Group #35323264 — subgroups

Subgroups — #35323264

Order 21248.

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×#14581738	C₂	1	2	yes	maximal
2	C₂×#19127505	C₂	1	2	yes	maximal
3	#24908324	C₂	1	1	yes	maximal, characteristic
4	#24905541	C₂	1	1	yes	maximal, characteristic
5	C₂×#494×C₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₃₂	C₂²	1	1	yes	characteristic
7	C₂×#14581738	—	2	4	no	—
8	C₂×#14581738	—	2	4	no	—
9	C₂×#14581738	—	2	4	no	—
10	C₂²×C₈₃⋊C₁₆	C₂²	1	2	yes	—
11	C₂×#14581726	C₂²	1	1	yes	characteristic
12	C₂×#14581717	—	2	1	no	—
13	#19127607	—	2	1	no	—
14	#19127505	—	2	4	no	—
15	C₂²×Q₁₆×C₈₃	—	2	1	no	—
16	C₂²×Q₁₆×C₈₃	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₈₃	—	2	1	no	—
18	#494×C₈₃	—	2	4	no	—
19	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
20	C₂²×Dic₁₆₆	—	2	1	no	—
21	C₂×Dic₃₃₂	—	2	2	no	—
22	C₂×Dic₃₃₂	—	2	2	no	—
23	C₂×Dic₃₃₂	—	2	1	no	—
24	C₂×Dic₃₃₂	D₄	1	2	yes	—
25	C₂×C₄⋊Dic₈₃	—	2	1	no	—
26	#14581738	—	2	16	no	—
27	C₂×C₈₃⋊C₁₆	—	2	2	no	—
28	C₂×C₈₃⋊C₁₆	—	2	2	no	—
29	C₂×C₈₃⋊C₁₆	D₄	1	4	yes	—
30	#14581726	—	2	2	no	—
31	#14581717	—	4	2	no	—
32	C₈₃⋊#95	—	4	2	no	—
33	C₂²×Q₈×C₈₃	—	2	2	no	—
34	C₂×Q₁₆×C₈₃	—	2	4	no	—
35	C₂×Q₁₆×C₈₃	—	2	2	no	—
36	C₂×Q₁₆×C₈₃	—	2	2	no	—
37	C₂×Q₁₆×C₈₃	—	2	2	no	—
38	C₂×Q₁₆×C₈₃	—	2	2	no	—
39	C₂×Q₁₆×C₈₃	—	2	2	no	—
40	C₂×Q₁₆×C₈₃	—	4	2	no	—
41	C₂×Q₁₆×C₈₃	—	4	2	no	—
42	C₂×Q₁₆×C₈₃	D₄	1	4	yes	—
43	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
45	C₄⋊Q₈×C₈₃	—	2	4	no	—
46	C₄⋊Q₈×C₈₃	—	4	2	no	—
47	C₂×C₄⋊C₄×C₈₃	—	4	2	no	—
48	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
49	C₄×C₈×C₈₃	—	2	2	no	—
50	C₂×Dic₁₆₆	—	2	2	no	—
51	C₂×Dic₁₆₆	—	4	1	no	—
52	C₂×Dic₁₆₆	—	4	1	no	—
53	C₂×Dic₁₆₆	—	4	1	no	—
54	C₂×Dic₁₆₆	—	4	1	no	—
55	C₂×Dic₁₆₆	—	4	1	no	—
56	C₂²×Dic₈₃	—	4	1	no	—
57	C₂²×Dic₈₃	—	4	1	no	—
58	Dic₃₃₂	—	2	4	no	—
59	Dic₃₃₂	—	4	2	no	—
60	C₄⋊Dic₈₃	—	4	1	no	—
61	C₄⋊Dic₈₃	—	4	1	no	—
62	C₈₃⋊C₁₆	—	2	4	no	—
63	C₂×Q₈×C₈₃	—	2	4	no	—
64	C₂×Q₈×C₈₃	—	4	2	no	—
65	C₂×Q₈×C₈₃	—	4	2	no	—
66	C₂×Q₈×C₈₃	—	4	2	no	—
67	C₂×Q₈×C₈₃	—	4	2	no	—
68	C₂×Q₈×C₈₃	—	4	2	no	—
69	C₂²×C₄×C₈₃	—	4	2	no	—
70	C₂²×C₄×C₈₃	D₈	1	2	yes	—
71	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
72	Q₁₆×C₈₃	—	2	4	no	—
73	Q₁₆×C₈₃	—	2	4	no	—
74	Q₁₆×C₈₃	—	4	8	no	—
75	Q₁₆×C₈₃	—	4	2	no	—
76	Q₁₆×C₈₃	—	4	2	no	—
77	C₂×C₈×C₈₃	—	2	1	no	—
78	C₂×C₈×C₈₃	—	2	1	no	—
79	C₂×C₈×C₈₃	D₈	1	2	yes	—
80	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
81	C₂×C₈×C₈₃	C₂×D₄	1	2	yes	—
82	C₂×C₈×C₈₃	C₂×D₄	1	2	yes	—
