Subgroups — C₇×#22718 #13199934

Order 1792.

796 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₄×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic
3	C₇×#1950	C₂	1	2	yes	maximal, complemented
4	C₇×#1855	C₂	1	2	yes	maximal, complemented
5	C₇×#1855	C₂	1	2	yes	maximal, complemented
6	C₇×#1838	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1811	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1810	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1778	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1738	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#341	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
13	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
14	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₇×#436	—	2	2	no	—
18	C₇×#435	—	2	2	no	—
19	C₇×#435	—	2	2	no	—
20	C₇×#435	C₄	1	4	yes	—
21	C₇×#435	C₄	1	4	yes	—
22	C₇×C₈×D₄	—	2	2	no	—
23	C₂×C₇×#108	C₂²	1	2	yes	—
24	C₂×C₇×#108	C₂²	1	2	yes	—
25	C₂×C₇×#108	C₂²	1	2	yes	—
26	C₇×#423	C₂²	1	2	yes	—
27	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₇×#407	C₂²	1	2	yes	—
29	C₇×#407	C₂²	1	2	yes	—
30	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₄×C₇×M₁₆	C₂²	1	2	yes	—
33	C₂×C₇×#97	C₂²	1	1	yes	characteristic
34	C₇×#341	C₂²	1	1	yes	characteristic
35	C₇×#341	C₂²	1	1	yes	characteristic
36	C₇×#341	C₂²	1	2	yes	—
37	C₇×#341	C₂²	1	1	yes	characteristic
38	C₇×#341	C₂²	1	2	yes	—
39	C₇×#341	C₂²	1	1	yes	characteristic
40	C₇×#341	C₂²	1	2	yes	—
41	#22718	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₇×D₄	Q₈	1	1	yes	characteristic
43	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
45	C₂×C₇×M₁₆	—	2	2	no	—
46	C₂×C₇×M₁₆	—	2	2	no	—
47	C₂×C₇×M₁₆	—	2	4	no	—
48	C₂×C₇×M₁₆	—	2	4	no	—
49	C₂×C₇×M₁₆	—	4	2	no	—
50	C₂×C₇×M₁₆	—	4	2	no	—
51	C₂×C₇×M₁₆	—	4	2	no	—
52	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	—
53	C₂×C₇×M₁₆	C₂³	1	2	yes	—
54	C₂×C₇×M₁₆	C₂³	1	2	yes	—
55	C₂×C₇×M₁₆	C₂³	1	2	yes	—
56	C₂×C₇×M₁₆	C₂³	1	2	yes	—
57	C₂²×C₇×C₈	—	2	2	no	—
58	C₂²×C₇×C₈	—	2	2	no	—
59	C₂²×C₇×C₈	—	4	2	no	—
60	C₂²×C₇×C₈	C₂×C₄	1	2	yes	—
61	C₂²×C₇×C₈	C₂×C₄	1	2	yes	—
62	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
66	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
67	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
68	C₄×C₇×D₄	D₄	1	2	yes	—
69	C₄×C₇×D₄	D₄	1	2	yes	—
70	C₂×C₇×C₄⋊C₄	Q₈	1	1	yes	characteristic
71	C₂×C₇×C₂²⋊C₄	Q₈	1	1	yes	characteristic
72	C₂×C₇×C₂²⋊C₄	Q₈	1	1	yes	characteristic
73	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
74	C₇×#108	—	2	4	no	—
75	C₇×#108	—	4	2	no	—
76	C₇×#108	—	4	2	no	—
77	C₇×C₄⋊C₈	—	2	2	no	—
78	C₇×C₄⋊C₈	—	2	2	no	—
79	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
80	C₇×C₂²⋊C₈	—	2	2	no	—
81	C₇×C₂²⋊C₈	—	2	2	no	—
82	C₇×C₂²⋊C₈	—	2	2	no	—
83	C₇×C₂²⋊C₈	—	2	2	no	—
84	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
85	C₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
86	C₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
87	C₇×#97	—	2	2	no	—
88	C₇×#97	C₂×C₄	1	4	yes	—
89	C₄×C₇×C₈	—	2	2	no	—
90	D₄×M₁₆	C₂×C₇	1	2	yes	—
91	C₂×#435	C₂×C₇	1	1	yes	characteristic
92	#1950	C₂×C₇	1	2	yes	complemented
93	#1855	C₂×C₇	1	2	yes	complemented
94	#1855	C₂×C₇	1	2	yes	complemented
95	#1838	C₂×C₇	1	1	yes	characteristic, complemented
96	#1811	C₂×C₇	1	1	yes	characteristic, complemented
