Subgroups — #36366983

Order 22144.

1140 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012118	C₂	1	1	yes	maximal, characteristic, complemented
2	#26012113	C₂	1	1	yes	maximal, characteristic, complemented
3	#26012111	C₂	1	2	yes	maximal, complemented
4	#26012096	C₂	1	1	yes	maximal, characteristic, complemented
5	#26012093	C₂	1	2	yes	maximal, complemented
6	#26012092	C₂	1	1	yes	maximal, characteristic, complemented
7	#26012080	C₂	1	2	yes	maximal, complemented
8	#26012075	C₂	1	2	yes	maximal, complemented
9	#26012071	C₂	1	1	yes	maximal, characteristic, complemented
10	#26012059	C₂	1	1	yes	maximal, characteristic, complemented
11	#26012057	C₂	1	1	yes	maximal, characteristic, complemented
12	#26012042	C₂	1	1	yes	maximal, characteristic, complemented
13	#26012040	C₂	1	2	yes	maximal, complemented
14	#26012036	C₂	1	1	yes	maximal, characteristic, complemented
15	#26012027	C₂	1	1	yes	maximal, characteristic, complemented
16	#26012024	C₂	1	2	yes	maximal, complemented
17	#26012020	C₂	1	1	yes	maximal, characteristic, complemented
18	#26012004	C₂	1	2	yes	maximal, complemented
19	#26011999	C₂	1	2	yes	maximal, complemented
20	C₄×#14583827	C₂	1	1	yes	maximal, characteristic, complemented
21	#26011959	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#542×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14583827	C₂²	1	1	yes	characteristic
25	C₂×#14583827	C₂²	1	2	yes	complemented
26	C₂×#14583826	C₂²	1	1	yes	characteristic
27	C₂×#14583825	C₂²	1	2	yes	complemented
28	C₂×D₄×D₁₇₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₇₃	C₂²	1	2	yes	—
30	#19149678	C₂²	1	1	yes	characteristic, complemented
31	#19149677	C₂²	1	2	yes	complemented
32	#19149676	C₂²	1	1	yes	characteristic
33	#19149675	C₂²	1	1	yes	characteristic
34	#19149675	C₂²	1	2	yes	—
35	#19149674	C₂²	1	2	yes	complemented
36	#19149673	C₂²	1	2	yes	complemented
37	#19149672	C₂²	1	2	yes	complemented
38	#19149671	C₂²	1	1	yes	characteristic, complemented
39	#19149670	C₂²	1	1	yes	characteristic, complemented
40	#19149669	C₂²	1	2	yes	complemented
41	#19149668	C₂²	1	1	yes	characteristic
42	#19149668	C₂²	1	2	yes	complemented
43	#19149667	C₂²	1	2	yes	complemented
44	#19149665	C₂²	1	2	yes	—
45	#19149665	C₂²	1	2	yes	complemented
46	#19149664	C₂²	1	2	yes	complemented
47	#19149664	C₂²	1	2	yes	complemented
48	#19149664	C₂²	1	2	yes	complemented
49	#19149663	C₂²	1	2	yes	complemented
50	#19149662	C₂²	1	2	yes	complemented
51	#19149661	C₂²	1	2	yes	complemented
52	#19149661	C₂²	1	2	yes	complemented
53	#19149657	C₂²	1	2	yes	—
54	#19149657	C₂²	1	2	yes	complemented
55	#19149657	C₂²	1	2	yes	complemented
56	#19149655	C₂²	1	2	yes	—
57	#19149655	C₂²	1	1	yes	characteristic, complemented
58	#19149654	C₂²	1	2	yes	—
