Subgroups — C₇×#23026 #13200242

Order 1792.

938 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#427	C₂	1	1	yes	maximal, characteristic
4	C₇×#2362	C₂	1	2	yes	maximal
5	C₇×#1969	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1927	C₂	1	2	yes	maximal, complemented
8	C₇×#1873	C₂	1	2	yes	maximal
9	C₇×#1865	C₂	1	2	yes	maximal, complemented
10	C₄×C₇×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
16	C₂×C₇×#117	C₂²	1	2	yes	—
17	C₇×#467	C₄	1	8	yes	complemented
18	C₄×C₇×Q₁₆	—	2	4	no	—
19	C₇×#427	—	2	4	no	—
20	C₂×C₇×#107	C₂²	1	1	yes	characteristic
21	C₂×C₇×#107	C₂²	1	1	yes	characteristic
22	C₂×C₇×#107	C₂²	1	1	yes	characteristic
23	C₂×C₇×#106	C₂²	1	2	yes	—
24	C₂×C₇×#103	C₂²	1	2	yes	—
25	C₂×C₇×#103	C₂²	1	2	yes	—
26	C₂×C₇×#103	C₂²	1	2	yes	—
27	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₇×#391	C₂²	1	2	yes	—
31	C₇×#389	C₂²	1	2	yes	—
32	C₇×#388	—	2	2	no	—
33	C₇×#388	—	2	2	no	—
34	C₇×#387	—	2	2	no	—
35	C₄×C₇×C₄⋊C₄	—	2	2	no	—
36	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₇×#340	C₂²	1	2	yes	—
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	1	yes	characteristic
41	C₇×#336	C₂²	1	1	yes	characteristic
42	#23026	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×Q₈	C₂³	1	2	yes	—
44	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
45	C₂×C₇×Q₁₆	—	2	2	no	—
46	C₂×C₇×Q₁₆	—	2	2	no	—
47	C₂×C₇×Q₁₆	C₂×C₄	1	4	yes	—
48	C₂²×C₇×C₈	—	2	2	no	—
49	C₂²×C₇×C₈	—	2	2	no	—
50	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
55	C₇×C₂²⋊Q₈	—	2	4	no	—
56	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
57	C₄×C₇×Q₈	—	2	4	no	—
58	C₄×C₇×Q₈	—	4	2	no	—
59	C₇×#117	—	2	4	no	—
60	C₇×#117	—	4	2	no	—
61	C₂×C₇×C₄⋊C₄	—	2	2	no	—
62	C₂×C₇×C₄⋊C₄	—	2	2	no	—
63	C₂×C₇×C₄⋊C₄	—	2	2	no	—
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	—	2	2	no	—
69	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₇	—	2	2	no	—
72	C₂×C₄²×C₇	—	2	2	no	—
73	C₂×C₄²×C₇	—	2	2	no	—
74	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
76	C₇×#107	—	2	2	no	—
77	C₇×#107	C₂×C₄	1	4	yes	—
78	C₇×#107	D₄	1	4	yes	—
79	C₇×#106	—	2	4	no	—
80	C₇×#103	—	2	4	no	—
81	C₇×#103	—	4	2	no	—
82	C₇×#103	C₂×C₄	1	8	yes	—
83	C₇×C₂²⋊C₈	—	2	2	no	—
84	C₄×C₇×C₈	—	2	2	no	—
85	C₄×C₇×C₈	—	2	2	no	—
86	C₇×#95	—	2	2	no	—
87	C₇×#95	—	2	2	no	—
88	C₇×#95	—	2	2	no	—
89	C₇×#95	—	2	2	no	—
90	C₇×#95	D₄	1	1	yes	characteristic
91	C₇×#95	D₄	1	1	yes	characteristic
92	C₂×#467	C₂×C₇	1	1	yes	characteristic
93	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
94	C₂×#427	C₂×C₇	1	1	yes	characteristic
95	#2362	C₂×C₇	1	2	yes	—
96	#1969	C₂×C₇	1	1	yes	characteristic, complemented
97	#1942	C₂×C₇	1	1	yes	characteristic, complemented
98	#1927	C₂×C₇	1	2	yes	complemented
99	#1873	C₂×C₇	1	2	yes	—
100	#1865	C₂×C₇	1	2	yes	complemented
101	C₄×#107	C₂×C₇	1	1	yes	characteristic, complemented
102	C₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
103	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
104	C₂×C₇×Q₈	—	2	2	no	—
105	C₂×C₇×Q₈	—	2	2	no	—
106	C₂×C₇×Q₈	—	2	2	no	—
107	C₂×C₇×Q₈	—	2	2	no	—
