Subgroups — #16923722

Order 4352.

714 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11762862	C₂	1	1	yes	maximal, characteristic
2	C₄×#10587612	C₂	1	1	yes	maximal, characteristic
3	#14526612	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₇×#431	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587612	C₄	1	2	yes	—
6	#11762862	—	2	1	no	—
7	#11762862	—	2	1	no	—
8	#11762862	C₄	1	2	yes	complemented
9	#11762862	C₂²	1	2	yes	—
10	C₂×C₄⋊#3622	—	2	1	no	—
11	C₂×C₂²⋊#3622	—	2	1	no	—
12	C₂×C₄×#3622	C₄	1	2	yes	complemented
13	C₄×C₄⋊Dic₁₇	—	2	1	no	—
14	C₄×C₄⋊Dic₁₇	—	2	1	no	—
15	C₄×C₂²⋊Dic₁₇	—	2	1	no	—
16	C₄×C₂²⋊Dic₁₇	—	2	1	no	—
17	#11762655	C₂²	1	2	yes	—
18	C₄²×Dic₁₇	C₄	1	2	yes	—
19	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
20	C₁₇×#431	—	2	1	no	—
21	C₁₇×#431	—	2	1	no	—
22	C₁₇×#431	C₄	1	2	yes	complemented
23	C₁₇×#431	C₂²	1	2	yes	—
24	C₂×C₁₇×C₄⋊C₈	—	2	1	no	—
25	C₂×C₁₇×C₂²⋊C₈	—	2	1	no	—
26	C₂×C₄×C₈×C₁₇	C₄	1	2	yes	complemented
27	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₇	—	2	2	no	—
31	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
41	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
43	C₂×C₂²⋊Dic₁₇	—	2	2	no	—
44	#10587612	—	2	4	no	—
45	#10587612	C₈	1	8	yes	complemented
46	C₂×C₄⋊Dic₁₇	—	2	2	no	—
47	C₂×C₄×Dic₁₇	—	2	2	no	—
48	C₂×C₄×Dic₁₇	—	2	2	no	—
49	C₂×C₄×Dic₁₇	C₂×C₄	1	4	yes	—
50	C₂²×#3622	—	2	2	no	—
51	C₁₇×C₄⋊C₈	—	2	2	no	—
52	C₁₇×C₄⋊C₈	—	2	2	no	—
53	C₁₇×C₂²⋊C₈	—	2	2	no	—
54	C₁₇×C₂²⋊C₈	—	2	2	no	—
55	C₄×C₈×C₁₇	—	2	2	no	—
56	C₄×C₈×C₁₇	C₂×C₄	1	4	yes	—
57	#10587502	—	2	2	no	—
58	#10587502	—	2	2	no	—
59	C₂²⋊#3622	—	2	2	no	—
60	C₂²⋊#3622	—	2	2	no	—
61	C₄⋊#3622	—	2	2	no	—
62	C₄⋊#3622	—	2	2	no	—
63	C₄×#3622	—	2	2	no	—
64	C₄×#3622	C₂×C₄	1	4	yes	—
65	C₂⁴×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₇	—	4	2	no	—
67	C₂²×C₄×C₁₇	—	4	2	no	—
68	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
69	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
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	1	yes	characteristic
76	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	C₂×C₈	1	4	yes	—
84	C₂²×C₄×C₁₇	M₁₆	1	4	yes	—
85	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×Dic₁₇	—	2	4	no	—
89	C₂×C₈×C₁₇	—	2	4	no	—
90	C₂×C₈×C₁₇	—	4	4	no	—
91	C₄²×C₁₇	C₄²	1	1	yes	characteristic
92	C₄²×C₁₇	C₄²	1	1	yes	characteristic
93	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
94	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₇	C₂×Q₈	1	1	yes	characteristic
107	C₂²⋊Dic₁₇	—	2	8	no	—
108	C₄⋊Dic₁₇	—	2	8	no	—
109	C₄×Dic₁₇	—	2	4	no	—
110	C₄×Dic₁₇	—	4	4	no	—
111	C₄×Dic₁₇	—	4	4	no	—
112	C₄×Dic₁₇	C₂×C₈	1	8	yes	complemented
113	C₂×#3622	—	2	4	no	—
114	C₂×#3622	—	4	4	no	—
115	#7854	—	17	1	no	maximal, Sylow
116	C₂³×C₁₇	—	4	1	no	—
117	C₂³×C₁₇	—	4	1	no	—
118	C₂³×C₁₇	#95	1	1	yes	characteristic
