Subgroups — C₂×C₄×#6548 #14260397

Order 1792.

12378 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6548	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#90489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×C₂²⋊D₇	C₂	1	4	yes	maximal, complemented
5	C₂×#90236	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×D₄×D₇	C₂	1	4	yes	maximal, complemented
7	C₄×#6548	C₂	1	32	yes	maximal, direct product factor
8	C₂×#90237	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×#1159	C₂	1	4	yes	maximal, complemented
10	C₂×#90195	C₂	1	2	yes	maximal, complemented
11	C₂×#90177	C₂	1	4	yes	maximal, complemented
12	C₂×C₄×#1157	C₂	1	2	yes	maximal, complemented
13	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₇	C₂²	1	2	yes	complemented
15	C₂³×C₂²⋊D₇	C₂²	1	4	yes	—
16	C₂×#6548	C₄	1	32	yes	direct product factor
17	C₂×#6548	C₂²	1	16	yes	—
18	C₂²×#1159	C₂²	1	4	yes	—
19	C₂²×D₄×D₇	C₂²	1	4	yes	—
20	C₂²×#1157	C₂²	1	2	yes	—
21	C₂³×C₄×D₇	C₂²	1	4	yes	complemented
22	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
23	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
24	C₂×C₄×C₇×D₄	C₂²	1	16	yes	complemented
25	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
27	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊Dic₇	C₂²	1	4	yes	complemented
29	#90489	C₂²	1	16	yes	complemented
30	C₂×D₄×Dic₇	C₂²	1	4	yes	complemented
31	C₂×D₄×Dic₇	C₂²	1	4	yes	complemented
32	C₂×C₄×C₂²⋊D₇	C₂²	1	4	yes	complemented
33	C₂×C₄×C₂²⋊D₇	C₂²	1	4	yes	complemented
34	C₂×C₄×C₂²⋊D₇	C₂²	1	8	yes	complemented
35	C₂×C₄×C₂²⋊D₇	C₂²	1	8	yes	complemented
36	C₂×C₄×C₂²⋊D₇	C₂²	1	8	yes	complemented
37	C₂×C₄×C₂²⋊D₇	C₂²	1	64	yes	complemented
38	C₂²×(C₂×D₇)⋊C₄	C₂²	1	4	yes	complemented
39	C₂×#6489	C₂²	1	2	yes	complemented
40	C₂²×Dic₇⋊C₄	C₂²	1	4	yes	complemented
41	C₂²×C₄×Dic₇	C₂²	1	4	yes	complemented
42	#90237	C₂²	1	64	yes	complemented
43	#90236	C₂²	1	64	yes	complemented
44	C₄×D₄×D₇	C₂²	1	64	yes	complemented
45	C₄×#1159	C₂²	1	64	yes	complemented
46	#90195	C₂²	1	32	yes	complemented
47	C₂×#6456	C₂²	1	4	yes	complemented
48	C₂×#6455	C₂²	1	4	yes	complemented
49	C₂×D₇×C₄⋊C₄	C₂²	1	4	yes	complemented
50	C₂×#6450	C₂²	1	4	yes	complemented
51	#90177	C₂²	1	64	yes	complemented
52	C₂×(C₂²⋊D₇)⋊C₄	C₂²	1	8	yes	complemented
53	C₂×(C₂²⋊D₇)⋊C₄	C₂²	1	8	yes	complemented
54	C₂×D₇×C₂²⋊C₄	C₂²	1	8	yes	complemented
55	C₂×#6440	C₂²	1	8	yes	complemented
56	C₄×#1157	C₂²	1	32	yes	complemented
57	C₂×C₄×D₂₈	C₂²	1	2	yes	complemented
58	C₂×C₄×D₂₈	C₂²	1	2	yes	complemented
59	C₂×#6435	C₂²	1	4	yes	complemented
60	C₂×C₄²×D₇	C₂²	1	4	yes	complemented
61	C₂×C₄×Dic₁₄	C₂²	1	2	yes	complemented
62	C₂×C₄×Dic₁₄	C₂²	1	2	yes	complemented
63	C₂×C₄×H(5,𝔽₂)	—	7	1	no	maximal, Sylow
64	C₂⁵×C₇	C₂³	1	2	yes	—
65	C₂⁴×D₇	C₂³	1	4	yes	—
66	C₂²×C₇×D₄	C₂×C₄	1	16	yes	complemented
67	C₂²×C₇×D₄	C₂³	1	4	yes	—
68	C₂²×C₇×D₄	C₂³	1	8	yes	—
69	C₂³×C₄×C₇	—	4	8	no	—
70	C₂³×C₄×C₇	C₂³	1	4	yes	—
71	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₇	C₂³	1	4	yes	—
73	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₇	C₂³	1	2	yes	—
