Subgroups — C₄×Q₈×D₁₇₂ #25256466

Order 11008.

3148 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₁₇₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈×D₄₃	C₂	1	2	yes	maximal, complemented
3	#19137653	C₂	1	3	yes	maximal, complemented
4	#19137602	C₂	1	6	yes	maximal, complemented
5	Q₈×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄⋊C₄×D₁₇₂	C₂	1	3	yes	maximal
7	Q₈×(C₂×D₄₃)⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₄×#13063325	C₂	1	3	yes	maximal, complemented
9	C₄×#13063305	C₂	1	6	yes	maximal, complemented
10	C₄²×D₁₇₂	C₂	1	3	yes	maximal
11	C₄²×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₈×D₄₃	C₂²	1	2	yes	—
13	Q₈×D₁₇₂	C₄	1	16	yes	direct product factor
14	C₂×#13063325	C₂²	1	3	yes	—
15	C₂×#13063305	C₂²	1	6	yes	—
16	C₂×Q₈×Dic₄₃	C₂²	1	2	yes	—
17	C₂×C₄×Dic₈₆	C₂²	1	6	yes	—
18	C₂×#13063290	C₂²	1	6	yes	—
19	C₄×Q₈×D₄₃	—	2	16	no	—
20	C₂×C₄×D₁₇₂	C₂²	1	3	yes	—
21	C₂×C₄×D₁₇₂	C₂²	1	3	yes	—
22	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₄×D₄₃	C₂²	1	6	yes	—
24	C₂×C₄²×D₄₃	C₂²	1	6	yes	—
25	#14582805	C₂²	1	6	yes	—
26	#14582804	C₂²	1	6	yes	—
27	#14582798	C₂²	1	6	yes	—
28	#14582797	C₂²	1	6	yes	—
29	#14582797	C₂²	1	6	yes	—
30	#14582784	C₂²	1	12	yes	—
31	#14582773	C₂²	1	12	yes	—
32	#14582769	C₂²	1	3	yes	—
33	#14582756	C₂²	1	6	yes	—
34	C₄×C₄⋊Dic₄₃	C₂²	1	6	yes	—
35	C₄×C₄⋊Dic₄₃	C₂²	1	3	yes	—
36	C₄×C₄⋊Dic₄₃	C₂²	1	3	yes	—
37	C₄×C₄⋊Dic₄₃	C₂²	1	3	yes	—
38	C₄×(C₂×D₄₃)⋊C₄	C₂²	1	6	yes	—
39	C₄×(C₂×D₄₃)⋊C₄	C₂²	1	6	yes	—
40	C₄×(C₂×D₄₃)⋊C₄	C₂²	1	6	yes	—
41	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
45	C₄×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
46	C₄×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
47	C₄³×C₄₃	C₂²	1	3	yes	—
48	C₂²×Dic₈₆	C₂³	1	6	yes	—
49	C₂×Q₈×D₄₃	—	2	8	no	—
50	C₂×Q₈×D₄₃	—	2	8	no	—
51	C₂×Q₈×D₄₃	C₂×C₄	1	16	yes	complemented
52	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
53	C₂²×C₄×D₄₃	C₂³	1	6	yes	—
54	C₂²×C₄×D₄₃	C₂³	1	6	yes	—
55	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
56	#13063325	C₂×C₄	1	24	yes	complemented
57	#13063305	C₂×C₄	1	48	yes	complemented
58	Q₈×Dic₄₃	—	2	8	no	—
59	C₄×Dic₈₆	—	2	24	no	—
60	#13063290	—	2	24	no	—
61	C₄×D₁₇₂	—	2	12	no	—
62	C₄×D₁₇₂	C₂×C₄	1	24	yes	—
63	C₄×D₁₇₂	Q₈	1	8	yes	direct product factor
64	C₂×C₄⋊Dic₄₃	C₂³	1	3	yes	—
65	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
66	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
67	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
68	C₂×C₄⋊Dic₄₃	C₂³	1	3	yes	—
69	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
70	C₂×Dic₄₃⋊C₄	C₂³	1	12	yes	—
71	C₄⋊C₄×D₄₃	—	2	24	no	—
72	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	6	yes	—
73	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	6	yes	—
