Group #26115183 — subgroups

Subgroups — #26115183

Order 12032.

586 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 147 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×C₄×D₃₇₆	C₂	1	1	yes	maximal, characteristic
2	#20244181	C₂	1	2	yes	maximal, complemented
3	C₂×#15688850	C₂	1	2	yes	maximal, complemented
4	C₂×#15688845	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₃₇₆	C₄	1	1	yes	characteristic
7	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
8	C₄×D₃₇₆	—	2	2	no	—
9	C₄×D₃₇₆	—	2	2	no	—
10	C₂×#13093958	C₄	1	1	yes	characteristic
11	C₂×#13093946	C₄	1	2	yes	—
12	C₂×(C₂×D₄₇)⋊C₈	—	2	4	no	—
13	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	#15688850	—	2	4	no	—
16	#15688845	—	2	2	no	—
17	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#334	—	2	2	no	—
20	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
21	C₂²×C₄×D₄₇	—	2	2	no	—
22	C₂×D₃₇₆	—	2	4	no	—
23	C₂×D₃₇₆	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	2	1	no	—
25	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
26	C₄×D₁₈₈	—	2	2	no	—
27	C₄×D₁₈₈	—	2	2	no	—
28	C₄×D₁₈₈	—	2	2	no	—
29	C₄×D₁₈₈	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
31	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
32	#13093958	—	2	2	no	—
33	#13093946	—	2	4	no	—
34	(C₂×D₄₇)⋊C₈	—	4	8	no	—
35	C₄×C₄₇⋊C₈	—	2	1	no	—
36	C₄×C₄₇⋊C₈	—	2	1	no	—
37	C₄×C₄₇⋊C₈	—	2	1	no	—
38	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
39	C₂²×C₈×C₄₇	—	2	2	no	—
40	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₄₇	—	2	2	no	—
44	C₄⋊C₈×C₄₇	—	2	2	no	—
45	C₄×C₈×C₄₇	D₄	1	2	yes	—
46	C₄×C₈×C₄₇	D₄	1	2	yes	—
47	C₂³×D₄₇	—	2	2	no	—
48	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
51	C₂²×Dic₄₇	—	2	2	no	—
52	C₂×D₁₈₈	—	2	2	no	—
53	C₂×D₁₈₈	—	2	2	no	—
54	C₂×D₁₈₈	—	2	2	no	—
55	C₂×D₁₈₈	—	2	2	no	—
56	C₂×D₁₈₈	—	2	2	no	—
57	C₂×D₁₈₈	M₁₆	1	4	yes	—
58	C₂×C₄×D₄₇	—	4	2	no	—
59	C₂×C₄×D₄₇	—	4	2	no	—
60	C₂×C₄×D₄₇	—	4	4	no	—
61	C₂×C₄×D₄₇	—	4	4	no	—
62	C₂×C₈×C₄₇	—	2	2	no	—
63	C₂×C₈×C₄₇	—	2	2	no	—
64	C₂×C₈×C₄₇	—	4	2	no	—
65	C₂×C₈×C₄₇	—	4	4	no	—
66	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
67	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
68	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₄₇	#41	1	1	yes	characteristic
72	(C₂×D₄₇)⋊C₄	—	4	2	no	—
73	(C₂×D₄₇)⋊C₄	—	4	2	no	—
74	C₄⋊Dic₄₇	—	2	2	no	—
75	C₄⋊Dic₄₇	—	2	2	no	—
76	C₂×C₄₇⋊C₈	—	2	4	no	—
77	C₂×C₄₇⋊C₈	—	2	2	no	—
78	C₂×C₄₇⋊C₈	—	2	2	no	—
79	C₂×C₄₇⋊C₈	—	2	4	no	—
80	D₃₇₆	—	2	8	no	—
81	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
82	C₂²×D₄₇	—	2	4	no	—
83	C₂²×D₄₇	—	4	2	no	—
84	C₂²×D₄₇	—	4	2	no	—
85	C₂²×D₄₇	—	4	4	no	—
86	C₂²×D₄₇	—	4	4	no	—
87	C₂×C₄×C₄₇	—	2	2	no	—
