Subgroups — #14542719

Order 2176.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763542	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763520	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763507	C₂	1	1	yes	maximal, characteristic, complemented
4	#11763504	C₂	1	2	yes	maximal, complemented
5	#11763494	C₂	1	1	yes	maximal, characteristic, complemented
6	#11763486	C₂	1	2	yes	maximal, complemented
7	#11763482	C₂	1	2	yes	maximal, complemented
8	#11763456	C₂	1	1	yes	maximal, characteristic, complemented
9	#11763455	C₂	1	1	yes	maximal, characteristic, complemented
10	#11763447	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	#11763412	C₂	1	1	yes	maximal, characteristic, complemented
14	#11763405	C₂	1	2	yes	maximal, complemented
15	#11763395	C₂	1	2	yes	maximal, complemented
16	#11763340	C₂	1	1	yes	maximal, characteristic, complemented
17	#11763339	C₂	1	1	yes	maximal, characteristic, complemented
18	#11763316	C₂	1	2	yes	maximal, complemented
19	#123×D₁₇	C₂	1	2	yes	maximal, complemented
20	#11763290	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763281	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#10587579	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₁₇	C₂²	1	2	yes	complemented
25	C₂×D₄×D₁₇	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₁₇	C₂²	1	2	yes	—
27	C₂×#63252	C₂²	1	1	yes	characteristic
28	C₂²×D₆₈	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₇	C₂²	1	2	yes	complemented
30	C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₇×#123	C₂²	1	2	yes	complemented
32	C₁₇×#123	C₂²	1	2	yes	complemented
33	C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₁₇×#121	C₂²	1	1	yes	characteristic
35	C₁₇×#121	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
40	#10587633	C₂²	1	2	yes	complemented
41	#10587632	C₂²	1	2	yes	complemented
42	#10587632	C₂²	1	2	yes	complemented
43	#10587632	C₂²	1	2	yes	complemented
44	#10587626	C₂²	1	1	yes	characteristic
45	#10587625	C₂²	1	1	yes	characteristic
46	#10587625	C₂²	1	2	yes	complemented
47	#10587624	C₂²	1	2	yes	complemented
48	#10587624	C₂²	1	2	yes	complemented
49	#10587623	C₂²	1	2	yes	—
50	#10587623	C₂²	1	2	yes	complemented
51	#10587623	C₂²	1	2	yes	complemented
52	#10587622	C₂²	1	1	yes	characteristic, complemented
53	#10587621	C₂²	1	2	yes	complemented
54	#10587621	C₂²	1	1	yes	characteristic, complemented
55	D₄×Dic₁₇	C₂²	1	2	yes	complemented
56	D₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
57	#10587616	C₂²	1	2	yes	complemented
58	#10587616	C₂²	1	1	yes	characteristic, complemented
59	#10587615	C₂²	1	2	yes	—
60	#10587615	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
63	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
68	C₂×#63227	C₂²	1	2	yes	complemented
