Subgroups — #14267653

Order 1792.

10894 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11744560	C₂	1	2	yes	maximal, complemented
2	C₂×C₇×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	#11744345	C₂	1	2	yes	maximal, complemented
4	#11744272	C₂	1	16	yes	maximal, complemented
5	#11744271	C₂	1	8	yes	maximal, complemented
6	D₇×#576	C₂	1	8	yes	maximal, complemented
7	#11744260	C₂	1	12	yes	maximal, complemented
8	#11744255	C₂	1	6	yes	maximal, complemented
9	C₂×#90448	C₂	1	6	yes	maximal, complemented
10	#11744231	C₂	1	1	yes	maximal, characteristic, complemented
11	#11744228	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	complemented
13	#90618	—	2	8	no	—
14	#90618	C₂²	1	16	yes	complemented
15	D₇×H(5,𝔽₂)	—	2	8	no	—
16	D₇×H(5,𝔽₂)	C₂²	1	16	yes	complemented
17	#90616	—	2	4	no	—
18	#90616	C₂²	1	1	yes	characteristic
19	#90616	C₂²	1	12	yes	complemented
20	#90616	C₂²	1	2	yes	complemented
21	C₂×#6548	—	2	12	no	—
22	C₂×#6548	C₂²	1	12	yes	complemented
23	C₇×#576	C₂²	1	8	yes	complemented
24	C₇×#576	C₂²	1	8	yes	complemented
25	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
26	C₂×C₇×#135	C₂²	1	3	yes	complemented
27	C₂²×C₇×D₈	C₂²	1	3	yes	complemented
28	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
29	#90527	C₂²	1	16	yes	complemented
30	#90526	C₂²	1	16	yes	complemented
31	#90513	C₂²	1	12	yes	complemented
32	#90510	C₂²	1	1	yes	characteristic, complemented
33	C₂×#6495	C₂²	1	12	yes	complemented
34	#90466	C₂²	1	48	yes	complemented
35	#90465	C₂²	1	48	yes	complemented
36	#90464	C₂²	1	48	yes	complemented
37	D₇×AGL(1,ℤ/8)	C₂²	1	48	yes	complemented
38	#90462	C₂²	1	12	yes	complemented
39	#90461	C₂²	1	24	yes	complemented
40	#90460	C₂²	1	12	yes	complemented
41	#90459	C₂²	1	24	yes	complemented
42	D₇×#135	C₂²	1	24	yes	complemented
43	#90457	C₂²	1	4	yes	complemented
44	#90453	C₂²	1	24	yes	complemented
45	#90448	C₂²	1	24	yes	complemented
46	#90448	C₂²	1	24	yes	complemented
47	#90448	C₂²	1	24	yes	complemented
48	#90448	C₂²	1	12	yes	complemented
49	C₂×#6475	C₂²	1	12	yes	complemented
50	C₂×#6474	C₂²	1	24	yes	complemented
51	C₂×D₇×D₈	C₂²	1	12	yes	complemented
52	#90444	C₂²	1	4	yes	complemented
53	#90443	C₂²	1	4	yes	complemented
54	#90442	C₂²	1	8	yes	complemented
55	#90441	C₂²	1	8	yes	complemented
56	D₇×#131	C₂²	1	8	yes	complemented
57	#90439	C₂²	1	6	yes	complemented
58	#90436	C₂²	1	6	yes	complemented
59	C₂×#6467	C₂²	1	6	yes	complemented
60	C₂×#6464	C₂²	1	6	yes	complemented
61	#63091	—	7	1	no	maximal, Sylow
62	C₇×H(5,𝔽₂)	—	2	8	no	—
63	C₇×H(5,𝔽₂)	C₂³	1	16	yes	complemented
64	C₂×C₇×#41	—	2	2	no	—
65	C₂×C₇×#41	C₂³	1	1	yes	characteristic
66	C₂×C₇×#41	C₂³	1	6	yes	complemented
67	C₂²×C₇×D₄	—	2	6	no	—
68	C₂²×C₇×D₄	C₂³	1	6	yes	complemented
69	C₂²×C₂²⋊D₇	—	2	24	no	—
70	#6554	—	2	16	no	—
71	#6554	—	2	12	no	—
72	#6554	D₄	1	4	yes	—
73	#6554	C₂³	1	24	yes	complemented
74	#6554	C₂³	1	8	yes	complemented
75	#6553	—	2	16	no	—