83	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
84	C₄⋊C₄×C₈₃	—	4	8	no	—
85	C₄²×C₈₃	—	2	1	no	—
86	C₄²×C₈₃	—	2	1	no	—
87	C₂³×C₈₃	C₂×D₈	1	1	yes	characteristic
88	Q₈×C₈₃	—	4	4	no	—
89	Q₈×C₈₃	—	4	4	no	—
90	Q₈×C₈₃	—	8	2	no	—
91	Q₈×C₈₃	—	8	2	no	—
92	C₂×C₄×C₈₃	—	2	2	no	—
93	C₂×C₄×C₈₃	—	2	2	no	—
94	C₂×C₄×C₈₃	—	4	4	no	—
95	C₂×C₄×C₈₃	—	8	2	no	—
96	C₂×C₄×C₈₃	—	8	2	no	—
97	C₂×C₄×C₈₃	Q₃₂	1	4	yes	complemented
98	C₂×C₄×C₈₃	#120	1	1	yes	characteristic
99	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
100	C₂×C₄×C₈₃	#127	1	1	yes	characteristic
101	C₂×C₄×C₈₃	C₂×D₈	1	1	yes	characteristic
102	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
104	C₂×Dic₈₃	—	4	2	no	—
105	C₂×Dic₈₃	—	8	1	no	—
106	C₂×Dic₈₃	—	8	1	no	—
107	C₂×Dic₈₃	—	8	1	no	—
108	C₂×Dic₈₃	—	8	2	no	—
109	Dic₁₆₆	—	4	2	no	—
110	Dic₁₆₆	—	4	2	no	—
111	Dic₁₆₆	—	8	1	no	—
112	Dic₁₆₆	—	8	1	no	—
113	C₈×C₈₃	—	2	2	no	—
114	C₈×C₈₃	#120	1	2	yes	—
115	C₈×C₈₃	#121	1	2	yes	—
116	C₂²×C₈₃	#447	1	1	yes	characteristic
117	C₂²×C₈₃	#459	1	1	yes	characteristic
118	C₂²×C₈₃	#493	1	1	yes	characteristic
119	C₂²×C₈₃	C₂×Q₃₂	1	2	yes	—
120	C₂²×C₈₃	#510	1	2	yes	—
121	C₄×C₈₃	—	2	4	no	—
122	C₄×C₈₃	—	8	4	no	—
123	C₄×C₈₃	#392	1	1	yes	characteristic
124	C₄×C₈₃	#447	1	1	yes	characteristic
125	C₄×C₈₃	#459	1	1	yes	characteristic
126	C₄×C₈₃	#496	1	1	yes	characteristic
127	Dic₈₃	—	8	2	no	—
128	Dic₈₃	—	16	1	no	—
129	#13330	—	83	1	no	maximal, Sylow
130	C₂×C₈₃	#2011	1	1	yes	characteristic
131	C₂×C₈₃	#2188	1	2	yes	—
132	C₂×C₈₃	#2209	1	2	yes	—
133	C₂×C₈₃	#2247	1	1	yes	characteristic
134	C₂×C₈₃	#2251	1	1	yes	characteristic
135	C₂²×Q₃₂	—	83	2	no	—
136	C₂×#494	D₈₃	1	1	yes	characteristic
137	C₂×#358	—	83	2	no	—
138	#1969	—	83	1	no	—
139	#1374	—	83	1	no	—
140	C₈₃	#13330	1	1	yes	characteristic, complemented, Sylow
141	C₂²×Q₁₆	—	2	1	no	—
142	C₂²×Q₁₆	—	83	1	no	—
143	C₂²×Q₁₆	C₂×D₈₃	1	2	yes	—
144	C₂×C₄⋊Q₈	—	2	1	no	—
145	C₂×Q₃₂	—	166	4	no	—
146	C₂×Q₃₂	—	166	4	no	—
147	C₂×Q₃₂	—	166	4	no	—
148	C₂²×C₁₆	—	83	2	no	—
149	#494	—	2	4	no	—
150	C₂×#107	—	83	1	no	—
151	C₂×#103	—	166	1	no	—
152	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
153	#391	—	166	1	no	—
154	#358	—	166	4	no	—
155	C₂²×Q₈	—	2	2	no	—
156	C₂²×Q₈	—	166	1	no	—
157	C₂×Q₁₆	—	2	4	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	—	2	2	no	—
163	C₂×Q₁₆	—	4	2	no	—
164	C₂×Q₁₆	—	4	2	no	—
165	C₂×Q₁₆	—	83	2	no	—
166	C₂×Q₁₆	—	166	2	no	—
167	C₂×Q₁₆	—	166	2	no	—
168	C₂×Q₁₆	—	166	1	no	—
169	C₂×Q₁₆	C₂²⋊D₈₃	1	4	yes	—
170	C₂²×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
