Subgroups — #14543353

Order 2176.

1032 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763561	C₂	1	2	yes	maximal, complemented
2	#11763555	C₂	1	2	yes	maximal, complemented
3	#11763532	C₂	1	1	yes	maximal, characteristic, complemented
4	#11763484	C₂	1	2	yes	maximal, complemented
5	#11763483	C₂	1	2	yes	maximal, complemented
6	Q₈×D₆₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#11763474	C₂	1	1	yes	maximal, characteristic, complemented
8	#11763471	C₂	1	1	yes	maximal, characteristic, complemented
9	#11763467	C₂	1	1	yes	maximal, characteristic, complemented
10	#11763454	C₂	1	1	yes	maximal, characteristic, complemented
11	#11763452	C₂	1	1	yes	maximal, characteristic, complemented
12	#11763434	C₂	1	2	yes	maximal, complemented
13	#11763431	C₂	1	1	yes	maximal, characteristic, complemented
14	#11763430	C₂	1	2	yes	maximal, complemented
15	#11763425	C₂	1	2	yes	maximal, complemented
16	#11763424	C₂	1	1	yes	maximal, characteristic, complemented
17	#11763398	C₂	1	2	yes	maximal, complemented
18	#11763384	C₂	1	1	yes	maximal, characteristic, complemented
19	#11763379	C₂	1	1	yes	maximal, characteristic, complemented
20	#11763363	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763346	C₂	1	1	yes	maximal, characteristic, complemented
22	#124×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#556	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	C₂×Q₈×D₁₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₁₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×#63254	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₁₇	C₂²	1	1	yes	characteristic
30	C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₇×#126	C₂²	1	2	yes	complemented
32	C₁₇×#126	C₂²	1	2	yes	complemented
33	C₁₇×#124	C₂²	1	1	yes	characteristic
34	C₁₇×#124	C₂²	1	1	yes	characteristic
35	C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
37	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
38	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
40	C₁₇×#117	C₂²	1	2	yes	complemented
41	#10587633	C₂²	1	1	yes	characteristic
42	#10587633	C₂²	1	1	yes	characteristic, complemented
43	#10587632	C₂²	1	1	yes	characteristic
44	#10587632	C₂²	1	1	yes	characteristic
45	#10587632	C₂²	1	1	yes	characteristic, complemented
46	#10587632	C₂²	1	2	yes	complemented
47	#10587630	C₂²	1	1	yes	characteristic, complemented
48	#10587624	C₂²	1	1	yes	characteristic
49	#10587622	C₂²	1	1	yes	characteristic
50	#10587616	C₂²	1	2	yes	—
51	#10587615	C₂²	1	2	yes	complemented
52	C₂×#63227	C₂²	1	2	yes	—
53	#10587610	C₂²	1	2	yes	complemented
54	#10587584	C₂²	1	2	yes	complemented
55	#10587584	C₂²	1	2	yes	complemented