88	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
90	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
91	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
92	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
93	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
94	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
95	C₂×C₄×C₄₇	#131	1	2	yes	—
96	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
97	C₂×Dic₄₇	—	4	2	no	—
98	C₂×Dic₄₇	—	4	4	no	—
99	D₁₈₈	—	2	4	no	—
100	D₁₈₈	—	2	4	no	—
101	D₁₈₈	—	4	2	no	—
102	D₁₈₈	—	4	2	no	—
103	C₄×D₄₇	—	8	4	no	—
104	C₄×D₄₇	—	8	2	no	—
105	C₄×D₄₇	—	8	2	no	—
106	C₈×C₄₇	—	2	2	no	—
107	C₈×C₄₇	—	2	2	no	—
108	C₈×C₄₇	—	8	2	no	—
109	C₄₇⋊C₈	—	2	4	no	—
110	C₄₇⋊C₈	—	4	2	no	—
111	#9665	—	47	1	no	maximal, Sylow
112	C₂²×C₄₇	#390	1	1	yes	characteristic
113	C₂²×C₄₇	#435	1	2	yes	—
114	C₂²×C₄₇	#442	1	2	yes	—
115	C₂²×C₄₇	#443	1	2	yes	—
116	C₂×D₄₇	—	4	8	no	—
117	C₂×D₄₇	—	4	4	no	—
118	C₂×D₄₇	—	8	4	no	—
119	C₂×D₄₇	—	8	2	no	—
120	C₂×D₄₇	—	8	2	no	—
121	C₄×C₄₇	—	2	1	no	—
122	C₄×C₄₇	—	2	1	no	—
123	C₄×C₄₇	#407	1	1	yes	characteristic
124	C₄×C₄₇	#408	1	1	yes	characteristic
125	C₄×C₄₇	#435	1	2	yes	—
126	C₄×C₄₇	#469	1	2	yes	—
127	C₄×C₄₇	#496	1	2	yes	—
128	Dic₄₇	—	8	2	no	—
129	C₂×C₄×D₈	—	47	1	no	—
130	#1954	—	47	2	no	—
131	C₂×#334	D₄₇	1	1	yes	characteristic, complemented
132	C₂×D₄⋊C₈	—	47	2	no	—
133	C₂×#322	—	47	1	no	—
134	C₂×C₄₇	#1586	1	4	yes	—
135	C₂×C₄₇	#1955	1	1	yes	characteristic
136	C₂×C₄₇	#1972	1	1	yes	characteristic
137	C₂×C₄₇	#1974	1	1	yes	characteristic
138	D₄₇	—	8	4	no	—
139	C₂²×D₈	—	47	1	no	—
140	C₂×C₄×D₄	—	47	2	no	—
141	C₄×D₈	—	94	2	no	—
142	C₄×D₈	—	94	2	no	—
143	C₂×#107	—	47	1	no	—
144	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
145	C₂×#102	—	47	2	no	—
146	C₂×C₂²⋊C₈	—	94	4	no	—
147	C₂×C₄×C₈	—	47	1	no	—
148	C₂×C₄×C₈	—	47	1	no	—
149	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
150	#334	—	2	2	no	—
151	D₄⋊C₈	—	94	4	no	—
152	#322	—	94	2	no	—
153	C₄₇	#9665	1	1	yes	characteristic, complemented, Sylow
154	C₂²×D₄	—	47	2	no	—
155	C₂³×C₄	—	94	2	no	—
156	C₂×D₈	—	94	4	no	—
157	C₂×D₈	—	94	2	no	—
158	C₂²×C₈	—	2	2	no	—
159	C₂²×C₈	—	47	2	no	—
160	C₂²×C₈	—	94	1	no	—
161	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
162	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
163	C₄×D₄	—	94	2	no	—
164	C₄×D₄	—	94	2	no	—
165	C₄×D₄	—	94	2	no	—
166	C₄×D₄	—	94	2	no	—
167	C₂×C₄⋊C₄	—	47	2	no	—
168	C₂×C₂²⋊C₄	—	94	2	no	—
169	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
170	#107	—	94	2	no	—
171	C₄⋊C₈	—	2	2	no	—
172	C₄⋊C₈	—	2	2	no	—
173	#102	—	94	4	no	—
174	C₂²⋊C₈	—	188	8	no	—
175	C₄×C₈	—	47	2	no	—
176	C₄×C₈	—	94	1	no	—
177	C₄×C₈	—	94	1	no	—
178	C₄×C₈	—	94	1	no	—
