Subgroups — #13261706

Order 1792.

958 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#389	C₂	1	1	yes	maximal, characteristic
2	C₂×#89707	C₂	1	1	yes	maximal, characteristic
3	C₂×#89324	C₂	1	2	yes	maximal
4	C₂×#89324	C₂	1	2	yes	maximal
5	C₂×#89319	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
7	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
8	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₇	—	2	1	no	—
11	C₂²×C₄⋊Dic₇	—	2	1	no	—
12	C₂²×C₄⋊Dic₇	C₂²	1	2	yes	—
13	C₂³×C₇⋊C₈	C₂²	1	2	yes	—
14	C₇×#389	—	2	2	no	—
15	C₇×#389	C₄	1	4	yes	complemented
16	C₂×C₇×#95	—	2	1	no	—
17	#89707	—	2	4	no	—
18	#89324	—	2	4	no	—
19	#89324	—	2	4	no	—
20	#89319	—	2	2	no	—
21	#11207	—	7	1	no	maximal, Sylow
22	C₂³×C₄×C₇	—	2	1	no	—
23	C₂³×C₄×C₇	—	2	1	no	—
24	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
27	C₂³×Dic₇	—	2	2	no	—
28	C₂×C₇×C₄⋊C₄	—	2	1	no	—
29	C₂×C₇×C₄⋊C₄	—	2	1	no	—
30	C₂×C₇×C₄⋊C₄	—	2	1	no	—
31	C₂×C₇×C₄⋊C₄	—	2	2	no	—
32	C₂×C₇×C₄⋊C₄	—	2	2	no	—
33	C₂×C₇×C₄⋊C₄	—	2	4	no	—
34	C₂×C₇×C₄⋊C₄	—	2	1	no	—
35	C₂×C₇×C₄⋊C₄	—	4	2	no	—
36	C₂×C₇×C₄⋊C₄	—	4	2	no	—
37	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
38	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
39	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
40	C₂×C₇×C₄⋊C₄	Q₈	1	2	yes	—
41	C₂×C₄²×C₇	—	2	2	no	—
42	C₂×C₄²×C₇	—	2	2	no	—
43	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₇	D₄	1	2	yes	—
45	C₂×C₄⋊Dic₇	—	2	2	no	—
46	C₂×C₄⋊Dic₇	—	2	2	no	—
47	C₂×C₄⋊Dic₇	—	2	2	no	—
48	C₂×C₄⋊Dic₇	—	2	2	no	—
49	C₂×C₄⋊Dic₇	—	2	4	no	—
50	C₂×C₄⋊Dic₇	—	2	4	no	—
51	C₂×C₄⋊Dic₇	—	2	2	no	—
52	C₂×C₄⋊Dic₇	—	4	2	no	—
53	C₂×C₄⋊Dic₇	—	4	2	no	—
54	C₂×C₄⋊Dic₇	—	4	2	no	—
55	C₂×C₄⋊Dic₇	—	4	2	no	—
56	C₂×C₄⋊Dic₇	D₄	1	4	yes	—
57	C₂²×C₇⋊C₈	—	2	2	no	—
58	C₂²×C₇⋊C₈	—	2	2	no	—
59	C₂²×C₇⋊C₈	—	2	2	no	—
60	C₂²×C₇⋊C₈	—	2	2	no	—
61	C₂²×C₇⋊C₈	—	2	2	no	—
62	C₂²×C₇⋊C₈	—	2	2	no	—
63	C₂²×C₇⋊C₈	Q₈	1	4	yes	—
64	C₇×#95	—	2	4	no	—
65	C₂×#389	D₇	1	1	yes	characteristic
66	C₂×#384	—	7	1	no	—
67	C₂×#340	—	7	2	no	—
68	C₂×#340	—	7	2	no	—
69	C₂×#336	—	7	1	no	—
70	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₇	—	2	1	no	—
72	C₂²×C₄×C₇	—	2	1	no	—
73	C₂²×C₄×C₇	—	2	1	no	—
74	C₂²×C₄×C₇	—	2	1	no	—
