Group #24999194 — subgroups

Subgroups — #24999194

Order 11008.

626 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 139 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	C₂×#14583279	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14583180	C₂	1	2	yes	maximal
3	#19135389	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582644	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Dic₁₇₂	—	2	2	no	—
7	C₂×#13063325	C₂²	1	2	yes	—
8	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
9	#14583279	—	2	4	no	—
10	#14583180	—	2	4	no	—
11	#14583180	—	2	4	no	—
12	C₂×#13063259	—	2	2	no	—
13	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#13063247	—	2	2	no	—
15	C₂×(C₂×D₄₃)⋊C₈	—	2	2	no	—
16	#14582644	—	2	4	no	—
17	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×Dic₈₆	—	2	2	no	—
20	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
21	C₂²×C₄×D₄₃	—	2	1	no	—
22	C₂×Dic₁₇₂	—	2	8	no	—
23	C₂×Dic₁₇₂	—	4	4	no	—
24	C₂×Dic₁₇₂	—	4	4	no	—
25	C₂²×C₄₃⋊C₈	—	2	1	no	—
26	#13063325	—	2	2	no	—
27	#13063325	—	2	2	no	—
28	#13063325	—	2	2	no	—
29	#13063325	D₄	1	4	yes	—
30	C₄×D₁₇₂	—	2	2	no	—
31	C₄×D₁₇₂	—	2	2	no	—
32	C₂×C₄⋊Dic₄₃	—	2	2	no	—
33	C₂×C₄⋊Dic₄₃	—	2	2	no	—
34	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
35	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
36	#13063259	—	2	8	no	—
37	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
38	#13063247	—	2	8	no	—
39	(C₂×D₄₃)⋊C₈	—	4	4	no	—
40	C₂²×C₈×C₄₃	—	2	2	no	—
41	C₂²×C₈×C₄₃	D₄	1	2	yes	—
42	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₄₃	—	2	2	no	—
44	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
45	C₄×C₈×C₄₃	—	2	2	no	—
46	C₂³×D₄₃	—	2	1	no	—
47	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
50	C₂²×Dic₄₃	—	2	1	no	—
51	C₂²×Dic₄₃	—	4	2	no	—
52	C₂×D₁₇₂	—	2	1	no	—
53	C₂×D₁₇₂	—	2	2	no	—
54	C₂×D₁₇₂	—	2	2	no	—
55	C₂×D₁₇₂	Q₁₆	1	2	yes	complemented
56	C₂×C₄×D₄₃	—	4	1	no	—
57	C₂×C₄×D₄₃	—	4	1	no	—
58	C₂×C₄×D₄₃	—	4	2	no	—
59	C₂×C₄×D₄₃	—	4	2	no	—
