Subgroups — #17982988

Order 4352.

756 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545933	C₂	1	1	yes	maximal, characteristic, complemented
2	#14545932	C₂	1	1	yes	maximal, characteristic
3	#14545932	C₂	1	1	yes	maximal, characteristic
4	#14545932	C₂	1	1	yes	maximal, characteristic
5	#14545931	C₂	1	1	yes	maximal, characteristic, complemented
6	#14545931	C₂	1	1	yes	maximal, characteristic, complemented
7	#14545931	C₂	1	1	yes	maximal, characteristic, complemented
8	#14545929	C₂	1	1	yes	maximal, characteristic
9	C₄⋊C₄×#3633	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₄×#3633	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₄⋊#3633	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²⋊C₄×#3633	C₂	1	1	yes	maximal, characteristic
13	C₂²⋊C₄×#3633	C₂	1	1	yes	maximal, characteristic
14	#14545918	C₂	1	1	yes	maximal, characteristic, complemented
15	#126×#595	C₂	1	1	yes	maximal, characteristic
16	C₂³×#3633	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊#3633	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊#3633	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊#3633	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#3633	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#3633	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊#3633	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊#3633	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊#3633	C₂²	1	1	yes	characteristic
25	C₂×C₄×#3633	C₂²	1	1	yes	characteristic
26	C₂×C₄×#3633	C₂²	1	1	yes	characteristic
27	C₂×C₄×#3633	C₂²	1	1	yes	characteristic
28	C₂×C₄×#3633	C₂²	1	1	yes	characteristic
29	C₂×C₄×#3633	C₂²	1	1	yes	characteristic
30	C₂×C₄×#3633	C₂²	1	1	yes	characteristic
31	C₂×C₄×#3633	C₂²	1	1	yes	characteristic
32	(C₂×#3633)⋊C₄	C₂²	1	1	yes	characteristic
33	(C₂×#3633)⋊C₄	C₂²	1	1	yes	characteristic
34	(C₂×#3633)⋊C₄	C₂²	1	1	yes	characteristic
35	(C₂×#3633)⋊C₄	C₂²	1	1	yes	characteristic
36	(C₂×#3633)⋊C₄	C₂²	1	1	yes	characteristic
37	(C₂×#3633)⋊C₄	C₂²	1	1	yes	characteristic
38	(C₂×#3633)⋊C₄	C₂²	1	1	yes	characteristic
39	(C₂×#3633)⋊C₄	C₂²	1	1	yes	characteristic
40	(C₂×#3633)⋊C₄	C₂²	1	1	yes	characteristic
41	(C₂×#3633)⋊C₄	C₂²	1	1	yes	characteristic
42	(C₂×#3633)⋊C₄	C₂²	1	1	yes	characteristic
43	(C₂×#3633)⋊C₄	C₂²	1	1	yes	characteristic
44	#11763759	C₄	1	1	yes	characteristic
45	#11763759	C₄	1	1	yes	characteristic
46	#11763759	C₄	1	1	yes	characteristic
47	#11763758	C₄	1	1	yes	characteristic
48	#11763758	C₄	1	1	yes	characteristic
49	#11763758	C₄	1	1	yes	characteristic
50	#11763754	C₄	1	1	yes	characteristic
51	C₄⋊C₄×#595	C₂²	1	1	yes	characteristic
52	C₄⋊C₄×#595	C₂²	1	1	yes	characteristic
53	C₄⋊C₄×#595	C₂²	1	1	yes	characteristic
54	C₂²⋊C₄×#595	C₂²	1	1	yes	characteristic
55	C₂²⋊C₄×#595	C₂²	1	1	yes	characteristic
56	C₂²⋊C₄×#595	C₂²	1	1	yes	characteristic
57	C₄²×#595	C₂²	1	1	yes	characteristic