97	#1810	C₂×C₇	1	1	yes	characteristic, complemented
98	#1778	C₂×C₇	1	1	yes	characteristic, complemented
99	#1738	C₂×C₇	1	1	yes	characteristic, complemented
100	C₂×#341	C₂×C₇	1	1	yes	characteristic, complemented
101	C₂⁴×C₇	C₂×Q₈	1	1	yes	characteristic
102	C₂⁴×C₇	C₂×Q₈	1	1	yes	characteristic
103	C₂×C₇×D₄	—	4	2	no	—
104	C₂×C₇×D₄	C₄⋊C₄	1	2	yes	—
105	C₂×C₇×D₄	C₄⋊C₄	1	2	yes	—
106	C₂²×C₄×C₇	—	2	2	no	—
107	C₂²×C₄×C₇	—	2	2	no	—
108	C₂²×C₄×C₇	—	2	2	no	—
109	C₂²×C₄×C₇	—	2	2	no	—
110	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
117	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
118	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
119	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
120	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
121	C₇×M₁₆	—	2	2	no	—
122	C₇×M₁₆	—	2	2	no	—
123	C₇×M₁₆	—	2	2	no	—
124	C₇×M₁₆	—	2	2	no	—
125	C₇×M₁₆	—	2	2	no	—
126	C₇×M₁₆	—	2	2	no	—
127	C₇×M₁₆	—	2	2	no	—
128	C₇×M₁₆	—	4	4	no	—
129	C₇×M₁₆	—	4	4	no	—
130	C₇×M₁₆	—	4	4	no	—
131	C₇×M₁₆	#41	1	4	yes	—
132	C₂×C₇×C₈	—	2	2	no	—
133	C₂×C₇×C₈	—	2	2	no	—
134	C₂×C₇×C₈	—	2	2	no	—
135	C₂×C₇×C₈	—	2	2	no	—
136	C₂×C₇×C₈	—	2	2	no	—
137	C₂×C₇×C₈	—	2	2	no	—
138	C₂×C₇×C₈	—	2	2	no	—
139	C₂×C₇×C₈	—	2	2	no	—
140	C₂×C₇×C₈	—	4	2	no	—
141	C₂×C₇×C₈	—	4	2	no	—
142	C₂×C₇×C₈	—	4	4	no	—
143	C₂×C₇×C₈	—	4	4	no	—
144	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
146	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
147	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
148	C₇×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
149	C₇×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
150	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
151	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
152	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
153	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
154	C₄²×C₇	C₂²×C₄	1	2	yes	—
155	C₄²×C₇	C₂×D₄	1	2	yes	—
156	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
157	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
158	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
159	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
160	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
161	#436	—	2	2	no	—
162	#435	—	2	2	no	—
163	#435	—	2	2	no	—
164	#435	C₄×C₇	1	4	yes	—
165	#435	C₄×C₇	1	4	yes	—
166	C₈×D₄	—	2	2	no	—
167	C₂×#108	C₂²×C₇	1	2	yes	—
168	C₂×#108	C₂²×C₇	1	2	yes	—
169	C₂×#108	C₂²×C₇	1	2	yes	—
170	#423	C₂²×C₇	1	2	yes	—
171	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
172	#407	C₂²×C₇	1	2	yes	—
173	#407	C₂²×C₇	1	2	yes	—
174	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
175	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
176	C₄×M₁₆	C₂²×C₇	1	2	yes	—
177	C₂×#97	C₂²×C₇	1	1	yes	characteristic
178	#341	C₂²×C₇	1	1	yes	characteristic
179	#341	C₂²×C₇	1	1	yes	characteristic
180	#341	C₂²×C₇	1	1	yes	characteristic
181	#341	C₂²×C₇	1	2	yes	—
182	#341	C₂²×C₇	1	2	yes	—
183	#341	C₂²×C₇	1	2	yes	—
184	#341	C₂²×C₇	1	1	yes	characteristic
185	C₂³×C₇	—	2	2	no	—
186	C₂³×C₇	—	2	2	no	—
187	C₂³×C₇	—	2	2	no	—
188	C₂³×C₇	—	4	1	no	—
189	C₂³×C₇	—	4	1	no	—
190	C₂³×C₇	—	4	1	no	—
191	C₂³×C₇	C₂×C₄⋊C₄	1	2	yes	—
192	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂³×C₇	C₂²×Q₈	1	1	yes	characteristic
195	C₇×D₄	—	2	4	no	—
196	C₇×D₄	—	4	2	no	—