76	#6553	—	2	12	no	—
77	#6553	D₄	1	4	yes	—
78	#6553	C₂³	1	24	yes	complemented
79	#6553	C₂³	1	8	yes	complemented
80	D₇×#41	—	2	8	no	—
81	D₇×#41	—	2	16	no	—
82	D₇×#41	—	2	16	no	—
83	D₇×#41	—	2	24	no	—
84	D₇×#41	C₂³	1	8	yes	—
85	D₇×#41	C₂³	1	48	yes	complemented
86	#6551	—	2	2	no	—
87	#6551	D₄	1	2	yes	—
88	#6551	C₂³	1	8	yes	complemented
89	#6548	—	2	6	no	—
90	#6548	—	2	24	no	—
91	#6548	—	2	48	no	—
92	#6548	—	2	48	no	—
93	#6548	—	2	24	no	—
94	#6548	—	2	24	no	—
95	#6548	D₄	1	6	yes	—
96	#6548	C₂³	1	24	yes	complemented
97	#6548	C₂³	1	48	yes	complemented
98	C₂×#1159	—	2	48	no	—
99	C₂×#1159	—	2	12	no	—
100	C₂×#1159	C₂³	1	24	yes	complemented
101	C₂×D₄×D₇	—	2	48	no	—
102	C₂×D₄×D₇	—	2	12	no	—
103	C₂×D₄×D₇	C₂³	1	24	yes	complemented
104	C₂×#1157	—	2	24	no	—
105	C₂×#1157	C₂³	1	6	yes	—
106	C₂×#1157	C₂³	1	12	yes	complemented
107	C₇×AGL(1,ℤ/8)	C₂³	1	48	yes	complemented
108	C₇×#135	C₂³	1	12	yes	complemented
109	C₇×#135	C₂³	1	12	yes	complemented
110	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic, complemented
111	C₂×C₇×SD₁₆	C₂³	1	6	yes	complemented
112	C₂×C₇×D₈	C₂³	1	12	yes	complemented
113	C₂×C₇×D₈	C₂³	1	12	yes	complemented
114	C₂×C₇×D₈	C₂³	1	3	yes	complemented
115	C₂×C₇×D₈	C₂³	1	6	yes	complemented
116	C₇×#131	C₂³	1	4	yes	complemented
117	C₇×#131	C₂³	1	4	yes	complemented
118	C₂×C₇×M₁₆	C₂³	1	3	yes	complemented
119	C₂²×C₇×C₈	C₂³	1	3	yes	complemented
120	#6514	C₂³	1	24	yes	complemented
121	#6513	C₂³	1	48	yes	complemented
122	#6512	C₂³	1	24	yes	complemented
123	#6511	C₂³	1	8	yes	complemented
124	#6505	C₂³	1	8	yes	complemented
125	C₂×#1142	C₂³	1	24	yes	complemented
126	#6495	C₂³	1	24	yes	complemented
127	#6495	C₂³	1	48	yes	complemented
128	C₂×#1141	C₂³	1	24	yes	complemented
129	C₂×#1136	C₂³	1	6	yes	complemented
130	#6482	C₂³	1	8	yes	complemented
131	#6481	C₂³	1	16	yes	complemented
132	D₇×Q₁₆	C₂³	1	8	yes	complemented
133	#6479	C₂³	1	48	yes	complemented
134	#6478	C₂³	1	48	yes	complemented
135	#6477	C₂³	1	48	yes	complemented
136	D₇×SD₁₆	C₂³	1	48	yes	complemented
137	#6475	C₂³	1	24	yes	complemented
138	#6475	C₂³	1	48	yes	complemented
139	#6474	C₂³	1	48	yes	complemented
140	#6474	C₂³	1	96	yes	complemented
141	D₇×D₈	C₂³	1	24	yes	complemented
142	D₇×D₈	C₂³	1	48	yes	complemented
143	#6472	C₂³	1	24	yes	complemented
144	#6471	C₂³	1	24	yes	complemented
145	#6470	C₂³	1	24	yes	complemented
146	D₇×M₁₆	C₂³	1	24	yes	complemented
147	C₂×Dic₂₈	C₂³	1	6	yes	complemented
148	#6467	C₂³	1	4	yes	complemented
149	#6467	C₂³	1	12	yes	complemented
150	#6467	C₂³	1	12	yes	complemented
151	#6467	C₂³	1	12	yes	complemented
152	C₂×D₅₆	C₂³	1	6	yes	complemented
153	C₂×#1132	C₂³	1	12	yes	complemented
154	#6464	C₂³	1	4	yes	complemented
155	#6464	C₂³	1	12	yes	complemented
156	#6464	C₂³	1	12	yes	complemented
157	#6464	C₂³	1	12	yes	complemented
158	C₂×#1131	C₂³	1	12	yes	complemented
159	C₂×C₈×D₇	C₂³	1	12	yes	complemented
160	H(7,𝔽₂)	—	7	2	no	—
