Subgroups — #13375504

Order 1792.

840 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#89796	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#89696	C₂	1	1	yes	maximal, characteristic
4	#11729389	C₂	1	1	yes	maximal, characteristic, complemented
5	#11729283	C₂	1	1	yes	maximal, characteristic
6	#11727239	C₂	1	1	yes	maximal, characteristic, complemented
7	#11727239	C₂	1	1	yes	maximal, characteristic, complemented
8	#11727238	C₂	1	1	yes	maximal, characteristic, complemented
9	#11727237	C₂	1	1	yes	maximal, characteristic, complemented
10	#11727236	C₂	1	1	yes	maximal, characteristic, complemented
11	#11727232	C₂	1	1	yes	maximal, characteristic, complemented
12	#11727204	C₂	1	1	yes	maximal, characteristic
13	#11727204	C₂	1	1	yes	maximal, characteristic
14	#11727202	C₂	1	1	yes	maximal, characteristic
15	#11727202	C₂	1	1	yes	maximal, characteristic
16	C₂×C₇×C₂²⋊Q₈	C₄	1	1	yes	characteristic
17	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
19	C₂²×#1136	C₂²	1	1	yes	characteristic
20	C₂²×#1136	C₂²	1	1	yes	characteristic
21	C₇×#391	C₄	1	1	yes	characteristic
22	C₇×#389	C₄	1	1	yes	characteristic
23	C₇×#387	C₄	1	1	yes	characteristic
24	C₇×#387	C₄	1	1	yes	characteristic
25	C₇×#385	C₄	1	1	yes	characteristic
26	C₇×#385	C₄	1	1	yes	characteristic
27	C₇×#380	C₄	1	1	yes	characteristic
28	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
35	#89796	—	2	4	no	—
36	#89696	—	2	4	no	—
37	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
45	C₂×#6377	C₂²	1	1	yes	characteristic
46	C₂×#6377	C₂²	1	1	yes	characteristic
47	C₂×#6377	C₂²	1	1	yes	characteristic
48	C₂×#6377	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
51	#89319	C₂²	1	1	yes	characteristic
52	#89319	C₂²	1	1	yes	characteristic
53	#89319	C₂²	1	1	yes	characteristic
54	#89319	C₂²	1	1	yes	characteristic
55	#89319	C₂²	1	1	yes	characteristic
56	#89319	C₂²	1	1	yes	characteristic
57	#89319	C₂²	1	1	yes	characteristic
58	#89319	C₂²	1	1	yes	characteristic
59	#89319	C₂²	1	1	yes	characteristic
60	#89319	C₂²	1	1	yes	characteristic
61	#22955	—	7	1	no	maximal, Sylow
62	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
66	C₇×C₂²⋊Q₈	—	2	4	no	—
67	C₄×C₇×Q₈	—	2	2	no	—
68	C₄×C₇×Q₈	—	2	2	no	—
69	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₇	—	2	2	no	—
83	C₂×C₄²×C₇	—	2	2	no	—
84	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
92	C₂×#1136	—	2	2	no	—
93	C₂×#1136	—	2	2	no	—
94	C₂×#1136	—	2	2	no	—
95	C₂×#1136	—	2	2	no	—
96	C₂×#1136	—	4	1	no	—
97	C₂×#1136	—	4	1	no	—
98	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
99	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
100	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
101	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
102	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
