Group #26107237 — subgroups

Subgroups — #26107237

Order 12032.

516 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 173 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	C₄⋊Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	#20243243	C₂	1	2	yes	maximal
3	C₂×#15688872	C₂	1	1	yes	maximal, characteristic
4	#20241272	C₂	1	2	yes	maximal
5	C₂×C₄₇×#333	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×Dic₄₇	C₄	1	2	yes	—
7	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
8	C₂×#13093934	—	2	2	no	—
9	#15689030	C₄	1	2	yes	—
10	#15689022	—	2	2	no	—
11	#15688993	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×Dic₄₇	—	2	2	no	—
13	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
14	#15688877	—	2	2	no	—
15	#15688872	C₄	1	4	yes	complemented
16	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
18	C₄₇×#333	C₄	1	4	yes	complemented
19	C₂²×C₄₇⋊C₈	—	2	2	no	—
20	Q₈×Dic₄₇	—	4	4	no	—
21	C₂×C₄⋊Dic₄₇	—	2	2	no	—
22	C₂×C₄⋊Dic₄₇	—	2	2	no	—
23	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
24	C₂×C₄×Dic₄₇	—	2	2	no	—
25	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
28	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
29	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
30	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
31	#13093934	—	4	4	no	—
32	C₄₇⋊#95	—	2	4	no	—
33	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₄₇	—	2	2	no	—
35	C₄⋊Q₈×C₄₇	—	2	2	no	—
36	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
37	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
38	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
39	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
40	C₄⋊C₈×C₄₇	—	2	2	no	—
41	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
42	C₂×Q₈×C₄₇	—	2	2	no	—
43	C₂×Q₈×C₄₇	—	4	2	no	—
44	C₂×Q₈×C₄₇	—	4	2	no	—
45	C₂×Q₈×C₄₇	C₄²	1	4	yes	—
46	C₂²×C₄×C₄₇	—	2	2	no	—
47	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
49	C₂²×Dic₄₇	—	2	2	no	—
50	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
51	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
53	C₂×C₈×C₄₇	—	2	4	no	—
54	C₂×C₈×C₄₇	—	4	2	no	—
55	C₂×C₈×C₄₇	—	4	2	no	—
56	C₄⋊C₄×C₄₇	—	2	4	no	—
57	C₄⋊C₄×C₄₇	—	2	4	no	—
58	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
59	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
60	C₄²×C₄₇	#41	1	2	yes	—
61	C₄⋊Dic₄₇	—	4	4	no	—
62	C₄⋊Dic₄₇	—	4	2	no	—
63	C₄⋊Dic₄₇	—	4	2	no	—
64	C₄⋊Dic₄₇	—	4	2	no	—
65	C₄×Dic₄₇	—	2	2	no	—
66	C₄×Dic₄₇	—	2	2	no	—
67	C₄×Dic₄₇	—	2	2	no	—
68	C₄×Dic₄₇	—	2	2	no	—
69	C₄×Dic₄₇	—	2	2	no	—
70	C₄×Dic₄₇	—	4	1	no	—
