Subgroups — #17053136

Order 4352.

832 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11762940	C₂	1	2	yes	maximal
2	#14529508	C₂	1	4	yes	maximal
3	#14529503	C₂	1	2	yes	maximal
4	#14528936	C₂	1	1	yes	maximal, characteristic
5	#14528936	C₂	1	2	yes	maximal
6	#14528637	C₂	1	2	yes	maximal
7	C₄×C₄⋊#3622	C₂	1	1	yes	maximal, characteristic
8	C₄²×Q₈×C₁₇	C₂	1	1	yes	maximal, characteristic
9	#11762940	—	2	8	no	—
10	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊#3622	C₂²	1	2	yes	—
12	C₂×C₄⋊#3622	C₂²	1	2	yes	—
13	C₂×C₄⋊#3622	C₂²	1	4	yes	—
14	C₂×C₄⋊#3622	C₂²	1	4	yes	—
15	C₂×C₄⋊#3622	C₂²	1	2	yes	—
16	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
17	C₂×#10587474	C₂²	1	4	yes	—
18	C₂×C₄×#3622	C₂²	1	2	yes	—
19	#11762564	C₂²	1	2	yes	—
20	#11762564	C₂²	1	4	yes	—
21	C₂×C₄×Q₈×C₁₇	C₄	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₇	C₄	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₁₇	C₄	1	2	yes	—
25	C₄×C₄⋊C₄×C₁₇	C₄	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₁₇	C₄	1	2	yes	—
27	C₄×C₄⋊C₄×C₁₇	C₄	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
30	C₄³×C₁₇	C₂²	1	1	yes	characteristic
31	C₄³×C₁₇	C₂²	1	2	yes	—
32	C₂²×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
33	C₄×Q₈×C₁₇	—	2	4	no	—
34	C₄×Q₈×C₁₇	—	2	4	no	—
35	C₄×Q₈×C₁₇	D₄	1	4	yes	—
36	C₄×Q₈×C₁₇	Q₈	1	4	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	2	yes	—
41	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×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	1	yes	characteristic
47	C₂×C₄²×C₁₇	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₁₇	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
53	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
56	C₂²×#3622	C₂³	1	2	yes	—
57	C₂²×#3622	C₂³	1	4	yes	—
58	C₂²×#3622	C₂³	1	2	yes	—
59	C₁₇×#95	C₂×C₄	1	2	yes	—
60	C₁₇×#95	C₂×C₄	1	2	yes	—
61	C₁₇×#95	C₂×C₄	1	2	yes	—
62	C₄⋊#3622	—	2	4	no	—
63	C₄⋊#3622	—	2	8	no	—
64	C₄⋊#3622	—	2	2	no	—
65	C₄⋊#3622	—	2	4	no	—
66	C₄⋊#3622	—	4	4	no	—
67	C₄⋊#3622	—	4	2	no	—
68	C₄⋊#3622	Q₈	1	4	yes	complemented
69	#10587474	—	2	8	no	—
70	C₄×#3622	—	2	4	no	—
71	C₂×Q₈×C₁₇	—	2	2	no	—
72	C₂×Q₈×C₁₇	—	2	2	no	—
73	C₂×Q₈×C₁₇	C₄⋊C₄	1	4	yes	—
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	2	yes	—
81	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
85	C₄⋊C₄×C₁₇	—	2	4	no	—
86	C₄⋊C₄×C₁₇	—	2	4	no	—
87	C₄⋊C₄×C₁₇	—	2	2	no	—
88	C₄⋊C₄×C₁₇	C₄⋊C₄	1	8	yes	—
89	C₄⋊C₄×C₁₇	C₄⋊C₄	1	4	yes	—
90	C₄⋊C₄×C₁₇	M₁₆	1	4	yes	—
91	C₄²×C₁₇	—	2	4	no	—
92	C₄²×C₁₇	—	2	2	no	—
93	C₄²×C₁₇	—	2	4	no	—
94	C₄²×C₁₇	—	2	4	no	—
95	C₄²×C₁₇	—	2	2	no	—
96	C₄²×C₁₇	—	2	1	no	—
97	C₄²×C₁₇	—	2	2	no	—
98	C₄²×C₁₇	—	2	1	no	—
99	C₄²×C₁₇	—	2	2	no	—
100	C₄²×C₁₇	—	4	1	no	—
101	C₄²×C₁₇	—	4	2	no	—
102	C₄²×C₁₇	M₁₆	1	4	yes	—
103	C₄²×C₁₇	C₂×D₄	1	2	yes	—
104	C₄²×C₁₇	C₂×D₄	1	4	yes	—