58	#126×D₁₇	C₄	1	1	yes	characteristic
59	C₂³×#595	C₂³	1	1	yes	characteristic
60	C₂²×#3633	—	2	2	no	—
61	C₂²×#3633	—	2	2	no	—
62	C₂²×#3633	—	4	1	no	—
63	C₂²×#3633	C₂³	1	1	yes	characteristic
64	C₂²×#3633	C₂³	1	1	yes	characteristic
65	C₂²×#3633	C₂³	1	1	yes	characteristic
66	C₂²×#3633	C₂³	1	1	yes	characteristic
67	C₂²×#3633	C₂³	1	1	yes	characteristic
68	C₂²×#3633	C₂³	1	1	yes	characteristic
69	C₂²×#3633	C₂³	1	1	yes	characteristic
70	C₂²×#3633	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊#595	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊#595	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊#595	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊#595	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊#595	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊#595	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×#595	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×#595	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×#595	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×#595	C₂³	1	1	yes	characteristic
81	C₂×C₄×#595	C₂³	1	1	yes	characteristic
82	C₂×C₄×#595	C₂³	1	1	yes	characteristic
83	C₂×C₄×#595	C₂³	1	1	yes	characteristic
84	C₂×C₄×#595	C₂³	1	1	yes	characteristic
85	C₂×C₄×#595	C₂³	1	1	yes	characteristic
86	C₂²⋊#3633	—	2	2	no	—
87	C₂²⋊#3633	—	2	2	no	—
88	C₂²⋊#3633	—	4	1	no	—
89	C₄⋊#3633	—	2	2	no	—
90	C₄⋊#3633	—	2	2	no	—
91	C₄⋊#3633	—	2	2	no	—
92	C₄⋊#3633	—	2	2	no	—
93	C₄⋊#3633	—	4	1	no	—
94	C₄×#3633	—	2	2	no	—
95	C₄×#3633	—	2	2	no	—
96	C₄×#3633	—	2	2	no	—
97	C₄×#3633	—	2	2	no	—
98	C₄×#3633	—	4	1	no	—
99	C₄×#3633	—	4	1	no	—
100	C₄×#3633	—	4	1	no	—
101	C₁₇×#126	C₈	1	1	yes	characteristic, complemented
102	#10587584	C₈	1	1	yes	characteristic, complemented
103	#10587584	C₈	1	1	yes	characteristic, complemented
104	#10587584	C₈	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
106	C₄⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
107	C₄⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
108	C₂²⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
109	C₂²⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
110	C₂²⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
111	#10587565	C₈	1	1	yes	characteristic, complemented
112	#10587565	C₈	1	1	yes	characteristic, complemented
113	#10587565	C₈	1	1	yes	characteristic, complemented
114	#10587562	C₈	1	1	yes	characteristic, complemented
115	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
116	(C₂×#595)⋊C₄	C₂×C₄	1	1	yes	characteristic
117	(C₂×#595)⋊C₄	C₂×C₄	1	1	yes	characteristic
118	(C₂×#595)⋊C₄	C₂×C₄	1	1	yes	characteristic
119	(C₂×#595)⋊C₄	C₂×C₄	1	1	yes	characteristic
120	(C₂×#595)⋊C₄	C₂×C₄	1	1	yes	characteristic
121	(C₂×#595)⋊C₄	C₂×C₄	1	1	yes	characteristic
122	(C₂×#595)⋊C₄	C₂×C₄	1	1	yes	characteristic
123	(C₂×#595)⋊C₄	C₂×C₄	1	1	yes	characteristic
