Subgroups — #17048256

Order 4352.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14539271	C₂	1	1	yes	maximal, characteristic
2	#14537637	C₂	1	1	yes	maximal, characteristic, complemented
3	#14529692	C₂	1	1	yes	maximal, characteristic, complemented
4	#14529683	C₂	1	1	yes	maximal, characteristic, complemented
5	#14529313	C₂	1	2	yes	maximal, complemented
6	#14529311	C₂	1	2	yes	maximal, complemented
7	#14529268	C₂	1	2	yes	maximal, complemented
8	#14529264	C₂	1	2	yes	maximal, complemented
9	#14528909	C₂	1	1	yes	maximal, characteristic, complemented
10	#14528539	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#2957	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10587635	C₂²	1	2	yes	—
13	C₂²×D₁₃₆	C₂²	1	1	yes	characteristic
14	#11763373	C₂²	1	2	yes	—
15	#11763283	C₂²	1	2	yes	—
16	#11763195	C₄	1	4	yes	complemented
17	#11763194	C₄	1	2	yes	complemented
18	#11763184	C₄	1	2	yes	complemented
19	#11762922	—	2	2	no	—
20	C₄×D₁₃₆	—	2	2	no	—
21	#11762847	C₂²	1	1	yes	characteristic
22	#11762826	C₂²	1	2	yes	—
23	#11762815	C₂²	1	2	yes	—
24	#11762815	C₂²	1	2	yes	—
25	C₂×#10587494	C₂²	1	2	yes	—
26	#11762783	C₂²	1	2	yes	—
27	#11762764	C₂²	1	1	yes	characteristic
28	#11762764	C₂²	1	1	yes	characteristic
29	#11762581	C₂²	1	2	yes	—
30	#11762567	C₂²	1	1	yes	characteristic
31	#11762566	C₂²	1	1	yes	characteristic
32	#11762566	C₂²	1	2	yes	—
33	#11762565	C₂²	1	1	yes	characteristic
34	#11762565	C₂²	1	1	yes	characteristic
35	C₂×C₁₇×#135	C₂²	1	1	yes	characteristic
36	C₁₇×#568	C₂²	1	2	yes	—
37	C₁₇×#444	—	2	2	no	—
38	C₁₇×#443	—	2	2	no	—
39	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic
40	C₁₇×#421	C₂²	1	2	yes	—
41	C₁₇×#405	C₂²	1	1	yes	characteristic
42	C₂×#41×C₁₇	C₂³	1	2	yes	—
43	C₂²×D₆₈	C₂³	1	2	yes	—
44	C₁₇×#135	—	2	1	no	—
45	C₁₇×#135	—	2	1	no	—
46	C₁₇×#135	—	2	1	no	—
47	C₁₇×#135	—	2	1	no	—
48	C₂×Q₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic, complemented
49	C₂×SD₁₆×C₁₇	C₂×C₄	1	2	yes	complemented
50	C₂×D₈×C₁₇	C₂×C₄	1	1	yes	characteristic, complemented
51	C₁₇×#131	—	2	4	no	—
52	C₁₇×#131	—	4	2	no	—
53	C₂×M₁₆×C₁₇	—	4	2	no	—
54	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
55	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
57	C₁₇×#117	C₂³	1	1	yes	characteristic
58	#10587635	—	4	2	no	—
59	#10587635	—	4	2	no	—
60	#10587633	C₂×C₄	1	4	yes	complemented
61	C₂×#63230	C₂×C₄	1	4	yes	complemented
62	#10587626	C₂×C₄	1	4	yes	complemented
63	#10587623	—	4	2	no	—
64	C₂×#63228	C₂×C₄	1	4	yes	complemented
65	#10587616	—	4	2	no	—
66	#10587612	C₂³	1	1	yes	characteristic
67	#10587612	C₂³	1	2	yes	—
68	#10587612	C₂³	1	1	yes	characteristic
69	C₂×#63223	C₂³	1	1	yes	characteristic
70	C₂×#63223	C₂³	1	1	yes	characteristic
71	C₂×D₁₃₆	—	2	1	no	—
72	C₂×D₁₃₆	—	2	1	no	—
