Group #26118874 — subgroups

Subgroups — #26118874

Order 12032.

626 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 139 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	C₂×#15689503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689403	C₂	1	2	yes	maximal
3	C₂×#15688870	C₂	1	2	yes	maximal, complemented
4	#20241223	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1954	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₈₈	—	2	2	no	—
7	C₂×#13094024	C₂²	1	2	yes	—
8	#15689503	—	2	4	no	—
9	#15689403	—	2	4	no	—
10	#15689403	—	2	4	no	—
11	C₂×#13093957	—	2	2	no	—
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	C₂×#13093945	—	2	2	no	—
14	#15688870	—	2	4	no	—
15	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
18	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×Dic₉₄	—	2	2	no	—
20	C₂×Dic₁₈₈	—	2	8	no	—
21	C₂×Dic₁₈₈	—	4	4	no	—
22	C₂×Dic₁₈₈	—	4	4	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	#13094024	—	2	2	no	—
25	#13094024	—	2	2	no	—
26	#13094024	—	2	2	no	—
27	#13094024	D₄	1	4	yes	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	#13093957	—	2	8	no	—
31	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
32	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
33	#13093945	—	2	8	no	—
34	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₄₇	—	2	1	no	—
36	C₂²×C₈×C₄₇	—	2	1	no	—
37	C₂²×C₈×C₄₇	D₄	1	2	yes	—
38	C₄×D₄×C₄₇	—	2	2	no	—
39	C₄×D₄×C₄₇	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
42	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₄₇	—	2	2	no	—
44	C₂²⋊C₈×C₄₇	—	4	4	no	—
45	C₄×C₈×C₄₇	—	2	2	no	—
46	C₂⁴×C₄₇	—	2	1	no	—
47	C₂×D₄×C₄₇	—	2	2	no	—
48	C₂×D₄×C₄₇	—	2	1	no	—
49	C₂×D₄×C₄₇	—	2	2	no	—
50	C₂×D₄×C₄₇	Q₁₆	1	2	yes	complemented
51	C₂²×C₄×C₄₇	—	2	1	no	—
52	C₂²×C₄×C₄₇	—	4	1	no	—
53	C₂²×C₄×C₄₇	—	4	1	no	—
54	C₂²×C₄×C₄₇	—	4	2	no	—
55	C₂²×C₄×C₄₇	—	4	2	no	—
56	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
59	C₂²×Dic₄₇	—	4	2	no	—
60	C₂×Dic₉₄	—	2	4	no	—
61	C₂×Dic₉₄	—	4	4	no	—
62	C₂×Dic₉₄	—	4	4	no	—
63	C₂×Dic₉₄	—	4	2	no	—
64	C₂×C₈×C₄₇	—	2	2	no	—
65	C₂×C₈×C₄₇	—	2	2	no	—
66	C₂×C₈×C₄₇	—	4	1	no	—
67	C₂×C₈×C₄₇	—	4	2	no	—
68	C₂×C₈×C₄₇	D₈	1	4	yes	—
69	C₄⋊C₄×C₄₇	—	2	2	no	—
70	C₂²⋊C₄×C₄₇	—	4	2	no	—
71	C₄²×C₄₇	C₂×D₄	1	2	yes	—
72	C₄²×C₄₇	C₂×D₄	1	2	yes	—
73	C₄⋊Dic₄₇	—	2	4	no	—
74	C₄⋊Dic₄₇	—	2	4	no	—
75	C₄⋊Dic₄₇	—	4	2	no	—
76	C₄⋊Dic₄₇	—	4	2	no	—
77	C₂×C₄₇⋊C₈	—	2	4	no	—
78	C₂×C₄₇⋊C₈	—	4	2	no	—
79	C₂×C₄₇⋊C₈	—	4	2	no	—
80	Dic₁₈₈	—	4	16	no	—
81	C₂³×C₄₇	—	2	2	no	—
82	C₂³×C₄₇	—	4	1	no	—
83	C₂³×C₄₇	—	4	2	no	—
84	C₂³×C₄₇	—	4	1	no	—
85	C₂³×C₄₇	—	4	2	no	—
86	C₂³×C₄₇	#121	1	1	yes	characteristic
87	D₄×C₄₇	—	2	4	no	—
88	D₄×C₄₇	—	4	2	no	—