119	C₂³×C₁₇	#95	1	1	yes	characteristic
120	C₂³×C₁₇	C₂²⋊C₈	1	4	yes	—
121	C₂³×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₇	—	2	2	no	—
123	C₂×C₄×C₁₇	—	2	2	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	2	no	—
128	C₂×C₄×C₁₇	—	4	1	no	—
129	C₂×C₄×C₁₇	—	4	1	no	—
130	C₂×C₄×C₁₇	—	4	1	no	—
131	C₂×C₄×C₁₇	—	4	1	no	—
132	C₂×C₄×C₁₇	—	4	1	no	—
133	C₂×C₄×C₁₇	—	4	1	no	—
134	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
135	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
136	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
137	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
138	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
139	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
140	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
141	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
142	C₂×C₄×C₁₇	#97	1	2	yes	—
143	C₂×C₄×C₁₇	#97	1	2	yes	—
144	C₂×C₄×C₁₇	C₂²⋊C₈	1	4	yes	—
145	C₂×C₄×C₁₇	C₄⋊C₈	1	4	yes	—
146	C₂×C₄×C₁₇	C₄⋊C₈	1	4	yes	—
147	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
154	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
155	C₂×Dic₁₇	—	2	8	no	—
156	C₂×Dic₁₇	—	4	4	no	—
157	C₂×Dic₁₇	—	4	4	no	—
158	C₈×C₁₇	—	4	4	no	—
159	#3622	—	4	4	no	—
160	C₂×#431	—	17	1	no	—
161	C₂×#431	D₁₇	1	1	yes	characteristic
162	C₄×#117	—	17	1	no	—
163	#1274	—	17	4	no	—
164	C₂²×C₁₇	—	2	1	no	—
165	C₂²×C₁₇	—	2	1	no	—
166	C₂²×C₁₇	—	2	1	no	—
167	C₂²×C₁₇	—	2	1	no	—
168	C₂²×C₁₇	—	2	1	no	—
169	C₂²×C₁₇	—	2	1	no	—
170	C₂²×C₁₇	—	4	4	no	—
171	C₂²×C₁₇	#336	1	2	yes	—
172	C₂²×C₁₇	#336	1	2	yes	—
173	C₂²×C₁₇	C₂×#95	1	1	yes	characteristic
174	C₂²×C₁₇	C₂×C₂²⋊C₈	1	2	yes	—
175	C₄×C₁₇	—	2	1	no	—
176	C₄×C₁₇	—	2	1	no	—
177	C₄×C₁₇	—	2	1	no	—
178	C₄×C₁₇	—	2	1	no	—
179	C₄×C₁₇	—	2	1	no	—
180	C₄×C₁₇	—	2	1	no	—
181	C₄×C₁₇	#336	1	2	yes	—
182	C₄×C₁₇	#336	1	2	yes	—
183	C₄×C₁₇	H(3,ℤ/4)	1	2	yes	—
184	C₄×C₁₇	H(3,ℤ/4)	1	2	yes	—
185	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
186	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
187	C₄×C₁₇	C₂×C₄⋊C₈	1	2	yes	—
188	Dic₁₇	—	4	8	no	—
189	C₂×#117	—	17	2	no	—
190	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
191	#431	—	2	1	no	—
192	#431	—	2	1	no	—
193	#431	—	17	2	no	—
194	#431	—	17	2	no	—
195	#431	—	34	1	no	—
196	#431	—	34	1	no	—
197	#431	Dic₁₇	1	2	yes	complemented
198	#431	C₂×D₁₇	1	2	yes	—
199	C₂×C₄⋊C₈	—	2	1	no	—
200	C₂×C₄⋊C₈	—	34	1	no	—
201	C₂×C₂²⋊C₈	—	2	1	no	—
202	C₂×C₂²⋊C₈	—	34	1	no	—
203	C₂×C₄×C₈	—	17	2	no	—
204	C₂×C₄×C₈	Dic₁₇	1	2	yes	complemented
205	C₄×C₄⋊C₄	—	34	1	no	—
206	C₄×C₄⋊C₄	—	34	1	no	—
207	C₄×C₂²⋊C₄	—	34	1	no	—
208	C₄×C₂²⋊C₄	—	34	1	no	—
209	#376	—	17	2	no	—
210	C₄³	—	17	2	no	—
211	C₂×C₁₇	—	2	2	no	—
212	C₂×C₁₇	—	2	2	no	—
213	C₂×C₁₇	—	2	2	no	—
214	C₂×C₁₇	C₂×#336	1	1	yes	characteristic
215	C₂×C₁₇	C₂×H(3,ℤ/4)	1	1	yes	characteristic
216	C₂×C₁₇	C₂×H(3,ℤ/4)	1	1	yes	characteristic
