Subgroups — #17054216

Order 4352.

784 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14529721	C₂	1	2	yes	maximal
2	#14529343	C₂	1	4	yes	maximal
3	#14528936	C₂	1	1	yes	maximal, characteristic
4	#14528901	C₂	1	2	yes	maximal
5	C₄⋊C₄×#3622	C₂	1	2	yes	maximal
6	C₄×C₄⋊#3622	C₂	1	1	yes	maximal, characteristic
7	C₄×C₄⋊#3622	C₂	1	2	yes	maximal
8	C₄²×Q₈×C₁₇	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊#3622	C₂²	1	2	yes	—
11	C₂×C₄⋊#3622	C₂²	1	2	yes	—
12	C₂×C₄⋊#3622	C₂²	1	2	yes	—
13	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
14	C₂×C₄×#3622	C₂²	1	2	yes	—
15	C₂×C₄×#3622	C₂²	1	4	yes	—
16	#11762564	C₂²	1	2	yes	—
17	#11762564	C₂²	1	4	yes	—
18	#11762564	C₂²	1	4	yes	—
19	#11762564	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₁₇	C₄	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₇	C₄	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₁₇	C₄	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₁₇	C₄	1	2	yes	—
25	C₄×C₄⋊C₄×C₁₇	C₄	1	2	yes	—
26	C₄×C₄⋊C₄×C₁₇	C₄	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
29	C₄³×C₁₇	C₂²	1	2	yes	—
30	C₄³×C₁₇	C₂²	1	1	yes	characteristic
31	C₂²×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
32	C₄×Q₈×C₁₇	—	2	4	no	—
33	C₄×Q₈×C₁₇	—	2	2	no	—
34	C₄×Q₈×C₁₇	—	2	2	no	—
35	C₄×Q₈×C₁₇	C₈	1	8	yes	complemented
36	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
37	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
39	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₇	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₇	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₁₇	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₇	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
51	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
52	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
55	C₂²×#3622	C₂³	1	2	yes	—
56	C₂²×#3622	C₂³	1	4	yes	—
57	C₂²×#3622	C₂³	1	2	yes	—
58	C₁₇×#95	C₂×C₄	1	2	yes	—
59	C₁₇×#95	C₂×C₄	1	2	yes	—
60	C₁₇×#95	C₂×C₄	1	2	yes	—
61	C₄⋊#3622	—	2	4	no	—
62	C₄⋊#3622	—	2	2	no	—
63	C₄⋊#3622	—	2	4	no	—
64	C₄⋊#3622	—	4	2	no	—
65	C₄⋊#3622	Q₈	1	4	yes	complemented
66	C₄×#3622	—	2	4	no	—
67	C₄×#3622	—	4	4	no	—
68	C₂×Q₈×C₁₇	—	2	2	no	—
69	C₂×Q₈×C₁₇	—	2	2	no	—
70	C₂×Q₈×C₁₇	C₂×C₈	1	4	yes	—
71	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
72	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
82	C₄⋊C₄×C₁₇	—	2	4	no	—
83	C₄⋊C₄×C₁₇	—	2	2	no	—
84	C₄⋊C₄×C₁₇	—	2	4	no	—
85	C₄⋊C₄×C₁₇	C₂×C₈	1	8	yes	—
86	C₄⋊C₄×C₁₇	C₂×C₈	1	4	yes	—
87	C₄⋊C₄×C₁₇	M₁₆	1	4	yes	—
88	C₄²×C₁₇	—	2	4	no	—
89	C₄²×C₁₇	—	2	2	no	—
90	C₄²×C₁₇	—	2	2	no	—
91	C₄²×C₁₇	—	2	4	no	—
92	C₄²×C₁₇	—	2	2	no	—
93	C₄²×C₁₇	—	2	2	no	—
94	C₄²×C₁₇	—	2	2	no	—
95	C₄²×C₁₇	—	2	1	no	—
96	C₄²×C₁₇	—	2	2	no	—
97	C₄²×C₁₇	—	2	1	no	—
98	C₄²×C₁₇	—	4	1	no	—
99	C₄²×C₁₇	—	4	2	no	—
100	C₄²×C₁₇	C₂×C₈	1	8	yes	—
101	C₄²×C₁₇	C₂×C₈	1	4	yes	—
