Subgroups — C₂×C₇×#3079 #13237698

Order 1792.

2358 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic
3	C₇×#3079	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#477	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#475	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#476	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#474	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#428	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#423	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#417	C₂	1	2	yes	maximal
11	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
12	C₂³×C₇×Q₈	—	2	1	no	—
13	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
14	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₇×C₄⋊Q₈	—	2	4	no	—
17	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₇×C₄⋊Q₈	C₂²	1	8	yes	complemented
20	C₄×C₇×#41	—	2	4	no	—
21	C₄×C₇×#41	C₂²	1	8	yes	—
22	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×D₄	—	2	1	no	—
25	C₂×C₄×C₇×D₄	—	2	1	no	—
26	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₇×#117	—	2	1	no	—
29	C₂×C₇×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
31	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₄²×C₇	—	2	1	no	—
33	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
34	C₇×#477	C₂²	1	16	yes	complemented
35	C₇×#476	C₂²	1	16	yes	complemented
36	C₇×#475	C₂²	1	16	yes	complemented
37	C₇×#474	C₂²	1	16	yes	complemented
38	C₇×#428	C₂²	1	16	yes	complemented
39	C₂×C₇×#107	C₂²	1	4	yes	—
40	C₂×C₇×#106	C₂²	1	4	yes	—
41	C₇×#423	C₂²	1	8	yes	complemented
42	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
43	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
44	C₇×#417	C₂²	1	16	yes	—
45	C₂×C₇×#103	C₂²	1	4	yes	—
46	C₂×C₇×#102	C₂²	1	4	yes	—
47	C₂×#3079	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	—	2	2	no	—
49	C₂×C₇×#41	—	2	4	no	—
50	C₂×C₇×#41	Q₈	1	8	yes	complemented
51	C₂×C₇×#41	C₂³	1	4	yes	—
52	C₂²×C₇×Q₈	—	2	2	no	—
53	C₂²×C₇×Q₈	—	2	2	no	—
54	C₂²×C₇×Q₈	—	2	8	no	—
55	C₂²×C₇×Q₈	—	4	8	no	—
56	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
57	C₂²×C₇×D₄	—	2	1	no	—
58	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₇	—	2	1	no	—
60	C₂³×C₄×C₇	—	2	2	no	—
61	C₂³×C₄×C₇	—	2	1	no	—
62	C₂³×C₄×C₇	—	2	1	no	—
63	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
66	C₂×C₇×M₁₆	—	2	8	no	—
67	C₂×C₇×M₁₆	C₂³	1	8	yes	—
68	C₂²×C₇×C₈	C₂³	1	4	yes	—
69	C₇×C₄⋊Q₈	—	2	4	no	—
70	C₇×C₄⋊Q₈	—	2	4	no	—
71	C₇×C₄⋊Q₈	—	2	8	no	—
72	C₇×C₄⋊Q₈	—	2	8	no	—
73	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
74	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
75	C₄×C₇×Q₈	—	2	2	no	—
76	C₄×C₇×Q₈	—	2	2	no	—
77	C₄×C₇×Q₈	C₂³	1	4	yes	—
78	C₄×C₇×Q₈	C₂³	1	4	yes	—
79	C₄×C₇×D₄	—	2	8	no	—
80	C₄×C₇×D₄	—	2	8	no	—
81	C₄×C₇×D₄	—	2	2	no	—
82	C₄×C₇×D₄	—	2	2	no	—
83	C₄×C₇×D₄	C₂³	1	4	yes	—
84	C₄×C₇×D₄	C₂³	1	4	yes	—
85	C₇×#117	—	2	2	no	—
86	C₇×#117	—	2	8	no	—
87	C₇×#117	C₂³	1	4	yes	—
88	C₂×C₇×C₄⋊C₄	—	2	2	no	—
