Subgroups — #36367713

Order 22144.

1336 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012234	C₂	1	1	yes	maximal, characteristic, complemented
2	#26012229	C₂	1	2	yes	maximal, complemented
3	#26012228	C₂	1	1	yes	maximal, characteristic, complemented
4	#26012172	C₂	1	1	yes	maximal, characteristic, complemented
5	#26012170	C₂	1	2	yes	maximal, complemented
6	#26012135	C₂	1	2	yes	maximal, complemented
7	#26012130	C₂	1	2	yes	maximal, complemented
8	#26012128	C₂	1	2	yes	maximal, complemented
9	D₄×C₂²⋊D₁₇₃	C₂	1	2	yes	maximal, complemented
10	#26012078	C₂	1	2	yes	maximal, complemented
11	#26012074	C₂	1	2	yes	maximal, complemented
12	#26012073	C₂	1	2	yes	maximal, complemented
13	#26012056	C₂	1	2	yes	maximal, complemented
14	#26012054	C₂	1	1	yes	maximal, characteristic, complemented
15	#26012051	C₂	1	1	yes	maximal, characteristic, complemented
16	#26012050	C₂	1	2	yes	maximal, complemented
17	C₂×#19149647	C₂	1	2	yes	maximal, complemented
18	#120×D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	D₄²×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₁₇₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14583825	C₂²	1	1	yes	characteristic, complemented
22	C₂×#14583825	C₂²	1	2	yes	complemented
23	C₂²×C₂²⋊D₁₇₃	C₂²	1	2	yes	complemented
24	C₂²×C₂²⋊D₁₇₃	C₂²	1	2	yes	complemented
25	C₂²×C₂²⋊D₁₇₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₄×D₁₇₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₄×D₁₇₃	C₂²	1	2	yes	complemented
28	#19149675	C₂²	1	2	yes	complemented
29	#19149675	C₂²	1	1	yes	characteristic, complemented
30	#19149674	C₂²	1	2	yes	complemented
31	#19149674	C₂²	1	2	yes	complemented
32	#19149673	C₂²	1	2	yes	complemented
33	#19149672	C₂²	1	2	yes	complemented
34	#19149667	C₂²	1	1	yes	characteristic, complemented
35	#19149666	C₂²	1	1	yes	characteristic, complemented
36	#19149666	C₂²	1	2	yes	complemented
37	#19149665	C₂²	1	2	yes	complemented
38	#19149665	C₂²	1	2	yes	complemented
39	#19149665	C₂²	1	2	yes	complemented
40	#19149665	C₂²	1	2	yes	complemented
41	#19149664	C₂²	1	2	yes	complemented
42	#19149663	C₂²	1	2	yes	complemented
43	#19149663	C₂²	1	1	yes	characteristic, complemented
44	#19149662	C₂²	1	2	yes	complemented
45	#19149662	C₂²	1	2	yes	complemented
46	#19149661	C₂²	1	2	yes	complemented
47	#19149660	C₂²	1	2	yes	complemented
48	#19149660	C₂²	1	2	yes	complemented
49	#19149660	C₂²	1	1	yes	characteristic, complemented
50	#19149660	C₂²	1	2	yes	complemented
51	#19149658	C₂²	1	2	yes	complemented
52	#19149657	C₂²	1	2	yes	complemented
53	#19149656	C₂²	1	2	yes	complemented
54	#19149653	C₂²	1	2	yes	complemented
55	#19149652	C₂²	1	2	yes	complemented
56	#19149652	C₂²	1	2	yes	complemented
57	#19149651	C₂²	1	2	yes	complemented
58	#19149651	C₂²	1	2	yes	complemented
59	#19149651	C₂²	1	2	yes	complemented
60	#19149651	C₂²	1	2	yes	complemented
61	#19149651	C₂²	1	2	yes	complemented
62	#19149651	C₂²	1	2	yes	complemented
63	#19149651	C₂²	1	2	yes	complemented
64	#19149651	C₂²	1	2	yes	complemented
65	#19149650	C₂²	1	2	yes	complemented
66	#19149650	C₂²	1	2	yes	complemented
67	#19149649	C₂²	1	1	yes	characteristic, complemented
68	#19149649	C₂²	1	2	yes	complemented
69	#19149648	C₂²	1	1	yes	characteristic, complemented
