Subgroups — C₂×#14526687 #16924613

Order 4352.

810 conjugacy classes of subgroups.

The subgroup lattice has 424 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	C₂×#11762833	C₂	1	1	yes	maximal, characteristic
3	#14526687	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₄⋊C₄×C₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#63223	—	2	1	no	—
6	#11762862	—	2	1	no	—
7	#11762862	—	2	1	no	—
8	#11762862	C₄	1	2	yes	complemented
9	#11762862	C₂²	1	2	yes	—
10	#11762833	—	2	1	no	—
11	#11762833	—	2	1	no	—
12	#11762833	C₄	1	2	yes	complemented
13	#11762833	C₂²	1	2	yes	—
14	C₂×C₄⋊#3622	—	2	1	no	—
15	C₂×C₄⋊#3622	C₄	1	2	yes	complemented
16	C₂×C₄⋊#3622	C₄	1	2	yes	complemented
17	C₂×C₂²⋊#3622	—	2	1	no	—
18	C₂×C₄×#3622	—	2	1	no	—
19	C₂²×C₄⋊C₄×C₁₇	—	2	1	no	—
20	C₂²×C₄²×C₁₇	—	2	1	no	—
21	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₁₇	—	2	1	no	—
23	C₄×C₄⋊C₄×C₁₇	—	2	1	no	—
24	C₄×C₄⋊C₄×C₁₇	C₄	1	2	yes	—
25	C₄×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
26	C₂×C₁₇×#95	C₄	1	2	yes	—
27	C₂³×C₄×C₁₇	—	2	2	no	—
28	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₁₇	—	2	8	no	—
32	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
34	C₂×C₄²×C₁₇	—	2	2	no	—
35	C₂×C₄²×C₁₇	—	2	2	no	—
36	C₂×C₄²×C₁₇	—	4	2	no	—
37	C₂×C₄²×C₁₇	—	4	2	no	—
38	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
48	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
49	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
50	C₂×#63223	—	2	2	no	—
51	C₂×#63223	—	2	2	no	—
52	C₂×#63223	—	4	2	no	—
53	C₂×#63223	—	4	2	no	—
54	C₂²×#3622	—	2	2	no	—
55	C₂²×#3622	—	2	2	no	—
56	C₁₇×#95	—	2	2	no	—
57	C₁₇×#95	C₂×C₄	1	4	yes	—
58	C₂²⋊#3622	—	2	2	no	—
59	C₂²⋊#3622	—	2	2	no	—
60	C₄⋊#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	complemented
65	C₄⋊#3622	C₂×C₄	1	4	yes	complemented
66	C₄×#3622	—	2	2	no	—
67	C₄×#3622	—	2	2	no	—
68	C₂⁴×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₇	—	2	4	no	—
70	C₂²×C₄×C₁₇	—	2	8	no	—
71	C₂²×C₄×C₁₇	—	2	4	no	—
72	C₂²×C₄×C₁₇	—	4	2	no	—
73	C₂²×C₄×C₁₇	—	4	4	no	—
74	C₂²×C₄×C₁₇	—	4	4	no	—
75	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
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	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₇	D₈	1	2	yes	—
91	C₂²×C₄×C₁₇	SD₁₆	1	2	yes	—
92	C₂²×C₄×C₁₇	SD₁₆	1	2	yes	—
93	C₂²×C₄×C₁₇	Q₁₆	1	2	yes	—
94	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
97	C₄⋊C₄×C₁₇	—	2	8	no	—
98	C₄⋊C₄×C₁₇	—	2	8	no	—
99	C₄²×C₁₇	—	4	4	no	—
100	C₄²×C₁₇	—	4	2	no	—
101	C₄²×C₁₇	—	4	2	no	—
102	C₄²×C₁₇	C₄²	1	1	yes	characteristic
103	C₄²×C₁₇	C₄²	1	1	yes	characteristic
104	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
108	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₁₇	C₂×Q₈	1	1	yes	characteristic
118	#63223	—	4	4	no	—
119	#63223	—	4	2	no	—
120	#63223	—	4	2	no	—
121	C₂×#3622	—	2	4	no	—
122	C₂×#3622	—	2	4	no	—
123	C₂×#3622	—	4	4	no	—
124	C₂×#3622	—	4	4	no	—
125	C₂×#1303	—	17	1	no	maximal, Sylow
126	C₂³×C₁₇	—	2	2	no	—
127	C₂³×C₁₇	—	2	2	no	—
128	C₂³×C₁₇	#95	1	1	yes	characteristic
129	C₂³×C₁₇	#95	1	1	yes	characteristic
130	C₂³×C₁₇	#102	1	2	yes	—
131	C₂³×C₁₇	#103	1	2	yes	—
132	C₂³×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₇	—	2	2	no	—
