Subgroups — #14543153

Order 2176.

1150 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763550	C₂	1	2	yes	maximal, complemented
2	#11763549	C₂	1	2	yes	maximal, complemented
3	#11763531	C₂	1	1	yes	maximal, characteristic, complemented
4	#11763510	C₂	1	2	yes	maximal, complemented
5	#11763481	C₂	1	1	yes	maximal, characteristic, complemented
6	#11763480	C₂	1	1	yes	maximal, characteristic, complemented
7	#11763477	C₂	1	1	yes	maximal, characteristic, complemented
8	#11763461	C₂	1	1	yes	maximal, characteristic, complemented
9	#11763454	C₂	1	1	yes	maximal, characteristic, complemented
10	#11763451	C₂	1	2	yes	maximal, complemented
11	#11763450	C₂	1	1	yes	maximal, characteristic, complemented
12	#11763443	C₂	1	1	yes	maximal, characteristic, complemented
13	#11763433	C₂	1	1	yes	maximal, characteristic, complemented
14	#11763399	C₂	1	2	yes	maximal, complemented
15	#11763393	C₂	1	2	yes	maximal, complemented
16	#11763389	C₂	1	2	yes	maximal, complemented
17	#11763378	C₂	1	1	yes	maximal, characteristic, complemented
18	#11763377	C₂	1	1	yes	maximal, characteristic, complemented
19	#11763377	C₂	1	2	yes	maximal, complemented
20	#11763360	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763358	C₂	1	1	yes	maximal, characteristic, complemented
22	#11763337	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#542	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#63256	C₂²	1	1	yes	characteristic, complemented
25	C₂×#63256	C₂²	1	1	yes	characteristic, complemented
26	C₂×#63256	C₂²	1	2	yes	complemented
27	C₂×#63254	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₄×D₁₇	C₂²	1	2	yes	—
29	C₂×D₄×D₁₇	C₂²	1	1	yes	characteristic
30	C₂×#63252	C₂²	1	1	yes	characteristic, complemented
31	C₂×#63252	C₂²	1	2	yes	complemented
32	C₂²×D₆₈	C₂²	1	1	yes	characteristic
33	C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₁₇×#126	C₂²	1	2	yes	complemented
35	C₁₇×#124	C₂²	1	1	yes	characteristic, complemented
36	C₁₇×#124	C₂²	1	2	yes	complemented
37	C₁₇×#123	C₂²	1	2	yes	complemented
38	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
40	C₁₇×#121	C₂²	1	1	yes	characteristic
41	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
42	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
43	C₁₇×#117	C₂²	1	1	yes	characteristic, complemented
44	#10587633	C₂²	1	1	yes	characteristic
45	#10587633	C₂²	1	2	yes	complemented
46	#10587633	C₂²	1	2	yes	complemented
47	#10587632	C₂²	1	2	yes	complemented
48	#10587630	C₂²	1	1	yes	characteristic, complemented
49	#10587626	C₂²	1	1	yes	characteristic
50	#10587626	C₂²	1	1	yes	characteristic, complemented
51	#10587626	C₂²	1	2	yes	complemented
52	#10587625	C₂²	1	2	yes	complemented
53	#10587623	C₂²	1	2	yes	—
54	#10587616	C₂²	1	2	yes	complemented
55	#10587616	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
58	C₂×#63227	C₂²	1	2	yes	complemented
59	#10587584	C₂²	1	2	yes	complemented
