Subgroups — C₂×#14543856 #17960538

Order 4352.

630 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763819	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10587533	C₂	1	1	yes	maximal, characteristic
3	#14543856	C₂	1	4	yes	maximal, direct product factor
4	C₂×M₃₂×D₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587677	—	2	1	no	—
6	C₂²×C₄⋊#595	—	2	1	no	—
7	#11763819	—	2	1	no	—
8	#11763819	—	2	1	no	—
9	#11763819	C₄	1	2	yes	complemented
10	#11763819	C₂²	1	2	yes	—
11	C₂×#10587534	C₄	1	2	yes	complemented
12	C₂×#10587533	—	2	1	no	—
13	C₂×#10587533	—	2	1	no	—
14	C₂×#10587533	—	2	1	no	—
15	C₂×#10587533	—	2	1	no	—
16	C₂×#10587533	C₄	1	2	yes	complemented
17	C₂×#10587533	C₄	1	2	yes	complemented
18	C₂×#10587533	C₂²	1	2	yes	—
19	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
20	C₂×#10587483	C₄	1	1	yes	characteristic, complemented
21	C₂×#10587469	—	2	1	no	—
22	M₃₂×D₁₇	—	2	1	no	—
23	M₃₂×D₁₇	—	2	1	no	—
24	M₃₂×D₁₇	C₄	1	2	yes	complemented
25	M₃₂×D₁₇	C₂²	1	2	yes	—
26	C₂×C₁₆×D₁₇	—	2	1	no	—
27	C₂×C₁₇×M₃₂	C₄	1	1	yes	characteristic, complemented
28	C₂³×#595	—	4	1	no	—
29	C₂²×C₄×D₁₇	D₄	1	1	yes	characteristic
30	C₂×C₂²⋊#595	—	4	1	no	—
31	#10587677	—	2	2	no	—
32	#10587677	—	2	2	no	—
33	#10587677	—	4	1	no	—
34	#10587677	—	4	1	no	—
35	C₂×C₄⋊#595	—	2	2	no	—
36	C₂×C₄⋊#595	—	2	2	no	—
37	C₂×C₄⋊#595	—	2	2	no	—
38	C₂×C₄⋊#595	—	2	2	no	—
39	C₂×C₄⋊#595	—	4	1	no	—
40	C₂×C₄⋊#595	—	4	1	no	—
41	C₂×C₄⋊#595	—	4	1	no	—
42	C₂×C₄×#595	—	4	1	no	—
43	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×#3622	Q₈	1	1	yes	characteristic
45	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
51	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
52	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
53	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
54	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
55	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
56	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
57	#10587534	—	2	2	no	—
58	#10587534	C₂×C₄	1	4	yes	complemented
59	#10587533	—	2	2	no	—
60	#10587533	—	2	2	no	—
61	#10587533	—	2	2	no	—
62	#10587533	—	2	2	no	—
63	#10587533	—	2	2	no	—
64	#10587533	C₂×C₄	1	4	yes	complemented
65	C₁₇×M₃₂	—	2	1	no	—
66	C₁₇×M₃₂	C₂×C₄	1	2	yes	complemented
67	C₂×C₁₆×C₁₇	—	2	1	no	—
68	#10587483	—	2	1	no	—
69	#10587483	C₂×C₄	1	2	yes	complemented
70	C₂×#63214	—	2	1	no	—
71	#10587469	—	2	2	no	—
72	#10587469	—	2	2	no	—
73	C₁₆×D₁₇	—	2	2	no	—
74	C₁₆×D₁₇	—	2	2	no	—
75	C₂³×D₁₇	D₈	1	1	yes	characteristic
76	C₂²×#595	—	4	2	no	—
77	C₂²×#595	—	4	2	no	—
78	C₂²×#595	—	4	2	no	—
79	C₂²×#595	—	4	2	no	—
80	C₂²×#595	—	8	4	no	—
81	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₁₇	Q₁₆	1	1	yes	characteristic
83	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₁₇	D₈	1	1	yes	characteristic
89	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
90	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