56	#10587584	C₂²	1	1	yes	characteristic, complemented
57	#10587584	C₂²	1	1	yes	characteristic, complemented
58	#10587583	C₂²	1	2	yes	—
59	#10587583	C₂²	1	1	yes	characteristic
60	#10587583	C₂²	1	1	yes	characteristic, complemented
61	#10587583	C₂²	1	2	yes	complemented
62	#10587583	C₂²	1	2	yes	complemented
63	#10587582	C₂²	1	2	yes	—
64	#10587582	C₂²	1	2	yes	—
65	#10587582	C₂²	1	2	yes	complemented
66	#10587582	C₂²	1	2	yes	complemented
67	#10587582	C₂²	1	2	yes	complemented
68	#10587582	C₂²	1	2	yes	complemented
69	#10587581	C₂²	1	1	yes	characteristic
70	#10587581	C₂²	1	1	yes	characteristic
71	#10587581	C₂²	1	2	yes	complemented
72	#10587580	C₂²	1	1	yes	characteristic
73	#10587580	C₂²	1	1	yes	characteristic
74	#10587580	C₂²	1	2	yes	complemented
75	#10587580	C₂²	1	2	yes	complemented
76	#10587580	C₂²	1	2	yes	complemented
77	#10587579	C₂²	1	2	yes	—
78	#10587578	C₂²	1	2	yes	complemented
79	#10587576	C₂²	1	1	yes	characteristic, complemented
80	#10587575	C₂²	1	2	yes	complemented
81	#10587574	C₂²	1	2	yes	complemented
82	#10587574	C₂²	1	1	yes	characteristic, complemented
83	#10587572	C₂²	1	2	yes	—
84	#10587571	C₂²	1	2	yes	—
85	#10587571	C₂²	1	2	yes	—
86	#10587571	C₂²	1	2	yes	complemented
87	#10587571	C₂²	1	2	yes	complemented
88	#10587570	C₂²	1	2	yes	—
89	#10587570	C₂²	1	2	yes	complemented
90	#10587569	C₂²	1	2	yes	—
91	#10587569	C₂²	1	2	yes	complemented
92	#10587569	C₂²	1	2	yes	complemented
93	#10587568	C₂²	1	2	yes	—
94	#10587568	C₂²	1	2	yes	—
95	#10587567	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
97	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
98	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
99	#10587565	C₂²	1	2	yes	complemented
100	#10587564	C₂²	1	2	yes	complemented
101	#10587564	C₂²	1	2	yes	complemented
102	#10587564	C₂²	1	2	yes	complemented
103	#10587562	C₂²	1	2	yes	complemented
104	#10587561	C₂²	1	1	yes	characteristic
105	#10587561	C₂²	1	1	yes	characteristic
106	#10587561	C₂²	1	2	yes	complemented
107	#10587561	C₂²	1	2	yes	complemented
108	C₄×D₆₈	C₂²	1	1	yes	characteristic
109	C₄×D₆₈	C₂²	1	2	yes	—
110	C₄×D₆₈	C₂²	1	1	yes	characteristic
111	C₄×D₆₈	C₂²	1	1	yes	characteristic
112	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
113	C₄×D₆₈	C₂²	1	2	yes	complemented
114	#10587558	C₂²	1	2	yes	—
115	#10587558	C₂²	1	1	yes	characteristic, complemented
116	#10587558	C₂²	1	1	yes	characteristic, complemented
117	C₄²×D₁₇	C₂²	1	1	yes	characteristic
118	#10587555	C₂²	1	1	yes	characteristic, complemented
119	#10587555	C₂²	1	2	yes	complemented
120	C₄×Dic₃₄	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₃₄	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₄	C₂²	1	2	yes	complemented
