Subgroups — C₂²×C₄×#63252 #17940898

Order 4352.

12878 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#63252	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#63252	C₂	1	48	yes	maximal, direct product factor
3	C₂²×C₄×Dic₃₄	C₂	1	2	yes	maximal, complemented
4	C₂²×C₄×D₆₈	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄×C₂²⋊D₁₇	C₂	1	4	yes	maximal, complemented
6	C₂²×#10587612	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#10587558	C₂	1	2	yes	maximal, complemented
8	C₂²×C₄²×D₁₇	C₂	1	2	yes	maximal, complemented
9	C₂³×C₄²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#63252	C₄	1	32	yes	direct product factor
11	C₂²×#63252	C₂²	1	24	yes	—
12	C₂³×Dic₃₄	C₂²	1	1	yes	characteristic
13	C₂³×D₆₈	C₂²	1	1	yes	characteristic
14	C₂³×C₂²⋊D₁₇	C₂²	1	2	yes	—
15	C₂³×C₄×D₁₇	C₂²	1	4	yes	—
16	C₂³×C₄×D₁₇	C₂²	1	2	yes	—
17	C₄×#63252	C₂²	1	256	yes	direct product factor
18	C₂×C₄×Dic₃₄	C₂²	1	48	yes	complemented
19	C₂×C₄×D₆₈	C₂²	1	48	yes	complemented
20	C₂×C₄×C₂²⋊D₁₇	C₂²	1	96	yes	complemented
21	C₂×#10587612	C₂²	1	24	yes	complemented
22	C₂×#10587558	C₂²	1	48	yes	complemented
23	C₂²×C₄⋊Dic₁₇	C₂²	1	2	yes	—
24	C₂²×#63225	C₂²	1	4	yes	—
25	C₂²×C₂²⋊Dic₁₇	C₂²	1	2	yes	—
26	C₂²×#63227	C₂²	1	4	yes	—
27	C₂²×C₄×Dic₁₇	C₂²	1	2	yes	—
28	C₂²×C₄×Dic₁₇	C₂²	1	4	yes	—
29	C₂×C₄²×D₁₇	C₂²	1	48	yes	complemented
30	C₂⁴×C₄×C₁₇	C₂²	1	2	yes	—
31	C₂⁴×C₄×C₁₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₇	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₇	C₂²	1	24	yes	complemented
36	C₂⁵×C₁₇	C₂³	1	1	yes	characteristic
37	C₂⁴×D₁₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₇	—	2	16	no	—
39	C₂³×C₄×C₁₇	C₂×C₄	1	16	yes	complemented
40	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₇	C₂³	1	24	yes	—
42	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₇	C₂³	1	12	yes	—
45	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
46	C₂²×C₂²⋊D₁₇	C₂×C₄	1	32	yes	complemented
47	C₂²×C₂²⋊D₁₇	C₂³	1	24	yes	—
48	C₂³×Dic₁₇	C₂³	1	4	yes	—
49	C₂³×Dic₁₇	C₂³	1	2	yes	—
50	C₂×#63252	C₂×C₄	1	384	yes	direct product factor
51	C₂×#63252	C₂³	1	64	yes	—
52	C₂²×D₆₈	C₂×C₄	1	16	yes	complemented
53	C₂²×D₆₈	C₂³	1	12	yes	—
54	C₂²×C₄×D₁₇	—	2	32	no	—
55	C₂²×C₄×D₁₇	C₂×C₄	1	32	yes	complemented
