Group #26113709 — subgroups

Subgroups — #26113709

Order 12032.

554 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 123 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	#20252473	C₂	1	1	yes	maximal, characteristic, complemented
2	#20243384	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242056	C₂	1	2	yes	maximal
4	#20241291	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2548	C₂	1	1	yes	maximal, characteristic
6	#15689254	—	2	4	no	—
7	#15689180	—	2	2	no	—
8	#15689176	C₂²	1	2	yes	—
9	#15689147	C₂²	1	2	yes	—
10	C₂×#13093943	—	2	1	no	—
11	#15688892	—	2	1	no	—
12	#15688867	—	2	4	no	—
13	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#124×C₄₇	—	2	1	no	—
15	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#394	C₄	1	4	yes	—
17	C₄₇×#390	—	2	1	no	—
18	C₄₇×#390	—	2	2	no	—
19	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×#10625329	—	2	2	no	—
21	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
22	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
23	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
24	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
25	#13093943	—	4	2	no	—
26	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
27	#13093935	—	2	4	no	—
28	C₄×C₄₇⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
30	C₂²×D₄×C₄₇	—	2	1	no	—
31	C₂²×D₄×C₄₇	—	2	1	no	—
32	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
33	#127×C₄₇	—	2	2	no	—
34	#127×C₄₇	—	2	2	no	—
35	#124×C₄₇	—	4	4	no	—
36	C₄×Q₈×C₄₇	—	2	2	no	—
37	C₄×Q₈×C₄₇	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
39	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
42	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
43	C₂×C₄²×C₄₇	—	2	1	no	—
44	C₂×C₄²×C₄₇	D₄	1	2	yes	—
45	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
46	#95×C₄₇	C₂×C₄	1	2	yes	—
47	C₂⁴×C₄₇	—	2	2	no	—
48	C₂×Q₈×C₄₇	—	2	2	no	—
49	C₂×Q₈×C₄₇	—	2	2	no	—
50	C₂×Q₈×C₄₇	—	2	1	no	—
51	C₂×Q₈×C₄₇	—	2	1	no	—
52	C₂×D₄×C₄₇	—	2	4	no	—
53	C₂×D₄×C₄₇	—	4	4	no	—
54	C₂×D₄×C₄₇	—	4	1	no	—
55	C₂×D₄×C₄₇	—	4	2	no	—
56	C₂×D₄×C₄₇	—	4	1	no	—
57	C₂×D₄×C₄₇	—	4	2	no	—
58	C₂×D₄×C₄₇	—	4	1	no	—
59	C₂×D₄×C₄₇	—	4	1	no	—
60	C₂×D₄×C₄₇	—	8	2	no	—
61	C₂²×C₄×C₄₇	—	2	2	no	—
62	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
67	C₄⋊C₄×C₄₇	—	2	4	no	—
68	C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₄⋊C₄×C₄₇	—	4	2	no	—
70	C₂²⋊C₄×C₄₇	—	4	8	no	—
71	C₂²⋊C₄×C₄₇	—	8	4	no	—
72	C₄²×C₄₇	—	2	2	no	—
73	C₄²×C₄₇	—	2	2	no	—
74	C₄²×C₄₇	—	4	2	no	—
75	C₄²×C₄₇	C₂×D₄	1	2	yes	—
76	C₄²×C₄₇	#41	1	2	yes	—
77	#10625329	—	4	2	no	—
78	#10625329	—	4	2	no	—
79	C₂×C₄₇⋊C₈	—	2	4	no	—
80	C₂×C₄₇⋊C₈	—	4	2	no	—
81	C₂³×C₄₇	—	4	4	no	—
82	C₂³×C₄₇	—	4	4	no	—
83	C₂³×C₄₇	—	4	2	no	—
84	C₂³×C₄₇	—	4	2	no	—
