Group #26107774 — subgroups

Subgroups — #26107774

Order 12032.

1030 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 227 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	#20243368	C₂	1	2	yes	maximal
2	C₂×#15688872	C₂	1	4	yes	maximal, complemented
3	C₂²×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
5	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
6	#15688878	—	2	2	no	—
7	#15688872	—	2	8	no	—
8	C₂³×Q₈×C₄₇	C₄	1	2	yes	—
9	C₂×C₄⋊Q₈×C₄₇	—	2	8	no	—
10	C₂×C₄⋊Q₈×C₄₇	—	2	2	no	—
11	C₂×C₄⋊Q₈×C₄₇	C₄	1	2	yes	—
12	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₄₇	—	2	2	no	—
14	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄₇⋊C₈	—	2	4	no	—
16	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
17	C₂²⋊(C₄₇⋊C₈)	—	4	4	no	—
18	C₂²×Q₈×C₄₇	—	2	8	no	—
19	C₂²×Q₈×C₄₇	—	2	2	no	—
20	C₂²×Q₈×C₄₇	—	4	4	no	—
21	C₂²×Q₈×C₄₇	—	4	4	no	—
22	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
23	C₂³×C₄×C₄₇	—	2	2	no	—
24	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₄₇	D₄	1	2	yes	—
26	C₄⋊Q₈×C₄₇	—	2	16	no	—
27	C₄⋊Q₈×C₄₇	—	2	8	no	—
28	C₄⋊Q₈×C₄₇	—	2	4	no	—
29	C₄⋊Q₈×C₄₇	D₄	1	8	yes	—
30	C₂×C₄⋊C₄×C₄₇	—	2	16	no	—
31	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
32	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
33	C₂×C₄²×C₄₇	—	2	4	no	—
34	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₄₇	D₄	1	2	yes	—
36	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
37	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×Q₈×C₄₇	—	2	8	no	—
39	C₂×Q₈×C₄₇	—	2	4	no	—
40	C₂×Q₈×C₄₇	—	4	32	no	—
41	C₂×Q₈×C₄₇	—	4	4	no	—
42	C₂×Q₈×C₄₇	—	4	4	no	—
43	C₂×Q₈×C₄₇	—	4	4	no	—
44	C₂×Q₈×C₄₇	—	4	4	no	—
45	C₂×Q₈×C₄₇	C₂²⋊C₄	1	8	yes	—
46	C₂²×C₄×C₄₇	—	2	2	no	—
47	C₂²×C₄×C₄₇	—	2	2	no	—
48	C₂²×C₄×C₄₇	—	2	2	no	—
49	C₂²×C₄×C₄₇	—	2	4	no	—
50	C₂²×C₄×C₄₇	—	2	4	no	—
51	C₂²×C₄×C₄₇	—	2	8	no	—
52	C₂²×C₄×C₄₇	—	2	4	no	—
53	C₂²×C₄×C₄₇	—	4	4	no	—
54	C₂²×C₄×C₄₇	—	4	4	no	—
55	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
58	C₂²×C₄×C₄₇	Q₁₆	1	4	yes	—
59	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
61	C₄⋊C₄×C₄₇	—	2	16	no	—
62	C₄⋊C₄×C₄₇	—	2	16	no	—
63	C₄²×C₄₇	—	2	2	no	—
64	C₄²×C₄₇	—	2	4	no	—
65	C₄²×C₄₇	C₂×D₄	1	4	yes	—
66	C₂×C₄₇⋊C₈	—	4	4	no	—
67	C₂×C₄₇⋊C₈	—	4	4	no	—
68	C₂×C₄₇⋊C₈	—	4	4	no	—
69	C₂³×C₄₇	—	2	1	no	—
70	C₂³×C₄₇	—	2	1	no	—
71	C₂³×C₄₇	—	2	2	no	—
72	C₂³×C₄₇	#100	1	2	yes	—
73	C₂³×C₄₇	#103	1	4	yes	—
74	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	Q₈×C₄₇	—	4	8	no	—