171	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
172	C₄⋊Q₈	—	2	4	no	—
173	C₄⋊Q₈	—	4	2	no	—
174	C₂×C₄⋊C₄	—	4	2	no	—
175	C₂×C₄⋊C₄	—	166	1	no	—
176	C₂×C₄²	C₂²⋊D₈₃	1	1	yes	characteristic
177	Q₃₂	—	166	16	no	—
178	C₂×C₁₆	—	83	4	no	—
179	C₂×C₁₆	—	166	2	no	—
180	C₂×C₁₆	—	166	2	no	—
181	#107	—	166	2	no	—
182	#103	—	332	2	no	—
183	C₄×C₈	—	2	2	no	—
184	#95	—	332	2	no	—
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	—	332	1	no	—
192	C₂×Q₈	—	332	1	no	—
193	C₂×Q₈	—	332	1	no	—
194	C₂×Q₈	—	332	1	no	—
195	C₂×Q₈	—	332	1	no	—
196	C₂×Q₈	—	166	2	no	—
197	C₂²×C₄	—	4	2	no	—
198	C₂²×C₄	—	332	1	no	—
199	C₂²×C₄	—	332	1	no	—
200	C₂²×C₄	#13050575	1	2	yes	—
201	C₂²×C₄	C₂×C₂²⋊D₈₃	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	—	332	2	no	—
208	Q₁₆	—	166	4	no	—
209	C₂×C₈	—	2	1	no	—
210	C₂×C₈	—	2	1	no	—
211	C₂×C₈	#13050575	1	2	yes	—
212	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
213	C₂×C₈	D₄×D₈₃	1	2	yes	—
214	C₂×C₈	C₂×C₂²⋊D₈₃	1	2	yes	—
215	C₂×C₈	#13050589	1	1	yes	characteristic
216	C₄⋊C₄	—	4	8	no	—
217	C₄⋊C₄	—	332	1	no	—
218	C₄⋊C₄	—	332	1	no	—
219	C₄²	—	2	1	no	—
220	C₄²	—	2	1	no	—
221	C₁₆	—	166	4	no	—
222	C₂³	C₂×#13050575	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	—	332	2	no	—
228	Q₈	—	332	2	no	—
229	Q₈	—	664	1	no	—
230	Q₈	—	664	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	—	332	2	no	—
237	C₂×C₄	—	664	1	no	—
238	C₂×C₄	—	664	2	no	—
239	C₂×C₄	—	664	1	no	—
240	C₂×C₄	—	664	1	no	—
241	C₂×C₄	#14581738	1	4	yes	complemented
242	C₂×C₄	#14581761	1	1	yes	characteristic
243	C₂×C₄	#14581763	1	1	yes	characteristic
244	C₂×C₄	#14581788	1	1	yes	characteristic
245	C₂×C₄	C₂×#13050575	1	1	yes	characteristic
246	C₂×C₄	#14581818	1	1	yes	characteristic
247	C₂×C₄	#14581818	1	1	yes	characteristic
248	C₈	—	2	2	no	—
249	C₈	#14581760	1	2	yes	—
250	C₈	#14581764	1	2	yes	—
251	C₂²	#19127835	1	1	yes	characteristic
252	C₂²	#19127893	1	1	yes	characteristic
253	C₂²	#19128077	1	1	yes	characteristic
254	C₂²	C₂×#14581738	1	2	yes	—
255	C₂²	#19128142	1	2	yes	—
256	C₄	—	2	4	no	—
257	C₄	—	8	4	no	—
258	C₄	—	1328	1	no	—
259	C₄	—	664	2	no	—
260	C₄	#19127609	1	1	yes	characteristic
261	C₄	#19127835	1	1	yes	characteristic
262	C₄	#19127893	1	1	yes	characteristic
263	C₄	#19128088	1	1	yes	characteristic
264	C₂	#24908534	1	1	yes	characteristic
265	C₂	#24909397	1	2	yes	—
266	C₂	#24909510	1	2	yes	—
267	C₂	#24909715	1	1	yes	characteristic
268	C₂	#24909732	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#14581738

