Group #25015459 — subgroups

Subgroups — #25015459

Order 11008.

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×Dic₃₄₄	C₂	1	2	yes	maximal
2	C₂×#14583279	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582704	C₂	1	2	yes	maximal
4	#19135456	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#1374	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₇₂	—	2	1	no	—
7	C₂²×Dic₁₇₂	C₂²	1	2	yes	—
8	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#13063325	—	2	1	no	—
10	C₂×Dic₃₄₄	—	2	4	no	—
11	C₂×Dic₃₄₄	—	2	4	no	—
12	C₂×Dic₃₄₄	—	2	4	no	—
13	#14583279	—	2	4	no	—
14	C₂×#13063259	C₂²	1	1	yes	characteristic
15	C₂×#13063250	—	2	1	no	—
16	#14582805	—	2	1	no	—
17	#14582704	—	2	4	no	—
18	C₂²×C₁₆×C₄₃	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×Dic₈₆	—	2	1	no	—
21	C₂²×Dic₈₆	—	2	2	no	—
22	C₂×Dic₁₇₂	—	2	2	no	—
23	C₂×Dic₁₇₂	—	2	2	no	—
24	C₂×Dic₁₇₂	—	2	2	no	—
25	C₂×Dic₁₇₂	—	2	2	no	—
26	C₂×Dic₁₇₂	—	2	2	no	—
27	C₂×Dic₁₇₂	—	2	2	no	—
28	C₂×Dic₁₇₂	—	2	4	no	—
29	C₂×Dic₁₇₂	—	2	2	no	—
30	C₂×Dic₁₇₂	—	2	1	no	—
31	C₂×Dic₁₇₂	—	4	2	no	—
32	C₂×Dic₁₇₂	—	4	2	no	—
33	C₂×Dic₁₇₂	D₄	1	2	yes	—
34	C₂×Dic₁₇₂	D₄	1	4	yes	—
35	#13063325	—	2	4	no	—
36	#13063325	—	4	2	no	—
37	C₂×C₄⋊Dic₄₃	—	2	1	no	—
38	C₂×C₄⋊Dic₄₃	—	4	2	no	—
39	Dic₃₄₄	—	2	16	no	—
40	#13063259	—	2	2	no	—
41	#13063250	—	4	2	no	—
42	C₄₃⋊#95	—	4	2	no	—
43	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
45	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
46	C₂×C₁₆×C₄₃	—	2	2	no	—
47	C₂×C₁₆×C₄₃	—	2	2	no	—
48	C₂×C₁₆×C₄₃	D₄	1	4	yes	—
49	C₄×C₈×C₄₃	—	2	2	no	—
50	C₂²×C₄×C₄₃	D₈	1	2	yes	—
51	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×Dic₄₃	—	4	1	no	—
53	C₂²×Dic₄₃	—	4	2	no	—
54	C₂²×Dic₄₃	—	4	1	no	—
55	C₂×Dic₈₆	—	2	4	no	—
56	C₂×Dic₈₆	—	2	2	no	—
57	C₂×Dic₈₆	—	4	1	no	—
58	C₂×Dic₈₆	—	4	2	no	—
59	C₂×Dic₈₆	—	4	1	no	—
60	C₂×Dic₈₆	—	4	2	no	—
61	C₂×Dic₈₆	—	4	1	no	—
62	C₂×Dic₈₆	—	4	2	no	—
63	C₂×Dic₈₆	—	4	2	no	—
64	C₂×Dic₈₆	—	4	1	no	—
65	C₂×Dic₈₆	—	4	2	no	—
66	C₂×Dic₈₆	—	4	1	no	—
67	C₂×C₈×C₄₃	—	2	1	no	—
68	C₂×C₈×C₄₃	—	2	1	no	—
69	C₂×C₈×C₄₃	D₈	1	2	yes	—
70	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
71	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
73	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
74	C₄²×C₄₃	—	2	1	no	—
75	C₄²×C₄₃	—	2	1	no	—
76	C₄⋊Dic₄₃	—	4	8	no	—
77	C₄⋊Dic₄₃	—	4	1	no	—
78	C₄⋊Dic₄₃	—	4	1	no	—
79	Dic₁₇₂	—	2	4	no	—
80	Dic₁₇₂	—	2	4	no	—
81	Dic₁₇₂	—	2	4	no	—
82	Dic₁₇₂	—	4	8	no	—
83	Dic₁₇₂	—	4	2	no	—
84	Dic₁₇₂	—	4	2	no	—
85	Dic₁₇₂	—	4	2	no	—
86	C₁₆×C₄₃	—	2	4	no	—
87	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
88	C₂×C₄×C₄₃	—	2	2	no	—
89	C₂×C₄×C₄₃	—	2	2	no	—