75	C₂²×C₄×C₇	—	2	1	no	—
76	C₂²×C₄×C₇	—	2	1	no	—
77	C₂²×C₄×C₇	—	2	1	no	—
78	C₂²×C₄×C₇	—	2	1	no	—
79	C₂²×C₄×C₇	—	2	2	no	—
80	C₂²×C₄×C₇	—	2	2	no	—
81	C₂²×C₄×C₇	—	2	2	no	—
82	C₂²×C₄×C₇	—	2	2	no	—
83	C₂²×C₄×C₇	—	4	1	no	—
84	C₂²×C₄×C₇	—	4	1	no	—
85	C₂²×C₄×C₇	—	4	1	no	—
86	C₂²×C₄×C₇	—	4	1	no	—
87	C₂²×C₄×C₇	—	4	1	no	—
88	C₂²×C₄×C₇	—	4	1	no	—
89	C₂²×C₄×C₇	—	4	1	no	—
90	C₂²×C₄×C₇	—	4	1	no	—
91	C₂²×C₄×C₇	—	4	1	no	—
92	C₂²×C₄×C₇	—	4	1	no	—
93	C₂²×C₄×C₇	C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄×C₇	C₂²⋊C₄	1	2	yes	—
95	C₂²×C₄×C₇	D₈	1	2	yes	—
96	C₂²×C₄×C₇	SD₁₆	1	2	yes	—
97	C₂²×C₄×C₇	SD₁₆	1	2	yes	—
98	C₂²×C₄×C₇	Q₁₆	1	2	yes	—
99	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
104	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
105	C₂²×C₄×C₇	#41	1	1	yes	characteristic
106	C₂²×C₄×C₇	#41	1	1	yes	characteristic
107	C₂²×C₄×C₇	#41	1	2	yes	—
108	C₂²×C₄×C₇	#41	1	2	yes	—
109	C₂²×Dic₇	—	2	4	no	—
110	C₂²×Dic₇	—	4	2	no	—
111	C₂²×Dic₇	—	4	2	no	—
112	C₂²×Dic₇	—	4	2	no	—
113	C₂²×Dic₇	—	4	2	no	—
114	C₂²×Dic₇	—	4	2	no	—
115	C₂²×Dic₇	—	4	2	no	—
116	C₇×C₄⋊C₄	—	2	2	no	—
117	C₇×C₄⋊C₄	—	2	2	no	—
118	C₇×C₄⋊C₄	—	2	2	no	—
119	C₇×C₄⋊C₄	—	2	4	no	—
120	C₇×C₄⋊C₄	—	4	8	no	—
121	C₇×C₄⋊C₄	—	4	2	no	—
122	C₇×C₄⋊C₄	C₄⋊C₄	1	4	yes	complemented
123	C₄²×C₇	—	2	4	no	—
124	C₄²×C₇	—	2	4	no	—
125	C₄⋊Dic₇	—	2	4	no	—
126	C₄⋊Dic₇	—	2	4	no	—
127	C₄⋊Dic₇	—	4	8	no	—
128	C₄⋊Dic₇	—	4	8	no	—
129	C₄⋊Dic₇	—	4	2	no	—
130	C₄⋊Dic₇	—	4	2	no	—
131	C₂×C₇⋊C₈	—	2	4	no	—
132	C₂×C₇⋊C₈	—	2	4	no	—
133	C₂×C₇⋊C₈	—	2	4	no	—
134	C₂×C₇⋊C₈	—	4	2	no	—
135	C₂×C₇⋊C₈	—	4	2	no	—
136	C₂×C₇⋊C₈	—	4	2	no	—
137	C₂×C₇⋊C₈	—	4	2	no	—
138	C₂³×C₈	—	7	2	no	—
139	C₂²×C₄⋊C₄	—	2	1	no	—
140	C₂²×C₄⋊C₄	—	7	2	no	—
141	C₂²×C₄⋊C₄	—	14	1	no	—
142	C₂²×C₄⋊C₄	—	14	1	no	—
143	C₂²×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
144	C₂²×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
145	C₂²×C₄²	C₂×D₇	1	1	yes	characteristic
146	#389	—	2	2	no	—
147	#389	Dic₇	1	4	yes	complemented
148	#384	—	14	4	no	—
149	C₂×#95	—	2	1	no	—
150	#340	—	14	4	no	—
151	#340	—	14	4	no	—
152	#336	—	14	2	no	—
153	C₂³×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂³×C₇	#120	1	1	yes	characteristic
155	C₂³×C₇	#121	1	1	yes	characteristic