71	C₄×Dic₄₇	—	4	4	no	—
72	C₂×C₄₇⋊C₈	—	2	4	no	—
73	C₂×C₄₇⋊C₈	—	4	2	no	—
74	C₂×C₄₇⋊C₈	—	4	2	no	—
75	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	Q₈×C₄₇	—	4	4	no	—
77	Q₈×C₄₇	—	4	4	no	—
78	C₂×C₄×C₄₇	—	2	1	no	—
79	C₂×C₄×C₄₇	—	2	1	no	—
80	C₂×C₄×C₄₇	—	2	4	no	—
81	C₂×C₄×C₄₇	—	4	2	no	—
82	C₂×C₄×C₄₇	—	4	2	no	—
83	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
84	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
85	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
86	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
87	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
88	C₂×C₄×C₄₇	#137	1	2	yes	—
89	C₂×C₄×C₄₇	#137	1	2	yes	—
90	C₂×C₄×C₄₇	#137	1	2	yes	—
91	C₂×Dic₄₇	—	2	2	no	—
92	C₂×Dic₄₇	—	2	1	no	—
93	C₂×Dic₄₇	—	2	2	no	—
94	C₂×Dic₄₇	—	2	2	no	—
95	C₂×Dic₄₇	—	2	2	no	—
96	C₂×Dic₄₇	—	2	2	no	—
97	C₂×Dic₄₇	—	4	2	no	—
98	C₂×Dic₄₇	—	4	4	no	—
99	C₂×Dic₄₇	#100	1	2	yes	—
100	C₈×C₄₇	—	4	4	no	—
101	C₄₇⋊C₈	—	4	4	no	—
102	#8232	—	47	1	no	maximal, Sylow
103	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
105	C₂²×C₄₇	#413	1	1	yes	characteristic
106	C₂²×C₄₇	#417	1	2	yes	—
107	C₂²×C₄₇	#419	1	2	yes	—
108	C₄×C₄₇	—	2	1	no	—
109	C₄×C₄₇	—	2	1	no	—
110	C₄×C₄₇	—	4	4	no	—
111	C₄×C₄₇	#440	1	2	yes	—
112	C₄×C₄₇	#440	1	2	yes	—
113	C₄×C₄₇	#441	1	2	yes	—
114	C₄×C₄₇	#441	1	2	yes	—
115	Dic₄₇	—	2	2	no	—
116	Dic₄₇	—	4	2	no	—
117	Dic₄₇	—	4	1	no	—
118	Dic₄₇	—	8	2	no	—
119	C₄×C₄⋊Q₈	—	47	1	no	—
120	#1767	—	47	2	no	—
121	C₂×#333	—	47	1	no	—
122	C₂×#333	D₄₇	1	1	yes	characteristic
123	#1296	—	47	2	no	—
124	C₂×C₄₇	#1558	1	1	yes	characteristic
125	C₂×C₄₇	#1559	1	2	yes	—
126	C₂×C₄₇	#1560	1	1	yes	characteristic
127	C₂×C₄₇	C₄×#100	1	1	yes	characteristic
128	C₂×C₄₇	#1763	1	2	yes	—
129	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
130	C₂×C₄×Q₈	—	47	2	no	—
131	C₂×C₄⋊C₈	—	47	2	no	—
132	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
133	C₂×#97	—	94	2	no	—
134	#391	—	47	2	no	—
135	#389	—	94	2	no	—
136	#384	—	47	1	no	—
137	C₄×C₄⋊C₄	—	94	2	no	—
138	C₄³	—	47	1	no	—
139	#336	—	94	2	no	—
140	#333	—	47	4	no	—
141	#333	Dic₄₇	1	4	yes	complemented
142	C₄₇	#8232	1	1	yes	characteristic, complemented, Sylow
143	C₂²×Q₈	C₄×D₄₇	1	2	yes	—
144	C₂²×C₈	—	2	2	no	—
145	C₂²×C₈	—	94	2	no	—
146	C₄⋊Q₈	—	2	2	no	—
147	C₄⋊Q₈	C₄×D₄₇	1	2	yes	—
148	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
149	C₄×Q₈	—	188	4	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	47	2	no	—
152	C₂×C₄⋊C₄	—	94	2	no	—
153	C₂×C₄⋊C₄	—	94	2	no	—
154	C₂×C₄²	—	47	1	no	—
155	C₂×C₄²	—	47	2	no	—
156	C₂×C₄²	—	47	2	no	—
157	C₂×C₄²	—	47	1	no	—
158	C₂×C₄²	—	94	2	no	—