59	#19149654	C₂²	1	1	yes	characteristic
60	#19149654	C₂²	1	1	yes	characteristic, complemented
61	#19149654	C₂²	1	2	yes	complemented
62	#19149653	C₂²	1	1	yes	characteristic
63	#19149653	C₂²	1	2	yes	complemented
64	#19149653	C₂²	1	1	yes	characteristic, complemented
65	#19149652	C₂²	1	2	yes	—
66	#19149652	C₂²	1	2	yes	—
67	#19149652	C₂²	1	2	yes	—
68	#19149652	C₂²	1	2	yes	complemented
69	#19149652	C₂²	1	2	yes	complemented
70	#19149652	C₂²	1	2	yes	complemented
71	#19149652	C₂²	1	2	yes	complemented
72	#19149651	C₂²	1	2	yes	complemented
73	#19149650	C₂²	1	1	yes	characteristic
74	#19149649	C₂²	1	2	yes	—
75	#19149649	C₂²	1	2	yes	—
76	#19149649	C₂²	1	2	yes	—
77	#19149647	C₂²	1	2	yes	—
78	Q₈×Dic₁₇₃	C₂²	1	1	yes	characteristic, complemented
79	#19149644	C₂²	1	1	yes	characteristic, complemented
80	#19149644	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₆₉₂	C₂²	1	1	yes	characteristic
82	C₄×D₆₉₂	C₂²	1	2	yes	—
83	C₄×D₆₉₂	C₂²	1	1	yes	characteristic, complemented
84	D₄×Dic₁₇₃	C₂²	1	1	yes	characteristic
85	#19149641	C₂²	1	1	yes	characteristic
86	#19149641	C₂²	1	1	yes	characteristic
87	#19149641	C₂²	1	1	yes	characteristic
88	#19149641	C₂²	1	2	yes	—
89	#19149641	C₂²	1	1	yes	characteristic, complemented
90	#19149641	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	—
92	#19149639	C₂²	1	2	yes	—
93	#19149639	C₂²	1	1	yes	characteristic
94	#19149639	C₂²	1	1	yes	characteristic
95	#19149639	C₂²	1	1	yes	characteristic, complemented
96	#19149639	C₂²	1	1	yes	characteristic, complemented
97	#19149639	C₂²	1	2	yes	complemented
98	#19149639	C₂²	1	2	yes	complemented
99	#19149639	C₂²	1	2	yes	complemented
100	#19149637	C₂²	1	1	yes	characteristic
101	#19149637	C₂²	1	2	yes	complemented
102	#19149637	C₂²	1	2	yes	complemented
103	#19149636	C₂²	1	1	yes	characteristic
104	#19149636	C₂²	1	1	yes	characteristic, complemented
105	#19149635	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₁₇₃	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₁₇₃	C₂²	1	2	yes	—
108	C₂×C₄×Dic₁₇₃	C₂²	1	1	yes	characteristic, complemented
109	C₄²×D₁₇₃	C₂²	1	1	yes	characteristic
110	C₄²×D₁₇₃	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₁₇₃	C₂²	1	2	yes	complemented
112	C₄⋊Q₈×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
113	#126×C₁₇₃	C₂²	1	2	yes	complemented
114	#124×C₁₇₃	C₂²	1	1	yes	characteristic
115	#124×C₁₇₃	C₂²	1	2	yes	complemented
116	#123×C₁₇₃	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₁₇₃	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
119	#121×C₁₇₃	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₁₇₃	C₂²	1	1	yes	characteristic
122	#117×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₇₃	C₂³	1	2	yes	—
124	#14583827	—	2	4	no	—
