Subgroups — #36367141

Order 22144.

1068 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012221	C₂	1	1	yes	maximal, characteristic, complemented
2	#26012218	C₂	1	2	yes	maximal, complemented
3	#26012216	C₂	1	1	yes	maximal, characteristic, complemented
4	#26012202	C₂	1	1	yes	maximal, characteristic, complemented
5	#26012199	C₂	1	2	yes	maximal, complemented
6	#26012197	C₂	1	2	yes	maximal, complemented
7	#26012195	C₂	1	4	yes	maximal, complemented
8	#26012156	C₂	1	1	yes	maximal, characteristic, complemented
9	#26012154	C₂	1	2	yes	maximal, complemented
10	#26012045	C₂	1	4	yes	maximal, complemented
11	#26012045	C₂	1	2	yes	maximal, complemented
12	#26012044	C₂	1	2	yes	maximal, complemented
13	C₄×#14583826	C₂	1	1	yes	maximal, characteristic
14	#26011959	C₂	1	2	yes	maximal
15	C₂×C₄×Dic₃₄₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×Q₈×D₁₇₃	C₂	1	2	yes	maximal, complemented
17	#533×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14583826	C₂²	1	1	yes	characteristic
19	C₂²×Dic₃₄₆	C₂²	1	1	yes	characteristic
20	C₂×Q₈×D₁₇₃	C₂²	1	2	yes	—
21	#19149678	C₂²	1	2	yes	—
22	#19149678	C₂²	1	2	yes	—
23	#19149678	C₂²	1	2	yes	—
24	#19149678	C₂²	1	4	yes	—
25	#19149677	C₂²	1	4	yes	—
26	#19149677	C₂²	1	2	yes	—
27	#19149670	C₂²	1	2	yes	—
28	#19149670	C₂²	1	2	yes	—
29	#19149669	C₂²	1	4	yes	—
30	#19149669	C₂²	1	4	yes	—
31	#19149669	C₂²	1	4	yes	—
32	#19149659	C₂²	1	4	yes	—
33	#19149659	C₂²	1	2	yes	—
34	#19149657	C₂²	1	4	yes	—
35	#19149657	C₂²	1	4	yes	—
36	#19149657	C₂²	1	4	yes	—
37	#19149656	C₂²	1	4	yes	—
38	#19149656	C₂²	1	4	yes	—
39	#19149655	C₂²	1	4	yes	—
40	#19149655	C₂²	1	2	yes	—
41	Q₈×Dic₁₇₃	C₂²	1	2	yes	—
42	C₄×Dic₃₄₆	C₂²	1	2	yes	—
43	C₄×Dic₃₄₆	C₂²	1	1	yes	characteristic
44	C₄×Dic₃₄₆	C₂²	1	1	yes	characteristic
45	C₄×Dic₃₄₆	C₂²	1	4	yes	—
46	C₄×Dic₃₄₆	C₂²	1	1	yes	characteristic
47	C₄×Dic₃₄₆	C₂²	1	2	yes	—
48	C₄×Dic₃₄₆	C₂²	1	1	yes	characteristic
49	C₄×Dic₃₄₆	C₂²	1	1	yes	characteristic
50	C₄×Dic₃₄₆	C₂²	1	1	yes	characteristic
51	C₄×Dic₃₄₆	C₂²	1	4	yes	—
52	#19149644	C₂²	1	4	yes	—
53	#19149644	C₂²	1	2	yes	—
54	#19149644	C₂²	1	2	yes	—
55	#19149644	C₂²	1	2	yes	—
56	C₄×D₆₉₂	C₂²	1	1	yes	characteristic
57	C₄×D₆₉₂	C₂²	1	1	yes	characteristic
58	#19149641	C₂²	1	2	yes	—
59	#19149641	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₁₇₃	C₂²	1	2	yes	—
62	#19149639	C₂²	1	4	yes	—
63	#19149639	C₂²	1	4	yes	—
64	#19149638	C₂²	1	1	yes	characteristic
