Subgroups — #14542528

Order 2176.

1022 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763526	C₂	1	2	yes	maximal, complemented
2	#11763515	C₂	1	2	yes	maximal, complemented
3	#11763497	C₂	1	2	yes	maximal, complemented
4	#11763495	C₂	1	2	yes	maximal, complemented
5	#11763491	C₂	1	2	yes	maximal, complemented
6	#11763491	C₂	1	2	yes	maximal, complemented
7	#11763484	C₂	1	2	yes	maximal, complemented
8	#11763484	C₂	1	2	yes	maximal, complemented
9	#11763439	C₂	1	1	yes	maximal, characteristic, complemented
10	#11763432	C₂	1	1	yes	maximal, characteristic, complemented
11	#11763430	C₂	1	1	yes	maximal, characteristic, complemented
12	#11763419	C₂	1	1	yes	maximal, characteristic, complemented
13	#11763384	C₂	1	1	yes	maximal, characteristic, complemented
14	#11763364	C₂	1	1	yes	maximal, characteristic, complemented
15	#11763363	C₂	1	1	yes	maximal, characteristic, complemented
16	#11763346	C₂	1	1	yes	maximal, characteristic, complemented
17	#11763344	C₂	1	1	yes	maximal, characteristic, complemented
18	#11763322	C₂	1	1	yes	maximal, characteristic
19	C₂²⋊Q₈×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#11763291	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763285	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#541	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#63256	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₇	C₂²	1	1	yes	characteristic
27	C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₁₇×#126	C₂²	1	2	yes	—
29	C₁₇×#126	C₂²	1	2	yes	—
30	C₁₇×#125	C₂²	1	2	yes	complemented
31	C₁₇×#125	C₂²	1	2	yes	complemented
32	C₁₇×#125	C₂²	1	1	yes	characteristic, complemented
33	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
36	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
37	C₁₇×#117	C₂²	1	1	yes	characteristic
38	#10587633	C₂²	1	1	yes	characteristic, complemented
39	#10587632	C₂²	1	1	yes	characteristic
40	#10587632	C₂²	1	1	yes	characteristic
41	Q₈×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
43	#10587630	C₂²	1	1	yes	characteristic, complemented
44	#10587616	C₂²	1	1	yes	characteristic
45	#10587612	C₂²	1	1	yes	characteristic
46	#10587610	C₂²	1	1	yes	characteristic
47	#10587584	C₂²	1	2	yes	complemented
48	#10587584	C₂²	1	2	yes	complemented
49	#10587584	C₂²	1	2	yes	complemented
50	#10587584	C₂²	1	2	yes	complemented
51	#10587583	C₂²	1	2	yes	—
52	#10587583	C₂²	1	2	yes	—
53	#10587583	C₂²	1	1	yes	characteristic
54	#10587583	C₂²	1	2	yes	complemented
55	#10587582	C₂²	1	2	yes	—
56	#10587582	C₂²	1	2	yes	—
57	#10587582	C₂²	1	2	yes	—