103	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
104	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
105	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
106	C₇×#95	C₂×C₄	1	1	yes	characteristic
107	C₇×#95	C₂×C₄	1	1	yes	characteristic
108	C₇×#95	C₂×C₄	1	1	yes	characteristic
109	C₇×#95	C₂×C₄	1	1	yes	characteristic
110	C₇×#95	C₂×C₄	1	1	yes	characteristic
111	C₇×#95	C₂×C₄	1	1	yes	characteristic
112	C₇×#95	C₂×C₄	1	1	yes	characteristic
113	C₇×#95	C₂×C₄	1	1	yes	characteristic
114	C₇×#95	C₂×C₄	1	1	yes	characteristic
115	C₇×#95	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
117	C₂²⋊(C₇⋊C₈)	Q₈	1	4	yes	complemented
118	C₄⋊(C₇⋊C₈)	—	2	2	no	—
119	C₄⋊(C₇⋊C₈)	—	2	2	no	—
120	C₄⋊(C₇⋊C₈)	—	2	2	no	—
121	C₄⋊(C₇⋊C₈)	—	2	2	no	—
122	C₄⋊(C₇⋊C₈)	—	2	2	no	—
123	C₄⋊(C₇⋊C₈)	—	4	1	no	—
124	C₄⋊(C₇⋊C₈)	—	4	1	no	—
125	C₄⋊(C₇⋊C₈)	D₄	1	4	yes	—
126	#6377	—	2	2	no	—
127	#6377	—	2	2	no	—
128	#6377	—	2	2	no	—
129	#6377	—	4	1	no	—
130	C₄×C₇⋊C₈	—	2	2	no	—
131	C₄×C₇⋊C₈	—	4	1	no	—
132	C₂×#446	—	7	1	no	—
133	C₂×#423	—	7	1	no	—
134	C₄×C₂²⋊Q₈	D₇	1	1	yes	characteristic
135	#1985	—	7	1	no	—
136	#1940	—	7	1	no	—
137	#1940	—	7	1	no	—
138	#1939	—	7	1	no	—
139	#1917	—	7	1	no	—
140	#1916	—	7	1	no	—
141	#1851	—	7	1	no	—
142	#1851	—	7	1	no	—
143	#1771	—	7	1	no	—
144	#1753	—	7	1	no	—
145	#1753	—	7	1	no	—
146	#1749	—	7	1	no	—
147	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₇×Q₈	—	2	2	no	—
149	C₂×C₇×Q₈	—	2	2	no	—
150	C₂×C₇×Q₈	—	4	1	no	—
151	C₂²×C₄×C₇	—	2	1	no	—
152	C₂²×C₄×C₇	—	2	1	no	—
153	C₂²×C₄×C₇	—	2	1	no	—
154	C₂²×C₄×C₇	—	2	1	no	—
155	C₂²×C₄×C₇	—	2	2	no	—
156	C₂²×C₄×C₇	—	2	2	no	—
157	C₂²×C₄×C₇	—	2	2	no	—
158	C₂²×C₄×C₇	—	4	1	no	—
159	C₂²×C₄×C₇	—	4	1	no	—
160	C₂²×C₄×C₇	—	4	1	no	—
161	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
175	C₂²×C₄×C₇	#41	1	2	yes	—
176	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
177	C₇×C₄⋊C₄	—	2	2	no	—
178	C₇×C₄⋊C₄	—	2	2	no	—
179	C₇×C₄⋊C₄	—	2	2	no	—
180	C₇×C₄⋊C₄	—	2	2	no	—
181	C₇×C₄⋊C₄	—	2	2	no	—
182	C₇×C₄⋊C₄	—	4	1	no	—
183	C₇×C₄⋊C₄	—	4	1	no	—
184	C₇×C₄⋊C₄	—	4	1	no	—
185	C₇×C₄⋊C₄	M₁₆	1	4	yes	complemented
186	C₇×C₂²⋊C₄	—	2	2	no	—
187	C₇×C₂²⋊C₄	—	2	2	no	—
188	C₇×C₂²⋊C₄	—	4	1	no	—
189	C₇×C₂²⋊C₄	—	4	1	no	—
190	C₄²×C₇	—	2	2	no	—
191	C₄²×C₇	—	2	2	no	—
192	C₄²×C₇	—	2	1	no	—
193	C₄²×C₇	—	2	1	no	—
194	C₄²×C₇	—	2	1	no	—
195	C₄²×C₇	—	2	1	no	—
196	C₄²×C₇	—	2	1	no	—
197	C₄²×C₇	—	2	1	no	—
198	C₄²×C₇	—	2	1	no	—
199	C₄²×C₇	—	2	1	no	—
200	C₄²×C₇	—	2	1	no	—
201	C₄²×C₇	—	2	1	no	—
202	C₄²×C₇	C₂×D₄	1	2	yes	—
203	C₄²×C₇	#41	1	2	yes	—
204	#1136	—	4	4	no	—
205	#1136	—	4	4	no	—
206	C₂×C₇⋊C₈	—	2	1	no	—
207	C₂×C₇⋊C₈	—	2	1	no	—
208	C₂×C₇⋊C₈	—	2	1	no	—
209	C₂×C₇⋊C₈	—	2	1	no	—
210	C₂×C₇⋊C₈	—	2	1	no	—
211	C₂×C₇⋊C₈	—	2	1	no	—
212	C₂×C₇⋊C₈	—	2	1	no	—
213	C₂×C₇⋊C₈	—	2	1	no	—