76	Q₈×C₄₇	—	4	16	no	—
77	Q₈×C₄₇	—	4	8	no	—
78	C₂×C₄×C₄₇	—	2	8	no	—
79	C₂×C₄×C₄₇	—	2	2	no	—
80	C₂×C₄×C₄₇	—	2	1	no	—
81	C₂×C₄×C₄₇	—	2	1	no	—
82	C₂×C₄×C₄₇	—	2	1	no	—
83	C₂×C₄×C₄₇	—	2	1	no	—
84	C₂×C₄×C₄₇	—	2	2	no	—
85	C₂×C₄×C₄₇	—	2	8	no	—
86	C₂×C₄×C₄₇	—	2	8	no	—
87	C₂×C₄×C₄₇	—	2	8	no	—
88	C₂×C₄×C₄₇	—	4	16	no	—
89	C₂×C₄×C₄₇	—	4	4	no	—
90	C₂×C₄×C₄₇	—	4	4	no	—
91	C₂×C₄×C₄₇	#100	1	2	yes	—
92	C₂×C₄×C₄₇	#103	1	4	yes	—
93	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
94	C₂×C₄×C₄₇	#120	1	4	yes	—
95	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
96	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
97	C₂×C₄×C₄₇	#137	1	4	yes	—
98	C₄₇⋊C₈	—	8	4	no	—
99	#8342	—	47	1	no	maximal, Sylow
100	C₂²×C₄₇	—	2	4	no	—
101	C₂²×C₄₇	—	2	2	no	—
102	C₂²×C₄₇	—	2	2	no	—
103	C₂²×C₄₇	—	2	4	no	—
104	C₂²×C₄₇	#333	1	4	yes	complemented
105	C₂²×C₄₇	#379	1	1	yes	characteristic
106	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
107	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
108	C₂²×C₄₇	C₂×#103	1	2	yes	—
109	C₂²×C₄₇	#419	1	2	yes	—
110	C₄×C₄₇	—	2	2	no	—
111	C₄×C₄₇	—	2	2	no	—
112	C₄×C₄₇	—	2	4	no	—
113	C₄×C₄₇	—	4	8	no	—
114	C₄×C₄₇	#448	1	4	yes	—
115	C₄×C₄₇	#451	1	4	yes	—
116	C₂²×C₄⋊Q₈	D₄₇	1	1	yes	characteristic
117	#1797	—	47	2	no	—
118	C₂×#333	—	47	4	no	—
119	C₂×C₄₇	—	2	4	no	—
120	C₂×C₄₇	C₂×#333	1	1	yes	characteristic
121	C₂×C₄₇	#1548	1	2	yes	—
122	C₂×C₄₇	#1558	1	1	yes	characteristic
123	C₂×C₄₇	#1783	1	1	yes	characteristic
124	C₂×C₄₇	#1787	1	2	yes	—
125	C₂³×Q₈	Dic₄₇	1	2	yes	—
126	C₂×C₄⋊Q₈	—	2	8	no	—
127	C₂×C₄⋊Q₈	—	2	2	no	—
128	C₂×C₄⋊Q₈	Dic₄₇	1	2	yes	—
129	C₂×C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
130	C₂²×C₄⋊C₄	—	2	2	no	—
131	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
132	C₂×C₄⋊C₈	—	47	4	no	—
133	C₂×C₂²⋊C₈	—	94	2	no	—
134	#336	—	94	2	no	—
135	#333	—	94	8	no	—
136	C₄₇	#8342	1	1	yes	characteristic, complemented, Sylow
137	C₂²×Q₈	—	2	8	no	—
138	C₂²×Q₈	—	2	2	no	—
139	C₂²×Q₈	—	4	4	no	—
140	C₂²×Q₈	—	4	4	no	—
141	C₂²×Q₈	C₂×Dic₄₇	1	4	yes	—
142	C₂³×C₄	—	2	2	no	—
143	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
144	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
145	C₂²×C₈	—	94	4	no	—
146	C₄⋊Q₈	—	2	16	no	—
147	C₄⋊Q₈	—	2	8	no	—
148	C₄⋊Q₈	—	2	4	no	—
149	C₄⋊Q₈	C₂²⋊D₄₇	1	8	yes	—
150	C₂×C₄⋊C₄	—	2	16	no	—
151	C₂×C₄⋊C₄	—	2	4	no	—
152	C₂×C₄⋊C₄	—	2	4	no	—
153	C₂×C₄²	—	2	4	no	—
154	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
155	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