161	#3585	—	7	2	no	—
162	#3585	—	7	16	no	—
163	#3585	—	7	12	no	—
164	#3584	—	7	8	no	—
165	#3584	—	7	6	no	—
166	#3584	—	7	1	no	—
167	C₂×#576	—	7	8	no	—
168	C₂×#576	—	7	6	no	—
169	C₂×#576	D₇	1	1	yes	characteristic, complemented
170	#3573	—	7	1	no	—
171	C₂⁴×C₇	—	2	6	no	—
172	C₂³×D₇	—	2	24	no	—
173	C₇×#41	—	2	16	no	—
174	C₇×#41	—	2	12	no	—
175	C₇×#41	C₂×D₄	1	4	yes	—
176	C₇×#41	C₂⁴	1	24	yes	—
177	C₇×#41	C₂⁴	1	4	yes	—
178	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
179	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
180	C₂×C₇×D₄	—	2	6	no	—
181	C₂×C₇×D₄	—	2	48	no	—
182	C₂×C₇×D₄	—	2	12	no	—
183	C₂×C₇×D₄	—	2	6	no	—
184	C₂×C₇×D₄	C₂×D₄	1	3	yes	—
185	C₂×C₇×D₄	C₂⁴	1	24	yes	—
186	C₂×C₇×D₄	C₂⁴	1	6	yes	—
187	C₂²×C₄×C₇	—	2	6	no	—
188	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
189	C₂×C₂²⋊D₇	—	2	12	no	—
190	C₂×C₂²⋊D₇	—	2	24	no	—
191	C₂×C₂²⋊D₇	—	2	48	no	—
192	C₂×C₂²⋊D₇	—	2	96	no	—
193	C₂×C₂²⋊D₇	—	2	24	no	—
194	C₂×C₂²⋊D₇	C₂×D₄	1	12	yes	—
195	C₂²×Dic₇	—	2	24	no	—
196	#1161	—	2	8	no	—
197	#1161	—	2	8	no	—
198	#1161	C₂×D₄	1	8	yes	—
199	#1161	C₂⁴	1	16	yes	—
200	Q₈×D₇	—	2	8	no	—
201	Q₈×D₇	—	2	8	no	—
202	Q₈×D₇	C₂×D₄	1	8	yes	—
203	Q₈×D₇	C₂⁴	1	16	yes	—
204	#1159	—	2	24	no	—
205	#1159	—	2	48	no	—
206	#1159	—	2	48	no	—
207	#1159	—	2	48	no	—
208	#1159	—	2	48	no	—
209	#1159	—	2	24	no	—
210	#1159	C₂×D₄	1	24	yes	—
211	#1159	C₂⁴	1	48	yes	—
212	D₄×D₇	—	2	48	no	—
213	D₄×D₇	—	2	24	no	—
214	D₄×D₇	—	2	48	no	—
215	D₄×D₇	—	2	48	no	—
216	D₄×D₇	—	2	24	no	—
217	D₄×D₇	—	2	48	no	—
218	D₄×D₇	C₂×D₄	1	24	yes	—
219	D₄×D₇	C₂⁴	1	48	yes	—
220	#1157	—	2	12	no	—
221	#1157	—	2	12	no	—
222	#1157	—	2	16	no	—
223	#1157	—	2	24	no	—
224	#1157	—	2	48	no	—
225	#1157	—	2	24	no	—
226	#1157	C₂×D₄	1	12	yes	—
227	#1157	C₂×D₄	1	12	yes	—
228	#1157	C₂⁴	1	4	yes	—
229	#1157	C₂⁴	1	12	yes	—
230	#1157	C₂⁴	1	8	yes	—
231	#1157	C₂⁴	1	24	yes	—
232	C₂×D₂₈	—	2	24	no	—
233	C₂×D₂₈	C₂×D₄	1	6	yes	—
234	C₂×D₂₈	C₂⁴	1	12	yes	—
235	C₂×C₄×D₇	—	2	12	no	—
236	C₂×C₄×D₇	—	2	48	no	—
237	C₂×C₄×D₇	C₂⁴	1	12	yes	—
238	C₂×Dic₁₄	—	2	24	no	—
239	C₂×Dic₁₄	C₂×D₄	1	6	yes	—
240	C₂×Dic₁₄	C₂⁴	1	12	yes	—
241	C₇×Q₁₆	C₂⁴	1	2	yes	—
242	C₇×Q₁₆	C₂⁴	1	2	yes	—
243	C₇×SD₁₆	C₂⁴	1	24	yes	—
244	C₇×D₈	C₂⁴	1	6	yes	—
245	C₇×D₈	C₂⁴	1	24	yes	—
246	C₇×D₈	C₂⁴	1	6	yes	—
247	C₇×M₁₆	C₂⁴	1	12	yes	—
248	C₂×C₇×C₈	C₂⁴	1	6	yes	—
249	C₂×C₇×C₈	C₂⁴	1	6	yes	—
250	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
251	C₂×C₇×C₈	C₂⁴	1	3	yes	—
252	#1144	C₂⁴	1	16	yes	—
253	#1143	C₂⁴	1	16	yes	—
254	#1142	C₂⁴	1	48	yes	—
255	#1141	C₂⁴	1	48	yes	—
256	#1136	C₂⁴	1	4	yes	—
257	#1136	C₂⁴	1	12	yes	—
258	C₂×C₇⋊C₈	C₂⁴	1	12	yes	—
259	Dic₂₈	C₂⁴	1	4	yes	—
260	Dic₂₈	C₂⁴	1	12	yes	—
261	D₅₆	C₂⁴	1	4	yes	—
262	D₅₆	C₂⁴	1	12	yes	—
263	#1132	C₂⁴	1	8	yes	—
264	#1132	C₂⁴	1	24	yes	—
265	#1131	C₂⁴	1	8	yes	—
266	#1131	C₂⁴	1	24	yes	—
267	C₈×D₇	C₂⁴	1	8	yes	—
268	C₈×D₇	C₂⁴	1	24	yes	—
269	#585	—	7	1	no	—
270	#585	—	7	16	no	—
271	#585	—	7	2	no	—
