Group #17958762 — subgroups

Subgroups — #17958762

Order 4352.

362 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545117	C₂	1	1	yes	maximal, characteristic
2	C₄×#10587530	C₂	1	1	yes	maximal, characteristic
3	#14543751	C₂	1	2	yes	maximal, complemented
4	Q₈⋊#63216	C₂	1	2	yes	maximal, complemented
5	C₈×Q₈×D₁₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10587530	—	2	1	no	—
7	C₂×#10587530	—	2	1	no	—
8	#11763730	—	2	1	no	—
9	C₄⋊#63216	C₂²	1	2	yes	—
10	#11763698	—	2	1	no	—
11	C₄×#63216	C₂²	1	2	yes	—
12	C₄×Q₈×D₁₇	C₄	1	1	yes	characteristic
13	Q₈×#3622	C₂²	1	1	yes	characteristic
14	C₈×Dic₃₄	—	2	1	no	—
15	C₈×Dic₃₄	C₄	1	1	yes	characteristic
16	#11762933	—	2	1	no	—
17	#11762933	C₂²	1	1	yes	characteristic
18	C₄⋊C₈×D₁₇	—	2	1	no	—
19	C₄⋊C₈×D₁₇	C₄	1	1	yes	characteristic
20	C₄×C₈×D₁₇	—	2	1	no	—
21	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
22	C₈×Q₈×C₁₇	C₄	1	1	yes	characteristic
23	C₂×Q₈×D₁₇	C₈	1	1	yes	characteristic
24	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
25	Q₈×Dic₁₇	C₈	1	1	yes	characteristic
26	C₂×C₈×D₁₇	—	2	1	no	—
27	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
28	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
29	C₄⋊C₄×D₁₇	—	2	1	no	—
30	C₄⋊C₄×D₁₇	C₈	1	1	yes	characteristic
31	#10587573	—	2	1	no	—
32	#10587573	C₈	1	1	yes	characteristic
33	C₄²×D₁₇	—	2	1	no	—
34	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
35	C₄×Dic₃₄	—	2	1	no	—
36	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
37	C₂×#63216	—	2	2	no	—
38	C₂×#63216	—	2	2	no	—
39	#10587530	—	2	4	no	—
40	#10587530	—	4	2	no	—
41	C₁₇×C₄⋊C₈	—	2	1	no	—
42	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₇	—	2	1	no	—
44	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
45	#10587485	—	2	1	no	—
46	#10587485	—	2	1	no	—
47	#10587485	—	2	1	no	—
48	C₈×Dic₁₇	—	2	1	no	—
49	C₈×Dic₁₇	—	2	1	no	—
50	C₈×Dic₁₇	D₄	1	1	yes	characteristic
51	C₈×Dic₁₇	D₄	1	1	yes	characteristic
52	C₄⋊#3622	—	2	1	no	—
53	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
54	C₄×#3622	—	2	1	no	—
55	C₄×#3622	C₂³	1	1	yes	characteristic
56	C₂×Q₈×C₁₇	C₂×C₈	1	1	yes	characteristic
57	Q₈×D₁₇	—	2	2	no	—
58	Q₈×D₁₇	—	2	2	no	—
59	C₂×C₄×D₁₇	—	2	1	no	—
60	C₂×C₄×D₁₇	—	2	1	no	—
61	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
63	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
64	C₂×Dic₃₄	—	2	1	no	—
65	C₂×Dic₃₄	C₂×C₈	1	1	yes	characteristic
66	C₂×C₈×C₁₇	—	2	1	no	—
67	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
69	C₄⋊C₄×C₁₇	—	2	1	no	—
70	C₄⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
71	C₄²×C₁₇	—	2	1	no	—
72	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
73	C₄⋊Dic₁₇	—	2	1	no	—
74	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
75	#63225	—	2	1	no	—
76	#63225	—	2	1	no	—
77	#63225	—	2	1	no	—
78	C₄×Dic₁₇	—	2	1	no	—