214	C₂×C₇⋊C₈	—	2	1	no	—
215	C₂×C₇⋊C₈	—	2	1	no	—
216	C₂×C₇⋊C₈	—	2	1	no	—
217	C₂×C₇⋊C₈	—	2	1	no	—
218	C₂×C₇⋊C₈	—	2	1	no	—
219	C₂×C₇⋊C₈	—	2	1	no	—
220	C₂×C₇⋊C₈	—	2	1	no	—
221	C₂×C₇⋊C₈	—	2	1	no	—
222	C₂×C₇⋊C₈	—	2	1	no	—
223	C₂×C₇⋊C₈	—	2	1	no	—
224	C₂×C₇⋊C₈	—	2	1	no	—
225	C₂×C₇⋊C₈	—	2	1	no	—
226	C₂×C₇⋊C₈	C₂×D₄	1	2	yes	—
227	C₂×C₇⋊C₈	C₂×D₄	1	2	yes	—
228	C₂×C₇⋊C₈	C₂×Q₈	1	2	yes	—
229	C₂×C₇⋊C₈	C₂×Q₈	1	2	yes	—
230	C₂²×M₁₆	—	7	1	no	—
231	C₂²×M₁₆	—	7	1	no	—
232	C₂×C₂²⋊Q₈	Dic₇	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂×D₇	1	1	yes	characteristic
234	C₂²×C₄²	C₂×D₇	1	1	yes	characteristic
235	#446	—	14	4	no	—
236	#423	—	14	4	no	—
237	C₂×C₄⋊C₈	—	7	1	no	—
238	C₂×C₄⋊C₈	—	7	1	no	—
239	C₂×C₄⋊C₈	—	7	1	no	—
240	C₂×C₄⋊C₈	—	7	1	no	—
241	C₂×C₄⋊C₈	—	7	1	no	—
242	C₂×C₄⋊C₈	—	7	1	no	—
243	C₂×C₄⋊C₈	—	7	1	no	—
244	C₂×C₄⋊C₈	—	7	1	no	—
245	C₂×C₂²⋊C₈	—	7	1	no	—
246	C₂×C₂²⋊C₈	—	7	1	no	—
247	C₂×#97	—	7	1	no	—
248	C₂×#97	—	7	1	no	—
249	C₂×#97	—	7	1	no	—
250	C₂×#97	—	7	1	no	—
251	C₂×C₄×C₈	—	7	1	no	—
252	C₂×C₄×C₈	—	7	1	no	—
253	#391	Dic₇	1	1	yes	characteristic
254	#389	Dic₇	1	1	yes	characteristic
255	#387	Dic₇	1	1	yes	characteristic
256	#387	Dic₇	1	1	yes	characteristic
257	#385	Dic₇	1	1	yes	characteristic
258	#385	Dic₇	1	1	yes	characteristic
259	#380	Dic₇	1	1	yes	characteristic
260	C₄×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
261	C₄×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
262	C₄×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
263	C₄×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
264	C₄×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
265	#336	—	7	1	no	—
266	#336	—	7	1	no	—
267	#336	—	7	1	no	—
268	#336	—	7	1	no	—
269	#336	—	7	1	no	—
270	#336	—	7	1	no	—
271	#336	—	7	1	no	—
272	#336	—	7	1	no	—
273	#336	—	7	1	no	—
274	#336	—	7	1	no	—
275	C₂³×C₇	—	2	1	no	—
276	C₂³×C₇	—	2	1	no	—
277	C₂³×C₇	—	2	1	no	—
278	C₂³×C₇	—	2	1	no	—
279	C₂³×C₇	—	2	1	no	—
280	C₂³×C₇	—	2	1	no	—
281	C₂³×C₇	C₄×Q₈	1	2	yes	—
282	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
283	C₇×Q₈	—	4	4	no	—
284	C₂×C₄×C₇	—	2	1	no	—
285	C₂×C₄×C₇	—	2	1	no	—
286	C₂×C₄×C₇	—	2	1	no	—
287	C₂×C₄×C₇	—	2	1	no	—
288	C₂×C₄×C₇	—	2	1	no	—
289	C₂×C₄×C₇	—	2	1	no	—
290	C₂×C₄×C₇	—	2	1	no	—
291	C₂×C₄×C₇	—	2	1	no	—
292	C₂×C₄×C₇	—	2	1	no	—
293	C₂×C₄×C₇	—	2	1	no	—
294	C₂×C₄×C₇	—	2	1	no	—
295	C₂×C₄×C₇	—	2	1	no	—
296	C₂×C₄×C₇	—	2	2	no	—
297	C₂×C₄×C₇	—	2	2	no	—
298	C₂×C₄×C₇	—	2	2	no	—
299	C₂×C₄×C₇	—	2	2	no	—
300	C₂×C₄×C₇	—	2	1	no	—
301	C₂×C₄×C₇	—	2	1	no	—
302	C₂×C₄×C₇	—	2	1	no	—
303	C₂×C₄×C₇	—	2	1	no	—
304	C₂×C₄×C₇	—	2	1	no	—
305	C₂×C₄×C₇	—	2	1	no	—
306	C₂×C₄×C₇	—	2	1	no	—
307	C₂×C₄×C₇	—	2	1	no	—
308	C₂×C₄×C₇	—	2	1	no	—
309	C₂×C₄×C₇	—	2	1	no	—
310	C₂×C₄×C₇	—	2	1	no	—
311	C₂×C₄×C₇	—	2	1	no	—
312	C₂×C₄×C₇	—	2	1	no	—
313	C₂×C₄×C₇	—	2	1	no	—
