Group #24999604 — subgroups

Subgroups — #24999604

Order 11008.

588 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 141 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	#19135522	C₂	1	2	yes	maximal
2	#19135400	C₂	1	1	yes	maximal, characteristic
3	#19132478	C₂	1	1	yes	maximal, characteristic, complemented
4	#19132436	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2551	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13063322	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
8	C₂×#13063245	—	2	2	no	—
9	C₂×#13063245	—	2	2	no	—
10	C₂×#13063245	—	2	2	no	—
11	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₄₃	—	2	2	no	—
13	C₄₃×#395	—	2	2	no	—
14	C₄₃×#389	—	2	2	no	—
15	C₄₃×#384	C₂²	1	1	yes	characteristic
16	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
17	C₂²×D₁₇₂	—	2	1	no	—
18	C₂²×D₁₇₂	—	2	2	no	—
19	C₂²×C₄₃⋊C₈	—	2	1	no	—
20	C₂²×C₄₃⋊C₈	—	2	2	no	—
21	#13063322	—	2	2	no	—
22	#13063322	—	2	1	no	—
23	#13063322	Q₈	1	2	yes	complemented
24	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
25	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
26	#13063245	—	4	4	no	—
27	#13063245	—	4	4	no	—
28	#13063245	—	4	4	no	—
29	C₄×C₄₃⋊C₈	—	2	2	no	—
30	C₂²×Q₈×C₄₃	—	2	2	no	—
31	C₄⋊Q₈×C₄₃	—	4	4	no	—
32	C₄⋊Q₈×C₄₃	—	4	4	no	—
33	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
34	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
35	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
36	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
37	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
38	C₂×C₄²×C₄₃	—	2	2	no	—
39	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
40	#95×C₄₃	—	2	2	no	—
41	#95×C₄₃	—	2	2	no	—
42	C₂³×D₄₃	—	4	1	no	—
43	C₂×Q₈×C₄₃	—	4	8	no	—
44	C₂×Q₈×C₄₃	—	8	2	no	—
45	C₂²×C₄×C₄₃	—	2	2	no	—
46	C₂²×C₄×C₄₃	—	2	2	no	—
47	C₂²×C₄×C₄₃	—	2	2	no	—
48	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
50	C₂×D₁₇₂	—	2	2	no	—
51	C₂×D₁₇₂	—	2	4	no	—
52	C₂×D₁₇₂	—	4	1	no	—
53	C₂×D₁₇₂	—	4	2	no	—
54	C₂×D₁₇₂	—	4	2	no	—
55	C₂×D₁₇₂	—	4	2	no	—
56	C₂×D₁₇₂	—	4	2	no	—
57	C₂×D₁₇₂	—	4	2	no	—
58	C₂×D₁₇₂	—	4	2	no	—
59	C₂×D₁₇₂	—	4	2	no	—
60	C₄⋊C₄×C₄₃	—	2	2	no	—
61	C₄⋊C₄×C₄₃	—	2	2	no	—
62	C₄⋊C₄×C₄₃	—	4	2	no	—
63	C₄⋊C₄×C₄₃	—	4	8	no	—
64	C₄⋊C₄×C₄₃	—	4	2	no	—
65	C₄⋊C₄×C₄₃	—	4	2	no	—
66	C₄⋊C₄×C₄₃	D₈	1	4	yes	—
67	C₄⋊C₄×C₄₃	SD₁₆	1	4	yes	—
68	C₄²×C₄₃	—	4	2	no	—
69	C₄²×C₄₃	—	4	2	no	—
70	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
71	C₄²×C₄₃	#41	1	2	yes	—
72	C₄²×C₄₃	#41	1	1	yes	characteristic
73	C₂×C₄₃⋊C₈	—	2	2	no	—
74	C₂×C₄₃⋊C₈	—	4	1	no	—
75	C₂×C₄₃⋊C₈	—	4	1	no	—
76	C₂×C₄₃⋊C₈	—	4	2	no	—
77	C₂×C₄₃⋊C₈	—	4	2	no	—
78	C₂×C₄₃⋊C₈	—	4	2	no	—
79	C₂³×C₄₃	#120	1	1	yes	characteristic
