Subgroups — C₂×#26012087 #36366913

Order 22144.

1144 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012087	C₂	1	16	yes	maximal, direct product factor
2	C₂×#19149674	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19149672	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19149669	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#19149669	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#19149664	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19149662	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#19149661	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#19149661	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19149655	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#19149655	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#19149652	C₂	1	1	yes	maximal, characteristic
13	C₂×#19149641	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×C₂²⋊D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄⋊C₄×D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂²⋊Q₈×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×D₆₉₂	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊D₁₇₃	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₁₇₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₁₇₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₁₇₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₁₇₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₁₇₃	C₂²	1	1	yes	characteristic
24	#19149674	C₂²	1	8	yes	complemented
25	#19149672	C₂²	1	8	yes	complemented
26	#19149669	C₂²	1	8	yes	complemented
27	#19149669	C₂²	1	8	yes	complemented
28	#19149664	C₂²	1	8	yes	complemented
29	#19149662	C₂²	1	8	yes	complemented
30	#19149661	C₂²	1	8	yes	complemented
31	#19149661	C₂²	1	8	yes	complemented
32	#19149655	C₂²	1	8	yes	complemented
33	#19149655	C₂²	1	8	yes	complemented
34	#19149652	C₂²	1	8	yes	—
35	#19149641	C₂²	1	8	yes	complemented
36	C₄×C₂²⋊D₁₇₃	C₂²	1	8	yes	complemented
37	C₂×C₄⋊Dic₁₇₃	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊Dic₁₇₃	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Dic₁₇₃	C₂²	1	1	yes	characteristic
40	C₂×#14583805	C₂²	1	1	yes	characteristic
41	C₂×#14583805	C₂²	1	1	yes	characteristic
42	C₂×#14583805	C₂²	1	1	yes	characteristic
43	C₂×#14583805	C₂²	1	1	yes	characteristic
44	C₂×#14583805	C₂²	1	1	yes	characteristic
45	C₂×#14583805	C₂²	1	1	yes	characteristic
46	C₂×#14583805	C₂²	1	1	yes	characteristic
47	C₂×#14583805	C₂²	1	1	yes	characteristic
48	C₄⋊C₄×D₁₇₃	C₂²	1	8	yes	complemented
49	C₂×C₂²⋊Dic₁₇₃	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊Dic₁₇₃	C₂²	1	1	yes	characteristic
51	C₂×#14583803	C₂²	1	1	yes	characteristic
52	C₂×#14583803	C₂²	1	1	yes	characteristic
53	C₂×#14583803	C₂²	1	1	yes	characteristic
54	C₂×#14583803	C₂²	1	1	yes	characteristic
55	C₂×#14583803	C₂²	1	1	yes	characteristic
56	C₂×#14583803	C₂²	1	1	yes	characteristic
