Subgroups — #17968592

Order 4352.

1010 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763819	C₂	1	1	yes	maximal, characteristic
2	#14545347	C₂	1	2	yes	maximal
3	C₂×#11763772	C₂	1	1	yes	maximal, characteristic
4	#14544593	C₂	1	4	yes	maximal, complemented
5	#14544589	C₂	1	4	yes	maximal, complemented
6	#14544466	C₂	1	2	yes	maximal
7	C₂×#108×D₁₇	C₂	1	1	yes	maximal, characteristic
8	C₂×D₁₇⋊M₁₆	C₂²	1	1	yes	characteristic
9	C₂×#10587677	C₂²	1	2	yes	—
10	C₂×#10587677	C₂²	1	1	yes	characteristic
11	#11763819	C₄	1	2	yes	complemented
12	#11763819	C₄	1	2	yes	complemented
13	#11763819	C₂²	1	2	yes	—
14	#11763819	C₂²	1	2	yes	—
15	C₂×#10587534	C₄	1	2	yes	complemented
16	C₂×#10587533	C₄	1	2	yes	complemented
17	#11763775	C₂²	1	8	yes	—
18	#11763772	—	2	4	no	—
19	#11763772	C₄	1	2	yes	complemented
20	#11763772	C₄	1	2	yes	complemented
21	#11763772	C₄	1	2	yes	complemented
22	#11763772	C₄	1	2	yes	complemented
23	M₁₆×#595	—	2	4	no	—
24	C₂×#10587532	C₂²	1	2	yes	—
25	C₂×C₈×#595	C₂²	1	2	yes	—
26	#11763681	C₂²	1	8	yes	—
27	C₂×M₁₆×D₁₇	C₂²	1	2	yes	—
28	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
29	C₂×#10587490	C₄	1	1	yes	characteristic, complemented
30	C₂×#10587493	C₄	1	2	yes	complemented
31	#108×D₁₇	C₄	1	2	yes	complemented
32	#108×D₁₇	C₄	1	2	yes	complemented
33	#108×D₁₇	C₂²	1	2	yes	—
34	#108×D₁₇	C₂²	1	2	yes	—
35	C₂×C₁₇×#108	C₄	1	1	yes	characteristic, complemented
36	C₂²×C₄×D₁₇	C₂³	1	1	yes	characteristic
37	C₂×C₂²⋊#595	—	2	1	no	—
38	C₂×C₂²⋊#595	—	2	2	no	—
39	C₂×#63247	Q₈	1	2	yes	—
40	#10587677	—	2	2	no	—
41	#10587677	—	2	2	no	—
42	#10587677	—	2	1	no	—
43	#10587677	—	2	1	no	—
44	#10587677	C₂×C₄	1	4	yes	—
45	#10587677	C₂×C₄	1	2	yes	—
46	#10587677	C₂×C₄	1	2	yes	—
47	#10587677	C₂³	1	4	yes	—
48	C₂×C₄⋊#595	—	2	1	no	—
49	C₂×C₄⋊#595	C₂×C₄	1	4	yes	—
50	C₂×C₄×#595	—	2	2	no	—
51	C₂×C₄×#595	C₂³	1	2	yes	—
52	D₁₇⋊M₁₆	C₂×C₄	1	2	yes	—
53	D₁₇⋊M₁₆	C₂×C₄	1	2	yes	—
54	D₁₇⋊M₁₆	D₄	1	2	yes	—
55	D₁₇⋊M₁₆	D₄	1	2	yes	—
56	C₂×#63243	Q₈	1	2	yes	—
57	C₂×#63242	C₂³	1	2	yes	—
58	C₂×M₁₆×C₁₇	C₂×C₄	1	2	yes	—
59	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
60	C₂×#63223	C₂×C₄	1	2	yes	—
61	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
62	M₁₆×D₁₇	—	2	2	no	—
63	M₁₆×D₁₇	—	2	2	no	—
64	M₁₆×D₁₇	C₂×C₄	1	4	yes	—
65	M₁₆×D₁₇	C₂³	1	4	yes	—
66	C₂×#63218	—	2	2	no	—
67	C₂×C₈×D₁₇	—	2	2	no	—
68	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
79	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
80	#10587534	C₂×C₄	1	4	yes	—
81	#10587534	C₂×C₄	1	4	yes	—
82	#10587533	C₂×C₄	1	4	yes	—
83	#10587533	C₂×C₄	1	4	yes	—
84	#10587532	—	2	8	no	—
85	#10587532	C₂×C₄	1	4	yes	complemented
86	#10587532	C₂×C₄	1	4	yes	complemented
87	C₈×#595	—	2	8	no	—
88	C₈×#595	C₂×C₄	1	4	yes	complemented