58	#10587582	C₂²	1	2	yes	complemented
59	#10587582	C₂²	1	2	yes	complemented
60	#10587582	C₂²	1	2	yes	complemented
61	#10587581	C₂²	1	1	yes	characteristic
62	#10587580	C₂²	1	2	yes	—
63	#10587580	C₂²	1	2	yes	—
64	#10587580	C₂²	1	2	yes	—
65	#10587580	C₂²	1	2	yes	—
66	#10587580	C₂²	1	2	yes	—
67	#10587579	C₂²	1	2	yes	—
68	#10587579	C₂²	1	2	yes	—
69	#10587579	C₂²	1	2	yes	—
70	#10587579	C₂²	1	1	yes	characteristic, complemented
71	#10587578	C₂²	1	2	yes	—
72	#10587578	C₂²	1	2	yes	—
73	#10587578	C₂²	1	1	yes	characteristic
74	#10587578	C₂²	1	1	yes	characteristic
75	#10587578	C₂²	1	1	yes	characteristic
76	#10587578	C₂²	1	2	yes	complemented
77	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic
78	C₄⋊C₄×D₁₇	C₂²	1	2	yes	—
79	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic
80	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic
81	C₄⋊C₄×D₁₇	C₂²	1	2	yes	complemented
82	#10587576	C₂²	1	2	yes	complemented
83	#10587576	C₂²	1	2	yes	complemented
84	#10587576	C₂²	1	1	yes	characteristic, complemented
85	#10587575	C₂²	1	2	yes	complemented
86	#10587575	C₂²	1	2	yes	complemented
87	#10587575	C₂²	1	2	yes	complemented
88	#10587574	C₂²	1	2	yes	complemented
89	#10587574	C₂²	1	1	yes	characteristic, complemented
90	#10587573	C₂²	1	2	yes	complemented
91	#10587573	C₂²	1	2	yes	complemented
92	#10587573	C₂²	1	1	yes	characteristic, complemented
93	#10587571	C₂²	1	2	yes	—
94	#10587571	C₂²	1	2	yes	—
95	#10587569	C₂²	1	2	yes	—
96	#10587569	C₂²	1	2	yes	—
97	#10587568	C₂²	1	2	yes	—
98	#10587567	C₂²	1	2	yes	—
99	C₂²⋊C₄×D₁₇	C₂²	1	1	yes	characteristic
100	C₂²⋊C₄×D₁₇	C₂²	1	1	yes	characteristic
101	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
102	#10587565	C₂²	1	2	yes	—
103	#10587565	C₂²	1	2	yes	—
104	#10587564	C₂²	1	2	yes	—
105	#10587563	C₂²	1	1	yes	characteristic
106	#10587563	C₂²	1	1	yes	characteristic
107	#10587561	C₂²	1	1	yes	characteristic, complemented
108	C₄×D₆₈	C₂²	1	2	yes	—
109	C₄×D₆₈	C₂²	1	2	yes	—
110	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
111	#10587558	C₂²	1	2	yes	—
112	#10587558	C₂²	1	2	yes	—
113	#10587558	C₂²	1	1	yes	characteristic
114	#10587558	C₂²	1	1	yes	characteristic
115	#10587558	C₂²	1	2	yes	complemented
116	#10587558	C₂²	1	2	yes	complemented
117	C₄²×D₁₇	C₂²	1	1	yes	characteristic
118	C₄²×D₁₇	C₂²	1	1	yes	characteristic
119	#10587555	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₃₄	C₂²	1	2	yes	complemented
121	C₄×Dic₃₄	C₂²	1	2	yes	complemented
122	C₄×Dic₃₄	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₇	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
