Subgroups — #36367121

Order 22144.

1132 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012211	C₂	1	1	yes	maximal, characteristic, complemented
2	#26012206	C₂	1	1	yes	maximal, characteristic, complemented
3	#26012198	C₂	1	1	yes	maximal, characteristic, complemented
4	#26012187	C₂	1	2	yes	maximal, complemented
5	#26012181	C₂	1	2	yes	maximal, complemented
6	#26012176	C₂	1	2	yes	maximal, complemented
7	#26012167	C₂	1	4	yes	maximal, complemented
8	#26012145	C₂	1	1	yes	maximal, characteristic, complemented
9	#26012135	C₂	1	2	yes	maximal, complemented
10	#26012048	C₂	1	1	yes	maximal, characteristic, complemented
11	#26012023	C₂	1	2	yes	maximal, complemented
12	#26012021	C₂	1	4	yes	maximal, complemented
13	#26012002	C₂	1	2	yes	maximal, complemented
14	C₄×#14583826	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#14583825	C₂	1	2	yes	maximal, complemented
16	C₂×#19149638	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14583826	C₂²	1	1	yes	characteristic
19	C₂×#14583825	C₂²	1	2	yes	—
20	#19149679	C₂²	1	1	yes	characteristic, complemented
21	#19149679	C₂²	1	1	yes	characteristic, complemented
22	#19149674	C₂²	1	4	yes	complemented
23	#19149672	C₂²	1	4	yes	complemented
24	#19149672	C₂²	1	4	yes	complemented
25	#19149671	C₂²	1	2	yes	complemented
26	#19149670	C₂²	1	2	yes	complemented
27	#19149669	C₂²	1	4	yes	complemented
28	#19149666	C₂²	1	2	yes	—
29	#19149665	C₂²	1	4	yes	complemented
30	#19149663	C₂²	1	4	yes	complemented
31	#19149662	C₂²	1	4	yes	—
32	#19149661	C₂²	1	4	yes	complemented
33	#19149660	C₂²	1	4	yes	—
34	#19149659	C₂²	1	2	yes	complemented
35	#19149658	C₂²	1	2	yes	—
36	#19149658	C₂²	1	2	yes	—
37	#19149658	C₂²	1	2	yes	complemented
38	#19149658	C₂²	1	2	yes	complemented
39	#19149656	C₂²	1	4	yes	complemented
40	#19149653	C₂²	1	2	yes	complemented
41	#19149653	C₂²	1	2	yes	complemented
42	#19149651	C₂²	1	4	yes	—
43	#19149650	C₂²	1	2	yes	—
44	#19149648	C₂²	1	4	yes	—
45	C₄×Dic₃₄₆	C₂²	1	1	yes	characteristic, complemented
46	C₄×Dic₃₄₆	C₂²	1	1	yes	characteristic, complemented
47	C₄×Dic₃₄₆	C₂²	1	2	yes	complemented
48	C₄×Dic₃₄₆	C₂²	1	2	yes	complemented
49	#19149644	C₂²	1	2	yes	complemented
50	C₄×D₆₉₂	C₂²	1	1	yes	characteristic, complemented
51	C₄×D₆₉₂	C₂²	1	1	yes	characteristic, complemented
52	D₄×Dic₁₇₃	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	—
55	C₄×C₂²⋊D₁₇₃	C₂²	1	4	yes	complemented
56	C₄×C₂²⋊D₁₇₃	C₂²	1	4	yes	complemented
57	#19149639	C₂²	1	4	yes	complemented
58	#19149638	C₂²	1	4	yes	—
59	#19149638	C₂²	1	1	yes	characteristic
60	#19149638	C₂²	1	2	yes	—
61	#19149638	C₂²	1	2	yes	complemented
62	#19149638	C₂²	1	2	yes	complemented
63	#19149638	C₂²	1	4	yes	complemented
64	#19149637	C₂²	1	2	yes	complemented
65	#19149636	C₂²	1	2	yes	complemented
