Group #26192152 — subgroups

Subgroups — C₂×#20242526 #26192152

Order 12032.

1010 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 219 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×#15689853	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689415	C₂	1	2	yes	maximal
3	#20242526	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688872	C₂	1	1	yes	maximal, characteristic
5	C₂×#15688855	C₂	1	2	yes	maximal
6	C₂×C₄₇×#494	C₂	1	1	yes	maximal, characteristic
7	#15689853	—	2	4	no	—
8	#15689853	—	2	2	no	—
9	#15689853	C₂²	1	4	yes	—
10	C₂×#13094023	—	2	2	no	—
11	C₂×#13094022	—	2	2	no	—
12	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
13	C₂×#13093989	—	2	2	no	—
14	#15689415	—	2	4	no	—
15	#15689415	C₂²	1	8	yes	—
16	C₂×#13093957	—	2	2	no	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×#13093947	—	2	2	no	—
19	#15688872	C₂²	1	4	yes	—
20	#15688855	C₂²	1	8	yes	—
21	C₂²×Q₁₆×C₄₇	—	2	2	no	—
22	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#494	—	2	2	no	—
25	C₄₇×#494	C₂²	1	4	yes	—
26	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×Dic₉₄	—	2	2	no	—
28	C₂²×Dic₉₄	D₄	1	2	yes	—
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	#13094023	—	2	8	no	—
31	#13094023	—	2	8	no	—
32	#13094022	—	2	8	no	—
33	#13094022	—	2	8	no	—
34	C₄×Dic₉₄	—	2	2	no	—
35	C₄×Dic₉₄	—	2	2	no	—
36	C₄×Dic₉₄	D₄	1	4	yes	—
37	C₄×Dic₉₄	C₂³	1	4	yes	—
38	#13093989	—	2	8	no	—
39	#13093989	—	2	8	no	—
40	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
41	C₂×Dic₄₇⋊C₄	—	2	4	no	—
42	C₂×Dic₄₇⋊C₄	—	2	2	no	—
43	C₂×C₄×Dic₄₇	—	2	2	no	—
44	C₂×C₄×Dic₄₇	—	2	2	no	—
45	#13093957	—	2	8	no	—
46	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
47	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
48	#13093947	—	2	8	no	—
49	C₂²×Q₈×C₄₇	—	2	1	no	—
50	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
51	C₂×Q₁₆×C₄₇	—	2	8	no	—
52	C₂×Q₁₆×C₄₇	—	4	8	no	—
53	C₂²×C₈×C₄₇	—	2	1	no	—
54	C₄⋊Q₈×C₄₇	—	2	2	no	—
55	C₄⋊Q₈×C₄₇	—	2	2	no	—
56	C₄⋊Q₈×C₄₇	—	2	1	no	—
57	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
58	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
62	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
63	C₄×C₈×C₄₇	—	2	1	no	—
64	C₄×C₈×C₄₇	C₂³	1	2	yes	—
65	C₂×Q₈×C₄₇	—	2	2	no	—
66	C₂×Q₈×C₄₇	—	2	2	no	—
67	C₂×Q₈×C₄₇	—	4	4	no	—
68	C₂×Q₈×C₄₇	—	4	4	no	—
69	C₂×Q₈×C₄₇	—	4	1	no	—
70	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	4	1	no	—
73	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
75	C₂²×Dic₄₇	—	2	2	no	—
76	C₂²×Dic₄₇	—	2	2	no	—
77	C₂×Dic₉₄	—	2	2	no	—
78	C₂×Dic₉₄	—	2	4	no	—
79	C₂×Dic₉₄	—	2	8	no	—
80	C₂×Dic₉₄	—	8	4	no	—
81	C₂×Dic₉₄	Q₁₆	1	8	yes	complemented
82	C₂×Dic₉₄	C₂×D₄	1	4	yes	—
83	Q₁₆×C₄₇	—	4	16	no	—
84	C₂×C₈×C₄₇	—	2	4	no	—
85	C₂×C₈×C₄₇	—	2	2	no	—
86	C₄⋊C₄×C₄₇	—	2	4	no	—
87	C₄⋊C₄×C₄₇	—	2	4	no	—
