Subgroups — #17983106

Order 4352.

598 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545990	C₂	1	2	yes	maximal, complemented
2	#14545989	C₂	1	2	yes	maximal, complemented
3	#14545984	C₂	1	1	yes	maximal, characteristic, complemented
4	#14545983	C₂	1	1	yes	maximal, characteristic, complemented
5	#14545982	C₂	1	1	yes	maximal, characteristic, complemented
6	#14545981	C₂	1	1	yes	maximal, characteristic, complemented
7	#14545975	C₂	1	2	yes	maximal, complemented
8	#14545954	C₂	1	2	yes	maximal
9	C₄×#10587670	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×#63241	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#10587678	C₂	1	1	yes	maximal, characteristic
12	C₂×#10587670	C₂²	1	2	yes	—
13	C₂²×#63241	C₂²	1	2	yes	—
14	#11763912	C₂²	1	2	yes	—
15	#11763912	C₂²	1	2	yes	—
16	C₄⋊#63241	C₂²	1	2	yes	—
17	C₄⋊#63241	C₂²	1	2	yes	—
18	#11763906	C₂²	1	2	yes	—
19	#11763906	C₂²	1	2	yes	—
20	C₂²⋊#63241	C₂²	1	2	yes	—
21	C₂²⋊#63241	C₂²	1	2	yes	—
22	#11763903	C₂²	1	2	yes	—
23	C₄×#63241	C₂²	1	1	yes	characteristic
24	C₄×#63241	C₂²	1	1	yes	characteristic
25	C₄×#63241	C₂²	1	2	yes	—
26	C₄×#63241	C₂²	1	1	yes	characteristic
27	C₄×#63241	C₂²	1	1	yes	characteristic
28	C₂×#10587678	C₄	1	1	yes	characteristic
29	C₂×#10587678	C₂²	1	1	yes	characteristic
30	#11763774	C₄	1	1	yes	characteristic
31	#11763774	C₂²	1	1	yes	characteristic
32	#11763773	C₄	1	1	yes	characteristic
33	#11763773	C₄	1	1	yes	characteristic
34	#11763773	C₂²	1	1	yes	characteristic
35	#11763773	C₂²	1	1	yes	characteristic
36	C₄×#63243	C₄	1	1	yes	characteristic
37	C₄×#63247	C₄	1	1	yes	characteristic
38	C₄×#63247	C₄	1	1	yes	characteristic
39	C₄×#63242	C₂²	1	1	yes	characteristic
40	C₂×C₄×#3624	C₂²	1	1	yes	characteristic
41	C₂×C₄×#3624	C₂²	1	1	yes	characteristic
42	C₄×#63254	C₄	1	1	yes	characteristic
43	C₂×#63254	C₂×C₄	1	1	yes	characteristic
44	C₂×#63247	C₂×C₄	1	1	yes	characteristic
45	C₂×#63247	C₂×C₄	1	1	yes	characteristic
46	C₂×#63247	C₂×C₄	1	1	yes	characteristic
47	C₂×#63247	C₂×C₄	1	1	yes	characteristic
48	C₂²×#3624	C₂×C₄	1	1	yes	characteristic
49	C₂²×#3624	C₂×C₄	1	1	yes	characteristic
50	C₂²×#3624	C₂³	1	1	yes	characteristic
51	C₂²×#3624	C₂³	1	1	yes	characteristic
52	#10587678	—	2	4	no	—
53	#10587678	—	2	4	no	—
54	C₂×#63243	C₂×C₄	1	1	yes	characteristic
55	C₂×#63243	C₂×C₄	1	1	yes	characteristic
56	C₂×#63242	C₂×C₄	1	1	yes	characteristic
57	C₂×#63242	C₂³	1	1	yes	characteristic
58	#10587670	—	2	4	no	—
59	C₂×#63241	—	2	4	no	—
60	C₂×#63241	C₂³	1	2	yes	—
61	C₂×#63241	C₂³	1	2	yes	—
62	C₂×#63241	C₂³	1	2	yes	—
63	C₂×#63241	C₂³	1	2	yes	—
64	C₄×D₄×C₁₇	C₈	1	1	yes	characteristic
65	D₄×Dic₁₇	C₈	1	1	yes	characteristic
66	C₄×C₂²⋊D₁₇	C₈	1	1	yes	characteristic
67	C₄×C₂²⋊D₁₇	C₈	1	1	yes	characteristic
68	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
70	#10587578	C₂×C₄	1	1	yes	characteristic
71	#10587573	C₈	1	1	yes	characteristic
72	#10587567	C₈	1	1	yes	characteristic