74	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
75	C₂×C₄×Dic₄₃	C₂³	1	6	yes	—
76	C₂×C₄×Dic₄₃	C₂³	1	6	yes	—
77	C₂×C₄×Dic₄₃	C₂³	1	6	yes	—
78	C₄²×D₄₃	—	2	24	no	—
79	C₄₃⋊#95	C₂³	1	6	yes	—
80	C₄₃⋊#95	C₂³	1	6	yes	—
81	C₄₃⋊#95	C₂³	1	12	yes	—
82	C₄₃⋊#95	C₂³	1	6	yes	—
83	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₄×Q₈×C₄₃	—	2	4	no	—
85	C₄×Q₈×C₄₃	C₂×C₄	1	8	yes	complemented
86	C₄×Q₈×C₄₃	D₄	1	8	yes	complemented
87	C₂×C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
88	C₂×C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
89	C₂×C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
90	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
91	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
92	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
93	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
94	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
95	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	#95×C₄₃	C₂³	1	6	yes	—
98	C₂³×D₄₃	C₂⁴	1	2	yes	—
99	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
100	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
101	C₂×Q₈×C₄₃	#41	1	4	yes	—
102	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
103	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
104	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
105	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
107	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
109	C₂²×Dic₄₃	C₂⁴	1	6	yes	—
110	C₂²×Dic₄₃	C₂⁴	1	6	yes	—
111	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
112	Q₈×D₄₃	—	2	64	no	—
113	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
114	C₂×D₁₇₂	C₂×Q₈	1	4	yes	—
115	C₂×D₁₇₂	#41	1	4	yes	—
116	C₂×C₄×D₄₃	—	2	4	no	—
117	C₂×C₄×D₄₃	—	2	12	no	—
118	C₂×C₄×D₄₃	—	2	12	no	—
119	C₂×C₄×D₄₃	—	2	4	no	—
120	C₂×C₄×D₄₃	—	2	12	no	—
121	C₂×C₄×D₄₃	—	2	12	no	—
122	C₂×C₄×D₄₃	—	4	6	no	—
123	C₂×C₄×D₄₃	C₂²×C₄	1	24	yes	—
124	C₂×C₄×D₄₃	C₂×Q₈	1	8	yes	complemented
125	C₂×Dic₈₆	—	2	12	no	—
126	C₂×Dic₈₆	—	2	12	no	—
127	C₂×Dic₈₆	C₂²×C₄	1	24	yes	—
128	C₄⋊C₄×C₄₃	—	2	6	no	—
129	C₄⋊C₄×C₄₃	C₂²×C₄	1	12	yes	—
130	C₄⋊C₄×C₄₃	C₂×D₄	1	12	yes	—
131	C₄²×C₄₃	—	2	6	no	—
132	C₄²×C₄₃	—	2	6	no	—
133	C₄²×C₄₃	—	2	6	no	—
134	C₄²×C₄₃	—	4	3	no	—
135	C₄²×C₄₃	C₂²×C₄	1	12	yes	—
136	C₄²×C₄₃	C₂×D₄	1	12	yes	—
137	C₄²×C₄₃	C₂×Q₈	1	4	yes	complemented
138	(C₂×D₄₃)⋊C₄	—	2	12	no	—
139	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	24	yes	—
140	(C₂×D₄₃)⋊C₄	C₂×Q₈	1	8	yes	complemented
141	C₄⋊Dic₄₃	—	2	12	no	—
142	C₄⋊Dic₄₃	—	2	6	no	—
143	C₄⋊Dic₄₃	—	4	6	no	—
144	C₄⋊Dic₄₃	C₂²×C₄	1	12	yes	—
145	C₄⋊Dic₄₃	C₂²×C₄	1	24	yes	—
146	C₄⋊Dic₄₃	C₂×Q₈	1	4	yes	complemented
147	Dic₄₃⋊C₄	—	2	24	no	—
148	C₄×Dic₄₃	—	2	12	no	—
149	C₄×Dic₄₃	—	2	12	no	—
150	C₄×Dic₄₃	—	2	12	no	—
151	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