60	#10587584	C₂²	1	2	yes	complemented
61	#10587584	C₂²	1	1	yes	characteristic, complemented
62	#10587583	C₂²	1	1	yes	characteristic, complemented
63	#10587582	C₂²	1	2	yes	complemented
64	#10587582	C₂²	1	1	yes	characteristic, complemented
65	#10587581	C₂²	1	1	yes	characteristic
66	#10587581	C₂²	1	1	yes	characteristic
67	#10587581	C₂²	1	1	yes	characteristic, complemented
68	#10587581	C₂²	1	2	yes	complemented
69	#10587581	C₂²	1	2	yes	complemented
70	#10587581	C₂²	1	2	yes	complemented
71	#10587581	C₂²	1	2	yes	complemented
72	#10587581	C₂²	1	2	yes	complemented
73	#10587581	C₂²	1	2	yes	complemented
74	#10587580	C₂²	1	2	yes	complemented
75	#10587580	C₂²	1	2	yes	complemented
76	#10587580	C₂²	1	1	yes	characteristic, complemented
77	#10587580	C₂²	1	2	yes	complemented
78	#10587579	C₂²	1	1	yes	characteristic
79	#10587579	C₂²	1	1	yes	characteristic, complemented
80	#10587579	C₂²	1	1	yes	characteristic, complemented
81	#10587579	C₂²	1	2	yes	complemented
82	C₄⋊C₄×D₁₇	C₂²	1	2	yes	complemented
83	#10587575	C₂²	1	1	yes	characteristic, complemented
84	#10587573	C₂²	1	1	yes	characteristic, complemented
85	#10587572	C₂²	1	2	yes	complemented
86	#10587571	C₂²	1	1	yes	characteristic
87	#10587570	C₂²	1	2	yes	—
88	#10587570	C₂²	1	2	yes	—
89	#10587570	C₂²	1	1	yes	characteristic
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	#10587570	C₂²	1	2	yes	complemented
96	#10587570	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	2	yes	complemented
102	#10587568	C₂²	1	2	yes	complemented
103	#10587568	C₂²	1	2	yes	complemented
104	#10587568	C₂²	1	2	yes	complemented
105	#10587568	C₂²	1	2	yes	complemented
106	#10587567	C₂²	1	2	yes	complemented
107	#10587567	C₂²	1	2	yes	complemented
108	#10587567	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	complemented
110	#10587565	C₂²	1	1	yes	characteristic, complemented
111	#10587562	C₂²	1	2	yes	complemented
112	#10587561	C₂²	1	1	yes	characteristic
113	#10587561	C₂²	1	1	yes	characteristic, complemented
114	#10587560	C₂²	1	1	yes	characteristic
115	#10587560	C₂²	1	1	yes	characteristic, complemented
116	#10587560	C₂²	1	2	yes	complemented
117	C₄×D₆₈	C₂²	1	2	yes	complemented
118	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
119	#10587558	C₂²	1	2	yes	complemented
120	#10587558	C₂²	1	1	yes	characteristic, complemented
121	C₄²×D₁₇	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₄	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₇	C₂³	1	2	yes	—
124	C₂³×D₁₇	C₂³	1	2	yes	—
125	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
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	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₇	C₂³	1	2	yes	—
141	#63256	—	4	4	no	—
142	#63256	—	4	2	no	—
143	#63256	—	4	2	no	—
144	#63254	—	4	2	no	—
145	D₄×D₁₇	—	4	2	no	—
146	D₄×D₁₇	—	4	4	no	—
147	#63252	—	4	4	no	—
148	#63252	—	4	2	no	—
149	C₂×D₆₈	—	4	2	no	—