73	#10587567	C₈	1	1	yes	characteristic
74	#10587563	C₂×C₄	1	1	yes	characteristic
75	#10587563	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
77	C₄×Dic₃₄	C₈	1	1	yes	characteristic
78	#10587542	C₂×C₄	1	1	yes	characteristic
79	#10587542	C₂×C₄	1	1	yes	characteristic
80	#10587542	C₂×C₄	1	1	yes	characteristic
81	#10587542	C₂×C₄	1	1	yes	characteristic
82	#10587542	C₂×C₄	1	1	yes	characteristic
83	#10587542	C₂×C₄	1	1	yes	characteristic
84	C₄×#3624	C₂×C₄	1	1	yes	characteristic
85	C₄×#3624	C₂×C₄	1	1	yes	characteristic
86	C₄×#3624	C₂×C₄	1	1	yes	characteristic
87	C₄×#3624	C₂×C₄	1	1	yes	characteristic
88	C₄×#3624	C₂×C₄	1	1	yes	characteristic
89	C₄×#3624	C₂×C₄	1	1	yes	characteristic
90	C₄×#3624	C₂³	1	1	yes	characteristic
91	C₄×#3624	C₂³	1	1	yes	characteristic
92	C₄×#3624	C₂³	1	1	yes	characteristic
93	C₄×#3624	C₂³	1	1	yes	characteristic
94	C₂×D₄×C₁₇	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
97	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
98	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
99	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
100	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
101	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
103	#63254	—	2	2	no	—
104	#63254	—	2	2	no	—
105	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
107	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×Dic₃₄	C₂×C₈	1	1	yes	characteristic
109	#63247	—	2	2	no	—
110	#63247	—	2	2	no	—
111	#63247	—	2	2	no	—
112	#63247	—	2	2	no	—
113	C₂×#3624	—	2	2	no	—
114	C₂×#3624	—	2	2	no	—
115	C₂×#3624	M₁₆	1	4	yes	—
116	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
117	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
118	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
119	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
120	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
121	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
122	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
123	C₂×#3624	#41	1	4	yes	—
124	C₂×#3624	C₂⁴	1	1	yes	characteristic
125	#63243	—	2	2	no	—
126	#63243	—	2	2	no	—
127	#63242	—	2	2	no	—
128	#63242	—	2	2	no	—
129	#63241	—	2	2	no	—
130	#63241	—	2	2	no	—
131	#63241	—	2	2	no	—
132	#63241	—	2	2	no	—
133	C₄⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
134	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
135	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
136	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
137	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
138	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
139	#63227	C₂×C₈	1	1	yes	characteristic
140	#63227	C₂×C₈	1	1	yes	characteristic
141	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
142	#63225	C₂×C₈	1	1	yes	characteristic
143	#63225	C₂×C₈	1	1	yes	characteristic
144	#63225	C₂×C₈	1	1	yes	characteristic
145	#63225	C₂×C₈	1	1	yes	characteristic