156	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
157	C₄⋊C₈	—	94	8	no	—
158	C₂²⋊C₈	—	188	4	no	—
159	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
160	C₂×Q₈	—	2	8	no	—
161	C₂×Q₈	—	2	4	no	—
162	C₂×Q₈	—	4	32	no	—
163	C₂×Q₈	—	4	4	no	—
164	C₂×Q₈	—	4	4	no	—
165	C₂×Q₈	—	4	4	no	—
166	C₂×Q₈	—	4	4	no	—
167	C₂×Q₈	C₂²⋊Dic₄₇	1	8	yes	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	2	2	no	—
171	C₂²×C₄	—	2	4	no	—
172	C₂²×C₄	—	2	4	no	—
173	C₂²×C₄	—	2	8	no	—
174	C₂²×C₄	—	2	4	no	—
175	C₂²×C₄	—	4	4	no	—
176	C₂²×C₄	—	4	4	no	—
177	C₂²×C₄	#10625336	1	4	yes	—
178	C₂²×C₄	#10625337	1	4	yes	—
179	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
180	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
181	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
182	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
183	C₂×C₈	—	188	4	no	—
184	C₂×C₈	—	188	4	no	—
185	C₂×C₈	—	188	4	no	—
186	C₄⋊C₄	—	2	16	no	—
187	C₄⋊C₄	—	2	16	no	—
188	C₄²	—	2	2	no	—
189	C₄²	—	2	4	no	—
190	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
191	C₂³	—	2	1	no	—
192	C₂³	—	2	1	no	—
193	C₂³	—	2	2	no	—
194	C₂³	#13093941	1	2	yes	—
195	C₂³	#13093948	1	4	yes	—
196	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
197	Q₈	—	4	8	no	—
198	Q₈	—	4	16	no	—
199	Q₈	—	4	8	no	—
200	C₂×C₄	—	2	8	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	8	no	—
208	C₂×C₄	—	2	8	no	—
209	C₂×C₄	—	2	8	no	—
210	C₂×C₄	—	4	16	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	4	no	—
213	C₂×C₄	#13093941	1	2	yes	—
214	C₂×C₄	#13093948	1	4	yes	—
215	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
216	C₂×C₄	#13093993	1	4	yes	—
217	C₂×C₄	C₂×#10625336	1	2	yes	—
218	C₂×C₄	C₂×#10625337	1	2	yes	—
219	C₂×C₄	#13094055	1	4	yes	—
220	C₈	—	376	4	no	—
221	C₂²	—	2	2	no	—
222	C₂²	—	2	4	no	—
223	C₂²	—	2	4	no	—
224	C₂²	—	2	2	no	—
225	C₂²	#15688872	1	4	yes	complemented
226	C₂²	#15688979	1	1	yes	characteristic
227	C₂²	C₂×#13093941	1	1	yes	characteristic
228	C₂²	C₂×#13093941	1	1	yes	characteristic
229	C₂²	C₂×#13093948	1	2	yes	—
230	C₂²	#15689132	1	2	yes	—
231	C₄	—	2	2	no	—
232	C₄	—	2	2	no	—
233	C₄	—	2	4	no	—
234	C₄	—	4	8	no	—
235	C₄	#15689262	1	4	yes	—
236	C₄	#15689279	1	4	yes	—
237	C₂	—	2	4	no	—
238	C₂	C₂×#15688872	1	1	yes	characteristic
239	C₂	#20242069	1	2	yes	—
240	C₂	#20242114	1	1	yes	characteristic
241	C₂	#20243309	1	1	yes	characteristic
242	C₂	#20243323	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20243368