69	C₂×#63227	C₂²	1	2	yes	complemented
70	#10587612	C₂²	1	2	yes	complemented
71	#10587612	C₂²	1	1	yes	characteristic, complemented
72	#10587610	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
74	#10587584	C₂²	1	2	yes	complemented
75	#10587584	C₂²	1	2	yes	complemented
76	#10587584	C₂²	1	1	yes	characteristic, complemented
77	#10587584	C₂²	1	2	yes	complemented
78	#10587583	C₂²	1	1	yes	characteristic, complemented
79	#10587583	C₂²	1	2	yes	complemented
80	#10587581	C₂²	1	1	yes	characteristic
81	#10587580	C₂²	1	2	yes	complemented
82	#10587580	C₂²	1	2	yes	complemented
83	#10587580	C₂²	1	2	yes	complemented
84	#10587579	C₂²	1	1	yes	characteristic
85	#10587579	C₂²	1	1	yes	characteristic
86	#10587579	C₂²	1	1	yes	characteristic
87	#10587579	C₂²	1	2	yes	complemented
88	#10587579	C₂²	1	1	yes	characteristic, complemented
89	#10587579	C₂²	1	2	yes	complemented
90	#10587579	C₂²	1	1	yes	characteristic, complemented
91	#10587578	C₂²	1	2	yes	complemented
92	#10587578	C₂²	1	1	yes	characteristic, complemented
93	C₄⋊C₄×D₁₇	C₂²	1	2	yes	complemented
94	C₄⋊C₄×D₁₇	C₂²	1	2	yes	complemented
95	#10587576	C₂²	1	1	yes	characteristic, complemented
96	#10587576	C₂²	1	1	yes	characteristic, complemented
97	#10587575	C₂²	1	2	yes	complemented
98	#10587575	C₂²	1	1	yes	characteristic, complemented
99	#10587573	C₂²	1	1	yes	characteristic, complemented
100	#10587573	C₂²	1	1	yes	characteristic, complemented
101	#10587572	C₂²	1	1	yes	characteristic
102	#10587572	C₂²	1	2	yes	complemented
103	#10587571	C₂²	1	2	yes	complemented
104	#10587571	C₂²	1	1	yes	characteristic, complemented
105	#10587570	C₂²	1	2	yes	—
106	#10587570	C₂²	1	2	yes	complemented
107	#10587569	C₂²	1	2	yes	complemented
108	#10587569	C₂²	1	2	yes	complemented
109	#10587569	C₂²	1	2	yes	complemented
110	#10587568	C₂²	1	2	yes	—
111	#10587567	C₂²	1	2	yes	complemented
112	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	complemented
113	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	complemented
114	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	complemented
115	#10587565	C₂²	1	1	yes	characteristic, complemented
116	#10587565	C₂²	1	2	yes	complemented
117	#10587564	C₂²	1	1	yes	characteristic, complemented
118	#10587563	C₂²	1	2	yes	complemented
119	#10587561	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₆₈	C₂²	1	1	yes	characteristic
121	#10587558	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	#41×C₁₇	—	4	4	no	—
126	C₂×Q₈×C₁₇	C₂³	1	2	yes	—
127	C₂×D₄×C₁₇	C₂³	1	2	yes	—
128	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₇	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
132	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
143	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