85	C₂³×C₄₇	—	4	2	no	—
86	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	Q₈×C₄₇	—	4	2	no	—
88	Q₈×C₄₇	—	4	2	no	—
89	D₄×C₄₇	—	8	4	no	—
90	D₄×C₄₇	—	8	2	no	—
91	D₄×C₄₇	—	8	2	no	—
92	D₄×C₄₇	—	8	2	no	—
93	D₄×C₄₇	—	8	2	no	—
94	C₂×C₄×C₄₇	—	2	2	no	—
95	C₂×C₄×C₄₇	—	2	2	no	—
96	C₂×C₄×C₄₇	—	2	2	no	—
97	C₂×C₄×C₄₇	—	2	2	no	—
98	C₂×C₄×C₄₇	—	2	2	no	—
99	C₂×C₄×C₄₇	—	4	1	no	—
100	C₂×C₄×C₄₇	—	4	2	no	—
101	C₂×C₄×C₄₇	—	4	2	no	—
102	C₂×C₄×C₄₇	—	4	2	no	—
103	C₂×C₄×C₄₇	—	4	2	no	—
104	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
105	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
106	C₂×C₄×C₄₇	#121	1	2	yes	—
107	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
108	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
109	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
110	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
111	C₄₇⋊C₈	—	4	4	no	—
112	C₄₇⋊C₈	—	8	2	no	—
113	#9406	—	47	1	no	maximal, Sylow
114	C₂²×C₄₇	—	2	1	no	—
115	C₂²×C₄₇	—	2	1	no	—
116	C₂²×C₄₇	—	8	4	no	—
117	C₂²×C₄₇	—	8	4	no	—
118	C₂²×C₄₇	—	8	2	no	—
119	C₂²×C₄₇	—	8	2	no	—
120	C₂²×C₄₇	—	8	2	no	—
121	C₂²×C₄₇	#386	1	1	yes	characteristic
122	C₂²×C₄₇	#417	1	1	yes	characteristic
123	C₂²×C₄₇	#418	1	1	yes	characteristic
124	C₄×C₄₇	—	2	1	no	—
125	C₄×C₄₇	—	2	2	no	—
126	C₄×C₄₇	—	4	2	no	—
127	C₄×C₄₇	—	4	2	no	—
128	C₄×C₄₇	—	8	2	no	—
129	C₄×C₄₇	#454	1	2	yes	—
130	C₄×C₄₇	#468	1	2	yes	—
131	C₄×C₄₇	#469	1	2	yes	—
132	#2983	—	47	1	no	—
133	#2548	D₄₇	1	1	yes	characteristic
134	#1801	—	47	1	no	—
135	#1545	—	47	2	no	—
136	#1303	—	47	2	no	—
137	C₂×C₄₇	—	2	1	no	—
138	C₂×C₄₇	—	2	1	no	—
139	C₂×C₄₇	—	16	2	no	—
140	C₂×C₄₇	#1888	1	1	yes	characteristic
141	C₂×C₄₇	#1895	1	1	yes	characteristic
142	C₂×C₄₇	#1914	1	1	yes	characteristic
143	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
144	C₂×#124	—	2	1	no	—
145	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
146	#446	—	94	4	no	—
147	#432	—	94	2	no	—
148	#431	—	47	2	no	—
149	#423	—	47	2	no	—
150	C₂×#101	—	94	1	no	—
151	#394	Dic₄₇	1	4	yes	—
152	#390	—	2	1	no	—
153	#390	—	2	2	no	—
154	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
155	#343	—	94	1	no	—
156	#331	—	94	4	no	—
157	C₄₇	#9406	1	1	yes	characteristic, complemented, Sylow
158	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
159	C₂²×D₄	—	2	1	no	—
160	C₂²×D₄	—	2	1	no	—
161	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
162	C₂×M₁₆	—	94	2	no	—
163	#127	—	2	2	no	—
164	#127	—	2	2	no	—
165	#124	—	4	4	no	—
166	C₄×Q₈	—	2	2	no	—
167	C₄×Q₈	—	2	2	no	—
168	C₂×C₄⋊C₄	—	2	1	no	—
169	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
170	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
171	C₂×C₂²⋊C₄	—	2	4	no	—
172	C₂×C₂²⋊C₄	—	2	4	no	—