65	#19149636	C₂²	1	4	yes	—
66	#19149636	C₂²	1	2	yes	—
67	C₂×C₄⋊Dic₁₇₃	C₂²	1	1	yes	characteristic
68	C₂×#14583805	C₂²	1	2	yes	—
69	C₄⋊C₄×D₁₇₃	C₂²	1	4	yes	—
70	C₄⋊C₄×D₁₇₃	C₂²	1	2	yes	—
71	C₂×C₄×Dic₁₇₃	C₂²	1	2	yes	—
72	C₄²×D₁₇₃	C₂²	1	4	yes	—
73	C₄²×D₁₇₃	C₂²	1	2	yes	—
74	C₄⋊Q₈×C₁₇₃	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₁₇₃	C₂²	1	1	yes	characteristic
76	#125×C₁₇₃	C₂²	1	2	yes	—
77	C₂²⋊Q₈×C₁₇₃	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₁₇₃	C₂²	1	2	yes	—
79	C₄×Q₈×C₁₇₃	C₂²	1	2	yes	—
80	C₄×Q₈×C₁₇₃	C₂²	1	2	yes	—
81	#117×C₁₇₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₁₇₃	C₂²	1	1	yes	characteristic
83	#14583826	Q₈	1	8	yes	complemented
84	C₂×Dic₃₄₆	—	2	4	no	—
85	C₂×Dic₃₄₆	C₂³	1	4	yes	—
86	C₂×Dic₃₄₆	C₂³	1	2	yes	—
87	C₂×Dic₃₄₆	C₂³	1	1	yes	characteristic
88	C₂×Dic₃₄₆	C₂³	1	4	yes	—
89	C₂×Dic₃₄₆	C₂³	1	1	yes	characteristic
90	C₂×Dic₃₄₆	C₂³	1	1	yes	characteristic
91	Q₈×D₁₇₃	—	2	8	no	—
92	C₂×D₆₉₂	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
94	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
95	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
96	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
97	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
98	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
99	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
100	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
101	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
102	C₄⋊Dic₁₇₃	C₂³	1	4	yes	—
103	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
105	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
106	C₄⋊Dic₁₇₃	C₂³	1	1	yes	characteristic
107	C₄⋊Dic₁₇₃	C₂³	1	4	yes	—
108	#14583805	C₂³	1	2	yes	—
109	#14583805	C₂³	1	4	yes	—
110	#14583805	C₂³	1	4	yes	—
111	#14583805	C₂³	1	2	yes	—
112	#14583805	C₂³	1	2	yes	—
113	#14583805	C₂³	1	2	yes	—
114	#14583805	C₂³	1	4	yes	—
115	#14583805	C₂³	1	4	yes	—
116	#14583805	C₂³	1	2	yes	—
117	#14583805	C₂³	1	2	yes	—
118	#14583805	C₂³	1	4	yes	—
119	#14583805	C₂³	1	4	yes	—
120	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
121	#14583803	C₂³	1	4	yes	—
122	#14583803	C₂³	1	4	yes	—
123	#14583803	C₂³	1	2	yes	—
124	#14583803	C₂³	1	2	yes	—
125	C₄×Dic₁₇₃	C₂³	1	2	yes	—
126	C₄×Dic₁₇₃	C₂³	1	2	yes	—
127	C₄×Dic₁₇₃	C₂³	1	4	yes	—
128	C₄×Dic₁₇₃	C₂³	1	4	yes	—
129	C₄×Dic₁₇₃	C₂³	1	2	yes	—
130	C₄×Dic₁₇₃	C₂³	1	2	yes	—
131	C₄×Dic₁₇₃	C₂³	1	2	yes	—
132	C₄×Dic₁₇₃	C₂³	1	2	yes	—
