Subgroups — #14543107

Order 2176.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763553	C₂	1	2	yes	maximal, complemented
2	#11763547	C₂	1	2	yes	maximal, complemented
3	#11763503	C₂	1	1	yes	maximal, characteristic, complemented
4	#11763498	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763483	C₂	1	2	yes	maximal, complemented
6	#11763477	C₂	1	1	yes	maximal, characteristic, complemented
7	#11763462	C₂	1	1	yes	maximal, characteristic, complemented
8	#11763455	C₂	1	1	yes	maximal, characteristic, complemented
9	#11763454	C₂	1	1	yes	maximal, characteristic, complemented
10	#11763452	C₂	1	2	yes	maximal, complemented
11	#11763443	C₂	1	1	yes	maximal, characteristic, complemented
12	#11763433	C₂	1	1	yes	maximal, characteristic, complemented
13	#11763414	C₂	1	2	yes	maximal, complemented
14	#11763410	C₂	1	1	yes	maximal, characteristic, complemented
15	#11763393	C₂	1	2	yes	maximal, complemented
16	#11763388	C₂	1	1	yes	maximal, characteristic, complemented
17	#11763378	C₂	1	1	yes	maximal, characteristic, complemented
18	#11763377	C₂	1	2	yes	maximal, complemented
19	#11763367	C₂	1	2	yes	maximal, complemented
20	#11763321	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763318	C₂	1	1	yes	maximal, characteristic, complemented
22	#121×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#555	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#63256	C₂²	1	2	yes	complemented
25	C₂×#63254	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₄×D₁₇	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₇	C₂²	1	2	yes	—
28	C₂×D₄×D₁₇	C₂²	1	2	yes	complemented
29	C₂×#63252	C₂²	1	1	yes	characteristic, complemented
30	C₂×#63252	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₆₈	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
33	C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₁₇×#124	C₂²	1	2	yes	complemented
35	C₁₇×#124	C₂²	1	2	yes	complemented
36	C₁₇×#121	C₂²	1	1	yes	characteristic, complemented
37	C₁₇×#121	C₂²	1	2	yes	complemented
38	C₁₇×#121	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
41	C₁₇×#117	C₂²	1	2	yes	complemented
42	C₁₇×#117	C₂²	1	1	yes	characteristic, complemented
43	C₁₇×#117	C₂²	1	1	yes	characteristic, complemented
44	#10587633	C₂²	1	2	yes	complemented
45	#10587632	C₂²	1	2	yes	complemented
46	#10587632	C₂²	1	2	yes	complemented
47	#10587626	C₂²	1	2	yes	complemented
48	#10587626	C₂²	1	1	yes	characteristic, complemented
49	#10587625	C₂²	1	2	yes	complemented
50	#10587625	C₂²	1	1	yes	characteristic, complemented
51	#10587625	C₂²	1	2	yes	complemented
52	#10587625	C₂²	1	2	yes	complemented
53	#10587624	C₂²	1	2	yes	complemented
54	#10587624	C₂²	1	1	yes	characteristic, complemented
55	#10587623	C₂²	1	1	yes	characteristic
56	#10587623	C₂²	1	2	yes	complemented
57	#10587623	C₂²	1	2	yes	complemented
58	#10587616	C₂²	1	1	yes	characteristic
59	#10587616	C₂²	1	2	yes	complemented
60	#10587616	C₂²	1	2	yes	complemented
61	#10587615	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
64	C₂×#63227	C₂²	1	2	yes	complemented
65	#10587610	C₂²	1	1	yes	characteristic, complemented
66	#10587584	C₂²	1	2	yes	complemented