91	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
92	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
93	C₂×C₄×D₁₇	Q₁₆	1	1	yes	characteristic
94	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
95	C₂²⋊#595	—	4	2	no	—
96	C₂²⋊#595	—	4	2	no	—
97	C₄⋊#595	—	2	4	no	—
98	C₄⋊#595	—	2	4	no	—
99	C₄⋊#595	—	4	2	no	—
100	C₄⋊#595	—	4	2	no	—
101	C₄⋊#595	—	4	2	no	—
102	C₄⋊#595	—	4	2	no	—
103	C₄×#595	—	4	2	no	—
104	C₄×#595	—	4	2	no	—
105	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
106	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
107	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
111	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
112	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
113	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
114	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
115	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
116	C₂×#3622	C₂×Q₈	1	1	yes	characteristic
117	C₈×D₁₇	C₄²	1	1	yes	characteristic
118	C₈×D₁₇	C₄²	1	1	yes	characteristic
119	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
120	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
121	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
122	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
123	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
124	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
125	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
126	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
127	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
128	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
129	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
130	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
131	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
132	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
133	C₁₆×C₁₇	—	2	2	no	—
134	#63214	—	2	2	no	—
135	C₂×#1386	—	17	1	no	maximal, Sylow
136	C₂³×C₁₇	#107	1	1	yes	characteristic
137	C₂²×D₁₇	—	2	4	no	—
138	C₂²×D₁₇	#102	1	1	yes	characteristic
139	C₂²×D₁₇	#102	1	1	yes	characteristic
140	C₂²×D₁₇	#102	1	1	yes	characteristic
141	C₂²×D₁₇	#102	1	1	yes	characteristic
142	C₂²×D₁₇	#107	1	1	yes	characteristic
143	C₂²×D₁₇	C₂×D₈	1	1	yes	characteristic
144	C₂×#595	—	4	4	no	—
145	C₂×#595	—	4	4	no	—
146	C₂×#595	—	8	4	no	—
147	C₂×#595	—	8	4	no	—
148	C₂×#595	—	8	4	no	—
149	C₂×#595	—	8	4	no	—
150	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
151	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
152	C₂×C₄×C₁₇	#106	1	1	yes	characteristic
153	C₂×C₄×C₁₇	#106	1	1	yes	characteristic
154	C₂×C₄×C₁₇	#107	1	1	yes	characteristic
155	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×Dic₁₇	#103	1	1	yes	characteristic
157	C₂×Dic₁₇	#103	1	1	yes	characteristic
158	C₂×Dic₁₇	#103	1	1	yes	characteristic
159	C₂×Dic₁₇	#103	1	1	yes	characteristic
160	C₂×Dic₁₇	#107	1	1	yes	characteristic
161	C₂×Dic₁₇	C₂×Q₁₆	1	1	yes	characteristic