56	C₂²×C₄×D₁₇	C₂³	1	48	yes	—
57	C₂²×C₄×D₁₇	C₂³	1	24	yes	—
58	C₂²×Dic₃₄	C₂×C₄	1	16	yes	complemented
59	C₂²×Dic₃₄	C₂³	1	12	yes	—
60	C₂×C₄²×C₁₇	C₂³	1	12	yes	—
61	C₂×C₄²×C₁₇	C₂³	1	12	yes	—
62	C₂×C₄²×C₁₇	C₂³	1	24	yes	—
63	C₂×C₄²×C₁₇	C₂³	1	64	yes	complemented
64	C₂×C₂²⋊Dic₁₇	C₂³	1	24	yes	—
65	C₄×C₂²⋊D₁₇	C₂³	1	256	yes	complemented
66	C₂×#63227	C₂³	1	48	yes	—
67	#10587612	C₂³	1	64	yes	complemented
68	C₂×C₄⋊Dic₁₇	C₂³	1	24	yes	—
69	C₂×#63225	C₂³	1	48	yes	—
70	C₂×C₄×Dic₁₇	C₂³	1	24	yes	—
71	C₂×C₄×Dic₁₇	C₂³	1	48	yes	—
72	C₄×D₆₈	C₂³	1	128	yes	complemented
73	#10587558	C₂³	1	128	yes	complemented
74	C₄²×D₁₇	C₂³	1	128	yes	complemented
75	C₄×Dic₃₄	C₂³	1	128	yes	complemented
76	C₂⁴×C₁₇	—	2	8	no	—
77	C₂⁴×C₁₇	C₂²×C₄	1	8	yes	—
78	C₂⁴×C₁₇	C₂⁴	1	6	yes	—
79	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
80	C₂³×D₁₇	—	2	16	no	—
81	C₂³×D₁₇	C₂²×C₄	1	16	yes	—
82	C₂³×D₁₇	C₂⁴	1	12	yes	—
83	C₂²×C₄×C₁₇	—	2	8	no	—
84	C₂²×C₄×C₁₇	—	2	96	no	—
85	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	—
86	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	—
87	C₂²×C₄×C₁₇	C₂²×C₄	1	96	yes	complemented
88	C₂²×C₄×C₁₇	#41	1	16	yes	complemented
89	C₂²×C₄×C₁₇	C₂⁴	1	12	yes	—
90	C₂²×C₄×C₁₇	C₂⁴	1	32	yes	—
91	C₂²×C₄×C₁₇	C₂⁴	1	6	yes	—
92	C₂²×C₄×C₁₇	C₂⁴	1	6	yes	—
93	C₂²×C₄×C₁₇	C₂⁴	1	16	yes	—
94	C₂²×C₄×C₁₇	C₂⁴	1	12	yes	—
95	C₂×C₂²⋊D₁₇	C₂²×C₄	1	192	yes	complemented
96	C₂×C₂²⋊D₁₇	C₂⁴	1	32	yes	—
97	C₂²×Dic₁₇	—	2	16	no	—
98	C₂²×Dic₁₇	C₂²×C₄	1	16	yes	—
99	C₂²×Dic₁₇	C₂⁴	1	24	yes	—
100	C₂²×Dic₁₇	C₂⁴	1	12	yes	—
101	#63252	C₂²×C₄	1	512	yes	direct product factor
102	C₂×D₆₈	C₂²×C₄	1	96	yes	complemented
103	C₂×D₆₈	C₂⁴	1	16	yes	—
104	C₂×C₄×D₁₇	—	2	192	no	—
105	C₂×C₄×D₁₇	C₂²×C₄	1	192	yes	complemented
106	C₂×C₄×D₁₇	C₂⁴	1	64	yes	—
107	C₂×C₄×D₁₇	C₂⁴	1	32	yes	—
108	C₂×Dic₃₄	C₂²×C₄	1	96	yes	complemented
109	C₂×Dic₃₄	C₂⁴	1	16	yes	—
110	C₄²×C₁₇	C₂⁴	1	32	yes	—
111	C₄²×C₁₇	C₂⁴	1	16	yes	—
112	C₄²×C₁₇	C₂⁴	1	16	yes	—
113	C₂²⋊Dic₁₇	C₂⁴	1	32	yes	—
114	#63227	C₂⁴	1	64	yes	—
115	C₄⋊Dic₁₇	C₂⁴	1	32	yes	—
116	#63225	C₂⁴	1	64	yes	—
117	C₄×Dic₁₇	C₂⁴	1	64	yes	—
118	C₄×Dic₁₇	C₂⁴	1	32	yes	—
119	C₂²×C₄×#41	—	17	1	no	maximal, Sylow
120	C₂³×C₁₇	—	2	32	no	—
121	C₂³×C₁₇	—	2	24	no	—