73	C₂×D₁₃₆	—	2	1	no	—
74	C₂×D₁₃₆	—	2	1	no	—
75	C₂×D₁₃₆	C₂×C₄	1	2	yes	—
76	C₂×D₁₃₆	C₂×C₄	1	2	yes	—
77	#10587579	—	4	2	no	—
78	C₂²⋊C₄×D₁₇	—	4	2	no	—
79	C₄×D₆₈	—	2	4	no	—
80	C₁₇×#108	—	2	1	no	—
81	C₁₇×#108	—	2	1	no	—
82	C₁₇×#104	—	2	4	no	—
83	C₁₇×#97	D₄	1	2	yes	complemented
84	C₄×C₈×C₁₇	D₄	1	2	yes	complemented
85	#10587508	—	4	2	no	—
86	#10587505	—	4	2	no	—
87	#10587494	—	4	2	no	—
88	#10587492	—	2	4	no	—
89	#10587492	—	4	2	no	—
90	#10587489	—	2	1	no	—
91	#10587488	—	2	1	no	—
92	#10587486	—	2	1	no	—
93	#10587486	C₂×C₄	1	2	yes	complemented
94	C₈×Dic₁₇	—	2	1	no	—
95	C₈×Dic₁₇	C₂×C₄	1	2	yes	complemented
96	C₂³×D₁₇	—	2	2	no	—
97	#41×C₁₇	—	2	2	no	—
98	#41×C₁₇	—	2	2	no	—
99	#41×C₁₇	—	2	2	no	—
100	#41×C₁₇	—	2	2	no	—
101	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₁₇	—	2	2	no	—
103	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₇	—	2	2	no	—
105	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
106	C₂×C₂²⋊D₁₇	—	4	4	no	—
107	C₂×D₆₈	—	2	2	no	—
108	C₂×D₆₈	—	2	2	no	—
109	C₂×D₆₈	—	2	2	no	—
110	C₂×D₆₈	—	2	2	no	—
111	C₂×D₆₈	—	2	2	no	—
112	C₂×D₆₈	C₂²×C₄	1	4	yes	—
113	C₂×C₄×D₁₇	—	4	4	no	—
114	Q₁₆×C₁₇	—	2	1	no	—
115	Q₁₆×C₁₇	—	2	1	no	—
116	SD₁₆×C₁₇	—	2	2	no	—
117	SD₁₆×C₁₇	—	2	2	no	—
118	D₈×C₁₇	—	2	1	no	—
119	D₈×C₁₇	—	2	1	no	—
120	M₁₆×C₁₇	—	2	1	no	—
121	M₁₆×C₁₇	—	2	1	no	—
122	M₁₆×C₁₇	—	2	2	no	—
123	M₁₆×C₁₇	—	2	2	no	—
124	M₁₆×C₁₇	—	4	4	no	—
125	C₂×C₈×C₁₇	—	2	2	no	—
126	C₂×C₈×C₁₇	—	4	4	no	—
127	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₇	#41	1	1	yes	characteristic
133	C₂×C₈×C₁₇	#41	1	1	yes	characteristic
134	C₄⋊C₄×C₁₇	—	2	1	no	—
135	C₂²⋊C₄×C₁₇	—	2	1	no	—
136	C₄²×C₁₇	C₂×D₄	1	2	yes	—
137	C₂²⋊Dic₁₇	—	2	1	no	—
138	C₂²⋊Dic₁₇	—	2	1	no	—
139	C₂²⋊Dic₁₇	—	2	2	no	—
140	#63230	—	4	4	no	—
141	#63228	—	4	4	no	—
142	#63227	—	4	4	no	—
143	#63227	—	4	4	no	—
144	C₄⋊Dic₁₇	—	2	1	no	—
145	C₄⋊Dic₁₇	—	2	2	no	—
146	C₄⋊Dic₁₇	—	2	1	no	—
147	C₄×Dic₁₇	—	2	1	no	—
148	C₄×Dic₁₇	—	2	2	no	—
149	C₄×Dic₁₇	C₂²×C₄	1	2	yes	—
150	#63223	—	2	1	no	—
151	#63223	—	2	1	no	—
152	#63223	—	2	1	no	—
153	#63223	—	2	1	no	—
154	C₂×#3622	—	2	1	no	—
155	C₂×#3622	C₂²×C₄	1	2	yes	—
156	D₁₃₆	—	2	2	no	—
157	D₁₃₆	—	2	2	no	—
158	D₁₃₆	—	2	2	no	—
159	D₁₃₆	—	2	2	no	—
160	#22286	—	17	1	no	maximal, Sylow
161	C₂³×C₁₇	—	2	2	no	—
162	C₂³×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂²×D₁₇	—	2	4	no	—
164	C₂²×D₁₇	—	4	2	no	—
165	C₂²×D₁₇	—	4	2	no	—
166	C₂²×D₁₇	—	16	2	no	—
167	Q₈×C₁₇	—	2	2	no	—
168	Q₈×C₁₇	—	2	2	no	—
169	D₄×C₁₇	—	2	2	no	—
170	D₄×C₁₇	—	2	2	no	—
171	D₄×C₁₇	—	4	2	no	—
172	D₄×C₁₇	—	4	2	no	—
173	C₂×C₄×C₁₇	—	2	2	no	—
174	C₂×C₄×C₁₇	—	2	2	no	—
175	C₂×C₄×C₁₇	—	4	2	no	—
176	C₂×C₄×C₁₇	—	4	2	no	—
177	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂²⋊D₁₇	—	16	4	no	—
184	C₂×Dic₁₇	—	2	2	no	—
