Subgroups — #36366972

Order 22144.

1160 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012117	C₂	1	1	yes	maximal, characteristic, complemented
2	#26012088	C₂	1	2	yes	maximal, complemented
3	#26012083	C₂	1	4	yes	maximal, complemented
4	#26012079	C₂	1	2	yes	maximal, complemented
5	#26012074	C₂	1	4	yes	maximal, complemented
6	#26012053	C₂	1	1	yes	maximal, characteristic, complemented
7	#26012050	C₂	1	2	yes	maximal, complemented
8	#26012025	C₂	1	2	yes	maximal, complemented
9	#26012021	C₂	1	4	yes	maximal, complemented
10	#26012002	C₂	1	2	yes	maximal, complemented
11	#26012000	C₂	1	4	yes	maximal, complemented
12	C₂×C₄×C₂²⋊D₁₇₃	C₂	1	2	yes	maximal, complemented
13	C₂×C₄×D₄×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14583826	C₂²	1	2	yes	complemented
15	C₂²×C₂²⋊D₁₇₃	C₂²	1	2	yes	—
16	C₂²×C₄×D₁₇₃	C₂²	1	2	yes	complemented
17	#19149674	C₂²	1	4	yes	complemented
18	#19149673	C₂²	1	4	yes	complemented
19	#19149672	C₂²	1	4	yes	complemented
20	#19149671	C₂²	1	2	yes	complemented
21	#19149669	C₂²	1	4	yes	complemented
22	#19149667	C₂²	1	2	yes	complemented
23	#19149665	C₂²	1	4	yes	complemented
24	#19149664	C₂²	1	4	yes	complemented
25	#19149663	C₂²	1	4	yes	complemented
26	#19149662	C₂²	1	4	yes	complemented
27	#19149662	C₂²	1	4	yes	complemented
28	#19149661	C₂²	1	4	yes	complemented
29	#19149660	C₂²	1	4	yes	complemented
30	#19149658	C₂²	1	2	yes	complemented
31	#19149658	C₂²	1	2	yes	complemented
32	#19149658	C₂²	1	2	yes	complemented
33	#19149657	C₂²	1	4	yes	complemented
34	#19149656	C₂²	1	4	yes	complemented
35	#19149656	C₂²	1	4	yes	complemented
36	#19149653	C₂²	1	2	yes	—
37	#19149653	C₂²	1	2	yes	—
38	#19149653	C₂²	1	2	yes	complemented
39	#19149652	C₂²	1	4	yes	complemented
40	#19149651	C₂²	1	4	yes	—
41	#19149651	C₂²	1	4	yes	—
42	#19149649	C₂²	1	4	yes	complemented
43	#19149648	C₂²	1	4	yes	complemented
44	#19149647	C₂²	1	4	yes	complemented
45	C₄×Dic₃₄₆	C₂²	1	2	yes	complemented
46	C₄×D₆₉₂	C₂²	1	2	yes	complemented
47	C₄×C₂²⋊D₁₇₃	C₂²	1	4	yes	complemented
48	C₄×C₂²⋊D₁₇₃	C₂²	1	4	yes	complemented
49	C₄×C₂²⋊D₁₇₃	C₂²	1	4	yes	complemented
50	C₄×C₂²⋊D₁₇₃	C₂²	1	4	yes	complemented
51	C₄×C₂²⋊D₁₇₃	C₂²	1	4	yes	complemented
52	#19149638	C₂²	1	2	yes	complemented
53	#19149636	C₂²	1	4	yes	complemented
54	C₂×#14583805	C₂²	1	2	yes	complemented
55	C₂×C₂²⋊Dic₁₇₃	C₂²	1	2	yes	—
56	C₂×#14583803	C₂²	1	2	yes	complemented
57	C₂×C₄×Dic₁₇₃	C₂²	1	2	yes	complemented
58	C₂²×D₄×C₁₇₃	C₂²	1	1	yes	characteristic
59	C₂³×C₄×C₁₇₃	C₂²	1	1	yes	characteristic
60	C₂³×C₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
61	C₄×D₄×C₁₇₃	C₂²	1	4	yes	complemented
62	C₄×D₄×C₁₇₃	C₂²	1	4	yes	complemented
63	C₂×C₄⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₂²⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄²×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
67	C₂³×D₁₇₃	C₂³	1	2	yes	—
68	#14583826	—	4	4	no	—
69	C₂×Dic₃₄₆	C₂³	1	2	yes	—
70	C₂×Dic₃₄₆	C₂³	1	2	yes	—
71	C₂×D₆₉₂	C₂³	1	2	yes	—
72	C₂×D₆₉₂	C₂³	1	2	yes	—
73	C₂×C₂²⋊D₁₇₃	—	2	8	no	—