134	C₂×C₄×C₁₇	—	2	2	no	—
135	C₂×C₄×C₁₇	—	2	2	no	—
136	C₂×C₄×C₁₇	—	2	2	no	—
137	C₂×C₄×C₁₇	—	2	2	no	—
138	C₂×C₄×C₁₇	—	2	2	no	—
139	C₂×C₄×C₁₇	—	2	2	no	—
140	C₂×C₄×C₁₇	—	2	8	no	—
141	C₂×C₄×C₁₇	—	4	1	no	—
142	C₂×C₄×C₁₇	—	4	1	no	—
143	C₂×C₄×C₁₇	—	4	1	no	—
144	C₂×C₄×C₁₇	—	4	1	no	—
145	C₂×C₄×C₁₇	—	4	16	no	—
146	C₂×C₄×C₁₇	—	4	4	no	—
147	C₂×C₄×C₁₇	—	4	4	no	—
148	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
149	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
150	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
151	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
152	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
153	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
154	C₂×C₄×C₁₇	#102	1	2	yes	—
155	C₂×C₄×C₁₇	#102	1	2	yes	—
156	C₂×C₄×C₁₇	#102	1	2	yes	—
157	C₂×C₄×C₁₇	#103	1	2	yes	—
158	C₂×C₄×C₁₇	#103	1	2	yes	—
159	C₂×C₄×C₁₇	#103	1	2	yes	—
160	C₂×C₄×C₁₇	#104	1	4	yes	—
161	C₂×C₄×C₁₇	#106	1	2	yes	—
162	C₂×C₄×C₁₇	#106	1	2	yes	—
163	C₂×C₄×C₁₇	#107	1	2	yes	—
164	C₂×C₄×C₁₇	#107	1	2	yes	—
165	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
173	C₂×C₄×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
174	C₂×C₄×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
175	#3622	—	4	4	no	—
176	#3622	—	4	4	no	—
177	C₂×#431	—	17	1	no	—
178	C₂×#423	—	17	1	no	—
179	C₂×C₄×C₄⋊C₄	D₁₇	1	1	yes	characteristic
180	#1303	—	17	4	no	—
181	C₂²×C₁₇	—	2	4	no	—
182	C₂²×C₁₇	—	2	4	no	—
183	C₂²×C₁₇	—	2	1	no	—
184	C₂²×C₁₇	—	2	1	no	—
185	C₂²×C₁₇	—	2	1	no	—
186	C₂²×C₁₇	—	2	1	no	—
187	C₂²×C₁₇	#339	1	2	yes	—
188	C₂²×C₁₇	#340	1	2	yes	—
189	C₂²×C₁₇	#340	1	2	yes	—
190	C₂²×C₁₇	#344	1	2	yes	—
191	C₂²×C₁₇	C₂×#95	1	1	yes	characteristic
192	C₂²×C₁₇	C₂×#102	1	1	yes	characteristic
193	C₂²×C₁₇	C₂×#103	1	1	yes	characteristic
194	C₄×C₁₇	—	2	1	no	—
195	C₄×C₁₇	—	2	1	no	—
196	C₄×C₁₇	—	2	1	no	—
197	C₄×C₁₇	—	2	1	no	—
198	C₄×C₁₇	—	2	1	no	—
199	C₄×C₁₇	—	2	1	no	—
200	C₄×C₁₇	—	4	8	no	—
201	C₄×C₁₇	#339	1	2	yes	—
202	C₄×C₁₇	#340	1	2	yes	—
203	C₄×C₁₇	#340	1	2	yes	—
204	C₄×C₁₇	C₂×#102	1	1	yes	characteristic
205	C₄×C₁₇	C₂×#103	1	1	yes	characteristic
206	C₄×C₁₇	C₂×#104	1	2	yes	—
207	C₄×C₁₇	C₂×#106	1	1	yes	characteristic
208	C₄×C₁₇	C₂×#107	1	1	yes	characteristic
209	C₂²×M₁₆	—	34	1	no	—
210	C₂²×C₄⋊C₄	—	2	1	no	—
211	C₂²×C₄²	—	2	1	no	—
212	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
213	#431	—	17	2	no	—
214	#431	—	17	2	no	—
215	#431	—	34	1	no	—
216	#431	—	34	1	no	—
217	#423	—	17	2	no	—
218	#423	—	17	2	no	—
219	#423	—	34	1	no	—
220	#423	—	34	1	no	—
221	C₂×C₄⋊C₈	—	17	2	no	—
222	C₂×C₄⋊C₈	—	17	2	no	—
223	C₂×C₄⋊C₈	—	34	1	no	—
224	C₂×C₂²⋊C₈	—	34	1	no	—
225	C₂×C₄×C₈	—	34	1	no	—
226	C₄×C₄⋊C₄	—	2	1	no	—
227	C₄×C₄⋊C₄	—	2	1	no	—
228	C₄×C₄⋊C₄	Dic₁₇	1	2	yes	—
229	C₄×C₄⋊C₄	C₂×D₁₇	1	2	yes	—
230	C₂×#95	Dic₁₇	1	2	yes	—
231	C₂×C₁₇	—	2	1	no	—
232	C₂×C₁₇	—	2	2	no	—
233	C₂×C₁₇	—	2	1	no	—
234	C₂×C₁₇	#1303	1	4	yes	complemented
235	C₂×C₁₇	C₂×#339	1	1	yes	characteristic
236	C₂×C₁₇	C₂×#340	1	1	yes	characteristic
237	C₂×C₁₇	C₂×#344	1	1	yes	characteristic
238	C₂³×C₄	—	2	2	no	—
239	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
240	C₂³×C₄	C₂²⋊D₁₇	1	1	yes	characteristic
241	C₂³×C₄	C₂²⋊D₁₇	1	1	yes	characteristic
242	C₂×M₁₆	—	34	2	no	—
243	C₂×M₁₆	—	34	2	no	—