80	C₂²×D₄₃	—	4	2	no	—
81	C₂²×D₄₃	—	8	2	no	—
82	C₂²×D₄₃	—	8	2	no	—
83	C₂²×D₄₃	—	8	1	no	—
84	C₂²×D₄₃	—	8	1	no	—
85	Q₈×C₄₃	—	8	8	no	—
86	C₂×C₄×C₄₃	—	2	1	no	—
87	C₂×C₄×C₄₃	—	2	1	no	—
88	C₂×C₄×C₄₃	—	2	4	no	—
89	C₂×C₄×C₄₃	—	2	4	no	—
90	C₂×C₄×C₄₃	—	4	2	no	—
91	C₂×C₄×C₄₃	—	4	2	no	—
92	C₂×C₄×C₄₃	—	4	2	no	—
93	C₂×C₄×C₄₃	—	4	2	no	—
94	C₂×C₄×C₄₃	—	4	4	no	—
95	C₂×C₄×C₄₃	—	4	2	no	—
96	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
97	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
98	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
99	C₂×C₄×C₄₃	#124	1	2	yes	—
100	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
101	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
102	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
103	C₂×C₄×C₄₃	#137	1	2	yes	—
104	D₁₇₂	—	4	4	no	—
105	D₁₇₂	—	4	4	no	—
106	D₁₇₂	—	4	4	no	—
107	D₁₇₂	—	8	2	no	—
108	D₁₇₂	—	8	2	no	—
109	D₁₇₂	—	8	2	no	—
110	C₄₃⋊C₈	—	4	2	no	—
111	C₄₃⋊C₈	—	8	2	no	—
112	#10348	—	43	1	no	maximal, Sylow
113	C₂²×C₄₃	#393	1	1	yes	characteristic
114	C₂²×C₄₃	#447	1	2	yes	—
115	C₂²×C₄₃	#448	1	2	yes	—
116	C₂²×C₄₃	#453	1	1	yes	characteristic
117	C₂²×C₄₃	#454	1	1	yes	characteristic
118	C₂×D₄₃	—	8	4	no	—
119	C₂×D₄₃	—	8	2	no	—
120	C₂×D₄₃	—	16	1	no	—
121	C₂×D₄₃	—	16	1	no	—
122	C₂×D₄₃	—	16	2	no	—
123	C₄×C₄₃	—	2	1	no	—
124	C₄×C₄₃	—	2	1	no	—
125	C₄×C₄₃	—	4	4	no	—
126	C₄×C₄₃	—	4	4	no	—
127	C₄×C₄₃	—	8	2	no	—
128	C₄×C₄₃	#474	1	2	yes	—
129	C₄×C₄₃	#476	1	2	yes	—
130	C₄×C₄₃	#486	1	2	yes	—
131	C₄×C₄₃	#489	1	2	yes	—
132	#2551	D₄₃	1	1	yes	characteristic, complemented
133	#1982	—	43	2	no	—
134	#1957	—	43	1	no	—
135	#1296	—	43	1	no	—
136	#1279	—	43	2	no	—
137	C₂×C₄₃	#1619	1	1	yes	characteristic
138	C₂×C₄₃	#1623	1	1	yes	characteristic
139	C₂×C₄₃	#1627	1	2	yes	—
140	C₂×C₄₃	#2023	1	2	yes	—
141	C₂×C₄₃	#2027	1	1	yes	characteristic
142	D₄₃	—	16	2	no	—
143	C₂×C₄⋊Q₈	—	2	2	no	—
144	C₂×#127	—	43	1	no	—
145	C₂×C₄⋊C₈	—	43	2	no	—
146	C₂×#102	—	86	2	no	—
147	C₂×#102	—	86	2	no	—
148	C₂×#102	—	86	2	no	—
149	C₂×C₄×C₈	—	43	1	no	—
150	#395	—	2	2	no	—
151	#389	—	2	2	no	—
152	#384	C₂×D₄₃	1	1	yes	characteristic
153	C₄×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
154	C₄₃	#10348	1	1	yes	characteristic, complemented, Sylow
155	C₂²×Q₈	—	2	2	no	—
156	C₂²×D₄	—	86	1	no	—
157	C₂²×D₄	—	86	2	no	—
158	C₂²×C₈	—	86	1	no	—
159	C₂²×C₈	—	86	2	no	—
160	C₄⋊Q₈	—	4	4	no	—
161	C₄⋊Q₈	—	4	4	no	—
162	#127	—	43	2	no	—
163	#127	—	86	2	no	—
164	#127	—	86	1	no	—
165	C₂×C₄⋊C₄	—	2	4	no	—
166	C₂×C₄⋊C₄	—	2	2	no	—
167	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
168	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
169	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
170	C₂×C₄²	—	2	2	no	—
