Subgroups — C₇×#22962 #13200178

Order 1792.

926 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#474	C₂	1	1	yes	maximal, characteristic
2	C₇×#2365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₇×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1947	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1942	C₂	1	2	yes	maximal, complemented
7	C₇×#1918	C₂	1	2	yes	maximal, complemented
8	C₇×#1862	C₂	1	2	yes	maximal
9	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₇×#102	C₂	1	2	yes	maximal
11	C₄×C₇×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₇×Q₈	—	2	1	no	—
14	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
15	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
17	C₇×#474	C₄	1	8	yes	complemented
18	C₂×C₇×#107	C₂²	1	2	yes	—
19	C₂×C₇×#107	C₂²	1	2	yes	—
20	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×#102	C₂²	1	1	yes	characteristic
22	C₂×C₇×#102	C₂²	1	2	yes	—
23	C₂×C₇×#102	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
26	C₇×#391	—	2	1	no	—
27	C₇×#389	C₂²	1	2	yes	—
28	C₇×#389	C₂²	1	2	yes	—
29	C₇×#387	—	2	2	no	—
30	C₇×#385	—	2	2	no	—
31	C₇×#384	C₂²	1	1	yes	characteristic
32	C₇×#380	—	2	1	no	—
33	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₇×C₄⋊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	1	yes	characteristic
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#340	C₂²	1	1	yes	characteristic
41	C₇×#336	C₂²	1	2	yes	—
42	#22962	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×Q₈	—	2	1	no	—
44	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₇	—	2	1	no	—
46	C₂³×C₄×C₇	—	2	2	no	—
47	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₇×C₈	C₂³	1	2	yes	—
49	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
50	C₇×C₄⋊Q₈	—	2	2	no	—
51	C₇×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
52	C₄×C₇×Q₈	—	4	4	no	—
53	C₄×C₇×D₄	—	2	4	no	—
54	C₄×C₇×D₄	—	2	2	no	—
55	C₄×C₇×D₄	—	4	2	no	—
56	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
57	C₂×C₇×C₄⋊C₄	—	2	1	no	—
58	C₂×C₇×C₄⋊C₄	—	2	1	no	—
59	C₂×C₇×C₄⋊C₄	—	2	2	no	—
60	C₂×C₇×C₄⋊C₄	—	2	2	no	—
61	C₂×C₇×C₄⋊C₄	—	2	1	no	—
62	C₂×C₇×C₄⋊C₄	—	4	4	no	—
63	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₄²×C₇	—	2	2	no	—
73	C₂×C₄²×C₇	—	2	1	no	—
74	C₂×C₄²×C₇	C₂³	1	2	yes	—
75	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
76	C₇×#107	—	4	2	no	—
77	C₇×#107	C₂×C₄	1	8	yes	complemented
78	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
79	C₇×#102	—	2	2	no	—
80	C₇×#102	C₂×C₄	1	8	yes	—
81	C₇×#102	Q₈	1	4	yes	complemented
82	C₄×C₇×C₈	—	2	2	no	—
83	C₄×C₇×C₈	—	4	2	no	—
84	C₇×#95	—	2	1	no	—
85	C₇×#95	—	2	2	no	—
86	C₇×#95	—	2	2	no	—
87	C₇×#95	—	2	2	no	—
88	C₇×#95	D₄	1	2	yes	—
89	C₂×#474	C₂×C₇	1	1	yes	characteristic
90	#2365	C₂×C₇	1	1	yes	characteristic, complemented
91	D₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic
92	#1990	C₂×C₇	1	1	yes	characteristic, complemented
93	#1947	C₂×C₇	1	1	yes	characteristic, complemented
94	#1942	C₂×C₇	1	2	yes	complemented
95	#1918	C₂×C₇	1	2	yes	complemented
96	#1862	C₂×C₇	1	2	yes	—
97	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
98	C₄×#102	C₂×C₇	1	2	yes	—
99	C₄×#102	C₂×C₇	1	1	yes	characteristic
100	C₂⁴×C₇	—	2	1	no	—
101	C₂×C₇×Q₈	—	2	4	no	—
102	C₂×C₇×Q₈	—	4	2	no	—
103	C₂×C₇×Q₈	—	4	2	no	—
104	C₂×C₇×D₄	—	2	1	no	—
105	C₂×C₇×D₄	—	2	1	no	—
106	C₂×C₇×D₄	—	2	1	no	—