60	C₂×Dic₈₆	—	2	4	no	—
61	C₂×Dic₈₆	—	4	4	no	—
62	C₂×Dic₈₆	—	4	4	no	—
63	C₂×Dic₈₆	—	4	2	no	—
64	C₂×C₈×C₄₃	—	2	2	no	—
65	C₂×C₈×C₄₃	—	2	2	no	—
66	C₂×C₈×C₄₃	—	2	4	no	—
67	C₂×C₈×C₄₃	—	4	2	no	—
68	C₂×C₈×C₄₃	—	4	2	no	—
69	C₂×C₈×C₄₃	D₈	1	4	yes	—
70	C₄²×C₄₃	C₂×D₄	1	2	yes	—
71	C₄²×C₄₃	C₂×D₄	1	2	yes	—
72	(C₂×D₄₃)⋊C₄	—	4	2	no	—
73	C₄⋊Dic₄₃	—	2	4	no	—
74	C₄⋊Dic₄₃	—	2	2	no	—
75	C₄⋊Dic₄₃	—	2	4	no	—
76	C₄⋊Dic₄₃	—	4	2	no	—
77	C₄⋊Dic₄₃	—	4	2	no	—
78	C₂×C₄₃⋊C₈	—	4	1	no	—
79	C₂×C₄₃⋊C₈	—	4	2	no	—
80	Dic₁₇₂	—	4	16	no	—
81	C₂³×C₄₃	#121	1	1	yes	characteristic
82	C₂²×D₄₃	—	2	2	no	—
83	C₂²×D₄₃	—	4	1	no	—
84	C₂²×D₄₃	—	4	2	no	—
85	C₂²×D₄₃	—	4	1	no	—
86	C₂²×D₄₃	—	4	2	no	—
87	C₂×C₄×C₄₃	—	2	2	no	—
88	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
89	C₂×C₄×C₄₃	#120	1	2	yes	—
90	C₂×C₄×C₄₃	#121	1	2	yes	—
91	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
92	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
93	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
94	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
95	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
96	C₂×C₄×C₄₃	#137	1	2	yes	—
97	C₂×Dic₄₃	—	4	4	no	—
98	C₂×Dic₄₃	—	4	1	no	—
99	C₂×Dic₄₃	—	4	2	no	—
100	C₂×Dic₄₃	—	8	4	no	—
101	D₁₇₂	—	2	4	no	—
102	D₁₇₂	—	4	2	no	—
103	C₄×D₄₃	—	8	2	no	—
104	C₄×D₄₃	—	8	1	no	—
105	C₄×D₄₃	—	8	1	no	—
106	Dic₈₆	—	4	8	no	—
107	Dic₈₆	—	8	2	no	—
108	Dic₈₆	—	8	2	no	—
109	C₈×C₄₃	—	2	4	no	—
110	C₈×C₄₃	—	4	4	no	—
111	C₄₃⋊C₈	—	8	1	no	—
112	#10274	—	43	1	no	maximal, Sylow
113	C₂²×C₄₃	#392	1	1	yes	characteristic
114	C₂²×C₄₃	#459	1	2	yes	—
115	C₂²×C₄₃	#467	1	1	yes	characteristic
116	C₂²×C₄₃	#470	1	1	yes	characteristic
117	C₂²×C₄₃	#473	1	2	yes	—
118	C₂×D₄₃	—	4	4	no	—
119	C₂×D₄₃	—	4	2	no	—
120	C₂×D₄₃	—	8	2	no	—
121	C₂×D₄₃	—	8	1	no	—
122	C₂×D₄₃	—	8	1	no	—
123	C₄×C₄₃	—	2	2	no	—
124	C₄×C₄₃	#447	1	2	yes	—
125	C₄×C₄₃	#451	1	2	yes	—
126	C₄×C₄₃	#452	1	2	yes	—
127	C₄×C₄₃	#493	1	1	yes	characteristic
128	C₄×C₄₃	#496	1	1	yes	characteristic