162	C₄×D₁₇	#95	1	1	yes	characteristic
163	C₄×D₁₇	#95	1	1	yes	characteristic
164	C₄×D₁₇	#102	1	1	yes	characteristic
165	C₄×D₁₇	#102	1	1	yes	characteristic
166	C₄×D₁₇	#102	1	1	yes	characteristic
167	C₄×D₁₇	#102	1	1	yes	characteristic
168	C₄×D₁₇	#103	1	1	yes	characteristic
169	C₄×D₁₇	#103	1	1	yes	characteristic
170	C₄×D₁₇	#103	1	1	yes	characteristic
171	C₄×D₁₇	#103	1	1	yes	characteristic
172	C₄×D₁₇	#106	1	1	yes	characteristic
173	C₄×D₁₇	#106	1	1	yes	characteristic
174	C₄×D₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₄×D₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₄×D₁₇	C₂×SD₁₆	1	1	yes	characteristic
177	C₄×D₁₇	C₂×SD₁₆	1	1	yes	characteristic
178	C₈×C₁₇	#95	1	1	yes	characteristic
179	C₈×C₁₇	#95	1	1	yes	characteristic
180	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
181	C₈×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	#3622	#95	1	1	yes	characteristic
183	#3622	#95	1	1	yes	characteristic
184	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
185	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂²×M₃₂	—	17	1	no	—
187	C₂×#427	—	17	1	no	—
188	C₂²×#106	—	17	1	no	—
189	#1386	—	17	4	no	—
190	C₂²×C₁₇	—	2	2	no	—
191	C₂²×C₁₇	#340	1	1	yes	characteristic
192	C₂²×C₁₇	#340	1	1	yes	characteristic
193	C₂²×C₁₇	C₂×#107	1	1	yes	characteristic
194	C₂×D₁₇	—	2	2	no	—
195	C₂×D₁₇	—	2	2	no	—
196	C₂×D₁₇	—	2	2	no	—
197	C₂×D₁₇	—	2	2	no	—
198	C₂×D₁₇	—	2	2	no	—
199	C₂×D₁₇	#340	1	1	yes	characteristic
200	C₂×D₁₇	#340	1	1	yes	characteristic
201	C₂×D₁₇	#360	1	4	yes	—
202	C₂×D₁₇	C₂×#102	1	1	yes	characteristic
203	C₂×D₁₇	C₂×#102	1	1	yes	characteristic
204	#595	—	8	4	no	—
205	#595	—	8	4	no	—
206	C₄×C₁₇	#340	1	1	yes	characteristic
207	C₄×C₁₇	#340	1	1	yes	characteristic
208	C₄×C₁₇	C₂×#95	1	1	yes	characteristic
209	C₄×C₁₇	C₂×#106	1	1	yes	characteristic
210	Dic₁₇	#340	1	1	yes	characteristic
211	Dic₁₇	#340	1	1	yes	characteristic
212	Dic₁₇	C₂×#103	1	1	yes	characteristic
213	Dic₁₇	C₂×#103	1	1	yes	characteristic
214	C₂³×C₈	—	17	1	no	—
215	C₂×#117	—	34	1	no	—
216	C₂²×C₄⋊C₄	—	34	1	no	—
217	C₂×M₃₂	—	17	1	no	—
218	C₂×M₃₂	—	17	2	no	—
219	C₂×M₃₂	—	17	2	no	—
220	C₂×M₃₂	—	34	1	no	—
221	C₂×M₃₂	—	34	1	no	—
222	C₂×M₃₂	—	34	1	no	—
223	C₂×M₃₂	#595	1	1	yes	characteristic, complemented
224	C₂²×C₁₆	—	34	1	no	—
225	#427	—	17	2	no	—
226	#427	—	17	2	no	—
227	#427	—	34	1	no	—
228	#427	—	34	1	no	—
229	C₂×#107	—	17	2	no	—
230	C₂×#106	—	17	2	no	—
231	C₂×#106	—	17	2	no	—
232	C₂×#106	—	17	2	no	—
233	C₂×#106	—	34	1	no	—
234	C₂×#106	—	34	1	no	—
235	C₂×#106	—	34	1	no	—
236	C₂×#106	—	34	1	no	—
237	C₂×C₁₇	—	2	1	no	—
238	C₂×C₁₇	—	2	1	no	—
239	C₂×C₁₇	#1386	1	2	yes	complemented
240	C₂×C₁₇	C₂×#340	1	1	yes	characteristic
241	D₁₇	—	2	1	no	—
242	D₁₇	—	2	1	no	—
243	D₁₇	#1386	1	2	yes	complemented
244	D₁₇	C₂×#360	1	2	yes	—
245	C₂³×C₄	—	17	1	no	—
246	C₂³×C₄	—	68	1	no	—
247	C₂²×C₈	—	17	1	no	—
248	C₂²×C₈	—	17	1	no	—
249	C₂²×C₈	—	17	1	no	—
250	C₂²×C₈	—	17	1	no	—
