Group #24991916 — subgroups

Subgroups — #24991916

Order 11008.

530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 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	#19145021	C₂	1	1	yes	maximal, characteristic
2	#19143662	C₂	1	1	yes	maximal, characteristic, complemented
3	#19133013	C₂	1	2	yes	maximal, complemented
4	#19132433	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1525	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13063345	—	2	2	no	—
7	#14583449	C₂²	1	1	yes	characteristic
8	#14583281	—	2	2	no	—
9	#14583278	C₄	1	1	yes	characteristic
10	#14583275	C₄	1	1	yes	characteristic
11	#14583273	C₄	1	1	yes	characteristic
12	#14583271	C₄	1	1	yes	characteristic
13	#14582977	—	2	2	no	—
14	D₄×C₄₃⋊C₈	—	2	2	no	—
15	#14582952	C₂²	1	2	yes	—
16	#14582866	—	2	2	no	—
17	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
18	#14582628	—	2	2	no	—
19	#14582628	—	2	2	no	—
20	C₄₃×#532	C₂²	1	1	yes	characteristic
21	C₄×M₁₆×C₄₃	C₂²	1	2	yes	—
22	C₄₃×#329	—	2	2	no	—
23	C₂×#10621898	—	2	1	no	—
24	#13063345	—	4	4	no	—
25	#13063345	—	4	4	no	—
26	C₂×#10621885	—	2	2	no	—
27	C₂×#10621883	—	2	2	no	—
28	C₂×#10621884	—	2	2	no	—
29	C₂×#10621882	—	2	2	no	—
30	C₂×#10621877	—	2	2	no	—
31	C₂²×C₄₃⋊C₈	—	2	1	no	—
32	C₂²×C₄₃⋊C₈	—	2	2	no	—
33	#13063325	C₂×C₄	1	1	yes	characteristic
34	#13063322	C₂×C₄	1	1	yes	characteristic
35	#13063313	—	2	1	no	—
36	#13063299	—	2	2	no	—
37	C₄×D₁₇₂	—	2	2	no	—
38	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
39	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
40	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
41	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
42	C₄×C₄₃⋊C₈	—	2	1	no	—
43	C₄×C₄₃⋊C₈	—	2	2	no	—
44	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
45	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
46	C₂×#41×C₄₃	D₄	1	2	yes	—
47	C₂×M₁₆×C₄₃	—	2	2	no	—
48	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
49	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
50	#124×C₄₃	D₄	1	2	yes	—
51	#121×C₄₃	—	2	2	no	—
52	C₄×D₄×C₄₃	—	2	2	no	—
53	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
54	#97×C₄₃	—	2	2	no	—
55	C₄×C₈×C₄₃	—	2	2	no	—
56	#41×C₄₃	—	4	2	no	—
57	#41×C₄₃	—	4	2	no	—
58	C₂×Q₈×C₄₃	C₂²⋊C₄	1	2	yes	—
59	C₂×D₄×C₄₃	—	2	2	no	—
60	C₂×D₄×C₄₃	—	2	2	no	—
61	C₂×D₄×C₄₃	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₄₃	—	2	2	no	—
63	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₃	#41	1	2	yes	—
65	C₂×C₂²⋊D₄₃	—	4	1	no	—
66	#10621898	—	4	2	no	—
67	#10621898	—	4	2	no	—
68	C₂×D₁₇₂	—	2	1	no	—
69	C₂×D₁₇₂	—	2	2	no	—
70	C₂×C₄×D₄₃	—	4	1	no	—
71	C₂×Dic₈₆	—	2	1	no	—
72	M₁₆×C₄₃	—	2	4	no	—
73	M₁₆×C₄₃	—	4	2	no	—
74	C₂×C₈×C₄₃	—	4	2	no	—
75	C₄⋊C₄×C₄₃	—	2	2	no	—
76	C₂²⋊C₄×C₄₃	—	2	4	no	—
77	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