217	C₂³×C₄	C₄×D₁₇	1	1	yes	characteristic
218	C₂³×C₄	D₆₈	1	1	yes	characteristic
219	C₂³×C₄	C₂²⋊D₁₇	1	1	yes	characteristic
220	C₂²×C₈	—	2	2	no	—
221	C₂²×C₈	—	34	2	no	—
222	#117	—	17	8	no	—
223	#117	—	34	4	no	—
224	C₂×C₄⋊C₄	—	34	2	no	—
225	C₂×C₂²⋊C₄	—	34	2	no	—
226	C₂×C₄²	—	17	4	no	—
227	C₂×C₄²	—	34	2	no	—
228	C₂×C₄²	—	34	2	no	—
229	C₂×C₄²	Dic₃₄	1	1	yes	characteristic
230	C₂×C₄²	Dic₃₄	1	1	yes	characteristic
231	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
232	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
233	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
234	C₂×C₄²	D₆₈	1	1	yes	characteristic
235	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
236	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
237	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
238	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
239	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
240	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	2	2	no	—
243	C₄⋊C₈	—	34	2	no	—
244	C₄⋊C₈	—	34	2	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	34	2	no	—
248	C₂²⋊C₈	—	34	2	no	—
249	C₄×C₈	—	2	2	no	—
250	C₄×C₈	—	17	4	no	—
251	C₄×C₈	—	34	2	no	—
252	C₄×C₈	C₂×Dic₁₇	1	4	yes	—
253	#95	—	34	2	no	—
254	#95	—	34	2	no	—
255	C₁₇	#7854	1	1	yes	characteristic, complemented, Sylow
256	C₂⁴	#63227	1	1	yes	characteristic
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	34	4	no	—
260	C₂²×C₄	C₈×D₁₇	1	4	yes	—
261	C₂²×C₄	#63218	1	4	yes	—
262	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
263	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
264	C₂²×C₄	#63225	1	1	yes	characteristic
265	C₂²×C₄	#63225	1	1	yes	characteristic
266	C₂²×C₄	#63225	1	1	yes	characteristic
267	C₂²×C₄	#63225	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
269	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
270	C₂²×C₄	#63227	1	1	yes	characteristic
271	C₂²×C₄	#63227	1	1	yes	characteristic
272	C₂²×C₄	#63227	1	1	yes	characteristic
273	C₂²×C₄	#63227	1	1	yes	characteristic
274	C₂²×C₄	#63227	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
276	C₂²×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	4	4	no	—
282	C₂×C₈	—	34	4	no	—
283	C₂×C₈	—	68	4	no	—
284	C₄⋊C₄	—	34	8	no	—
285	C₂²⋊C₄	—	34	8	no	—
286	C₄²	—	17	8	no	—
287	C₄²	—	34	4	no	—
288	C₄²	—	68	4	no	—
289	C₄²	—	68	4	no	—
290	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
291	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
292	C₄²	#63225	1	1	yes	characteristic
293	C₄²	#63225	1	1	yes	characteristic
294	C₄²	#63225	1	1	yes	characteristic
295	C₄²	#63225	1	1	yes	characteristic
296	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
297	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
298	C₄²	#63227	1	1	yes	characteristic
299	C₄²	#63227	1	1	yes	characteristic