122	C₂³×C₁₇	C₂³×C₄	1	24	yes	—
123	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
124	C₂³×C₁₇	C₂×#41	1	8	yes	—
125	C₂³×C₁₇	C₂⁵	1	4	yes	—
126	C₂³×C₁₇	C₂⁵	1	3	yes	—
127	C₂²×D₁₇	—	2	64	no	—
128	C₂²×D₁₇	—	2	48	no	—
129	C₂²×D₁₇	C₂³×C₄	1	48	yes	—
130	C₂²×D₁₇	C₂⁵	1	8	yes	—
131	C₂×C₄×C₁₇	—	2	24	no	—
132	C₂×C₄×C₁₇	—	2	64	no	—
133	C₂×C₄×C₁₇	C₂³×C₄	1	24	yes	—
134	C₂×C₄×C₁₇	C₂³×C₄	1	24	yes	—
135	C₂×C₄×C₁₇	C₂³×C₄	1	64	yes	complemented
136	C₂×C₄×C₁₇	C₂×#41	1	48	yes	complemented
137	C₂×C₄×C₁₇	C₂⁵	1	8	yes	—
138	C₂×C₄×C₁₇	C₂⁵	1	4	yes	—
139	C₂×C₄×C₁₇	C₂⁵	1	4	yes	—
140	C₂×C₄×C₁₇	C₂⁵	1	8	yes	—
141	C₂²⋊D₁₇	C₂³×C₄	1	128	yes	complemented
142	C₂×Dic₁₇	—	2	48	no	—
143	C₂×Dic₁₇	C₂³×C₄	1	48	yes	—
144	C₂×Dic₁₇	C₂⁵	1	16	yes	—
145	C₂×Dic₁₇	C₂⁵	1	8	yes	—
146	D₆₈	C₂³×C₄	1	64	yes	complemented
147	C₄×D₁₇	—	2	128	no	—
148	C₄×D₁₇	C₂³×C₄	1	128	yes	complemented
149	Dic₃₄	C₂³×C₄	1	64	yes	complemented
150	C₂³×#41	—	17	1	no	—
151	C₂×C₄×#41	—	17	48	no	—
152	C₂²×C₄×Q₈	—	17	2	no	—
153	C₂²×C₄×D₄	—	17	2	no	—
154	C₂²×C₄×D₄	—	17	4	no	—
155	C₂²×#117	—	17	2	no	—
156	C₂²×#117	—	17	1	no	—
157	C₂³×C₄²	—	17	2	no	—
158	C₂³×C₄²	D₁₇	1	1	yes	characteristic, complemented
159	C₂²×C₁₇	—	2	8	no	—
160	C₂²×C₁₇	—	2	48	no	—
161	C₂²×C₁₇	C₄×#41	1	16	yes	complemented
162	C₂²×C₁₇	C₂⁴×C₄	1	8	yes	—
163	C₂²×C₁₇	C₂⁴×C₄	1	6	yes	—
164	C₂²×C₁₇	C₂²×#41	1	12	yes	—
165	C₂²×C₁₇	C₂⁶	1	1	yes	characteristic
166	C₂×D₁₇	—	2	16	no	—
167	C₂×D₁₇	—	2	96	no	—
168	C₂×D₁₇	C₂⁴×C₄	1	16	yes	—
169	C₄×C₁₇	—	2	8	no	—
170	C₄×C₁₇	C₂⁴×C₄	1	8	yes	—
171	C₄×C₁₇	C₂⁴×C₄	1	8	yes	—
172	C₄×C₁₇	C₂²×#41	1	16	yes	complemented
173	Dic₁₇	—	2	16	no	—
174	Dic₁₇	C₂⁴×C₄	1	16	yes	—
175	C₂²×#41	—	17	32	no	—
176	C₂²×#41	—	17	24	no	—
177	C₂³×Q₈	—	17	1	no	—
178	C₂³×D₄	—	17	2	no	—
179	C₂³×D₄	—	17	1	no	—
180	C₂⁴×C₄	—	17	2	no	—
181	C₂⁴×C₄	—	17	4	no	—
182	C₂⁴×C₄	C₂×D₁₇	1	2	yes	—
183	C₂⁴×C₄	C₂×D₁₇	1	1	yes	characteristic
184	C₄×#41	—	17	256	no	—
185	C₂×C₄×Q₈	—	17	48	no	—
186	C₂×C₄×D₄	—	17	96	no	—
187	C₂×C₄×D₄	—	17	48	no	—
188	C₂×#117	—	17	24	no	—
189	C₂×#117	—	17	48	no	—
190	C₂²×C₄⋊C₄	—	17	4	no	—
191	C₂²×C₄⋊C₄	—	17	2	no	—
192	C₂²×C₂²⋊C₄	—	17	2	no	—
193	C₂²×C₂²⋊C₄	—	17	4	no	—
194	C₂²×C₄²	—	17	2	no	—
195	C₂²×C₄²	—	17	4	no	—
196	C₂²×C₄²	—	17	48	no	—