C₂

yes

maximal

C₂×#19127505

C₂

yes

maximal

#24908324

C₂

yes

maximal, characteristic

#24905541

C₂

yes

maximal, characteristic

C₂×#494×C₈₃

C₂

yes

maximal, characteristic

C₂²×Dic₃₃₂

C₂²

yes

—

—

—

C₂²×C₈₃⋊C₁₆

C₂²

yes

—

C₂×#14581726

C₂²

yes

—

—

—

C₂²×Q₁₆×C₈₃

—

C₂²×Q₁₆×C₈₃

C₂²

yes

—

C₂×C₄⋊Q₈×C₈₃

—

#494×C₈₃

—

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

C₂²×Dic₁₆₆

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

D₄

yes

—

C₂×C₄⋊Dic₈₃

—

#14581738

—

C₂×C₈₃⋊C₁₆

—

C₂×C₈₃⋊C₁₆

—

C₂×C₈₃⋊C₁₆

D₄

yes

—

#14581726

—

#14581717

—

C₈₃⋊#95

—

C₂²×Q₈×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

D₄

yes

—

C₂²×C₈×C₈₃

D₄

yes

characteristic

C₂²×C₈×C₈₃

C₂³

yes

characteristic

C₄⋊Q₈×C₈₃

—

C₄⋊Q₈×C₈₃

—

C₂×C₄⋊C₄×C₈₃

—

C₂×C₄²×C₈₃

D₄

yes

characteristic

C₄×C₈×C₈₃

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂²×Dic₈₃

—

C₂²×Dic₈₃

—

Dic₃₃₂

—

Dic₃₃₂

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₈₃⋊C₁₆

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

D₈

yes

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

Q₁₆×C₈₃

—

Q₁₆×C₈₃

—

Q₁₆×C₈₃

—

Q₁₆×C₈₃

—

Q₁₆×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

D₈

yes

—

C₂×C₈×C₈₃

C₂×D₄

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

—

C₂×C₈×C₈₃

C₂×D₄

yes

—

C₂×C₈×C₈₃

#41

yes

characteristic

C₄⋊C₄×C₈₃

—

C₄²×C₈₃

—

C₄²×C₈₃

—

C₂³×C₈₃

C₂×D₈

yes

characteristic

Q₈×C₈₃

—

Q₈×C₈₃

—

Q₈×C₈₃

—

Q₈×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

Q₃₂

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

100

C₂×C₄×C₈₃

#127

yes

characteristic

101

C₂×C₄×C₈₃

C₂×D₈

yes

characteristic

102

C₂×C₄×C₈₃

AGL(1,ℤ/8)