146	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
147	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
148	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
149	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
150	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
151	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
153	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
154	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
155	#33420	—	17	1	no	maximal, Sylow
156	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
157	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
158	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
159	D₄×C₁₇	—	2	2	no	—
160	C₂×C₄×C₁₇	—	2	2	no	—
161	C₂×C₄×C₁₇	—	2	2	no	—
162	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
163	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
164	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
165	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
166	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
167	C₂²⋊D₁₇	—	2	2	no	—
168	C₂²⋊D₁₇	—	2	2	no	—
169	C₂×Dic₁₇	—	2	1	no	—
170	C₂×Dic₁₇	—	2	1	no	—
171	C₂×Dic₁₇	—	2	2	no	—
172	C₂×Dic₁₇	—	2	2	no	—
173	C₂×Dic₁₇	#117	1	2	yes	—
174	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
175	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
176	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
177	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
180	C₂×Dic₁₇	C₂×M₁₆	1	2	yes	—
181	C₂×Dic₁₇	C₂³×C₄	1	1	yes	characteristic
182	C₄×D₁₇	—	2	2	no	—
183	C₄×D₁₇	—	2	1	no	—
184	C₄×D₁₇	—	2	1	no	—
185	C₄×D₁₇	—	2	2	no	—
186	Dic₃₄	—	2	2	no	—
187	#3624	—	2	1	no	—
188	#3624	—	2	1	no	—
189	#3624	—	2	1	no	—
190	#3624	—	2	1	no	—
191	#3624	#117	1	2	yes	—
192	#3624	C₂×M₁₆	1	2	yes	—
193	#3624	C₂×M₁₆	1	2	yes	—
194	#3624	C₂×#41	1	2	yes	—
195	C₄×#131	—	17	1	no	—
196	#2164	—	17	2	no	—
197	#2164	—	17	2	no	—
198	#2162	—	17	1	no	—
199	#2162	—	17	1	no	—
200	#2162	—	17	1	no	—
201	#2162	—	17	1	no	—
202	#2151	—	17	2	no	—
203	#2113	—	17	2	no	—
204	C₄×M₃₂	—	17	1	no	—
205	C₂×C₄×C₁₆	—	17	1	no	—
206	C₂²×C₁₇	—	2	1	no	—
207	C₂²×C₁₇	—	2	1	no	—
208	C₂²×C₁₇	—	2	1	no	—
209	C₂²×C₁₇	—	2	1	no	—
210	C₂²×C₁₇	—	2	1	no	—
211	C₂²×C₁₇	#431	1	2	yes	—
212	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
213	C₂×D₁₇	—	2	1	no	—
214	C₂×D₁₇	—	2	1	no	—
215	C₂×D₁₇	—	2	1	no	—
216	C₄×C₁₇	—	2	1	no	—
217	C₄×C₁₇	—	2	1	no	—
218	C₄×C₁₇	—	2	1	no	—
219	C₄×C₁₇	—	2	1	no	—
220	C₄×C₁₇	#504	1	2	yes	—
221	Dic₁₇	—	2	1	no	—
222	Dic₁₇	—	2	1	no	—
223	Dic₁₇	—	2	1	no	—
224	Dic₁₇	—	2	1	no	—
225	Dic₁₇	#431	1	2	yes	—
226	Dic₁₇	#504	1	2	yes	—
227	Dic₁₇	C₂×#117	1	1	yes	characteristic
228	Dic₁₇	C₂²×M₁₆	1	1	yes	characteristic
229	C₂×#131	—	17	1	no	—
230	C₂×#131	—	17	1	no	—
231	C₄×#41	—	17	1	no	—
232	C₂×M₃₂	—	17	2	no	—
233	C₂²×C₁₆	—	17	2	no	—
234	#405	—	17	1	no	—
235	#405	—	17	1	no	—
236	#405	—	17	1	no	—
237	#405	—	17	1	no	—
238	#405	—	17	1	no	—