88	C₄⋊C₄×C₄₇	—	2	4	no	—
89	C₄⋊C₄×C₄₇	—	4	2	no	—
90	C₄²×C₄₇	C₂×D₄	1	2	yes	—
91	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
93	C₄⋊Dic₄₇	—	2	2	no	—
94	C₄⋊Dic₄₇	C₂×D₄	1	4	yes	—
95	Dic₄₇⋊C₄	—	2	16	no	—
96	Dic₄₇⋊C₄	—	2	4	no	—
97	Dic₄₇⋊C₄	—	2	4	no	—
98	C₄×Dic₄₇	—	2	8	no	—
99	C₄×Dic₄₇	—	2	4	no	—
100	C₄×Dic₄₇	—	2	4	no	—
101	C₂×C₄₇⋊C₈	—	2	4	no	—
102	C₂×C₄₇⋊C₈	—	4	4	no	—
103	C₂³×C₄₇	#120	1	1	yes	characteristic
104	Q₈×C₄₇	—	4	4	no	—
105	Q₈×C₄₇	—	4	4	no	—
106	Q₈×C₄₇	—	8	2	no	—
107	Q₈×C₄₇	—	8	2	no	—
108	C₂×C₄×C₄₇	—	2	2	no	—
109	C₂×C₄×C₄₇	—	2	4	no	—
110	C₂×C₄×C₄₇	—	4	4	no	—
111	C₂×C₄×C₄₇	—	4	2	no	—
112	C₂×C₄×C₄₇	—	8	2	no	—
113	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
114	C₂×C₄×C₄₇	#120	1	2	yes	—
115	C₂×C₄×C₄₇	C₂×Q₁₆	1	4	yes	—
116	C₂×C₄×C₄₇	#137	1	4	yes	—
117	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
118	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
119	C₂×Dic₄₇	—	2	4	no	—
120	C₂×Dic₄₇	—	2	8	no	—
121	C₂×Dic₄₇	—	2	4	no	—
122	C₂×Dic₄₇	—	4	4	no	—
123	Dic₉₄	—	2	4	no	—
124	Dic₉₄	—	2	8	no	—
125	Dic₉₄	—	8	8	no	—
126	Dic₉₄	C₂×Q₁₆	1	8	yes	complemented
127	C₈×C₄₇	—	2	4	no	—
128	C₄₇⋊C₈	—	4	4	no	—
129	C₂×#1633	—	47	1	no	maximal, Sylow
130	C₂²×C₄₇	#451	1	4	yes	—
131	C₂²×C₄₇	#453	1	2	yes	—
132	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
133	C₄×C₄₇	—	2	1	no	—
134	C₄×C₄₇	—	2	1	no	—
135	C₄×C₄₇	—	4	4	no	—
136	C₄×C₄₇	—	8	2	no	—
137	C₄×C₄₇	#451	1	4	yes	—
138	C₄×C₄₇	C₂²×Q₁₆	1	2	yes	—
139	C₄×C₄₇	C₂×#137	1	2	yes	—
140	Dic₄₇	—	2	8	no	—
141	Dic₄₇	—	4	4	no	—
142	C₂×Q₈²	—	47	1	no	—
143	C₂×#494	D₄₇	1	1	yes	characteristic
144	C₂×#477	—	47	2	no	—
145	#1633	—	47	8	no	—
146	C₂×#333	—	47	1	no	—
147	C₂×Q₈⋊C₈	—	47	2	no	—
148	C₂×C₄₇	#1633	1	4	yes	complemented
149	C₂×C₄₇	C₂×#451	1	2	yes	—
150	C₂×C₄₇	C₂×#453	1	1	yes	characteristic
151	C₂²×Q₁₆	—	2	2	no	—
152	Q₈²	—	47	4	no	—
153	Q₈²	—	94	4	no	—
154	Q₈²	—	94	2	no	—
155	C₂×C₄⋊Q₈	—	94	2	no	—
156	C₂×C₄⋊Q₈	—	94	2	no	—
157	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
158	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
159	C₂×C₄×Q₈	—	47	2	no	—
160	C₂×C₄×Q₈	—	94	2	no	—
161	#494	—	2	2	no	—
162	#494	C₂×D₄₇	1	4	yes	—
163	#477	—	47	8	no	—
164	#477	—	94	4	no	—
165	C₂×#107	—	94	2	no	—
166	C₂×C₄⋊C₈	—	47	2	no	—
167	C₂×#103	—	94	2	no	—
168	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
169	#333	—	47	4	no	—
170	Q₈⋊C₈	—	47	8	no	—
171	C₄₇	C₂×#1633	1	1	yes	characteristic, complemented, Sylow
172	C₂²×Q₈	—	2	1	no	—
173	C₂²×Q₈	—	47	2	no	—
174	C₂²×Q₈	—	94	2	no	—
175	C₂²×Q₈	C₂²⋊D₄₇	1	2	yes	—
176	C₂×Q₁₆	—	2	8	no	—
177	C₂×Q₁₆	—	4	8	no	—
178	C₂²×C₈	—	2	1	no	—
179	C₂²×C₈	—	94	2	no	—
180	C₄⋊Q₈	—	2	2	no	—
181	C₄⋊Q₈	—	2	2	no	—
182	C₄⋊Q₈	—	2	1	no	—
183	C₄⋊Q₈	—	94	8	no	—
184	C₄⋊Q₈	—	94	8	no	—
185	C₄⋊Q₈	—	94	8	no	—
186	C₄⋊Q₈	—	94	8	no	—