150	C₂×D₆₈	C₂³	1	1	yes	characteristic
151	C₂×D₆₈	C₂³	1	1	yes	characteristic
152	C₂×D₆₈	C₂³	1	1	yes	characteristic
153	C₂×D₆₈	C₂³	1	2	yes	—
154	C₂×D₆₈	C₂³	1	2	yes	—
155	C₂×D₆₈	C₂³	1	2	yes	—
156	C₂×D₆₈	C₂³	1	2	yes	—
157	C₂×D₆₈	C₂³	1	2	yes	—
158	C₂×D₆₈	C₂³	1	2	yes	—
159	C₂×D₆₈	C₂³	1	2	yes	—
160	C₂×D₆₈	C₂³	1	2	yes	—
161	C₂×D₆₈	C₂³	1	1	yes	characteristic
162	C₂×D₆₈	C₂³	1	2	yes	—
163	C₂×D₆₈	C₂³	1	2	yes	—
164	C₂×C₄×D₁₇	C₂³	1	2	yes	—
165	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₁₇	C₂³	1	2	yes	—
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	2	yes	—
171	C₂×C₄×D₁₇	C₂³	1	2	yes	—
172	C₂×C₄×D₁₇	C₂³	1	2	yes	—
173	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
174	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
175	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
176	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
177	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
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	2	yes	—
184	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
187	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
189	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
190	C₄²×C₁₇	C₂³	1	2	yes	—
191	C₄²×C₁₇	C₂³	1	1	yes	characteristic
192	C₄²×C₁₇	C₂³	1	1	yes	characteristic
193	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
194	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
195	#63227	C₂³	1	2	yes	—
196	#63227	C₂³	1	1	yes	characteristic
197	#63227	C₂³	1	2	yes	—
198	#63227	C₂³	1	1	yes	characteristic
199	#63227	C₂³	1	2	yes	—
200	#63227	C₂³	1	1	yes	characteristic
201	#63227	C₂³	1	2	yes	—
202	#63227	C₂³	1	1	yes	characteristic
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	2	yes	—
208	#63227	C₂³	1	2	yes	—
209	#63227	C₂³	1	1	yes	characteristic
210	#63227	C₂³	1	2	yes	—
211	#63227	C₂³	1	2	yes	—
212	#63227	C₂³	1	2	yes	—
213	#63227	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₁₇	C₂³	1	2	yes	—
217	#63225	C₂³	1	1	yes	characteristic
218	#63225	C₂³	1	1	yes	characteristic
219	#63225	C₂³	1	1	yes	characteristic
220	#63225	C₂³	1	2	yes	—
221	#63225	C₂³	1	1	yes	characteristic
222	#63225	C₂³	1	2	yes	—
223	#63225	C₂³	1	2	yes	—
224	#63225	C₂³	1	1	yes	characteristic
225	#63225	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
228	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
229	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
230	C₄×Dic₁₇	C₂³	1	2	yes	—
231	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
232	C₂³×C₁₇	C₂⁴	1	2	yes	—
233	C₂²×D₁₇	—	4	2	no	—
234	C₂²×D₁₇	—	4	2	no	—
235	C₂²×D₁₇	—	4	2	no	—
236	C₂²×D₁₇	—	4	2	no	—
237	C₂²×D₁₇	—	4	2	no	—
238	C₂²×D₁₇	—	4	2	no	—
239	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
240	C₂²×D₁₇	C₂⁴	1	2	yes	—
241	C₂²×D₁₇	C₂⁴	1	2	yes	—
242	C₂²×D₁₇	C₂⁴	1	2	yes	—
243	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
244	Q₈×C₁₇	—	2	2	no	—
245	Q₈×C₁₇	—	4	2	no	—
246	D₄×C₁₇	—	2	2	no	—
