Subgroups — C₂×C₇×#3330 #13238366

Order 1792.

2374 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3330	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#484	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#468	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#449	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#417	C₂	1	2	yes	maximal, complemented
13	C₂²×C₇×#41	—	2	1	no	—
14	C₂²×C₇×#41	C₂²	1	2	yes	—
15	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
17	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
18	C₇×#547	—	2	4	no	—
19	C₇×#547	—	2	4	no	—
20	C₇×#547	C₂²	1	8	yes	complemented
21	C₇×#547	C₂²	1	8	yes	complemented
22	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×#123	—	2	2	no	—
25	C₂×C₇×#123	—	2	2	no	—
26	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₇×#121	—	2	1	no	—
29	C₂×C₇×#121	C₂²	1	2	yes	—
30	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
33	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
34	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
35	C₇×#487	C₂²	1	8	yes	complemented
36	C₇×#484	C₂²	1	16	yes	complemented
37	C₇×#474	C₂²	1	8	yes	complemented
38	C₇×#468	C₂²	1	16	yes	complemented
39	C₇×#461	C₂²	1	8	yes	complemented
40	C₇×#449	C₂²	1	16	yes	complemented
41	C₄×C₇×D₈	C₂²	1	8	yes	complemented
42	C₇×#436	C₂²	1	8	yes	complemented
43	C₂×C₇×#107	C₂²	1	1	yes	characteristic
44	C₂×C₇×#107	C₂²	1	2	yes	—
45	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₇×#417	C₂²	1	16	yes	complemented
47	C₂×C₇×#103	C₂²	1	2	yes	—
48	C₂×C₇×#103	C₂²	1	2	yes	—
49	C₂×C₇×#103	C₂²	1	2	yes	—
50	C₂×C₇×#102	C₂²	1	1	yes	characteristic
51	C₂×C₇×#102	C₂²	1	1	yes	characteristic
52	C₂×C₇×#102	C₂²	1	2	yes	—
53	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
54	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
55	C₂×#3330	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂×C₇×#41	—	2	8	no	—
57	C₂×C₇×#41	—	2	4	no	—
58	C₂×C₇×#41	—	2	8	no	—
59	C₂×C₇×#41	—	4	4	no	—
60	C₂×C₇×#41	—	4	8	no	—
61	C₂×C₇×#41	C₂³	1	8	yes	—
62	C₂²×C₇×Q₈	—	2	1	no	—
63	C₂²×C₇×Q₈	C₂³	1	2	yes	—
64	C₂²×C₇×D₄	—	2	2	no	—
65	C₂²×C₇×D₄	—	2	2	no	—
66	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
67	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
68	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₇	—	2	2	no	—
70	C₂³×C₄×C₇	—	2	1	no	—
71	C₂³×C₄×C₇	—	2	2	no	—
72	C₂³×C₄×C₇	—	2	1	no	—
73	C₂³×C₄×C₇	C₂³	1	2	yes	—
74	C₂×C₇×SD₁₆	—	4	4	no	—
75	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
76	C₂×C₇×D₈	—	2	4	no	—
77	C₂×C₇×D₈	C₂³	1	4	yes	—
78	C₂×C₇×M₁₆	—	4	4	no	—
79	C₂×C₇×M₁₆	C₂³	1	8	yes	—
80	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₇×C₈	C₂³	1	2	yes	—
83	C₇×C₄⋊Q₈	—	2	2	no	—
84	C₇×C₄⋊Q₈	—	2	2	no	—
85	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
86	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
87	C₇×#123	—	2	16	no	—
88	C₇×#123	—	2	16	no	—
89	C₇×C₂²⋊Q₈	—	2	4	no	—
90	C₇×C₂²⋊Q₈	—	2	8	no	—
91	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
92	C₇×#121	—	2	8	no	—
93	C₇×#121	—	2	4	no	—
94	C₇×#121	C₂³	1	8	yes	—
95	C₄×C₇×D₄	—	2	2	no	—
96	C₄×C₇×D₄	—	2	2	no	—