124	(C₂×#595)⋊C₄	C₂×C₄	1	1	yes	characteristic
125	(C₂×#595)⋊C₄	C₂×C₄	1	1	yes	characteristic
126	(C₂×#595)⋊C₄	C₂×C₄	1	1	yes	characteristic
127	(C₂×#595)⋊C₄	C₂×C₄	1	1	yes	characteristic
128	C₂³×D₁₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×#595	—	2	1	no	—
130	C₂²×#595	—	2	1	no	—
131	C₂²×#595	—	2	1	no	—
132	C₂²×#595	—	2	1	no	—
133	C₂²×#595	—	2	1	no	—
134	C₂²×#595	—	2	1	no	—
135	C₂²×#595	C₂²×C₄	1	1	yes	characteristic
136	C₂²×#595	C₂²×C₄	1	1	yes	characteristic
137	C₂²×#595	C₂²×C₄	1	1	yes	characteristic
138	C₂²×#595	C₂²×C₄	1	1	yes	characteristic
139	C₂²×#595	C₂²×C₄	1	1	yes	characteristic
140	C₂²×#595	C₂²×C₄	1	1	yes	characteristic
141	C₂²×#595	C₂²×C₄	1	1	yes	characteristic
142	C₂²×#595	C₂⁴	1	1	yes	characteristic
143	C₂×#3633	—	2	1	no	—
144	C₂×#3633	—	2	1	no	—
145	C₂×#3633	—	2	1	no	—
146	C₂×#3633	—	2	1	no	—
147	C₂×#3633	—	2	1	no	—
148	C₂×#3633	—	2	1	no	—
149	C₂×#3633	—	2	1	no	—
150	C₂×#3633	—	2	1	no	—
151	C₂×#3633	—	2	1	no	—
152	C₂×#3633	—	2	1	no	—
153	C₂×#3633	—	2	1	no	—
154	C₂×#3633	—	2	1	no	—
155	C₂×#3633	—	2	1	no	—
156	C₂×#3633	—	2	1	no	—
157	C₂×#3633	—	2	1	no	—
158	C₂×#3633	—	2	1	no	—
159	C₂×#3633	—	2	1	no	—
160	C₂×#3633	—	2	1	no	—
161	C₂×#3633	—	2	1	no	—
162	C₂×#3633	—	2	1	no	—
163	C₂×#3633	—	4	4	no	—
164	C₂×#3633	#41	1	2	yes	—
165	C₂×#3633	#41	1	2	yes	—
166	C₂×#3633	#41	1	2	yes	—
167	C₂×#3633	#41	1	2	yes	—
168	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
174	C₂²⋊#595	—	2	2	no	—
175	C₂²⋊#595	—	2	2	no	—
176	C₂²⋊#595	—	4	1	no	—
177	C₄⋊#595	—	2	2	no	—
178	C₄⋊#595	—	2	2	no	—
179	C₄⋊#595	—	4	1	no	—
180	C₄×#595	—	2	2	no	—
181	C₄×#595	—	2	2	no	—
182	C₄×#595	—	2	1	no	—
183	C₄×#595	—	2	1	no	—
184	C₄×#595	—	2	1	no	—
185	C₄×#595	—	2	1	no	—
186	C₄×#595	—	2	1	no	—
187	C₄×#595	—	2	1	no	—
188	C₄×#595	—	2	1	no	—
189	C₄×#595	—	2	1	no	—
190	C₄×#595	—	2	1	no	—
191	C₄×#595	—	2	1	no	—
192	C₄×#595	—	2	1	no	—
193	C₄×#595	—	2	1	no	—
194	C₄×#595	—	4	1	no	—
195	C₄⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic, complemented
196	C₄⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic, complemented
197	C₄⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic, complemented
198	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
199	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
200	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
201	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic, complemented
202	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
203	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
204	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
205	#63227	C₂×C₈	1	1	yes	characteristic
206	#63227	C₂×C₈	1	1	yes	characteristic
207	#63227	C₂×C₈	1	1	yes	characteristic
208	#63227	C₂×C₈	1	1	yes	characteristic
209	#63227	C₂×C₈	1	1	yes	characteristic
210	#63227	C₂×C₈	1	1	yes	characteristic
211	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic, complemented
