Subgroups — C₂×C₄×#6553 #14260399

Order 1792.

12378 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6553	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#90518	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#6553	C₂	1	32	yes	maximal, direct product factor
5	C₂×#90265	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×#1161	C₂	1	2	yes	maximal, complemented
7	C₂×#90236	C₂	1	6	yes	maximal, complemented
8	C₂×C₄×D₄×D₇	C₂	1	6	yes	maximal, complemented
9	C₂×#90214	C₂	1	3	yes	maximal, complemented
10	C₂×#90212	C₂	1	3	yes	maximal, complemented
11	C₂²×C₄×D₂₈	C₂	1	3	yes	maximal, complemented
12	C₂×C₄×#1157	C₂	1	3	yes	maximal, complemented
13	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
14	C₂×#6553	C₄	1	32	yes	direct product factor
15	C₂×#6553	C₂²	1	16	yes	—
16	C₂²×#1161	C₂²	1	2	yes	—
17	C₂²×D₄×D₇	C₂²	1	6	yes	—
18	C₂²×#1157	C₂²	1	3	yes	—
19	C₂³×D₂₈	C₂²	1	3	yes	—
20	C₂³×C₄×D₇	C₂²	1	6	yes	complemented
21	C₄×C₇×#41	C₂²	1	16	yes	complemented
22	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄×C₇×D₄	C₂²	1	3	yes	complemented
25	C₂×C₄×C₇×D₄	C₂²	1	3	yes	complemented
26	C₂×C₇×#117	C₂²	1	3	yes	complemented
27	C₂²×C₄²×C₇	C₂²	1	3	yes	complemented
28	#90518	C₂²	1	16	yes	complemented
29	C₂×Q₈×Dic₇	C₂²	1	2	yes	complemented
30	C₂×D₄×Dic₇	C₂²	1	6	yes	complemented
31	C₂×C₄×C₂²⋊D₇	C₂²	1	6	yes	complemented
32	C₂×C₄×C₂²⋊D₇	C₂²	1	6	yes	complemented
33	C₂²×(C₂×D₇)⋊C₄	C₂²	1	6	yes	complemented
34	C₂×#6489	C₂²	1	3	yes	complemented
35	C₂²×C₄⋊Dic₇	C₂²	1	3	yes	complemented
36	#90265	C₂²	1	32	yes	complemented
37	C₄×#1161	C₂²	1	32	yes	complemented
38	#90236	C₂²	1	96	yes	complemented
39	C₄×D₄×D₇	C₂²	1	96	yes	complemented
40	#90214	C₂²	1	48	yes	complemented
41	#90212	C₂²	1	48	yes	complemented
42	C₂×#6456	C₂²	1	6	yes	complemented
43	C₂×#6456	C₂²	1	6	yes	complemented
44	C₂×#6455	C₂²	1	6	yes	complemented
45	C₂×D₇×C₄⋊C₄	C₂²	1	6	yes	complemented
46	C₂×(C₂²⋊D₇)⋊C₄	C₂²	1	12	yes	complemented
47	C₂×D₇×C₂²⋊C₄	C₂²	1	12	yes	complemented
48	C₄×#1157	C₂²	1	48	yes	complemented
49	C₂×C₄×D₂₈	C₂²	1	3	yes	complemented
50	C₂×C₄×D₂₈	C₂²	1	3	yes	complemented
51	C₂×C₄×D₂₈	C₂²	1	6	yes	complemented
52	C₂×C₄×D₂₈	C₂²	1	6	yes	complemented
53	C₂×C₄×D₂₈	C₂²	1	6	yes	complemented
54	C₂×C₄×D₂₈	C₂²	1	48	yes	complemented
55	C₂×#6435	C₂²	1	6	yes	complemented
56	C₂×C₄²×D₇	C₂²	1	6	yes	complemented
57	C₂×C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×Dic₁₄	C₂²	1	3	yes	complemented
59	C₂×C₄×H(5,𝔽₂)	—	7	1	no	maximal, Sylow
60	C₂⁴×D₇	C₂³	1	6	yes	—
61	C₂×C₇×#41	C₂×C₄	1	16	yes	complemented
62	C₂×C₇×#41	C₂³	1	8	yes	—
63	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇×D₄	C₂³	1	3	yes	—
65	C₂³×C₄×C₇	C₂³	1	3	yes	—
66	C₂³×C₄×C₇	C₂³	1	3	yes	—
67	C₂³×C₄×C₇	C₂³	1	3	yes	—