314	C₂×C₄×C₇	—	2	1	no	—
315	C₂×C₄×C₇	—	2	1	no	—
316	C₂×C₄×C₇	—	2	1	no	—
317	C₂×C₄×C₇	—	2	1	no	—
318	C₂×C₄×C₇	—	2	1	no	—
319	C₂×C₄×C₇	—	2	1	no	—
320	C₂×C₄×C₇	—	2	1	no	—
321	C₂×C₄×C₇	—	4	4	no	—
322	C₂×C₄×C₇	—	4	4	no	—
323	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
324	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
325	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
326	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
327	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
328	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
329	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
331	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
332	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
335	C₇⋊C₈	—	2	2	no	—
336	C₇⋊C₈	—	2	2	no	—
337	C₇⋊C₈	—	2	2	no	—
338	C₇⋊C₈	—	2	2	no	—
339	C₇⋊C₈	—	4	1	no	—
340	C₇⋊C₈	—	4	1	no	—
341	C₇⋊C₈	—	4	1	no	—
342	C₇⋊C₈	—	4	1	no	—
343	C₂²×Q₈	C₂×Dic₇	1	1	yes	characteristic
344	C₂³×C₄	C₂×Dic₇	1	1	yes	characteristic
345	C₂³×C₄	C₂×Dic₇	1	1	yes	characteristic
346	C₂³×C₄	C₂²×D₇	1	1	yes	characteristic
347	C₂×M₁₆	—	14	2	no	—
348	C₂×M₁₆	—	14	2	no	—
349	C₂×M₁₆	—	14	2	no	—
350	C₂×M₁₆	—	14	2	no	—
351	C₂×M₁₆	—	28	1	no	—
352	C₂×M₁₆	—	28	1	no	—
353	C₂²×C₈	—	7	1	no	—
354	C₂²×C₈	—	7	1	no	—
355	C₂²×C₈	—	7	1	no	—
356	C₂²×C₈	—	7	1	no	—
357	C₂²×C₈	—	7	1	no	—
358	C₂²×C₈	—	7	1	no	—
359	C₂²×C₈	—	7	1	no	—
360	C₂²×C₈	—	7	1	no	—
361	C₂²⋊Q₈	—	2	4	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
377	C₂×C₄²	—	2	2	no	—
378	C₂×C₄²	—	2	2	no	—
379	C₂×C₄²	C₂×Dic₇	1	1	yes	characteristic
380	C₂×C₄²	C₂×Dic₇	1	1	yes	characteristic
381	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
382	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
383	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
384	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
385	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
386	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
387	C₄⋊C₈	—	7	4	no	—
388	C₄⋊C₈	—	14	2	no	—
389	C₄⋊C₈	—	14	2	no	—
390	C₄⋊C₈	—	14	2	no	—
391	C₄⋊C₈	—	14	2	no	—
392	C₄⋊C₈	—	14	2	no	—
393	C₄⋊C₈	—	28	1	no	—
394	C₄⋊C₈	—	28	1	no	—
395	C₂²⋊C₈	—	7	4	no	—
396	C₂²⋊C₈	—	14	2	no	—
397	#97	—	14	2	no	—
398	#97	—	14	2	no	—
399	#97	—	14	2	no	—
400	#97	—	28	1	no	—
401	C₄×C₈	—	14	2	no	—
402	C₄×C₈	—	28	1	no	—
403	#95	C₂×Dic₇	1	1	yes	characteristic
404	#95	C₂×Dic₇	1	1	yes	characteristic
405	#95	C₂×Dic₇	1	1	yes	characteristic
406	#95	C₂×Dic₇	1	1	yes	characteristic
407	#95	C₂×Dic₇	1	1	yes	characteristic
408	#95	C₂×Dic₇	1	1	yes	characteristic
409	#95	C₂×Dic₇	1	1	yes	characteristic
410	#95	C₂×Dic₇	1	1	yes	characteristic
411	#95	C₂×Dic₇	1	1	yes	characteristic
412	#95	C₂×Dic₇	1	1	yes	characteristic
413	C₂²×C₇	—	2	2	no	—
414	C₂²×C₇	—	2	2	no	—
415	C₂²×C₇	—	2	2	no	—