133	C₄×Dic₁₇₃	C₂³	1	2	yes	—
134	C₂×Q₈×C₁₇₃	C₂³	1	2	yes	—
135	C₂×Q₈×C₁₇₃	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
139	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
140	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
141	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
142	C₄⋊C₄×C₁₇₃	C₂³	1	2	yes	—
143	C₄⋊C₄×C₁₇₃	C₂³	1	4	yes	—
144	C₄⋊C₄×C₁₇₃	C₂³	1	4	yes	—
145	C₂²⋊C₄×C₁₇₃	C₂³	1	4	yes	—
146	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
147	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
148	C₄²×C₁₇₃	C₂³	1	4	yes	—
149	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
150	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
151	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
152	Dic₃₄₆	—	2	2	no	—
153	Dic₃₄₆	—	2	8	no	—
154	Dic₃₄₆	—	2	4	no	—
155	Dic₃₄₆	—	4	4	no	—
156	Dic₃₄₆	C₂×Q₈	1	4	yes	complemented
157	Dic₃₄₆	#41	1	4	yes	complemented
158	D₆₉₂	C₂×Q₈	1	4	yes	complemented
159	C₂²⋊D₁₇₃	C₂×Q₈	1	8	yes	complemented
160	C₂×Dic₁₇₃	—	2	4	no	—
161	C₂×Dic₁₇₃	—	4	2	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	2	yes	—
166	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
167	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
168	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
169	C₄×D₁₇₃	—	2	4	no	—
170	C₄×D₁₇₃	—	2	8	no	—
171	C₄×D₁₇₃	—	4	4	no	—
172	C₄×D₁₇₃	—	4	2	no	—
173	C₄×D₁₇₃	C₂×Q₈	1	8	yes	complemented
174	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
175	Q₈×C₁₇₃	—	2	4	no	—
176	Q₈×C₁₇₃	—	4	2	no	—
177	C₂×C₄×C₁₇₃	—	2	2	no	—
178	C₂×C₄×C₁₇₃	—	4	1	no	—
179	C₂×C₄×C₁₇₃	C₂×Q₈	1	4	yes	complemented
180	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₁₇₃	C₂⁴	1	4	yes	—
182	C₂×C₄×C₁₇₃	C₂⁴	1	4	yes	—
183	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
184	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
185	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
187	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
188	C₂²×C₁₇₃	—	2	1	no	—
189	C₂²×C₁₇₃	—	2	1	no	—
190	C₂²×C₁₇₃	C₂²×Q₈	1	2	yes	—
191	C₂²×C₁₇₃	C₂⁵	1	1	yes	characteristic
192	C₂×D₁₇₃	—	2	2	no	—
193	C₂×D₁₇₃	—	2	2	no	—
194	C₂×D₁₇₃	C₂²×Q₈	1	4	yes	—
195	C₄×C₁₇₃	—	2	1	no	—
196	C₄×C₁₇₃	—	2	4	no	—
197	C₄×C₁₇₃	—	2	1	no	—
198	C₄×C₁₇₃	—	2	1	no	—
199	C₄×C₁₇₃	—	2	4	no	—
200	C₄×C₁₇₃	C₂²×Q₈	1	2	yes	—
201	C₄×C₁₇₃	C₂²×Q₈	1	2	yes	—
202	C₄×C₁₇₃	C₂×#41	1	2	yes	—
203	Dic₁₇₃	—	2	2	no	—
204	Dic₁₇₃	—	2	2	no	—
205	Dic₁₇₃	—	2	2	no	—