173	C₂×C₄²	—	2	1	no	—
174	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
175	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
176	C₄⋊C₈	—	47	4	no	—
177	C₄⋊C₈	—	94	4	no	—
178	C₄⋊C₈	—	94	2	no	—
179	C₄⋊C₈	—	94	2	no	—
180	#101	—	188	2	no	—
181	C₂²⋊C₈	—	94	2	no	—
182	#97	—	94	4	no	—
183	C₄×C₈	—	94	2	no	—
184	#95	C₂×Dic₄₇	1	2	yes	—
185	C₂⁴	—	2	2	no	—
186	C₂×Q₈	—	2	2	no	—
187	C₂×Q₈	—	2	1	no	—
188	C₂×Q₈	—	2	2	no	—
189	C₂×Q₈	—	2	1	no	—
190	C₂×D₄	—	2	4	no	—
191	C₂×D₄	—	4	4	no	—
192	C₂×D₄	—	4	1	no	—
193	C₂×D₄	—	4	2	no	—
194	C₂×D₄	—	4	1	no	—
195	C₂×D₄	—	4	1	no	—
196	C₂×D₄	—	4	2	no	—
197	C₂×D₄	—	4	1	no	—
198	C₂×D₄	—	8	2	no	—
199	C₂²×C₄	—	2	2	no	—
200	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
201	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
202	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
203	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
204	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
205	M₁₆	—	188	2	no	—
206	M₁₆	—	188	2	no	—
207	C₂×C₈	—	94	4	no	—
208	C₂×C₈	—	188	2	no	—
209	C₄⋊C₄	—	2	4	no	—
210	C₄⋊C₄	—	2	2	no	—
211	C₄⋊C₄	—	4	2	no	—
212	C₂²⋊C₄	—	4	8	no	—
213	C₂²⋊C₄	—	8	4	no	—
214	C₄²	—	2	2	no	—
215	C₄²	—	2	2	no	—
216	C₄²	—	4	2	no	—
217	C₄²	D₄×D₄₇	1	2	yes	—
218	C₄²	#10625352	1	2	yes	—
219	C₂³	—	4	4	no	—
220	C₂³	—	4	4	no	—
221	C₂³	—	4	2	no	—
222	C₂³	—	4	2	no	—
223	C₂³	—	4	2	no	—
224	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
225	Q₈	—	4	2	no	—
226	Q₈	—	4	2	no	—
227	D₄	—	8	4	no	—
228	D₄	—	8	2	no	—
229	D₄	—	8	2	no	—
230	D₄	—	8	2	no	—
231	D₄	—	8	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	4	1	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂×C₄	—	4	2	no	—
241	C₂×C₄	—	4	2	no	—
242	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
243	C₂×C₄	#13093992	1	1	yes	characteristic
244	C₂×C₄	#13093996	1	2	yes	—
245	C₂×C₄	#13094005	1	1	yes	characteristic
246	C₂×C₄	#13094049	1	1	yes	characteristic
247	C₂×C₄	#13094050	1	2	yes	—
248	C₂×C₄	#13094054	1	1	yes	characteristic
249	C₈	—	376	2	no	—
250	C₈	—	188	4	no	—
251	C₂²	—	2	1	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	8	4	no	—
254	C₂²	—	8	4	no	—
255	C₂²	—	8	2	no	—
256	C₂²	—	8	2	no	—
257	C₂²	—	8	2	no	—
258	C₂²	#15689003	1	1	yes	characteristic
259	C₂²	#15689124	1	1	yes	characteristic
260	C₂²	#15689128	1	1	yes	characteristic
261	C₄	—	2	1	no	—
262	C₄	—	2	2	no	—
263	C₄	—	4	2	no	—
264	C₄	—	4	2	no	—
265	C₄	—	8	2	no	—
266	C₄	#15689295	1	2	yes	—
267	C₄	#15689367	1	2	yes	—
268	C₄	#15689374	1	2	yes	—
269	C₂	—	2	1	no	—
270	C₂	—	2	1	no	—
271	C₂	—	16	2	no	—
272	C₂	#20243792	1	1	yes	characteristic
273	C₂	#20243827	1	1	yes	characteristic
274	C₂	#20243936	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20252473