156	C₂³×C₇	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂³×C₇	#123	1	1	yes	characteristic
158	C₂³×C₇	#124	1	1	yes	characteristic
159	C₂³×C₇	C₄⋊Q₈	1	1	yes	characteristic
160	C₂³×C₇	C₂×D₈	1	1	yes	characteristic
161	C₂³×C₇	C₂×SD₁₆	1	1	yes	characteristic
162	C₂³×C₇	C₂×SD₁₆	1	1	yes	characteristic
163	C₂³×C₇	C₂×Q₁₆	1	1	yes	characteristic
164	C₂³×C₇	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂³×C₇	AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₂³×C₇	#137	1	1	yes	characteristic
167	C₂³×C₇	#137	1	1	yes	characteristic
168	C₂×C₄×C₇	—	2	2	no	—
169	C₂×C₄×C₇	—	2	2	no	—
170	C₂×C₄×C₇	—	2	2	no	—
171	C₂×C₄×C₇	—	2	2	no	—
172	C₂×C₄×C₇	—	2	2	no	—
173	C₂×C₄×C₇	—	2	2	no	—
174	C₂×C₄×C₇	—	2	2	no	—
175	C₂×C₄×C₇	—	2	2	no	—
176	C₂×C₄×C₇	—	2	2	no	—
177	C₂×C₄×C₇	—	2	2	no	—
178	C₂×C₄×C₇	—	2	2	no	—
179	C₂×C₄×C₇	—	2	2	no	—
180	C₂×C₄×C₇	—	2	4	no	—
181	C₂×C₄×C₇	—	4	2	no	—
182	C₂×C₄×C₇	—	4	2	no	—
183	C₂×C₄×C₇	—	4	2	no	—
184	C₂×C₄×C₇	—	4	2	no	—
185	C₂×C₄×C₇	—	4	2	no	—
186	C₂×C₄×C₇	—	4	2	no	—
187	C₂×C₄×C₇	—	4	2	no	—
188	C₂×C₄×C₇	—	4	2	no	—
189	C₂×C₄×C₇	—	4	2	no	—
190	C₂×C₄×C₇	—	8	1	no	—
191	C₂×C₄×C₇	—	8	1	no	—
192	C₂×C₄×C₇	—	8	1	no	—
193	C₂×C₄×C₇	—	8	1	no	—
194	C₂×C₄×C₇	#102	1	4	yes	—
195	C₂×C₄×C₇	#103	1	4	yes	—
196	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₇	#117	1	1	yes	characteristic
198	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
199	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
200	C₂×C₄×C₇	#121	1	2	yes	—
201	C₂×C₄×C₇	#121	1	1	yes	characteristic
202	C₂×C₄×C₇	#121	1	2	yes	—
203	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
204	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
205	C₂×C₄×C₇	C₂²⋊Q₈	1	1	yes	characteristic
206	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
207	C₂×C₄×C₇	#123	1	2	yes	—
208	C₂×C₄×C₇	#125	1	2	yes	—
209	C₂×C₄×C₇	#125	1	2	yes	—
210	C₂×C₄×C₇	#126	1	2	yes	—
211	C₂×C₄×C₇	C₄⋊Q₈	1	2	yes	—
212	C₂×Dic₇	—	4	4	no	—
213	C₂×Dic₇	—	4	4	no	—
214	C₂×Dic₇	—	4	4	no	—
215	C₂×Dic₇	—	8	2	no	—
216	C₂×Dic₇	—	8	2	no	—
217	C₂×Dic₇	—	8	2	no	—
218	C₂×Dic₇	—	8	2	no	—
219	C₇⋊C₈	—	4	4	no	—
220	C₂³×C₄	—	2	1	no	—
221	C₂³×C₄	—	2	1	no	—
222	C₂³×C₄	—	14	2	no	—