125	#14583827	—	4	4	no	—
126	#14583826	—	2	4	no	—
127	#14583825	—	4	4	no	—
128	C₂×Dic₃₄₆	C₂³	1	1	yes	characteristic
129	C₂×Dic₃₄₆	C₂³	1	2	yes	—
130	C₂×D₆₉₂	C₂³	1	1	yes	characteristic
131	C₂×D₆₉₂	C₂³	1	2	yes	—
132	C₂×D₆₉₂	C₂³	1	1	yes	characteristic
133	C₂×D₆₉₂	C₂³	1	1	yes	characteristic
134	C₂×D₆₉₂	C₂³	1	2	yes	—
135	C₂×D₆₉₂	C₂³	1	2	yes	—
136	C₂×D₆₉₂	C₂³	1	2	yes	—
137	C₂×D₆₉₂	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₇₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₇₃	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
146	D₄×D₁₇₃	—	2	4	no	—
147	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
148	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
149	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
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	2	yes	—
154	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
156	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
157	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
160	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
161	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
162	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
166	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
174	#14583805	C₂³	1	2	yes	—
175	#14583805	C₂³	1	2	yes	—
176	#14583805	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
179	#14583803	C₂³	1	2	yes	—
180	#14583803	C₂³	1	2	yes	—
181	#14583803	C₂³	1	1	yes	characteristic
182	#14583803	C₂³	1	1	yes	characteristic
183	#14583803	C₂³	1	1	yes	characteristic
184	#14583803	C₂³	1	1	yes	characteristic
185	#14583803	C₂³	1	2	yes	—
186	#14583803	C₂³	1	2	yes	—
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	#14583803	C₂³	1	2	yes	—
192	#14583803	C₂³	1	2	yes	—
193	#14583803	C₂³	1	2	yes	—
194	#14583803	C₂³	1	2	yes	—
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	1	yes	characteristic
199	C₄×Dic₁₇₃	C₂³	1	2	yes	—
200	C₄×Dic₁₇₃	C₂³	1	2	yes	—
201	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
205	C₂×Q₈×C₁₇₃	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₁₇₃	C₂³	1	2	yes	—
207	C₂×D₄×C₁₇₃	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
209	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
211	C₄⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
225	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
226	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
227	C₄²×C₁₇₃	C₂³	1	2	yes	—
228	C₂²×D₁₇₃	—	2	4	no	—
229	C₂²×D₁₇₃	—	4	2	no	—
230	C₂²×D₁₇₃	—	4	2	no	—
231	C₂²×D₁₇₃	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
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	D₆₉₂	—	2	4	no	—
239	D₆₉₂	—	2	2	no	—
240	D₆₉₂	—	2	2	no	—
241	D₆₉₂	—	4	2	no	—
242	D₆₉₂	—	4	2	no	—
243	D₆₉₂	—	4	2	no	—