68	C₂²×C₂²⋊D₇	C₂³	1	6	yes	—
69	C₂³×Dic₇	C₂³	1	6	yes	—
70	#6553	C₂×C₄	1	256	yes	direct product factor
71	C₂×#1161	C₂×C₄	1	32	yes	complemented
72	C₂×#1161	C₂³	1	16	yes	—
73	C₂×D₄×D₇	C₂×C₄	1	96	yes	complemented
74	C₂×D₄×D₇	C₂³	1	48	yes	—
75	C₂×#1157	C₂×C₄	1	48	yes	complemented
76	C₂×#1157	C₂³	1	24	yes	—
77	C₂²×D₂₈	C₂×C₄	1	48	yes	complemented
78	C₂²×D₂₈	C₂³	1	3	yes	—
79	C₂²×D₂₈	C₂³	1	6	yes	—
80	C₂²×D₂₈	C₂³	1	24	yes	—
81	C₂²×C₄×D₇	—	4	24	no	—
82	C₂²×C₄×D₇	C₂³	1	6	yes	—
83	C₂²×C₄×D₇	C₂³	1	6	yes	—
84	C₂²×C₄×D₇	C₂³	1	12	yes	—
85	C₂²×C₄×D₇	C₂³	1	6	yes	—
86	C₂²×C₄×D₇	C₂³	1	48	yes	complemented
87	C₂²×Dic₁₄	C₂³	1	1	yes	characteristic
88	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
89	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
90	C₄×C₇×D₄	C₂³	1	24	yes	complemented
91	C₄×C₇×D₄	C₂³	1	24	yes	complemented
92	C₇×#117	C₂³	1	24	yes	complemented
93	C₂×C₇×C₄⋊C₄	C₂³	1	3	yes	—
94	C₂×C₇×C₄⋊C₄	C₂³	1	3	yes	—
95	C₂×C₇×C₂²⋊C₄	C₂³	1	6	yes	—
96	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇	C₂³	1	3	yes	—
98	C₂×C₄²×C₇	C₂³	1	3	yes	—
99	C₂×C₄²×C₇	C₂³	1	3	yes	—
100	C₂×C₄²×C₇	C₂³	1	24	yes	complemented
101	C₂×C₂²⋊Dic₇	C₂³	1	6	yes	—
102	Q₈×Dic₇	C₂³	1	16	yes	complemented
103	D₄×Dic₇	C₂³	1	48	yes	complemented
104	C₄×C₂²⋊D₇	C₂³	1	48	yes	complemented
105	C₄×C₂²⋊D₇	C₂³	1	48	yes	complemented
106	C₂×(C₂×D₇)⋊C₄	C₂³	1	6	yes	—
107	C₂×(C₂×D₇)⋊C₄	C₂³	1	6	yes	—
108	C₂×(C₂×D₇)⋊C₄	C₂³	1	12	yes	—
109	C₂×(C₂×D₇)⋊C₄	C₂³	1	48	yes	complemented
110	#6489	C₂³	1	24	yes	complemented
111	C₂×C₄⋊Dic₇	C₂³	1	3	yes	—
112	C₂×C₄⋊Dic₇	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊Dic₇	C₂³	1	6	yes	—
114	C₂×C₄⋊Dic₇	C₂³	1	24	yes	complemented
115	C₂×Dic₇⋊C₄	C₂³	1	2	yes	—
116	C₂×Dic₇⋊C₄	C₂³	1	6	yes	—
117	C₂×C₄×Dic₇	C₂³	1	2	yes	—
118	C₂×C₄×Dic₇	C₂³	1	6	yes	—
119	C₂×C₄×Dic₇	C₂³	1	6	yes	—
120	#6456	C₂³	1	48	yes	complemented
121	#6456	C₂³	1	48	yes	complemented
122	#6455	C₂³	1	48	yes	complemented
123	D₇×C₄⋊C₄	C₂³	1	48	yes	complemented
124	(C₂²⋊D₇)⋊C₄	C₂³	1	96	yes	complemented
125	D₇×C₂²⋊C₄	C₂³	1	96	yes	complemented
126	C₄×D₂₈	C₂³	1	24	yes	complemented
127	C₄×D₂₈	C₂³	1	48	yes	complemented
128	C₄×D₂₈	C₂³	1	48	yes	complemented
129	C₄×D₂₈	C₂³	1	48	yes	complemented
130	C₄×D₂₈	C₂³	1	24	yes	complemented
131	#6435	C₂³	1	48	yes	complemented
132	C₄²×D₇	C₂³	1	48	yes	complemented
133	C₄×Dic₁₄	C₂³	1	8	yes	complemented
134	C₄×Dic₁₄	C₂³	1	24	yes	complemented
135	C₂²×H(5,𝔽₂)	—	7	1	no	—
136	C₄×H(5,𝔽₂)	—	7	32	no	—
137	C₂×#520	—	7	1	no	—
138	C₂×#520	—	7	2	no	—
139	C₂×#520	—	7	3	no	—
140	C₂×#518	—	7	6	no	—
141	C₂×#518	—	7	3	no	—
142	C₂×C₄×#41	—	7	3	no	—
143	C₂×C₄×#41	—	7	2	no	—
144	C₂×C₄×#41	D₇	1	1	yes	characteristic, complemented
145	C₂²×C₄×D₄	—	7	3	no	—
146	C₂²×C₄×D₄	—	7	6	no	—
