Subgroups — C₇×#36594 #13213810

Order 1792.

2330 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#556	C₂	1	2	yes	maximal, complemented
2	C₇×#2868	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2858	C₂	1	2	yes	maximal
4	C₇×#2547	C₂	1	2	yes	maximal, complemented
5	C₇×#2545	C₂	1	4	yes	maximal, complemented
6	C₇×#2538	C₂	1	4	yes	maximal, complemented
7	C₇×#2512	C₂	1	8	yes	maximal, complemented
8	C₇×#2354	C₂	1	4	yes	maximal, complemented
9	C₄×C₇×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
10	C₄×C₇×#127	C₂	1	1	yes	maximal, characteristic
11	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#556	—	2	16	no	—
13	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₇×#127	C₂²	1	1	yes	characteristic
17	C₂×C₇×#126	C₂²	1	8	yes	—
18	C₂×C₇×#124	C₂²	1	4	yes	—
19	C₂×C₇×#124	C₂²	1	4	yes	—
20	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
21	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
22	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	—
23	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
25	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
26	C₂×C₇×#117	C₂²	1	4	yes	—
27	C₇×#397	C₂²	1	8	yes	—
28	C₇×#396	C₂²	1	16	yes	—
29	C₇×#391	C₂²	1	4	yes	—
30	C₇×#390	C₂²	1	4	yes	—
31	C₇×#390	C₂²	1	8	yes	—
32	C₇×#390	C₂²	1	8	yes	—
33	C₇×#390	C₂²	1	2	yes	—
34	C₇×#389	C₂²	1	8	yes	—
35	C₇×#388	C₂²	1	16	yes	—
36	C₇×#384	C₂²	1	4	yes	—
37	C₇×#384	C₂²	1	4	yes	—
38	C₇×#384	C₂²	1	1	yes	characteristic
39	C₇×#380	C₂²	1	8	yes	—
40	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
41	C₄×C₇×C₄⋊C₄	C₂²	1	8	yes	—
42	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
43	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
45	C₄³×C₇	C₂²	1	1	yes	characteristic
46	C₄³×C₇	C₂²	1	2	yes	—
47	#36594	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂²×C₇×Q₈	C₂³	1	4	yes	—
49	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
50	C₂²×C₇×D₄	C₂³	1	2	yes	—
51	C₂²×C₇×D₄	C₂³	1	4	yes	—
52	C₂³×C₄×C₇	C₂³	1	4	yes	—
53	C₇×C₄⋊Q₈	—	2	8	no	—
54	C₇×C₄⋊Q₈	—	2	8	no	—
55	C₇×C₄⋊Q₈	—	4	4	no	—
56	C₇×#127	—	2	4	no	—
57	C₇×#126	—	2	32	no	—
58	C₇×#124	—	2	16	no	—
59	C₇×#124	—	4	8	no	—
60	C₇×C₂²⋊Q₈	—	2	16	no	—
61	C₄×C₇×Q₈	—	2	16	no	—
62	C₄×C₇×Q₈	—	2	8	no	—
63	C₄×C₇×Q₈	D₄	1	8	yes	complemented
64	C₄×C₇×D₄	—	2	8	no	—
65	C₄×C₇×D₄	—	2	16	no	—
66	C₇×#117	—	2	16	no	—
67	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
71	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
72	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
74	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
75	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
76	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
79	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
80	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
81	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
82	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
83	C₂×C₄²×C₇	C₂³	1	4	yes	—
84	C₂×C₄²×C₇	C₂³	1	2	yes	—
85	C₂×C₄²×C₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₇	C₂³	1	4	yes	—
88	C₂×C₄²×C₇	C₂³	1	8	yes	—
89	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₇	C₂³	1	2	yes	—
91	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₇	C₂³	1	2	yes	—
93	C₇×#95	C₂³	1	4	yes	—
94	C₇×#95	C₂³	1	2	yes	—
95	C₇×#95	C₂³	1	16	yes	—
96	C₂×#556	C₂×C₇	1	2	yes	complemented
97	#2868	C₂×C₇	1	1	yes	characteristic, complemented
98	#2858	C₂×C₇	1	2	yes	—
99	#2547	C₂×C₇	1	2	yes	complemented
100	#2545	C₂×C₇	1	4	yes	complemented
101	#2538	C₂×C₇	1	4	yes	complemented
102	#2512	C₂×C₇	1	8	yes	complemented
103	#2354	C₂×C₇	1	4	yes	complemented
104	C₄×C₄⋊Q₈	C₂×C₇	1	2	yes	complemented
