Subgroups — #36367757

Order 22144.

1166 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012238	C₂	1	2	yes	maximal, complemented
2	#26012231	C₂	1	2	yes	maximal, complemented
3	#26012189	C₂	1	2	yes	maximal, complemented
4	#26012164	C₂	1	2	yes	maximal, complemented
5	#26012133	C₂	1	2	yes	maximal, complemented
6	#26012131	C₂	1	2	yes	maximal, complemented
7	#26012131	C₂	1	2	yes	maximal, complemented
8	D₄×C₂²⋊D₁₇₃	C₂	1	2	yes	maximal, complemented
9	#26012093	C₂	1	2	yes	maximal, complemented
10	#26012088	C₂	1	1	yes	maximal, characteristic, complemented
11	#26012085	C₂	1	2	yes	maximal, complemented
12	#26012079	C₂	1	1	yes	maximal, characteristic, complemented
13	#26012077	C₂	1	2	yes	maximal, complemented
14	#26012072	C₂	1	1	yes	maximal, characteristic, complemented
15	#26012053	C₂	1	1	yes	maximal, characteristic, complemented
16	#26012052	C₂	1	2	yes	maximal, complemented
17	#26012002	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#19149653	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#123×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14583826	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14583826	C₂²	1	2	yes	complemented
22	C₂²×D₆₉₂	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₂²⋊D₁₇₃	C₂²	1	2	yes	complemented
24	C₂²×C₂²⋊D₁₇₃	C₂²	1	2	yes	complemented
25	C₂×D₄×D₁₇₃	C₂²	1	2	yes	complemented
26	#19149675	C₂²	1	2	yes	complemented
27	#19149674	C₂²	1	2	yes	complemented
28	#19149674	C₂²	1	2	yes	complemented
29	#19149674	C₂²	1	2	yes	complemented
30	#19149672	C₂²	1	2	yes	complemented
31	#19149670	C₂²	1	2	yes	complemented
32	#19149669	C₂²	1	2	yes	complemented
33	#19149665	C₂²	1	2	yes	complemented
34	#19149665	C₂²	1	2	yes	complemented
35	#19149665	C₂²	1	2	yes	complemented
36	#19149664	C₂²	1	2	yes	complemented
37	#19149664	C₂²	1	2	yes	complemented
38	#19149664	C₂²	1	2	yes	complemented
39	#19149663	C₂²	1	2	yes	complemented
40	#19149663	C₂²	1	2	yes	complemented
41	#19149662	C₂²	1	2	yes	complemented
42	#19149662	C₂²	1	2	yes	complemented
43	#19149661	C₂²	1	2	yes	complemented
44	#19149661	C₂²	1	2	yes	complemented
45	#19149661	C₂²	1	2	yes	complemented
46	#19149659	C₂²	1	2	yes	complemented
47	#19149659	C₂²	1	2	yes	complemented
48	#19149658	C₂²	1	1	yes	characteristic, complemented
49	#19149658	C₂²	1	1	yes	characteristic, complemented
50	#19149657	C₂²	1	2	yes	complemented
51	#19149656	C₂²	1	2	yes	complemented
52	#19149656	C₂²	1	2	yes	complemented
53	#19149654	C₂²	1	2	yes	complemented
54	#19149654	C₂²	1	2	yes	complemented
55	#19149654	C₂²	1	2	yes	complemented
56	#19149653	C₂²	1	1	yes	characteristic
57	#19149653	C₂²	1	2	yes	complemented
58	#19149653	C₂²	1	2	yes	complemented
59	#19149653	C₂²	1	2	yes	complemented
60	#19149653	C₂²	1	1	yes	characteristic, complemented
61	#19149653	C₂²	1	2	yes	complemented
62	#19149653	C₂²	1	1	yes	characteristic, complemented
63	#19149653	C₂²	1	1	yes	characteristic, complemented