129	Dic₄₃	—	8	4	no	—
130	Dic₄₃	—	8	1	no	—
131	C₂×#494	—	43	1	no	—
132	C₂×#474	—	43	2	no	—
133	#1954	—	43	1	no	—
134	C₂×#332	—	43	2	no	—
135	#1277	D₄₃	1	1	yes	characteristic, complemented
136	C₂×C₄₃	#1669	1	2	yes	—
137	C₂×C₄₃	#1689	1	2	yes	—
138	C₂×C₄₃	#2001	1	1	yes	characteristic
139	C₂×C₄₃	#2011	1	1	yes	characteristic
140	C₂×C₄₃	#2020	1	1	yes	characteristic
141	D₄₃	—	8	2	no	—
142	C₂²×Q₁₆	—	86	2	no	—
143	C₂×C₄⋊Q₈	—	43	2	no	—
144	C₂×C₄×D₄	—	43	1	no	—
145	#494	—	86	4	no	—
146	#474	—	86	4	no	—
147	#474	—	86	4	no	—
148	C₂×#107	—	86	2	no	—
149	C₂×C₄⋊C₈	—	43	1	no	—
150	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
151	C₂×#102	—	86	2	no	—
152	C₂×C₂²⋊C₈	—	86	2	no	—
153	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
154	#332	—	86	4	no	—
155	C₄₃	#10274	1	1	yes	characteristic, complemented, Sylow
156	C₂²×Q₈	—	86	2	no	—
157	C₂²×D₄	—	43	1	no	—
158	C₂³×C₄	—	86	1	no	—
159	C₂×Q₁₆	—	86	8	no	—
160	C₂×Q₁₆	—	172	4	no	—
161	C₂×Q₁₆	—	172	4	no	—
162	C₂²×C₈	—	2	2	no	—
163	C₂²×C₈	—	86	1	no	—
164	C₂²×C₈	D₁₇₂	1	2	yes	—
165	C₄⋊Q₈	—	43	4	no	—
166	C₄⋊Q₈	—	86	2	no	—
167	C₄⋊Q₈	—	86	2	no	—
168	C₄⋊Q₈	—	86	2	no	—
169	C₄×D₄	—	86	2	no	—
170	C₄×D₄	—	86	2	no	—
171	C₂×C₄⋊C₄	—	43	1	no	—
172	C₂×C₄⋊C₄	—	86	2	no	—
173	C₂×C₄⋊C₄	—	86	2	no	—
174	C₂×C₂²⋊C₄	—	86	1	no	—
175	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
176	#107	—	86	8	no	—
177	C₄⋊C₈	—	2	2	no	—
178	C₄⋊C₈	—	86	2	no	—
179	C₄⋊C₈	D₁₇₂	1	4	yes	—
180	#102	—	86	8	no	—
181	C₂²⋊C₈	—	172	4	no	—
182	C₄×C₈	—	2	2	no	—
183	C₂⁴	—	86	1	no	—
184	C₂×Q₈	—	86	4	no	—
185	C₂×Q₈	—	172	4	no	—
186	C₂×Q₈	—	172	4	no	—
187	C₂×Q₈	—	172	2	no	—
188	C₂×D₄	—	43	2	no	—
189	C₂×D₄	—	86	2	no	—
190	C₂×D₄	—	86	1	no	—
191	C₂×D₄	—	86	2	no	—
192	C₂²×C₄	—	86	1	no	—
193	C₂²×C₄	—	172	2	no	—
194	C₂²×C₄	—	172	1	no	—
195	C₂²×C₄	—	172	1	no	—
196	C₂²×C₄	—	172	2	no	—
197	C₂²×C₄	—	172	2	no	—
198	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
199	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
200	C₂²×C₄	#10621902	1	1	yes	characteristic