70	#19149648	C₂²	1	2	yes	complemented
71	#19149648	C₂²	1	1	yes	characteristic, complemented
72	#19149648	C₂²	1	2	yes	complemented
73	#19149647	C₂²	1	2	yes	—
74	#19149647	C₂²	1	2	yes	complemented
75	#19149647	C₂²	1	1	yes	characteristic, complemented
76	#19149647	C₂²	1	2	yes	complemented
77	#19149647	C₂²	1	2	yes	complemented
78	#19149647	C₂²	1	2	yes	complemented
79	#19149647	C₂²	1	2	yes	complemented
80	#19149647	C₂²	1	2	yes	complemented
81	#19149647	C₂²	1	2	yes	complemented
82	#19149647	C₂²	1	2	yes	complemented
83	#19149647	C₂²	1	2	yes	complemented
84	D₄×Dic₁₇₃	C₂²	1	2	yes	complemented
85	D₄×Dic₁₇₃	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	#19149636	C₂²	1	1	yes	characteristic, complemented
90	#19149635	C₂²	1	2	yes	complemented
91	C₂×C₂²⋊Dic₁₇₃	C₂²	1	2	yes	complemented
92	C₂×C₂²⋊Dic₁₇₃	C₂²	1	2	yes	complemented
93	C₂×#14583803	C₂²	1	2	yes	complemented
94	C₂×#14583803	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₁₇₃	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₁₇₃	C₂²	1	1	yes	characteristic, complemented
97	C₂²⋊C₄×D₁₇₃	C₂²	1	1	yes	characteristic, complemented
98	C₂²×D₄×C₁₇₃	C₂²	1	2	yes	complemented
99	C₂²×D₄×C₁₇₃	C₂²	1	2	yes	complemented
100	#127×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
101	#121×C₁₇₃	C₂²	1	2	yes	complemented
102	#121×C₁₇₃	C₂²	1	2	yes	complemented
103	#120×C₁₇₃	C₂²	1	1	yes	characteristic
104	#120×C₁₇₃	C₂²	1	2	yes	complemented
105	#120×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
106	C₄×D₄×C₁₇₃	C₂²	1	2	yes	complemented
107	C₂³×D₁₇₃	—	4	4	no	—
108	C₂³×D₁₇₃	—	4	2	no	—
109	C₂³×D₁₇₃	C₂³	1	2	yes	—
110	C₂³×D₁₇₃	C₂³	1	1	yes	characteristic
111	C₂³×D₁₇₃	C₂³	1	1	yes	characteristic
112	C₂³×D₁₇₃	C₂³	1	2	yes	—
113	C₂³×D₁₇₃	C₂³	1	1	yes	characteristic
114	#14583825	—	4	4	no	—
115	#14583825	—	4	2	no	—
116	C₂×Dic₃₄₆	C₂³	1	1	yes	characteristic, complemented
117	C₂×Dic₃₄₆	C₂³	1	2	yes	complemented
118	C₂×D₆₉₂	C₂³	1	1	yes	characteristic
119	C₂×D₆₉₂	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₁₇₃	—	4	4	no	—
121	C₂×C₂²⋊D₁₇₃	—	4	4	no	—
122	C₂×C₂²⋊D₁₇₃	—	4	2	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	1	yes	characteristic
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	C₂×C₂²⋊D₁₇₃	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	complemented
136	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	complemented
137	D₄×D₁₇₃	—	4	4	no	—
138	D₄×D₁₇₃	—	4	2	no	—
139	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
140	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
141	C₂²×Dic₁₇₃	C₂³	1	2	yes	complemented
142	C₂²×Dic₁₇₃	C₂³	1	2	yes	complemented
143	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic, complemented
144	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
146	C₂×C₄×D₁₇₃	C₂³	1	2	yes	complemented
147	C₄⋊Dic₁₇₃	C₂³	1	2	yes	complemented
148	C₄⋊Dic₁₇₃	C₂³	1	2	yes	complemented
149	#14583805	C₂³	1	2	yes	complemented
150	#14583805	C₂³	1	2	yes	complemented
151	#14583805	C₂³	1	2	yes	complemented
152	#14583805	C₂³	1	2	yes	complemented
153	#14583805	C₂³	1	2	yes	complemented
154	#14583805	C₂³	1	2	yes	complemented
155	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
156	C₂²⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
