Subgroups — #535×D₁₇₃ #36366867

Order 22144.

1896 conjugacy classes of subgroups.

The subgroup lattice has 480 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	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#26012060	C₂	1	1	yes	maximal, characteristic, complemented
4	#26012059	C₂	1	2	yes	maximal, complemented
5	#26012058	C₂	1	1	yes	maximal, characteristic, complemented
6	#26012057	C₂	1	4	yes	maximal, complemented
7	#26012056	C₂	1	4	yes	maximal, complemented
8	#26012055	C₂	1	1	yes	maximal, characteristic, complemented
9	#26012054	C₂	1	2	yes	maximal, complemented
10	#127×D₁₇₃	C₂	1	2	yes	maximal, complemented
11	#124×D₁₇₃	C₂	1	2	yes	maximal, complemented
12	#121×D₁₇₃	C₂	1	4	yes	maximal, complemented
13	#120×D₁₇₃	C₂	1	4	yes	maximal, complemented
14	#117×D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#535×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×D₁₇₃	C₂²	1	2	yes	—
17	C₂×#14583827	C₂²	1	1	yes	characteristic, complemented
18	C₂×#14583826	C₂²	1	2	yes	complemented
19	C₂×#14583826	C₂²	1	1	yes	characteristic, complemented
20	C₂×#14583825	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14583825	C₂²	1	2	yes	complemented
22	#41×D₁₇₃	—	2	8	no	—
23	C₂×Q₈×D₁₇₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×D₆₉₂	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₂²⋊D₁₇₃	C₂²	1	2	yes	complemented
26	C₂×D₄×D₁₇₃	—	2	8	no	—
27	C₂×D₄×D₁₇₃	C₂²	1	2	yes	—
28	C₂×D₄×D₁₇₃	C₂²	1	2	yes	—
29	C₂×D₄×D₁₇₃	C₂²	1	2	yes	—
30	C₂×D₄×D₁₇₃	C₂²	1	2	yes	complemented
31	C₂×D₄×D₁₇₃	C₂²	1	2	yes	complemented
32	C₂×D₄×D₁₇₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×D₄×D₁₇₃	C₂²	1	8	yes	complemented
34	C₂²×C₄×D₁₇₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄×D₁₇₃	C₂²	1	2	yes	complemented
36	#19149676	C₂²	1	2	yes	complemented
37	#19149675	C₂²	1	8	yes	complemented
38	#19149675	C₂²	1	2	yes	complemented
39	#19149675	C₂²	1	2	yes	complemented
40	#19149668	C₂²	1	2	yes	complemented
41	#19149667	C₂²	1	2	yes	complemented
42	#19149666	C₂²	1	2	yes	complemented
43	#19149665	C₂²	1	8	yes	complemented
44	#19149654	C₂²	1	4	yes	complemented
45	#19149653	C₂²	1	4	yes	complemented
46	#19149652	C₂²	1	8	yes	complemented
47	#19149651	C₂²	1	8	yes	complemented
48	#19149650	C₂²	1	4	yes	complemented
49	#19149649	C₂²	1	4	yes	complemented
50	#19149649	C₂²	1	8	yes	complemented
