Subgroups — C₇×#26060 #13203276

Order 1792.

894 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₇×#106	C₂	1	1	yes	maximal, characteristic
3	C₇×#2440	C₂	1	2	yes	maximal
4	C₇×#2084	C₂	1	2	yes	maximal, complemented
5	C₇×#2058	C₂	1	2	yes	maximal, complemented
6	C₇×#1941	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1853	C₂	1	2	yes	maximal
9	C₇×#1844	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1807	C₂	1	1	yes	maximal, characteristic
11	C₇×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
15	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
16	C₇×#498	—	2	4	no	—
17	C₂×C₇×#106	—	2	4	no	—
18	C₂×C₇×#106	C₂²	1	1	yes	characteristic
19	C₂×C₇×#106	C₂²	1	2	yes	—
20	C₂×C₇×#106	C₂²	1	2	yes	—
21	C₂×C₇×#106	C₂²	1	1	yes	characteristic
22	C₂×C₇×#106	C₂²	1	1	yes	characteristic
23	C₂×C₇×#106	C₂²	1	2	yes	—
24	C₂×C₇×#106	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
28	C₇×#398	—	2	2	no	—
29	C₇×#395	—	2	2	no	—
30	C₇×#389	C₂²	1	2	yes	—
31	C₇×#389	C₂²	1	2	yes	—
32	C₇×#385	—	2	2	no	—
33	C₇×#384	C₂²	1	2	yes	—
34	C₇×#380	C₂²	1	2	yes	—
35	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₇×#340	C₂²	1	2	yes	—
37	C₇×#340	C₂²	1	2	yes	—
38	C₇×#340	C₂²	1	2	yes	—
39	C₇×#336	C₂²	1	1	yes	characteristic
40	C₇×#336	C₂²	1	1	yes	characteristic
41	#26060	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₇×Q₈	—	2	2	no	—
43	C₂³×C₄×C₇	—	2	2	no	—
44	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
45	C₂²×C₇×C₈	—	2	2	no	—
46	C₂²×C₇×C₈	—	2	2	no	—
47	C₂²×C₇×C₈	Q₈	1	4	yes	complemented
48	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₇×C₄⋊Q₈	—	2	4	no	—
53	C₇×C₄⋊Q₈	—	4	2	no	—
54	C₇×C₂²⋊Q₈	—	4	8	no	—
55	C₂×C₇×C₄⋊C₄	—	2	4	no	—
56	C₂×C₇×C₄⋊C₄	—	2	2	no	—
57	C₂×C₇×C₄⋊C₄	—	2	2	no	—
58	C₂×C₇×C₄⋊C₄	—	2	2	no	—
59	C₂×C₇×C₄⋊C₄	—	2	2	no	—
60	C₂×C₇×C₄⋊C₄	—	2	2	no	—
61	C₂×C₇×C₄⋊C₄	—	2	2	no	—
62	C₂×C₇×C₄⋊C₄	—	4	2	no	—
63	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
69	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
71	C₇×#106	—	2	2	no	—
72	C₇×#106	—	2	2	no	—
73	C₇×#106	—	2	2	no	—
74	C₇×#106	—	2	4	no	—
75	C₇×#106	—	2	4	no	—
76	C₇×#106	—	4	2	no	—
77	C₇×#106	D₄	1	4	yes	—
78	C₇×C₂²⋊C₈	Q₈	1	4	yes	complemented
79	C₄×C₇×C₈	—	2	2	no	—
80	C₄×C₇×C₈	—	2	2	no	—
81	C₇×#95	—	2	2	no	—
82	C₇×#95	—	2	2	no	—
83	C₇×#95	—	2	2	no	—
84	C₇×#95	D₄	1	2	yes	—
85	C₂×#498	C₂×C₇	1	1	yes	characteristic, complemented
86	C₂²×#106	C₂×C₇	1	1	yes	characteristic
87	#2440	C₂×C₇	1	2	yes	—
88	#2084	C₂×C₇	1	2	yes	complemented
89	#2058	C₂×C₇	1	2	yes	complemented
90	#1941	C₂×C₇	1	1	yes	characteristic, complemented
91	#1941	C₂×C₇	1	1	yes	characteristic, complemented
92	#1853	C₂×C₇	1	2	yes	—
93	#1844	C₂×C₇	1	1	yes	characteristic, complemented
94	#1807	C₂×C₇	1	1	yes	characteristic
95	C₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
96	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
97	C₂×C₇×Q₈	—	4	4	no	—
98	C₂×C₇×Q₈	—	4	4	no	—
99	C₂×C₇×Q₈	—	8	2	no	—
100	C₂²×C₄×C₇	—	2	1	no	—
101	C₂²×C₄×C₇	—	2	1	no	—
102	C₂²×C₄×C₇	—	2	1	no	—
