊C₄	—	173	2	no	—
520	C₂²⋊C₄	—	173	1	no	—
521	C₂²⋊C₄	—	173	1	no	—
522	C₂²⋊C₄	—	173	2	no	—
523	C₂²⋊C₄	—	173	1	no	—
524	C₂²⋊C₄	—	173	2	no	—
525	C₂²⋊C₄	—	173	2	no	—
526	C₂²⋊C₄	—	173	2	no	—
527	C₂²⋊C₄	—	173	2	no	—
528	C₂²⋊C₄	—	173	1	no	—
529	C₂²⋊C₄	—	173	2	no	—
530	C₂²⋊C₄	—	173	2	no	—
531	C₂²⋊C₄	—	173	2	no	—
532	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
537	C₄²	—	173	2	no	—
538	C₄²	—	173	2	no	—
539	C₄²	—	173	1	no	—
540	C₄²	—	173	1	no	—
541	C₄²	—	173	2	no	—
542	C₄²	—	173	2	no	—
543	C₄²	—	173	2	no	—
544	C₄²	—	173	1	no	—
545	C₄²	—	173	1	no	—
546	C₄²	—	173	2	no	—
547	C₄²	—	173	1	no	—
548	C₄²	—	173	2	no	—
549	C₄²	—	173	1	no	—
550	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
551	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
552	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
553	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
554	C₄²	C₂²×D₁₇₃	1	2	yes	—
555	C₂³	—	173	1	no	—
556	C₂³	—	173	2	no	—
557	C₂³	—	173	1	no	—
558	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
559	C₂³	C₂³×D₁₇₃	1	2	yes	—
560	Q₈	—	2	2	no	—
561	Q₈	—	346	4	no	—
562	Q₈	—	346	4	no	—
563	Q₈	—	346	2	no	—
564	Q₈	—	173	4	no	—
565	D₄	—	2	2	no	—
566	D₄	—	4	2	no	—
567	D₄	—	346	4	no	—
568	D₄	—	346	2	no	—
569	D₄	—	346	2	no	—
570	D₄	—	346	4	no	—
571	D₄	—	346	4	no	—
572	D₄	—	346	4	no	—
573	D₄	—	346	2	no	—
574	D₄	—	346	4	no	—
575	D₄	—	346	2	no	—
576	D₄	—	692	2	no	—
577	D₄	—	692	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	346	4	no	—
583	C₂×C₄	—	346	4	no	—
584	C₂×C₄	—	346	4	no	—
585	C₂×C₄	—	346	2	no	—
586	C₂×C₄	—	346	2	no	—
587	C₂×C₄	—	346	2	no	—
588	C₂×C₄	—	346	4	no	—
589	C₂×C₄	—	173	1	no	—
590	C₂×C₄	—	173	2	no	—
591	C₂×C₄	—	173	1	no	—
592	C₂×C₄	—	173	1	no	—
593	C₂×C₄	—	173	1	no	—
594	C₂×C₄	—	173	2	no	—
595	C₂×C₄	—	173	1	no	—
596	C₂×C₄	—	173	1	no	—
597	C₂×C₄	—	173	2	no	—
598	C₂×C₄	—	173	4	no	—
599	C₂×C₄	—	692	2	no	—
600	C₂×C₄	—	692	1	no	—
601	C₂×C₄	—	692	1	no	—
602	C₂×C₄	—	692	2	no	—
603	C₂×C₄	—	692	2	no	—
604	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
608	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
609	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
610	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
613	C₂²	—	2	1	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	346	1	no	—
620	C₂²	—	346	1	no	—
621	C₂²	—	346	1	no	—
622	C₂²	—	346	2	no	—
623	C₂²	—	346	2	no	—
624	C₂²	—	346	1	no	—
625	C₂²	—	346	1	no	—
626	C₂²	—	346	2	no	—
627	C₂²	—	173	2	no	—
628	C₂²	C₂⁴×D₁₇₃	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	2	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	346	1	no	—
637	C₄	—	346	1	no	—
638	C₄	—	346	2	no	—
639	C₄	—	346	1	no	—
640	C₄	—	346	2	no	—
641	C₄	—	346	1	no	—
642	C₄	—	346	1	no	—
643	C₄	—	173	4	no	—
644	C₄	—	173	2	no	—
645	C₄	#41×D₁₇₃	1	2	yes	—
646	C₄	#41×D₁₇₃	1	2	yes	—
647	C₂	—	4	1	no	—
648	C₂	—	4	2	no	—
649	C₂	—	346	2	no	—
650	C₂	—	692	1	no	—
651	C₂	—	692	2	no	—
652	C₂	C₂×#41×D₁₇₃	1	1	yes	characteristic
653	C₂	C₂×#41×D₁₇₃	1	1	yes	characteristic
654	C₂	#26012327	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₇₃
commutator, socle, cosocle	C₂²×C₁₇₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₇₃
Fitting	#529×C₁₇₃	C₂
hypercenter	#529	D₁₇₃
hypocenter	C₁₇₃	#3480
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #26012225	C₂	semidirect
2. #26012223	C₂	semidirect
3. #26012218	C₂	semidirect
4. #26012212	C₂	semidirect
5. #26012208	C₂	semidirect
6. #26012194	C₂	semidirect
7. #26012192	C₂	semidirect
8. #26012188	C₂	semidirect
9. #26012186	C₂	semidirect
10. #26012159	C₂	semidirect
11. #26012151	C₂	semidirect
12. #26012149	C₂	semidirect
13. #26012038	C₂	semidirect
14. #26012038	C₂	semidirect
15. #26012028	C₂	semidirect
16. #26012021	C₂	semidirect
17. #26012019	C₂	semidirect
18. C₄×#14583826	C₂	semidirect
19. C₄×#14583826	C₂	semidirect
20. #26011959	C₂	semidirect
21. C₄×#14583825	C₂	semidirect
22. C₄×Q₈×D₁₇₃	C₂	semidirect
23. #529×C₁₇₃	C₂	semidirect
233. Dic₃₄₆	#41	semidirect
266. C₄×D₁₇₃	#41	semidirect
327. C₁₇₃	#3480	semidirect
346. #529	D₁₇₃	semidirect

Maximal subgroups

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

subgroup	index
#26012225	2
#26012223	2
#26012218	2
#26012212	2
#26012208	2
#26012194	2
#26012192	2
#26012188	2
#26012186	2
#26012159	2
#26012151	2
#26012149	2
#26012038	2
#26012028	2
#26012021	2
#26012019	2
C₄×#14583826	2
#26011959	2
C₄×#14583825	2
C₄×Q₈×D₁₇₃	2
#529×C₁₇₃	2
#3480	173