Subgroups — #13507301

Order 1792.

498 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11737362	C₂	1	1	yes	maximal, characteristic
2	C₇×#2183	C₂	1	1	yes	maximal, characteristic, complemented
3	#11728703	C₂	1	1	yes	maximal, characteristic, complemented
4	#11727039	C₂	1	1	yes	maximal, characteristic
5	#11727039	C₂	1	1	yes	maximal, characteristic
6	D₇×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
7	#11727036	C₂	1	1	yes	maximal, characteristic, complemented
8	#11727036	C₂	1	1	yes	maximal, characteristic, complemented
9	#11727034	C₂	1	1	yes	maximal, characteristic, complemented
10	#11726826	C₂	1	1	yes	maximal, characteristic
11	#11726825	C₂	1	1	yes	maximal, characteristic
12	#11726822	C₂	1	1	yes	maximal, characteristic, complemented
13	#11726822	C₂	1	1	yes	maximal, characteristic, complemented
14	#11726805	C₂	1	1	yes	maximal, characteristic
15	C₁₆×Dic₁₄	C₂	1	1	yes	maximal, characteristic, complemented
16	#90269	C₄	1	1	yes	characteristic
17	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
18	#89796	C₄	1	1	yes	characteristic
19	C₂×#6372	C₂²	1	1	yes	characteristic
20	C₂×#6372	C₂²	1	1	yes	characteristic
21	C₂×D₇×C₁₆	C₂²	1	1	yes	characteristic
22	C₂×D₇×C₁₆	C₂²	1	1	yes	characteristic
23	#89611	C₄	1	1	yes	characteristic
24	#89611	C₄	1	1	yes	characteristic
25	#89609	C₄	1	1	yes	characteristic
26	#89603	C₄	1	1	yes	characteristic
27	#89600	C₄	1	1	yes	characteristic
28	#89600	C₄	1	1	yes	characteristic
29	#89461	C₂²	1	1	yes	characteristic
30	#89461	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
32	C₈×Dic₁₄	C₂²	1	1	yes	characteristic
33	C₈×Dic₁₄	C₂²	1	1	yes	characteristic
34	C₈×Dic₁₄	C₂²	1	1	yes	characteristic
35	C₇×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₇×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₇×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₇×#346	C₂²	1	1	yes	characteristic
39	C₇×#346	C₂²	1	1	yes	characteristic
40	C₄×C₇×C₁₆	C₂²	1	1	yes	characteristic
41	#89297	C₂²	1	1	yes	characteristic
42	#89297	C₂²	1	1	yes	characteristic
43	Dic₇⋊C₁₆	C₂²	1	1	yes	characteristic
44	Dic₇⋊C₁₆	C₂²	1	1	yes	characteristic
45	Dic₇⋊C₁₆	C₂²	1	1	yes	characteristic
46	Dic₇⋊C₁₆	C₂²	1	1	yes	characteristic
47	Dic₇⋊C₁₆	C₂²	1	1	yes	characteristic
48	Dic₇⋊C₁₆	C₂²	1	1	yes	characteristic
49	C₁₆×Dic₇	C₂²	1	1	yes	characteristic
50	C₁₆×Dic₇	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₇	C₂²	1	1	yes	characteristic
52	C₁₆×Dic₇	C₂²	1	1	yes	characteristic
53	C₄⋊(C₇⋊C₁₆)	C₂²	1	1	yes	characteristic
54	C₄⋊(C₇⋊C₁₆)	C₂²	1	1	yes	characteristic
55	C₄⋊(C₇⋊C₁₆)	C₂²	1	1	yes	characteristic
56	#89256	C₂²	1	1	yes	characteristic
57	#89256	C₂²	1	1	yes	characteristic
58	C₄×C₇⋊C₁₆	C₂²	1	1	yes	characteristic
59	#33476	—	7	1	no	maximal, Sylow
60	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
61	#6509	C₈	1	1	yes	characteristic
62	#6507	C₈	1	1	yes	characteristic
63	C₂×#1131	C₂×C₄	1	1	yes	characteristic
64	C₂×#1131	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₇	C₂³	1	1	yes	characteristic
67	#6460	C₈	1	1	yes	characteristic
68	#6459	C₈	1	1	yes	characteristic