105	C₄²×C₁₇	C₂×Q₈	1	4	yes	—
106	C₄²×C₁₇	C₂×Q₈	1	2	yes	—
107	C₄²×C₁₇	C₂×Q₈	1	2	yes	—
108	C₄²×C₁₇	#41	1	2	yes	—
109	C₂×#3622	—	2	2	no	—
110	C₂×#3622	—	2	2	no	—
111	C₂×#3622	—	2	2	no	—
112	C₂×#3622	—	2	4	no	—
113	C₂×#3622	—	2	2	no	—
114	C₂×#3622	—	2	4	no	—
115	C₂×#3622	—	2	2	no	—
116	C₂×#3622	—	2	4	no	—
117	C₂×#3622	C₂×Q₈	1	4	yes	—
118	#22722	—	17	1	no	maximal, Sylow
119	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
120	Q₈×C₁₇	—	2	8	no	—
121	C₂×C₄×C₁₇	—	2	1	no	—
122	C₂×C₄×C₁₇	—	2	2	no	—
123	C₂×C₄×C₁₇	—	2	1	no	—
124	C₂×C₄×C₁₇	—	2	2	no	—
125	C₂×C₄×C₁₇	—	2	2	no	—
126	C₂×C₄×C₁₇	—	2	2	no	—
127	C₂×C₄×C₁₇	—	2	1	no	—
128	C₂×C₄×C₁₇	—	2	2	no	—
129	C₂×C₄×C₁₇	—	2	1	no	—
130	C₂×C₄×C₁₇	—	2	1	no	—
131	C₂×C₄×C₁₇	—	2	2	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	—	2	1	no	—
137	C₂×C₄×C₁₇	—	2	1	no	—
138	C₂×C₄×C₁₇	—	2	2	no	—
139	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
140	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	4	yes	—
141	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	4	yes	—
142	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×C₄×C₁₇	C₄×Q₈	1	2	yes	—
144	C₂×C₄×C₁₇	C₄×Q₈	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	C₂×M₁₆	1	2	yes	—
148	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
149	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
150	C₂×C₄×C₁₇	#131	1	2	yes	—
151	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
157	#3622	—	2	4	no	—
158	#3622	—	4	2	no	—
159	#3622	—	4	4	no	—
160	C₂×#446	—	17	2	no	—
161	C₄²×Q₈	D₁₇	1	1	yes	characteristic
162	#1940	—	17	4	no	—
163	#1939	—	17	2	no	—
164	#1842	—	17	1	no	—
165	#1842	—	17	2	no	—
166	#1767	—	17	2	no	—
167	C₄×C₄⋊C₈	—	17	1	no	—
168	C₂²×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
169	C₂²×C₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
170	C₂²×C₁₇	#520	1	1	yes	characteristic
171	C₂²×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
172	C₂²×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
173	C₂²×C₁₇	C₂×#131	1	1	yes	characteristic
174	C₂²×C₁₇	#568	1	1	yes	characteristic
175	C₄×C₁₇	—	2	4	no	—
176	C₄×C₁₇	—	2	2	no	—
177	C₄×C₁₇	—	2	4	no	—
178	C₄×C₁₇	—	2	2	no	—
179	C₄×C₁₇	—	2	2	no	—
180	C₄×C₁₇	—	2	4	no	—
181	C₄×C₁₇	—	4	2	no	—
182	C₄×C₁₇	—	4	1	no	—
183	C₄×C₁₇	#423	1	4	yes	—
184	C₄×C₁₇	#446	1	4	yes	complemented
185	C₄×C₁₇	D₄×Q₈	1	1	yes	characteristic
186	C₄×C₁₇	#550	1	1	yes	characteristic
187	C₄×C₁₇	#557	1	1	yes	characteristic
188	C₄×C₁₇	Q₈²	1	1	yes	characteristic
189	C₂×C₄×Q₈	Dic₁₇	1	1	yes	characteristic
190	C₂×C₄×Q₈	Dic₁₇	1	1	yes	characteristic
191	C₂×C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic
192	#446	—	34	8	no	—
193	C₂×C₄⋊C₈	—	17	1	no	—
194	C₂×C₄⋊C₈	—	17	1	no	—
195	C₂×C₄⋊C₈	—	17	2	no	—
196	C₂×C₄⋊C₈	—	17	2	no	—
197	C₂×C₄⋊C₈	—	17	4	no	—
198	C₂×C₄⋊C₈	—	17	4	no	—
199	C₂×C₄⋊C₈	—	17	2	no	—