89	C₂×C₄×C₄₇	—	2	2	no	—
90	C₂×C₄×C₄₇	—	4	1	no	—
91	C₂×C₄×C₄₇	—	4	2	no	—
92	C₂×C₄×C₄₇	—	8	2	no	—
93	C₂×C₄×C₄₇	—	8	1	no	—
94	C₂×C₄×C₄₇	—	8	1	no	—
95	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
96	C₂×C₄×C₄₇	#120	1	2	yes	—
97	C₂×C₄×C₄₇	#121	1	2	yes	—
98	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
99	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
100	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
101	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
102	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
103	C₂×C₄×C₄₇	#137	1	2	yes	—
104	C₂×Dic₄₇	—	4	4	no	—
105	C₂×Dic₄₇	—	8	4	no	—
106	Dic₉₄	—	4	8	no	—
107	Dic₉₄	—	8	2	no	—
108	Dic₉₄	—	8	2	no	—
109	C₈×C₄₇	—	2	4	no	—
110	C₈×C₄₇	—	8	1	no	—
111	C₄₇⋊C₈	—	4	4	no	—
112	#10274	—	47	1	no	maximal, Sylow
113	C₂²×C₄₇	—	4	4	no	—
114	C₂²×C₄₇	—	4	2	no	—
115	C₂²×C₄₇	—	8	2	no	—
116	C₂²×C₄₇	—	8	1	no	—
117	C₂²×C₄₇	—	8	1	no	—
118	C₂²×C₄₇	#392	1	1	yes	characteristic
119	C₂²×C₄₇	#459	1	2	yes	—
120	C₂²×C₄₇	#467	1	1	yes	characteristic
121	C₂²×C₄₇	#470	1	1	yes	characteristic
122	C₂²×C₄₇	#473	1	2	yes	—
123	C₄×C₄₇	—	2	2	no	—
124	C₄×C₄₇	—	8	1	no	—
125	C₄×C₄₇	#447	1	2	yes	—
126	C₄×C₄₇	#451	1	2	yes	—
127	C₄×C₄₇	#452	1	2	yes	—
128	C₄×C₄₇	#493	1	1	yes	characteristic
129	C₄×C₄₇	#496	1	1	yes	characteristic
130	Dic₄₇	—	8	4	no	—
131	C₂×#494	—	47	1	no	—
132	C₂×#474	—	47	2	no	—
133	#1954	D₄₇	1	1	yes	characteristic
134	C₂×#332	—	47	2	no	—
135	#1277	—	47	1	no	—
136	C₂×C₄₇	—	8	2	no	—
137	C₂×C₄₇	#1669	1	2	yes	—
138	C₂×C₄₇	#1689	1	2	yes	—
139	C₂×C₄₇	#2001	1	1	yes	characteristic
140	C₂×C₄₇	#2011	1	1	yes	characteristic
141	C₂×C₄₇	#2020	1	1	yes	characteristic
142	C₂²×Q₁₆	—	94	2	no	—
143	C₂×C₄⋊Q₈	—	47	2	no	—
144	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
145	#494	—	94	4	no	—
146	#474	—	94	4	no	—
147	#474	—	94	4	no	—
148	C₂×#107	—	94	2	no	—
149	C₂×C₄⋊C₈	—	47	2	no	—
150	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
151	C₂×#102	—	94	2	no	—
152	C₂×C₂²⋊C₈	—	2	2	no	—
153	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
154	#332	—	94	4	no	—
155	C₄₇	#10274	1	1	yes	characteristic, complemented, Sylow
156	C₂²×Q₈	—	94	2	no	—
157	C₂²×D₄	D₁₈₈	1	1	yes	characteristic
158	C₂³×C₄	—	2	1	no	—
159	C₂×Q₁₆	—	94	8	no	—
160	C₂×Q₁₆	—	188	4	no	—
161	C₂×Q₁₆	—	188	4	no	—
162	C₂²×C₈	—	2	1	no	—
163	C₂²×C₈	—	94	2	no	—
164	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
165	C₄⋊Q₈	—	47	4	no	—
166	C₄⋊Q₈	—	94	2	no	—
167	C₄⋊Q₈	—	94	2	no	—
168	C₄⋊Q₈	—	94	2	no	—
169	C₄×D₄	—	2	2	no	—
170	C₄×D₄	—	2	2	no	—
171	C₂×C₄⋊C₄	—	94	2	no	—
172	C₂×C₄⋊C₄	—	94	2	no	—
173	C₂×C₄⋊C₄	D₁₈₈	1	1	yes	characteristic
174	C₂×C₂²⋊C₄	—	2	1	no	—