51	#19149648	C₂²	1	4	yes	complemented
52	#19149647	C₂²	1	8	yes	complemented
53	#19149647	C₂²	1	4	yes	complemented
54	#19149638	C₂²	1	1	yes	characteristic, complemented
55	#19149637	C₂²	1	2	yes	complemented
56	#19149636	C₂²	1	2	yes	complemented
57	#19149635	C₂²	1	2	yes	complemented
58	C₄⋊C₄×D₁₇₃	C₂²	1	2	yes	complemented
59	C₂²⋊C₄×D₁₇₃	C₂²	1	2	yes	—
60	C₂²⋊C₄×D₁₇₃	C₂²	1	8	yes	complemented
61	C₄²×D₁₇₃	C₂²	1	2	yes	complemented
62	C₂×#41×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
63	C₂²×D₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
64	#127×C₁₇₃	C₂²	1	2	yes	complemented
65	#124×C₁₇₃	C₂²	1	2	yes	complemented
66	#121×C₁₇₃	C₂²	1	4	yes	complemented
67	#120×C₁₇₃	C₂²	1	4	yes	complemented
68	#117×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
69	C₂³×D₁₇₃	—	2	8	no	—
70	C₂³×D₁₇₃	—	4	8	no	—
71	C₂³×D₁₇₃	C₂³	1	4	yes	—
72	C₂³×D₁₇₃	C₂³	1	2	yes	—
73	C₂³×D₁₇₃	C₂³	1	1	yes	characteristic
74	C₂³×D₁₇₃	C₂³	1	4	yes	—
75	C₂³×D₁₇₃	C₂³	1	2	yes	—
76	#14583827	—	2	4	no	—
77	#14583826	—	2	8	no	—
78	#14583826	—	2	4	no	—
79	#14583825	—	2	8	no	—
80	#14583825	—	2	4	no	—
81	C₂×Dic₃₄₆	C₂³	1	2	yes	complemented
82	C₂×Dic₃₄₆	C₂³	1	1	yes	characteristic, complemented
83	Q₈×D₁₇₃	—	2	4	no	—
84	C₂×D₆₉₂	—	2	4	no	—
85	C₂×D₆₉₂	C₂³	1	2	yes	—
86	C₂×D₆₉₂	C₂³	1	2	yes	—
87	C₂×D₆₉₂	C₂³	1	2	yes	—
88	C₂×D₆₉₂	C₂³	1	1	yes	characteristic, complemented
89	C₂×D₆₉₂	C₂³	1	8	yes	complemented
90	C₂×C₂²⋊D₁₇₃	—	2	8	no	—
91	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	complemented
96	C₂×C₂²⋊D₁₇₃	C₂³	1	8	yes	complemented
97	C₂×C₂²⋊D₁₇₃	C₂³	1	8	yes	complemented
98	D₄×D₁₇₃	—	2	8	no	—
99	D₄×D₁₇₃	—	2	8	no	—
100	D₄×D₁₇₃	—	2	8	no	—
101	D₄×D₁₇₃	—	2	4	no	—
102	D₄×D₁₇₃	—	2	8	no	—
103	D₄×D₁₇₃	—	2	8	no	—
104	D₄×D₁₇₃	—	4	16	no	—
105	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
106	C₂²×Dic₁₇₃	C₂³	1	2	yes	complemented
107	C₂×C₄×D₁₇₃	—	2	8	no	—
108	C₂×C₄×D₁₇₃	D₄	1	8	yes	complemented
109	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
110	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
111	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
112	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
113	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
114	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
115	C₂×C₄×D₁₇₃	C₂³	1	2	yes	complemented