64	#19149653	C₂²	1	1	yes	characteristic, complemented
65	#19149653	C₂²	1	1	yes	characteristic, complemented
66	#19149652	C₂²	1	2	yes	complemented
67	#19149652	C₂²	1	2	yes	complemented
68	#19149652	C₂²	1	2	yes	complemented
69	#19149652	C₂²	1	2	yes	complemented
70	#19149652	C₂²	1	2	yes	complemented
71	#19149651	C₂²	1	2	yes	—
72	#19149651	C₂²	1	2	yes	complemented
73	#19149650	C₂²	1	2	yes	complemented
74	#19149649	C₂²	1	2	yes	complemented
75	#19149649	C₂²	1	2	yes	complemented
76	#19149649	C₂²	1	2	yes	complemented
77	#19149649	C₂²	1	2	yes	complemented
78	#19149648	C₂²	1	2	yes	complemented
79	#19149648	C₂²	1	2	yes	complemented
80	#19149647	C₂²	1	2	yes	—
81	#19149647	C₂²	1	2	yes	complemented
82	D₄×Dic₁₇₃	C₂²	1	2	yes	complemented
83	#19149641	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	complemented
87	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	complemented
88	#19149639	C₂²	1	2	yes	complemented
89	#19149639	C₂²	1	2	yes	complemented
90	#19149638	C₂²	1	1	yes	characteristic, complemented
91	#19149637	C₂²	1	2	yes	complemented
92	C₂×C₄⋊Dic₁₇₃	C₂²	1	1	yes	characteristic, complemented
93	C₂×#14583803	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₁₇₃	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₁₇₃	C₂²	1	2	yes	complemented
96	C₂²×D₄×C₁₇₃	C₂²	1	1	yes	characteristic
97	C₂³×C₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
98	#123×C₁₇₃	C₂²	1	2	yes	complemented
99	#123×C₁₇₃	C₂²	1	2	yes	complemented
100	#123×C₁₇₃	C₂²	1	2	yes	complemented
101	#123×C₁₇₃	C₂²	1	2	yes	complemented
102	C₂×C₄⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₄⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₂²⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₂²⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₂²⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₇₃	C₂³	1	2	yes	—
108	C₂³×D₁₇₃	C₂³	1	2	yes	—
109	#14583826	—	4	4	no	—
110	#14583826	—	4	2	no	—
111	C₂×Dic₃₄₆	C₂³	1	2	yes	—
112	C₂×Dic₃₄₆	C₂³	1	1	yes	characteristic
113	C₂×D₆₉₂	—	4	2	no	—
114	C₂×D₆₉₂	C₂³	1	2	yes	—
115	C₂×D₆₉₂	C₂³	1	2	yes	—
116	C₂×D₆₉₂	C₂³	1	1	yes	characteristic
117	C₂×D₆₉₂	C₂³	1	1	yes	characteristic
118	C₂×D₆₉₂	C₂³	1	2	yes	—
119	C₂×D₆₉₂	C₂³	1	1	yes	characteristic
120	C₂×D₆₉₂	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₁₇₃	—	4	4	no	—
122	C₂×C₂²⋊D₁₇₃	—	4	4	no	—
123	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
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	2	yes	—
134	D₄×D₁₇₃	—	4	4	no	—
135	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
136	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
137	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
138	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
139	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
140	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
141	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