147	C₂⁴×C₇	C₂⁴	1	3	yes	—
148	C₂³×D₇	—	4	12	no	—
149	C₂³×D₇	—	4	12	no	—
150	C₂³×D₇	C₂²×C₄	1	48	yes	complemented
151	C₂³×D₇	C₂⁴	1	6	yes	—
152	C₂³×D₇	C₂⁴	1	24	yes	—
153	C₇×#41	C₂²×C₄	1	64	yes	complemented
154	C₂×C₇×Q₈	C₂²×C₄	1	8	yes	complemented
155	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
156	C₂×C₇×D₄	C₂²×C₄	1	24	yes	complemented
157	C₂×C₇×D₄	C₂⁴	1	12	yes	—
158	C₂²×C₄×C₇	—	2	12	no	—
159	C₂²×C₄×C₇	—	4	6	no	—
160	C₂²×C₄×C₇	C₂²×C₄	1	24	yes	complemented
161	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
162	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
164	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
165	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
166	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
167	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
169	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
170	C₂×C₂²⋊D₇	C₂²×C₄	1	48	yes	complemented
171	C₂×C₂²⋊D₇	C₂⁴	1	24	yes	—
172	C₂²×Dic₇	—	4	12	no	—
173	C₂²×Dic₇	C₂⁴	1	2	yes	—
174	C₂²×Dic₇	C₂⁴	1	6	yes	—
175	C₂²×Dic₇	C₂⁴	1	24	yes	—
176	C₂²×Dic₇	C₂⁴	1	2	yes	—
177	#1161	C₂²×C₄	1	128	yes	complemented
178	D₄×D₇	C₂²×C₄	1	384	yes	complemented
179	#1157	C₂²×C₄	1	192	yes	complemented
180	C₂×D₂₈	C₂²×C₄	1	24	yes	complemented
181	C₂×D₂₈	C₂²×C₄	1	48	yes	complemented
182	C₂×D₂₈	C₂²×C₄	1	192	yes	complemented
183	C₂×D₂₈	C₂⁴	1	12	yes	—
184	C₂×D₂₈	C₂⁴	1	24	yes	—
185	C₂×C₄×D₇	—	2	24	no	—
186	C₂×C₄×D₇	—	4	96	no	—
187	C₂×C₄×D₇	—	4	24	no	—
188	C₂×C₄×D₇	—	4	12	no	—
189	C₂×C₄×D₇	C₂²×C₄	1	48	yes	complemented
190	C₂×C₄×D₇	C₂⁴	1	24	yes	—
191	C₂×C₄×D₇	C₂⁴	1	24	yes	—
192	C₂×C₄×D₇	C₂⁴	1	48	yes	—
193	C₂×C₄×D₇	C₂⁴	1	24	yes	—
194	C₂×Dic₁₄	C₂²×C₄	1	8	yes	complemented
195	C₂×Dic₁₄	C₂⁴	1	4	yes	—
196	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
197	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
198	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
199	C₄²×C₇	C₂⁴	1	4	yes	—
200	C₄²×C₇	C₂⁴	1	12	yes	—
201	C₄²×C₇	C₂⁴	1	12	yes	—
202	C₄²×C₇	C₂⁴	1	12	yes	—
203	C₂²⋊Dic₇	C₂⁴	1	24	yes	—
204	(C₂×D₇)⋊C₄	C₂⁴	1	24	yes	—
205	(C₂×D₇)⋊C₄	C₂⁴	1	24	yes	—
206	(C₂×D₇)⋊C₄	C₂⁴	1	48	yes	—
207	C₄⋊Dic₇	C₂⁴	1	12	yes	—
208	C₄⋊Dic₇	C₂⁴	1	4	yes	—
209	C₄⋊Dic₇	C₂⁴	1	24	yes	—
210	Dic₇⋊C₄	C₂⁴	1	8	yes	—
211	Dic₇⋊C₄	C₂⁴	1	24	yes	—
212	C₄×Dic₇	C₂⁴	1	8	yes	—
213	C₄×Dic₇	C₂⁴	1	24	yes	—
214	C₄×Dic₇	C₂⁴	1	24	yes	—
215	C₂×H(5,𝔽₂)	—	7	32	no	—
216	C₂×H(5,𝔽₂)	—	7	16	no	—
217	C₂²×#41	—	7	2	no	—
218	C₂²×#41	—	7	3	no	—
219	C₂²×#41	C₂×D₇	1	1	yes	characteristic
220	C₂³×D₄	—	7	6	no	—
221	C₂³×D₄	—	7	3	no	—
222	C₂⁴×C₄	—	7	6	no	—
223	#520	—	7	16	no	—
224	#520	—	7	32	no	—
225	#520	—	7	48	no	—
226	#518	—	7	96	no	—
227	#518	—	7	48	no	—
228	C₄×#41	—	7	32	no	—
229	C₄×#41	—	7	48	no	—