89	C₈×#595	C₂×C₄	1	4	yes	complemented
90	C₁₇×#108	C₂×C₄	1	2	yes	complemented
91	C₁₇×#108	C₂×C₄	1	2	yes	complemented
92	#10587493	C₂×C₄	1	4	yes	complemented
93	#10587493	C₂×C₄	1	4	yes	complemented
94	#10587490	C₂×C₄	1	2	yes	complemented
95	#10587490	C₂×C₄	1	2	yes	complemented
96	C₂³×D₁₇	#41	1	1	yes	characteristic
97	C₂²×#595	—	2	2	no	—
98	C₂²×#595	—	2	4	no	—
99	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
101	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
108	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
110	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
111	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
112	C₂×C₄×D₁₇	C₂⁴	1	1	yes	characteristic
113	C₂²⋊#595	—	2	2	no	—
114	C₂²⋊#595	—	2	2	no	—
115	C₂²⋊#595	—	2	4	no	—
116	C₂²⋊#595	—	2	4	no	—
117	#63247	C₄⋊C₄	1	4	yes	—
118	#63247	C₄⋊C₄	1	4	yes	—
119	C₂×#3624	C₂×Q₈	1	4	yes	—
120	C₄⋊#595	—	2	2	no	—
121	C₄⋊#595	—	2	2	no	—
122	C₄⋊#595	—	2	4	no	—
123	C₄⋊#595	C₂²×C₄	1	8	yes	—
124	C₄×#595	—	2	4	no	—
125	C₄×#595	—	2	4	no	—
126	C₄×#595	—	2	2	no	—
127	C₄×#595	C₂²×C₄	1	4	yes	—
128	#63243	C₄⋊C₄	1	4	yes	—
129	#63243	C₄⋊C₄	1	4	yes	—
130	#63242	C₂²×C₄	1	4	yes	—
131	#63242	C₂×D₄	1	4	yes	—
132	M₁₆×C₁₇	—	2	2	no	—
133	M₁₆×C₁₇	C₂²×C₄	1	4	yes	—
134	C₂×C₈×C₁₇	—	2	2	no	—
135	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
136	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
137	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
138	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
139	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
141	#63223	—	2	2	no	—
142	#63223	C₂²×C₄	1	4	yes	—
143	C₂×#3622	—	2	2	no	—
144	C₂×#3622	C₄²	1	1	yes	characteristic
145	C₂×#3622	C₄²	1	1	yes	characteristic
146	C₂×#3622	C₄²	1	1	yes	characteristic
147	C₂×#3622	C₄²	1	1	yes	characteristic
148	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
149	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
150	#63218	—	2	4	no	—
151	#63218	—	2	4	no	—
152	C₈×D₁₇	—	2	4	no	—
153	C₈×D₁₇	—	2	4	no	—
154	C₈×D₁₇	C₄²	1	1	yes	characteristic
155	C₈×D₁₇	C₄²	1	1	yes	characteristic
156	C₈×D₁₇	C₄²	1	1	yes	characteristic
157	C₈×D₁₇	C₄²	1	1	yes	characteristic
158	C₈×D₁₇	C₄²	1	1	yes	characteristic
159	C₈×D₁₇	C₄²	1	1	yes	characteristic
160	C₈×D₁₇	C₄²	1	1	yes	characteristic
161	C₈×D₁₇	C₄²	1	1	yes	characteristic
162	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
163	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
164	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
165	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
166	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
167	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
168	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