C₂

yes

maximal, characteristic, complemented

#20243384

C₂

yes

maximal, characteristic, complemented

#20242056

C₂

yes

maximal

#20241291

C₂

yes

maximal, complemented

C₄₇×#2548

C₂

yes

maximal, characteristic

#15689254

—

#15689180

—

#15689176

C₂²

yes

—

#15689147

C₂²

yes

—

C₂×#13093943

—

#15688892

—

#15688867

—

C₂×#127×C₄₇

C₂²

yes

characteristic

C₂×#124×C₄₇

—

C₂×C₄×Q₈×C₄₇

C₂²

yes

characteristic

C₄₇×#394

C₄

yes

—

C₄₇×#390

—

C₄₇×#390

—

C₄×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×#10625329

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

#13093943

—

C₂²⋊(C₄₇⋊C₈)

—

#13093935

—

C₄×C₄₇⋊C₈

—

C₂²×Q₈×C₄₇

D₄

yes

characteristic

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

C₂×C₄

yes

—

#127×C₄₇

—

#127×C₄₇

—

#124×C₄₇

—

C₄×Q₈×C₄₇

—

C₄×Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#95×C₄₇

C₂×C₄

yes

—

C₂⁴×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

100

C₂×C₄×C₄₇

—

101

C₂×C₄×C₄₇

—

102

C₂×C₄×C₄₇

—

103

C₂×C₄×C₄₇

—

104

C₂×C₄×C₄₇

C₄×D₄

yes

—

105

C₂×C₄×C₄₇

#120

yes

characteristic

106

C₂×C₄×C₄₇

#121

yes

—

107

C₂×C₄×C₄₇

#123

yes

characteristic

108

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

characteristic

109

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

110

C₂×C₄×C₄₇

#137

yes

characteristic

111

C₄₇⋊C₈

—

112

C₄₇⋊C₈

—

113

#9406

—

maximal, Sylow

114

C₂²×C₄₇

—

115

C₂²×C₄₇

—

116

C₂²×C₄₇

—

117

C₂²×C₄₇

—

118

C₂²×C₄₇

—

119

C₂²×C₄₇

—

120

C₂²×C₄₇

—

121

C₂²×C₄₇

#386

yes

characteristic

122

C₂²×C₄₇

#417

yes

characteristic

123

C₂²×C₄₇

#418

yes

characteristic

124

C₄×C₄₇

—

125

C₄×C₄₇

—

126

C₄×C₄₇

—

127

C₄×C₄₇

—

128

C₄×C₄₇

—

129

C₄×C₄₇

#454

yes

—

130

C₄×C₄₇

#468

yes

—

131

C₄×C₄₇

#469

yes

—

132

#2983

—

133

#2548

D₄₇

yes

characteristic

134

#1801

—

135

#1545

—

136

#1303

—

137

C₂×C₄₇

—

138

C₂×C₄₇

—

139

C₂×C₄₇

—

140

C₂×C₄₇

#1888

yes

characteristic

141

C₂×C₄₇

#1895

yes

characteristic

142

C₂×C₄₇

#1914

yes

characteristic

143

C₂×#127

C₂×D₄₇

yes

characteristic

144

C₂×#124

—

145

C₂×C₄×Q₈

C₂×D₄₇

yes

characteristic

146

#446

—

147

#432

—

148

#431

—

149

#423

—

150

C₂×#101

—

151

#394

Dic₄₇

yes

—

152

#390

—

153

#390

—

154

C₄×C₄⋊C₄

C₂×D₄₇

yes

characteristic

155

#343

—

156

#331

—

157

C₄₇

#9406

yes

characteristic, complemented, Sylow

158

C₂²×Q₈

C₂²⋊D₄₇

yes

characteristic

159

C₂²×D₄

—

160

C₂²×D₄

—

161

C₂²×D₄

C₂×Dic₄₇

yes

—

162

C₂×M₁₆

—

163

#127

—

164

#127

—

165

#124

—

166

C₄×Q₈

—

167

C₄×Q₈

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

C₂×Dic₄₇

yes

—

170

C₂×C₄⋊C₄

C₂²⋊D₄₇

yes

characteristic

171

C₂×C₂²⋊C₄

—

172

C₂×C₂²⋊C₄

—

173

C₂×C₄²

—

174

C₂×C₄²

C₂²⋊D₄₇

yes

—