74	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
75	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
76	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
77	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
78	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
79	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
80	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
81	C₂×C₄×D₁₇₃	—	4	4	no	—
82	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
83	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
84	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
85	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
86	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
87	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
88	#14583805	C₂³	1	4	yes	—
89	#14583805	C₂³	1	4	yes	—
90	#14583805	C₂³	1	4	yes	—
91	#14583805	C₂³	1	4	yes	—
92	#14583805	C₂³	1	4	yes	—
93	#14583805	C₂³	1	4	yes	—
94	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
95	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
96	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
97	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
98	#14583803	C₂³	1	4	yes	—
99	#14583803	C₂³	1	4	yes	—
100	#14583803	C₂³	1	4	yes	—
101	#14583803	C₂³	1	4	yes	—
102	#14583803	C₂³	1	4	yes	—
103	#14583803	C₂³	1	4	yes	—
104	C₄×Dic₁₇₃	C₂³	1	4	yes	—
105	C₄×Dic₁₇₃	C₂³	1	4	yes	—
106	C₂⁴×C₁₇₃	C₂³	1	1	yes	characteristic
107	C₂⁴×C₁₇₃	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₁₇₃	—	2	4	no	—
109	C₂×D₄×C₁₇₃	C₂³	1	4	yes	—
110	C₂²×C₄×C₁₇₃	—	4	2	no	—
111	C₂²×C₄×C₁₇₃	—	4	2	no	—
112	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
114	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
115	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
117	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
120	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
121	C₄⋊C₄×C₁₇₃	C₂³	1	4	yes	—
122	C₂²⋊C₄×C₁₇₃	C₂³	1	4	yes	—
123	C₂²⋊C₄×C₁₇₃	C₂³	1	4	yes	—
124	C₄²×C₁₇₃	C₂³	1	2	yes	—
125	C₄²×C₁₇₃	C₂³	1	2	yes	—
126	C₂²×D₁₇₃	—	2	4	no	—
127	C₂²×D₁₇₃	—	4	2	no	—
128	C₂²×D₁₇₃	—	4	2	no	—
129	C₂²×D₁₇₃	C₂⁴	1	4	yes	—
130	Dic₃₄₆	—	4	2	no	—
131	Dic₃₄₆	—	4	2	no	—
132	D₆₉₂	—	4	2	no	—
133	D₆₉₂	—	4	2	no	—
134	C₂²⋊D₁₇₃	—	2	8	no	—
135	C₂²⋊D₁₇₃	—	2	8	no	—
136	C₂²⋊D₁₇₃	—	4	4	no	—
137	C₂²⋊D₁₇₃	—	4	4	no	—
138	C₂×Dic₁₇₃	—	2	4	no	—
139	C₂×Dic₁₇₃	—	4	2	no	—
140	C₂×Dic₁₇₃	—	4	2	no	—
141	C₂×Dic₁₇₃	C₂⁴	1	4	yes	—
142	C₂×Dic₁₇₃	C₂⁴	1	4	yes	—
143	C₂×Dic₁₇₃	C₂⁴	1	4	yes	—
144	C₄×D₁₇₃	—	2	8	no	—
145	C₄×D₁₇₃	—	4	4	no	—
146	C₂³×C₁₇₃	—	2	2	no	—
147	C₂³×C₁₇₃	—	4	1	no	—
148	C₂³×C₁₇₃	—	4	1	no	—
149	C₂³×C₁₇₃	—	4	1	no	—
150	C₂³×C₁₇₃	—	4	1	no	—
151	C₂³×C₁₇₃	#41	1	4	yes	complemented
152	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
153	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
154	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
155	D₄×C₁₇₃	—	2	8	no	—
156	C₂×C₄×C₁₇₃	—	2	2	no	—
157	C₂×C₄×C₁₇₃	—	2	4	no	—
158	C₂×C₄×C₁₇₃	—	2	4	no	—
159	C₂×C₄×C₁₇₃	—	2	2	no	—
160	C₂×C₄×C₁₇₃	—	4	2	no	—
