Group #16953184 — subgroups

Subgroups — #16953184

Order 4352.

558 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 129 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	C₂²×#10587500	C₂	1	2	yes	maximal
2	C₂×#11762613	C₂	1	2	yes	maximal
3	#14529645	C₂	1	1	yes	maximal, characteristic
4	#14526862	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₇×#494	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₆₈	C₂²	1	1	yes	characteristic
7	C₂×#10587500	—	2	4	no	—
8	C₂×#10587500	—	2	4	no	—
9	C₂×#10587500	—	2	4	no	—
10	C₂²×#63214	C₂²	1	2	yes	—
11	C₂×#10587489	C₂²	1	1	yes	characteristic
12	C₂×#10587487	—	2	1	no	—
13	#11762715	—	2	1	no	—
14	#11762613	—	2	4	no	—
15	C₂²×Q₁₆×C₁₇	—	2	1	no	—
16	C₂²×Q₁₆×C₁₇	C₂²	1	2	yes	—
17	C₂×C₁₇×C₄⋊Q₈	—	2	1	no	—
18	C₁₇×#494	—	2	4	no	—
19	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₁₇	—	2	2	no	—
21	C₂²×Dic₃₄	—	2	1	no	—
22	C₂×Q₁₆×C₁₇	—	2	4	no	—
23	C₂×Q₁₆×C₁₇	—	2	2	no	—
24	C₂×Q₁₆×C₁₇	—	2	2	no	—
25	C₂×Q₁₆×C₁₇	—	2	2	no	—
26	C₂×Q₁₆×C₁₇	—	2	2	no	—
27	C₂×Q₁₆×C₁₇	—	2	2	no	—
28	C₂×Q₁₆×C₁₇	—	4	2	no	—
29	C₂×Q₁₆×C₁₇	—	4	2	no	—
30	C₂×Q₁₆×C₁₇	D₄	1	4	yes	—
31	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
33	C₁₇×C₄⋊Q₈	—	2	4	no	—
34	C₁₇×C₄⋊Q₈	—	4	2	no	—
35	C₂×C₄⋊C₄×C₁₇	—	4	2	no	—
36	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
37	C₂×C₄⋊Dic₁₇	—	2	1	no	—
38	C₂×Dic₆₈	—	2	2	no	—
39	C₂×Dic₆₈	—	2	2	no	—
40	C₂×Dic₆₈	—	2	1	no	—
41	C₂×Dic₆₈	D₄	1	2	yes	—
42	C₄×C₈×C₁₇	—	2	2	no	—
43	#10587502	—	4	2	no	—
44	#10587500	—	2	16	no	—
45	#10587489	—	2	2	no	—
46	#10587487	—	4	2	no	—
47	C₂×#63214	—	2	2	no	—
48	C₂×#63214	—	2	2	no	—
49	C₂×#63214	D₄	1	4	yes	—
50	C₂×Q₈×C₁₇	—	2	4	no	—
51	C₂×Q₈×C₁₇	—	4	2	no	—
52	C₂×Q₈×C₁₇	—	4	2	no	—
53	C₂×Q₈×C₁₇	—	4	2	no	—
54	C₂×Q₈×C₁₇	—	4	2	no	—
55	C₂×Q₈×C₁₇	—	4	2	no	—
56	C₂²×C₄×C₁₇	—	4	2	no	—
57	C₂²×C₄×C₁₇	D₈	1	2	yes	—
58	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
59	C₂²×Dic₁₇	—	4	1	no	—
60	C₂²×Dic₁₇	—	4	1	no	—
61	C₂×Dic₃₄	—	2	2	no	—
62	C₂×Dic₃₄	—	4	1	no	—
63	C₂×Dic₃₄	—	4	1	no	—
64	C₂×Dic₃₄	—	4	1	no	—
65	C₂×Dic₃₄	—	4	1	no	—
66	C₂×Dic₃₄	—	4	1	no	—
67	Q₁₆×C₁₇	—	2	4	no	—
68	Q₁₆×C₁₇	—	2	4	no	—
69	Q₁₆×C₁₇	—	4	8	no	—
70	Q₁₆×C₁₇	—	4	2	no	—
71	Q₁₆×C₁₇	—	4	2	no	—
72	C₂×C₈×C₁₇	—	2	1	no	—
73	C₂×C₈×C₁₇	—	2	1	no	—
74	C₂×C₈×C₁₇	D₈	1	2	yes	—
75	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
76	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
77	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
78	C₂×C₈×C₁₇	#41	1	1	yes	characteristic
79	C₄⋊C₄×C₁₇	—	4	8	no	—
80	C₄²×C₁₇	—	2	1	no	—
81	C₄²×C₁₇	—	2	1	no	—
82	C₄⋊Dic₁₇	—	4	1	no	—
83	C₄⋊Dic₁₇	—	4	1	no	—
84	Dic₆₈	—	2	4	no	—
85	Dic₆₈	—	4	2	no	—