66	#19149635	C₂²	1	4	yes	complemented
67	C₂×C₄⋊Dic₁₇₃	C₂²	1	2	yes	complemented
68	C₂×C₄⋊Dic₁₇₃	C₂²	1	2	yes	complemented
69	C₂×C₂²⋊Dic₁₇₃	C₂²	1	4	yes	—
70	C₂×C₄×Dic₁₇₃	C₂²	1	4	yes	complemented
71	C₄²×D₁₇₃	C₂²	1	2	yes	complemented
72	C₂²×D₄×C₁₇₃	C₂²	1	1	yes	characteristic
73	C₂³×C₄×C₁₇₃	C₂²	1	2	yes	—
74	C₄×D₄×C₁₇₃	C₂²	1	2	yes	—
75	C₄×D₄×C₁₇₃	C₂²	1	1	yes	characteristic
76	C₄×D₄×C₁₇₃	C₂²	1	1	yes	characteristic
77	C₄×D₄×C₁₇₃	C₂²	1	1	yes	characteristic
78	C₄×D₄×C₁₇₃	C₂²	1	2	yes	—
79	C₄×D₄×C₁₇₃	C₂²	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₇₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₁₇₃	C₂²	1	1	yes	characteristic
83	#14583826	—	2	4	no	—
84	#14583825	—	2	8	no	—
85	C₂×Dic₃₄₆	C₂³	1	2	yes	—
86	C₂×Dic₃₄₆	C₂³	1	1	yes	characteristic
87	C₂×Dic₃₄₆	C₂³	1	2	yes	—
88	C₂×D₆₉₂	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
92	C₂²×Dic₁₇₃	C₂³	1	4	yes	—
93	C₂²×Dic₁₇₃	C₂³	1	4	yes	—
94	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
95	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
96	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
97	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
99	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
100	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
101	C₄⋊Dic₁₇₃	C₂³	1	4	yes	—
102	C₄⋊Dic₁₇₃	C₂³	1	4	yes	—
103	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
104	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
105	#14583805	C₂³	1	4	yes	—
106	#14583805	C₂³	1	4	yes	—
107	#14583805	C₂³	1	2	yes	—
108	#14583805	C₂³	1	2	yes	—
109	#14583805	C₂³	1	4	yes	—
110	#14583805	C₂³	1	4	yes	—
111	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
112	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
113	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
114	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
115	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
116	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
117	#14583803	C₂³	1	2	yes	—
118	#14583803	C₂³	1	2	yes	—
119	#14583803	C₂³	1	4	yes	—
120	#14583803	C₂³	1	4	yes	—
121	C₄×Dic₁₇₃	C₂³	1	2	yes	—
122	C₄×Dic₁₇₃	C₂³	1	2	yes	—
123	C₄×Dic₁₇₃	C₂³	1	2	yes	—
124	C₄×Dic₁₇₃	C₂³	1	4	yes	—
125	C₄×Dic₁₇₃	C₂³	1	4	yes	—
126	C₄×Dic₁₇₃	C₂³	1	4	yes	—
127	C₂⁴×C₁₇₃	C₂³	1	2	yes	—
128	C₂×D₄×C₁₇₃	—	2	4	no	—
129	C₂×D₄×C₁₇₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
131	C₂×D₄×C₁₇₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₇₃	—	2	8	no	—
133	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
138	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₁₇₃	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
145	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
148	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