67	#10587583	C₂²	1	1	yes	characteristic, complemented
68	#10587583	C₂²	1	1	yes	characteristic, complemented
69	#10587582	C₂²	1	1	yes	characteristic, complemented
70	#10587581	C₂²	1	1	yes	characteristic
71	#10587581	C₂²	1	1	yes	characteristic
72	#10587581	C₂²	1	1	yes	characteristic, complemented
73	#10587581	C₂²	1	1	yes	characteristic, complemented
74	#10587581	C₂²	1	1	yes	characteristic, complemented
75	#10587580	C₂²	1	2	yes	complemented
76	#10587580	C₂²	1	2	yes	complemented
77	#10587580	C₂²	1	2	yes	complemented
78	#10587580	C₂²	1	1	yes	characteristic, complemented
79	#10587580	C₂²	1	2	yes	complemented
80	#10587579	C₂²	1	1	yes	characteristic, complemented
81	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
82	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
83	#10587576	C₂²	1	1	yes	characteristic, complemented
84	#10587573	C₂²	1	1	yes	characteristic, complemented
85	#10587572	C₂²	1	2	yes	complemented
86	#10587572	C₂²	1	2	yes	complemented
87	#10587570	C₂²	1	1	yes	characteristic
88	#10587570	C₂²	1	2	yes	complemented
89	#10587570	C₂²	1	2	yes	complemented
90	#10587570	C₂²	1	2	yes	complemented
91	#10587570	C₂²	1	2	yes	complemented
92	#10587570	C₂²	1	2	yes	complemented
93	#10587570	C₂²	1	2	yes	complemented
94	#10587570	C₂²	1	2	yes	complemented
95	#10587569	C₂²	1	2	yes	—
96	#10587569	C₂²	1	2	yes	complemented
97	#10587569	C₂²	1	2	yes	complemented
98	#10587569	C₂²	1	1	yes	characteristic, complemented
99	#10587568	C₂²	1	2	yes	—
100	#10587568	C₂²	1	2	yes	complemented
101	#10587568	C₂²	1	1	yes	characteristic, complemented
102	#10587568	C₂²	1	2	yes	complemented
103	#10587568	C₂²	1	2	yes	complemented
104	#10587568	C₂²	1	2	yes	complemented
105	#10587567	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	complemented
108	#10587565	C₂²	1	2	yes	complemented
109	#10587564	C₂²	1	2	yes	complemented
110	#10587564	C₂²	1	1	yes	characteristic, complemented
111	#10587562	C₂²	1	2	yes	complemented
112	#10587561	C₂²	1	2	yes	complemented
113	#10587561	C₂²	1	1	yes	characteristic, complemented
114	#10587560	C₂²	1	2	yes	complemented
115	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₆₈	C₂²	1	2	yes	complemented
118	C₄×D₆₈	C₂²	1	2	yes	complemented
119	C₄×D₆₈	C₂²	1	2	yes	complemented
120	#10587558	C₂²	1	2	yes	complemented
121	#10587558	C₂²	1	1	yes	characteristic, complemented
122	#10587556	C₂²	1	2	yes	complemented
123	C₂³×D₁₇	C₂³	1	1	yes	characteristic
124	C₂³×D₁₇	C₂³	1	2	yes	—
125	C₂³×D₁₇	C₂³	1	2	yes	—
126	C₂×Q₈×C₁₇	C₂³	1	2	yes	—
127	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₇	C₂³	1	2	yes	—
129	C₂×D₄×C₁₇	C₂³	1	2	yes	—
130	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
145	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
146	C₂²×Dic₁₇	C₂³	1	2	yes	—
147	#63256	—	4	4	no	—
148	#63254	—	4	2	no	—
149	D₄×D₁₇	—	4	2	no	—
150	D₄×D₁₇	—	4	4	no	—
151	D₄×D₁₇	—	4	4	no	—
152	#63252	—	4	2	no	—
153	#63252	—	4	2	no	—
154	C₂×D₆₈	—	4	2	no	—
155	C₂×D₆₈	C₂³	1	1	yes	characteristic
156	C₂×D₆₈	C₂³	1	1	yes	characteristic
157	C₂×D₆₈	C₂³	1	2	yes	—
158	C₂×D₆₈	C₂³	1	1	yes	characteristic
159	C₂×D₆₈	C₂³	1	2	yes	—
160	C₂×D₆₈	C₂³	1	1	yes	characteristic