272	#585	—	7	12	no	—
273	#585	—	14	4	no	—
274	#585	—	14	8	no	—
275	C₂×H(5,𝔽₂)	—	7	16	no	—
276	C₂×H(5,𝔽₂)	—	7	12	no	—
277	C₂×H(5,𝔽₂)	—	14	12	no	—
278	C₂×H(5,𝔽₂)	—	14	8	no	—
279	C₂×H(5,𝔽₂)	C₂×D₇	1	2	yes	complemented
280	#578	—	7	12	no	—
281	#578	—	7	4	no	—
282	#578	—	7	4	no	—
283	#577	—	7	16	no	—
284	#577	—	7	48	no	—
285	#577	—	7	24	no	—
286	#577	—	7	24	no	—
287	#577	—	7	8	no	—
288	#576	—	7	16	no	—
289	#576	—	7	48	no	—
290	#576	—	7	12	no	—
291	#576	—	7	24	no	—
292	#576	—	7	12	no	—
293	#576	—	7	24	no	—
294	#576	—	7	24	no	—
295	#576	—	7	4	no	—
296	#576	C₂×D₇	1	8	yes	complemented
297	#576	C₂×D₇	1	8	yes	complemented
298	#575	—	7	12	no	—
299	#575	—	7	48	no	—
300	#575	—	7	24	no	—
301	#575	—	7	6	no	—
302	C₂×AGL(1,ℤ/8)	—	7	12	no	—
303	C₂×AGL(1,ℤ/8)	—	7	48	no	—
304	C₂×AGL(1,ℤ/8)	—	7	24	no	—
305	C₂×AGL(1,ℤ/8)	C₂×D₇	1	6	yes	complemented
306	C₂×#135	—	7	24	no	—
307	C₂×#135	—	7	12	no	—
308	C₂×#135	—	7	6	no	—
309	C₂×#135	C₂×D₇	1	3	yes	complemented
310	C₂²×D₈	—	7	12	no	—
311	C₂²×D₈	C₂×D₇	1	3	yes	complemented
312	#568	—	7	1	no	—
313	#568	—	7	8	no	—
314	#568	—	7	6	no	—
315	C₂×#131	—	7	8	no	—
316	C₂×#131	—	7	6	no	—
317	C₂×#131	C₂×D₇	1	1	yes	characteristic, complemented
318	C₂³×C₇	—	2	24	no	—
319	C₂³×C₇	—	2	6	no	—
320	C₂³×C₇	—	16	6	no	—
321	C₂³×C₇	C₂²×D₄	1	3	yes	—
322	C₂²×D₇	—	2	12	no	—
323	C₂²×D₇	—	2	48	no	—
324	C₂²×D₇	—	16	24	no	—
325	C₂²×D₇	C₂²×D₄	1	12	yes	—
326	C₇×Q₈	—	2	2	no	—
327	C₇×Q₈	C₂²×D₄	1	4	yes	—
328	C₇×Q₈	C₂⁵	1	4	yes	—
329	C₇×D₄	—	2	24	no	—
330	C₇×D₄	—	2	24	no	—
331	C₇×D₄	—	2	6	no	—
332	C₇×D₄	C₂²×D₄	1	12	yes	—
333	C₇×D₄	C₂⁵	1	12	yes	—
334	C₂×C₄×C₇	—	2	2	no	—
335	C₂×C₄×C₇	—	2	24	no	—
336	C₂×C₄×C₇	C₂²×D₄	1	6	yes	—
337	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
338	C₂×C₄×C₇	C₂⁵	1	6	yes	—
339	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
340	C₂²⋊D₇	—	2	8	no	—
341	C₂²⋊D₇	—	2	24	no	—
342	C₂²⋊D₇	—	2	48	no	—
343	C₂²⋊D₇	—	2	48	no	—
344	C₂²⋊D₇	C₂²×D₄	1	8	yes	—
345	C₂²⋊D₇	C₂²×D₄	1	24	yes	—
346	C₂×Dic₇	—	2	12	no	—
347	C₂×Dic₇	—	2	48	no	—
348	C₂×Dic₇	C₂²×D₄	1	12	yes	—
349	D₂₈	—	2	16	no	—
350	D₂₈	—	2	12	no	—
351	D₂₈	C₂²×D₄	1	12	yes	—
352	D₂₈	C₂²×D₄	1	4	yes	—
353	D₂₈	C₂⁵	1	8	yes	—
354	C₄×D₇	—	2	16	no	—
355	C₄×D₇	—	2	24	no	—
356	C₄×D₇	—	2	8	no	—
357	C₄×D₇	—	2	16	no	—
358	C₄×D₇	C₂²×D₄	1	24	yes	—
359	C₄×D₇	C₂⁵	1	8	yes	—
360	Dic₁₄	—	2	12	no	—
361	Dic₁₄	—	2	16	no	—
362	Dic₁₄	C₂²×D₄	1	12	yes	—
363	Dic₁₄	C₂²×D₄	1	4	yes	—
364	Dic₁₄	C₂⁵	1	8	yes	—
365	C₇×C₈	C₂⁵	1	1	yes	characteristic
366	C₇×C₈	C₂⁵	1	6	yes	—
367	C₇×C₈	C₂⁵	1	1	yes	characteristic
368	C₇⋊C₈	C₂⁵	1	8	yes	—
369	2₋¹⁺⁴	—	7	4	no	—
370	2₋¹⁺⁴	—	7	2	no	—
371	2₋¹⁺⁴	—	7	24	no	—
372	2₋¹⁺⁴	—	7	8	no	—
373	2₋¹⁺⁴	—	7	8	no	—
374	2₋¹⁺⁴	—	14	16	no	—
375	2₋¹⁺⁴	—	14	12	no	—
376	2₋¹⁺⁴	—	14	2	no	—
377	H(5,𝔽₂)	—	2	8	no	—
378	H(5,𝔽₂)	—	7	4	no	—
379	H(5,𝔽₂)	—	7	6	no	—
380	H(5,𝔽₂)	—	7	24	no	—
381	H(5,𝔽₂)	—	7	8	no	—
382	H(5,𝔽₂)	—	7	48	no	—
383	H(5,𝔽₂)	—	7	24	no	—
384	H(5,𝔽₂)	—	14	24	no	—