152	C₂²×D₄₃	—	2	2	no	—
153	C₂²×D₄₃	—	2	2	no	—
154	C₂²×D₄₃	—	2	2	no	—
155	C₂²×D₄₃	—	2	2	no	—
156	C₂²×D₄₃	C₂³×C₄	1	4	yes	—
157	C₂²×D₄₃	C₂²×Q₈	1	4	yes	—
158	C₂²×D₄₃	C₂×#41	1	4	yes	—
159	Q₈×C₄₃	C₄×D₄	1	16	yes	complemented
160	C₂×C₄×C₄₃	—	2	1	no	—
161	C₂×C₄×C₄₃	—	2	3	no	—
162	C₂×C₄×C₄₃	—	2	3	no	—
163	C₂×C₄×C₄₃	—	2	3	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	3	no	—
166	C₂×C₄×C₄₃	—	2	3	no	—
167	C₂×C₄×C₄₃	—	2	3	no	—
168	C₂×C₄×C₄₃	—	2	3	no	—
169	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
170	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
171	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
172	C₂×C₄×C₄₃	C₂²×D₄	1	6	yes	—
173	C₂×C₄×C₄₃	C₂²×D₄	1	6	yes	—
174	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
176	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
177	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
178	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
179	C₂×C₄×C₄₃	C₂×#41	1	6	yes	—
180	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
181	C₂×Dic₄₃	—	2	2	no	—
182	C₂×Dic₄₃	—	2	6	no	—
183	C₂×Dic₄₃	—	2	6	no	—
184	C₂×Dic₄₃	—	2	2	no	—
185	C₂×Dic₄₃	—	2	6	no	—
186	C₂×Dic₄₃	—	2	6	no	—
187	C₂×Dic₄₃	—	2	6	no	—
188	C₂×Dic₄₃	C₂³×C₄	1	12	yes	—
189	C₂×Dic₄₃	C₂²×Q₈	1	4	yes	—
190	D₁₇₂	C₄×Q₈	1	16	yes	direct product factor
191	C₄×D₄₃	—	2	48	no	—
192	C₄×D₄₃	—	2	16	no	—
193	C₄×D₄₃	—	4	24	no	—
194	Dic₈₆	—	2	48	no	—
195	C₄×D₄×Q₈	—	43	1	no	maximal, Sylow
196	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
197	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
198	C₂²×C₄₃	C₂³×Q₈	1	1	yes	characteristic
199	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
200	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
201	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
202	C₂²×C₄₃	#585	1	1	yes	characteristic
203	C₂×D₄₃	—	2	4	no	—
204	C₂×D₄₃	—	2	4	no	—
205	C₂×D₄₃	—	2	4	no	—
206	C₂×D₄₃	—	2	4	no	—
207	C₂×D₄₃	—	2	4	no	—
208	C₂×D₄₃	—	2	4	no	—
209	C₂×D₄₃	C₂×C₄×Q₈	1	8	yes	complemented
210	C₄×C₄₃	—	2	6	no	—
211	C₄×C₄₃	—	2	6	no	—
212	C₄×C₄₃	—	2	2	no	—
213	C₄×C₄₃	—	4	3	no	—
214	C₄×C₄₃	C₂×C₄×D₄	1	12	yes	—
215	C₄×C₄₃	C₂×C₄×Q₈	1	4	yes	complemented
216	C₄×C₄₃	D₄×Q₈	1	4	yes	complemented
217	Dic₄₃	—	2	12	no	—
218	Dic₄₃	—	2	4	no	—
219	Dic₄₃	—	4	6	no	—
220	C₂×D₄×Q₈	—	43	1	no	—
221	C₂²×C₄×Q₈	—	43	2	no	—
222	#2365	—	43	3	no	—
223	#2360	—	43	6	no	—
224	Q₈×C₄⋊C₄	—	43	1	no	—
225	D₄×C₄⋊C₄	—	43	3	no	—
226	Q₈×C₂²⋊C₄	—	43	2	no	—
227	C₄×C₄⋊Q₈	—	43	3	no	—
228	C₄×C₂²⋊Q₈	—	43	6	no	—
229	C₄²×Q₈	D₄₃	1	1	yes	characteristic, complemented
230	C₄²×D₄	—	43	3	no	—
231	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
232	C₂×C₄₃	C₂²×C₄×Q₈	1	1	yes	characteristic
233	C₂×C₄₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