175	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
176	#107	—	94	8	no	—
177	C₄⋊C₈	—	2	2	no	—
178	C₄⋊C₈	—	47	4	no	—
179	C₄⋊C₈	—	94	2	no	—
180	#102	—	94	8	no	—
181	C₂²⋊C₈	—	4	4	no	—
182	C₄×C₈	—	2	2	no	—
183	C₂⁴	—	2	1	no	—
184	C₂×Q₈	—	94	4	no	—
185	C₂×Q₈	—	188	4	no	—
186	C₂×Q₈	—	188	4	no	—
187	C₂×Q₈	—	188	2	no	—
188	C₂×D₄	—	2	2	no	—
189	C₂×D₄	—	2	1	no	—
190	C₂×D₄	—	2	2	no	—
191	C₂×D₄	Dic₁₈₈	1	2	yes	complemented
192	C₂²×C₄	—	2	1	no	—
193	C₂²×C₄	—	4	1	no	—
194	C₂²×C₄	—	4	1	no	—
195	C₂²×C₄	—	4	2	no	—
196	C₂²×C₄	—	4	2	no	—
197	C₂²×C₄	—	188	2	no	—
198	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
199	C₂²×C₄	#10625350	1	1	yes	characteristic
200	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
201	Q₁₆	—	188	16	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	4	1	no	—
205	C₂×C₈	—	4	2	no	—
206	C₂×C₈	—	94	4	no	—
207	C₂×C₈	—	188	2	no	—
208	C₂×C₈	—	188	2	no	—
209	C₂×C₈	#10625334	1	4	yes	—
210	C₄⋊C₄	—	2	2	no	—
211	C₄⋊C₄	—	94	4	no	—
212	C₄⋊C₄	—	94	4	no	—
213	C₄⋊C₄	—	188	2	no	—
214	C₄⋊C₄	—	188	2	no	—
215	C₂²⋊C₄	—	4	2	no	—
216	C₄²	D₄×D₄₇	1	2	yes	—
217	C₄²	D₄×D₄₇	1	2	yes	—
218	C₂³	—	2	2	no	—
219	C₂³	—	4	1	no	—
220	C₂³	—	4	2	no	—
221	C₂³	—	4	1	no	—
222	C₂³	—	4	2	no	—
223	C₂³	#13093998	1	1	yes	characteristic
224	Q₈	—	376	2	no	—
225	Q₈	—	376	2	no	—
226	Q₈	—	188	8	no	—
227	D₄	—	2	4	no	—
228	D₄	—	4	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	4	1	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	8	1	no	—
233	C₂×C₄	—	8	2	no	—
234	C₂×C₄	—	8	1	no	—
235	C₂×C₄	—	376	4	no	—
236	C₂×C₄	—	188	4	no	—
237	C₂×C₄	#13093992	1	1	yes	characteristic
238	C₂×C₄	#13093994	1	2	yes	—
239	C₂×C₄	#13093997	1	2	yes	—
240	C₂×C₄	#13094020	1	1	yes	characteristic
241	C₂×C₄	C₂×#10625334	1	2	yes	—
242	C₂×C₄	C₂×Dic₁₈₈	1	1	yes	characteristic
243	C₂×C₄	#13094046	1	1	yes	characteristic
244	C₂×C₄	#13094049	1	2	yes	—
245	C₂×C₄	#13094057	1	2	yes	—
246	C₈	—	2	4	no	—
247	C₈	—	8	1	no	—
248	C₈	—	188	4	no	—
249	C₂²	—	4	4	no	—
250	C₂²	—	4	2	no	—
251	C₂²	—	8	1	no	—
252	C₂²	—	8	2	no	—
253	C₂²	—	8	1	no	—
254	C₂²	#15689032	1	1	yes	characteristic
255	C₂²	#15689318	1	2	yes	—
256	C₂²	#15689364	1	1	yes	characteristic
257	C₂²	#15689381	1	1	yes	characteristic
258	C₂²	#15689398	1	2	yes	—
259	C₄	—	2	2	no	—
260	C₄	—	8	1	no	—
261	C₄	—	376	4	no	—
262	C₄	#15689256	1	2	yes	—
263	C₄	#15689281	1	2	yes	—
264	C₄	#15689287	1	2	yes	—
265	C₄	#15689499	1	1	yes	characteristic
266	C₄	#15689513	1	1	yes	characteristic
267	C₂	—	8	2	no	—
268	C₂	#20242753	1	2	yes	—
269	C₂	#20242877	1	2	yes	—
270	C₂	#20244398	1	1	yes	characteristic
271	C₂	#20244458	1	1	yes	characteristic
272	C₂	#20244509	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689503