78	C₄²×C₄₃	C₂×D₄	1	2	yes	—
79	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
80	#10621885	—	4	4	no	—
81	#10621884	—	4	4	no	—
82	#10621883	—	4	4	no	—
83	#10621882	—	4	4	no	—
84	(C₂×D₄₃)⋊C₄	—	4	2	no	—
85	C₄⋊Dic₄₃	—	2	2	no	—
86	#10621877	—	8	2	no	—
87	C₂×C₄₃⋊C₈	—	2	2	no	—
88	C₂×C₄₃⋊C₈	—	2	2	no	—
89	C₂×C₄₃⋊C₈	—	2	1	no	—
90	C₂×C₄₃⋊C₈	—	2	1	no	—
91	C₂×C₄₃⋊C₈	—	2	2	no	—
92	C₂×C₄₃⋊C₈	—	2	2	no	—
93	C₂×C₄₃⋊C₈	—	8	2	no	—
94	C₂³×C₄₃	—	2	2	no	—
95	C₂³×C₄₃	#123	1	1	yes	characteristic
96	C₂²×D₄₃	—	4	1	no	—
97	Q₈×C₄₃	—	4	2	no	—
98	D₄×C₄₃	—	4	2	no	—
99	D₄×C₄₃	—	4	2	no	—
100	D₄×C₄₃	—	4	2	no	—
101	D₄×C₄₃	—	8	2	no	—
102	C₂×C₄×C₄₃	—	2	2	no	—
103	C₂×C₄×C₄₃	—	2	2	no	—
104	C₂×C₄×C₄₃	—	2	1	no	—
105	C₂×C₄×C₄₃	—	2	1	no	—
106	C₂×C₄×C₄₃	—	2	2	no	—
107	C₂×C₄×C₄₃	—	4	2	no	—
108	C₂×C₄×C₄₃	—	4	2	no	—
109	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
111	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
112	C₂×C₄×C₄₃	#121	1	2	yes	—
113	C₂²⋊D₄₃	—	8	2	no	—
114	C₂×Dic₄₃	—	4	1	no	—
115	D₁₇₂	—	4	2	no	—
116	D₁₇₂	—	4	2	no	—
117	D₁₇₂	—	4	2	no	—
118	C₄×D₄₃	—	8	1	no	—
119	C₄×D₄₃	—	8	1	no	—
120	Dic₈₆	—	4	2	no	—
121	C₈×C₄₃	—	4	4	no	—
122	C₄₃⋊C₈	—	2	2	no	—
123	C₄₃⋊C₈	—	2	2	no	—
124	C₄₃⋊C₈	—	4	2	no	—
125	C₄₃⋊C₈	—	4	2	no	—
126	#9069	—	43	1	no	maximal, Sylow
127	C₂²×C₄₃	—	2	2	no	—
128	C₂²×C₄₃	—	2	1	no	—
129	C₂²×C₄₃	—	4	4	no	—
130	C₂²×C₄₃	—	4	2	no	—
131	C₂²×C₄₃	#386	1	1	yes	characteristic
132	C₂×D₄₃	—	8	2	no	—
133	C₂×D₄₃	—	8	1	no	—
134	C₄×C₄₃	—	2	2	no	—
135	C₄×C₄₃	—	2	1	no	—
136	C₄×C₄₃	—	4	2	no	—
137	C₄×C₄₃	#443	1	2	yes	—
138	C₄×C₄₃	#444	1	2	yes	—
139	C₄×C₄₃	#453	1	1	yes	characteristic
140	C₄×C₄₃	#453	1	1	yes	characteristic
141	Dic₄₃	—	8	1	no	—
142	#3147	—	43	1	no	—
143	#2979	—	43	1	no	—
144	#1525	D₄₃	1	1	yes	characteristic, complemented
145	#1484	—	43	2	no	—
146	#1278	—	43	2	no	—
147	C₂×C₄₃	—	4	1	no	—
148	C₂×C₄₃	—	8	2	no	—
149	C₂×C₄₃	#1876	1	2	yes	—
150	C₂×C₄₃	#1887	1	1	yes	characteristic
151	D₄₃	—	16	1	no	—
152	C₂×#135	—	86	2	no	—
153	#532	—	43	1	no	—
154	#532	C₂×D₄₃	1	1	yes	characteristic
155	#495	—	86	2	no	—
156	#494	—	43	1	no	—
157	#493	—	43	1	no	—
158	#492	—	43	1	no	—
159	#492	—	43	1	no	—
160	#436	—	86	2	no	—
161	C₈×D₄	—	86	2	no	—
162	#431	—	43	2	no	—
163	#408	—	86	2	no	—
164	C₄×M₁₆	C₂×D₄₃	1	2	yes	—
165	C₂×C₄×C₈	—	43	1	no	—
166	#329	—	2	2	no	—
167	D₄⋊C₈	—	86	2	no	—
168	D₄⋊C₈	—	86	2	no	—
169	C₄₃	#9069	1	1	yes	characteristic, complemented, Sylow
170	C₂×#41	—	86	1	no	—
171	C₂×#41	D₁₇₂	1	2	yes	—
172	#135	—	172	4	no	—
173	#135	—	172	4	no	—
174	C₂×Q₁₆	—	86	2	no	—
175	C₂×SD₁₆	—	86	2	no	—
176	C₂×SD₁₆	—	86	2	no	—
177	C₂×D₈	—	86	2	no	—
178	C₂×M₁₆	—	2	2	no	—
179	C₂×M₁₆	—	86	2	no	—
180	C₂²×C₈	—	86	1	no	—
181	C₂²×C₈	—	86	2	no	—
182	C₄⋊Q₈	—	43	1	no	—
183	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
184	#127	—	43	1	no	—