161	C₂×C₄×C₁₇₃	—	4	2	no	—
162	C₂×C₄×C₁₇₃	—	4	1	no	—
163	C₂×C₄×C₁₇₃	—	4	1	no	—
164	C₂×C₄×C₁₇₃	—	4	1	no	—
165	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
170	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
171	C₂²×C₁₇₃	—	2	1	no	—
172	C₂²×C₁₇₃	—	2	2	no	—
173	C₂²×C₁₇₃	—	2	1	no	—
174	C₂²×C₁₇₃	—	2	2	no	—
175	C₂²×C₁₇₃	—	2	2	no	—
176	C₂²×C₁₇₃	—	2	2	no	—
177	C₂²×C₁₇₃	—	2	2	no	—
178	C₂²×C₁₇₃	—	4	4	no	—
179	C₂²×C₁₇₃	—	4	4	no	—
180	C₂²×C₁₇₃	C₂×#41	1	2	yes	—
181	C₂²×C₁₇₃	C₂×#41	1	4	yes	—
182	C₂²×C₁₇₃	C₂⁵	1	1	yes	characteristic
183	C₂×D₁₇₃	—	2	4	no	—
184	C₂×D₁₇₃	—	2	4	no	—
185	C₂×D₁₇₃	—	2	4	no	—
186	C₂×D₁₇₃	—	4	8	no	—
187	C₄×C₁₇₃	—	2	2	no	—
188	C₄×C₁₇₃	—	2	1	no	—
189	C₄×C₁₇₃	—	2	2	no	—
190	C₄×C₁₇₃	—	2	2	no	—
191	C₄×C₁₇₃	—	2	2	no	—
192	C₄×C₁₇₃	H(5,𝔽₂)	1	2	yes	—
193	Dic₁₇₃	—	2	4	no	—
194	Dic₁₇₃	—	2	4	no	—
195	Dic₁₇₃	—	2	4	no	—
196	C₂×C₁₇₃	—	2	4	no	—
197	C₂×C₁₇₃	—	2	2	no	—
198	C₂×C₁₇₃	—	4	2	no	—
199	C₂×C₁₇₃	C₂²×#41	1	1	yes	characteristic
200	C₂×C₁₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₁₇₃	#585	1	1	yes	characteristic
202	D₁₇₃	—	4	4	no	—
203	C₁₇₃	#3459	1	1	yes	characteristic, complemented, Sylow
204	#3459	—	173	1	no	maximal, Sylow
205	#543	—	173	1	no	—
206	#539	—	173	4	no	—
207	#539	—	173	2	no	—
208	#538	—	173	4	no	—
209	#538	—	173	2	no	—
210	#534	—	173	2	no	—
211	#534	—	173	1	no	—
212	#529	—	173	4	no	—
213	#529	—	173	2	no	—
214	#525	—	173	2	no	—
215	#525	—	173	4	no	—
216	C₂×C₄×D₄	—	173	2	no	—
217	C₂×C₄×D₄	D₁₇₃	1	1	yes	characteristic, complemented
218	C₂×#41	—	173	2	no	—
219	C₂²×D₄	—	173	2	no	—
220	C₂²×D₄	C₂×D₁₇₃	1	1	yes	characteristic
221	C₂³×C₄	—	173	2	no	—
222	C₂³×C₄	C₂×D₁₇₃	1	1	yes	characteristic
223	C₂³×C₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
224	#126	—	173	4	no	—
225	#126	—	173	4	no	—
226	#126	—	173	4	no	—
227	#125	—	173	4	no	—
228	#125	—	173	2	no	—
229	#124	—	173	4	no	—
230	#124	—	173	2	no	—
231	#123	—	173	4	no	—
232	#123	—	173	4	no	—
233	#123	—	173	4	no	—
234	#123	—	173	4	no	—
235	#123	—	173	4	no	—
236	#123	—	173	4	no	—
237	C₂²⋊Q₈	—	173	2	no	—
238	C₂²⋊Q₈	—	173	2	no	—
239	C₂²⋊Q₈	—	173	2	no	—
240	C₂²⋊Q₈	—	173	4	no	—
241	C₂²⋊Q₈	—	173	4	no	—
242	C₂²⋊Q₈	—	173	4	no	—
243	#121	—	173	4	no	—
244	#121	—	173	4	no	—
245	#121	—	173	2	no	—
246	#121	—	173	2	no	—
247	#121	—	173	2	no	—
248	#121	—	173	4	no	—
249	#120	—	173	4	no	—
250	#120	—	173	4	no	—
251	#120	—	173	4	no	—
252	C₄×Q₈	—	173	2	no	—
253	C₄×D₄	—	173	4	no	—
254	C₄×D₄	—	173	4	no	—
255	C₄×D₄	—	173	4	no	—
256	C₄×D₄	—	173	4	no	—
257	C₄×D₄	—	173	4	no	—
258	C₄×D₄	—	173	2	no	—
259	C₄×D₄	C₂×D₁₇₃	1	4	yes	complemented
260	C₄×D₄	C₂×D₁₇₃	1	4	yes	complemented
261	#117	—	173	2	no	—
262	#117	—	173	4	no	—
263	C₂×C₄⋊C₄	—	173	2	no	—
264	C₂×C₄⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
265	C₂×C₂²⋊C₄	—	173	2	no	—
266	C₂×C₂²⋊C₄	—	173	2	no	—
267	C₂×C₂²⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
269	C₂×C₄²	—	173	2	no	—
270	C₂×C₄²	C₂×D₁₇₃	1	1	yes	characteristic, complemented
271	C₂⁴	—	173	2	no	—
272	C₂⁴	C₂²×D₁₇₃	1	1	yes	characteristic