244	C₂×M₁₆	—	68	2	no	—
245	C₂×M₁₆	—	68	2	no	—
246	C₂²×C₈	—	34	2	no	—
247	C₂²×C₈	—	34	2	no	—
248	C₂×C₄⋊C₄	—	2	8	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	4	2	no	—
254	C₂×C₄²	—	4	2	no	—
255	C₂×C₄²	Dic₃₄	1	1	yes	characteristic
256	C₂×C₄²	Dic₃₄	1	1	yes	characteristic
257	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
258	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
259	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
260	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
261	C₂×C₄²	D₆₈	1	1	yes	characteristic
262	C₂×C₄²	D₆₈	1	1	yes	characteristic
263	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
264	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
265	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
266	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
267	C₄⋊C₈	—	17	4	no	—
268	C₄⋊C₈	—	17	4	no	—
269	C₄⋊C₈	—	34	2	no	—
270	C₄⋊C₈	—	34	2	no	—
271	C₄⋊C₈	—	34	2	no	—
272	C₄⋊C₈	—	34	2	no	—
273	C₂²⋊C₈	—	34	2	no	—
274	C₂²⋊C₈	—	34	2	no	—
275	C₄×C₈	—	34	2	no	—
276	C₄×C₈	—	34	2	no	—
277	#95	—	2	2	no	—
278	#95	C₂×Dic₁₇	1	4	yes	—
279	C₁₇	C₂×#1303	1	1	yes	characteristic, complemented, Sylow
280	C₂⁴	C₂²⋊Dic₁₇	1	1	yes	characteristic
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	8	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	4	no	—
286	C₂²×C₄	—	4	4	no	—
287	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
288	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
289	C₂²×C₄	#63225	1	1	yes	characteristic
290	C₂²×C₄	#63225	1	1	yes	characteristic
291	C₂²×C₄	#63225	1	1	yes	characteristic
292	C₂²×C₄	#63225	1	1	yes	characteristic
293	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
294	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
295	C₂²×C₄	#63227	1	1	yes	characteristic
296	C₂²×C₄	#63227	1	1	yes	characteristic
297	C₂²×C₄	#63227	1	1	yes	characteristic
298	C₂²×C₄	#63227	1	1	yes	characteristic
299	C₂²×C₄	#63228	1	2	yes	—
300	C₂²×C₄	#63229	1	2	yes	—
301	C₂²×C₄	#63230	1	2	yes	—
302	C₂²×C₄	#63231	1	2	yes	—
303	C₂²×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
304	C₂²×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
305	C₂²×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
306	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
309	M₁₆	—	68	4	no	—
310	M₁₆	—	68	2	no	—
311	M₁₆	—	68	2	no	—
312	C₂×C₈	—	34	4	no	—
313	C₂×C₈	—	34	4	no	—
314	C₂×C₈	—	68	4	no	—
315	C₂×C₈	—	68	4	no	—
316	C₄⋊C₄	—	2	8	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄²	—	4	4	no	—
319	C₄²	—	4	2	no	—
320	C₄²	—	4	2	no	—
321	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
322	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
323	C₄²	#63225	1	1	yes	characteristic
324	C₄²	#63225	1	1	yes	characteristic
325	C₄²	#63225	1	1	yes	characteristic
326	C₄²	#63225	1	1	yes	characteristic
327	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
328	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
329	C₄²	#63227	1	1	yes	characteristic
330	C₄²	#63227	1	1	yes	characteristic
331	C₄²	#63227	1	1	yes	characteristic
332	C₄²	#63227	1	1	yes	characteristic
333	C₄²	C₂×Dic₃₄	1	1	yes	characteristic
334	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