128	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
129	#63256	—	2	4	no	—
130	Q₈×D₁₇	—	2	4	no	—
131	C₂×D₆₈	C₂³	1	2	yes	—
132	C₂×D₆₈	C₂³	1	1	yes	characteristic
133	C₂×D₆₈	C₂³	1	2	yes	—
134	C₂×C₄×D₁₇	—	2	4	no	—
135	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₇	C₂³	1	2	yes	—
139	C₂×C₄×D₁₇	C₂³	1	2	yes	—
140	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₇	C₂³	1	2	yes	—
145	C₂×C₄×D₁₇	C₂³	1	2	yes	—
146	C₂×C₄×D₁₇	C₂³	1	2	yes	—
147	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
148	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
149	C₂×Dic₃₄	C₂³	1	2	yes	—
150	C₂×Dic₃₄	C₂³	1	2	yes	—
151	C₂×Dic₃₄	C₂³	1	2	yes	—
152	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
153	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
154	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
157	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
158	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
161	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
162	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
163	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
167	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
168	C₄²×C₁₇	C₂³	1	2	yes	—
169	C₄²×C₁₇	C₂³	1	2	yes	—
170	C₄²×C₁₇	C₂³	1	1	yes	characteristic
171	C₄²×C₁₇	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
175	#63227	C₂³	1	1	yes	characteristic
176	#63227	C₂³	1	1	yes	characteristic
177	#63227	C₂³	1	1	yes	characteristic
178	#63227	C₂³	1	1	yes	characteristic
179	#63227	C₂³	1	2	yes	—
180	#63227	C₂³	1	2	yes	—
181	#63227	C₂³	1	2	yes	—
182	#63227	C₂³	1	2	yes	—
183	#63227	C₂³	1	2	yes	—
184	#63227	C₂³	1	2	yes	—
185	#63227	C₂³	1	2	yes	—
186	#63227	C₂³	1	2	yes	—
187	#63227	C₂³	1	2	yes	—
188	#63227	C₂³	1	2	yes	—
189	#63227	C₂³	1	2	yes	—
190	#63227	C₂³	1	2	yes	—
191	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₇	C₂³	1	2	yes	—
193	C₄⋊Dic₁₇	C₂³	1	2	yes	—
194	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₁₇	C₂³	1	2	yes	—
196	C₄⋊Dic₁₇	C₂³	1	2	yes	—
197	C₄⋊Dic₁₇	C₂³	1	2	yes	—
198	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
200	#63225	C₂³	1	1	yes	characteristic
201	#63225	C₂³	1	2	yes	—
202	#63225	C₂³	1	2	yes	—
203	#63225	C₂³	1	2	yes	—
204	#63225	C₂³	1	1	yes	characteristic
205	#63225	C₂³	1	1	yes	characteristic
206	#63225	C₂³	1	1	yes	characteristic
207	#63225	C₂³	1	2	yes	—
208	#63225	C₂³	1	2	yes	—
209	#63225	C₂³	1	2	yes	—
210	#63225	C₂³	1	2	yes	—
211	#63225	C₂³	1	2	yes	—
212	#63225	C₂³	1	2	yes	—
213	#63225	C₂³	1	2	yes	—