169	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
170	#20446	—	17	1	no	maximal, Sylow
171	C₂³×C₁₇	C₄×Q₈	1	1	yes	characteristic
172	C₂²×D₁₇	—	4	2	no	—
173	C₂²×D₁₇	#117	1	1	yes	characteristic
174	C₂²×D₁₇	#117	1	1	yes	characteristic
175	C₂²×D₁₇	C₄×D₄	1	1	yes	characteristic
176	C₂²×D₁₇	C₄×D₄	1	1	yes	characteristic
177	C₂²×D₁₇	C₄×Q₈	1	1	yes	characteristic
178	C₂²×D₁₇	C₂×#41	1	1	yes	characteristic
179	C₂×#595	—	2	4	no	—
180	C₂×#595	—	2	8	no	—
181	C₂×#595	—	4	4	no	—
182	C₂×#595	—	8	4	no	—
183	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
184	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
185	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
189	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×Dic₁₇	C₄×Q₈	1	1	yes	characteristic
192	C₂×Dic₁₇	C₄×Q₈	1	1	yes	characteristic
193	C₂×Dic₁₇	C₄×Q₈	1	1	yes	characteristic
194	C₂×Dic₁₇	C₂²×Q₈	1	1	yes	characteristic
195	C₄×D₁₇	C₂×C₄²	1	1	yes	characteristic
196	C₄×D₁₇	C₂×C₄²	1	1	yes	characteristic
197	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₄×D₁₇	#117	1	1	yes	characteristic
200	C₄×D₁₇	#117	1	1	yes	characteristic
201	C₄×D₁₇	C₄×D₄	1	1	yes	characteristic
202	C₄×D₁₇	C₄×D₄	1	1	yes	characteristic
203	C₄×D₁₇	C₄×D₄	1	1	yes	characteristic
204	C₄×D₁₇	C₄×D₄	1	1	yes	characteristic
205	C₄×D₁₇	C₄×Q₈	1	1	yes	characteristic
206	C₄×D₁₇	C₄×Q₈	1	1	yes	characteristic
207	C₄×D₁₇	C₂³×C₄	1	1	yes	characteristic
208	C₄×D₁₇	C₂³×C₄	1	1	yes	characteristic
209	C₄×D₁₇	C₂²×D₄	1	1	yes	characteristic
210	C₄×D₁₇	C₂×#41	1	1	yes	characteristic
211	#3624	C₂×C₄⋊C₄	1	8	yes	—
212	C₈×C₁₇	—	2	4	no	—
213	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
214	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
215	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
216	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
217	#3622	—	2	4	no	—
218	#3622	C₂×C₄²	1	1	yes	characteristic
219	#3622	C₂×C₄²	1	1	yes	characteristic
220	#3622	C₂×C₄²	1	1	yes	characteristic
221	#3622	C₂×C₄²	1	1	yes	characteristic
222	C₂²×#108	—	17	1	no	—
223	C₂×#427	—	17	1	no	—
224	#2873	—	17	2	no	—
225	C₂×#405	—	17	1	no	—
226	#1773	—	17	4	no	—
227	#1772	—	17	4	no	—
228	#1733	—	17	2	no	—
229	C₂²×C₁₇	—	4	1	no	—
230	C₂²×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
231	C₂²×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
232	C₂²×C₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
233	C₂×D₁₇	—	2	2	no	—
234	C₂×D₁₇	—	2	2	no	—
235	C₂×D₁₇	—	2	2	no	—
236	C₂×D₁₇	—	4	1	no	—
237	C₂×D₁₇	—	4	1	no	—
238	C₂×D₁₇	—	4	1	no	—
239	C₂×D₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
240	C₂×D₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
241	C₂×D₁₇	C₂×#117	1	1	yes	characteristic
242	C₂×D₁₇	C₂×C₄×D₄	1	1	yes	characteristic