161	C₂×D₆₈	C₂³	1	2	yes	—
162	C₂×D₆₈	C₂³	1	2	yes	—
163	C₂×D₆₈	C₂³	1	2	yes	—
164	C₂×D₆₈	C₂³	1	2	yes	—
165	C₂×C₄×D₁₇	—	4	2	no	—
166	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₁₇	C₂³	1	2	yes	—
170	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
171	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
172	C₂×C₄×D₁₇	C₂³	1	2	yes	—
173	C₂×C₄×D₁₇	C₂³	1	2	yes	—
174	C₂×C₄×D₁₇	C₂³	1	2	yes	—
175	C₂×C₄×D₁₇	C₂³	1	2	yes	—
176	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
177	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
179	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
180	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
181	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
182	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
183	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
184	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
185	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
190	C₄²×C₁₇	C₂³	1	2	yes	—
191	C₄²×C₁₇	C₂³	1	2	yes	—
192	C₄²×C₁₇	C₂³	1	1	yes	characteristic
193	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
194	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
195	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
196	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
197	#63227	C₂³	1	1	yes	characteristic
198	#63227	C₂³	1	2	yes	—
199	#63227	C₂³	1	1	yes	characteristic
200	#63227	C₂³	1	1	yes	characteristic
201	#63227	C₂³	1	1	yes	characteristic
202	#63227	C₂³	1	2	yes	—
203	#63227	C₂³	1	2	yes	—
204	#63227	C₂³	1	2	yes	—
205	#63227	C₂³	1	2	yes	—
206	#63227	C₂³	1	2	yes	—
207	#63227	C₂³	1	1	yes	characteristic
208	#63227	C₂³	1	1	yes	characteristic
209	#63227	C₂³	1	2	yes	—
210	#63227	C₂³	1	2	yes	—
211	#63227	C₂³	1	2	yes	—
212	#63227	C₂³	1	2	yes	—
213	#63227	C₂³	1	2	yes	—
214	#63227	C₂³	1	2	yes	—
215	C₄⋊Dic₁₇	C₂³	1	2	yes	—
216	C₄⋊Dic₁₇	C₂³	1	2	yes	—
217	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₁₇	C₂³	1	2	yes	—
219	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
220	#63225	C₂³	1	1	yes	characteristic
221	#63225	C₂³	1	2	yes	—
222	#63225	C₂³	1	2	yes	—
223	#63225	C₂³	1	2	yes	—
224	#63225	C₂³	1	2	yes	—
225	#63225	C₂³	1	1	yes	characteristic
226	#63225	C₂³	1	1	yes	characteristic
227	#63225	C₂³	1	1	yes	characteristic
228	#63225	C₂³	1	2	yes	—
229	C₄×Dic₁₇	C₂³	1	2	yes	—
230	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
231	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
232	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
233	C₂³×C₁₇	C₂⁴	1	2	yes	—
234	C₂²×D₁₇	—	2	2	no	—
235	C₂²×D₁₇	—	2	4	no	—
236	C₂²×D₁₇	—	4	1	no	—
237	C₂²×D₁₇	—	4	1	no	—
238	C₂²×D₁₇	—	4	2	no	—
239	C₂²×D₁₇	—	4	2	no	—
240	C₂²×D₁₇	—	4	2	no	—
241	C₂²×D₁₇	—	4	2	no	—
242	C₂²×D₁₇	—	4	2	no	—
243	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
244	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
245	C₂²×D₁₇	C₂⁴	1	2	yes	—
246	C₂²×D₁₇	C₂⁴	1	2	yes	—
247	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
248	Q₈×C₁₇	—	4	2	no	—
249	D₄×C₁₇	—	2	2	no	—
250	D₄×C₁₇	—	4	2	no	—
251	D₄×C₁₇	—	4	2	no	—
252	D₄×C₁₇	—	4	1	no	—
253	C₂×C₄×C₁₇	—	2	2	no	—