90	C₂×C₄×C₄₃	Q₃₂	1	4	yes	complemented
91	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
92	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
93	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
94	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
95	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
96	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
97	C₂×Dic₄₃	—	4	4	no	—
98	C₂×Dic₄₃	—	4	2	no	—
99	C₂×Dic₄₃	—	8	1	no	—
100	C₂×Dic₄₃	—	8	2	no	—
101	C₂×Dic₄₃	—	8	1	no	—
102	C₂×Dic₄₃	—	8	2	no	—
103	C₂×Dic₄₃	—	8	1	no	—
104	C₂×Dic₄₃	—	8	2	no	—
105	Dic₈₆	—	4	2	no	—
106	Dic₈₆	—	4	4	no	—
107	Dic₈₆	—	4	4	no	—
108	Dic₈₆	—	4	2	no	—
109	Dic₈₆	—	8	1	no	—
110	Dic₈₆	—	8	2	no	—
111	Dic₈₆	—	8	2	no	—
112	Dic₈₆	—	8	1	no	—
113	C₈×C₄₃	—	2	2	no	—
114	C₈×C₄₃	#120	1	2	yes	—
115	C₈×C₄₃	#121	1	2	yes	—
116	#13330	—	43	1	no	maximal, Sylow
117	C₂²×C₄₃	#447	1	1	yes	characteristic
118	C₂²×C₄₃	#459	1	1	yes	characteristic
119	C₂²×C₄₃	#493	1	1	yes	characteristic
120	C₂²×C₄₃	C₂×Q₃₂	1	2	yes	—
121	C₂²×C₄₃	#510	1	2	yes	—
122	C₄×C₄₃	—	2	4	no	—
123	C₄×C₄₃	#392	1	1	yes	characteristic
124	C₄×C₄₃	#447	1	1	yes	characteristic
125	C₄×C₄₃	#459	1	1	yes	characteristic
126	C₄×C₄₃	#496	1	1	yes	characteristic
127	Dic₄₃	—	8	4	no	—
128	Dic₄₃	—	8	2	no	—
129	Dic₄₃	—	16	1	no	—
130	C₂²×Q₃₂	—	43	2	no	—
131	C₂×#494	—	43	1	no	—
132	C₂×#358	—	43	2	no	—
133	#1969	—	43	1	no	—
134	#1374	D₄₃	1	1	yes	characteristic
135	C₂×C₄₃	#2011	1	1	yes	characteristic
136	C₂×C₄₃	#2188	1	2	yes	—
137	C₂×C₄₃	#2209	1	2	yes	—
138	C₂×C₄₃	#2247	1	1	yes	characteristic
139	C₂×C₄₃	#2251	1	1	yes	characteristic
140	C₂²×Q₁₆	—	43	2	no	—
141	C₂²×Q₁₆	—	43	1	no	—
142	C₂²×Q₁₆	—	86	1	no	—
143	C₂×C₄⋊Q₈	—	86	1	no	—
144	C₂×Q₃₂	—	86	4	no	—
145	C₂×Q₃₂	—	86	4	no	—
146	C₂×Q₃₂	—	86	4	no	—
147	C₂²×C₁₆	C₂×D₄₃	1	2	yes	—
148	#494	—	86	4	no	—
149	C₂×#107	—	43	1	no	—
150	C₂×#103	—	86	1	no	—
151	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
152	#391	—	86	1	no	—
153	#358	—	86	4	no	—
154	C₄₃	#13330	1	1	yes	characteristic, complemented, Sylow
155	C₂²×Q₈	—	86	2	no	—
156	C₂²×Q₈	—	86	1	no	—
157	C₂×Q₁₆	—	43	4	no	—
158	C₂×Q₁₆	—	43	2	no	—
159	C₂×Q₁₆	—	86	4	no	—
160	C₂×Q₁₆	—	86	2	no	—
161	C₂×Q₁₆	—	86	2	no	—
162	C₂×Q₁₆	—	86	2	no	—
163	C₂×Q₁₆	—	86	2	no	—
164	C₂×Q₁₆	—	86	2	no	—
165	C₂×Q₁₆	—	86	2	no	—
166	C₂×Q₁₆	—	86	2	no	—
167	C₂×Q₁₆	—	86	1	no	—
168	C₂×Q₁₆	—	172	2	no	—
169	C₂×Q₁₆	—	172	2	no	—
170	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
171	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
172	C₄⋊Q₈	—	86	4	no	—
173	C₄⋊Q₈	—	172	2	no	—
174	C₂×C₄⋊C₄	—	86	1	no	—
175	C₂×C₄⋊C₄	—	172	2	no	—
176	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