335	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
336	C₄²	C₂×D₆₈	1	1	yes	characteristic
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	#10587502	1	1	yes	characteristic
340	C₂³	#10587502	1	1	yes	characteristic
341	C₂³	#10587503	1	2	yes	—
342	C₂³	#10587506	1	2	yes	—
343	C₂³	C₂×C₂²⋊Dic₁₇	1	1	yes	characteristic
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	16	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	#10587476	1	4	yes	—
360	C₂×C₄	#10587478	1	2	yes	—
361	C₂×C₄	#10587478	1	2	yes	—
362	C₂×C₄	#10587479	1	2	yes	—
363	C₂×C₄	#10587479	1	2	yes	—
364	C₂×C₄	#10587480	1	2	yes	—
365	C₂×C₄	#10587480	1	2	yes	—
366	C₂×C₄	#10587481	1	2	yes	—
367	C₂×C₄	#10587481	1	2	yes	—
368	C₂×C₄	#10587502	1	1	yes	characteristic
369	C₂×C₄	#10587502	1	1	yes	characteristic
370	C₂×C₄	#10587502	1	1	yes	characteristic
371	C₂×C₄	#10587502	1	1	yes	characteristic
372	C₂×C₄	#10587502	1	1	yes	characteristic
373	C₂×C₄	#10587502	1	1	yes	characteristic
374	C₂×C₄	#10587503	1	2	yes	—
375	C₂×C₄	#10587506	1	2	yes	—
376	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
377	C₂×C₄	C₂×#63225	1	1	yes	characteristic
378	C₂×C₄	C₂×#63225	1	1	yes	characteristic
379	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
380	C₂×C₄	C₂×#63227	1	1	yes	characteristic
381	C₂×C₄	C₂×#63227	1	1	yes	characteristic
382	C₂×C₄	C₂×#63228	1	1	yes	characteristic
383	C₂×C₄	C₂×#63229	1	1	yes	characteristic
384	C₂×C₄	C₂×#63230	1	1	yes	characteristic
385	C₂×C₄	C₂×#63231	1	1	yes	characteristic
386	C₈	—	68	4	no	—
387	C₈	—	68	4	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	#11762569	1	2	yes	—
395	C₂²	#11762571	1	2	yes	—
396	C₂²	#11762571	1	2	yes	—
397	C₂²	#11762579	1	2	yes	—
398	C₂²	C₂×#10587502	1	1	yes	characteristic
399	C₂²	C₂×#10587503	1	1	yes	characteristic
400	C₂²	C₂×#10587506	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	4	8	no	—
408	C₄	#11762569	1	2	yes	—
409	C₄	#11762571	1	2	yes	—
410	C₄	#11762571	1	2	yes	—
411	C₄	C₂×#10587480	1	1	yes	characteristic
412	C₄	C₂×#10587481	1	1	yes	characteristic
413	C₄	C₂×#10587476	1	2	yes	—
414	C₄	C₂×#10587479	1	1	yes	characteristic
415	C₄	C₂×#10587478	1	1	yes	characteristic
416	C₂	—	2	1	no	—
417	C₂	—	2	1	no	—
418	C₂	—	2	2	no	—
419	C₂	#14526687	1	4	yes	direct product factor
420	C₂	C₂×#11762569	1	1	yes	characteristic
421	C₂	C₂×#11762571	1	1	yes	characteristic
422	C₂	C₂×#11762579	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#63227
commutator	C₂×C₄×C₁₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₂×C₄×C₄⋊C₄×C₁₇	C₂
socle	C₂³×C₁₇	#95
prime radical	C₂⁴×C₁₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₁₇
hypocenter	C₁₇	C₂×#1303
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #14526687	C₂	direct (N × H)
8. #11762862	C₄	semidirect
12. #11762833	C₄	semidirect
15. C₂×C₄⋊#3622	C₄	semidirect
16. C₂×C₄⋊#3622	C₄	semidirect
64. C₄⋊#3622	C₂×C₄	semidirect
65. C₄⋊#3622	C₂×C₄	semidirect
234. C₂×C₁₇	#1303	semidirect
279. C₁₇	C₂×#1303	semidirect
419. C₂	#14526687	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×#11762862	2
C₂×#11762833	2
#14526687	2
C₂×C₄×C₄⋊C₄×C₁₇	2
C₂×#1303	17

Subgroups — C2×#14526687 #16924613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14526687 #16924613