123	C₂³×D₁₇	C₂³	1	2	yes	—
124	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
126	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
132	C₂²×Dic₁₇	C₂³	1	2	yes	—
133	#63256	—	4	2	no	—
134	Q₈×D₁₇	—	4	2	no	—
135	Q₈×D₁₇	—	4	2	no	—
136	Q₈×D₁₇	—	4	2	no	—
137	#63254	—	4	2	no	—
138	D₄×D₁₇	—	4	2	no	—
139	C₂×D₆₈	C₂³	1	1	yes	characteristic
140	C₂×D₆₈	C₂³	1	1	yes	characteristic
141	C₂×D₆₈	C₂³	1	1	yes	characteristic
142	C₂×D₆₈	C₂³	1	2	yes	—
143	C₂×D₆₈	C₂³	1	2	yes	—
144	C₂×D₆₈	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₇	C₂³	1	2	yes	—
150	C₂×C₄×D₁₇	C₂³	1	2	yes	—
151	C₂×C₄×D₁₇	C₂³	1	2	yes	—
152	C₂×C₄×D₁₇	C₂³	1	2	yes	—
153	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₇	C₂³	1	2	yes	—
155	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
156	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
157	C₂×Dic₃₄	C₂³	1	2	yes	—
158	C₂×Dic₃₄	C₂³	1	2	yes	—
159	C₂×Dic₃₄	C₂³	1	2	yes	—
160	C₂×Dic₃₄	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	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
165	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
167	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
169	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
174	C₄²×C₁₇	C₂³	1	1	yes	characteristic
175	C₄²×C₁₇	C₂³	1	1	yes	characteristic
176	C₄²×C₁₇	C₂³	1	2	yes	—
177	C₄²×C₁₇	C₂³	1	2	yes	—
178	C₄²×C₁₇	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
182	#63227	C₂³	1	2	yes	—
183	#63227	C₂³	1	2	yes	—
184	#63227	C₂³	1	1	yes	characteristic
185	#63227	C₂³	1	1	yes	characteristic
186	#63227	C₂³	1	1	yes	characteristic
187	#63227	C₂³	1	1	yes	characteristic
188	#63227	C₂³	1	2	yes	—
189	#63227	C₂³	1	2	yes	—
190	#63227	C₂³	1	1	yes	characteristic
191	#63227	C₂³	1	1	yes	characteristic
192	#63227	C₂³	1	1	yes	characteristic
193	#63227	C₂³	1	1	yes	characteristic
194	#63227	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	2	yes	—
199	#63227	C₂³	1	2	yes	—
200	#63227	C₂³	1	2	yes	—
201	#63227	C₂³	1	2	yes	—
202	#63227	C₂³	1	2	yes	—
203	#63227	C₂³	1	2	yes	—
204	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₁₇	C₂³	1	2	yes	—
206	C₄⋊Dic₁₇	C₂³	1	2	yes	—
207	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₇	C₂³	1	2	yes	—
209	C₄⋊Dic₁₇	C₂³	1	2	yes	—
210	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
212	#63225	C₂³	1	2	yes	—
213	#63225	C₂³	1	2	yes	—
214	#63225	C₂³	1	2	yes	—
215	#63225	C₂³	1	2	yes	—
216	#63225	C₂³	1	2	yes	—
217	#63225	C₂³	1	2	yes	—
218	#63225	C₂³	1	1	yes	characteristic
219	#63225	C₂³	1	1	yes	characteristic
220	#63225	C₂³	1	1	yes	characteristic
221	#63225	C₂³	1	1	yes	characteristic
222	#63225	C₂³	1	2	yes	—