79	C₄×Dic₁₇	—	2	1	no	—
80	C₄×Dic₁₇	—	2	1	no	—
81	C₄×Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
83	C₄×Dic₁₇	M₁₆	1	1	yes	characteristic
84	C₂×#3622	—	2	1	no	—
85	C₂×#3622	C₂×D₄	1	1	yes	characteristic
86	C₂×#3622	C₂×D₄	1	1	yes	characteristic
87	C₈×D₁₇	—	2	2	no	—
88	C₈×D₁₇	—	4	2	no	—
89	C₈×D₁₇	SD₁₆	1	2	yes	—
90	C₈×D₁₇	Q₁₆	1	2	yes	—
91	#63216	—	2	4	no	—
92	#63216	—	4	2	no	—
93	#11607	—	17	1	no	maximal, Sylow
94	C₂²×D₁₇	C₂²⋊C₈	1	1	yes	characteristic
95	Q₈×C₁₇	—	2	1	no	—
96	Q₈×C₁₇	M₃₂	1	2	yes	complemented
97	C₂×C₄×C₁₇	—	2	1	no	—
98	C₂×C₄×C₁₇	—	2	1	no	—
99	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
101	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
102	C₂×Dic₁₇	—	2	1	no	—
103	C₂×Dic₁₇	—	2	1	no	—
104	C₂×Dic₁₇	C₂²⋊C₈	1	1	yes	characteristic
105	C₂×Dic₁₇	C₂²⋊C₈	1	1	yes	characteristic
106	C₂×Dic₁₇	C₂²⋊C₈	1	1	yes	characteristic
107	C₄×D₁₇	—	2	4	no	—
108	C₄×D₁₇	—	2	1	no	—
109	C₄×D₁₇	—	2	1	no	—
110	C₄×D₁₇	—	4	1	no	—
111	C₄×D₁₇	—	4	2	no	—
112	C₄×D₁₇	#103	1	2	yes	—
113	C₄×D₁₇	#104	1	2	yes	—
114	Dic₃₄	—	2	4	no	—
115	Dic₃₄	—	2	1	no	—
116	Dic₃₄	M₃₂	1	2	yes	complemented
117	C₈×C₁₇	—	2	1	no	—
118	C₈×C₁₇	—	4	1	no	—
119	C₈×C₁₇	#103	1	2	yes	—
120	#3622	—	2	1	no	—
121	#3622	—	4	1	no	—
122	#3622	C₂×SD₁₆	1	1	yes	characteristic
123	#3622	C₂×Q₁₆	1	1	yes	characteristic
124	C₂×C₈×Q₈	—	17	1	no	—
125	#2150	—	17	1	no	—
126	C₄×M₃₂	—	17	1	no	—
127	Q₈⋊C₁₆	—	17	2	no	—
128	Q₈⋊C₁₆	—	17	2	no	—
129	C₂²×C₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
130	C₂×D₁₇	—	2	1	no	—
131	C₂×D₁₇	—	2	1	no	—
132	C₂×D₁₇	Q₈⋊C₈	1	2	yes	—
133	C₄×C₁₇	—	2	2	no	—
134	C₄×C₁₇	—	2	1	no	—
135	C₄×C₁₇	—	4	1	no	—
136	C₄×C₁₇	C₂×#103	1	1	yes	characteristic
137	C₄×C₁₇	C₂×#104	1	1	yes	characteristic
138	C₄×C₁₇	C₂×M₃₂	1	1	yes	characteristic
139	C₄×C₁₇	C₂×M₃₂	1	1	yes	characteristic
140	Dic₁₇	—	2	1	no	—
141	Dic₁₇	—	2	2	no	—
142	Dic₁₇	—	2	1	no	—
143	Dic₁₇	—	4	1	no	—
144	Dic₁₇	Q₈⋊C₈	1	2	yes	—
145	C₂×C₄×Q₈	—	17	1	no	—
146	C₂×M₃₂	—	34	1	no	—
147	C₂×M₃₂	—	34	1	no	—
148	C₈×Q₈	—	17	1	no	—
149	C₈×Q₈	—	17	1	no	—
150	C₈×Q₈	—	17	1	no	—
151	C₈×Q₈	—	34	1	no	—
152	C₈×Q₈	—	34	1	no	—
153	C₈×Q₈	#595	1	1	yes	characteristic
154	C₂×C₄⋊C₈	—	17	1	no	—
155	C₂×C₄⋊C₈	—	34	1	no	—
156	C₂×C₄×C₈	—	17	1	no	—
157	C₂×C₄×C₈	—	34	1	no	—
158	C₄⋊C₁₆	—	17	2	no	—
159	C₄⋊C₁₆	—	34	1	no	—
160	#346	—	34	1	no	—
161	C₄×C₁₆	—	17	2	no	—
162	C₂×C₁₇	C₂×Q₈⋊C₈	1	1	yes	characteristic
163	C₂×C₁₇	#2112	1	1	yes	characteristic
164	C₂×C₁₇	#2117	1	1	yes	characteristic
165	D₁₇	—	2	2	no	—
166	C₂²×Q₈	—	17	1	no	—
167	C₂²×C₈	—	17	1	no	—
168	C₂²×C₈	—	17	1	no	—
169	C₂²×C₈	—	34	1	no	—
170	C₄×Q₈	—	17	1	no	—
171	C₄×Q₈	—	17	1	no	—
172	C₄×Q₈	—	17	1	no	—
173	C₄×Q₈	—	34	1	no	—
174	C₄×Q₈	—	34	1	no	—
175	C₄×Q₈	C₂×#595	1	1	yes	characteristic
176	C₂×C₄⋊C₄	—	17	1	no	—
177	C₂×C₄⋊C₄	—	34	1	no	—
178	C₂×C₄²	—	17	1	no	—
179	C₂×C₄²	—	34	1	no	—