105	C₄×#127	C₂×C₇	1	1	yes	characteristic
106	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
107	C₂⁴×C₇	C₂⁴	1	4	yes	—
108	C₂×C₇×Q₈	—	2	8	no	—
109	C₂×C₇×Q₈	—	2	4	no	—
110	C₂×C₇×Q₈	—	2	8	no	—
111	C₂×C₇×Q₈	—	2	8	no	—
112	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
113	C₂×C₇×D₄	—	2	4	no	—
114	C₂×C₇×D₄	—	2	8	no	—
115	C₂×C₇×D₄	—	2	4	no	—
116	C₂×C₇×D₄	—	2	8	no	—
117	C₂×C₇×D₄	—	2	4	no	—
118	C₂×C₇×D₄	—	2	8	no	—
119	C₂²×C₄×C₇	—	2	8	no	—
120	C₂²×C₄×C₇	—	2	16	no	—
121	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
124	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
126	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
127	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
129	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
130	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
131	C₇×C₄⋊C₄	—	2	8	no	—
132	C₇×C₄⋊C₄	—	2	4	no	—
133	C₇×C₄⋊C₄	—	2	16	no	—
134	C₇×C₄⋊C₄	—	2	8	no	—
135	C₇×C₄⋊C₄	—	2	8	no	—
136	C₇×C₄⋊C₄	—	2	8	no	—
137	C₇×C₄⋊C₄	—	2	4	no	—
138	C₇×C₄⋊C₄	—	2	16	no	—
139	C₇×C₄⋊C₄	—	4	8	no	—
140	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
141	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
142	C₇×C₂²⋊C₄	—	2	16	no	—
143	C₇×C₂²⋊C₄	—	2	8	no	—
144	C₇×C₂²⋊C₄	—	2	16	no	—
145	C₇×C₂²⋊C₄	—	2	16	no	—
146	C₇×C₂²⋊C₄	—	4	16	no	—
147	C₄²×C₇	—	2	16	no	—
148	C₄²×C₇	—	2	8	no	—
149	C₄²×C₇	—	2	4	no	—
150	C₄²×C₇	—	2	2	no	—
151	C₄²×C₇	—	2	4	no	—
152	C₄²×C₇	—	2	8	no	—
153	C₄²×C₇	C₂×D₄	1	4	yes	—
154	C₄²×C₇	C₂×D₄	1	8	yes	—
155	C₄²×C₇	#41	1	8	yes	—
156	C₄²×C₇	#41	1	4	yes	—
157	#556	—	2	16	no	—
158	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
159	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
160	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
161	C₂×#127	C₂²×C₇	1	1	yes	characteristic
162	C₂×#126	C₂²×C₇	1	8	yes	—
163	C₂×#124	C₂²×C₇	1	4	yes	—
164	C₂×#124	C₂²×C₇	1	4	yes	—
165	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
166	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	—
167	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
168	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
169	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
170	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
171	C₂×#117	C₂²×C₇	1	4	yes	—
172	#397	C₂²×C₇	1	8	yes	—
173	#396	C₂²×C₇	1	16	yes	—
174	#391	C₂²×C₇	1	4	yes	—
175	#390	C₂²×C₇	1	4	yes	—
176	#390	C₂²×C₇	1	2	yes	—
177	#390	C₂²×C₇	1	8	yes	—
178	#390	C₂²×C₇	1	8	yes	—
179	#389	C₂²×C₇	1	8	yes	—
180	#388	C₂²×C₇	1	16	yes	—
181	#384	C₂²×C₇	1	1	yes	characteristic
182	#384	C₂²×C₇	1	4	yes	—
183	#384	C₂²×C₇	1	4	yes	—
184	#380	C₂²×C₇	1	8	yes	—
185	C₄×C₄⋊C₄	C₂²×C₇	1	8	yes	—
186	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
187	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
188	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
189	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
190	C₄³	C₂²×C₇	1	1	yes	characteristic
191	C₄³	C₂²×C₇	1	2	yes	—
192	C₂³×C₇	—	2	4	no	—
193	C₂³×C₇	—	2	8	no	—
194	C₂³×C₇	—	2	4	no	—
195	C₂³×C₇	—	2	4	no	—
196	C₂³×C₇	—	2	8	no	—
197	C₂³×C₇	C₂⁵	1	1	yes	characteristic
198	C₇×Q₈	—	2	8	no	—
199	C₇×Q₈	—	4	16	no	—
200	C₇×D₄	—	4	8	no	—
201	C₇×D₄	—	4	16	no	—
202	C₂×C₄×C₇	—	2	4	no	—
203	C₂×C₄×C₇	—	2	2	no	—
204	C₂×C₄×C₇	—	2	4	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	2	no	—
207	C₂×C₄×C₇	—	2	4	no	—
208	C₂×C₄×C₇	—	2	8	no	—
209	C₂×C₄×C₇	—	2	4	no	—
210	C₂×C₄×C₇	—	2	8	no	—
211	C₂×C₄×C₇	—	2	8	no	—
212	C₂×C₄×C₇	—	2	4	no	—
213	C₂×C₄×C₇	—	2	8	no	—
214	C₂×C₄×C₇	—	2	4	no	—
215	C₂×C₄×C₇	—	4	16	no	—
216	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