251	C₂²×C₈	—	17	1	no	—
252	C₂²×C₈	—	17	1	no	—
253	C₂²×C₈	—	17	1	no	—
254	C₂²×C₈	—	17	1	no	—
255	C₂²×C₈	—	17	1	no	—
256	C₂²×C₈	—	17	1	no	—
257	C₂²×C₈	—	17	1	no	—
258	C₂²×C₈	—	17	1	no	—
259	C₂²×C₈	—	17	1	no	—
260	C₂²×C₈	C₂×#595	1	1	yes	characteristic
261	#117	—	34	2	no	—
262	#117	—	34	2	no	—
263	#117	—	68	1	no	—
264	#117	—	68	1	no	—
265	C₂×C₄⋊C₄	—	34	2	no	—
266	C₂×C₄⋊C₄	—	34	2	no	—
267	C₂×C₄⋊C₄	—	34	2	no	—
268	C₂×C₄⋊C₄	—	34	2	no	—
269	C₂×C₄⋊C₄	—	68	1	no	—
270	C₂×C₄⋊C₄	—	68	1	no	—
271	C₂×C₄⋊C₄	—	68	1	no	—
272	C₂×C₂²⋊C₄	—	68	1	no	—
273	C₂×C₄²	—	68	1	no	—
274	M₃₂	—	2	1	no	—
275	M₃₂	—	17	2	no	—
276	M₃₂	—	34	2	no	—
277	M₃₂	—	34	2	no	—
278	M₃₂	—	34	1	no	—
279	M₃₂	C₂×#595	1	2	yes	complemented
280	C₂×C₁₆	—	2	1	no	—
281	C₂×C₁₆	—	34	2	no	—
282	C₂×C₁₆	—	34	2	no	—
283	C₂×C₁₆	—	34	1	no	—
284	#107	—	17	4	no	—
285	#107	—	34	2	no	—
286	#106	—	17	4	no	—
287	#106	—	34	2	no	—
288	#106	—	34	2	no	—
289	#106	—	34	2	no	—
290	#106	—	34	2	no	—
291	#106	—	34	2	no	—
292	C₁₇	C₂×#1386	1	1	yes	characteristic, complemented, Sylow
293	C₂⁴	—	17	1	no	—
294	C₂²×C₄	—	17	1	no	—
295	C₂²×C₄	—	17	1	no	—
296	C₂²×C₄	—	17	1	no	—
297	C₂²×C₄	—	17	1	no	—
298	C₂²×C₄	—	17	1	no	—
299	C₂²×C₄	—	17	1	no	—
300	C₂²×C₄	—	17	1	no	—
301	C₂²×C₄	—	17	1	no	—
302	C₂²×C₄	—	17	1	no	—
303	C₂²×C₄	—	17	1	no	—
304	C₂²×C₄	—	17	1	no	—
305	C₂²×C₄	—	17	1	no	—
306	C₂²×C₄	—	17	1	no	—
307	C₂²×C₄	—	68	2	no	—
308	C₂²×C₄	—	68	2	no	—
309	C₂²×C₄	—	68	2	no	—
310	C₂²×C₄	—	68	2	no	—
311	C₂²×C₄	—	136	4	no	—
312	C₂²×C₄	C₄⋊#595	1	1	yes	characteristic
313	C₂×C₈	—	17	1	no	—
314	C₂×C₈	—	17	1	no	—
315	C₂×C₈	—	17	1	no	—
316	C₂×C₈	—	17	1	no	—
317	C₂×C₈	—	17	1	no	—
318	C₂×C₈	—	17	1	no	—
319	C₂×C₈	—	17	1	no	—
320	C₂×C₈	—	17	1	no	—
321	C₂×C₈	—	17	1	no	—
322	C₂×C₈	—	17	1	no	—
323	C₂×C₈	—	17	1	no	—
324	C₂×C₈	—	17	1	no	—
325	C₂×C₈	—	17	1	no	—
326	C₂×C₈	—	17	1	no	—
327	C₂×C₈	—	17	1	no	—
328	C₂×C₈	—	17	1	no	—
329	C₂×C₈	—	17	1	no	—
330	C₂×C₈	—	17	1	no	—
331	C₂×C₈	—	17	1	no	—
332	C₂×C₈	—	17	1	no	—
333	C₂×C₈	—	17	1	no	—
334	C₂×C₈	—	17	1	no	—
335	C₂×C₈	C₄×#595	1	1	yes	characteristic
336	C₂×C₈	C₄×#595	1	1	yes	characteristic
337	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
338	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
339	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
340	C₂×C₈	C₂²×#595	1	1	yes	characteristic
341	C₄⋊C₄	—	34	4	no	—
342	C₄⋊C₄	—	34	4	no	—
343	C₄⋊C₄	—	68	2	no	—
344	C₄⋊C₄	—	68	2	no	—
345	C₄⋊C₄	—	68	2	no	—
346	C₄⋊C₄	—	68	2	no	—
347	C₂²⋊C₄	—	68	2	no	—
348	C₂²⋊C₄	—	68	2	no	—
349	C₄²	—	68	2	no	—
350	C₄²	—	68	2	no	—
351	C₁₆	—	2	2	no	—
352	C₁₆	—	34	2	no	—
353	C₂³	—	17	1	no	—
354	C₂³	—	17	1	no	—
355	C₂³	—	17	1	no	—
356	C₂³	—	17	1	no	—
357	C₂³	—	17	1	no	—
358	C₂³	—	17	1	no	—
359	C₂³	—	34	4	no	—
360	C₂³	#10587534	1	1	yes	characteristic
361	C₂×C₄	—	17	1	no	—
362	C₂×C₄	—	17	1	no	—
363	C₂×C₄	—	17	1	no	—
364	C₂×C₄	—	17	1	no	—
365	C₂×C₄	—	17	1	no	—
366	C₂×C₄	—	17	1	no	—
367	C₂×C₄	—	17	1	no	—
