Subgroups — C₂²×#11763316 #17940977

Order 4352.

14334 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11763316	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#10587621	C₂	1	2	yes	maximal, complemented
4	C₂²×#10587632	C₂	1	2	yes	maximal, complemented
5	C₂²×#10587624	C₂	1	2	yes	maximal, complemented
6	C₂²×#10587623	C₂	1	2	yes	maximal, complemented
7	C₂²×C₄×C₂²⋊D₁₇	C₂	1	4	yes	maximal, complemented
8	C₂²×#10587612	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×#41×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁵×D₁₇	C₂²	1	1	yes	characteristic
11	C₂³×C₂²⋊D₁₇	C₂²	1	4	yes	—
12	C₂⁴×Dic₁₇	C₂²	1	1	yes	characteristic
13	C₂³×C₄×D₁₇	—	2	16	no	—
14	C₂³×C₄×D₁₇	C₂²	1	2	yes	—
15	C₂³×C₄×D₁₇	C₂²	1	2	yes	—
16	C₂³×C₄×D₁₇	C₂²	1	24	yes	complemented
17	#11763316	C₂²	1	256	yes	direct product factor
18	C₂×#10587621	C₂²	1	48	yes	complemented
19	C₂×#10587632	C₂²	1	48	yes	complemented
20	C₂×#10587624	C₂²	1	48	yes	complemented
21	C₂×#10587623	C₂²	1	48	yes	complemented
22	C₂×C₄×C₂²⋊D₁₇	C₂²	1	96	yes	complemented
23	C₂×#10587612	C₂²	1	24	yes	complemented
24	C₂²×C₄⋊Dic₁₇	C₂²	1	2	yes	complemented
25	C₂²×#63225	C₂²	1	4	yes	complemented
26	C₂²×C₂²⋊Dic₁₇	C₂²	1	2	yes	—
27	C₂²×C₂²⋊Dic₁₇	C₂²	1	4	yes	complemented
28	C₂²×#63227	C₂²	1	4	yes	—
29	C₂²×C₄×Dic₁₇	C₂²	1	2	yes	complemented
30	C₂²×#41×C₁₇	—	2	16	no	—
31	C₂²×#41×C₁₇	C₂²	1	24	yes	complemented
32	C₂³×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
33	C₂³×D₄×C₁₇	C₂²	1	2	yes	—
34	C₂³×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
35	C₂⁴×C₄×C₁₇	C₂²	1	1	yes	characteristic
36	C₂⁴×C₄×C₁₇	C₂²	1	2	yes	complemented
37	C₂⁵×C₁₇	C₂³	1	2	yes	—
38	C₂⁵×C₁₇	C₂³	1	1	yes	characteristic
39	C₂⁴×D₁₇	—	2	8	no	—
40	C₂⁴×D₁₇	—	2	16	no	—
41	C₂⁴×D₁₇	C₂³	1	12	yes	—
42	C₂⁴×D₁₇	C₂³	1	2	yes	—
43	C₂×#41×C₁₇	—	2	192	no	—
44	C₂×#41×C₁₇	C₂³	1	64	yes	complemented
45	C₂²×Q₈×C₁₇	—	2	8	no	—
46	C₂²×Q₈×C₁₇	C₂³	1	12	yes	complemented
47	C₂²×D₄×C₁₇	—	2	16	no	—
48	C₂²×D₄×C₁₇	—	2	8	no	—
49	C₂²×D₄×C₁₇	C₂³	1	24	yes	—
50	C₂²×D₄×C₁₇	C₂³	1	12	yes	complemented
51	C₂³×C₄×C₁₇	—	2	16	no	—