223	C₂³×C₄	C₂²⋊D₇	1	1	yes	characteristic
224	C₂³×C₄	C₂²⋊D₇	1	1	yes	characteristic
225	C₂³×C₄	C₂²×D₇	1	1	yes	characteristic
226	C₂²×C₈	—	7	4	no	—
227	C₂²×C₈	—	14	2	no	—
228	C₂²×C₈	—	14	2	no	—
229	C₂²×C₈	—	14	2	no	—
230	C₂²×C₈	—	14	2	no	—
231	C₂²×C₈	—	14	2	no	—
232	C₂²×C₈	—	14	2	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	4	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	4	2	no	—
241	C₂×C₄⋊C₄	—	4	2	no	—
242	C₂×C₄⋊C₄	—	7	4	no	—
243	C₂×C₄⋊C₄	—	14	2	no	—
244	C₂×C₄⋊C₄	—	14	2	no	—
245	C₂×C₄⋊C₄	—	14	2	no	—
246	C₂×C₄⋊C₄	—	14	2	no	—
247	C₂×C₄⋊C₄	—	14	4	no	—
248	C₂×C₄⋊C₄	—	14	4	no	—
249	C₂×C₄⋊C₄	—	14	2	no	—
250	C₂×C₄⋊C₄	—	28	2	no	—
251	C₂×C₄⋊C₄	—	28	2	no	—
252	C₂×C₄⋊C₄	—	28	2	no	—
253	C₂×C₄⋊C₄	—	28	2	no	—
254	C₂×C₄⋊C₄	Dic₁₄	1	2	yes	—
255	C₂×C₄⋊C₄	D₂₈	1	2	yes	—
256	C₂×C₄⋊C₄	C₂×Dic₇	1	2	yes	—
257	C₂×C₄⋊C₄	C₂×Dic₇	1	2	yes	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	—	2	2	no	—
260	C₂×C₄²	C₂×Dic₇	1	2	yes	—
261	C₂×C₄²	C₂²⋊D₇	1	2	yes	—
262	#95	—	2	4	no	—
263	C₂²×C₇	#380	1	1	yes	characteristic
264	C₂²×C₇	#386	1	1	yes	characteristic
265	C₂²×C₇	#391	1	1	yes	characteristic
266	C₂²×C₇	#394	1	1	yes	characteristic
267	C₂²×C₇	#395	1	1	yes	characteristic
268	C₂²×C₇	#398	1	1	yes	characteristic
269	C₂²×C₇	#400	1	1	yes	characteristic
270	C₂²×C₇	C₂×#102	1	1	yes	characteristic
271	C₂²×C₇	C₂×#103	1	1	yes	characteristic
272	C₂²×C₇	#417	1	1	yes	characteristic
273	C₂²×C₇	#417	1	1	yes	characteristic
274	C₂²×C₇	#447	1	1	yes	characteristic
275	C₂²×C₇	#448	1	1	yes	characteristic
276	C₂²×C₇	#450	1	1	yes	characteristic
277	C₂²×C₇	#451	1	1	yes	characteristic
278	C₂²×C₇	#459	1	1	yes	characteristic
279	C₂²×C₇	#460	1	1	yes	characteristic
280	C₂²×C₇	#461	1	1	yes	characteristic
281	C₂²×C₇	#462	1	1	yes	characteristic
282	C₂²×C₇	#474	1	1	yes	characteristic
283	C₂²×C₇	#475	1	1	yes	characteristic
284	C₂²×C₇	#476	1	1	yes	characteristic
285	C₂²×C₇	#477	1	1	yes	characteristic
286	C₂²×C₇	#480	1	1	yes	characteristic
287	C₂²×C₇	#481	1	1	yes	characteristic
288	C₂²×C₇	#483	1	1	yes	characteristic
289	C₂²×C₇	#484	1	1	yes	characteristic
290	C₂²×C₇	#486	1	1	yes	characteristic
291	C₂²×C₇	#487	1	1	yes	characteristic
292	C₂²×C₇	#490	1	1	yes	characteristic
