Subgroups — #13323022

Order 1792.

610 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	#11736730	C₂	1	2	yes	maximal
2	C₈×#1157	C₂	1	1	yes	maximal, characteristic
3	C₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
4	#11728501	C₂	1	2	yes	maximal, complemented
5	#11727486	C₂	1	1	yes	maximal, characteristic, complemented
6	#11726327	C₂	1	2	yes	maximal, complemented
7	#11726326	C₂	1	2	yes	maximal, complemented
8	#11726284	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726283	C₂	1	1	yes	maximal, characteristic, complemented
10	#11726281	C₂	1	1	yes	maximal, characteristic, complemented
11	D₇×#334	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#1157	C₂²	1	1	yes	characteristic
13	C₇×#431	C₂²	1	2	yes	—
14	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
15	C₈×C₂²⋊D₇	C₄	1	1	yes	characteristic
16	C₈×C₂²⋊D₇	C₄	1	1	yes	characteristic
17	C₈×C₂²⋊D₇	C₄	1	1	yes	characteristic
18	C₈×C₂²⋊D₇	C₄	1	1	yes	characteristic
19	#89698	C₂²	1	2	yes	—
20	#89697	C₂²	1	1	yes	characteristic
21	#89609	C₂²	1	2	yes	—
22	#89607	C₂²	1	2	yes	—
23	#89605	C₂²	1	2	yes	—
24	D₇×C₄⋊C₈	C₂²	1	2	yes	—
25	#89499	—	2	2	no	—
26	#89492	—	2	2	no	—
27	#89462	—	2	2	no	—
28	#89461	—	2	2	no	—
29	C₈×D₂₈	C₄	1	1	yes	characteristic
30	C₈×D₂₈	C₄	1	1	yes	characteristic
31	#89457	C₂²	1	1	yes	characteristic
32	#89457	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
35	C₈×Dic₁₄	C₄	1	1	yes	characteristic
36	C₈×Dic₁₄	C₄	1	1	yes	characteristic
37	C₇×#335	C₂²	1	2	yes	—
38	C₇×#334	C₂²	1	1	yes	characteristic
39	C₇×#334	C₂²	1	1	yes	characteristic
40	#89275	C₂²	1	2	yes	—
41	#89275	C₂²	1	2	yes	—
42	#89274	C₂²	1	2	yes	—
43	#89274	C₂²	1	2	yes	—
44	#89253	C₂²	1	2	yes	—
45	#89252	C₂²	1	1	yes	characteristic
46	#89252	C₂²	1	1	yes	characteristic
47	#17827	—	7	1	no	maximal, Sylow
48	C₂×#1157	D₄	1	1	yes	characteristic
49	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
52	C₄×C₂²⋊D₇	C₂×C₄	1	1	yes	characteristic
53	C₄×C₂²⋊D₇	C₂×C₄	1	1	yes	characteristic
54	C₄×C₂²⋊D₇	Q₈	1	1	yes	characteristic
55	C₄×C₂²⋊D₇	Q₈	1	1	yes	characteristic
56	#6489	D₄	1	1	yes	characteristic
57	C₂×#1131	—	2	2	no	—
58	C₂×C₈×D₇	—	2	2	no	—
59	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
63	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
64	C₄×D₂₈	Q₈	1	1	yes	characteristic
65	#6435	D₄	1	1	yes	characteristic
66	#6435	D₄	1	1	yes	characteristic
67	C₄²×D₇	C₂³	1	1	yes	characteristic
68	C₄²×D₇	C₂³	1	1	yes	characteristic
69	C₄×Dic₁₄	C₂×C₄	1	1	yes	characteristic
70	C₄×Dic₁₄	Q₈	1	1	yes	characteristic
71	C₇×C₄⋊C₈	C₂³	1	2	yes	—
72	C₇×C₄⋊C₈	C₂³	1	2	yes	—
73	C₇×C₂²⋊C₈	—	2	2	no	—
74	C₄×C₇×C₈	—	2	2	no	—
75	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
76	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