243	#595	—	4	4	no	—
244	#595	—	4	8	no	—
245	C₄×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
246	C₄×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
247	C₄×C₁₇	C₂²×C₄²	1	1	yes	characteristic
248	C₄×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
249	Dic₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
250	Dic₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
251	Dic₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
252	Dic₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
253	C₂²×M₁₆	—	17	1	no	—
254	C₂²×M₁₆	—	17	2	no	—
255	C₂³×C₈	—	17	1	no	—
256	C₂×#117	—	17	1	no	—
257	C₂×#117	—	17	2	no	—
258	C₂×#108	—	17	2	no	—
259	C₂×#108	—	17	1	no	—
260	C₂×#108	—	17	2	no	—
261	C₂×#108	—	17	2	no	—
262	C₂×#108	—	17	2	no	—
263	C₂×#108	—	17	2	no	—
264	C₂×#108	#595	1	1	yes	characteristic, complemented
265	#427	—	17	2	no	—
266	#427	—	17	2	no	—
267	#427	—	17	2	no	—
268	#427	—	17	2	no	—
269	C₂×#107	—	17	2	no	—
270	C₂×#106	—	17	2	no	—
271	#405	—	17	2	no	—
272	#405	—	17	2	no	—
273	#405	—	17	2	no	—
274	#405	—	17	2	no	—
275	#405	—	17	8	no	—
276	#405	—	34	4	no	—
277	C₄×M₁₆	—	34	4	no	—
278	C₂×#97	—	17	2	no	—
279	C₂×C₄×C₈	—	17	2	no	—
280	#339	—	17	8	no	—
281	C₂×C₁₇	—	2	1	no	—
282	C₂×C₁₇	—	2	1	no	—
283	C₂×C₁₇	—	2	1	no	—
284	C₂×C₁₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
285	D₁₇	—	2	1	no	—
286	D₁₇	—	2	1	no	—
287	D₁₇	—	2	1	no	—
288	D₁₇	#2957	1	2	yes	—
289	C₂³×C₄	—	17	1	no	—
290	C₂×M₁₆	—	17	2	no	—
291	C₂×M₁₆	—	17	2	no	—
292	C₂×M₁₆	—	17	2	no	—
293	C₂×M₁₆	—	17	2	no	—
294	C₂×M₁₆	—	17	2	no	—
295	C₂×M₁₆	—	17	2	no	—
296	C₂×M₁₆	—	17	2	no	—
297	C₂×M₁₆	—	17	4	no	—
298	C₂×M₁₆	—	17	4	no	—
299	C₂×M₁₆	—	34	2	no	—
300	C₂×M₁₆	—	34	2	no	—
301	C₂×M₁₆	—	34	2	no	—
302	C₂×M₁₆	C₂×#595	1	2	yes	—
303	C₂²×C₈	—	17	2	no	—
304	C₂²×C₈	—	17	1	no	—
305	C₂²×C₈	—	17	1	no	—
306	C₂²×C₈	—	17	1	no	—
307	C₂²×C₈	—	17	1	no	—
308	C₂²×C₈	—	17	1	no	—
309	C₂²×C₈	—	17	1	no	—
310	C₂²×C₈	—	17	1	no	—
311	C₂²×C₈	—	17	1	no	—
312	C₂²×C₈	—	17	1	no	—
313	C₂²×C₈	—	17	1	no	—
314	C₂²×C₈	—	17	1	no	—
315	C₂²×C₈	—	17	1	no	—
316	C₂²×C₈	—	17	1	no	—
317	C₂²×C₈	—	34	2	no	—
318	C₂²×C₈	C₂×#595	1	1	yes	characteristic
319	#117	—	17	2	no	—
320	#117	—	17	2	no	—
321	#117	—	17	4	no	—
322	#117	—	17	4	no	—
323	#117	—	34	1	no	—
324	#117	—	34	1	no	—
325	#117	—	34	2	no	—
326	#117	—	34	2	no	—
327	C₂×C₄⋊C₄	—	17	4	no	—
328	C₂×C₄⋊C₄	—	34	1	no	—
329	C₂×C₂²⋊C₄	—	34	1	no	—
330	C₂×C₂²⋊C₄	—	34	2	no	—
331	C₂×C₄²	—	17	2	no	—
332	C₂×C₄²	—	34	2	no	—
333	#108	—	17	4	no	—
334	#108	—	17	4	no	—
335	#108	—	17	2	no	—
336	#108	—	17	2	no	—
337	#108	C₂×#595	1	2	yes	complemented
338	#108	C₂×#595	1	2	yes	complemented
339	#107	—	17	4	no	—
340	#107	—	17	4	no	—
341	#106	—	17	4	no	—
342	#106	—	17	4	no	—
343	#97	—	17	4	no	—