75	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₇	C₂³	1	16	yes	complemented
77	C₂²×C₂²⋊D₇	C₂×C₄	1	64	yes	complemented
78	C₂²×C₂²⋊D₇	C₂³	1	8	yes	—
79	C₂²×C₂²⋊D₇	C₂³	1	32	yes	—
80	C₂²×C₂²⋊D₇	C₂³	1	4	yes	—
81	C₂³×Dic₇	C₂³	1	4	yes	—
82	C₂³×Dic₇	C₂³	1	4	yes	—
83	C₂³×Dic₇	C₂³	1	4	yes	—
84	#6548	C₂×C₄	1	256	yes	direct product factor
85	C₂×#1159	C₂×C₄	1	64	yes	complemented
86	C₂×#1159	C₂³	1	32	yes	—
87	C₂×D₄×D₇	C₂×C₄	1	64	yes	complemented
88	C₂×D₄×D₇	C₂³	1	32	yes	—
89	C₂×#1157	C₂×C₄	1	32	yes	complemented
90	C₂×#1157	C₂³	1	16	yes	—
91	C₂²×D₂₈	C₂³	1	2	yes	—
92	C₂²×C₄×D₇	—	4	16	no	—
93	C₂²×C₄×D₇	C₂³	1	4	yes	—
94	C₂²×C₄×D₇	C₂³	1	4	yes	—
95	C₂²×C₄×D₇	C₂³	1	8	yes	—
96	C₂²×C₄×D₇	C₂³	1	4	yes	—
97	C₂²×C₄×D₇	C₂³	1	32	yes	complemented
98	C₂²×Dic₁₄	C₂³	1	2	yes	—
99	C₄×C₇×D₄	C₂³	1	32	yes	complemented
100	C₄×C₇×D₄	C₂³	1	32	yes	complemented
101	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
103	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
104	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	complemented
105	C₂×C₄²×C₇	C₂³	1	2	yes	—
106	C₂×C₄²×C₇	C₂³	1	2	yes	—
107	C₂×C₄²×C₇	C₂³	1	8	yes	complemented
108	C₂×C₂²⋊Dic₇	C₂³	1	8	yes	—
109	C₂×C₂²⋊Dic₇	C₂³	1	4	yes	—
110	C₂×C₂²⋊Dic₇	C₂³	1	32	yes	complemented
111	D₄×Dic₇	C₂³	1	32	yes	complemented
112	D₄×Dic₇	C₂³	1	32	yes	complemented
113	C₄×C₂²⋊D₇	C₂³	1	32	yes	complemented
114	C₄×C₂²⋊D₇	C₂³	1	32	yes	complemented
115	C₄×C₂²⋊D₇	C₂³	1	64	yes	complemented
116	C₄×C₂²⋊D₇	C₂³	1	64	yes	complemented
117	C₄×C₂²⋊D₇	C₂³	1	64	yes	complemented
118	C₂×(C₂×D₇)⋊C₄	C₂³	1	4	yes	—
119	C₂×(C₂×D₇)⋊C₄	C₂³	1	4	yes	—
120	C₂×(C₂×D₇)⋊C₄	C₂³	1	8	yes	—
121	C₂×(C₂×D₇)⋊C₄	C₂³	1	32	yes	complemented
122	#6489	C₂³	1	16	yes	complemented
123	C₂×C₄⋊Dic₇	C₂³	1	2	yes	—
124	C₂×C₄⋊Dic₇	C₂³	1	2	yes	—
125	C₂×Dic₇⋊C₄	C₂³	1	4	yes	—
126	C₂×Dic₇⋊C₄	C₂³	1	4	yes	—
127	C₂×Dic₇⋊C₄	C₂³	1	8	yes	—
128	C₂×Dic₇⋊C₄	C₂³	1	32	yes	complemented
129	C₂×C₄×Dic₇	C₂³	1	4	yes	—
130	C₂×C₄×Dic₇	C₂³	1	4	yes	—
131	C₂×C₄×Dic₇	C₂³	1	4	yes	—
132	C₂×C₄×Dic₇	C₂³	1	8	yes	—
133	C₂×C₄×Dic₇	C₂³	1	32	yes	complemented
134	#6456	C₂³	1	32	yes	complemented
135	#6455	C₂³	1	32	yes	complemented
136	D₇×C₄⋊C₄	C₂³	1	32	yes	complemented
137	#6450	C₂³	1	32	yes	complemented
138	(C₂²⋊D₇)⋊C₄	C₂³	1	64	yes	complemented
139	(C₂²⋊D₇)⋊C₄	C₂³	1	64	yes	complemented
140	D₇×C₂²⋊C₄	C₂³	1	64	yes	complemented
141	#6440	C₂³	1	64	yes	complemented
142	C₄×D₂₈	C₂³	1	16	yes	complemented
143	C₄×D₂₈	C₂³	1	16	yes	complemented
144	#6435	C₂³	1	32	yes	complemented
145	C₄²×D₇	C₂³	1	32	yes	complemented
146	C₄×Dic₁₄	C₂³	1	16	yes	complemented
147	C₄×Dic₁₄	C₂³	1	16	yes	complemented
148	C₂²×H(5,𝔽₂)	—	7	1	no	—
149	C₄×H(5,𝔽₂)	—	7	32	no	—
150	C₂×#520	—	7	4	no	—
151	C₂×#520	—	7	2	no	—
152	C₂×#518	—	7	1	no	—
153	C₂×#518	—	7	4	no	—
154	C₂×#518	—	7	4	no	—
155	C₂×C₄×#41	—	7	2	no	—
156	C₂×C₄×#41	—	7	4	no	—
157	C₂²×C₄×D₄	—	7	4	no	—
158	C₂²×C₄×D₄	—	7	4	no	—
159	C₂²×C₄×D₄	D₇	1	1	yes	characteristic, complemented
160	C₂⁴×C₇	—	4	4	no	—
161	C₂⁴×C₇	—	4	4	no	—
