Group #26133661 — subgroups

Subgroups — #26133661

Order 12032.

508 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 143 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	C₂³×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15688930	C₂	1	2	yes	maximal, complemented
3	#20243426	C₂	1	1	yes	maximal, characteristic, complemented
4	#20241483	C₂	1	2	yes	maximal, complemented
5	C₄₇×#3050	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₇⋊C₁₆	—	2	4	no	—
7	C₂²×C₄₇⋊C₁₆	—	2	2	no	—
8	C₂²×C₄₇⋊C₁₆	C₂²	1	2	yes	—
9	C₂×#13093960	C₂²	1	2	yes	—
10	#15689087	—	2	1	no	—
11	#15688930	—	2	4	no	—
12	#15688888	—	2	1	no	—
13	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₄₇×#525	—	2	1	no	—
16	C₄₇×#467	C₄	1	2	yes	—
17	C₄₇×#466	C₄	1	2	yes	—
18	C₄₇×#465	—	2	2	no	—
19	C₄₇×#427	C₂²	1	1	yes	characteristic
20	C₄₇×#416	—	2	1	no	—
21	C₂×#10625329	—	2	2	no	—
22	C₂×C₄₇⋊C₁₆	—	2	8	no	—
23	C₂×C₄₇⋊C₁₆	—	2	2	no	—
24	C₂×C₄₇⋊C₁₆	—	2	2	no	—
25	C₂×C₄₇⋊C₁₆	D₄	1	4	yes	complemented
26	#13093960	—	2	2	no	—
27	#13093960	—	2	2	no	—
28	C₂²⋊(C₄₇⋊C₈)	—	4	2	no	—
29	C₂×#41×C₄₇	—	2	1	no	—
30	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
31	#135×C₄₇	—	2	2	no	—
32	#135×C₄₇	—	2	2	no	—
33	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂×SD₁₆×C₄₇	—	2	1	no	—
35	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₈×C₄₇	—	2	2	no	—
37	C₂²×C₈×C₄₇	—	2	2	no	—
38	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₄₇	D₄	1	2	yes	—
41	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
42	#123×C₄₇	—	4	1	no	—
43	C₂²⋊Q₈×C₄₇	—	2	2	no	—
44	#121×C₄₇	—	2	2	no	—
45	#120×C₄₇	—	4	1	no	—
46	C₄×D₄×C₄₇	—	4	2	no	—
47	#117×C₄₇	—	2	1	no	—
48	#107×C₄₇	C₂×C₄	1	2	yes	—
49	#106×C₄₇	—	2	1	no	—
50	#103×C₄₇	—	2	2	no	—
51	#102×C₄₇	—	2	2	no	—
52	C₂⁴×C₄₇	SD₁₆	1	1	yes	characteristic
53	#41×C₄₇	—	4	2	no	—
54	#41×C₄₇	—	4	2	no	—
55	C₂×Q₈×C₄₇	—	2	1	no	—
56	C₂×D₄×C₄₇	—	2	1	no	—
57	C₂×D₄×C₄₇	—	4	2	no	—
58	C₂×D₄×C₄₇	—	4	1	no	—
59	C₂²×C₄×C₄₇	—	2	2	no	—
60	C₂²×C₄×C₄₇	—	2	2	no	—
61	C₂²×C₄×C₄₇	—	4	1	no	—
62	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₄₇	D₈	1	2	yes	—
64	C₂²×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
66	Q₁₆×C₄₇	—	2	2	no	—
67	SD₁₆×C₄₇	—	4	1	no	—
68	SD₁₆×C₄₇	—	4	1	no	—
69	D₈×C₄₇	—	2	2	no	—
70	C₂×C₈×C₄₇	—	2	2	no	—
71	C₂×C₈×C₄₇	—	2	4	no	—
72	C₂×C₈×C₄₇	—	2	2	no	—
73	C₂×C₈×C₄₇	—	2	2	no	—
74	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
75	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
77	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₄₇	#41	1	2	yes	—
79	C₄⋊C₄×C₄₇	—	2	2	no	—
80	C₄⋊C₄×C₄₇	—	4	2	no	—
81	C₂²⋊C₄×C₄₇	—	4	2	no	—
82	C₂²⋊C₄×C₄₇	—	4	1	no	—
83	C₂²⋊C₄×C₄₇	—	4	2	no	—
84	C₄²×C₄₇	—	4	1	no	—
85	#10625329	—	4	2	no	—
86	#10625329	—	4	2	no	—
