Group #24995698 — subgroups

Subgroups — #24995698

Order 11008.

610 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 151 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	#19142952	C₂	1	1	yes	maximal, characteristic
2	#19134448	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14582647	C₂	1	2	yes	maximal, complemented
4	C₂×#14582642	C₂	1	2	yes	maximal
5	C₄₃×#1842	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13063325	C₂²	1	1	yes	characteristic
7	C₂×#13063322	C₂²	1	1	yes	characteristic
8	C₂×#13063313	C₄	1	4	yes	—
9	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
10	C₂×#13063236	—	2	1	no	—
11	#14582801	—	2	1	no	—
12	#14582801	—	2	1	no	—
13	#14582801	—	2	2	no	—
14	#14582654	—	2	1	no	—
15	#14582647	—	2	4	no	—
16	#14582642	—	2	4	no	—
17	C₂×C₄⋊C₈×C₄₃	—	2	2	no	—
18	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
19	C₄³×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×Dic₈₆	C₂×C₄	1	2	yes	—
21	C₂²×D₁₇₂	—	2	1	no	—
22	C₂²×D₁₇₂	—	2	1	no	—
23	C₂²×D₁₇₂	C₂×C₄	1	2	yes	—
24	C₂²×C₄₃⋊C₈	—	2	2	no	—
25	#13063325	—	2	2	no	—
26	#13063325	—	2	2	no	—
27	#13063322	—	2	2	no	—
28	#13063322	—	2	2	no	—
29	#13063313	—	4	8	no	—
30	C₂×C₄⋊Dic₄₃	—	2	1	no	—
31	C₂×C₄⋊Dic₄₃	—	2	1	no	—
32	C₂×(C₂×D₄₃)⋊C₄	—	2	4	no	—
33	C₂×(C₂×D₄₃)⋊C₄	—	2	4	no	—
34	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
35	C₄⋊(C₄₃⋊C₈)	D₄	1	4	yes	—
36	#13063236	—	4	2	no	—
37	C₂²×C₈×C₄₃	—	2	2	no	—
38	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
41	C₂×C₄²×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	—	2	2	no	—
45	C₄⋊C₈×C₄₃	—	4	4	no	—
46	C₂³×D₄₃	—	2	2	no	—
47	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×Dic₄₃	—	2	2	no	—
53	C₂×D₁₇₂	—	2	4	no	—
54	C₂×D₁₇₂	—	4	2	no	—
55	C₂×D₁₇₂	—	4	1	no	—
56	C₂×D₁₇₂	—	4	1	no	—
57	C₂×D₁₇₂	—	4	2	no	—
58	C₂×D₁₇₂	—	4	2	no	—
59	C₂×D₁₇₂	—	4	1	no	—
60	C₂×D₁₇₂	—	4	2	no	—
61	C₂×D₁₇₂	—	4	1	no	—
62	C₂×D₁₇₂	—	4	4	no	—
63	C₂×Dic₈₆	—	2	4	no	—
64	C₂×Dic₈₆	—	4	4	no	—
65	C₂×C₈×C₄₃	—	4	2	no	—
66	C₂×C₈×C₄₃	—	4	4	no	—
67	C₄²×C₄₃	—	2	4	no	—
68	C₄²×C₄₃	—	2	2	no	—
69	C₄²×C₄₃	—	2	2	no	—
70	C₄²×C₄₃	—	2	1	no	—
71	C₄²×C₄₃	—	2	2	no	—
72	C₄²×C₄₃	—	2	1	no	—
73	C₄²×C₄₃	C₂×D₄	1	2	yes	—
74	C₄²×C₄₃	#41	1	2	yes	—
75	(C₂×D₄₃)⋊C₄	—	4	8	no	—
76	(C₂×D₄₃)⋊C₄	—	4	8	no	—
77	C₄⋊Dic₄₃	—	4	2	no	—
78	C₄⋊Dic₄₃	—	4	1	no	—
79	C₄⋊Dic₄₃	—	4	1	no	—
80	C₂×C₄₃⋊C₈	—	2	4	no	—
81	C₂×C₄₃⋊C₈	—	4	2	no	—
82	C₂×C₄₃⋊C₈	—	4	2	no	—
83	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×D₄₃	—	4	2	no	—
85	C₂²×D₄₃	—	4	4	no	—
86	C₂²×D₄₃	—	4	2	no	—
87	C₂²×D₄₃	—	4	4	no	—
88	C₂²×D₄₃	—	4	2	no	—
89	C₂×C₄×C₄₃	—	2	2	no	—
90	C₂×C₄×C₄₃	—	2	2	no	—
91	C₂×C₄×C₄₃	—	2	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	#100	1	4	yes	—