162	C₂⁴×C₇	C₂²×C₄	1	16	yes	complemented
163	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
164	C₂⁴×C₇	C₂⁴	1	4	yes	—
165	C₂⁴×C₇	C₂⁴	1	8	yes	—
166	C₂³×D₇	—	4	8	no	—
167	C₂³×D₇	—	4	8	no	—
168	C₂³×D₇	C₂²×C₄	1	32	yes	complemented
169	C₂³×D₇	C₂⁴	1	4	yes	—
170	C₂³×D₇	C₂⁴	1	16	yes	—
171	C₂×C₇×D₄	C₂²×C₄	1	32	yes	complemented
172	C₂×C₇×D₄	C₂²×C₄	1	64	yes	complemented
173	C₂×C₇×D₄	C₂⁴	1	16	yes	—
174	C₂²×C₄×C₇	—	2	16	no	—
175	C₂²×C₄×C₇	—	2	4	no	—
176	C₂²×C₄×C₇	—	4	32	no	—
177	C₂²×C₄×C₇	—	4	4	no	—
178	C₂²×C₄×C₇	—	4	8	no	—
179	C₂²×C₄×C₇	—	4	2	no	—
180	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	complemented
181	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
184	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
187	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
189	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
192	C₂×C₂²⋊D₇	C₂²×C₄	1	32	yes	complemented
193	C₂×C₂²⋊D₇	C₂²×C₄	1	64	yes	complemented
194	C₂×C₂²⋊D₇	C₂²×C₄	1	256	yes	complemented
195	C₂×C₂²⋊D₇	C₂⁴	1	32	yes	—
196	C₂×C₂²⋊D₇	C₂⁴	1	16	yes	—
197	C₂²×Dic₇	—	4	8	no	—
198	C₂²×Dic₇	—	4	8	no	—
199	C₂²×Dic₇	C₂²×C₄	1	32	yes	complemented
200	C₂²×Dic₇	C₂⁴	1	4	yes	—
201	C₂²×Dic₇	C₂⁴	1	4	yes	—
202	C₂²×Dic₇	C₂⁴	1	16	yes	—
203	C₂²×Dic₇	C₂⁴	1	16	yes	—
204	C₂²×Dic₇	C₂⁴	1	4	yes	—
205	C₂²×Dic₇	C₂⁴	1	16	yes	—
206	#1159	C₂²×C₄	1	256	yes	complemented
207	D₄×D₇	C₂²×C₄	1	256	yes	complemented
208	#1157	C₂²×C₄	1	128	yes	complemented
209	C₂×D₂₈	C₂²×C₄	1	16	yes	complemented
210	C₂×D₂₈	C₂⁴	1	8	yes	—
211	C₂×C₄×D₇	—	2	16	no	—
212	C₂×C₄×D₇	—	4	64	no	—
213	C₂×C₄×D₇	—	4	16	no	—
214	C₂×C₄×D₇	—	4	8	no	—
215	C₂×C₄×D₇	C₂²×C₄	1	32	yes	complemented
216	C₂×C₄×D₇	C₂⁴	1	16	yes	—
217	C₂×C₄×D₇	C₂⁴	1	16	yes	—
218	C₂×C₄×D₇	C₂⁴	1	32	yes	—
219	C₂×C₄×D₇	C₂⁴	1	16	yes	—
220	C₂×Dic₁₄	C₂²×C₄	1	16	yes	complemented
221	C₂×Dic₁₄	C₂⁴	1	8	yes	—
222	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
223	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
224	C₄²×C₇	C₂⁴	1	8	yes	—
225	C₄²×C₇	C₂⁴	1	8	yes	—
226	C₂²⋊Dic₇	C₂⁴	1	32	yes	—
227	C₂²⋊Dic₇	C₂⁴	1	16	yes	—
228	(C₂×D₇)⋊C₄	C₂⁴	1	16	yes	—
229	(C₂×D₇)⋊C₄	C₂⁴	1	16	yes	—
230	(C₂×D₇)⋊C₄	C₂⁴	1	32	yes	—
231	C₄⋊Dic₇	C₂⁴	1	8	yes	—
232	C₄⋊Dic₇	C₂⁴	1	8	yes	—
233	Dic₇⋊C₄	C₂⁴	1	16	yes	—
234	Dic₇⋊C₄	C₂⁴	1	16	yes	—
235	Dic₇⋊C₄	C₂⁴	1	32	yes	—
236	C₄×Dic₇	C₂⁴	1	16	yes	—
237	C₄×Dic₇	C₂⁴	1	16	yes	—
238	C₄×Dic₇	C₂⁴	1	16	yes	—
239	C₄×Dic₇	C₂⁴	1	32	yes	—
240	C₂×H(5,𝔽₂)	—	7	32	no	—
241	C₂×H(5,𝔽₂)	—	7	16	no	—
242	C₂²×#41	—	7	4	no	—
243	C₂²×#41	—	7	2	no	—
244	C₂³×D₄	—	7	4	no	—
245	C₂³×D₄	—	7	4	no	—
246	C₂³×D₄	C₂×D₇	1	1	yes	characteristic
247	C₂⁴×C₄	—	7	4	no	—
248	C₂⁴×C₄	C₂×D₇	1	2	yes	complemented
249	#520	—	7	64	no	—
250	#520	—	7	32	no	—
251	#518	—	7	16	no	—
252	#518	—	7	64	no	—
253	#518	—	7	64	no	—
254	C₄×#41	—	7	64	no	—
255	C₄×#41	—	7	32	no	—
256	C₂×C₄×Q₈	—	7	4	no	—
257	C₂×C₄×Q₈	—	7	2	no	—
258	C₂×C₄×Q₈	—	7	2	no	—
259	C₂×C₄×D₄	—	7	4	no	—
260	C₂×C₄×D₄	—	7	4	no	—
261	C₂×C₄×D₄	—	7	4	no	—
262	C₂×C₄×D₄	—	7	8	no	—
263	C₂×C₄×D₄	—	7	8	no	—