157	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
158	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
159	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
160	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
161	C₂²⋊Dic₁₇₃	C₂³	1	1	yes	characteristic, complemented
162	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	complemented
163	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	complemented
164	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	complemented
165	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	complemented
166	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	complemented
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	#14583803	C₂³	1	2	yes	—
175	#14583803	C₂³	1	2	yes	—
176	#14583803	C₂³	1	2	yes	—
177	#14583803	C₂³	1	2	yes	—
178	#14583803	C₂³	1	2	yes	complemented
179	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic, complemented
180	C₄×Dic₁₇₃	C₂³	1	2	yes	complemented
181	C₄×Dic₁₇₃	C₂³	1	2	yes	complemented
182	C₂⁴×C₁₇₃	C₂³	1	1	yes	characteristic
183	C₂⁴×C₁₇₃	C₂³	1	2	yes	—
184	C₂⁴×C₁₇₃	C₂³	1	1	yes	characteristic, complemented
185	C₂×D₄×C₁₇₃	—	4	4	no	—
186	C₂×D₄×C₁₇₃	—	4	4	no	—
187	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
188	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
189	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
190	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
191	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
192	C₂×D₄×C₁₇₃	C₂³	1	1	yes	characteristic
193	C₂×D₄×C₁₇₃	C₂³	1	2	yes	complemented
194	C₂×D₄×C₁₇₃	C₂³	1	2	yes	complemented
195	C₂×D₄×C₁₇₃	C₂³	1	1	yes	characteristic, complemented
196	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
197	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	complemented
198	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	complemented
199	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
201	C₂²⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic, complemented
202	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	complemented
203	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	complemented
204	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic, complemented
205	C₂²×D₁₇₃	—	2	4	no	—
206	C₂²×D₁₇₃	—	2	4	no	—
207	C₂²×D₁₇₃	—	2	2	no	—
208	C₂²×D₁₇₃	—	2	4	no	—
209	C₂²×D₁₇₃	—	2	2	no	—
210	C₂²×D₁₇₃	—	4	2	no	—
211	C₂²×D₁₇₃	—	4	2	no	—
212	C₂²×D₁₇₃	—	4	1	no	—
213	C₂²×D₁₇₃	—	4	2	no	—
214	C₂²×D₁₇₃	—	4	2	no	—
215	C₂²×D₁₇₃	—	4	2	no	—
216	C₂²×D₁₇₃	—	4	2	no	—
217	C₂²×D₁₇₃	—	4	16	no	—
218	C₂²×D₁₇₃	C₂⁴	1	1	yes	characteristic
219	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
220	C₂²×D₁₇₃	C₂⁴	1	1	yes	characteristic
221	C₂²×D₁₇₃	C₂⁴	1	1	yes	characteristic
222	Dic₃₄₆	—	4	2	no	—
223	Dic₃₄₆	—	4	1	no	—
224	D₆₉₂	—	4	2	no	—
225	D₆₉₂	—	4	1	no	—
226	C₂²⋊D₁₇₃	—	2	4	no	—
227	C₂²⋊D₁₇₃	—	2	4	no	—
228	C₂²⋊D₁₇₃	—	2	4	no	—
229	C₂²⋊D₁₇₃	—	4	1	no	—
230	C₂²⋊D₁₇₃	—	4	1	no	—
231	C₂²⋊D₁₇₃	—	4	2	no	—
232	C₂²⋊D₁₇₃	—	4	2	no	—
233	C₂²⋊D₁₇₃	—	4	2	no	—
234	C₂²⋊D₁₇₃	—	4	2	no	—
235	C₂²⋊D₁₇₃	—	4	2	no	—
236	C₂²⋊D₁₇₃	—	4	2	no	—
237	C₂²⋊D₁₇₃	—	4	2	no	—
238	C₂²⋊D₁₇₃	—	4	2	no	—
239	C₂²⋊D₁₇₃	—	4	2	no	—
240	C₂×Dic₁₇₃	—	2	4	no	—
241	C₂×Dic₁₇₃	—	4	2	no	—