197	C₂×C₄×C₇	—	2	2	no	—
198	C₂×C₄×C₇	—	2	2	no	—
199	C₂×C₄×C₇	—	2	1	no	—
200	C₂×C₄×C₇	—	2	1	no	—
201	C₂×C₄×C₇	—	2	2	no	—
202	C₂×C₄×C₇	—	2	1	no	—
203	C₂×C₄×C₇	—	2	1	no	—
204	C₂×C₄×C₇	—	2	2	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	2	no	—
207	C₂×C₄×C₇	—	2	2	no	—
208	C₂×C₄×C₇	—	2	2	no	—
209	C₂×C₄×C₇	—	4	1	no	—
210	C₂×C₄×C₇	—	4	1	no	—
211	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
212	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
213	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
216	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₇	C₂×#41	1	2	yes	—
219	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
220	C₇×C₈	—	2	2	no	—
221	C₇×C₈	—	2	2	no	—
222	C₇×C₈	—	2	2	no	—
223	C₇×C₈	—	2	2	no	—
224	C₇×C₈	—	2	4	no	—
225	C₇×C₈	—	4	2	no	—
226	C₇×C₈	—	4	2	no	—
227	C₇×C₈	—	4	2	no	—
228	C₂²×D₄	C₇×Q₈	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
230	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	—	2	4	no	—
234	C₂×M₁₆	—	2	4	no	—
235	C₂×M₁₆	—	4	2	no	—
236	C₂×M₁₆	—	4	2	no	—
237	C₂×M₁₆	—	4	2	no	—
238	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	—
239	C₂×M₁₆	C₂³×C₇	1	2	yes	—
240	C₂×M₁₆	C₂³×C₇	1	2	yes	—
241	C₂×M₁₆	C₂³×C₇	1	2	yes	—
242	C₂×M₁₆	C₂³×C₇	1	2	yes	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	—	4	2	no	—
246	C₂²×C₈	C₂×C₄×C₇	1	2	yes	—
247	C₂²×C₈	C₂×C₄×C₇	1	2	yes	—
248	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
252	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
253	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
254	C₄×D₄	C₇×D₄	1	2	yes	—
255	C₄×D₄	C₇×D₄	1	2	yes	—
256	C₂×C₄⋊C₄	C₇×Q₈	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	C₇×Q₈	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	C₇×Q₈	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
260	#108	—	2	4	no	—
261	#108	—	4	2	no	—
262	#108	—	4	2	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	—
266	C₂²⋊C₈	—	2	2	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	—	2	2	no	—
269	C₂²⋊C₈	—	2	2	no	—
270	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	—
271	C₂²⋊C₈	C₂×C₄×C₇	1	2	yes	—
272	C₂²⋊C₈	C₂×C₄×C₇	1	2	yes	—
273	#97	—	2	2	no	—
274	#97	C₂×C₄×C₇	1	4	yes	—
275	C₄×C₈	—	2	2	no	—
276	C₂²×C₇	—	2	1	no	—
277	C₂²×C₇	—	2	1	no	—
278	C₂²×C₇	—	2	1	no	—
279	C₂²×C₇	—	2	1	no	—
280	C₂²×C₇	—	2	1	no	—
281	C₂²×C₇	—	2	2	no	—
282	C₂²×C₇	—	2	2	no	—
283	C₂²×C₇	—	2	1	no	—
284	C₂²×C₇	—	2	1	no	—
285	C₂²×C₇	—	2	2	no	—
286	C₂²×C₇	—	4	4	no	—
287	C₂²×C₇	—	8	2	no	—
288	C₂²×C₇	#430	1	2	yes	—
289	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
290	C₂²×C₇	#554	1	2	yes	—
291	C₄×C₇	—	2	1	no	—
292	C₄×C₇	—	2	1	no	—
293	C₄×C₇	—	2	2	no	—
294	C₄×C₇	—	2	2	no	—
295	C₄×C₇	—	2	2	no	—
296	C₄×C₇	C₄×#41	1	1	yes	characteristic
297	C₄×C₇	#518	1	1	yes	characteristic
298	C₄×C₇	#546	1	2	yes	—
299	C₂⁴	C₂×C₇×Q₈	1	1	yes	characteristic
300	C₂⁴	C₂×C₇×Q₈	1	1	yes	characteristic
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	C₇×C₄⋊C₄	1	2	yes	—
303	C₂×D₄	C₇×C₄⋊C₄	1	2	yes	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
311	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
313	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
318	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
319	M₁₆	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	4	4	no	—
327	M₁₆	—	4	4	no	—
328	M₁₆	—	4	4	no	—