108	C₂×C₇×Q₈	—	2	2	no	—
109	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
110	C₂²×C₄×C₇	—	2	1	no	—
111	C₂²×C₄×C₇	—	2	1	no	—
112	C₂²×C₄×C₇	—	2	1	no	—
113	C₂²×C₄×C₇	—	2	1	no	—
114	C₂²×C₄×C₇	—	2	2	no	—
115	C₂²×C₄×C₇	—	2	2	no	—
116	C₂²×C₄×C₇	—	2	2	no	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇	#41	1	2	yes	—
125	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
126	C₇×Q₁₆	—	2	8	no	—
127	C₂×C₇×C₈	—	2	1	no	—
128	C₂×C₇×C₈	—	2	1	no	—
129	C₂×C₇×C₈	—	2	8	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	—	2	1	no	—
134	C₂×C₇×C₈	—	2	1	no	—
135	C₂×C₇×C₈	—	2	1	no	—
136	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
138	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
139	C₂×C₇×C₈	#41	1	2	yes	—
140	C₇×C₄⋊C₄	—	2	8	no	—
141	C₇×C₄⋊C₄	—	2	2	no	—
142	C₇×C₄⋊C₄	—	2	2	no	—
143	C₇×C₄⋊C₄	—	2	2	no	—
144	C₇×C₄⋊C₄	—	2	2	no	—
145	C₇×C₄⋊C₄	—	4	4	no	—
146	C₇×C₄⋊C₄	—	4	4	no	—
147	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
148	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
149	C₇×C₂²⋊C₄	—	2	8	no	—
150	C₇×C₂²⋊C₄	—	2	2	no	—
151	C₇×C₂²⋊C₄	—	2	2	no	—
152	C₇×C₂²⋊C₄	—	4	4	no	—
153	C₄²×C₇	—	2	1	no	—
154	C₄²×C₇	—	2	1	no	—
155	C₄²×C₇	—	2	1	no	—
156	C₄²×C₇	—	2	1	no	—
157	C₄²×C₇	—	4	4	no	—
158	C₄²×C₇	—	4	4	no	—
159	C₄²×C₇	—	4	4	no	—
160	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
161	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
162	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
163	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
164	C₂×#117	C₂²×C₇	1	2	yes	—
165	#467	C₄×C₇	1	8	yes	complemented
166	C₄×Q₁₆	—	2	4	no	—
167	#427	—	2	4	no	—
168	C₂×#107	C₂²×C₇	1	1	yes	characteristic
169	C₂×#107	C₂²×C₇	1	1	yes	characteristic
170	C₂×#107	C₂²×C₇	1	1	yes	characteristic
171	C₂×#106	C₂²×C₇	1	2	yes	—
172	C₂×#103	C₂²×C₇	1	2	yes	—
173	C₂×#103	C₂²×C₇	1	2	yes	—
174	C₂×#103	C₂²×C₇	1	2	yes	—
175	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
176	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
177	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
178	#391	C₂²×C₇	1	2	yes	—
179	#389	C₂²×C₇	1	2	yes	—
180	#388	—	2	2	no	—
181	#388	—	2	2	no	—
182	#387	—	2	2	no	—
183	C₄×C₄⋊C₄	—	2	2	no	—
184	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
185	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
186	#340	C₂²×C₇	1	2	yes	—
187	#340	C₂²×C₇	1	2	yes	—
188	#336	C₂²×C₇	1	1	yes	characteristic
189	#336	C₂²×C₇	1	1	yes	characteristic
190	C₂³×C₇	—	2	1	no	—
191	C₂³×C₇	—	2	1	no	—
192	C₂³×C₇	—	2	1	no	—
193	C₂³×C₇	—	2	1	no	—
194	C₂³×C₇	—	2	1	no	—
195	C₂³×C₇	—	2	1	no	—
196	C₂³×C₇	C₄×D₄	1	2	yes	—
197	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
198	C₇×Q₈	—	2	4	no	—
199	C₇×Q₈	—	2	4	no	—
200	C₇×Q₈	—	4	2	no	—
201	C₇×Q₈	—	4	2	no	—
202	C₂×C₄×C₇	—	2	1	no	—
203	C₂×C₄×C₇	—	2	1	no	—
204	C₂×C₄×C₇	—	2	1	no	—
205	C₂×C₄×C₇	—	2	1	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	2	1	no	—
208	C₂×C₄×C₇	—	2	2	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	4	no	—
213	C₂×C₄×C₇	—	2	4	no	—