142	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
144	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
146	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
149	#14583805	C₂³	1	2	yes	—
150	#14583805	C₂³	1	2	yes	—
151	#14583805	C₂³	1	2	yes	—
152	#14583805	C₂³	1	2	yes	—
153	#14583805	C₂³	1	2	yes	—
154	#14583805	C₂³	1	2	yes	—
155	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
156	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
157	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
158	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
159	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
160	#14583803	C₂³	1	2	yes	—
161	#14583803	C₂³	1	2	yes	—
162	#14583803	C₂³	1	2	yes	—
163	#14583803	C₂³	1	2	yes	—
164	#14583803	C₂³	1	2	yes	—
165	#14583803	C₂³	1	2	yes	—
166	#14583803	C₂³	1	2	yes	—
167	#14583803	C₂³	1	2	yes	—
168	#14583803	C₂³	1	2	yes	—
169	#14583803	C₂³	1	2	yes	—
170	#14583803	C₂³	1	2	yes	—
171	#14583803	C₂³	1	2	yes	—
172	#14583803	C₂³	1	2	yes	—
173	#14583803	C₂³	1	2	yes	—
174	C₄×Dic₁₇₃	C₂³	1	2	yes	—
175	C₄×Dic₁₇₃	C₂³	1	2	yes	—
176	C₄×Dic₁₇₃	C₂³	1	2	yes	—
177	C₂⁴×C₁₇₃	C₂³	1	1	yes	characteristic
178	C₂⁴×C₁₇₃	C₂³	1	1	yes	characteristic
179	C₂×D₄×C₁₇₃	—	4	2	no	—
180	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
181	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
182	C₂²×C₄×C₁₇₃	—	4	2	no	—
183	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
184	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
186	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
187	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
188	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
189	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
190	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
191	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
192	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
193	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
194	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
195	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
201	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
202	C₂²×D₁₇₃	—	2	4	no	—
203	C₂²×D₁₇₃	—	4	2	no	—
204	C₂²×D₁₇₃	—	4	2	no	—
205	C₂²×D₁₇₃	—	4	2	no	—
206	C₂²×D₁₇₃	—	4	2	no	—
207	C₂²×D₁₇₃	—	4	2	no	—
208	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
209	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
210	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
211	Dic₃₄₆	—	4	1	no	—
212	Dic₃₄₆	—	4	2	no	—
213	D₆₉₂	—	4	2	no	—
214	D₆₉₂	—	4	1	no	—
215	D₆₉₂	—	4	2	no	—
216	D₆₉₂	—	4	1	no	—
217	D₆₉₂	—	4	2	no	—
218	D₆₉₂	—	4	1	no	—
219	D₆₉₂	—	4	2	no	—
220	C₂²⋊D₁₇₃	—	2	4	no	—
221	C₂²⋊D₁₇₃	—	2	4	no	—
222	C₂²⋊D₁₇₃	—	2	4	no	—
223	C₂²⋊D₁₇₃	—	2	4	no	—
224	C₂²⋊D₁₇₃	—	4	2	no	—
225	C₂²⋊D₁₇₃	—	4	2	no	—
226	C₂²⋊D₁₇₃	—	4	2	no	—
227	C₂²⋊D₁₇₃	—	4	2	no	—
228	C₂²⋊D₁₇₃	—	4	2	no	—
229	C₂²⋊D₁₇₃	—	4	2	no	—
230	C₂²⋊D₁₇₃	—	4	2	no	—
231	C₂×Dic₁₇₃	—	4	2	no	—