78	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
79	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
80	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
81	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
82	(C₂×D₇)⋊C₈	—	2	2	no	—
83	(C₂×D₇)⋊C₈	—	2	2	no	—
84	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
85	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
86	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
87	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
88	#6389	—	2	2	no	—
89	Dic₇⋊C₈	—	2	2	no	—
90	Dic₇⋊C₈	—	2	2	no	—
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	C₈×Dic₇	—	2	2	no	—
96	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
100	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
101	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
102	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
103	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
104	#6377	—	2	2	no	—
105	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
106	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
107	C₈×#41	—	7	1	no	—
108	#2925	—	7	2	no	—
109	#1572	—	7	2	no	—
110	#1572	—	7	2	no	—
111	#1571	—	7	2	no	—
112	#1568	—	7	1	no	—
113	#1568	—	7	1	no	—
114	#1566	—	7	1	no	—
115	#1564	—	7	1	no	—
116	#1564	D₇	1	1	yes	characteristic, complemented
117	C₂×#334	—	7	1	no	—
118	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
121	C₂×C₂²⋊D₇	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₂²⋊D₇	C₄⋊C₄	1	1	yes	characteristic
123	#1157	—	2	4	no	—
124	C₂×D₂₈	C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×D₇	C₂×Q₈	1	1	yes	characteristic
130	C₂×C₄×D₇	C₂×Q₈	1	1	yes	characteristic
131	C₂×Dic₁₄	C₄⋊C₄	1	1	yes	characteristic
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	—	4	1	no	—
136	C₂×C₇×C₈	C₂²×C₄	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	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₇	C₂×Q₈	1	1	yes	characteristic
143	C₄²×C₇	C₂⁴	1	1	yes	characteristic
144	C₂²⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
145	C₂²⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
146	(C₂×D₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
147	(C₂×D₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
148	(C₂×D₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
149	(C₂×D₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
150	C₄⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
151	C₄⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
152	Dic₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
153	Dic₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
154	Dic₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
155	Dic₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