89	C₂×C₇×C₄⋊C₄	—	2	2	no	—
90	C₂×C₇×C₄⋊C₄	—	2	8	no	—
91	C₂×C₇×C₄⋊C₄	—	2	4	no	—
92	C₂×C₇×C₄⋊C₄	—	2	2	no	—
93	C₂×C₇×C₄⋊C₄	—	2	1	no	—
94	C₂×C₇×C₄⋊C₄	—	2	1	no	—
95	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
97	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₄²×C₇	—	2	1	no	—
103	C₂×C₄²×C₇	—	2	1	no	—
104	C₂×C₄²×C₇	—	2	1	no	—
105	C₂×C₄²×C₇	—	2	8	no	—
106	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₇	D₄	1	4	yes	—
109	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₇	C₂³	1	4	yes	—
112	C₇×#107	C₂³	1	16	yes	—
113	C₇×#106	C₂³	1	16	yes	—
114	C₇×C₄⋊C₈	C₂³	1	8	yes	—
115	C₇×C₄⋊C₈	C₂³	1	8	yes	—
116	C₇×#103	C₂³	1	16	yes	—
117	C₇×#102	C₂³	1	16	yes	—
118	C₂²×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
119	C₂×C₄×#41	C₂×C₇	1	1	yes	characteristic
120	#3079	C₂×C₇	1	16	yes	direct product factor
121	C₂×#477	C₂×C₇	1	2	yes	complemented
122	C₂×#475	C₂×C₇	1	2	yes	complemented
123	C₂×#476	C₂×C₇	1	2	yes	complemented
124	C₂×#474	C₂×C₇	1	2	yes	complemented
125	C₂×#428	C₂×C₇	1	2	yes	complemented
126	C₂×#423	C₂×C₇	1	1	yes	characteristic, complemented
127	C₂×#417	C₂×C₇	1	2	yes	—
128	C₂⁴×C₇	—	2	1	no	—
129	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
130	C₇×#41	—	2	16	no	—
131	C₇×#41	—	2	8	no	—
132	C₇×#41	C₂×Q₈	1	16	yes	complemented
133	C₂×C₇×Q₈	—	2	1	no	—
134	C₂×C₇×Q₈	—	2	8	no	—
135	C₂×C₇×Q₈	—	2	8	no	—
136	C₂×C₇×Q₈	—	2	2	no	—
137	C₂×C₇×Q₈	—	4	8	no	—
138	C₂×C₇×Q₈	—	4	32	no	—
139	C₂×C₇×Q₈	—	4	8	no	—
140	C₂×C₇×Q₈	C₂×Q₈	1	4	yes	complemented
141	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
142	C₂×C₇×D₄	—	2	8	no	—
143	C₂×C₇×D₄	—	2	4	no	—
144	C₂×C₇×D₄	—	2	1	no	—
145	C₂×C₇×D₄	—	2	2	no	—
146	C₂×C₇×D₄	C₂×Q₈	1	4	yes	complemented
147	C₂×C₇×D₄	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₇	—	2	1	no	—
149	C₂²×C₄×C₇	—	2	8	no	—
150	C₂²×C₄×C₇	—	2	4	no	—
151	C₂²×C₄×C₇	—	2	4	no	—
152	C₂²×C₄×C₇	—	2	4	no	—
153	C₂²×C₄×C₇	—	2	8	no	—
154	C₂²×C₄×C₇	—	2	1	no	—
155	C₂²×C₄×C₇	—	2	1	no	—
156	C₂²×C₄×C₇	—	2	4	no	—
157	C₂²×C₄×C₇	—	2	4	no	—
158	C₂²×C₄×C₇	—	2	4	no	—
159	C₂²×C₄×C₇	—	4	8	no	—
160	C₂²×C₄×C₇	—	4	4	no	—
161	C₂²×C₄×C₇	—	4	4	no	—
162	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
171	C₂²×C₄×C₇	#41	1	4	yes	—
172	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
174	C₇×M₁₆	—	2	16	no	—
175	C₂×C₇×C₈	—	2	8	no	—
176	C₂×C₇×C₈	C₂⁴	1	8	yes	—
177	C₇×C₄⋊C₄	—	2	8	no	—
178	C₇×C₄⋊C₄	—	2	8	no	—
179	C₇×C₄⋊C₄	—	2	8	no	—
180	C₇×C₄⋊C₄	—	2	4	no	—
181	C₇×C₄⋊C₄	—	2	4	no	—
182	C₇×C₄⋊C₄	—	2	4	no	—
183	C₇×C₄⋊C₄	—	2	1	no	—
184	C₇×C₄⋊C₄	—	2	1	no	—
185	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
186	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
187	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
188	C₇×C₂²⋊C₄	—	2	4	no	—
189	C₇×C₂²⋊C₄	—	2	4	no	—
190	C₇×C₂²⋊C₄	—	2	4	no	—
191	C₄²×C₇	—	2	4	no	—
192	C₄²×C₇	—	2	4	no	—
193	C₄²×C₇	—	2	4	no	—
194	C₄²×C₇	C₂×D₄	1	4	yes	—
195	C₄²×C₇	C₂×D₄	1	4	yes	—
196	C₄²×C₇	C₂×D₄	1	2	yes	—
