Group #24995665 — subgroups

Subgroups — #24995665

Order 11008.

602 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 159 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	#19134712	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14582648	C₂	1	2	yes	maximal, complemented
4	C₂×#14582643	C₂	1	2	yes	maximal
5	C₄₃×#2858	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
9	#14582654	—	2	1	no	—
10	#14582654	—	2	2	no	—
11	#14582648	—	2	4	no	—
12	#14582643	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#124×C₄₃	C₄	1	4	yes	—
16	C₄₃×#390	—	2	1	no	—
17	C₄₃×#390	—	2	1	no	—
18	C₄₃×#390	—	2	2	no	—
19	C₄³×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄₃⋊C₈	—	2	2	no	—
21	C₂²×C₄₃⋊C₈	—	2	2	no	—
22	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
23	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
24	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
25	C₄⋊(C₄₃⋊C₈)	D₄	1	4	yes	—
26	C₄×C₄₃⋊C₈	—	4	2	no	—
27	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
28	C₂²×D₄×C₄₃	—	2	1	no	—
29	C₂²×D₄×C₄₃	—	2	1	no	—
30	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
31	C₄⋊Q₈×C₄₃	—	2	2	no	—
32	C₄⋊Q₈×C₄₃	—	2	2	no	—
33	#127×C₄₃	—	2	2	no	—
34	#127×C₄₃	—	2	2	no	—
35	#124×C₄₃	—	4	8	no	—
36	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
37	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
38	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
39	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
40	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₄₃	D₄	1	2	yes	—
44	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
45	C₂⁴×C₄₃	—	2	2	no	—
46	C₂×Q₈×C₄₃	—	2	4	no	—
47	C₂×Q₈×C₄₃	—	4	4	no	—
48	C₂×D₄×C₄₃	—	2	4	no	—
49	C₂×D₄×C₄₃	—	4	2	no	—
50	C₂×D₄×C₄₃	—	4	1	no	—
51	C₂×D₄×C₄₃	—	4	1	no	—
52	C₂×D₄×C₄₃	—	4	2	no	—
53	C₂×D₄×C₄₃	—	4	4	no	—
54	C₂×D₄×C₄₃	—	4	1	no	—
55	C₂×D₄×C₄₃	—	4	1	no	—
56	C₂×D₄×C₄₃	—	4	4	no	—
57	C₂²×C₄×C₄₃	—	2	2	no	—
58	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
59	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
63	C₄⋊C₄×C₄₃	—	4	2	no	—
64	C₄⋊C₄×C₄₃	—	4	1	no	—
65	C₄⋊C₄×C₄₃	—	4	1	no	—
66	C₂²⋊C₄×C₄₃	—	4	8	no	—
67	C₂²⋊C₄×C₄₃	—	4	8	no	—
68	C₄²×C₄₃	—	2	4	no	—
69	C₄²×C₄₃	—	2	4	no	—
70	C₄²×C₄₃	—	2	2	no	—
71	C₄²×C₄₃	—	2	1	no	—
72	C₄²×C₄₃	—	2	1	no	—
73	C₄²×C₄₃	C₂×D₄	1	2	yes	—
74	C₄²×C₄₃	#41	1	2	yes	—
75	C₂×C₄₃⋊C₈	—	2	4	no	—
76	C₂×C₄₃⋊C₈	—	4	2	no	—
77	C₂×C₄₃⋊C₈	—	4	2	no	—
78	C₂×C₄₃⋊C₈	—	4	2	no	—
79	C₂×C₄₃⋊C₈	—	4	4	no	—
80	C₂³×C₄₃	—	4	2	no	—
81	C₂³×C₄₃	—	4	4	no	—
82	C₂³×C₄₃	—	4	2	no	—
83	C₂³×C₄₃	—	4	4	no	—
84	C₂³×C₄₃	—	4	2	no	—
85	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	Q₈×C₄₃	—	8	4	no	—