385	H(5,𝔽₂)	—	14	48	no	—
386	H(5,𝔽₂)	—	14	48	no	—
387	H(5,𝔽₂)	—	14	24	no	—
388	H(5,𝔽₂)	—	14	24	no	—
389	H(5,𝔽₂)	—	14	12	no	—
390	H(5,𝔽₂)	—	14	16	no	—
391	H(5,𝔽₂)	—	14	6	no	—
392	H(5,𝔽₂)	C₂²×D₇	1	16	yes	complemented
393	C₂×#41	—	2	2	no	—
394	C₂×#41	—	7	8	no	—
395	C₂×#41	—	7	6	no	—
396	C₂×#41	—	7	48	no	—
397	C₂×#41	—	7	24	no	—
398	C₂×#41	—	7	12	no	—
399	C₂×#41	—	14	24	no	—
400	C₂×#41	—	14	12	no	—
401	C₂×#41	—	14	48	no	—
402	C₂×#41	—	14	16	no	—
403	C₂×#41	—	14	16	no	—
404	C₂×#41	—	14	24	no	—
405	C₂×#41	—	14	8	no	—
406	C₂×#41	C₂²×D₇	1	1	yes	characteristic
407	C₂×#41	C₂²×D₇	1	6	yes	complemented
408	C₂²×D₄	—	2	6	no	—
409	C₂²×D₄	—	7	24	no	—
410	C₂²×D₄	—	14	48	no	—
411	C₂²×D₄	—	14	12	no	—
412	C₂²×D₄	—	14	24	no	—
413	C₂²×D₄	C₂²×D₇	1	6	yes	complemented
414	#137	—	7	24	no	—
415	#137	—	7	8	no	—
416	#137	—	7	16	no	—
417	#137	—	7	48	no	—
418	#137	—	7	24	no	—
419	AGL(1,ℤ/8)	—	7	24	no	—
420	AGL(1,ℤ/8)	—	7	48	no	—
421	AGL(1,ℤ/8)	—	7	24	no	—
422	AGL(1,ℤ/8)	—	7	48	no	—
423	AGL(1,ℤ/8)	—	7	96	no	—
424	AGL(1,ℤ/8)	—	7	48	no	—
425	AGL(1,ℤ/8)	—	7	24	no	—
426	AGL(1,ℤ/8)	C₂²×D₇	1	48	yes	complemented
427	#135	—	7	48	no	—
428	#135	—	7	8	no	—
429	#135	—	7	48	no	—
430	#135	—	7	24	no	—
431	#135	—	7	48	no	—
432	#135	—	7	12	no	—
433	#135	—	7	4	no	—
434	#135	—	7	12	no	—
435	#135	—	7	12	no	—
436	#135	C₂²×D₇	1	12	yes	complemented
437	#135	C₂²×D₇	1	12	yes	complemented
438	C₂×Q₁₆	—	7	8	no	—
439	C₂×Q₁₆	—	7	6	no	—
440	C₂×Q₁₆	C₂²×D₇	1	1	yes	characteristic, complemented
441	C₂×SD₁₆	—	7	24	no	—
442	C₂×SD₁₆	—	7	48	no	—
443	C₂×SD₁₆	—	7	12	no	—
444	C₂×SD₁₆	C₂²×D₇	1	6	yes	complemented
445	C₂×D₈	—	7	24	no	—
446	C₂×D₈	—	7	24	no	—
447	C₂×D₈	—	7	48	no	—
448	C₂×D₈	—	7	6	no	—
449	C₂×D₈	C₂²×D₇	1	12	yes	complemented
450	C₂×D₈	C₂²×D₇	1	3	yes	complemented
451	C₂×D₈	C₂²×D₇	1	12	yes	complemented
452	C₂×D₈	C₂²×D₇	1	6	yes	complemented
453	#131	—	7	8	no	—
454	#131	—	7	24	no	—
455	#131	—	7	12	no	—
456	#131	—	7	4	no	—
457	#131	—	7	12	no	—
458	#131	—	7	12	no	—
459	#131	C₂²×D₇	1	4	yes	complemented
460	#131	C₂²×D₇	1	4	yes	complemented
461	C₂×M₁₆	—	7	6	no	—
462	C₂×M₁₆	—	7	24	no	—
463	C₂×M₁₆	—	7	12	no	—
464	C₂×M₁₆	C₂²×D₇	1	3	yes	complemented
465	C₂²×C₈	—	7	12	no	—
466	C₂²×C₈	C₂²×D₇	1	3	yes	complemented
467	C₂²×C₇	—	2	12	no	—
468	C₂²×C₇	—	4	3	no	—
469	C₂²×C₇	—	8	24	no	—
470	C₂²×C₇	—	8	6	no	—
471	C₂²×C₇	C₂³×D₄	1	6	yes	—
472	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
473	C₂×D₇	—	2	8	no	—
474	C₂×D₇	—	4	12	no	—
475	C₂×D₇	—	8	48	no	—
476	C₂×D₇	—	8	12	no	—
477	C₂×D₇	C₂³×D₄	1	8	yes	—
478	C₄×C₇	—	2	4	no	—
479	C₄×C₇	C₂³×D₄	1	6	yes	—
480	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
481	C₄×C₇	C₂⁶	1	1	yes	characteristic
482	Dic₇	—	2	8	no	—
483	Dic₇	C₂³×D₄	1	8	yes	—
484	C₂⁴	—	2	6	no	—
485	C₂⁴	—	14	24	no	—
486	#41	—	2	16	no	—
487	#41	—	2	12	no	—
488	#41	—	7	8	no	—
489	#41	—	7	24	no	—
490	#41	—	7	12	no	—
491	#41	—	7	12	no	—
492	#41	—	7	12	no	—