177	Q₃₂	—	86	16	no	—
178	C₂×C₁₆	—	2	2	no	—
179	C₂×C₁₆	—	2	2	no	—
180	C₂×C₁₆	D₁₇₂	1	4	yes	—
181	#107	—	86	2	no	—
182	#103	—	172	2	no	—
183	C₄×C₈	—	2	2	no	—
184	#95	—	172	2	no	—
185	C₂×Q₈	—	86	4	no	—
186	C₂×Q₈	—	86	2	no	—
187	C₂×Q₈	—	172	1	no	—
188	C₂×Q₈	—	172	2	no	—
189	C₂×Q₈	—	172	2	no	—
190	C₂×Q₈	—	172	1	no	—
191	C₂×Q₈	—	172	1	no	—
192	C₂×Q₈	—	172	2	no	—
193	C₂×Q₈	—	172	2	no	—
194	C₂×Q₈	—	172	1	no	—
195	C₂×Q₈	—	172	2	no	—
196	C₂×Q₈	—	172	1	no	—
197	C₂²×C₄	—	172	1	no	—
198	C₂²×C₄	—	172	1	no	—
199	C₂²×C₄	—	172	2	no	—
200	C₂²×C₄	D₃₄₄	1	2	yes	—
201	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
202	Q₁₆	—	86	4	no	—
203	Q₁₆	—	86	4	no	—
204	Q₁₆	—	86	4	no	—
205	Q₁₆	—	172	8	no	—
206	Q₁₆	—	172	2	no	—
207	Q₁₆	—	172	2	no	—
208	Q₁₆	—	172	2	no	—
209	C₂×C₈	—	2	1	no	—
210	C₂×C₈	—	2	1	no	—
211	C₂×C₈	D₃₄₄	1	2	yes	—
212	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
213	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
214	C₂×C₈	D₄×D₄₃	1	2	yes	—
215	C₂×C₈	#10621902	1	1	yes	characteristic
216	C₄⋊C₄	—	172	8	no	—
217	C₄⋊C₄	—	172	1	no	—
218	C₄⋊C₄	—	172	1	no	—
219	C₄²	—	2	1	no	—
220	C₄²	—	2	1	no	—
221	C₁₆	—	2	4	no	—
222	C₂³	C₂×D₃₄₄	1	1	yes	characteristic
223	Q₈	—	344	2	no	—
224	Q₈	—	344	2	no	—
225	Q₈	—	344	1	no	—
226	Q₈	—	344	1	no	—
227	Q₈	—	172	2	no	—
228	Q₈	—	172	4	no	—
229	Q₈	—	172	2	no	—
230	Q₈	—	172	4	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	344	2	no	—
234	C₂×C₄	—	344	1	no	—
235	C₂×C₄	—	344	2	no	—
236	C₂×C₄	—	344	1	no	—
237	C₂×C₄	—	344	2	no	—
238	C₂×C₄	—	344	1	no	—
239	C₂×C₄	—	172	2	no	—
240	C₂×C₄	—	172	4	no	—
241	C₂×C₄	Dic₃₄₄	1	4	yes	complemented
242	C₂×C₄	#13063295	1	1	yes	characteristic
243	C₂×C₄	#13063300	1	1	yes	characteristic
244	C₂×C₄	#13063322	1	1	yes	characteristic
245	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
246	C₂×C₄	#13063353	1	1	yes	characteristic
247	C₂×C₄	#13063353	1	1	yes	characteristic
248	C₈	—	2	2	no	—
249	C₈	#13063295	1	2	yes	—
250	C₈	#13063300	1	2	yes	—
251	C₂²	#14583035	1	1	yes	characteristic
252	C₂²	#14583095	1	1	yes	characteristic
253	C₂²	#14583276	1	1	yes	characteristic
254	C₂²	C₂×Dic₃₄₄	1	2	yes	—
255	C₂²	#14583342	1	2	yes	—
256	C₄	—	2	4	no	—
257	C₄	—	344	4	no	—
258	C₄	—	344	2	no	—
259	C₄	—	688	1	no	—
260	C₄	#14582809	1	1	yes	characteristic
261	C₄	#14583035	1	1	yes	characteristic
262	C₄	#14583095	1	1	yes	characteristic
263	C₄	#14583288	1	1	yes	characteristic
264	C₂	#19135668	1	1	yes	characteristic
265	C₂	#19136531	1	2	yes	—
266	C₂	#19136646	1	2	yes	—
267	C₂	#19136848	1	1	yes	characteristic
268	C₂	#19136866	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₃₄₄