69	#6459	C₈	1	1	yes	characteristic
70	#6452	C₈	1	1	yes	characteristic
71	#6452	C₈	1	1	yes	characteristic
72	#6451	C₈	1	1	yes	characteristic
73	#6435	C₂×C₄	1	1	yes	characteristic
74	#6435	C₂×C₄	1	1	yes	characteristic
75	C₄²×D₇	C₂×C₄	1	1	yes	characteristic
76	C₄×Dic₁₄	C₂×C₄	1	1	yes	characteristic
77	C₄×Dic₁₄	C₂×C₄	1	1	yes	characteristic
78	C₄×Dic₁₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
83	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
84	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
87	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
88	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
89	#6389	C₂×C₄	1	1	yes	characteristic
90	#6389	C₂×C₄	1	1	yes	characteristic
91	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
92	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
93	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
94	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
95	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
96	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₇	C₂³	1	1	yes	characteristic
99	C₈×Dic₇	C₂³	1	1	yes	characteristic
100	C₈×Dic₇	C₂³	1	1	yes	characteristic
101	C₂×C₇⋊C₁₆	C₂³	1	1	yes	characteristic
102	C₂×C₇⋊C₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₇⋊C₁₆	C₂³	1	1	yes	characteristic
104	C₂×C₇⋊C₁₆	C₂³	1	1	yes	characteristic
105	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
106	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
107	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
108	#6377	C₂×C₄	1	1	yes	characteristic
109	#6377	C₂×C₄	1	1	yes	characteristic
110	C₄×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
111	#6372	—	2	2	no	—
112	#6372	Q₈	1	4	yes	complemented
113	D₇×C₁₆	—	2	2	no	—
114	D₇×C₁₆	—	2	2	no	—
115	#2960	—	7	1	no	—
116	#2183	—	7	1	no	—
117	#2183	—	7	1	no	—
118	#2183	—	7	1	no	—
119	#2183	—	7	1	no	—
120	#2183	—	7	1	no	—
121	#2183	D₇	1	1	yes	characteristic, complemented
122	Q₈×C₁₆	—	7	1	no	—
123	Q₈×C₁₆	—	7	1	no	—
124	#2151	—	7	1	no	—
125	#2151	—	7	1	no	—
126	C₂×C₄⋊C₁₆	—	7	1	no	—
127	#2108	—	7	1	no	—
128	#2108	—	7	1	no	—
129	C₄×M₃₂	—	7	1	no	—
130	C₂×C₇×Q₈	C₂×C₈	1	1	yes	characteristic
131	C₂×C₄×D₇	C₂×C₈	1	1	yes	characteristic
132	C₂×C₄×D₇	C₂×C₈	1	1	yes	characteristic
133	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×Dic₁₄	C₂×C₈	1	1	yes	characteristic
135	C₂×Dic₁₄	C₂×C₈	1	1	yes	characteristic
136	C₂×Dic₁₄	C₂×C₈	1	1	yes	characteristic
137	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
141	C₇×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
142	C₇×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
143	C₇×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
144	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
147	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
148	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
149	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
150	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
151	C₄⋊Dic₇	C₂×C₈	1	1	yes	characteristic
152	C₄⋊Dic₇	C₂×C₈	1	1	yes	characteristic
153	C₄⋊Dic₇	C₂×C₈	1	1	yes	characteristic