171	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
172	C₄⋊C₈	—	86	2	no	—
173	C₄⋊C₈	—	86	2	no	—
174	#102	—	172	4	no	—
175	#102	—	172	4	no	—
176	#102	—	172	4	no	—
177	C₄×C₈	—	86	2	no	—
178	#95	—	2	2	no	—
179	#95	—	2	2	no	—
180	C₂⁴	—	172	1	no	—
181	C₂×Q₈	—	4	8	no	—
182	C₂×Q₈	—	8	2	no	—
183	C₂×D₄	—	86	2	no	—
184	C₂×D₄	—	86	4	no	—
185	C₂×D₄	—	172	2	no	—
186	C₂×D₄	—	172	2	no	—
187	C₂×D₄	—	172	1	no	—
188	C₂×D₄	—	172	2	no	—
189	C₂×D₄	—	172	2	no	—
190	C₂×D₄	—	172	2	no	—
191	C₂×D₄	—	172	2	no	—
192	C₂×D₄	—	172	2	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	2	2	no	—
195	C₂²×C₄	—	2	2	no	—
196	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
197	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
198	C₂×C₈	—	86	2	no	—
199	C₂×C₈	—	172	2	no	—
200	C₂×C₈	—	172	2	no	—
201	C₂×C₈	—	172	2	no	—
202	C₂×C₈	—	172	1	no	—
203	C₂×C₈	—	172	1	no	—
204	C₄⋊C₄	—	2	2	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₄⋊C₄	—	4	8	no	—
208	C₄⋊C₄	—	4	2	no	—
209	C₄⋊C₄	—	4	2	no	—
210	C₄⋊C₄	#10621882	1	4	yes	—
211	C₄⋊C₄	#10621884	1	4	yes	—
212	C₄²	—	4	2	no	—
213	C₄²	—	4	2	no	—
214	C₄²	Q₈×D₄₃	1	1	yes	characteristic
215	C₄²	#10621902	1	2	yes	—
216	C₄²	#10621902	1	1	yes	characteristic
217	C₂³	—	344	1	no	—
218	C₂³	—	344	1	no	—
219	C₂³	—	344	2	no	—
220	C₂³	—	344	2	no	—
221	C₂³	—	172	2	no	—
222	C₂³	#13063294	1	1	yes	characteristic
223	Q₈	—	8	8	no	—
224	D₄	—	344	2	no	—
225	D₄	—	344	2	no	—
226	D₄	—	344	2	no	—
227	D₄	—	172	4	no	—
228	D₄	—	172	4	no	—
229	D₄	—	172	4	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	4	no	—
233	C₂×C₄	—	2	4	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	4	4	no	—
240	C₂×C₄	#13063301	1	1	yes	characteristic
241	C₂×C₄	#13063301	1	2	yes	—
242	C₂×C₄	#13063314	1	1	yes	characteristic
243	C₂×C₄	#13063314	1	2	yes	—
244	C₂×C₄	C₂×#10621882	1	2	yes	—
245	C₂×C₄	C₂×#10621884	1	2	yes	—
246	C₂×C₄	#13063351	1	2	yes	—
247	C₂×C₄	#13063356	1	2	yes	—
248	C₈	—	344	2	no	—
249	C₈	—	172	2	no	—
250	C₂²	—	344	2	no	—
251	C₂²	—	344	4	no	—
252	C₂²	—	688	2	no	—
253	C₂²	—	688	1	no	—
254	C₂²	—	688	1	no	—
255	C₂²	#14582810	1	1	yes	characteristic
256	C₂²	#14583033	1	2	yes	—
257	C₂²	#14583038	1	2	yes	—
258	C₂²	#14583067	1	1	yes	characteristic
259	C₂²	#14583072	1	1	yes	characteristic
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	4	4	no	—
263	C₄	—	4	4	no	—
264	C₄	—	8	2	no	—
265	C₄	#14583176	1	2	yes	—
266	C₄	#14583186	1	2	yes	—
267	C₄	#14583247	1	2	yes	—
268	C₄	#14583261	1	2	yes	—
269	C₂	—	688	2	no	—
270	C₂	#19133649	1	1	yes	characteristic
271	C₂	#19133673	1	1	yes	characteristic
272	C₂	#19133698	1	2	yes	—
273	C₂	#19135728	1	2	yes	—
274	C₂	#19135748	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19135522