52	C₂³×C₄×C₁₇	D₄	1	16	yes	complemented
53	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₇	C₂³	1	12	yes	—
57	C₂³×C₄×C₁₇	C₂³	1	24	yes	complemented
58	C₂²×C₂²⋊D₁₇	—	2	32	no	—
59	C₂²×C₂²⋊D₁₇	C₂³	1	48	yes	—
60	C₂³×Dic₁₇	—	2	8	no	—
61	C₂³×Dic₁₇	C₂³	1	4	yes	—
62	C₂³×Dic₁₇	C₂³	1	2	yes	—
63	C₂³×Dic₁₇	C₂³	1	12	yes	—
64	C₂²×C₄×D₁₇	—	2	16	no	—
65	C₂²×C₄×D₁₇	—	2	16	no	—
66	C₂²×C₄×D₁₇	—	2	192	no	—
67	C₂²×C₄×D₁₇	C₂³	1	24	yes	—
68	C₂²×C₄×D₁₇	C₂³	1	24	yes	—
69	C₂²×C₄×D₁₇	C₂³	1	64	yes	complemented
70	C₂×C₂²⋊Dic₁₇	C₂³	1	24	yes	—
71	C₂×C₂²⋊Dic₁₇	C₂³	1	48	yes	complemented
72	#10587632	C₂³	1	128	yes	complemented
73	#10587624	C₂³	1	128	yes	complemented
74	#10587623	C₂³	1	128	yes	complemented
75	#10587621	C₂³	1	128	yes	complemented
76	C₄×C₂²⋊D₁₇	C₂³	1	256	yes	complemented
77	C₂×#63227	C₂³	1	48	yes	—
78	#10587612	C₂³	1	64	yes	complemented
79	C₂×C₄⋊Dic₁₇	C₂³	1	24	yes	complemented
80	C₂×#63225	C₂³	1	48	yes	complemented
81	C₂×C₄×Dic₁₇	C₂³	1	24	yes	complemented
82	C₂⁴×C₁₇	—	2	8	no	—
83	C₂⁴×C₁₇	—	2	8	no	—
84	C₂⁴×C₁₇	—	2	16	no	—
85	C₂⁴×C₁₇	C₂×D₄	1	8	yes	—
86	C₂⁴×C₁₇	C₂⁴	1	12	yes	—
87	C₂⁴×C₁₇	C₂⁴	1	6	yes	—
88	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
89	C₂³×D₁₇	—	2	128	no	—
90	C₂³×D₁₇	—	2	48	no	—
91	C₂³×D₁₇	—	2	8	no	—
92	C₂³×D₁₇	—	2	8	no	—
93	C₂³×D₁₇	—	2	96	no	—
94	C₂³×D₁₇	#41	1	16	yes	complemented
95	C₂³×D₁₇	C₂⁴	1	16	yes	—
96	C₂³×D₁₇	C₂⁴	1	12	yes	—
97	#41×C₁₇	—	2	256	no	—
98	C₂×Q₈×C₁₇	—	2	48	no	—
99	C₂×Q₈×C₁₇	C₂⁴	1	16	yes	complemented
100	C₂×D₄×C₁₇	—	2	96	no	—
101	C₂×D₄×C₁₇	—	2	48	no	—
102	C₂×D₄×C₁₇	C₂⁴	1	32	yes	—
103	C₂×D₄×C₁₇	C₂⁴	1	16	yes	complemented
104	C₂²×C₄×C₁₇	—	2	8	no	—
105	C₂²×C₄×C₁₇	—	2	96	no	—
106	C₂²×C₄×C₁₇	C₂×D₄	1	8	yes	—
107	C₂²×C₄×C₁₇	C₂×D₄	1	8	yes	—
108	C₂²×C₄×C₁₇	C₂×D₄	1	96	yes	complemented
109	C₂²×C₄×C₁₇	C₂⁴	1	12	yes	—
110	C₂²×C₄×C₁₇	C₂⁴	1	6	yes	—
111	C₂²×C₄×C₁₇	C₂⁴	1	6	yes	—
112	C₂²×C₄×C₁₇	C₂⁴	1	16	yes	—
113	C₂²×C₄×C₁₇	C₂⁴	1	32	yes	complemented
114	C₂×C₂²⋊D₁₇	—	2	192	no	—
115	C₂×C₂²⋊D₁₇	C₂⁴	1	64	yes	—
116	C₂²×Dic₁₇	—	2	48	no	—
117	C₂²×Dic₁₇	—	2	8	no	—
118	C₂²×Dic₁₇	—	2	16	no	—
119	C₂²×Dic₁₇	C₂⁴	1	12	yes	—