206	Dic₁₇₃	—	2	2	no	—
207	Dic₁₇₃	—	2	2	no	—
208	Dic₁₇₃	C₂²×Q₈	1	4	yes	—
209	Dic₁₇₃	C₂×#41	1	4	yes	—
210	C₂×C₁₇₃	—	2	2	no	—
211	C₂×C₁₇₃	C₂³×Q₈	1	1	yes	characteristic
212	C₂×C₁₇₃	C₂²×#41	1	1	yes	characteristic
213	C₂×C₁₇₃	#585	1	1	yes	characteristic
214	D₁₇₃	—	2	4	no	—
215	C₁₇₃	Q₈×#41	1	1	yes	characteristic, complemented, Sylow
216	Q₈×#41	—	173	1	no	maximal, Sylow
217	Q₈²	—	173	1	no	—
218	#557	—	173	1	no	—
219	#557	—	173	2	no	—
220	#554	—	173	1	no	—
221	#554	—	173	2	no	—
222	#554	—	173	4	no	—
223	#554	—	173	2	no	—
224	D₄×Q₈	—	173	1	no	—
225	D₄×Q₈	—	173	2	no	—
226	#533	—	173	4	no	—
227	#533	—	173	2	no	—
228	#533	—	173	2	no	—
229	#533	D₁₇₃	1	1	yes	characteristic, complemented
230	C₄×#41	—	173	2	no	—
231	C₄×#41	—	173	1	no	—
232	C₂×C₄×Q₈	—	173	2	no	—
233	C₂×C₄×Q₈	—	173	1	no	—
234	C₂×#41	—	173	1	no	—
235	C₂²×Q₈	—	173	2	no	—
236	C₂²×Q₈	—	173	1	no	—
237	C₄⋊Q₈	—	173	2	no	—
238	C₄⋊Q₈	—	173	4	no	—
239	C₄⋊Q₈	—	173	4	no	—
240	C₄⋊Q₈	—	173	2	no	—
241	C₄⋊Q₈	—	173	2	no	—
242	C₄⋊Q₈	—	173	2	no	—
243	C₄⋊Q₈	C₂×D₁₇₃	1	1	yes	characteristic
244	C₄⋊Q₈	C₂×D₁₇₃	1	1	yes	characteristic
245	#125	—	173	4	no	—
246	#125	—	173	4	no	—
247	#125	—	173	4	no	—
248	#125	—	173	2	no	—
249	#125	—	173	2	no	—
250	#125	C₂×D₁₇₃	1	2	yes	—
251	C₂²⋊Q₈	—	173	2	no	—
252	C₂²⋊Q₈	—	173	4	no	—
253	C₂²⋊Q₈	—	173	4	no	—
254	C₂²⋊Q₈	—	173	4	no	—
255	C₂²⋊Q₈	—	173	2	no	—
256	C₂²⋊Q₈	—	173	4	no	—
257	C₂²⋊Q₈	—	173	4	no	—
258	C₂²⋊Q₈	—	173	4	no	—
259	C₂²⋊Q₈	—	173	4	no	—
260	C₂²⋊Q₈	C₂×D₁₇₃	1	2	yes	—
261	C₂²⋊Q₈	C₂×D₁₇₃	1	2	yes	—
262	C₄×Q₈	—	173	2	no	—
263	C₄×Q₈	—	173	2	no	—
264	C₄×Q₈	—	173	4	no	—
265	C₄×Q₈	—	173	2	no	—
266	C₄×Q₈	—	173	2	no	—
267	C₄×Q₈	—	173	1	no	—
268	C₄×Q₈	—	173	4	no	—
269	C₄×Q₈	—	173	2	no	—
270	C₄×Q₈	—	173	1	no	—
271	C₄×Q₈	—	173	1	no	—
272	C₄×Q₈	—	173	1	no	—
273	C₄×Q₈	—	173	2	no	—
274	C₄×Q₈	—	173	1	no	—
275	C₄×Q₈	—	173	1	no	—
276	C₄×Q₈	—	173	4	no	—
277	C₄×Q₈	C₂×D₁₇₃	1	2	yes	—
278	C₄×Q₈	C₂×D₁₇₃	1	2	yes	—
279	C₄×D₄	—	173	2	no	—
280	C₄×D₄	—	173	2	no	—
281	C₄×D₄	—	173	2	no	—
282	C₄×D₄	—	173	2	no	—
283	C₄×D₄	—	173	4	no	—
284	C₄×D₄	—	173	4	no	—
285	C₄×D₄	—	173	1	no	—
286	C₄×D₄	—	173	1	no	—
287	#117	—	173	1	no	—
288	#117	—	173	4	no	—
289	#117	—	173	2	no	—
290	#117	C₂×D₁₇₃	1	2	yes	—
291	C₂×C₄⋊C₄	—	173	2	no	—
292	C₂×C₄⋊C₄	—	173	1	no	—
293	C₂×C₄⋊C₄	—	173	4	no	—
294	C₂×C₄⋊C₄	—	173	2	no	—
295	C₂×C₄²	—	173	2	no	—
296	C₂×C₄²	—	173	4	no	—
297	C₂×C₄²	—	173	2	no	—
298	C₂×C₄²	C₂×D₁₇₃	1	1	yes	characteristic