180	M₃₂	—	34	4	no	—
181	M₃₂	—	68	2	no	—
182	C₂×C₁₆	—	34	2	no	—
183	C₂×C₁₆	—	34	2	no	—
184	C₄⋊C₈	—	2	1	no	—
185	C₄⋊C₈	—	17	1	no	—
186	C₄⋊C₈	—	34	1	no	—
187	C₄⋊C₈	—	34	1	no	—
188	C₄⋊C₈	—	34	1	no	—
189	C₄⋊C₈	—	34	1	no	—
190	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
191	C₄×C₈	—	2	1	no	—
192	C₄×C₈	—	17	1	no	—
193	C₄×C₈	—	17	1	no	—
194	C₄×C₈	—	17	1	no	—
195	C₄×C₈	—	34	1	no	—
196	C₄×C₈	—	34	1	no	—
197	C₄×C₈	—	34	1	no	—
198	C₄×C₈	C₂×#595	1	1	yes	characteristic
199	C₁₇	#11607	1	1	yes	characteristic, complemented, Sylow
200	C₂×Q₈	—	17	1	no	—
201	C₂×Q₈	—	34	1	no	—
202	C₂×Q₈	—	34	2	no	—
203	C₂×Q₈	—	34	2	no	—
204	C₂×Q₈	#63242	1	1	yes	characteristic
205	C₂²×C₄	—	17	1	no	—
206	C₂²×C₄	—	17	1	no	—
207	C₂²×C₄	—	17	1	no	—
208	C₂²×C₄	—	34	1	no	—
209	C₂²×C₄	—	34	1	no	—
210	C₂×C₈	—	2	1	no	—
211	C₂×C₈	—	17	1	no	—
212	C₂×C₈	—	17	2	no	—
213	C₂×C₈	—	17	2	no	—
214	C₂×C₈	—	17	1	no	—
215	C₂×C₈	—	34	2	no	—
216	C₂×C₈	—	34	1	no	—
217	C₂×C₈	—	68	2	no	—
218	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
219	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
220	C₄⋊C₄	—	2	1	no	—
221	C₄⋊C₄	—	17	1	no	—
222	C₄⋊C₄	—	34	1	no	—
223	C₄⋊C₄	—	34	1	no	—
224	C₄⋊C₄	—	34	1	no	—
225	C₄⋊C₄	—	34	1	no	—
226	C₄⋊C₄	#63242	1	1	yes	characteristic
227	C₄²	—	2	1	no	—
228	C₄²	—	17	1	no	—
229	C₄²	—	17	1	no	—
230	C₄²	—	17	1	no	—
231	C₄²	—	34	1	no	—
232	C₄²	—	34	1	no	—
233	C₄²	—	34	1	no	—
234	C₄²	C₂²×#595	1	1	yes	characteristic
235	C₁₆	—	34	4	no	—
236	C₁₆	—	68	2	no	—
237	C₂³	—	17	1	no	—
238	Q₈	—	2	1	no	—
239	Q₈	—	17	2	no	—
240	Q₈	—	34	4	no	—
241	Q₈	—	34	1	no	—
242	Q₈	#10587530	1	2	yes	complemented
243	C₂×C₄	—	2	1	no	—
244	C₂×C₄	—	2	1	no	—
245	C₂×C₄	—	17	1	no	—
246	C₂×C₄	—	17	2	no	—
247	C₂×C₄	—	17	2	no	—
248	C₂×C₄	—	17	1	no	—
249	C₂×C₄	—	17	1	no	—
250	C₂×C₄	—	34	4	no	—
251	C₂×C₄	—	34	1	no	—
252	C₂×C₄	—	34	1	no	—
253	C₂×C₄	—	34	1	no	—
254	C₂×C₄	—	34	1	no	—
255	C₂×C₄	—	68	1	no	—
256	C₂×C₄	—	68	2	no	—
257	C₂×C₄	C₂×#63242	1	1	yes	characteristic
258	C₂×C₄	D₁₇⋊M₁₆	1	1	yes	characteristic
259	C₂×C₄	C₂×C₂²⋊#595	1	1	yes	characteristic
260	C₈	—	2	1	no	—
261	C₈	—	4	1	no	—
262	C₈	—	17	1	no	—
263	C₈	—	17	1	no	—
264	C₈	—	34	1	no	—
265	C₈	—	68	1	no	—
266	C₈	#10587549	1	2	yes	—
267	C₂²	—	17	2	no	—
268	C₂²	—	34	1	no	—
269	C₂²	—	34	1	no	—
270	C₂²	#11763777	1	1	yes	characteristic
271	C₄	—	2	2	no	—
272	C₄	—	2	1	no	—
273	C₄	—	4	1	no	—
274	C₄	—	17	2	no	—
275	C₄	—	34	1	no	—
276	C₄	—	34	2	no	—
277	C₄	—	34	1	no	—
278	C₄	—	68	1	no	—
279	C₄	C₂×#10587549	1	1	yes	characteristic
280	C₄	D₁₇⋊#104	1	1	yes	characteristic
281	C₄	#11763865	1	1	yes	characteristic
282	C₄	C₂×#10587530	1	1	yes	characteristic
283	C₂	—	34	2	no	—
284	C₂	#14544073	1	1	yes	characteristic
285	C₂	#14545012	1	1	yes	characteristic
286	C₂	#14545027	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14545117