217	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
219	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₇	C₂×#41	1	4	yes	—
222	C₂×C₄×C₇	C₂×#41	1	4	yes	—
223	C₂×C₄×C₇	C₂×#41	1	2	yes	—
224	C₂×C₄×C₇	C₂×#41	1	4	yes	—
225	C₂×C₄×C₇	C₂×#41	1	4	yes	—
226	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
227	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
228	C₂²×Q₈	C₂³×C₇	1	4	yes	—
229	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
230	C₂²×D₄	C₂³×C₇	1	2	yes	—
231	C₂²×D₄	C₂³×C₇	1	4	yes	—
232	C₂³×C₄	C₂³×C₇	1	4	yes	—
233	C₄⋊Q₈	—	2	8	no	—
234	C₄⋊Q₈	—	2	8	no	—
235	C₄⋊Q₈	—	4	4	no	—
236	#127	—	2	4	no	—
237	#126	—	2	32	no	—
238	#124	—	2	16	no	—
239	#124	—	4	8	no	—
240	C₂²⋊Q₈	—	2	16	no	—
241	C₄×Q₈	—	2	16	no	—
242	C₄×Q₈	—	2	8	no	—
243	C₄×Q₈	C₇×D₄	1	8	yes	complemented
244	C₄×D₄	—	2	8	no	—
245	C₄×D₄	—	2	16	no	—
246	#117	—	2	16	no	—
247	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
248	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
250	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
251	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
253	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
254	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
255	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
256	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
258	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
259	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
260	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
261	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
262	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
263	C₂×C₄²	C₂³×C₇	1	8	yes	—
264	C₂×C₄²	C₂³×C₇	1	4	yes	—
265	C₂×C₄²	C₂³×C₇	1	2	yes	—
266	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₇	1	4	yes	—
268	C₂×C₄²	C₂³×C₇	1	2	yes	—
269	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₇	1	2	yes	—
271	C₂×C₄²	C₂³×C₇	1	2	yes	—
272	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
273	#95	C₂³×C₇	1	4	yes	—
274	#95	C₂³×C₇	1	2	yes	—
275	#95	C₂³×C₇	1	16	yes	—
276	C₂²×C₇	—	4	4	no	—
277	C₂²×C₇	—	4	4	no	—
278	C₂²×C₇	—	4	8	no	—
279	C₂²×C₇	—	4	4	no	—
280	C₂²×C₇	—	4	8	no	—
281	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
282	C₂²×C₇	C₂²×#41	1	2	yes	—
283	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
284	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
285	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
286	C₄×C₇	—	2	4	no	—
287	C₄×C₇	—	2	4	no	—
288	C₄×C₇	—	2	2	no	—
289	C₄×C₇	—	2	4	no	—
290	C₄×C₇	—	4	4	no	—
291	C₄×C₇	—	4	8	no	—
292	C₄×C₇	—	4	4	no	—
293	C₄×C₇	#532	1	4	yes	—
294	C₄×C₇	#550	1	4	yes	—
295	C₄×C₇	#556	1	8	yes	complemented
296	C₂⁴	C₂⁴×C₇	1	4	yes	—
297	C₂×Q₈	—	2	8	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	2	8	no	—
300	C₂×Q₈	—	2	8	no	—
301	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	8	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	8	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	8	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	2	16	no	—
310	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
311	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
312	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
313	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
315	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
316	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
318	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
319	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
320	C₄⋊C₄	—	2	8	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	16	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	—	2	8	no	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	16	no	—