214	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
215	C₄×Dic₁₇	C₂³	1	2	yes	—
216	C₄×Dic₁₇	C₂³	1	2	yes	—
217	C₄×Dic₁₇	C₂³	1	2	yes	—
218	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₇	C₂³	1	2	yes	—
224	C₄×Dic₁₇	C₂³	1	2	yes	—
225	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
226	C₂²×D₁₇	—	2	2	no	—
227	C₂²×D₁₇	—	2	2	no	—
228	C₂²×D₁₇	—	4	1	no	—
229	C₂²×D₁₇	C₂⁴	1	2	yes	—
230	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
232	Q₈×C₁₇	—	2	2	no	—
233	Q₈×C₁₇	—	2	2	no	—
234	C₂×C₄×C₁₇	—	2	2	no	—
235	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
239	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
241	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
245	C₂²⋊D₁₇	—	4	2	no	—
246	C₂×Dic₁₇	—	2	2	no	—
247	C₂×Dic₁₇	C₂⁴	1	2	yes	—
248	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₇	C₂⁴	1	2	yes	—
250	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₇	C₂⁴	1	2	yes	—
254	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
256	D₆₈	—	2	4	no	—
257	D₆₈	—	2	4	no	—
258	D₆₈	—	2	2	no	—
259	C₄×D₁₇	—	2	2	no	—
260	C₄×D₁₇	—	2	4	no	—
261	C₄×D₁₇	—	2	2	no	—
262	C₄×D₁₇	—	2	2	no	—
263	C₄×D₁₇	—	2	2	no	—
264	C₄×D₁₇	—	2	2	no	—
265	C₄×D₁₇	—	2	4	no	—
266	C₄×D₁₇	—	4	1	no	—
267	C₄×D₁₇	—	4	2	no	—
268	C₄×D₁₇	—	4	2	no	—
269	C₄×D₁₇	—	4	1	no	—
270	C₄×D₁₇	—	4	2	no	—
271	C₄×D₁₇	#41	1	4	yes	—
272	Dic₃₄	—	2	2	no	—
273	Dic₃₄	—	2	4	no	—
274	Dic₃₄	—	4	2	no	—
275	Dic₃₄	—	4	2	no	—
276	#3495	—	17	1	no	maximal, Sylow
277	C₂²×C₁₇	—	2	1	no	—
278	C₂²×C₁₇	—	2	1	no	—
279	C₂²×C₁₇	—	2	1	no	—
280	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
281	C₂×D₁₇	—	2	1	no	—
282	C₂×D₁₇	—	2	1	no	—
283	C₂×D₁₇	—	2	1	no	—
284	C₂×D₁₇	—	2	1	no	—
285	C₂×D₁₇	—	2	2	no	—
286	C₂×D₁₇	—	2	2	no	—
287	C₂×D₁₇	—	2	2	no	—
288	C₂×D₁₇	—	4	4	no	—
289	C₂×D₁₇	C₂×#41	1	2	yes	—
290	C₂×D₁₇	2₋¹⁺⁴	1	2	yes	—
291	C₄×C₁₇	—	2	2	no	—
292	C₄×C₁₇	—	2	1	no	—
293	C₄×C₁₇	—	2	2	no	—
294	C₄×C₁₇	—	2	1	no	—
295	C₄×C₁₇	—	2	1	no	—
296	C₄×C₁₇	—	2	2	no	—
297	C₄×C₁₇	—	2	1	no	—
298	C₄×C₁₇	—	2	2	no	—
299	C₄×C₁₇	—	2	1	no	—
300	C₄×C₁₇	C₂×#41	1	2	yes	—
301	Dic₁₇	—	2	2	no	—
302	Dic₁₇	—	2	1	no	—
303	Dic₁₇	—	2	1	no	—
304	Dic₁₇	—	2	1	no	—
305	Dic₁₇	—	2	1	no	—
306	Dic₁₇	—	2	2	no	—
307	Dic₁₇	—	2	2	no	—
308	Dic₁₇	—	2	1	no	—
309	Dic₁₇	C₂×#41	1	2	yes	—
310	#556	—	17	2	no	—
311	#554	—	17	2	no	—
312	#552	—	17	2	no	—
313	#552	—	17	2	no	—
314	#552	—	17	2	no	—
315	#552	—	17	2	no	—
316	#551	—	17	2	no	—
317	#551	—	17	2	no	—
318	#544	—	17	1	no	—
319	#542	—	17	1	no	—
320	#542	—	17	1	no	—
321	#541	—	17	1	no	—
322	#541	D₁₇	1	1	yes	characteristic, complemented
