Subgroups — #17983115

Order 4352.

600 conjugacy classes of subgroups.

The subgroup lattice has 450 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	#14545990	C₂	1	2	yes	maximal, complemented
3	#14545988	C₂	1	1	yes	maximal, characteristic, complemented
4	#14545987	C₂	1	1	yes	maximal, characteristic, complemented
5	#14545984	C₂	1	1	yes	maximal, characteristic, complemented
6	#14545983	C₂	1	1	yes	maximal, characteristic, complemented
7	#14545975	C₂	1	2	yes	maximal, complemented
8	#14545953	C₂	1	1	yes	maximal, characteristic
9	C₂×#11763906	C₂	1	1	yes	maximal, characteristic
10	#14545945	C₂	1	2	yes	maximal, complemented
11	#14545344	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	complemented
15	#11763912	C₂²	1	2	yes	complemented
16	C₄⋊#63241	C₂²	1	2	yes	complemented
17	C₄⋊#63241	C₂²	1	2	yes	complemented
18	#11763906	C₂²	1	1	yes	characteristic
19	#11763906	C₂²	1	1	yes	characteristic
20	#11763906	C₂²	1	2	yes	—
21	#11763906	C₂²	1	1	yes	characteristic
22	#11763906	C₂²	1	1	yes	characteristic
23	#11763906	C₂²	1	2	yes	—
24	#11763903	C₂²	1	2	yes	complemented
25	#11763903	C₂²	1	2	yes	complemented
26	C₄×#63241	C₂²	1	2	yes	complemented
27	C₄×#63241	C₂²	1	2	yes	complemented
28	C₂×D₁₇⋊M₁₆	C₄	1	1	yes	characteristic
29	C₂²×#63242	C₂²	1	1	yes	characteristic
30	#11763774	C₄	1	1	yes	characteristic
31	#11763774	C₄	1	1	yes	characteristic
32	#11763774	C₂²	1	1	yes	characteristic
33	#11763774	C₂²	1	1	yes	characteristic
34	#11763773	C₄	1	1	yes	characteristic
35	#11763773	C₄	1	1	yes	characteristic
36	#11763773	C₂²	1	1	yes	characteristic
37	#11763773	C₂²	1	1	yes	characteristic
38	#11763768	C₄	1	1	yes	characteristic
39	#11763768	C₄	1	1	yes	characteristic
40	C₄×#63242	C₂²	1	1	yes	characteristic
41	C₄×#63242	C₂²	1	1	yes	characteristic
42	#117×D₁₇	C₄	1	1	yes	characteristic
43	C₂²×C₄×D₁₇	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	C₂²×#3624	C₂×C₄	1	1	yes	characteristic
47	C₂²×#3624	C₂³	1	1	yes	characteristic
48	D₁₇⋊M₁₆	—	2	4	no	—
49	C₂×#63243	C₂×C₄	1	1	yes	characteristic
50	C₂×#63243	C₂×C₄	1	1	yes	characteristic
51	C₂×#63242	—	2	4	no	—
52	C₂×#63242	C₂×C₄	1	1	yes	characteristic
53	C₂×#63242	C₂×C₄	1	1	yes	characteristic
54	C₂×#63242	C₂×C₄	1	1	yes	characteristic
55	C₂×#63242	C₂×C₄	1	1	yes	characteristic
56	C₂×#63242	C₂³	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	C₁₇×#117	C₈	1	1	yes	characteristic
65	#10587612	C₈	1	1	yes	characteristic
66	#10587578	C₂×C₄	1	1	yes	characteristic
67	#10587578	C₂×C₄	1	1	yes	characteristic
68	C₄⋊C₄×D₁₇	C₈	1	1	yes	characteristic
69	C₄⋊C₄×D₁₇	C₈	1	1	yes	characteristic
70	C₂²⋊C₄×D₁₇	C₈	1	1	yes	characteristic
71	C₂²⋊C₄×D₁₇	C₈	1	1	yes	characteristic
72	#10587563	C₂×C₄	1	1	yes	characteristic
73	#10587563	C₂×C₄	1	1	yes	characteristic
74	#10587558	C₈	1	1	yes	characteristic
75	#10587558	C₈	1	1	yes	characteristic
76	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
77	C₄²×D₁₇	C₂×C₄	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	#10587542	C₂×C₄	1	1	yes	characteristic