230	C₄×#41	C₂×D₇	1	16	yes	complemented
231	C₂×C₄×Q₈	—	7	2	no	—
232	C₂×C₄×Q₈	—	7	1	no	—
233	C₂×C₄×Q₈	—	7	3	no	—
234	C₂×C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
235	C₂×C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
236	C₂×C₄×D₄	—	7	6	no	—
237	C₂×C₄×D₄	—	7	6	no	—
238	C₂×C₄×D₄	—	7	6	no	—
239	C₂×C₄×D₄	—	7	96	no	—
240	C₂×C₄×D₄	—	7	6	no	—
241	C₂×C₄×D₄	—	7	6	no	—
242	C₂×C₄×D₄	—	7	12	no	—
243	C₂×C₄×D₄	—	7	3	no	—
244	C₂×C₄×D₄	—	7	6	no	—
245	C₂×C₄×D₄	—	7	6	no	—
246	C₂×C₄×D₄	—	7	6	no	—
247	C₂×C₄×D₄	—	7	3	no	—
248	C₂×C₄×D₄	—	7	48	no	—
249	C₂×C₄×D₄	C₂×D₇	1	3	yes	complemented
250	C₂×C₄×D₄	C₂×D₇	1	3	yes	complemented
251	C₂×#117	—	7	3	no	—
252	C₂×#117	—	7	6	no	—
253	C₂×#117	—	7	6	no	—
254	C₂×#117	C₂×D₇	1	3	yes	complemented
255	C₂²×C₄⋊C₄	—	7	3	no	—
256	C₂²×C₄⋊C₄	—	7	6	no	—
257	C₂²×C₂²⋊C₄	—	7	6	no	—
258	C₂²×C₂²⋊C₄	—	7	12	no	—
259	C₂²×C₄²	—	7	6	no	—
260	C₂²×C₄²	C₂×D₇	1	3	yes	complemented
261	C₂³×C₇	—	2	6	no	—
262	C₂³×C₇	—	2	6	no	—
263	C₂³×C₇	C₂³×C₄	1	12	yes	—
264	C₂³×C₇	C₂⁵	1	6	yes	—
265	C₂³×C₇	C₂⁵	1	1	yes	characteristic
266	C₂²×D₇	—	2	12	no	—
267	C₂²×D₇	—	2	12	no	—
268	C₂²×D₇	—	4	24	no	—
269	C₂²×D₇	—	4	96	no	—
270	C₂²×D₇	—	4	24	no	—
271	C₂²×D₇	C₂³×C₄	1	24	yes	—
272	C₂²×D₇	C₂³×C₄	1	96	yes	complemented
273	C₂²×D₇	C₂⁵	1	12	yes	—
274	C₇×Q₈	C₂³×C₄	1	16	yes	complemented
275	C₇×D₄	C₂³×C₄	1	48	yes	complemented
276	C₂×C₄×C₇	—	2	6	no	—
277	C₂×C₄×C₇	—	2	6	no	—
278	C₂×C₄×C₇	—	2	2	no	—
279	C₂×C₄×C₇	—	2	24	no	—
280	C₂×C₄×C₇	—	4	12	no	—
281	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
282	C₂×C₄×C₇	C₂³×C₄	1	12	yes	—
283	C₂×C₄×C₇	C₂³×C₄	1	48	yes	complemented
284	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	complemented
285	C₂×C₄×C₇	C₂⁵	1	6	yes	—
286	C₂×C₄×C₇	C₂⁵	1	2	yes	—
287	C₂×C₄×C₇	C₂⁵	1	6	yes	—
288	C₂×C₄×C₇	C₂⁵	1	6	yes	—
289	C₂×C₄×C₇	C₂⁵	1	2	yes	—
290	C₂×C₄×C₇	C₂⁵	1	2	yes	—
291	C₂²⋊D₇	C₂³×C₄	1	96	yes	complemented
292	C₂×Dic₇	—	2	12	no	—
293	C₂×Dic₇	—	2	4	no	—
294	C₂×Dic₇	—	4	24	no	—
295	C₂×Dic₇	C₂³×C₄	1	8	yes	—
296	C₂×Dic₇	C₂⁵	1	4	yes	—
297	C₂×Dic₇	C₂⁵	1	12	yes	—
298	C₂×Dic₇	C₂⁵	1	4	yes	—
299	D₂₈	C₂³×C₄	1	48	yes	complemented
300	D₂₈	C₂³×C₄	1	96	yes	complemented
301	C₄×D₇	—	2	48	no	—
302	C₄×D₇	—	4	48	no	—
303	C₄×D₇	—	4	24	no	—
304	C₄×D₇	C₂³×C₄	1	96	yes	complemented
305	Dic₁₄	C₂³×C₄	1	16	yes	complemented
306	C₂⁵	—	7	6	no	—
307	H(5,𝔽₂)	—	7	256	no	—
308	C₂×#41	—	7	32	no	—
309	C₂×#41	—	7	16	no	—
310	C₂×#41	—	7	48	no	—
311	C₂×#41	—	7	24	no	—
312	C₂×#41	C₄×D₇	1	16	yes	complemented
313	C₂×#41	C₂²×D₇	1	8	yes	—
314	C₂²×Q₈	—	7	1	no	—
315	C₂²×Q₈	C₂²×D₇	1	1	yes	characteristic
316	C₂²×D₄	—	7	6	no	—
317	C₂²×D₄	—	7	96	no	—
318	C₂²×D₄	—	7	48	no	—
319	C₂²×D₄	—	7	48	no	—
320	C₂²×D₄	—	7	6	no	—
321	C₂²×D₄	—	7	3	no	—
322	C₂²×D₄	—	7	24	no	—