185	#127	C₄×D₄₃	1	1	yes	characteristic
186	#124	—	86	1	no	—
187	#124	C₂²⋊D₄₃	1	2	yes	—
188	#121	—	2	2	no	—
189	#121	—	86	2	no	—
190	C₄×D₄	—	2	2	no	—
191	C₄×D₄	—	86	2	no	—
192	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
193	C₄⋊C₈	—	43	2	no	—
194	C₄⋊C₈	—	43	2	no	—
195	C₂²⋊C₈	—	86	4	no	—
196	C₂²⋊C₈	—	86	2	no	—
197	#97	—	2	2	no	—
198	C₄×C₈	—	2	2	no	—
199	C₄×C₈	—	43	1	no	—
200	C₄×C₈	—	43	1	no	—
201	C₄×C₈	—	86	2	no	—
202	C₄×C₈	—	86	1	no	—
203	#41	—	4	2	no	—
204	#41	—	4	2	no	—
205	#41	—	172	2	no	—
206	#41	—	172	2	no	—
207	C₂×Q₈	—	86	1	no	—
208	C₂×Q₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
209	C₂×D₄	—	2	2	no	—
210	C₂×D₄	—	2	2	no	—
211	C₂×D₄	—	86	1	no	—
212	C₂×D₄	—	86	2	no	—
213	C₂×D₄	—	172	1	no	—
214	C₂×D₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
215	C₂²×C₄	—	2	2	no	—
216	C₂²×C₄	—	172	1	no	—
217	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
218	C₂²×C₄	#10621900	1	2	yes	—
219	Q₁₆	—	172	4	no	—
220	SD₁₆	—	172	4	no	—
221	SD₁₆	—	172	4	no	—
222	D₈	—	172	4	no	—
223	M₁₆	—	2	4	no	—
224	M₁₆	—	4	2	no	—
225	M₁₆	—	344	2	no	—
226	C₂×C₈	—	4	2	no	—
227	C₂×C₈	—	86	2	no	—
228	C₂×C₈	—	86	2	no	—
229	C₂×C₈	—	86	1	no	—
230	C₂×C₈	—	86	1	no	—
231	C₂×C₈	—	86	2	no	—
232	C₂×C₈	—	86	2	no	—
233	C₂×C₈	—	344	2	no	—
234	C₄⋊C₄	—	2	2	no	—
235	C₄⋊C₄	—	86	2	no	—
236	C₂²⋊C₄	—	2	4	no	—
237	C₂²⋊C₄	—	172	2	no	—
238	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
239	C₄²	D₄×D₄₃	1	2	yes	—
240	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
241	C₂³	—	2	2	no	—
242	C₂³	—	172	1	no	—
243	C₂³	#13063309	1	1	yes	characteristic
244	Q₈	—	4	2	no	—
245	Q₈	—	172	2	no	—
246	D₄	—	4	2	no	—
247	D₄	—	4	2	no	—
248	D₄	—	4	2	no	—
249	D₄	—	8	2	no	—
250	D₄	—	344	2	no	—
251	D₄	—	172	2	no	—
252	D₄	—	172	2	no	—
253	D₄	—	172	2	no	—
254	C₂×C₄	—	2	1	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	2	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	344	1	no	—
262	C₂×C₄	—	344	1	no	—
263	C₂×C₄	—	172	1	no	—
264	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
265	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
266	C₂×C₄	#13063295	1	1	yes	characteristic
267	C₂×C₄	#13063297	1	2	yes	—
268	C₈	—	4	4	no	—
269	C₈	—	86	2	no	—
270	C₈	—	86	2	no	—
271	C₈	—	172	2	no	—
272	C₈	—	172	2	no	—
273	C₂²	—	2	1	no	—
274	C₂²	—	2	2	no	—
275	C₂²	—	4	2	no	—
276	C₂²	—	4	4	no	—
277	C₂²	—	344	1	no	—
278	C₂²	—	344	2	no	—
279	C₂²	#14582776	1	1	yes	characteristic
280	C₄	—	2	1	no	—
281	C₄	—	2	2	no	—
282	C₄	—	4	2	no	—
283	C₄	—	344	1	no	—
284	C₄	#14583013	1	2	yes	—
285	C₄	#14583018	1	2	yes	—
286	C₄	#14583069	1	1	yes	characteristic
287	C₄	#14583069	1	1	yes	characteristic
288	C₂	—	4	1	no	—
289	C₂	—	8	2	no	—
290	C₂	—	688	1	no	—
291	C₂	#19134920	1	2	yes	—
292	C₂	#19134991	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19145021