214	C₂×C₄×C₇	—	2	1	no	—
215	C₂×C₄×C₇	—	2	4	no	—
216	C₂×C₄×C₇	—	2	1	no	—
217	C₂×C₄×C₇	—	2	1	no	—
218	C₂×C₄×C₇	—	2	1	no	—
219	C₂×C₄×C₇	—	2	1	no	—
220	C₂×C₄×C₇	—	2	1	no	—
221	C₂×C₄×C₇	—	4	2	no	—
222	C₂×C₄×C₇	—	4	2	no	—
223	C₂×C₄×C₇	—	4	2	no	—
224	C₂×C₄×C₇	—	4	2	no	—
225	C₂×C₄×C₇	—	4	2	no	—
226	C₂×C₄×C₇	—	4	2	no	—
227	C₂×C₄×C₇	—	4	2	no	—
228	C₂×C₄×C₇	—	4	2	no	—
229	C₂×C₄×C₇	—	4	2	no	—
230	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
231	C₂×C₄×C₇	#135	1	2	yes	—
232	C₂×C₄×C₇	#135	1	2	yes	—
233	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
234	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
239	C₇×C₈	—	2	2	no	—
240	C₇×C₈	—	4	1	no	—
241	C₇×C₈	—	4	1	no	—
242	C₇×C₈	C₄×D₄	1	4	yes	—
243	C₂²×Q₈	C₂³×C₇	1	2	yes	—
244	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
245	C₂×Q₁₆	—	2	2	no	—
246	C₂×Q₁₆	—	2	2	no	—
247	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	C₂×C₄×C₇	1	4	yes	—
251	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
255	C₂²⋊Q₈	—	2	4	no	—
256	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
257	C₄×Q₈	—	2	4	no	—
258	C₄×Q₈	—	4	2	no	—
259	#117	—	2	4	no	—
260	#117	—	4	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
276	#107	—	2	2	no	—
277	#107	C₂×C₄×C₇	1	4	yes	—
278	#107	C₇×D₄	1	4	yes	—
279	#106	—	2	4	no	—
280	#103	—	2	4	no	—
281	#103	—	4	2	no	—
282	#103	C₂×C₄×C₇	1	8	yes	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₄×C₈	—	2	2	no	—
285	C₄×C₈	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	C₇×D₄	1	1	yes	characteristic
291	#95	C₇×D₄	1	1	yes	characteristic
292	C₂²×C₇	—	2	2	no	—
293	C₂²×C₇	—	2	2	no	—
294	C₂²×C₇	—	2	2	no	—
295	C₂²×C₇	—	4	1	no	—
296	C₂²×C₇	—	4	1	no	—
297	C₂²×C₇	—	4	1	no	—
298	C₂²×C₇	—	4	1	no	—
299	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
300	C₂²×C₇	D₄²	1	1	yes	characteristic
301	C₂²×C₇	#547	1	1	yes	characteristic
302	C₂²×C₇	C₂×#135	1	1	yes	characteristic
303	C₂²×C₇	C₂×#135	1	1	yes	characteristic
304	C₂²×C₇	#578	1	1	yes	characteristic
305	C₂²×C₇	#578	1	1	yes	characteristic
306	C₄×C₇	—	2	2	no	—
307	C₄×C₇	—	2	2	no	—
308	C₄×C₇	—	2	2	no	—
309	C₄×C₇	—	4	1	no	—
310	C₄×C₇	—	4	4	no	—
311	C₄×C₇	—	4	4	no	—
312	C₄×C₇	—	4	1	no	—
313	C₄×C₇	—	4	4	no	—
314	C₄×C₇	—	8	2	no	—
315	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
316	C₄×C₇	#520	1	1	yes	characteristic
317	C₄×C₇	#548	1	1	yes	characteristic
318	C₄×C₇	#553	1	1	yes	characteristic
319	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
335	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
340	C₂²×C₄	C₇×#41	1	2	yes	—
341	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
342	Q₁₆	—	2	8	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	8	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
353	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
354	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
355	C₂×C₈	C₇×#41	1	2	yes	—
356	C₄⋊C₄	—	2	8	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	—	4	4	no	—
363	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