57	C₂×C₄×Dic₁₇₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₁₇₃	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₇₃	C₂²	1	1	yes	characteristic
60	C₂³×C₄×C₁₇₃	C₂²	1	1	yes	characteristic
61	C₂²⋊Q₈×C₁₇₃	C₂²	1	8	yes	complemented
62	C₂×C₄⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic
67	C₂³×D₁₇₃	C₂³	1	1	yes	characteristic
68	C₂³×D₁₇₃	C₂³	1	1	yes	characteristic
69	C₂×D₆₉₂	—	2	4	no	—
70	C₂×D₆₉₂	C₂³	1	4	yes	—
71	C₂×C₂²⋊D₁₇₃	—	2	4	no	—
72	C₂×C₂²⋊D₁₇₃	—	4	2	no	—
73	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
74	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
75	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
76	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
77	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
78	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
79	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
80	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₁₇₃	—	2	4	no	—
82	C₂×C₄×D₁₇₃	—	4	2	no	—
83	C₂×C₄×D₁₇₃	—	4	2	no	—
84	C₂×C₄×D₁₇₃	—	4	2	no	—
85	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
86	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
87	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
88	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
89	C₄⋊Dic₁₇₃	C₂³	1	4	yes	—
90	C₄⋊Dic₁₇₃	C₂³	1	4	yes	—
91	C₄⋊Dic₁₇₃	C₂³	1	4	yes	—
92	#14583805	C₂³	1	4	yes	—
93	#14583805	C₂³	1	4	yes	—
94	#14583805	C₂³	1	4	yes	—
95	#14583805	C₂³	1	4	yes	—
96	#14583805	C₂³	1	4	yes	—
97	#14583805	C₂³	1	4	yes	—
98	#14583805	C₂³	1	4	yes	—
99	#14583805	C₂³	1	4	yes	—
100	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
101	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
102	#14583803	C₂³	1	4	yes	—
103	#14583803	C₂³	1	4	yes	—
104	#14583803	C₂³	1	4	yes	—
105	#14583803	C₂³	1	4	yes	—
106	#14583803	C₂³	1	4	yes	—
107	#14583803	C₂³	1	4	yes	—
108	C₄×Dic₁₇₃	C₂³	1	4	yes	—
109	C₄×Dic₁₇₃	C₂³	1	4	yes	—
110	C₂⁴×C₁₇₃	C₂³	1	1	yes	characteristic
111	C₂×Q₈×C₁₇₃	—	4	2	no	—
112	C₂×Q₈×C₁₇₃	C₂³	1	4	yes	—
113	C₂²×C₄×C₁₇₃	—	4	2	no	—
114	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₁₇₃	C₂³	1	4	yes	—
121	C₄⋊C₄×C₁₇₃	C₂³	1	4	yes	—
122	C₄⋊C₄×C₁₇₃	C₂³	1	4	yes	—
123	C₄⋊C₄×C₁₇₃	C₂³	1	4	yes	—
124	C₂²⋊C₄×C₁₇₃	C₂³	1	4	yes	—
125	C₂²⋊C₄×C₁₇₃	C₂³	1	4	yes	—
126	C₂²×D₁₇₃	—	2	2	no	—
127	C₂²×D₁₇₃	—	2	2	no	—
128	C₂²×D₁₇₃	—	2	2	no	—
129	C₂²×D₁₇₃	—	2	2	no	—
130	C₂²×D₁₇₃	—	2	2	no	—
131	C₂²×D₁₇₃	#41	1	4	yes	—
132	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
133	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
134	D₆₉₂	—	2	8	no	—
135	C₂²⋊D₁₇₃	—	2	8	no	—
136	C₂²⋊D₁₇₃	—	4	4	no	—
137	C₂×Dic₁₇₃	—	2	2	no	—
138	C₂×Dic₁₇₃	—	2	2	no	—
139	C₂×Dic₁₇₃	—	2	2	no	—
140	C₂×Dic₁₇₃	—	2	2	no	—
141	C₂×Dic₁₇₃	—	2	2	no	—
142	C₂×Dic₁₇₃	—	2	2	no	—
143	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
144	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
145	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