154	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
155	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
156	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
157	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
158	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
159	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
160	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
161	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
162	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
163	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
164	C₄×Dic₇	C₂×C₈	1	1	yes	characteristic
165	C₄×Dic₇	C₂×C₈	1	1	yes	characteristic
166	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
167	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
168	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
173	#1131	—	2	2	no	—
174	#1131	—	2	2	no	—
175	C₈×D₇	—	2	2	no	—
176	C₈×D₇	C₂×Q₈	1	2	yes	—
177	C₈×D₇	#41	1	2	yes	—
178	C₇×C₁₆	—	2	1	no	—
179	C₇×C₁₆	—	2	1	no	—
180	C₇×C₁₆	—	2	1	no	—
181	C₇×C₁₆	C₂×Q₈	1	2	yes	—
182	C₇⋊C₁₆	—	2	1	no	—
183	C₇⋊C₁₆	—	2	1	no	—
184	C₇⋊C₁₆	—	2	1	no	—
185	C₇⋊C₁₆	C₂×Q₈	1	2	yes	—
186	#533	—	7	1	no	—
187	C₂×M₃₂	—	7	1	no	—
188	C₂×M₃₂	—	7	1	no	—
189	C₂²×C₁₆	—	7	1	no	—
190	C₂²×C₁₆	—	7	1	no	—
191	#446	—	7	1	no	—
192	#446	—	7	1	no	—
193	#446	—	7	1	no	—
194	#446	—	7	1	no	—
195	C₈×Q₈	—	7	1	no	—
196	C₈×Q₈	—	7	1	no	—
197	C₈×Q₈	—	7	1	no	—
198	C₈×Q₈	C₂×D₇	1	1	yes	characteristic
199	#424	—	7	1	no	—
200	#424	—	7	1	no	—
201	#423	—	7	1	no	—
202	#405	—	7	1	no	—
203	#405	—	7	1	no	—
204	C₂×C₄×C₈	—	7	1	no	—
205	C₄⋊C₁₆	—	7	1	no	—
206	C₄⋊C₁₆	—	7	1	no	—
207	C₄⋊C₁₆	—	7	1	no	—
208	C₄⋊C₁₆	—	7	1	no	—
209	C₄⋊C₁₆	—	7	1	no	—
210	C₄⋊C₁₆	—	7	1	no	—
211	C₄⋊C₁₆	—	7	1	no	—
212	C₄⋊C₁₆	—	7	1	no	—
213	C₄⋊C₁₆	—	7	1	no	—
214	C₄⋊C₁₆	C₂×D₇	1	1	yes	characteristic
215	C₄⋊C₁₆	C₂×D₇	1	1	yes	characteristic
216	C₄⋊C₁₆	C₂×D₇	1	1	yes	characteristic
217	#346	—	7	1	no	—
218	#346	—	7	1	no	—
219	#346	—	7	1	no	—
220	#346	—	7	1	no	—
221	#346	C₂×D₇	1	1	yes	characteristic
222	#346	C₂×D₇	1	1	yes	characteristic
223	C₄×C₁₆	—	7	1	no	—
224	C₄×C₁₆	—	7	1	no	—
225	C₄×C₁₆	—	7	1	no	—
226	C₄×C₁₆	—	7	1	no	—
227	C₄×C₁₆	—	7	1	no	—
228	C₄×C₁₆	C₂×D₇	1	1	yes	characteristic
229	C₂²×D₇	C₂²×C₈	1	1	yes	characteristic
230	C₇×Q₈	—	4	1	no	—
231	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
232	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
233	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
234	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
235	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
236	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
237	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
238	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
239	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
240	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
241	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
242	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
243	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