254	C₂×C₄×C₁₇	—	2	2	no	—
255	C₂×C₄×C₁₇	—	4	2	no	—
256	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
259	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
261	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
262	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
264	C₂²⋊D₁₇	—	2	2	no	—
265	C₂²⋊D₁₇	—	4	2	no	—
266	C₂²⋊D₁₇	—	4	1	no	—
267	C₂²⋊D₁₇	—	4	1	no	—
268	C₂²⋊D₁₇	—	4	2	no	—
269	C₂²⋊D₁₇	—	4	2	no	—
270	C₂²⋊D₁₇	—	4	2	no	—
271	C₂²⋊D₁₇	—	4	2	no	—
272	C₂²⋊D₁₇	—	4	2	no	—
273	C₂²⋊D₁₇	—	4	1	no	—
274	C₂²⋊D₁₇	—	4	2	no	—
275	C₂×Dic₁₇	—	4	1	no	—
276	C₂×Dic₁₇	—	4	2	no	—
277	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₁₇	C₂⁴	1	2	yes	—
279	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₇	C₂⁴	1	2	yes	—
281	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
284	D₆₈	—	2	4	no	—
285	D₆₈	—	2	2	no	—
286	D₆₈	—	2	2	no	—
287	D₆₈	—	2	2	no	—
288	D₆₈	—	4	2	no	—
289	D₆₈	—	4	2	no	—
290	D₆₈	—	4	2	no	—
291	D₆₈	—	4	1	no	—
292	D₆₈	—	4	2	no	—
293	D₆₈	—	4	2	no	—
294	C₄×D₁₇	—	2	4	no	—
295	C₄×D₁₇	—	2	2	no	—
296	C₄×D₁₇	—	2	2	no	—
297	C₄×D₁₇	—	2	2	no	—
298	C₄×D₁₇	—	4	1	no	—
299	C₄×D₁₇	—	4	1	no	—
300	C₄×D₁₇	—	4	2	no	—
301	C₄×D₁₇	—	4	2	no	—
302	C₄×D₁₇	—	4	2	no	—
303	C₄×D₁₇	—	4	2	no	—
304	Dic₃₄	—	2	2	no	—
305	Dic₃₄	—	4	1	no	—
306	#3542	—	17	1	no	maximal, Sylow
307	C₂²×C₁₇	—	2	1	no	—
308	C₂²×C₁₇	—	2	2	no	—
309	C₂²×C₁₇	—	2	1	no	—
310	C₂²×C₁₇	—	2	1	no	—
311	C₂²×C₁₇	—	2	1	no	—
312	C₂²×C₁₇	—	2	2	no	—
313	C₂²×C₁₇	—	2	2	no	—
314	C₂²×C₁₇	—	2	1	no	—
315	C₂²×C₁₇	—	2	1	no	—
316	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
317	C₂×D₁₇	—	2	1	no	—
318	C₂×D₁₇	—	2	1	no	—
319	C₂×D₁₇	—	2	1	no	—
320	C₂×D₁₇	—	2	1	no	—
321	C₂×D₁₇	—	2	1	no	—
322	C₂×D₁₇	—	2	2	no	—
323	C₂×D₁₇	—	2	2	no	—
324	C₂×D₁₇	—	2	2	no	—
325	C₂×D₁₇	—	2	2	no	—
326	C₂×D₁₇	—	2	1	no	—
327	C₂×D₁₇	—	2	1	no	—
328	C₂×D₁₇	—	2	1	no	—
329	C₂×D₁₇	—	2	2	no	—
330	C₂×D₁₇	—	2	2	no	—
331	C₂×D₁₇	—	4	4	no	—
332	C₂×D₁₇	—	8	4	no	—
333	C₂×D₁₇	—	8	4	no	—
334	C₂×D₁₇	H(5,𝔽₂)	1	2	yes	—
335	C₄×C₁₇	—	2	1	no	—
336	C₄×C₁₇	—	2	2	no	—
337	C₄×C₁₇	—	2	1	no	—
338	C₄×C₁₇	—	2	2	no	—
339	C₄×C₁₇	—	2	1	no	—
340	C₄×C₁₇	—	2	2	no	—
341	C₄×C₁₇	—	2	1	no	—
342	C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
343	Dic₁₇	—	2	2	no	—
344	Dic₁₇	—	2	1	no	—
345	Dic₁₇	—	2	1	no	—
346	Dic₁₇	—	2	2	no	—
347	Dic₁₇	—	2	1	no	—
348	Dic₁₇	—	2	1	no	—
349	Dic₁₇	—	2	1	no	—
350	#562	—	17	2	no	—
351	#560	—	17	2	no	—
352	#555	D₁₇	1	1	yes	characteristic, complemented
353	#553	—	17	1	no	—
354	#552	—	17	1	no	—
355	#551	—	17	2	no	—
356	#550	—	17	1	no	—
357	#547	—	17	1	no	—
358	#546	—	17	2	no	—
359	#546	—	17	1	no	—
360	#546	—	17	1	no	—
361	D₄²	—	17	1	no	—
362	#542	—	17	1	no	—
363	#540	—	17	1	no	—
364	#540	—	17	2	no	—
365	#538	—	17	2	no	—
366	#537	—	17	1	no	—
367	#535	—	17	2	no	—
368	#535	—	17	1	no	—
369	#534	—	17	2	no	—
370	#525	—	17	1	no	—
371	#525	—	17	1	no	—
372	C₂×#121	—	17	1	no	—
373	C₂×C₁₇	—	4	1	no	—
374	C₂×C₁₇	—	4	1	no	—
375	C₂×C₁₇	—	4	2	no	—
376	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂×C₁₇	#585	1	1	yes	characteristic
379	D₁₇	—	2	2	no	—
380	D₁₇	—	4	1	no	—
381	D₁₇	—	4	1	no	—
382	D₁₇	—	4	2	no	—
383	D₁₇	—	4	2	no	—
384	C₂×#41	—	17	2	no	—