96	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
97	C₂×C₄×C₄₃	#121	1	2	yes	—
98	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
99	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
100	C₂×C₄×C₄₃	#135	1	2	yes	—
101	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
102	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×C₄×C₄₃	#137	1	2	yes	—
104	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
105	C₂×Dic₄₃	—	4	2	no	—
106	C₂×Dic₄₃	—	4	4	no	—
107	D₁₇₂	—	8	4	no	—
108	D₁₇₂	—	8	2	no	—
109	D₁₇₂	—	8	2	no	—
110	D₁₇₂	—	8	2	no	—
111	D₁₇₂	—	8	1	no	—
112	D₁₇₂	—	8	1	no	—
113	Dic₈₆	—	8	4	no	—
114	C₈×C₄₃	—	8	2	no	—
115	C₄₃⋊C₈	—	4	4	no	—
116	#9707	—	43	1	no	maximal, Sylow
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	#417	1	2	yes	—
121	C₂²×C₄₃	#417	1	1	yes	characteristic
122	C₂×D₄₃	—	8	4	no	—
123	C₂×D₄₃	—	8	4	no	—
124	C₂×D₄₃	—	8	2	no	—
125	C₂×D₄₃	—	8	2	no	—
126	C₂×D₄₃	—	8	2	no	—
127	C₄×C₄₃	—	2	4	no	—
128	C₄×C₄₃	—	2	2	no	—
129	C₄×C₄₃	—	4	2	no	—
130	C₄×C₄₃	#463	1	2	yes	—
131	C₄×C₄₃	#464	1	2	yes	—
132	C₄×C₄₃	#489	1	2	yes	—
133	C₄×C₄₃	#496	1	1	yes	characteristic
134	C₄×C₄₃	#497	1	1	yes	characteristic
135	Dic₄₃	—	8	2	no	—
136	#2858	—	43	1	no	—
137	#1842	D₄₃	1	1	yes	characteristic, complemented
138	#1767	—	43	1	no	—
139	C₂×#333	—	43	2	no	—
140	C₂×#331	—	43	2	no	—
141	C₂×C₄₃	#1551	1	2	yes	—
142	C₂×C₄₃	#1560	1	2	yes	—
143	C₂×C₄₃	#1959	1	1	yes	characteristic
144	C₂×C₄₃	#1965	1	1	yes	characteristic
145	C₂×C₄₃	#1983	1	1	yes	characteristic
146	D₄₃	—	16	2	no	—
147	C₂×C₄⋊Q₈	—	43	1	no	—
148	C₂×#127	—	43	1	no	—
149	C₂×#124	—	43	4	no	—
150	C₂×C₄⋊C₈	—	2	2	no	—
151	C₂×C₄⋊C₈	—	43	2	no	—
152	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
153	C₂×#97	—	86	1	no	—
154	#390	—	86	1	no	—
155	#390	—	86	1	no	—
156	#390	—	86	2	no	—
157	C₄³	C₂×D₄₃	1	1	yes	characteristic
158	#336	—	86	1	no	—
159	#333	—	86	4	no	—
160	#331	—	86	4	no	—
161	C₄₃	#9707	1	1	yes	characteristic, complemented, Sylow
162	C₂²×Q₈	—	43	2	no	—
163	C₂²×D₄	—	43	2	no	—
164	C₂²×D₄	—	86	1	no	—
165	C₂²×D₄	—	86	1	no	—
166	C₂²×C₈	—	2	2	no	—
167	C₂²×C₈	—	86	2	no	—
168	C₄⋊Q₈	—	86	2	no	—
169	C₄⋊Q₈	—	86	2	no	—
170	#127	—	86	2	no	—
171	#127	—	86	2	no	—
172	#124	—	172	8	no	—
173	C₂×C₄⋊C₄	—	86	1	no	—
174	C₂×C₄⋊C₄	—	86	1	no	—
175	C₂×C₂²⋊C₄	—	86	4	no	—
176	C₂×C₂²⋊C₄	—	86	4	no	—
177	C₂×C₄²	C₄×D₄₃	1	2	yes	—
178	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
179	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
180	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
181	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
182	C₄⋊C₈	—	2	2	no	—
183	C₄⋊C₈	—	2	2	no	—
184	C₄⋊C₈	—	4	4	no	—
