Group #25253046 — subgroups

Subgroups — #25253046

Order 11008.

488 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 143 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	#19145234	C₂	1	2	yes	maximal, complemented
2	#19136743	C₂	1	2	yes	maximal, complemented
3	#19136738	C₂	1	2	yes	maximal, complemented
4	#19136703	C₂	1	1	yes	maximal, characteristic, complemented
5	#19136698	C₂	1	1	yes	maximal, characteristic
6	#19136691	C₂	1	2	yes	maximal, complemented
7	#19136658	C₂	1	2	yes	maximal, complemented
8	#19136651	C₂	1	2	yes	maximal, complemented
9	C₄₃×#2151	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583520	—	2	2	no	—
11	C₂×Dic₃₄₄	C₂²	1	1	yes	characteristic
12	C₂×#13063270	C₂²	1	2	yes	—
13	C₂×D₆₈₈	C₂²	1	1	yes	characteristic
14	#14583304	C₂²	1	2	yes	—
15	#14583283	C₂²	1	2	yes	—
16	#14583259	—	2	2	no	—
17	#14583145	—	2	2	no	—
18	#14583140	C₂²	1	2	yes	—
19	#14583135	C₂²	1	2	yes	—
20	#14583001	—	2	2	no	—
21	C₄×Dic₁₇₂	C₂²	1	2	yes	—
22	C₄×D₃₄₄	C₂²	1	2	yes	—
23	#14582727	C₂²	1	2	yes	—
24	#14582727	C₂²	1	1	yes	characteristic
25	#14582727	C₂²	1	1	yes	characteristic
26	#14582704	C₂²	1	2	yes	—
27	#14582704	C₂²	1	2	yes	—
28	#14582701	C₂²	1	2	yes	—
29	#14582701	C₂²	1	2	yes	—
30	C₂×M₃₂×C₄₃	C₂²	1	1	yes	characteristic
31	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#405	C₂²	1	1	yes	characteristic
33	C₄₃×C₄⋊C₁₆	C₂²	1	2	yes	—
34	C₄₃×C₄⋊C₁₆	C₂²	1	2	yes	—
35	C₂×Dic₁₇₂	C₂³	1	2	yes	—
36	C₂×#10621873	—	2	2	no	—
37	C₂×D₃₄₄	C₂³	1	2	yes	—
38	#13063325	—	2	2	no	—
39	#13063320	—	4	2	no	—
40	#13063313	—	2	2	no	—
41	#13063311	—	4	2	no	—
42	#13063307	—	4	2	no	—
43	#13063304	—	2	2	no	—
44	#13063303	—	4	2	no	—
45	#13063299	—	2	2	no	—
46	C₄×Dic₈₆	—	2	2	no	—
47	C₄×D₁₇₂	—	2	2	no	—
48	Dic₃₄₄	—	4	1	no	—
49	#13063270	—	4	2	no	—
50	D₆₈₈	—	4	1	no	—
51	#13063259	—	2	2	no	—
52	#13063259	C₂³	1	2	yes	—
53	#13063259	C₂³	1	2	yes	—
54	#13063250	—	2	2	no	—
55	#13063250	—	2	2	no	—
56	#13063247	—	2	2	no	—
57	#13063247	—	2	2	no	—
58	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
59	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
60	#117×C₄₃	D₄	1	1	yes	characteristic
61	M₃₂×C₄₃	—	4	1	no	—
62	C₂×C₁₆×C₄₃	—	4	1	no	—
63	C₂×C₁₆×C₄₃	C₂³	1	2	yes	—
64	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
66	#97×C₄₃	D₄	1	2	yes	—
67	C₄×C₈×C₄₃	C₂³	1	2	yes	—
68	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
69	C₂×C₂²⋊D₄₃	—	4	2	no	—
70	C₂×D₁₇₂	—	2	2	no	—
71	C₂×C₄×D₄₃	—	4	2	no	—
72	C₂×Dic₈₆	—	2	2	no	—
73	C₂×Dic₈₆	—	4	2	no	—
74	M₁₆×C₄₃	—	4	1	no	—
75	C₂×C₈×C₄₃	—	2	1	no	—
76	C₂×C₈×C₄₃	—	2	1	no	—
77	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
78	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
80	C₄⋊C₄×C₄₃	D₈	1	2	yes	—
81	C₂²⋊C₄×C₄₃	D₈	1	1	yes	characteristic
82	C₂²⋊C₄×C₄₃	D₈	1	1	yes	characteristic
83	C₄²×C₄₃	C₂×D₄	1	2	yes	—