264	C₂×C₄×D₄	—	7	8	no	—
265	C₂×C₄×D₄	—	7	4	no	—
266	C₂×C₄×D₄	—	7	64	no	—
267	C₂×C₄×D₄	—	7	64	no	—
268	C₂×C₄×D₄	—	7	4	no	—
269	C₂×C₄×D₄	—	7	8	no	—
270	C₂×C₄×D₄	—	7	8	no	—
271	C₂×C₄×D₄	—	7	2	no	—
272	C₂×C₄×D₄	—	7	2	no	—
273	C₂×C₄×D₄	C₂×D₇	1	4	yes	complemented
274	C₂×C₄×D₄	C₂×D₇	1	4	yes	complemented
275	C₂×C₄×D₄	C₂×D₇	1	16	yes	complemented
276	C₂×#117	—	7	2	no	—
277	C₂×#117	—	7	4	no	—
278	C₂×#117	—	7	8	no	—
279	C₂×#117	—	7	4	no	—
280	C₂²×C₄⋊C₄	—	7	4	no	—
281	C₂²×C₄⋊C₄	—	7	4	no	—
282	C₂²×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
283	C₂²×C₂²⋊C₄	—	7	4	no	—
284	C₂²×C₂²⋊C₄	—	7	4	no	—
285	C₂²×C₂²⋊C₄	—	7	8	no	—
286	C₂²×C₂²⋊C₄	C₂×D₇	1	2	yes	complemented
287	C₂²×C₄²	—	7	4	no	—
288	C₂²×C₄²	—	7	4	no	—
289	C₂²×C₄²	C₂×D₇	1	1	yes	characteristic, complemented
290	C₂³×C₇	—	2	8	no	—
291	C₂³×C₇	—	2	2	no	—
292	C₂³×C₇	—	2	8	no	—
293	C₂³×C₇	—	2	2	no	—
294	C₂³×C₇	—	4	8	no	—
295	C₂³×C₇	—	4	32	no	—
296	C₂³×C₇	—	4	8	no	—
297	C₂³×C₇	C₂³×C₄	1	16	yes	—
298	C₂³×C₇	C₂³×C₄	1	4	yes	—
299	C₂³×C₇	C₂³×C₄	1	32	yes	complemented
300	C₂³×C₇	C₂⁵	1	2	yes	—
301	C₂³×C₇	C₂⁵	1	8	yes	—
302	C₂³×C₇	C₂⁵	1	1	yes	characteristic
303	C₂²×D₇	—	2	8	no	—
304	C₂²×D₇	—	2	8	no	—
305	C₂²×D₇	—	4	16	no	—
306	C₂²×D₇	—	4	64	no	—
307	C₂²×D₇	—	4	16	no	—
308	C₂²×D₇	C₂³×C₄	1	16	yes	—
309	C₂²×D₇	C₂³×C₄	1	64	yes	complemented
310	C₂²×D₇	C₂⁵	1	8	yes	—
311	C₇×D₄	C₂³×C₄	1	64	yes	complemented
312	C₂×C₄×C₇	—	2	8	no	—
313	C₂×C₄×C₇	—	2	2	no	—
314	C₂×C₄×C₇	—	2	4	no	—
315	C₂×C₄×C₇	—	2	32	no	—
316	C₂×C₄×C₇	—	2	8	no	—
317	C₂×C₄×C₇	—	4	8	no	—
318	C₂×C₄×C₇	—	4	16	no	—
319	C₂×C₄×C₇	—	4	4	no	—
320	C₂×C₄×C₇	C₂³×C₄	1	8	yes	—
321	C₂×C₄×C₇	C₂³×C₄	1	16	yes	complemented
322	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	complemented
323	C₂×C₄×C₇	C₂⁵	1	4	yes	—
324	C₂×C₄×C₇	C₂⁵	1	8	yes	—
325	C₂×C₄×C₇	C₂⁵	1	2	yes	—
326	C₂×C₄×C₇	C₂⁵	1	4	yes	—
327	C₂×C₄×C₇	C₂⁵	1	2	yes	—
328	C₂²⋊D₇	C₂³×C₄	1	64	yes	complemented
329	C₂²⋊D₇	C₂³×C₄	1	128	yes	complemented
330	C₂×Dic₇	—	2	8	no	—
331	C₂×Dic₇	—	2	8	no	—
332	C₂×Dic₇	—	4	16	no	—
333	C₂×Dic₇	—	4	16	no	—
334	C₂×Dic₇	C₂³×C₄	1	16	yes	—
335	C₂×Dic₇	C₂³×C₄	1	64	yes	complemented
336	C₂×Dic₇	C₂⁵	1	8	yes	—
337	C₂×Dic₇	C₂⁵	1	8	yes	—
338	C₂×Dic₇	C₂⁵	1	8	yes	—
339	D₂₈	C₂³×C₄	1	32	yes	complemented
340	C₄×D₇	—	2	32	no	—
341	C₄×D₇	—	4	32	no	—
342	C₄×D₇	—	4	16	no	—
343	C₄×D₇	C₂³×C₄	1	64	yes	complemented
344	Dic₁₄	C₂³×C₄	1	32	yes	complemented
345	C₂⁵	—	7	4	no	—
346	C₂⁵	C₂²×D₇	1	2	yes	—
347	H(5,𝔽₂)	—	7	256	no	—
348	C₂×#41	—	7	64	no	—
349	C₂×#41	—	7	32	no	—
350	C₂×#41	—	7	32	no	—
351	C₂×#41	—	7	16	no	—
352	C₂²×Q₈	—	7	2	no	—
353	C₂²×D₄	—	7	64	no	—
354	C₂²×D₄	—	7	4	no	—
355	C₂²×D₄	—	7	8	no	—
356	C₂²×D₄	—	7	32	no	—
357	C₂²×D₄	—	7	64	no	—
358	C₂²×D₄	—	7	32	no	—
359	C₂²×D₄	—	7	2	no	—
360	C₂²×D₄	C₄×D₇	1	16	yes	complemented
361	C₂²×D₄	C₂²×D₇	1	4	yes	—
362	C₂²×D₄	C₂²×D₇	1	8	yes	—
363	C₂³×C₄	—	4	8	no	—
364	C₂³×C₄	—	7	4	no	—
365	C₂³×C₄	—	7	4	no	—
366	C₂³×C₄	—	7	4	no	—
367	C₂³×C₄	—	7	4	no	—
368	C₂³×C₄	—	7	4	no	—
369	C₂³×C₄	—	7	4	no	—
370	C₂³×C₄	—	7	8	no	—