273	C₂⁴	C₂²×D₁₇₃	1	1	yes	characteristic
274	#41	—	692	4	no	—
275	C₂×Q₈	—	173	2	no	—
276	C₂×Q₈	—	173	2	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	346	8	no	—
279	C₂×D₄	—	173	4	no	—
280	C₂×D₄	—	173	4	no	—
281	C₂×D₄	—	173	4	no	—
282	C₂×D₄	—	173	4	no	—
283	C₂×D₄	—	173	2	no	—
284	C₂×D₄	—	173	2	no	—
285	C₂×D₄	C₂²×D₁₇₃	1	4	yes	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	173	2	no	—
289	C₂²×C₄	—	173	4	no	—
290	C₂²×C₄	—	173	2	no	—
291	C₂²×C₄	—	173	2	no	—
292	C₂²×C₄	—	173	4	no	—
293	C₂²×C₄	—	692	4	no	—
294	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
295	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
296	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
297	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
298	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
299	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
300	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
301	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
303	C₄⋊C₄	—	173	4	no	—
304	C₄⋊C₄	—	173	4	no	—
305	C₄⋊C₄	—	173	4	no	—
306	C₄⋊C₄	—	173	2	no	—
307	C₄⋊C₄	—	173	4	no	—
308	C₄⋊C₄	—	173	2	no	—
309	C₄⋊C₄	—	173	4	no	—
310	C₄⋊C₄	—	173	2	no	—
311	C₄⋊C₄	—	173	4	no	—
312	C₄⋊C₄	—	173	2	no	—
313	C₄⋊C₄	C₂²×D₁₇₃	1	4	yes	—
314	C₂²⋊C₄	—	173	4	no	—
315	C₂²⋊C₄	—	173	4	no	—
316	C₂²⋊C₄	—	173	4	no	—
317	C₂²⋊C₄	—	173	4	no	—
318	C₂²⋊C₄	—	173	4	no	—
319	C₂²⋊C₄	—	173	4	no	—
320	C₂²⋊C₄	—	173	4	no	—
321	C₂²⋊C₄	—	173	4	no	—
322	C₂²⋊C₄	—	173	4	no	—
323	C₂²⋊C₄	—	173	4	no	—
324	C₂²⋊C₄	C₂²×D₁₇₃	1	4	yes	—
325	C₂²⋊C₄	C₂²×D₁₇₃	1	4	yes	—
326	C₄²	—	173	4	no	—
327	C₄²	—	173	4	no	—
328	C₄²	C₂²×D₁₇₃	1	2	yes	—
329	C₄²	C₂²×D₁₇₃	1	2	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	4	1	no	—
332	C₂³	—	4	1	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	4	1	no	—
335	C₂³	—	346	4	no	—
336	C₂³	—	173	4	no	—
337	C₂³	—	692	2	no	—
338	C₂³	—	692	2	no	—
339	C₂³	#14583826	1	4	yes	complemented
340	C₂³	C₂³×D₁₇₃	1	2	yes	—
341	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
342	C₂³	C₂³×D₁₇₃	1	2	yes	—
343	Q₈	—	692	2	no	—
344	Q₈	—	692	2	no	—
345	D₄	—	2	8	no	—
346	D₄	—	346	8	no	—
347	D₄	—	346	8	no	—
348	D₄	—	692	2	no	—
349	D₄	—	692	2	no	—
350	D₄	—	692	4	no	—
351	D₄	—	692	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	346	4	no	—
362	C₂×C₄	—	346	8	no	—
363	C₂×C₄	—	173	4	no	—
364	C₂×C₄	—	173	4	no	—
365	C₂×C₄	—	173	4	no	—
366	C₂×C₄	—	692	4	no	—
367	C₂×C₄	—	692	2	no	—
368	C₂×C₄	—	692	2	no	—
369	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
370	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
371	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
372	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
373	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
374	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
375	C₂²	—	2	1	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	346	4	no	—
385	C₂²	—	346	4	no	—
386	C₂²	—	346	4	no	—
387	C₂²	—	692	8	no	—
388	C₂²	C₂×#14583826	1	2	yes	—
389	C₂²	C₂×#14583826	1	4	yes	—