97	C₄×C₇×D₄	D₄	1	4	yes	—
98	C₄×C₇×D₄	C₂³	1	4	yes	—
99	C₄×C₇×D₄	C₂³	1	4	yes	—
100	C₄×C₇×D₄	C₂³	1	4	yes	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	—	2	2	no	—
103	C₂×C₇×C₄⋊C₄	—	2	2	no	—
104	C₂×C₇×C₄⋊C₄	—	2	4	no	—
105	C₂×C₇×C₄⋊C₄	—	2	1	no	—
106	C₂×C₇×C₄⋊C₄	—	2	1	no	—
107	C₂×C₇×C₄⋊C₄	—	2	8	no	—
108	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
109	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
110	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
118	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
119	C₇×#107	C₂³	1	8	yes	—
120	C₇×#107	C₂³	1	4	yes	—
121	C₇×C₄⋊C₈	C₂³	1	4	yes	—
122	C₇×#103	C₂³	1	8	yes	—
123	C₇×#103	C₂³	1	8	yes	—
124	C₇×#103	C₂³	1	8	yes	—
125	C₇×#102	C₂³	1	4	yes	—
126	C₇×#102	C₂³	1	8	yes	—
127	C₇×#102	C₂³	1	4	yes	—
128	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
129	C₄×C₇×C₈	C₂³	1	4	yes	—
130	C₂×#547	C₂×C₇	1	1	yes	characteristic, complemented
131	C₂×#547	C₂×C₇	1	1	yes	characteristic, complemented
132	#3330	C₂×C₇	1	16	yes	direct product factor
133	C₂×#487	C₂×C₇	1	1	yes	characteristic, complemented
134	C₂×#484	C₂×C₇	1	2	yes	complemented
135	C₂×#474	C₂×C₇	1	1	yes	characteristic, complemented
136	C₂×#468	C₂×C₇	1	2	yes	complemented
137	C₂×#461	C₂×C₇	1	1	yes	characteristic, complemented
138	C₂×#449	C₂×C₇	1	2	yes	complemented
139	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
140	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
141	C₂×#417	C₂×C₇	1	2	yes	complemented
142	C₂⁴×C₇	—	2	1	no	—
143	C₂⁴×C₇	—	2	1	no	—
144	C₂⁴×C₇	C₂×D₄	1	2	yes	—
145	C₇×#41	—	2	16	no	—
146	C₇×#41	—	4	8	no	—
147	C₇×#41	—	4	16	no	—
148	C₇×#41	—	4	32	no	—
149	C₂×C₇×Q₈	—	2	2	no	—
150	C₂×C₇×Q₈	—	2	4	no	—
151	C₂×C₇×Q₈	—	2	4	no	—
152	C₂×C₇×Q₈	—	2	4	no	—
153	C₂×C₇×Q₈	—	4	4	no	—
154	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
155	C₂×C₇×D₄	—	2	8	no	—
156	C₂×C₇×D₄	—	2	8	no	—
157	C₂×C₇×D₄	—	2	4	no	—
158	C₂×C₇×D₄	—	2	1	no	—
159	C₂×C₇×D₄	—	2	1	no	—
160	C₂×C₇×D₄	—	2	2	no	—
161	C₂×C₇×D₄	—	2	2	no	—
162	C₂×C₇×D₄	—	2	2	no	—
163	C₂×C₇×D₄	—	4	8	no	—
164	C₂×C₇×D₄	—	4	8	no	—
165	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
166	C₂×C₇×D₄	#41	1	4	yes	complemented
167	C₂×C₇×D₄	C₂⁴	1	2	yes	—
168	C₂×C₇×D₄	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₇	—	2	4	no	—
170	C₂²×C₄×C₇	—	2	4	no	—
171	C₂²×C₄×C₇	—	2	8	no	—
172	C₂²×C₄×C₇	—	2	1	no	—
173	C₂²×C₄×C₇	—	2	2	no	—
174	C₂²×C₄×C₇	—	2	1	no	—
175	C₂²×C₄×C₇	—	2	2	no	—
176	C₂²×C₄×C₇	—	2	4	no	—
177	C₂²×C₄×C₇	—	2	8	no	—
178	C₂²×C₄×C₇	—	2	4	no	—
179	C₂²×C₄×C₇	—	4	8	no	—
180	C₂²×C₄×C₇	—	4	8	no	—
181	C₂²×C₄×C₇	—	4	4	no	—
182	C₂²×C₄×C₇	—	4	4	no	—
183	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
184	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
186	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
189	C₇×SD₁₆	—	4	8	no	—
190	C₇×D₈	—	2	8	no	—
191	C₇×M₁₆	—	4	8	no	—
192	C₂×C₇×C₈	—	2	2	no	—
193	C₂×C₇×C₈	—	2	2	no	—
194	C₂×C₇×C₈	—	2	4	no	—
195	C₂×C₇×C₈	C₂⁴	1	2	yes	—
196	C₂×C₇×C₈	C₂⁴	1	2	yes	—
197	C₂×C₇×C₈	C₂⁴	1	4	yes	—
198	C₇×C₄⋊C₄	—	2	1	no	—
199	C₇×C₄⋊C₄	—	2	4	no	—
200	C₇×C₄⋊C₄	—	2	8	no	—
201	C₇×C₄⋊C₄	—	2	2	no	—
202	C₇×C₄⋊C₄	—	2	8	no	—