179	C₄×C₈	D₁₈₈	1	2	yes	—
180	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
181	C₂⁴	—	94	2	no	—
182	C₂×D₄	—	47	4	no	—
183	C₂×D₄	—	94	2	no	—
184	C₂×D₄	—	94	2	no	—
185	C₂×D₄	—	94	2	no	—
186	C₂×D₄	—	94	2	no	—
187	C₂×D₄	—	94	2	no	—
188	C₂²×C₄	—	94	2	no	—
189	C₂²×C₄	—	188	2	no	—
190	C₂²×C₄	—	188	2	no	—
191	C₂²×C₄	—	188	4	no	—
192	C₂²×C₄	—	188	4	no	—
193	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
194	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
195	C₂²×C₄	#10625354	1	1	yes	characteristic
196	D₈	—	94	8	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	2	2	no	—
199	C₂×C₈	—	4	2	no	—
200	C₂×C₈	—	4	4	no	—
201	C₂×C₈	—	94	4	no	—
202	C₂×C₈	—	94	2	no	—
203	C₂×C₈	—	94	2	no	—
204	C₂×C₈	—	94	4	no	—
205	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
206	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
207	C₄⋊C₄	—	94	2	no	—
208	C₄⋊C₄	—	94	2	no	—
209	C₂²⋊C₄	—	188	2	no	—
210	C₂²⋊C₄	—	188	2	no	—
211	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
212	C₄²	D₄×D₄₇	1	1	yes	characteristic
213	C₄²	#10625354	1	1	yes	characteristic
214	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
215	C₂³	—	94	4	no	—
216	C₂³	—	188	4	no	—
217	C₂³	—	188	4	no	—
218	C₂³	—	188	2	no	—
219	C₂³	—	188	2	no	—
220	C₂³	#13093986	1	1	yes	characteristic
221	D₄	—	94	4	no	—
222	D₄	—	94	4	no	—
223	D₄	—	188	2	no	—
224	D₄	—	188	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	376	2	no	—
227	C₂×C₄	—	376	2	no	—
228	C₂×C₄	—	376	4	no	—
229	C₂×C₄	—	188	4	no	—
230	C₂×C₄	—	188	2	no	—
231	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
232	C₂×C₄	#13093986	1	1	yes	characteristic
233	C₂×C₄	#13093999	1	1	yes	characteristic
234	C₂×C₄	#13093999	1	1	yes	characteristic
235	C₂×C₄	#13094013	1	1	yes	characteristic
236	C₂×C₄	#13094020	1	1	yes	characteristic
237	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
238	C₂×C₄	#13094030	1	2	yes	—
239	C₂×C₄	#13094051	1	4	yes	—
240	C₈	—	2	2	no	—
241	C₈	—	2	2	no	—
242	C₈	—	8	2	no	—
243	C₈	—	94	4	no	—
244	C₈	—	188	2	no	—
245	C₂²	—	376	2	no	—
246	C₂²	—	376	2	no	—
247	C₂²	—	376	4	no	—
248	C₂²	—	188	8	no	—
249	C₂²	—	188	4	no	—
250	C₂²	#15689024	1	1	yes	characteristic
251	C₂²	#15689193	1	2	yes	—
252	C₂²	#15689234	1	2	yes	—
253	C₂²	#15689239	1	2	yes	—
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	376	2	no	—
257	C₄	#15689086	1	1	yes	characteristic
258	C₄	#15689089	1	1	yes	characteristic
259	C₄	#15689193	1	2	yes	—
260	C₄	#15689377	1	2	yes	—
261	C₄	#15689509	1	2	yes	—
262	C₂	—	376	4	no	—
263	C₂	#20242251	1	4	yes	—
264	C₂	#20244185	1	1	yes	characteristic
265	C₂	#20244262	1	1	yes	characteristic
266	C₂	#20244274	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×D₃₇₆