385	C₂×#41	—	17	1	no	—
386	C₂×#41	—	17	1	no	—
387	C₂×#41	—	17	1	no	—
388	C₂²×D₄	—	17	2	no	—
389	C₂²×D₄	—	17	1	no	—
390	C₂²×D₄	—	17	2	no	—
391	C₂²×D₄	—	17	1	no	—
392	C₂³×C₄	—	17	1	no	—
393	C₄⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
394	#127	—	17	2	no	—
395	#127	—	17	1	no	—
396	#127	—	17	2	no	—
397	#126	—	17	2	no	—
398	#126	—	17	2	no	—
399	#126	—	17	2	no	—
400	#125	—	17	1	no	—
401	#125	—	17	2	no	—
402	#124	—	17	2	no	—
403	#124	—	17	2	no	—
404	#124	—	17	1	no	—
405	#124	C₂×D₁₇	1	2	yes	complemented
406	#124	C₂×D₁₇	1	2	yes	complemented
407	#123	—	17	2	no	—
408	#123	—	17	1	no	—
409	#123	—	17	2	no	—
410	#123	—	17	2	no	—
411	#123	—	17	2	no	—
412	#123	—	17	2	no	—
413	#123	—	17	1	no	—
414	#123	—	17	2	no	—
415	#123	—	17	2	no	—
416	#123	—	17	2	no	—
417	#123	—	17	2	no	—
418	#123	—	17	2	no	—
419	C₂²⋊Q₈	—	17	2	no	—
420	C₂²⋊Q₈	—	17	2	no	—
421	C₂²⋊Q₈	—	17	1	no	—
422	C₂²⋊Q₈	—	17	1	no	—
423	C₂²⋊Q₈	—	17	1	no	—
424	C₂²⋊Q₈	—	17	1	no	—
425	C₂²⋊Q₈	—	17	1	no	—
426	C₂²⋊Q₈	—	17	2	no	—
427	#121	—	17	1	no	—
428	#121	—	17	2	no	—
429	#121	—	17	1	no	—
430	#121	—	17	2	no	—
431	#121	—	17	2	no	—
432	#121	—	17	2	no	—
433	#121	—	17	1	no	—
434	#121	—	17	2	no	—
435	#121	—	17	2	no	—
436	#121	—	17	1	no	—
437	#121	—	17	1	no	—
438	#121	—	17	1	no	—
439	#121	—	17	1	no	—
440	#121	—	17	1	no	—
441	#121	—	17	2	no	—
442	#121	—	17	1	no	—
443	#121	—	17	2	no	—
444	#121	—	17	2	no	—
445	#121	—	17	2	no	—
446	#121	—	17	2	no	—
447	#121	—	17	2	no	—
448	#121	—	17	2	no	—
449	#121	C₂×D₁₇	1	1	yes	characteristic, complemented
450	#121	C₂×D₁₇	1	2	yes	complemented
451	#121	C₂×D₁₇	1	1	yes	characteristic, complemented
452	#120	—	17	1	no	—
453	#120	—	17	2	no	—
454	#120	—	17	2	no	—
455	#120	—	17	2	no	—
456	#120	—	17	1	no	—
457	#120	—	17	2	no	—
458	#120	—	17	2	no	—
459	#120	—	17	2	no	—
460	#120	—	17	2	no	—
461	C₄×Q₈	—	17	1	no	—
462	C₄×D₄	—	17	1	no	—
463	C₄×D₄	—	17	1	no	—
464	C₄×D₄	—	17	1	no	—
465	C₄×D₄	—	17	2	no	—
466	C₄×D₄	—	17	2	no	—
467	C₄×D₄	—	17	1	no	—
468	C₄×D₄	—	17	2	no	—
469	C₄×D₄	—	17	1	no	—
470	C₄×D₄	—	17	2	no	—
471	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
472	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
473	#117	—	17	1	no	—
474	#117	—	17	2	no	—
475	#117	C₂×D₁₇	1	1	yes	characteristic, complemented
476	#117	C₂×D₁₇	1	1	yes	characteristic, complemented
477	#117	C₂×D₁₇	1	2	yes	complemented
478	C₂×C₄⋊C₄	—	17	1	no	—
479	C₂×C₄⋊C₄	—	17	1	no	—
480	C₂×C₂²⋊C₄	—	17	2	no	—
481	C₂×C₂²⋊C₄	—	17	2	no	—
482	C₂×C₂²⋊C₄	—	17	2	no	—
483	C₁₇	#3542	1	1	yes	characteristic, complemented, Sylow
484	C₂⁴	—	17	2	no	—
485	C₂⁴	—	17	1	no	—
486	C₂⁴	—	17	2	no	—
487	#41	—	68	2	no	—
488	#41	—	68	2	no	—
489	#41	—	68	2	no	—
490	#41	—	68	4	no	—
491	C₂×Q₈	—	17	1	no	—
492	C₂×Q₈	—	17	1	no	—
493	C₂×Q₈	C₂²×D₁₇	1	2	yes	—
494	C₂×D₄	—	17	1	no	—
495	C₂×D₄	—	17	2	no	—
496	C₂×D₄	—	17	1	no	—
497	C₂×D₄	—	17	1	no	—
498	C₂×D₄	—	17	1	no	—
499	C₂×D₄	—	17	2	no	—
500	C₂×D₄	—	17	2	no	—
501	C₂×D₄	—	17	2	no	—
502	C₂×D₄	—	17	2	no	—
503	C₂×D₄	—	17	2	no	—
504	C₂×D₄	—	17	2	no	—
505	C₂×D₄	—	17	1	no	—
506	C₂×D₄	—	17	2	no	—
507	C₂×D₄	—	17	1	no	—
508	C₂×D₄	—	17	1	no	—
509	C₂×D₄	—	17	2	no	—
510	C₂×D₄	—	17	2	no	—