87	C₂×C₄₇⋊C₈	—	4	2	no	—
88	C₄₇⋊C₁₆	—	2	4	no	—
89	C₂³×C₄₇	—	2	4	no	—
90	C₂³×C₄₇	—	2	2	no	—
91	C₂³×C₄₇	—	4	1	no	—
92	C₂³×C₄₇	#102	1	2	yes	—
93	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
94	Q₈×C₄₇	—	4	1	no	—
95	Q₈×C₄₇	—	4	1	no	—
96	D₄×C₄₇	—	4	1	no	—
97	D₄×C₄₇	—	4	1	no	—
98	D₄×C₄₇	—	8	4	no	—
99	D₄×C₄₇	—	8	2	no	—
100	C₂×C₄×C₄₇	—	2	2	no	—
101	C₂×C₄×C₄₇	—	2	2	no	—
102	C₂×C₄×C₄₇	—	2	2	no	—
103	C₂×C₄×C₄₇	—	2	4	no	—
104	C₂×C₄×C₄₇	—	4	2	no	—
105	C₂×C₄×C₄₇	—	4	1	no	—
106	C₂×C₄×C₄₇	—	8	2	no	—
107	C₂×C₄×C₄₇	#102	1	2	yes	—
108	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₄×C₄₇	#121	1	2	yes	—
110	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
111	C₂×C₄×C₄₇	#135	1	2	yes	—
112	C₈×C₄₇	—	2	2	no	—
113	C₈×C₄₇	C₄×D₄	1	2	yes	—
114	C₈×C₄₇	#120	1	1	yes	characteristic
115	C₈×C₄₇	#123	1	1	yes	characteristic
116	C₄₇⋊C₈	—	8	2	no	—
117	#13063	—	47	1	no	maximal, Sylow
118	C₂²×C₄₇	—	2	8	no	—
119	C₂²×C₄₇	—	2	2	no	—
120	C₂²×C₄₇	—	2	2	no	—
121	C₂²×C₄₇	—	2	2	no	—
122	C₂²×C₄₇	—	8	2	no	—
123	C₂²×C₄₇	—	8	1	no	—
124	C₂²×C₄₇	#359	1	4	yes	complemented
125	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
126	C₂²×C₄₇	#465	1	2	yes	—
127	C₄×C₄₇	—	2	2	no	—
128	C₄×C₄₇	—	8	2	no	—
129	C₄×C₄₇	—	8	1	no	—
130	C₄×C₄₇	#386	1	1	yes	characteristic
131	C₄×C₄₇	#416	1	1	yes	characteristic
132	C₄×C₄₇	#466	1	2	yes	—
133	C₂³×C₁₆	—	47	1	no	—
134	#3050	D₄₇	1	1	yes	characteristic
135	C₂×#359	—	47	2	no	—
136	#1810	—	47	1	no	—
137	#1382	—	47	2	no	—
138	C₂×C₄₇	—	2	4	no	—
139	C₂×C₄₇	—	2	2	no	—
140	C₂×C₄₇	—	16	1	no	—
141	C₂×C₄₇	#1893	1	1	yes	characteristic
142	C₂×C₄₇	C₂×#359	1	2	yes	—
143	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
144	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
145	#525	—	2	1	no	—
146	C₂²×C₁₆	—	47	2	no	—
147	C₂²×C₁₆	—	94	4	no	—
148	C₂²×C₁₆	—	94	2	no	—
149	#467	Dic₄₇	1	2	yes	—
150	#466	Dic₄₇	1	2	yes	—
151	#465	—	2	2	no	—
152	C₂×#108	—	47	2	no	—
153	#427	C₂×D₄₇	1	1	yes	characteristic
154	#416	—	2	1	no	—
155	#407	—	94	1	no	—
156	#359	—	94	4	no	—
157	#341	—	94	1	no	—
158	C₄₇	#13063	1	1	yes	characteristic, complemented, Sylow
159	C₂×#41	—	2	1	no	—
160	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
161	#135	—	2	2	no	—
162	#135	—	2	2	no	—
163	C₂×Q₁₆	C₂×Dic₄₇	1	1	yes	characteristic
164	C₂×SD₁₆	—	2	1	no	—
165	C₂×D₈	C₂×Dic₄₇	1	1	yes	characteristic
166	C₂×M₁₆	—	94	2	no	—
167	C₂²×C₈	—	2	2	no	—
168	C₂²×C₈	—	2	2	no	—
169	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
170	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
171	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
172	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
173	#123	—	4	1	no	—
174	C₂²⋊Q₈	—	2	2	no	—
175	#121	—	2	2	no	—
176	#120	—	4	1	no	—
177	C₄×D₄	—	4	2	no	—