149	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
150	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
151	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
152	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
153	Dic₃₄₆	—	2	4	no	—
154	Dic₃₄₆	—	2	2	no	—
155	Dic₃₄₆	—	4	2	no	—
156	D₆₉₂	—	2	2	no	—
157	C₂²⋊D₁₇₃	—	2	8	no	—
158	C₂²⋊D₁₇₃	—	2	4	no	—
159	C₂²⋊D₁₇₃	—	4	4	no	—
160	C₂×Dic₁₇₃	—	2	8	no	—
161	C₂×Dic₁₇₃	—	4	4	no	—
162	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
163	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
164	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
165	C₂×Dic₁₇₃	C₂⁴	1	4	yes	—
166	C₂×Dic₁₇₃	C₂⁴	1	4	yes	—
167	C₄×D₁₇₃	—	2	4	no	—
168	C₄×D₁₇₃	—	2	4	no	—
169	C₄×D₁₇₃	—	4	2	no	—
170	C₂³×C₁₇₃	—	2	4	no	—
171	C₂³×C₁₇₃	—	2	4	no	—
172	C₂³×C₁₇₃	—	4	2	no	—
173	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
174	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
175	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
176	D₄×C₁₇₃	—	2	4	no	—
177	D₄×C₁₇₃	—	2	2	no	—
178	D₄×C₁₇₃	#41	1	4	yes	complemented
179	C₂×C₄×C₁₇₃	—	2	4	no	—
180	C₂×C₄×C₁₇₃	—	2	4	no	—
181	C₂×C₄×C₁₇₃	—	2	4	no	—
182	C₂×C₄×C₁₇₃	—	2	4	no	—
183	C₂×C₄×C₁₇₃	—	2	4	no	—
184	C₂×C₄×C₁₇₃	—	2	2	no	—
185	C₂×C₄×C₁₇₃	—	4	1	no	—
186	C₂×C₄×C₁₇₃	#41	1	4	yes	complemented
187	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
188	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
189	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
191	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
192	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
194	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
195	C₂²×C₁₇₃	—	2	2	no	—
196	C₂²×C₁₇₃	—	2	1	no	—
197	C₂²×C₁₇₃	—	2	1	no	—
198	C₂²×C₁₇₃	—	2	2	no	—
199	C₂²×C₁₇₃	—	2	2	no	—
200	C₂²×C₁₇₃	—	2	2	no	—
201	C₂²×C₁₇₃	—	2	2	no	—
202	C₂²×C₁₇₃	—	4	8	no	—
203	C₂²×C₁₇₃	C₂×#41	1	2	yes	—
204	C₂²×C₁₇₃	C₂×#41	1	4	yes	—
205	C₂²×C₁₇₃	C₂⁵	1	1	yes	characteristic
206	C₂×D₁₇₃	—	2	2	no	—
207	C₂×D₁₇₃	—	2	2	no	—
208	C₂×D₁₇₃	—	2	2	no	—
209	C₄×C₁₇₃	—	2	2	no	—
210	C₄×C₁₇₃	—	2	2	no	—
211	C₄×C₁₇₃	—	2	1	no	—
212	C₄×C₁₇₃	—	2	1	no	—
213	C₄×C₁₇₃	—	2	1	no	—
214	C₄×C₁₇₃	C₂×#41	1	2	yes	—
215	C₄×C₁₇₃	C₂×#41	1	2	yes	—
216	C₄×C₁₇₃	C₂×#41	1	2	yes	—
217	Dic₁₇₃	—	2	2	no	—
218	Dic₁₇₃	—	2	2	no	—
219	Dic₁₇₃	—	2	4	no	—
220	Dic₁₇₃	—	2	2	no	—
221	Dic₁₇₃	—	2	4	no	—
222	C₂×C₁₇₃	—	2	2	no	—
223	C₂×C₁₇₃	—	2	4	no	—
224	C₂×C₁₇₃	—	4	2	no	—
225	C₂×C₁₇₃	C₂²×#41	1	1	yes	characteristic
226	C₂×C₁₇₃	C₂²×#41	1	1	yes	characteristic
227	C₂×C₁₇₃	#585	1	1	yes	characteristic
228	D₁₇₃	—	4	2	no	—
229	C₁₇₃	#3475	1	1	yes	characteristic, complemented, Sylow
230	#3475	—	173	1	no	maximal, Sylow
231	#556	—	173	1	no	—
232	#555	—	173	1	no	—
233	#554	—	173	1	no	—
234	#553	—	173	2	no	—
235	#552	—	173	2	no	—