300	C₄²	C₂²⋊Dic₁₇	1	1	yes	characteristic
301	C₄²	C₂²⋊Dic₁₇	1	1	yes	characteristic
302	C₄²	C₂×Dic₃₄	1	1	yes	characteristic
303	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
304	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
305	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
306	C₂³	—	4	1	no	—
307	C₂³	—	4	1	no	—
308	C₂³	#10587491	1	4	yes	—
309	C₂³	#10587502	1	1	yes	characteristic
310	C₂³	#10587502	1	1	yes	characteristic
311	C₂³	C₂×#63227	1	1	yes	characteristic
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	34	8	no	—
325	C₂×C₄	—	68	4	no	—
326	C₂×C₄	—	68	4	no	—
327	C₂×C₄	C₈×Dic₁₇	1	2	yes	—
328	C₂×C₄	C₈×Dic₁₇	1	2	yes	—
329	C₂×C₄	#10587485	1	4	yes	—
330	C₂×C₄	#10587485	1	4	yes	—
331	C₂×C₄	#10587486	1	2	yes	—
332	C₂×C₄	#10587486	1	2	yes	—
333	C₂×C₄	#10587491	1	4	yes	—
334	C₂×C₄	#10587502	1	1	yes	characteristic
335	C₂×C₄	#10587502	1	1	yes	characteristic
336	C₂×C₄	#10587502	1	1	yes	characteristic
337	C₂×C₄	#10587502	1	1	yes	characteristic
338	C₂×C₄	#10587502	1	1	yes	characteristic
339	C₂×C₄	#10587502	1	1	yes	characteristic
340	C₂×C₄	C₂×C₈×D₁₇	1	2	yes	—
341	C₂×C₄	C₂×#63218	1	2	yes	—
342	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
343	C₂×C₄	C₂×#63225	1	1	yes	characteristic
344	C₂×C₄	C₂×#63225	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
346	C₂×C₄	C₂×#63227	1	1	yes	characteristic
347	C₂×C₄	C₂×C₂²⋊Dic₁₇	1	1	yes	characteristic
348	C₈	—	4	4	no	—
349	C₈	—	68	4	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	4	4	no	—
357	C₂²	#11762563	1	2	yes	—
358	C₂²	#11762563	1	2	yes	—
359	C₂²	C₂×#10587502	1	1	yes	characteristic
360	C₂²	C₂×#10587491	1	2	yes	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	68	8	no	—
368	C₄	#11762563	1	2	yes	—
369	C₄	#11762563	1	2	yes	—
370	C₄	#11762565	1	2	yes	—
371	C₄	#11762566	1	2	yes	—
372	C₄	C₂×C₈×Dic₁₇	1	1	yes	characteristic
373	C₄	C₂×#10587486	1	1	yes	characteristic
374	C₄	C₂×#10587485	1	2	yes	—
375	C₂	—	2	2	no	—
376	C₂	—	2	2	no	—
377	C₂	—	2	2	no	—
378	C₂	C₂×#11762563	1	1	yes	characteristic
379	C₂	C₂×#11762565	1	1	yes	characteristic
380	C₂	C₂×#11762566	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₄×Dic₁₇
commutator	C₄×C₁₇	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₂×C₁₇×#431	C₂
socle	C₂²×C₁₇	C₂×#95
prime radical	C₂⁴×C₁₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	C₂×#431	D₁₇
hypocenter	C₁₇	#7854
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #14526612	C₂	semidirect
8. #11762862	C₄	semidirect
12. C₂×C₄×#3622	C₄	semidirect
22. C₁₇×#431	C₄	semidirect
26. C₂×C₄×C₈×C₁₇	C₄	semidirect
45. #10587612	C₈	semidirect
112. C₄×Dic₁₇	C₂×C₈	semidirect
197. #431	Dic₁₇	semidirect
204. C₂×C₄×C₈	Dic₁₇	semidirect
255. C₁₇	#7854	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11762862	2
C₄×#10587612	2
#14526612	2
C₂×C₁₇×#431	2
#7854	17