116	C₂×C₄×D₁₇₃	C₂³	1	2	yes	complemented
117	C₄⋊Dic₁₇₃	C₂³	1	2	yes	complemented
118	#14583805	C₂³	1	4	yes	complemented
119	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
120	C₂²⋊Dic₁₇₃	C₂³	1	8	yes	complemented
121	#14583803	C₂³	1	4	yes	—
122	#14583803	C₂³	1	8	yes	complemented
123	#14583803	C₂³	1	8	yes	complemented
124	C₄×Dic₁₇₃	C₂³	1	4	yes	complemented
125	C₄×Dic₁₇₃	C₂³	1	2	yes	complemented
126	C₂⁴×C₁₇₃	C₂³	1	2	yes	—
127	#41×C₁₇₃	—	2	4	no	—
128	C₂×Q₈×C₁₇₃	C₂³	1	1	yes	characteristic, complemented
129	C₂×D₄×C₁₇₃	—	2	4	no	—
130	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
131	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
132	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
133	C₂×D₄×C₁₇₃	C₂³	1	1	yes	characteristic, complemented
134	C₂×D₄×C₁₇₃	C₂³	1	8	yes	complemented
135	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	complemented
137	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	complemented
138	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
139	C₂²⋊C₄×C₁₇₃	C₂³	1	8	yes	complemented
140	C₄²×C₁₇₃	C₂³	1	2	yes	complemented
141	C₂²×D₁₇₃	—	2	4	no	—
142	C₂²×D₁₇₃	—	2	4	no	—
143	C₂²×D₁₇₃	—	2	4	no	—
144	C₂²×D₁₇₃	—	2	8	no	—
145	C₂²×D₁₇₃	—	2	8	no	—
146	C₂²×D₁₇₃	—	2	8	no	—
147	C₂²×D₁₇₃	—	2	16	no	—
148	C₂²×D₁₇₃	—	4	8	no	—
149	C₂²×D₁₇₃	—	4	4	no	—
150	C₂²×D₁₇₃	—	4	32	no	—
151	C₂²×D₁₇₃	C₂×D₄	1	4	yes	—
152	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
153	C₂²×D₁₇₃	C₂⁴	1	4	yes	—
154	C₂²×D₁₇₃	C₂⁴	1	1	yes	characteristic
155	C₂²×D₁₇₃	C₂⁴	1	1	yes	characteristic
156	Dic₃₄₆	—	2	2	no	—
157	Dic₃₄₆	—	2	4	no	—
158	D₆₉₂	—	2	4	no	—
159	D₆₉₂	—	2	4	no	—
160	D₆₉₂	—	2	4	no	—
161	D₆₉₂	—	2	2	no	—
162	D₆₉₂	—	4	8	no	—
163	C₂²⋊D₁₇₃	—	2	4	no	—
164	C₂²⋊D₁₇₃	—	2	4	no	—
165	C₂²⋊D₁₇₃	—	2	8	no	—
166	C₂²⋊D₁₇₃	—	2	8	no	—
167	C₂²⋊D₁₇₃	—	2	4	no	—
168	C₂²⋊D₁₇₃	—	4	8	no	—
169	C₂²⋊D₁₇₃	—	4	8	no	—
170	C₂×Dic₁₇₃	—	2	4	no	—
171	C₂×Dic₁₇₃	C₂×D₄	1	4	yes	complemented
172	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
173	C₂×Dic₁₇₃	C₂⁴	1	4	yes	—
174	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
175	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
176	C₄×D₁₇₃	—	2	4	no	—
177	C₄×D₁₇₃	—	2	8	no	—
178	C₄×D₁₇₃	—	2	4	no	—
179	C₄×D₁₇₃	—	2	4	no	—
180	C₄×D₁₇₃	C₂×D₄	1	4	yes	—
181	C₄×D₁₇₃	C₂×D₄	1	4	yes	—
182	C₄×D₁₇₃	C₂×D₄	1	4	yes	complemented