236	#552	—	173	2	no	—
237	#551	—	173	4	no	—
238	#547	—	173	1	no	—
239	#546	—	173	2	no	—
240	#533	—	173	1	no	—
241	#529	—	173	4	no	—
242	#529	—	173	2	no	—
243	#525	—	173	2	no	—
244	C₄×#41	—	173	2	no	—
245	C₄×#41	—	173	1	no	—
246	C₂×C₄×D₄	D₁₇₃	1	1	yes	characteristic, complemented
247	C₂×#117	—	173	2	no	—
248	C₂×#41	—	173	2	no	—
249	C₂×#41	—	173	1	no	—
250	C₂²×D₄	C₂×D₁₇₃	1	1	yes	characteristic
251	C₂³×C₄	C₂×D₁₇₃	1	2	yes	—
252	C₄⋊Q₈	—	173	1	no	—
253	C₄⋊Q₈	—	173	1	no	—
254	#126	—	173	4	no	—
255	#126	—	173	4	no	—
256	#126	—	173	4	no	—
257	#125	—	173	4	no	—
258	#125	—	173	2	no	—
259	#125	—	173	2	no	—
260	#124	—	173	2	no	—
261	#124	—	173	4	no	—
262	#123	—	173	4	no	—
263	#123	—	173	4	no	—
264	#123	—	173	4	no	—
265	#123	—	173	4	no	—
266	C₂²⋊Q₈	—	173	2	no	—
267	C₂²⋊Q₈	—	173	2	no	—
268	C₂²⋊Q₈	—	173	2	no	—
269	C₂²⋊Q₈	—	173	2	no	—
270	C₂²⋊Q₈	—	173	2	no	—
271	C₂²⋊Q₈	—	173	4	no	—
272	#121	—	173	4	no	—
273	#121	—	173	2	no	—
274	#121	—	173	2	no	—
275	#121	—	173	2	no	—
276	#120	—	173	4	no	—
277	C₄×Q₈	—	173	2	no	—
278	C₄×Q₈	—	173	2	no	—
279	C₄×Q₈	—	173	1	no	—
280	C₄×Q₈	—	173	1	no	—
281	C₄×Q₈	—	173	2	no	—
282	C₄×D₄	—	173	2	no	—
283	C₄×D₄	—	173	4	no	—
284	C₄×D₄	—	173	2	no	—
285	C₄×D₄	—	173	2	no	—
286	C₄×D₄	—	173	4	no	—
287	C₄×D₄	—	173	4	no	—
288	C₄×D₄	—	173	1	no	—
289	C₄×D₄	—	173	1	no	—
290	C₄×D₄	C₂×D₁₇₃	1	1	yes	characteristic
291	C₄×D₄	C₂×D₁₇₃	1	1	yes	characteristic
292	C₄×D₄	C₂×D₁₇₃	1	2	yes	—
293	C₄×D₄	C₂×D₁₇₃	1	1	yes	characteristic
294	C₄×D₄	C₂×D₁₇₃	1	2	yes	—
295	C₄×D₄	C₂×D₁₇₃	1	1	yes	characteristic
296	#117	—	173	1	no	—
297	#117	—	173	2	no	—
298	#117	—	173	4	no	—
299	#117	—	173	4	no	—
300	#117	—	173	2	no	—
301	#117	—	173	2	no	—
302	#117	—	173	2	no	—
303	#117	—	173	4	no	—
304	#117	—	173	2	no	—
305	C₂×C₄⋊C₄	—	173	2	no	—
306	C₂×C₄⋊C₄	—	173	2	no	—
307	C₂×C₄⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	173	4	no	—
309	C₂×C₂²⋊C₄	C₂×D₁₇₃	1	2	yes	—
310	C₂×C₄²	—	173	4	no	—
311	C₂×C₄²	—	173	2	no	—
312	C₂×C₄²	C₂×D₁₇₃	1	1	yes	characteristic
313	C₂⁴	C₂²×D₁₇₃	1	2	yes	—
314	#41	—	346	8	no	—
315	#41	—	346	4	no	—
316	C₂×Q₈	—	173	1	no	—
317	C₂×Q₈	—	173	2	no	—
318	C₂×Q₈	—	173	2	no	—
319	C₂×D₄	—	2	4	no	—
320	C₂×D₄	—	173	2	no	—
321	C₂×D₄	—	173	4	no	—
322	C₂×D₄	—	173	4	no	—
323	C₂×D₄	—	173	1	no	—
324	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
325	C₂×D₄	C₂²×D₁₇₃	1	1	yes	characteristic
326	C₂×D₄	C₂²×D₁₇₃	1	1	yes	characteristic
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	173	4	no	—
329	C₂²×C₄	—	173	2	no	—
330	C₂²×C₄	—	173	2	no	—
331	C₂²×C₄	—	173	4	no	—
332	C₂²×C₄	—	173	2	no	—
333	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
334	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
335	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
336	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