299	#41	—	173	8	no	—
300	C₂×Q₈	—	346	4	no	—
301	C₂×Q₈	—	346	8	no	—
302	C₂×Q₈	—	173	1	no	—
303	C₂×Q₈	—	173	4	no	—
304	C₂×Q₈	—	173	2	no	—
305	C₂×Q₈	—	173	1	no	—
306	C₂×Q₈	—	173	1	no	—
307	C₂×Q₈	—	173	4	no	—
308	C₂×Q₈	C₂²×D₁₇₃	1	2	yes	—
309	C₂×Q₈	C₂²×D₁₇₃	1	2	yes	—
310	C₂×D₄	—	173	2	no	—
311	C₂×D₄	—	173	1	no	—
312	C₂²×C₄	—	173	2	no	—
313	C₂²×C₄	—	173	4	no	—
314	C₂²×C₄	—	173	2	no	—
315	C₂²×C₄	—	173	2	no	—
316	C₂²×C₄	—	173	2	no	—
317	C₂²×C₄	—	173	4	no	—
318	C₂²×C₄	—	173	2	no	—
319	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
321	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
322	C₄⋊C₄	—	173	2	no	—
323	C₄⋊C₄	—	173	1	no	—
324	C₄⋊C₄	—	173	4	no	—
325	C₄⋊C₄	—	173	2	no	—
326	C₄⋊C₄	—	173	2	no	—
327	C₄⋊C₄	—	173	4	no	—
328	C₄⋊C₄	—	173	2	no	—
329	C₄⋊C₄	—	173	4	no	—
330	C₄⋊C₄	—	173	2	no	—
331	C₄⋊C₄	—	173	1	no	—
332	C₄⋊C₄	—	173	4	no	—
333	C₄⋊C₄	—	173	4	no	—
334	C₄⋊C₄	—	173	2	no	—
335	C₄⋊C₄	—	173	2	no	—
336	C₄⋊C₄	—	173	1	no	—
337	C₄⋊C₄	—	173	1	no	—
338	C₄⋊C₄	—	173	4	no	—
339	C₄⋊C₄	—	173	4	no	—
340	C₄⋊C₄	—	173	4	no	—
341	C₄⋊C₄	C₂²×D₁₇₃	1	4	yes	—
342	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
343	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
344	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
345	C₄⋊C₄	C₂²×D₁₇₃	1	2	yes	—
346	C₄⋊C₄	C₂²×D₁₇₃	1	4	yes	—
347	C₂²⋊C₄	—	173	2	no	—
348	C₂²⋊C₄	—	173	4	no	—
349	C₂²⋊C₄	—	173	4	no	—
350	C₂²⋊C₄	—	173	2	no	—
351	C₂²⋊C₄	—	173	2	no	—
352	C₂²⋊C₄	C₂²×D₁₇₃	1	4	yes	—
353	C₄²	—	173	2	no	—
354	C₄²	—	173	4	no	—
355	C₄²	—	173	2	no	—
356	C₄²	—	173	2	no	—
357	C₄²	—	173	2	no	—
358	C₄²	—	173	4	no	—
359	C₄²	—	173	2	no	—
360	C₄²	—	173	2	no	—
361	C₄²	—	173	2	no	—
362	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
363	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
364	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
365	C₄²	C₂²×D₁₇₃	1	4	yes	—
366	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
367	C₂³	—	173	2	no	—
368	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
369	Q₈	—	2	4	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	346	4	no	—
372	Q₈	—	346	8	no	—
373	Q₈	—	346	2	no	—
374	Q₈	—	173	4	no	—
375	Q₈	—	173	4	no	—
376	Q₈	—	692	4	no	—
377	D₄	—	173	8	no	—
378	D₄	—	173	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	346	8	no	—
382	C₂×C₄	—	346	4	no	—
383	C₂×C₄	—	346	4	no	—
384	C₂×C₄	—	173	2	no	—
385	C₂×C₄	—	173	2	no	—
386	C₂×C₄	—	173	2	no	—