183	C₄×D₁₇₃	C₂×D₄	1	4	yes	complemented
184	C₂³×C₁₇₃	—	2	4	no	—
185	C₂³×C₁₇₃	—	4	4	no	—
186	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
187	C₂³×C₁₇₃	C₂⁴	1	4	yes	—
188	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
189	Q₈×C₁₇₃	—	2	2	no	—
190	D₄×C₁₇₃	—	2	4	no	—
191	D₄×C₁₇₃	—	2	4	no	—
192	D₄×C₁₇₃	—	2	4	no	—
193	D₄×C₁₇₃	—	2	2	no	—
194	D₄×C₁₇₃	—	4	8	no	—
195	C₂×C₄×C₁₇₃	—	2	4	no	—
196	C₂×C₄×C₁₇₃	C₂×D₄	1	4	yes	complemented
197	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
198	C₂×C₄×C₁₇₃	C₂⁴	1	4	yes	—
199	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
200	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
201	C₂²×C₁₇₃	—	2	2	no	—
202	C₂²×C₁₇₃	—	2	2	no	—
203	C₂²×C₁₇₃	—	2	4	no	—
204	C₂²×C₁₇₃	—	2	4	no	—
205	C₂²×C₁₇₃	—	2	8	no	—
206	C₂²×C₁₇₃	—	4	8	no	—
207	C₂²×C₁₇₃	C₂²×D₄	1	2	yes	—
208	C₂²×C₁₇₃	C₂⁵	1	1	yes	characteristic
209	C₂×D₁₇₃	—	2	2	no	—
210	C₂×D₁₇₃	—	2	8	no	—
211	C₂×D₁₇₃	—	2	2	no	—
212	C₂×D₁₇₃	—	2	4	no	—
213	C₂×D₁₇₃	—	2	4	no	—
214	C₂×D₁₇₃	—	2	8	no	—
215	C₂×D₁₇₃	—	4	16	no	—
216	C₂×D₁₇₃	—	4	8	no	—
217	C₂×D₁₇₃	—	4	8	no	—
218	C₂×D₁₇₃	—	4	16	no	—
219	C₂×D₁₇₃	C₂²×D₄	1	2	yes	—
220	C₂×D₁₇₃	C₂²×D₄	1	2	yes	—
221	C₂×D₁₇₃	H(5,𝔽₂)	1	4	yes	—
222	C₄×C₁₇₃	—	2	2	no	—
223	C₄×C₁₇₃	—	2	4	no	—
224	C₄×C₁₇₃	C₂²×D₄	1	2	yes	—
225	C₄×C₁₇₃	C₂²×D₄	1	2	yes	—
226	Dic₁₇₃	—	2	2	no	—
227	Dic₁₇₃	—	2	4	no	—
228	Dic₁₇₃	C₂²×D₄	1	2	yes	—
229	Dic₁₇₃	C₂²×D₄	1	2	yes	—
230	C₂×C₁₇₃	—	2	2	no	—
231	C₂×C₁₇₃	—	4	4	no	—
232	C₂×C₁₇₃	—	4	2	no	—
233	C₂×C₁₇₃	C₂³×D₄	1	1	yes	characteristic
234	C₂×C₁₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
235	D₁₇₃	—	2	2	no	—
236	D₁₇₃	—	4	2	no	—
237	D₁₇₃	—	4	4	no	—
238	D₁₇₃	#535	1	4	yes	direct product factor
239	C₁₇₃	C₂×#535	1	1	yes	characteristic, complemented, Sylow
240	C₂×#535	—	173	1	no	maximal, Sylow
241	C₂²×#41	—	173	1	no	—
242	C₂³×D₄	—	173	1	no	—
243	#535	—	173	1	no	—
244	#535	—	173	1	no	—
245	#535	—	173	2	no	—
246	#535	—	173	2	no	—
247	#535	—	173	4	no	—
248	#535	—	173	4	no	—
249	#535	—	173	1	no	—
250	#535	D₁₇₃	1	1	yes	characteristic, direct product factor
251	C₂×#127	—	173	2	no	—
252	C₂×#124	—	173	2	no	—
253	C₂×#121	—	173	4	no	—
254	C₂×#120	—	173	4	no	—
255	C₂×#117	—	173	1	no	—
256	C₂⁵	—	173	2	no	—
257	C₂×#41	—	346	8	no	—
258	C₂×#41	—	173	1	no	—
259	C₂×#41	—	173	2	no	—
260	C₂×#41	—	173	1	no	—
261	C₂×#41	—	173	1	no	—
262	C₂×#41	—	173	2	no	—