337	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
338	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
339	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
340	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
341	C₄⋊C₄	—	173	1	no	—
342	C₄⋊C₄	—	173	1	no	—
343	C₄⋊C₄	—	173	2	no	—
344	C₄⋊C₄	—	173	2	no	—
345	C₄⋊C₄	—	173	4	no	—
346	C₄⋊C₄	—	173	4	no	—
347	C₄⋊C₄	—	173	2	no	—
348	C₄⋊C₄	—	173	2	no	—
349	C₄⋊C₄	—	173	4	no	—
350	C₄⋊C₄	—	173	4	no	—
351	C₄⋊C₄	—	173	2	no	—
352	C₄⋊C₄	—	173	4	no	—
353	C₄⋊C₄	—	173	4	no	—
354	C₄⋊C₄	—	173	2	no	—
355	C₄⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
356	C₄⋊C₄	C₂²×D₁₇₃	1	1	yes	characteristic
357	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
358	C₂²⋊C₄	—	173	2	no	—
359	C₂²⋊C₄	—	173	4	no	—
360	C₂²⋊C₄	—	173	4	no	—
361	C₂²⋊C₄	—	173	4	no	—
362	C₂²⋊C₄	—	173	4	no	—
363	C₂²⋊C₄	—	173	4	no	—
364	C₂²⋊C₄	—	173	2	no	—
365	C₂²⋊C₄	—	173	4	no	—
366	C₂²⋊C₄	—	173	2	no	—
367	C₂²⋊C₄	—	173	4	no	—
368	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
369	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
370	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
371	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
372	C₄²	—	173	4	no	—
373	C₄²	—	173	4	no	—
374	C₄²	—	173	2	no	—
375	C₄²	—	173	2	no	—
376	C₄²	—	173	2	no	—
377	C₄²	—	173	4	no	—
378	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
379	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
380	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
381	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
382	C₂³	—	2	4	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	173	2	no	—
386	C₂³	C₂³×D₁₇₃	1	2	yes	—
387	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
388	C₂³	C₂³×D₁₇₃	1	2	yes	—
389	Q₈	—	346	2	no	—
390	Q₈	—	346	4	no	—
391	Q₈	—	692	2	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	2	no	—
394	D₄	—	346	4	no	—
395	D₄	—	346	8	no	—
396	D₄	—	346	2	no	—
397	D₄	—	692	4	no	—
398	D₄	#14583826	1	4	yes	complemented
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	346	8	no	—
407	C₂×C₄	—	346	4	no	—
408	C₂×C₄	—	346	4	no	—
409	C₂×C₄	—	173	2	no	—
410	C₂×C₄	—	173	2	no	—
411	C₂×C₄	—	173	2	no	—
412	C₂×C₄	—	173	4	no	—
413	C₂×C₄	—	173	4	no	—
414	C₂×C₄	—	692	2	no	—
415	C₂×C₄	—	692	4	no	—
416	C₂×C₄	#14583825	1	4	yes	complemented
417	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
418	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
419	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
420	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
422	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
425	C₂²	—	2	2	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	4	8	no	—
433	C₂²	—	346	2	no	—
434	C₂²	—	346	2	no	—