C₂

yes

maximal, characteristic

C₄×#10587530

C₂

yes

maximal, characteristic

#14543751

C₂

yes

maximal, complemented

Q₈⋊#63216

C₂

yes

maximal, complemented

C₈×Q₈×D₁₇

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

#11763698

—

C₄×#63216

C₂²

yes

—

C₄×Q₈×D₁₇

C₄

yes

characteristic

Q₈×#3622

C₂²

yes

characteristic

C₈×Dic₃₄

—

C₈×Dic₃₄

C₄

yes

characteristic

#11762933

—

#11762933

C₂²

yes

characteristic

C₄⋊C₈×D₁₇

—

C₄⋊C₈×D₁₇

C₄

yes

characteristic

C₄×C₈×D₁₇

—

C₄×C₈×D₁₇

C₂²

yes

characteristic

C₈×Q₈×C₁₇

C₄

yes

characteristic

C₂×Q₈×D₁₇

C₈

yes

characteristic

C₄×Q₈×C₁₇

C₂×C₄

yes

characteristic

Q₈×Dic₁₇

C₈

yes

characteristic

C₂×C₈×D₁₇

—

C₂×C₈×D₁₇

D₄

yes

characteristic

C₂×C₈×D₁₇

D₄

yes

characteristic

C₄⋊C₄×D₁₇

—

C₄⋊C₄×D₁₇

C₈

yes

characteristic

#10587573

—

#10587573

C₈

yes

characteristic

C₄²×D₁₇

—

C₄²×D₁₇

C₂×C₄

yes

characteristic

C₄×Dic₃₄

—

C₄×Dic₃₄

C₂×C₄

yes

—

—

—

—

C₁₇×C₄⋊C₈

—

C₁₇×C₄⋊C₈

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

—

C₄×C₈×C₁₇

C₂×C₄

yes

—

—

—

C₈×Dic₁₇

—

C₈×Dic₁₇

—

C₈×Dic₁₇

D₄

yes

characteristic

C₈×Dic₁₇

D₄

yes

characteristic

C₄⋊#3622

—

C₄⋊#3622

C₂×C₄

yes

characteristic

C₄×#3622

—

C₄×#3622

C₂³

yes

characteristic

C₂×Q₈×C₁₇

C₂×C₈

yes

characteristic

Q₈×D₁₇

—

Q₈×D₁₇

—

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×D₁₇

C₂×C₈

yes

characteristic

C₂×C₄×D₁₇

M₁₆

yes

characteristic

C₂×Dic₃₄

—

C₂×Dic₃₄

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

C₂×C₈

yes

characteristic

C₄²×C₁₇

—

C₄²×C₁₇

C₂²×C₄

yes

characteristic

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

C₂×C₈

yes

—

—

—

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

C₂²⋊C₄

yes

characteristic

C₄×Dic₁₇

C₂×C₈

yes

characteristic

C₄×Dic₁₇

M₁₆

yes

characteristic

C₂×#3622

—

C₂×#3622

C₂×D₄

yes

characteristic

C₂×#3622

C₂×D₄

yes

characteristic

C₈×D₁₇

—

C₈×D₁₇

—

C₈×D₁₇

SD₁₆

yes

—

C₈×D₁₇

Q₁₆

yes

—

—

—

—

C₂²×D₁₇

C₂²⋊C₈

yes

characteristic

Q₈×C₁₇

—

Q₈×C₁₇

M₃₂

yes

complemented

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

100

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

101

C₂×C₄×C₁₇

C₂×M₁₆

yes

characteristic

102

C₂×Dic₁₇

—

103

C₂×Dic₁₇

—

104

C₂×Dic₁₇

C₂²⋊C₈

yes

characteristic

105

C₂×Dic₁₇

C₂²⋊C₈

yes