223	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₇	C₂³	1	2	yes	—
225	C₄×Dic₁₇	C₂³	1	2	yes	—
226	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
228	C₂³×C₁₇	C₂⁴	1	2	yes	—
229	C₂²×D₁₇	—	2	4	no	—
230	C₂²×D₁₇	—	4	2	no	—
231	C₂²×D₁₇	—	4	2	no	—
232	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₇	C₂⁴	1	2	yes	—
235	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
236	Q₈×C₁₇	—	2	2	no	—
237	Q₈×C₁₇	—	2	2	no	—
238	Q₈×C₁₇	—	4	1	no	—
239	D₄×C₁₇	—	2	2	no	—
240	C₂×C₄×C₁₇	—	4	2	no	—
241	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
244	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
246	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₁₇	—	4	2	no	—
252	C₂²⋊D₁₇	—	4	2	no	—
253	C₂²⋊D₁₇	—	4	2	no	—
254	C₂×Dic₁₇	—	4	2	no	—
255	C₂×Dic₁₇	C₂⁴	1	2	yes	—
256	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₇	C₂⁴	1	2	yes	—
260	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₇	C₂⁴	1	2	yes	—
262	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
263	D₆₈	—	2	2	no	—
264	D₆₈	—	2	2	no	—
265	D₆₈	—	2	2	no	—
266	D₆₈	—	4	2	no	—
267	D₆₈	—	4	1	no	—
268	D₆₈	—	4	2	no	—
269	C₄×D₁₇	—	2	2	no	—
270	C₄×D₁₇	—	2	2	no	—
271	C₄×D₁₇	—	2	2	no	—
272	C₄×D₁₇	—	2	2	no	—
273	C₄×D₁₇	—	4	1	no	—
274	C₄×D₁₇	—	4	2	no	—
275	C₄×D₁₇	—	4	2	no	—
276	C₄×D₁₇	—	4	2	no	—
277	C₄×D₁₇	—	4	2	no	—
278	C₄×D₁₇	—	4	2	no	—
279	Dic₃₄	—	2	2	no	—
280	Dic₃₄	—	2	2	no	—
281	Dic₃₄	—	4	2	no	—
282	Dic₃₄	—	4	2	no	—
283	Dic₃₄	—	4	2	no	—
284	Dic₃₄	—	4	2	no	—
285	#3561	—	17	1	no	maximal, Sylow
286	C₂²×C₁₇	—	2	2	no	—
287	C₂²×C₁₇	—	2	2	no	—
288	C₂²×C₁₇	—	2	2	no	—
289	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
290	C₂×D₁₇	—	2	1	no	—
291	C₂×D₁₇	—	2	1	no	—
292	C₂×D₁₇	—	2	1	no	—
293	C₂×D₁₇	—	2	1	no	—
294	C₂×D₁₇	—	2	2	no	—
295	C₂×D₁₇	—	2	1	no	—
296	C₂×D₁₇	—	2	1	no	—
297	C₂×D₁₇	—	2	2	no	—
298	C₂×D₁₇	—	2	2	no	—
299	C₂×D₁₇	—	2	1	no	—
300	C₂×D₁₇	—	2	1	no	—
301	C₂×D₁₇	—	8	4	no	—
302	C₂×D₁₇	2₋¹⁺⁴	1	2	yes	—
303	C₄×C₁₇	—	2	2	no	—
304	C₄×C₁₇	—	2	2	no	—
305	C₄×C₁₇	—	2	1	no	—
306	C₄×C₁₇	—	2	1	no	—
307	C₄×C₁₇	—	2	1	no	—
308	C₄×C₁₇	—	2	2	no	—
309	C₄×C₁₇	—	2	1	no	—
310	C₄×C₁₇	—	2	1	no	—
311	C₄×C₁₇	—	2	1	no	—
312	C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
313	Dic₁₇	—	2	2	no	—
314	Dic₁₇	—	2	2	no	—
315	Dic₁₇	—	2	1	no	—
316	Dic₁₇	—	2	1	no	—
317	Dic₁₇	—	2	1	no	—
318	Dic₁₇	—	2	1	no	—
319	Dic₁₇	—	2	1	no	—
320	Dic₁₇	—	2	2	no	—
321	#563	—	17	2	no	—
322	#562	—	17	2	no	—
323	#556	—	17	1	no	—
324	#556	D₁₇	1	1	yes	characteristic, complemented
325	#551	—	17	2	no	—
326	#551	—	17	2	no	—
327	D₄×Q₈	—	17	1	no	—
328	D₄×Q₈	—	17	1	no	—
329	#548	—	17	1	no	—
330	#548	—	17	1	no	—
331	#546	—	17	1	no	—
332	#546	—	17	1	no	—