C₂

yes

maximal

#19135400

C₂

yes

maximal, characteristic

#19132478

C₂

yes

maximal, characteristic, complemented

#19132436

C₂

yes

maximal, complemented

C₄₃×#2551

C₂

yes

maximal, characteristic, complemented

C₂×#13063322

C₂²

yes

characteristic

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₂×#13063245

—

C₂×#13063245

—

C₂×#13063245

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Q₈×C₄₃

—

C₄₃×#395

—

C₄₃×#389

—

C₄₃×#384

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂²×D₁₇₂

—

C₂²×D₁₇₂

—

C₂²×C₄₃⋊C₈

—

C₂²×C₄₃⋊C₈

—

#13063322

—

#13063322

—

#13063322

Q₈

yes

complemented

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

#13063245

—

#13063245

—

#13063245

—

C₄×C₄₃⋊C₈

—

C₂²×Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#95×C₄₃

—

#95×C₄₃

—

C₂³×D₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

D₈

yes

—

C₄⋊C₄×C₄₃

SD₁₆

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×Q₈

yes

characteristic

C₄²×C₄₃

#41

yes

—

C₄²×C₄₃

#41

yes

characteristic

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#120

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₃

#124

yes

characteristic

C₂×C₄×C₄₃

#124

yes

—

100

C₂×C₄×C₄₃

C₂×D₈

yes

—

101

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

102

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

103

C₂×C₄×C₄₃

#137

yes

—

104

D₁₇₂

—

105

D₁₇₂

—

106

D₁₇₂

—

107

D₁₇₂

—

108

D₁₇₂

—

109

D₁₇₂

—

110

C₄₃⋊C₈

—

111

C₄₃⋊C₈

—

112

#10348

—

maximal, Sylow

113

C₂²×C₄₃

#393

yes

characteristic

114

C₂²×C₄₃

#447

yes

—

115

C₂²×C₄₃

#448

yes

—

116

C₂²×C₄₃

#453

yes

characteristic

117

C₂²×C₄₃

#454

yes

characteristic

118

C₂×D₄₃

—

119

C₂×D₄₃

—

120

C₂×D₄₃

—

121

C₂×D₄₃

—

122

C₂×D₄₃

—

123

C₄×C₄₃

—

124

C₄×C₄₃

—

125

C₄×C₄₃

—

126

C₄×C₄₃

—

127

C₄×C₄₃

—

128

C₄×C₄₃

#474

yes

—

129

C₄×C₄₃

#476

yes

—

130

C₄×C₄₃

#486

yes

—

131

C₄×C₄₃

#489

yes

—

132

#2551

D₄₃

yes

characteristic, complemented

133

#1982

—

134

#1957

—

135

#1296

—

136

#1279

—

137

C₂×C₄₃

#1619

yes

characteristic

138

C₂×C₄₃

#1623

yes

characteristic

139

C₂×C₄₃

#1627

yes

—

140

C₂×C₄₃

#2023

yes

—

141

C₂×C₄₃

#2027

yes

characteristic

142

D₄₃

—

143

C₂×C₄⋊Q₈

—

144

C₂×#127

—

145

C₂×C₄⋊C₈

—

146

C₂×#102

—

147

C₂×#102

—

148

C₂×#102

—

149

C₂×C₄×C₈

—

150

#395

—

151

#389

—

152

#384

C₂×D₄₃

yes

characteristic

153

C₄×C₄⋊C₄

C₂×D₄₃

yes

—

154

C₄₃

#10348

yes

characteristic, complemented, Sylow

155

C₂²×Q₈

—

156

C₂²×D₄

—

157

C₂²×D₄

—

158

C₂²×C₈

—

159

C₂²×C₈

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

#127

—

163

#127

—

164

#127

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

168

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

169

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

170

C₂×C₄²

—

171

C₂×C₄²

C₂²×D₄₃

yes

characteristic

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

#102

—

172

—

175

#102

—

172

—

176

#102

—

172

—

177