197	C₄²×C₇	C₂×D₄	1	2	yes	—
198	C₄²×C₇	C₂⁴	1	2	yes	—
199	C₄²×C₇	C₂⁴	1	2	yes	—
200	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
201	C₂³×Q₈	—	2	1	no	—
202	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
203	C₂×C₄⋊Q₈	—	2	1	no	—
204	C₂×C₄⋊Q₈	—	2	4	no	—
205	C₂×C₄⋊Q₈	—	2	1	no	—
206	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
207	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
208	C₂×C₄⋊Q₈	C₂²×C₇	1	8	yes	complemented
209	C₄×#41	—	2	4	no	—
210	C₄×#41	C₂²×C₇	1	8	yes	—
211	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
212	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
213	C₂×C₄×D₄	—	2	1	no	—
214	C₂×C₄×D₄	—	2	1	no	—
215	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
217	C₂×#117	—	2	1	no	—
218	C₂×#117	C₂²×C₇	1	1	yes	characteristic
219	C₂²×C₄⋊C₄	—	2	1	no	—
220	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
221	C₂²×C₄²	—	2	1	no	—
222	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
223	#477	C₂²×C₇	1	16	yes	complemented
224	#476	C₂²×C₇	1	16	yes	complemented
225	#475	C₂²×C₇	1	16	yes	complemented
226	#474	C₂²×C₇	1	16	yes	complemented
227	#428	C₂²×C₇	1	16	yes	complemented
228	C₂×#107	C₂²×C₇	1	4	yes	—
229	C₂×#106	C₂²×C₇	1	4	yes	—
230	#423	C₂²×C₇	1	8	yes	complemented
231	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
232	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
233	#417	C₂²×C₇	1	16	yes	—
234	C₂×#103	C₂²×C₇	1	4	yes	—
235	C₂×#102	C₂²×C₇	1	4	yes	—
236	C₂³×C₇	—	2	2	no	—
237	C₂³×C₇	—	2	2	no	—
238	C₂³×C₇	—	2	4	no	—
239	C₂³×C₇	—	2	2	no	—
240	C₂³×C₇	—	4	2	no	—
241	C₂³×C₇	—	4	2	no	—
242	C₂³×C₇	C₂²⋊Q₈	1	4	yes	—
243	C₂³×C₇	C₂²×D₄	1	2	yes	—
244	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
245	C₇×Q₈	—	2	4	no	—
246	C₇×Q₈	—	2	2	no	—
247	C₇×Q₈	—	4	16	no	—
248	C₇×Q₈	—	4	16	no	—
249	C₇×Q₈	C₂²×Q₈	1	4	yes	complemented
250	C₇×D₄	—	2	16	no	—
251	C₇×D₄	—	2	4	no	—
252	C₇×D₄	—	2	2	no	—
253	C₇×D₄	C₂²×Q₈	1	4	yes	complemented
254	C₂×C₄×C₇	—	2	4	no	—
255	C₂×C₄×C₇	—	2	2	no	—
256	C₂×C₄×C₇	—	2	2	no	—
257	C₂×C₄×C₇	—	2	2	no	—
258	C₂×C₄×C₇	—	2	16	no	—
259	C₂×C₄×C₇	—	2	8	no	—
260	C₂×C₄×C₇	—	2	8	no	—
261	C₂×C₄×C₇	—	2	2	no	—
262	C₂×C₄×C₇	—	2	2	no	—
263	C₂×C₄×C₇	—	2	8	no	—
264	C₂×C₄×C₇	—	4	16	no	—
265	C₂×C₄×C₇	—	4	2	no	—
266	C₂×C₄×C₇	—	4	8	no	—
267	C₂×C₄×C₇	—	4	2	no	—
268	C₂×C₄×C₇	—	4	8	no	—
269	C₂×C₄×C₇	—	4	8	no	—
270	C₂×C₄×C₇	C₂²⋊Q₈	1	4	yes	—
271	C₂×C₄×C₇	C₂²⋊Q₈	1	8	yes	—
272	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
273	C₂×C₄×C₇	#137	1	4	yes	—
274	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
279	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
281	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
282	C₂×C₄×C₇	C₂×#41	1	2	yes	—
283	C₂×C₄×C₇	C₂×#41	1	4	yes	—
284	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
285	C₇×C₈	—	2	8	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	4	no	—
288	C₂×#41	C₇×Q₈	1	8	yes	complemented
289	C₂×#41	C₂³×C₇	1	4	yes	—
290	C₂²×Q₈	—	2	2	no	—