293	C₂²×C₇	#491	1	1	yes	characteristic
294	C₂²×C₇	#498	1	1	yes	characteristic
295	C₂²×C₇	#500	1	1	yes	characteristic
296	C₂²×C₇	#501	1	1	yes	characteristic
297	C₂²×C₇	#501	1	1	yes	characteristic
298	C₄×C₇	—	2	4	no	—
299	C₄×C₇	—	2	4	no	—
300	C₄×C₇	—	4	4	no	—
301	C₄×C₇	—	8	2	no	—
302	C₄×C₇	#387	1	2	yes	—
303	C₄×C₇	#389	1	2	yes	—
304	C₄×C₇	#396	1	2	yes	—
305	C₄×C₇	#398	1	2	yes	—
306	Dic₇	—	8	4	no	—
307	C₂⁴	C₂×C₂²⋊D₇	1	1	yes	characteristic
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	14	4	no	—
331	C₂²×C₄	—	28	2	no	—
332	C₂²×C₄	—	28	2	no	—
333	C₂²×C₄	—	28	2	no	—
334	C₂²×C₄	—	28	2	no	—
335	C₂²×C₄	—	28	2	no	—
336	C₂²×C₄	—	28	2	no	—
337	C₂²×C₄	#1141	1	2	yes	—
338	C₂²×C₄	#1142	1	2	yes	—
339	C₂²×C₄	#1143	1	2	yes	—
340	C₂²×C₄	#1144	1	2	yes	—
341	C₂²×C₄	C₂²⋊Dic₇	1	2	yes	—
342	C₂²×C₄	C₂²⋊Dic₇	1	2	yes	—
343	C₂²×C₄	C₂×Dic₁₄	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₂₈	1	1	yes	characteristic
345	C₂²×C₄	#1157	1	1	yes	characteristic
346	C₂²×C₄	#1157	1	1	yes	characteristic
347	C₂²×C₄	D₄×D₇	1	2	yes	—
348	C₂²×C₄	#1159	1	2	yes	—
349	C₂²×C₄	Q₈×D₇	1	2	yes	—
350	C₂²×C₄	#1161	1	2	yes	—
351	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
353	C₂×C₈	—	14	4	no	—
354	C₂×C₈	—	14	4	no	—
355	C₂×C₈	—	14	4	no	—
356	C₂×C₈	—	28	2	no	—
357	C₂×C₈	—	28	2	no	—
358	C₂×C₈	—	28	2	no	—
359	C₂×C₈	—	28	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	4	8	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	14	4	no	—
367	C₄⋊C₄	—	14	4	no	—
368	C₄⋊C₄	—	28	8	no	—
369	C₄⋊C₄	—	28	8	no	—
370	C₄⋊C₄	—	28	2	no	—
371	C₄⋊C₄	—	28	2	no	—
372	C₄⋊C₄	C₄⋊Dic₇	1	4	yes	complemented
373	C₄²	—	2	4	no	—
374	C₄²	—	2	4	no	—
375	C₂×C₇	#1441	1	1	yes	characteristic
376	C₂×C₇	#1802	1	1	yes	characteristic
377	C₂×C₇	#1803	1	1	yes	characteristic
378	C₂×C₇	#1872	1	1	yes	characteristic
379	C₂×C₇	#1874	1	1	yes	characteristic
380	C₂×C₇	#1990	1	1	yes	characteristic
381	C₂×C₇	#1992	1	1	yes	characteristic
382	C₂×C₇	#2041	1	1	yes	characteristic
383	C₂×C₇	#2043	1	1	yes	characteristic
384	C₂×C₇	#2057	1	1	yes	characteristic
385	C₂×C₇	#2058	1	1	yes	characteristic
386	C₂×C₇	#2083	1	1	yes	characteristic
387	C₂×C₇	#2084	1	1	yes	characteristic
388	C₂×C₇	#2099	1	1	yes	characteristic