203	C₇×C₄⋊C₄	—	2	4	no	—
204	C₇×C₄⋊C₄	—	2	4	no	—
205	C₇×C₄⋊C₄	—	2	1	no	—
206	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
207	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
208	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
209	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
210	C₇×C₂²⋊C₄	—	2	8	no	—
211	C₇×C₂²⋊C₄	—	2	4	no	—
212	C₇×C₂²⋊C₄	—	2	4	no	—
213	C₇×C₂²⋊C₄	—	2	8	no	—
214	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
215	C₄²×C₇	C₂×D₄	1	2	yes	—
216	C₄²×C₇	C₂⁴	1	2	yes	—
217	C₂²×#41	—	2	1	no	—
218	C₂²×#41	C₂²×C₇	1	2	yes	—
219	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
220	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
221	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
222	#547	—	2	4	no	—
223	#547	—	2	4	no	—
224	#547	C₂²×C₇	1	8	yes	complemented
225	#547	C₂²×C₇	1	8	yes	complemented
226	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
227	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
228	C₂×#123	—	2	2	no	—
229	C₂×#123	—	2	2	no	—
230	C₂×C₂²⋊Q₈	—	2	1	no	—
231	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
232	C₂×#121	—	2	1	no	—
233	C₂×#121	C₂²×C₇	1	2	yes	—
234	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	—	2	1	no	—
238	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
239	#487	C₂²×C₇	1	8	yes	complemented
240	#484	C₂²×C₇	1	16	yes	complemented
241	#474	C₂²×C₇	1	8	yes	complemented
242	#468	C₂²×C₇	1	16	yes	complemented
243	#461	C₂²×C₇	1	8	yes	complemented
244	#449	C₂²×C₇	1	16	yes	complemented
245	C₄×D₈	C₂²×C₇	1	8	yes	complemented
246	#436	C₂²×C₇	1	8	yes	complemented
247	C₂×#107	C₂²×C₇	1	1	yes	characteristic
248	C₂×#107	C₂²×C₇	1	2	yes	—
249	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
250	#417	C₂²×C₇	1	16	yes	complemented
251	C₂×#103	C₂²×C₇	1	2	yes	—
252	C₂×#103	C₂²×C₇	1	2	yes	—
253	C₂×#103	C₂²×C₇	1	2	yes	—
254	C₂×#102	C₂²×C₇	1	1	yes	characteristic
255	C₂×#102	C₂²×C₇	1	2	yes	—
256	C₂×#102	C₂²×C₇	1	1	yes	characteristic
257	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
258	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
259	C₂³×C₇	—	2	4	no	—
260	C₂³×C₇	—	2	4	no	—
261	C₂³×C₇	—	2	4	no	—
262	C₂³×C₇	—	2	4	no	—
263	C₂³×C₇	—	2	2	no	—
264	C₂³×C₇	—	2	2	no	—
265	C₂³×C₇	—	4	2	no	—
266	C₂³×C₇	—	4	2	no	—
267	C₂³×C₇	—	4	2	no	—
268	C₂³×C₇	—	4	2	no	—
269	C₂³×C₇	—	4	2	no	—
270	C₂³×C₇	C₂²×D₄	1	4	yes	—
271	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
272	C₇×Q₈	—	2	4	no	—
273	C₇×Q₈	—	2	4	no	—
274	C₇×Q₈	—	4	4	no	—
275	C₇×Q₈	—	4	8	no	—
276	C₇×D₄	—	2	4	no	—
277	C₇×D₄	—	2	8	no	—
278	C₇×D₄	—	2	2	no	—
279	C₇×D₄	—	2	2	no	—
280	C₇×D₄	—	2	2	no	—
281	C₇×D₄	—	4	16	no	—
282	C₇×D₄	—	4	16	no	—
283	C₇×D₄	—	4	2	no	—
284	C₇×D₄	C₂×#41	1	4	yes	complemented
285	C₂×C₄×C₇	—	2	4	no	—
286	C₂×C₄×C₇	—	2	2	no	—
287	C₂×C₄×C₇	—	2	8	no	—
288	C₂×C₄×C₇	—	2	4	no	—
289	C₂×C₄×C₇	—	2	4	no	—
290	C₂×C₄×C₇	—	2	2	no	—
291	C₂×C₄×C₇	—	2	4	no	—
292	C₂×C₄×C₇	—	2	2	no	—
293	C₂×C₄×C₇	—	2	4	no	—
294	C₂×C₄×C₇	—	4	16	no	—
295	C₂×C₄×C₇	—	4	16	no	—
296	C₂×C₄×C₇	—	4	4	no	—
297	C₂×C₄×C₇	—	4	2	no	—
298	C₂×C₄×C₇	—	4	2	no	—
299	C₂×C₄×C₇	—	4	4	no	—
300	C₂×C₄×C₇	—	4	8	no	—