493	#41	—	7	4	no	—
494	#41	—	7	16	no	—
495	#41	—	7	48	no	—
496	#41	—	7	24	no	—
497	#41	—	7	8	no	—
498	#41	—	14	48	no	—
499	#41	—	14	16	no	—
500	#41	—	14	24	no	—
501	#41	—	14	24	no	—
502	#41	—	14	48	no	—
503	#41	—	14	48	no	—
504	#41	—	14	48	no	—
505	#41	—	14	24	no	—
506	#41	—	14	48	no	—
507	#41	—	14	8	no	—
508	#41	—	14	8	no	—
509	#41	—	14	24	no	—
510	#41	—	14	12	no	—
511	#41	—	14	12	no	—
512	#41	D₄×D₇	1	4	yes	—
513	#41	C₂³×D₇	1	24	yes	—
514	#41	C₂³×D₇	1	4	yes	—
515	C₂×Q₈	—	7	8	no	—
516	C₂×Q₈	—	7	6	no	—
517	C₂×Q₈	—	7	16	no	—
518	C₂×Q₈	—	7	12	no	—
519	C₂×Q₈	—	14	24	no	—
520	C₂×Q₈	—	14	8	no	—
521	C₂×Q₈	—	14	8	no	—
522	C₂×Q₈	D₄×D₇	1	1	yes	characteristic
523	C₂×Q₈	C₂³×D₇	1	2	yes	—
524	C₂×D₄	—	2	6	no	—
525	C₂×D₄	—	2	48	no	—
526	C₂×D₄	—	2	6	no	—
527	C₂×D₄	—	2	12	no	—
528	C₂×D₄	—	7	12	no	—
529	C₂×D₄	—	7	24	no	—
530	C₂×D₄	—	7	48	no	—
531	C₂×D₄	—	7	6	no	—
532	C₂×D₄	—	7	12	no	—
533	C₂×D₄	—	14	24	no	—
534	C₂×D₄	—	14	48	no	—
535	C₂×D₄	—	14	24	no	—
536	C₂×D₄	—	14	48	no	—
537	C₂×D₄	—	14	48	no	—
538	C₂×D₄	—	14	24	no	—
539	C₂×D₄	—	14	48	no	—
540	C₂×D₄	—	14	48	no	—
541	C₂×D₄	—	14	96	no	—
542	C₂×D₄	—	14	24	no	—
543	C₂×D₄	—	14	12	no	—
544	C₂×D₄	—	14	24	no	—
545	C₂×D₄	D₄×D₇	1	3	yes	—
546	C₂×D₄	C₂³×D₇	1	24	yes	—
547	C₂×D₄	C₂³×D₇	1	6	yes	—
548	C₂²×C₄	—	2	6	no	—
549	C₂²×C₄	—	7	12	no	—
550	C₂²×C₄	—	14	48	no	—
551	C₂²×C₄	—	14	24	no	—
552	C₂²×C₄	—	14	12	no	—
553	C₂²×C₄	C₂³×D₇	1	3	yes	—
554	Q₁₆	—	7	16	no	—
555	Q₁₆	—	7	4	no	—
556	Q₁₆	—	7	12	no	—
557	Q₁₆	C₂³×D₇	1	2	yes	—
558	Q₁₆	C₂³×D₇	1	2	yes	—
559	SD₁₆	—	7	16	no	—
560	SD₁₆	—	7	48	no	—
561	SD₁₆	—	7	24	no	—
562	SD₁₆	—	7	8	no	—
563	SD₁₆	C₂³×D₇	1	24	yes	—
564	D₈	—	7	48	no	—
565	D₈	—	7	4	no	—
566	D₈	—	7	12	no	—
567	D₈	C₂³×D₇	1	6	yes	—
568	D₈	C₂³×D₇	1	24	yes	—
569	D₈	C₂³×D₇	1	6	yes	—
570	M₁₆	—	7	12	no	—
571	M₁₆	—	7	4	no	—
572	M₁₆	—	7	24	no	—
573	M₁₆	—	7	8	no	—
574	M₁₆	C₂³×D₇	1	12	yes	—
575	C₂×C₈	—	7	12	no	—
576	C₂×C₈	—	7	8	no	—
577	C₂×C₈	—	7	24	no	—
578	C₂×C₈	C₂³×D₇	1	6	yes	—
579	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
580	C₂×C₈	C₂³×D₇	1	6	yes	—
581	C₂×C₈	C₂³×D₇	1	3	yes	—
582	C₂×C₇	—	2	6	no	—
583	C₂×C₇	—	2	1	no	—
584	C₂×C₇	—	4	12	no	—
585	C₂×C₇	C₂⁴×D₄	1	1	yes	characteristic
586	D₇	—	2	8	no	—
587	D₇	—	4	8	no	—
588	C₂³	—	2	6	no	—
589	C₂³	—	2	24	no	—
590	C₂³	—	7	12	no	—
591	C₂³	—	14	48	no	—
592	C₂³	—	14	12	no	—
593	C₂³	—	16	6	no	—
594	C₂³	—	112	24	no	—
595	C₂³	C₂×D₄×D₇	1	3	yes	—
596	Q₈	—	2	2	no	—
597	Q₈	—	7	12	no	—
598	Q₈	—	7	4	no	—
599	Q₈	—	7	8	no	—
600	Q₈	—	14	16	no	—
601	Q₈	—	14	12	no	—
602	Q₈	C₂×D₄×D₇	1	4	yes	—
603	Q₈	C₂⁴×D₇	1	4	yes	—
604	D₄	—	2	24	no	—
605	D₄	—	2	24	no	—
606	D₄	—	2	6	no	—
607	D₄	—	7	8	no	—
608	D₄	—	7	24	no	—
609	D₄	—	7	8	no	—
610	D₄	—	7	12	no	—
611	D₄	—	7	4	no	—
612	D₄	—	14	16	no	—
613	D₄	—	14	48	no	—
614	D₄	—	14	48	no	—
615	D₄	—	14	8	no	—
616	D₄	—	14	24	no	—
617	D₄	—	14	12	no	—
618	D₄	C₂×D₄×D₇	1	12	yes	—
619	D₄	C₂⁴×D₇	1	12	yes	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	24	no	—