389	C₂×C₇	#2100	1	1	yes	characteristic
390	C₂³	#6487	1	1	yes	characteristic
391	C₂³	#6493	1	1	yes	characteristic
392	C₂³	C₂×#1141	1	1	yes	characteristic
393	C₂³	C₂×#1142	1	1	yes	characteristic
394	C₂³	#6498	1	1	yes	characteristic
395	C₂³	#6500	1	1	yes	characteristic
396	C₂³	C₂×#1143	1	1	yes	characteristic
397	C₂³	C₂×#1144	1	1	yes	characteristic
398	C₂³	#6507	1	1	yes	characteristic
399	C₂³	#6510	1	1	yes	characteristic
400	C₂³	#6512	1	1	yes	characteristic
401	C₂³	#6512	1	1	yes	characteristic
402	C₂³	#6514	1	1	yes	characteristic
403	C₂³	#6514	1	1	yes	characteristic
404	C₂³	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	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	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	8	1	no	—
428	C₂×C₄	—	8	1	no	—
429	C₂×C₄	—	8	1	no	—
430	C₂×C₄	—	8	1	no	—
431	C₂×C₄	—	28	4	no	—
432	C₂×C₄	—	28	4	no	—
433	C₂×C₄	—	28	4	no	—
434	C₂×C₄	—	56	2	no	—
435	C₂×C₄	—	56	2	no	—
436	C₂×C₄	—	56	2	no	—
437	C₂×C₄	—	56	2	no	—
438	C₂×C₄	#6406	1	4	yes	—
439	C₂×C₄	#6409	1	4	yes	—
440	C₂×C₄	#6451	1	2	yes	—
441	C₂×C₄	#6452	1	2	yes	—
442	C₂×C₄	#6453	1	2	yes	—
443	C₂×C₄	#6457	1	2	yes	—
444	C₂×C₄	#6458	1	2	yes	—
445	C₂×C₄	#6459	1	2	yes	—
446	C₂×C₄	#6460	1	2	yes	—
447	C₂×C₄	#6461	1	2	yes	—
448	C₂×C₄	#6487	1	1	yes	characteristic
449	C₂×C₄	C₂×C₄⋊Dic₇	1	1	yes	characteristic
450	C₂×C₄	#6489	1	1	yes	characteristic
451	C₂×C₄	#6493	1	1	yes	characteristic
452	C₂×C₄	D₄×Dic₇	1	2	yes	—
453	C₂×C₄	#6502	1	2	yes	—
454	C₂×C₄	Q₈×Dic₇	1	2	yes	—
455	C₂×C₄	#6509	1	2	yes	—
456	C₈	—	28	4	no	—
457	C₇	#11207	1	1	yes	characteristic, complemented, Sylow
458	C₂²	#89751	1	1	yes	characteristic
459	C₂²	#89755	1	1	yes	characteristic
460	C₂²	#89758	1	1	yes	characteristic
461	C₂²	#89763	1	1	yes	characteristic
462	C₂²	#89779	1	1	yes	characteristic
463	C₂²	#89780	1	1	yes	characteristic
464	C₂²	#89787	1	1	yes	characteristic
465	C₂²	#89791	1	1	yes	characteristic
466	C₂²	#89792	1	1	yes	characteristic
467	C₂²	#89793	1	1	yes	characteristic
468	C₂²	#89799	1	1	yes	characteristic
469	C₂²	#89803	1	1	yes	characteristic
470	C₂²	#89805	1	1	yes	characteristic
471	C₂²	#89806	1	1	yes	characteristic
472	C₂²	#89808	1	1	yes	characteristic