387	C₂×C₄	—	173	2	no	—
388	C₂×C₄	—	173	2	no	—
389	C₂×C₄	—	173	2	no	—
390	C₂×C₄	—	173	2	no	—
391	C₂×C₄	—	173	8	no	—
392	C₂×C₄	—	692	2	no	—
393	C₂×C₄	—	692	4	no	—
394	C₂×C₄	—	692	2	no	—
395	C₂×C₄	Q₈×D₁₇₃	1	4	yes	complemented
396	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
397	C₂×C₄	C₂³×D₁₇₃	1	4	yes	—
398	C₂×C₄	C₂³×D₁₇₃	1	4	yes	—
399	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
400	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
403	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	346	2	no	—
407	C₂²	—	346	2	no	—
408	C₂²	—	173	4	no	—
409	C₂²	C₂×Q₈×D₁₇₃	1	2	yes	—
410	C₂²	C₂⁴×D₁₇₃	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	4	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	4	no	—
416	C₄	—	346	2	no	—
417	C₄	—	346	2	no	—
418	C₄	—	346	2	no	—
419	C₄	—	346	2	no	—
420	C₄	—	346	2	no	—
421	C₄	—	173	4	no	—
422	C₄	—	173	4	no	—
423	C₄	C₂×Q₈×D₁₇₃	1	2	yes	—
424	C₄	C₂×Q₈×D₁₇₃	1	2	yes	—
425	C₄	#41×D₁₇₃	1	2	yes	—
426	C₂	—	2	2	no	—
427	C₂	—	346	4	no	—
428	C₂	C₂²×Q₈×D₁₇₃	1	1	yes	characteristic
429	C₂	C₂×#41×D₁₇₃	1	1	yes	characteristic
430	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	#533×C₁₇₃	C₂
prime radical	C₂×#14583826	C₂²
hypercenter	#533	D₁₇₃
hypocenter	C₁₇₃	Q₈×#41
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #533

Complements

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

N	H ≅ G/N	type
1. #26012221	C₂	semidirect
2. #26012218	C₂	semidirect
3. #26012216	C₂	semidirect
4. #26012202	C₂	semidirect
5. #26012199	C₂	semidirect
6. #26012197	C₂	semidirect
7. #26012195	C₂	semidirect
8. #26012156	C₂	semidirect
9. #26012154	C₂	semidirect
10. #26012045	C₂	semidirect
11. #26012045	C₂	semidirect
12. #26012044	C₂	semidirect
15. C₂×C₄×Dic₃₄₆	C₂	semidirect
16. C₄×Q₈×D₁₇₃	C₂	semidirect
17. #533×C₁₇₃	C₂	semidirect
83. #14583826	Q₈	semidirect
156. Dic₃₄₆	C₂×Q₈	semidirect
157. Dic₃₄₆	#41	semidirect
158. D₆₉₂	C₂×Q₈	semidirect
159. C₂²⋊D₁₇₃	C₂×Q₈	semidirect
173. C₄×D₁₇₃	C₂×Q₈	semidirect
179. C₂×C₄×C₁₇₃	C₂×Q₈	semidirect
215. C₁₇₃	Q₈×#41	semidirect
229. #533	D₁₇₃	semidirect
395. C₂×C₄	Q₈×D₁₇₃	semidirect

Maximal subgroups

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

subgroup	index
#26012221	2
#26012218	2
#26012216	2
#26012202	2
#26012199	2
#26012197	2
#26012195	2
#26012156	2
#26012154	2
#26012045	2
#26012044	2
C₄×#14583826	2
#26011959	2
C₂×C₄×Dic₃₄₆	2
C₄×Q₈×D₁₇₃	2
#533×C₁₇₃	2
Q₈×#41	173