323	#536	—	17	1	no	—
324	#533	—	17	1	no	—
325	#533	—	17	1	no	—
326	#529	—	17	1	no	—
327	#529	—	17	1	no	—
328	#525	—	17	1	no	—
329	C₂×C₂²⋊Q₈	—	17	1	no	—
330	#520	—	17	1	no	—
331	#519	—	17	1	no	—
332	C₂×#117	—	17	1	no	—
333	C₂×C₁₇	—	4	1	no	—
334	C₂×C₁₇	C₂²×#41	1	1	yes	characteristic
335	C₂×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
336	C₂×C₁₇	#585	1	1	yes	characteristic
337	D₁₇	—	2	2	no	—
338	D₁₇	—	2	2	no	—
339	D₁₇	—	4	2	no	—
340	C₂×#41	—	17	1	no	—
341	C₂²×Q₈	—	17	1	no	—
342	C₂³×C₄	—	17	1	no	—
343	C₄⋊Q₈	—	17	1	no	—
344	C₄⋊Q₈	—	17	1	no	—
345	C₄⋊Q₈	—	17	2	no	—
346	C₄⋊Q₈	—	17	1	no	—
347	C₄⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
348	#126	—	17	2	no	—
349	#126	—	17	2	no	—
350	#126	—	17	2	no	—
351	#126	—	17	2	no	—
352	#126	—	17	2	no	—
353	#126	—	17	2	no	—
354	#126	C₂×D₁₇	1	2	yes	—
355	#126	C₂×D₁₇	1	2	yes	—
356	#125	—	17	1	no	—
357	#125	—	17	2	no	—
358	#125	—	17	2	no	—
359	#125	—	17	2	no	—
360	#125	—	17	2	no	—
361	#125	—	17	2	no	—
362	#125	C₂×D₁₇	1	1	yes	characteristic, complemented
363	#125	C₂×D₁₇	1	2	yes	complemented
364	#125	C₂×D₁₇	1	2	yes	complemented
365	#124	—	17	1	no	—
366	#124	—	17	2	no	—
367	#124	—	17	2	no	—
368	#124	—	17	1	no	—
369	#123	—	17	2	no	—
370	#123	—	17	2	no	—
371	#123	—	17	2	no	—
372	#123	—	17	2	no	—
373	#123	—	17	2	no	—
374	#123	—	17	2	no	—
375	#123	—	17	2	no	—
376	C₂²⋊Q₈	—	17	1	no	—
377	C₂²⋊Q₈	—	17	1	no	—
378	C₂²⋊Q₈	—	17	1	no	—
379	C₂²⋊Q₈	—	17	1	no	—
380	C₂²⋊Q₈	—	17	2	no	—
381	C₂²⋊Q₈	—	17	2	no	—
382	C₂²⋊Q₈	—	17	2	no	—
383	C₂²⋊Q₈	—	17	2	no	—
384	C₂²⋊Q₈	—	17	2	no	—
385	C₂²⋊Q₈	—	17	2	no	—
386	C₂²⋊Q₈	—	17	2	no	—
387	C₂²⋊Q₈	—	17	2	no	—
388	C₂²⋊Q₈	—	17	2	no	—
389	C₂²⋊Q₈	—	17	2	no	—
390	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic
391	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic
392	#121	—	17	1	no	—
393	#121	—	17	1	no	—
394	#120	—	17	2	no	—
395	C₄×Q₈	—	17	1	no	—
396	C₄×Q₈	—	17	1	no	—
397	C₄×Q₈	—	17	1	no	—
398	C₄×Q₈	—	17	2	no	—
399	C₄×Q₈	—	17	2	no	—
400	C₄×Q₈	—	17	1	no	—
401	C₄×Q₈	—	17	2	no	—
402	C₄×Q₈	—	17	2	no	—
403	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
404	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
405	C₄×D₄	—	17	1	no	—
406	C₄×D₄	—	17	2	no	—
407	C₄×D₄	—	17	2	no	—
408	C₄×D₄	—	17	2	no	—
409	C₄×D₄	—	17	2	no	—
410	C₄×D₄	—	17	1	no	—
411	C₄×D₄	—	17	2	no	—
412	C₄×D₄	—	17	2	no	—
413	#117	—	17	1	no	—
414	#117	—	17	1	no	—
415	#117	—	17	1	no	—
416	#117	—	17	1	no	—
417	#117	—	17	2	no	—
418	#117	—	17	2	no	—
419	#117	—	17	2	no	—
420	#117	—	17	1	no	—
421	#117	—	17	1	no	—