244	D₆₉₂	—	4	2	no	—
245	C₂²⋊D₁₇₃	—	2	2	no	—
246	C₂²⋊D₁₇₃	—	2	4	no	—
247	C₂²⋊D₁₇₃	—	2	2	no	—
248	C₂²⋊D₁₇₃	—	4	2	no	—
249	C₂²⋊D₁₇₃	—	4	2	no	—
250	C₂²⋊D₁₇₃	—	4	2	no	—
251	C₂²⋊D₁₇₃	—	4	2	no	—
252	C₂²⋊D₁₇₃	—	4	2	no	—
253	C₂×Dic₁₇₃	—	2	4	no	—
254	C₂×Dic₁₇₃	—	2	2	no	—
255	C₂×Dic₁₇₃	—	4	1	no	—
256	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
257	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
259	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
264	C₄×D₁₇₃	—	2	2	no	—
265	C₄×D₁₇₃	—	2	4	no	—
266	C₄×D₁₇₃	—	2	2	no	—
267	C₄×D₁₇₃	—	2	4	no	—
268	C₄×D₁₇₃	—	2	4	no	—
269	C₄×D₁₇₃	—	2	2	no	—
270	C₄×D₁₇₃	—	4	2	no	—
271	C₄×D₁₇₃	—	4	2	no	—
272	C₄×D₁₇₃	—	4	1	no	—
273	C₄×D₁₇₃	—	4	1	no	—
274	C₄×D₁₇₃	—	4	2	no	—
275	C₄×D₁₇₃	#41	1	4	yes	complemented
276	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
277	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
278	Q₈×C₁₇₃	—	2	2	no	—
279	Q₈×C₁₇₃	—	4	2	no	—
280	D₄×C₁₇₃	—	2	2	no	—
281	D₄×C₁₇₃	—	4	2	no	—
282	C₂×C₄×C₁₇₃	—	2	2	no	—
283	C₂×C₄×C₁₇₃	—	4	2	no	—
284	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
287	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
290	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
291	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
292	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₁₇₃	—	2	1	no	—
294	C₂²×C₁₇₃	—	2	2	no	—
295	C₂²×C₁₇₃	—	2	2	no	—
296	C₂²×C₁₇₃	—	2	1	no	—
297	C₂²×C₁₇₃	—	2	1	no	—
298	C₂²×C₁₇₃	—	2	2	no	—
299	C₂²×C₁₇₃	C₂⁵	1	1	yes	characteristic
300	C₂×D₁₇₃	—	2	1	no	—
301	C₂×D₁₇₃	—	2	1	no	—
302	C₂×D₁₇₃	—	2	1	no	—
303	C₂×D₁₇₃	—	2	2	no	—
304	C₂×D₁₇₃	—	2	2	no	—
305	C₂×D₁₇₃	—	2	2	no	—
306	C₂×D₁₇₃	—	2	2	no	—
307	C₂×D₁₇₃	—	2	1	no	—
308	C₂×D₁₇₃	—	2	1	no	—
309	C₂×D₁₇₃	—	2	2	no	—
310	C₂×D₁₇₃	—	2	2	no	—
311	C₂×D₁₇₃	—	4	8	no	—
312	C₂×D₁₇₃	C₂×#41	1	2	yes	—
313	C₄×C₁₇₃	—	2	1	no	—
314	C₄×C₁₇₃	—	2	2	no	—
315	C₄×C₁₇₃	—	2	1	no	—
316	C₄×C₁₇₃	—	2	2	no	—
317	C₄×C₁₇₃	—	2	2	no	—
318	C₄×C₁₇₃	—	2	1	no	—
319	C₄×C₁₇₃	—	2	1	no	—
320	C₄×C₁₇₃	—	2	1	no	—
321	C₄×C₁₇₃	C₂×#41	1	2	yes	—
322	Dic₁₇₃	—	2	1	no	—
323	Dic₁₇₃	—	2	2	no	—
324	Dic₁₇₃	—	2	1	no	—
325	Dic₁₇₃	—	2	1	no	—
326	Dic₁₇₃	—	2	2	no	—
327	Dic₁₇₃	—	2	1	no	—
328	Dic₁₇₃	C₂×#41	1	2	yes	—
329	Dic₁₇₃	H(5,𝔽₂)	1	2	yes	—
330	C₂×C₁₇₃	—	4	2	no	—
331	C₂×C₁₇₃	—	4	1	no	—
332	C₂×C₁₇₃	C₂²×#41	1	1	yes	characteristic
333	C₂×C₁₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₁₇₃	#585	1	1	yes	characteristic
335	D₁₇₃	—	2	2	no	—
336	D₁₇₃	—	4	1	no	—
337	D₁₇₃	—	4	2	no	—
338	D₁₇₃	—	4	2	no	—
339	C₁₇₃	#3460	1	1	yes	characteristic, complemented, Sylow
340	#3460	—	173	1	no	maximal, Sylow
341	#544	—	173	1	no	—
342	#542	—	173	2	no	—
343	#542	—	173	1	no	—
344	#542	D₁₇₃	1	1	yes	characteristic, complemented
345	#540	—	173	2	no	—