120	C₂²×Dic₁₇	C₂⁴	1	16	yes	—
121	C₂²×Dic₁₇	C₂⁴	1	24	yes	—
122	C₂×C₄×D₁₇	—	2	96	no	—
123	C₂×C₄×D₁₇	—	2	96	no	—
124	C₂×C₄×D₁₇	—	2	256	no	—
125	C₂×C₄×D₁₇	C₂⁴	1	32	yes	—
126	C₂×C₄×D₁₇	C₂⁴	1	32	yes	—
127	C₂²⋊Dic₁₇	C₂⁴	1	32	yes	—
128	C₂²⋊Dic₁₇	C₂⁴	1	64	yes	complemented
129	#63227	C₂⁴	1	64	yes	—
130	C₄⋊Dic₁₇	C₂⁴	1	32	yes	complemented
131	#63225	C₂⁴	1	64	yes	complemented
132	C₄×Dic₁₇	C₂⁴	1	32	yes	complemented
133	C₂²×#525	—	17	1	no	maximal, Sylow
134	C₂³×C₁₇	—	2	32	no	—
135	C₂³×C₁₇	—	2	24	no	—
136	C₂³×C₁₇	—	2	24	no	—
137	C₂³×C₁₇	—	2	48	no	—
138	C₂³×C₁₇	—	4	32	no	—
139	C₂³×C₁₇	C₂²×D₄	1	24	yes	—
140	C₂³×C₁₇	C₂²×D₄	1	4	yes	—
141	C₂³×C₁₇	C₂×#41	1	8	yes	—
142	C₂³×C₁₇	C₂⁵	1	8	yes	—
143	C₂³×C₁₇	C₂⁵	1	4	yes	—
144	C₂³×C₁₇	C₂⁵	1	3	yes	—
145	C₂²×D₁₇	—	2	384	no	—
146	C₂²×D₁₇	—	2	64	no	—
147	C₂²×D₁₇	—	2	32	no	—
148	C₂²×D₁₇	—	2	24	no	—
149	C₂²×D₁₇	—	2	24	no	—
150	C₂²×D₁₇	—	2	64	no	—
151	C₂²×D₁₇	C₂×#41	1	48	yes	complemented
152	C₂²×D₁₇	C₂⁵	1	8	yes	—
153	Q₈×C₁₇	—	2	32	no	—
154	D₄×C₁₇	—	2	64	no	—
155	D₄×C₁₇	—	2	32	no	—
156	C₂×C₄×C₁₇	—	2	24	no	—
157	C₂×C₄×C₁₇	—	2	64	no	—
158	C₂×C₄×C₁₇	C₂²×D₄	1	24	yes	—
159	C₂×C₄×C₁₇	C₂²×D₄	1	24	yes	—
160	C₂×C₄×C₁₇	C₂²×D₄	1	64	yes	complemented
161	C₂×C₄×C₁₇	C₂⁵	1	8	yes	—
162	C₂×C₄×C₁₇	C₂⁵	1	4	yes	—
163	C₂×C₄×C₁₇	C₂⁵	1	4	yes	—
164	C₂²⋊D₁₇	—	2	128	no	—
165	C₂×Dic₁₇	—	2	32	no	—
166	C₂×Dic₁₇	—	2	24	no	—
167	C₂×Dic₁₇	—	2	48	no	—
168	C₂×Dic₁₇	C₂⁵	1	16	yes	—
169	C₂×Dic₁₇	C₂⁵	1	8	yes	—
170	C₄×D₁₇	—	2	64	no	—
171	C₄×D₁₇	—	2	64	no	—
172	C₂³×#41	D₁₇	1	1	yes	characteristic, complemented
173	C₂⁵×C₄	—	17	1	no	—
174	C₂×#525	—	17	48	no	—
175	C₂²×#123	—	17	2	no	—
176	C₂²×C₂²⋊Q₈	—	17	2	no	—
177	C₂²×#121	—	17	2	no	—
178	C₂²×#120	—	17	2	no	—
179	C₂²×C₄×D₄	—	17	4	no	—
180	C₂²×#117	—	17	1	no	—
181	C₂²×C₁₇	—	2	8	no	—
182	C₂²×C₁₇	—	2	48	no	—
183	C₂²×C₁₇	—	2	8	no	—
184	C₂²×C₁₇	—	2	16	no	—
185	C₂²×C₁₇	—	4	48	no	—
186	C₂²×C₁₇	#525	1	16	yes	complemented
187	C₂²×C₁₇	C₂³×D₄	1	8	yes	—
188	C₂²×C₁₇	C₂³×D₄	1	6	yes	—
189	C₂²×C₁₇	C₂²×#41	1	12	yes	—
190	C₂²×C₁₇	C₂⁶	1	1	yes	characteristic
191	C₂×D₁₇	—	2	128	no	—
192	C₂×D₁₇	—	2	8	no	—