247	D₄×C₁₇	—	4	2	no	—
248	C₂×C₄×C₁₇	—	2	2	no	—
249	C₂×C₄×C₁₇	—	4	2	no	—
250	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
258	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
259	C₂²⋊D₁₇	—	2	4	no	—
260	C₂²⋊D₁₇	—	2	2	no	—
261	C₂²⋊D₁₇	—	4	2	no	—
262	C₂²⋊D₁₇	—	4	2	no	—
263	C₂²⋊D₁₇	—	4	2	no	—
264	C₂²⋊D₁₇	—	4	2	no	—
265	C₂²⋊D₁₇	—	4	2	no	—
266	C₂²⋊D₁₇	—	4	1	no	—
267	C₂²⋊D₁₇	—	4	2	no	—
268	C₂×Dic₁₇	—	4	2	no	—
269	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₇	C₂⁴	1	2	yes	—
274	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
276	D₆₈	—	2	2	no	—
277	D₆₈	—	2	2	no	—
278	D₆₈	—	2	2	no	—
279	D₆₈	—	4	2	no	—
280	D₆₈	—	4	2	no	—
281	D₆₈	—	4	1	no	—
282	D₆₈	—	4	2	no	—
283	D₆₈	—	4	2	no	—
284	D₆₈	—	4	2	no	—
285	D₆₈	—	4	2	no	—
286	D₆₈	—	4	2	no	—
287	D₆₈	—	4	2	no	—
288	D₆₈	—	4	2	no	—
289	D₆₈	—	4	2	no	—
290	C₄×D₁₇	—	2	2	no	—
291	C₄×D₁₇	—	2	2	no	—
292	C₄×D₁₇	—	2	4	no	—
293	C₄×D₁₇	—	2	4	no	—
294	C₄×D₁₇	—	2	2	no	—
295	C₄×D₁₇	—	4	1	no	—
296	C₄×D₁₇	—	4	2	no	—
297	C₄×D₁₇	—	4	2	no	—
298	C₄×D₁₇	—	4	2	no	—
299	C₄×D₁₇	—	4	2	no	—
300	Dic₃₄	—	2	2	no	—
301	Dic₃₄	—	2	2	no	—
302	#3546	—	17	1	no	maximal, Sylow
303	C₂²×C₁₇	—	2	2	no	—
304	C₂²×C₁₇	—	2	2	no	—
305	C₂²×C₁₇	—	2	1	no	—
306	C₂²×C₁₇	—	2	1	no	—
307	C₂²×C₁₇	—	2	2	no	—
308	C₂²×C₁₇	—	2	1	no	—
309	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
310	C₂×D₁₇	—	2	1	no	—
311	C₂×D₁₇	—	2	2	no	—
312	C₂×D₁₇	—	2	1	no	—
313	C₂×D₁₇	—	2	2	no	—
314	C₂×D₁₇	—	2	1	no	—
315	C₂×D₁₇	—	2	2	no	—
316	C₂×D₁₇	—	2	2	no	—
317	C₂×D₁₇	—	2	2	no	—
318	C₂×D₁₇	—	2	2	no	—
319	C₂×D₁₇	—	2	1	no	—
320	C₂×D₁₇	—	2	1	no	—
321	C₂×D₁₇	—	2	2	no	—
322	C₂×D₁₇	—	2	2	no	—
323	C₂×D₁₇	—	2	2	no	—
324	C₂×D₁₇	—	2	1	no	—
325	C₂×D₁₇	—	8	4	no	—
326	C₂×D₁₇	—	8	4	no	—
327	C₄×C₁₇	—	2	1	no	—
328	C₄×C₁₇	—	2	2	no	—
329	C₄×C₁₇	—	2	2	no	—
330	C₄×C₁₇	—	2	1	no	—
331	C₄×C₁₇	—	2	1	no	—
332	C₄×C₁₇	—	2	2	no	—
333	C₄×C₁₇	—	2	1	no	—
334	C₄×C₁₇	—	2	1	no	—
335	C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
336	Dic₁₇	—	2	1	no	—
337	Dic₁₇	—	2	2	no	—
338	Dic₁₇	—	2	1	no	—
339	Dic₁₇	—	2	1	no	—
340	Dic₁₇	—	2	1	no	—
341	Dic₁₇	—	2	1	no	—
342	Dic₁₇	H(5,𝔽₂)	1	2	yes	—
343	#560	—	17	2	no	—
344	#560	—	17	2	no	—
345	#556	—	17	1	no	—
346	#553	—	17	2	no	—
347	#550	—	17	1	no	—
348	#550	—	17	1	no	—
349	#550	—	17	1	no	—
350	#547	—	17	1	no	—
351	#546	—	17	2	no	—
352	#546	—	17	1	no	—
353	#546	—	17	1	no	—
354	D₄²	—	17	1	no	—
355	#542	—	17	1	no	—
356	#542	D₁₇	1	1	yes	characteristic, complemented
357	#538	—	17	2	no	—
358	#538	—	17	2	no	—
359	#537	—	17	2	no	—
360	#535	—	17	1	no	—
361	#535	—	17	2	no	—
362	#535	—	17	1	no	—
363	#532	—	17	1	no	—
364	#532	—	17	1	no	—
365	#529	—	17	1	no	—
366	C₂×C₁₇	—	4	1	no	—
367	C₂×C₁₇	—	4	2	no	—
368	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
369	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂×C₁₇	#585	1	1	yes	characteristic
371	D₁₇	—	4	1	no	—
372	D₁₇	—	4	2	no	—
373	D₁₇	—	4	2	no	—