178	#117	—	2	1	no	—
179	C₂×C₁₆	—	47	4	no	—
180	C₂×C₁₆	—	94	8	no	—
181	C₂×C₁₆	—	94	2	no	—
182	C₂×C₁₆	—	94	2	no	—
183	#108	—	94	2	no	—
184	#108	—	94	2	no	—
185	#107	C₂×Dic₄₇	1	2	yes	—
186	#106	—	2	1	no	—
187	#103	—	2	2	no	—
188	#102	—	2	2	no	—
189	C₂²⋊C₈	—	188	2	no	—
190	C₂⁴	#10625335	1	1	yes	characteristic
191	#41	—	4	2	no	—
192	#41	—	4	2	no	—
193	C₂×Q₈	—	2	1	no	—
194	C₂×D₄	—	2	1	no	—
195	C₂×D₄	—	4	2	no	—
196	C₂×D₄	—	4	1	no	—
197	C₂²×C₄	—	2	2	no	—
198	C₂²×C₄	—	2	2	no	—
199	C₂²×C₄	—	4	1	no	—
200	C₂²×C₄	#10625334	1	2	yes	—
201	C₂²×C₄	#10625335	1	1	yes	characteristic
202	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
203	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
204	Q₁₆	—	2	2	no	—
205	SD₁₆	—	4	1	no	—
206	SD₁₆	—	4	1	no	—
207	D₈	—	2	2	no	—
208	M₁₆	—	188	2	no	—
209	M₁₆	—	188	2	no	—
210	C₂×C₈	—	2	2	no	—
211	C₂×C₈	—	2	4	no	—
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	—	2	2	no	—
214	C₂×C₈	—	188	2	no	—
215	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
216	C₂×C₈	D₄×D₄₇	1	2	yes	—
217	C₂×C₈	#10625352	1	2	yes	—
218	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
219	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
220	C₄⋊C₄	—	2	2	no	—
221	C₄⋊C₄	—	4	2	no	—
222	C₂²⋊C₄	—	4	2	no	—
223	C₂²⋊C₄	—	4	1	no	—
224	C₂²⋊C₄	—	4	2	no	—
225	C₄²	—	4	1	no	—
226	C₁₆	—	94	4	no	—
227	C₂³	—	2	2	no	—
228	C₂³	—	2	4	no	—
229	C₂³	—	4	1	no	—
230	C₂³	#13093945	1	2	yes	—
231	C₂³	C₂×#10625335	1	1	yes	characteristic
232	Q₈	—	4	1	no	—
233	Q₈	—	4	1	no	—
234	D₄	—	4	1	no	—
235	D₄	—	4	1	no	—
236	D₄	—	8	2	no	—
237	D₄	—	8	4	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	4	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	4	2	no	—
243	C₂×C₄	—	4	1	no	—
244	C₂×C₄	—	8	2	no	—
245	C₂×C₄	#13093945	1	2	yes	—
246	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
247	C₂×C₄	#13093996	1	2	yes	—
248	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
249	C₂×C₄	#13094044	1	2	yes	—
250	C₈	—	2	2	no	—
251	C₈	—	376	2	no	—
252	C₈	D₄×Dic₄₇	1	2	yes	—
253	C₈	#13093992	1	1	yes	characteristic
254	C₈	#13094005	1	1	yes	characteristic
255	C₂²	—	2	8	no	—
256	C₂²	—	2	2	no	—
257	C₂²	—	2	2	no	—
258	C₂²	—	2	2	no	—
259	C₂²	—	8	1	no	—
260	C₂²	—	8	2	no	—
261	C₂²	#15688930	1	4	yes	complemented
262	C₂²	C₂×#13093945	1	1	yes	characteristic
263	C₂²	#15689350	1	2	yes	—
264	C₄	—	2	2	no	—
265	C₄	—	8	1	no	—
266	C₄	—	8	2	no	—
267	C₄	#15689003	1	1	yes	characteristic
268	C₄	#15689119	1	1	yes	characteristic
269	C₄	#15689357	1	2	yes	—
270	C₂	—	2	2	no	—
271	C₂	—	2	4	no	—
272	C₂	—	16	1	no	—
273	C₂	#20243817	1	1	yes	characteristic
274	C₂	C₂×#15688930	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×C₄₇⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×#15688930