85	#10587542	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	C₂³×D₁₇	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
96	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₇	—	2	2	no	—
98	C₂×C₄×D₁₇	—	2	2	no	—
99	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
100	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
107	#63247	—	2	2	no	—
108	#63247	M₁₆	1	4	yes	—
109	C₂×#3624	—	2	2	no	—
110	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
111	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
112	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
113	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
114	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
115	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
116	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
117	C₂×#3624	#41	1	4	yes	—
118	C₂×#3624	C₂⁴	1	1	yes	characteristic
119	#63243	—	2	2	no	—
120	#63243	—	2	2	no	—
121	#63242	—	2	2	no	—
122	#63242	—	2	2	no	—
123	#63242	—	2	2	no	—
124	#63242	—	2	2	no	—
125	#63242	—	2	2	no	—
126	#63242	—	2	2	no	—
127	#63241	—	2	2	no	—
128	#63241	—	2	2	no	—
129	#63241	—	2	2	no	—
130	#63241	—	2	2	no	—
131	C₄⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
132	C₄⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
133	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
134	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
135	C₄²×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	#63227	C₂×C₈	1	1	yes	characteristic
142	#63227	C₂×C₈	1	1	yes	characteristic
143	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
144	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
145	#63225	C₂×C₈	1	1	yes	characteristic
146	#63225	C₂×C₈	1	1	yes	characteristic
147	#63225	C₂×C₈	1	1	yes	characteristic
148	#63225	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	#33422	—	17	1	no	maximal, Sylow
156	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
157	C₂²×D₁₇	—	2	2	no	—
158	C₂²×D₁₇	—	2	2	no	—
159	C₂²×D₁₇	—	4	1	no	—
160	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
161	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₁₇	—	2	2	no	—
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	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
169	C₂×Dic₁₇	#117	1	2	yes	—
170	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
171	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
172	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
173	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
174	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
175	C₂×Dic₁₇	C₂×M₁₆	1	2	yes	—
176	C₂×Dic₁₇	C₂³×C₄	1	1	yes	characteristic
177	C₄×D₁₇	—	2	2	no	—
178	C₄×D₁₇	—	2	2	no	—
179	C₄×D₁₇	—	2	1	no	—
180	C₄×D₁₇	—	2	1	no	—
181	C₄×D₁₇	—	2	1	no	—
182	C₄×D₁₇	—	2	1	no	—
183	C₄×D₁₇	—	2	2	no	—
184	C₄×D₁₇	—	2	2	no	—
185	C₄×D₁₇	—	4	1	no	—
186	C₄×D₁₇	—	4	1	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	C₂×#405	—	17	1	no	—
196	#2164	—	17	2	no	—
197	#2164	—	17	2	no	—
198	#2163	—	17	1	no	—
199	#2163	—	17	1	no	—
200	#2162	—	17	1	no	—
201	#2162	—	17	1	no	—