622	C₂×C₄	—	7	12	no	—
623	C₂×C₄	—	7	8	no	—
624	C₂×C₄	—	7	24	no	—
625	C₂×C₄	—	14	16	no	—
626	C₂×C₄	—	14	16	no	—
627	C₂×C₄	—	14	48	no	—
628	C₂×C₄	—	14	12	no	—
629	C₂×C₄	—	14	24	no	—
630	C₂×C₄	—	14	8	no	—
631	C₂×C₄	C₂×D₄×D₇	1	3	yes	—
632	C₂×C₄	C₂×D₄×D₇	1	6	yes	—
633	C₂×C₄	C₂⁴×D₇	1	6	yes	—
634	C₂×C₄	C₂⁴×D₇	1	1	yes	characteristic
635	C₈	—	7	8	no	—
636	C₈	C₂⁴×D₇	1	1	yes	characteristic
637	C₈	C₂⁴×D₇	1	6	yes	—
638	C₈	C₂⁴×D₇	1	1	yes	characteristic
639	C₇	#63091	1	1	yes	characteristic, complemented, Sylow
640	C₂²	—	2	12	no	—
641	C₂²	—	4	3	no	—
642	C₂²	—	7	8	no	—
643	C₂²	—	8	6	no	—
644	C₂²	—	8	24	no	—
645	C₂²	—	14	8	no	—
646	C₂²	—	28	12	no	—
647	C₂²	—	56	12	no	—
648	C₂²	—	56	48	no	—
649	C₂²	C₂²×D₄×D₇	1	1	yes	characteristic
650	C₂²	C₂²×D₄×D₇	1	6	yes	—
651	C₄	—	2	4	no	—
652	C₄	—	7	8	no	—
653	C₄	—	14	8	no	—
654	C₄	C₂²×D₄×D₇	1	6	yes	—
655	C₄	C₂²×D₄×D₇	1	1	yes	characteristic
656	C₄	C₂⁵×D₇	1	1	yes	characteristic
657	C₂	—	2	1	no	—
658	C₂	—	2	6	no	—
659	C₂	—	4	12	no	—
660	C₂	—	14	8	no	—
661	C₂	—	28	8	no	—
662	C₂	C₂³×D₄×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂³×D₄×D₇
commutator, cosocle	C₄×C₇	C₂⁶
Frattini	C₄	C₂⁵×D₇
Fitting	C₂×C₇×#576	C₂
socle	C₂×C₇	C₂⁴×D₄
hypercenter	C₂×#576	D₇
hypocenter	C₇	#63091
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ C₂×#576

Complements

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

N	H ≅ G/N	type
1. #11744560	C₂	semidirect
2. C₂×C₇×#576	C₂	semidirect
3. #11744345	C₂	semidirect
4. #11744272	C₂	semidirect
5. #11744271	C₂	semidirect
6. D₇×#576	C₂	semidirect
7. #11744260	C₂	semidirect
8. #11744255	C₂	semidirect
9. C₂×#90448	C₂	semidirect
10. #11744231	C₂	semidirect
11. #11744228	C₂	semidirect
12. C₂×C₇×H(5,𝔽₂)	C₂²	semidirect
14. #90618	C₂²	semidirect
16. D₇×H(5,𝔽₂)	C₂²	semidirect
19. #90616	C₂²	semidirect
20. #90616	C₂²	semidirect
22. C₂×#6548	C₂²	semidirect
23. C₇×#576	C₂²	semidirect
24. C₇×#576	C₂²	semidirect
25. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₇×#135	C₂²	semidirect
27. C₂²×C₇×D₈	C₂²	semidirect
28. C₂×C₇×#131	C₂²	semidirect
29. #90527	C₂²	semidirect
30. #90526	C₂²	semidirect
31. #90513	C₂²	semidirect
32. #90510	C₂²	semidirect
33. C₂×#6495	C₂²	semidirect
34. #90466	C₂²	semidirect
35. #90465	C₂²	semidirect
36. #90464	C₂²	semidirect
37. D₇×AGL(1,ℤ/8)	C₂²	semidirect
38. #90462	C₂²	semidirect
39. #90461	C₂²	semidirect
40. #90460	C₂²	semidirect
41. #90459	C₂²	semidirect
42. D₇×#135	C₂²	semidirect
43. #90457	C₂²	semidirect
44. #90453	C₂²	semidirect
45. #90448	C₂²	semidirect
46. #90448	C₂²	semidirect
47. #90448	C₂²	semidirect
48. #90448	C₂²	semidirect
49. C₂×#6475	C₂²	semidirect
50. C₂×#6474	C₂²	semidirect
51. C₂×D₇×D₈	C₂²	semidirect
52. #90444	C₂²	semidirect
53. #90443	C₂²	semidirect
54. #90442	C₂²	semidirect
55. #90441	C₂²	semidirect
56. D₇×#131	C₂²	semidirect
57. #90439	C₂²	semidirect
58. #90436	C₂²	semidirect