144	C₂²×Dic₁₇	C₂³	1	2	yes	—
145	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
146	D₄×D₁₇	—	2	4	no	—
147	D₄×D₁₇	—	4	4	no	—
148	#63252	—	2	4	no	—
149	C₂×D₆₈	—	2	4	no	—
150	C₂×D₆₈	C₂³	1	1	yes	characteristic
151	C₂×D₆₈	C₂³	1	2	yes	—
152	C₂×D₆₈	C₂³	1	2	yes	—
153	C₂×D₆₈	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₇	—	4	4	no	—
155	C₂×C₄×D₁₇	C₂³	1	2	yes	—
156	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₇	C₂³	1	2	yes	—
158	C₂×C₄×D₁₇	C₂³	1	2	yes	—
159	C₂×C₄×D₁₇	C₂³	1	2	yes	—
160	C₂×C₄×D₁₇	C₂³	1	2	yes	—
161	C₂×C₄×D₁₇	C₂³	1	2	yes	—
162	C₂×C₄×D₁₇	C₂³	1	2	yes	—
163	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
164	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
165	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
167	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
168	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
169	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
170	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
171	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
172	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
175	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
176	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
177	C₄²×C₁₇	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₇	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	2	yes	—
191	#63227	C₂³	1	1	yes	characteristic
192	#63227	C₂³	1	2	yes	—
193	#63227	C₂³	1	2	yes	—
194	#63227	C₂³	1	2	yes	—
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	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₁₇	C₂³	1	2	yes	—
206	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₁₇	C₂³	1	2	yes	—
208	C₄⋊Dic₁₇	C₂³	1	2	yes	—
209	#63225	C₂³	1	1	yes	characteristic
210	#63225	C₂³	1	1	yes	characteristic
211	#63225	C₂³	1	1	yes	characteristic
212	#63225	C₂³	1	1	yes	characteristic
213	#63225	C₂³	1	2	yes	—
214	#63225	C₂³	1	2	yes	—
215	#63225	C₂³	1	1	yes	characteristic
216	#63225	C₂³	1	1	yes	characteristic
217	#63225	C₂³	1	2	yes	—
218	#63225	C₂³	1	2	yes	—
219	#63225	C₂³	1	2	yes	—
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	1	yes	characteristic
224	C₄×Dic₁₇	C₂³	1	2	yes	—
225	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₇	C₂³	1	2	yes	—
227	C₄×Dic₁₇	C₂³	1	2	yes	—
228	C₂³×C₁₇	C₂⁴	1	2	yes	—
229	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₇	—	2	4	no	—
232	C₂²×D₁₇	—	2	4	no	—
233	C₂²×D₁₇	—	2	4	no	—
234	C₂²×D₁₇	—	4	2	no	—
235	C₂²×D₁₇	—	4	2	no	—
236	C₂²×D₁₇	—	4	2	no	—
237	C₂²×D₁₇	C₂⁴	1	2	yes	—
238	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
239	C₂²×D₁₇	C₂⁴	1	2	yes	—
240	Q₈×C₁₇	—	4	2	no	—
241	D₄×C₁₇	—	2	4	no	—
242	D₄×C₁₇	—	2	2	no	—
243	D₄×C₁₇	—	2	2	no	—
244	D₄×C₁₇	—	4	2	no	—
245	C₂×C₄×C₁₇	—	2	4	no	—