193	C₂×D₁₇	—	2	8	no	—
194	C₂×D₁₇	—	2	96	no	—
195	C₂×D₁₇	C₂²×#41	1	16	yes	complemented
196	C₄×C₁₇	—	2	8	no	—
197	C₄×C₁₇	C₂³×D₄	1	8	yes	—
198	C₄×C₁₇	C₂³×D₄	1	8	yes	—
199	Dic₁₇	—	2	8	no	—
200	Dic₁₇	—	2	16	no	—
201	C₂⁶	—	17	1	no	—
202	C₂²×#41	—	2	16	no	—
203	C₂²×#41	C₂×D₁₇	1	24	yes	complemented
204	C₂³×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
205	C₂³×D₄	—	17	4	no	—
206	C₂³×D₄	C₂×D₁₇	1	2	yes	—
207	C₂³×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
208	C₂⁴×C₄	—	17	1	no	—
209	C₂⁴×C₄	—	17	2	no	—
210	C₂⁴×C₄	—	17	24	no	—
211	C₂⁴×C₄	—	17	2	no	—
212	C₂⁴×C₄	—	34	16	no	—
213	C₂⁴×C₄	C₂×D₁₇	1	1	yes	characteristic
214	C₂⁴×C₄	C₂×D₁₇	1	2	yes	complemented
215	#525	—	17	256	no	—
216	C₂×#123	—	17	48	no	—
217	C₂×C₂²⋊Q₈	—	17	48	no	—
218	C₂×#121	—	17	48	no	—
219	C₂×#120	—	17	48	no	—
220	C₂×C₄×D₄	—	17	96	no	—
221	C₂×#117	—	17	24	no	—
222	C₂²×C₄⋊C₄	—	17	4	no	—
223	C₂²×C₄⋊C₄	—	17	2	no	—
224	C₂²×C₂²⋊C₄	—	17	2	no	—
225	C₂²×C₂²⋊C₄	—	17	4	no	—
226	C₂²×C₂²⋊C₄	—	17	4	no	—
227	C₂²×C₄²	—	17	2	no	—
228	C₂×C₁₇	—	2	8	no	—
229	C₂×C₁₇	—	4	8	no	—
230	C₂×C₁₇	C₂×#525	1	12	yes	complemented
231	C₂×C₁₇	C₂⁴×D₄	1	1	yes	characteristic
232	C₂×C₁₇	C₂³×#41	1	2	yes	—
233	D₁₇	—	2	16	no	—
234	C₂⁵	—	17	2	no	—
235	C₂⁵	—	17	12	no	—
236	C₂⁵	—	34	16	no	—
237	C₂⁵	—	34	8	no	—
238	C₂⁵	C₂²×D₁₇	1	2	yes	—
239	C₂⁵	C₂²×D₁₇	1	1	yes	characteristic
240	C₂×#41	—	2	192	no	—
241	C₂×#41	C₂²×D₁₇	1	64	yes	complemented
242	C₂²×Q₈	—	2	8	no	—
243	C₂²×Q₈	C₂²×D₁₇	1	12	yes	complemented
244	C₂²×D₄	—	2	16	no	—
245	C₂²×D₄	—	2	8	no	—
246	C₂²×D₄	—	17	48	no	—
247	C₂²×D₄	—	34	32	no	—
248	C₂²×D₄	C₂²×D₁₇	1	24	yes	—
249	C₂²×D₄	C₂²×D₁₇	1	12	yes	complemented
250	C₂³×C₄	—	2	16	no	—
251	C₂³×C₄	—	17	4	no	—
252	C₂³×C₄	—	17	2	no	—
253	C₂³×C₄	—	17	12	no	—
254	C₂³×C₄	—	17	24	no	—
255	C₂³×C₄	—	17	24	no	—
256	C₂³×C₄	—	17	64	no	—
257	C₂³×C₄	—	34	8	no	—
258	C₂³×C₄	—	34	16	no	—
259	C₂³×C₄	—	34	16	no	—
260	C₂³×C₄	—	34	192	no	—
261	C₂³×C₄	C₂²⋊D₁₇	1	16	yes	complemented
262	C₂³×C₄	C₂²×D₁₇	1	2	yes	—
263	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
264	C₂³×C₄	C₂²×D₁₇	1	12	yes	—