107	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
108	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
109	C₂×C₇×D₄	#41	1	2	yes	—
110	C₂²×C₄×C₇	—	2	1	no	—
111	C₂²×C₄×C₇	—	2	2	no	—
112	C₂²×C₄×C₇	—	2	1	no	—
113	C₂²×C₄×C₇	—	2	4	no	—
114	C₂²×C₄×C₇	—	2	1	no	—
115	C₂²×C₄×C₇	—	2	2	no	—
116	C₂²×C₄×C₇	—	4	4	no	—
117	C₂²×C₄×C₇	—	4	2	no	—
118	C₂²×C₄×C₇	—	4	2	no	—
119	C₂²×C₄×C₇	—	4	4	no	—
120	C₂²×C₄×C₇	—	8	2	no	—
121	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
126	C₂×C₇×C₈	—	2	1	no	—
127	C₂×C₇×C₈	—	2	1	no	—
128	C₂×C₇×C₈	—	2	2	no	—
129	C₂×C₇×C₈	—	2	2	no	—
130	C₂×C₇×C₈	—	2	1	no	—
131	C₂×C₇×C₈	—	2	1	no	—
132	C₂×C₇×C₈	—	2	1	no	—
133	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
134	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
135	C₇×C₄⋊C₄	—	2	4	no	—
136	C₇×C₄⋊C₄	—	2	2	no	—
137	C₇×C₄⋊C₄	—	2	1	no	—
138	C₇×C₄⋊C₄	—	2	2	no	—
139	C₇×C₄⋊C₄	—	2	1	no	—
140	C₇×C₄⋊C₄	—	2	1	no	—
141	C₇×C₄⋊C₄	—	2	2	no	—
142	C₇×C₄⋊C₄	—	2	1	no	—
143	C₇×C₄⋊C₄	—	2	2	no	—
144	C₇×C₄⋊C₄	—	4	4	no	—
145	C₇×C₄⋊C₄	—	4	2	no	—
146	C₇×C₄⋊C₄	—	4	4	no	—
147	C₇×C₄⋊C₄	—	8	1	no	—
148	C₇×C₄⋊C₄	D₈	1	4	yes	—
149	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
150	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
151	C₇×C₄⋊C₄	C₂×Q₈	1	2	yes	—
152	C₇×C₂²⋊C₄	—	2	4	no	—
153	C₇×C₂²⋊C₄	—	4	4	no	—
154	C₄²×C₇	—	2	2	no	—
155	C₄²×C₇	—	2	2	no	—
156	C₄²×C₇	—	4	4	no	—
157	C₄²×C₇	—	4	2	no	—
158	C₄²×C₇	C₂²×C₄	1	2	yes	—
159	C₄²×C₇	#41	1	2	yes	—
160	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
161	C₂×C₄×Q₈	—	2	1	no	—
162	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
163	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
164	C₂²×C₄⋊C₄	—	2	1	no	—
165	#474	C₄×C₇	1	8	yes	complemented
166	C₂×#107	C₂²×C₇	1	2	yes	—
167	C₂×#107	C₂²×C₇	1	2	yes	—
168	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
169	C₂×#102	C₂²×C₇	1	1	yes	characteristic
170	C₂×#102	C₂²×C₇	1	2	yes	—
171	C₂×#102	C₂²×C₇	1	1	yes	characteristic
172	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
173	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
174	#391	—	2	1	no	—
175	#389	C₂²×C₇	1	2	yes	—
176	#389	C₂²×C₇	1	2	yes	—
177	#387	—	2	2	no	—
178	#385	—	2	2	no	—
179	#384	C₂²×C₇	1	1	yes	characteristic
180	#380	—	2	1	no	—
181	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
182	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
183	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
184	#340	C₂²×C₇	1	2	yes	—
185	#340	C₂²×C₇	1	1	yes	characteristic
186	#340	C₂²×C₇	1	2	yes	—
187	#340	C₂²×C₇	1	1	yes	characteristic
188	#340	C₂²×C₇	1	2	yes	—
189	#336	C₂²×C₇	1	2	yes	—
190	C₂³×C₇	—	2	2	no	—
191	C₂³×C₇	—	2	2	no	—
192	C₂³×C₇	—	2	2	no	—
193	C₂³×C₇	—	4	1	no	—
194	C₂³×C₇	—	4	1	no	—
195	C₂³×C₇	—	4	1	no	—
196	C₂³×C₇	—	4	1	no	—
197	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
198	C₇×Q₈	—	4	8	no	—
199	C₇×D₄	—	2	2	no	—
200	C₇×D₄	—	2	2	no	—
201	C₇×D₄	—	2	2	no	—
202	C₇×D₄	C₄×Q₈	1	4	yes	complemented
203	C₂×C₄×C₇	—	2	2	no	—
204	C₂×C₄×C₇	—	2	1	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	2	2	no	—
208	C₂×C₄×C₇	—	2	4	no	—
209	C₂×C₄×C₇	—	2	2	no	—
210	C₂×C₄×C₇	—	2	2	no	—
211	C₂×C₄×C₇	—	2	2	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	4	1	no	—
214	C₂×C₄×C₇	—	4	2	no	—
215	C₂×C₄×C₇	—	4	1	no	—
216	C₂×C₄×C₇	—	4	1	no	—
217	C₂×C₄×C₇	—	4	2	no	—
218	C₂×C₄×C₇	—	4	1	no	—
219	C₂×C₄×C₇	—	4	8	no	—