242	C₂×Dic₁₇₃	—	4	1	no	—
243	C₂×Dic₁₇₃	—	4	2	no	—
244	C₂×Dic₁₇₃	—	4	2	no	—
245	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
247	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
248	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
249	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
250	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
251	C₄×D₁₇₃	—	2	2	no	—
252	C₄×D₁₇₃	—	4	2	no	—
253	C₄×D₁₇₃	—	4	2	no	—
254	C₂³×C₁₇₃	—	2	4	no	—
255	C₂³×C₁₇₃	—	2	4	no	—
256	C₂³×C₁₇₃	—	4	1	no	—
257	C₂³×C₁₇₃	—	4	2	no	—
258	C₂³×C₁₇₃	—	4	1	no	—
259	C₂³×C₁₇₃	—	4	2	no	—
260	C₂³×C₁₇₃	—	4	2	no	—
261	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
262	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
263	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
264	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
265	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
266	D₄×C₁₇₃	—	2	4	no	—
267	D₄×C₁₇₃	—	2	4	no	—
268	D₄×C₁₇₃	—	2	4	no	—
269	D₄×C₁₇₃	—	4	1	no	—
270	D₄×C₁₇₃	—	4	1	no	—
271	D₄×C₁₇₃	—	4	2	no	—
272	D₄×C₁₇₃	—	4	2	no	—
273	D₄×C₁₇₃	—	4	2	no	—
274	D₄×C₁₇₃	—	4	2	no	—
275	C₂×C₄×C₁₇₃	—	4	2	no	—
276	C₂×C₄×C₁₇₃	—	4	2	no	—
277	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
279	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
280	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
281	C₂²×C₁₇₃	—	2	2	no	—
282	C₂²×C₁₇₃	—	2	2	no	—
283	C₂²×C₁₇₃	—	2	2	no	—
284	C₂²×C₁₇₃	—	2	2	no	—
285	C₂²×C₁₇₃	—	2	2	no	—
286	C₂²×C₁₇₃	—	2	2	no	—
287	C₂²×C₁₇₃	—	2	2	no	—
288	C₂²×C₁₇₃	—	2	2	no	—
289	C₂²×C₁₇₃	—	2	2	no	—
290	C₂²×C₁₇₃	—	2	1	no	—
291	C₂²×C₁₇₃	—	2	1	no	—
292	C₂²×C₁₇₃	—	2	2	no	—
293	C₂²×C₁₇₃	—	4	4	no	—
294	C₂²×C₁₇₃	—	8	4	no	—
295	C₂²×C₁₇₃	—	8	2	no	—
296	C₂²×C₁₇₃	H(5,𝔽₂)	1	4	yes	—
297	C₂²×C₁₇₃	C₂⁵	1	1	yes	characteristic
298	C₂×D₁₇₃	—	2	2	no	—
299	C₂×D₁₇₃	—	2	2	no	—
300	C₂×D₁₇₃	—	2	1	no	—
301	C₂×D₁₇₃	—	2	2	no	—
302	C₂×D₁₇₃	—	2	2	no	—
303	C₂×D₁₇₃	—	2	2	no	—
304	C₂×D₁₇₃	—	2	1	no	—
305	C₂×D₁₇₃	—	2	2	no	—
306	C₂×D₁₇₃	—	4	8	no	—
307	C₂×D₁₇₃	—	4	4	no	—
308	C₂×D₁₇₃	—	4	8	no	—
309	C₂×D₁₇₃	—	4	4	no	—
310	C₂×D₁₇₃	—	8	2	no	—
311	C₂×D₁₇₃	H(5,𝔽₂)	1	2	yes	—
312	C₄×C₁₇₃	—	2	2	no	—
313	C₄×C₁₇₃	—	2	2	no	—
314	C₄×C₁₇₃	—	2	2	no	—
315	C₄×C₁₇₃	—	2	1	no	—
316	Dic₁₇₃	—	2	1	no	—
317	Dic₁₇₃	—	2	2	no	—
318	Dic₁₇₃	—	2	2	no	—
319	Dic₁₇₃	—	2	2	no	—
320	Dic₁₇₃	—	2	2	no	—
321	Dic₁₇₃	—	2	2	no	—
322	C₂×C₁₇₃	—	2	4	no	—
323	C₂×C₁₇₃	—	4	1	no	—
324	C₂×C₁₇₃	—	4	1	no	—
325	C₂×C₁₇₃	—	4	2	no	—
326	C₂×C₁₇₃	—	4	2	no	—
327	C₂×C₁₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
328	C₂×C₁₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
329	D₁₇₃	—	2	2	no	—
330	D₁₇₃	—	4	2	no	—
331	D₁₇₃	—	4	1	no	—
332	D₁₇₃	—	4	1	no	—
333	C₁₇₃	#3532	1	1	yes	characteristic, complemented, Sylow
334	#3532	—	173	1	no	maximal, Sylow
335	H(3,𝔽₄)	—	173	1	no	—
336	#560	—	173	1	no	—
337	#560	—	173	2	no	—
338	#551	—	173	1	no	—
339	#551	—	173	2	no	—
340	#546	—	173	2	no	—
341	#546	—	173	2	no	—
342	#546	—	173	2	no	—
343	D₄²	—	173	2	no	—
344	D₄²	D₁₇₃	1	1	yes	characteristic, complemented
345	#538	—	173	2	no	—
346	#538	—	173	2	no	—
347	#538	—	173	2	no	—
348	#535	—	173	1	no	—
349	#535	—	173	2	no	—
350	#534	—	173	2	no	—
351	#534	—	173	1	no	—
352	C₂×#120	—	173	2	no	—
353	C₂×#120	—	173	1	no	—