C₂

yes

maximal, characteristic

#19143662

C₂

yes

maximal, characteristic, complemented

#19133013

C₂

yes

maximal, complemented

#19132433

C₂

yes

maximal, complemented

C₄₃×#1525

C₂

yes

maximal, characteristic, complemented

C₂×#13063345

—

#14583449

C₂²

yes

characteristic

#14583281

—

#14583278

C₄

yes

characteristic

#14583275

C₄

yes

characteristic

#14583273

C₄

yes

characteristic

#14583271

C₄

yes

characteristic

#14582977

—

D₄×C₄₃⋊C₈

—

#14582952

C₂²

yes

—

#14582866

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

#14582628

—

#14582628

—

C₄₃×#532

C₂²

yes

characteristic

C₄×M₁₆×C₄₃

C₂²

yes

—

C₄₃×#329

—

—

—

—

—

—

—

—

—

C₂²×C₄₃⋊C₈

—

C₂²×C₄₃⋊C₈

—

#13063325

C₂×C₄

yes

characteristic

#13063322

C₂×C₄

yes

characteristic

#13063313

—

#13063299

—

C₄×D₁₇₂

—

C₄⋊(C₄₃⋊C₈)

D₄

yes

—

C₄⋊(C₄₃⋊C₈)

D₄

yes

—

C₂²⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₄×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂×#41×C₄₃