333	#543	—	17	2	no	—
334	#542	—	17	2	no	—
335	#542	—	17	1	no	—
336	#542	—	17	1	no	—
337	#542	—	17	2	no	—
338	#538	—	17	2	no	—
339	#536	—	17	1	no	—
340	#536	—	17	1	no	—
341	#533	—	17	1	no	—
342	#529	—	17	1	no	—
343	C₂×#124	—	17	1	no	—
344	C₂×C₁₇	—	4	2	no	—
345	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
347	C₂×C₁₇	#585	1	1	yes	characteristic
348	D₁₇	—	2	2	no	—
349	D₁₇	—	4	1	no	—
350	D₁₇	—	4	1	no	—
351	D₁₇	—	4	2	no	—
352	C₂×#41	—	17	1	no	—
353	C₂×#41	—	17	1	no	—
354	C₂²×Q₈	—	17	1	no	—
355	C₂²×Q₈	—	17	1	no	—
356	C₂²×Q₈	—	17	1	no	—
357	C₂²×D₄	—	17	1	no	—
358	C₄⋊Q₈	—	17	1	no	—
359	C₄⋊Q₈	—	17	1	no	—
360	C₄⋊Q₈	—	17	2	no	—
361	C₄⋊Q₈	—	17	1	no	—
362	C₄⋊Q₈	—	17	2	no	—
363	C₄⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
364	#126	—	17	1	no	—
365	#126	—	17	1	no	—
366	#126	—	17	2	no	—
367	#126	—	17	2	no	—
368	#126	—	17	2	no	—
369	#126	—	17	2	no	—
370	#126	C₂×D₁₇	1	2	yes	complemented
371	#126	C₂×D₁₇	1	2	yes	complemented
372	#125	—	17	1	no	—
373	#125	—	17	2	no	—
374	#124	—	17	1	no	—
375	#124	—	17	1	no	—
376	#124	—	17	1	no	—
377	#124	—	17	2	no	—
378	#124	—	17	2	no	—
379	#124	—	17	2	no	—
380	#124	—	17	2	no	—
381	#124	—	17	1	no	—
382	#124	—	17	1	no	—
383	#124	—	17	2	no	—
384	#124	—	17	2	no	—
385	#124	C₂×D₁₇	1	1	yes	characteristic
386	#124	C₂×D₁₇	1	1	yes	characteristic
387	#123	—	17	2	no	—
388	#123	—	17	1	no	—
389	#123	—	17	1	no	—
390	#123	—	17	2	no	—
391	#123	—	17	2	no	—
392	#123	—	17	2	no	—
393	#123	—	17	2	no	—
394	#123	—	17	2	no	—
395	#123	—	17	2	no	—
396	#123	—	17	2	no	—
397	C₂²⋊Q₈	—	17	1	no	—
398	C₂²⋊Q₈	—	17	1	no	—
399	C₂²⋊Q₈	—	17	1	no	—
400	C₂²⋊Q₈	—	17	2	no	—
401	C₂²⋊Q₈	—	17	2	no	—
402	C₂²⋊Q₈	—	17	2	no	—
403	C₂²⋊Q₈	—	17	1	no	—
404	C₂²⋊Q₈	—	17	2	no	—
405	C₂²⋊Q₈	—	17	2	no	—
406	C₂²⋊Q₈	—	17	2	no	—
407	C₂²⋊Q₈	—	17	1	no	—
408	C₂²⋊Q₈	—	17	2	no	—
409	C₂²⋊Q₈	—	17	2	no	—
410	C₂²⋊Q₈	—	17	2	no	—
411	C₂²⋊Q₈	—	17	2	no	—
412	C₂²⋊Q₈	—	17	2	no	—
413	C₂²⋊Q₈	—	17	2	no	—
414	C₂²⋊Q₈	—	17	2	no	—
415	C₂²⋊Q₈	—	17	2	no	—
416	C₂²⋊Q₈	C₂×D₁₇	1	2	yes	complemented
417	#121	—	17	1	no	—
418	#121	—	17	2	no	—
419	#121	—	17	1	no	—
420	#121	—	17	2	no	—
421	#121	—	17	1	no	—
422	#121	—	17	2	no	—
423	#121	—	17	2	no	—
424	#120	—	17	2	no	—
425	#120	—	17	2	no	—
426	C₄×Q₈	—	17	2	no	—
427	C₄×Q₈	—	17	1	no	—
428	C₄×Q₈	—	17	1	no	—
429	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
430	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
431	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
432	C₄×D₄	—	17	2	no	—
433	C₄×D₄	—	17	2	no	—
434	C₄×D₄	—	17	1	no	—
435	C₄×D₄	—	17	1	no	—
436	C₄×D₄	—	17	1	no	—
437	C₄×D₄	—	17	2	no	—
438	C₄×D₄	—	17	1	no	—
439	C₄×D₄	—	17	2	no	—
440	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic
441	#117	—	17	2	no	—
442	#117	—	17	1	no	—
443	#117	—	17	1	no	—
444	#117	—	17	2	no	—
445	#117	C₂×D₁₇	1	2	yes	complemented
446	C₂×C₂²⋊C₄	—	17	2	no	—
447	C₂×C₂²⋊C₄	—	17	2	no	—
448	C₂×C₂²⋊C₄	—	17	2	no	—
449	C₂×C₂²⋊C₄	—	17	2	no	—
450	C₂×C₄²	—	17	1	no	—
451	C₁₇	#3561	1	1	yes	characteristic, complemented, Sylow
452	C₂⁴	—	17	2	no	—
453	#41	—	68	2	no	—
454	#41	—	68	2	no	—
455	C₂×Q₈	—	17	1	no	—
456	C₂×Q₈	—	17	1	no	—
457	C₂×Q₈	—	17	2	no	—
458	C₂×Q₈	—	17	2	no	—
459	C₂×Q₈	—	17	2	no	—
460	C₂×Q₈	—	17	2	no	—
461	C₂×Q₈	—	68	2	no	—
462	C₂×Q₈	—	68	2	no	—
463	C₂×Q₈	—	68	2	no	—
464	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
465	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
466	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
467	C₂×D₄	—	17	2	no	—
468	C₂×D₄	—	17	2	no	—
469	C₂×D₄	—	17	2	no	—
470	C₂×D₄	—	17	1	no	—
471	C₂×D₄	—	17	1	no	—
472	C₂×D₄	—	17	1	no	—
473	C₂×D₄	—	17	2	no	—
474	C₂×D₄	—	17	1	no	—
475	C₂×D₄	—	17	2	no	—
476	C₂×D₄	—	68	2	no	—
477	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
478	C₂²×C₄	—	17	2	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	2	no	—
485	C₂²×C₄	—	17	2	no	—
486	C₂²×C₄	—	17	2	no	—
487	C₂²×C₄	—	17	2	no	—
488	C₂²×C₄	—	17	2	no	—
489	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
490	C₄⋊C₄	—	17	1	no	—
491	C₄⋊C₄	—	17	1	no	—
492	C₄⋊C₄	—	17	2	no	—
493	C₄⋊C₄	—	17	2	no	—
494	C₄⋊C₄	—	17	1	no	—
495	C₄⋊C₄	—	17	1	no	—
496	C₄⋊C₄	—	17	2	no	—
497	C₄⋊C₄	—	17	1	no	—
498	C₄⋊C₄	—	17	1	no	—
499	C₄⋊C₄	—	17	2	no	—
500	C₄⋊C₄	—	17	2	no	—
501	C₄⋊C₄	—	17	2	no	—
502	C₄⋊C₄	—	17	1	no	—
503	C₄⋊C₄	—	17	1	no	—
504	C₄⋊C₄	—	17	2	no	—
505	C₄⋊C₄	—	17	2	no	—
506	C₄⋊C₄	—	17	2	no	—
507	C₄⋊C₄	—	17	2	no	—
508	C₄⋊C₄	—	17	2	no	—
509	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
512	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
513	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
515	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
517	C₂²⋊C₄	—	17	2	no	—
518	C₂²⋊C₄	—	17	2	no	—
519	C₂²⋊C₄	—	17	2	no	—
520	C₂²⋊C₄	—	17	1	no	—
521	C₂²⋊C₄	—	17	1	no	—
522	C₂²⋊C₄	—	17	2	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	—	17	2	no	—
528	C₂²⋊C₄	—	17	2	no	—
529	C₂²⋊C₄	—	17	2	no	—
530	C₂²⋊C₄	—	17	2	no	—
531	C₂²⋊C₄	—	17	1	no	—
532	C₂²⋊C₄	—	17	1	no	—
533	C₂²⋊C₄	—	17	1	no	—
534	C₂²⋊C₄	—	17	1	no	—
535	C₂²⋊C₄	—	17	1	no	—
536	C₂²⋊C₄	—	17	1	no	—
537	C₂²⋊C₄	—	17	2	no	—
538	C₂²⋊C₄	—	17	1	no	—
539	C₂²⋊C₄	—	17	1	no	—
540	C₂²⋊C₄	—	17	2	no	—
541	C₂²⋊C₄	—	17	2	no	—
542	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
547	C₄²	—	17	1	no	—
548	C₄²	—	17	1	no	—
549	C₄²	—	17	1	no	—
550	C₄²	—	17	2	no	—
551	C₄²	—	17	2	no	—