146	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
147	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
148	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
149	C₄×D₁₇₃	—	2	8	no	—
150	C₄×D₁₇₃	—	4	4	no	—
151	C₄×D₁₇₃	—	4	4	no	—
152	C₄×D₁₇₃	—	4	4	no	—
153	C₂³×C₁₇₃	—	2	2	no	—
154	C₂³×C₁₇₃	—	2	2	no	—
155	C₂³×C₁₇₃	—	2	2	no	—
156	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
157	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
158	Q₈×C₁₇₃	—	4	4	no	—
159	C₂×C₄×C₁₇₃	—	2	2	no	—
160	C₂×C₄×C₁₇₃	—	2	2	no	—
161	C₂×C₄×C₁₇₃	—	2	2	no	—
162	C₂×C₄×C₁₇₃	—	2	2	no	—
163	C₂×C₄×C₁₇₃	—	2	2	no	—
164	C₂×C₄×C₁₇₃	—	2	2	no	—
165	C₂×C₄×C₁₇₃	—	4	4	no	—
166	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
171	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
172	C₂²×C₁₇₃	—	2	2	no	—
173	C₂²×C₁₇₃	—	2	2	no	—
174	C₂²×C₁₇₃	—	2	2	no	—
175	C₂²×C₁₇₃	—	4	4	no	—
176	C₂²×C₁₇₃	C₂×#41	1	2	yes	—
177	C₂²×C₁₇₃	H(5,𝔽₂)	1	2	yes	—
178	C₂²×C₁₇₃	2₋¹⁺⁴	1	2	yes	—
179	C₂²×C₁₇₃	C₂⁵	1	1	yes	characteristic
180	C₂×D₁₇₃	—	2	8	no	—
181	C₂×D₁₇₃	—	2	2	no	—
182	C₂×D₁₇₃	—	2	2	no	—
183	C₂×D₁₇₃	—	2	2	no	—
184	C₂×D₁₇₃	—	2	2	no	—
185	C₂×D₁₇₃	—	2	2	no	—
186	C₂×D₁₇₃	—	4	4	no	—
187	C₂×D₁₇₃	C₂×#41	1	4	yes	—
188	C₄×C₁₇₃	—	2	2	no	—
189	C₄×C₁₇₃	—	2	2	no	—
190	C₄×C₁₇₃	—	2	2	no	—
191	C₄×C₁₇₃	—	2	2	no	—
192	C₄×C₁₇₃	—	2	2	no	—
193	C₄×C₁₇₃	—	2	2	no	—
194	Dic₁₇₃	—	2	2	no	—
195	Dic₁₇₃	—	2	2	no	—
196	Dic₁₇₃	—	2	2	no	—
197	Dic₁₇₃	—	2	2	no	—
198	Dic₁₇₃	—	2	2	no	—
199	Dic₁₇₃	—	2	2	no	—
200	C₂×C₁₇₃	—	4	2	no	—
201	C₂×C₁₇₃	#539	1	4	yes	complemented
202	C₂×C₁₇₃	C₂²×#41	1	1	yes	characteristic
203	C₂×C₁₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₁₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
205	D₁₇₃	—	2	4	no	—
206	D₁₇₃	—	4	2	no	—
207	C₁₇₃	C₂×#539	1	1	yes	characteristic, complemented, Sylow
208	C₂×#539	—	173	1	no	maximal, Sylow
209	#539	—	173	16	no	—
210	C₂×#126	—	173	1	no	—
211	C₂×#126	—	173	1	no	—
212	C₂×#125	—	173	1	no	—
213	C₂×#125	—	173	1	no	—
214	C₂×#123	—	173	1	no	—
215	C₂×#123	—	173	1	no	—
216	C₂×#123	—	173	1	no	—
217	C₂×#123	—	173	1	no	—
218	C₂×C₂²⋊Q₈	—	173	1	no	—
219	C₂×C₂²⋊Q₈	—	173	1	no	—
220	C₂×C₂²⋊Q₈	D₁₇₃	1	1	yes	characteristic, complemented
221	C₂×#121	—	173	1	no	—
222	C₂×C₄×D₄	—	173	1	no	—
223	C₂×C₄×D₄	—	173	1	no	—
224	C₂²×C₄⋊C₄	—	173	1	no	—
225	C₂²×Q₈	C₂×D₁₇₃	1	1	yes	characteristic
226	C₂²×D₄	—	173	1	no	—
227	C₂²×D₄	—	173	1	no	—
228	C₂²×D₄	—	173	1	no	—
229	C₂³×C₄	—	173	1	no	—
230	C₂³×C₄	—	173	1	no	—
231	C₂³×C₄	—	173	1	no	—
232	C₂³×C₄	—	173	1	no	—
233	C₂³×C₄	C₂×D₁₇₃	1	1	yes	characteristic
234	#126	—	173	8	no	—
235	#126	—	173	8	no	—
236	#125	—	173	8	no	—
237	#125	—	173	8	no	—
238	#123	—	173	8	no	—
239	#123	—	173	8	no	—
240	#123	—	173	8	no	—
241	#123	—	173	8	no	—
242	C₂²⋊Q₈	—	173	8	no	—
243	C₂²⋊Q₈	—	173	8	no	—
244	C₂²⋊Q₈	C₂×D₁₇₃	1	8	yes	complemented
245	#121	—	173	8	no	—
246	C₄×D₄	—	173	8	no	—