D₄

yes

—

C₂×M₁₆×C₄₃

—

C₄⋊Q₈×C₄₃

C₂×C₄

yes

characteristic

#127×C₄₃

C₂×C₄

yes

characteristic

#124×C₄₃

D₄

yes

—

#121×C₄₃

—

C₄×D₄×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#97×C₄₃

—

C₄×C₈×C₄₃

—

#41×C₄₃

—

#41×C₄₃

—

C₂×Q₈×C₄₃

C₂²⋊C₄

yes

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

—

C₂×C₂²⋊D₄₃

—

#10621898

—

#10621898

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

C₂×D₄

yes

—

—

—

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

#123

yes

characteristic

C₂²×D₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

100

D₄×C₄₃

—

101

D₄×C₄₃

—

102

C₂×C₄×C₄₃

—

103

C₂×C₄×C₄₃

—

104

C₂×C₄×C₄₃

—

105

C₂×C₄×C₄₃

—

106

C₂×C₄×C₄₃

—

107

C₂×C₄×C₄₃

—

108

C₂×C₄×C₄₃

—

109

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

110

C₂×C₄×C₄₃

C₄×D₄

yes

—

111

C₂×C₄×C₄₃

#120

yes

characteristic

112

C₂×C₄×C₄₃

#121

yes

—

113

C₂²⋊D₄₃

—

114

C₂×Dic₄₃

—

115

D₁₇₂

—

116

D₁₇₂

—

117

D₁₇₂

—

118

C₄×D₄₃

—

119

C₄×D₄₃

—

120

Dic₈₆

—

121

C₈×C₄₃

—

122

C₄₃⋊C₈

—

123

C₄₃⋊C₈

—

124

C₄₃⋊C₈

—

125

C₄₃⋊C₈

—

126

#9069

—

maximal, Sylow

127

C₂²×C₄₃

—

128

C₂²×C₄₃

—

129

C₂²×C₄₃

—

130

C₂²×C₄₃

—

131

C₂²×C₄₃

#386

yes

characteristic

132

C₂×D₄₃

—

133

C₂×D₄₃

—

134

C₄×C₄₃

—

135

C₄×C₄₃

—

136

C₄×C₄₃

—

137

C₄×C₄₃

#443

yes

—

138

C₄×C₄₃

#444

yes

—

139

C₄×C₄₃

#453

yes

characteristic

140

C₄×C₄₃

#453

yes

characteristic

141

Dic₄₃

—

142

#3147

—

143

#2979

—

144

#1525

D₄₃

yes

characteristic, complemented

145

#1484

—

146

#1278

—

147

C₂×C₄₃

—

148

C₂×C₄₃

—

149

C₂×C₄₃

#1876

yes

—

150

C₂×C₄₃

#1887

yes

characteristic

151

D₄₃

—

152

C₂×#135

—

153

#532

—

154

#532

C₂×D₄₃

yes

characteristic

155

#495

—

156

#494

—

157

#493

—

158

#492

—

159

#492

—

160

#436

—

161

C₈×D₄

—

162

#431

—

163

#408

—

164

C₄×M₁₆

C₂×D₄₃

yes

—

165

C₂×C₄×C₈

—

166

#329

—

167

D₄⋊C₈

—

168

D₄⋊C₈

—

169

C₄₃

#9069

yes

characteristic, complemented, Sylow

170

C₂×#41

—

171

C₂×#41

D₁₇₂

yes

—

172

#135

—

172

—

173

#135

—

172

—

174

C₂×Q₁₆

—

175

C₂×SD₁₆

—

176

C₂×SD₁₆

—

177

C₂×D₈

—

178

C₂×M₁₆

—

179

C₂×M₁₆

—

180

C₂²×C₈

—

181

C₂²×C₈

—

182

C₄⋊Q₈

—

183

C₄⋊Q₈

C₄×D₄₃

yes

characteristic

184

#127

—

185

#127

C₄×D₄₃

yes

characteristic

186

#124

—

187

#124

C₂²⋊D₄₃

yes

—

188

#121

—

189

#121

—

190

C₄×D₄

—

191

C₄×D₄

—

192

C₂×C₄²

C₂²×D₄₃

yes

characteristic

193

C₄⋊C₈

—

194

C₄⋊C₈

—

195

C₂²⋊C₈

—

196

C₂²⋊C₈

—

197

#97

—

198

C₄×C₈

—

199

C₄×C₈

—

200

C₄×C₈

—

201

C₄×C₈

—

202

C₄×C₈

—

203

#41

—

204

#41

—

205

#41

—

172

—

206

#41

—

172

—

207

C₂×Q₈

—

208

C₂×Q₈

(C₂×D₄₃)⋊C₄

yes