346	#540	—	173	1	no	—
347	#540	—	173	1	no	—
348	#538	—	173	2	no	—
349	#538	—	173	2	no	—
350	#537	—	173	1	no	—
351	#535	—	173	1	no	—
352	#535	—	173	1	no	—
353	#532	—	173	1	no	—
354	#532	—	173	2	no	—
355	#532	—	173	1	no	—
356	#529	—	173	2	no	—
357	#529	—	173	1	no	—
358	#529	—	173	1	no	—
359	#525	—	173	2	no	—
360	#525	—	173	2	no	—
361	C₄×#41	—	173	1	no	—
362	C₄×#41	—	173	1	no	—
363	C₂×C₄×D₄	—	173	1	no	—
364	C₂×#41	—	173	1	no	—
365	C₂×#41	—	173	2	no	—
366	C₂×#41	—	173	2	no	—
367	C₂×#41	—	173	1	no	—
368	C₂²×D₄	—	173	1	no	—
369	C₂³×C₄	—	173	2	no	—
370	C₄⋊Q₈	—	173	2	no	—
371	C₄⋊Q₈	—	173	1	no	—
372	C₄⋊Q₈	C₂×D₁₇₃	1	1	yes	characteristic, complemented
373	#127	—	173	2	no	—
374	#127	—	173	1	no	—
375	#127	—	173	1	no	—
376	#126	—	173	2	no	—
377	#126	—	173	2	no	—
378	#126	—	173	2	no	—
379	#126	C₂×D₁₇₃	1	2	yes	complemented
380	#125	—	173	2	no	—
381	#125	—	173	1	no	—
382	#125	—	173	1	no	—
383	#124	—	173	1	no	—
384	#124	—	173	2	no	—
385	#124	—	173	2	no	—
386	#124	—	173	2	no	—
387	#124	—	173	2	no	—
388	#124	C₂×D₁₇₃	1	1	yes	characteristic
389	#124	C₂×D₁₇₃	1	2	yes	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	2	no	—
399	C₂²⋊Q₈	—	173	1	no	—
400	C₂²⋊Q₈	—	173	2	no	—
401	C₂²⋊Q₈	—	173	2	no	—
402	C₂²⋊Q₈	—	173	2	no	—
403	C₂²⋊Q₈	C₂×D₁₇₃	1	2	yes	complemented
404	C₂²⋊Q₈	C₂×D₁₇₃	1	1	yes	characteristic, complemented
405	#121	—	173	1	no	—
406	#121	—	173	2	no	—
407	#121	—	173	2	no	—
408	#121	—	173	1	no	—
409	#121	—	173	1	no	—
410	#121	—	173	2	no	—
411	#121	—	173	1	no	—
412	#121	—	173	1	no	—
413	#121	—	173	2	no	—
414	#121	—	173	2	no	—
415	#121	—	173	2	no	—
416	#121	—	173	2	no	—
417	#121	—	173	2	no	—
418	#121	—	173	2	no	—
419	#121	—	173	2	no	—
420	#121	—	173	2	no	—
421	#121	C₂×D₁₇₃	1	1	yes	characteristic
422	#120	—	173	2	no	—
423	#120	—	173	2	no	—
424	#120	—	173	2	no	—
425	#120	—	173	2	no	—
426	C₄×Q₈	—	173	1	no	—
427	C₄×Q₈	—	173	1	no	—
428	C₄×Q₈	—	173	1	no	—
429	C₄×Q₈	C₂×D₁₇₃	1	1	yes	characteristic, complemented
430	C₄×D₄	—	173	1	no	—
431	C₄×D₄	—	173	2	no	—
432	C₄×D₄	—	173	1	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	2	no	—
438	C₄×D₄	—	173	2	no	—
439	C₄×D₄	—	173	1	no	—
440	C₄×D₄	—	173	1	no	—
441	C₄×D₄	—	173	1	no	—
442	C₄×D₄	—	173	1	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	2	no	—
448	C₄×D₄	—	173	1	no	—
449	C₄×D₄	C₂×D₁₇₃	1	1	yes	characteristic
450	#117	—	173	1	no	—
451	#117	—	173	2	no	—
452	#117	—	173	2	no	—
453	#117	—	173	2	no	—
454	#117	—	173	1	no	—
455	#117	—	173	1	no	—
456	#117	C₂×D₁₇₃	1	1	yes	characteristic, complemented
457	C₂×C₄⋊C₄	—	173	1	no	—
458	C₂×C₂²⋊C₄	—	173	2	no	—
459	C₂×C₄²	—	173	1	no	—
460	C₂×C₄²	—	173	1	no	—
461	C₂×C₄²	—	173	2	no	—
462	C₂×C₄²	—	173	1	no	—
463	C₂⁴	—	173	2	no	—
464	#41	—	346	4	no	—
465	#41	—	346	4	no	—