265	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
266	C₂³×C₄	C₂²×D₁₇	1	24	yes	complemented
267	#123	—	17	128	no	—
268	C₂²⋊Q₈	—	17	128	no	—
269	#121	—	17	128	no	—
270	#120	—	17	128	no	—
271	C₄×D₄	—	17	256	no	—
272	#117	—	17	64	no	—
273	C₂×C₄⋊C₄	—	17	24	no	—
274	C₂×C₄⋊C₄	—	17	48	no	—
275	C₂×C₂²⋊C₄	—	17	24	no	—
276	C₂×C₂²⋊C₄	—	17	48	no	—
277	C₂×C₂²⋊C₄	—	17	48	no	—
278	C₂×C₄²	—	17	24	no	—
279	C₁₇	C₂²×#525	1	1	yes	characteristic, complemented, Sylow
280	C₂⁴	—	2	8	no	—
281	C₂⁴	—	2	16	no	—
282	C₂⁴	—	2	8	no	—
283	C₂⁴	—	17	16	no	—
284	C₂⁴	—	17	12	no	—
285	C₂⁴	—	17	16	no	—
286	C₂⁴	—	34	96	no	—
287	C₂⁴	—	34	128	no	—
288	C₂⁴	—	34	8	no	—
289	C₂⁴	—	34	48	no	—
290	C₂⁴	—	34	8	no	—
291	C₂⁴	C₂×C₂²⋊D₁₇	1	8	yes	—
292	C₂⁴	C₂³×D₁₇	1	12	yes	—
293	C₂⁴	C₂³×D₁₇	1	6	yes	—
294	C₂⁴	C₂³×D₁₇	1	1	yes	characteristic
295	#41	—	2	256	no	—
296	C₂×Q₈	—	2	48	no	—
297	C₂×Q₈	C₂³×D₁₇	1	16	yes	complemented
298	C₂×D₄	—	2	96	no	—
299	C₂×D₄	—	2	48	no	—
300	C₂×D₄	—	17	64	no	—
301	C₂×D₄	—	34	192	no	—
302	C₂×D₄	C₂³×D₁₇	1	32	yes	—
303	C₂×D₄	C₂³×D₁₇	1	16	yes	complemented
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	2	96	no	—
306	C₂²×C₄	—	17	24	no	—
307	C₂²×C₄	—	17	12	no	—
308	C₂²×C₄	—	17	16	no	—
309	C₂²×C₄	—	17	32	no	—
310	C₂²×C₄	—	17	32	no	—
311	C₂²×C₄	—	34	16	no	—
312	C₂²×C₄	—	34	48	no	—
313	C₂²×C₄	—	34	8	no	—
314	C₂²×C₄	—	34	96	no	—
315	C₂²×C₄	—	34	96	no	—
316	C₂²×C₄	—	34	256	no	—
317	C₂²×C₄	C₂×C₂²⋊D₁₇	1	8	yes	—
318	C₂²×C₄	C₂×C₂²⋊D₁₇	1	8	yes	—
319	C₂²×C₄	C₂×C₂²⋊D₁₇	1	96	yes	complemented
320	C₂²×C₄	C₂³×D₁₇	1	12	yes	—
321	C₂²×C₄	C₂³×D₁₇	1	6	yes	—
322	C₂²×C₄	C₂³×D₁₇	1	6	yes	—
323	C₂²×C₄	C₂³×D₁₇	1	16	yes	—
324	C₂²×C₄	C₂³×D₁₇	1	32	yes	complemented
325	C₄⋊C₄	—	17	32	no	—
326	C₄⋊C₄	—	17	64	no	—
327	C₂²⋊C₄	—	17	32	no	—
328	C₂²⋊C₄	—	17	64	no	—
329	C₂²⋊C₄	—	17	64	no	—
330	C₄²	—	17	32	no	—
331	C₂³	—	2	32	no	—
332	C₂³	—	2	24	no	—
333	C₂³	—	2	24	no	—
334	C₂³	—	2	48	no	—
335	C₂³	—	4	32	no	—
336	C₂³	—	17	48	no	—
337	C₂³	—	17	8	no	—
338	C₂³	—	34	64	no	—
339	C₂³	—	34	384	no	—
340	C₂³	—	34	64	no	—
341	C₂³	—	34	32	no	—
342	C₂³	—	34	24	no	—
343	C₂³	—	34	24	no	—