87	D₄×C₄₃	—	8	4	no	—
88	D₄×C₄₃	—	8	2	no	—
89	D₄×C₄₃	—	8	2	no	—
90	D₄×C₄₃	—	8	2	no	—
91	D₄×C₄₃	—	8	2	no	—
92	C₂×C₄×C₄₃	—	2	2	no	—
93	C₂×C₄×C₄₃	—	2	2	no	—
94	C₂×C₄×C₄₃	—	2	2	no	—
95	C₂×C₄×C₄₃	—	2	2	no	—
96	C₂×C₄×C₄₃	—	2	2	no	—
97	C₂×C₄×C₄₃	—	2	2	no	—
98	C₂×C₄×C₄₃	—	4	2	no	—
99	C₂×C₄×C₄₃	—	4	4	no	—
100	C₂×C₄×C₄₃	#100	1	4	yes	—
101	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
102	C₂×C₄×C₄₃	#121	1	2	yes	—
103	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
104	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
105	C₂×C₄×C₄₃	#135	1	2	yes	—
106	C₂×C₄×C₄₃	#135	1	4	yes	—
107	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
108	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
109	C₄₃⋊C₈	—	4	4	no	—
110	C₄₃⋊C₈	—	8	2	no	—
111	#9699	—	43	1	no	maximal, Sylow
112	C₂²×C₄₃	—	8	4	no	—
113	C₂²×C₄₃	—	8	4	no	—
114	C₂²×C₄₃	—	8	2	no	—
115	C₂²×C₄₃	—	8	2	no	—
116	C₂²×C₄₃	—	8	2	no	—
117	C₂²×C₄₃	#390	1	1	yes	characteristic
118	C₂²×C₄₃	C₂×#100	1	2	yes	—
119	C₂²×C₄₃	#416	1	1	yes	characteristic
120	C₂²×C₄₃	#416	1	2	yes	—
121	C₂²×C₄₃	#417	1	1	yes	characteristic
122	C₄×C₄₃	—	2	4	no	—
123	C₄×C₄₃	—	2	2	no	—
124	C₄×C₄₃	—	4	2	no	—
125	C₄×C₄₃	—	8	2	no	—
126	C₄×C₄₃	#463	1	2	yes	—
127	C₄×C₄₃	#464	1	2	yes	—
128	C₄×C₄₃	#488	1	2	yes	—
129	C₄×C₄₃	#495	1	2	yes	—
130	#2858	D₄₃	1	1	yes	characteristic
131	#1831	—	43	1	no	—
132	C₄×C₄⋊C₈	—	43	1	no	—
133	C₂×#333	—	43	2	no	—
134	C₂×#331	—	43	2	no	—
135	C₂×C₄₃	—	16	2	no	—
136	C₂×C₄₃	#1543	1	2	yes	—
137	C₂×C₄₃	#1551	1	2	yes	—
138	C₂×C₄₃	#1958	1	1	yes	characteristic
139	C₂×C₄₃	#1965	1	1	yes	characteristic
140	C₂×C₄₃	#1983	1	1	yes	characteristic
141	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
142	C₂×#127	C₂×D₄₃	1	1	yes	characteristic
143	C₂×#124	Dic₄₃	1	4	yes	—
144	C₂×C₄⋊C₈	—	43	2	no	—
145	C₂×C₄⋊C₈	—	43	2	no	—
146	C₂×C₄×C₈	—	86	1	no	—
147	#390	—	2	1	no	—
148	#390	—	2	2	no	—
149	#390	—	2	1	no	—
150	C₄³	C₂×D₄₃	1	1	yes	characteristic
151	#336	—	86	2	no	—
152	#336	—	86	1	no	—
153	#333	—	86	4	no	—
154	#331	—	86	4	no	—
155	C₄₃	#9699	1	1	yes	characteristic, complemented, Sylow
156	C₂²×Q₈	C₂×Dic₄₃	1	2	yes	—
157	C₂²×D₄	—	2	1	no	—
158	C₂²×D₄	—	2	1	no	—
159	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
160	C₂²×C₈	—	86	2	no	—
161	C₂²×C₈	—	86	2	no	—
162	C₄⋊Q₈	—	2	2	no	—
163	C₄⋊Q₈	—	2	2	no	—
164	#127	—	2	2	no	—
165	#127	—	2	2	no	—
166	#124	—	4	8	no	—
167	C₂×C₄⋊C₄	—	2	1	no	—
168	C₂×C₄⋊C₄	—	2	1	no	—
169	C₂×C₂²⋊C₄	—	2	4	no	—
170	C₂×C₂²⋊C₄	—	2	4	no	—
171	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
172	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