C₂

yes

maximal, characteristic

#20244181

C₂

yes

maximal, complemented

C₂×#15688850

C₂

yes

maximal, complemented

C₂×#15688845

C₂

yes

maximal, characteristic, complemented

C₂×C₄₇×#334

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₇₆

C₄

yes

characteristic

C₂×C₄×D₁₈₈

C₂²

yes

—

C₄×D₃₇₆

—

C₄×D₃₇₆

—

C₂×#13093958

C₄

yes

characteristic

C₂×#13093946

C₄

yes

—

C₂×(C₂×D₄₇)⋊C₈

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₄₇⋊C₈

C₂²

yes

characteristic

#15688850

—

#15688845

—

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#334

—

C₂²×D₁₈₈

C₂×C₄

yes

—

C₂²×C₄×D₄₇

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

D₄

yes

—

C₄×D₁₈₈

—

C₄×D₁₈₈

—

C₄×D₁₈₈

—

C₄×D₁₈₈

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

—

C₂×(C₂×D₄₇)⋊C₄

—

#13093958

—

#13093946

—

(C₂×D₄₇)⋊C₈

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₄×C₈×C₄₇

D₄

yes

—

C₄×C₈×C₄₇

D₄

yes

—

C₂³×D₄₇

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

#41

yes

characteristic

C₂²×Dic₄₇

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

M₁₆

yes

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

#41

yes

characteristic

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

D₃₇₆

—

C₂³×C₄₇

C₄×D₄

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

C₂×M₁₆

yes

—

C₂×C₄×C₄₇

#131

yes

—

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

100

D₁₈₈

—

101

D₁₈₈

—

102

D₁₈₈

—

103

C₄×D₄₇

—

104

C₄×D₄₇

—

105

C₄×D₄₇

—

106

C₈×C₄₇

—

107

C₈×C₄₇

—

108

C₈×C₄₇

—

109

C₄₇⋊C₈

—

110

C₄₇⋊C₈

—

111

#9665

—

maximal, Sylow

112

C₂²×C₄₇

#390

yes

characteristic

113

C₂²×C₄₇

#435

yes

—

114

C₂²×C₄₇

#442

yes

—

115

C₂²×C₄₇

#443

yes

—

116

C₂×D₄₇

—

117

C₂×D₄₇

—

118

C₂×D₄₇

—

119

C₂×D₄₇

—

120

C₂×D₄₇

—

121

C₄×C₄₇

—

122

C₄×C₄₇

—

123

C₄×C₄₇

#407

yes

characteristic

124

C₄×C₄₇

#408

yes

characteristic

125

C₄×C₄₇

#435

yes

—

126

C₄×C₄₇

#469

yes

—

127

C₄×C₄₇

#496

yes

—

128

Dic₄₇

—

129

C₂×C₄×D₈

—

130

#1954

—

131

C₂×#334

D₄₇

yes

characteristic, complemented

132

C₂×D₄⋊C₈

—

133

C₂×#322

—

134

C₂×C₄₇

#1586

yes

—

135

C₂×C₄₇

#1955

yes

characteristic

136

C₂×C₄₇

#1972

yes

characteristic

137

C₂×C₄₇

#1974

yes

characteristic

138

D₄₇

—

139

C₂²×D₈

—

140

C₂×C₄×D₄

—

141

C₄×D₈

—

142

C₄×D₈

—

143

C₂×#107

—

144

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

145

C₂×#102

—

146

C₂×C₂²⋊C₈

—

147

C₂×C₄×C₈

—

148

C₂×C₄×C₈

—

149

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

150

#334

—

151

D₄⋊C₈

—

152

#322

—

153

C₄₇

#9665

yes

characteristic, complemented, Sylow

154

C₂²×D₄

—

155

C₂³×C₄

—

156

C₂×D₈

—

157

C₂×D₈

—

158

C₂²×C₈

—

159

C₂²×C₈

—

160

C₂²×C₈

—

161

C₂²×C₈

C₄×D₄₇

yes

characteristic

162

C₂²×C₈

C₄×D₄₇

yes

characteristic

163

C₄×D₄

—

164

C₄×D₄

—

165

C₄×D₄

—

166

C₄×D₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₂²⋊C₄

—

169

C₂×C₄²

C₂²×D₄₇

yes

characteristic

170

#107

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

#102

—

174

C₂²⋊C₈

—

188

—

175

C₄×C₈

—

176

C₄×C₈

—

177