263	C₂×#41	C₂×D₁₇₃	1	1	yes	characteristic, complemented
264	C₂²×Q₈	—	173	1	no	—
265	C₂²×D₄	—	346	8	no	—
266	C₂²×D₄	—	173	2	no	—
267	C₂²×D₄	—	173	2	no	—
268	C₂²×D₄	—	173	2	no	—
269	C₂²×D₄	—	173	2	no	—
270	C₂²×D₄	—	173	2	no	—
271	C₂²×D₄	—	173	2	no	—
272	C₂²×D₄	—	173	1	no	—
273	C₂²×D₄	—	173	8	no	—
274	C₂²×D₄	—	173	1	no	—
275	C₂²×D₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
276	C₂³×C₄	—	173	2	no	—
277	C₂³×C₄	—	173	1	no	—
278	#127	—	173	2	no	—
279	#127	—	173	8	no	—
280	#127	—	173	2	no	—
281	#127	—	173	2	no	—
282	#127	C₂×D₁₇₃	1	2	yes	complemented
283	#124	—	173	2	no	—
284	#124	—	173	2	no	—
285	#124	—	173	8	no	—
286	#124	—	173	2	no	—
287	#124	C₂×D₁₇₃	1	2	yes	complemented
288	#121	—	173	4	no	—
289	#121	—	173	8	no	—
290	#121	—	173	4	no	—
291	#121	—	173	4	no	—
292	#121	—	173	8	no	—
293	#121	C₂×D₁₇₃	1	4	yes	complemented
294	#120	—	173	4	no	—
295	#120	—	173	4	no	—
296	#120	—	173	8	no	—
297	#120	—	173	4	no	—
298	#120	—	173	8	no	—
299	#120	C₂×D₁₇₃	1	4	yes	complemented
300	#117	—	173	1	no	—
301	#117	—	173	2	no	—
302	#117	—	173	2	no	—
303	#117	—	173	2	no	—
304	#117	C₂×D₁₇₃	1	1	yes	characteristic, complemented
305	C₂×C₄⋊C₄	—	173	2	no	—
306	C₂×C₂²⋊C₄	—	173	2	no	—
307	C₂×C₂²⋊C₄	—	173	8	no	—
308	C₂×C₄²	—	173	2	no	—
309	C₂⁴	—	346	8	no	—
310	C₂⁴	—	173	4	no	—
311	C₂⁴	—	173	2	no	—
312	C₂⁴	—	173	1	no	—
313	C₂⁴	—	173	4	no	—
314	C₂⁴	—	173	2	no	—
315	C₂⁴	—	692	8	no	—
316	C₂⁴	C₂²×D₁₇₃	1	2	yes	—
317	#41	—	2	4	no	—
318	#41	—	346	8	no	—
319	#41	—	346	8	no	—
320	#41	—	346	4	no	—
321	#41	—	346	4	no	—
322	#41	—	346	4	no	—
323	C₂×Q₈	—	346	4	no	—
324	C₂×Q₈	—	173	1	no	—
325	C₂×Q₈	—	173	2	no	—
326	C₂×Q₈	C₂²×D₁₇₃	1	1	yes	characteristic, complemented
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	346	8	no	—
329	C₂×D₄	—	346	8	no	—
330	C₂×D₄	—	346	8	no	—
331	C₂×D₄	—	346	8	no	—
332	C₂×D₄	—	346	8	no	—
333	C₂×D₄	—	346	4	no	—
334	C₂×D₄	—	346	8	no	—
335	C₂×D₄	—	346	4	no	—
336	C₂×D₄	—	173	2	no	—
337	C₂×D₄	—	173	2	no	—
338	C₂×D₄	—	173	4	no	—
339	C₂×D₄	—	173	4	no	—
340	C₂×D₄	—	173	2	no	—
341	C₂×D₄	—	173	8	no	—
342	C₂×D₄	—	173	8	no	—
343	C₂×D₄	—	173	2	no	—
344	C₂×D₄	—	173	2	no	—
345	C₂×D₄	—	173	2	no	—
346	C₂×D₄	—	173	1	no	—
347	C₂×D₄	—	173	8	no	—
348	C₂×D₄	—	692	16	no	—
349	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
350	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