C₂

yes

maximal

C₂×#14583279

C₂

yes

maximal, characteristic

C₂×#14582704

C₂

yes

maximal

#19135456

C₂

yes

maximal, characteristic

C₄₃×#1374

C₂

yes

maximal, characteristic

C₂²×Dic₁₇₂

—

C₂²×Dic₁₇₂

C₂²

yes

—

C₂²×Dic₁₇₂

C₂²

yes

characteristic

C₂×#13063325

—

C₂×Dic₃₄₄

—

C₂×Dic₃₄₄

—

C₂×Dic₃₄₄

—

#14583279

—

C₂×#13063259

C₂²

yes

—

—

—

C₂²×C₁₆×C₄₃

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂²×Dic₈₆

—

C₂²×Dic₈₆

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

D₄

yes

—

C₂×Dic₁₇₂

D₄

yes

—

#13063325

—

#13063325

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

Dic₃₄₄

—

#13063259

—

#13063250

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

D₄

yes

—

C₄×C₈×C₄₃

—

C₂²×C₄×C₄₃

D₈

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₈

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

#41

yes

characteristic

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

C₁₆×C₄₃

—

C₂³×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

Q₃₂

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×D₈

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

100

C₂×Dic₄₃

—

101

C₂×Dic₄₃

—

102

C₂×Dic₄₃

—

103

C₂×Dic₄₃

—

104

C₂×Dic₄₃

—

105

Dic₈₆

—

106

Dic₈₆

—

107

Dic₈₆

—

108

Dic₈₆

—

109

Dic₈₆

—

110

Dic₈₆

—

111

Dic₈₆

—

112

Dic₈₆

—

113

C₈×C₄₃

—

114

C₈×C₄₃

#120

yes

—

115

C₈×C₄₃

#121

yes

—

116

#13330

—

maximal, Sylow

117

C₂²×C₄₃

#447

yes

characteristic

118

C₂²×C₄₃

#459

yes

characteristic

119

C₂²×C₄₃

#493

yes

characteristic

120

C₂²×C₄₃

C₂×Q₃₂

yes

—

121

C₂²×C₄₃

#510

yes

—

122

C₄×C₄₃

—

123

C₄×C₄₃

#392

yes

characteristic

124

C₄×C₄₃

#447

yes

characteristic

125

C₄×C₄₃

#459

yes

characteristic

126

C₄×C₄₃

#496

yes

characteristic

127

Dic₄₃

—

128

Dic₄₃

—

129

Dic₄₃

—

130

C₂²×Q₃₂

—

131

C₂×#494

—

132

C₂×#358

—

133

#1969

—

134

#1374

D₄₃

yes

characteristic

135

C₂×C₄₃

#2011

yes

characteristic

136

C₂×C₄₃

#2188

yes

—

137

C₂×C₄₃

#2209

yes

—

138

C₂×C₄₃

#2247

yes

characteristic

139

C₂×C₄₃

#2251

yes

characteristic

140

C₂²×Q₁₆

—

141

C₂²×Q₁₆

—

142

C₂²×Q₁₆

—

143

C₂×C₄⋊Q₈

—

144

C₂×Q₃₂

—

145

C₂×Q₃₂

—

146

C₂×Q₃₂

—

147

C₂²×C₁₆

C₂×D₄₃

yes

—

148

#494

—

149

C₂×#107

—

150

C₂×#103

—

151

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

152

#391

—

153

#358

—

154

C₄₃

#13330

yes

characteristic, complemented, Sylow

155

C₂²×Q₈

—

156

C₂²×Q₈

—

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

—

172

—

169

C₂×Q₁₆

—

172

—

170

C₂²×C₈

D₁₇₂

yes

characteristic

171

C₂²×C₈

C₂²×D₄₃

yes

characteristic

172

C₄⋊Q₈

—

173

C₄⋊Q₈

—

172

—

174

C₂×C₄⋊C₄

—

175

C₂×C₄⋊C₄

—

172

—

176

C₂×C₄²

D₁₇₂

yes

characteristic

177

Q₃₂

—

178

C₂×C₁₆

—

179

C₂×C₁₆

—

180

C₂×C₁₆

D₁₇₂

yes

—

181

#107

—

182

#103

—

172

—

183

C₄×C₈

—

184

#95

—

172

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

172

—

188

C₂×Q₈

—

172

—

189

C₂×Q₈

—

172

—

190

C₂×Q₈

—

172

—

191

C₂×Q₈

—

172

—

192

C₂×Q₈

—