232	C₂×Dic₁₇₃	—	4	2	no	—
233	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
234	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
235	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
236	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
237	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
238	C₄×D₁₇₃	—	4	2	no	—
239	C₄×D₁₇₃	—	4	2	no	—
240	C₄×D₁₇₃	—	4	2	no	—
241	C₄×D₁₇₃	—	4	2	no	—
242	C₄×D₁₇₃	—	4	2	no	—
243	C₂³×C₁₇₃	—	2	2	no	—
244	C₂³×C₁₇₃	—	2	2	no	—
245	C₂³×C₁₇₃	—	2	2	no	—
246	C₂³×C₁₇₃	—	4	1	no	—
247	C₂³×C₁₇₃	—	4	1	no	—
248	C₂³×C₁₇₃	—	4	1	no	—
249	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
250	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
251	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
252	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
253	D₄×C₁₇₃	—	2	4	no	—
254	D₄×C₁₇₃	—	4	2	no	—
255	C₂×C₄×C₁₇₃	—	2	2	no	—
256	C₂×C₄×C₁₇₃	—	2	2	no	—
257	C₂×C₄×C₁₇₃	—	2	2	no	—
258	C₂×C₄×C₁₇₃	—	4	1	no	—
259	C₂×C₄×C₁₇₃	—	4	1	no	—
260	C₂×C₄×C₁₇₃	—	4	1	no	—
261	C₂×C₄×C₁₇₃	—	4	1	no	—
262	C₂×C₄×C₁₇₃	—	4	1	no	—
263	C₂×C₄×C₁₇₃	—	4	1	no	—
264	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
265	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
267	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
268	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₁₇₃	—	2	1	no	—
272	C₂²×C₁₇₃	—	2	1	no	—
273	C₂²×C₁₇₃	—	2	1	no	—
274	C₂²×C₁₇₃	—	2	1	no	—
275	C₂²×C₁₇₃	—	2	1	no	—
276	C₂²×C₁₇₃	—	2	2	no	—
277	C₂²×C₁₇₃	—	2	2	no	—
278	C₂²×C₁₇₃	—	2	1	no	—
279	C₂²×C₁₇₃	—	2	1	no	—
280	C₂²×C₁₇₃	—	2	2	no	—
281	C₂²×C₁₇₃	—	4	4	no	—
282	C₂²×C₁₇₃	—	8	2	no	—
283	C₂²×C₁₇₃	H(5,𝔽₂)	1	2	yes	—
284	C₂²×C₁₇₃	H(5,𝔽₂)	1	2	yes	—
285	C₂²×C₁₇₃	C₂⁵	1	1	yes	characteristic
286	C₂×D₁₇₃	—	2	2	no	—
287	C₂×D₁₇₃	—	2	2	no	—
288	C₂×D₁₇₃	—	2	2	no	—
289	C₂×D₁₇₃	—	2	2	no	—
290	C₂×D₁₇₃	—	2	2	no	—
291	C₂×D₁₇₃	—	2	2	no	—
292	C₂×D₁₇₃	—	2	2	no	—
293	C₂×D₁₇₃	—	2	2	no	—
294	C₂×D₁₇₃	—	2	2	no	—
295	C₂×D₁₇₃	—	8	4	no	—
296	C₂×D₁₇₃	—	8	4	no	—
297	C₄×C₁₇₃	—	2	1	no	—
298	C₄×C₁₇₃	—	2	1	no	—
299	C₄×C₁₇₃	—	2	1	no	—
300	C₄×C₁₇₃	—	2	1	no	—
301	C₄×C₁₇₃	—	2	2	no	—
302	C₄×C₁₇₃	—	2	2	no	—
303	C₄×C₁₇₃	—	2	2	no	—
304	Dic₁₇₃	—	2	2	no	—
305	Dic₁₇₃	—	2	2	no	—
306	Dic₁₇₃	—	2	2	no	—
307	Dic₁₇₃	—	2	2	no	—
308	Dic₁₇₃	—	2	2	no	—
309	C₂×C₁₇₃	—	2	2	no	—
310	C₂×C₁₇₃	—	2	2	no	—
311	C₂×C₁₇₃	—	4	2	no	—
312	C₂×C₁₇₃	—	4	1	no	—
313	C₂×C₁₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂×C₁₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂×C₁₇₃	#585	1	1	yes	characteristic
316	D₁₇₃	—	4	2	no	—
317	D₁₇₃	—	4	2	no	—
318	D₁₇₃	—	4	2	no	—
319	C₁₇₃	#3534	1	1	yes	characteristic, complemented, Sylow
320	#3534	—	173	1	no	maximal, Sylow
321	#562	—	173	2	no	—
322	#560	—	173	2	no	—
323	#553	—	173	2	no	—
324	#551	—	173	2	no	—
325	#546	—	173	2	no	—
326	#546	—	173	2	no	—
327	#546	—	173	2	no	—
328	D₄²	—	173	2	no	—
329	#540	—	173	2	no	—
330	#539	—	173	2	no	—
331	#539	—	173	1	no	—