201	Q₁₆	—	172	16	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	2	4	no	—
205	C₂×C₈	—	4	2	no	—
206	C₂×C₈	—	4	2	no	—
207	C₂×C₈	—	172	1	no	—
208	C₂×C₈	—	172	2	no	—
209	C₂×C₈	D₃₄₄	1	4	yes	—
210	C₄⋊C₄	—	86	4	no	—
211	C₄⋊C₄	—	86	2	no	—
212	C₄⋊C₄	—	86	4	no	—
213	C₄⋊C₄	—	172	2	no	—
214	C₄⋊C₄	—	172	2	no	—
215	C₂²⋊C₄	—	172	2	no	—
216	C₄²	C₂×D₁₇₂	1	2	yes	—
217	C₄²	D₄×D₄₃	1	2	yes	—
218	C₂³	—	86	2	no	—
219	C₂³	—	172	1	no	—
220	C₂³	—	172	2	no	—
221	C₂³	—	172	1	no	—
222	C₂³	—	172	2	no	—
223	C₂³	#13063300	1	1	yes	characteristic
224	Q₈	—	344	2	no	—
225	Q₈	—	344	2	no	—
226	Q₈	—	172	8	no	—
227	D₄	—	86	4	no	—
228	D₄	—	172	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	344	4	no	—
231	C₂×C₄	—	344	1	no	—
232	C₂×C₄	—	344	1	no	—
233	C₂×C₄	—	344	2	no	—
234	C₂×C₄	—	172	1	no	—
235	C₂×C₄	—	172	4	no	—
236	C₂×C₄	—	172	2	no	—
237	C₂×C₄	#13063295	1	2	yes	—
238	C₂×C₄	#13063295	1	1	yes	characteristic
239	C₂×C₄	#13063300	1	2	yes	—
240	C₂×C₄	#13063322	1	1	yes	characteristic
241	C₂×C₄	C₂×D₃₄₄	1	2	yes	—
242	C₂×C₄	Q₁₆×D₄₃	1	1	yes	characteristic
243	C₂×C₄	#13063344	1	1	yes	characteristic
244	C₂×C₄	#13063353	1	2	yes	—
245	C₂×C₄	#13063354	1	2	yes	—
246	C₈	—	2	4	no	—
247	C₈	—	4	4	no	—
248	C₈	—	344	1	no	—
249	C₂²	—	344	2	no	—
250	C₂²	—	344	1	no	—
251	C₂²	—	344	1	no	—
252	C₂²	—	172	4	no	—
253	C₂²	—	172	2	no	—
254	C₂²	#14582809	1	1	yes	characteristic
255	C₂²	#14583095	1	2	yes	—
256	C₂²	#14583141	1	1	yes	characteristic
257	C₂²	#14583158	1	1	yes	characteristic
258	C₂²	#14583175	1	2	yes	—
259	C₄	—	2	2	no	—
260	C₄	—	344	1	no	—
261	C₄	—	344	4	no	—
262	C₄	#14583035	1	2	yes	—
263	C₄	#14583056	1	2	yes	—
264	C₄	#14583062	1	2	yes	—
265	C₄	#14583276	1	1	yes	characteristic
266	C₄	#14583288	1	1	yes	characteristic
267	C₂	—	344	2	no	—
268	C₂	#19133961	1	2	yes	—
269	C₂	#19134085	1	2	yes	—
270	C₂	#19135606	1	1	yes	characteristic
271	C₂	#19135668	1	1	yes	characteristic
272	C₂	#19135717	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583279