390	C₂²	C₂⁴×D₁₇₃	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	346	4	no	—
397	C₄	—	346	4	no	—
398	C₄	—	346	4	no	—
399	C₄	#19149724	1	2	yes	—
400	C₂	—	2	2	no	—
401	C₂	—	2	4	no	—
402	C₂	—	4	2	no	—
403	C₂	—	692	4	no	—
404	C₂	C₂²×#14583826	1	1	yes	characteristic
405	C₂	C₂×#19149724	1	1	yes	characteristic
406	C₂	#26012327	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₇₃
commutator, socle, cosocle	C₂²×C₁₇₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₇₃
Fitting	C₂×C₄×D₄×C₁₇₃	C₂
hypercenter	C₂×C₄×D₄	D₁₇₃
hypocenter	C₁₇₃	#3459
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #26012117	C₂	semidirect
2. #26012088	C₂	semidirect
3. #26012083	C₂	semidirect
4. #26012079	C₂	semidirect
5. #26012074	C₂	semidirect
6. #26012053	C₂	semidirect
7. #26012050	C₂	semidirect
8. #26012025	C₂	semidirect
9. #26012021	C₂	semidirect
10. #26012002	C₂	semidirect
11. #26012000	C₂	semidirect
12. C₂×C₄×C₂²⋊D₁₇₃	C₂	semidirect
13. C₂×C₄×D₄×C₁₇₃	C₂	semidirect
14. C₂×#14583826	C₂²	semidirect
16. C₂²×C₄×D₁₇₃	C₂²	semidirect
17. #19149674	C₂²	semidirect
18. #19149673	C₂²	semidirect
19. #19149672	C₂²	semidirect
20. #19149671	C₂²	semidirect
21. #19149669	C₂²	semidirect
22. #19149667	C₂²	semidirect
23. #19149665	C₂²	semidirect
24. #19149664	C₂²	semidirect
25. #19149663	C₂²	semidirect
26. #19149662	C₂²	semidirect
27. #19149662	C₂²	semidirect
28. #19149661	C₂²	semidirect
29. #19149660	C₂²	semidirect
30. #19149658	C₂²	semidirect
31. #19149658	C₂²	semidirect
32. #19149658	C₂²	semidirect
33. #19149657	C₂²	semidirect
34. #19149656	C₂²	semidirect
35. #19149656	C₂²	semidirect
38. #19149653	C₂²	semidirect
39. #19149652	C₂²	semidirect
42. #19149649	C₂²	semidirect
43. #19149648	C₂²	semidirect
44. #19149647	C₂²	semidirect
45. C₄×Dic₃₄₆	C₂²	semidirect
46. C₄×D₆₉₂	C₂²	semidirect
47. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
48. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
49. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
50. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
51. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
52. #19149638	C₂²	semidirect
53. #19149636	C₂²	semidirect
54. C₂×#14583805	C₂²	semidirect
56. C₂×#14583803	C₂²	semidirect
57. C₂×C₄×Dic₁₇₃	C₂²	semidirect
60. C₂³×C₄×C₁₇₃	C₂²	semidirect
61. C₄×D₄×C₁₇₃	C₂²	semidirect
62. C₄×D₄×C₁₇₃	C₂²	semidirect
63. C₂×C₄⋊C₄×C₁₇₃	C₂²	semidirect
65. C₂×C₂²⋊C₄×C₁₇₃	C₂²	semidirect
66. C₂×C₄²×C₁₇₃	C₂²	semidirect
151. C₂³×C₁₇₃	#41	semidirect
203. C₁₇₃	#3459	semidirect
217. C₂×C₄×D₄	D₁₇₃	semidirect
223. C₂³×C₄	C₂×D₁₇₃	semidirect
259. C₄×D₄	C₂×D₁₇₃	semidirect
260. C₄×D₄	C₂×D₁₇₃	semidirect
264. C₂×C₄⋊C₄	C₂×D₁₇₃	semidirect
268. C₂×C₂²⋊C₄	C₂×D₁₇₃	semidirect
270. C₂×C₄²	C₂×D₁₇₃	semidirect
339. C₂³	#14583826	semidirect

Maximal subgroups

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

subgroup	index
#26012117	2
#26012088	2
#26012083	2
#26012079	2
#26012074	2
#26012053	2
#26012050	2
#26012025	2
#26012021	2
#26012002	2
#26012000	2
C₂×C₄×C₂²⋊D₁₇₃	2
C₂×C₄×D₄×C₁₇₃	2
#3459	173