84	C₂²⋊Dic₄₃	—	4	2	no	—
85	(C₂×D₄₃)⋊C₄	—	4	2	no	—
86	(C₂×D₄₃)⋊C₄	—	4	2	no	—
87	(C₂×D₄₃)⋊C₄	—	4	2	no	—
88	(C₂×D₄₃)⋊C₄	—	4	2	no	—
89	C₄⋊Dic₄₃	—	2	2	no	—
90	C₄⋊Dic₄₃	—	2	2	no	—
91	C₄⋊Dic₄₃	—	4	2	no	—
92	Dic₄₃⋊C₄	—	4	2	no	—
93	Dic₄₃⋊C₄	—	4	2	no	—
94	C₄×Dic₄₃	—	4	2	no	—
95	Dic₁₇₂	—	2	2	no	—
96	Dic₁₇₂	—	2	2	no	—
97	D₃₄₄	—	2	2	no	—
98	D₃₄₄	—	2	2	no	—
99	#10621873	—	4	4	no	—
100	C₁₆×C₄₃	—	2	2	no	—
101	C₁₆×C₄₃	—	2	1	no	—
102	C₁₆×C₄₃	—	2	1	no	—
103	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
104	C₂²×D₄₃	—	4	2	no	—
105	C₂×C₄×C₄₃	—	2	1	no	—
106	C₂×C₄×C₄₃	—	2	1	no	—
107	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
108	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
109	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
110	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
111	C₂²⋊D₄₃	—	16	2	no	—
112	C₂×Dic₄₃	—	4	2	no	—
113	C₂×Dic₄₃	—	4	2	no	—
114	C₂×Dic₄₃	—	4	2	no	—
115	D₁₇₂	—	4	2	no	—
116	D₁₇₂	—	4	2	no	—
117	C₄×D₄₃	—	16	2	no	—
118	Dic₈₆	—	4	2	no	—
119	Dic₈₆	—	4	2	no	—
120	Dic₈₆	—	16	2	no	—
121	C₈×C₄₃	—	2	1	no	—
122	C₈×C₄₃	—	2	2	no	—
123	C₈×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
124	C₈×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
125	#33829	—	43	1	no	maximal, Sylow
126	C₂²×C₄₃	—	2	2	no	—
127	C₂²×C₄₃	—	2	1	no	—
128	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
129	C₂×D₄₃	—	8	2	no	—
130	C₂×D₄₃	—	8	2	no	—
131	C₂×D₄₃	—	8	2	no	—
132	C₄×C₄₃	—	2	2	no	—
133	C₄×C₄₃	—	2	2	no	—
134	C₄×C₄₃	—	2	1	no	—
135	C₄×C₄₃	#537	1	1	yes	characteristic
136	C₄×C₄₃	#575	1	1	yes	characteristic
137	Dic₄₃	—	8	2	no	—
138	Dic₄₃	—	8	2	no	—
139	Dic₄₃	—	8	2	no	—
140	#3175	—	43	2	no	—
141	#2226	—	43	2	no	—
142	#2225	—	43	2	no	—
143	#2219	—	43	1	no	—
144	#2218	—	43	1	no	—
145	#2217	—	43	2	no	—
146	#2211	—	43	2	no	—
147	#2210	—	43	2	no	—
148	#2151	D₄₃	1	1	yes	characteristic, complemented
149	C₂×C₄₃	—	4	1	no	—
150	C₂×C₄₃	#3245	1	1	yes	characteristic
151	C₂×C₄₃	#3416	1	2	yes	—
152	D₄₃	—	16	2	no	—
153	#542	—	86	2	no	—
154	C₂×Q₃₂	—	43	1	no	—
155	C₂×SD₃₂	—	43	2	no	—
156	C₂×D₁₆	—	43	1	no	—
157	C₂×M₃₂	C₂×D₄₃	1	1	yes	characteristic
158	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
159	#500	—	43	2	no	—
160	#495	—	43	2	no	—
161	#489	—	86	2	no	—
162	#468	—	86	2	no	—
163	#467	—	43	2	no	—
164	#466	—	43	2	no	—
165	#440	—	86	2	no	—
166	C₄×Q₁₆	—	43	2	no	—
167	C₄×D₈	—	43	2	no	—
168	#405	C₂×D₄₃	1	1	yes	characteristic
169	#367	—	43	2	no	—
170	#367	—	43	1	no	—
171	#367	—	43	1	no	—
172	C₄⋊C₁₆	C₂×D₄₃	1	2	yes	—
173	C₄⋊C₁₆	C₂×D₄₃	1	2	yes	—
174	#358	—	43	2	no	—
175	#358	—	43	2	no	—
176	#357	—	43	2	no	—
177	#357	—	43	2	no	—
178	C₄₃	#33829	1	1	yes	characteristic, complemented, Sylow
179	C₂×Q₁₆	—	43	2	no	—
180	C₂×SD₁₆	—	86	2	no	—
181	C₂×D₈	—	43	2	no	—
182	C₂×M₁₆	D₁₇₂	1	1	yes	characteristic
183	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