239	#405	—	17	1	no	—
240	C₄×M₁₆	—	17	1	no	—
241	C₄×M₁₆	—	17	1	no	—
242	C₄×M₁₆	—	17	1	no	—
243	C₂×C₄×C₈	—	17	1	no	—
244	C₂×C₄×C₈	—	17	1	no	—
245	C₂×C₄×C₈	—	17	1	no	—
246	C₄⋊C₁₆	—	17	2	no	—
247	C₄⋊C₁₆	—	17	2	no	—
248	C₄⋊C₁₆	—	17	2	no	—
249	C₄⋊C₁₆	—	17	2	no	—
250	C₂²⋊C₁₆	—	17	2	no	—
251	C₂²⋊C₁₆	—	17	2	no	—
252	C₂²⋊C₁₆	—	17	2	no	—
253	C₂²⋊C₁₆	—	17	2	no	—
254	#346	—	17	2	no	—
255	C₄×C₁₆	—	17	1	no	—
256	C₄×C₁₆	—	17	1	no	—
257	C₄×C₁₆	—	17	2	no	—
258	C₄×C₁₆	—	17	1	no	—
259	C₄×C₁₆	—	17	1	no	—
260	C₂×C₁₇	—	2	2	no	—
261	C₂×C₁₇	—	4	1	no	—
262	C₂×C₁₇	C₂×#431	1	1	yes	characteristic
263	C₂×C₁₇	C₂×#504	1	1	yes	characteristic
264	C₂×C₁₇	C₂×#504	1	1	yes	characteristic
265	D₁₇	—	4	1	no	—
266	C₂×#41	—	17	1	no	—
267	#131	—	34	4	no	—
268	#131	—	34	4	no	—
269	C₂×M₁₆	—	17	1	no	—
270	C₂×M₁₆	—	17	1	no	—
271	C₂×M₁₆	—	17	1	no	—
272	C₂×M₁₆	—	17	1	no	—
273	C₂×M₁₆	—	17	1	no	—
274	C₂×M₁₆	—	17	1	no	—
275	C₂²×C₈	—	17	1	no	—
276	C₂²×C₈	—	17	1	no	—
277	C₂²×C₈	—	17	1	no	—
278	C₂²×C₈	—	17	1	no	—
279	C₂²×C₈	—	17	1	no	—
280	C₂²×C₈	—	17	1	no	—
281	C₄×Q₈	—	17	1	no	—
282	C₄×Q₈	—	17	1	no	—
283	C₄×D₄	—	17	1	no	—
284	C₄×D₄	—	17	1	no	—
285	C₄×D₄	—	17	1	no	—
286	C₄×D₄	—	17	1	no	—
287	C₄×D₄	—	17	1	no	—
288	C₄×D₄	#3633	1	1	yes	characteristic
289	#117	—	17	1	no	—
290	#117	—	17	1	no	—
291	#117	—	17	1	no	—
292	C₂×C₄²	—	17	1	no	—
293	C₂×C₄²	—	17	1	no	—
294	C₂×C₄²	—	17	1	no	—
295	M₃₂	—	34	4	no	—
296	C₂×C₁₆	—	17	2	no	—
297	C₂×C₁₆	—	17	2	no	—
298	C₂×C₁₆	—	17	2	no	—
299	C₂×C₁₆	—	17	2	no	—
300	C₂×C₁₆	—	34	4	no	—
301	#97	—	17	1	no	—
302	#97	—	17	1	no	—
303	#97	—	17	1	no	—
304	#97	—	17	1	no	—
305	#97	—	17	1	no	—
306	#97	—	17	1	no	—
307	C₄×C₈	—	17	1	no	—
308	C₄×C₈	—	17	1	no	—
309	C₄×C₈	—	17	1	no	—
310	C₄×C₈	—	17	1	no	—
311	C₄×C₈	—	17	1	no	—
312	C₄×C₈	—	17	1	no	—
313	C₄×C₈	—	17	1	no	—
314	C₄×C₈	—	17	1	no	—
315	C₄×C₈	—	17	1	no	—
316	C₄×C₈	—	17	1	no	—
317	C₁₇	#33420	1	1	yes	characteristic, complemented, Sylow
318	#41	—	34	2	no	—
319	#41	—	34	2	no	—
320	C₂×Q₈	—	17	1	no	—
321	C₂×D₄	—	17	1	no	—
322	C₂×D₄	—	17	1	no	—
323	C₂×D₄	C₂×#3633	1	1	yes	characteristic
324	C₂²×C₄	—	17	1	no	—
325	C₂²×C₄	—	17	1	no	—
326	C₂²×C₄	—	17	1	no	—
327	C₂²×C₄	—	17	1	no	—
328	C₂²×C₄	—	17	1	no	—
329	C₂²×C₄	—	17	1	no	—
330	C₂²×C₄	—	17	1	no	—
331	C₂²×C₄	C₂×#3633	1	1	yes	characteristic
332	C₂²×C₄	C₂×#3633	1	1	yes	characteristic
333	M₁₆	—	34	2	no	—
334	M₁₆	—	34	2	no	—
335	M₁₆	—	34	2	no	—
336	M₁₆	—	34	2	no	—
337	M₁₆	—	34	2	no	—
338	M₁₆	—	34	2	no	—
339	C₂×C₈	—	17	4	no	—
340	C₂×C₈	—	17	1	no	—
341	C₂×C₈	—	17	1	no	—
342	C₂×C₈	—	17	1	no	—
343	C₂×C₈	—	17	4	no	—
344	C₂×C₈	—	17	1	no	—
345	C₂×C₈	—	17	1	no	—
346	C₂×C₈	—	17	1	no	—
347	C₂×C₈	—	17	1	no	—
348	C₂×C₈	—	17	1	no	—
349	C₂×C₈	—	34	2	no	—
350	C₂×C₈	—	34	2	no	—
351	C₂×C₈	—	34	2	no	—
352	C₂×C₈	—	34	2	no	—
353	C₄⋊C₄	—	17	1	no	—
354	C₄⋊C₄	—	17	1	no	—
355	C₄⋊C₄	—	17	1	no	—
356	C₄⋊C₄	—	17	1	no	—
357	C₄⋊C₄	—	17	1	no	—
358	C₄⋊C₄	C₂×#3633	1	1	yes	characteristic