102	C₄²×C₁₇	C₂×Q₈	1	2	yes	—
103	C₄²×C₁₇	#41	1	2	yes	—
104	C₄²×C₁₇	#41	1	2	yes	—
105	C₄²×C₁₇	#41	1	2	yes	—
106	C₂×#3622	—	2	2	no	—
107	C₂×#3622	—	2	2	no	—
108	C₂×#3622	—	2	2	no	—
109	C₂×#3622	—	2	4	no	—
110	C₂×#3622	—	2	2	no	—
111	C₂×#3622	—	2	4	no	—
112	C₂×#3622	—	2	4	no	—
113	C₂×#3622	—	2	2	no	—
114	C₂×#3622	C₂×Q₈	1	4	yes	—
115	#22821	—	17	1	no	maximal, Sylow
116	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
117	Q₈×C₁₇	—	2	8	no	—
118	C₂×C₄×C₁₇	—	2	2	no	—
119	C₂×C₄×C₁₇	—	2	2	no	—
120	C₂×C₄×C₁₇	—	2	1	no	—
121	C₂×C₄×C₁₇	—	2	2	no	—
122	C₂×C₄×C₁₇	—	2	1	no	—
123	C₂×C₄×C₁₇	—	2	2	no	—
124	C₂×C₄×C₁₇	—	2	1	no	—
125	C₂×C₄×C₁₇	—	2	2	no	—
126	C₂×C₄×C₁₇	—	2	1	no	—
127	C₂×C₄×C₁₇	—	2	1	no	—
128	C₂×C₄×C₁₇	—	2	1	no	—
129	C₂×C₄×C₁₇	—	2	2	no	—
130	C₂×C₄×C₁₇	—	2	2	no	—
131	C₂×C₄×C₁₇	—	2	1	no	—
132	C₂×C₄×C₁₇	—	2	1	no	—
133	C₂×C₄×C₁₇	—	2	2	no	—
134	C₂×C₄×C₁₇	—	2	1	no	—
135	C₂×C₄×C₁₇	—	2	2	no	—
136	C₂×C₄×C₁₇	#117	1	2	yes	—
137	C₂×C₄×C₁₇	#117	1	2	yes	—
138	C₂×C₄×C₁₇	C₄×Q₈	1	2	yes	—
139	C₂×C₄×C₁₇	C₄×Q₈	1	2	yes	—
140	C₂×C₄×C₁₇	C₂²×C₈	1	4	yes	—
141	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
142	C₂×C₄×C₁₇	C₂²×C₈	1	4	yes	—
143	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
144	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
145	C₂×C₄×C₁₇	C₂×M₁₆	1	4	yes	—
146	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
147	C₂×C₄×C₁₇	#131	1	2	yes	—
148	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
153	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
154	#3622	—	2	4	no	—
155	#3622	—	4	2	no	—
156	#3622	—	4	4	no	—
157	C₄²×Q₈	D₁₇	1	1	yes	characteristic
158	#1984	—	17	2	no	—
159	#1916	—	17	4	no	—
160	#1842	—	17	1	no	—
161	#1831	—	17	2	no	—
162	C₈×C₄⋊C₄	—	17	2	no	—
163	C₄×C₄⋊C₈	—	17	1	no	—
164	C₄×C₄⋊C₈	—	17	2	no	—
165	C₂²×C₁₇	C₂×#117	1	1	yes	characteristic
166	C₂²×C₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
167	C₂²×C₁₇	#520	1	1	yes	characteristic
168	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
169	C₂²×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
170	C₂²×C₁₇	C₂×#131	1	1	yes	characteristic
171	C₂²×C₁₇	#568	1	1	yes	characteristic
172	C₄×C₁₇	—	2	4	no	—
173	C₄×C₁₇	—	2	2	no	—
174	C₄×C₁₇	—	2	2	no	—
175	C₄×C₁₇	—	2	4	no	—
176	C₄×C₁₇	—	2	2	no	—
177	C₄×C₁₇	—	2	4	no	—
178	C₄×C₁₇	—	4	2	no	—
179	C₄×C₁₇	—	4	1	no	—
180	C₄×C₁₇	#431	1	4	yes	—
181	C₄×C₁₇	C₈×Q₈	1	4	yes	—
182	C₄×C₁₇	#554	1	1	yes	characteristic
183	C₄×C₁₇	#556	1	1	yes	characteristic
184	C₄×C₁₇	#557	1	1	yes	characteristic
185	C₄×C₁₇	#559	1	1	yes	characteristic
186	C₂×C₄×Q₈	Dic₁₇	1	1	yes	characteristic
187	C₂×C₄×Q₈	Dic₁₇	1	1	yes	characteristic
188	C₂×C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic
189	C₂×C₄⋊C₈	—	17	1	no	—
190	C₂×C₄⋊C₈	—	17	1	no	—
191	C₂×C₄⋊C₈	—	17	2	no	—
192	C₂×C₄⋊C₈	—	17	2	no	—
193	C₂×C₄⋊C₈	—	17	2	no	—
194	C₂×C₄×C₈	—	17	2	no	—
195	C₂×C₄×C₈	—	17	4	no	—