184	C₄⋊Q₈	—	86	2	no	—
185	#126	—	172	2	no	—
186	#124	—	86	2	no	—
187	#124	—	172	2	no	—
188	#123	—	172	2	no	—
189	C₂²⋊Q₈	—	86	2	no	—
190	C₂²⋊Q₈	—	172	2	no	—
191	#121	—	86	2	no	—
192	C₄×Q₈	—	86	2	no	—
193	C₄×D₄	—	86	2	no	—
194	#117	D₁₇₂	1	1	yes	characteristic
195	Q₃₂	—	172	1	no	—
196	SD₃₂	—	172	2	no	—
197	D₁₆	—	172	1	no	—
198	M₃₂	—	4	1	no	—
199	C₂×C₁₆	—	4	1	no	—
200	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
201	C₂×C₁₆	C₂²×D₄₃	1	2	yes	—
202	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
203	#107	—	43	2	no	—
204	#107	—	43	2	no	—
205	#107	—	86	2	no	—
206	#103	—	86	2	no	—
207	#103	—	86	2	no	—
208	#102	—	86	2	no	—
209	#102	—	86	2	no	—
210	#97	D₁₇₂	1	2	yes	—
211	C₄×C₈	C₂²×D₄₃	1	2	yes	—
212	C₂×Q₈	—	86	2	no	—
213	C₂×Q₈	—	172	2	no	—
214	C₂×D₄	—	86	2	no	—
215	C₂×D₄	—	172	2	no	—
216	C₂²×C₄	—	172	2	no	—
217	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
218	Q₁₆	—	86	2	no	—
219	Q₁₆	—	86	2	no	—
220	SD₁₆	—	172	4	no	—
221	D₈	—	86	2	no	—
222	D₈	—	86	2	no	—
223	M₁₆	—	4	1	no	—
224	C₂×C₈	—	2	1	no	—
225	C₂×C₈	—	2	1	no	—
226	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
227	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
228	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
229	C₄⋊C₄	—	86	2	no	—
230	C₄⋊C₄	—	86	2	no	—
231	C₄⋊C₄	—	172	2	no	—
232	C₄⋊C₄	—	172	2	no	—
233	C₄⋊C₄	—	172	2	no	—
234	C₄⋊C₄	D₃₄₄	1	2	yes	—
235	C₂²⋊C₄	—	172	2	no	—
236	C₂²⋊C₄	—	172	2	no	—
237	C₂²⋊C₄	—	172	2	no	—
238	C₂²⋊C₄	—	172	2	no	—
239	C₂²⋊C₄	—	172	2	no	—
240	C₂²⋊C₄	D₃₄₄	1	1	yes	characteristic
241	C₂²⋊C₄	D₃₄₄	1	1	yes	characteristic
242	C₄²	—	172	2	no	—
243	C₄²	C₂×D₁₇₂	1	2	yes	—
244	C₁₆	—	2	2	no	—
245	C₁₆	—	2	1	no	—
246	C₁₆	—	2	1	no	—
247	C₂³	—	172	2	no	—
248	C₂³	C₂×D₃₄₄	1	1	yes	characteristic
249	Q₈	—	172	2	no	—
250	Q₈	—	172	2	no	—
251	Q₈	—	688	2	no	—
252	D₄	—	172	2	no	—
253	D₄	—	172	2	no	—
254	D₄	—	688	2	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	172	2	no	—
258	C₂×C₄	—	172	2	no	—
259	C₂×C₄	—	172	2	no	—
260	C₂×C₄	—	688	2	no	—
261	C₂×C₄	C₂×D₃₄₄	1	2	yes	—
262	C₂×C₄	C₂×D₃₄₄	1	2	yes	—
263	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
264	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
265	C₈	—	2	2	no	—
266	C₈	—	2	1	no	—
267	C₈	#13063370	1	1	yes	characteristic
268	C₈	#13063373	1	1	yes	characteristic
269	C₂²	—	2	1	no	—
270	C₂²	—	2	2	no	—
271	C₂²	—	344	2	no	—
272	C₂²	—	344	2	no	—
273	C₂²	—	344	2	no	—
274	C₂²	C₂²×D₃₄₄	1	1	yes	characteristic
275	C₄	—	2	1	no	—
276	C₄	—	2	2	no	—
277	C₄	—	2	2	no	—
278	C₄	—	344	2	no	—
279	C₄	—	344	2	no	—
280	C₄	—	344	2	no	—
281	C₄	#14583480	1	1	yes	characteristic
282	C₄	#14583699	1	1	yes	characteristic
283	C₂	—	4	1	no	—
284	C₂	—	688	2	no	—
285	C₂	#19145905	1	1	yes	characteristic
286	C₂	#19147743	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19145234