200	C₂×#97	—	17	4	no	—
201	C₂×C₄×C₈	—	17	2	no	—
202	C₄×C₄⋊C₄	Dic₁₇	1	2	yes	—
203	C₄×C₄⋊C₄	Dic₁₇	1	1	yes	characteristic
204	C₄×C₄⋊C₄	Dic₁₇	1	2	yes	—
205	C₄×C₄⋊C₄	Dic₁₇	1	1	yes	characteristic
206	C₄×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
207	C₄×C₄⋊C₄	C₂×D₁₇	1	2	yes	—
208	C₄³	C₂×D₁₇	1	1	yes	characteristic
209	C₄³	C₂×D₁₇	1	2	yes	—
210	#336	—	17	4	no	—
211	#336	—	17	2	no	—
212	C₂×C₁₇	Q₈×C₄⋊C₄	1	1	yes	characteristic
213	C₂×C₁₇	C₂×#423	1	1	yes	characteristic
214	C₂×C₁₇	#2906	1	1	yes	characteristic
215	C₂×C₁₇	C₂×#446	1	1	yes	characteristic
216	C₂×C₁₇	Q₈×M₁₆	1	1	yes	characteristic
217	C₂×C₁₇	#2989	1	1	yes	characteristic
218	C₂×C₁₇	#2990	1	1	yes	characteristic
219	C₂²×Q₈	C₂×Dic₁₇	1	1	yes	characteristic
220	C₂²×C₈	—	17	2	no	—
221	C₂²×C₈	—	17	2	no	—
222	C₂²×C₈	—	17	4	no	—
223	C₄×Q₈	—	2	4	no	—
224	C₄×Q₈	—	2	4	no	—
225	C₄×Q₈	Dic₃₄	1	4	yes	—
226	C₄×Q₈	D₆₈	1	4	yes	—
227	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂×Dic₁₇	1	2	yes	—
229	C₂×C₄⋊C₄	C₂×Dic₁₇	1	2	yes	—
230	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂×Dic₁₇	1	2	yes	—
232	C₂×C₄⋊C₄	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	C₂×Dic₁₇	1	2	yes	—
238	C₂×C₄²	C₂×Dic₁₇	1	2	yes	—
239	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
240	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
241	C₂×C₄²	C₂²×D₁₇	1	2	yes	—
242	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
244	C₂×C₄²	C₂²×D₁₇	1	2	yes	—
245	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
246	C₄⋊C₈	—	17	4	no	—
247	C₄⋊C₈	—	34	4	no	—
248	C₄⋊C₈	—	34	8	no	—
249	C₄⋊C₈	—	34	2	no	—
250	C₄⋊C₈	—	34	4	no	—
251	C₄⋊C₈	—	68	4	no	—
252	C₄⋊C₈	—	68	2	no	—
253	#97	—	34	8	no	—
254	C₄×C₈	—	34	4	no	—
255	#95	C₂×Dic₁₇	1	2	yes	—
256	#95	C₂×Dic₁₇	1	2	yes	—
257	#95	C₂×Dic₁₇	1	2	yes	—
258	C₁₇	#22722	1	1	yes	characteristic, complemented, Sylow
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	C₄⋊Dic₁₇	1	4	yes	—
262	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
263	C₂²×C₄	C₂²×Dic₁₇	1	2	yes	—
264	C₂²×C₄	C₂²×Dic₁₇	1	2	yes	—
265	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
266	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
267	C₂²×C₄	C₂²×Dic₁₇	1	2	yes	—
268	C₂²×C₄	C₂²×Dic₁₇	1	2	yes	—
269	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
270	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
271	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
272	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
273	C₂×C₈	—	17	4	no	—
274	C₂×C₈	—	34	2	no	—
275	C₂×C₈	—	34	2	no	—
276	C₂×C₈	—	34	2	no	—
277	C₂×C₈	—	34	4	no	—
278	C₂×C₈	—	34	2	no	—
279	C₂×C₈	—	34	4	no	—
280	C₂×C₈	—	34	2	no	—
281	C₂×C₈	—	34	4	no	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	2	4	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	#63223	1	4	yes	—