291	C₂²×Q₈	—	2	2	no	—
292	C₂²×Q₈	—	2	8	no	—
293	C₂²×Q₈	—	4	8	no	—
294	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
297	C₂³×C₄	—	2	1	no	—
298	C₂³×C₄	—	2	2	no	—
299	C₂³×C₄	—	2	1	no	—
300	C₂³×C₄	—	2	1	no	—
301	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
302	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
304	C₂×M₁₆	—	2	8	no	—
305	C₂×M₁₆	C₂³×C₇	1	8	yes	—
306	C₂²×C₈	C₂³×C₇	1	4	yes	—
307	C₄⋊Q₈	—	2	4	no	—
308	C₄⋊Q₈	—	2	4	no	—
309	C₄⋊Q₈	—	2	8	no	—
310	C₄⋊Q₈	—	2	8	no	—
311	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
312	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
313	C₄×Q₈	—	2	2	no	—
314	C₄×Q₈	—	2	2	no	—
315	C₄×Q₈	C₂³×C₇	1	4	yes	—
316	C₄×Q₈	C₂³×C₇	1	4	yes	—
317	C₄×D₄	—	2	8	no	—
318	C₄×D₄	—	2	8	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	C₂³×C₇	1	4	yes	—
322	C₄×D₄	C₂³×C₇	1	4	yes	—
323	#117	—	2	2	no	—
324	#117	—	2	8	no	—
325	#117	C₂³×C₇	1	4	yes	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	8	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	4	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
334	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
335	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	—	2	8	no	—
344	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
345	C₂×C₄²	C₇×D₄	1	4	yes	—
346	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
347	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₇	1	4	yes	—
350	#107	C₂³×C₇	1	16	yes	—
351	#106	C₂³×C₇	1	16	yes	—
352	C₄⋊C₈	C₂³×C₇	1	8	yes	—
353	C₄⋊C₈	C₂³×C₇	1	8	yes	—
354	#103	C₂³×C₇	1	16	yes	—
355	#102	C₂³×C₇	1	16	yes	—
356	C₂²×C₇	—	2	8	no	—
357	C₂²×C₇	—	2	2	no	—
358	C₂²×C₇	—	2	2	no	—
359	C₂²×C₇	—	2	4	no	—
360	C₂²×C₇	—	4	8	no	—
361	C₂²×C₇	—	4	2	no	—
362	C₂²×C₇	—	4	2	no	—
363	C₂²×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
364	C₂²×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
365	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
366	C₂²×C₇	C₂×#137	1	2	yes	—
367	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
368	C₄×C₇	—	2	4	no	—
369	C₄×C₇	—	2	2	no	—
370	C₄×C₇	—	2	2	no	—
371	C₄×C₇	—	4	2	no	—
372	C₄×C₇	—	4	8	no	—
373	C₄×C₇	—	4	2	no	—
374	C₄×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
375	C₄×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
376	C₄×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
377	C₄×C₇	C₂×#137	1	4	yes	—
378	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
379	C₄×C₇	C₂²×#41	1	1	yes	characteristic
380	C₂⁴	—	2	1	no	—
381	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
382	#41	—	2	16	no	—
383	#41	—	2	8	no	—
384	#41	C₂×C₇×Q₈	1	16	yes	complemented
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	8	no	—
387	C₂×Q₈	—	2	8	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	4	8	no	—
390	C₂×Q₈	—	4	32	no	—
391	C₂×Q₈	—	4	8	no	—
392	C₂×Q₈	C₂×C₇×Q₈	1	4	yes	complemented
393	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	C₂×C₇×Q₈	1	4	yes	complemented