246	C₂×C₄×C₁₇	—	2	2	no	—
247	C₂×C₄×C₁₇	—	2	2	no	—
248	C₂×C₄×C₁₇	—	4	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	1	yes	characteristic
253	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
258	C₂²⋊D₁₇	—	2	2	no	—
259	C₂²⋊D₁₇	—	2	4	no	—
260	C₂²⋊D₁₇	—	2	4	no	—
261	C₂²⋊D₁₇	—	4	2	no	—
262	C₂²⋊D₁₇	—	4	1	no	—
263	C₂²⋊D₁₇	—	4	2	no	—
264	C₂²⋊D₁₇	—	4	2	no	—
265	C₂×Dic₁₇	—	2	2	no	—
266	C₂×Dic₁₇	—	4	1	no	—
267	C₂×Dic₁₇	—	4	2	no	—
268	C₂×Dic₁₇	C₂⁴	1	2	yes	—
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	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
277	D₆₈	—	2	4	no	—
278	D₆₈	—	2	2	no	—
279	D₆₈	—	4	2	no	—
280	D₆₈	#41	1	4	yes	complemented
281	C₄×D₁₇	—	2	4	no	—
282	C₄×D₁₇	—	2	2	no	—
283	C₄×D₁₇	—	4	2	no	—
284	C₄×D₁₇	—	4	2	no	—
285	C₄×D₁₇	—	4	2	no	—
286	C₄×D₁₇	—	4	2	no	—
287	C₄×D₁₇	—	4	2	no	—
288	C₄×D₁₇	—	4	2	no	—
289	Dic₃₄	—	2	2	no	—
290	Dic₃₄	—	4	1	no	—
291	#3513	—	17	1	no	maximal, Sylow
292	C₂²×C₁₇	—	2	1	no	—
293	C₂²×C₁₇	—	2	1	no	—
294	C₂²×C₁₇	—	2	1	no	—
295	C₂²×C₁₇	—	2	2	no	—
296	C₂²×C₁₇	—	2	2	no	—
297	C₂²×C₁₇	—	2	1	no	—
298	C₂²×C₁₇	—	2	2	no	—
299	C₂²×C₁₇	—	2	1	no	—
300	C₂²×C₁₇	H(5,𝔽₂)	1	2	yes	—
301	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
302	C₂×D₁₇	—	2	2	no	—
303	C₂×D₁₇	—	2	2	no	—
304	C₂×D₁₇	—	2	1	no	—
305	C₂×D₁₇	—	2	2	no	—
306	C₂×D₁₇	—	2	2	no	—
307	C₂×D₁₇	—	2	1	no	—
308	C₂×D₁₇	—	2	2	no	—
309	C₂×D₁₇	—	2	1	no	—
310	C₂×D₁₇	—	4	8	no	—
311	C₂×D₁₇	—	8	4	no	—
312	C₂×D₁₇	C₂×#41	1	4	yes	—
313	C₄×C₁₇	—	2	1	no	—
314	C₄×C₁₇	—	2	1	no	—
315	C₄×C₁₇	—	2	2	no	—
316	C₄×C₁₇	—	2	2	no	—
317	C₄×C₁₇	—	2	2	no	—
318	C₄×C₁₇	—	2	1	no	—
319	C₄×C₁₇	—	2	1	no	—
320	C₄×C₁₇	C₂×#41	1	2	yes	—
321	Dic₁₇	—	2	2	no	—
322	Dic₁₇	—	2	1	no	—
323	Dic₁₇	—	2	1	no	—
324	Dic₁₇	—	2	1	no	—
325	Dic₁₇	—	2	1	no	—
326	Dic₁₇	—	2	1	no	—
327	Dic₁₇	—	2	1	no	—
328	Dic₁₇	—	2	2	no	—
329	Dic₁₇	—	2	1	no	—
330	#559	—	17	1	no	—
331	#554	—	17	1	no	—
332	#553	—	17	2	no	—
333	#553	—	17	1	no	—
334	#552	—	17	1	no	—
335	#551	—	17	2	no	—
336	#551	—	17	2	no	—
337	#547	D₁₇	1	1	yes	characteristic, complemented
338	#546	—	17	2	no	—
339	#546	—	17	1	no	—
340	#546	—	17	1	no	—
341	D₄²	—	17	1	no	—
342	#542	—	17	1	no	—
343	#540	—	17	1	no	—
344	#539	—	17	2	no	—
345	#538	—	17	2	no	—
346	#529	—	17	1	no	—
347	#529	—	17	1	no	—
348	#525	—	17	2	no	—
349	C₂×#123	—	17	2	no	—
350	#520	—	17	1	no	—
351	#518	—	17	1	no	—
352	C₂×C₄×D₄	—	17	1	no	—
353	C₂×C₁₇	—	2	2	no	—
354	C₂×C₁₇	—	4	2	no	—
355	C₂×C₁₇	—	4	1	no	—
356	C₂×C₁₇	C₂²×#41	1	1	yes	characteristic
357	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
358	C₂×C₁₇	#585	1	1	yes	characteristic
359	D₁₇	—	2	4	no	—
360	D₁₇	—	4	2	no	—
361	D₁₇	—	4	1	no	—
362	C₂×#41	—	17	1	no	—
363	C₂×#41	C₂×D₁₇	1	2	yes	complemented
364	C₂²×D₄	—	17	1	no	—
365	C₂²×D₄	—	17	2	no	—
366	C₂²×D₄	—	17	1	no	—