354	C₂⁵	—	173	1	no	—
355	C₂×#41	—	173	2	no	—
356	C₂×#41	—	173	1	no	—
357	C₂²×D₄	—	173	2	no	—
358	C₂²×D₄	—	173	2	no	—
359	C₂²×D₄	—	173	1	no	—
360	C₂²×D₄	—	173	1	no	—
361	C₂²×D₄	—	173	2	no	—
362	C₂²×D₄	C₂×D₁₇₃	1	2	yes	complemented
363	C₂²×D₄	C₂×D₁₇₃	1	2	yes	complemented
364	#127	—	173	1	no	—
365	#127	—	173	2	no	—
366	#127	C₂×D₁₇₃	1	1	yes	characteristic, complemented
367	#126	—	173	2	no	—
368	#126	—	173	2	no	—
369	#126	—	173	2	no	—
370	#126	—	173	2	no	—
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	—	173	1	no	—
378	#123	—	173	2	no	—
379	#123	—	173	2	no	—
380	#123	—	173	1	no	—
381	#123	—	173	2	no	—
382	#123	—	173	2	no	—
383	#123	—	173	2	no	—
384	#123	—	173	2	no	—
385	#123	—	173	1	no	—
386	#123	—	173	2	no	—
387	#123	—	173	2	no	—
388	C₂²⋊Q₈	—	173	2	no	—
389	C₂²⋊Q₈	—	173	2	no	—
390	C₂²⋊Q₈	—	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	#121	—	173	2	no	—
401	#121	—	173	2	no	—
402	#121	—	173	2	no	—
403	#121	—	173	2	no	—
404	#121	C₂×D₁₇₃	1	2	yes	complemented
405	#121	C₂×D₁₇₃	1	2	yes	complemented
406	#120	—	173	1	no	—
407	#120	—	173	2	no	—
408	#120	—	173	1	no	—
409	#120	—	173	2	no	—
410	#120	—	173	2	no	—
411	#120	—	173	2	no	—
412	#120	—	173	2	no	—
413	#120	—	173	2	no	—
414	#120	—	173	2	no	—
415	#120	—	173	2	no	—
416	#120	—	173	2	no	—
417	#120	—	173	2	no	—
418	#120	—	173	2	no	—
419	#120	—	173	1	no	—
420	#120	—	173	2	no	—
421	#120	—	173	2	no	—
422	#120	—	173	1	no	—
423	#120	C₂×D₁₇₃	1	1	yes	characteristic
424	#120	C₂×D₁₇₃	1	2	yes	complemented
425	#120	C₂×D₁₇₃	1	1	yes	characteristic, complemented
426	C₄×D₄	—	173	2	no	—
427	C₄×D₄	—	173	2	no	—
428	C₄×D₄	—	173	2	no	—
429	C₄×D₄	—	173	2	no	—
430	C₄×D₄	—	173	2	no	—
431	C₄×D₄	C₂×D₁₇₃	1	2	yes	complemented
432	#117	—	173	2	no	—
433	#117	—	173	1	no	—
434	C₂×C₂²⋊C₄	—	173	2	no	—
435	C₂×C₂²⋊C₄	—	173	2	no	—
436	C₂×C₂²⋊C₄	—	173	2	no	—
437	C₂×C₂²⋊C₄	—	173	2	no	—
438	C₂×C₂²⋊C₄	—	173	1	no	—
439	C₂×C₂²⋊C₄	—	173	2	no	—
440	C₂×C₂²⋊C₄	—	173	1	no	—
441	C₂⁴	—	173	2	no	—
442	C₂⁴	—	173	1	no	—
443	C₂⁴	—	173	2	no	—
444	C₂⁴	—	173	1	no	—
445	C₂⁴	—	173	1	no	—
446	C₂⁴	—	692	4	no	—
447	C₂⁴	—	692	2	no	—
448	C₂⁴	C₂²×D₁₇₃	1	1	yes	characteristic
449	C₂⁴	C₂²×D₁₇₃	1	2	yes	—
450	C₂⁴	C₂²×D₁₇₃	1	1	yes	characteristic, complemented
451	#41	—	692	4	no	—
452	#41	—	692	2	no	—
453	C₂×Q₈	—	173	2	no	—
454	C₂×Q₈	—	173	1	no	—
455	C₂×D₄	—	4	4	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	173	2	no	—
458	C₂×D₄	—	173	2	no	—
459	C₂×D₄	—	173	2	no	—
460	C₂×D₄	—	173	1	no	—
461	C₂×D₄	—	173	2	no	—
462	C₂×D₄	—	173	2	no	—
463	C₂×D₄	—	173	2	no	—
464	C₂×D₄	—	173	2	no	—
465	C₂×D₄	—	173	2	no	—
466	C₂×D₄	—	173	1	no	—
467	C₂×D₄	—	173	2	no	—
468	C₂×D₄	—	173	2	no	—
469	C₂×D₄	—	173	2	no	—
470	C₂×D₄	—	173	2	no	—
471	C₂×D₄	—	173	2	no	—
472	C₂×D₄	—	173	1	no	—
473	C₂×D₄	—	692	2	no	—
474	C₂×D₄	—	692	4	no	—
475	C₂×D₄	—	692	4	no	—
476	C₂×D₄	—	692	2	no	—
477	C₂×D₄	—	692	4	no	—
478	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
479	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
480	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
481	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
482	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
483	C₂×D₄	C₂²×D₁₇₃	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₁₇₃	1	2	yes	complemented