351	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
352	C₂×D₄	C₂²×D₁₇₃	1	1	yes	characteristic, complemented
353	C₂×D₄	C₂²×D₁₇₃	1	8	yes	complemented
354	C₂²×C₄	—	346	8	no	—
355	C₂²×C₄	—	173	2	no	—
356	C₂²×C₄	—	173	4	no	—
357	C₂²×C₄	—	173	2	no	—
358	C₂²×C₄	—	173	2	no	—
359	C₂²×C₄	—	173	2	no	—
360	C₂²×C₄	—	173	1	no	—
361	C₂²×C₄	—	173	8	no	—
362	C₂²×C₄	—	173	1	no	—
363	C₂²×C₄	—	173	1	no	—
364	C₂²×C₄	—	173	1	no	—
365	C₂²×C₄	—	173	1	no	—
366	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
367	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	complemented
368	C₄⋊C₄	—	173	4	no	—
369	C₄⋊C₄	—	173	2	no	—
370	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	complemented
371	C₂²⋊C₄	—	173	2	no	—
372	C₂²⋊C₄	—	173	8	no	—
373	C₂²⋊C₄	—	173	4	no	—
374	C₂²⋊C₄	—	173	8	no	—
375	C₂²⋊C₄	—	173	8	no	—
376	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
377	C₂²⋊C₄	C₂²×D₁₇₃	1	8	yes	complemented
378	C₄²	—	173	2	no	—
379	C₄²	—	173	4	no	—
380	C₄²	C₂²×D₁₇₃	1	2	yes	complemented
381	C₂³	—	2	4	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	346	4	no	—
384	C₂³	—	346	4	no	—
385	C₂³	—	346	8	no	—
386	C₂³	—	346	8	no	—
387	C₂³	—	346	8	no	—
388	C₂³	—	346	16	no	—
389	C₂³	—	346	4	no	—
390	C₂³	—	173	4	no	—
391	C₂³	—	173	2	no	—
392	C₂³	—	173	4	no	—
393	C₂³	—	173	1	no	—
394	C₂³	—	173	1	no	—
395	C₂³	—	692	4	no	—
396	C₂³	—	692	8	no	—
397	C₂³	—	692	32	no	—
398	C₂³	C₂³×D₁₇₃	1	4	yes	—
399	C₂³	C₂³×D₁₇₃	1	2	yes	—
400	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
401	Q₈	—	2	2	no	—
402	Q₈	—	346	4	no	—
403	Q₈	—	346	2	no	—
404	D₄	—	2	4	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	2	no	—
408	D₄	—	4	8	no	—
409	D₄	—	346	4	no	—
410	D₄	—	346	4	no	—
411	D₄	—	346	4	no	—
412	D₄	—	346	8	no	—
413	D₄	—	346	8	no	—
414	D₄	—	346	4	no	—
415	D₄	—	346	4	no	—
416	D₄	—	346	4	no	—
417	D₄	—	346	2	no	—
418	D₄	—	692	8	no	—
419	D₄	—	692	8	no	—
420	D₄	—	692	8	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	346	4	no	—
423	C₂×C₄	—	346	8	no	—
424	C₂×C₄	—	346	4	no	—
425	C₂×C₄	—	346	4	no	—
426	C₂×C₄	—	346	4	no	—
427	C₂×C₄	—	173	4	no	—
428	C₂×C₄	—	173	2	no	—
429	C₂×C₄	—	173	4	no	—
430	C₂×C₄	—	173	1	no	—
431	C₂×C₄	—	173	1	no	—
432	C₂×C₄	—	173	4	no	—
433	C₂×C₄	—	173	4	no	—
434	C₂×C₄	—	173	4	no	—
435	C₂×C₄	—	173	4	no	—
436	C₂×C₄	D₄×D₁₇₃	1	4	yes	complemented