367	C₂³×C₄	—	17	2	no	—
368	C₄⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
369	#127	—	17	1	no	—
370	#126	—	17	1	no	—
371	#126	—	17	2	no	—
372	#126	—	17	2	no	—
373	#126	—	17	2	no	—
374	#126	—	17	2	no	—
375	#126	—	17	1	no	—
376	#125	—	17	1	no	—
377	#125	—	17	1	no	—
378	#125	—	17	2	no	—
379	#125	—	17	1	no	—
380	#124	—	17	2	no	—
381	#124	—	17	1	no	—
382	#124	—	17	1	no	—
383	#124	—	17	2	no	—
384	#124	—	17	1	no	—
385	#123	—	17	2	no	—
386	#123	—	17	1	no	—
387	#123	—	17	2	no	—
388	#123	—	17	2	no	—
389	#123	—	17	2	no	—
390	#123	—	17	2	no	—
391	#123	—	17	2	no	—
392	#123	—	17	1	no	—
393	#123	—	17	2	no	—
394	#123	—	17	2	no	—
395	#123	—	17	2	no	—
396	#123	—	17	2	no	—
397	#123	C₂×D₁₇	1	2	yes	complemented
398	#123	C₂×D₁₇	1	2	yes	complemented
399	C₂²⋊Q₈	—	17	2	no	—
400	C₂²⋊Q₈	—	17	2	no	—
401	C₂²⋊Q₈	—	17	2	no	—
402	C₂²⋊Q₈	—	17	1	no	—
403	C₂²⋊Q₈	—	17	2	no	—
404	C₂²⋊Q₈	—	17	1	no	—
405	C₂²⋊Q₈	—	17	1	no	—
406	C₂²⋊Q₈	C₂×D₁₇	1	2	yes	complemented
407	#121	—	17	2	no	—
408	#121	—	17	2	no	—
409	#121	—	17	1	no	—
410	#121	—	17	2	no	—
411	#121	—	17	2	no	—
412	#121	—	17	1	no	—
413	#121	—	17	1	no	—
414	#121	—	17	2	no	—
415	#121	—	17	2	no	—
416	#121	C₂×D₁₇	1	1	yes	characteristic
417	#121	C₂×D₁₇	1	1	yes	characteristic, complemented
418	#120	—	17	2	no	—
419	#120	—	17	2	no	—
420	#120	—	17	2	no	—
421	#120	—	17	2	no	—
422	C₄×Q₈	—	17	1	no	—
423	C₄×Q₈	—	17	1	no	—
424	C₄×Q₈	—	17	1	no	—
425	C₄×D₄	—	17	1	no	—
426	C₄×D₄	—	17	2	no	—
427	C₄×D₄	—	17	2	no	—
428	C₄×D₄	—	17	2	no	—
429	C₄×D₄	—	17	2	no	—
430	C₄×D₄	—	17	2	no	—
431	C₄×D₄	—	17	2	no	—
432	C₄×D₄	—	17	1	no	—
433	C₄×D₄	—	17	1	no	—
434	C₄×D₄	—	17	1	no	—
435	C₄×D₄	—	17	2	no	—
436	C₄×D₄	—	17	1	no	—
437	C₄×D₄	—	17	1	no	—
438	C₄×D₄	—	17	2	no	—
439	C₄×D₄	—	17	1	no	—
440	C₄×D₄	—	17	1	no	—
441	C₄×D₄	—	17	2	no	—
442	C₄×D₄	—	17	1	no	—
443	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
444	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
445	#117	—	17	1	no	—
446	#117	—	17	2	no	—
447	#117	—	17	1	no	—
448	#117	—	17	2	no	—
449	#117	—	17	2	no	—
450	#117	—	17	1	no	—
451	C₂×C₄⋊C₄	—	17	2	no	—
452	C₂×C₄⋊C₄	—	17	2	no	—
453	C₂×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic, complemented
454	C₂×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic, complemented
455	C₂×C₂²⋊C₄	—	17	2	no	—
456	C₂×C₂²⋊C₄	—	17	2	no	—
457	C₂×C₂²⋊C₄	—	17	2	no	—
458	C₂×C₂²⋊C₄	—	17	2	no	—
459	C₂×C₂²⋊C₄	—	17	2	no	—
460	C₂×C₄²	—	17	1	no	—
461	C₁₇	#3513	1	1	yes	characteristic, complemented, Sylow
462	C₂⁴	—	17	2	no	—
463	C₂⁴	—	17	2	no	—
464	#41	—	4	4	no	—
465	#41	—	34	4	no	—
466	C₂×Q₈	—	17	1	no	—
467	C₂×Q₈	—	17	1	no	—
468	C₂×Q₈	C₂²×D₁₇	1	2	yes	—
469	C₂×D₄	—	17	2	no	—
470	C₂×D₄	—	17	2	no	—
471	C₂×D₄	—	17	1	no	—
472	C₂×D₄	—	17	1	no	—
473	C₂×D₄	—	17	2	no	—