C₂

yes

maximal, complemented

#19136743

C₂

yes

maximal, complemented

#19136738

C₂

yes

maximal, complemented

#19136703

C₂

yes

maximal, characteristic, complemented

#19136698

C₂

yes

maximal, characteristic

#19136691

C₂

yes

maximal, complemented

#19136658

C₂

yes

maximal, complemented

#19136651

C₂

yes

maximal, complemented

C₄₃×#2151

C₂

yes

maximal, characteristic, complemented

#14583520

—

C₂×Dic₃₄₄

C₂²

yes

characteristic

C₂×#13063270

C₂²

yes

—

C₂×D₆₈₈

C₂²

yes

characteristic

#14583304

C₂²

yes

—

#14583283

C₂²

yes

—

#14583259

—

#14583145

—

#14583140

C₂²

yes

—

#14583135

C₂²

yes

—

#14583001

—

C₄×Dic₁₇₂

C₂²

yes

—

C₄×D₃₄₄

C₂²

yes

—

#14582727

C₂²

yes

—

#14582727

C₂²

yes

characteristic

#14582727

C₂²

yes

characteristic

#14582704

C₂²

yes

—

#14582704

C₂²

yes

—

#14582701

C₂²

yes

—

#14582701

C₂²

yes

—

C₂×M₃₂×C₄₃

C₂²

yes

characteristic

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₄₃×#405

C₂²

yes

characteristic

C₄₃×C₄⋊C₁₆

C₂²

yes

—

C₄₃×C₄⋊C₁₆

C₂²

yes

—

C₂×Dic₁₇₂

C₂³

yes

—

C₂×#10621873

—

C₂×D₃₄₄

C₂³

yes

—

—

—

—

—

—

—

—

—

C₄×Dic₈₆

—

C₄×D₁₇₂

—

Dic₃₄₄

—

#13063270

—

D₆₈₈

—

#13063259

—

#13063259

C₂³

yes

—

#13063259

C₂³

yes

—

—

—

—

—

C₂×M₁₆×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

C₂³

yes

characteristic

#117×C₄₃

D₄

yes

characteristic

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

C₂³

yes

—

C₂×C₁₆×C₄₃

C₂³

yes

characteristic

C₂×C₁₆×C₄₃

C₂³

yes

characteristic

#97×C₄₃

D₄

yes

—

C₄×C₈×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₄₃

—

C₂×D₁₇₂

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂⁴

yes

characteristic

C₄⋊C₄×C₄₃

D₈

yes

—

C₂²⋊C₄×C₄₃

D₈

yes

characteristic

C₂²⋊C₄×C₄₃

D₈

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

—

C₂²⋊Dic₄₃

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

—

D₃₄₄

—

D₃₄₄

—

#10621873

—

100

C₁₆×C₄₃

—

101

C₁₆×C₄₃

—

102

C₁₆×C₄₃

—

103

C₂³×C₄₃

C₂×D₈

yes

characteristic

104

C₂²×D₄₃

—

105

C₂×C₄×C₄₃

—

106

C₂×C₄×C₄₃

—

107

C₂×C₄×C₄₃

C₂×D₈

yes

—

108

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

109

C₂×C₄×C₄₃

C₂×D₈

yes

—

110

C₂×C₄×C₄₃

C₂²×D₄

yes

characteristic

111

C₂²⋊D₄₃

—

112

C₂×Dic₄₃

—

113

C₂×Dic₄₃

—

114

C₂×Dic₄₃

—

115

D₁₇₂

—

116

D₁₇₂

—

117

C₄×D₄₃

—

118

Dic₈₆

—

119

Dic₈₆

—

120

Dic₈₆

—

121

C₈×C₄₃

—

122

C₈×C₄₃

—

123

C₈×C₄₃

H(5,𝔽₂)