329	M₁₆	C₇×#41	1	4	yes	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	4	2	no	—
339	C₂×C₈	—	4	2	no	—
340	C₂×C₈	—	4	4	no	—
341	C₂×C₈	—	4	4	no	—
342	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
343	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
344	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
345	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
346	C₄⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
347	C₄⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
348	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
349	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
350	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
351	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
352	C₄²	C₂²×C₄×C₇	1	2	yes	—
353	C₄²	C₂×C₇×D₄	1	2	yes	—
354	C₂×C₇	—	2	2	no	—
355	C₂×C₇	—	2	2	no	—
356	C₂×C₇	—	4	1	no	—
357	C₂×C₇	—	4	2	no	—
358	C₂×C₇	#2349	1	1	yes	characteristic
359	C₂×C₇	C₂×#430	1	1	yes	characteristic
360	C₂×C₇	#2916	1	1	yes	characteristic
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	C₂×C₇×C₄⋊C₄	1	2	yes	—
368	C₂³	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
369	C₂³	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
370	C₂³	C₂²×C₇×Q₈	1	1	yes	characteristic
371	D₄	—	2	4	no	—
372	D₄	—	4	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
388	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
389	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
390	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
391	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
392	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
394	C₂×C₄	C₂×C₇×#41	1	2	yes	—
395	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	2	2	no	—
399	C₈	—	2	2	no	—
400	C₈	—	2	4	no	—
401	C₈	—	4	2	no	—
402	C₈	—	4	2	no	—
403	C₈	—	4	2	no	—
404	C₇	#22718	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	8	2	no	—
417	C₂²	C₇×#430	1	2	yes	—
418	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
419	C₂²	C₇×#554	1	2	yes	—
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	2	no	—
425	C₄	C₄×C₇×#41	1	1	yes	characteristic
426	C₄	C₇×#518	1	1	yes	characteristic
427	C₄	C₇×#546	1	2	yes	—
428	C₂	—	2	2	no	—
429	C₂	—	2	2	no	—
430	C₂	—	4	1	no	—
431	C₂	—	4	2	no	—
432	C₂	C₇×#2349	1	1	yes	characteristic
433	C₂	C₂×C₇×#430	1	1	yes	characteristic
434	C₂	C₇×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂²×C₄⋊C₄
prime radical	C₂²×C₇×D₄	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#1950	C₂	semidirect
4. C₇×#1855	C₂	semidirect
5. C₇×#1855	C₂	semidirect
6. C₇×#1838	C₂	semidirect
7. C₇×#1811	C₂	semidirect
8. C₇×#1810	C₂	semidirect
9. C₇×#1778	C₂	semidirect
10. C₇×#1738	C₂	semidirect
11. C₂×C₇×#341	C₂	semidirect
41. #22718	C₇	direct (N × H)
92. #1950	C₂×C₇	semidirect
93. #1855	C₂×C₇	semidirect
94. #1855	C₂×C₇	semidirect
95. #1838	C₂×C₇	semidirect
96. #1811	C₂×C₇	semidirect
97. #1810	C₂×C₇	semidirect
98. #1778	C₂×C₇	semidirect
99. #1738	C₂×C₇	semidirect
100. C₂×#341	C₂×C₇	semidirect
404. C₇	#22718	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×D₄×M₁₆	2
C₂×C₇×#435	2
C₇×#1950	2
C₇×#1855	2
C₇×#1838	2
C₇×#1811	2
C₇×#1810	2
C₇×#1778	2
C₇×#1738	2
C₂×C₇×#341	2
#22718	7

Subgroups — C7×#22718 #13199934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22718 #13199934