466	#41	—	692	4	no	—
467	#41	—	692	4	no	—
468	C₂×Q₈	—	173	1	no	—
469	C₂×Q₈	—	173	2	no	—
470	C₂×Q₈	C₂²×D₁₇₃	1	1	yes	characteristic
471	C₂×Q₈	C₂²×D₁₇₃	1	2	yes	—
472	C₂×D₄	—	346	4	no	—
473	C₂×D₄	—	173	1	no	—
474	C₂×D₄	—	173	2	no	—
475	C₂×D₄	—	173	1	no	—
476	C₂×D₄	—	173	2	no	—
477	C₂×D₄	—	173	2	no	—
478	C₂×D₄	—	173	2	no	—
479	C₂×D₄	—	173	2	no	—
480	C₂×D₄	—	173	2	no	—
481	C₂×D₄	—	173	1	no	—
482	C₂×D₄	—	173	2	no	—
483	C₂×D₄	—	173	1	no	—
484	C₂×D₄	—	173	1	no	—
485	C₂×D₄	—	173	2	no	—
486	C₂×D₄	—	173	2	no	—
487	C₂×D₄	—	173	2	no	—
488	C₂×D₄	—	173	2	no	—
489	C₂×D₄	C₂²×D₁₇₃	1	1	yes	characteristic
490	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
491	C₂²×C₄	—	173	1	no	—
492	C₂²×C₄	—	173	2	no	—
493	C₂²×C₄	—	173	2	no	—
494	C₂²×C₄	—	173	1	no	—
495	C₂²×C₄	—	173	1	no	—
496	C₂²×C₄	—	173	2	no	—
497	C₂²×C₄	—	173	1	no	—
498	C₂²×C₄	—	173	2	no	—
499	C₂²×C₄	—	173	1	no	—
500	C₂²×C₄	—	173	1	no	—
501	C₂²×C₄	—	173	1	no	—
502	C₂²×C₄	—	173	1	no	—
503	C₂²×C₄	—	173	2	no	—
504	C₂²×C₄	—	173	2	no	—
505	C₂²×C₄	—	173	2	no	—
506	C₂²×C₄	—	692	4	no	—
507	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
508	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
509	C₄⋊C₄	—	173	2	no	—
510	C₄⋊C₄	—	173	1	no	—
511	C₄⋊C₄	—	173	1	no	—
512	C₄⋊C₄	—	173	1	no	—
513	C₄⋊C₄	—	173	1	no	—
514	C₄⋊C₄	—	173	1	no	—
515	C₄⋊C₄	—	173	1	no	—
516	C₄⋊C₄	—	173	2	no	—
517	C₄⋊C₄	—	173	2	no	—
518	C₄⋊C₄	—	173	2	no	—
519	C₄⋊C₄	—	173	2	no	—
520	C₄⋊C₄	—	173	2	no	—
521	C₄⋊C₄	—	173	2	no	—
522	C₄⋊C₄	—	173	2	no	—
523	C₄⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
526	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
527	C₄⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
530	C₂²⋊C₄	—	173	2	no	—
531	C₂²⋊C₄	—	173	2	no	—
532	C₂²⋊C₄	—	173	2	no	—
533	C₂²⋊C₄	—	173	2	no	—
534	C₂²⋊C₄	—	173	2	no	—
535	C₂²⋊C₄	—	173	1	no	—
536	C₂²⋊C₄	—	173	1	no	—
537	C₂²⋊C₄	—	173	2	no	—
538	C₂²⋊C₄	—	173	1	no	—
539	C₂²⋊C₄	—	173	2	no	—
540	C₂²⋊C₄	—	173	1	no	—
541	C₂²⋊C₄	—	173	2	no	—
542	C₂²⋊C₄	—	173	2	no	—
543	C₂²⋊C₄	—	173	2	no	—
544	C₂²⋊C₄	—	173	2	no	—
545	C₂²⋊C₄	—	173	2	no	—
546	C₂²⋊C₄	—	173	2	no	—
547	C₂²⋊C₄	—	173	2	no	—
548	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
551	C₂²⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
552	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
555	C₄²	—	173	1	no	—
556	C₄²	—	173	1	no	—
557	C₄²	—	173	1	no	—
558	C₄²	—	173	1	no	—
559	C₄²	—	173	1	no	—
560	C₄²	—	173	2	no	—
561	C₄²	—	173	1	no	—
562	C₄²	—	173	2	no	—
563	C₄²	—	173	1	no	—
564	C₄²	—	173	1	no	—
565	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
566	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
567	C₄²	C₂²×D₁₇₃	1	2	yes	—
568	C₂³	—	346	4	no	—
569	C₂³	—	173	2	no	—
570	C₂³	—	173	1	no	—