C₂

yes

maximal, characteristic, complemented

C₂×#15689403

C₂

yes

maximal

C₂×#15688870

C₂

yes

maximal, complemented

#20241223

C₂

yes

maximal, characteristic, complemented

C₄₇×#1954

C₂

yes

maximal, characteristic

C₂²×Dic₁₈₈

—

C₂×#13094024

C₂²

yes

—

—

—

—

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₂×#13093945

—

#15688870

—

C₂×C₄×D₄×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₄₇

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂²×Dic₉₄

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂²×C₄₇⋊C₈

—

—

—

—

D₄

yes

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

#13093957

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

#13093945

—

C₂²×D₄×C₄₇

D₄

yes

characteristic

C₂³×C₄×C₄₇

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

D₄

yes

—

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₂²⋊C₈×C₄₇

—

C₄×C₈×C₄₇

—

C₂⁴×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

Q₁₆

yes

complemented

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

#41

yes

characteristic

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₈

yes

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

Dic₁₈₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#121

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#120

yes

characteristic

C₂×C₄×C₄₇

#120

yes

—

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

#127

yes

characteristic

C₂×C₄×C₄₇

C₂×D₈

yes

—

100

C₂×C₄×C₄₇

C₂×Q₁₆

yes

characteristic

101

C₂×C₄×C₄₇

#135

yes

characteristic

102

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

103

C₂×C₄×C₄₇

#137

yes

—

104

C₂×Dic₄₇

—

105

C₂×Dic₄₇

—

106

Dic₉₄

—

107

Dic₉₄

—

108

Dic₉₄

—

109

C₈×C₄₇

—

110

C₈×C₄₇

—

111

C₄₇⋊C₈

—

112

#10274

—

maximal, Sylow

113

C₂²×C₄₇

—

114

C₂²×C₄₇

—

115

C₂²×C₄₇

—

116

C₂²×C₄₇

—

117

C₂²×C₄₇

—

118

C₂²×C₄₇

#392

yes

characteristic

119

C₂²×C₄₇

#459

yes

—

120

C₂²×C₄₇

#467

yes

characteristic

121

C₂²×C₄₇

#470

yes

characteristic

122

C₂²×C₄₇

#473

yes

—

123

C₄×C₄₇

—

124

C₄×C₄₇

—

125

C₄×C₄₇

#447

yes

—

126

C₄×C₄₇

#451

yes

—

127

C₄×C₄₇

#452

yes

—

128

C₄×C₄₇

#493

yes

characteristic

129

C₄×C₄₇

#496

yes

characteristic

130

Dic₄₇

—

131

C₂×#494

—

132

C₂×#474

—

133

#1954

D₄₇

yes

characteristic

134

C₂×#332

—

135

#1277

—

136

C₂×C₄₇

—

137

C₂×C₄₇

#1669

yes

—

138

C₂×C₄₇

#1689

yes

—

139

C₂×C₄₇

#2001

yes

characteristic

140

C₂×C₄₇

#2011

yes

characteristic

141

C₂×C₄₇

#2020

yes

characteristic

142

C₂²×Q₁₆

—

143

C₂×C₄⋊Q₈

—

144

C₂×C₄×D₄

C₂×D₄₇

yes

characteristic

145

#494

—

146

#474

—

147

#474

—

148

C₂×#107

—

149

C₂×C₄⋊C₈

—

150

C₂×C₄⋊C₈

C₂×D₄₇

yes

characteristic

151

C₂×#102

—

152

C₂×C₂²⋊C₈

—

153

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

154

#332

—

155

C₄₇

#10274

yes

characteristic, complemented, Sylow

156

C₂²×Q₈

—

157

C₂²×D₄

D₁₈₈

yes

characteristic

158

C₂³×C₄

—

159

C₂×Q₁₆

—

160

C₂×Q₁₆

—

188

—

161

C₂×Q₁₆

—

188

—

162

C₂²×C₈

—

163

C₂²×C₈

—

164

C₂²×C₈

C₂²⋊D₄₇

yes

—

165

C₄⋊Q₈

—

166

C₄⋊Q₈

—

167

C₄⋊Q₈

—

168

C₄⋊Q₈

—

169

C₄×D₄

—

170

C₄×D₄

—

171

C₂×C₄⋊C₄

—

172

C₂×C₄⋊C₄

—

173

C₂×C₄⋊C₄

D₁₈₈

yes

characteristic

174