159	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
160	C₄⋊C₈	—	2	2	no	—
161	C₄⋊C₈	—	47	4	no	—
162	C₄⋊C₈	—	94	2	no	—
163	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	—
164	#97	—	188	4	no	—
165	#95	—	94	4	no	—
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	4	2	no	—
168	C₂×Q₈	—	4	2	no	—
169	C₂×Q₈	C₄×Dic₄₇	1	4	yes	—
170	C₂²×C₄	—	2	2	no	—
171	C₂²×C₄	—	47	1	no	—
172	C₂²×C₄	—	47	2	no	—
173	C₂²×C₄	—	47	1	no	—
174	C₂²×C₄	—	94	2	no	—
175	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
176	C₂²×C₄	D₄×D₄₇	1	2	yes	—
177	C₂×C₈	—	2	4	no	—
178	C₂×C₈	—	4	2	no	—
179	C₂×C₈	—	4	2	no	—
180	C₂×C₈	—	94	4	no	—
181	C₂×C₈	—	188	2	no	—
182	C₂×C₈	—	188	2	no	—
183	C₄⋊C₄	—	2	4	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	188	2	no	—
186	C₄⋊C₄	—	188	4	no	—
187	C₄⋊C₄	—	188	2	no	—
188	C₄⋊C₄	—	188	2	no	—
189	C₄²	—	94	2	no	—
190	C₄²	—	94	2	no	—
191	C₄²	—	94	2	no	—
192	C₄²	—	94	2	no	—
193	C₄²	—	94	2	no	—
194	C₄²	—	188	1	no	—
195	C₄²	—	188	4	no	—
196	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
197	C₄²	#10625352	1	2	yes	—
198	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
199	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
200	Q₈	—	4	4	no	—
201	Q₈	—	4	4	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	4	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	47	2	no	—
208	C₂×C₄	—	94	2	no	—
209	C₂×C₄	—	94	1	no	—
210	C₂×C₄	—	94	2	no	—
211	C₂×C₄	—	94	2	no	—
212	C₂×C₄	—	94	2	no	—
213	C₂×C₄	—	94	2	no	—
214	C₂×C₄	—	188	2	no	—
215	C₂×C₄	—	188	4	no	—
216	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
217	C₂×C₄	#13093980	1	1	yes	characteristic
218	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
219	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
220	C₂×C₄	#13094051	1	2	yes	—
221	C₂×C₄	#13094053	1	2	yes	—
222	C₂×C₄	#13094056	1	2	yes	—
223	C₂×C₄	#13094056	1	2	yes	—
224	C₈	—	4	4	no	—
225	C₈	—	188	4	no	—
226	C₂²	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
227	C₂²	#100×D₄₇	1	1	yes	characteristic
228	C₂²	#15689104	1	1	yes	characteristic
229	C₂²	#15689123	1	2	yes	—
230	C₂²	#15689130	1	2	yes	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	4	4	no	—
234	C₄	—	94	2	no	—
235	C₄	—	376	2	no	—
236	C₄	—	188	2	no	—
237	C₄	—	188	1	no	—
238	C₄	#15689224	1	2	yes	—
239	C₄	#15689226	1	2	yes	—
240	C₄	#15689227	1	2	yes	—
241	C₄	#15689230	1	2	yes	—
242	C₂	#20242112	1	1	yes	characteristic
243	C₂	#20242115	1	2	yes	—
244	C₂	#20242122	1	1	yes	characteristic
245	C₂	#100×Dic₄₇	1	1	yes	characteristic
246	C₂	#20243220	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊Q₈×Dic₄₇