244	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
245	C₄×D₇	—	2	2	no	—
246	C₄×D₇	—	4	1	no	—
247	C₄×D₇	C₄×Q₈	1	2	yes	—
248	C₄×D₇	#131	1	2	yes	—
249	Dic₁₄	—	2	2	no	—
250	Dic₁₄	—	2	2	no	—
251	Dic₁₄	—	4	1	no	—
252	C₇×C₈	—	2	1	no	—
253	C₇×C₈	—	2	1	no	—
254	C₇×C₈	—	2	1	no	—
255	C₇×C₈	C₂²×Q₈	1	1	yes	characteristic
256	C₇×C₈	C₂×#41	1	1	yes	characteristic
257	C₇⋊C₈	—	2	1	no	—
258	C₇⋊C₈	—	2	1	no	—
259	C₇⋊C₈	—	2	1	no	—
260	C₇⋊C₈	C₄×Q₈	1	2	yes	—
261	C₂×M₁₆	—	7	1	no	—
262	C₂×M₁₆	—	7	1	no	—
263	C₂²×C₈	—	7	1	no	—
264	C₂²×C₈	—	7	1	no	—
265	C₄⋊Q₈	—	7	1	no	—
266	C₄⋊Q₈	—	7	1	no	—
267	#125	—	7	1	no	—
268	#125	—	7	1	no	—
269	C₂²⋊Q₈	—	7	1	no	—
270	C₂²⋊Q₈	—	7	1	no	—
271	C₂²⋊Q₈	—	7	1	no	—
272	C₂²⋊Q₈	—	7	1	no	—
273	C₄×Q₈	—	7	1	no	—
274	C₄×Q₈	—	7	1	no	—
275	C₄×Q₈	—	7	1	no	—
276	C₄×Q₈	C₄×D₇	1	1	yes	characteristic
277	#117	—	7	1	no	—
278	#117	—	7	1	no	—
279	C₂×C₄²	—	7	1	no	—
280	M₃₂	—	7	4	no	—
281	M₃₂	—	14	2	no	—
282	C₂×C₁₆	—	7	1	no	—
283	C₂×C₁₆	—	7	1	no	—
284	C₂×C₁₆	—	7	1	no	—
285	C₂×C₁₆	—	7	1	no	—
286	C₂×C₁₆	—	14	2	no	—
287	C₂×C₁₆	—	14	2	no	—
288	C₂×C₁₆	C₂²×D₇	1	1	yes	characteristic
289	C₂×C₁₆	C₂²×D₇	1	1	yes	characteristic
290	C₂×C₁₆	C₂²×D₇	1	1	yes	characteristic
291	C₂×C₁₆	C₂²×D₇	1	1	yes	characteristic
292	C₄⋊C₈	—	7	1	no	—
293	C₄⋊C₈	—	7	1	no	—
294	C₄⋊C₈	—	7	1	no	—
295	C₄⋊C₈	—	7	1	no	—
296	C₄⋊C₈	—	7	1	no	—
297	C₄⋊C₈	—	7	1	no	—
298	C₄⋊C₈	—	7	1	no	—
299	C₄⋊C₈	—	7	1	no	—
300	C₄⋊C₈	—	7	1	no	—
301	C₄⋊C₈	C₄×D₇	1	1	yes	characteristic
302	C₄⋊C₈	C₄×D₇	1	1	yes	characteristic
303	C₄⋊C₈	C₄×D₇	1	1	yes	characteristic
304	#97	—	7	1	no	—
305	#97	—	7	1	no	—
306	#97	—	7	1	no	—
307	#97	—	7	1	no	—
308	C₄×C₈	—	7	1	no	—
309	C₄×C₈	—	7	1	no	—
310	C₄×C₈	—	7	1	no	—
311	C₄×C₈	—	7	1	no	—
312	C₄×C₈	—	7	1	no	—
313	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
316	C₂²×C₇	C₂³×C₈	1	1	yes	characteristic
317	C₂×D₇	—	2	1	no	—
318	C₂×D₇	—	2	1	no	—
319	C₂×D₇	C₈×Q₈	1	2	yes	—
320	C₄×C₇	—	2	1	no	—
321	C₄×C₇	—	2	1	no	—
322	C₄×C₇	—	2	1	no	—
323	C₄×C₇	—	2	1	no	—
324	C₄×C₇	—	2	1	no	—
325	C₄×C₇	—	2	1	no	—
326	C₄×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
327	C₄×C₇	C₂×#131	1	1	yes	characteristic
328	Dic₇	—	2	1	no	—
329	Dic₇	—	2	1	no	—
330	Dic₇	—	2	1	no	—
331	Dic₇	—	2	1	no	—
332	Dic₇	—	2	1	no	—
333	Dic₇	C₈×Q₈	1	2	yes	—
334	Dic₇	#504	1	2	yes	—
335	C₂×Q₈	—	7	1	no	—
336	C₂×Q₈	—	7	1	no	—
337	C₂×Q₈	—	7	1	no	—
338	C₂×Q₈	C₈×D₇	1	1	yes	characteristic
339	C₂²×C₄	—	7	1	no	—
340	C₂²×C₄	—	7	1	no	—
341	C₂²×C₄	—	7	1	no	—
342	M₁₆	—	14	2	no	—
343	M₁₆	—	14	2	no	—
344	C₂×C₈	—	7	1	no	—
345	C₂×C₈	—	7	2	no	—
346	C₂×C₈	—	7	2	no	—
347	C₂×C₈	—	7	1	no	—
348	C₂×C₈	—	7	1	no	—
349	C₂×C₈	—	7	1	no	—
350	C₂×C₈	—	14	2	no	—
351	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
352	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
353	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
354	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
355	C₄⋊C₄	—	7	1	no	—
356	C₄⋊C₄	—	7	1	no	—
357	C₄⋊C₄	—	7	1	no	—
358	C₄⋊C₄	—	7	1	no	—
359	C₄⋊C₄	—	7	1	no	—
360	C₄⋊C₄	—	7	1	no	—
361	C₄⋊C₄	—	7	1	no	—
362	C₄⋊C₄	—	7	1	no	—
363	C₄⋊C₄	—	7	1	no	—
364	C₄⋊C₄	—	7	1	no	—