C₂

yes

maximal, characteristic, complemented

C₂×#14583180

C₂

yes

maximal

#19135389

C₂

yes

maximal, characteristic

C₂×#14582644

C₂

yes

maximal, complemented

C₄₃×#1277

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₁₇₂

—

C₂×#13063325

C₂²

yes

—

C₂×C₄×D₁₇₂

C₂²

yes

—

—

—

—

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₂×#13063247

—

C₂×(C₂×D₄₃)⋊C₈

—

#14582644

—

C₂×C₄⋊C₈×C₄₃

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂²×Dic₈₆

—

C₂²×D₁₇₂

D₄

yes

characteristic

C₂²×C₄×D₄₃

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂²×C₄₃⋊C₈

—

—

—

—

D₄

yes

—

C₄×D₁₇₂

—

C₄×D₁₇₂

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

D₄

yes

characteristic

C₂×(C₂×D₄₃)⋊C₄

—

#13063259

—

C₄⋊(C₄₃⋊C₈)

—

#13063247

—

(C₂×D₄₃)⋊C₈

—

C₂²×C₈×C₄₃

—

C₂²×C₈×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

D₄

yes

—

C₄×C₈×C₄₃

—

C₂³×D₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

Q₁₆

yes

complemented

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₈

yes

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

C₂×D₄

yes

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

—

C₂³×C₄₃

#121

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#120

yes

characteristic

C₂×C₄×C₄₃

#120

yes

—

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

#127

yes

characteristic

C₂×C₄×C₄₃

C₂×D₈

yes

—

C₂×C₄×C₄₃

C₂×Q₁₆

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

100

C₂×Dic₄₃

—

101

D₁₇₂

—

102

D₁₇₂

—

103

C₄×D₄₃

—

104

C₄×D₄₃

—

105

C₄×D₄₃

—

106

Dic₈₆

—

107

Dic₈₆

—

108

Dic₈₆

—

109

C₈×C₄₃

—

110

C₈×C₄₃

—

111

C₄₃⋊C₈

—

112

#10274

—

maximal, Sylow

113

C₂²×C₄₃

#392

yes

characteristic

114

C₂²×C₄₃

#459

yes

—

115

C₂²×C₄₃

#467

yes

characteristic

116

C₂²×C₄₃

#470

yes

characteristic

117

C₂²×C₄₃

#473

yes

—

118

C₂×D₄₃

—

119

C₂×D₄₃

—

120

C₂×D₄₃

—

121

C₂×D₄₃

—

122

C₂×D₄₃

—

123

C₄×C₄₃

—

124

C₄×C₄₃

#447

yes

—

125

C₄×C₄₃

#451

yes

—

126

C₄×C₄₃

#452

yes

—

127

C₄×C₄₃

#493

yes

characteristic

128

C₄×C₄₃

#496

yes

characteristic

129

Dic₄₃

—

130

Dic₄₃

—

131

C₂×#494

—

132

C₂×#474

—

133

#1954

—

134

C₂×#332

—

135

#1277

D₄₃

yes

characteristic, complemented

136

C₂×C₄₃

#1669

yes

—

137

C₂×C₄₃

#1689

yes

—

138

C₂×C₄₃

#2001

yes

characteristic

139

C₂×C₄₃

#2011

yes

characteristic

140

C₂×C₄₃

#2020

yes

characteristic

141

D₄₃

—

142

C₂²×Q₁₆

—

143

C₂×C₄⋊Q₈

—

144

C₂×C₄×D₄

—

145

#494

—

146

#474

—

147

#474

—

148

C₂×#107

—

149

C₂×C₄⋊C₈

—

150

C₂×C₄⋊C₈

C₂×D₄₃

yes

—

151

C₂×#102

—

152

C₂×C₂²⋊C₈

—

153

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

154

#332

—

155

C₄₃

#10274

yes

characteristic, complemented, Sylow

156

C₂²×Q₈

—

157

C₂²×D₄

—

158

C₂³×C₄

—

159

C₂×Q₁₆

—

160

C₂×Q₁₆

—

172

—

161

C₂×Q₁₆

—

172

—

162

C₂²×C₈

—

163

C₂²×C₈

—

164

C₂²×C₈

D₁₇₂

yes

—

165

C₄⋊Q₈

—

166

C₄⋊Q₈

—

167

C₄⋊Q₈

—

168

C₄⋊Q₈

—

169

C₄×D₄

—

170

C₄×D₄

—

171

C₂×C₄⋊C₄

—

172

C₂×C₄⋊C₄

—

173

C₂×C₄⋊C₄

—

174

C₂×C₂²⋊C₄

—

175

C₂×C₄²

C₂²×D₄₃

yes

characteristic

176

#107

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

D₁₇₂

yes

—

180

#102

—

181

C₂²⋊C₈

—