435	C₂²	—	346	2	no	—
436	C₂²	C₂×#14583825	1	2	yes	—
437	C₂²	C₂×#14583826	1	4	yes	—
438	C₂²	C₂⁴×D₁₇₃	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	346	2	no	—
445	C₄	—	346	2	no	—
446	C₄	—	346	4	no	—
447	C₄	—	346	2	no	—
448	C₄	—	346	4	no	—
449	C₄	C₂×#14583825	1	2	yes	—
450	C₄	C₂×#14583825	1	2	yes	—
451	C₄	C₂×#14583826	1	2	yes	—
452	C₂	—	2	2	no	—
453	C₂	—	2	4	no	—
454	C₂	—	4	2	no	—
455	C₂	—	692	2	no	—
456	C₂	C₂²×#14583825	1	1	yes	characteristic
457	C₂	C₂²×#14583826	1	1	yes	characteristic
458	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	#3475
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. #26012211	C₂	semidirect
2. #26012206	C₂	semidirect
3. #26012198	C₂	semidirect
4. #26012187	C₂	semidirect
5. #26012181	C₂	semidirect
6. #26012176	C₂	semidirect
7. #26012167	C₂	semidirect
8. #26012145	C₂	semidirect
9. #26012135	C₂	semidirect
10. #26012048	C₂	semidirect
11. #26012023	C₂	semidirect
12. #26012021	C₂	semidirect
13. #26012002	C₂	semidirect
14. C₄×#14583826	C₂	semidirect
15. C₄×#14583825	C₂	semidirect
16. C₂×#19149638	C₂	semidirect
17. C₂×C₄×D₄×C₁₇₃	C₂	semidirect
20. #19149679	C₂²	semidirect
21. #19149679	C₂²	semidirect
22. #19149674	C₂²	semidirect
23. #19149672	C₂²	semidirect
24. #19149672	C₂²	semidirect
25. #19149671	C₂²	semidirect
26. #19149670	C₂²	semidirect
27. #19149669	C₂²	semidirect
29. #19149665	C₂²	semidirect
30. #19149663	C₂²	semidirect
32. #19149661	C₂²	semidirect
34. #19149659	C₂²	semidirect
37. #19149658	C₂²	semidirect
38. #19149658	C₂²	semidirect
39. #19149656	C₂²	semidirect
40. #19149653	C₂²	semidirect
41. #19149653	C₂²	semidirect
45. C₄×Dic₃₄₆	C₂²	semidirect
46. C₄×Dic₃₄₆	C₂²	semidirect
47. C₄×Dic₃₄₆	C₂²	semidirect
48. C₄×Dic₃₄₆	C₂²	semidirect
49. #19149644	C₂²	semidirect
50. C₄×D₆₉₂	C₂²	semidirect
51. C₄×D₆₉₂	C₂²	semidirect
55. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
56. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
57. #19149639	C₂²	semidirect
61. #19149638	C₂²	semidirect
62. #19149638	C₂²	semidirect
63. #19149638	C₂²	semidirect
64. #19149637	C₂²	semidirect
65. #19149636	C₂²	semidirect
66. #19149635	C₂²	semidirect
67. C₂×C₄⋊Dic₁₇₃	C₂²	semidirect
68. C₂×C₄⋊Dic₁₇₃	C₂²	semidirect
70. C₂×C₄×Dic₁₇₃	C₂²	semidirect
71. C₄²×D₁₇₃	C₂²	semidirect
178. D₄×C₁₇₃	#41	semidirect
186. C₂×C₄×C₁₇₃	#41	semidirect
229. C₁₇₃	#3475	semidirect
246. C₂×C₄×D₄	D₁₇₃	semidirect
398. D₄	#14583826	semidirect
416. C₂×C₄	#14583825	semidirect

Maximal subgroups

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

subgroup	index
#26012211	2
#26012206	2
#26012198	2
#26012187	2
#26012181	2
#26012176	2
#26012167	2
#26012145	2
#26012135	2
#26012048	2
#26012023	2
#26012021	2
#26012002	2
C₄×#14583826	2
C₄×#14583825	2
C₂×#19149638	2
C₂×C₄×D₄×C₁₇₃	2
#3475	173