C₂

yes

maximal, characteristic

#20243243

C₂

yes

maximal

C₂×#15688872

C₂

yes

maximal, characteristic

#20241272

C₂

yes

maximal

C₂×C₄₇×#333

C₂

yes

maximal, characteristic

C₂×Q₈×Dic₄₇

C₄

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₂×#13093934

—

#15689030

C₄

yes

—

#15689022

—

#15688993

C₂²

yes

characteristic

C₄⋊C₄×Dic₄₇

—

C₄²×Dic₄₇

C₂²

yes

characteristic

#15688877

—

#15688872

C₄

yes

complemented

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₄₇×#333

C₄

yes

complemented

C₂²×C₄₇⋊C₈

—

Q₈×Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₇

D₄

yes

—

C₂×C₄×Dic₄₇

D₄

yes

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

C₂×C₄

yes

—

#13093934

—

C₄₇⋊#95

—

C₂²×Q₈×C₄₇

C₂×C₄

yes

—

C₂²×C₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

C₂×C₄

yes

—

C₄⋊Q₈×C₄₇

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

C₂×C₄

yes

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₄²

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂²⋊C₄

yes

—

C₂²×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₂²×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

#41

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₇

#117

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

#100

yes

—

100

C₈×C₄₇

—

101

C₄₇⋊C₈

—

102

#8232

—

maximal, Sylow

103

C₂²×C₄₇

C₄×C₂²⋊C₄

yes

characteristic

104

C₂²×C₄₇

C₂×#100

yes

characteristic

105

C₂²×C₄₇

#413

yes

characteristic

106

C₂²×C₄₇

#417

yes

—

107

C₂²×C₄₇

#419

yes

—

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

—

111

C₄×C₄₇

#440

yes

—

112

C₄×C₄₇

#440

yes

—

113

C₄×C₄₇

#441

yes

—

114

C₄×C₄₇

#441

yes

—

115

Dic₄₇

—

116

Dic₄₇

—

117

Dic₄₇

—

118

Dic₄₇

—

119

C₄×C₄⋊Q₈

—

120

#1767

—

121

C₂×#333

—

122

C₂×#333

D₄₇

yes

characteristic

123

#1296

—

124

C₂×C₄₇

#1558

yes

characteristic

125

C₂×C₄₇

#1559

yes

—

126

C₂×C₄₇

#1560

yes

characteristic

127

C₂×C₄₇

C₄×#100

yes

characteristic

128

C₂×C₄₇

#1763

yes

—

129

C₂×C₄⋊Q₈

C₂×D₄₇

yes

characteristic

130

C₂×C₄×Q₈

—

131

C₂×C₄⋊C₈

—

132

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

133

C₂×#97

—

134

#391

—

135

#389

—

136

#384

—

137

C₄×C₄⋊C₄

—

138

C₄³

—

139

#336

—

140

#333

—

141

#333

Dic₄₇

yes

complemented

142

C₄₇

#8232

yes

characteristic, complemented, Sylow

143

C₂²×Q₈

C₄×D₄₇

yes

—

144

C₂²×C₈

—

145

C₂²×C₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

C₄×D₄₇

yes

—

148

C₄⋊Q₈

C₂×Dic₄₇

yes

—

149

C₄×Q₈

—

188

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄²

—

155

C₂×C₄²

—

156

C₂×C₄²

—

157

C₂×C₄²

—

158

C₂×C₄²

—

159

C₂×C₄²

C₂²×D₄₇

yes

characteristic

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

C₂×Dic₄₇

yes

—

164

#97

—

188

—

165

#95

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

C₄×Dic₄₇

yes

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

176

C₂²×C₄

D₄×D₄₇

yes

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

188

—

182

C₂×C₈

—

188

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

188

—

186

C₄⋊C₄

—

188

—

187

C₄⋊C₄

—

188

—

188

C₄⋊C₄

—

188

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

194

C₄²

—

188

—

195

C₄²

—

188

—

196

C₄²

C₂×C₄×D₄₇

yes

characteristic

197

C₄²

#10625352

yes

—

198

C₄²

C₂²×Dic₄₇

yes

characteristic

199

C₂³

C₂²⋊C₄×D₄₇

yes

characteristic

200

Q₈

—

201

Q₈

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

188

—

215

C₂×C₄

—

188

—

216

C₂×C₄

C₂×C₄×Dic₄₇

yes

characteristic

217

C₂×C₄

#13093980

yes

characteristic

218

C₂×C₄

(C₂²⋊D₄₇)⋊C₄

yes

—

219

C₂×C₄

D₄×Dic₄₇

yes

—

220

C₂×C₄

#13094051

yes

—

221

C₂×C₄

#13094053

yes

—

222

C₂×C₄

#13094056

yes

—

223

C₂×C₄

#13094056

yes

—

224

C₈

—

225

C₈

—

188

—

226

C₂²

C₂²⋊C₄×Dic₄₇

yes

characteristic

227

C₂²

#100×D₄₇

yes

characteristic

228

C₂²

#15689104

yes

characteristic

229

C₂²

#15689123

yes

—

230

C₂²

#15689130

yes

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

376

—

236

C₄

—

188

—

237

C₄

—

188

—

238

C₄

#15689224

yes

—

239

C₄

#15689226

yes

—

240

C₄

#15689227

yes

—

241

C₄

#15689230

yes

—

242

C₂

#20242112

yes

characteristic

243

C₂

#20242115

yes

—

244

C₂

#20242122

yes

characteristic

245

C₂

#100×Dic₄₇

yes

characteristic

246

C₂

#20243220

yes

—

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×#333	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#333	D₄₇
hypocenter	C₄₇	#8232
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

subgroup

G/H

center

C₂³

C₂²⋊C₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₂×C₄₇×#333

C₂

socle, prime radical

C₂³×C₄₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

N	H ≅ G/N	type
15. #15688872	C₄	semidirect
18. C₄₇×#333	C₄	semidirect
141. #333	Dic₄₇	semidirect
142. C₄₇	#8232	semidirect

H ≅ G/N

type

15. #15688872

C₄

semidirect

18. C₄₇×#333

C₄

semidirect

141. #333

Dic₄₇

semidirect

142. C₄₇

#8232

semidirect

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

subgroup	index
C₄⋊Q₈×Dic₄₇	2
#20243243	2
C₂×#15688872	2
#20241272	2
C₂×C₄₇×#333	2
#8232	47

subgroup

index

C₄⋊Q₈×Dic₄₇

C₂×C₄₇×#333

Subgroups — #26107237

Conjugacy classes of subgroups

Complements

Maximal subgroups