C₂

yes

maximal

C₂×#15688872

C₂

yes

maximal, complemented

C₂²×C₄⋊Q₈×C₄₇

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₂×C₂²⋊(C₄₇⋊C₈)

—

#15688878

—

#15688872

—

C₂³×Q₈×C₄₇

C₄

yes

—

C₂×C₄⋊Q₈×C₄₇

—

C₂×C₄⋊Q₈×C₄₇

—

C₂×C₄⋊Q₈×C₄₇

C₄

yes

—

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

—

C₂²×C₄⋊C₄×C₄₇

—

C₂²×C₄²×C₄₇

C₂²

yes

characteristic

C₂²×C₄₇⋊C₈

—

C₄⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

C₂×C₄

yes

—

C₂³×C₄×C₄₇

—

C₂³×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₇

D₄

yes

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

D₄

yes

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₂⁴×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

SD₁₆

yes

—

C₂²×C₄×C₄₇

Q₁₆

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#100

yes

—

C₂³×C₄₇

#103

yes

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#100

yes

—

C₂×C₄×C₄₇

#103

yes

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

#120

yes

—

C₂×C₄×C₄₇

C₂×SD₁₆

yes

—

C₂×C₄×C₄₇

C₂×Q₁₆

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₄₇⋊C₈

—

#8342

—

maximal, Sylow

100

C₂²×C₄₇

—

101

C₂²×C₄₇

—

102

C₂²×C₄₇

—

103

C₂²×C₄₇

—

104

C₂²×C₄₇

#333

yes

complemented

105

C₂²×C₄₇

#379

yes

characteristic

106

C₂²×C₄₇

C₂×#100

yes

characteristic

107

C₂²×C₄₇

C₂×#100

yes

characteristic

108

C₂²×C₄₇

C₂×#103

yes

—

109

C₂²×C₄₇

#419

yes

—

110

C₄×C₄₇

—

111

C₄×C₄₇

—

112

C₄×C₄₇

—

113

C₄×C₄₇

—

114

C₄×C₄₇

#448

yes

—

115

C₄×C₄₇

#451

yes

—

116

C₂²×C₄⋊Q₈

D₄₇

yes

characteristic

117

#1797

—

118

C₂×#333

—

119

C₂×C₄₇

—

120

C₂×C₄₇

C₂×#333

yes

characteristic

121

C₂×C₄₇

#1548

yes

—

122

C₂×C₄₇

#1558

yes

characteristic

123

C₂×C₄₇

#1783

yes

characteristic

124

C₂×C₄₇

#1787

yes

—

125

C₂³×Q₈

Dic₄₇

yes

—

126

C₂×C₄⋊Q₈

—

127

C₂×C₄⋊Q₈

—

128

C₂×C₄⋊Q₈

Dic₄₇

yes

—

129

C₂×C₄⋊Q₈

C₂×D₄₇

yes

—

130

C₂²×C₄⋊C₄

—

131

C₂²×C₄²

C₂×D₄₇

yes

characteristic

132

C₂×C₄⋊C₈

—

133

C₂×C₂²⋊C₈

—

134

#336

—

135

#333

—

136

C₄₇

#8342

yes

characteristic, complemented, Sylow

137

C₂²×Q₈

—

138

C₂²×Q₈

—

139

C₂²×Q₈

—

140

C₂²×Q₈

—

141

C₂²×Q₈

C₂×Dic₄₇

yes

—

142

C₂³×C₄

—

143

C₂³×C₄

C₂×Dic₄₇

yes

characteristic

144

C₂³×C₄

C₂²⋊D₄₇

yes

—

145

C₂²×C₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

C₄⋊Q₈

C₂²⋊D₄₇

yes

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄²

—

154

C₂×C₄²

C₂×Dic₄₇

yes

characteristic

155

C₂×C₄²

C₂²⋊D₄₇

yes

—

156

C₂×C₄²

C₂²×D₄₇

yes

characteristic

157

C₄⋊C₈

—

158

C₂²⋊C₈

—

188

—

159

C₂⁴

C₂²⋊Dic₄₇

yes

characteristic

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

C₂²⋊Dic₄₇

yes

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

#10625336

yes

—

178

C₂²×C₄

#10625337

yes

—

179

C₂²×C₄

C₂²⋊Dic₄₇

yes

characteristic

180

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

181

C₂²×C₄

C₂²×Dic₄₇

yes

characteristic

182

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

—

183

C₂×C₈

—

188

—

184

C₂×C₈

—

188

—

185

C₂×C₈

—

188

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄²

—

189

C₄²

—

190

C₄²

C₂×C₂²⋊D₄₇

yes

—

191

C₂³

—

192

C₂³

—

193

C₂³

—

194

C₂³

#13093941

yes

—

195

C₂³

#13093948

yes

—

196

C₂³

C₂×C₂²⋊Dic₄₇

yes

characteristic

197

Q₈

—

198

Q₈

—

199

Q₈

—

200

C₂×C₄

—

201

C₂×C₄

—

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

#13093941

yes

—

214

C₂×C₄

#13093948

yes

—

215

C₂×C₄

C₂×C₂²⋊Dic₄₇

yes

—

216

C₂×C₄

#13093993

yes

—

217

C₂×C₄

C₂×#10625336

yes

—

218

C₂×C₄

C₂×#10625337

yes

—

219

C₂×C₄

#13094055

yes

—

220

C₈

—

376

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

#15688872

yes

complemented

226

C₂²

#15688979

yes

characteristic

227

C₂²

C₂×#13093941

yes

characteristic

228

C₂²

C₂×#13093941

yes

characteristic

229

C₂²

C₂×#13093948

yes

—

230

C₂²

#15689132

yes

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

#15689262

yes

—

236

C₄

#15689279

yes

—

237

C₂

—

238

C₂

C₂×#15688872

yes

characteristic

239

C₂

#20242069

yes

—

240

C₂

#20242114

yes

characteristic

241

C₂

#20243309

yes

characteristic

242

C₂

#20243323

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂²×C₄⋊Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂²×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	#8342
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₄₇

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₂²×C₄⋊Q₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂×C₂²⋊C₄

prime radical

C₂⁴×C₄₇

C₂²⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

hypercenter

C₂²×C₄⋊Q₈

D₄₇

hypocenter

C₄₇

#8342

LCS

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×C₄⋊Q₈

N	H ≅ G/N	type
2. C₂×#15688872	C₂	semidirect
104. C₂²×C₄₇	#333	semidirect
136. C₄₇	#8342	semidirect
225. C₂²	#15688872	semidirect

H ≅ G/N

type

2. C₂×#15688872

C₂

semidirect

104. C₂²×C₄₇

#333

semidirect

136. C₄₇

#8342

semidirect

225. C₂²

#15688872

semidirect

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

subgroup	index
#20243368	2
C₂×#15688872	2
C₂²×C₄⋊Q₈×C₄₇	2
#8342	47

subgroup

index

#20243368

C₂×#15688872

C₂²×C₄⋊Q₈×C₄₇

#8342

Subgroups — #26107774

Conjugacy classes of subgroups

Complements

Maximal subgroups