185	C₂×Dic₁₇	—	4	2	no	—
186	C₂×Dic₁₇	—	4	1	no	—
187	D₆₈	—	2	4	no	—
188	D₆₈	—	2	4	no	—
189	D₆₈	—	4	2	no	—
190	D₆₈	—	4	2	no	—
191	C₄×D₁₇	—	16	4	no	—
192	C₈×C₁₇	—	2	2	no	—
193	C₈×C₁₇	—	4	2	no	—
194	C₈×C₁₇	C₄×D₄	1	1	yes	characteristic
195	C₈×C₁₇	C₄×D₄	1	1	yes	characteristic
196	C₈×C₁₇	C₄×D₄	1	1	yes	characteristic
197	C₈×C₁₇	C₄×D₄	1	1	yes	characteristic
198	#3622	—	2	2	no	—
199	#3622	—	4	1	no	—
200	#3155	—	17	1	no	—
201	#2957	D₁₇	1	1	yes	characteristic, complemented
202	#2948	—	17	1	no	—
203	#1978	—	17	1	no	—
204	#1976	—	17	1	no	—
205	#1911	—	17	2	no	—
206	#1910	—	17	2	no	—
207	#1904	—	17	2	no	—
208	#1903	—	17	2	no	—
209	#1833	—	17	1	no	—
210	#1747	—	17	1	no	—
211	C₂²×C₁₇	—	4	1	no	—
212	C₂²×C₁₇	—	4	2	no	—
213	C₂²×C₁₇	—	8	2	no	—
214	C₂²×C₁₇	#518	1	1	yes	characteristic
215	C₂²×C₁₇	#535	1	1	yes	characteristic
216	C₂²×C₁₇	#540	1	1	yes	characteristic
217	C₂×D₁₇	—	4	4	no	—
218	C₂×D₁₇	—	8	4	no	—
219	C₂×D₁₇	—	8	4	no	—
220	C₂×D₁₇	—	16	2	no	—
221	C₄×C₁₇	—	4	2	no	—
222	C₄×C₁₇	—	4	2	no	—
223	C₄×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
224	C₄×C₁₇	#518	1	1	yes	characteristic
225	C₄×C₁₇	#535	1	1	yes	characteristic
226	C₄×C₁₇	#540	1	1	yes	characteristic
227	Dic₁₇	—	4	2	no	—
228	Dic₁₇	—	8	2	no	—
229	Dic₁₇	—	8	1	no	—
230	C₂×AGL(1,ℤ/8)	—	17	2	no	—
231	C₂×#135	C₂×D₁₇	1	1	yes	characteristic
232	C₂²×D₈	—	17	1	no	—
233	#568	C₂×D₁₇	1	2	yes	—
234	#535	—	17	2	no	—
235	#518	—	17	2	no	—
236	#496	—	17	4	no	—
237	#495	—	17	2	no	—
238	#493	—	17	2	no	—
239	#444	—	2	2	no	—
240	#443	—	2	2	no	—
241	#442	—	34	2	no	—
242	C₄×D₈	—	34	2	no	—
243	C₂×#108	C₂×D₁₇	1	1	yes	characteristic
244	#427	—	17	1	no	—
245	#421	—	17	2	no	—
246	#421	C₂×D₁₇	1	2	yes	—
247	#418	—	17	2	no	—
248	#418	—	17	2	no	—
249	C₂×#100	—	17	2	no	—
250	#410	—	17	2	no	—
251	#405	—	17	1	no	—
252	#405	—	17	1	no	—
253	#405	C₂×D₁₇	1	1	yes	characteristic
254	#344	—	17	2	no	—
255	#338	—	17	1	no	—
256	H(3,ℤ/4)	—	17	2	no	—
257	H(3,ℤ/4)	—	17	1	no	—
258	H(3,ℤ/4)	—	17	1	no	—
259	H(3,ℤ/4)	—	17	1	no	—
260	C₂×C₁₇	—	2	1	no	—
261	C₂×C₁₇	—	2	1	no	—
262	C₂×C₁₇	—	2	1	no	—
263	C₂×C₁₇	—	8	2	no	—
264	C₂×C₁₇	#2328	1	1	yes	characteristic
265	D₁₇	—	8	4	no	—
266	C₂×#41	C₂²×D₁₇	1	2	yes	—
267	C₂²×D₄	—	17	2	no	—
268	AGL(1,ℤ/8)	—	68	2	no	—
269	AGL(1,ℤ/8)	—	68	2	no	—
270	#135	—	2	1	no	—
271	#135	—	2	1	no	—
272	#135	—	2	1	no	—
273	#135	—	2	1	no	—
274	C₂×Q₁₆	C₄×D₁₇	1	1	yes	characteristic, complemented
275	C₂×SD₁₆	—	17	4	no	—
276	C₂×SD₁₆	C₄×D₁₇	1	2	yes	complemented
277	C₂×D₈	—	17	4	no	—
278	C₂×D₈	—	17	2	no	—
279	C₂×D₈	—	17	2	no	—
280	C₂×D₈	—	34	1	no	—
281	C₂×D₈	—	34	1	no	—
282	C₂×D₈	—	34	1	no	—
283	C₂×D₈	—	34	1	no	—
284	C₂×D₈	C₄×D₁₇	1	1	yes	characteristic, complemented
285	#131	—	2	4	no	—
286	#131	—	4	2	no	—
287	C₂×M₁₆	—	4	2	no	—