175

C₂×C₄²

C₂²×D₄₇

yes

characteristic

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

#101

—

188

—

181

C₂²⋊C₈

—

182

#97

—

183

C₄×C₈

—

184

#95

C₂×Dic₄₇

yes

—

185

C₂⁴

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂×D₄

—

198

C₂×D₄

—

199

C₂²×C₄

—

200

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

201

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

202

C₂²×C₄

C₂²×Dic₄₇

yes

characteristic

203

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

204

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

205

M₁₆

—

188

—

206

M₁₆

—

188

—

207

C₂×C₈

—

208

C₂×C₈

—

188

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₂²⋊C₄

—

213

C₂²⋊C₄

—

214

C₄²

—

215

C₄²

—

216

C₄²

—

217

C₄²

D₄×D₄₇

yes

—

218

C₄²

#10625352

yes

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

C₂×C₂²⋊Dic₄₇

yes

characteristic

225

Q₈

—

226

Q₈

—

227

D₄

—

228

D₄

—

229

D₄

—

230

D₄

—

231

D₄

—

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

—

241

C₂×C₄

—

242

C₂×C₄

D₄×Dic₄₇

yes

—

243

C₂×C₄

#13093992

yes

characteristic

244

C₂×C₄

#13093996

yes

—

245

C₂×C₄

#13094005

yes

characteristic

246

C₂×C₄

#13094049

yes

characteristic

247

C₂×C₄

#13094050

yes

—

248

C₂×C₄

#13094054

yes

characteristic

249

C₈

—

376

—

250

C₈

—

188

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

#15689003

yes

characteristic

259

C₂²

#15689124

yes

characteristic

260

C₂²

#15689128

yes

characteristic

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

—

266

C₄

#15689295

yes

—

267

C₄

#15689367

yes

—

268

C₄

#15689374

yes

—

269

C₂

—

270

C₂

—

271

C₂

—

272

C₂

#20243792

yes

characteristic

273

C₂

#20243827

yes

characteristic

274

C₂

#20243936

yes

characteristic

	subgroup	G/H
center	C₂²	#15689003
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#2548	C₂
socle	C₂²×C₄₇	#386
prime radical	C₂×#127×C₄₇	C₂²
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#2548	D₄₇
hypocenter	C₄₇	#9406
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2548

subgroup

G/H

center

C₂²

#15689003

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#2548

C₂

socle

C₂²×C₄₇

#386

prime radical

C₂×#127×C₄₇

C₂²

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2548

N	H ≅ G/N	type
1. #20252473	C₂	semidirect
2. #20243384	C₂	semidirect
4. #20241291	C₂	semidirect
157. C₄₇	#9406	semidirect

H ≅ G/N

type

1. #20252473

C₂

semidirect

2. #20243384

C₂

semidirect

4. #20241291

C₂

semidirect

157. C₄₇

#9406

semidirect

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

subgroup	index
#20252473	2
#20243384	2
#20242056	2
#20241291	2
C₄₇×#2548	2
#9406	47

subgroup

index

C₄₇×#2548

Subgroups — #26113709

Conjugacy classes of subgroups

Complements

Maximal subgroups