86	#63214	—	2	4	no	—
87	#13330	—	17	1	no	maximal, Sylow
88	C₂³×C₁₇	C₂×D₈	1	1	yes	characteristic
89	Q₈×C₁₇	—	4	4	no	—
90	Q₈×C₁₇	—	4	4	no	—
91	Q₈×C₁₇	—	8	2	no	—
92	Q₈×C₁₇	—	8	2	no	—
93	C₂×C₄×C₁₇	—	2	2	no	—
94	C₂×C₄×C₁₇	—	2	2	no	—
95	C₂×C₄×C₁₇	—	4	4	no	—
96	C₂×C₄×C₁₇	—	8	2	no	—
97	C₂×C₄×C₁₇	—	8	2	no	—
98	C₂×C₄×C₁₇	Q₃₂	1	4	yes	complemented
99	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
100	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
101	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
102	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
103	C₂×C₄×C₁₇	AGL(1,ℤ/8)	1	1	yes	characteristic
104	C₂×C₄×C₁₇	AGL(1,ℤ/8)	1	1	yes	characteristic
105	C₂×Dic₁₇	—	4	2	no	—
106	C₂×Dic₁₇	—	8	1	no	—
107	C₂×Dic₁₇	—	8	1	no	—
108	C₂×Dic₁₇	—	8	1	no	—
109	C₂×Dic₁₇	—	8	2	no	—
110	Dic₃₄	—	4	2	no	—
111	Dic₃₄	—	4	2	no	—
112	Dic₃₄	—	8	1	no	—
113	Dic₃₄	—	8	1	no	—
114	C₈×C₁₇	—	2	2	no	—
115	C₈×C₁₇	#120	1	2	yes	—
116	C₈×C₁₇	#121	1	2	yes	—
117	C₂²×Q₃₂	—	17	2	no	—
118	C₂×#494	D₁₇	1	1	yes	characteristic
119	C₂×#358	—	17	2	no	—
120	#1969	—	17	1	no	—
121	#1374	—	17	1	no	—
122	C₂²×C₁₇	#447	1	1	yes	characteristic
123	C₂²×C₁₇	#459	1	1	yes	characteristic
124	C₂²×C₁₇	#493	1	1	yes	characteristic
125	C₂²×C₁₇	C₂×Q₃₂	1	2	yes	—
126	C₂²×C₁₇	#510	1	2	yes	—
127	C₄×C₁₇	—	2	4	no	—
128	C₄×C₁₇	—	8	4	no	—
129	C₄×C₁₇	#392	1	1	yes	characteristic
130	C₄×C₁₇	#447	1	1	yes	characteristic
131	C₄×C₁₇	#459	1	1	yes	characteristic
132	C₄×C₁₇	#496	1	1	yes	characteristic
133	Dic₁₇	—	8	2	no	—
134	Dic₁₇	—	16	1	no	—
135	C₂²×Q₁₆	—	2	1	no	—
136	C₂²×Q₁₆	—	17	1	no	—
137	C₂²×Q₁₆	C₂×D₁₇	1	2	yes	—
138	C₂×C₄⋊Q₈	—	2	1	no	—
139	C₂×Q₃₂	—	34	4	no	—
140	C₂×Q₃₂	—	34	4	no	—
141	C₂×Q₃₂	—	34	4	no	—
142	C₂²×C₁₆	—	17	2	no	—
143	#494	—	2	4	no	—
144	C₂×#107	—	17	1	no	—
145	C₂×#103	—	34	1	no	—
146	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
147	#391	—	34	1	no	—
148	#358	—	34	4	no	—
149	C₂×C₁₇	#2011	1	1	yes	characteristic
150	C₂×C₁₇	#2188	1	2	yes	—
151	C₂×C₁₇	#2209	1	2	yes	—
152	C₂×C₁₇	#2247	1	1	yes	characteristic
153	C₂×C₁₇	#2251	1	1	yes	characteristic
154	C₂²×Q₈	—	2	2	no	—
155	C₂²×Q₈	—	34	1	no	—
156	C₂×Q₁₆	—	2	4	no	—
157	C₂×Q₁₆	—	2	2	no	—
158	C₂×Q₁₆	—	2	2	no	—
159	C₂×Q₁₆	—	2	2	no	—
160	C₂×Q₁₆	—	2	2	no	—
161	C₂×Q₁₆	—	2	2	no	—
162	C₂×Q₁₆	—	4	2	no	—
163	C₂×Q₁₆	—	4	2	no	—
164	C₂×Q₁₆	—	17	2	no	—
165	C₂×Q₁₆	—	34	2	no	—
166	C₂×Q₁₆	—	34	1	no	—
167	C₂×Q₁₆	—	34	2	no	—
168	C₂×Q₁₆	C₂²⋊D₁₇	1	4	yes	—
169	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
170	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
171	C₄⋊Q₈	—	2	4	no	—
172	C₄⋊Q₈	—	4	2	no	—
173	C₂×C₄⋊C₄	—	4	2	no	—
174	C₂×C₄⋊C₄	—	34	1	no	—