247	C₄×D₄	—	173	8	no	—
248	C₂×C₄⋊C₄	—	173	1	no	—
249	C₂×C₄⋊C₄	—	173	1	no	—
250	C₂×C₄⋊C₄	—	173	1	no	—
251	C₂×C₄⋊C₄	—	173	1	no	—
252	C₂×C₄⋊C₄	—	173	1	no	—
253	C₂×C₄⋊C₄	—	173	1	no	—
254	C₂×C₄⋊C₄	—	173	1	no	—
255	C₂×C₄⋊C₄	—	173	1	no	—
256	C₂×C₄⋊C₄	—	173	1	no	—
257	C₂×C₄⋊C₄	—	173	1	no	—
258	C₂×C₄⋊C₄	—	173	1	no	—
259	C₂×C₄⋊C₄	—	173	8	no	—
260	C₂×C₄⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	173	1	no	—
264	C₂×C₂²⋊C₄	—	173	1	no	—
265	C₂×C₂²⋊C₄	—	173	1	no	—
266	C₂×C₂²⋊C₄	—	173	1	no	—
267	C₂×C₂²⋊C₄	—	173	1	no	—
268	C₂×C₂²⋊C₄	—	173	1	no	—
269	C₂×C₂²⋊C₄	—	173	1	no	—
270	C₂×C₂²⋊C₄	—	173	1	no	—
271	C₂×C₂²⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic
273	C₂×C₄²	—	173	1	no	—
274	C₂×C₄²	—	173	1	no	—
275	C₂⁴	—	173	1	no	—
276	C₂⁴	—	173	1	no	—
277	C₂⁴	C₂²×D₁₇₃	1	1	yes	characteristic
278	C₂×Q₈	—	4	2	no	—
279	C₂×Q₈	C₂²×D₁₇₃	1	4	yes	—
280	C₂×D₄	—	346	4	no	—
281	C₂×D₄	—	346	4	no	—
282	C₂×D₄	—	173	4	no	—
283	C₂×D₄	—	173	4	no	—
284	C₂×D₄	—	173	4	no	—
285	C₂×D₄	—	692	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	346	4	no	—
288	C₂²×C₄	—	173	1	no	—
289	C₂²×C₄	—	173	1	no	—
290	C₂²×C₄	—	173	1	no	—
291	C₂²×C₄	—	173	1	no	—
292	C₂²×C₄	—	173	1	no	—
293	C₂²×C₄	—	173	1	no	—
294	C₂²×C₄	—	173	4	no	—
295	C₂²×C₄	—	173	4	no	—
296	C₂²×C₄	—	173	4	no	—
297	C₂²×C₄	—	173	4	no	—
298	C₂²×C₄	—	692	2	no	—
299	C₂²×C₄	—	692	2	no	—
300	C₂²×C₄	—	692	2	no	—
301	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
305	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
306	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
307	C₂²×C₄	C₂²×D₁₇₃	1	4	yes	—
308	C₄⋊C₄	—	173	4	no	—
309	C₄⋊C₄	—	173	4	no	—
310	C₄⋊C₄	—	173	4	no	—
311	C₄⋊C₄	—	173	4	no	—
312	C₄⋊C₄	—	173	4	no	—
313	C₄⋊C₄	—	173	4	no	—
314	C₄⋊C₄	—	173	4	no	—
315	C₄⋊C₄	—	173	4	no	—
316	C₄⋊C₄	—	173	4	no	—
317	C₄⋊C₄	—	173	4	no	—
318	C₄⋊C₄	—	173	4	no	—
319	C₄⋊C₄	C₂²×D₁₇₃	1	4	yes	—
320	C₄⋊C₄	C₂²×D₁₇₃	1	4	yes	—
321	C₄⋊C₄	C₂²×D₁₇₃	1	4	yes	—
322	C₂²⋊C₄	—	173	4	no	—
323	C₂²⋊C₄	—	173	4	no	—
324	C₂²⋊C₄	—	173	4	no	—
325	C₂²⋊C₄	—	173	4	no	—
326	C₂²⋊C₄	—	173	4	no	—
327	C₂²⋊C₄	—	173	4	no	—
328	C₂²⋊C₄	—	173	4	no	—
329	C₂²⋊C₄	—	173	4	no	—
330	C₂²⋊C₄	C₂²×D₁₇₃	1	4	yes	—
331	C₂²⋊C₄	C₂²×D₁₇₃	1	4	yes	—
332	C₄²	—	173	4	no	—
333	C₄²	—	173	4	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	346	2	no	—
338	C₂³	—	346	2	no	—
339	C₂³	—	346	2	no	—
340	C₂³	—	346	2	no	—
341	C₂³	—	346	2	no	—
342	C₂³	—	173	2	no	—
343	C₂³	—	173	4	no	—
344	C₂³	—	173	2	no	—
345	C₂³	C₂³×D₁₇₃	1	2	yes	—
346	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
347	Q₈	—	4	4	no	—
348	D₄	—	346	8	no	—
349	D₄	—	346	8	no	—
350	D₄	—	692	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	346	8	no	—
359	C₂×C₄	—	346	2	no	—
360	C₂×C₄	—	346	2	no	—
361	C₂×C₄	—	346	2	no	—
362	C₂×C₄	—	346	2	no	—
363	C₂×C₄	—	346	2	no	—
364	C₂×C₄	—	346	2	no	—
365	C₂×C₄	—	173	2	no	—
366	C₂×C₄	—	173	2	no	—
367	C₂×C₄	—	173	2	no	—
368	C₂×C₄	—	173	2	no	—
369	C₂×C₄	—	173	2	no	—