C₄×C₈

—

178

C₄×C₈

—

179

C₄×C₈

D₁₈₈

yes

—

180

C₄×C₈

C₂²⋊D₄₇

yes

—

181

C₂⁴

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

188

—

190

C₂²×C₄

—

188

—

191

C₂²×C₄

—

188

—

192

C₂²×C₄

—

188

—

193

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

194

C₂²×C₄

D₄×D₄₇

yes

characteristic

195

C₂²×C₄

#10625354

yes

characteristic

196

D₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

206

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₂²⋊C₄

—

188

—

210

C₂²⋊C₄

—

188

—

211

C₄²

C₂×D₁₈₈

yes

characteristic

212

C₄²

D₄×D₄₇

yes

characteristic

213

C₄²

#10625354

yes

characteristic

214

C₄²

C₂×C₂²⋊D₄₇

yes

characteristic

215

C₂³

—

216

C₂³

—

188

—

217

C₂³

—

188

—

218

C₂³

—

188

—

219

C₂³

—

188

—

220

C₂³

#13093986

yes

characteristic

221

D₄

—

222

D₄

—

223

D₄

—

188

—

224

D₄

—

188

—

225

C₂×C₄

—

226

C₂×C₄

—

376

—

227

C₂×C₄

—

376

—

228

C₂×C₄

—

376

—

229

C₂×C₄

—

188

—

230

C₂×C₄

—

188

—

231

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

232

C₂×C₄

#13093986

yes

characteristic

233

C₂×C₄

#13093999

yes

characteristic

234

C₂×C₄

#13093999

yes

characteristic

235

C₂×C₄

#13094013

yes

characteristic

236

C₂×C₄

#13094020

yes

characteristic

237

C₂×C₄

M₁₆×D₄₇

yes

—

238

C₂×C₄

#13094030

yes

—

239

C₂×C₄

#13094051

yes

—

240

C₈

—

241

C₈

—

242

C₈

—

243

C₈

—

244

C₈

—

188

—

245

C₂²

—

376

—

246

C₂²

—

376

—

247

C₂²

—

376

—

248

C₂²

—

188

—

249

C₂²

—

188

—

250

C₂²

#15689024

yes

characteristic

251

C₂²

#15689193

yes

—

252

C₂²

#15689234

yes

—

253

C₂²

#15689239

yes

—

254

C₄

—

255

C₄

—

256

C₄

—

376

—

257

C₄

#15689086

yes

characteristic

258

C₄

#15689089

yes

characteristic

259

C₄

#15689193

yes

—

260

C₄

#15689377

yes

—

261

C₄

#15689509

yes

—

262

C₂

—

376

—

263

C₂

#20242251

yes

—

264

C₂

#20244185

yes

characteristic

265

C₂

#20244262

yes

characteristic

266

C₂

#20244274

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×#334	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂²×D₃₇₆	C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#334	D₄₇
hypocenter	C₄₇	#9665
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

subgroup

G/H

center

C₂²×C₄

D₄×D₄₇

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₂×C₄₇×#334

C₂

socle

C₂³×C₄₇

C₄×D₄

prime radical

C₂²×D₃₇₆

C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

N	H ≅ G/N	type
2. #20244181	C₂	semidirect
3. C₂×#15688850	C₂	semidirect
4. C₂×#15688845	C₂	semidirect
5. C₂×C₄₇×#334	C₂	semidirect
131. C₂×#334	D₄₇	semidirect
153. C₄₇	#9665	semidirect

H ≅ G/N

type

2. #20244181

C₂

semidirect

3. C₂×#15688850

C₂

semidirect

4. C₂×#15688845

C₂

semidirect

5. C₂×C₄₇×#334

C₂

semidirect

131. C₂×#334

D₄₇

semidirect

153. C₄₇

#9665

semidirect

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

subgroup	index
C₂×C₄×D₃₇₆	2
#20244181	2
C₂×#15688850	2
C₂×#15688845	2
C₂×C₄₇×#334	2
#9665	47

subgroup

index

C₂×C₄×D₃₇₆

C₂×C₄₇×#334

Subgroups — #26115183

Conjugacy classes of subgroups

Complements

Maximal subgroups