323	C₂²×D₄	C₂²×D₇	1	3	yes	—
324	C₂³×C₄	—	7	6	no	—
325	C₂³×C₄	—	7	6	no	—
326	C₂³×C₄	—	7	6	no	—
327	C₂³×C₄	—	7	6	no	—
328	C₂³×C₄	—	7	12	no	—
329	C₂³×C₄	—	7	48	no	—
330	C₂³×C₄	—	28	24	no	—
331	C₂³×C₄	C₂²×D₇	1	3	yes	—
332	C₂³×C₄	C₂²×D₇	1	3	yes	—
333	C₂³×C₄	C₂²×D₇	1	3	yes	—
334	C₄×Q₈	—	7	16	no	—
335	C₄×Q₈	—	7	8	no	—
336	C₄×Q₈	—	7	24	no	—
337	C₄×Q₈	C₂²×D₇	1	8	yes	complemented
338	C₄×Q₈	C₂²×D₇	1	8	yes	complemented
339	C₄×D₄	—	7	48	no	—
340	C₄×D₄	—	7	48	no	—
341	C₄×D₄	—	7	48	no	—
342	C₄×D₄	—	7	48	no	—
343	C₄×D₄	—	7	48	no	—
344	C₄×D₄	—	7	96	no	—
345	C₄×D₄	—	7	48	no	—
346	C₄×D₄	—	7	24	no	—
347	C₄×D₄	—	7	48	no	—
348	C₄×D₄	—	7	48	no	—
349	C₄×D₄	—	7	24	no	—
350	C₄×D₄	C₂²×D₇	1	24	yes	complemented
351	C₄×D₄	C₂²×D₇	1	24	yes	complemented
352	#117	—	7	24	no	—
353	#117	—	7	48	no	—
354	#117	—	7	48	no	—
355	#117	C₂²×D₇	1	24	yes	complemented
356	C₂×C₄⋊C₄	—	7	6	no	—
357	C₂×C₄⋊C₄	—	7	6	no	—
358	C₂×C₄⋊C₄	—	7	3	no	—
359	C₂×C₄⋊C₄	—	7	24	no	—
360	C₂×C₄⋊C₄	—	7	2	no	—
361	C₂×C₄⋊C₄	—	7	1	no	—
362	C₂×C₄⋊C₄	—	7	48	no	—
363	C₂×C₄⋊C₄	C₂²×D₇	1	3	yes	—
364	C₂×C₄⋊C₄	C₂²×D₇	1	3	yes	—
365	C₂×C₂²⋊C₄	—	7	6	no	—
366	C₂×C₂²⋊C₄	—	7	6	no	—
367	C₂×C₂²⋊C₄	—	7	12	no	—
368	C₂×C₂²⋊C₄	—	7	6	no	—
369	C₂×C₂²⋊C₄	—	7	48	no	—
370	C₂×C₂²⋊C₄	—	7	96	no	—
371	C₂×C₂²⋊C₄	C₂²×D₇	1	6	yes	—
372	C₂×C₄²	—	7	6	no	—
373	C₂×C₄²	—	7	6	no	—
374	C₂×C₄²	—	7	2	no	—
375	C₂×C₄²	—	7	48	no	—
376	C₂×C₄²	C₂²×D₇	1	3	yes	—
377	C₂×C₄²	C₂²×D₇	1	3	yes	—
378	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
379	C₂×C₄²	C₂²×D₇	1	3	yes	—
380	C₂×C₄²	C₂²×D₇	1	24	yes	complemented
381	C₂²×C₇	—	2	6	no	—
382	C₂²×C₇	—	2	6	no	—
383	C₂²×C₇	—	2	24	no	—
384	C₂²×C₇	C₂⁴×C₄	1	12	yes	—
385	C₂²×C₇	C₂⁴×C₄	1	2	yes	—
386	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
387	C₂²×C₇	#585	1	2	yes	—
388	C₂²×C₇	C₂⁶	1	1	yes	characteristic
389	C₂×D₇	—	2	12	no	—
390	C₂×D₇	—	2	12	no	—
391	C₂×D₇	—	2	48	no	—
392	C₂×D₇	—	4	96	no	—
393	C₂×D₇	C₂⁴×C₄	1	24	yes	—
394	C₄×C₇	—	2	6	no	—
395	C₄×C₇	—	2	6	no	—
396	C₄×C₇	—	2	2	no	—
397	C₄×C₇	C₂⁴×C₄	1	4	yes	—
398	C₄×C₇	C₂⁴×C₄	1	12	yes	—
399	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	complemented
400	Dic₇	—	2	12	no	—
401	Dic₇	—	2	4	no	—
402	Dic₇	C₂⁴×C₄	1	8	yes	—
403	C₂⁴	—	7	6	no	—
404	C₂⁴	—	7	48	no	—
405	C₂⁴	—	7	24	no	—
406	C₂⁴	—	28	12	no	—
407	C₂⁴	—	28	12	no	—
408	C₂⁴	C₂³×D₇	1	3	yes	—
409	#41	—	7	128	no	—
410	#41	—	7	192	no	—
411	#41	C₂×C₄×D₇	1	64	yes	complemented
412	C₂×Q₈	—	7	8	no	—
413	C₂×Q₈	—	7	4	no	—
414	C₂×Q₈	C₂×C₄×D₇	1	8	yes	complemented
415	C₂×Q₈	C₂³×D₇	1	4	yes	—
416	C₂×D₄	—	7	48	no	—
417	C₂×D₄	—	7	24	no	—
418	C₂×D₄	—	7	384	no	—
419	C₂×D₄	—	7	48	no	—
420	C₂×D₄	—	7	24	no	—
421	C₂×D₄	—	7	192	no	—
422	C₂×D₄	—	7	24	no	—
423	C₂×D₄	—	7	12	no	—
424	C₂×D₄	C₂×C₄×D₇	1	24	yes	complemented
425	C₂×D₄	C₂³×D₇	1	12	yes	—