485	C₂×D₄	C₂²×D₁₇₃	1	1	yes	characteristic, complemented
486	C₂×D₄	C₂²×D₁₇₃	1	2	yes	complemented
487	C₂²×C₄	—	173	2	no	—
488	C₂²×C₄	—	173	1	no	—
489	C₂²×C₄	—	173	2	no	—
490	C₂²×C₄	—	173	2	no	—
491	C₂²×C₄	—	173	2	no	—
492	C₂²×C₄	—	173	1	no	—
493	C₂²×C₄	—	173	2	no	—
494	C₂²×C₄	—	173	2	no	—
495	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
496	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	complemented
497	C₄⋊C₄	—	173	2	no	—
498	C₄⋊C₄	—	173	2	no	—
499	C₄⋊C₄	—	173	2	no	—
500	C₄⋊C₄	—	173	2	no	—
501	C₄⋊C₄	—	173	2	no	—
502	C₄⋊C₄	—	173	2	no	—
503	C₄⋊C₄	—	173	2	no	—
504	C₄⋊C₄	—	173	2	no	—
505	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	complemented
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	1	no	—
512	C₂²⋊C₄	—	173	1	no	—
513	C₂²⋊C₄	—	173	2	no	—
514	C₂²⋊C₄	—	173	2	no	—
515	C₂²⋊C₄	—	173	2	no	—
516	C₂²⋊C₄	—	173	2	no	—
517	C₂²⋊C₄	—	173	2	no	—
518	C₂²⋊C₄	—	173	2	no	—
519	C₂²⋊C₄	—	173	2	no	—
520	C₂²⋊C₄	—	173	2	no	—
521	C₂²⋊C₄	—	173	2	no	—
522	C₂²⋊C₄	—	173	2	no	—
523	C₂²⋊C₄	—	173	2	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	2	no	—
529	C₂²⋊C₄	—	173	2	no	—
530	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
532	C₂²⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic, complemented
533	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	complemented
534	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	complemented
535	C₄²	—	173	1	no	—
536	C₄²	—	173	2	no	—
537	C₄²	—	173	2	no	—
538	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic, complemented
539	C₂³	—	2	4	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	2	no	—
543	C₂³	—	4	2	no	—
544	C₂³	—	4	2	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	346	2	no	—
547	C₂³	—	346	4	no	—
548	C₂³	—	346	2	no	—
549	C₂³	—	346	4	no	—
550	C₂³	—	346	4	no	—
551	C₂³	—	173	2	no	—
552	C₂³	—	173	1	no	—
553	C₂³	—	173	1	no	—
554	C₂³	—	173	1	no	—
555	C₂³	—	692	2	no	—
556	C₂³	—	692	2	no	—
557	C₂³	—	692	2	no	—
558	C₂³	—	692	2	no	—
559	C₂³	—	692	1	no	—
560	C₂³	—	692	2	no	—
561	C₂³	—	692	2	no	—
562	C₂³	—	692	16	no	—
563	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
564	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
565	C₂³	C₂³×D₁₇₃	1	2	yes	—
566	C₂³	C₂³×D₁₇₃	1	2	yes	—
567	C₂³	C₂³×D₁₇₃	1	2	yes	—
568	Q₈	—	692	1	no	—
569	Q₈	—	692	2	no	—
570	D₄	—	2	4	no	—
571	D₄	—	2	4	no	—
572	D₄	—	2	4	no	—
573	D₄	—	4	2	no	—
574	D₄	—	4	2	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	1	no	—
578	D₄	—	4	1	no	—
579	D₄	—	346	4	no	—
580	D₄	—	346	4	no	—
581	D₄	—	346	4	no	—
582	D₄	—	692	1	no	—
583	D₄	—	692	2	no	—
584	D₄	—	692	1	no	—
585	D₄	—	692	1	no	—
586	D₄	—	692	2	no	—
587	D₄	—	692	2	no	—
588	D₄	—	692	2	no	—
589	D₄	—	692	2	no	—
590	D₄	—	692	2	no	—
591	D₄	—	692	2	no	—
592	D₄	—	692	2	no	—
593	D₄	—	692	2	no	—
594	D₄	—	692	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	346	2	no	—
598	C₂×C₄	—	346	4	no	—
599	C₂×C₄	—	173	2	no	—
600	C₂×C₄	—	173	2	no	—
601	C₂×C₄	—	173	2	no	—
602	C₂×C₄	—	173	2	no	—
603	C₂×C₄	—	173	1	no	—
604	C₂×C₄	—	173	2	no	—
605	C₂×C₄	—	692	2	no	—
606	C₂×C₄	—	692	2	no	—
607	C₂×C₄	—	692	1	no	—
608	C₂×C₄	—	692	2	no	—
609	C₂×C₄	—	692	2	no	—
610	C₂×C₄	—	692	2	no	—