364	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
365	C₂²⋊C₄	—	2	8	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	4	4	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	4	4	no	—
374	C₄²	—	4	4	no	—
375	C₄²	—	4	4	no	—
376	C₂×C₇	—	4	2	no	—
377	C₂×C₇	#2361	1	1	yes	characteristic
378	C₂×C₇	C₄×#135	1	1	yes	characteristic
379	C₂×C₇	#2950	1	1	yes	characteristic
380	C₂×C₇	#3283	1	1	yes	characteristic
381	C₂×C₇	#3285	1	1	yes	characteristic
382	C₂×C₇	#3336	1	1	yes	characteristic
383	C₂×C₇	#3342	1	1	yes	characteristic
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	1	no	—
390	C₂³	C₄×C₇×D₄	1	2	yes	—
391	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
392	Q₈	—	2	4	no	—
393	Q₈	—	2	4	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
425	C₂×C₄	C₇×#135	1	2	yes	—
426	C₂×C₄	C₇×#135	1	2	yes	—
427	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
429	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
430	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
431	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
432	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	4	1	no	—
435	C₈	—	4	1	no	—
436	C₈	C₄×C₇×D₄	1	4	yes	—
437	C₇	#23026	1	1	yes	characteristic, direct product factor, Sylow
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
446	C₂²	C₇×D₄²	1	1	yes	characteristic
447	C₂²	C₇×#547	1	1	yes	characteristic
448	C₂²	C₂×C₇×#135	1	1	yes	characteristic
449	C₂²	C₂×C₇×#135	1	1	yes	characteristic
450	C₂²	C₇×#578	1	1	yes	characteristic
451	C₂²	C₇×#578	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	4	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	4	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	4	no	—
460	C₄	—	8	2	no	—
461	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
462	C₄	C₇×#520	1	1	yes	characteristic
463	C₄	C₇×#548	1	1	yes	characteristic
464	C₄	C₇×#553	1	1	yes	characteristic
465	C₂	—	4	2	no	—
466	C₂	C₇×#2361	1	1	yes	characteristic
467	C₂	C₄×C₇×#135	1	1	yes	characteristic
468	C₂	C₇×#2950	1	1	yes	characteristic
469	C₂	C₇×#3283	1	1	yes	characteristic
470	C₂	C₇×#3285	1	1	yes	characteristic
471	C₂	C₇×#3336	1	1	yes	characteristic
472	C₂	C₇×#3342	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	C₂⁴×C₇	C₂×D₄
LCS	G ▷ C₂×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
2. C₂×C₄×C₇×Q₁₆	C₂	semidirect
5. C₇×#1969	C₂	semidirect
6. C₇×#1942	C₂	semidirect
7. C₇×#1927	C₂	semidirect
9. C₇×#1865	C₂	semidirect
10. C₄×C₇×#107	C₂	semidirect
17. C₇×#467	C₄	semidirect
42. #23026	C₇	direct (N × H)
93. C₂×C₄×Q₁₆	C₂×C₇	semidirect
96. #1969	C₂×C₇	semidirect
97. #1942	C₂×C₇	semidirect
98. #1927	C₂×C₇	semidirect
100. #1865	C₂×C₇	semidirect
101. C₄×#107	C₂×C₇	semidirect
165. #467	C₄×C₇	semidirect
437. C₇	#23026	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×#467	2
C₂×C₄×C₇×Q₁₆	2
C₂×C₇×#427	2
C₇×#2362	2
C₇×#1969	2
C₇×#1942	2
C₇×#1927	2
C₇×#1873	2
C₇×#1865	2
C₄×C₇×#107	2
C₇×C₈×C₂²⋊C₄	2
#23026	7

Subgroups — C7×#23026 #13200242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23026 #13200242