426	C₂²×C₄	—	2	12	no	—
427	C₂²×C₄	—	4	6	no	—
428	C₂²×C₄	—	7	2	no	—
429	C₂²×C₄	—	7	48	no	—
430	C₂²×C₄	—	7	24	no	—
431	C₂²×C₄	—	7	2	no	—
432	C₂²×C₄	—	7	6	no	—
433	C₂²×C₄	—	7	24	no	—
434	C₂²×C₄	—	7	24	no	—
435	C₂²×C₄	—	7	24	no	—
436	C₂²×C₄	—	7	48	no	—
437	C₂²×C₄	—	14	24	no	—
438	C₂²×C₄	—	28	96	no	—
439	C₂²×C₄	—	28	12	no	—
440	C₂²×C₄	—	28	24	no	—
441	C₂²×C₄	—	28	12	no	—
442	C₂²×C₄	C₂×C₄×D₇	1	24	yes	complemented
443	C₂²×C₄	C₂³×D₇	1	3	yes	—
444	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
445	C₂²×C₄	C₂³×D₇	1	3	yes	—
446	C₂²×C₄	C₂³×D₇	1	12	yes	—
447	C₂²×C₄	C₂³×D₇	1	12	yes	—
448	C₂²×C₄	C₂³×D₇	1	3	yes	—
449	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
450	C₂²×C₄	C₂³×D₇	1	12	yes	—
451	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
452	C₄⋊C₄	—	7	24	no	—
453	C₄⋊C₄	—	7	8	no	—
454	C₄⋊C₄	—	7	24	no	—
455	C₄⋊C₄	—	7	12	no	—
456	C₄⋊C₄	—	7	4	no	—
457	C₄⋊C₄	C₂³×D₇	1	12	yes	—
458	C₄⋊C₄	C₂³×D₇	1	12	yes	—
459	C₂²⋊C₄	—	7	24	no	—
460	C₂²⋊C₄	—	7	24	no	—
461	C₂²⋊C₄	—	7	48	no	—
462	C₂²⋊C₄	—	7	24	no	—
463	C₂²⋊C₄	C₂³×D₇	1	24	yes	—
464	C₄²	—	7	8	no	—
465	C₄²	—	7	24	no	—
466	C₄²	—	7	24	no	—
467	C₄²	C₂³×D₇	1	12	yes	—
468	C₄²	C₂³×D₇	1	4	yes	—
469	C₄²	C₂³×D₇	1	12	yes	—
470	C₄²	C₂³×D₇	1	12	yes	—
471	C₂×C₇	—	2	12	no	—
472	C₂×C₇	C₄×H(5,𝔽₂)	1	4	yes	complemented
473	C₂×C₇	C₂⁵×C₄	1	1	yes	characteristic
474	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
475	C₂×C₇	C₂×#585	1	1	yes	characteristic
476	D₇	—	2	24	no	—
477	C₂³	—	2	6	no	—
478	C₂³	—	2	6	no	—
479	C₂³	—	7	12	no	—
480	C₂³	—	7	24	no	—
481	C₂³	—	7	96	no	—
482	C₂³	—	14	12	no	—
483	C₂³	—	14	12	no	—
484	C₂³	—	28	24	no	—
485	C₂³	—	28	24	no	—
486	C₂³	—	28	96	no	—
487	C₂³	C₂²×C₄×D₇	1	12	yes	—
488	C₂³	C₂⁴×D₇	1	6	yes	—
489	C₂³	C₂⁴×D₇	1	1	yes	characteristic
490	Q₈	—	7	16	no	—
491	Q₈	C₂²×C₄×D₇	1	16	yes	complemented
492	D₄	—	7	96	no	—
493	D₄	—	7	96	no	—
494	D₄	—	7	48	no	—
495	D₄	C₂²×C₄×D₇	1	48	yes	complemented
496	C₂×C₄	—	2	6	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	6	no	—
499	C₂×C₄	—	2	24	no	—
500	C₂×C₄	—	4	12	no	—
501	C₂×C₄	—	7	4	no	—
502	C₂×C₄	—	7	8	no	—
503	C₂×C₄	—	7	96	no	—
504	C₂×C₄	—	7	4	no	—
505	C₂×C₄	—	7	12	no	—
506	C₂×C₄	—	14	12	no	—
507	C₂×C₄	—	14	4	no	—
508	C₂×C₄	—	14	48	no	—
509	C₂×C₄	—	28	24	no	—
510	C₂×C₄	—	28	48	no	—
511	C₂×C₄	—	28	24	no	—
512	C₂×C₄	C₂²×C₄×D₇	1	12	yes	—
513	C₂×C₄	C₂²×C₄×D₇	1	4	yes	—
514	C₂×C₄	C₂²×C₄×D₇	1	48	yes	complemented
515	C₂×C₄	#6553	1	4	yes	direct product factor
516	C₂×C₄	C₂⁴×D₇	1	6	yes	—
517	C₂×C₄	C₂⁴×D₇	1	2	yes	—
518	C₂×C₄	C₂⁴×D₇	1	6	yes	—
519	C₂×C₄	C₂⁴×D₇	1	6	yes	—
520	C₂×C₄	C₂⁴×D₇	1	2	yes	—
521	C₂×C₄	C₂⁴×D₇	1	2	yes	—
522	C₇	C₂×C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
523	C₂²	—	2	6	no	—
524	C₂²	—	2	6	no	—