552	C₄²	C₂²×D₁₇	1	1	yes	characteristic
553	C₄²	C₂²×D₁₇	1	2	yes	—
554	C₄²	C₂²×D₁₇	1	1	yes	characteristic
555	C₄²	C₂²×D₁₇	1	1	yes	characteristic
556	C₄²	C₂²×D₁₇	1	2	yes	—
557	C₂³	—	17	1	no	—
558	C₂³	—	17	2	no	—
559	C₂³	—	17	1	no	—
560	C₂³	—	17	1	no	—
561	C₂³	—	34	4	no	—
562	C₂³	—	68	2	no	—
563	C₂³	—	68	2	no	—
564	C₂³	C₂³×D₁₇	1	2	yes	—
565	Q₈	—	2	2	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	4	1	no	—
568	Q₈	—	34	2	no	—
569	Q₈	—	34	2	no	—
570	Q₈	—	68	2	no	—
571	Q₈	—	68	2	no	—
572	Q₈	—	68	2	no	—
573	Q₈	—	68	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	34	2	no	—
576	D₄	—	34	2	no	—
577	D₄	—	34	2	no	—
578	D₄	—	68	2	no	—
579	D₄	—	68	2	no	—
580	D₄	—	68	1	no	—
581	D₄	—	68	2	no	—
582	D₄	—	68	2	no	—
583	D₄	—	68	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	17	1	no	—
586	C₂×C₄	—	17	1	no	—
587	C₂×C₄	—	17	2	no	—
588	C₂×C₄	—	17	1	no	—
589	C₂×C₄	—	17	2	no	—
590	C₂×C₄	—	17	2	no	—
591	C₂×C₄	—	17	1	no	—
592	C₂×C₄	—	17	1	no	—
593	C₂×C₄	—	34	2	no	—
594	C₂×C₄	—	34	2	no	—
595	C₂×C₄	—	34	2	no	—
596	C₂×C₄	—	34	2	no	—
597	C₂×C₄	—	68	2	no	—
598	C₂×C₄	—	68	2	no	—
599	C₂×C₄	—	68	2	no	—
600	C₂×C₄	—	68	2	no	—
601	C₂×C₄	—	68	2	no	—
602	C₂×C₄	—	68	1	no	—
603	C₂×C₄	—	68	2	no	—
604	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₁₇	1	2	yes	—
609	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₇	1	2	yes	—
612	C₂×C₄	C₂³×D₁₇	1	2	yes	—
613	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	17	2	no	—
618	C₂²	—	34	1	no	—
619	C₂²	—	34	1	no	—
620	C₂²	—	34	1	no	—
621	C₂²	—	34	1	no	—
622	C₂²	—	34	2	no	—
623	C₂²	—	34	1	no	—
624	C₂²	—	34	1	no	—
625	C₂²	—	34	2	no	—
626	C₂²	—	34	2	no	—
627	C₂²	—	34	1	no	—
628	C₂²	—	34	1	no	—
629	C₂²	—	136	4	no	—
630	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	34	1	no	—
641	C₄	—	34	1	no	—
642	C₄	—	34	1	no	—
643	C₄	—	34	2	no	—
644	C₄	—	34	2	no	—
645	C₄	—	34	1	no	—
646	C₄	—	34	2	no	—
647	C₄	—	34	1	no	—
648	C₄	#10587696	1	2	yes	—
649	C₂	—	4	2	no	—
650	C₂	—	34	2	no	—
651	C₂	—	68	2	no	—
652	C₂	—	68	1	no	—
653	C₂	—	68	1	no	—
654	C₂	C₂×#10587696	1	1	yes	characteristic
655	C₂	2₋¹⁺⁴×D₁₇	1	1	yes	characteristic
656	C₂	#11763645	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#556	C₂
hypercenter	#556	D₁₇
hypocenter	C₁₇	#3561
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #11763561	C₂	semidirect
2. #11763555	C₂	semidirect
3. #11763532	C₂	semidirect
4. #11763484	C₂	semidirect
5. #11763483	C₂	semidirect
6. Q₈×D₆₈	C₂	semidirect
7. #11763474	C₂	semidirect
8. #11763471	C₂	semidirect
9. #11763467	C₂	semidirect
10. #11763454	C₂	semidirect
11. #11763452	C₂	semidirect
12. #11763434	C₂	semidirect
13. #11763431	C₂	semidirect
14. #11763430	C₂	semidirect