197	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
198	C₂²×C₄²	C₂×D₁₇	1	2	yes	—
199	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
200	C₂²×C₄²	C₂×D₁₇	1	24	yes	complemented
201	C₂×C₁₇	—	2	8	no	—
202	C₂×C₁₇	C₂×C₄×#41	1	12	yes	complemented
203	C₂×C₁₇	C₂⁵×C₄	1	1	yes	characteristic
204	C₂×C₁₇	C₂³×#41	1	2	yes	—
205	D₁₇	—	2	16	no	—
206	C₂⁵	—	17	2	no	—
207	C₂⁵	C₂²×D₁₇	1	1	yes	characteristic
208	C₂×#41	—	17	384	no	—
209	C₂×#41	—	17	64	no	—
210	C₂²×Q₈	—	17	16	no	—
211	C₂²×Q₈	—	17	12	no	—
212	C₂²×D₄	—	17	32	no	—
213	C₂²×D₄	—	17	24	no	—
214	C₂²×D₄	—	17	16	no	—
215	C₂²×D₄	—	17	12	no	—
216	C₂³×C₄	—	2	16	no	—
217	C₂³×C₄	—	17	2	no	—
218	C₂³×C₄	—	17	32	no	—
219	C₂³×C₄	—	17	24	no	—
220	C₂³×C₄	—	17	4	no	—
221	C₂³×C₄	—	17	48	no	—
222	C₂³×C₄	—	34	32	no	—
223	C₂³×C₄	C₄×D₁₇	1	16	yes	complemented
224	C₂³×C₄	C₂²×D₁₇	1	2	yes	—
225	C₂³×C₄	C₂²×D₁₇	1	24	yes	—
226	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
227	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
228	C₂³×C₄	C₂²×D₁₇	1	12	yes	—
229	C₂³×C₄	C₂²×D₁₇	1	2	yes	—
230	C₄×Q₈	—	17	128	no	—
231	C₄×D₄	—	17	256	no	—
232	C₄×D₄	—	17	128	no	—
233	#117	—	17	64	no	—
234	#117	—	17	128	no	—
235	C₂×C₄⋊C₄	—	17	48	no	—
236	C₂×C₄⋊C₄	—	17	24	no	—
237	C₂×C₂²⋊C₄	—	17	24	no	—
238	C₂×C₂²⋊C₄	—	17	48	no	—
239	C₂×C₄²	—	17	24	no	—
240	C₂×C₄²	—	17	48	no	—
241	C₂×C₄²	—	17	128	no	—
242	C₂×C₄²	C₂²×D₁₇	1	12	yes	—
243	C₂×C₄²	C₂²×D₁₇	1	24	yes	—
244	C₂×C₄²	C₂²×D₁₇	1	12	yes	—
245	C₂×C₄²	C₂²×D₁₇	1	64	yes	complemented
246	C₁₇	C₂²×C₄×#41	1	1	yes	characteristic, complemented, Sylow
247	C₂⁴	—	2	8	no	—
248	C₂⁴	—	17	16	no	—
249	C₂⁴	—	17	12	no	—
250	C₂⁴	—	34	16	no	—
251	C₂⁴	C₂×C₄×D₁₇	1	8	yes	—
252	C₂⁴	C₂³×D₁₇	1	6	yes	—
253	C₂⁴	C₂³×D₁₇	1	1	yes	characteristic
254	#41	—	17	512	no	—
255	C₂×Q₈	—	17	96	no	—
256	C₂×Q₈	—	17	16	no	—
257	C₂×D₄	—	17	192	no	—
258	C₂×D₄	—	17	32	no	—
259	C₂×D₄	—	17	96	no	—
260	C₂×D₄	—	17	16	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	96	no	—
263	C₂²×C₄	—	17	16	no	—
264	C₂²×C₄	—	17	12	no	—
265	C₂²×C₄	—	17	192	no	—
266	C₂²×C₄	—	17	32	no	—
267	C₂²×C₄	—	17	24	no	—
268	C₂²×C₄	—	17	64	no	—
269	C₂²×C₄	—	34	16	no	—
270	C₂²×C₄	—	34	192	no	—
271	C₂²×C₄	C₂×C₄×D₁₇	1	8	yes	—
272	C₂²×C₄	C₂×C₄×D₁₇	1	8	yes	—