525	C₂²	—	2	24	no	—
526	C₂²	—	7	24	no	—
527	C₂²	—	14	12	no	—
528	C₂²	—	14	12	no	—
529	C₂²	—	14	48	no	—
530	C₂²	—	28	96	no	—
531	C₂²	C₂³×C₄×D₇	1	12	yes	—
532	C₂²	C₂³×C₄×D₇	1	2	yes	—
533	C₂²	C₂×#6553	1	2	yes	—
534	C₂²	#90616	1	2	yes	—
535	C₂²	C₂⁵×D₇	1	1	yes	characteristic
536	C₄	—	2	6	no	—
537	C₄	—	2	2	no	—
538	C₄	—	2	6	no	—
539	C₄	—	7	8	no	—
540	C₄	—	14	12	no	—
541	C₄	—	14	4	no	—
542	C₄	C₂³×C₄×D₇	1	12	yes	—
543	C₄	C₂³×C₄×D₇	1	4	yes	—
544	C₄	C₂×#6553	1	4	yes	direct product factor
545	C₂	—	2	12	no	—
546	C₂	—	14	24	no	—
547	C₂	C₄×#6553	1	4	yes	direct product factor
548	C₂	C₂⁴×C₄×D₇	1	1	yes	characteristic
549	C₂	C₂²×#6553	1	1	yes	characteristic
550	C₂	C₂×#90616	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₇
commutator	C₂×C₇	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₇
Fitting	C₂×C₄×C₇×#41	C₂
socle	C₂³×C₇	C₂⁵
prime radical	C₂²×#6553	C₂
cosocle	C₂²×C₇	C₂⁶
hypercenter	C₂×C₄×#41	D₇
hypocenter	C₇	C₂×C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₄×C₇×#41	C₂	semidirect
3. C₂×#90518	C₂	semidirect
4. C₄×#6553	C₂	direct (N × H)
5. C₂×#90265	C₂	semidirect
6. C₂×C₄×#1161	C₂	semidirect
7. C₂×#90236	C₂	semidirect
8. C₂×C₄×D₄×D₇	C₂	semidirect
9. C₂×#90214	C₂	semidirect
10. C₂×#90212	C₂	semidirect
11. C₂²×C₄×D₂₈	C₂	semidirect
12. C₂×C₄×#1157	C₂	semidirect
14. C₂×#6553	C₄	direct (N × H)
20. C₂³×C₄×D₇	C₂²	semidirect
21. C₄×C₇×#41	C₂²	semidirect
22. C₂×C₄×C₇×Q₈	C₂²	semidirect
23. C₂×C₄×C₇×Q₈	C₂²	semidirect
24. C₂×C₄×C₇×D₄	C₂²	semidirect
25. C₂×C₄×C₇×D₄	C₂²	semidirect
26. C₂×C₇×#117	C₂²	semidirect
27. C₂²×C₄²×C₇	C₂²	semidirect
28. #90518	C₂²	semidirect
29. C₂×Q₈×Dic₇	C₂²	semidirect
30. C₂×D₄×Dic₇	C₂²	semidirect
31. C₂×C₄×C₂²⋊D₇	C₂²	semidirect
32. C₂×C₄×C₂²⋊D₇	C₂²	semidirect
33. C₂²×(C₂×D₇)⋊C₄	C₂²	semidirect
34. C₂×#6489	C₂²	semidirect
35. C₂²×C₄⋊Dic₇	C₂²	semidirect
36. #90265	C₂²	semidirect
37. C₄×#1161	C₂²	semidirect
38. #90236	C₂²	semidirect
39. C₄×D₄×D₇	C₂²	semidirect
40. #90214	C₂²	semidirect
41. #90212	C₂²	semidirect
42. C₂×#6456	C₂²	semidirect
43. C₂×#6456	C₂²	semidirect
44. C₂×#6455	C₂²	semidirect
45. C₂×D₇×C₄⋊C₄	C₂²	semidirect
46. C₂×(C₂²⋊D₇)⋊C₄	C₂²	semidirect
47. C₂×D₇×C₂²⋊C₄	C₂²	semidirect
48. C₄×#1157	C₂²	semidirect
49. C₂×C₄×D₂₈	C₂²	semidirect
50. C₂×C₄×D₂₈	C₂²	semidirect
51. C₂×C₄×D₂₈	C₂²	semidirect
52. C₂×C₄×D₂₈	C₂²	semidirect
53. C₂×C₄×D₂₈	C₂²	semidirect
54. C₂×C₄×D₂₈	C₂²	semidirect
55. C₂×#6435	C₂²	semidirect
56. C₂×C₄²×D₇	C₂²	semidirect
57. C₂×C₄×Dic₁₄	C₂²	semidirect
58. C₂×C₄×Dic₁₄	C₂²	semidirect
61. C₂×C₇×#41	C₂×C₄	semidirect
70. #6553	C₂×C₄	direct (N × H)
71. C₂×#1161	C₂×C₄	semidirect
73. C₂×D₄×D₇	C₂×C₄	semidirect
75. C₂×#1157	C₂×C₄	semidirect
77. C₂²×D₂₈	C₂×C₄	semidirect
86. C₂²×C₄×D₇	C₂³	semidirect