212	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic, complemented
213	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic, complemented
214	#63225	C₂×C₈	1	1	yes	characteristic, complemented
215	#63225	C₂×C₈	1	1	yes	characteristic, complemented
216	#63225	C₂×C₈	1	1	yes	characteristic, complemented
217	#63225	C₂×C₈	1	1	yes	characteristic, complemented
218	#63225	C₂×C₈	1	1	yes	characteristic, complemented
219	#63225	C₂×C₈	1	1	yes	characteristic, complemented
220	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic, complemented
221	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic, complemented
222	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic, complemented
223	#23278	—	17	1	no	maximal, Sylow
224	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
225	C₂²×D₁₇	—	2	1	no	—
226	C₂²×D₁₇	—	2	1	no	—
227	C₂²×D₁₇	—	2	1	no	—
228	C₂²×D₁₇	—	2	1	no	—
229	C₂²×D₁₇	—	2	1	no	—
230	C₂²×D₁₇	—	2	1	no	—
231	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
232	C₂²×D₁₇	C₂³×C₄	1	1	yes	characteristic
233	C₂×#595	—	2	1	no	—
234	C₂×#595	—	2	1	no	—
235	C₂×#595	—	2	1	no	—
236	C₂×#595	—	2	1	no	—
237	C₂×#595	—	2	1	no	—
238	C₂×#595	—	2	1	no	—
239	C₂×#595	—	2	1	no	—
240	C₂×#595	—	2	1	no	—
241	C₂×#595	—	2	1	no	—
242	C₂×#595	—	2	1	no	—
243	C₂×#595	—	2	1	no	—
244	C₂×#595	—	2	1	no	—
245	C₂×#595	—	2	1	no	—
246	C₂×#595	—	2	1	no	—
247	C₂×#595	—	2	1	no	—
248	C₂×#595	—	2	1	no	—
249	C₂×#595	—	2	1	no	—
250	C₂×#595	—	2	1	no	—
251	C₂×#595	—	2	1	no	—
252	C₂×#595	—	4	1	no	—
253	C₂×#595	—	4	1	no	—
254	C₂×#595	—	4	1	no	—
255	C₂×#595	—	4	1	no	—
256	C₂×#595	#131	1	2	yes	—
257	C₂×#595	#131	1	2	yes	—
258	C₂×#595	C₂×#41	1	1	yes	characteristic
259	C₂×#595	C₂×#41	1	1	yes	characteristic
260	C₂×#595	C₂×#41	1	1	yes	characteristic
261	C₂×#595	C₂×#41	1	1	yes	characteristic
262	C₂×#595	H(5,𝔽₂)	1	1	yes	characteristic
263	C₂×#595	2₋¹⁺⁴	1	1	yes	characteristic
264	#3633	—	2	2	no	—
265	#3633	—	2	2	no	—
266	#3633	—	2	2	no	—
267	#3633	—	2	2	no	—
268	#3633	—	4	1	no	—
269	#3633	—	4	1	no	—
270	#3633	—	4	1	no	—
271	#3633	—	4	1	no	—
272	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
273	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
274	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
275	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
276	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
277	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
278	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
279	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
280	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
281	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
282	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
283	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
284	C₄×D₁₇	—	2	1	no	—
285	C₄×D₁₇	—	2	1	no	—