328	C₄⋊C₄	—	4	8	no	—
329	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
330	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
331	C₂²⋊C₄	—	2	16	no	—
332	C₂²⋊C₄	—	2	8	no	—
333	C₂²⋊C₄	—	2	16	no	—
334	C₂²⋊C₄	—	2	16	no	—
335	C₂²⋊C₄	—	4	16	no	—
336	C₄²	—	2	16	no	—
337	C₄²	—	2	8	no	—
338	C₄²	—	2	4	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	4	no	—
341	C₄²	—	2	8	no	—
342	C₄²	C₂×C₇×D₄	1	4	yes	—
343	C₄²	C₂×C₇×D₄	1	8	yes	—
344	C₄²	C₇×#41	1	8	yes	—
345	C₄²	C₇×#41	1	4	yes	—
346	C₂×C₇	—	8	4	no	—
347	C₂×C₇	C₂×#532	1	1	yes	characteristic
348	C₂×C₇	C₂×#550	1	1	yes	characteristic
349	C₂×C₇	C₂×#556	1	2	yes	—
350	C₂×C₇	#3499	1	1	yes	characteristic
351	C₂×C₇	#3511	1	2	yes	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	8	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	8	no	—
357	C₂³	C₂⁵×C₇	1	1	yes	characteristic
358	Q₈	—	2	8	no	—
359	Q₈	—	4	16	no	—
360	D₄	—	4	8	no	—
361	D₄	—	4	16	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	8	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	4	16	no	—
376	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
377	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
378	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
379	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
380	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
381	C₂×C₄	C₂×C₇×#41	1	4	yes	—
382	C₂×C₄	C₂×C₇×#41	1	4	yes	—
383	C₂×C₄	C₂×C₇×#41	1	2	yes	—
384	C₂×C₄	C₂×C₇×#41	1	4	yes	—
385	C₂×C₄	C₂×C₇×#41	1	4	yes	—
386	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
387	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
388	C₇	#36594	1	1	yes	characteristic, direct product factor, Sylow
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	8	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	8	no	—
394	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
395	C₂²	C₂²×C₇×#41	1	2	yes	—
396	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
397	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
399	C₄	—	2	4	no	—
400	C₄	—	2	4	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	4	no	—
403	C₄	—	4	4	no	—
404	C₄	—	4	8	no	—
405	C₄	—	4	4	no	—
406	C₄	C₇×#532	1	4	yes	—
407	C₄	C₇×#550	1	4	yes	—
408	C₄	C₇×#556	1	8	yes	complemented
409	C₂	—	8	4	no	—
410	C₂	C₂×C₇×#532	1	1	yes	characteristic
411	C₂	C₂×C₇×#550	1	1	yes	characteristic
412	C₂	C₂×C₇×#556	1	2	yes	—
413	C₂	C₇×#3499	1	1	yes	characteristic
414	C₂	C₇×#3511	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂×C₇×#127	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#556	C₂	semidirect
2. C₇×#2868	C₂	semidirect
4. C₇×#2547	C₂	semidirect
5. C₇×#2545	C₂	semidirect
6. C₇×#2538	C₂	semidirect
7. C₇×#2512	C₂	semidirect
8. C₇×#2354	C₂	semidirect
9. C₄×C₇×C₄⋊Q₈	C₂	semidirect
11. C₄²×C₇×Q₈	C₂	semidirect
47. #36594	C₇	direct (N × H)
63. C₄×C₇×Q₈	D₄	semidirect
96. C₂×#556	C₂×C₇	semidirect
97. #2868	C₂×C₇	semidirect
99. #2547	C₂×C₇	semidirect
100. #2545	C₂×C₇	semidirect
101. #2538	C₂×C₇	semidirect
102. #2512	C₂×C₇	semidirect
103. #2354	C₂×C₇	semidirect
104. C₄×C₄⋊Q₈	C₂×C₇	semidirect
106. C₄²×Q₈	C₂×C₇	semidirect
243. C₄×Q₈	C₇×D₄	semidirect
295. C₄×C₇	#556	semidirect
388. C₇	#36594	direct (N × H)
408. C₄	C₇×#556	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#556	2
C₇×#2868	2
C₇×#2858	2
C₇×#2547	2
C₇×#2545	2
C₇×#2538	2
C₇×#2512	2
C₇×#2354	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×#127	2
C₄²×C₇×Q₈	2
#36594	7

Subgroups — C7×#36594 #13213810

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#36594 #13213810