332	#538	—	173	2	no	—
333	#538	—	173	1	no	—
334	#537	—	173	1	no	—
335	#534	—	173	2	no	—
336	#534	—	173	1	no	—
337	#525	—	173	1	no	—
338	C₂×#123	D₁₇₃	1	1	yes	characteristic, complemented
339	C₂×#121	—	173	1	no	—
340	C₂×#41	—	173	1	no	—
341	C₂×#41	—	173	2	no	—
342	C₂²×D₄	—	173	2	no	—
343	C₂²×D₄	—	173	2	no	—
344	C₂²×D₄	—	173	2	no	—
345	C₂²×D₄	—	173	1	no	—
346	C₂²×D₄	C₂×D₁₇₃	1	1	yes	characteristic
347	C₂³×C₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
348	#127	—	173	2	no	—
349	#126	—	173	2	no	—
350	#126	—	173	2	no	—
351	#126	—	173	2	no	—
352	#126	—	173	2	no	—
353	#125	—	173	2	no	—
354	#125	—	173	2	no	—
355	#124	—	173	2	no	—
356	#124	—	173	2	no	—
357	#124	—	173	2	no	—
358	#123	—	173	2	no	—
359	#123	—	173	2	no	—
360	#123	—	173	2	no	—
361	#123	—	173	2	no	—
362	#123	—	173	2	no	—
363	#123	—	173	2	no	—
364	#123	—	173	2	no	—
365	#123	—	173	2	no	—
366	#123	—	173	2	no	—
367	#123	—	173	2	no	—
368	#123	C₂×D₁₇₃	1	2	yes	complemented
369	#123	C₂×D₁₇₃	1	2	yes	complemented
370	#123	C₂×D₁₇₃	1	2	yes	complemented
371	#123	C₂×D₁₇₃	1	2	yes	complemented
372	C₂²⋊Q₈	—	173	1	no	—
373	C₂²⋊Q₈	—	173	1	no	—
374	C₂²⋊Q₈	—	173	2	no	—
375	C₂²⋊Q₈	—	173	2	no	—
376	C₂²⋊Q₈	—	173	2	no	—
377	C₂²⋊Q₈	—	173	2	no	—
378	C₂²⋊Q₈	—	173	2	no	—
379	#121	—	173	2	no	—
380	#121	—	173	2	no	—
381	#121	—	173	2	no	—
382	#121	—	173	1	no	—
383	#121	—	173	1	no	—
384	#121	—	173	1	no	—
385	#121	—	173	1	no	—
386	#121	—	173	2	no	—
387	#121	—	173	2	no	—
388	#121	—	173	1	no	—
389	#121	—	173	1	no	—
390	#121	—	173	2	no	—
391	#121	—	173	2	no	—
392	#121	—	173	2	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	—	173	2	no	—
399	#121	—	173	2	no	—
400	#120	—	173	2	no	—
401	#120	—	173	2	no	—
402	#120	—	173	2	no	—
403	#120	—	173	2	no	—
404	#120	—	173	2	no	—
405	#120	—	173	2	no	—
406	#120	—	173	2	no	—
407	#120	—	173	2	no	—
408	C₄×D₄	—	173	2	no	—
409	C₄×D₄	—	173	2	no	—
410	C₄×D₄	—	173	2	no	—
411	C₄×D₄	—	173	2	no	—
412	C₄×D₄	—	173	2	no	—
413	C₄×D₄	—	173	2	no	—
414	C₄×D₄	—	173	2	no	—
415	C₄×D₄	—	173	2	no	—
416	#117	—	173	1	no	—
417	#117	—	173	2	no	—
418	C₂×C₄⋊C₄	—	173	1	no	—
419	C₂×C₄⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
420	C₂×C₄⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
421	C₂×C₂²⋊C₄	—	173	2	no	—
422	C₂×C₂²⋊C₄	—	173	2	no	—
423	C₂×C₂²⋊C₄	—	173	2	no	—
424	C₂×C₂²⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
425	C₂×C₂²⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
426	C₂×C₂²⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
427	C₂⁴	—	173	2	no	—
428	C₂⁴	—	173	2	no	—
429	C₂⁴	C₂²×D₁₇₃	1	1	yes	characteristic
430	C₂⁴	C₂²×D₁₇₃	1	1	yes	characteristic
431	#41	—	692	2	no	—
432	#41	—	692	4	no	—
433	C₂×Q₈	—	173	1	no	—
434	C₂×Q₈	—	173	2	no	—
435	C₂×D₄	—	4	2	no	—
436	C₂×D₄	—	173	2	no	—
437	C₂×D₄	—	173	2	no	—
438	C₂×D₄	—	173	2	no	—
439	C₂×D₄	—	173	2	no	—
440	C₂×D₄	—	173	2	no	—
441	C₂×D₄	—	173	2	no	—
442	C₂×D₄	—	173	2	no	—
443	C₂×D₄	—	173	2	no	—