172

—

193

C₂×Q₈

—

172

—

194

C₂×Q₈

—

172

—

195

C₂×Q₈

—

172

—

196

C₂×Q₈

—

172

—

197

C₂²×C₄

—

172

—

198

C₂²×C₄

—

172

—

199

C₂²×C₄

—

172

—

200

C₂²×C₄

D₃₄₄

yes

—

201

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

202

Q₁₆

—

203

Q₁₆

—

204

Q₁₆

—

205

Q₁₆

—

172

—

206

Q₁₆

—

172

—

207

Q₁₆

—

172

—

208

Q₁₆

—

172

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

D₃₄₄

yes

—

212

C₂×C₈

C₂×D₁₇₂

yes

—

213

C₂×C₈

D₄×D₄₃

yes

characteristic

214

C₂×C₈

D₄×D₄₃

yes

—

215

C₂×C₈

#10621902

yes

characteristic

216

C₄⋊C₄

—

172

—

217

C₄⋊C₄

—

172

—

218

C₄⋊C₄

—

172

—

219

C₄²

—

220

C₄²

—

221

C₁₆

—

222

C₂³

C₂×D₃₄₄

yes

characteristic

223

Q₈

—

344

—

224

Q₈

—

344

—

225

Q₈

—

344

—

226

Q₈

—

344

—

227

Q₈

—

172

—

228

Q₈

—

172

—

229

Q₈

—

172

—

230

Q₈

—

172

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

344

—

234

C₂×C₄

—

344

—

235

C₂×C₄

—

344

—

236

C₂×C₄

—

344

—

237

C₂×C₄

—

344

—

238

C₂×C₄

—

344

—

239

C₂×C₄

—

172

—

240

C₂×C₄

—

172

—

241

C₂×C₄

Dic₃₄₄

yes

complemented

242

C₂×C₄

#13063295

yes

characteristic

243

C₂×C₄

#13063300

yes

characteristic

244

C₂×C₄

#13063322

yes

characteristic

245

C₂×C₄

C₂×D₃₄₄

yes

characteristic

246

C₂×C₄

#13063353

yes

characteristic

247

C₂×C₄

#13063353

yes

characteristic

248

C₈

—

249

C₈

#13063295

yes

—

250

C₈

#13063300

yes

—

251

C₂²

#14583035

yes

characteristic

252

C₂²

#14583095

yes

characteristic

253

C₂²

#14583276

yes

characteristic

254

C₂²

C₂×Dic₃₄₄

yes

—

255

C₂²

#14583342

yes

—

256

C₄

—

257

C₄

—

344

—

258

C₄

—

344

—

259

C₄

—

688

—

260

C₄

#14582809

yes

characteristic

261

C₄

#14583035

yes

characteristic

262

C₄

#14583095

yes

characteristic

263

C₄

#14583288

yes

characteristic

264

C₂

#19135668

yes

characteristic

265

C₂

#19136531

yes

—

266

C₂

#19136646

yes

—

267

C₂

#19136848

yes

characteristic

268

C₂

#19136866

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₃₄₄
commutator, cosocle	C₂²×C₈×C₄₃	C₂³
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#1374	C₂
socle, prime radical	C₂³×C₄₃	C₂×D₈
hypercenter	#1374	D₄₃
hypocenter	C₄₃	#13330
LCS	G ▷ C₂²×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

subgroup

G/H

center

C₂³

C₂×D₃₄₄

commutator, cosocle

C₂²×C₈×C₄₃

C₂³

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₄₃×#1374

C₂

socle, prime radical

C₂³×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂²×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

N	H ≅ G/N	type
90. C₂×C₄×C₄₃	Q₃₂	semidirect
154. C₄₃	#13330	semidirect
241. C₂×C₄	Dic₃₄₄	semidirect

H ≅ G/N

type

90. C₂×C₄×C₄₃

Q₃₂

semidirect

154. C₄₃

#13330

semidirect

241. C₂×C₄

Dic₃₄₄

semidirect

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

subgroup	index
C₂²×Dic₃₄₄	2
C₂×#14583279	2
C₂×#14582704	2
#19135456	2
C₄₃×#1374	2
#13330	43

subgroup

index

C₂²×Dic₃₄₄

C₄₃×#1374

Subgroups — #25015459

Conjugacy classes of subgroups

Complements

Maximal subgroups