571	C₂³	—	173	2	no	—
572	C₂³	—	173	1	no	—
573	C₂³	—	692	2	no	—
574	C₂³	—	692	2	no	—
575	C₂³	C₂³×D₁₇₃	1	2	yes	—
576	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
577	Q₈	—	2	2	no	—
578	Q₈	—	4	2	no	—
579	Q₈	—	346	2	no	—
580	Q₈	—	692	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	346	2	no	—
584	D₄	—	346	4	no	—
585	D₄	—	346	2	no	—
586	D₄	—	346	4	no	—
587	D₄	—	346	2	no	—
588	D₄	—	346	2	no	—
589	D₄	—	346	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	D₄	—	692	2	no	—
596	D₄	—	692	2	no	—
597	D₄	—	692	2	no	—
598	D₄	—	692	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	346	2	no	—
602	C₂×C₄	—	346	4	no	—
603	C₂×C₄	—	346	4	no	—
604	C₂×C₄	—	346	4	no	—
605	C₂×C₄	—	346	2	no	—
606	C₂×C₄	—	346	4	no	—
607	C₂×C₄	—	346	2	no	—
608	C₂×C₄	—	346	2	no	—
609	C₂×C₄	—	173	1	no	—
610	C₂×C₄	—	173	1	no	—
611	C₂×C₄	—	173	2	no	—
612	C₂×C₄	—	173	1	no	—
613	C₂×C₄	—	173	1	no	—
614	C₂×C₄	—	173	2	no	—
615	C₂×C₄	—	173	1	no	—
616	C₂×C₄	—	173	1	no	—
617	C₂×C₄	—	173	4	no	—
618	C₂×C₄	—	692	1	no	—
619	C₂×C₄	—	692	2	no	—
620	C₂×C₄	—	692	1	no	—
621	C₂×C₄	—	692	2	no	—
622	C₂×C₄	—	692	2	no	—
623	C₂×C₄	—	692	1	no	—
624	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
627	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
629	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
632	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	346	1	no	—
640	C₂²	—	346	1	no	—
641	C₂²	—	346	2	no	—
642	C₂²	—	346	1	no	—
643	C₂²	—	346	2	no	—
644	C₂²	—	346	2	no	—
645	C₂²	—	346	1	no	—
646	C₂²	—	346	2	no	—
647	C₂²	—	346	2	no	—
648	C₂²	—	346	1	no	—
649	C₂²	—	346	2	no	—
650	C₂²	—	173	2	no	—
651	C₂²	—	692	8	no	—
652	C₂²	C₂⁴×D₁₇₃	1	1	yes	characteristic
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	346	1	no	—
662	C₄	—	346	2	no	—
663	C₄	—	346	1	no	—
664	C₄	—	346	1	no	—
665	C₄	—	346	2	no	—
666	C₄	—	346	1	no	—
667	C₄	—	173	2	no	—
668	C₄	—	173	2	no	—
669	C₄	#41×D₁₇₃	1	2	yes	—
670	C₂	—	4	1	no	—
671	C₂	—	4	2	no	—
672	C₂	—	346	2	no	—
673	C₂	—	692	1	no	—
674	C₂	—	692	2	no	—
675	C₂	—	692	2	no	—
676	C₂	C₂×#41×D₁₇₃	1	1	yes	characteristic
677	C₂	H(5,𝔽₂)×D₁₇₃	1	1	yes	characteristic
678	C₂	#26012328	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇₃
commutator, socle, cosocle	C₂²×C₁₇₃	C₂⁵
Fitting	#542×C₁₇₃	C₂
hypercenter	#542	D₁₇₃
hypocenter	C₁₇₃	#3460
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #26012118	C₂	semidirect
2. #26012113	C₂	semidirect
3. #26012111	C₂	semidirect
4. #26012096	C₂	semidirect
5. #26012093	C₂	semidirect
6. #26012092	C₂	semidirect
7. #26012080	C₂	semidirect
8. #26012075	C₂	semidirect
9. #26012071	C₂	semidirect
10. #26012059	C₂	semidirect
11. #26012057	C₂	semidirect
12. #26012042	C₂	semidirect
13. #26012040	C₂	semidirect