473	C₂²	#89812	1	1	yes	characteristic
474	C₂²	#89815	1	1	yes	characteristic
475	C₂²	#89816	1	1	yes	characteristic
476	C₂²	#89818	1	1	yes	characteristic
477	C₂²	#89822	1	1	yes	characteristic
478	C₂²	#89837	1	1	yes	characteristic
479	C₂²	#89837	1	1	yes	characteristic
480	C₂²	#89839	1	1	yes	characteristic
481	C₂²	#89841	1	1	yes	characteristic
482	C₂²	#89850	1	1	yes	characteristic
483	C₂²	#89851	1	1	yes	characteristic
484	C₂²	#89860	1	1	yes	characteristic
485	C₂²	#89865	1	1	yes	characteristic
486	C₂²	#89984	1	1	yes	characteristic
487	C₂²	C₂×#6406	1	1	yes	characteristic
488	C₂²	#89992	1	1	yes	characteristic
489	C₂²	C₂×#6409	1	1	yes	characteristic
490	C₂²	#90002	1	1	yes	characteristic
491	C₂²	#90004	1	1	yes	characteristic
492	C₂²	#90004	1	1	yes	characteristic
493	C₄	—	2	4	no	—
494	C₄	—	2	4	no	—
495	C₄	—	4	4	no	—
496	C₄	—	8	2	no	—
497	C₄	—	56	4	no	—
498	C₄	#89753	1	2	yes	—
499	C₄	#89756	1	2	yes	—
500	C₄	#89757	1	2	yes	—
501	C₄	#89766	1	2	yes	—
502	C₂	#11727358	1	1	yes	characteristic
503	C₂	#11727359	1	1	yes	characteristic
504	C₂	#11727361	1	1	yes	characteristic
505	C₂	#11727362	1	1	yes	characteristic
506	C₂	#11727365	1	1	yes	characteristic
507	C₂	#11727366	1	1	yes	characteristic
508	C₂	#11727381	1	1	yes	characteristic
509	C₂	#11727387	1	1	yes	characteristic
510	C₂	#11729319	1	1	yes	characteristic
511	C₂	#11729358	1	1	yes	characteristic
512	C₂	#11729380	1	1	yes	characteristic
513	C₂	#11729431	1	1	yes	characteristic
514	C₂	#11729446	1	1	yes	characteristic
515	C₂	#11729495	1	1	yes	characteristic
516	C₂	#11729541	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₇
commutator	C₂²×C₄×C₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₇
Fitting	C₂×C₇×#389	C₂
socle, prime radical	C₂⁴×C₇	C₂×D₄
cosocle	C₂³×C₄×C₇	C₂³
hypercenter	C₂×#389	D₇
hypocenter	C₇	#11207
LCS	G ▷ C₂²×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#389

Complements

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

N	H ≅ G/N	type
15. C₇×#389	C₄	semidirect
122. C₇×C₄⋊C₄	C₄⋊C₄	semidirect
147. #389	Dic₇	semidirect
372. C₄⋊C₄	C₄⋊Dic₇	semidirect
457. C₇	#11207	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#389	2
C₂×#89707	2
C₂×#89324	2
C₂×#89319	2
#11207	7