422	#117	—	17	1	no	—
423	#117	—	17	1	no	—
424	#117	—	17	2	no	—
425	#117	—	17	2	no	—
426	#117	—	17	2	no	—
427	#117	—	17	2	no	—
428	#117	C₂×D₁₇	1	1	yes	characteristic
429	C₂×C₄⋊C₄	—	17	1	no	—
430	C₂×C₄⋊C₄	—	17	1	no	—
431	C₂×C₄⋊C₄	—	17	1	no	—
432	C₂×C₄⋊C₄	—	17	2	no	—
433	C₂×C₄⋊C₄	—	17	2	no	—
434	C₂×C₂²⋊C₄	—	17	1	no	—
435	C₂×C₂²⋊C₄	—	17	1	no	—
436	C₂×C₂²⋊C₄	—	17	2	no	—
437	C₂×C₄²	—	17	1	no	—
438	C₂×C₄²	—	17	1	no	—
439	C₁₇	#3495	1	1	yes	characteristic, complemented, Sylow
440	C₂⁴	—	17	1	no	—
441	#41	—	34	4	no	—
442	C₂×Q₈	—	17	2	no	—
443	C₂×Q₈	—	17	1	no	—
444	C₂×Q₈	—	17	2	no	—
445	C₂×Q₈	—	17	2	no	—
446	C₂×Q₈	—	34	4	no	—
447	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
448	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
449	C₂×D₄	—	17	2	no	—
450	C₂×D₄	—	17	2	no	—
451	C₂×D₄	—	17	2	no	—
452	C₂×D₄	—	17	1	no	—
453	C₂²×C₄	—	17	1	no	—
454	C₂²×C₄	—	17	1	no	—
455	C₂²×C₄	—	17	1	no	—
456	C₂²×C₄	—	17	1	no	—
457	C₂²×C₄	—	17	1	no	—
458	C₂²×C₄	—	17	2	no	—
459	C₂²×C₄	—	17	1	no	—
460	C₂²×C₄	—	17	1	no	—
461	C₂²×C₄	—	17	2	no	—
462	C₂²×C₄	—	17	1	no	—
463	C₂²×C₄	—	17	1	no	—
464	C₂²×C₄	—	17	2	no	—
465	C₂²×C₄	—	17	2	no	—
466	C₂²×C₄	—	17	2	no	—
467	C₂²×C₄	—	34	4	no	—
468	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
469	C₄⋊C₄	—	17	1	no	—
470	C₄⋊C₄	—	17	2	no	—
471	C₄⋊C₄	—	17	1	no	—
472	C₄⋊C₄	—	17	1	no	—
473	C₄⋊C₄	—	17	1	no	—
474	C₄⋊C₄	—	17	1	no	—
475	C₄⋊C₄	—	17	1	no	—
476	C₄⋊C₄	—	17	2	no	—
477	C₄⋊C₄	—	17	2	no	—
478	C₄⋊C₄	—	17	1	no	—
479	C₄⋊C₄	—	17	2	no	—
480	C₄⋊C₄	—	17	2	no	—
481	C₄⋊C₄	—	17	1	no	—
482	C₄⋊C₄	—	17	2	no	—
483	C₄⋊C₄	—	17	2	no	—
484	C₄⋊C₄	—	17	2	no	—
485	C₄⋊C₄	—	17	2	no	—
486	C₄⋊C₄	—	17	2	no	—
487	C₄⋊C₄	—	17	2	no	—
488	C₄⋊C₄	—	17	2	no	—
489	C₄⋊C₄	—	17	2	no	—
490	C₄⋊C₄	—	17	2	no	—
491	C₄⋊C₄	—	17	2	no	—
492	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
493	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
496	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
497	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
499	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
500	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
502	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
503	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
504	C₂²⋊C₄	—	17	1	no	—
505	C₂²⋊C₄	—	17	1	no	—
506	C₂²⋊C₄	—	17	2	no	—
507	C₂²⋊C₄	—	17	1	no	—
508	C₂²⋊C₄	—	17	1	no	—
509	C₂²⋊C₄	—	17	1	no	—
510	C₂²⋊C₄	—	17	1	no	—
511	C₂²⋊C₄	—	17	2	no	—
512	C₂²⋊C₄	—	17	2	no	—
513	C₂²⋊C₄	—	17	2	no	—
514	C₂²⋊C₄	—	17	2	no	—
515	C₂²⋊C₄	—	17	2	no	—
516	C₂²⋊C₄	—	17	2	no	—