301	C₂×C₄×C₇	—	4	8	no	—
302	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
303	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
305	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
307	C₂×C₄×C₇	C₂×#41	1	2	yes	—
308	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
309	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
310	C₇×C₈	—	2	2	no	—
311	C₇×C₈	—	2	2	no	—
312	C₇×C₈	—	2	4	no	—
313	C₂×#41	—	2	8	no	—
314	C₂×#41	—	2	4	no	—
315	C₂×#41	—	2	8	no	—
316	C₂×#41	—	4	4	no	—
317	C₂×#41	—	4	8	no	—
318	C₂×#41	C₂³×C₇	1	8	yes	—
319	C₂²×Q₈	—	2	1	no	—
320	C₂²×Q₈	C₂³×C₇	1	2	yes	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	—	2	2	no	—
323	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
324	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
325	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
326	C₂³×C₄	—	2	2	no	—
327	C₂³×C₄	—	2	1	no	—
328	C₂³×C₄	—	2	2	no	—
329	C₂³×C₄	—	2	1	no	—
330	C₂³×C₄	C₂³×C₇	1	2	yes	—
331	C₂×SD₁₆	—	4	4	no	—
332	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
333	C₂×D₈	—	2	4	no	—
334	C₂×D₈	C₂³×C₇	1	4	yes	—
335	C₂×M₁₆	—	4	4	no	—
336	C₂×M₁₆	C₂³×C₇	1	8	yes	—
337	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₇	1	2	yes	—
339	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
340	C₄⋊Q₈	—	2	2	no	—
341	C₄⋊Q₈	—	2	2	no	—
342	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
343	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
344	#123	—	2	16	no	—
345	#123	—	2	16	no	—
346	C₂²⋊Q₈	—	2	4	no	—
347	C₂²⋊Q₈	—	2	8	no	—
348	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
349	#121	—	2	8	no	—
350	#121	—	2	4	no	—
351	#121	C₂³×C₇	1	8	yes	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	C₇×D₄	1	4	yes	—
355	C₄×D₄	C₂³×C₇	1	4	yes	—
356	C₄×D₄	C₂³×C₇	1	4	yes	—
357	C₄×D₄	C₂³×C₇	1	4	yes	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	—	2	4	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	8	no	—
365	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
369	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
375	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
376	#107	C₂³×C₇	1	4	yes	—
377	#107	C₂³×C₇	1	8	yes	—
378	C₄⋊C₈	C₂³×C₇	1	4	yes	—
379	#103	C₂³×C₇	1	8	yes	—
380	#103	C₂³×C₇	1	8	yes	—
381	#103	C₂³×C₇	1	8	yes	—
382	#102	C₂³×C₇	1	4	yes	—
383	#102	C₂³×C₇	1	8	yes	—
384	#102	C₂³×C₇	1	4	yes	—
385	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
386	C₄×C₈	C₂³×C₇	1	4	yes	—
387	C₂²×C₇	—	2	4	no	—
388	C₂²×C₇	—	2	4	no	—
389	C₂²×C₇	—	2	4	no	—
390	C₂²×C₇	—	2	4	no	—
391	C₂²×C₇	—	4	8	no	—
392	C₂²×C₇	—	4	8	no	—
393	C₂²×C₇	—	4	2	no	—
394	C₂²×C₇	—	4	2	no	—
395	C₂²×C₇	—	4	2	no	—
396	C₂²×C₇	—	4	2	no	—
397	C₂²×C₇	—	4	2	no	—
398	C₂²×C₇	—	8	4	no	—
399	C₂²×C₇	#546	1	2	yes	—
400	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
401	C₂²×C₇	#578	1	2	yes	—
402	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
403	C₄×C₇	—	2	4	no	—
404	C₄×C₇	—	2	2	no	—
405	C₄×C₇	—	4	4	no	—
406	C₄×C₇	—	4	2	no	—
407	C₄×C₇	—	4	2	no	—
408	C₄×C₇	—	4	4	no	—
409	C₄×C₇	#546	1	2	yes	—
410	C₄×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
411	C₄×C₇	C₂²×#41	1	1	yes	characteristic