88. C₄×C₇×Q₈	C₂³	semidirect
89. C₄×C₇×Q₈	C₂³	semidirect
90. C₄×C₇×D₄	C₂³	semidirect
91. C₄×C₇×D₄	C₂³	semidirect
92. C₇×#117	C₂³	semidirect
100. C₂×C₄²×C₇	C₂³	semidirect
102. Q₈×Dic₇	C₂³	semidirect
103. D₄×Dic₇	C₂³	semidirect
104. C₄×C₂²⋊D₇	C₂³	semidirect
105. C₄×C₂²⋊D₇	C₂³	semidirect
109. C₂×(C₂×D₇)⋊C₄	C₂³	semidirect
110. #6489	C₂³	semidirect
114. C₂×C₄⋊Dic₇	C₂³	semidirect
120. #6456	C₂³	semidirect
121. #6456	C₂³	semidirect
122. #6455	C₂³	semidirect
123. D₇×C₄⋊C₄	C₂³	semidirect
124. (C₂²⋊D₇)⋊C₄	C₂³	semidirect
125. D₇×C₂²⋊C₄	C₂³	semidirect
126. C₄×D₂₈	C₂³	semidirect
127. C₄×D₂₈	C₂³	semidirect
128. C₄×D₂₈	C₂³	semidirect
129. C₄×D₂₈	C₂³	semidirect
130. C₄×D₂₈	C₂³	semidirect
131. #6435	C₂³	semidirect
132. C₄²×D₇	C₂³	semidirect
133. C₄×Dic₁₄	C₂³	semidirect
134. C₄×Dic₁₄	C₂³	semidirect
144. C₂×C₄×#41	D₇	semidirect
150. C₂³×D₇	C₂²×C₄	semidirect
153. C₇×#41	C₂²×C₄	semidirect
154. C₂×C₇×Q₈	C₂²×C₄	semidirect
156. C₂×C₇×D₄	C₂²×C₄	semidirect
160. C₂²×C₄×C₇	C₂²×C₄	semidirect
170. C₂×C₂²⋊D₇	C₂²×C₄	semidirect
177. #1161	C₂²×C₄	semidirect
178. D₄×D₇	C₂²×C₄	semidirect
179. #1157	C₂²×C₄	semidirect
180. C₂×D₂₈	C₂²×C₄	semidirect
181. C₂×D₂₈	C₂²×C₄	semidirect
182. C₂×D₂₈	C₂²×C₄	semidirect
189. C₂×C₄×D₇	C₂²×C₄	semidirect
194. C₂×Dic₁₄	C₂²×C₄	semidirect
230. C₄×#41	C₂×D₇	semidirect
234. C₂×C₄×Q₈	C₂×D₇	semidirect
235. C₂×C₄×Q₈	C₂×D₇	semidirect
249. C₂×C₄×D₄	C₂×D₇	semidirect
250. C₂×C₄×D₄	C₂×D₇	semidirect
254. C₂×#117	C₂×D₇	semidirect
260. C₂²×C₄²	C₂×D₇	semidirect
272. C₂²×D₇	C₂³×C₄	semidirect
274. C₇×Q₈	C₂³×C₄	semidirect
275. C₇×D₄	C₂³×C₄	semidirect
283. C₂×C₄×C₇	C₂³×C₄	semidirect
284. C₂×C₄×C₇	H(5,𝔽₂)	semidirect
291. C₂²⋊D₇	C₂³×C₄	semidirect
299. D₂₈	C₂³×C₄	semidirect
300. D₂₈	C₂³×C₄	semidirect
304. C₄×D₇	C₂³×C₄	semidirect
305. Dic₁₄	C₂³×C₄	semidirect
312. C₂×#41	C₄×D₇	semidirect
337. C₄×Q₈	C₂²×D₇	semidirect
338. C₄×Q₈	C₂²×D₇	semidirect
350. C₄×D₄	C₂²×D₇	semidirect
351. C₄×D₄	C₂²×D₇	semidirect
355. #117	C₂²×D₇	semidirect
380. C₂×C₄²	C₂²×D₇	semidirect
399. C₄×C₇	C₂×H(5,𝔽₂)	semidirect
411. #41	C₂×C₄×D₇	semidirect
414. C₂×Q₈	C₂×C₄×D₇	semidirect
424. C₂×D₄	C₂×C₄×D₇	semidirect
442. C₂²×C₄	C₂×C₄×D₇	semidirect
472. C₂×C₇	C₄×H(5,𝔽₂)	semidirect
491. Q₈	C₂²×C₄×D₇	semidirect
495. D₄	C₂²×C₄×D₇	semidirect
514. C₂×C₄	C₂²×C₄×D₇	semidirect
515. C₂×C₄	#6553	direct (N × H)
522. C₇	C₂×C₄×H(5,𝔽₂)	semidirect
544. C₄	C₂×#6553	direct (N × H)
547. C₂	C₄×#6553	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#6553	2
C₂×C₄×C₇×#41	2
C₂×#90518	2
C₄×#6553	2
C₂×#90265	2
C₂×C₄×#1161	2
C₂×#90236	2
C₂×C₄×D₄×D₇	2
C₂×#90214	2
C₂×#90212	2
C₂²×C₄×D₂₈	2
C₂×C₄×#1157	2
C₂×C₄×H(5,𝔽₂)	7

Subgroups — C2×C4×#6553 #14260399

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#6553 #14260399