437	C₂×C₄	C₂³×D₁₇₃	1	4	yes	—
438	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
439	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	8	no	—
446	C₂²	—	4	8	no	—
447	C₂²	—	346	8	no	—
448	C₂²	—	346	2	no	—
449	C₂²	—	346	2	no	—
450	C₂²	—	346	4	no	—
451	C₂²	—	346	4	no	—
452	C₂²	—	346	8	no	—
453	C₂²	—	173	2	no	—
454	C₂²	—	173	2	no	—
455	C₂²	—	173	4	no	—
456	C₂²	—	692	8	no	—
457	C₂²	—	692	16	no	—
458	C₂²	—	692	16	no	—
459	C₂²	—	692	8	no	—
460	C₂²	C₂×D₄×D₁₇₃	1	2	yes	—
461	C₂²	C₂⁴×D₁₇₃	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	4	no	—
464	C₄	—	346	2	no	—
465	C₄	—	346	4	no	—
466	C₄	—	173	2	no	—
467	C₄	—	173	2	no	—
468	C₄	C₂×D₄×D₁₇₃	1	2	yes	—
469	C₄	C₂×D₄×D₁₇₃	1	2	yes	—
470	C₂	—	2	2	no	—
471	C₂	—	4	4	no	—
472	C₂	—	4	2	no	—
473	C₂	—	346	2	no	—
474	C₂	—	173	4	no	—
475	C₂	—	692	2	no	—
476	C₂	—	692	4	no	—
477	C₂	C₂²×D₄×D₁₇₃	1	1	yes	characteristic
478	C₂	H(5,𝔽₂)×D₁₇₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇₃
commutator, socle, cosocle	C₂²×C₁₇₃	C₂⁵
Fitting	#535×C₁₇₃	C₂
hypercenter	#535	D₁₇₃
hypocenter	C₁₇₃	C₂×#535
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₇₃	C₂	semidirect
2. C₂²×D₄×D₁₇₃	C₂	semidirect
3. #26012060	C₂	semidirect
4. #26012059	C₂	semidirect
5. #26012058	C₂	semidirect
6. #26012057	C₂	semidirect
7. #26012056	C₂	semidirect
8. #26012055	C₂	semidirect
9. #26012054	C₂	semidirect
10. #127×D₁₇₃	C₂	semidirect
11. #124×D₁₇₃	C₂	semidirect
12. #121×D₁₇₃	C₂	semidirect
13. #120×D₁₇₃	C₂	semidirect
14. #117×D₁₇₃	C₂	semidirect
15. #535×C₁₇₃	C₂	semidirect
17. C₂×#14583827	C₂²	semidirect
18. C₂×#14583826	C₂²	semidirect
19. C₂×#14583826	C₂²	semidirect
20. C₂×#14583825	C₂²	semidirect
21. C₂×#14583825	C₂²	semidirect
23. C₂×Q₈×D₁₇₃	C₂²	semidirect
24. C₂²×D₆₉₂	C₂²	semidirect
25. C₂²×C₂²⋊D₁₇₃	C₂²	semidirect
30. C₂×D₄×D₁₇₃	C₂²	semidirect
31. C₂×D₄×D₁₇₃	C₂²	semidirect
32. C₂×D₄×D₁₇₃	C₂²	semidirect
33. C₂×D₄×D₁₇₃	C₂²	semidirect
35. C₂²×C₄×D₁₇₃	C₂²	semidirect
36. #19149676	C₂²	semidirect
37. #19149675	C₂²	semidirect
38. #19149675	C₂²	semidirect
39. #19149675	C₂²	semidirect
40. #19149668	C₂²	semidirect
41. #19149667	C₂²	semidirect
42. #19149666	C₂²	semidirect
43. #19149665	C₂²	semidirect
44. #19149654	C₂²	semidirect
45. #19149653	C₂²	semidirect
46. #19149652	C₂²	semidirect
47. #19149651	C₂²	semidirect
48. #19149650	C₂²	semidirect
49. #19149649	C₂²	semidirect