399	C₂×D₄	C₂⁴×C₇	1	2	yes	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	8	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	8	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	4	8	no	—
412	C₂²×C₄	—	4	4	no	—
413	C₂²×C₄	—	4	4	no	—
414	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
415	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
416	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
417	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
418	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
419	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
420	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
421	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
422	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
423	C₂²×C₄	C₇×#41	1	4	yes	—
424	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
426	M₁₆	—	2	16	no	—
427	C₂×C₈	—	2	8	no	—
428	C₂×C₈	C₂⁴×C₇	1	8	yes	—
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	2	8	no	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
438	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
439	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₄²	—	2	4	no	—
444	C₄²	—	2	4	no	—
445	C₄²	—	2	4	no	—
446	C₄²	C₂×C₇×D₄	1	4	yes	—
447	C₄²	C₂×C₇×D₄	1	4	yes	—
448	C₄²	C₂×C₇×D₄	1	2	yes	—
449	C₄²	C₂×C₇×D₄	1	2	yes	—
450	C₄²	C₂⁴×C₇	1	2	yes	—
451	C₄²	C₂⁴×C₇	1	2	yes	—
452	C₂×C₇	—	2	4	no	—
453	C₂×C₇	—	4	4	no	—
454	C₂×C₇	#3079	1	4	yes	direct product factor
455	C₂×C₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
456	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
457	C₂×C₇	C₂²×#137	1	1	yes	characteristic
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	C₇×C₂²⋊Q₈	1	4	yes	—
465	C₂³	C₂²×C₇×D₄	1	2	yes	—
466	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
467	Q₈	—	2	2	no	—
468	Q₈	—	2	4	no	—
469	Q₈	—	4	16	no	—
470	Q₈	—	4	16	no	—
471	Q₈	C₂²×C₇×Q₈	1	4	yes	complemented
472	D₄	—	2	16	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	4	no	—
475	D₄	C₂²×C₇×Q₈	1	4	yes	complemented
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	16	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	8	no	—
486	C₂×C₄	—	4	16	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	8	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	8	no	—
491	C₂×C₄	—	4	8	no	—
492	C₂×C₄	C₇×C₂²⋊Q₈	1	4	yes	—
493	C₂×C₄	C₇×C₂²⋊Q₈	1	8	yes	—
494	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
495	C₂×C₄	C₇×#137	1	4	yes	—
496	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
497	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
498	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
499	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
500	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
501	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
502	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
503	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