103	C₂²×C₄×C₇	—	2	1	no	—
104	C₂²×C₄×C₇	—	2	2	no	—
105	C₂²×C₄×C₇	—	2	2	no	—
106	C₂²×C₄×C₇	—	2	2	no	—
107	C₂²×C₄×C₇	—	2	2	no	—
108	C₂²×C₄×C₇	—	4	4	no	—
109	C₂²×C₄×C₇	—	4	4	no	—
110	C₂²×C₄×C₇	—	8	2	no	—
111	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
115	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
116	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
117	C₂×C₇×C₈	—	2	1	no	—
118	C₂×C₇×C₈	—	2	1	no	—
119	C₂×C₇×C₈	—	2	1	no	—
120	C₂×C₇×C₈	—	2	1	no	—
121	C₂×C₇×C₈	—	2	1	no	—
122	C₂×C₇×C₈	—	2	1	no	—
123	C₂×C₇×C₈	—	2	8	no	—
124	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
125	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
126	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
127	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
128	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
129	C₂×C₇×C₈	#41	1	2	yes	—
130	C₇×C₄⋊C₄	—	2	2	no	—
131	C₇×C₄⋊C₄	—	2	2	no	—
132	C₇×C₄⋊C₄	—	2	2	no	—
133	C₇×C₄⋊C₄	—	2	2	no	—
134	C₇×C₄⋊C₄	—	2	2	no	—
135	C₇×C₄⋊C₄	—	2	2	no	—
136	C₇×C₄⋊C₄	—	2	2	no	—
137	C₇×C₄⋊C₄	—	4	4	no	—
138	C₇×C₄⋊C₄	—	4	4	no	—
139	C₇×C₄⋊C₄	—	4	4	no	—
140	C₇×C₄⋊C₄	—	4	4	no	—
141	C₇×C₄⋊C₄	—	4	4	no	—
142	C₇×C₄⋊C₄	—	8	2	no	—
143	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
144	C₇×C₂²⋊C₄	—	4	4	no	—
145	C₇×C₂²⋊C₄	SD₁₆	1	8	yes	—
146	C₄²×C₇	—	2	1	no	—
147	C₄²×C₇	—	2	1	no	—
148	C₄²×C₇	—	2	1	no	—
149	C₄²×C₇	—	2	1	no	—
150	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
151	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
152	C₂×C₂²⋊Q₈	—	2	2	no	—
153	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
154	#498	—	2	4	no	—
155	C₂×#106	—	2	4	no	—
156	C₂×#106	C₂²×C₇	1	2	yes	—
157	C₂×#106	C₂²×C₇	1	1	yes	characteristic
158	C₂×#106	C₂²×C₇	1	1	yes	characteristic
159	C₂×#106	C₂²×C₇	1	2	yes	—
160	C₂×#106	C₂²×C₇	1	1	yes	characteristic
161	C₂×#106	C₂²×C₇	1	2	yes	—
162	C₂×#106	C₂²×C₇	1	1	yes	characteristic
163	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
164	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
165	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
166	#398	—	2	2	no	—
167	#395	—	2	2	no	—
168	#389	C₂²×C₇	1	2	yes	—
169	#389	C₂²×C₇	1	2	yes	—
170	#385	—	2	2	no	—
171	#384	C₂²×C₇	1	2	yes	—
172	#380	C₂²×C₇	1	2	yes	—
173	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
174	#340	C₂²×C₇	1	2	yes	—
175	#340	C₂²×C₇	1	2	yes	—
176	#340	C₂²×C₇	1	2	yes	—
177	#336	C₂²×C₇	1	1	yes	characteristic
178	#336	C₂²×C₇	1	1	yes	characteristic
179	C₂³×C₇	—	2	1	no	—
180	C₂³×C₇	—	2	1	no	—
181	C₂³×C₇	—	2	2	no	—
182	C₂³×C₇	C₄⋊Q₈	1	2	yes	—
183	C₂³×C₇	C₂×SD₁₆	1	4	yes	—
184	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
185	C₇×Q₈	—	8	8	no	—
186	C₂×C₄×C₇	—	2	2	no	—
187	C₂×C₄×C₇	—	2	1	no	—
188	C₂×C₄×C₇	—	2	2	no	—
189	C₂×C₄×C₇	—	2	1	no	—
190	C₂×C₄×C₇	—	2	2	no	—
191	C₂×C₄×C₇	—	2	2	no	—
192	C₂×C₄×C₇	—	2	2	no	—
193	C₂×C₄×C₇	—	2	2	no	—
194	C₂×C₄×C₇	—	2	2	no	—
195	C₂×C₄×C₇	—	2	2	no	—
196	C₂×C₄×C₇	—	2	4	no	—
197	C₂×C₄×C₇	—	4	2	no	—
198	C₂×C₄×C₇	—	4	2	no	—
199	C₂×C₄×C₇	—	4	2	no	—