416	C₂²×C₇	—	4	1	no	—
417	C₂²×C₇	—	4	1	no	—
418	C₂²×C₇	—	4	1	no	—
419	C₂²×C₇	—	4	1	no	—
420	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
421	C₂²×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
422	C₂²×C₇	#520	1	1	yes	characteristic
423	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
424	C₂²×C₇	#568	1	1	yes	characteristic
425	C₂²×C₇	#568	1	1	yes	characteristic
426	C₂²×C₇	#568	1	1	yes	characteristic
427	C₄×C₇	—	2	2	no	—
428	C₄×C₇	—	2	2	no	—
429	C₄×C₇	—	2	2	no	—
430	C₄×C₇	—	2	2	no	—
431	C₄×C₇	—	2	2	no	—
432	C₄×C₇	—	2	2	no	—
433	C₄×C₇	—	4	1	no	—
434	C₄×C₇	—	4	1	no	—
435	C₄×C₇	—	4	1	no	—
436	C₄×C₇	—	4	1	no	—
437	C₄×C₇	—	4	1	no	—
438	C₄×C₇	—	4	1	no	—
439	C₄×C₇	—	4	1	no	—
440	C₄×C₇	#546	1	1	yes	characteristic
441	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
442	C₄×C₇	#552	1	1	yes	characteristic
443	C₄×C₇	#554	1	1	yes	characteristic
444	C₂⁴	C₂²×Dic₇	1	1	yes	characteristic
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	4	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	Q₈×D₇	1	2	yes	—
459	C₂²×C₄	#1161	1	2	yes	—
460	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
461	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
462	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
463	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
464	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
465	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
466	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
467	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
468	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
469	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
470	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
471	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
472	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
473	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
474	M₁₆	—	28	4	no	—
475	M₁₆	—	28	4	no	—
476	C₂×C₈	—	7	2	no	—
477	C₂×C₈	—	7	2	no	—
478	C₂×C₈	—	7	2	no	—
479	C₂×C₈	—	7	2	no	—
480	C₂×C₈	—	14	1	no	—
481	C₂×C₈	—	14	1	no	—
482	C₂×C₈	—	14	1	no	—
483	C₂×C₈	—	14	1	no	—
484	C₂×C₈	—	14	1	no	—
485	C₂×C₈	—	14	1	no	—
486	C₂×C₈	—	14	1	no	—
487	C₂×C₈	—	14	1	no	—
488	C₂×C₈	—	14	1	no	—
489	C₂×C₈	—	14	1	no	—
490	C₂×C₈	—	14	1	no	—
491	C₂×C₈	—	14	1	no	—
492	C₂×C₈	—	14	1	no	—
493	C₂×C₈	—	14	1	no	—
494	C₂×C₈	—	14	1	no	—
495	C₂×C₈	—	14	1	no	—
496	C₂×C₈	—	14	1	no	—
497	C₂×C₈	—	14	1	no	—
498	C₂×C₈	—	14	1	no	—
499	C₂×C₈	—	14	1	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	4	1	no	—
506	C₄⋊C₄	—	4	1	no	—
507	C₄⋊C₄	—	4	1	no	—
508	C₄⋊C₄	#1136	1	4	yes	complemented
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₂²⋊C₄	—	4	1	no	—
513	C₄²	—	2	2	no	—
514	C₄²	—	2	2	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	D₄×D₇	1	2	yes	—