370	C₂×C₄	—	173	2	no	—
371	C₂×C₄	—	692	4	no	—
372	C₂×C₄	—	692	4	no	—
373	C₂×C₄	—	692	4	no	—
374	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
375	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
376	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
377	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
378	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
379	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	346	2	no	—
385	C₂²	—	346	2	no	—
386	C₂²	—	346	8	no	—
387	C₂²	—	346	2	no	—
388	C₂²	—	346	2	no	—
389	C₂²	—	346	2	no	—
390	C₂²	—	173	4	no	—
391	C₂²	—	692	4	no	—
392	C₂²	#41×D₁₇₃	1	2	yes	—
393	C₂²	#19149724	1	2	yes	—
394	C₂²	#19149727	1	2	yes	—
395	C₂²	C₂⁴×D₁₇₃	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	346	2	no	—
403	C₄	—	346	2	no	—
404	C₄	—	346	2	no	—
405	C₄	—	346	2	no	—
406	C₄	—	346	2	no	—
407	C₄	—	346	2	no	—
408	C₂	—	4	2	no	—
409	C₂	—	346	4	no	—
410	C₂	—	692	2	no	—
411	C₂	#26012087	1	4	yes	direct product factor
412	C₂	C₂×#41×D₁₇₃	1	1	yes	characteristic
413	C₂	C₂×#19149724	1	1	yes	characteristic
414	C₂	C₂×#19149727	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₇₃
commutator, cosocle	C₂²×C₁₇₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₇₃
Fitting	C₂×C₂²⋊Q₈×C₁₇₃	C₂
socle	C₂³×C₁₇₃	C₂⁴
prime radical	C₂×#19149652	C₂
hypercenter	C₂×C₂²⋊Q₈	D₁₇₃
hypocenter	C₁₇₃	C₂×#539
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #26012087	C₂	direct (N × H)
2. C₂×#19149674	C₂	semidirect
3. C₂×#19149672	C₂	semidirect
4. C₂×#19149669	C₂	semidirect
5. C₂×#19149669	C₂	semidirect
6. C₂×#19149664	C₂	semidirect
7. C₂×#19149662	C₂	semidirect
8. C₂×#19149661	C₂	semidirect
9. C₂×#19149661	C₂	semidirect
10. C₂×#19149655	C₂	semidirect
11. C₂×#19149655	C₂	semidirect
13. C₂×#19149641	C₂	semidirect
14. C₂×C₄×C₂²⋊D₁₇₃	C₂	semidirect
15. C₂×C₄⋊C₄×D₁₇₃	C₂	semidirect
16. C₂×C₂²⋊Q₈×C₁₇₃	C₂	semidirect
24. #19149674	C₂²	semidirect
25. #19149672	C₂²	semidirect
26. #19149669	C₂²	semidirect
27. #19149669	C₂²	semidirect
28. #19149664	C₂²	semidirect
29. #19149662	C₂²	semidirect
30. #19149661	C₂²	semidirect
31. #19149661	C₂²	semidirect
32. #19149655	C₂²	semidirect
33. #19149655	C₂²	semidirect
35. #19149641	C₂²	semidirect
36. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
48. C₄⋊C₄×D₁₇₃	C₂²	semidirect
61. C₂²⋊Q₈×C₁₇₃	C₂²	semidirect
201. C₂×C₁₇₃	#539	semidirect
207. C₁₇₃	C₂×#539	semidirect
220. C₂×C₂²⋊Q₈	D₁₇₃	semidirect
244. C₂²⋊Q₈	C₂×D₁₇₃	semidirect
411. C₂	#26012087	direct (N × H)

Maximal subgroups

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

subgroup	index
#26012087	2
C₂×#19149674	2
C₂×#19149672	2
C₂×#19149669	2
C₂×#19149664	2
C₂×#19149662	2
C₂×#19149661	2
C₂×#19149655	2
C₂×#19149652	2
C₂×#19149641	2
C₂×C₄×C₂²⋊D₁₇₃	2
C₂×C₄⋊C₄×D₁₇₃	2
C₂×C₂²⋊Q₈×C₁₇₃	2
C₂×#539	173

Subgroups — C2×#26012087 #36366913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26012087 #36366913