374	D₁₇	—	4	2	no	—
375	D₁₇	—	4	1	no	—
376	C₂×#41	—	17	2	no	—
377	C₂×#41	—	17	1	no	—
378	C₂×#41	—	17	1	no	—
379	C₂×#41	—	17	1	no	—
380	C₂×#41	—	17	1	no	—
381	C₂×#41	—	17	2	no	—
382	C₂²×D₄	—	17	2	no	—
383	C₂²×D₄	—	17	1	no	—
384	C₂²×D₄	—	17	1	no	—
385	C₄⋊Q₈	—	17	1	no	—
386	C₄⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
387	#127	—	17	1	no	—
388	#127	—	17	1	no	—
389	#127	—	17	2	no	—
390	#127	—	17	1	no	—
391	#127	—	17	1	no	—
392	#127	—	17	2	no	—
393	#126	—	17	1	no	—
394	#126	—	17	2	no	—
395	#126	—	17	2	no	—
396	#126	—	17	1	no	—
397	#126	—	17	2	no	—
398	#126	C₂×D₁₇	1	2	yes	complemented
399	#125	—	17	1	no	—
400	#124	—	17	2	no	—
401	#124	—	17	2	no	—
402	#124	—	17	1	no	—
403	#124	—	17	1	no	—
404	#124	—	17	1	no	—
405	#124	—	17	1	no	—
406	#124	C₂×D₁₇	1	1	yes	characteristic, complemented
407	#124	C₂×D₁₇	1	2	yes	complemented
408	#123	—	17	1	no	—
409	#123	—	17	2	no	—
410	#123	—	17	2	no	—
411	#123	—	17	2	no	—
412	#123	—	17	1	no	—
413	#123	—	17	2	no	—
414	#123	—	17	2	no	—
415	#123	C₂×D₁₇	1	2	yes	complemented
416	C₂²⋊Q₈	—	17	2	no	—
417	C₂²⋊Q₈	—	17	1	no	—
418	C₂²⋊Q₈	—	17	2	no	—
419	C₂²⋊Q₈	—	17	1	no	—
420	C₂²⋊Q₈	C₂×D₁₇	1	2	yes	complemented
421	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
422	#121	—	17	2	no	—
423	#121	—	17	2	no	—
424	#121	—	17	2	no	—
425	#121	—	17	1	no	—
426	#121	—	17	1	no	—
427	#121	—	17	2	no	—
428	#121	—	17	2	no	—
429	#121	—	17	2	no	—
430	#121	—	17	2	no	—
431	#121	—	17	2	no	—
432	#121	—	17	2	no	—
433	#121	—	17	1	no	—
434	#121	—	17	1	no	—
435	#121	—	17	2	no	—
436	#121	—	17	2	no	—
437	#121	—	17	2	no	—
438	#121	—	17	2	no	—
439	#121	—	17	2	no	—
440	#121	—	17	2	no	—
441	#121	—	17	2	no	—
442	#121	—	17	2	no	—
443	#121	—	17	2	no	—
444	#121	C₂×D₁₇	1	1	yes	characteristic
445	#120	—	17	2	no	—
446	#120	—	17	2	no	—
447	#120	—	17	2	no	—
448	#120	—	17	2	no	—
449	#120	—	17	2	no	—
450	#120	—	17	2	no	—
451	#120	—	17	2	no	—
452	#120	—	17	2	no	—
453	C₄×Q₈	—	17	1	no	—
454	C₄×Q₈	—	17	1	no	—
455	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
456	C₄×D₄	—	17	1	no	—
457	C₄×D₄	—	17	1	no	—
458	C₄×D₄	—	17	1	no	—
459	C₄×D₄	—	17	2	no	—
460	C₄×D₄	—	17	1	no	—
461	C₄×D₄	—	17	1	no	—
462	C₄×D₄	—	17	2	no	—
463	C₄×D₄	—	17	2	no	—
464	C₄×D₄	—	17	2	no	—
465	C₄×D₄	—	17	1	no	—
466	C₄×D₄	—	17	2	no	—
467	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
468	#117	—	17	1	no	—
469	#117	—	17	2	no	—
470	#117	C₂×D₁₇	1	1	yes	characteristic, complemented
471	C₂×C₄⋊C₄	—	17	2	no	—
472	C₂×C₂²⋊C₄	—	17	2	no	—
473	C₂×C₂²⋊C₄	—	17	2	no	—
474	C₂×C₄²	—	17	1	no	—
475	C₁₇	#3546	1	1	yes	characteristic, complemented, Sylow
476	C₂⁴	—	17	2	no	—
477	C₂⁴	—	17	2	no	—
478	#41	—	68	2	no	—
479	#41	—	68	4	no	—
480	#41	—	68	4	no	—
481	#41	—	68	2	no	—
482	#41	—	68	2	no	—
483	#41	—	68	2	no	—
484	C₂×Q₈	—	17	1	no	—
485	C₂×Q₈	—	17	1	no	—
486	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
487	C₂×Q₈	C₂²×D₁₇	1	2	yes	—
488	C₂×D₄	—	17	1	no	—