444	C₂×D₄	—	173	2	no	—
445	C₂×D₄	—	173	2	no	—
446	C₂×D₄	—	173	2	no	—
447	C₂×D₄	—	173	2	no	—
448	C₂×D₄	—	173	1	no	—
449	C₂×D₄	—	173	2	no	—
450	C₂×D₄	—	173	1	no	—
451	C₂×D₄	—	173	2	no	—
452	C₂×D₄	—	173	1	no	—
453	C₂×D₄	—	173	2	no	—
454	C₂×D₄	—	692	2	no	—
455	C₂×D₄	—	692	4	no	—
456	C₂×D₄	—	692	4	no	—
457	C₂×D₄	—	692	4	no	—
458	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
459	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
460	C₂²×C₄	—	4	2	no	—
461	C₂²×C₄	—	173	2	no	—
462	C₂²×C₄	—	173	2	no	—
463	C₂²×C₄	—	173	2	no	—
464	C₂²×C₄	—	173	2	no	—
465	C₂²×C₄	—	173	2	no	—
466	C₂²×C₄	—	173	2	no	—
467	C₂²×C₄	—	173	2	no	—
468	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
469	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
470	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
471	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
472	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
473	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
475	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
476	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
477	C₄⋊C₄	—	173	1	no	—
478	C₄⋊C₄	—	173	2	no	—
479	C₄⋊C₄	—	173	1	no	—
480	C₄⋊C₄	—	173	1	no	—
481	C₄⋊C₄	—	173	2	no	—
482	C₄⋊C₄	—	173	1	no	—
483	C₄⋊C₄	—	173	2	no	—
484	C₄⋊C₄	—	173	2	no	—
485	C₄⋊C₄	—	173	2	no	—
486	C₄⋊C₄	—	173	2	no	—
487	C₄⋊C₄	—	173	2	no	—
488	C₄⋊C₄	—	173	2	no	—
489	C₄⋊C₄	—	173	2	no	—
490	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
491	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
492	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
493	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
494	C₂²⋊C₄	—	173	2	no	—
495	C₂²⋊C₄	—	173	2	no	—
496	C₂²⋊C₄	—	173	2	no	—
497	C₂²⋊C₄	—	173	2	no	—
498	C₂²⋊C₄	—	173	2	no	—
499	C₂²⋊C₄	—	173	2	no	—
500	C₂²⋊C₄	—	173	2	no	—
501	C₂²⋊C₄	—	173	2	no	—
502	C₂²⋊C₄	—	173	2	no	—
503	C₂²⋊C₄	—	173	2	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	—	173	2	no	—
511	C₂²⋊C₄	—	173	2	no	—
512	C₂²⋊C₄	—	173	2	no	—
513	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
514	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
515	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
516	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
517	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
518	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
519	C₄²	—	173	2	no	—
520	C₄²	—	173	2	no	—
521	C₄²	—	173	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	346	4	no	—
529	C₂³	—	173	2	no	—
530	C₂³	—	173	2	no	—
531	C₂³	—	173	2	no	—
532	C₂³	—	692	2	no	—
533	C₂³	—	692	2	no	—
534	C₂³	—	692	2	no	—
535	C₂³	—	692	2	no	—
536	C₂³	—	692	2	no	—
537	C₂³	C₂³×D₁₇₃	1	2	yes	—
538	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
539	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
540	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
541	Q₈	—	692	1	no	—
542	Q₈	—	692	2	no	—
543	D₄	—	2	4	no	—
544	D₄	—	4	2	no	—