196	C₄×C₄⋊C₄	Dic₁₇	1	1	yes	characteristic
197	C₄×C₄⋊C₄	Dic₁₇	1	2	yes	—
198	C₄×C₄⋊C₄	Dic₁₇	1	2	yes	—
199	C₄×C₄⋊C₄	Dic₁₇	1	1	yes	characteristic
200	C₄×C₄⋊C₄	C₂×D₁₇	1	2	yes	—
201	C₄×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
202	C₄³	C₂×D₁₇	1	2	yes	—
203	C₄³	C₂×D₁₇	1	1	yes	characteristic
204	#336	—	17	4	no	—
205	#336	—	17	4	no	—
206	#336	—	17	2	no	—
207	#336	—	17	4	no	—
208	C₂×C₁₇	#2355	1	1	yes	characteristic
209	C₂×C₁₇	C₂×#431	1	1	yes	characteristic
210	C₂×C₁₇	#2925	1	1	yes	characteristic
211	C₂×C₁₇	C₂×C₈×Q₈	1	1	yes	characteristic
212	C₂×C₁₇	Q₈×M₁₆	1	1	yes	characteristic
213	C₂×C₁₇	#2988	1	1	yes	characteristic
214	C₂×C₁₇	#2990	1	1	yes	characteristic
215	C₂²×Q₈	C₂×Dic₁₇	1	1	yes	characteristic
216	C₂²×C₈	—	17	2	no	—
217	C₂²×C₈	—	17	2	no	—
218	C₂²×C₈	—	17	4	no	—
219	C₄×Q₈	—	2	4	no	—
220	C₄×Q₈	—	2	2	no	—
221	C₄×Q₈	—	2	2	no	—
222	C₄×Q₈	#3622	1	8	yes	complemented
223	C₂×C₄⋊C₄	C₂×Dic₁₇	1	2	yes	—
224	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂×Dic₁₇	1	2	yes	—
226	C₂×C₄⋊C₄	C₂×Dic₁₇	1	2	yes	—
227	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
229	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
230	C₂×C₄²	C₂×Dic₁₇	1	2	yes	—
231	C₂×C₄²	C₂×Dic₁₇	1	2	yes	—
232	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
233	C₂×C₄²	C₂×Dic₁₇	1	2	yes	—
234	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
235	C₂×C₄²	C₂×Dic₁₇	1	2	yes	—
236	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
237	C₂×C₄²	C₂²×D₁₇	1	2	yes	—
238	C₂×C₄²	C₂²×D₁₇	1	2	yes	—
239	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
240	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
241	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
242	C₄⋊C₈	—	17	4	no	—
243	C₄⋊C₈	—	34	4	no	—
244	C₄⋊C₈	—	34	2	no	—
245	C₄⋊C₈	—	34	4	no	—
246	C₄⋊C₈	—	68	2	no	—
247	C₄×C₈	—	34	4	no	—
248	C₄×C₈	—	68	4	no	—
249	#95	C₂×Dic₁₇	1	2	yes	—
250	#95	C₂×Dic₁₇	1	2	yes	—
251	#95	C₂×Dic₁₇	1	2	yes	—
252	C₁₇	#22821	1	1	yes	characteristic, complemented, Sylow
253	C₂×Q₈	—	2	2	no	—
254	C₂×Q₈	—	2	2	no	—
255	C₂×Q₈	C₂×#3622	1	4	yes	—
256	C₂²×C₄	C₂²×Dic₁₇	1	2	yes	—
257	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
258	C₂²×C₄	C₂²×Dic₁₇	1	2	yes	—
259	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
260	C₂²×C₄	C₂²×Dic₁₇	1	2	yes	—
261	C₂²×C₄	C₂²×Dic₁₇	1	2	yes	—
262	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
263	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
264	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
265	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
266	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
267	C₂×C₈	—	17	4	no	—
268	C₂×C₈	—	34	2	no	—
269	C₂×C₈	—	34	2	no	—
270	C₂×C₈	—	34	2	no	—
271	C₂×C₈	—	34	4	no	—
272	C₂×C₈	—	34	2	no	—
273	C₂×C₈	—	34	4	no	—
274	C₂×C₈	—	34	4	no	—
275	C₂×C₈	—	34	2	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	C₂×#3622	1	8	yes	—