234	C₂×C₄₃	C₂×D₄×Q₈	1	1	yes	characteristic
235	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
236	C₂×C₄₃	Q₈×#41	1	1	yes	characteristic
237	C₂×C₄₃	#3482	1	1	yes	characteristic
238	D₄₃	—	2	8	no	—
239	C₂³×Q₈	—	43	2	no	—
240	D₄×Q₈	—	43	16	no	—
241	C₂×C₄⋊Q₈	—	43	3	no	—
242	C₂×C₂²⋊Q₈	—	43	6	no	—
243	C₂×C₄×Q₈	—	43	2	no	—
244	C₂×C₄×Q₈	—	43	6	no	—
245	C₂×C₄×Q₈	—	43	6	no	—
246	C₂×C₄×Q₈	—	86	16	no	—
247	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
248	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
249	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
250	C₂×C₄×D₄	—	43	3	no	—
251	C₂×C₄×D₄	—	43	1	no	—
252	C₂×C₄×D₄	—	43	3	no	—
253	C₂²×C₄⋊C₄	—	43	6	no	—
254	C₂²×C₄²	—	43	6	no	—
255	#391	—	43	6	no	—
256	#391	—	43	6	no	—
257	#389	—	43	6	no	—
258	#389	—	43	6	no	—
259	#389	—	43	6	no	—
260	#387	—	43	12	no	—
261	#385	—	43	12	no	—
262	#384	—	43	3	no	—
263	#380	—	43	6	no	—
264	C₄×C₄⋊C₄	—	43	3	no	—
265	C₄×C₄⋊C₄	—	43	6	no	—
266	C₄×C₄⋊C₄	—	43	3	no	—
267	C₄×C₄⋊C₄	—	43	3	no	—
268	C₄×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
269	C₄×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
270	C₄×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
271	C₄×C₂²⋊C₄	—	43	6	no	—
272	C₄×C₂²⋊C₄	—	43	6	no	—
273	C₄×C₂²⋊C₄	—	43	6	no	—
274	C₄³	C₂×D₄₃	1	3	yes	—
275	C₄₃	C₄×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
276	C₂²×Q₈	—	43	16	no	—
277	C₂²×Q₈	—	43	6	no	—
278	C₂²×Q₈	—	86	8	no	—
279	C₂²×Q₈	—	86	8	no	—
280	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
281	C₂²×D₄	—	43	1	no	—
282	C₂³×C₄	—	43	6	no	—
283	C₂³×C₄	—	43	2	no	—
284	C₂³×C₄	—	43	6	no	—
285	C₄⋊Q₈	—	43	24	no	—
286	C₂²⋊Q₈	—	43	48	no	—
287	C₄×Q₈	—	2	4	no	—
288	C₄×Q₈	—	86	8	no	—
289	C₄×Q₈	—	86	24	no	—
290	C₄×Q₈	—	86	24	no	—
291	C₄×Q₈	C₄×D₄₃	1	8	yes	complemented
292	C₄×Q₈	D₁₇₂	1	8	yes	direct product factor
293	C₄×D₄	—	43	24	no	—
294	C₄×D₄	—	43	8	no	—
295	C₄×D₄	—	86	12	no	—
296	C₂×C₄⋊C₄	—	43	3	no	—
297	C₂×C₄⋊C₄	—	43	1	no	—
298	C₂×C₄⋊C₄	—	43	6	no	—
299	C₂×C₄⋊C₄	—	43	12	no	—
300	C₂×C₄⋊C₄	—	43	6	no	—
301	C₂×C₄⋊C₄	—	43	3	no	—
302	C₂×C₄⋊C₄	—	43	6	no	—
303	C₂×C₄⋊C₄	—	86	24	no	—
304	C₂×C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
305	C₂×C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
306	C₂×C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
307	C₂×C₂²⋊C₄	—	43	6	no	—
308	C₂×C₂²⋊C₄	—	43	2	no	—
309	C₂×C₂²⋊C₄	—	43	6	no	—
310	C₂×C₄²	—	43	6	no	—
311	C₂×C₄²	—	43	6	no	—
312	C₂×C₄²	—	43	6	no	—
313	C₂×C₄²	—	86	24	no	—
314	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
315	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
316	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
317	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
318	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