173	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
174	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
175	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
176	C₄⋊C₈	—	43	4	no	—
177	C₄⋊C₈	—	86	2	no	—
178	C₄⋊C₈	—	86	2	no	—
179	C₄⋊C₈	—	86	2	no	—
180	C₄×C₈	—	172	2	no	—
181	C₂⁴	—	2	2	no	—
182	C₂×Q₈	—	2	4	no	—
183	C₂×Q₈	—	4	4	no	—
184	C₂×D₄	—	2	4	no	—
185	C₂×D₄	—	4	4	no	—
186	C₂×D₄	—	4	2	no	—
187	C₂×D₄	—	4	1	no	—
188	C₂×D₄	—	4	1	no	—
189	C₂×D₄	—	4	2	no	—
190	C₂×D₄	—	4	4	no	—
191	C₂×D₄	—	4	1	no	—
192	C₂×D₄	—	4	1	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	C₂²⋊Dic₄₃	1	2	yes	—
195	C₂²×C₄	C₂²⋊Dic₄₃	1	2	yes	—
196	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
197	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
198	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
199	C₂×C₈	—	86	4	no	—
200	C₂×C₈	—	172	2	no	—
201	C₂×C₈	—	172	4	no	—
202	C₂×C₈	—	172	2	no	—
203	C₂×C₈	—	172	2	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	4	1	no	—
206	C₄⋊C₄	—	4	1	no	—
207	C₂²⋊C₄	—	4	8	no	—
208	C₂²⋊C₄	—	4	8	no	—
209	C₄²	—	2	4	no	—
210	C₄²	—	2	4	no	—
211	C₄²	—	2	2	no	—
212	C₄²	—	2	1	no	—
213	C₄²	—	2	1	no	—
214	C₄²	D₄×D₄₃	1	2	yes	—
215	C₄²	#10621900	1	2	yes	—
216	C₂³	—	4	2	no	—
217	C₂³	—	4	4	no	—
218	C₂³	—	4	2	no	—
219	C₂³	—	4	4	no	—
220	C₂³	—	4	2	no	—
221	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
222	Q₈	—	8	4	no	—
223	D₄	—	8	4	no	—
224	D₄	—	8	2	no	—
225	D₄	—	8	2	no	—
226	D₄	—	8	2	no	—
227	D₄	—	8	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	4	4	no	—
236	C₂×C₄	#13063242	1	4	yes	—
237	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
238	C₂×C₄	#13063296	1	2	yes	—
239	C₂×C₄	#13063312	1	1	yes	characteristic
240	C₂×C₄	#13063321	1	1	yes	characteristic
241	C₂×C₄	#13063345	1	2	yes	—
242	C₂×C₄	#13063345	1	4	yes	—
243	C₂×C₄	#13063350	1	1	yes	characteristic
244	C₂×C₄	#13063355	1	1	yes	characteristic
245	C₈	—	344	2	no	—
246	C₈	—	172	4	no	—
247	C₂²	—	8	2	no	—
248	C₂²	—	8	4	no	—
249	C₂²	—	8	4	no	—
250	C₂²	—	8	2	no	—
251	C₂²	—	8	2	no	—
252	C₂²	#14582802	1	1	yes	characteristic
253	C₂²	C₂×#13063242	1	2	yes	—
254	C₂²	#14582895	1	1	yes	characteristic
255	C₂²	#14582895	1	2	yes	—
256	C₂²	#14582900	1	1	yes	characteristic
257	C₄	—	2	4	no	—
258	C₄	—	2	2	no	—
259	C₄	—	4	2	no	—
260	C₄	—	8	2	no	—
261	C₄	#14583111	1	2	yes	—
262	C₄	#14583118	1	2	yes	—
263	C₄	#14583253	1	2	yes	—
264	C₄	#14583281	1	2	yes	—
265	C₂	—	16	2	no	—
266	C₂	#19133257	1	2	yes	—
267	C₂	#19133290	1	2	yes	—
268	C₂	#19135407	1	1	yes	characteristic
269	C₂	#19135436	1	1	yes	characteristic
270	C₂	#19135528	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19134712