371	C₂³×C₄	—	7	32	no	—
372	C₂³×C₄	—	28	16	no	—
373	C₂³×C₄	C₂²×D₇	1	1	yes	characteristic
374	C₂³×C₄	C₂²×D₇	1	4	yes	—
375	C₂³×C₄	C₂²×D₇	1	4	yes	—
376	C₂³×C₄	C₂²×D₇	1	1	yes	characteristic
377	C₂³×C₄	C₂²×D₇	1	2	yes	—
378	C₂³×C₄	C₂²×D₇	1	1	yes	characteristic
379	C₂³×C₄	C₂²×D₇	1	16	yes	complemented
380	C₄×Q₈	—	7	32	no	—
381	C₄×Q₈	—	7	16	no	—
382	C₄×Q₈	—	7	16	no	—
383	C₄×D₄	—	7	32	no	—
384	C₄×D₄	—	7	32	no	—
385	C₄×D₄	—	7	64	no	—
386	C₄×D₄	—	7	32	no	—
387	C₄×D₄	—	7	64	no	—
388	C₄×D₄	—	7	64	no	—
389	C₄×D₄	—	7	32	no	—
390	C₄×D₄	—	7	32	no	—
391	C₄×D₄	—	7	64	no	—
392	C₄×D₄	—	7	64	no	—
393	C₄×D₄	—	7	16	no	—
394	C₄×D₄	—	7	16	no	—
395	C₄×D₄	C₂²×D₇	1	32	yes	complemented
396	C₄×D₄	C₂²×D₇	1	32	yes	complemented
397	#117	—	7	16	no	—
398	#117	—	7	32	no	—
399	#117	—	7	64	no	—
400	#117	—	7	32	no	—
401	C₂×C₄⋊C₄	—	7	8	no	—
402	C₂×C₄⋊C₄	—	7	4	no	—
403	C₂×C₄⋊C₄	—	7	2	no	—
404	C₂×C₄⋊C₄	—	7	32	no	—
405	C₂×C₄⋊C₄	—	7	4	no	—
406	C₂×C₄⋊C₄	—	7	2	no	—
407	C₂×C₄⋊C₄	—	7	32	no	—
408	C₂×C₄⋊C₄	C₂²×D₇	1	4	yes	—
409	C₂×C₄⋊C₄	C₂²×D₇	1	8	yes	complemented
410	C₂×C₂²⋊C₄	—	7	4	no	—
411	C₂×C₂²⋊C₄	—	7	8	no	—
412	C₂×C₂²⋊C₄	—	7	32	no	—
413	C₂×C₂²⋊C₄	—	7	8	no	—
414	C₂×C₂²⋊C₄	—	7	4	no	—
415	C₂×C₂²⋊C₄	—	7	4	no	—
416	C₂×C₂²⋊C₄	—	7	32	no	—
417	C₂×C₂²⋊C₄	—	7	64	no	—
418	C₂×C₂²⋊C₄	C₂²×D₇	1	8	yes	—
419	C₂×C₂²⋊C₄	C₂²×D₇	1	16	yes	complemented
420	C₂×C₄²	—	7	8	no	—
421	C₂×C₄²	—	7	4	no	—
422	C₂×C₄²	—	7	4	no	—
423	C₂×C₄²	—	7	32	no	—
424	C₂×C₄²	—	7	4	no	—
425	C₂×C₄²	—	7	32	no	—
426	C₂×C₄²	C₂²×D₇	1	2	yes	—
427	C₂×C₄²	C₂²×D₇	1	2	yes	—
428	C₂×C₄²	C₂²×D₇	1	8	yes	complemented
429	C₂²×C₇	—	2	8	no	—
430	C₂²×C₇	—	2	2	no	—
431	C₂²×C₇	—	2	8	no	—
432	C₂²×C₇	—	2	2	no	—
433	C₂²×C₇	—	2	32	no	—
434	C₂²×C₇	—	2	8	no	—
435	C₂²×C₇	—	4	32	no	—
436	C₂²×C₇	C₂⁴×C₄	1	16	yes	—
437	C₂²×C₇	C₂⁴×C₄	1	4	yes	—
438	C₂²×C₇	C₂⁴×C₄	1	2	yes	—
439	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
440	C₂²×C₇	#585	1	2	yes	—
441	C₂²×C₇	C₂⁶	1	1	yes	characteristic
442	C₂×D₇	—	2	8	no	—
443	C₂×D₇	—	2	8	no	—
444	C₂×D₇	—	2	32	no	—
445	C₂×D₇	—	4	64	no	—
446	C₂×D₇	C₂⁴×C₄	1	16	yes	—
447	C₄×C₇	—	2	8	no	—
448	C₄×C₇	—	2	2	no	—
449	C₄×C₇	—	2	4	no	—
450	C₄×C₇	C₂⁴×C₄	1	8	yes	—
451	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	complemented
452	Dic₇	—	2	8	no	—
453	Dic₇	—	2	8	no	—
454	Dic₇	C₂⁴×C₄	1	16	yes	—
455	C₂⁴	—	4	4	no	—
456	C₂⁴	—	4	4	no	—
457	C₂⁴	—	7	4	no	—
458	C₂⁴	—	7	32	no	—
459	C₂⁴	—	7	16	no	—
460	C₂⁴	—	28	8	no	—
461	C₂⁴	—	28	8	no	—
462	C₂⁴	C₂×C₄×D₇	1	16	yes	complemented
463	C₂⁴	C₂³×D₇	1	1	yes	characteristic
464	C₂⁴	C₂³×D₇	1	4	yes	—
465	C₂⁴	C₂³×D₇	1	8	yes	—
466	#41	—	7	256	no	—
467	#41	—	7	128	no	—
468	C₂×Q₈	—	7	16	no	—
469	C₂×Q₈	—	7	8	no	—
470	C₂×D₄	—	7	64	no	—
471	C₂×D₄	—	7	32	no	—
472	C₂×D₄	—	7	256	no	—
473	C₂×D₄	—	7	16	no	—
474	C₂×D₄	—	7	32	no	—
475	C₂×D₄	—	7	256	no	—
476	C₂×D₄	—	7	16	no	—
477	C₂×D₄	—	7	8	no	—
478	C₂×D₄	C₂×C₄×D₇	1	32	yes	complemented
479	C₂×D₄	C₂×C₄×D₇	1	64	yes	complemented
480	C₂×D₄	C₂³×D₇	1	16	yes	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	16	no	—