yes

characteristic

124

C₈×C₄₃

2₋¹⁺⁴

yes

characteristic

125

#33829

—

maximal, Sylow

126

C₂²×C₄₃

—

127

C₂²×C₄₃

—

128

C₂²×C₄₃

C₂²×D₈

yes

characteristic

129

C₂×D₄₃

—

130

C₂×D₄₃

—

131

C₂×D₄₃

—

132

C₄×C₄₃

—

133

C₄×C₄₃

—

134

C₄×C₄₃

—

135

C₄×C₄₃

#537

yes

characteristic

136

C₄×C₄₃

#575

yes

characteristic

137

Dic₄₃

—

138

Dic₄₃

—

139

Dic₄₃

—

140

#3175

—

141

#2226

—

142

#2225

—

143

#2219

—

144

#2218

—

145

#2217

—

146

#2211

—

147

#2210

—

148

#2151

D₄₃

yes

characteristic, complemented

149

C₂×C₄₃

—

150

C₂×C₄₃

#3245

yes

characteristic

151

C₂×C₄₃

#3416

yes

—

152

D₄₃

—

153

#542

—

154

C₂×Q₃₂

—

155

C₂×SD₃₂

—

156

C₂×D₁₆

—

157

C₂×M₃₂

C₂×D₄₃

yes

characteristic

158

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

159

#500

—

160

#495

—

161

#489

—

162

#468

—

163

#467

—

164

#466

—

165

#440

—

166

C₄×Q₁₆

—

167

C₄×D₈

—

168

#405

C₂×D₄₃

yes

characteristic

169

#367

—

170

#367

—

171

#367

—

172

C₄⋊C₁₆

C₂×D₄₃

yes

—

173

C₄⋊C₁₆

C₂×D₄₃

yes

—

174

#358

—

175

#358

—

176

#357

—

177

#357

—

178

C₄₃

#33829

yes

characteristic, complemented, Sylow

179

C₂×Q₁₆

—

180

C₂×SD₁₆

—

181

C₂×D₈

—

182

C₂×M₁₆

D₁₇₂

yes

characteristic

183

C₂²×C₈

C₂²×D₄₃

yes

characteristic

184

C₄⋊Q₈

—

185

#126

—

172

—

186

#124

—

187

#124

—

172

—

188

#123

—

172

—

189

C₂²⋊Q₈

—

190

C₂²⋊Q₈

—

172

—

191

#121

—

192

C₄×Q₈

—

193

C₄×D₄

—

194

#117

D₁₇₂

yes

characteristic

195

Q₃₂

—

172

—

196

SD₃₂

—

172

—

197

D₁₆

—

172

—

198

M₃₂

—

199

C₂×C₁₆

—

200

C₂×C₁₆

C₂²×D₄₃

yes

characteristic

201

C₂×C₁₆

C₂²×D₄₃

yes

—

202

C₂×C₁₆

C₂²×D₄₃

yes

characteristic

203

#107

—

204

#107

—

205

#107

—

206

#103

—

207

#103

—

208

#102

—

209

#102

—

210

#97

D₁₇₂

yes

—

211

C₄×C₈

C₂²×D₄₃

yes

—

212

C₂×Q₈

—

213

C₂×Q₈

—

172

—

214

C₂×D₄

—

215

C₂×D₄

—

172

—

216

C₂²×C₄

—

172

—

217

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

218

Q₁₆

—

219

Q₁₆

—

220

SD₁₆

—

172

—

221

D₈

—

222

D₈

—

223

M₁₆

—

224

C₂×C₈

—

225

C₂×C₈

—

226

C₂×C₈

C₂×D₁₇₂

yes

—

227

C₂×C₈

C₂×D₁₇₂

yes

characteristic

228

C₂×C₈

C₂³×D₄₃

yes

characteristic

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

172

—

232

C₄⋊C₄

—

172

—

233

C₄⋊C₄

—

172

—

234

C₄⋊C₄

D₃₄₄

yes

—

235

C₂²⋊C₄

—

172

—

236

C₂²⋊C₄

—

172

—

237

C₂²⋊C₄

—

172

—

238

C₂²⋊C₄

—

172

—

239

C₂²⋊C₄

—

172

—