545	D₄	—	346	4	no	—
546	D₄	—	346	4	no	—
547	D₄	—	346	4	no	—
548	D₄	—	346	4	no	—
549	D₄	—	692	2	no	—
550	D₄	—	692	1	no	—
551	D₄	—	692	2	no	—
552	D₄	—	692	1	no	—
553	D₄	—	692	2	no	—
554	D₄	—	692	1	no	—
555	D₄	—	692	2	no	—
556	D₄	—	692	2	no	—
557	D₄	—	692	2	no	—
558	D₄	—	692	2	no	—
559	D₄	—	692	2	no	—
560	D₄	—	692	2	no	—
561	D₄	—	692	2	no	—
562	D₄	—	692	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	173	2	no	—
573	C₂×C₄	—	173	2	no	—
574	C₂×C₄	—	173	2	no	—
575	C₂×C₄	—	173	2	no	—
576	C₂×C₄	—	173	2	no	—
577	C₂×C₄	—	692	2	no	—
578	C₂×C₄	—	692	2	no	—
579	C₂×C₄	—	692	2	no	—
580	C₂×C₄	—	692	2	no	—
581	C₂×C₄	—	692	2	no	—
582	C₂×C₄	—	692	2	no	—
583	C₂×C₄	—	692	2	no	—
584	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
586	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
587	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
589	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	8	2	no	—
603	C₂²	—	346	2	no	—
604	C₂²	—	346	2	no	—
605	C₂²	—	346	2	no	—
606	C₂²	—	346	2	no	—
607	C₂²	—	346	2	no	—
608	C₂²	—	346	2	no	—
609	C₂²	—	346	2	no	—
610	C₂²	—	346	2	no	—
611	C₂²	—	346	2	no	—
612	C₂²	—	1384	4	no	—
613	C₂²	—	1384	4	no	—
614	C₂²	#19149724	1	2	yes	—
615	C₂²	#19149725	1	2	yes	—
616	C₂²	C₂⁴×D₁₇₃	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	346	2	no	—
625	C₄	—	346	2	no	—
626	C₄	—	346	2	no	—
627	C₄	—	346	2	no	—
628	C₄	—	346	2	no	—
629	C₂	—	2	2	no	—
630	C₂	—	2	2	no	—
631	C₂	—	4	1	no	—
632	C₂	—	4	2	no	—
633	C₂	—	692	2	no	—
634	C₂	—	692	2	no	—
635	C₂	—	692	2	no	—
636	C₂	C₂×#19149724	1	1	yes	characteristic
637	C₂	C₂×#19149725	1	1	yes	characteristic
638	C₂	#26012327	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇₃
commutator, socle, cosocle	C₂²×C₁₇₃	C₂⁵
Fitting	C₂×#123×C₁₇₃	C₂
hypercenter	C₂×#123	D₁₇₃
hypocenter	C₁₇₃	#3534
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂² ◁ C₂×#123

Complements

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

N	H ≅ G/N	type
1. #26012238	C₂	semidirect
2. #26012231	C₂	semidirect
3. #26012189	C₂	semidirect
4. #26012164	C₂	semidirect
5. #26012133	C₂	semidirect
6. #26012131	C₂	semidirect
7. #26012131	C₂	semidirect
8. D₄×C₂²⋊D₁₇₃	C₂	semidirect
9. #26012093	C₂	semidirect
10. #26012088	C₂	semidirect
11. #26012085	C₂	semidirect
12. #26012079	C₂	semidirect
13. #26012077	C₂	semidirect
14. #26012072	C₂	semidirect
15. #26012053	C₂	semidirect
16. #26012052	C₂	semidirect
17. #26012002	C₂	semidirect
18. C₂×#19149653	C₂	semidirect
19. C₂×#123×C₁₇₃	C₂	semidirect
20. C₂×#14583826	C₂²	semidirect
21. C₂×#14583826	C₂²	semidirect
22. C₂²×D₆₉₂	C₂²	semidirect
23. C₂²×C₂²⋊D₁₇₃	C₂²	semidirect
24. C₂²×C₂²⋊D₁₇₃	C₂²	semidirect
25. C₂×D₄×D₁₇₃	C₂²	semidirect
26. #19149675	C₂²	semidirect
27. #19149674	C₂²	semidirect
28. #19149674	C₂²	semidirect
29. #19149674	C₂²	semidirect
30. #19149672	C₂²	semidirect
31. #19149670	C₂²	semidirect
32. #19149669	C₂²	semidirect
33. #19149665	C₂²	semidirect