200	C₂×C₄×C₇	—	4	2	no	—
201	C₂×C₄×C₇	—	4	2	no	—
202	C₂×C₄×C₇	—	4	2	no	—
203	C₂×C₄×C₇	—	4	2	no	—
204	C₂×C₄×C₇	—	4	2	no	—
205	C₂×C₄×C₇	—	4	2	no	—
206	C₂×C₄×C₇	—	4	2	no	—
207	C₂×C₄×C₇	—	4	2	no	—
208	C₂×C₄×C₇	—	8	8	no	—
209	C₂×C₄×C₇	C₄⋊Q₈	1	2	yes	—
210	C₂×C₄×C₇	C₂×SD₁₆	1	4	yes	—
211	C₂×C₄×C₇	C₂×SD₁₆	1	4	yes	—
212	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
215	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
218	C₇×C₈	—	2	2	no	—
219	C₇×C₈	—	2	2	no	—
220	C₇×C₈	—	2	2	no	—
221	C₇×C₈	C₂²⋊Q₈	1	4	yes	complemented
222	C₂²×Q₈	—	2	2	no	—
223	C₂³×C₄	—	2	2	no	—
224	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	—	2	2	no	—
227	C₂²×C₈	C₇×Q₈	1	4	yes	complemented
228	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
232	C₄⋊Q₈	—	2	4	no	—
233	C₄⋊Q₈	—	4	2	no	—
234	C₂²⋊Q₈	—	4	8	no	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	4	2	no	—
243	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
244	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
249	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
251	#106	—	2	2	no	—
252	#106	—	2	2	no	—
253	#106	—	2	2	no	—
254	#106	—	2	4	no	—
255	#106	—	2	4	no	—
256	#106	—	4	2	no	—
257	#106	C₇×D₄	1	4	yes	—
258	C₂²⋊C₈	C₇×Q₈	1	4	yes	complemented
259	C₄×C₈	—	2	2	no	—
260	C₄×C₈	—	2	2	no	—
261	#95	—	2	2	no	—
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	#95	C₇×D₄	1	2	yes	—
265	C₂²×C₇	—	2	4	no	—
266	C₂²×C₇	—	2	2	no	—
267	C₂²×C₇	—	2	2	no	—
268	C₂²×C₇	—	2	4	no	—
269	C₂²×C₇	#498	1	4	yes	complemented
270	C₂²×C₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
271	C₂²×C₇	D₄²	1	1	yes	characteristic
272	C₂²×C₇	#547	1	1	yes	characteristic
273	C₂²×C₇	C₂²×SD₁₆	1	2	yes	—
274	C₂²×C₇	#577	1	2	yes	—
275	C₄×C₇	—	2	4	no	—
276	C₄×C₇	—	2	2	no	—
277	C₄×C₇	—	2	4	no	—
278	C₄×C₇	—	4	4	no	—
279	C₄×C₇	—	8	2	no	—
280	C₄×C₇	—	8	2	no	—
281	C₄×C₇	—	8	2	no	—
282	C₄×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
283	C₄×C₇	#544	1	1	yes	characteristic
284	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
285	C₄×C₇	#554	1	1	yes	characteristic
286	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
287	C₂×Q₈	—	4	4	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×Q₈	—	8	2	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	—	8	2	no	—
301	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
303	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
304	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
305	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	8	no	—
314	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
315	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
316	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
317	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
318	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
319	C₂×C₈	C₇×#41	1	2	yes	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	4	4	no	—
328	C₄⋊C₄	—	4	4	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	—	8	2	no	—