59. C₂×#6467	C₂²	semidirect
60. C₂×#6464	C₂²	semidirect
63. C₇×H(5,𝔽₂)	C₂³	semidirect
66. C₂×C₇×#41	C₂³	semidirect
68. C₂²×C₇×D₄	C₂³	semidirect
73. #6554	C₂³	semidirect
74. #6554	C₂³	semidirect
78. #6553	C₂³	semidirect
79. #6553	C₂³	semidirect
85. D₇×#41	C₂³	semidirect
88. #6551	C₂³	semidirect
96. #6548	C₂³	semidirect
97. #6548	C₂³	semidirect
100. C₂×#1159	C₂³	semidirect
103. C₂×D₄×D₇	C₂³	semidirect
106. C₂×#1157	C₂³	semidirect
107. C₇×AGL(1,ℤ/8)	C₂³	semidirect
108. C₇×#135	C₂³	semidirect
109. C₇×#135	C₂³	semidirect
110. C₂×C₇×Q₁₆	C₂³	semidirect
111. C₂×C₇×SD₁₆	C₂³	semidirect
112. C₂×C₇×D₈	C₂³	semidirect
113. C₂×C₇×D₈	C₂³	semidirect
114. C₂×C₇×D₈	C₂³	semidirect
115. C₂×C₇×D₈	C₂³	semidirect
116. C₇×#131	C₂³	semidirect
117. C₇×#131	C₂³	semidirect
118. C₂×C₇×M₁₆	C₂³	semidirect
119. C₂²×C₇×C₈	C₂³	semidirect
120. #6514	C₂³	semidirect
121. #6513	C₂³	semidirect
122. #6512	C₂³	semidirect
123. #6511	C₂³	semidirect
124. #6505	C₂³	semidirect
125. C₂×#1142	C₂³	semidirect
126. #6495	C₂³	semidirect
127. #6495	C₂³	semidirect
128. C₂×#1141	C₂³	semidirect
129. C₂×#1136	C₂³	semidirect
130. #6482	C₂³	semidirect
131. #6481	C₂³	semidirect
132. D₇×Q₁₆	C₂³	semidirect
133. #6479	C₂³	semidirect
134. #6478	C₂³	semidirect
135. #6477	C₂³	semidirect
136. D₇×SD₁₆	C₂³	semidirect
137. #6475	C₂³	semidirect
138. #6475	C₂³	semidirect
139. #6474	C₂³	semidirect
140. #6474	C₂³	semidirect
141. D₇×D₈	C₂³	semidirect
142. D₇×D₈	C₂³	semidirect
143. #6472	C₂³	semidirect
144. #6471	C₂³	semidirect
145. #6470	C₂³	semidirect
146. D₇×M₁₆	C₂³	semidirect
147. C₂×Dic₂₈	C₂³	semidirect
148. #6467	C₂³	semidirect
149. #6467	C₂³	semidirect
150. #6467	C₂³	semidirect
151. #6467	C₂³	semidirect
152. C₂×D₅₆	C₂³	semidirect
153. C₂×#1132	C₂³	semidirect
154. #6464	C₂³	semidirect
155. #6464	C₂³	semidirect
156. #6464	C₂³	semidirect
157. #6464	C₂³	semidirect
158. C₂×#1131	C₂³	semidirect
159. C₂×C₈×D₇	C₂³	semidirect
169. C₂×#576	D₇	semidirect
279. C₂×H(5,𝔽₂)	C₂×D₇	semidirect
296. #576	C₂×D₇	semidirect
297. #576	C₂×D₇	semidirect
305. C₂×AGL(1,ℤ/8)	C₂×D₇	semidirect
309. C₂×#135	C₂×D₇	semidirect
311. C₂²×D₈	C₂×D₇	semidirect
317. C₂×#131	C₂×D₇	semidirect
392. H(5,𝔽₂)	C₂²×D₇	semidirect
407. C₂×#41	C₂²×D₇	semidirect
413. C₂²×D₄	C₂²×D₇	semidirect
426. AGL(1,ℤ/8)	C₂²×D₇	semidirect
436. #135	C₂²×D₇	semidirect
437. #135	C₂²×D₇	semidirect
440. C₂×Q₁₆	C₂²×D₇	semidirect
444. C₂×SD₁₆	C₂²×D₇	semidirect
449. C₂×D₈	C₂²×D₇	semidirect
450. C₂×D₈	C₂²×D₇	semidirect
451. C₂×D₈	C₂²×D₇	semidirect
452. C₂×D₈	C₂²×D₇	semidirect
459. #131	C₂²×D₇	semidirect
460. #131	C₂²×D₇	semidirect
464. C₂×M₁₆	C₂²×D₇	semidirect
466. C₂²×C₈	C₂²×D₇	semidirect
639. C₇	#63091	semidirect

Maximal subgroups

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

subgroup	index
#11744560	2
C₂×C₇×#576	2
#11744345	2
#11744272	2
#11744271	2
D₇×#576	2
#11744260	2
#11744255	2
C₂×#90448	2
#11744231	2
#11744228	2
#63091	7