286	C₄⋊C₄	C₄⋊Dic₁₇	1	8	yes	—
287	C₄⋊C₄	C₄⋊Dic₁₇	1	4	yes	—
288	C₄²	—	2	1	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	2	1	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	4	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	2	4	no	—
295	C₄²	—	2	4	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	4	1	no	—
298	C₄²	—	4	2	no	—
299	C₄²	#63223	1	4	yes	—
300	C₄²	C₂×Dic₃₄	1	4	yes	—
301	C₄²	C₂×Dic₃₄	1	2	yes	—
302	C₄²	C₂×D₆₈	1	2	yes	—
303	C₄²	C₂×D₆₈	1	4	yes	—
304	C₄²	Q₈×D₁₇	1	2	yes	—
305	C₄²	#63256	1	2	yes	—
306	C₂³	C₂³×Dic₁₇	1	1	yes	characteristic
307	Q₈	—	2	8	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	C₂×#63223	1	4	yes	—
327	C₂×C₄	C₂×#63223	1	2	yes	—
328	C₂×C₄	C₂×#63223	1	2	yes	—
329	C₂×C₄	C₂×#63223	1	2	yes	—
330	C₂×C₄	C₂×#63223	1	2	yes	—
331	C₂×C₄	C₂×C₄⋊Dic₁₇	1	2	yes	—
332	C₂×C₄	C₂×C₄⋊Dic₁₇	1	4	yes	—
333	C₂×C₄	C₂×C₄⋊Dic₁₇	1	4	yes	—
334	C₂×C₄	C₂×C₄⋊Dic₁₇	1	2	yes	—
335	C₂×C₄	Q₈×Dic₁₇	1	2	yes	—
336	C₂×C₄	Q₈×Dic₁₇	1	2	yes	—
337	C₂×C₄	#10587634	1	2	yes	—
338	C₂×C₄	C₂²×Dic₃₄	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
340	C₂×C₄	C₂×Q₈×D₁₇	1	1	yes	characteristic
341	C₂×C₄	C₂×#63256	1	1	yes	characteristic
342	C₂×C₄	#10587696	1	1	yes	characteristic
343	C₂×C₄	#10587697	1	1	yes	characteristic
344	C₈	—	34	4	no	—
345	C₈	—	68	2	no	—
346	C₈	—	68	4	no	—
347	C₂²	C₂²×C₄⋊Dic₁₇	1	1	yes	characteristic
348	C₂²	C₂×Q₈×Dic₁₇	1	1	yes	characteristic
349	C₂²	#11763292	1	1	yes	characteristic
350	C₂²	C₂²×#63223	1	1	yes	characteristic
351	C₂²	C₂²×#63223	1	1	yes	characteristic
352	C₂²	C₂×#10587634	1	1	yes	characteristic
353	C₂²	#11763576	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	4	no	—
356	C₄	—	2	2	no	—
357	C₄	—	2	4	no	—
358	C₄	—	2	2	no	—
359	C₄	—	2	4	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	1	no	—
362	C₄	#11762833	1	4	yes	—
363	C₄	#11762940	1	4	yes	complemented
364	C₄	Q₈×D₆₈	1	1	yes	characteristic
365	C₄	#11763481	1	1	yes	characteristic
366	C₄	#11763538	1	1	yes	characteristic
367	C₄	Q₈×Dic₃₄	1	1	yes	characteristic
368	C₂	Q₈×C₄⋊Dic₁₇	1	1	yes	characteristic
369	C₂	C₂×#11762833	1	1	yes	characteristic
370	C₂	#14537352	1	1	yes	characteristic
371	C₂	C₂×#11762940	1	1	yes	characteristic
372	C₂	Q₈×#63223	1	1	yes	characteristic
373	C₂	#14537901	1	1	yes	characteristic
374	C₂	#14537909	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₇
commutator, socle, prime radical	C₂³×C₁₇	C₂³×C₄
Fitting	C₄²×Q₈×C₁₇	C₂
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	C₄²×Q₈	D₁₇
hypocenter	C₁₇	#22722
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
68. C₄⋊#3622	Q₈	semidirect
184. C₄×C₁₇	#446	semidirect
258. C₁₇	#22722	semidirect
363. C₄	#11762940	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11762940	2
#14529508	2
#14529503	2
#14528936	2
#14528637	2
C₄×C₄⋊#3622	2
C₄²×Q₈×C₁₇	2
#22722	17