C₄×C₈

—

178

#95

—

179

#95

—

180

C₂⁴

—

172

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

—

172

—

186

C₂×D₄

—

172

—

187

C₂×D₄

—

172

—

188

C₂×D₄

—

172

—

189

C₂×D₄

—

172

—

190

C₂×D₄

—

172

—

191

C₂×D₄

—

172

—

192

C₂×D₄

—

172

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

197

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

198

C₂×C₈

—

199

C₂×C₈

—

172

—

200

C₂×C₈

—

172

—

201

C₂×C₈

—

172

—

202

C₂×C₈

—

172

—

203

C₂×C₈

—

172

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

#10621882

yes

—

211

C₄⋊C₄

#10621884

yes

—

212

C₄²

—

213

C₄²

—

214

C₄²

Q₈×D₄₃

yes

characteristic

215

C₄²

#10621902

yes

—

216

C₄²

#10621902

yes

characteristic

217

C₂³

—

344

—

218

C₂³

—

344

—

219

C₂³

—

344

—

220

C₂³

—

344

—

221

C₂³

—

172

—

222

C₂³

#13063294

yes

characteristic

223

Q₈

—

224

D₄

—

344

—

225

D₄

—

344

—

226

D₄

—

344

—

227

D₄

—

172

—

228

D₄

—

172

—

229

D₄

—

172

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

#13063301

yes

characteristic

241

C₂×C₄

#13063301

yes

—

242

C₂×C₄

#13063314

yes

characteristic

243

C₂×C₄

#13063314

yes

—

244

C₂×C₄

C₂×#10621882

yes

—

245

C₂×C₄

C₂×#10621884

yes

—

246

C₂×C₄

#13063351

yes

—

247

C₂×C₄

#13063356

yes

—

248

C₈

—

344

—

249

C₈

—

172

—

250

C₂²

—

344

—

251

C₂²

—

344

—

252

C₂²

—

688

—

253

C₂²

—

688

—

254

C₂²

—

688

—

255

C₂²

#14582810

yes

characteristic

256

C₂²

#14583033

yes

—

257

C₂²

#14583038

yes

—

258

C₂²

#14583067

yes

characteristic

259

C₂²

#14583072

yes

characteristic

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

#14583176

yes

—

266

C₄

#14583186

yes

—

267

C₄

#14583247

yes

—

268

C₄

#14583261

yes

—

269

C₂

—

688

—

270

C₂

#19133649

yes

characteristic

271

C₂

#19133673

yes

characteristic

272

C₂

#19133698

yes

—

273

C₂

#19135728

yes

—

274

C₂

#19135748

yes

characteristic

	subgroup	G/H
center	C₂³	#13063294
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#2551	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂×#13063322	C₂²
hypercenter	#2551	D₄₃
hypocenter	C₄₃	#10348
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2551

subgroup

G/H

center

C₂³

#13063294

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#2551

C₂

C₂³×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2551

N	H ≅ G/N	type
3. #19132478	C₂	semidirect
4. #19132436	C₂	semidirect
5. C₄₃×#2551	C₂	semidirect
23. #13063322	Q₈	semidirect
132. #2551	D₄₃	semidirect
154. C₄₃	#10348	semidirect

H ≅ G/N

type

3. #19132478

C₂

semidirect

4. #19132436

C₂

semidirect

5. C₄₃×#2551

C₂

semidirect

23. #13063322

Q₈

semidirect

132. #2551

D₄₃

semidirect

154. C₄₃

#10348

semidirect

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

subgroup	index
#19135522	2
#19135400	2
#19132478	2
#19132436	2
C₄₃×#2551	2
#10348	43

subgroup

index

C₄₃×#2551

Subgroups — #24999604

Conjugacy classes of subgroups

Complements

Maximal subgroups