365	C₄⋊C₄	—	7	1	no	—
366	C₄⋊C₄	—	7	1	no	—
367	C₄⋊C₄	—	7	1	no	—
368	C₄⋊C₄	C₈×D₇	1	1	yes	characteristic
369	C₄⋊C₄	C₈×D₇	1	1	yes	characteristic
370	C₄⋊C₄	C₈×D₇	1	1	yes	characteristic
371	C₂²⋊C₄	—	7	1	no	—
372	C₂²⋊C₄	—	7	1	no	—
373	C₂²⋊C₄	—	7	1	no	—
374	C₂²⋊C₄	—	7	1	no	—
375	C₄²	—	7	1	no	—
376	C₄²	—	7	1	no	—
377	C₄²	—	7	1	no	—
378	C₄²	—	7	1	no	—
379	C₄²	—	7	1	no	—
380	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
381	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
382	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
383	C₁₆	—	2	1	no	—
384	C₁₆	—	2	1	no	—
385	C₁₆	—	2	1	no	—
386	C₁₆	—	7	2	no	—
387	C₁₆	—	14	1	no	—
388	C₁₆	—	14	1	no	—
389	C₁₆	—	14	1	no	—
390	C₁₆	Q₈×D₇	1	2	yes	—
391	C₂×C₇	C₂×C₈×Q₈	1	1	yes	characteristic
392	C₂×C₇	C₂×#504	1	1	yes	characteristic
393	C₂×C₇	#3407	1	1	yes	characteristic
394	D₇	—	2	2	no	—
395	C₂³	—	7	1	no	—
396	Q₈	—	4	1	no	—
397	Q₈	—	14	2	no	—
398	Q₈	—	14	2	no	—
399	Q₈	—	28	1	no	—
400	C₂×C₄	—	7	1	no	—
401	C₂×C₄	—	7	1	no	—
402	C₂×C₄	—	7	2	no	—
403	C₂×C₄	—	7	2	no	—
404	C₂×C₄	—	7	1	no	—
405	C₂×C₄	—	7	1	no	—
406	C₂×C₄	—	7	1	no	—
407	C₂×C₄	—	7	1	no	—
408	C₂×C₄	—	7	1	no	—
409	C₂×C₄	—	14	2	no	—
410	C₂×C₄	—	28	1	no	—
411	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
412	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
413	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
414	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
415	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
416	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	7	2	no	—
422	C₈	—	14	1	no	—
423	C₈	—	14	1	no	—
424	C₈	—	14	1	no	—
425	C₈	C₂×Q₈×D₇	1	1	yes	characteristic
426	C₈	D₇×#41	1	1	yes	characteristic
427	C₇	#33476	1	1	yes	characteristic, complemented, Sylow
428	C₂²	—	7	2	no	—
429	C₂²	—	14	1	no	—
430	C₂²	—	14	1	no	—
431	C₂²	C₂²×C₈×D₇	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	7	2	no	—
439	C₄	—	7	2	no	—
440	C₄	—	14	1	no	—
441	C₄	—	14	1	no	—
442	C₄	—	14	1	no	—
443	C₄	—	14	1	no	—
444	C₄	—	14	1	no	—
445	C₄	C₄×Q₈×D₇	1	1	yes	characteristic
446	C₄	D₇×#131	1	1	yes	characteristic
447	C₂	—	14	2	no	—
448	C₂	C₈×Q₈×D₇	1	1	yes	characteristic
449	C₂	#11739452	1	1	yes	characteristic
450	C₂	D₇×#504	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₇
commutator, socle	C₂²×C₇	C₂³×C₈
Fitting	C₇×#2183	C₂
prime radical	C₂²×D₇	C₂²×C₈
cosocle	C₂×C₇×C₈	C₂⁴
hypercenter	#2183	D₇
hypocenter	C₇	#33476
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₈ ◁ #2183

Complements

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

N	H ≅ G/N	type
2. C₇×#2183	C₂	semidirect
3. #11728703	C₂	semidirect
7. #11727036	C₂	semidirect
8. #11727036	C₂	semidirect
9. #11727034	C₂	semidirect
12. #11726822	C₂	semidirect
13. #11726822	C₂	semidirect
15. C₁₆×Dic₁₄	C₂	semidirect
112. #6372	Q₈	semidirect
121. #2183	D₇	semidirect
427. C₇	#33476	semidirect

Maximal subgroups

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

subgroup	index
#11737362	2
C₇×#2183	2
#11728703	2
#11727039	2
D₇×C₄⋊C₁₆	2
#11727036	2
#11727034	2
#11726826	2
#11726825	2
#11726822	2
#11726805	2
C₁₆×Dic₁₄	2
#33476	7