273	C₂²×C₄	C₂×C₄×D₁₇	1	96	yes	complemented
274	C₂²×C₄	#63252	1	16	yes	direct product factor
275	C₂²×C₄	C₂³×D₁₇	1	12	yes	—
276	C₂²×C₄	C₂³×D₁₇	1	32	yes	—
277	C₂²×C₄	C₂³×D₁₇	1	6	yes	—
278	C₂²×C₄	C₂³×D₁₇	1	6	yes	—
279	C₂²×C₄	C₂³×D₁₇	1	16	yes	—
280	C₂²×C₄	C₂³×D₁₇	1	12	yes	—
281	C₄⋊C₄	—	17	64	no	—
282	C₄⋊C₄	—	17	32	no	—
283	C₂²⋊C₄	—	17	32	no	—
284	C₂²⋊C₄	—	17	64	no	—
285	C₄²	—	17	32	no	—
286	C₄²	—	17	64	no	—
287	C₄²	C₂³×D₁₇	1	16	yes	—
288	C₄²	C₂³×D₁₇	1	16	yes	—
289	C₄²	C₂³×D₁₇	1	32	yes	—
290	C₂³	—	2	32	no	—
291	C₂³	—	2	24	no	—
292	C₂³	—	17	48	no	—
293	C₂³	—	17	8	no	—
294	C₂³	—	34	64	no	—
295	C₂³	—	34	48	no	—
296	C₂³	C₂²×C₄×D₁₇	1	24	yes	—
297	C₂³	C₂²×C₄×D₁₇	1	4	yes	—
298	C₂³	C₂×#63252	1	8	yes	—
299	C₂³	C₂⁴×D₁₇	1	4	yes	—
300	C₂³	C₂⁴×D₁₇	1	3	yes	—
301	Q₈	—	17	64	no	—
302	D₄	—	17	128	no	—
303	D₄	—	17	64	no	—
304	C₂×C₄	—	2	24	no	—
305	C₂×C₄	—	2	64	no	—
306	C₂×C₄	—	17	48	no	—
307	C₂×C₄	—	17	8	no	—
308	C₂×C₄	—	17	128	no	—
309	C₂×C₄	—	17	16	no	—
310	C₂×C₄	—	34	48	no	—
311	C₂×C₄	—	34	128	no	—
312	C₂×C₄	C₂²×C₄×D₁₇	1	24	yes	—
313	C₂×C₄	C₂²×C₄×D₁₇	1	24	yes	—
314	C₂×C₄	C₂²×C₄×D₁₇	1	64	yes	complemented
315	C₂×C₄	C₂×#63252	1	48	yes	direct product factor
316	C₂×C₄	C₂⁴×D₁₇	1	8	yes	—
317	C₂×C₄	C₂⁴×D₁₇	1	4	yes	—
318	C₂×C₄	C₂⁴×D₁₇	1	4	yes	—
319	C₂×C₄	C₂⁴×D₁₇	1	8	yes	—
320	C₂²	—	2	48	no	—
321	C₂²	—	2	8	no	—
322	C₂²	—	17	16	no	—
323	C₂²	—	34	96	no	—
324	C₂²	—	34	16	no	—
325	C₂²	C₄×#63252	1	16	yes	direct product factor
326	C₂²	C₂³×C₄×D₁₇	1	8	yes	—
327	C₂²	C₂³×C₄×D₁₇	1	6	yes	—
328	C₂²	C₂²×#63252	1	12	yes	—
329	C₂²	C₂⁵×D₁₇	1	1	yes	characteristic
330	C₄	—	2	8	no	—
331	C₄	—	17	16	no	—
332	C₄	—	34	16	no	—
333	C₄	C₂³×C₄×D₁₇	1	8	yes	—
334	C₄	C₂³×C₄×D₁₇	1	8	yes	—
335	C₄	C₂²×#63252	1	16	yes	direct product factor
336	C₂	—	2	8	no	—
337	C₂	—	34	16	no	—
338	C₂	C₂×C₄×#63252	1	12	yes	direct product factor
339	C₂	C₂⁴×C₄×D₁₇	1	1	yes	characteristic
340	C₂	C₂³×#63252	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄²	C₂×D₁₇
commutator	C₂×C₁₇	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₁₇
Fitting	C₂³×C₄²×C₁₇	C₂
socle	C₂⁴×C₁₇	C₂⁴
prime radical	C₂³×#63252	C₂
cosocle	C₂²×C₁₇	C₂⁶
hypercenter	C₂³×C₄²	D₁₇
hypocenter	C₁₇	C₂²×C₄×#41