156	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
157	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
158	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
159	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
160	C₄×Dic₇	C₂×Q₈	1	1	yes	characteristic
161	C₄×Dic₇	C₂×Q₈	1	1	yes	characteristic
162	C₂×C₇⋊C₈	—	2	2	no	—
163	C₂×C₇⋊C₈	—	2	2	no	—
164	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
168	#1131	—	4	4	no	—
169	C₈×D₇	—	2	2	no	—
170	C₈×D₇	—	2	2	no	—
171	C₈×D₇	—	4	1	no	—
172	C₈×D₇	—	4	1	no	—
173	C₈×D₇	—	4	4	no	—
174	C₄×#41	—	7	1	no	—
175	C₈×Q₈	—	7	1	no	—
176	C₈×Q₈	—	7	1	no	—
177	C₈×D₄	—	7	1	no	—
178	C₈×D₄	—	7	1	no	—
179	C₈×D₄	—	7	1	no	—
180	C₈×D₄	—	7	1	no	—
181	C₈×D₄	—	7	1	no	—
182	C₈×D₄	—	7	1	no	—
183	#433	—	14	2	no	—
184	#433	—	14	2	no	—
185	#432	—	7	2	no	—
186	#432	—	7	2	no	—
187	#431	—	7	1	no	—
188	#431	—	7	1	no	—
189	#431	—	7	1	no	—
190	#431	—	7	2	no	—
191	#431	C₂×D₇	1	2	yes	—
192	#423	—	7	2	no	—
193	C₂×C₄⋊C₈	—	7	2	no	—
194	#408	—	14	2	no	—
195	#405	—	14	2	no	—
196	C₂×C₄×C₈	—	7	1	no	—
197	C₂×C₄×C₈	—	7	1	no	—
198	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic
199	#335	—	7	2	no	—
200	#335	—	7	2	no	—
201	#335	—	7	2	no	—
202	#335	C₂×D₇	1	2	yes	—
203	#334	—	7	2	no	—
204	#334	—	7	2	no	—
205	#334	—	7	1	no	—
206	#334	—	7	1	no	—
207	#334	C₂×D₇	1	1	yes	characteristic
208	#334	C₂×D₇	1	1	yes	characteristic
209	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂²×D₇	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂²×D₇	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₇	—	2	1	no	—
213	C₂×C₄×C₇	—	2	1	no	—
214	C₂×C₄×C₇	—	2	2	no	—
215	C₂×C₄×C₇	—	4	1	no	—
216	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
222	C₂²⋊D₇	—	2	2	no	—
223	C₂²⋊D₇	—	2	2	no	—
224	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
230	D₂₈	—	2	2	no	—
231	C₄×D₇	—	2	1	no	—
232	C₄×D₇	—	2	1	no	—
233	C₄×D₇	—	2	1	no	—
234	C₄×D₇	—	2	1	no	—
235	C₄×D₇	—	2	2	no	—
236	C₄×D₇	—	4	1	no	—
237	C₄×D₇	—	4	1	no	—
238	C₄×D₇	#135	1	4	yes	—
239	Dic₁₄	—	2	2	no	—
240	C₇×C₈	—	2	1	no	—
241	C₇×C₈	—	2	1	no	—
242	C₇×C₈	—	2	1	no	—
243	C₇×C₈	—	4	2	no	—
244	C₇×C₈	—	4	2	no	—
245	C₇×C₈	#131	1	2	yes	—
246	C₇⋊C₈	—	2	1	no	—
247	C₇⋊C₈	—	2	1	no	—
248	C₇⋊C₈	—	2	1	no	—
249	C₇⋊C₈	—	2	1	no	—
250	C₇⋊C₈	—	4	2	no	—
251	C₇⋊C₈	—	4	2	no	—
252	C₂×#41	—	7	1	no	—
253	C₂×M₁₆	—	14	2	no	—
254	C₂²×C₈	—	7	1	no	—
255	C₂²×C₈	—	7	1	no	—
256	C₂²×C₈	—	7	1	no	—
257	C₂²×C₈	—	7	1	no	—
258	C₂²×C₈	—	14	2	no	—
259	C₂²×C₈	C₄×D₇	1	1	yes	characteristic
260	C₂²×C₈	C₄×D₇	1	1	yes	characteristic
261	C₄×Q₈	—	7	1	no	—
262	C₄×Q₈	—	7	1	no	—
263	C₄×D₄	—	7	1	no	—
264	C₄×D₄	—	7	1	no	—
265	C₄×D₄	—	7	1	no	—
266	C₄×D₄	—	7	1	no	—
267	C₄×D₄	—	7	1	no	—
268	C₄×D₄	—	7	1	no	—
269	#117	—	7	1	no	—
270	#117	—	7	1	no	—
271	#117	—	7	1	no	—
272	C₂×C₄²	—	7	1	no	—