185	C₄⋊C₈	—	43	4	no	—
186	C₄⋊C₈	—	86	2	no	—
187	#97	—	172	2	no	—
188	C₂⁴	—	86	2	no	—
189	C₂×Q₈	—	86	4	no	—
190	C₂×Q₈	—	172	4	no	—
191	C₂×D₄	—	86	4	no	—
192	C₂×D₄	—	172	4	no	—
193	C₂×D₄	—	172	2	no	—
194	C₂×D₄	—	172	1	no	—
195	C₂×D₄	—	172	1	no	—
196	C₂×D₄	—	172	2	no	—
197	C₂×D₄	—	172	2	no	—
198	C₂×D₄	—	172	1	no	—
199	C₂×D₄	—	172	2	no	—
200	C₂×D₄	—	172	1	no	—
201	C₂²×C₄	—	86	2	no	—
202	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
203	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
204	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
205	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
206	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
207	C₂×C₈	—	4	2	no	—
208	C₂×C₈	—	4	4	no	—
209	C₂×C₈	—	86	4	no	—
210	C₂×C₈	—	172	2	no	—
211	C₂×C₈	—	172	2	no	—
212	C₄⋊C₄	—	172	2	no	—
213	C₄⋊C₄	—	172	1	no	—
214	C₄⋊C₄	—	172	1	no	—
215	C₂²⋊C₄	—	172	8	no	—
216	C₂²⋊C₄	—	172	8	no	—
217	C₄²	—	2	4	no	—
218	C₄²	—	2	2	no	—
219	C₄²	—	2	2	no	—
220	C₄²	—	2	1	no	—
221	C₄²	—	2	2	no	—
222	C₄²	—	2	1	no	—
223	C₄²	D₄×D₄₃	1	2	yes	—
224	C₄²	#10621902	1	2	yes	—
225	C₂³	—	172	2	no	—
226	C₂³	—	172	4	no	—
227	C₂³	—	172	2	no	—
228	C₂³	—	172	4	no	—
229	C₂³	—	172	2	no	—
230	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
231	Q₈	—	344	4	no	—
232	D₄	—	344	4	no	—
233	D₄	—	344	2	no	—
234	D₄	—	344	2	no	—
235	D₄	—	344	2	no	—
236	D₄	—	344	1	no	—
237	D₄	—	344	1	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	172	2	no	—
245	C₂×C₄	—	172	4	no	—
246	C₂×C₄	#13063241	1	4	yes	—
247	C₂×C₄	#13063287	1	2	yes	—
248	C₂×C₄	#13063300	1	2	yes	—
249	C₂×C₄	#13063314	1	1	yes	characteristic
250	C₂×C₄	#13063321	1	1	yes	characteristic
251	C₂×C₄	#13063347	1	2	yes	—
252	C₂×C₄	#13063351	1	2	yes	—
253	C₂×C₄	#13063353	1	1	yes	characteristic
254	C₂×C₄	#13063356	1	2	yes	—
255	C₂×C₄	#13063358	1	1	yes	characteristic
256	C₈	—	8	2	no	—
257	C₈	—	172	4	no	—
258	C₂²	—	344	2	no	—
259	C₂²	—	344	4	no	—
260	C₂²	—	344	4	no	—
261	C₂²	—	344	2	no	—
262	C₂²	—	344	2	no	—
263	C₂²	#14582800	1	1	yes	characteristic
264	C₂²	C₂×#13063241	1	2	yes	—
265	C₂²	#14582896	1	1	yes	characteristic
266	C₂²	#14582898	1	2	yes	—
267	C₂²	#14582901	1	1	yes	characteristic
268	C₄	—	2	4	no	—
269	C₄	—	2	2	no	—
270	C₄	—	4	2	no	—
271	C₄	—	344	2	no	—
272	C₄	#14583115	1	2	yes	—
273	C₄	#14583122	1	2	yes	—
274	C₄	#14583261	1	2	yes	—
275	C₄	#14583286	1	1	yes	characteristic
276	C₄	#14583291	1	1	yes	characteristic
277	C₂	—	688	2	no	—
278	C₂	#19133288	1	2	yes	—
279	C₂	#19133328	1	2	yes	—
280	C₂	#19135409	1	1	yes	characteristic
281	C₂	#19135434	1	1	yes	characteristic
282	C₂	#19135525	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19142952