C₂

yes

maximal, complemented

#20243426

C₂

yes

maximal, characteristic, complemented

#20241483

C₂

yes

maximal, complemented

C₄₇×#3050

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₁₆

—

C₂²×C₄₇⋊C₁₆

—

C₂²×C₄₇⋊C₁₆

C₂²

yes

—

C₂×#13093960

C₂²

yes

—

#15689087

—

#15688930

—

#15688888

—

C₂×#135×C₄₇

C₂²

yes

characteristic

C₂³×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#525

—

C₄₇×#467

C₄

yes

—

C₄₇×#466

C₄

yes

—

C₄₇×#465

—

C₄₇×#427

C₂²

yes

characteristic

C₄₇×#416

—

C₂×#10625329

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

D₄

yes

complemented

#13093960

—

#13093960

—

C₂²⋊(C₄₇⋊C₈)

—

C₂×#41×C₄₇

—

C₂³×C₄×C₄₇

D₄

yes

characteristic

#135×C₄₇

—

#135×C₄₇

—

C₂×Q₁₆×C₄₇

C₂×C₄

yes

characteristic

C₂×SD₁₆×C₄₇

—

C₂×D₈×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

C₂×C₄

yes

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

#123×C₄₇

—

C₂²⋊Q₈×C₄₇

—

#121×C₄₇

—

#120×C₄₇

—

C₄×D₄×C₄₇

—

#117×C₄₇

—

#107×C₄₇

C₂×C₄

yes

—

#106×C₄₇

—

#103×C₄₇

—

#102×C₄₇

—

C₂⁴×C₄₇

SD₁₆

yes

characteristic

#41×C₄₇

—

#41×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

D₈

yes

—

C₂²×C₄×C₄₇

SD₁₆

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

Q₁₆×C₄₇

—

SD₁₆×C₄₇

—

SD₁₆×C₄₇

—

D₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

#41

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#102

yes

—

C₂³×C₄₇

C₂×SD₁₆

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

100

C₂×C₄×C₄₇

—

101

C₂×C₄×C₄₇

—

102

C₂×C₄×C₄₇

—

103

C₂×C₄×C₄₇

—

104

C₂×C₄×C₄₇

—

105

C₂×C₄×C₄₇

—

106

C₂×C₄×C₄₇

—

107

C₂×C₄×C₄₇

#102

yes

—

108

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

109

C₂×C₄×C₄₇

#121

yes

—

110

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

111

C₂×C₄×C₄₇

#135

yes

—

112

C₈×C₄₇

—

113

C₈×C₄₇

C₄×D₄

yes

—

114

C₈×C₄₇

#120

yes

characteristic

115

C₈×C₄₇

#123

yes

characteristic

116

C₄₇⋊C₈

—

117

#13063

—

maximal, Sylow

118

C₂²×C₄₇

—

119

C₂²×C₄₇

—

120

C₂²×C₄₇

—

121

C₂²×C₄₇

—

122

C₂²×C₄₇

—

123

C₂²×C₄₇

—

124

C₂²×C₄₇

#359

yes

complemented

125

C₂²×C₄₇

C₂×#102

yes

characteristic

126

C₂²×C₄₇

#465

yes

—

127

C₄×C₄₇

—

128

C₄×C₄₇

—

129

C₄×C₄₇

—

130

C₄×C₄₇

#386

yes

characteristic

131

C₄×C₄₇

#416

yes

characteristic

132

C₄×C₄₇

#466

yes

—

133

C₂³×C₁₆

—

134

#3050

D₄₇

yes

characteristic

135

C₂×#359

—

136

#1810

—

137

#1382

—

138

C₂×C₄₇

—

139

C₂×C₄₇

—

140

C₂×C₄₇

—

141

C₂×C₄₇

#1893

yes

characteristic

142

C₂×C₄₇

C₂×#359

yes

—

143

C₂×#135

C₂×D₄₇

yes

characteristic

144

C₂³×C₈

C₂×D₄₇

yes

characteristic

145

#525

—

146

C₂²×C₁₆

—

147

C₂²×C₁₆

—

148

C₂²×C₁₆

—

149

#467

Dic₄₇

yes

—

150

#466

Dic₄₇

yes

—

151

#465

—

152

C₂×#108

—

153

#427

C₂×D₄₇

yes

characteristic

154

#416

—

155

#407

—

156

#359

—

157

#341

—

158

C₄₇

#13063

yes

characteristic, complemented, Sylow

159

C₂×#41

—

160

C₂³×C₄

C₂²⋊D₄₇

yes

characteristic

161

#135

—

162

#135

—

163

C₂×Q₁₆

C₂×Dic₄₇

yes

characteristic

164

C₂×SD₁₆

—

165

C₂×D₈

C₂×Dic₄₇

yes

characteristic

166

C₂×M₁₆

—

167

C₂²×C₈

—

168

C₂²×C₈

—

169

C₂²×C₈

C₂×Dic₄₇

yes

—

170

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

171

C₂²×C₈

C₂²⋊D₄₇

yes

—

172

C₂²×C₈