526	C₄²	#1159	1	2	yes	—
527	C₂×C₇	—	4	2	no	—
528	C₂×C₇	#2360	1	1	yes	characteristic
529	C₂×C₇	#2930	1	1	yes	characteristic
530	C₂×C₇	D₄×M₁₆	1	1	yes	characteristic
531	C₂×C₇	#2961	1	1	yes	characteristic
532	C₂×C₇	Q₈×M₁₆	1	1	yes	characteristic
533	C₂×C₇	#2989	1	1	yes	characteristic
534	C₂×C₇	#2995	1	1	yes	characteristic
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	Q₈×Dic₇	1	2	yes	—
542	C₂³	C₂³×Dic₇	1	1	yes	characteristic
543	Q₈	—	4	4	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	4	4	no	—
583	C₂×C₄	C₂×#1136	1	2	yes	—
584	C₂×C₄	C₂×#1136	1	2	yes	—
585	C₂×C₄	C₂×#1136	1	2	yes	—
586	C₂×C₄	D₄×Dic₇	1	2	yes	—
587	C₂×C₄	D₄×Dic₇	1	2	yes	—
588	C₂×C₄	Q₈×Dic₇	1	2	yes	—
589	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
590	C₂×C₄	C₂×#1159	1	1	yes	characteristic
591	C₂×C₄	C₂×Q₈×D₇	1	1	yes	characteristic
592	C₂×C₄	C₂×#1161	1	1	yes	characteristic
593	C₂×C₄	#6553	1	1	yes	characteristic
594	C₂×C₄	#6554	1	1	yes	characteristic
595	C₈	—	14	2	no	—
596	C₈	—	14	2	no	—
597	C₈	—	14	2	no	—
598	C₈	—	14	2	no	—
599	C₈	—	28	1	no	—
600	C₈	—	28	1	no	—
601	C₈	—	28	1	no	—
602	C₈	—	28	1	no	—
603	C₇	#22955	1	1	yes	characteristic, complemented, Sylow
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	C₂²×#1136	1	1	yes	characteristic
612	C₂²	C₂×D₄×Dic₇	1	1	yes	characteristic
613	C₂²	C₂×Q₈×Dic₇	1	1	yes	characteristic
614	C₂²	#90510	1	1	yes	characteristic
615	C₂²	#90510	1	1	yes	characteristic
616	C₂²	#90510	1	1	yes	characteristic
617	C₂²	#90518	1	1	yes	characteristic
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	#90321	1	1	yes	characteristic
632	C₄	#90323	1	1	yes	characteristic
633	C₄	#90326	1	1	yes	characteristic
634	C₄	#90333	1	1	yes	characteristic
635	C₂	—	4	2	no	—
636	C₂	D₄×#1136	1	1	yes	characteristic
637	C₂	Q₈×#1136	1	1	yes	characteristic
638	C₂	#11739966	1	1	yes	characteristic
639	C₂	#11740192	1	1	yes	characteristic
640	C₂	#11740362	1	1	yes	characteristic
641	C₂	#11740578	1	1	yes	characteristic
642	C₂	#11740774	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇
commutator, socle	C₂³×C₇	C₂³×C₄
Fitting	C₄×C₇×C₂²⋊Q₈	C₂
prime radical	C₂⁴×C₇	C₂²×C₄
cosocle	C₂²×C₄×C₇	C₂⁴
hypercenter	C₄×C₂²⋊Q₈	D₇
hypocenter	C₇	#22955
LCS	G ▷ C₂³×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×#89796	C₂	semidirect
4. #11729389	C₂	semidirect
6. #11727239	C₂	semidirect
7. #11727239	C₂	semidirect
8. #11727238	C₂	semidirect
9. #11727237	C₂	semidirect
10. #11727236	C₂	semidirect
11. #11727232	C₂	semidirect
117. C₂²⋊(C₇⋊C₈)	Q₈	semidirect
185. C₇×C₄⋊C₄	M₁₆	semidirect
508. C₄⋊C₄	#1136	semidirect
603. C₇	#22955	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₇×C₂²⋊Q₈	2
C₂×#89796	2
C₂×#89696	2
#11729389	2
#11729283	2
#11727239	2
#11727238	2
#11727237	2
#11727236	2
#11727232	2
#11727204	2
#11727202	2
#22955	7