483	C₂²×C₄	—	4	32	no	—
484	C₂²×C₄	—	4	8	no	—
485	C₂²×C₄	—	4	4	no	—
486	C₂²×C₄	—	4	2	no	—
487	C₂²×C₄	—	7	32	no	—
488	C₂²×C₄	—	7	4	no	—
489	C₂²×C₄	—	7	16	no	—
490	C₂²×C₄	—	7	32	no	—
491	C₂²×C₄	—	7	16	no	—
492	C₂²×C₄	—	7	4	no	—
493	C₂²×C₄	—	7	4	no	—
494	C₂²×C₄	—	7	16	no	—
495	C₂²×C₄	—	7	16	no	—
496	C₂²×C₄	—	7	16	no	—
497	C₂²×C₄	—	7	16	no	—
498	C₂²×C₄	—	7	32	no	—
499	C₂²×C₄	—	14	16	no	—
500	C₂²×C₄	—	28	64	no	—
501	C₂²×C₄	—	28	8	no	—
502	C₂²×C₄	—	28	16	no	—
503	C₂²×C₄	—	28	8	no	—
504	C₂²×C₄	—	28	8	no	—
505	C₂²×C₄	C₂×C₄×D₇	1	8	yes	complemented
506	C₂²×C₄	C₂³×D₇	1	2	yes	—
507	C₂²×C₄	C₂³×D₇	1	4	yes	—
508	C₂²×C₄	C₂³×D₇	1	16	yes	—
509	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
510	C₂²×C₄	C₂³×D₇	1	4	yes	—
511	C₂²×C₄	C₂³×D₇	1	4	yes	—
512	C₂²×C₄	C₂³×D₇	1	16	yes	—
513	C₂²×C₄	C₂³×D₇	1	8	yes	—
514	C₂²×C₄	C₂³×D₇	1	2	yes	—
515	C₂²×C₄	C₂³×D₇	1	4	yes	—
516	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
517	C₄⋊C₄	—	7	32	no	—
518	C₄⋊C₄	—	7	16	no	—
519	C₄⋊C₄	—	7	16	no	—
520	C₄⋊C₄	—	7	8	no	—
521	C₄⋊C₄	—	7	8	no	—
522	C₄⋊C₄	C₂³×D₇	1	16	yes	—
523	C₂²⋊C₄	—	7	16	no	—
524	C₂²⋊C₄	—	7	32	no	—
525	C₂²⋊C₄	—	7	32	no	—
526	C₂²⋊C₄	—	7	16	no	—
527	C₂²⋊C₄	—	7	16	no	—
528	C₂²⋊C₄	C₂³×D₇	1	32	yes	—
529	C₄²	—	7	16	no	—
530	C₄²	—	7	32	no	—
531	C₄²	—	7	16	no	—
532	C₄²	—	7	16	no	—
533	C₄²	C₂³×D₇	1	8	yes	—
534	C₄²	C₂³×D₇	1	8	yes	—
535	C₂×C₇	—	2	16	no	—
536	C₂×C₇	—	2	4	no	—
537	C₂×C₇	C₄×H(5,𝔽₂)	1	4	yes	complemented
538	C₂×C₇	C₂⁵×C₄	1	1	yes	characteristic
539	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
540	C₂×C₇	C₂×#585	1	1	yes	characteristic
541	D₇	—	2	16	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	8	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	8	no	—
546	C₂³	—	4	8	no	—
547	C₂³	—	4	32	no	—
548	C₂³	—	4	8	no	—
549	C₂³	—	7	8	no	—
550	C₂³	—	7	16	no	—
551	C₂³	—	7	64	no	—
552	C₂³	—	14	8	no	—
553	C₂³	—	14	8	no	—
554	C₂³	—	28	16	no	—
555	C₂³	—	28	16	no	—
556	C₂³	—	28	64	no	—
557	C₂³	C₂²×C₄×D₇	1	16	yes	—
558	C₂³	C₂²×C₄×D₇	1	4	yes	—
559	C₂³	C₂²×C₄×D₇	1	32	yes	complemented
560	C₂³	C₂⁴×D₇	1	2	yes	—
561	C₂³	C₂⁴×D₇	1	8	yes	—
562	C₂³	C₂⁴×D₇	1	1	yes	characteristic
563	Q₈	—	7	32	no	—
564	D₄	—	7	128	no	—
565	D₄	—	7	64	no	—
566	D₄	—	7	32	no	—
567	D₄	C₂²×C₄×D₇	1	64	yes	complemented
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	8	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	32	no	—
573	C₂×C₄	—	4	16	no	—
574	C₂×C₄	—	4	8	no	—
575	C₂×C₄	—	4	4	no	—
576	C₂×C₄	—	7	8	no	—
577	C₂×C₄	—	7	16	no	—
578	C₂×C₄	—	7	64	no	—
579	C₂×C₄	—	7	64	no	—
580	C₂×C₄	—	7	8	no	—
581	C₂×C₄	—	7	8	no	—
582	C₂×C₄	—	14	8	no	—
583	C₂×C₄	—	14	8	no	—
584	C₂×C₄	—	14	32	no	—
585	C₂×C₄	—	28	16	no	—
586	C₂×C₄	—	28	32	no	—
587	C₂×C₄	—	28	16	no	—
588	C₂×C₄	—	28	16	no	—
589	C₂×C₄	C₂²×C₄×D₇	1	8	yes	—
590	C₂×C₄	C₂²×C₄×D₇	1	16	yes	complemented
591	C₂×C₄	#6548	1	4	yes	direct product factor
592	C₂×C₄	C₂⁴×D₇	1	4	yes	—
593	C₂×C₄	C₂⁴×D₇	1	8	yes	—
594	C₂×C₄	C₂⁴×D₇	1	2	yes	—
595	C₂×C₄	C₂⁴×D₇	1	4	yes	—
596	C₂×C₄	C₂⁴×D₇	1	2	yes	—