412	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂⁴	—	2	1	no	—
414	C₂⁴	—	2	1	no	—
415	C₂⁴	C₂×C₇×D₄	1	2	yes	—
416	#41	—	2	16	no	—
417	#41	—	4	8	no	—
418	#41	—	4	16	no	—
419	#41	—	4	32	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	4	no	—
422	C₂×Q₈	—	2	4	no	—
423	C₂×Q₈	—	2	4	no	—
424	C₂×Q₈	—	4	4	no	—
425	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
426	C₂×D₄	—	2	8	no	—
427	C₂×D₄	—	2	8	no	—
428	C₂×D₄	—	2	4	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	4	8	no	—
435	C₂×D₄	—	4	8	no	—
436	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
437	C₂×D₄	C₇×#41	1	4	yes	complemented
438	C₂×D₄	C₂⁴×C₇	1	2	yes	—
439	C₂×D₄	C₂⁴×C₇	1	2	yes	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	8	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	8	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	4	8	no	—
451	C₂²×C₄	—	4	8	no	—
452	C₂²×C₄	—	4	4	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
456	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
457	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
459	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
460	SD₁₆	—	4	8	no	—
461	D₈	—	2	8	no	—
462	M₁₆	—	4	8	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	4	no	—
466	C₂×C₈	C₂⁴×C₇	1	2	yes	—
467	C₂×C₈	C₂⁴×C₇	1	2	yes	—
468	C₂×C₈	C₂⁴×C₇	1	4	yes	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	8	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	8	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
478	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
479	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
480	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
481	C₂²⋊C₄	—	2	8	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	8	no	—
485	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
486	C₄²	C₂×C₇×D₄	1	2	yes	—
487	C₄²	C₂⁴×C₇	1	2	yes	—
488	C₂×C₇	—	4	4	no	—
489	C₂×C₇	—	4	4	no	—
490	C₂×C₇	—	8	2	no	—
491	C₂×C₇	#3330	1	4	yes	direct product factor
492	C₂×C₇	C₂×#546	1	1	yes	characteristic
493	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
494	C₂×C₇	C₂×#578	1	1	yes	characteristic
495	C₂³	—	2	2	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	C₂²×C₇×D₄	1	4	yes	—
507	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
508	Q₈	—	2	4	no	—
509	Q₈	—	2	4	no	—
510	Q₈	—	4	4	no	—
511	Q₈	—	4	8	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	2	no	—
514	D₄	—	2	2	no	—
515	D₄	—	2	4	no	—
516	D₄	—	2	8	no	—
517	D₄	—	4	16	no	—
518	D₄	—	4	16	no	—
519	D₄	—	4	2	no	—
520	D₄	C₂×C₇×#41	1	4	yes	complemented
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	8	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	4	16	no	—
531	C₂×C₄	—	4	16	no	—
532	C₂×C₄	—	4	4	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	8	no	—
537	C₂×C₄	—	4	8	no	—
538	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
539	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
540	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
541	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
542	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
543	C₂×C₄	C₂×C₇×#41	1	2	yes	—