504	C₂×C₄	C₂×C₇×#41	1	2	yes	—
505	C₂×C₄	C₂×C₇×#41	1	4	yes	—
506	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
507	C₈	—	2	8	no	—
508	C₇	C₂×#3079	1	1	yes	characteristic, direct product factor, Sylow
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	8	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	8	no	—
516	C₂²	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
517	C₂²	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
518	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
519	C₂²	C₂×C₇×#137	1	2	yes	—
520	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	4	no	—
524	C₄	—	4	8	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
528	C₄	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
529	C₄	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
530	C₄	C₂×C₇×#137	1	4	yes	—
531	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
532	C₄	C₂²×C₇×#41	1	1	yes	characteristic
533	C₂	—	2	4	no	—
534	C₂	—	4	4	no	—
535	C₂	C₇×#3079	1	4	yes	direct product factor
536	C₂	C₂²×C₇×C₂²⋊Q₈	1	1	yes	characteristic
537	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
538	C₂	C₂²×C₇×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂²×C₇×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×C₄⋊Q₈	C₂	semidirect
3. C₇×#3079	C₂	direct (N × H)
4. C₂×C₇×#477	C₂	semidirect
5. C₂×C₇×#475	C₂	semidirect
6. C₂×C₇×#476	C₂	semidirect
7. C₂×C₇×#474	C₂	semidirect
8. C₂×C₇×#428	C₂	semidirect
9. C₂×C₇×#423	C₂	semidirect
19. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
34. C₇×#477	C₂²	semidirect
35. C₇×#476	C₂²	semidirect
36. C₇×#475	C₂²	semidirect
37. C₇×#474	C₂²	semidirect
38. C₇×#428	C₂²	semidirect
41. C₇×#423	C₂²	semidirect
47. C₂×#3079	C₇	direct (N × H)
50. C₂×C₇×#41	Q₈	semidirect
118. C₂²×C₄⋊Q₈	C₂×C₇	semidirect
120. #3079	C₂×C₇	direct (N × H)
121. C₂×#477	C₂×C₇	semidirect
122. C₂×#475	C₂×C₇	semidirect
123. C₂×#476	C₂×C₇	semidirect
124. C₂×#474	C₂×C₇	semidirect
125. C₂×#428	C₂×C₇	semidirect
126. C₂×#423	C₂×C₇	semidirect
132. C₇×#41	C₂×Q₈	semidirect
140. C₂×C₇×Q₈	C₂×Q₈	semidirect
146. C₂×C₇×D₄	C₂×Q₈	semidirect
208. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
223. #477	C₂²×C₇	semidirect
224. #476	C₂²×C₇	semidirect
225. #475	C₂²×C₇	semidirect
226. #474	C₂²×C₇	semidirect
227. #428	C₂²×C₇	semidirect
230. #423	C₂²×C₇	semidirect
249. C₇×Q₈	C₂²×Q₈	semidirect
253. C₇×D₄	C₂²×Q₈	semidirect
288. C₂×#41	C₇×Q₈	semidirect
384. #41	C₂×C₇×Q₈	semidirect
392. C₂×Q₈	C₂×C₇×Q₈	semidirect
398. C₂×D₄	C₂×C₇×Q₈	semidirect
454. C₂×C₇	#3079	direct (N × H)
471. Q₈	C₂²×C₇×Q₈	semidirect
475. D₄	C₂²×C₇×Q₈	semidirect
508. C₇	C₂×#3079	direct (N × H)
535. C₂	C₇×#3079	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×C₇×C₄⋊Q₈	2
C₂×C₄×C₇×#41	2
C₇×#3079	2
C₂×C₇×#477	2
C₂×C₇×#475	2
C₂×C₇×#476	2
C₂×C₇×#474	2
C₂×C₇×#428	2
C₂×C₇×#423	2
C₂×C₇×#417	2
C₂×#3079	7

Subgroups — C2×C7×#3079 #13237698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3079 #13237698