273	C₂×C₄²	—	7	1	no	—
274	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
275	C₄⋊C₈	—	7	1	no	—
276	C₄⋊C₈	—	7	1	no	—
277	C₄⋊C₈	—	7	1	no	—
278	C₄⋊C₈	—	7	1	no	—
279	C₄⋊C₈	—	7	1	no	—
280	C₄⋊C₈	—	7	1	no	—
281	C₄⋊C₈	—	7	2	no	—
282	C₄⋊C₈	—	7	2	no	—
283	C₄⋊C₈	—	14	2	no	—
284	C₄⋊C₈	—	14	2	no	—
285	C₄⋊C₈	C₂²×D₇	1	2	yes	—
286	C₄⋊C₈	C₂²×D₇	1	2	yes	—
287	C₂²⋊C₈	—	2	2	no	—
288	C₂²⋊C₈	—	7	1	no	—
289	C₂²⋊C₈	—	7	1	no	—
290	C₂²⋊C₈	—	7	1	no	—
291	C₂²⋊C₈	—	7	1	no	—
292	C₂²⋊C₈	—	7	1	no	—
293	C₂²⋊C₈	—	7	1	no	—
294	C₂²⋊C₈	—	14	2	no	—
295	C₂²⋊C₈	—	14	2	no	—
296	C₂²⋊C₈	—	14	2	no	—
297	#97	—	14	2	no	—
298	#97	—	14	2	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	—	7	1	no	—
301	C₄×C₈	—	7	1	no	—
302	C₄×C₈	—	7	1	no	—
303	C₄×C₈	—	7	1	no	—
304	C₄×C₈	—	7	1	no	—
305	C₄×C₈	—	7	1	no	—
306	C₄×C₈	—	14	2	no	—
307	C₄×C₈	C₄×D₇	1	1	yes	characteristic
308	C₄×C₈	C₄×D₇	1	1	yes	characteristic
309	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
311	C₂²×C₇	—	2	1	no	—
312	C₂²×C₇	—	2	1	no	—
313	C₂²×C₇	—	2	1	no	—
314	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
315	C₂×D₇	—	2	1	no	—
316	C₂×D₇	—	2	1	no	—
317	C₂×D₇	—	2	1	no	—
318	C₂×D₇	—	2	1	no	—
319	C₂×D₇	—	2	1	no	—
320	C₂×D₇	#427	1	2	yes	—
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	C₂×#131	1	1	yes	characteristic
326	C₄×C₇	#568	1	1	yes	characteristic
327	C₄×C₇	C₂×#135	1	2	yes	—
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	#427	1	2	yes	—
334	#41	—	14	4	no	—
335	C₂×Q₈	—	7	1	no	—
336	C₂×D₄	—	7	1	no	—
337	C₂×D₄	—	7	1	no	—
338	C₂×D₄	—	7	1	no	—
339	C₂²×C₄	—	7	1	no	—
340	C₂²×C₄	—	7	1	no	—
341	C₂²×C₄	—	7	1	no	—
342	C₂²×C₄	—	7	1	no	—
343	C₂²×C₄	—	7	1	no	—
344	C₂²×C₄	—	7	1	no	—
345	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
347	C₂²×C₄	Q₈×D₇	1	1	yes	characteristic
348	M₁₆	—	28	4	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	7	1	no	—
354	C₂×C₈	—	7	1	no	—
355	C₂×C₈	—	7	1	no	—
356	C₂×C₈	—	7	1	no	—
357	C₂×C₈	—	14	2	no	—
358	C₂×C₈	—	14	2	no	—
359	C₂×C₈	—	14	2	no	—
360	C₂×C₈	—	14	2	no	—
361	C₂×C₈	—	28	1	no	—
362	C₂×C₈	—	28	1	no	—
363	C₂×C₈	—	28	4	no	—
364	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
365	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
367	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
368	C₄⋊C₄	—	7	1	no	—
369	C₄⋊C₄	—	7	1	no	—
370	C₄⋊C₄	—	7	1	no	—
371	C₄⋊C₄	—	7	1	no	—
372	C₄⋊C₄	—	7	1	no	—
373	C₄⋊C₄	—	7	1	no	—
374	C₂²⋊C₄	—	7	1	no	—
375	C₂²⋊C₄	—	7	1	no	—
376	C₂²⋊C₄	—	7	1	no	—
377	C₂²⋊C₄	—	7	1	no	—
378	C₂²⋊C₄	—	7	1	no	—
379	C₂²⋊C₄	—	7	1	no	—
380	C₄²	—	7	1	no	—
381	C₄²	—	7	1	no	—
382	C₄²	—	7	1	no	—
383	C₄²	—	7	1	no	—
384	C₄²	—	7	1	no	—
385	C₄²	—	7	1	no	—
386	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
387	C₄²	D₄×D₇	1	1	yes	characteristic
388	C₄²	Q₈×D₇	1	1	yes	characteristic