288	C₂×M₁₆	—	17	1	no	—
289	C₂×M₁₆	—	17	1	no	—
290	C₂×M₁₆	C₂²×D₁₇	1	2	yes	—
291	C₂×M₁₆	C₂²×D₁₇	1	1	yes	characteristic
292	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
293	#127	—	17	4	no	—
294	#124	—	17	4	no	—
295	#121	—	68	2	no	—
296	#120	—	68	2	no	—
297	C₄×D₄	—	34	4	no	—
298	C₄×D₄	—	68	2	no	—
299	#117	—	17	1	no	—
300	#117	—	17	2	no	—
301	#117	—	17	1	no	—
302	#117	C₂²×D₁₇	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	—	68	2	no	—
304	#108	—	2	1	no	—
305	#108	—	2	1	no	—
306	#107	—	34	1	no	—
307	#106	—	34	1	no	—
308	#104	—	2	4	no	—
309	#104	—	68	2	no	—
310	#102	—	34	4	no	—
311	#102	—	68	2	no	—
312	#100	—	68	2	no	—
313	#99	—	68	2	no	—
314	#97	—	17	2	no	—
315	#97	—	34	1	no	—
316	#97	C₂²⋊D₁₇	1	2	yes	complemented
317	C₄×C₈	—	17	2	no	—
318	C₄×C₈	—	34	1	no	—
319	C₄×C₈	C₂²⋊D₁₇	1	2	yes	complemented
320	C₁₇	#22286	1	1	yes	characteristic, complemented, Sylow
321	C₂⁴	—	34	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	C₂×Q₈	C₂×C₄×D₁₇	1	2	yes	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	17	4	no	—
329	C₂×D₄	—	34	2	no	—
330	C₂×D₄	—	34	2	no	—
331	C₂×D₄	—	34	2	no	—
332	C₂×D₄	—	34	2	no	—
333	C₂×D₄	—	34	2	no	—
334	C₂×D₄	—	68	4	no	—
335	C₂×D₄	C₂×C₄×D₁₇	1	2	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	68	4	no	—
338	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
339	Q₁₆	—	2	1	no	—
340	Q₁₆	—	2	1	no	—
341	SD₁₆	—	2	2	no	—
342	SD₁₆	—	2	2	no	—
343	SD₁₆	—	68	4	no	—
344	D₈	—	2	1	no	—
345	D₈	—	2	1	no	—
346	D₈	—	34	2	no	—
347	D₈	—	34	2	no	—
348	D₈	—	34	2	no	—
349	D₈	—	34	2	no	—
350	D₈	—	68	4	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	4	4	no	—
356	M₁₆	—	34	1	no	—
357	M₁₆	—	34	1	no	—
358	M₁₆	—	34	1	no	—
359	M₁₆	—	34	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	4	4	no	—
362	C₂×C₈	—	17	2	no	—
363	C₂×C₈	—	34	1	no	—
364	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
365	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
366	C₂×C₈	#63252	1	1	yes	characteristic
367	C₂×C₈	#63252	1	1	yes	characteristic
368	C₂×C₈	C₂×C₂²⋊D₁₇	1	2	yes	—
369	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
370	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	34	1	no	—
373	C₄⋊C₄	—	34	1	no	—
374	C₄⋊C₄	—	34	2	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	34	1	no	—
377	C₂²⋊C₄	—	34	1	no	—
378	C₂²⋊C₄	—	34	2	no	—
379	C₂²⋊C₄	—	68	4	no	—
380	C₂²⋊C₄	—	68	4	no	—
381	C₄²	—	17	2	no	—
382	C₄²	—	34	1	no	—
383	C₄²	—	34	2	no	—
384	C₄²	C₂×C₂²⋊D₁₇	1	2	yes	—
385	C₂³	—	2	2	no	—
386	C₂³	—	272	2	no	—
387	C₂³	—	34	4	no	—
388	C₂³	—	68	2	no	—
389	C₂³	—	68	2	no	—
390	C₂³	#10587696	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	272	4	no	—
398	D₄	—	34	4	no	—
399	D₄	—	34	4	no	—
400	D₄	—	68	2	no	—
401	D₄	—	68	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	272	4	no	—