597	C₇	C₂×C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
598	C₂²	—	2	2	no	—
599	C₂²	—	2	8	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	8	no	—
602	C₂²	—	2	8	no	—
603	C₂²	—	2	32	no	—
604	C₂²	—	4	32	no	—
605	C₂²	—	7	16	no	—
606	C₂²	—	14	8	no	—
607	C₂²	—	14	8	no	—
608	C₂²	—	14	32	no	—
609	C₂²	—	28	64	no	—
610	C₂²	C₂³×C₄×D₇	1	16	yes	—
611	C₂²	C₂³×C₄×D₇	1	4	yes	—
612	C₂²	C₂³×C₄×D₇	1	2	yes	—
613	C₂²	C₂×#6548	1	2	yes	—
614	C₂²	#90616	1	2	yes	—
615	C₂²	C₂⁵×D₇	1	1	yes	characteristic
616	C₄	—	2	2	no	—
617	C₄	—	2	8	no	—
618	C₄	—	2	4	no	—
619	C₄	—	7	16	no	—
620	C₄	—	14	8	no	—
621	C₄	—	14	8	no	—
622	C₄	C₂³×C₄×D₇	1	8	yes	—
623	C₄	C₂×#6548	1	4	yes	direct product factor
624	C₂	—	2	4	no	—
625	C₂	—	2	16	no	—
626	C₂	—	14	16	no	—
627	C₂	C₄×#6548	1	4	yes	direct product factor
628	C₂	C₂⁴×C₄×D₇	1	1	yes	characteristic
629	C₂	C₂²×#6548	1	1	yes	characteristic
630	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	C₂²×C₄×C₇×D₄	C₂
socle	C₂³×C₇	C₂⁵
prime radical	C₂²×#6548	C₂
cosocle	C₂²×C₇	C₂⁶
hypercenter	C₂²×C₄×D₄	D₇
hypocenter	C₇	C₂×C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₇×D₄	C₂	semidirect
3. C₂×#90489	C₂	semidirect
4. C₂²×C₄×C₂²⋊D₇	C₂	semidirect
5. C₂×#90236	C₂	semidirect
6. C₂×C₄×D₄×D₇	C₂	semidirect
7. C₄×#6548	C₂	direct (N × H)
8. C₂×#90237	C₂	semidirect
9. C₂×C₄×#1159	C₂	semidirect
10. C₂×#90195	C₂	semidirect
11. C₂×#90177	C₂	semidirect
12. C₂×C₄×#1157	C₂	semidirect
14. C₂⁴×C₄×C₇	C₂²	semidirect
16. C₂×#6548	C₄	direct (N × H)
21. C₂³×C₄×D₇	C₂²	semidirect
22. C₂×C₄×C₇×D₄	C₂²	semidirect
23. C₂×C₄×C₇×D₄	C₂²	semidirect
24. C₂×C₄×C₇×D₄	C₂²	semidirect
25. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
26. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
27. C₂²×C₄²×C₇	C₂²	semidirect
28. C₂²×C₂²⋊Dic₇	C₂²	semidirect
29. #90489	C₂²	semidirect
30. C₂×D₄×Dic₇	C₂²	semidirect
31. C₂×D₄×Dic₇	C₂²	semidirect
32. C₂×C₄×C₂²⋊D₇	C₂²	semidirect
33. C₂×C₄×C₂²⋊D₇	C₂²	semidirect
34. C₂×C₄×C₂²⋊D₇	C₂²	semidirect
35. C₂×C₄×C₂²⋊D₇	C₂²	semidirect
36. C₂×C₄×C₂²⋊D₇	C₂²	semidirect
37. C₂×C₄×C₂²⋊D₇	C₂²	semidirect
38. C₂²×(C₂×D₇)⋊C₄	C₂²	semidirect
39. C₂×#6489	C₂²	semidirect
40. C₂²×Dic₇⋊C₄	C₂²	semidirect
41. C₂²×C₄×Dic₇	C₂²	semidirect
42. #90237	C₂²	semidirect
43. #90236	C₂²	semidirect
44. C₄×D₄×D₇	C₂²	semidirect
45. C₄×#1159	C₂²	semidirect
46. #90195	C₂²	semidirect
47. C₂×#6456	C₂²	semidirect
48. C₂×#6455	C₂²	semidirect
49. C₂×D₇×C₄⋊C₄	C₂²	semidirect
50. C₂×#6450	C₂²	semidirect
51. #90177	C₂²	semidirect
52. C₂×(C₂²⋊D₇)⋊C₄	C₂²	semidirect
53. C₂×(C₂²⋊D₇)⋊C₄	C₂²	semidirect
54. C₂×D₇×C₂²⋊C₄	C₂²	semidirect
55. C₂×#6440	C₂²	semidirect
56. C₄×#1157	C₂²	semidirect
57. C₂×C₄×D₂₈	C₂²	semidirect
58. C₂×C₄×D₂₈	C₂²	semidirect
59. C₂×#6435	C₂²	semidirect
60. C₂×C₄²×D₇	C₂²	semidirect
61. C₂×C₄×Dic₁₄	C₂²	semidirect
62. C₂×C₄×Dic₁₄	C₂²	semidirect
66. C₂²×C₇×D₄	C₂×C₄	semidirect
76. C₂³×C₄×C₇	C₂³	semidirect
77. C₂²×C₂²⋊D₇	C₂×C₄	semidirect
84. #6548	C₂×C₄	direct (N × H)
85. C₂×#1159	C₂×C₄	semidirect
87. C₂×D₄×D₇	C₂×C₄	semidirect
89. C₂×#1157	C₂×C₄	semidirect