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄² ◁ C₂³×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#63252	C₂	direct (N × H)
3. C₂²×C₄×Dic₃₄	C₂	semidirect
4. C₂²×C₄×D₆₈	C₂	semidirect
5. C₂²×C₄×C₂²⋊D₁₇	C₂	semidirect
6. C₂²×#10587612	C₂	semidirect
7. C₂²×#10587558	C₂	semidirect
8. C₂²×C₄²×D₁₇	C₂	semidirect
9. C₂³×C₄²×C₁₇	C₂	semidirect
10. C₂²×#63252	C₄	direct (N × H)
17. C₄×#63252	C₂²	direct (N × H)
18. C₂×C₄×Dic₃₄	C₂²	semidirect
19. C₂×C₄×D₆₈	C₂²	semidirect
20. C₂×C₄×C₂²⋊D₁₇	C₂²	semidirect
21. C₂×#10587612	C₂²	semidirect
22. C₂×#10587558	C₂²	semidirect
29. C₂×C₄²×D₁₇	C₂²	semidirect
35. C₂²×C₄²×C₁₇	C₂²	semidirect
39. C₂³×C₄×C₁₇	C₂×C₄	semidirect
46. C₂²×C₂²⋊D₁₇	C₂×C₄	semidirect
50. C₂×#63252	C₂×C₄	direct (N × H)
52. C₂²×D₆₈	C₂×C₄	semidirect
55. C₂²×C₄×D₁₇	C₂×C₄	semidirect
58. C₂²×Dic₃₄	C₂×C₄	semidirect
63. C₂×C₄²×C₁₇	C₂³	semidirect
65. C₄×C₂²⋊D₁₇	C₂³	semidirect
67. #10587612	C₂³	semidirect
72. C₄×D₆₈	C₂³	semidirect
73. #10587558	C₂³	semidirect
74. C₄²×D₁₇	C₂³	semidirect
75. C₄×Dic₃₄	C₂³	semidirect
87. C₂²×C₄×C₁₇	C₂²×C₄	semidirect
88. C₂²×C₄×C₁₇	#41	semidirect
95. C₂×C₂²⋊D₁₇	C₂²×C₄	semidirect
101. #63252	C₂²×C₄	direct (N × H)
102. C₂×D₆₈	C₂²×C₄	semidirect
105. C₂×C₄×D₁₇	C₂²×C₄	semidirect
108. C₂×Dic₃₄	C₂²×C₄	semidirect
135. C₂×C₄×C₁₇	C₂³×C₄	semidirect
136. C₂×C₄×C₁₇	C₂×#41	semidirect
141. C₂²⋊D₁₇	C₂³×C₄	semidirect
146. D₆₈	C₂³×C₄	semidirect
148. C₄×D₁₇	C₂³×C₄	semidirect
149. Dic₃₄	C₂³×C₄	semidirect
158. C₂³×C₄²	D₁₇	semidirect
161. C₂²×C₁₇	C₄×#41	semidirect
172. C₄×C₁₇	C₂²×#41	semidirect
200. C₂²×C₄²	C₂×D₁₇	semidirect
202. C₂×C₁₇	C₂×C₄×#41	semidirect
223. C₂³×C₄	C₄×D₁₇	semidirect
245. C₂×C₄²	C₂²×D₁₇	semidirect
246. C₁₇	C₂²×C₄×#41	semidirect
273. C₂²×C₄	C₂×C₄×D₁₇	semidirect
274. C₂²×C₄	#63252	direct (N × H)
314. C₂×C₄	C₂²×C₄×D₁₇	semidirect
315. C₂×C₄	C₂×#63252	direct (N × H)
325. C₂²	C₄×#63252	direct (N × H)
335. C₄	C₂²×#63252	direct (N × H)
338. C₂	C₂×C₄×#63252	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#63252	2
C₂×C₄×#63252	2
C₂²×C₄×Dic₃₄	2
C₂²×C₄×D₆₈	2
C₂²×C₄×C₂²⋊D₁₇	2
C₂²×#10587612	2
C₂²×#10587558	2
C₂²×C₄²×D₁₇	2
C₂³×C₄²×C₁₇	2
C₂²×C₄×#41	17

Subgroups — C22×C4×#63252 #17940898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×#63252 #17940898