15. #11763425	C₂	semidirect
16. #11763424	C₂	semidirect
17. #11763398	C₂	semidirect
18. #11763384	C₂	semidirect
19. #11763379	C₂	semidirect
20. #11763363	C₂	semidirect
21. #11763346	C₂	semidirect
22. #124×D₁₇	C₂	semidirect
23. C₁₇×#556	C₂	semidirect
26. C₂×Q₈×D₁₇	C₂²	semidirect
27. C₂×Q₈×D₁₇	C₂²	semidirect
30. C₁₇×C₄⋊Q₈	C₂²	semidirect
31. C₁₇×#126	C₂²	semidirect
32. C₁₇×#126	C₂²	semidirect
35. C₁₇×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₁₇	C₂²	semidirect
37. C₄×Q₈×C₁₇	C₂²	semidirect
38. C₄×Q₈×C₁₇	C₂²	semidirect
40. C₁₇×#117	C₂²	semidirect
42. #10587633	C₂²	semidirect
45. #10587632	C₂²	semidirect
46. #10587632	C₂²	semidirect
47. #10587630	C₂²	semidirect
51. #10587615	C₂²	semidirect
53. #10587610	C₂²	semidirect
54. #10587584	C₂²	semidirect
55. #10587584	C₂²	semidirect
56. #10587584	C₂²	semidirect
57. #10587584	C₂²	semidirect
60. #10587583	C₂²	semidirect
61. #10587583	C₂²	semidirect
62. #10587583	C₂²	semidirect
65. #10587582	C₂²	semidirect
66. #10587582	C₂²	semidirect
67. #10587582	C₂²	semidirect
68. #10587582	C₂²	semidirect
71. #10587581	C₂²	semidirect
74. #10587580	C₂²	semidirect
75. #10587580	C₂²	semidirect
76. #10587580	C₂²	semidirect
78. #10587578	C₂²	semidirect
79. #10587576	C₂²	semidirect
80. #10587575	C₂²	semidirect
81. #10587574	C₂²	semidirect
82. #10587574	C₂²	semidirect
86. #10587571	C₂²	semidirect
87. #10587571	C₂²	semidirect
89. #10587570	C₂²	semidirect
91. #10587569	C₂²	semidirect
92. #10587569	C₂²	semidirect
95. #10587567	C₂²	semidirect
99. #10587565	C₂²	semidirect
100. #10587564	C₂²	semidirect
101. #10587564	C₂²	semidirect
102. #10587564	C₂²	semidirect
103. #10587562	C₂²	semidirect
106. #10587561	C₂²	semidirect
107. #10587561	C₂²	semidirect
112. C₄×D₆₈	C₂²	semidirect
113. C₄×D₆₈	C₂²	semidirect
115. #10587558	C₂²	semidirect
116. #10587558	C₂²	semidirect
118. #10587555	C₂²	semidirect
119. #10587555	C₂²	semidirect
120. C₄×Dic₃₄	C₂²	semidirect
121. C₄×Dic₃₄	C₂²	semidirect
122. C₄×Dic₃₄	C₂²	semidirect
324. #556	D₁₇	semidirect
363. C₄⋊Q₈	C₂×D₁₇	semidirect
370. #126	C₂×D₁₇	semidirect
371. #126	C₂×D₁₇	semidirect
416. C₂²⋊Q₈	C₂×D₁₇	semidirect
429. C₄×Q₈	C₂×D₁₇	semidirect
430. C₄×Q₈	C₂×D₁₇	semidirect
431. C₄×Q₈	C₂×D₁₇	semidirect
445. #117	C₂×D₁₇	semidirect
451. C₁₇	#3561	semidirect

Maximal subgroups

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

subgroup	index
#11763561	2
#11763555	2
#11763532	2
#11763484	2
#11763483	2
Q₈×D₆₈	2
#11763474	2
#11763471	2
#11763467	2
#11763454	2
#11763452	2
#11763434	2
#11763431	2
#11763430	2
#11763425	2
#11763424	2
#11763398	2
#11763384	2
#11763379	2
#11763363	2
#11763346	2
#124×D₁₇	2
C₁₇×#556	2
#3561	17