344	C₂³	#41×D₁₇	1	8	yes	—
345	C₂³	C₂²×C₂²⋊D₁₇	1	24	yes	—
346	C₂³	C₂²×C₂²⋊D₁₇	1	4	yes	—
347	C₂³	C₂⁴×D₁₇	1	8	yes	—
348	C₂³	C₂⁴×D₁₇	1	4	yes	—
349	C₂³	C₂⁴×D₁₇	1	3	yes	—
350	Q₈	—	2	32	no	—
351	D₄	—	2	64	no	—
352	D₄	—	2	32	no	—
353	D₄	—	34	128	no	—
354	C₂×C₄	—	2	24	no	—
355	C₂×C₄	—	2	64	no	—
356	C₂×C₄	—	17	16	no	—
357	C₂×C₄	—	17	8	no	—
358	C₂×C₄	—	34	32	no	—
359	C₂×C₄	—	34	24	no	—
360	C₂×C₄	—	34	48	no	—
361	C₂×C₄	—	34	64	no	—
362	C₂×C₄	—	34	64	no	—
363	C₂×C₄	C₂²×C₂²⋊D₁₇	1	24	yes	—
364	C₂×C₄	C₂²×C₂²⋊D₁₇	1	24	yes	—
365	C₂×C₄	C₂²×C₂²⋊D₁₇	1	64	yes	complemented
366	C₂×C₄	C₂⁴×D₁₇	1	8	yes	—
367	C₂×C₄	C₂⁴×D₁₇	1	4	yes	—
368	C₂×C₄	C₂⁴×D₁₇	1	4	yes	—
369	C₂²	—	2	48	no	—
370	C₂²	—	2	8	no	—
371	C₂²	—	2	8	no	—
372	C₂²	—	2	16	no	—
373	C₂²	—	4	48	no	—
374	C₂²	—	17	16	no	—
375	C₂²	—	34	128	no	—
376	C₂²	—	34	96	no	—
377	C₂²	—	34	8	no	—
378	C₂²	—	34	8	no	—
379	C₂²	#11763316	1	16	yes	direct product factor
380	C₂²	C₂³×C₂²⋊D₁₇	1	8	yes	—
381	C₂²	C₂³×C₂²⋊D₁₇	1	6	yes	—
382	C₂²	C₂×#41×D₁₇	1	12	yes	—
383	C₂²	C₂⁵×D₁₇	1	1	yes	characteristic
384	C₄	—	2	8	no	—
385	C₄	—	34	8	no	—
386	C₄	—	34	16	no	—
387	C₄	C₂³×C₂²⋊D₁₇	1	8	yes	—
388	C₄	C₂³×C₂²⋊D₁₇	1	8	yes	—
389	C₂	—	2	8	no	—
390	C₂	—	4	8	no	—
391	C₂	—	34	16	no	—
392	C₂	C₂×#11763316	1	12	yes	direct product factor
393	C₂	C₂⁴×C₂²⋊D₁₇	1	1	yes	characteristic
394	C₂	C₂²×#41×D₁₇	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₁₇
commutator, cosocle	C₂²×C₁₇	C₂⁶
Frattini	C₂²	C₂⁵×D₁₇
Fitting	C₂³×#41×C₁₇	C₂
socle	C₂⁴×C₁₇	C₂⁴
hypercenter	C₂³×#41	D₁₇
hypocenter	C₁₇	C₂²×#525
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₄×D₁₇	C₂	semidirect
2. C₂×#11763316	C₂	direct (N × H)
3. C₂²×#10587621	C₂	semidirect
4. C₂²×#10587632	C₂	semidirect
5. C₂²×#10587624	C₂	semidirect
6. C₂²×#10587623	C₂	semidirect
7. C₂²×C₄×C₂²⋊D₁₇	C₂	semidirect
8. C₂²×#10587612	C₂	semidirect
9. C₂³×#41×C₁₇	C₂	semidirect
16. C₂³×C₄×D₁₇	C₂²	semidirect
17. #11763316	C₂²	direct (N × H)
18. C₂×#10587621	C₂²	semidirect
19. C₂×#10587632	C₂²	semidirect
20. C₂×#10587624	C₂²	semidirect
21. C₂×#10587623	C₂²	semidirect
22. C₂×C₄×C₂²⋊D₁₇	C₂²	semidirect