C₂

yes

maximal, characteristic, complemented

C₄×C₄⋊(C₄₃⋊C₈)

C₂

yes

maximal, characteristic, complemented

C₂×#14582648

C₂

yes

maximal, complemented

C₂×#14582643

C₂

yes

maximal

C₄₃×#2858

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₂×C₄×C₄₃⋊C₈

—

—

—

—

—

C₂×C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₂×#127×C₄₃

C₂²

yes

characteristic

C₂×#124×C₄₃

C₄

yes

—

C₄₃×#390

—

C₄₃×#390

—

C₄₃×#390

—

C₄³×C₄₃

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

—

C₂²×C₄₃⋊C₈

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

D₄

yes

—

C₄×C₄₃⋊C₈

—

C₂²×Q₈×C₄₃

C₂×C₄

yes

—

C₂²×D₄×C₄₃

—

C₂²×D₄×C₄₃

—

C₂²×D₄×C₄₃

C₂×C₄

yes

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

#127×C₄₃

—

#127×C₄₃

—

#124×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₂²⋊C₄×C₄₃

—

C₂×C₂²⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₂⁴×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×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

—

100

C₂×C₄×C₄₃

#100

yes

—

101

C₂×C₄×C₄₃

C₄×D₄

yes

—

102

C₂×C₄×C₄₃

#121

yes

—

103

C₂×C₄×C₄₃

#124

yes

characteristic

104

C₂×C₄×C₄₃

#127

yes

characteristic

105

C₂×C₄×C₄₃

#135

yes

—

106

C₂×C₄×C₄₃

#135

yes

—

107

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

characteristic

108

C₂×C₄×C₄₃

#137

yes

characteristic

109

C₄₃⋊C₈

—

110

C₄₃⋊C₈

—

111

#9699

—

maximal, Sylow

112

C₂²×C₄₃

—

113

C₂²×C₄₃

—

114

C₂²×C₄₃

—

115

C₂²×C₄₃

—

116

C₂²×C₄₃

—

117

C₂²×C₄₃

#390

yes

characteristic

118

C₂²×C₄₃

C₂×#100

yes

—

119

C₂²×C₄₃

#416

yes

characteristic

120

C₂²×C₄₃

#416

yes

—

121

C₂²×C₄₃

#417

yes

characteristic

122

C₄×C₄₃

—

123

C₄×C₄₃

—

124

C₄×C₄₃

—

125

C₄×C₄₃

—

126

C₄×C₄₃

#463

yes

—

127

C₄×C₄₃

#464

yes

—

128

C₄×C₄₃

#488

yes

—

129

C₄×C₄₃

#495

yes

—

130

#2858

D₄₃

yes

characteristic

131

#1831

—

132

C₄×C₄⋊C₈

—

133

C₂×#333

—

134

C₂×#331

—

135

C₂×C₄₃

—

136

C₂×C₄₃

#1543

yes

—

137

C₂×C₄₃

#1551

yes

—

138

C₂×C₄₃

#1958

yes

characteristic

139

C₂×C₄₃

#1965

yes

characteristic

140

C₂×C₄₃

#1983

yes

characteristic

141

C₂×C₄⋊Q₈

C₂×D₄₃

yes

characteristic

142

C₂×#127

C₂×D₄₃

yes

characteristic

143

C₂×#124

Dic₄₃

yes

—

144

C₂×C₄⋊C₈

—

145

C₂×C₄⋊C₈

—

146

C₂×C₄×C₈

—

147

#390

—

148

#390

—

149

#390

—

150

C₄³

C₂×D₄₃

yes

characteristic

151

#336

—

152

#336

—

153

#333

—

154

#331

—

155

C₄₃

#9699

yes

characteristic, complemented, Sylow

156

C₂²×Q₈

C₂×Dic₄₃

yes

—

157

C₂²×D₄

—

158

C₂²×D₄

—

159

C₂²×D₄

C₂×Dic₄₃

yes

—

160

C₂²×C₈

—

161

C₂²×C₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

—

164

#127

—

165

#127

—

166

#124

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₂²⋊C₄

—

170

C₂×C₂²⋊C₄

—

171

C₂×C₄²

C₂×Dic₄₃

yes

—

172

C₂×C₄²

C₂²⋊D₄₃

yes

characteristic

173

C₂×C₄²

C₂²⋊D₄₃