474	C₂×D₄	—	17	2	no	—
475	C₂×D₄	—	17	2	no	—
476	C₂×D₄	—	17	1	no	—
477	C₂×D₄	—	17	2	no	—
478	C₂×D₄	—	17	1	no	—
479	C₂×D₄	—	17	2	no	—
480	C₂×D₄	—	34	4	no	—
481	C₂×D₄	—	34	4	no	—
482	C₂×D₄	—	68	4	no	—
483	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₁₇	1	2	yes	—
485	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
486	C₂×D₄	C₂²×D₁₇	1	2	yes	—
487	C₂²×C₄	—	17	1	no	—
488	C₂²×C₄	—	17	1	no	—
489	C₂²×C₄	—	17	2	no	—
490	C₂²×C₄	—	17	2	no	—
491	C₂²×C₄	—	17	1	no	—
492	C₂²×C₄	—	17	2	no	—
493	C₂²×C₄	—	17	2	no	—
494	C₂²×C₄	—	17	2	no	—
495	C₂²×C₄	—	17	2	no	—
496	C₂²×C₄	—	17	2	no	—
497	C₂²×C₄	—	17	2	no	—
498	C₂²×C₄	—	68	4	no	—
499	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
501	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
503	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
504	C₄⋊C₄	—	17	1	no	—
505	C₄⋊C₄	—	17	1	no	—
506	C₄⋊C₄	—	17	2	no	—
507	C₄⋊C₄	—	17	2	no	—
508	C₄⋊C₄	—	17	2	no	—
509	C₄⋊C₄	—	17	2	no	—
510	C₄⋊C₄	—	17	1	no	—
511	C₄⋊C₄	—	17	1	no	—
512	C₄⋊C₄	—	17	1	no	—
513	C₄⋊C₄	—	17	1	no	—
514	C₄⋊C₄	—	17	2	no	—
515	C₄⋊C₄	—	17	2	no	—
516	C₄⋊C₄	—	17	2	no	—
517	C₄⋊C₄	—	17	1	no	—
518	C₄⋊C₄	—	17	1	no	—
519	C₄⋊C₄	—	17	2	no	—
520	C₄⋊C₄	—	17	1	no	—
521	C₄⋊C₄	—	17	1	no	—
522	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
523	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
524	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
527	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
529	C₂²⋊C₄	—	17	2	no	—
530	C₂²⋊C₄	—	17	2	no	—
531	C₂²⋊C₄	—	17	2	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	2	no	—
537	C₂²⋊C₄	—	17	2	no	—
538	C₂²⋊C₄	—	17	2	no	—
539	C₂²⋊C₄	—	17	1	no	—
540	C₂²⋊C₄	—	17	1	no	—
541	C₂²⋊C₄	—	17	1	no	—
542	C₂²⋊C₄	—	17	2	no	—
543	C₂²⋊C₄	—	17	2	no	—
544	C₂²⋊C₄	—	17	2	no	—
545	C₂²⋊C₄	—	17	2	no	—
546	C₂²⋊C₄	—	17	2	no	—
547	C₂²⋊C₄	—	17	2	no	—
548	C₂²⋊C₄	—	17	2	no	—
549	C₂²⋊C₄	—	17	2	no	—
550	C₂²⋊C₄	—	17	1	no	—
551	C₂²⋊C₄	—	17	2	no	—
552	C₂²⋊C₄	—	17	2	no	—
553	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
558	C₄²	—	17	1	no	—
559	C₄²	—	17	1	no	—
560	C₄²	—	17	1	no	—
561	C₄²	—	17	1	no	—
562	C₄²	—	17	2	no	—
563	C₄²	—	17	2	no	—
564	C₄²	—	17	2	no	—
565	C₄²	—	17	1	no	—
566	C₄²	C₂²×D₁₇	1	1	yes	characteristic
567	C₂³	—	17	2	no	—
568	C₂³	—	17	1	no	—
569	C₂³	—	17	2	no	—
570	C₂³	—	34	4	no	—
571	C₂³	—	34	4	no	—
572	C₂³	—	34	4	no	—
573	C₂³	—	68	2	no	—
574	C₂³	—	68	2	no	—
575	C₂³	—	68	2	no	—
576	C₂³	C₂³×D₁₇	1	2	yes	—
577	C₂³	C₂³×D₁₇	1	1	yes	characteristic
578	C₂³	C₂³×D₁₇	1	1	yes	characteristic
579	Q₈	—	4	2	no	—
580	Q₈	—	34	2	no	—
581	Q₈	—	68	1	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	17	4	no	—
587	D₄	—	34	4	no	—
588	D₄	—	34	4	no	—
589	D₄	—	34	4	no	—
590	D₄	—	34	2	no	—
591	D₄	—	34	2	no	—
592	D₄	—	68	2	no	—