175	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
176	Q₃₂	—	34	16	no	—
177	C₂×C₁₆	—	17	4	no	—
178	C₂×C₁₆	—	34	2	no	—
179	C₂×C₁₆	—	34	2	no	—
180	#107	—	34	2	no	—
181	#103	—	68	2	no	—
182	C₄×C₈	—	2	2	no	—
183	#95	—	68	2	no	—
184	C₁₇	#13330	1	1	yes	characteristic, complemented, Sylow
185	C₂×Q₈	—	2	4	no	—
186	C₂×Q₈	—	4	2	no	—
187	C₂×Q₈	—	4	2	no	—
188	C₂×Q₈	—	4	2	no	—
189	C₂×Q₈	—	4	2	no	—
190	C₂×Q₈	—	4	2	no	—
191	C₂×Q₈	—	34	2	no	—
192	C₂×Q₈	—	68	1	no	—
193	C₂×Q₈	—	68	1	no	—
194	C₂×Q₈	—	68	1	no	—
195	C₂×Q₈	—	68	1	no	—
196	C₂×Q₈	—	68	1	no	—
197	C₂²×C₄	—	4	2	no	—
198	C₂²×C₄	—	68	1	no	—
199	C₂²×C₄	—	68	1	no	—
200	C₂²×C₄	#63228	1	2	yes	—
201	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
202	Q₁₆	—	2	4	no	—
203	Q₁₆	—	2	4	no	—
204	Q₁₆	—	4	8	no	—
205	Q₁₆	—	4	2	no	—
206	Q₁₆	—	4	2	no	—
207	Q₁₆	—	34	4	no	—
208	Q₁₆	—	68	2	no	—
209	C₂×C₈	—	2	1	no	—
210	C₂×C₈	—	2	1	no	—
211	C₂×C₈	#63228	1	2	yes	—
212	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
213	C₂×C₈	D₄×D₁₇	1	2	yes	—
214	C₂×C₈	#63254	1	1	yes	characteristic
215	C₂×C₈	C₂×C₂²⋊D₁₇	1	2	yes	—
216	C₄⋊C₄	—	4	8	no	—
217	C₄⋊C₄	—	68	1	no	—
218	C₄⋊C₄	—	68	1	no	—
219	C₄²	—	2	1	no	—
220	C₄²	—	2	1	no	—
221	C₁₆	—	34	4	no	—
222	C₂³	C₂×#63228	1	1	yes	characteristic
223	Q₈	—	4	4	no	—
224	Q₈	—	4	4	no	—
225	Q₈	—	8	2	no	—
226	Q₈	—	8	2	no	—
227	Q₈	—	68	2	no	—
228	Q₈	—	68	2	no	—
229	Q₈	—	136	1	no	—
230	Q₈	—	136	1	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	4	4	no	—
234	C₂×C₄	—	8	2	no	—
235	C₂×C₄	—	8	2	no	—
236	C₂×C₄	—	68	2	no	—
237	C₂×C₄	—	136	2	no	—
238	C₂×C₄	—	136	1	no	—
239	C₂×C₄	—	136	1	no	—
240	C₂×C₄	—	136	1	no	—
241	C₂×C₄	#10587500	1	4	yes	complemented
242	C₂×C₄	C₂×#63228	1	1	yes	characteristic
243	C₂×C₄	#10587618	1	1	yes	characteristic
244	C₂×C₄	#10587618	1	1	yes	characteristic
245	C₂×C₄	#10587624	1	1	yes	characteristic
246	C₂×C₄	#10587626	1	1	yes	characteristic
247	C₂×C₄	#10587639	1	1	yes	characteristic
248	C₈	—	2	2	no	—
249	C₈	#10587623	1	2	yes	—
250	C₈	#10587625	1	2	yes	—
251	C₂²	#11762943	1	1	yes	characteristic
252	C₂²	#11763001	1	1	yes	characteristic
253	C₂²	#11763185	1	1	yes	characteristic
254	C₂²	C₂×#10587500	1	2	yes	—
255	C₂²	#11763250	1	2	yes	—
256	C₄	—	2	4	no	—
257	C₄	—	8	4	no	—
258	C₄	—	272	1	no	—
259	C₄	—	136	2	no	—
260	C₄	#11762717	1	1	yes	characteristic
261	C₄	#11762943	1	1	yes	characteristic
262	C₄	#11763001	1	1	yes	characteristic
263	C₄	#11763196	1	1	yes	characteristic
264	C₂	#14529855	1	1	yes	characteristic
265	C₂	#14530718	1	2	yes	—
266	C₂	#14530831	1	2	yes	—
267	C₂	#14531036	1	1	yes	characteristic
268	C₂	#14531053	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#10587500