C₂×C₂²⋊C₄

—

175

C₂×C₄²

C₂²×D₄₇

yes

characteristic

176

#107

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

#102

—

181

C₂²⋊C₈

—

182

C₄×C₈

—

183

C₂⁴

—

184

C₂×Q₈

—

185

C₂×Q₈

—

188

—

186

C₂×Q₈

—

188

—

187

C₂×Q₈

—

188

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

Dic₁₈₈

yes

complemented

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

—

188

—

198

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

199

C₂²×C₄

#10625350

yes

characteristic

200

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

201

Q₁₆

—

188

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

188

—

208

C₂×C₈

—

188

—

209

C₂×C₈

#10625334

yes

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

188

—

214

C₄⋊C₄

—

188

—

215

C₂²⋊C₄

—

216

C₄²

D₄×D₄₇

yes

—

217

C₄²

D₄×D₄₇

yes

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

#13093998

yes

characteristic

224

Q₈

—

376

—

225

Q₈

—

376

—

226

Q₈

—

188

—

227

D₄

—

228

D₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

376

—

236

C₂×C₄

—

188

—

237

C₂×C₄

#13093992

yes

characteristic

238

C₂×C₄

#13093994

yes

—

239

C₂×C₄

#13093997

yes

—

240

C₂×C₄

#13094020

yes

characteristic

241

C₂×C₄

C₂×#10625334

yes

—

242

C₂×C₄

C₂×Dic₁₈₈

yes

characteristic

243

C₂×C₄

#13094046

yes

characteristic

244

C₂×C₄

#13094049

yes

—

245

C₂×C₄

#13094057

yes

—

246

C₈

—

247

C₈

—

248

C₈

—

188

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

#15689032

yes

characteristic

255

C₂²

#15689318

yes

—

256

C₂²

#15689364

yes

characteristic

257

C₂²

#15689381

yes

characteristic

258

C₂²

#15689398

yes

—

259

C₄

—

260

C₄

—

261

C₄

—

376

—

262

C₄

#15689256

yes

—

263

C₄

#15689281

yes

—

264

C₄

#15689287

yes

—

265

C₄

#15689499

yes

characteristic

266

C₄

#15689513

yes

characteristic

267

C₂

—

268

C₂

#20242753

yes

—

269

C₂

#20242877

yes

—

270

C₂

#20244398

yes

characteristic

271

C₂

#20244458

yes

characteristic

272

C₂

#20244509

yes

characteristic

	subgroup	G/H
center	C₂³	#13093998
commutator, cosocle	C₂×C₄²×C₄₇	C₂³
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1954	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂²×D₄×C₄₇	D₄
hypercenter	#1954	D₄₇
hypocenter	C₄₇	#10274
LCS	G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

subgroup

G/H

center

C₂³

#13093998

commutator, cosocle

C₂×C₄²×C₄₇

C₂³

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1954

C₂

socle

C₂³×C₄₇

#121

prime radical

C₂²×D₄×C₄₇

D₄

D₄₇

C₄₇

G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

N	H ≅ G/N	type
1. C₂×#15689503	C₂	semidirect
3. C₂×#15688870	C₂	semidirect
4. #20241223	C₂	semidirect
50. C₂×D₄×C₄₇	Q₁₆	semidirect
155. C₄₇	#10274	semidirect
191. C₂×D₄	Dic₁₈₈	semidirect

H ≅ G/N

type

1. C₂×#15689503

C₂

semidirect

3. C₂×#15688870

C₂

semidirect

4. #20241223

C₂

semidirect

50. C₂×D₄×C₄₇

Q₁₆

semidirect

155. C₄₇

#10274

semidirect

191. C₂×D₄

Dic₁₈₈

semidirect

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

subgroup	index
C₂×#15689503	2
C₂×#15689403	2
C₂×#15688870	2
#20241223	2
C₄₇×#1954	2
#10274	47

subgroup

index

C₄₇×#1954

Subgroups — #26118874

Conjugacy classes of subgroups

Complements

Maximal subgroups