517	C₂²⋊C₄	—	17	2	no	—
518	C₂²⋊C₄	—	17	2	no	—
519	C₂²⋊C₄	—	17	2	no	—
520	C₂²⋊C₄	—	17	2	no	—
521	C₂²⋊C₄	—	17	2	no	—
522	C₂²⋊C₄	—	17	2	no	—
523	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
524	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
525	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
527	C₄²	—	17	1	no	—
528	C₄²	—	17	1	no	—
529	C₄²	—	17	1	no	—
530	C₄²	—	17	1	no	—
531	C₄²	—	17	1	no	—
532	C₄²	—	17	1	no	—
533	C₄²	—	17	2	no	—
534	C₄²	—	17	2	no	—
535	C₄²	—	17	2	no	—
536	C₄²	—	17	2	no	—
537	C₄²	—	17	2	no	—
538	C₄²	C₂²×D₁₇	1	1	yes	characteristic
539	C₄²	C₂²×D₁₇	1	1	yes	characteristic
540	C₄²	C₂²×D₁₇	1	2	yes	—
541	C₄²	C₂²×D₁₇	1	2	yes	—
542	C₂³	—	17	1	no	—
543	C₂³	—	17	1	no	—
544	C₂³	—	17	2	no	—
545	C₂³	—	34	2	no	—
546	C₂³	—	34	2	no	—
547	C₂³	—	68	1	no	—
548	C₂³	C₂³×D₁₇	1	1	yes	characteristic
549	Q₈	—	2	2	no	—
550	Q₈	—	2	2	no	—
551	Q₈	—	34	4	no	—
552	Q₈	—	34	2	no	—
553	Q₈	—	68	2	no	—
554	Q₈	—	68	2	no	—
555	D₄	—	34	4	no	—
556	D₄	—	34	4	no	—
557	D₄	—	34	2	no	—
558	D₄	—	68	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	17	1	no	—
561	C₂×C₄	—	17	4	no	—
562	C₂×C₄	—	17	1	no	—
563	C₂×C₄	—	17	1	no	—
564	C₂×C₄	—	17	1	no	—
565	C₂×C₄	—	17	2	no	—
566	C₂×C₄	—	17	1	no	—
567	C₂×C₄	—	17	2	no	—
568	C₂×C₄	—	17	1	no	—
569	C₂×C₄	—	17	2	no	—
570	C₂×C₄	—	34	2	no	—
571	C₂×C₄	—	34	4	no	—
572	C₂×C₄	—	34	2	no	—
573	C₂×C₄	—	34	4	no	—
574	C₂×C₄	—	34	2	no	—
575	C₂×C₄	—	34	2	no	—
576	C₂×C₄	—	34	2	no	—
577	C₂×C₄	—	34	2	no	—
578	C₂×C₄	—	68	2	no	—
579	C₂×C₄	—	68	1	no	—
580	C₂×C₄	—	68	2	no	—
581	C₂×C₄	—	68	2	no	—
582	C₂×C₄	—	68	1	no	—
583	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₁₇	1	2	yes	—
585	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₁₇	1	2	yes	—
588	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₁₇	1	2	yes	—
590	C₂×C₄	C₂³×D₁₇	1	2	yes	—
591	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	17	2	no	—
597	C₂²	—	17	2	no	—
598	C₂²	—	34	1	no	—
599	C₂²	—	34	1	no	—
600	C₂²	—	34	1	no	—
601	C₂²	—	34	1	no	—
602	C₂²	—	34	2	no	—
603	C₂²	—	34	2	no	—
604	C₂²	—	34	2	no	—
605	C₂²	—	68	4	no	—
606	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	1	no	—
616	C₄	—	17	2	no	—
617	C₄	—	34	1	no	—
618	C₄	—	34	2	no	—
619	C₄	—	34	1	no	—
620	C₄	—	34	1	no	—
621	C₄	—	34	1	no	—
622	C₄	—	34	2	no	—
623	C₄	—	34	1	no	—
624	C₄	—	34	2	no	—
625	C₄	#41×D₁₇	1	2	yes	—
626	C₂	—	4	1	no	—
627	C₂	—	34	2	no	—
628	C₂	—	34	2	no	—
629	C₂	—	68	2	no	—
630	C₂	C₂×#41×D₁₇	1	1	yes	characteristic
631	C₂	2₋¹⁺⁴×D₁₇	1	1	yes	characteristic