187	C₄⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
188	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
189	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
190	C₄×Q₈	—	47	4	no	—
191	C₄×Q₈	—	47	4	no	—
192	C₄×Q₈	—	94	8	no	—
193	C₄×Q₈	—	94	8	no	—
194	C₄×Q₈	—	94	2	no	—
195	C₄×Q₈	—	94	2	no	—
196	C₂×C₄⋊C₄	—	2	2	no	—
197	C₂×C₄⋊C₄	—	2	2	no	—
198	C₂×C₄⋊C₄	—	47	2	no	—
199	C₂×C₄⋊C₄	—	94	4	no	—
200	C₂×C₄⋊C₄	—	94	2	no	—
201	C₂×C₄²	—	94	2	no	—
202	C₂×C₄²	—	94	2	no	—
203	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
204	#107	—	94	8	no	—
205	C₄⋊C₈	—	47	4	no	—
206	C₄⋊C₈	—	94	2	no	—
207	#103	—	94	8	no	—
208	C₄×C₈	—	2	1	no	—
209	C₄×C₈	C₂²×D₄₇	1	2	yes	—
210	C₂×Q₈	—	2	2	no	—
211	C₂×Q₈	—	2	2	no	—
212	C₂×Q₈	—	4	4	no	—
213	C₂×Q₈	—	4	4	no	—
214	C₂×Q₈	—	4	1	no	—
215	C₂×Q₈	—	47	8	no	—
216	C₂×Q₈	—	47	4	no	—
217	C₂×Q₈	—	94	8	no	—
218	C₂×Q₈	—	94	2	no	—
219	C₂×Q₈	—	94	4	no	—
220	C₂×Q₈	—	376	4	no	—
221	C₂×Q₈	C₂×C₂²⋊D₄₇	1	4	yes	—
222	C₂²×C₄	—	2	2	no	—
223	C₂²×C₄	—	4	1	no	—
224	C₂²×C₄	—	94	2	no	—
225	C₂²×C₄	—	94	2	no	—
226	C₂²×C₄	D₄×D₄₇	1	2	yes	—
227	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
228	Q₁₆	—	4	16	no	—
229	C₂×C₈	—	2	4	no	—
230	C₂×C₈	—	2	2	no	—
231	C₂×C₈	—	94	4	no	—
232	C₂×C₈	—	188	4	no	—
233	C₄⋊C₄	—	2	4	no	—
234	C₄⋊C₄	—	2	4	no	—
235	C₄⋊C₄	—	2	4	no	—
236	C₄⋊C₄	—	4	2	no	—
237	C₄⋊C₄	—	47	4	no	—
238	C₄⋊C₄	—	94	16	no	—
239	C₄⋊C₄	—	94	4	no	—
240	C₄⋊C₄	—	94	2	no	—
241	C₄⋊C₄	—	94	4	no	—
242	C₄²	—	94	8	no	—
243	C₄²	—	94	4	no	—
244	C₄²	—	94	4	no	—
245	C₄²	D₄×D₄₇	1	2	yes	—
246	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
247	C₄²	C₂³×D₄₇	1	1	yes	characteristic
248	C₂³	#13093992	1	1	yes	characteristic
249	Q₈	—	4	4	no	—
250	Q₈	—	4	4	no	—
251	Q₈	—	8	2	no	—
252	Q₈	—	8	2	no	—
253	Q₈	—	47	8	no	—
254	Q₈	—	94	8	no	—
255	Q₈	—	94	4	no	—
256	Q₈	—	376	8	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	2	4	no	—
259	C₂×C₄	—	4	4	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	8	2	no	—
262	C₂×C₄	—	94	8	no	—
263	C₂×C₄	—	94	4	no	—
264	C₂×C₄	—	94	4	no	—
265	C₂×C₄	—	188	4	no	—
266	C₂×C₄	#13093992	1	1	yes	characteristic
267	C₂×C₄	#13093992	1	2	yes	—
268	C₂×C₄	Q₁₆×D₄₇	1	4	yes	—
269	C₂×C₄	#13094056	1	4	yes	—
270	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
271	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
272	C₈	—	2	4	no	—
273	C₈	—	188	4	no	—
274	C₂²	#15689277	1	4	yes	—
275	C₂²	#15689290	1	2	yes	—
276	C₂²	C₂×#13093992	1	1	yes	characteristic
277	C₄	—	2	1	no	—
278	C₄	—	2	1	no	—
279	C₄	—	4	4	no	—
280	C₄	—	8	2	no	—
281	C₄	—	94	8	no	—
282	C₄	—	188	4	no	—
283	C₄	#15689277	1	4	yes	—
284	C₄	C₂×Q₁₆×D₄₇	1	2	yes	—
285	C₄	C₂×#13094056	1	2	yes	—
286	C₂	#20242526	1	4	yes	direct product factor
287	C₂	C₂×#15689277	1	2	yes	—
288	C₂	C₂×#15689290	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689853