333	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
334	C₂²⋊C₄	—	4	4	no	—
335	C₂²⋊C₄	C₇×SD₁₆	1	8	yes	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₂×C₇	—	2	4	no	—
341	C₂×C₇	#2440	1	1	yes	characteristic
342	C₂×C₇	C₂×#498	1	1	yes	characteristic
343	C₂×C₇	#3163	1	1	yes	characteristic
344	C₂×C₇	D₄×SD₁₆	1	2	yes	—
345	C₂×C₇	#3335	1	2	yes	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	2	no	—
349	C₂³	C₇×C₄⋊Q₈	1	2	yes	—
350	C₂³	C₂×C₇×SD₁₆	1	4	yes	—
351	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
352	Q₈	—	8	8	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	8	8	no	—
376	C₂×C₄	C₇×C₄⋊Q₈	1	2	yes	—
377	C₂×C₄	C₂×C₇×SD₁₆	1	4	yes	—
378	C₂×C₄	C₂×C₇×SD₁₆	1	4	yes	—
379	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
381	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
382	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
383	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
384	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
385	C₈	—	2	2	no	—
386	C₈	—	2	2	no	—
387	C₈	—	2	2	no	—
388	C₈	C₇×C₂²⋊Q₈	1	4	yes	complemented
389	C₇	#26060	1	1	yes	characteristic, direct product factor, Sylow
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	2	4	no	—
394	C₂²	C₇×#498	1	4	yes	complemented
395	C₂²	C₂×C₇×C₄⋊Q₈	1	1	yes	characteristic
396	C₂²	C₇×D₄²	1	1	yes	characteristic
397	C₂²	C₇×#547	1	1	yes	characteristic
398	C₂²	C₂²×C₇×SD₁₆	1	2	yes	—
399	C₂²	C₇×#577	1	2	yes	—
400	C₄	—	2	2	no	—
401	C₄	—	2	4	no	—
402	C₄	—	2	4	no	—
403	C₄	—	4	4	no	—
404	C₄	—	8	2	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	2	no	—
407	C₄	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
408	C₄	C₇×#544	1	1	yes	characteristic
409	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
410	C₄	C₇×#554	1	1	yes	characteristic
411	C₂	—	2	4	no	—
412	C₂	C₇×#2440	1	1	yes	characteristic
413	C₂	C₂×C₇×#498	1	1	yes	characteristic
414	C₂	C₇×#3163	1	1	yes	characteristic
415	C₂	C₇×D₄×SD₁₆	1	2	yes	—
416	C₂	C₇×#3335	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂⁴×C₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄×C₇×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#498	C₂	semidirect
4. C₇×#2084	C₂	semidirect
5. C₇×#2058	C₂	semidirect
6. C₇×#1941	C₂	semidirect
7. C₇×#1941	C₂	semidirect
9. C₇×#1844	C₂	semidirect
41. #26060	C₇	direct (N × H)
47. C₂²×C₇×C₈	Q₈	semidirect
78. C₇×C₂²⋊C₈	Q₈	semidirect
85. C₂×#498	C₂×C₇	semidirect
88. #2084	C₂×C₇	semidirect
89. #2058	C₂×C₇	semidirect
90. #1941	C₂×C₇	semidirect
91. #1941	C₂×C₇	semidirect
93. #1844	C₂×C₇	semidirect
221. C₇×C₈	C₂²⋊Q₈	semidirect
227. C₂²×C₈	C₇×Q₈	semidirect
258. C₂²⋊C₈	C₇×Q₈	semidirect
269. C₂²×C₇	#498	semidirect
388. C₈	C₇×C₂²⋊Q₈	semidirect
389. C₇	#26060	direct (N × H)
394. C₂²	C₇×#498	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#498	2
C₂²×C₇×#106	2
C₇×#2440	2
C₇×#2084	2
C₇×#2058	2
C₇×#1941	2
C₇×#1853	2
C₇×#1844	2
C₇×#1807	2
C₇×C₈×C₂²⋊C₄	2
#26060	7

Subgroups — C7×#26060 #13203276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#26060 #13203276