611	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
613	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
614	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	4	4	no	—
628	C₂²	—	8	4	no	—
629	C₂²	—	8	2	no	—
630	C₂²	—	346	2	no	—
631	C₂²	—	346	1	no	—
632	C₂²	—	346	1	no	—
633	C₂²	—	346	2	no	—
634	C₂²	—	346	2	no	—
635	C₂²	—	346	2	no	—
636	C₂²	—	346	2	no	—
637	C₂²	—	346	2	no	—
638	C₂²	—	1384	2	no	—
639	C₂²	—	173	2	no	—
640	C₂²	—	692	8	no	—
641	C₂²	—	692	8	no	—
642	C₂²	—	692	4	no	—
643	C₂²	—	692	4	no	—
644	C₂²	#19149724	1	4	yes	—
645	C₂²	C₂⁴×D₁₇₃	1	1	yes	characteristic
646	C₄	—	2	1	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	346	1	no	—
651	C₄	—	346	2	no	—
652	C₄	—	346	2	no	—
653	C₄	—	346	2	no	—
654	C₄	—	346	2	no	—
655	C₄	—	346	2	no	—
656	C₂	—	2	4	no	—
657	C₂	—	4	1	no	—
658	C₂	—	4	2	no	—
659	C₂	—	4	2	no	—
660	C₂	—	4	1	no	—
661	C₂	—	346	2	no	—
662	C₂	—	692	1	no	—
663	C₂	—	692	2	no	—
664	C₂	—	692	1	no	—
665	C₂	H(5,𝔽₂)×D₁₇₃	1	1	yes	characteristic
666	C₂	C₂×#19149724	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇₃
commutator, socle, cosocle	C₂²×C₁₇₃	C₂⁵
Fitting	D₄²×C₁₇₃	C₂
hypercenter	D₄²	D₁₇₃
hypocenter	C₁₇₃	#3532
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. #26012234	C₂	semidirect
2. #26012229	C₂	semidirect
3. #26012228	C₂	semidirect
4. #26012172	C₂	semidirect
5. #26012170	C₂	semidirect
6. #26012135	C₂	semidirect
7. #26012130	C₂	semidirect
8. #26012128	C₂	semidirect
9. D₄×C₂²⋊D₁₇₃	C₂	semidirect
10. #26012078	C₂	semidirect
11. #26012074	C₂	semidirect
12. #26012073	C₂	semidirect
13. #26012056	C₂	semidirect
14. #26012054	C₂	semidirect
15. #26012051	C₂	semidirect
16. #26012050	C₂	semidirect
17. C₂×#19149647	C₂	semidirect
18. #120×D₁₇₃	C₂	semidirect
19. D₄²×C₁₇₃	C₂	semidirect
20. C₂⁴×D₁₇₃	C₂²	semidirect
21. C₂×#14583825	C₂²	semidirect
22. C₂×#14583825	C₂²	semidirect
23. C₂²×C₂²⋊D₁₇₃	C₂²	semidirect
24. C₂²×C₂²⋊D₁₇₃	C₂²	semidirect
25. C₂²×C₂²⋊D₁₇₃	C₂²	semidirect
26. C₂×D₄×D₁₇₃	C₂²	semidirect
27. C₂×D₄×D₁₇₃	C₂²	semidirect
28. #19149675	C₂²	semidirect
29. #19149675	C₂²	semidirect
30. #19149674	C₂²	semidirect
31. #19149674	C₂²	semidirect
32. #19149673	C₂²	semidirect
33. #19149672	C₂²	semidirect
34. #19149667	C₂²	semidirect
35. #19149666	C₂²	semidirect
36. #19149666	C₂²	semidirect
37. #19149665	C₂²	semidirect
38. #19149665	C₂²	semidirect
39. #19149665	C₂²	semidirect
40. #19149665	C₂²	semidirect
41. #19149664	C₂²	semidirect
42. #19149663	C₂²	semidirect
43. #19149663	C₂²	semidirect
44. #19149662	C₂²	semidirect
45. #19149662	C₂²	semidirect
46. #19149661	C₂²	semidirect
47. #19149660	C₂²	semidirect
48. #19149660	C₂²	semidirect
49. #19149660	C₂²	semidirect
50. #19149660	C₂²	semidirect
51. #19149658	C₂²	semidirect
52. #19149657	C₂²	semidirect
53. #19149656	C₂²	semidirect
54. #19149653	C₂²	semidirect
55. #19149652	C₂²	semidirect
56. #19149652	C₂²	semidirect
57. #19149651	C₂²	semidirect
58. #19149651	C₂²	semidirect
59. #19149651	C₂²	semidirect
60. #19149651	C₂²	semidirect
61. #19149651	C₂²	semidirect
62. #19149651	C₂²	semidirect
63. #19149651	C₂²	semidirect
64. #19149651	C₂²	semidirect
65. #19149650	C₂²	semidirect
66. #19149650	C₂²	semidirect
67. #19149649	C₂²	semidirect
68. #19149649	C₂²	semidirect