286	C₄×D₁₇	—	2	1	no	—
287	C₄×D₁₇	—	2	1	no	—
288	C₄×D₁₇	—	2	1	no	—
289	C₄×D₁₇	—	2	1	no	—
290	C₄×D₁₇	—	2	1	no	—
291	C₄×D₁₇	—	2	1	no	—
292	C₄×D₁₇	—	2	1	no	—
293	C₄×D₁₇	—	2	1	no	—
294	C₄×D₁₇	—	2	1	no	—
295	C₄×D₁₇	—	2	1	no	—
296	C₄×#126	—	17	1	no	—
297	#1939	—	17	1	no	—
298	#1923	—	17	1	no	—
299	#1923	—	17	1	no	—
300	#1923	—	17	1	no	—
301	#1916	—	17	1	no	—
302	#1916	—	17	1	no	—
303	#1916	—	17	1	no	—
304	#1850	—	17	1	no	—
305	C₈×C₄⋊C₄	—	17	1	no	—
306	C₈×C₄⋊C₄	—	17	1	no	—
307	C₄×C₄⋊C₈	—	17	1	no	—
308	C₈×C₂²⋊C₄	—	17	1	no	—
309	C₈×C₂²⋊C₄	—	17	1	no	—
310	#1744	—	17	1	no	—
311	C₂²×C₁₇	—	2	1	no	—
312	C₂²×C₁₇	—	2	1	no	—
313	C₂²×C₁₇	—	2	1	no	—
314	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
315	C₂×D₁₇	—	2	1	no	—
316	C₂×D₁₇	—	2	1	no	—
317	C₂×D₁₇	—	2	1	no	—
318	C₂×D₁₇	—	4	1	no	—
319	C₂×D₁₇	—	4	1	no	—
320	C₂×D₁₇	—	4	1	no	—
321	C₂×D₁₇	—	4	1	no	—
322	C₂×D₁₇	C₄×#41	1	1	yes	characteristic
323	C₂×D₁₇	C₄×#41	1	1	yes	characteristic
324	C₂×D₁₇	#520	1	1	yes	characteristic
325	C₂×D₁₇	C₂×#131	1	1	yes	characteristic
326	C₂×D₁₇	C₂×#131	1	1	yes	characteristic
327	C₂×D₁₇	#568	1	1	yes	characteristic
328	#595	—	2	2	no	—
329	#595	—	2	2	no	—
330	#595	—	4	1	no	—
331	#595	—	4	1	no	—
332	#595	—	4	1	no	—
333	#595	—	4	1	no	—
334	#595	—	4	1	no	—
335	#595	#551	1	1	yes	characteristic
336	#595	#552	1	1	yes	characteristic
337	#595	#553	1	1	yes	characteristic
338	#595	#556	1	1	yes	characteristic
339	C₄×C₁₇	—	2	1	no	—
340	C₄×C₁₇	—	2	1	no	—
341	C₄×C₁₇	—	2	1	no	—
342	C₄×C₁₇	—	2	1	no	—
343	C₄×C₁₇	—	2	1	no	—
344	C₄×C₁₇	—	2	1	no	—
345	Dic₁₇	—	2	1	no	—
346	Dic₁₇	—	2	1	no	—
347	Dic₁₇	—	2	1	no	—
348	Dic₁₇	—	2	1	no	—
349	Dic₁₇	—	2	1	no	—
350	Dic₁₇	—	2	1	no	—
351	C₂³×C₈	—	17	1	no	—
352	C₂×#126	—	17	1	no	—
353	C₂×C₄⋊C₈	—	17	1	no	—
354	C₂×C₄⋊C₈	—	17	1	no	—
355	C₂×C₄⋊C₈	—	17	1	no	—
356	C₂×C₄⋊C₈	—	17	1	no	—
357	C₂×C₄⋊C₈	—	17	1	no	—
358	C₂×C₂²⋊C₈	—	17	1	no	—
359	C₂×C₂²⋊C₈	—	17	1	no	—
360	C₂×C₂²⋊C₈	—	17	1	no	—
361	C₂×C₄×C₈	—	17	1	no	—
362	C₂×C₄×C₈	—	17	1	no	—
363	C₂×C₄×C₈	—	17	1	no	—
364	C₂×C₄×C₈	—	17	1	no	—
365	C₂×C₄×C₈	—	17	1	no	—
366	C₂×C₄×C₈	—	17	1	no	—
367	C₂×C₄×C₈	—	17	1	no	—
368	#388	—	17	1	no	—
369	#388	—	17	1	no	—
370	#388	—	17	1	no	—
371	#387	—	17	1	no	—
372	#387	—	17	1	no	—
373	#387	—	17	1	no	—
374	#383	—	17	1	no	—
375	C₄×C₄⋊C₄	—	17	1	no	—
376	C₄×C₄⋊C₄	—	17	1	no	—
377	C₄×C₄⋊C₄	—	17	1	no	—
378	C₄×C₂²⋊C₄	—	17	1	no	—
379	C₄×C₂²⋊C₄	—	17	1	no	—
380	C₄×C₂²⋊C₄	—	17	1	no	—
381	C₄³	—	17	1	no	—
382	#336	—	17	1	no	—
383	#336	—	17	1	no	—
384	#336	—	17	1	no	—
385	#336	—	17	1	no	—
386	#336	—	17	1	no	—
387	#336	—	17	1	no	—
388	#336	—	17	1	no	—
389	#336	—	17	1	no	—
390	#336	—	17	1	no	—
391	#336	—	17	1	no	—
392	#336	—	17	1	no	—
393	#336	—	17	1	no	—
394	C₂×C₁₇	—	4	1	no	—
395	C₂×C₁₇	C₈×#41	1	1	yes	characteristic
396	C₂×C₁₇	C₈×#41	1	1	yes	characteristic
397	C₂×C₁₇	#2988	1	1	yes	characteristic
398	D₁₇	—	4	1	no	—
399	D₁₇	#2373	1	1	yes	characteristic