511	C₂×D₄	—	17	2	no	—
512	C₂×D₄	—	17	2	no	—
513	C₂×D₄	—	17	2	no	—
514	C₂×D₄	—	17	1	no	—
515	C₂×D₄	—	68	2	no	—
516	C₂×D₄	—	68	2	no	—
517	C₂×D₄	—	68	4	no	—
518	C₂×D₄	—	68	4	no	—
519	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
520	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
521	C₂×D₄	C₂²×D₁₇	1	2	yes	—
522	C₂×D₄	C₂²×D₁₇	1	2	yes	—
523	C₂²×C₄	—	17	2	no	—
524	C₂²×C₄	—	17	1	no	—
525	C₂²×C₄	—	17	2	no	—
526	C₂²×C₄	—	17	1	no	—
527	C₂²×C₄	—	17	1	no	—
528	C₂²×C₄	—	17	1	no	—
529	C₂²×C₄	—	17	1	no	—
530	C₂²×C₄	—	17	2	no	—
531	C₂²×C₄	—	17	2	no	—
532	C₂²×C₄	—	17	2	no	—
533	C₂²×C₄	—	17	1	no	—
534	C₂²×C₄	—	17	2	no	—
535	C₂²×C₄	—	68	2	no	—
536	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
537	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
538	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
539	C₄⋊C₄	—	17	1	no	—
540	C₄⋊C₄	—	17	2	no	—
541	C₄⋊C₄	—	17	2	no	—
542	C₄⋊C₄	—	17	2	no	—
543	C₄⋊C₄	—	17	2	no	—
544	C₄⋊C₄	—	17	1	no	—
545	C₄⋊C₄	—	17	1	no	—
546	C₄⋊C₄	—	17	1	no	—
547	C₄⋊C₄	—	17	1	no	—
548	C₄⋊C₄	—	17	2	no	—
549	C₄⋊C₄	—	17	2	no	—
550	C₄⋊C₄	—	17	2	no	—
551	C₄⋊C₄	—	17	1	no	—
552	C₄⋊C₄	—	17	2	no	—
553	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
554	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
555	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
556	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
557	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
558	C₂²⋊C₄	—	17	2	no	—
559	C₂²⋊C₄	—	17	2	no	—
560	C₂²⋊C₄	—	17	1	no	—
561	C₂²⋊C₄	—	17	1	no	—
562	C₂²⋊C₄	—	17	1	no	—
563	C₂²⋊C₄	—	17	2	no	—
564	C₂²⋊C₄	—	17	2	no	—
565	C₂²⋊C₄	—	17	2	no	—
566	C₂²⋊C₄	—	17	2	no	—
567	C₂²⋊C₄	—	17	2	no	—
568	C₂²⋊C₄	—	17	2	no	—
569	C₂²⋊C₄	—	17	1	no	—
570	C₂²⋊C₄	—	17	1	no	—
571	C₂²⋊C₄	—	17	1	no	—
572	C₂²⋊C₄	—	17	1	no	—
573	C₂²⋊C₄	—	17	2	no	—
574	C₂²⋊C₄	—	17	2	no	—
575	C₂²⋊C₄	—	17	2	no	—
576	C₂²⋊C₄	—	17	2	no	—
577	C₂²⋊C₄	—	17	2	no	—
578	C₂²⋊C₄	—	17	2	no	—
579	C₂²⋊C₄	—	17	1	no	—
580	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
581	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
582	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
583	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
584	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
585	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
586	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
587	C₄²	—	17	1	no	—
588	C₄²	—	17	2	no	—
589	C₄²	C₂²×D₁₇	1	2	yes	—
590	C₄²	C₂²×D₁₇	1	1	yes	characteristic
591	C₄²	C₂²×D₁₇	1	2	yes	—
592	C₂³	—	17	1	no	—
593	C₂³	—	17	2	no	—
594	C₂³	—	17	2	no	—
595	C₂³	—	17	1	no	—
596	C₂³	—	17	1	no	—
597	C₂³	—	34	2	no	—
598	C₂³	—	34	4	no	—
599	C₂³	—	68	1	no	—
600	C₂³	—	68	1	no	—
601	C₂³	—	68	2	no	—
602	C₂³	—	68	2	no	—
603	C₂³	—	68	2	no	—
604	C₂³	—	68	2	no	—
605	C₂³	—	68	2	no	—
606	C₂³	C₂³×D₁₇	1	1	yes	characteristic
607	C₂³	C₂³×D₁₇	1	1	yes	characteristic
608	C₂³	C₂³×D₁₇	1	2	yes	—
609	Q₈	—	4	2	no	—
610	Q₈	—	34	2	no	—
611	Q₈	—	68	1	no	—
612	D₄	—	2	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	1	no	—
616	D₄	—	34	4	no	—
617	D₄	—	34	2	no	—
618	D₄	—	34	2	no	—
619	D₄	—	34	2	no	—
620	D₄	—	34	2	no	—