C₂²×D₄₇

yes

characteristic

173

#123

—

174

C₂²⋊Q₈

—

175

#121

—

176

#120

—

177

C₄×D₄

—

178

#117

—

179

C₂×C₁₆

—

180

C₂×C₁₆

—

181

C₂×C₁₆

—

182

C₂×C₁₆

—

183

#108

—

184

#108

—

185

#107

C₂×Dic₄₇

yes

—

186

#106

—

187

#103

—

188

#102

—

189

C₂²⋊C₈

—

188

—

190

C₂⁴

#10625335

yes

characteristic

191

#41

—

192

#41

—

193

C₂×Q₈

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

—

200

C₂²×C₄

#10625334

yes

—

201

C₂²×C₄

#10625335

yes

characteristic

202

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

203

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

204

Q₁₆

—

205

SD₁₆

—

206

SD₁₆

—

207

D₈

—

208

M₁₆

—

188

—

209

M₁₆

—

188

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

188

—

215

C₂×C₈

C₂²⋊Dic₄₇

yes

—

216

C₂×C₈

D₄×D₄₇

yes

—

217

C₂×C₈

#10625352

yes

—

218

C₂×C₈

C₂²×Dic₄₇

yes

characteristic

219

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₂²⋊C₄

—

223

C₂²⋊C₄

—

224

C₂²⋊C₄

—

225

C₄²

—

226

C₁₆

—

227

C₂³

—

228

C₂³

—

229

C₂³

—

230

C₂³

#13093945

yes

—

231

C₂³

C₂×#10625335

yes

characteristic

232

Q₈

—

233

Q₈

—

234

D₄

—

235

D₄

—

236

D₄

—

237

D₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

#13093945

yes

—

246

C₂×C₄

C₂×C₂²⋊Dic₄₇

yes

characteristic

247

C₂×C₄

#13093996

yes

—

248

C₂×C₄

C₂×#10625334

yes

characteristic

249

C₂×C₄

#13094044

yes

—

250

C₈

—

251

C₈

—

376

—

252

C₈

D₄×Dic₄₇

yes

—

253

C₈

#13093992

yes

characteristic

254

C₈

#13094005

yes

characteristic

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

—

259

C₂²

—

260

C₂²

—

261

C₂²

#15688930

yes

complemented

262

C₂²

C₂×#13093945

yes

characteristic

263

C₂²

#15689350

yes

—

264

C₄

—

265

C₄

—

266

C₄

—

267

C₄

#15689003

yes

characteristic

268

C₄

#15689119

yes

characteristic

269

C₄

#15689357

yes

—

270

C₂

—

271

C₂

—

272

C₂

—

273

C₂

#20243817

yes

characteristic

274

C₂

C₂×#15688930

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×#10625334
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting, prime radical	C₄₇×#3050	C₂
socle	C₂²×C₄₇	C₂×#102
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#3050	D₄₇
hypocenter	C₄₇	#13063
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #3050

subgroup

G/H

center

C₂×C₄

C₂×#10625334

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting, prime radical

C₄₇×#3050

C₂

socle

C₂²×C₄₇

C₂×#102

cosocle

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #3050

N	H ≅ G/N	type
1. C₂³×C₄₇⋊C₁₆	C₂	semidirect
2. C₂×#15688930	C₂	semidirect
3. #20243426	C₂	semidirect
4. #20241483	C₂	semidirect
25. C₂×C₄₇⋊C₁₆	D₄	semidirect
124. C₂²×C₄₇	#359	semidirect
158. C₄₇	#13063	semidirect
261. C₂²	#15688930	semidirect

H ≅ G/N

type

1. C₂³×C₄₇⋊C₁₆

C₂

semidirect

2. C₂×#15688930

C₂

semidirect

3. #20243426

C₂

semidirect

4. #20241483

C₂

semidirect

25. C₂×C₄₇⋊C₁₆

D₄

semidirect

124. C₂²×C₄₇

#359

semidirect

158. C₄₇

#13063

semidirect

261. C₂²

#15688930

semidirect

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

subgroup	index
C₂³×C₄₇⋊C₁₆	2
C₂×#15688930	2
#20243426	2
#20241483	2
C₄₇×#3050	2
#13063	47

subgroup

index

C₂³×C₄₇⋊C₁₆

C₄₇×#3050

Subgroups — #26133661

Conjugacy classes of subgroups

Complements

Maximal subgroups