544	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
545	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
546	C₈	—	2	2	no	—
547	C₈	—	2	2	no	—
548	C₈	—	2	4	no	—
549	C₇	C₂×#3330	1	1	yes	characteristic, direct product factor, Sylow
550	C₂²	—	2	4	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	2	4	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	8	no	—
557	C₂²	—	4	8	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	8	4	no	—
562	C₂²	C₇×#546	1	2	yes	—
563	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
564	C₂²	C₇×#578	1	2	yes	—
565	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
566	C₄	—	2	2	no	—
567	C₄	—	2	4	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	4	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	4	no	—
572	C₄	C₇×#546	1	2	yes	—
573	C₄	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
574	C₄	C₂²×C₇×#41	1	1	yes	characteristic
575	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
576	C₂	—	4	4	no	—
577	C₂	—	4	4	no	—
578	C₂	—	8	2	no	—
579	C₂	C₇×#3330	1	4	yes	direct product factor
580	C₂	C₂×C₇×#546	1	1	yes	characteristic
581	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
582	C₂	C₂×C₇×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#547	C₂	semidirect
2. C₂×C₇×#547	C₂	semidirect
3. C₇×#3330	C₂	direct (N × H)
4. C₂×C₇×#487	C₂	semidirect
5. C₂×C₇×#484	C₂	semidirect
6. C₂×C₇×#474	C₂	semidirect
7. C₂×C₇×#468	C₂	semidirect
8. C₂×C₇×#461	C₂	semidirect
9. C₂×C₇×#449	C₂	semidirect
10. C₂×C₄×C₇×D₈	C₂	semidirect
11. C₂×C₇×#436	C₂	semidirect
12. C₂×C₇×#417	C₂	semidirect
20. C₇×#547	C₂²	semidirect
21. C₇×#547	C₂²	semidirect
35. C₇×#487	C₂²	semidirect
36. C₇×#484	C₂²	semidirect
37. C₇×#474	C₂²	semidirect
38. C₇×#468	C₂²	semidirect
39. C₇×#461	C₂²	semidirect
40. C₇×#449	C₂²	semidirect
41. C₄×C₇×D₈	C₂²	semidirect
42. C₇×#436	C₂²	semidirect
46. C₇×#417	C₂²	semidirect
55. C₂×#3330	C₇	direct (N × H)
130. C₂×#547	C₂×C₇	semidirect
131. C₂×#547	C₂×C₇	semidirect
132. #3330	C₂×C₇	direct (N × H)
133. C₂×#487	C₂×C₇	semidirect
134. C₂×#484	C₂×C₇	semidirect
135. C₂×#474	C₂×C₇	semidirect
136. C₂×#468	C₂×C₇	semidirect
137. C₂×#461	C₂×C₇	semidirect
138. C₂×#449	C₂×C₇	semidirect
139. C₂×C₄×D₈	C₂×C₇	semidirect
140. C₂×#436	C₂×C₇	semidirect
141. C₂×#417	C₂×C₇	semidirect
166. C₂×C₇×D₄	#41	semidirect
224. #547	C₂²×C₇	semidirect
225. #547	C₂²×C₇	semidirect
239. #487	C₂²×C₇	semidirect
240. #484	C₂²×C₇	semidirect
241. #474	C₂²×C₇	semidirect
242. #468	C₂²×C₇	semidirect
243. #461	C₂²×C₇	semidirect
244. #449	C₂²×C₇	semidirect
245. C₄×D₈	C₂²×C₇	semidirect
246. #436	C₂²×C₇	semidirect
250. #417	C₂²×C₇	semidirect
284. C₇×D₄	C₂×#41	semidirect
437. C₂×D₄	C₇×#41	semidirect
491. C₂×C₇	#3330	direct (N × H)
520. D₄	C₂×C₇×#41	semidirect
549. C₇	C₂×#3330	direct (N × H)
579. C₂	C₇×#3330	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#547	2
C₇×#3330	2
C₂×C₇×#487	2
C₂×C₇×#484	2
C₂×C₇×#474	2
C₂×C₇×#468	2
C₂×C₇×#461	2
C₂×C₇×#449	2
C₂×C₄×C₇×D₈	2
C₂×C₇×#436	2
C₂×C₇×#417	2
C₂×#3330	7

Subgroups — C2×C7×#3330 #13238366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3330 #13238366