characteristic

106

C₂×Dic₁₇

C₂²⋊C₈

yes

characteristic

107

C₄×D₁₇

—

108

C₄×D₁₇

—

109

C₄×D₁₇

—

110

C₄×D₁₇

—

111

C₄×D₁₇

—

112

C₄×D₁₇

#103

yes

—

113

C₄×D₁₇

#104

yes

—

114

Dic₃₄

—

115

Dic₃₄

—

116

Dic₃₄

M₃₂

yes

complemented

117

C₈×C₁₇

—

118

C₈×C₁₇

—

119

C₈×C₁₇

#103

yes

—

120

#3622

—

121

#3622

—

122

#3622

C₂×SD₁₆

yes

characteristic

123

#3622

C₂×Q₁₆

yes

characteristic

124

C₂×C₈×Q₈

—

125

#2150

—

126

C₄×M₃₂

—

127

Q₈⋊C₁₆

—

128

Q₈⋊C₁₆

—

129

C₂²×C₁₇

C₂×C₂²⋊C₈

yes

characteristic

130

C₂×D₁₇

—

131

C₂×D₁₇

—

132

C₂×D₁₇

Q₈⋊C₈

yes

—

133

C₄×C₁₇

—

134

C₄×C₁₇

—

135

C₄×C₁₇

—

136

C₄×C₁₇

C₂×#103

yes

characteristic

137

C₄×C₁₇

C₂×#104

yes

characteristic

138

C₄×C₁₇

C₂×M₃₂

yes

characteristic

139

C₄×C₁₇

C₂×M₃₂

yes

characteristic

140

Dic₁₇

—

141

Dic₁₇

—

142

Dic₁₇

—

143

Dic₁₇

—

144

Dic₁₇

Q₈⋊C₈

yes

—

145

C₂×C₄×Q₈

—

146

C₂×M₃₂

—

147

C₂×M₃₂

—

148

C₈×Q₈

—

149

C₈×Q₈

—

150

C₈×Q₈

—

151

C₈×Q₈

—

152

C₈×Q₈

—

153

C₈×Q₈

#595

yes

characteristic

154

C₂×C₄⋊C₈

—

155

C₂×C₄⋊C₈

—

156

C₂×C₄×C₈

—

157

C₂×C₄×C₈

—

158

C₄⋊C₁₆

—

159

C₄⋊C₁₆

—

160

#346

—

161

C₄×C₁₆

—

162

C₂×C₁₇

C₂×Q₈⋊C₈

yes

characteristic

163

C₂×C₁₇

#2112

yes

characteristic

164

C₂×C₁₇

#2117

yes

characteristic

165

D₁₇

—

166

C₂²×Q₈

—

167

C₂²×C₈

—

168

C₂²×C₈

—

169

C₂²×C₈

—

170

C₄×Q₈

—

171

C₄×Q₈

—

172

C₄×Q₈

—

173

C₄×Q₈

—

174

C₄×Q₈

—

175

C₄×Q₈

C₂×#595

yes

characteristic

176

C₂×C₄⋊C₄

—

177

C₂×C₄⋊C₄

—

178

C₂×C₄²

—

179

C₂×C₄²

—

180

M₃₂

—

181

M₃₂

—

182

C₂×C₁₆

—

183

C₂×C₁₆

—

184

C₄⋊C₈

—

185

C₄⋊C₈

—

186

C₄⋊C₈

—

187

C₄⋊C₈

—

188

C₄⋊C₈

—

189

C₄⋊C₈

—

190

C₄⋊C₈

C₂×#595

yes

characteristic

191

C₄×C₈

—

192

C₄×C₈

—

193

C₄×C₈

—

194

C₄×C₈

—

195

C₄×C₈

—

196

C₄×C₈

—

197

C₄×C₈

—

198

C₄×C₈

C₂×#595

yes

characteristic

199

C₁₇

#11607

yes

characteristic, complemented, Sylow

200

C₂×Q₈

—

201

C₂×Q₈

—

202

C₂×Q₈

—

203

C₂×Q₈

—

204

C₂×Q₈

#63242

yes

characteristic

205

C₂²×C₄

—

206

C₂²×C₄

—

207

C₂²×C₄

—

208

C₂²×C₄

—

209

C₂²×C₄

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₂×C₈

—

218

C₂×C₈

C₂²⋊#595

yes

characteristic

219

C₂×C₈

C₂²⋊#595

yes

characteristic

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