489	C₂×D₄	—	17	2	no	—
490	C₂×D₄	—	17	2	no	—
491	C₂×D₄	—	17	1	no	—
492	C₂×D₄	—	17	2	no	—
493	C₂×D₄	—	17	2	no	—
494	C₂×D₄	—	17	2	no	—
495	C₂×D₄	—	17	2	no	—
496	C₂×D₄	—	17	2	no	—
497	C₂×D₄	—	17	1	no	—
498	C₂×D₄	—	17	1	no	—
499	C₂×D₄	—	17	1	no	—
500	C₂×D₄	—	17	2	no	—
501	C₂×D₄	—	17	1	no	—
502	C₂×D₄	—	17	2	no	—
503	C₂×D₄	—	17	2	no	—
504	C₂×D₄	—	17	2	no	—
505	C₂×D₄	—	17	2	no	—
506	C₂×D₄	—	17	2	no	—
507	C₂×D₄	—	17	2	no	—
508	C₂×D₄	—	17	2	no	—
509	C₂×D₄	—	17	2	no	—
510	C₂×D₄	—	17	2	no	—
511	C₂×D₄	—	68	2	no	—
512	C₂×D₄	—	68	2	no	—
513	C₂×D₄	—	68	4	no	—
514	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
515	C₂×D₄	C₂²×D₁₇	1	2	yes	—
516	C₂²×C₄	—	17	2	no	—
517	C₂²×C₄	—	17	1	no	—
518	C₂²×C₄	—	17	1	no	—
519	C₂²×C₄	—	17	2	no	—
520	C₂²×C₄	—	17	2	no	—
521	C₂²×C₄	—	17	1	no	—
522	C₂²×C₄	—	17	1	no	—
523	C₂²×C₄	—	17	2	no	—
524	C₂²×C₄	—	17	2	no	—
525	C₂²×C₄	—	17	2	no	—
526	C₂²×C₄	—	17	2	no	—
527	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
528	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
529	C₄⋊C₄	—	17	1	no	—
530	C₄⋊C₄	—	17	2	no	—
531	C₄⋊C₄	—	17	2	no	—
532	C₄⋊C₄	—	17	1	no	—
533	C₄⋊C₄	—	17	1	no	—
534	C₄⋊C₄	—	17	1	no	—
535	C₄⋊C₄	—	17	1	no	—
536	C₄⋊C₄	—	17	1	no	—
537	C₄⋊C₄	—	17	2	no	—
538	C₄⋊C₄	—	17	2	no	—
539	C₄⋊C₄	—	17	1	no	—
540	C₄⋊C₄	—	17	1	no	—
541	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
542	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
544	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
546	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
547	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
548	C₂²⋊C₄	—	17	1	no	—
549	C₂²⋊C₄	—	17	1	no	—
550	C₂²⋊C₄	—	17	1	no	—
551	C₂²⋊C₄	—	17	2	no	—
552	C₂²⋊C₄	—	17	2	no	—
553	C₂²⋊C₄	—	17	2	no	—
554	C₂²⋊C₄	—	17	2	no	—
555	C₂²⋊C₄	—	17	2	no	—
556	C₂²⋊C₄	—	17	2	no	—
557	C₂²⋊C₄	—	17	1	no	—
558	C₂²⋊C₄	—	17	1	no	—
559	C₂²⋊C₄	—	17	2	no	—
560	C₂²⋊C₄	—	17	2	no	—
561	C₂²⋊C₄	—	17	1	no	—
562	C₂²⋊C₄	—	17	2	no	—
563	C₂²⋊C₄	—	17	2	no	—
564	C₂²⋊C₄	—	17	2	no	—
565	C₂²⋊C₄	—	17	2	no	—
566	C₂²⋊C₄	—	17	1	no	—
567	C₂²⋊C₄	—	17	1	no	—
568	C₂²⋊C₄	—	17	2	no	—
569	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
570	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
571	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
572	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
576	C₄²	—	17	1	no	—
577	C₄²	—	17	1	no	—
578	C₄²	—	17	1	no	—
579	C₄²	—	17	1	no	—
580	C₄²	—	17	2	no	—
581	C₄²	C₂²×D₁₇	1	1	yes	characteristic
582	C₄²	C₂²×D₁₇	1	2	yes	—
583	C₄²	C₂²×D₁₇	1	1	yes	characteristic
584	C₂³	—	17	2	no	—
585	C₂³	—	17	1	no	—
586	C₂³	—	17	2	no	—
587	C₂³	—	17	1	no	—
588	C₂³	—	17	2	no	—
589	C₂³	—	68	2	no	—
590	C₂³	—	68	2	no	—
591	C₂³	—	68	2	no	—
592	C₂³	—	68	2	no	—
593	C₂³	—	68	2	no	—
594	C₂³	—	68	2	no	—
595	C₂³	C₂³×D₁₇	1	1	yes	characteristic
596	C₂³	C₂³×D₁₇	1	2	yes	—
597	Q₈	—	2	2	no	—
598	Q₈	—	4	2	no	—
599	Q₈	—	34	2	no	—