C₂

yes

maximal, characteristic

C₂×#15689415

C₂

yes

maximal

#20242526

C₂

yes

maximal, direct product factor

C₂×#15688872

C₂

yes

maximal, characteristic

C₂×#15688855

C₂

yes

maximal

C₂×C₄₇×#494

C₂

yes

maximal, characteristic

#15689853

—

#15689853

—

#15689853

C₂²

yes

—

C₂×#13094023

—

C₂×#13094022

—

C₂×C₄×Dic₉₄

C₂²

yes

—

C₂×#13093989

—

#15689415

—

#15689415

C₂²

yes

—

C₂×#13093957

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₂×#13093947

—

#15688872

C₂²

yes

—

#15688855

C₂²

yes

—

C₂²×Q₁₆×C₄₇

—

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₄₇×#494

—

C₄₇×#494

C₂²

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂²×Dic₉₄

—

C₂²×Dic₉₄

D₄

yes

—

C₂²×C₄₇⋊C₈

—

—

—

—

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₄×Dic₉₄

D₄

yes

—

C₄×Dic₉₄

C₂³

yes

—

#13093989

—

#13093989

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×Dic₄₇⋊C₄

—

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

—

#13093957

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

C₂³

yes

—

#13093947

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

D₄

yes

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂²×C₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

D₄

yes

—

C₄⋊Q₈×C₄₇

C₂³

yes

—

C₄⋊Q₈×C₄₇

C₂³

yes

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄×C₈×C₄₇

—

C₄×C₈×C₄₇

C₂³

yes

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂×D₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