632	C₂	#11763646	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#541	C₂
prime radical	#11763322	C₂
hypercenter	#541	D₁₇
hypocenter	C₁₇	#3495
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. #11763526	C₂	semidirect
2. #11763515	C₂	semidirect
3. #11763497	C₂	semidirect
4. #11763495	C₂	semidirect
5. #11763491	C₂	semidirect
6. #11763491	C₂	semidirect
7. #11763484	C₂	semidirect
8. #11763484	C₂	semidirect
9. #11763439	C₂	semidirect
10. #11763432	C₂	semidirect
11. #11763430	C₂	semidirect
12. #11763419	C₂	semidirect
13. #11763384	C₂	semidirect
14. #11763364	C₂	semidirect
15. #11763363	C₂	semidirect
16. #11763346	C₂	semidirect
17. #11763344	C₂	semidirect
19. C₂²⋊Q₈×D₁₇	C₂	semidirect
20. #11763291	C₂	semidirect
21. #11763285	C₂	semidirect
22. #117×D₁₇	C₂	semidirect
23. C₁₇×#541	C₂	semidirect
27. C₁₇×C₄⋊Q₈	C₂²	semidirect
30. C₁₇×#125	C₂²	semidirect
31. C₁₇×#125	C₂²	semidirect
32. C₁₇×#125	C₂²	semidirect
35. C₄×Q₈×C₁₇	C₂²	semidirect
36. C₄×Q₈×C₁₇	C₂²	semidirect
38. #10587633	C₂²	semidirect
41. Q₈×Dic₁₇	C₂²	semidirect
42. Q₈×Dic₁₇	C₂²	semidirect
43. #10587630	C₂²	semidirect
47. #10587584	C₂²	semidirect
48. #10587584	C₂²	semidirect
49. #10587584	C₂²	semidirect
50. #10587584	C₂²	semidirect
54. #10587583	C₂²	semidirect
58. #10587582	C₂²	semidirect
59. #10587582	C₂²	semidirect
60. #10587582	C₂²	semidirect
70. #10587579	C₂²	semidirect
76. #10587578	C₂²	semidirect
81. C₄⋊C₄×D₁₇	C₂²	semidirect
82. #10587576	C₂²	semidirect
83. #10587576	C₂²	semidirect
84. #10587576	C₂²	semidirect
85. #10587575	C₂²	semidirect
86. #10587575	C₂²	semidirect
87. #10587575	C₂²	semidirect
88. #10587574	C₂²	semidirect
89. #10587574	C₂²	semidirect
90. #10587573	C₂²	semidirect
91. #10587573	C₂²	semidirect
92. #10587573	C₂²	semidirect
107. #10587561	C₂²	semidirect
110. C₄×D₆₈	C₂²	semidirect
115. #10587558	C₂²	semidirect
116. #10587558	C₂²	semidirect
119. #10587555	C₂²	semidirect
120. C₄×Dic₃₄	C₂²	semidirect
121. C₄×Dic₃₄	C₂²	semidirect
122. C₄×Dic₃₄	C₂²	semidirect
322. #541	D₁₇	semidirect
347. C₄⋊Q₈	C₂×D₁₇	semidirect
362. #125	C₂×D₁₇	semidirect
363. #125	C₂×D₁₇	semidirect
364. #125	C₂×D₁₇	semidirect
403. C₄×Q₈	C₂×D₁₇	semidirect
404. C₄×Q₈	C₂×D₁₇	semidirect
439. C₁₇	#3495	semidirect

Maximal subgroups

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

subgroup	index
#11763526	2
#11763515	2
#11763497	2
#11763495	2
#11763491	2
#11763484	2
#11763439	2
#11763432	2
#11763430	2
#11763419	2
#11763384	2
#11763364	2
#11763363	2
#11763346	2
#11763344	2
#11763322	2
C₂²⋊Q₈×D₁₇	2
#11763291	2
#11763285	2
#117×D₁₇	2
C₁₇×#541	2
#3495	17