621	D₄	—	68	2	no	—
622	D₄	—	68	2	no	—
623	D₄	—	68	2	no	—
624	D₄	—	68	1	no	—
625	D₄	—	68	2	no	—
626	D₄	—	68	2	no	—
627	D₄	—	68	2	no	—
628	D₄	—	68	2	no	—
629	D₄	—	68	2	no	—
630	D₄	—	68	2	no	—
631	D₄	—	68	1	no	—
632	D₄	—	68	1	no	—
633	D₄	—	68	2	no	—
634	D₄	—	68	2	no	—
635	D₄	—	68	2	no	—
636	D₄	—	68	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	17	1	no	—
641	C₂×C₄	—	17	2	no	—
642	C₂×C₄	—	17	1	no	—
643	C₂×C₄	—	17	1	no	—
644	C₂×C₄	—	17	1	no	—
645	C₂×C₄	—	17	2	no	—
646	C₂×C₄	—	17	1	no	—
647	C₂×C₄	—	34	4	no	—
648	C₂×C₄	—	34	2	no	—
649	C₂×C₄	—	34	2	no	—
650	C₂×C₄	—	34	2	no	—
651	C₂×C₄	—	68	1	no	—
652	C₂×C₄	—	68	1	no	—
653	C₂×C₄	—	68	2	no	—
654	C₂×C₄	—	68	2	no	—
655	C₂×C₄	—	68	2	no	—
656	C₂×C₄	—	68	2	no	—
657	C₂×C₄	—	68	1	no	—
658	C₂×C₄	—	68	2	no	—
659	C₂×C₄	C₂³×D₁₇	1	2	yes	—
660	C₂×C₄	C₂³×D₁₇	1	2	yes	—
661	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
663	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
665	C₂×C₄	C₂³×D₁₇	1	2	yes	—
666	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	17	2	no	—
677	C₂²	—	34	1	no	—
678	C₂²	—	34	1	no	—
679	C₂²	—	34	1	no	—
680	C₂²	—	34	2	no	—
681	C₂²	—	34	2	no	—
682	C₂²	—	34	1	no	—
683	C₂²	—	34	1	no	—
684	C₂²	—	34	1	no	—
685	C₂²	—	34	2	no	—
686	C₂²	—	34	2	no	—
687	C₂²	—	34	1	no	—
688	C₂²	—	34	1	no	—
689	C₂²	—	34	2	no	—
690	C₂²	—	34	2	no	—
691	C₂²	—	68	4	no	—
692	C₂²	—	136	4	no	—
693	C₂²	—	136	4	no	—
694	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
695	C₄	—	2	2	no	—
696	C₄	—	2	2	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	2	1	no	—
701	C₄	—	2	2	no	—
702	C₄	—	34	2	no	—
703	C₄	—	34	1	no	—
704	C₄	—	34	1	no	—
705	C₄	—	34	1	no	—
706	C₄	—	34	1	no	—
707	C₄	—	34	2	no	—
708	C₄	—	34	1	no	—
709	C₄	#10587696	1	2	yes	—
710	C₂	—	4	1	no	—
711	C₂	—	4	1	no	—
712	C₂	—	4	2	no	—
713	C₂	—	34	2	no	—
714	C₂	—	68	1	no	—
715	C₂	—	68	2	no	—
716	C₂	—	68	2	no	—
717	C₂	—	68	1	no	—
718	C₂	H(5,𝔽₂)×D₁₇	1	1	yes	characteristic
719	C₂	C₂×#10587696	1	1	yes	characteristic
720	C₂	#11763645	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#555	C₂
hypercenter	#555	D₁₇
hypocenter	C₁₇	#3542
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #555

Complements

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

N	H ≅ G/N	type
1. #11763553	C₂	semidirect
2. #11763547	C₂	semidirect
3. #11763503	C₂	semidirect
4. #11763498	C₂	semidirect
5. #11763483	C₂	semidirect
6. #11763477	C₂	semidirect
7. #11763462	C₂	semidirect
8. #11763455	C₂	semidirect
9. #11763454	C₂	semidirect
10. #11763452	C₂	semidirect
11. #11763443	C₂	semidirect
12. #11763433	C₂	semidirect
13. #11763414	C₂	semidirect
14. #11763410	C₂	semidirect
15. #11763393	C₂	semidirect
16. #11763388	C₂	semidirect
17. #11763378	C₂	semidirect
18. #11763377	C₂	semidirect
19. #11763367	C₂	semidirect
20. #11763321	C₂	semidirect
21. #11763318	C₂	semidirect
22. #121×D₁₇	C₂	semidirect
23. C₁₇×#555	C₂	semidirect
24. C₂×#63256	C₂²	semidirect
25. C₂×#63254	C₂²	semidirect
28. C₂×D₄×D₁₇	C₂²	semidirect
29. C₂×#63252	C₂²	semidirect
30. C₂×#63252	C₂²	semidirect
31. C₂²×D₆₈	C₂²	semidirect
32. C₂²×C₄×D₁₇	C₂²	semidirect
33. C₁₇×C₄⋊Q₈	C₂²	semidirect