368	C₂×C₄	—	17	1	no	—
369	C₂×C₄	—	17	1	no	—
370	C₂×C₄	—	17	1	no	—
371	C₂×C₄	—	17	1	no	—
372	C₂×C₄	—	17	1	no	—
373	C₂×C₄	—	17	1	no	—
374	C₂×C₄	—	17	1	no	—
375	C₂×C₄	—	17	1	no	—
376	C₂×C₄	—	17	1	no	—
377	C₂×C₄	—	17	1	no	—
378	C₂×C₄	—	17	1	no	—
379	C₂×C₄	—	17	1	no	—
380	C₂×C₄	—	17	1	no	—
381	C₂×C₄	—	17	1	no	—
382	C₂×C₄	—	17	1	no	—
383	C₂×C₄	—	68	4	no	—
384	C₂×C₄	—	68	4	no	—
385	C₂×C₄	—	136	4	no	—
386	C₂×C₄	—	136	4	no	—
387	C₂×C₄	—	136	4	no	—
388	C₂×C₄	—	136	4	no	—
389	C₂×C₄	#10587533	1	1	yes	characteristic
390	C₂×C₄	#10587533	1	1	yes	characteristic
391	C₂×C₄	#10587534	1	1	yes	characteristic
392	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
393	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
394	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
395	C₈	—	17	1	no	—
396	C₈	—	17	1	no	—
397	C₈	—	17	1	no	—
398	C₈	—	17	1	no	—
399	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
400	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
401	C₈	C₂×C₄×#595	1	1	yes	characteristic
402	C₈	C₂×C₂²⋊#595	1	1	yes	characteristic
403	C₂²	—	2	2	no	—
404	C₂²	—	17	1	no	—
405	C₂²	—	17	1	no	—
406	C₂²	—	17	4	no	—
407	C₂²	—	17	1	no	—
408	C₂²	—	17	1	no	—
409	C₂²	—	34	2	no	—
410	C₂²	—	34	2	no	—
411	C₂²	—	34	2	no	—
412	C₂²	—	34	2	no	—
413	C₂²	—	34	2	no	—
414	C₂²	#11763683	1	1	yes	characteristic
415	C₂²	#11763683	1	1	yes	characteristic
416	C₂²	C₂×#10587534	1	1	yes	characteristic
417	C₄	—	17	1	no	—
418	C₄	—	17	1	no	—
419	C₄	—	17	1	no	—
420	C₄	—	17	1	no	—
421	C₄	—	136	4	no	—
422	C₄	—	136	4	no	—
423	C₄	#11763683	1	1	yes	characteristic
424	C₄	#11763683	1	1	yes	characteristic
425	C₄	C₂×(C₂×#595)⋊C₄	1	1	yes	characteristic
426	C₄	C₂×#10587533	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	17	2	no	—
430	C₂	—	17	2	no	—
431	C₂	—	34	1	no	—
432	C₂	—	34	1	no	—
433	C₂	#14543856	1	2	yes	direct product factor
434	C₂	C₂×#11763683	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11763683
commutator	C₈×C₁₇	C₂×C₄²
Frattini	C₂×C₈	C₂²×#595
Fitting	C₂×C₁₇×M₃₂	C₄
socle	C₂²×C₁₇	#340
prime radical	C₂³×D₁₇	D₈
cosocle	C₂×C₈×D₁₇	C₂³
hypercenter	C₂×M₃₂	#595
hypocenter	C₁₇	C₂×#1386
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #14543856	C₂	direct (N × H)
9. #11763819	C₄	semidirect
11. C₂×#10587534	C₄	semidirect
16. C₂×#10587533	C₄	semidirect
17. C₂×#10587533	C₄	semidirect
20. C₂×#10587483	C₄	semidirect
24. M₃₂×D₁₇	C₄	semidirect
27. C₂×C₁₇×M₃₂	C₄	semidirect
58. #10587534	C₂×C₄	semidirect
64. #10587533	C₂×C₄	semidirect
66. C₁₇×M₃₂	C₂×C₄	semidirect
69. #10587483	C₂×C₄	semidirect
223. C₂×M₃₂	#595	semidirect
239. C₂×C₁₇	#1386	semidirect
243. D₁₇	#1386	semidirect
279. M₃₂	C₂×#595	semidirect
292. C₁₇	C₂×#1386	semidirect
433. C₂	#14543856	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×#11763819	2
C₂²×#10587533	2
#14543856	2
C₂×M₃₂×D₁₇	2
C₂×#1386	17

Subgroups — C2×#14543856 #17960538

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14543856 #17960538