359	C₂²⋊C₄	—	17	1	no	—
360	C₂²⋊C₄	—	17	1	no	—
361	C₂²⋊C₄	—	17	1	no	—
362	C₂²⋊C₄	—	17	1	no	—
363	C₂²⋊C₄	C₂×#3633	1	1	yes	characteristic
364	C₂²⋊C₄	C₂×#3633	1	1	yes	characteristic
365	C₄²	—	17	1	no	—
366	C₄²	—	17	1	no	—
367	C₄²	—	17	1	no	—
368	C₄²	—	17	1	no	—
369	C₄²	—	17	1	no	—
370	C₄²	—	17	1	no	—
371	C₄²	—	17	1	no	—
372	C₄²	—	17	1	no	—
373	C₄²	—	17	1	no	—
374	C₄²	C₂×#3633	1	1	yes	characteristic
375	C₁₆	—	34	2	no	—
376	C₁₆	—	34	2	no	—
377	C₁₆	—	34	2	no	—
378	C₁₆	—	34	2	no	—
379	C₂³	—	17	1	no	—
380	C₂³	C₂²×#3633	1	1	yes	characteristic
381	C₂³	C₂²×#3633	1	1	yes	characteristic
382	Q₈	—	34	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	34	2	no	—
385	D₄	—	34	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	17	2	no	—
389	C₂×C₄	—	17	2	no	—
390	C₂×C₄	—	17	1	no	—
391	C₂×C₄	—	17	1	no	—
392	C₂×C₄	—	17	1	no	—
393	C₂×C₄	—	17	1	no	—
394	C₂×C₄	—	17	1	no	—
395	C₂×C₄	—	17	1	no	—
396	C₂×C₄	—	17	1	no	—
397	C₂×C₄	—	34	1	no	—
398	C₂×C₄	—	34	1	no	—
399	C₂×C₄	—	34	2	no	—
400	C₂×C₄	—	34	1	no	—
401	C₂×C₄	—	34	1	no	—
402	C₂×C₄	—	34	2	no	—
403	C₂×C₄	—	34	2	no	—
404	C₂×C₄	—	34	2	no	—
405	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
406	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
407	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
408	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
409	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
410	C₈	—	17	2	no	—
411	C₈	—	17	2	no	—
412	C₈	—	17	2	no	—
413	C₈	—	17	2	no	—
414	C₈	—	34	1	no	—
415	C₈	—	34	1	no	—
416	C₈	—	34	1	no	—
417	C₈	—	34	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	34	1	no	—
424	C₂²	—	34	1	no	—
425	C₂²	—	34	1	no	—
426	C₂²	#11763922	1	2	yes	—
427	C₂²	C₂³×#3633	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	17	1	no	—
433	C₄	—	17	1	no	—
434	C₄	—	17	2	no	—
435	C₄	—	17	2	no	—
436	C₄	—	34	1	no	—
437	C₄	—	34	1	no	—
438	C₄	—	34	1	no	—
439	C₄	—	34	1	no	—
440	C₄	#11763930	1	2	yes	—
441	C₂	—	2	2	no	—
442	C₂	—	4	1	no	—
443	C₂	—	68	1	no	—
444	C₂	C₂×#11763922	1	1	yes	characteristic
445	C₂	C₂×#11763930	1	1	yes	characteristic
446	C₂	#14546035	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#3633
commutator, socle	C₂²×C₁₇	C₂³×C₈
Frattini	C₂²	C₂³×#3633
Fitting	C₄×D₄×C₁₇	C₈
prime radical	C₂×#63254	C₂×C₄
cosocle	C₂×#3624	C₂⁴
hypercenter	C₄×D₄	#3633
hypocenter	C₁₇	#33420
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #14545990	C₂	semidirect
2. #14545989	C₂	semidirect
3. #14545984	C₂	semidirect
4. #14545983	C₂	semidirect
5. #14545982	C₂	semidirect
6. #14545981	C₂	semidirect
7. #14545975	C₂	semidirect
9. C₄×#10587670	C₂	semidirect
10. C₂×C₄×#63241	C₂	semidirect
317. C₁₇	#33420	semidirect

Maximal subgroups

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

subgroup	index
#14545990	2
#14545989	2
#14545984	2
#14545983	2
#14545982	2
#14545981	2
#14545975	2
#14545954	2
C₄×#10587670	2
C₂×C₄×#63241	2
C₄×#10587678	2
#33420	17