593	D₄	—	68	2	no	—
594	D₄	—	68	2	no	—
595	D₄	—	68	1	no	—
596	D₄	—	68	2	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	17	1	no	—
603	C₂×C₄	—	17	1	no	—
604	C₂×C₄	—	17	2	no	—
605	C₂×C₄	—	17	1	no	—
606	C₂×C₄	—	17	1	no	—
607	C₂×C₄	—	17	1	no	—
608	C₂×C₄	—	17	1	no	—
609	C₂×C₄	—	17	2	no	—
610	C₂×C₄	—	17	1	no	—
611	C₂×C₄	—	34	4	no	—
612	C₂×C₄	—	34	2	no	—
613	C₂×C₄	—	34	2	no	—
614	C₂×C₄	—	68	2	no	—
615	C₂×C₄	—	68	2	no	—
616	C₂×C₄	—	68	2	no	—
617	C₂×C₄	—	68	2	no	—
618	C₂×C₄	—	68	2	no	—
619	C₂×C₄	—	68	2	no	—
620	C₂×C₄	—	68	2	no	—
621	C₂×C₄	—	68	1	no	—
622	C₂×C₄	C₂³×D₁₇	1	2	yes	—
623	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₇	1	2	yes	—
625	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₇	1	2	yes	—
629	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	17	4	no	—
639	C₂²	—	34	2	no	—
640	C₂²	—	34	2	no	—
641	C₂²	—	34	1	no	—
642	C₂²	—	34	2	no	—
643	C₂²	—	34	2	no	—
644	C₂²	—	34	1	no	—
645	C₂²	—	34	2	no	—
646	C₂²	—	34	1	no	—
647	C₂²	—	68	8	no	—
648	C₂²	—	136	4	no	—
649	C₂²	#10587691	1	2	yes	—
650	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	34	1	no	—
659	C₄	—	34	2	no	—
660	C₄	—	34	1	no	—
661	C₄	—	34	1	no	—
662	C₄	—	34	1	no	—
663	C₄	—	34	1	no	—
664	C₄	—	34	2	no	—
665	C₄	—	34	1	no	—
666	C₄	—	34	1	no	—
667	C₄	#41×D₁₇	1	2	yes	—
668	C₂	—	2	2	no	—
669	C₂	—	4	2	no	—
670	C₂	—	4	1	no	—
671	C₂	—	34	4	no	—
672	C₂	—	68	2	no	—
673	C₂	—	68	1	no	—
674	C₂	C₂×#41×D₁₇	1	1	yes	characteristic
675	C₂	C₂×#10587691	1	1	yes	characteristic
676	C₂	#11763646	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#547	C₂
hypercenter	#547	D₁₇
hypocenter	C₁₇	#3513
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. #11763542	C₂	semidirect
2. #11763520	C₂	semidirect
3. #11763507	C₂	semidirect
4. #11763504	C₂	semidirect
5. #11763494	C₂	semidirect
6. #11763486	C₂	semidirect
7. #11763482	C₂	semidirect
8. #11763456	C₂	semidirect
9. #11763455	C₂	semidirect
10. #11763447	C₂	semidirect
11. #11763443	C₂	semidirect
12. #11763433	C₂	semidirect
13. #11763412	C₂	semidirect
14. #11763405	C₂	semidirect
15. #11763395	C₂	semidirect
16. #11763340	C₂	semidirect
17. #11763339	C₂	semidirect
18. #11763316	C₂	semidirect
19. #123×D₁₇	C₂	semidirect
20. #11763290	C₂	semidirect
21. #11763281	C₂	semidirect
22. C₂×#10587579	C₂	semidirect
23. C₁₇×#547	C₂	semidirect
24. C₂×#41×C₁₇	C₂²	semidirect
29. C₂²×C₄×D₁₇	C₂²	semidirect
30. C₁₇×C₄⋊Q₈	C₂²	semidirect
31. C₁₇×#123	C₂²	semidirect
32. C₁₇×#123	C₂²	semidirect
33. C₁₇×C₂²⋊Q₈	C₂²	semidirect
35. C₁₇×#121	C₂²	semidirect
36. C₄×D₄×C₁₇	C₂²	semidirect
37. C₄×D₄×C₁₇	C₂²	semidirect
38. C₂×C₄⋊C₄×C₁₇	C₂²	semidirect
39. C₂×C₄⋊C₄×C₁₇	C₂²	semidirect
40. #10587633	C₂²	semidirect
41. #10587632	C₂²	semidirect
42. #10587632	C₂²	semidirect
43. #10587632	C₂²	semidirect