yes

characteristic

103

C₂×C₄×C₈₃

AGL(1,ℤ/8)

yes

characteristic

104

C₂×Dic₈₃

—

105

C₂×Dic₈₃

—

106

C₂×Dic₈₃

—

107

C₂×Dic₈₃

—

108

C₂×Dic₈₃

—

109

Dic₁₆₆

—

110

Dic₁₆₆

—

111

Dic₁₆₆

—

112

Dic₁₆₆

—

113

C₈×C₈₃

—

114

C₈×C₈₃

#120

yes

—

115

C₈×C₈₃

#121

yes

—

116

C₂²×C₈₃

#447

yes

characteristic

117

C₂²×C₈₃

#459

yes

characteristic

118

C₂²×C₈₃

#493

yes

characteristic

119

C₂²×C₈₃

C₂×Q₃₂

yes

—

120

C₂²×C₈₃

#510

yes

—

121

C₄×C₈₃

—

122

C₄×C₈₃

—

123

C₄×C₈₃

#392

yes

characteristic

124

C₄×C₈₃

#447

yes

characteristic

125

C₄×C₈₃

#459

yes

characteristic

126

C₄×C₈₃

#496

yes

characteristic

127

Dic₈₃

—

128

Dic₈₃

—

129

#13330

—

maximal, Sylow

130

C₂×C₈₃

#2011

yes

characteristic

131

C₂×C₈₃

#2188

yes

—

132

C₂×C₈₃

#2209

yes

—

133

C₂×C₈₃

#2247

yes

characteristic

134

C₂×C₈₃

#2251

yes

characteristic

135

C₂²×Q₃₂

—

136

C₂×#494

D₈₃

yes

characteristic

137

C₂×#358

—

138

#1969

—

139

#1374

—

140

C₈₃

#13330

yes

characteristic, complemented, Sylow

141

C₂²×Q₁₆

—

142

C₂²×Q₁₆

—

143

C₂²×Q₁₆

C₂×D₈₃

yes

—

144

C₂×C₄⋊Q₈

—

145

C₂×Q₃₂

—

166

—

146

C₂×Q₃₂

—

166

—

147

C₂×Q₃₂

—

166

—

148

C₂²×C₁₆

—

149

#494

—

150

C₂×#107

—

151

C₂×#103

—

166

—

152

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

153

#391

—

166

—

154

#358

—

166

—

155

C₂²×Q₈

—

156

C₂²×Q₈

—

166

—

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

—

166

—

167

C₂×Q₁₆

—

166

—

168

C₂×Q₁₆

—

166

—

169

C₂×Q₁₆

C₂²⋊D₈₃

yes

—

170

C₂²×C₈

C₂²⋊D₈₃

yes

characteristic

171

C₂²×C₈

C₂²×D₈₃

yes

characteristic

172

C₄⋊Q₈

—

173

C₄⋊Q₈

—

174

C₂×C₄⋊C₄

—

175

C₂×C₄⋊C₄

—

166

—

176

C₂×C₄²

C₂²⋊D₈₃

yes

characteristic

177

Q₃₂

—

166

—

178

C₂×C₁₆

—

179

C₂×C₁₆

—

166

—

180

C₂×C₁₆

—

166

—

181

#107

—

166

—

182

#103

—

332

—

183

C₄×C₈

—

184

#95

—

332

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

—

332

—

192

C₂×Q₈

—

332

—

193

C₂×Q₈

—

332

—

194

C₂×Q₈

—

332

—

195

C₂×Q₈

—

332

—

196

C₂×Q₈

—

166

—

197

C₂²×C₄

—

198

C₂²×C₄

—

332

—

199

C₂²×C₄

—

332

—

200

C₂²×C₄

#13050575

yes

—

201

C₂²×C₄

C₂×C₂²⋊D₈₃

yes

characteristic

202

Q₁₆

—

203

Q₁₆

—

204

Q₁₆

—

205

Q₁₆

—

206

Q₁₆

—

207

Q₁₆

—

332

—

208

Q₁₆

—

166

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

#13050575

yes

—

212

C₂×C₈

D₄×D₈₃

yes

characteristic

213

C₂×C₈

D₄×D₈₃

yes

—

214