yes

—

174

C₂×C₄²

C₂²⋊D₄₃

yes

characteristic

175

C₂×C₄²

C₂²×D₄₃

yes

characteristic

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄×C₈

—

172

—

181

C₂⁴

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂²×C₄

—

194

C₂²×C₄

C₂²⋊Dic₄₃

yes

—

195

C₂²×C₄

C₂²⋊Dic₄₃

yes

—

196

C₂²×C₄

C₂²×Dic₄₃

yes

characteristic

197

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

198

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

199

C₂×C₈

—

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

C₂²⋊C₄

—

208

C₂²⋊C₄

—

209

C₄²

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₄²

D₄×D₄₃

yes

—

215

C₄²

#10621900

yes

—

216

C₂³

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

C₂×C₂²⋊Dic₄₃

yes

characteristic

222

Q₈

—

223

D₄

—

224

D₄

—

225

D₄

—

226

D₄

—

227

D₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

#13063242

yes

—

237

C₂×C₄

D₄×Dic₄₃

yes

—

238

C₂×C₄

#13063296

yes

—

239

C₂×C₄

#13063312

yes

characteristic

240

C₂×C₄

#13063321

yes

characteristic

241

C₂×C₄

#13063345

yes

—

242

C₂×C₄

#13063345

yes

—

243

C₂×C₄

#13063350

yes

characteristic

244

C₂×C₄

#13063355

yes

characteristic

245

C₈

—

344

—

246

C₈

—

172

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

#14582802

yes

characteristic

253

C₂²

C₂×#13063242

yes

—

254

C₂²

#14582895

yes

characteristic

255

C₂²

#14582895

yes

—

256

C₂²

#14582900

yes

characteristic

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

#14583111

yes

—

262

C₄

#14583118

yes

—

263

C₄

#14583253

yes

—

264

C₄

#14583281

yes

—

265

C₂

—

266

C₂

#19133257

yes

—

267

C₂

#19133290

yes

—

268

C₂

#19135407

yes

characteristic

269

C₂

#19135436

yes

characteristic

270

C₂

#19135528

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₃
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#2858	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂×#127×C₄₃	C₂²
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#2858	D₄₃
hypocenter	C₄₃	#9699
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2858

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₄₃

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#2858

C₂

socle

C₂³×C₄₃

C₂×C₂²⋊C₄

prime radical

C₂×#127×C₄₃

C₂²

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #2858

N	H ≅ G/N	type
1. #19134712	C₂	semidirect
2. C₄×C₄⋊(C₄₃⋊C₈)	C₂	semidirect
3. C₂×#14582648	C₂	semidirect
155. C₄₃	#9699	semidirect

H ≅ G/N

type

1. #19134712

C₂

semidirect

2. C₄×C₄⋊(C₄₃⋊C₈)

C₂

semidirect

3. C₂×#14582648

C₂

semidirect

155. C₄₃

#9699

semidirect

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

subgroup	index
#19134712	2
C₄×C₄⋊(C₄₃⋊C₈)	2
C₂×#14582648	2
C₂×#14582643	2
C₄₃×#2858	2
#9699	43

subgroup

index

C₄×C₄⋊(C₄₃⋊C₈)

C₄₃×#2858

Subgroups — #24995665

Conjugacy classes of subgroups

Complements

Maximal subgroups