34. C₁₇×#124	C₂²	semidirect
35. C₁₇×#124	C₂²	semidirect
36. C₁₇×#121	C₂²	semidirect
37. C₁₇×#121	C₂²	semidirect
38. C₁₇×#121	C₂²	semidirect
39. C₄×D₄×C₁₇	C₂²	semidirect
40. C₄×D₄×C₁₇	C₂²	semidirect
41. C₁₇×#117	C₂²	semidirect
42. C₁₇×#117	C₂²	semidirect
43. C₁₇×#117	C₂²	semidirect
44. #10587633	C₂²	semidirect
45. #10587632	C₂²	semidirect
46. #10587632	C₂²	semidirect
47. #10587626	C₂²	semidirect
48. #10587626	C₂²	semidirect
49. #10587625	C₂²	semidirect
50. #10587625	C₂²	semidirect
51. #10587625	C₂²	semidirect
52. #10587625	C₂²	semidirect
53. #10587624	C₂²	semidirect
54. #10587624	C₂²	semidirect
56. #10587623	C₂²	semidirect
57. #10587623	C₂²	semidirect
59. #10587616	C₂²	semidirect
60. #10587616	C₂²	semidirect
61. #10587615	C₂²	semidirect
63. C₄×C₂²⋊D₁₇	C₂²	semidirect
64. C₂×#63227	C₂²	semidirect
65. #10587610	C₂²	semidirect
66. #10587584	C₂²	semidirect
67. #10587583	C₂²	semidirect
68. #10587583	C₂²	semidirect
69. #10587582	C₂²	semidirect
72. #10587581	C₂²	semidirect
73. #10587581	C₂²	semidirect
74. #10587581	C₂²	semidirect
75. #10587580	C₂²	semidirect
76. #10587580	C₂²	semidirect
77. #10587580	C₂²	semidirect
78. #10587580	C₂²	semidirect
79. #10587580	C₂²	semidirect
80. #10587579	C₂²	semidirect
81. C₄⋊C₄×D₁₇	C₂²	semidirect
82. C₄⋊C₄×D₁₇	C₂²	semidirect
83. #10587576	C₂²	semidirect
84. #10587573	C₂²	semidirect
85. #10587572	C₂²	semidirect
86. #10587572	C₂²	semidirect
88. #10587570	C₂²	semidirect
89. #10587570	C₂²	semidirect
90. #10587570	C₂²	semidirect
91. #10587570	C₂²	semidirect
92. #10587570	C₂²	semidirect
93. #10587570	C₂²	semidirect
94. #10587570	C₂²	semidirect
96. #10587569	C₂²	semidirect
97. #10587569	C₂²	semidirect
98. #10587569	C₂²	semidirect
100. #10587568	C₂²	semidirect
101. #10587568	C₂²	semidirect
102. #10587568	C₂²	semidirect
103. #10587568	C₂²	semidirect
104. #10587568	C₂²	semidirect
105. #10587567	C₂²	semidirect
106. C₂²⋊C₄×D₁₇	C₂²	semidirect
107. C₂²⋊C₄×D₁₇	C₂²	semidirect
108. #10587565	C₂²	semidirect
109. #10587564	C₂²	semidirect
110. #10587564	C₂²	semidirect
111. #10587562	C₂²	semidirect
112. #10587561	C₂²	semidirect
113. #10587561	C₂²	semidirect
114. #10587560	C₂²	semidirect
115. C₄×D₆₈	C₂²	semidirect
116. C₄×D₆₈	C₂²	semidirect
117. C₄×D₆₈	C₂²	semidirect
118. C₄×D₆₈	C₂²	semidirect
119. C₄×D₆₈	C₂²	semidirect
120. #10587558	C₂²	semidirect
121. #10587558	C₂²	semidirect
122. #10587556	C₂²	semidirect
352. #555	D₁₇	semidirect
393. C₄⋊Q₈	C₂×D₁₇	semidirect
405. #124	C₂×D₁₇	semidirect
406. #124	C₂×D₁₇	semidirect
449. #121	C₂×D₁₇	semidirect
450. #121	C₂×D₁₇	semidirect
451. #121	C₂×D₁₇	semidirect
471. C₄×D₄	C₂×D₁₇	semidirect
472. C₄×D₄	C₂×D₁₇	semidirect
475. #117	C₂×D₁₇	semidirect
476. #117	C₂×D₁₇	semidirect
477. #117	C₂×D₁₇	semidirect
483. C₁₇	#3542	semidirect

Maximal subgroups

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

subgroup	index
#11763553	2
#11763547	2
#11763503	2
#11763498	2
#11763483	2
#11763477	2
#11763462	2
#11763455	2
#11763454	2
#11763452	2
#11763443	2
#11763433	2
#11763414	2
#11763410	2
#11763393	2
#11763388	2
#11763378	2
#11763377	2
#11763367	2
#11763321	2
#11763318	2
#121×D₁₇	2
C₁₇×#555	2
#3542	17