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂×D₄

—

213

C₂×D₄

—

172

—

214

C₂×D₄

(C₂×D₄₃)⋊C₄

yes

—

215

C₂²×C₄

—

216

C₂²×C₄

—

172

—

217

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

218

C₂²×C₄

#10621900

yes

—

219

Q₁₆

—

172

—

220

SD₁₆

—

172

—

221

SD₁₆

—

172

—

222

D₈

—

172

—

223

M₁₆

—

224

M₁₆

—

225

M₁₆

—

344

—

226

C₂×C₈

—

227

C₂×C₈

—

228

C₂×C₈

—

229

C₂×C₈

—

230

C₂×C₈

—

231

C₂×C₈

—

232

C₂×C₈

—

233

C₂×C₈

—

344

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₂²⋊C₄

—

237

C₂²⋊C₄

—

172

—

238

C₄²

C₂×C₄×D₄₃

yes

characteristic

239

C₄²

D₄×D₄₃

yes

—

240

C₄²

C₂×C₂²⋊D₄₃

yes

characteristic

241

C₂³

—

242

C₂³

—

172

—

243

C₂³

#13063309

yes

characteristic

244

Q₈

—

245

Q₈

—

172

—

246

D₄

—

247

D₄

—

248

D₄

—

249

D₄

—

250

D₄

—

344

—

251

D₄

—

172

—

252

D₄

—

172

—

253

D₄

—

172

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

344

—

262

C₂×C₄

—

344

—

263

C₂×C₄

—

172

—

264

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

265

C₂×C₄

(C₂²⋊D₄₃)⋊C₄

yes

—

266

C₂×C₄

#13063295

yes

characteristic

267

C₂×C₄

#13063297

yes

—

268

C₈

—

269

C₈

—

270

C₈

—

271

C₈

—

172

—

272

C₈

—

172

—

273

C₂²

—

274

C₂²

—

275

C₂²

—

276

C₂²

—

277

C₂²

—

344

—

278

C₂²

—

344

—

279

C₂²

#14582776

yes

characteristic

280

C₄

—

281

C₄

—

282

C₄

—

283

C₄

—

344

—

284

C₄

#14583013

yes

—

285

C₄

#14583018

yes

—

286

C₄

#14583069

yes

characteristic

287

C₄

#14583069

yes

characteristic

288

C₂

—

289

C₂

—

290

C₂

—

688

—

291

C₂

#19134920

yes

—

292

C₂

#19134991

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13063295
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1525	C₂
socle	C₂²×C₄₃	#386
prime radical	#19145021	C₂
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1525	D₄₃
hypocenter	C₄₃	#9069
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1525

subgroup

G/H

center

C₂×C₄

#13063295

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1525

C₂

C₂²×C₄₃

C₂

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1525

N	H ≅ G/N	type
2. #19143662	C₂	semidirect
3. #19133013	C₂	semidirect
4. #19132433	C₂	semidirect
5. C₄₃×#1525	C₂	semidirect
144. #1525	D₄₃	semidirect
169. C₄₃	#9069	semidirect

H ≅ G/N

type

2. #19143662

C₂

semidirect

3. #19133013

C₂

semidirect

4. #19132433

C₂

semidirect

5. C₄₃×#1525

C₂

semidirect

144. #1525

D₄₃

semidirect

169. C₄₃

#9069

semidirect

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

subgroup	index
#19145021	2
#19143662	2
#19133013	2
#19132433	2
C₄₃×#1525	2
#9069	43

subgroup

index

C₄₃×#1525

Subgroups — #24991916

Conjugacy classes of subgroups

Complements

Maximal subgroups