Q₁₆

yes

complemented

C₂×Dic₉₄

C₂×D₄

yes

—

Q₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂⁴

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂×D₄

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

100

C₄×Dic₄₇

—

101

C₂×C₄₇⋊C₈

—

102

C₂×C₄₇⋊C₈

—

103

C₂³×C₄₇

#120

yes

characteristic

104

Q₈×C₄₇

—

105

Q₈×C₄₇

—

106

Q₈×C₄₇

—

107

Q₈×C₄₇

—

108

C₂×C₄×C₄₇

—

109

C₂×C₄×C₄₇

—

110

C₂×C₄×C₄₇

—

111

C₂×C₄×C₄₇

—

112

C₂×C₄×C₄₇

—

113

C₂×C₄×C₄₇

#120

yes

characteristic

114

C₂×C₄×C₄₇

#120

yes

—

115

C₂×C₄×C₄₇

C₂×Q₁₆

yes

—

116

C₂×C₄×C₄₇

#137

yes

—

117

C₂×C₄×C₄₇

C₂²×D₄

yes

—

118

C₂×C₄×C₄₇

C₂²×D₄

yes

characteristic

119

C₂×Dic₄₇

—

120

C₂×Dic₄₇

—

121

C₂×Dic₄₇

—

122

C₂×Dic₄₇

—

123

Dic₉₄

—

124

Dic₉₄

—

125

Dic₉₄

—

126

Dic₉₄

C₂×Q₁₆

yes

complemented

127

C₈×C₄₇

—

128

C₄₇⋊C₈

—

129

C₂×#1633

—

maximal, Sylow

130

C₂²×C₄₇

#451

yes

—

131

C₂²×C₄₇

#453

yes

—

132

C₂²×C₄₇

C₂×#120

yes

characteristic

133

C₄×C₄₇

—

134

C₄×C₄₇

—

135

C₄×C₄₇

—

136

C₄×C₄₇

—

137

C₄×C₄₇

#451

yes

—

138

C₄×C₄₇

C₂²×Q₁₆

yes

—

139

C₄×C₄₇

C₂×#137

yes

—

140

Dic₄₇

—

141

Dic₄₇

—

142

C₂×Q₈²

—

143

C₂×#494

D₄₇

yes

characteristic

144

C₂×#477

—

145

#1633

—

146

C₂×#333

—

147

C₂×Q₈⋊C₈

—

148

C₂×C₄₇

#1633

yes

complemented

149

C₂×C₄₇

C₂×#451

yes

—

150

C₂×C₄₇

C₂×#453

yes

characteristic

151

C₂²×Q₁₆

—

152

Q₈²

—

153

Q₈²

—

154

Q₈²

—

155

C₂×C₄⋊Q₈

—

156

C₂×C₄⋊Q₈

—

157

C₂×C₄⋊Q₈

C₂×D₄₇

yes

characteristic

158

C₂×C₄⋊Q₈

C₂×D₄₇

yes

characteristic

159

C₂×C₄×Q₈

—

160

C₂×C₄×Q₈

—

161

#494

—

162

#494

C₂×D₄₇

yes

—

163

#477

—

164

#477

—

165

C₂×#107

—

166

C₂×C₄⋊C₈

—

167

C₂×#103

—

168

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

169

#333

—

170

Q₈⋊C₈

—

171

C₄₇

C₂×#1633

yes

characteristic, complemented, Sylow

172

C₂²×Q₈

—

173

C₂²×Q₈

—

174

C₂²×Q₈

—

175

C₂²×Q₈

C₂²⋊D₄₇

yes

—

176

C₂×Q₁₆

—

177

C₂×Q₁₆

—

178

C₂²×C₈

—

179

C₂²×C₈

—

180

C₄⋊Q₈

—

181

C₄⋊Q₈

—

182

C₄⋊Q₈

—

183

C₄⋊Q₈

—

184

C₄⋊Q₈

—

185

C₄⋊Q₈

—

186

C₄⋊Q₈

—

187

C₄⋊Q₈

C₂²⋊D₄₇

yes

—

188

C₄⋊Q₈

C₂²×D₄₇

yes

—

189

C₄⋊Q₈

C₂²×D₄₇

yes

—

190

C₄×Q₈

—

191

C₄×Q₈

—

192

C₄×Q₈

—

193

C₄×Q₈

—

194

C₄×Q₈

—

195

C₄×Q₈

—

196

C₂×C₄⋊C₄

—

197

C₂×C₄⋊C₄

—

198

C₂×C₄⋊C₄

—

199

C₂×C₄⋊C₄

—

200

C₂×C₄⋊C₄

—

201

C₂×C₄²

—

202

C₂×C₄²

—

203

C₂×C₄²

C₂²×D₄₇

yes

characteristic

204

#107

—

205

C₄⋊C₈

—

206

C₄⋊C₈

—

207

#103

—

208

C₄×C₈

—

209

C₄×C₈

C₂²×D₄₇

yes

—

210

C₂×Q₈

—

211

C₂×Q₈

—

212

C₂×Q₈

—

213

C₂×Q₈

—

214

C₂×Q₈

—

215

C₂×Q₈

—