C₂

yes

maximal

C₂×#11762613

C₂

yes

maximal

#14529645

C₂

yes

maximal, characteristic

#14526862

C₂

yes

maximal, characteristic

C₂×C₁₇×#494

C₂

yes

maximal, characteristic

C₂²×Dic₆₈

C₂²

yes

—

—

—

C₂²×#63214

C₂²

yes

—

C₂×#10587489

C₂²

yes

—

—

—

C₂²×Q₁₆×C₁₇

—

C₂²×Q₁₆×C₁₇

C₂²

yes

—

C₂×C₁₇×C₄⋊Q₈

—

C₁₇×#494

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₂²×Q₈×C₁₇

—

C₂²×Dic₃₄

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

D₄

yes

—

C₂²×C₈×C₁₇

D₄

yes

characteristic

C₂²×C₈×C₁₇

C₂³

yes

characteristic

C₁₇×C₄⋊Q₈

—

C₁₇×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₇

—

C₂×C₄²×C₁₇

D₄

yes

characteristic

C₂×C₄⋊Dic₁₇

—

C₂×Dic₆₈

—

C₂×Dic₆₈

—

C₂×Dic₆₈

—

C₂×Dic₆₈

D₄

yes

—

C₄×C₈×C₁₇

—

—

—

—

—

—

—

D₄

yes

—

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂²×C₄×C₁₇

—

C₂²×C₄×C₁₇

D₈

yes

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×Dic₁₇

—

C₂²×Dic₁₇

—

C₂×Dic₃₄

—

C₂×Dic₃₄

—

C₂×Dic₃₄

—

C₂×Dic₃₄

—

C₂×Dic₃₄

—

C₂×Dic₃₄

—

Q₁₆×C₁₇

—

Q₁₆×C₁₇

—

Q₁₆×C₁₇

—

Q₁₆×C₁₇

—

Q₁₆×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

D₈

yes

—

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₂×C₈×C₁₇

C₂×D₄

yes

—

C₂×C₈×C₁₇

C₂×D₄

yes

—

C₂×C₈×C₁₇

#41

yes

characteristic

C₄⋊C₄×C₁₇

—

C₄²×C₁₇

—

C₄²×C₁₇

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

Dic₆₈

—

Dic₆₈

—

#63214

—

#13330

—

maximal, Sylow

C₂³×C₁₇

C₂×D₈

yes

characteristic

Q₈×C₁₇

—

Q₈×C₁₇

—

Q₈×C₁₇

—

Q₈×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

Q₃₂

yes

complemented

C₂×C₄×C₁₇

#120

yes

characteristic

100

C₂×C₄×C₁₇

#121

yes

characteristic

101

C₂×C₄×C₁₇

#127

yes

characteristic

102

C₂×C₄×C₁₇

C₂×D₈

yes

characteristic

103

C₂×C₄×C₁₇

AGL(1,ℤ/8)

yes

characteristic

104

C₂×C₄×C₁₇

AGL(1,ℤ/8)