400	D₁₇	#2968	1	1	yes	characteristic
401	D₁₇	#2969	1	1	yes	characteristic
402	D₁₇	#2994	1	1	yes	characteristic
403	C₂³×C₄	—	17	1	no	—
404	C₂²×C₈	—	17	1	no	—
405	C₂²×C₈	—	17	1	no	—
406	C₂²×C₈	—	17	1	no	—
407	C₂²×C₈	—	17	1	no	—
408	C₂²×C₈	—	17	1	no	—
409	C₂²×C₈	—	17	1	no	—
410	C₂²×C₈	—	17	1	no	—
411	C₂²×C₈	—	17	1	no	—
412	C₂²×C₈	—	34	2	no	—
413	C₂²×C₈	—	34	2	no	—
414	C₂²×C₈	—	68	1	no	—
415	#126	—	17	1	no	—
416	#126	—	17	1	no	—
417	#126	—	17	1	no	—
418	#126	—	17	1	no	—
419	#126	—	17	1	no	—
420	#126	—	17	1	no	—
421	#126	—	17	1	no	—
422	#126	#3633	1	1	yes	characteristic, complemented
423	C₂×C₄⋊C₄	—	17	1	no	—
424	C₂×C₄⋊C₄	—	17	1	no	—
425	C₂×C₄⋊C₄	—	17	1	no	—
426	C₂×C₄⋊C₄	—	17	1	no	—
427	C₂×C₄⋊C₄	—	17	1	no	—
428	C₂×C₄⋊C₄	—	17	1	no	—
429	C₂×C₂²⋊C₄	—	17	1	no	—
430	C₂×C₂²⋊C₄	—	17	1	no	—
431	C₂×C₂²⋊C₄	—	17	1	no	—
432	C₂×C₂²⋊C₄	—	17	1	no	—
433	C₂×C₂²⋊C₄	—	17	1	no	—
434	C₂×C₂²⋊C₄	—	17	1	no	—
435	C₂×C₄²	—	17	1	no	—
436	C₂×C₄²	—	17	1	no	—
437	C₂×C₄²	—	17	1	no	—
438	C₂×C₄²	—	17	1	no	—
439	C₂×C₄²	—	17	1	no	—
440	C₂×C₄²	—	17	1	no	—
441	C₂×C₄²	—	17	1	no	—
442	C₂×C₄²	—	17	1	no	—
443	C₂×C₄²	—	17	1	no	—
444	C₂×C₄²	—	17	1	no	—
445	C₄⋊C₈	—	34	2	no	—
446	C₄⋊C₈	—	34	2	no	—
447	C₄⋊C₈	—	34	2	no	—
448	C₄⋊C₈	—	34	2	no	—
449	C₄⋊C₈	—	68	1	no	—
450	C₂²⋊C₈	—	34	2	no	—
451	C₂²⋊C₈	—	34	2	no	—
452	C₂²⋊C₈	—	68	1	no	—
453	C₄×C₈	—	34	2	no	—
454	C₄×C₈	—	34	2	no	—
455	C₄×C₈	—	34	2	no	—
456	C₄×C₈	—	34	2	no	—
457	C₄×C₈	—	68	1	no	—
458	C₄×C₈	—	68	1	no	—
459	C₄×C₈	—	68	1	no	—
460	#95	—	17	1	no	—
461	#95	—	17	1	no	—
462	#95	—	17	1	no	—
463	#95	—	17	1	no	—
464	#95	—	17	1	no	—
465	#95	—	17	1	no	—
466	#95	—	17	1	no	—
467	#95	—	17	1	no	—
468	#95	—	17	1	no	—
469	#95	—	17	1	no	—
470	#95	—	17	1	no	—
471	#95	—	17	1	no	—
472	C₁₇	#23278	1	1	yes	characteristic, complemented, Sylow
473	C₂⁴	—	17	1	no	—
474	C₂²×C₄	—	17	1	no	—
475	C₂²×C₄	—	17	1	no	—
476	C₂²×C₄	—	17	1	no	—
477	C₂²×C₄	—	17	1	no	—
478	C₂²×C₄	—	17	1	no	—
479	C₂²×C₄	—	17	1	no	—
480	C₂²×C₄	—	17	1	no	—
481	C₂²×C₄	—	17	1	no	—
482	C₂²×C₄	—	17	1	no	—
483	C₂²×C₄	—	17	1	no	—
484	C₂²×C₄	—	17	1	no	—
485	C₂²×C₄	—	17	1	no	—
486	C₂²×C₄	—	17	1	no	—
487	C₂²×C₄	—	17	1	no	—
488	C₂²×C₄	—	34	1	no	—
489	C₂²×C₄	—	34	1	no	—
490	C₂²×C₄	—	34	1	no	—
491	C₂²×C₄	—	34	1	no	—
492	C₂²×C₄	—	34	1	no	—
493	C₂²×C₄	—	34	1	no	—
494	C₂×C₈	—	17	2	no	—
495	C₂×C₈	—	17	2	no	—
496	C₂×C₈	—	17	2	no	—
497	C₂×C₈	—	17	2	no	—
498	C₂×C₈	—	34	1	no	—
499	C₂×C₈	—	34	1	no	—
500	C₂×C₈	—	34	1	no	—
501	C₂×C₈	—	34	1	no	—
502	C₂×C₈	—	34	1	no	—
503	C₂×C₈	—	34	1	no	—
504	C₂×C₈	—	34	1	no	—
505	C₂×C₈	—	34	1	no	—
506	C₂×C₈	—	34	1	no	—
507	C₂×C₈	—	34	1	no	—
508	C₂×C₈	—	34	1	no	—
509	C₂×C₈	—	34	1	no	—
510	C₂×C₈	—	34	1	no	—
511	C₂×C₈	—	34	1	no	—
512	C₂×C₈	—	34	1	no	—
513	C₂×C₈	—	34	1	no	—
514	C₂×C₈	—	34	1	no	—
515	C₂×C₈	—	34	1	no	—
516	C₂×C₈	—	34	1	no	—
517	C₂×C₈	—	34	1	no	—
518	C₂×C₈	—	68	4	no	—