50. #19149649	C₂²	semidirect
51. #19149648	C₂²	semidirect
52. #19149647	C₂²	semidirect
53. #19149647	C₂²	semidirect
54. #19149638	C₂²	semidirect
55. #19149637	C₂²	semidirect
56. #19149636	C₂²	semidirect
57. #19149635	C₂²	semidirect
58. C₄⋊C₄×D₁₇₃	C₂²	semidirect
60. C₂²⋊C₄×D₁₇₃	C₂²	semidirect
61. C₄²×D₁₇₃	C₂²	semidirect
62. C₂×#41×C₁₇₃	C₂²	semidirect
63. C₂²×D₄×C₁₇₃	C₂²	semidirect
64. #127×C₁₇₃	C₂²	semidirect
65. #124×C₁₇₃	C₂²	semidirect
66. #121×C₁₇₃	C₂²	semidirect
67. #120×C₁₇₃	C₂²	semidirect
68. #117×C₁₇₃	C₂²	semidirect
81. C₂×Dic₃₄₆	C₂³	semidirect
82. C₂×Dic₃₄₆	C₂³	semidirect
88. C₂×D₆₉₂	C₂³	semidirect
89. C₂×D₆₉₂	C₂³	semidirect
95. C₂×C₂²⋊D₁₇₃	C₂³	semidirect
96. C₂×C₂²⋊D₁₇₃	C₂³	semidirect
97. C₂×C₂²⋊D₁₇₃	C₂³	semidirect
106. C₂²×Dic₁₇₃	C₂³	semidirect
108. C₂×C₄×D₁₇₃	D₄	semidirect
115. C₂×C₄×D₁₇₃	C₂³	semidirect
116. C₂×C₄×D₁₇₃	C₂³	semidirect
117. C₄⋊Dic₁₇₃	C₂³	semidirect
118. #14583805	C₂³	semidirect
120. C₂²⋊Dic₁₇₃	C₂³	semidirect
122. #14583803	C₂³	semidirect
123. #14583803	C₂³	semidirect
124. C₄×Dic₁₇₃	C₂³	semidirect
125. C₄×Dic₁₇₃	C₂³	semidirect
128. C₂×Q₈×C₁₇₃	C₂³	semidirect
133. C₂×D₄×C₁₇₃	C₂³	semidirect
134. C₂×D₄×C₁₇₃	C₂³	semidirect
136. C₂²×C₄×C₁₇₃	C₂³	semidirect
137. C₄⋊C₄×C₁₇₃	C₂³	semidirect
139. C₂²⋊C₄×C₁₇₃	C₂³	semidirect
140. C₄²×C₁₇₃	C₂³	semidirect
171. C₂×Dic₁₇₃	C₂×D₄	semidirect
182. C₄×D₁₇₃	C₂×D₄	semidirect
183. C₄×D₁₇₃	C₂×D₄	semidirect
196. C₂×C₄×C₁₇₃	C₂×D₄	semidirect
238. D₁₇₃	#535	direct (N × H)
239. C₁₇₃	C₂×#535	semidirect
250. #535	D₁₇₃	direct (N × H)
263. C₂×#41	C₂×D₁₇₃	semidirect
275. C₂²×D₄	C₂×D₁₇₃	semidirect
282. #127	C₂×D₁₇₃	semidirect
287. #124	C₂×D₁₇₃	semidirect
293. #121	C₂×D₁₇₃	semidirect
299. #120	C₂×D₁₇₃	semidirect
304. #117	C₂×D₁₇₃	semidirect
326. C₂×Q₈	C₂²×D₁₇₃	semidirect
352. C₂×D₄	C₂²×D₁₇₃	semidirect
353. C₂×D₄	C₂²×D₁₇₃	semidirect
367. C₂²×C₄	C₂²×D₁₇₃	semidirect
370. C₄⋊C₄	C₂²×D₁₇₃	semidirect
377. C₂²⋊C₄	C₂²×D₁₇₃	semidirect
380. C₄²	C₂²×D₁₇₃	semidirect
436. C₂×C₄	D₄×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
C₂²×D₄×D₁₇₃	2
#26012060	2
#26012059	2
#26012058	2
#26012057	2
#26012056	2
#26012055	2
#26012054	2
#127×D₁₇₃	2
#124×D₁₇₃	2
#121×D₁₇₃	2
#120×D₁₇₃	2
#117×D₁₇₃	2
#535×C₁₇₃	2
C₂×#535	173

Subgroups — #535×D173 #36366867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #535×D₁₇₃ #36366867