C₂

yes

maximal, characteristic

#19134448

C₂

yes

maximal, characteristic, complemented

C₂×#14582647

C₂

yes

maximal, complemented

C₂×#14582642

C₂

yes

maximal

C₄₃×#1842

C₂

yes

maximal, characteristic, complemented

C₂×#13063325

C₂²

yes

characteristic

C₂×#13063322

C₂²

yes

characteristic

C₂×#13063313

C₄

yes

—

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

—

—

—

—

—

—

—

C₂×C₄⋊C₈×C₄₃

—

C₂×C₄⋊C₈×C₄₃

C₂²

yes

—

C₄³×C₄₃

C₂²

yes

characteristic

C₂²×Dic₈₆

C₂×C₄

yes

—

C₂²×D₁₇₂

—

C₂²×D₁₇₂

—

C₂²×D₁₇₂

C₂×C₄

yes

—

C₂²×C₄₃⋊C₈

—

—

—

—

—

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×(C₂×D₄₃)⋊C₄

—

C₂×(C₂×D₄₃)⋊C₄

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

D₄

yes

—

#13063236

—

C₂²×C₈×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

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₂³×D₄₃

—

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

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#100

yes

—

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

100

C₂×C₄×C₄₃

#135

yes

—

101

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

102

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

characteristic

103

C₂×C₄×C₄₃

#137

yes

—

104

C₂×C₄×C₄₃

#137

yes

characteristic

105

C₂×Dic₄₃

—

106

C₂×Dic₄₃

—

107

D₁₇₂

—

108

D₁₇₂

—

109

D₁₇₂

—

110

D₁₇₂

—

111

D₁₇₂

—

112

D₁₇₂

—

113

Dic₈₆

—

114

C₈×C₄₃

—

115

C₄₃⋊C₈

—

116

#9707

—

maximal, Sylow

117

C₂²×C₄₃

#390

yes

characteristic

118

C₂²×C₄₃

C₂×#100

yes

—

119

C₂²×C₄₃

#416

yes

characteristic

120

C₂²×C₄₃

#417

yes

—

121

C₂²×C₄₃

#417

yes

characteristic

122

C₂×D₄₃

—

123

C₂×D₄₃

—

124

C₂×D₄₃

—

125

C₂×D₄₃

—

126

C₂×D₄₃

—

127

C₄×C₄₃

—

128

C₄×C₄₃

—

129

C₄×C₄₃

—

130

C₄×C₄₃

#463

yes

—

131

C₄×C₄₃

#464

yes

—

132

C₄×C₄₃

#489

yes

—

133

C₄×C₄₃

#496

yes

characteristic

134

C₄×C₄₃

#497

yes

characteristic

135

Dic₄₃

—

136

#2858

—

137

#1842

D₄₃

yes

characteristic, complemented

138

#1767

—

139

C₂×#333

—

140

C₂×#331

—

141

C₂×C₄₃

#1551

yes

—

142

C₂×C₄₃

#1560

yes

—

143

C₂×C₄₃

#1959

yes

characteristic

144

C₂×C₄₃

#1965

yes

characteristic

145

C₂×C₄₃

#1983

yes

characteristic

146

D₄₃

—

147

C₂×C₄⋊Q₈

—

148

C₂×#127

—

149

C₂×#124

—

150

C₂×C₄⋊C₈

—

151

C₂×C₄⋊C₈

—

152

C₂×C₄⋊C₈

C₂×D₄₃

yes

—

153

C₂×#97

—

154

#390

—

155

#390

—

156

#390

—

157

C₄³

C₂×D₄₃

yes

characteristic

158

#336

—

159

#333

—

160

#331

—

161

C₄₃

#9707

yes

characteristic, complemented, Sylow

162

C₂²×Q₈

—

163

C₂²×D₄

—

164

C₂²×D₄

—

165

C₂²×D₄

—

166

C₂²×C₈

—

167

C₂²×C₈

—

168

C₄⋊Q₈

—

169

C₄⋊Q₈

—

170

#127

—

171

#127

—

172

#124

—

172

—

173

C₂×C₄⋊C₄

—

174

C₂×C₄⋊C₄

—

175

C₂×C₂²⋊C₄

—

176

C₂×C₂²⋊C₄

—

177

C₂×C₄²

C₄×D₄₃

yes

—

178

C₂×C₄²

D₁₇₂

yes

characteristic

179

C₂×C₄²

D₁₇₂

yes

characteristic

180

C₂×C₄²

C₂²⋊D₄₃

yes

—

181

C₂×C₄²

C₂²×D₄₃

yes

characteristic

182

C₄⋊C₈

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

C₄⋊C₈

—

186

C₄⋊C₈

—

187

#97

—

172

—

188

C₂⁴

—

189

C₂×Q₈

—

190

C₂×Q₈

—

172

—

191

C₂×D₄

—

192

C₂×D₄

—

172

—

193

C₂×D₄

—

172

—

194

C₂×D₄

—

172

—

195

C₂×D₄

—

172

—

196