319	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
320	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
321	#95	—	43	6	no	—
322	#95	—	43	6	no	—
323	#95	—	43	6	no	—
324	#95	—	43	12	no	—
325	#95	C₂²×D₄₃	1	6	yes	—
326	C₂⁴	—	43	2	no	—
327	C₂×Q₈	—	43	24	no	—
328	C₂×Q₈	—	86	64	no	—
329	C₂×Q₈	—	86	12	no	—
330	C₂×Q₈	—	86	12	no	—
331	C₂×Q₈	C₂×C₄×D₄₃	1	4	yes	—
332	C₂×Q₈	C₂×D₁₇₂	1	4	yes	—
333	C₂×Q₈	#10621898	1	4	yes	—
334	C₂×D₄	—	43	4	no	—
335	C₂×D₄	—	43	4	no	—
336	C₂×D₄	—	43	4	no	—
337	C₂²×C₄	—	43	2	no	—
338	C₂²×C₄	—	43	6	no	—
339	C₂²×C₄	—	43	24	no	—
340	C₂²×C₄	—	43	8	no	—
341	C₂²×C₄	—	43	6	no	—
342	C₂²×C₄	—	86	12	no	—
343	C₂²×C₄	—	86	4	no	—
344	C₂²×C₄	—	86	12	no	—
345	C₂²×C₄	—	86	12	no	—
346	C₂²×C₄	—	86	4	no	—
347	C₂²×C₄	—	86	12	no	—
348	C₂²×C₄	—	172	6	no	—
349	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
350	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
351	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
352	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
353	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
354	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
355	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
356	C₄⋊C₄	—	2	6	no	—
357	C₄⋊C₄	—	43	12	no	—
358	C₄⋊C₄	—	43	24	no	—
359	C₄⋊C₄	—	43	4	no	—
360	C₄⋊C₄	—	86	24	no	—
361	C₄⋊C₄	—	86	12	no	—
362	C₄⋊C₄	—	86	6	no	—
363	C₄⋊C₄	—	172	6	no	—
364	C₄⋊C₄	C₂×C₄×D₄₃	1	12	yes	—
365	C₄⋊C₄	C₂×D₁₇₂	1	12	yes	—
366	C₂²⋊C₄	—	43	24	no	—
367	C₂²⋊C₄	—	43	8	no	—
368	C₂²⋊C₄	—	86	12	no	—
369	C₄²	—	2	6	no	—
370	C₄²	—	2	6	no	—
371	C₄²	—	2	6	no	—
372	C₄²	—	4	3	no	—
373	C₄²	—	86	12	no	—
374	C₄²	—	86	12	no	—
375	C₄²	—	86	12	no	—
376	C₄²	C₂×C₄×D₄₃	1	12	yes	—
377	C₄²	C₂×D₁₇₂	1	12	yes	—
378	C₄²	Q₈×D₄₃	1	4	yes	complemented
379	C₂³	—	43	4	no	—
380	C₂³	—	43	4	no	—
381	C₂³	—	43	4	no	—
382	C₂³	—	86	2	no	—
383	C₂³	—	86	2	no	—
384	C₂³	—	86	2	no	—
385	C₂³	—	86	2	no	—
386	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
387	Q₈	—	86	48	no	—
388	Q₈	C₄×D₁₇₂	1	16	yes	direct product factor
389	D₄	—	43	16	no	—
390	C₂×C₄	—	2	3	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	3	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	3	no	—
395	C₂×C₄	—	2	3	no	—
396	C₂×C₄	—	2	3	no	—
397	C₂×C₄	—	2	3	no	—
398	C₂×C₄	—	2	3	no	—
399	C₂×C₄	—	43	12	no	—
400	C₂×C₄	—	43	4	no	—
401	C₂×C₄	—	86	2	no	—
402	C₂×C₄	—	86	6	no	—
403	C₂×C₄	—	86	6	no	—
404	C₂×C₄	—	86	2	no	—
405	C₂×C₄	—	86	16	no	—
406	C₂×C₄	—	86	48	no	—
407	C₂×C₄	—	86	6	no	—
408	C₂×C₄	—	86	6	no	—
409	C₂×C₄	—	86	6	no	—
410	C₂×C₄	—	172	24	no	—
411	C₂×C₄	C₂²×C₄×D₄₃	1	6	yes	—
412	C₂×C₄	C₂²×C₄×D₄₃	1	6	yes	—
413	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
414	C₂×C₄	C₂²×D₁₇₂	1	6	yes	—
415	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
416	C₂×C₄	C₂²×D₁₇₂	1	6	yes	—