600	Q₈	—	34	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	4	2	no	—
603	D₄	—	34	2	no	—
604	D₄	—	34	4	no	—
605	D₄	—	34	2	no	—
606	D₄	—	34	2	no	—
607	D₄	—	34	2	no	—
608	D₄	—	68	2	no	—
609	D₄	—	68	2	no	—
610	D₄	—	68	2	no	—
611	D₄	—	68	2	no	—
612	D₄	—	68	2	no	—
613	D₄	—	68	2	no	—
614	D₄	—	68	2	no	—
615	D₄	—	68	2	no	—
616	D₄	—	68	2	no	—
617	D₄	—	68	1	no	—
618	D₄	—	68	2	no	—
619	D₄	—	68	2	no	—
620	D₄	—	68	2	no	—
621	D₄	—	68	2	no	—
622	D₄	—	68	2	no	—
623	D₄	—	68	2	no	—
624	D₄	—	68	2	no	—
625	D₄	—	68	1	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	17	1	no	—
629	C₂×C₄	—	17	1	no	—
630	C₂×C₄	—	17	1	no	—
631	C₂×C₄	—	17	1	no	—
632	C₂×C₄	—	17	1	no	—
633	C₂×C₄	—	17	2	no	—
634	C₂×C₄	—	17	1	no	—
635	C₂×C₄	—	34	4	no	—
636	C₂×C₄	—	34	4	no	—
637	C₂×C₄	—	34	2	no	—
638	C₂×C₄	—	34	2	no	—
639	C₂×C₄	—	34	2	no	—
640	C₂×C₄	—	68	2	no	—
641	C₂×C₄	—	68	2	no	—
642	C₂×C₄	—	68	2	no	—
643	C₂×C₄	—	68	2	no	—
644	C₂×C₄	—	68	1	no	—
645	C₂×C₄	—	68	2	no	—
646	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₁₇	1	2	yes	—
649	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₇	1	2	yes	—
652	C₂×C₄	C₂³×D₁₇	1	2	yes	—
653	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
655	C₂²	—	2	2	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	34	1	no	—
662	C₂²	—	34	2	no	—
663	C₂²	—	34	2	no	—
664	C₂²	—	34	2	no	—
665	C₂²	—	34	1	no	—
666	C₂²	—	34	1	no	—
667	C₂²	—	34	1	no	—
668	C₂²	—	34	2	no	—
669	C₂²	—	34	2	no	—
670	C₂²	—	34	2	no	—
671	C₂²	—	34	1	no	—
672	C₂²	—	34	2	no	—
673	C₂²	—	34	2	no	—
674	C₂²	—	34	2	no	—
675	C₂²	—	34	1	no	—
676	C₂²	—	136	4	no	—
677	C₂²	—	136	4	no	—
678	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	17	2	no	—
688	C₄	—	34	1	no	—
689	C₄	—	34	1	no	—
690	C₄	—	34	1	no	—
691	C₄	—	34	2	no	—
692	C₄	—	34	1	no	—
693	C₄	—	34	1	no	—
694	C₄	#10587696	1	2	yes	—
695	C₂	—	4	1	no	—
696	C₂	—	4	2	no	—
697	C₂	—	68	2	no	—
698	C₂	—	68	1	no	—
699	C₂	—	68	2	no	—
700	C₂	—	68	1	no	—
701	C₂	—	68	2	no	—
702	C₂	H(5,𝔽₂)×D₁₇	1	1	yes	characteristic
703	C₂	C₂×#10587696	1	1	yes	characteristic
704	C₂	#11763646	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#542	C₂
hypercenter	#542	D₁₇
hypocenter	C₁₇	#3546
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #11763550	C₂	semidirect
2. #11763549	C₂	semidirect
3. #11763531	C₂	semidirect
4. #11763510	C₂	semidirect
5. #11763481	C₂	semidirect
6. #11763480	C₂	semidirect
7. #11763477	C₂	semidirect
8. #11763461	C₂	semidirect
9. #11763454	C₂	semidirect
10. #11763451	C₂	semidirect
11. #11763450	C₂	semidirect
12. #11763443	C₂	semidirect
13. #11763433	C₂	semidirect
14. #11763399	C₂	semidirect
15. #11763393	C₂	semidirect
16. #11763389	C₂	semidirect
17. #11763378	C₂	semidirect
18. #11763377	C₂	semidirect
19. #11763377	C₂	semidirect
20. #11763360	C₂	semidirect
21. #11763358	C₂	semidirect
22. #11763337	C₂	semidirect
23. C₁₇×#542	C₂	semidirect
24. C₂×#63256	C₂²	semidirect
25. C₂×#63256	C₂²	semidirect