216

C₂×Q₈

—

217

C₂×Q₈

—

218

C₂×Q₈

—

219

C₂×Q₈

—

220

C₂×Q₈

—

376

—

221

C₂×Q₈

C₂×C₂²⋊D₄₇

yes

—

222

C₂²×C₄

—

223

C₂²×C₄

—

224

C₂²×C₄

—

225

C₂²×C₄

—

226

C₂²×C₄

D₄×D₄₇

yes

—

227

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

228

Q₁₆

—

229

C₂×C₈

—

230

C₂×C₈

—

231

C₂×C₈

—

232

C₂×C₈

—

188

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

237

C₄⋊C₄

—

238

C₄⋊C₄

—

239

C₄⋊C₄

—

240

C₄⋊C₄

—

241

C₄⋊C₄

—

242

C₄²

—

243

C₄²

—

244

C₄²

—

245

C₄²

D₄×D₄₇

yes

—

246

C₄²

C₂×C₂²⋊D₄₇

yes

characteristic

247

C₄²

C₂³×D₄₇

yes

characteristic

248

C₂³

#13093992

yes

characteristic

249

Q₈

—

250

Q₈

—

251

Q₈

—

252

Q₈

—

253

Q₈

—

254

Q₈

—

255

Q₈

—

256

Q₈

—

376

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

—

264

C₂×C₄

—

265

C₂×C₄

—

188

—

266

C₂×C₄

#13093992

yes

characteristic

267

C₂×C₄

#13093992

yes

—

268

C₂×C₄

Q₁₆×D₄₇

yes

—

269

C₂×C₄

#13094056

yes

—

270

C₂×C₄

C₂×D₄×D₄₇

yes

—

271

C₂×C₄

C₂²×C₂²⋊D₄₇

yes

characteristic

272

C₈

—

273

C₈

—

188

—

274

C₂²

#15689277

yes

—

275

C₂²

#15689290

yes

—

276

C₂²

C₂×#13093992

yes

characteristic

277

C₄

—

278

C₄

—

279

C₄

—

280

C₄

—

281

C₄

—

282

C₄

—

188

—

283

C₄

#15689277

yes

—

284

C₄

C₂×Q₁₆×D₄₇

yes

—

285

C₄

C₂×#13094056

yes

—

286

C₂

#20242526

yes

direct product factor

287

C₂

C₂×#15689277

yes

—

288

C₂

C₂×#15689290

yes

characteristic

	subgroup	G/H
center	C₂³	#13093992
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#494	C₂
socle, prime radical	C₂³×C₄₇	#120
hypercenter	C₂×#494	D₄₇
hypocenter	C₄₇	C₂×#1633
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

subgroup

G/H

center

C₂³

#13093992

commutator, cosocle

C₄²×C₄₇

C₂⁴

Frattini

C₄²

C₂³×D₄₇

Fitting

C₂×C₄₇×#494

C₂

C₂³×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

N	H ≅ G/N	type
3. #20242526	C₂	direct (N × H)
81. C₂×Dic₉₄	Q₁₆	semidirect
126. Dic₉₄	C₂×Q₁₆	semidirect
148. C₂×C₄₇	#1633	semidirect
171. C₄₇	C₂×#1633	semidirect
286. C₂	#20242526	direct (N × H)

H ≅ G/N

type

3. #20242526

C₂

direct (N × H)

81. C₂×Dic₉₄

Q₁₆

semidirect

126. Dic₉₄

C₂×Q₁₆

semidirect

148. C₂×C₄₇

#1633

semidirect

171. C₄₇

C₂×#1633

semidirect

286. C₂

#20242526

direct (N × H)

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

subgroup	index
C₂×#15689853	2
C₂×#15689415	2
#20242526	2
C₂×#15688872	2
C₂×#15688855	2
C₂×C₄₇×#494	2
C₂×#1633	47

subgroup

index

C₂×C₄₇×#494

Subgroups — C₂×#20242526 #26192152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#20242526 #26192152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242526 #26192152