yes

characteristic

105

C₂×Dic₁₇

—

106

C₂×Dic₁₇

—

107

C₂×Dic₁₇

—

108

C₂×Dic₁₇

—

109

C₂×Dic₁₇

—

110

Dic₃₄

—

111

Dic₃₄

—

112

Dic₃₄

—

113

Dic₃₄

—

114

C₈×C₁₇

—

115

C₈×C₁₇

#120

yes

—

116

C₈×C₁₇

#121

yes

—

117

C₂²×Q₃₂

—

118

C₂×#494

D₁₇

yes

characteristic

119

C₂×#358

—

120

#1969

—

121

#1374

—

122

C₂²×C₁₇

#447

yes

characteristic

123

C₂²×C₁₇

#459

yes

characteristic

124

C₂²×C₁₇

#493

yes

characteristic

125

C₂²×C₁₇

C₂×Q₃₂

yes

—

126

C₂²×C₁₇

#510

yes

—

127

C₄×C₁₇

—

128

C₄×C₁₇

—

129

C₄×C₁₇

#392

yes

characteristic

130

C₄×C₁₇

#447

yes

characteristic

131

C₄×C₁₇

#459

yes

characteristic

132

C₄×C₁₇

#496

yes

characteristic

133

Dic₁₇

—

134

Dic₁₇

—

135

C₂²×Q₁₆

—

136

C₂²×Q₁₆

—

137

C₂²×Q₁₆

C₂×D₁₇

yes

—

138

C₂×C₄⋊Q₈

—

139

C₂×Q₃₂

—

140

C₂×Q₃₂

—

141

C₂×Q₃₂

—

142

C₂²×C₁₆

—

143

#494

—

144

C₂×#107

—

145

C₂×#103

—

146

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

147

#391

—

148

#358

—

149

C₂×C₁₇

#2011

yes

characteristic

150

C₂×C₁₇

#2188

yes

—

151

C₂×C₁₇

#2209

yes

—

152

C₂×C₁₇

#2247

yes

characteristic

153

C₂×C₁₇

#2251

yes

characteristic

154

C₂²×Q₈

—

155

C₂²×Q₈

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

—

158

C₂×Q₁₆

—

159

C₂×Q₁₆

—

160

C₂×Q₁₆

—

161

C₂×Q₁₆

—

162

C₂×Q₁₆

—

163

C₂×Q₁₆

—

164

C₂×Q₁₆

—

165

C₂×Q₁₆

—

166

C₂×Q₁₆

—

167

C₂×Q₁₆

—

168

C₂×Q₁₆

C₂²⋊D₁₇

yes

—

169

C₂²×C₈

C₂²⋊D₁₇

yes

characteristic

170

C₂²×C₈

C₂²×D₁₇

yes

characteristic

171

C₄⋊Q₈

—

172

C₄⋊Q₈

—

173

C₂×C₄⋊C₄

—

174

C₂×C₄⋊C₄

—

175

C₂×C₄²

C₂²⋊D₁₇

yes

characteristic

176

Q₃₂

—

177

C₂×C₁₆

—

178

C₂×C₁₆

—

179

C₂×C₁₆

—

180

#107

—

181

#103

—

182

C₄×C₈

—

183

#95

—

184

C₁₇

#13330

yes

characteristic, complemented, Sylow

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂×Q₈

—

194

C₂×Q₈

—

195

C₂×Q₈

—

196

C₂×Q₈

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

—

200

C₂²×C₄

#63228

yes

—

201

C₂²×C₄

C₂×C₂²⋊D₁₇

yes

characteristic

202

Q₁₆

—

203

Q₁₆

—

204

Q₁₆

—

205

Q₁₆

—

206

Q₁₆

—

207

Q₁₆

—

208

Q₁₆

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

#63228

yes

—

212

C₂×C₈

D₄×D₁₇

yes

characteristic

213

C₂×C₈

D₄×D₁₇

yes

—

214

C₂×C₈

#63254

yes

characteristic

215

C₂×C₈

C₂×C₂²⋊D₁₇