519	C₄⋊C₄	—	17	1	no	—
520	C₄⋊C₄	—	17	1	no	—
521	C₄⋊C₄	—	17	1	no	—
522	C₄⋊C₄	—	17	1	no	—
523	C₄⋊C₄	—	17	1	no	—
524	C₄⋊C₄	—	17	1	no	—
525	C₄⋊C₄	—	17	1	no	—
526	C₄⋊C₄	—	17	1	no	—
527	C₄⋊C₄	—	17	1	no	—
528	C₄⋊C₄	—	34	2	no	—
529	C₄⋊C₄	—	34	2	no	—
530	C₄⋊C₄	—	68	1	no	—
531	C₄⋊C₄	C₂×#3633	1	1	yes	characteristic, complemented
532	C₄⋊C₄	C₂×#3633	1	1	yes	characteristic, complemented
533	C₄⋊C₄	C₂×#3633	1	1	yes	characteristic, complemented
534	C₂²⋊C₄	—	17	1	no	—
535	C₂²⋊C₄	—	17	1	no	—
536	C₂²⋊C₄	—	17	1	no	—
537	C₂²⋊C₄	—	17	1	no	—
538	C₂²⋊C₄	—	17	1	no	—
539	C₂²⋊C₄	—	17	1	no	—
540	C₂²⋊C₄	—	17	1	no	—
541	C₂²⋊C₄	—	17	1	no	—
542	C₂²⋊C₄	—	17	1	no	—
543	C₂²⋊C₄	—	34	2	no	—
544	C₂²⋊C₄	—	34	2	no	—
545	C₂²⋊C₄	—	68	1	no	—
546	C₂²⋊C₄	C₂×#3633	1	1	yes	characteristic
547	C₂²⋊C₄	C₂×#3633	1	1	yes	characteristic
548	C₂²⋊C₄	C₂×#3633	1	1	yes	characteristic
549	C₄²	—	17	1	no	—
550	C₄²	—	17	1	no	—
551	C₄²	—	17	1	no	—
552	C₄²	—	34	1	no	—
553	C₄²	—	34	1	no	—
554	C₄²	—	34	1	no	—
555	C₄²	—	34	1	no	—
556	C₄²	—	34	1	no	—
557	C₄²	—	34	1	no	—
558	C₄²	—	34	1	no	—
559	C₄²	—	34	1	no	—
560	C₄²	—	34	1	no	—
561	C₄²	—	34	1	no	—
562	C₄²	—	34	1	no	—
563	C₄²	—	34	1	no	—
564	C₄²	—	34	2	no	—
565	C₄²	—	34	2	no	—
566	C₄²	—	68	1	no	—
567	C₄²	C₂×#3633	1	1	yes	characteristic, complemented
568	C₂³	—	17	1	no	—
569	C₂³	—	17	1	no	—
570	C₂³	—	34	1	no	—
571	C₂³	—	34	1	no	—
572	C₂³	—	34	1	no	—
573	C₂³	—	34	1	no	—
574	C₂³	—	34	1	no	—
575	C₂³	—	34	1	no	—
576	C₂³	C₂²×#3633	1	1	yes	characteristic
577	C₂×C₄	—	17	1	no	—
578	C₂×C₄	—	17	1	no	—
579	C₂×C₄	—	17	1	no	—
580	C₂×C₄	—	17	1	no	—
581	C₂×C₄	—	17	1	no	—
582	C₂×C₄	—	17	1	no	—
583	C₂×C₄	—	17	2	no	—
584	C₂×C₄	—	17	2	no	—
585	C₂×C₄	—	17	1	no	—
586	C₂×C₄	—	17	1	no	—
587	C₂×C₄	—	17	1	no	—
588	C₂×C₄	—	17	1	no	—
589	C₂×C₄	—	17	1	no	—
590	C₂×C₄	—	17	1	no	—
591	C₂×C₄	—	34	1	no	—
592	C₂×C₄	—	34	1	no	—
593	C₂×C₄	—	34	1	no	—
594	C₂×C₄	—	34	1	no	—
595	C₂×C₄	—	34	1	no	—
596	C₂×C₄	—	34	1	no	—
597	C₂×C₄	—	34	1	no	—
598	C₂×C₄	—	34	1	no	—
599	C₂×C₄	—	34	1	no	—
600	C₂×C₄	—	34	1	no	—
601	C₂×C₄	—	34	1	no	—
602	C₂×C₄	—	34	1	no	—
603	C₂×C₄	—	34	1	no	—
604	C₂×C₄	—	34	1	no	—
605	C₂×C₄	—	34	1	no	—
606	C₂×C₄	—	34	1	no	—
607	C₂×C₄	—	34	1	no	—
608	C₂×C₄	—	34	1	no	—
609	C₂×C₄	—	34	1	no	—
610	C₂×C₄	—	34	1	no	—
611	C₂×C₄	—	34	1	no	—
612	C₂×C₄	—	34	1	no	—
613	C₂×C₄	—	34	1	no	—
614	C₂×C₄	—	34	1	no	—
615	C₂×C₄	—	34	1	no	—
616	C₂×C₄	—	34	1	no	—
617	C₂×C₄	—	34	1	no	—
618	C₂×C₄	—	34	1	no	—
619	C₂×C₄	—	34	1	no	—
620	C₂×C₄	—	34	1	no	—
621	C₂×C₄	—	34	1	no	—
622	C₂×C₄	—	68	1	no	—
623	C₂×C₄	—	68	1	no	—
624	C₂×C₄	—	68	1	no	—
625	C₂×C₄	—	68	1	no	—
626	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
627	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
628	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
629	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
630	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