407	C₂×C₄	—	34	2	no	—
408	C₂×C₄	—	68	2	no	—
409	C₂×C₄	—	68	1	no	—
410	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
411	C₂×C₄	C₂×#63252	1	1	yes	characteristic
412	C₂×C₄	#10587691	1	1	yes	characteristic
413	C₂×C₄	#10587691	1	1	yes	characteristic
414	C₂×C₄	#10587696	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	34	2	no	—
419	C₈	—	68	1	no	—
420	C₈	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
421	C₈	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
422	C₈	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
423	C₈	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	272	2	no	—
428	C₂²	—	68	4	no	—
429	C₂²	—	136	4	no	—
430	C₂²	—	136	4	no	—
431	C₂²	#11763281	1	1	yes	characteristic
432	C₂²	#11763373	1	1	yes	characteristic
433	C₂²	#11763410	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	68	2	no	—
437	C₄	—	136	2	no	—
438	C₄	—	136	1	no	—
439	C₄	C₂×C₄×C₂²⋊D₁₇	1	1	yes	characteristic
440	C₄	#11763281	1	1	yes	characteristic
441	C₄	#11763376	1	1	yes	characteristic
442	C₄	#11763410	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	8	2	no	—
447	C₂	—	136	4	no	—
448	C₂	#14531506	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14531506
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₇
Fitting	C₁₇×#2957	C₂
socle	C₂×C₁₇	#2328
prime radical	#14539271	C₂
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	#2957	D₁₇
hypocenter	C₁₇	#22286
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2957

Complements

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

N	H ≅ G/N	type
2. #14537637	C₂	semidirect
3. #14529692	C₂	semidirect
4. #14529683	C₂	semidirect
5. #14529313	C₂	semidirect
6. #14529311	C₂	semidirect
7. #14529268	C₂	semidirect
8. #14529264	C₂	semidirect
9. #14528909	C₂	semidirect
10. #14528539	C₂	semidirect
11. C₁₇×#2957	C₂	semidirect
16. #11763195	C₄	semidirect
17. #11763194	C₄	semidirect
18. #11763184	C₄	semidirect
48. C₂×Q₁₆×C₁₇	C₂×C₄	semidirect
49. C₂×SD₁₆×C₁₇	C₂×C₄	semidirect
50. C₂×D₈×C₁₇	C₂×C₄	semidirect
60. #10587633	C₂×C₄	semidirect
61. C₂×#63230	C₂×C₄	semidirect
62. #10587626	C₂×C₄	semidirect
64. C₂×#63228	C₂×C₄	semidirect
83. C₁₇×#97	D₄	semidirect
84. C₄×C₈×C₁₇	D₄	semidirect
93. #10587486	C₂×C₄	semidirect
95. C₈×Dic₁₇	C₂×C₄	semidirect
201. #2957	D₁₇	semidirect
274. C₂×Q₁₆	C₄×D₁₇	semidirect
276. C₂×SD₁₆	C₄×D₁₇	semidirect
284. C₂×D₈	C₄×D₁₇	semidirect
316. #97	C₂²⋊D₁₇	semidirect
319. C₄×C₈	C₂²⋊D₁₇	semidirect
320. C₁₇	#22286	semidirect

Maximal subgroups

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

subgroup	index
#14539271	2
#14537637	2
#14529692	2
#14529683	2
#14529313	2
#14529311	2
#14529268	2
#14529264	2
#14528909	2
#14528539	2
C₁₇×#2957	2
#22286	17