14. #26012036	C₂	semidirect
15. #26012027	C₂	semidirect
16. #26012024	C₂	semidirect
17. #26012020	C₂	semidirect
18. #26012004	C₂	semidirect
19. #26011999	C₂	semidirect
20. C₄×#14583827	C₂	semidirect
21. #26011959	C₂	semidirect
22. C₄×D₄×D₁₇₃	C₂	semidirect
23. #542×C₁₇₃	C₂	semidirect
25. C₂×#14583827	C₂²	semidirect
27. C₂×#14583825	C₂²	semidirect
30. #19149678	C₂²	semidirect
31. #19149677	C₂²	semidirect
35. #19149674	C₂²	semidirect
36. #19149673	C₂²	semidirect
37. #19149672	C₂²	semidirect
38. #19149671	C₂²	semidirect
39. #19149670	C₂²	semidirect
40. #19149669	C₂²	semidirect
42. #19149668	C₂²	semidirect
43. #19149667	C₂²	semidirect
45. #19149665	C₂²	semidirect
46. #19149664	C₂²	semidirect
47. #19149664	C₂²	semidirect
48. #19149664	C₂²	semidirect
49. #19149663	C₂²	semidirect
50. #19149662	C₂²	semidirect
51. #19149661	C₂²	semidirect
52. #19149661	C₂²	semidirect
54. #19149657	C₂²	semidirect
55. #19149657	C₂²	semidirect
57. #19149655	C₂²	semidirect
60. #19149654	C₂²	semidirect
61. #19149654	C₂²	semidirect
63. #19149653	C₂²	semidirect
64. #19149653	C₂²	semidirect
68. #19149652	C₂²	semidirect
69. #19149652	C₂²	semidirect
70. #19149652	C₂²	semidirect
71. #19149652	C₂²	semidirect
72. #19149651	C₂²	semidirect
78. Q₈×Dic₁₇₃	C₂²	semidirect
79. #19149644	C₂²	semidirect
80. #19149644	C₂²	semidirect
83. C₄×D₆₉₂	C₂²	semidirect
89. #19149641	C₂²	semidirect
90. #19149641	C₂²	semidirect
95. #19149639	C₂²	semidirect
96. #19149639	C₂²	semidirect
97. #19149639	C₂²	semidirect
98. #19149639	C₂²	semidirect
99. #19149639	C₂²	semidirect
101. #19149637	C₂²	semidirect
102. #19149637	C₂²	semidirect
104. #19149636	C₂²	semidirect
105. #19149635	C₂²	semidirect
108. C₂×C₄×Dic₁₇₃	C₂²	semidirect
110. C₄²×D₁₇₃	C₂²	semidirect
111. C₄²×D₁₇₃	C₂²	semidirect
112. C₄⋊Q₈×C₁₇₃	C₂²	semidirect
113. #126×C₁₇₃	C₂²	semidirect
115. #124×C₁₇₃	C₂²	semidirect
116. #123×C₁₇₃	C₂²	semidirect
117. C₂²⋊Q₈×C₁₇₃	C₂²	semidirect
118. C₂²⋊Q₈×C₁₇₃	C₂²	semidirect
120. C₄×Q₈×C₁₇₃	C₂²	semidirect
122. #117×C₁₇₃	C₂²	semidirect
275. C₄×D₁₇₃	#41	semidirect
339. C₁₇₃	#3460	semidirect
344. #542	D₁₇₃	semidirect
372. C₄⋊Q₈	C₂×D₁₇₃	semidirect
379. #126	C₂×D₁₇₃	semidirect
389. #124	C₂×D₁₇₃	semidirect
397. #123	C₂×D₁₇₃	semidirect
403. C₂²⋊Q₈	C₂×D₁₇₃	semidirect
404. C₂²⋊Q₈	C₂×D₁₇₃	semidirect
429. C₄×Q₈	C₂×D₁₇₃	semidirect
456. #117	C₂×D₁₇₃	semidirect

Maximal subgroups

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

subgroup	index
#26012118	2
#26012113	2
#26012111	2
#26012096	2
#26012093	2
#26012092	2
#26012080	2
#26012075	2
#26012071	2
#26012059	2
#26012057	2
#26012042	2
#26012040	2
#26012036	2
#26012027	2
#26012024	2
#26012020	2
#26012004	2
#26011999	2
C₄×#14583827	2
#26011959	2
C₄×D₄×D₁₇₃	2
#542×C₁₇₃	2
#3460	173