yes

—

216

C₄⋊C₄

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄²

—

220

C₄²

—

221

C₁₆

—

222

C₂³

C₂×#63228

yes

characteristic

223

Q₈

—

224

Q₈

—

225

Q₈

—

226

Q₈

—

227

Q₈

—

228

Q₈

—

229

Q₈

—

136

—

230

Q₈

—

136

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

136

—

238

C₂×C₄

—

136

—

239

C₂×C₄

—

136

—

240

C₂×C₄

—

136

—

241

C₂×C₄

#10587500

yes

complemented

242

C₂×C₄

C₂×#63228

yes

characteristic

243

C₂×C₄

#10587618

yes

characteristic

244

C₂×C₄

#10587618

yes

characteristic

245

C₂×C₄

#10587624

yes

characteristic

246

C₂×C₄

#10587626

yes

characteristic

247

C₂×C₄

#10587639

yes

characteristic

248

C₈

—

249

C₈

#10587623

yes

—

250

C₈

#10587625

yes

—

251

C₂²

#11762943

yes

characteristic

252

C₂²

#11763001

yes

characteristic

253

C₂²

#11763185

yes

characteristic

254

C₂²

C₂×#10587500

yes

—

255

C₂²

#11763250

yes

—

256

C₄

—

257

C₄

—

258

C₄

—

272

—

259

C₄

—

136

—

260

C₄

#11762717

yes

characteristic

261

C₄

#11762943

yes

characteristic

262

C₄

#11763001

yes

characteristic

263

C₄

#11763196

yes

characteristic

264

C₂

#14529855

yes

characteristic

265

C₂

#14530718

yes

—

266

C₂

#14530831

yes

—

267

C₂

#14531036

yes

characteristic

268

C₂

#14531053

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×#63228
commutator, cosocle	C₂²×C₈×C₁₇	C₂³
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting	C₂×C₁₇×#494	C₂
socle, prime radical	C₂³×C₁₇	C₂×D₈
hypercenter	C₂×#494	D₁₇
hypocenter	C₁₇	#13330
LCS	G ▷ C₂²×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#494

subgroup

G/H

center

C₂³

C₂×#63228

commutator, cosocle

C₂²×C₈×C₁₇

C₂³

Frattini

C₂²×C₈

C₂²×D₁₇

Fitting

C₂×C₁₇×#494

C₂

socle, prime radical

C₂³×C₁₇

C₂×D₈

D₁₇

C₁₇

G ▷ C₂²×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#494

N	H ≅ G/N	type
98. C₂×C₄×C₁₇	Q₃₂	semidirect
184. C₁₇	#13330	semidirect
241. C₂×C₄	#10587500	semidirect

H ≅ G/N

type

98. C₂×C₄×C₁₇

Q₃₂

semidirect

184. C₁₇

#13330

semidirect

241. C₂×C₄

#10587500

semidirect

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

subgroup	index
C₂²×#10587500	2
C₂×#11762613	2
#14529645	2
#14526862	2
C₂×C₁₇×#494	2
#13330	17

subgroup

index

C₂×C₁₇×#494

Subgroups — #16953184

Conjugacy classes of subgroups

Complements

Maximal subgroups