C₂×C₈

C₂×C₂²⋊D₈₃

yes

—

215

C₂×C₈

#13050589

yes

characteristic

216

C₄⋊C₄

—

217

C₄⋊C₄

—

332

—

218

C₄⋊C₄

—

332

—

219

C₄²

—

220

C₄²

—

221

C₁₆

—

166

—

222

C₂³

C₂×#13050575

yes

characteristic

223

Q₈

—

224

Q₈

—

225

Q₈

—

226

Q₈

—

227

Q₈

—

332

—

228

Q₈

—

332

—

229

Q₈

—

664

—

230

Q₈

—

664

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

332

—

237

C₂×C₄

—

664

—

238

C₂×C₄

—

664

—

239

C₂×C₄

—

664

—

240

C₂×C₄

—

664

—

241

C₂×C₄

#14581738

yes

complemented

242

C₂×C₄

#14581761

yes

characteristic

243

C₂×C₄

#14581763

yes

characteristic

244

C₂×C₄

#14581788

yes

characteristic

245

C₂×C₄

C₂×#13050575

yes

characteristic

246

C₂×C₄

#14581818

yes

characteristic

247

C₂×C₄

#14581818

yes

characteristic

248

C₈

—

249

C₈

#14581760

yes

—

250

C₈

#14581764

yes

—

251

C₂²

#19127835

yes

characteristic

252

C₂²

#19127893

yes

characteristic

253

C₂²

#19128077

yes

characteristic

254

C₂²

C₂×#14581738

yes

—

255

C₂²

#19128142

yes

—

256

C₄

—

257

C₄

—

258

C₄

—

1328

—

259

C₄

—

664

—

260

C₄

#19127609

yes

characteristic

261

C₄

#19127835

yes

characteristic

262

C₄

#19127893

yes

characteristic

263

C₄

#19128088

yes

characteristic

264

C₂

#24908534

yes

characteristic

265

C₂

#24909397

yes

—

266

C₂

#24909510

yes

—

267

C₂

#24909715

yes

characteristic

268

C₂

#24909732

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×#13050575
commutator, cosocle	C₂²×C₈×C₈₃	C₂³
Frattini	C₂²×C₈	C₂²×D₈₃
Fitting	C₂×#494×C₈₃	C₂
socle, prime radical	C₂³×C₈₃	C₂×D₈
hypercenter	C₂×#494	D₈₃
hypocenter	C₈₃	#13330
LCS	G ▷ C₂²×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#494

subgroup

G/H

center

C₂³

C₂×#13050575

commutator, cosocle

C₂²×C₈×C₈₃

C₂³

Frattini

C₂²×C₈

C₂²×D₈₃

Fitting

C₂×#494×C₈₃

C₂

socle, prime radical

C₂³×C₈₃

C₂×D₈

D₈₃

C₈₃

G ▷ C₂²×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

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

N	H ≅ G/N	type
97. C₂×C₄×C₈₃	Q₃₂	semidirect
140. C₈₃	#13330	semidirect
241. C₂×C₄	#14581738	semidirect

H ≅ G/N

type

97. C₂×C₄×C₈₃

Q₃₂

semidirect

140. C₈₃

#13330

semidirect

241. C₂×C₄

#14581738

semidirect

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

subgroup	index
C₂²×#14581738	2
C₂×#19127505	2
#24908324	2
#24905541	2
C₂×#494×C₈₃	2
#13330	83

subgroup

index

C₂×#494×C₈₃

Subgroups — #35323264

Conjugacy classes of subgroups

Complements

Maximal subgroups