34. #19149665	C₂²	semidirect
35. #19149665	C₂²	semidirect
36. #19149664	C₂²	semidirect
37. #19149664	C₂²	semidirect
38. #19149664	C₂²	semidirect
39. #19149663	C₂²	semidirect
40. #19149663	C₂²	semidirect
41. #19149662	C₂²	semidirect
42. #19149662	C₂²	semidirect
43. #19149661	C₂²	semidirect
44. #19149661	C₂²	semidirect
45. #19149661	C₂²	semidirect
46. #19149659	C₂²	semidirect
47. #19149659	C₂²	semidirect
48. #19149658	C₂²	semidirect
49. #19149658	C₂²	semidirect
50. #19149657	C₂²	semidirect
51. #19149656	C₂²	semidirect
52. #19149656	C₂²	semidirect
53. #19149654	C₂²	semidirect
54. #19149654	C₂²	semidirect
55. #19149654	C₂²	semidirect
57. #19149653	C₂²	semidirect
58. #19149653	C₂²	semidirect
59. #19149653	C₂²	semidirect
60. #19149653	C₂²	semidirect
61. #19149653	C₂²	semidirect
62. #19149653	C₂²	semidirect
63. #19149653	C₂²	semidirect
64. #19149653	C₂²	semidirect
65. #19149653	C₂²	semidirect
66. #19149652	C₂²	semidirect
67. #19149652	C₂²	semidirect
68. #19149652	C₂²	semidirect
69. #19149652	C₂²	semidirect
70. #19149652	C₂²	semidirect
72. #19149651	C₂²	semidirect
73. #19149650	C₂²	semidirect
74. #19149649	C₂²	semidirect
75. #19149649	C₂²	semidirect
76. #19149649	C₂²	semidirect
77. #19149649	C₂²	semidirect
78. #19149648	C₂²	semidirect
79. #19149648	C₂²	semidirect
81. #19149647	C₂²	semidirect
82. D₄×Dic₁₇₃	C₂²	semidirect
83. #19149641	C₂²	semidirect
84. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
85. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
86. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
87. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
88. #19149639	C₂²	semidirect
89. #19149639	C₂²	semidirect
90. #19149638	C₂²	semidirect
91. #19149637	C₂²	semidirect
92. C₂×C₄⋊Dic₁₇₃	C₂²	semidirect
93. C₂×#14583803	C₂²	semidirect
94. C₂²⋊C₄×D₁₇₃	C₂²	semidirect
95. C₂²⋊C₄×D₁₇₃	C₂²	semidirect
97. C₂³×C₄×C₁₇₃	C₂²	semidirect
98. #123×C₁₇₃	C₂²	semidirect
99. #123×C₁₇₃	C₂²	semidirect
100. #123×C₁₇₃	C₂²	semidirect
101. #123×C₁₇₃	C₂²	semidirect
102. C₂×C₄⋊C₄×C₁₇₃	C₂²	semidirect
103. C₂×C₄⋊C₄×C₁₇₃	C₂²	semidirect
104. C₂×C₂²⋊C₄×C₁₇₃	C₂²	semidirect
105. C₂×C₂²⋊C₄×C₁₇₃	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₁₇₃	C₂²	semidirect
319. C₁₇₃	#3534	semidirect
338. C₂×#123	D₁₇₃	semidirect
347. C₂³×C₄	C₂×D₁₇₃	semidirect
368. #123	C₂×D₁₇₃	semidirect
369. #123	C₂×D₁₇₃	semidirect
370. #123	C₂×D₁₇₃	semidirect
371. #123	C₂×D₁₇₃	semidirect
419. C₂×C₄⋊C₄	C₂×D₁₇₃	semidirect
420. C₂×C₄⋊C₄	C₂×D₁₇₃	semidirect
424. C₂×C₂²⋊C₄	C₂×D₁₇₃	semidirect
425. C₂×C₂²⋊C₄	C₂×D₁₇₃	semidirect
426. C₂×C₂²⋊C₄	C₂×D₁₇₃	semidirect

Maximal subgroups

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

subgroup	index
#26012238	2
#26012231	2
#26012189	2
#26012164	2
#26012133	2
#26012131	2
D₄×C₂²⋊D₁₇₃	2
#26012093	2
#26012088	2
#26012085	2
#26012079	2
#26012077	2
#26012072	2
#26012053	2
#26012052	2
#26012002	2
C₂×#19149653	2
C₂×#123×C₁₇₃	2
#3534	173