240

C₂²⋊C₄

D₃₄₄

yes

characteristic

241

C₂²⋊C₄

D₃₄₄

yes

characteristic

242

C₄²

—

172

—

243

C₄²

C₂×D₁₇₂

yes

—

244

C₁₆

—

245

C₁₆

—

246

C₁₆

—

247

C₂³

—

172

—

248

C₂³

C₂×D₃₄₄

yes

characteristic

249

Q₈

—

172

—

250

Q₈

—

172

—

251

Q₈

—

688

—

252

D₄

—

172

—

253

D₄

—

172

—

254

D₄

—

688

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

172

—

258

C₂×C₄

—

172

—

259

C₂×C₄

—

172

—

260

C₂×C₄

—

688

—

261

C₂×C₄

C₂×D₃₄₄

yes

—

262

C₂×C₄

C₂×D₃₄₄

yes

—

263

C₂×C₄

C₂×D₃₄₄

yes

characteristic

264

C₂×C₄

C₂²×D₁₇₂

yes

characteristic

265

C₈

—

266

C₈

—

267

C₈

#13063370

yes

characteristic

268

C₈

#13063373

yes

characteristic

269

C₂²

—

270

C₂²

—

271

C₂²

—

344

—

272

C₂²

—

344

—

273

C₂²

—

344

—

274

C₂²

C₂²×D₃₄₄

yes

characteristic

275

C₄

—

276

C₄

—

277

C₄

—

278

C₄

—

344

—

279

C₄

—

344

—

280

C₄

—

344

—

281

C₄

#14583480

yes

characteristic

282

C₄

#14583699

yes

characteristic

283

C₂

—

284

C₂

—

688

—

285

C₂

#19145905

yes

characteristic

286

C₂

#19147743

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₃₄₄
commutator, cosocle	C₂×C₈×C₄₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₄₃×#2151	C₂
socle	C₂²×C₄₃	C₂²×D₈
prime radical	#19136698	C₂
hypercenter	#2151	D₄₃
hypocenter	C₄₃	#33829
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405 ◁ #2151

subgroup

G/H

center

C₂²

C₂²×D₃₄₄

commutator, cosocle

C₂×C₈×C₄₃

C₂⁴

Frattini

C₂×C₈

C₂³×D₄₃

Fitting

C₄₃×#2151

C₂

socle

C₂²×C₄₃

C₂²×D₈

C₂

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ #117 ◁ #405 ◁ #2151

N	H ≅ G/N	type
1. #19145234	C₂	semidirect
2. #19136743	C₂	semidirect
3. #19136738	C₂	semidirect
4. #19136703	C₂	semidirect
6. #19136691	C₂	semidirect
7. #19136658	C₂	semidirect
8. #19136651	C₂	semidirect
9. C₄₃×#2151	C₂	semidirect
148. #2151	D₄₃	semidirect
178. C₄₃	#33829	semidirect

H ≅ G/N

type

1. #19145234

C₂

semidirect

2. #19136743

C₂

semidirect

3. #19136738

C₂

semidirect

4. #19136703

C₂

semidirect

6. #19136691

C₂

semidirect

7. #19136658

C₂

semidirect

8. #19136651

C₂

semidirect

9. C₄₃×#2151

C₂

semidirect

148. #2151

D₄₃

semidirect

178. C₄₃

#33829

semidirect

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

subgroup	index
#19145234	2
#19136743	2
#19136738	2
#19136703	2
#19136698	2
#19136691	2
#19136658	2
#19136651	2
C₄₃×#2151	2
#33829	43

subgroup

index

C₄₃×#2151

Subgroups — #25253046

Conjugacy classes of subgroups

Complements

Maximal subgroups