23. C₂×#10587612	C₂²	semidirect
24. C₂²×C₄⋊Dic₁₇	C₂²	semidirect
25. C₂²×#63225	C₂²	semidirect
27. C₂²×C₂²⋊Dic₁₇	C₂²	semidirect
29. C₂²×C₄×Dic₁₇	C₂²	semidirect
31. C₂²×#41×C₁₇	C₂²	semidirect
32. C₂³×Q₈×C₁₇	C₂²	semidirect
34. C₂³×D₄×C₁₇	C₂²	semidirect
36. C₂⁴×C₄×C₁₇	C₂²	semidirect
44. C₂×#41×C₁₇	C₂³	semidirect
46. C₂²×Q₈×C₁₇	C₂³	semidirect
50. C₂²×D₄×C₁₇	C₂³	semidirect
52. C₂³×C₄×C₁₇	D₄	semidirect
57. C₂³×C₄×C₁₇	C₂³	semidirect
69. C₂²×C₄×D₁₇	C₂³	semidirect
71. C₂×C₂²⋊Dic₁₇	C₂³	semidirect
72. #10587632	C₂³	semidirect
73. #10587624	C₂³	semidirect
74. #10587623	C₂³	semidirect
75. #10587621	C₂³	semidirect
76. C₄×C₂²⋊D₁₇	C₂³	semidirect
78. #10587612	C₂³	semidirect
79. C₂×C₄⋊Dic₁₇	C₂³	semidirect
80. C₂×#63225	C₂³	semidirect
81. C₂×C₄×Dic₁₇	C₂³	semidirect
94. C₂³×D₁₇	#41	semidirect
99. C₂×Q₈×C₁₇	C₂⁴	semidirect
103. C₂×D₄×C₁₇	C₂⁴	semidirect
108. C₂²×C₄×C₁₇	C₂×D₄	semidirect
113. C₂²×C₄×C₁₇	C₂⁴	semidirect
128. C₂²⋊Dic₁₇	C₂⁴	semidirect
130. C₄⋊Dic₁₇	C₂⁴	semidirect
131. #63225	C₂⁴	semidirect
132. C₄×Dic₁₇	C₂⁴	semidirect
151. C₂²×D₁₇	C₂×#41	semidirect
160. C₂×C₄×C₁₇	C₂²×D₄	semidirect
172. C₂³×#41	D₁₇	semidirect
186. C₂²×C₁₇	#525	semidirect
195. C₂×D₁₇	C₂²×#41	semidirect
203. C₂²×#41	C₂×D₁₇	semidirect
204. C₂³×Q₈	C₂×D₁₇	semidirect
207. C₂³×D₄	C₂×D₁₇	semidirect
214. C₂⁴×C₄	C₂×D₁₇	semidirect
230. C₂×C₁₇	C₂×#525	semidirect
241. C₂×#41	C₂²×D₁₇	semidirect
243. C₂²×Q₈	C₂²×D₁₇	semidirect
249. C₂²×D₄	C₂²×D₁₇	semidirect
261. C₂³×C₄	C₂²⋊D₁₇	semidirect
266. C₂³×C₄	C₂²×D₁₇	semidirect
279. C₁₇	C₂²×#525	semidirect
297. C₂×Q₈	C₂³×D₁₇	semidirect
303. C₂×D₄	C₂³×D₁₇	semidirect
319. C₂²×C₄	C₂×C₂²⋊D₁₇	semidirect
324. C₂²×C₄	C₂³×D₁₇	semidirect
365. C₂×C₄	C₂²×C₂²⋊D₁₇	semidirect
379. C₂²	#11763316	direct (N × H)
392. C₂	C₂×#11763316	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₄×D₁₇	2
C₂×#11763316	2
C₂²×#10587621	2
C₂²×#10587632	2
C₂²×#10587624	2
C₂²×#10587623	2
C₂²×C₄×C₂²⋊D₁₇	2
C₂²×#10587612	2
C₂³×#41×C₁₇	2
C₂²×#525	17

Subgroups — C22×#11763316 #17940977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11763316 #17940977