344	#97	—	17	4	no	—
345	#97	—	34	8	no	—
346	C₄×C₈	—	17	4	no	—
347	C₄×C₈	—	17	4	no	—
348	C₄×C₈	—	34	8	no	—
349	C₁₇	#20446	1	1	yes	characteristic, complemented, Sylow
350	C₂⁴	—	17	1	no	—
351	C₂²×C₄	—	17	1	no	—
352	C₂²×C₄	—	17	1	no	—
353	C₂²×C₄	—	17	1	no	—
354	C₂²×C₄	—	17	1	no	—
355	C₂²×C₄	—	17	1	no	—
356	C₂²×C₄	—	17	1	no	—
357	C₂²×C₄	—	17	1	no	—
358	C₂²×C₄	—	17	1	no	—
359	C₂²×C₄	—	17	1	no	—
360	C₂²×C₄	—	17	1	no	—
361	C₂²×C₄	—	17	1	no	—
362	C₂²×C₄	—	17	1	no	—
363	C₂²×C₄	—	17	1	no	—
364	C₂²×C₄	—	34	2	no	—
365	C₂²×C₄	—	34	4	no	—
366	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
367	M₁₆	—	2	2	no	—
368	M₁₆	—	17	4	no	—
369	M₁₆	—	17	4	no	—
370	M₁₆	—	17	4	no	—
371	M₁₆	—	17	4	no	—
372	M₁₆	—	17	4	no	—
373	M₁₆	—	34	4	no	—
374	M₁₆	—	34	4	no	—
375	M₁₆	—	34	2	no	—
376	M₁₆	C₂²×#595	1	4	yes	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	17	4	no	—
379	C₂×C₈	—	17	4	no	—
380	C₂×C₈	—	17	4	no	—
381	C₂×C₈	—	17	1	no	—
382	C₂×C₈	—	17	1	no	—
383	C₂×C₈	—	17	1	no	—
384	C₂×C₈	—	17	1	no	—
385	C₂×C₈	—	17	1	no	—
386	C₂×C₈	—	17	1	no	—
387	C₂×C₈	—	17	1	no	—
388	C₂×C₈	—	17	1	no	—
389	C₂×C₈	—	17	1	no	—
390	C₂×C₈	—	17	1	no	—
391	C₂×C₈	—	17	1	no	—
392	C₂×C₈	—	17	1	no	—
393	C₂×C₈	—	17	1	no	—
394	C₂×C₈	—	17	1	no	—
395	C₂×C₈	—	17	1	no	—
396	C₂×C₈	—	17	1	no	—
397	C₂×C₈	—	17	1	no	—
398	C₂×C₈	—	17	1	no	—
399	C₂×C₈	—	17	1	no	—
400	C₂×C₈	—	17	1	no	—
401	C₂×C₈	—	17	1	no	—
402	C₂×C₈	—	17	1	no	—
403	C₂×C₈	—	34	4	no	—
404	C₂×C₈	—	34	4	no	—
405	C₂×C₈	—	34	2	no	—
406	C₂×C₈	C₄×#595	1	1	yes	characteristic
407	C₂×C₈	C₄×#595	1	1	yes	characteristic
408	C₂×C₈	C₄×#595	1	1	yes	characteristic
409	C₂×C₈	C₄×#595	1	1	yes	characteristic
410	C₂×C₈	C₂²×#595	1	1	yes	characteristic
411	C₂×C₈	C₂²×#595	1	1	yes	characteristic
412	C₄⋊C₄	—	17	8	no	—
413	C₄⋊C₄	—	34	4	no	—
414	C₄⋊C₄	—	34	2	no	—
415	C₄⋊C₄	—	34	2	no	—
416	C₂²⋊C₄	—	34	2	no	—
417	C₂²⋊C₄	—	34	2	no	—
418	C₂²⋊C₄	—	34	4	no	—
419	C₂²⋊C₄	—	34	4	no	—
420	C₄²	—	17	4	no	—
421	C₄²	—	34	4	no	—
422	C₄²	—	34	2	no	—
423	C₄²	—	34	4	no	—
424	C₂³	—	17	1	no	—
425	C₂³	—	17	1	no	—
426	C₂³	—	17	1	no	—
427	C₂³	—	17	1	no	—
428	C₂³	—	17	1	no	—
429	C₂³	—	17	1	no	—
430	C₂³	—	68	2	no	—
431	C₂³	Q₈×#595	1	1	yes	characteristic
432	C₂×C₄	—	17	1	no	—
433	C₂×C₄	—	17	1	no	—
434	C₂×C₄	—	17	1	no	—
435	C₂×C₄	—	17	1	no	—
436	C₂×C₄	—	17	1	no	—
437	C₂×C₄	—	17	1	no	—
438	C₂×C₄	—	17	1	no	—
439	C₂×C₄	—	17	1	no	—
440	C₂×C₄	—	17	1	no	—
441	C₂×C₄	—	17	1	no	—
442	C₂×C₄	—	17	1	no	—
443	C₂×C₄	—	17	1	no	—
444	C₂×C₄	—	17	1	no	—
445	C₂×C₄	—	17	1	no	—
446	C₂×C₄	—	17	1	no	—
447	C₂×C₄	—	17	1	no	—
448	C₂×C₄	—	17	1	no	—
449	C₂×C₄	—	17	1	no	—
450	C₂×C₄	—	17	1	no	—
451	C₂×C₄	—	17	1	no	—
452	C₂×C₄	—	17	1	no	—
453	C₂×C₄	—	17	1	no	—
454	C₂×C₄	—	34	4	no	—
455	C₂×C₄	—	34	8	no	—
456	C₂×C₄	—	68	4	no	—