172

—

182

C₄×C₈

—

183

C₂⁴

—

184

C₂×Q₈

—

185

C₂×Q₈

—

172

—

186

C₂×Q₈

—

172

—

187

C₂×Q₈

—

172

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

172

—

194

C₂²×C₄

—

172

—

195

C₂²×C₄

—

172

—

196

C₂²×C₄

—

172

—

197

C₂²×C₄

—

172

—

198

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

199

C₂²×C₄

D₄×D₄₃

yes

characteristic

200

C₂²×C₄

#10621902

yes

characteristic

201

Q₁₆

—

172

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

172

—

208

C₂×C₈

—

172

—

209

C₂×C₈

D₃₄₄

yes

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

172

—

214

C₄⋊C₄

—

172

—

215

C₂²⋊C₄

—

172

—

216

C₄²

C₂×D₁₇₂

yes

—

217

C₄²

D₄×D₄₃

yes

—

218

C₂³

—

219

C₂³

—

172

—

220

C₂³

—

172

—

221

C₂³

—

172

—

222

C₂³

—

172

—

223

C₂³

#13063300

yes

characteristic

224

Q₈

—

344

—

225

Q₈

—

344

—

226

Q₈

—

172

—

227

D₄

—

228

D₄

—

172

—

229

C₂×C₄

—

230

C₂×C₄

—

344

—

231

C₂×C₄

—

344

—

232

C₂×C₄

—

344

—

233

C₂×C₄

—

344

—

234

C₂×C₄

—

172

—

235

C₂×C₄

—

172

—

236

C₂×C₄

—

172

—

237

C₂×C₄

#13063295

yes

—

238

C₂×C₄

#13063295

yes

characteristic

239

C₂×C₄

#13063300

yes

—

240

C₂×C₄

#13063322

yes

characteristic

241

C₂×C₄

C₂×D₃₄₄

yes

—

242

C₂×C₄

Q₁₆×D₄₃

yes

characteristic

243

C₂×C₄

#13063344

yes

characteristic

244

C₂×C₄

#13063353

yes

—

245

C₂×C₄

#13063354

yes

—

246

C₈

—

247

C₈

—

248

C₈

—

344

—

249

C₂²

—

344

—

250

C₂²

—

344

—

251

C₂²

—

344

—

252

C₂²

—

172

—

253

C₂²

—

172

—

254

C₂²

#14582809

yes

characteristic

255

C₂²

#14583095

yes

—

256

C₂²

#14583141

yes

characteristic

257

C₂²

#14583158

yes

characteristic

258

C₂²

#14583175

yes

—

259

C₄

—

260

C₄

—

344

—

261

C₄

—

344

—

262

C₄

#14583035

yes

—

263

C₄

#14583056

yes

—

264

C₄

#14583062

yes

—

265

C₄

#14583276

yes

characteristic

266

C₄

#14583288

yes

characteristic

267

C₂

—

344

—

268

C₂

#19133961

yes

—

269

C₂

#19134085

yes

—

270

C₂

#19135606

yes

characteristic

271

C₂

#19135668

yes

characteristic

272

C₂

#19135717

yes

characteristic

	subgroup	G/H
center	C₂³	#13063300
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1277	C₂
socle	C₂³×C₄₃	#121
prime radical	C₂²×D₁₇₂	D₄
hypercenter	#1277	D₄₃
hypocenter	C₄₃	#10274
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

subgroup

G/H

center

C₂³

#13063300

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1277

C₂

socle

C₂³×C₄₃

#121

prime radical

C₂²×D₁₇₂

D₄

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

N	H ≅ G/N	type
1. C₂×#14583279	C₂	semidirect
4. C₂×#14582644	C₂	semidirect
5. C₄₃×#1277	C₂	semidirect
55. C₂×D₁₇₂	Q₁₆	semidirect
135. #1277	D₄₃	semidirect
155. C₄₃	#10274	semidirect

H ≅ G/N

type

1. C₂×#14583279

C₂

semidirect

4. C₂×#14582644

C₂

semidirect

5. C₄₃×#1277

C₂

semidirect

55. C₂×D₁₇₂

Q₁₆

semidirect

135. #1277

D₄₃

semidirect

155. C₄₃

#10274

semidirect

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

subgroup	index
C₂×#14583279	2
C₂×#14583180	2
#19135389	2
C₂×#14582644	2
C₄₃×#1277	2
#10274	43

subgroup

index

C₄₃×#1277

Subgroups — #24999194

Conjugacy classes of subgroups

Complements

Maximal subgroups