220	C₂×C₄×C₇	—	4	2	no	—
221	C₂×C₄×C₇	—	4	1	no	—
222	C₂×C₄×C₇	—	4	1	no	—
223	C₂×C₄×C₇	—	4	2	no	—
224	C₂×C₄×C₇	—	4	2	no	—
225	C₂×C₄×C₇	—	4	1	no	—
226	C₂×C₄×C₇	—	8	8	no	—
227	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
229	C₂×C₄×C₇	C₂×D₈	1	4	yes	—
230	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
231	C₂×C₄×C₇	#135	1	2	yes	—
232	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
234	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
238	C₇×C₈	—	2	4	no	—
239	C₇×C₈	—	2	2	no	—
240	C₇×C₈	—	4	1	no	—
241	C₂²×Q₈	—	2	1	no	—
242	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
243	C₂³×C₄	—	2	1	no	—
244	C₂³×C₄	—	2	2	no	—
245	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₇	1	2	yes	—
247	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
248	C₄⋊Q₈	—	2	2	no	—
249	C₄⋊Q₈	C₂×C₄×C₇	1	4	yes	complemented
250	C₄×Q₈	—	4	4	no	—
251	C₄×D₄	—	2	4	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	—	4	2	no	—
254	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	4	4	no	—
261	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	C₂³×C₇	1	2	yes	—
273	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
274	#107	—	4	2	no	—
275	#107	C₂×C₄×C₇	1	8	yes	complemented
276	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
277	#102	—	2	2	no	—
278	#102	C₂×C₄×C₇	1	8	yes	—
279	#102	C₇×Q₈	1	4	yes	complemented
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	—	4	2	no	—
282	#95	—	2	1	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	C₇×D₄	1	2	yes	—
287	C₂²×C₇	—	2	4	no	—
288	C₂²×C₇	—	4	2	no	—
289	C₂²×C₇	—	4	2	no	—
290	C₂²×C₇	—	4	2	no	—
291	C₂²×C₇	—	4	2	no	—
292	C₂²×C₇	—	4	2	no	—
293	C₂²×C₇	—	4	2	no	—
294	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
295	C₂²×C₇	#546	1	1	yes	characteristic
296	C₂²×C₇	D₄×Q₈	1	1	yes	characteristic
297	C₂²×C₇	C₂²×D₈	1	1	yes	characteristic
298	C₂²×C₇	C₂×#135	1	1	yes	characteristic
299	C₂²×C₇	#577	1	1	yes	characteristic
300	C₂²×C₇	#578	1	1	yes	characteristic
301	C₄×C₇	—	2	2	no	—
302	C₄×C₇	—	2	4	no	—
303	C₄×C₇	—	4	2	no	—
304	C₄×C₇	—	4	2	no	—
305	C₄×C₇	—	4	4	no	—
306	C₄×C₇	—	4	2	no	—
307	C₄×C₇	—	8	1	no	—
308	C₄×C₇	—	8	2	no	—
309	C₄×C₇	C₄×D₈	1	4	yes	—
310	C₄×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
311	C₄×C₇	#520	1	1	yes	characteristic
312	C₄×C₇	#552	1	1	yes	characteristic
313	C₄×C₇	#554	1	1	yes	characteristic
314	C₂⁴	—	2	1	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	4	2	no	—
317	C₂×Q₈	—	4	2	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
322	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
323	C₂×D₄	C₇×#41	1	2	yes	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	4	no	—
334	C₂²×C₄	—	8	2	no	—
335	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
336	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
338	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
339	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
348	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	4	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	—	8	1	no	—
362	C₄⋊C₄	C₇×D₈	1	4	yes	—
363	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
364	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
365	C₄⋊C₄	C₂×C₇×Q₈	1	2	yes	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	4	4	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	4	4	no	—
371	C₄²	—	4	2	no	—