457	C₂×C₄	—	136	4	no	—
458	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
459	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
460	C₂×C₄	D₄×#595	1	1	yes	characteristic
461	C₂×C₄	D₄×#595	1	1	yes	characteristic
462	C₂×C₄	Q₈×#595	1	1	yes	characteristic
463	C₂×C₄	C₂³×#595	1	1	yes	characteristic
464	C₈	—	2	4	no	—
465	C₈	—	17	8	no	—
466	C₈	—	17	1	no	—
467	C₈	—	17	1	no	—
468	C₈	—	17	1	no	—
469	C₈	—	17	1	no	—
470	C₈	—	34	4	no	—
471	C₈	C₂×C₄×#595	1	1	yes	characteristic
472	C₈	C₂×C₄×#595	1	1	yes	characteristic
473	C₈	C₂×C₄×#595	1	1	yes	characteristic
474	C₈	C₂×C₄×#595	1	1	yes	characteristic
475	C₂²	—	4	1	no	—
476	C₂²	—	17	1	no	—
477	C₂²	—	17	1	no	—
478	C₂²	—	17	1	no	—
479	C₂²	—	17	1	no	—
480	C₂²	—	34	2	no	—
481	C₂²	—	34	2	no	—
482	C₂²	—	34	2	no	—
483	C₂²	—	68	1	no	—
484	C₂²	—	68	1	no	—
485	C₂²	—	68	1	no	—
486	C₂²	C₄⋊C₄×#595	1	1	yes	characteristic
487	C₂²	C₄⋊C₄×#595	1	1	yes	characteristic
488	C₂²	C₂×Q₈×#595	1	1	yes	characteristic
489	C₄	—	17	1	no	—
490	C₄	—	17	1	no	—
491	C₄	—	17	1	no	—
492	C₄	—	17	1	no	—
493	C₄	—	68	8	no	—
494	C₄	—	68	4	no	—
495	C₄	C₄⋊C₄×#595	1	1	yes	characteristic
496	C₄	C₄⋊C₄×#595	1	1	yes	characteristic
497	C₄	C₂²×C₄×#595	1	1	yes	characteristic
498	C₄	C₂×D₄×#595	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	2	1	no	—
502	C₂	—	17	2	no	—
503	C₂	—	34	1	no	—
504	C₂	—	34	1	no	—
505	C₂	—	34	1	no	—
506	C₂	C₂×C₄⋊C₄×#595	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×#595
commutator	C₄×C₁₇	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#595
Fitting	C₂×C₁₇×#108	C₄
socle	C₂×C₁₇	C₂×C₄×C₄⋊C₄
prime radical	C₂³×D₁₇	#41
cosocle	C₂×C₄×D₁₇	C₂⁴
hypercenter	C₂×#108	#595
hypocenter	C₁₇	#20446
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
4. #14544593	C₂	semidirect
5. #14544589	C₂	semidirect
11. #11763819	C₄	semidirect
12. #11763819	C₄	semidirect
15. C₂×#10587534	C₄	semidirect
16. C₂×#10587533	C₄	semidirect
19. #11763772	C₄	semidirect
20. #11763772	C₄	semidirect
21. #11763772	C₄	semidirect
22. #11763772	C₄	semidirect
29. C₂×#10587490	C₄	semidirect
30. C₂×#10587493	C₄	semidirect
31. #108×D₁₇	C₄	semidirect
32. #108×D₁₇	C₄	semidirect
35. C₂×C₁₇×#108	C₄	semidirect
85. #10587532	C₂×C₄	semidirect
86. #10587532	C₂×C₄	semidirect
88. C₈×#595	C₂×C₄	semidirect
89. C₈×#595	C₂×C₄	semidirect
90. C₁₇×#108	C₂×C₄	semidirect
91. C₁₇×#108	C₂×C₄	semidirect
92. #10587493	C₂×C₄	semidirect
93. #10587493	C₂×C₄	semidirect
94. #10587490	C₂×C₄	semidirect
95. #10587490	C₂×C₄	semidirect
264. C₂×#108	#595	semidirect
337. #108	C₂×#595	semidirect
338. #108	C₂×#595	semidirect
349. C₁₇	#20446	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11763819	2
#14545347	2
C₂×#11763772	2
#14544593	2
#14544589	2
#14544466	2
C₂×#108×D₁₇	2
#20446	17