280	C₄⋊C₄	C₂×#3622	1	4	yes	—
281	C₄⋊C₄	#63223	1	4	yes	—
282	C₄²	—	2	2	no	—
283	C₄²	—	2	2	no	—
284	C₄²	—	2	2	no	—
285	C₄²	—	2	1	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	2	1	no	—
288	C₄²	—	2	4	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	2	4	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	4	1	no	—
293	C₄²	—	4	2	no	—
294	C₄²	C₂×#3622	1	8	yes	—
295	C₄²	C₂×#3622	1	4	yes	—
296	C₄²	#63252	1	2	yes	—
297	C₄²	#63252	1	2	yes	—
298	C₄²	Q₈×D₁₇	1	2	yes	—
299	C₄²	#63256	1	2	yes	—
300	C₂³	C₂³×Dic₁₇	1	1	yes	characteristic
301	Q₈	—	2	8	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	C₂²×#3622	1	4	yes	—
321	C₂×C₄	C₂²×#3622	1	2	yes	—
322	C₂×C₄	C₂²×#3622	1	4	yes	—
323	C₂×C₄	C₂²×#3622	1	2	yes	—
324	C₂×C₄	C₂²×#3622	1	2	yes	—
325	C₂×C₄	C₂×#63223	1	4	yes	—
326	C₂×C₄	C₂×#63223	1	2	yes	—
327	C₂×C₄	#10587612	1	2	yes	—
328	C₂×C₄	#10587612	1	2	yes	—
329	C₂×C₄	Q₈×Dic₁₇	1	2	yes	—
330	C₂×C₄	Q₈×Dic₁₇	1	2	yes	—
331	C₂×C₄	#10587634	1	2	yes	—
332	C₂×C₄	C₂×#63252	1	1	yes	characteristic
333	C₂×C₄	C₂×#63252	1	1	yes	characteristic
334	C₂×C₄	C₂×Q₈×D₁₇	1	1	yes	characteristic
335	C₂×C₄	C₂×#63256	1	1	yes	characteristic
336	C₂×C₄	#10587696	1	1	yes	characteristic
337	C₂×C₄	#10587697	1	1	yes	characteristic
338	C₈	—	34	4	no	—
339	C₈	—	68	2	no	—
340	C₈	—	68	4	no	—
341	C₂²	C₂×#10587612	1	1	yes	characteristic
342	C₂²	C₂×Q₈×Dic₁₇	1	1	yes	characteristic
343	C₂²	#11763292	1	1	yes	characteristic
344	C₂²	C₂³×#3622	1	1	yes	characteristic
345	C₂²	C₂²×#63223	1	1	yes	characteristic
346	C₂²	C₂×#10587634	1	1	yes	characteristic
347	C₂²	#11763576	1	1	yes	characteristic
348	C₄	—	2	2	no	—
349	C₄	—	2	4	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	4	no	—
352	C₄	—	2	4	no	—
353	C₄	—	2	2	no	—
354	C₄	—	4	1	no	—
355	C₄	—	4	2	no	—
356	C₄	#11762862	1	4	yes	—
357	C₄	Q₈×#3622	1	4	yes	—
358	C₄	#11763519	1	1	yes	characteristic
359	C₄	#11763532	1	1	yes	characteristic
360	C₄	#11763537	1	1	yes	characteristic
361	C₄	#11763544	1	1	yes	characteristic
362	C₂	#14531741	1	1	yes	characteristic
363	C₂	C₂×#11762862	1	1	yes	characteristic
364	C₂	#14537450	1	1	yes	characteristic
365	C₂	C₂×Q₈×#3622	1	1	yes	characteristic
366	C₂	Q₈×#63223	1	1	yes	characteristic
367	C₂	#14537895	1	1	yes	characteristic
368	C₂	#14537909	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₇
commutator	C₂²×C₁₇	C₂³×C₈
Fitting	C₄²×Q₈×C₁₇	C₂
socle, prime radical	C₂³×C₁₇	C₂³×C₄
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	C₄²×Q₈	D₁₇
hypocenter	C₁₇	#22821
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
35. C₄×Q₈×C₁₇	C₈	semidirect
65. C₄⋊#3622	Q₈	semidirect
222. C₄×Q₈	#3622	semidirect
252. C₁₇	#22821	semidirect

Maximal subgroups

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

subgroup	index
#14529721	2
#14529343	2
#14528936	2
#14528901	2
C₄⋊C₄×#3622	2
C₄×C₄⋊#3622	2
C₄²×Q₈×C₁₇	2
#22821	17