372	C₄²	C₂²×C₄×C₇	1	2	yes	—
373	C₄²	C₇×#41	1	2	yes	—
374	C₂×C₇	—	4	4	no	—
375	C₂×C₇	#2360	1	1	yes	characteristic
376	C₂×C₇	C₂×C₄×D₈	1	1	yes	characteristic
377	C₂×C₇	#2947	1	1	yes	characteristic
378	C₂×C₇	#3294	1	1	yes	characteristic
379	C₂×C₇	#3302	1	1	yes	characteristic
380	C₂×C₇	Q₈×D₈	1	1	yes	characteristic
381	C₂×C₇	#3381	1	1	yes	characteristic
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
390	Q₈	—	4	8	no	—
391	D₄	—	2	2	no	—
392	D₄	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	C₄×C₇×Q₈	1	4	yes	complemented
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	8	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	8	8	no	—
419	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
420	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
421	C₂×C₄	C₂×C₇×D₈	1	4	yes	—
422	C₂×C₄	C₂×C₇×D₈	1	2	yes	—
423	C₂×C₄	C₇×#135	1	2	yes	—
424	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
425	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
426	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
427	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
428	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
429	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
430	C₈	—	2	4	no	—
431	C₈	—	2	2	no	—
432	C₈	—	4	1	no	—
433	C₇	#22962	1	1	yes	characteristic, direct product factor, Sylow
434	C₂²	—	2	4	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
442	C₂²	C₇×#546	1	1	yes	characteristic
443	C₂²	C₇×D₄×Q₈	1	1	yes	characteristic
444	C₂²	C₂²×C₇×D₈	1	1	yes	characteristic
445	C₂²	C₂×C₇×#135	1	1	yes	characteristic
446	C₂²	C₇×#577	1	1	yes	characteristic
447	C₂²	C₇×#578	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	4	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	4	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	8	2	no	—
455	C₄	—	8	1	no	—
456	C₄	C₄×C₇×D₈	1	4	yes	—
457	C₄	C₂×C₄×C₇×Q₈	1	1	yes	characteristic
458	C₄	C₇×#520	1	1	yes	characteristic
459	C₄	C₇×#552	1	1	yes	characteristic
460	C₄	C₇×#554	1	1	yes	characteristic
461	C₂	—	4	4	no	—
462	C₂	C₇×#2360	1	1	yes	characteristic
463	C₂	C₂×C₄×C₇×D₈	1	1	yes	characteristic
464	C₂	C₇×#2947	1	1	yes	characteristic
465	C₂	C₇×#3294	1	1	yes	characteristic
466	C₂	C₇×#3302	1	1	yes	characteristic
467	C₂	C₇×Q₈×D₈	1	1	yes	characteristic
468	C₂	C₇×#3381	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₇×#2365	C₂	semidirect
4. C₇×#1990	C₂	semidirect
5. C₇×#1947	C₂	semidirect
6. C₇×#1942	C₂	semidirect
7. C₇×#1918	C₂	semidirect
9. C₇×C₈×C₄⋊C₄	C₂	semidirect
17. C₇×#474	C₄	semidirect
42. #22962	C₇	direct (N × H)
51. C₇×C₄⋊Q₈	C₂×C₄	semidirect
77. C₇×#107	C₂×C₄	semidirect
78. C₇×C₄⋊C₈	C₂×C₄	semidirect
81. C₇×#102	Q₈	semidirect
90. #2365	C₂×C₇	semidirect
92. #1990	C₂×C₇	semidirect
93. #1947	C₂×C₇	semidirect
94. #1942	C₂×C₇	semidirect
95. #1918	C₂×C₇	semidirect
97. C₈×C₄⋊C₄	C₂×C₇	semidirect
165. #474	C₄×C₇	semidirect
202. C₇×D₄	C₄×Q₈	semidirect
249. C₄⋊Q₈	C₂×C₄×C₇	semidirect
275. #107	C₂×C₄×C₇	semidirect
276. C₄⋊C₈	C₂×C₄×C₇	semidirect
279. #102	C₇×Q₈	semidirect
394. D₄	C₄×C₇×Q₈	semidirect
433. C₇	#22962	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×#474	2
C₇×#2365	2
C₇×D₄×C₄⋊C₄	2
C₇×#1990	2
C₇×#1947	2
C₇×#1942	2
C₇×#1918	2
C₇×#1862	2
C₇×C₈×C₄⋊C₄	2
C₄×C₇×#102	2
#22962	7

Subgroups — C7×#22962 #13200178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22962 #13200178