389	C₄²	C₂³×D₇	1	1	yes	characteristic
390	C₂×C₇	—	4	1	no	—
391	C₂×C₇	#2906	1	1	yes	characteristic
392	C₂×C₇	C₂×#427	1	1	yes	characteristic
393	C₂×C₇	#2916	1	1	yes	characteristic
394	D₇	—	2	2	no	—
395	D₇	—	4	1	no	—
396	C₂³	—	7	1	no	—
397	C₂³	—	7	1	no	—
398	C₂³	D₇×C₄⋊C₄	1	1	yes	characteristic
399	Q₈	—	14	2	no	—
400	D₄	—	14	2	no	—
401	D₄	—	14	2	no	—
402	D₄	—	14	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	7	1	no	—
408	C₂×C₄	—	7	4	no	—
409	C₂×C₄	—	7	1	no	—
410	C₂×C₄	—	7	1	no	—
411	C₂×C₄	—	7	1	no	—
412	C₂×C₄	—	7	1	no	—
413	C₂×C₄	—	7	1	no	—
414	C₂×C₄	—	14	1	no	—
415	C₂×C₄	—	14	1	no	—
416	C₂×C₄	—	14	1	no	—
417	C₂×C₄	—	14	1	no	—
418	C₂×C₄	—	14	2	no	—
419	C₂×C₄	—	28	1	no	—
420	C₂×C₄	—	28	1	no	—
421	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
422	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
423	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
424	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
425	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
426	C₂×C₄	C₂×Q₈×D₇	1	1	yes	characteristic
427	C₈	—	2	1	no	—
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	4	2	no	—
431	C₈	—	4	2	no	—
432	C₈	—	14	1	no	—
433	C₈	—	14	1	no	—
434	C₈	—	14	1	no	—
435	C₈	—	14	1	no	—
436	C₈	—	28	2	no	—
437	C₈	—	28	2	no	—
438	C₈	#6464	1	2	yes	—
439	C₇	#17827	1	1	yes	characteristic, complemented, Sylow
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	7	2	no	—
444	C₂²	—	14	1	no	—
445	C₂²	—	14	1	no	—
446	C₂²	—	14	1	no	—
447	C₂²	—	14	1	no	—
448	C₂²	—	14	1	no	—
449	C₂²	C₂×D₇×C₄⋊C₄	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	7	2	no	—
455	C₄	—	14	1	no	—
456	C₄	—	14	1	no	—
457	C₄	—	14	1	no	—
458	C₄	—	14	1	no	—
459	C₄	—	14	1	no	—
460	C₄	C₂×#6464	1	1	yes	characteristic
461	C₄	#90436	1	1	yes	characteristic
462	C₄	D₇×#135	1	2	yes	—
463	C₂	—	4	1	no	—
464	C₂	—	14	2	no	—
465	C₂	—	28	1	no	—
466	C₂	#11736457	1	1	yes	characteristic
467	C₂	D₇×#427	1	1	yes	characteristic
468	C₂	#11736697	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting	C₇×#1564	C₂
socle	C₂²×C₇	C₂²×C₄⋊C₄
prime radical	C₂×#1157	D₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1564	D₇
hypocenter	C₇	#17827
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
3. C₇×#1564	C₂	semidirect
4. #11728501	C₂	semidirect
5. #11727486	C₂	semidirect
6. #11726327	C₂	semidirect
7. #11726326	C₂	semidirect
8. #11726284	C₂	semidirect
9. #11726283	C₂	semidirect
10. #11726281	C₂	semidirect
11. D₇×#334	C₂	semidirect
116. #1564	D₇	semidirect
439. C₇	#17827	semidirect

Maximal subgroups

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

subgroup	index
#11736730	2
C₈×#1157	2
C₇×#1564	2
#11728501	2
#11727486	2
#11726327	2
#11726326	2
#11726284	2
#11726283	2
#11726281	2
D₇×#334	2
#17827	7