417	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
418	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
419	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
420	C₂×C₄	#41×D₄₃	1	2	yes	—
421	C₂×C₄	C₂×#10621898	1	6	yes	—
422	C₂×C₄	#13063372	1	2	yes	—
423	C₂²	—	43	8	no	—
424	C₂²	—	86	4	no	—
425	C₂²	—	86	4	no	—
426	C₂²	—	86	4	no	—
427	C₂²	—	86	4	no	—
428	C₂²	—	86	4	no	—
429	C₂²	—	86	4	no	—
430	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
431	C₂²	C₂³×D₁₇₂	1	1	yes	characteristic
432	C₂²	C₂²×Q₈×D₄₃	1	1	yes	characteristic
433	C₂²	C₂×#41×D₄₃	1	1	yes	characteristic
434	C₂²	C₂²×#10621898	1	1	yes	characteristic
435	C₂²	C₂×#13063372	1	1	yes	characteristic
436	C₂²	#14583735	1	1	yes	characteristic
437	C₄	—	2	6	no	—
438	C₄	—	2	6	no	—
439	C₄	—	2	2	no	—
440	C₄	—	4	3	no	—
441	C₄	—	86	4	no	—
442	C₄	—	86	12	no	—
443	C₄	—	172	6	no	—
444	C₄	C₂×C₄×D₁₇₂	1	12	yes	—
445	C₄	C₄×Q₈×D₄₃	1	4	yes	complemented
446	C₄	Q₈×D₁₇₂	1	4	yes	direct product factor
447	C₂	—	86	8	no	—
448	C₂	C₂²×C₄×D₁₇₂	1	1	yes	characteristic
449	C₂	C₂×C₄×Q₈×D₄₃	1	1	yes	characteristic
450	C₂	C₄×#13063372	1	1	yes	characteristic
451	C₂	C₂×Q₈×D₁₇₂	1	1	yes	characteristic
452	C₂	#41×D₁₇₂	1	1	yes	characteristic
453	C₂	Q₈×#10621898	1	1	yes	characteristic
454	C₂	#19148217	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₃
Fitting	C₄²×Q₈×C₄₃	C₂
socle, cosocle	C₂³×C₄₃	C₂⁵
prime radical	C₂²×D₁₇₂	C₂³
hypercenter	C₄²×Q₈	D₄₃
hypocenter	C₄₃	C₄×D₄×Q₈
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₈×D₄₃	C₂	semidirect
3. #19137653	C₂	semidirect
4. #19137602	C₂	semidirect
5. Q₈×C₄⋊Dic₄₃	C₂	semidirect
7. Q₈×(C₂×D₄₃)⋊C₄	C₂	semidirect
8. C₄×#13063325	C₂	semidirect
9. C₄×#13063305	C₂	semidirect
11. C₄²×Q₈×C₄₃	C₂	semidirect
13. Q₈×D₁₇₂	C₄	direct (N × H)
51. C₂×Q₈×D₄₃	C₂×C₄	semidirect
56. #13063325	C₂×C₄	semidirect
57. #13063305	C₂×C₄	semidirect
63. C₄×D₁₇₂	Q₈	direct (N × H)
85. C₄×Q₈×C₄₃	C₂×C₄	semidirect
86. C₄×Q₈×C₄₃	D₄	semidirect
124. C₂×C₄×D₄₃	C₂×Q₈	semidirect
137. C₄²×C₄₃	C₂×Q₈	semidirect
140. (C₂×D₄₃)⋊C₄	C₂×Q₈	semidirect
146. C₄⋊Dic₄₃	C₂×Q₈	semidirect
159. Q₈×C₄₃	C₄×D₄	semidirect
190. D₁₇₂	C₄×Q₈	direct (N × H)
209. C₂×D₄₃	C₂×C₄×Q₈	semidirect
215. C₄×C₄₃	C₂×C₄×Q₈	semidirect
216. C₄×C₄₃	D₄×Q₈	semidirect
229. C₄²×Q₈	D₄₃	semidirect
275. C₄₃	C₄×D₄×Q₈	semidirect
291. C₄×Q₈	C₄×D₄₃	semidirect
292. C₄×Q₈	D₁₇₂	direct (N × H)
378. C₄²	Q₈×D₄₃	semidirect
388. Q₈	C₄×D₁₇₂	direct (N × H)
445. C₄	C₄×Q₈×D₄₃	semidirect
446. C₄	Q₈×D₁₇₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₈×D₁₇₂	2
C₂×C₄×Q₈×D₄₃	2
#19137653	2
#19137602	2
Q₈×C₄⋊Dic₄₃	2
C₄⋊C₄×D₁₇₂	2
Q₈×(C₂×D₄₃)⋊C₄	2
C₄×#13063325	2
C₄×#13063305	2
C₄²×D₁₇₂	2
C₄²×Q₈×C₄₃	2
C₄×D₄×Q₈	43

Subgroups — C4×Q8×D172 #25256466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Q₈×D₁₇₂ #25256466