26. C₂×#63256	C₂²	semidirect
27. C₂×#63254	C₂²	semidirect
30. C₂×#63252	C₂²	semidirect
31. C₂×#63252	C₂²	semidirect
33. C₁₇×C₄⋊Q₈	C₂²	semidirect
34. C₁₇×#126	C₂²	semidirect
35. C₁₇×#124	C₂²	semidirect
36. C₁₇×#124	C₂²	semidirect
37. C₁₇×#123	C₂²	semidirect
38. C₁₇×C₂²⋊Q₈	C₂²	semidirect
39. C₁₇×C₂²⋊Q₈	C₂²	semidirect
41. C₄×Q₈×C₁₇	C₂²	semidirect
42. C₄×D₄×C₁₇	C₂²	semidirect
43. C₁₇×#117	C₂²	semidirect
45. #10587633	C₂²	semidirect
46. #10587633	C₂²	semidirect
47. #10587632	C₂²	semidirect
48. #10587630	C₂²	semidirect
50. #10587626	C₂²	semidirect
51. #10587626	C₂²	semidirect
52. #10587625	C₂²	semidirect
54. #10587616	C₂²	semidirect
55. #10587616	C₂²	semidirect
57. C₄×C₂²⋊D₁₇	C₂²	semidirect
58. C₂×#63227	C₂²	semidirect
59. #10587584	C₂²	semidirect
60. #10587584	C₂²	semidirect
61. #10587584	C₂²	semidirect
62. #10587583	C₂²	semidirect
63. #10587582	C₂²	semidirect
64. #10587582	C₂²	semidirect
67. #10587581	C₂²	semidirect
68. #10587581	C₂²	semidirect
69. #10587581	C₂²	semidirect
70. #10587581	C₂²	semidirect
71. #10587581	C₂²	semidirect
72. #10587581	C₂²	semidirect
73. #10587581	C₂²	semidirect
74. #10587580	C₂²	semidirect
75. #10587580	C₂²	semidirect
76. #10587580	C₂²	semidirect
77. #10587580	C₂²	semidirect
79. #10587579	C₂²	semidirect
80. #10587579	C₂²	semidirect
81. #10587579	C₂²	semidirect
82. C₄⋊C₄×D₁₇	C₂²	semidirect
83. #10587575	C₂²	semidirect
84. #10587573	C₂²	semidirect
85. #10587572	C₂²	semidirect
90. #10587570	C₂²	semidirect
91. #10587570	C₂²	semidirect
92. #10587570	C₂²	semidirect
93. #10587570	C₂²	semidirect
94. #10587570	C₂²	semidirect
95. #10587570	C₂²	semidirect
96. #10587570	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. #10587568	C₂²	semidirect
106. #10587567	C₂²	semidirect
107. #10587567	C₂²	semidirect
108. #10587567	C₂²	semidirect
109. C₂²⋊C₄×D₁₇	C₂²	semidirect
110. #10587565	C₂²	semidirect
111. #10587562	C₂²	semidirect
113. #10587561	C₂²	semidirect
115. #10587560	C₂²	semidirect
116. #10587560	C₂²	semidirect
117. C₄×D₆₈	C₂²	semidirect
118. C₄×D₆₈	C₂²	semidirect
119. #10587558	C₂²	semidirect
120. #10587558	C₂²	semidirect
121. C₄²×D₁₇	C₂²	semidirect
122. C₄×Dic₃₄	C₂²	semidirect
356. #542	D₁₇	semidirect
386. C₄⋊Q₈	C₂×D₁₇	semidirect
398. #126	C₂×D₁₇	semidirect
406. #124	C₂×D₁₇	semidirect
407. #124	C₂×D₁₇	semidirect
415. #123	C₂×D₁₇	semidirect
420. C₂²⋊Q₈	C₂×D₁₇	semidirect
421. C₂²⋊Q₈	C₂×D₁₇	semidirect
455. C₄×Q₈	C₂×D₁₇	semidirect
467. C₄×D₄	C₂×D₁₇	semidirect
470. #117	C₂×D₁₇	semidirect
475. C₁₇	#3546	semidirect

Maximal subgroups

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

subgroup	index
#11763550	2
#11763549	2
#11763531	2
#11763510	2
#11763481	2
#11763480	2
#11763477	2
#11763461	2
#11763454	2
#11763451	2
#11763450	2
#11763443	2
#11763433	2
#11763399	2
#11763393	2
#11763389	2
#11763378	2
#11763377	2
#11763360	2
#11763358	2
#11763337	2
C₁₇×#542	2
#3546	17