97. C₂²×C₄×D₇	C₂³	semidirect
99. C₄×C₇×D₄	C₂³	semidirect
100. C₄×C₇×D₄	C₂³	semidirect
102. C₂×C₇×C₄⋊C₄	C₂³	semidirect
104. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
107. C₂×C₄²×C₇	C₂³	semidirect
110. C₂×C₂²⋊Dic₇	C₂³	semidirect
111. D₄×Dic₇	C₂³	semidirect
112. D₄×Dic₇	C₂³	semidirect
113. C₄×C₂²⋊D₇	C₂³	semidirect
114. C₄×C₂²⋊D₇	C₂³	semidirect
115. C₄×C₂²⋊D₇	C₂³	semidirect
116. C₄×C₂²⋊D₇	C₂³	semidirect
117. C₄×C₂²⋊D₇	C₂³	semidirect
121. C₂×(C₂×D₇)⋊C₄	C₂³	semidirect
122. #6489	C₂³	semidirect
128. C₂×Dic₇⋊C₄	C₂³	semidirect
133. C₂×C₄×Dic₇	C₂³	semidirect
134. #6456	C₂³	semidirect
135. #6455	C₂³	semidirect
136. D₇×C₄⋊C₄	C₂³	semidirect
137. #6450	C₂³	semidirect
138. (C₂²⋊D₇)⋊C₄	C₂³	semidirect
139. (C₂²⋊D₇)⋊C₄	C₂³	semidirect
140. D₇×C₂²⋊C₄	C₂³	semidirect
141. #6440	C₂³	semidirect
142. C₄×D₂₈	C₂³	semidirect
143. C₄×D₂₈	C₂³	semidirect
144. #6435	C₂³	semidirect
145. C₄²×D₇	C₂³	semidirect
146. C₄×Dic₁₄	C₂³	semidirect
147. C₄×Dic₁₄	C₂³	semidirect
159. C₂²×C₄×D₄	D₇	semidirect
162. C₂⁴×C₇	C₂²×C₄	semidirect
168. C₂³×D₇	C₂²×C₄	semidirect
171. C₂×C₇×D₄	C₂²×C₄	semidirect
172. C₂×C₇×D₄	C₂²×C₄	semidirect
180. C₂²×C₄×C₇	C₂²×C₄	semidirect
192. C₂×C₂²⋊D₇	C₂²×C₄	semidirect
193. C₂×C₂²⋊D₇	C₂²×C₄	semidirect
194. C₂×C₂²⋊D₇	C₂²×C₄	semidirect
199. C₂²×Dic₇	C₂²×C₄	semidirect
206. #1159	C₂²×C₄	semidirect
207. D₄×D₇	C₂²×C₄	semidirect
208. #1157	C₂²×C₄	semidirect
209. C₂×D₂₈	C₂²×C₄	semidirect
215. C₂×C₄×D₇	C₂²×C₄	semidirect
220. C₂×Dic₁₄	C₂²×C₄	semidirect
248. C₂⁴×C₄	C₂×D₇	semidirect
273. C₂×C₄×D₄	C₂×D₇	semidirect
274. C₂×C₄×D₄	C₂×D₇	semidirect
275. C₂×C₄×D₄	C₂×D₇	semidirect
282. C₂²×C₄⋊C₄	C₂×D₇	semidirect
286. C₂²×C₂²⋊C₄	C₂×D₇	semidirect
289. C₂²×C₄²	C₂×D₇	semidirect
299. C₂³×C₇	C₂³×C₄	semidirect
309. C₂²×D₇	C₂³×C₄	semidirect
311. C₇×D₄	C₂³×C₄	semidirect
321. C₂×C₄×C₇	C₂³×C₄	semidirect
322. C₂×C₄×C₇	H(5,𝔽₂)	semidirect
328. C₂²⋊D₇	C₂³×C₄	semidirect
329. C₂²⋊D₇	C₂³×C₄	semidirect
335. C₂×Dic₇	C₂³×C₄	semidirect
339. D₂₈	C₂³×C₄	semidirect
343. C₄×D₇	C₂³×C₄	semidirect
344. Dic₁₄	C₂³×C₄	semidirect
360. C₂²×D₄	C₄×D₇	semidirect
379. C₂³×C₄	C₂²×D₇	semidirect
395. C₄×D₄	C₂²×D₇	semidirect
396. C₄×D₄	C₂²×D₇	semidirect
409. C₂×C₄⋊C₄	C₂²×D₇	semidirect
419. C₂×C₂²⋊C₄	C₂²×D₇	semidirect
428. C₂×C₄²	C₂²×D₇	semidirect
451. C₄×C₇	C₂×H(5,𝔽₂)	semidirect
462. C₂⁴	C₂×C₄×D₇	semidirect
478. C₂×D₄	C₂×C₄×D₇	semidirect
479. C₂×D₄	C₂×C₄×D₇	semidirect
505. C₂²×C₄	C₂×C₄×D₇	semidirect
537. C₂×C₇	C₄×H(5,𝔽₂)	semidirect
559. C₂³	C₂²×C₄×D₇	semidirect
567. D₄	C₂²×C₄×D₇	semidirect
590. C₂×C₄	C₂²×C₄×D₇	semidirect
591. C₂×C₄	#6548	direct (N × H)
597. C₇	C₂×C₄×H(5,𝔽₂)	semidirect
623. C₄	C₂×#6548	direct (N × H)
627. C₂	C₄×#6548	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×#6548	2
C₂²×C₄×C₇×D₄	2
C₂×#90489	2
C₂²×C₄×C₂²⋊D₇	2
C₂×#90236	2
C₂×C₄×D₄×D₇	2
C₄×#6548	2
C₂×#90237	2
C₂×C₄×#1159	2
C₂×#90195	2
C₂×#90177	2
C₂×C₄×#1157	2
C₂×C₄×H(5,𝔽₂)	7

Subgroups — C2×C4×#6548 #14260397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#6548 #14260397