69. #19149648	C₂²	semidirect
70. #19149648	C₂²	semidirect
71. #19149648	C₂²	semidirect
72. #19149648	C₂²	semidirect
74. #19149647	C₂²	semidirect
75. #19149647	C₂²	semidirect
76. #19149647	C₂²	semidirect
77. #19149647	C₂²	semidirect
78. #19149647	C₂²	semidirect
79. #19149647	C₂²	semidirect
80. #19149647	C₂²	semidirect
81. #19149647	C₂²	semidirect
82. #19149647	C₂²	semidirect
83. #19149647	C₂²	semidirect
84. D₄×Dic₁₇₃	C₂²	semidirect
85. D₄×Dic₁₇₃	C₂²	semidirect
86. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
87. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
88. #19149639	C₂²	semidirect
89. #19149636	C₂²	semidirect
90. #19149635	C₂²	semidirect
91. C₂×C₂²⋊Dic₁₇₃	C₂²	semidirect
92. C₂×C₂²⋊Dic₁₇₃	C₂²	semidirect
93. C₂×#14583803	C₂²	semidirect
94. C₂×#14583803	C₂²	semidirect
95. C₂²⋊C₄×D₁₇₃	C₂²	semidirect
96. C₂²⋊C₄×D₁₇₃	C₂²	semidirect
97. C₂²⋊C₄×D₁₇₃	C₂²	semidirect
98. C₂²×D₄×C₁₇₃	C₂²	semidirect
99. C₂²×D₄×C₁₇₃	C₂²	semidirect
100. #127×C₁₇₃	C₂²	semidirect
101. #121×C₁₇₃	C₂²	semidirect
102. #121×C₁₇₃	C₂²	semidirect
104. #120×C₁₇₃	C₂²	semidirect
105. #120×C₁₇₃	C₂²	semidirect
106. C₄×D₄×C₁₇₃	C₂²	semidirect
116. C₂×Dic₃₄₆	C₂³	semidirect
117. C₂×Dic₃₄₆	C₂³	semidirect
135. C₂×C₂²⋊D₁₇₃	C₂³	semidirect
136. C₂×C₂²⋊D₁₇₃	C₂³	semidirect
141. C₂²×Dic₁₇₃	C₂³	semidirect
142. C₂²×Dic₁₇₃	C₂³	semidirect
143. C₂²×Dic₁₇₃	C₂³	semidirect
146. C₂×C₄×D₁₇₃	C₂³	semidirect
147. C₄⋊Dic₁₇₃	C₂³	semidirect
148. C₄⋊Dic₁₇₃	C₂³	semidirect
149. #14583805	C₂³	semidirect
150. #14583805	C₂³	semidirect
151. #14583805	C₂³	semidirect
152. #14583805	C₂³	semidirect
153. #14583805	C₂³	semidirect
154. #14583805	C₂³	semidirect
161. C₂²⋊Dic₁₇₃	C₂³	semidirect
162. C₂²⋊Dic₁₇₃	C₂³	semidirect
163. C₂²⋊Dic₁₇₃	C₂³	semidirect
164. C₂²⋊Dic₁₇₃	C₂³	semidirect
165. C₂²⋊Dic₁₇₃	C₂³	semidirect
166. C₂²⋊Dic₁₇₃	C₂³	semidirect
178. #14583803	C₂³	semidirect
179. C₄×Dic₁₇₃	C₂³	semidirect
180. C₄×Dic₁₇₃	C₂³	semidirect
181. C₄×Dic₁₇₃	C₂³	semidirect
184. C₂⁴×C₁₇₃	C₂³	semidirect
193. C₂×D₄×C₁₇₃	C₂³	semidirect
194. C₂×D₄×C₁₇₃	C₂³	semidirect
195. C₂×D₄×C₁₇₃	C₂³	semidirect
197. C₂²×C₄×C₁₇₃	C₂³	semidirect
198. C₄⋊C₄×C₁₇₃	C₂³	semidirect
201. C₂²⋊C₄×C₁₇₃	C₂³	semidirect
202. C₂²⋊C₄×C₁₇₃	C₂³	semidirect
203. C₂²⋊C₄×C₁₇₃	C₂³	semidirect
204. C₄²×C₁₇₃	C₂³	semidirect
333. C₁₇₃	#3532	semidirect
344. D₄²	D₁₇₃	semidirect
362. C₂²×D₄	C₂×D₁₇₃	semidirect
363. C₂²×D₄	C₂×D₁₇₃	semidirect
366. #127	C₂×D₁₇₃	semidirect
404. #121	C₂×D₁₇₃	semidirect
405. #121	C₂×D₁₇₃	semidirect
424. #120	C₂×D₁₇₃	semidirect
425. #120	C₂×D₁₇₃	semidirect
431. C₄×D₄	C₂×D₁₇₃	semidirect
450. C₂⁴	C₂²×D₁₇₃	semidirect
484. C₂×D₄	C₂²×D₁₇₃	semidirect
485. C₂×D₄	C₂²×D₁₇₃	semidirect
486. C₂×D₄	C₂²×D₁₇₃	semidirect
496. C₂²×C₄	C₂²×D₁₇₃	semidirect
505. C₄⋊C₄	C₂²×D₁₇₃	semidirect
532. C₂²⋊C₄	C₂²×D₁₇₃	semidirect
533. C₂²⋊C₄	C₂²×D₁₇₃	semidirect
534. C₂²⋊C₄	C₂²×D₁₇₃	semidirect
538. C₄²	C₂²×D₁₇₃	semidirect

Maximal subgroups

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

subgroup	index
#26012234	2
#26012229	2
#26012228	2
#26012172	2
#26012170	2
#26012135	2
#26012130	2
#26012128	2
D₄×C₂²⋊D₁₇₃	2
#26012078	2
#26012074	2
#26012073	2
#26012056	2
#26012054	2
#26012051	2
#26012050	2
C₂×#19149647	2
#120×D₁₇₃	2
D₄²×C₁₇₃	2
#3532	173