202	#2151	—	17	2	no	—
203	#2112	—	17	1	no	—
204	C₂×C₂²⋊C₁₆	—	17	1	no	—
205	#2108	—	17	2	no	—
206	C₂²×C₁₇	—	2	1	no	—
207	C₂²×C₁₇	—	2	1	no	—
208	C₂²×C₁₇	#431	1	2	yes	—
209	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
210	C₂×D₁₇	—	2	1	no	—
211	C₂×D₁₇	—	2	1	no	—
212	C₂×D₁₇	—	2	1	no	—
213	C₂×D₁₇	—	2	1	no	—
214	C₂×D₁₇	—	2	1	no	—
215	C₂×D₁₇	—	4	4	no	—
216	C₂×D₁₇	#504	1	2	yes	—
217	C₄×C₁₇	—	2	1	no	—
218	C₄×C₁₇	—	2	1	no	—
219	C₄×C₁₇	—	2	1	no	—
220	C₄×C₁₇	—	2	1	no	—
221	C₄×C₁₇	—	2	1	no	—
222	C₄×C₁₇	—	2	1	no	—
223	Dic₁₇	—	2	1	no	—
224	Dic₁₇	—	2	1	no	—
225	Dic₁₇	—	2	1	no	—
226	Dic₁₇	—	2	1	no	—
227	Dic₁₇	#431	1	2	yes	—
228	Dic₁₇	C₂×#117	1	1	yes	characteristic
229	Dic₁₇	C₂²×M₁₆	1	1	yes	characteristic
230	C₂²×M₁₆	—	17	1	no	—
231	C₂³×C₈	—	17	1	no	—
232	C₂×#117	—	17	1	no	—
233	C₂×M₃₂	—	17	2	no	—
234	C₂²×C₁₆	—	17	2	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	#405	—	17	1	no	—
241	#405	—	17	1	no	—
242	#405	—	17	1	no	—
243	C₂×#97	—	17	1	no	—
244	C₂×#97	—	17	1	no	—
245	C₂×C₄×C₈	—	17	1	no	—
246	C₂×C₄×C₈	—	17	1	no	—
247	C₄⋊C₁₆	—	17	2	no	—
248	C₄⋊C₁₆	—	17	2	no	—
249	C₄⋊C₁₆	—	17	2	no	—
250	C₄⋊C₁₆	—	17	2	no	—
251	C₂²⋊C₁₆	—	17	1	no	—
252	C₂²⋊C₁₆	—	17	1	no	—
253	C₂²⋊C₁₆	—	17	2	no	—
254	C₂²⋊C₁₆	—	17	1	no	—
255	C₂²⋊C₁₆	—	17	1	no	—
256	C₂²⋊C₁₆	—	17	2	no	—
257	#346	—	17	2	no	—
258	#346	—	17	2	no	—
259	C₄×C₁₆	—	17	2	no	—
260	C₄×C₁₆	—	17	2	no	—
261	C₂×C₁₇	—	2	2	no	—
262	C₂×C₁₇	C₂×#431	1	1	yes	characteristic
263	C₂×C₁₇	C₂×#504	1	1	yes	characteristic
264	C₂×C₁₇	#3407	1	1	yes	characteristic
265	D₁₇	—	2	2	no	—
266	D₁₇	—	4	1	no	—
267	C₂³×C₄	—	17	1	no	—
268	C₂×M₁₆	—	17	1	no	—
269	C₂×M₁₆	—	17	1	no	—
270	C₂×M₁₆	—	17	1	no	—
271	C₂×M₁₆	—	17	1	no	—
272	C₂×M₁₆	—	34	4	no	—
273	C₂²×C₈	—	17	1	no	—
274	C₂²×C₈	—	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	C₂²×C₈	—	34	4	no	—
282	#117	—	17	1	no	—
283	#117	—	17	1	no	—
284	#117	—	17	1	no	—
285	#117	—	17	1	no	—
286	#117	—	17	1	no	—
287	#117	—	17	1	no	—
288	#117	—	17	1	no	—
289	#117	#3633	1	1	yes	characteristic
290	C₂×C₄⋊C₄	—	17	1	no	—
291	C₂×C₄⋊C₄	—	17	1	no	—
292	C₂×C₂²⋊C₄	—	17	1	no	—
293	C₂×C₂²⋊C₄	—	17	1	no	—
294	C₂×C₄²	—	17	1	no	—
295	C₂×C₄²	—	17	1	no	—
296	M₃₂	—	34	4	no	—
297	C₂×C₁₆	—	17	2	no	—
298	C₂×C₁₆	—	17	2	no	—
299	C₂×C₁₆	—	17	2	no	—
300	C₂×C₁₆	—	17	2	no	—
301	C₂×C₁₆	—	34	4	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	#97	—	17	1	no	—
308	#97	—	17	1	no	—
309	#97	—	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	C₄×C₈	—	17	1	no	—
318	C₁₇	#33422	1	1	yes	characteristic, complemented, Sylow
319	C₂⁴	—	17	1	no	—
320	C₂²×C₄	—	17	1	no	—
321	C₂²×C₄	—	17	1	no	—
322	C₂²×C₄	—	17	1	no	—
323	C₂²×C₄	—	17	1	no	—
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	—	34	2	no	—
330	C₂²×C₄	—	34	2	no	—
331	C₂²×C₄	C₂×#3633	1	1	yes	characteristic
332	M₁₆	—	17	4	no	—
333	M₁₆	—	34	2	no	—
334	M₁₆	—	34	2	no	—
335	M₁₆	—	34	2	no	—
336	C₂×C₈	—	17	1	no	—
337	C₂×C₈	—	17	1	no	—
338	C₂×C₈	—	17	1	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	1	no	—
344	C₂×C₈	—	17	1	no	—
345	C₂×C₈	—	34	2	no	—
346	C₂×C₈	—	34	2	no	—