C₂×D₄

—

172

—

197

C₂×D₄

—

172

—

198

C₂×D₄

—

172

—

199

C₂×D₄

—

172

—

200

C₂×D₄

—

172

—

201

C₂²×C₄

—

202

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

203

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

204

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

205

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

206

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

—

172

—

211

C₂×C₈

—

172

—

212

C₄⋊C₄

—

172

—

213

C₄⋊C₄

—

172

—

214

C₄⋊C₄

—

172

—

215

C₂²⋊C₄

—

172

—

216

C₂²⋊C₄

—

172

—

217

C₄²

—

218

C₄²

—

219

C₄²

—

220

C₄²

—

221

C₄²

—

222

C₄²

—

223

C₄²

D₄×D₄₃

yes

—

224

C₄²

#10621902

yes

—

225

C₂³

—

172

—

226

C₂³

—

172

—

227

C₂³

—

172

—

228

C₂³

—

172

—

229

C₂³

—

172

—

230

C₂³

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

231

Q₈

—

344

—

232

D₄

—

344

—

233

D₄

—

344

—

234

D₄

—

344

—

235

D₄

—

344

—

236

D₄

—

344

—

237

D₄

—

344

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

172

—

245

C₂×C₄

—

172

—

246

C₂×C₄

#13063241

yes

—

247

C₂×C₄

#13063287

yes

—

248

C₂×C₄

#13063300

yes

—

249

C₂×C₄

#13063314

yes

characteristic

250

C₂×C₄

#13063321

yes

characteristic

251

C₂×C₄

#13063347

yes

—

252

C₂×C₄

#13063351

yes

—

253

C₂×C₄

#13063353

yes

characteristic

254

C₂×C₄

#13063356

yes

—

255

C₂×C₄

#13063358

yes

characteristic

256

C₈

—

257

C₈

—

172

—

258

C₂²

—

344

—

259

C₂²

—

344

—

260

C₂²

—

344

—

261

C₂²

—

344

—

262

C₂²

—

344

—

263

C₂²

#14582800

yes

characteristic

264

C₂²

C₂×#13063241

yes

—

265

C₂²

#14582896

yes

characteristic

266

C₂²

#14582898

yes

—

267

C₂²

#14582901

yes

characteristic

268

C₄

—

269

C₄

—

270

C₄

—

271

C₄

—

344

—

272

C₄

#14583115

yes

—

273

C₄

#14583122

yes

—

274

C₄

#14583261

yes

—

275

C₄

#14583286

yes

characteristic

276

C₄

#14583291

yes

characteristic

277

C₂

—

688

—

278

C₂

#19133288

yes

—

279

C₂

#19133328

yes

—

280

C₂

#19135409

yes

characteristic

281

C₂

#19135434

yes

characteristic

282

C₂

#19135525

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₃)⋊C₄
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1842	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂×#13063322	C₂²
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1842	D₄₃
hypocenter	C₄₃	#9707
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1842

subgroup

G/H

center

C₂³

C₂×(C₂×D₄₃)⋊C₄

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1842

C₂

socle

C₂³×C₄₃

C₂×C₂²⋊C₄

prime radical

C₂×#13063322

C₂²

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1842

N	H ≅ G/N	type
2. #19134448	C₂	semidirect
3. C₂×#14582647	C₂	semidirect
5. C₄₃×#1842	C₂	semidirect
137. #1842	D₄₃	semidirect
161. C₄₃	#9707	semidirect

H ≅ G/N

type

2. #19134448

C₂

semidirect

3. C₂×#14582647

C₂

semidirect

5. C₄₃×#1842

C₂

semidirect

137. #1842

D₄₃

semidirect

161. C₄₃

#9707

semidirect

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

subgroup	index
#19142952	2
#19134448	2
C₂×#14582647	2
C₂×#14582642	2
C₄₃×#1842	2
#9707	43

subgroup

index

C₄₃×#1842

Subgroups — #24995698

Conjugacy classes of subgroups

Complements

Maximal subgroups