631	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
632	C₈	—	34	2	no	—
633	C₈	—	34	2	no	—
634	C₈	—	34	2	no	—
635	C₈	—	34	2	no	—
636	C₈	—	68	1	no	—
637	C₈	—	68	1	no	—
638	C₈	—	68	1	no	—
639	C₈	—	68	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	17	1	no	—
644	C₂²	—	17	1	no	—
645	C₂²	—	17	1	no	—
646	C₂²	—	17	1	no	—
647	C₂²	—	17	1	no	—
648	C₂²	—	17	1	no	—
649	C₂²	—	34	1	no	—
650	C₂²	—	34	1	no	—
651	C₂²	—	34	1	no	—
652	C₂²	—	68	1	no	—
653	C₂²	—	68	1	no	—
654	C₂²	—	68	1	no	—
655	C₂²	—	68	1	no	—
656	C₂²	C₂³×#3633	1	1	yes	characteristic
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	17	1	no	—
664	C₄	—	17	1	no	—
665	C₄	—	17	1	no	—
666	C₄	—	17	1	no	—
667	C₄	—	34	2	no	—
668	C₄	—	34	2	no	—
669	C₄	—	34	1	no	—
670	C₄	—	34	1	no	—
671	C₄	—	34	1	no	—
672	C₄	—	34	1	no	—
673	C₄	—	34	1	no	—
674	C₄	—	34	1	no	—
675	C₄	—	68	1	no	—
676	C₄	—	68	1	no	—
677	C₄	—	68	1	no	—
678	C₄	—	68	1	no	—
679	C₄	—	68	1	no	—
680	C₂	—	4	1	no	—
681	C₂	—	17	1	no	—
682	C₂	—	17	1	no	—
683	C₂	—	17	1	no	—
684	C₂	—	17	1	no	—
685	C₂	—	68	1	no	—
686	C₂	#41×#3633	1	1	yes	characteristic
687	C₂	#41×#3633	1	1	yes	characteristic
688	C₂	#14546028	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#3633
commutator, socle	C₂²×C₁₇	C₂³×C₈
Fitting	C₁₇×#126	C₈
prime radical	C₂³×D₁₇	C₂²×C₄
cosocle	C₂²×#595	C₂⁴
hypercenter	#126	#3633
hypocenter	C₁₇	#23278
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #126

Complements

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

N	H ≅ G/N	type
1. #14545933	C₂	semidirect
5. #14545931	C₂	semidirect
6. #14545931	C₂	semidirect
7. #14545931	C₂	semidirect
9. C₄⋊C₄×#3633	C₂	semidirect
10. C₄⋊C₄×#3633	C₂	semidirect
11. C₄×C₄⋊#3633	C₂	semidirect
14. #14545918	C₂	semidirect
101. C₁₇×#126	C₈	semidirect
102. #10587584	C₈	semidirect
103. #10587584	C₈	semidirect
104. #10587584	C₈	semidirect
111. #10587565	C₈	semidirect
112. #10587565	C₈	semidirect
113. #10587565	C₈	semidirect
114. #10587562	C₈	semidirect
195. C₄⋊C₄×C₁₇	C₂×C₈	semidirect
196. C₄⋊C₄×C₁₇	C₂×C₈	semidirect
197. C₄⋊C₄×C₁₇	C₂×C₈	semidirect
201. C₄²×C₁₇	C₂×C₈	semidirect
211. C₄⋊Dic₁₇	C₂×C₈	semidirect
212. C₄⋊Dic₁₇	C₂×C₈	semidirect
213. C₄⋊Dic₁₇	C₂×C₈	semidirect
214. #63225	C₂×C₈	semidirect
215. #63225	C₂×C₈	semidirect
216. #63225	C₂×C₈	semidirect
217. #63225	C₂×C₈	semidirect
218. #63225	C₂×C₈	semidirect
219. #63225	C₂×C₈	semidirect
220. C₄×Dic₁₇	C₂×C₈	semidirect
221. C₄×Dic₁₇	C₂×C₈	semidirect
222. C₄×Dic₁₇	C₂×C₈	semidirect
422. #126	#3633	semidirect
472. C₁₇	#23278	semidirect
531. C₄⋊C₄	C₂×#3633	semidirect
532. C₄⋊C₄	C₂×#3633	semidirect
533. C₄⋊C₄	C₂×#3633	semidirect
567. C₄²	C₂×#3633	semidirect

Maximal subgroups

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

subgroup	index
#14545933	2
#14545932	2
#14545931	2
#14545929	2
C₄⋊C₄×#3633	2
C₄×C₄⋊#3633	2
C₂²⋊C₄×#3633	2
#14545918	2
#126×#595	2
#23278	17