347	C₂×C₈	—	34	2	no	—
348	C₂×C₈	—	34	2	no	—
349	C₂×C₈	—	34	2	no	—
350	C₂×C₈	—	34	2	no	—
351	C₂×C₈	—	34	2	no	—
352	C₄⋊C₄	—	17	1	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	C₄⋊C₄	C₂×#3633	1	1	yes	characteristic
360	C₂²⋊C₄	—	17	1	no	—
361	C₂²⋊C₄	—	17	1	no	—
362	C₂²⋊C₄	—	17	1	no	—
363	C₂²⋊C₄	—	17	1	no	—
364	C₂²⋊C₄	—	17	1	no	—
365	C₂²⋊C₄	—	17	1	no	—
366	C₂²⋊C₄	C₂×#3633	1	1	yes	characteristic
367	C₂²⋊C₄	C₂×#3633	1	1	yes	characteristic
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	C₄²	C₂×#3633	1	1	yes	characteristic
376	C₁₆	—	34	2	no	—
377	C₁₆	—	34	2	no	—
378	C₁₆	—	34	2	no	—
379	C₁₆	—	34	2	no	—
380	C₂³	—	17	1	no	—
381	C₂³	—	17	1	no	—
382	C₂³	—	34	2	no	—
383	C₂³	—	34	2	no	—
384	C₂³	—	68	1	no	—
385	C₂³	C₂²×#3633	1	1	yes	characteristic
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	17	2	no	—
388	C₂×C₄	—	17	2	no	—
389	C₂×C₄	—	17	1	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	—	34	1	no	—
396	C₂×C₄	—	34	1	no	—
397	C₂×C₄	—	34	1	no	—
398	C₂×C₄	—	34	1	no	—
399	C₂×C₄	—	34	2	no	—
400	C₂×C₄	—	34	2	no	—
401	C₂×C₄	—	34	2	no	—
402	C₂×C₄	—	34	2	no	—
403	C₂×C₄	—	68	1	no	—
404	C₂×C₄	—	68	1	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	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
411	C₈	—	17	2	no	—
412	C₈	—	17	2	no	—
413	C₈	—	17	2	no	—
414	C₈	—	17	2	no	—
415	C₈	—	34	1	no	—
416	C₈	—	34	1	no	—
417	C₈	—	34	1	no	—
418	C₈	—	34	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	17	2	no	—
422	C₂²	—	34	1	no	—
423	C₂²	—	34	1	no	—
424	C₂²	—	34	1	no	—
425	C₂²	—	34	1	no	—
426	C₂²	—	34	1	no	—
427	C₂²	—	68	4	no	—
428	C₂²	#11763922	1	2	yes	—
429	C₂²	C₂³×#3633	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	17	1	no	—
437	C₄	—	17	1	no	—
438	C₄	—	17	2	no	—
439	C₄	—	34	1	no	—
440	C₄	—	34	1	no	—
441	C₄	—	34	1	no	—
442	C₄	—	34	1	no	—
443	C₂	—	2	2	no	—
444	C₂	—	34	2	no	—
445	C₂	—	68	1	no	—
446	C₂	C₂×#11763922	1	1	yes	characteristic
447	C₂	#14546035	1	1	yes	characteristic
448	C₂	#14546038	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#3633
commutator, socle	C₂²×C₁₇	C₂³×C₈
Fitting	C₁₇×#117	C₈
prime radical	C₂³×D₁₇	C₂×C₈
cosocle	C₂×#3624	C₂⁴
hypercenter	#117	#3633
hypocenter	C₁₇	#33422
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #117

Complements

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

N	H ≅ G/N	type
1. #14545990	C₂	semidirect
2. #14545990	C₂	semidirect
3. #14545988	C₂	semidirect
4. #14545987	C₂	semidirect
5. #14545984	C₂	semidirect
6. #14545983	C₂	semidirect
7. #14545975	C₂	semidirect
10. #14545945	C₂	semidirect
14. #11763912	C₂²	semidirect
15. #11763912	C₂²	semidirect
16. C₄⋊#63241	C₂²	semidirect
17. C₄⋊#63241	C₂²	semidirect
24. #11763903	C₂²	semidirect
25. #11763903	C₂²	semidirect
26. C₄×#63241	C₂²	semidirect
27. C₄×#63241	C₂²	semidirect
318. C₁₇	#33422	semidirect

Maximal subgroups

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

subgroup	index
#14545990	2
#14545988	2
#14545987	2
#14545984	2
#14545983	2
#14545975	2
#14545953	2
C₂×#11763906	2
#14545945	2
#14545344	2
#33422	17