46. #10587625	C₂²	semidirect
47. #10587624	C₂²	semidirect
48. #10587624	C₂²	semidirect
50. #10587623	C₂²	semidirect
51. #10587623	C₂²	semidirect
52. #10587622	C₂²	semidirect
53. #10587621	C₂²	semidirect
54. #10587621	C₂²	semidirect
55. D₄×Dic₁₇	C₂²	semidirect
56. D₄×Dic₁₇	C₂²	semidirect
57. #10587616	C₂²	semidirect
58. #10587616	C₂²	semidirect
60. #10587615	C₂²	semidirect
62. C₄×C₂²⋊D₁₇	C₂²	semidirect
63. C₄×C₂²⋊D₁₇	C₂²	semidirect
64. C₄×C₂²⋊D₁₇	C₂²	semidirect
65. C₄×C₂²⋊D₁₇	C₂²	semidirect
66. C₄×C₂²⋊D₁₇	C₂²	semidirect
67. C₄×C₂²⋊D₁₇	C₂²	semidirect
68. C₂×#63227	C₂²	semidirect
69. C₂×#63227	C₂²	semidirect
70. #10587612	C₂²	semidirect
71. #10587612	C₂²	semidirect
72. #10587610	C₂²	semidirect
73. C₂×C₄×Dic₁₇	C₂²	semidirect
74. #10587584	C₂²	semidirect
75. #10587584	C₂²	semidirect
76. #10587584	C₂²	semidirect
77. #10587584	C₂²	semidirect
78. #10587583	C₂²	semidirect
79. #10587583	C₂²	semidirect
81. #10587580	C₂²	semidirect
82. #10587580	C₂²	semidirect
83. #10587580	C₂²	semidirect
87. #10587579	C₂²	semidirect
88. #10587579	C₂²	semidirect
89. #10587579	C₂²	semidirect
90. #10587579	C₂²	semidirect
91. #10587578	C₂²	semidirect
92. #10587578	C₂²	semidirect
93. C₄⋊C₄×D₁₇	C₂²	semidirect
94. C₄⋊C₄×D₁₇	C₂²	semidirect
95. #10587576	C₂²	semidirect
96. #10587576	C₂²	semidirect
97. #10587575	C₂²	semidirect
98. #10587575	C₂²	semidirect
99. #10587573	C₂²	semidirect
100. #10587573	C₂²	semidirect
102. #10587572	C₂²	semidirect
103. #10587571	C₂²	semidirect
104. #10587571	C₂²	semidirect
106. #10587570	C₂²	semidirect
107. #10587569	C₂²	semidirect
108. #10587569	C₂²	semidirect
109. #10587569	C₂²	semidirect
111. #10587567	C₂²	semidirect
112. C₂²⋊C₄×D₁₇	C₂²	semidirect
113. C₂²⋊C₄×D₁₇	C₂²	semidirect
114. C₂²⋊C₄×D₁₇	C₂²	semidirect
115. #10587565	C₂²	semidirect
116. #10587565	C₂²	semidirect
117. #10587564	C₂²	semidirect
118. #10587563	C₂²	semidirect
119. #10587561	C₂²	semidirect
121. #10587558	C₂²	semidirect
122. C₄×Dic₃₄	C₂²	semidirect
280. D₆₈	#41	semidirect
337. #547	D₁₇	semidirect
363. C₂×#41	C₂×D₁₇	semidirect
368. C₄⋊Q₈	C₂×D₁₇	semidirect
397. #123	C₂×D₁₇	semidirect
398. #123	C₂×D₁₇	semidirect
406. C₂²⋊Q₈	C₂×D₁₇	semidirect
417. #121	C₂×D₁₇	semidirect
443. C₄×D₄	C₂×D₁₇	semidirect
444. C₄×D₄	C₂×D₁₇	semidirect
453. C₂×C₄⋊C₄	C₂×D₁₇	semidirect
454. C₂×C₄⋊C₄	C₂×D₁₇	semidirect
461. C₁₇	#3513	semidirect

Maximal subgroups

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

subgroup	index
#11763542	2
#11763520	2
#11763507	2
#11763504	2
#11763494	2
#11763486	2
#11763482	2
#11763456	2
#11763455	2
#11763447	2
#11763443	2
#11763433	2
#11763412	2
#11763405	2
#11763395	2
#11763340	2
#11763339	2
#11763316	2
#123×D₁₇	2
#11763290	2
#11763281	2
C₂×#10587579	2
C₁₇×#547	2
#3513	17