225

C₄⋊C₄

—

226

C₄⋊C₄

#63242

yes

characteristic

227

C₄²

—

228

C₄²

—

229

C₄²

—

230

C₄²

—

231

C₄²

—

232

C₄²

—

233

C₄²

—

234

C₄²

C₂²×#595

yes

characteristic

235

C₁₆

—

236

C₁₆

—

237

C₂³

—

238

Q₈

—

239

Q₈

—

240

Q₈

—

241

Q₈

—

242

Q₈

#10587530

yes

complemented

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

252

C₂×C₄

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

C₂×#63242

yes

characteristic

258

C₂×C₄

D₁₇⋊M₁₆

yes

characteristic

259

C₂×C₄

C₂×C₂²⋊#595

yes

characteristic

260

C₈

—

261

C₈

—

262

C₈

—

263

C₈

—

264

C₈

—

265

C₈

—

266

C₈

#10587549

yes

—

267

C₂²

—

268

C₂²

—

269

C₂²

—

270

C₂²

#11763777

yes

characteristic

271

C₄

—

272

C₄

—

273

C₄

—

274

C₄

—

275

C₄

—

276

C₄

—

277

C₄

—

278

C₄

—

279

C₄

C₂×#10587549

yes

characteristic

280

C₄

D₁₇⋊#104

yes

characteristic

281

C₄

#11763865

yes

characteristic

282

C₄

C₂×#10587530

yes

characteristic

283

C₂

—

284

C₂

#14544073

yes

characteristic

285

C₂

#14545012

yes

characteristic

286

C₂

#14545027

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊#595
commutator	C₂×C₄×C₁₇	C₂²×C₈
Frattini	C₄²	C₂²×#595
Fitting	C₈×Q₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₂²⋊C₈
prime radical	C₂²×D₁₇	C₂²⋊C₈
cosocle	C₄×#3622	C₂³
hypercenter	C₈×Q₈	#595
hypocenter	C₁₇	#11607
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×Q₈

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊#595

commutator

C₂×C₄×C₁₇

C₂²×C₈

Frattini

C₄²

C₂²×#595

Fitting

C₈×Q₈×C₁₇

C₄

socle

C₂²×C₁₇

C₂×C₂²⋊C₈

prime radical

C₂²×D₁₇

C₂²⋊C₈

C₂³

C₈×Q₈

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×Q₈

N	H ≅ G/N	type
3. #14543751	C₂	semidirect
4. Q₈⋊#63216	C₂	semidirect
96. Q₈×C₁₇	M₃₂	semidirect
116. Dic₃₄	M₃₂	semidirect
199. C₁₇	#11607	semidirect
242. Q₈	#10587530	semidirect

H ≅ G/N

type

3. #14543751

C₂

semidirect

4. Q₈⋊#63216

C₂

semidirect

96. Q₈×C₁₇

M₃₂

semidirect

116. Dic₃₄

M₃₂

semidirect

199. C₁₇

#11607

semidirect

242. Q₈

#10587530

semidirect

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

subgroup	index
#14545117	2
C₄×#10587530	2
#14543751	2
Q₈⋊#63216	2
C₈×Q₈×D₁₇	2
#11607	17

subgroup

index

C₈×Q₈×D₁₇

Subgroups — #17958762

Conjugacy classes of subgroups

Complements

Maximal subgroups