Subgroups — #13371145

Order 1792.

894 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#416	C₂	1	1	yes	maximal, characteristic
2	#11741520	C₂	1	1	yes	maximal, characteristic
3	#11739655	C₂	1	1	yes	maximal, characteristic, complemented
4	#11729892	C₂	1	1	yes	maximal, characteristic
5	#11729731	C₂	1	1	yes	maximal, characteristic, complemented
6	#11729721	C₂	1	1	yes	maximal, characteristic, complemented
7	#11729344	C₂	1	1	yes	maximal, characteristic, complemented
8	#11728046	C₂	1	2	yes	maximal, complemented
9	#11728045	C₂	1	2	yes	maximal, complemented
10	#11728044	C₂	1	2	yes	maximal, complemented
11	#11728042	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
13	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×#117	C₂²	1	1	yes	characteristic
15	C₂×#6511	C₂²	1	2	yes	—
16	C₇×#416	C₄	1	1	yes	characteristic, complemented
17	C₇×#416	C₄	1	1	yes	characteristic, complemented
18	C₇×#416	C₄	1	1	yes	characteristic, complemented
19	C₇×#416	C₄	1	1	yes	characteristic, complemented
20	C₇×#416	C₂²	1	1	yes	characteristic
21	C₇×#416	C₂²	1	1	yes	characteristic
22	C₇×#416	C₂²	1	1	yes	characteristic
23	C₇×#416	C₂²	1	1	yes	characteristic
24	C₂×C₇×#103	C₄	1	1	yes	characteristic, complemented
25	C₂×C₇×#103	C₄	1	1	yes	characteristic, complemented
26	C₂×C₇×#102	C₄	1	1	yes	characteristic, complemented
27	C₂×C₇×#102	C₄	1	1	yes	characteristic, complemented
28	C₂×#6411	C₂²	1	2	yes	—
29	C₂×#6411	C₂²	1	2	yes	—
30	#90006	—	2	2	no	—
31	#90006	C₂²	1	2	yes	—
32	C₄×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
33	#89979	—	2	1	no	—
34	#89979	C₂²	1	1	yes	characteristic
35	#89979	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊(C₇⋊C₈)	—	2	1	no	—
37	C₂×C₂²⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
38	C₂×#6393	C₂²	1	2	yes	complemented
39	C₂×#6389	C₂²	1	2	yes	complemented
40	#89772	—	2	2	no	—
41	#89771	C₂²	1	2	yes	complemented
42	#89769	C₂²	1	2	yes	complemented
43	#89698	—	2	1	no	—
44	#89697	—	2	1	no	—
45	#89347	C₂²	1	2	yes	complemented
46	#89345	C₂²	1	2	yes	complemented
47	#89327	C₂²	1	2	yes	complemented
48	#89327	C₂²	1	2	yes	complemented
49	#22586	—	7	1	no	maximal, Sylow
50	C₂×C₇×#41	—	2	1	no	—
51	C₂×C₇×#41	—	2	1	no	—
52	C₂×C₇×#41	—	2	4	no	—
53	C₂×C₇×#41	—	4	2	no	—
54	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
55	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
56	C₂×C₇×#41	C₂³	1	1	yes	characteristic
57	C₂×C₇×#41	C₂³	1	1	yes	characteristic
58	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₇×D₄	—	2	1	no	—
60	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₇	—	2	1	no	—
62	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
63	C₂²×C₇×C₈	—	4	2	no	—
64	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₇×#117	—	2	1	no	—
71	C₇×#117	—	2	1	no	—
72	C₇×#117	C₂×C₄	1	1	yes	characteristic
73	C₇×#117	C₂×C₄	1	1	yes	characteristic
74	C₇×#117	C₂³	1	1	yes	characteristic
75	C₇×#117	C₂³	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	—	2	1	no	—
79	C₂×C₄²×C₇	—	2	1	no	—
80	C₂×C₂²⋊Dic₇	—	2	1	no	—
81	#6511	—	2	4	no	—
82	#6511	—	4	2	no	—
83	C₂×C₄×Dic₇	C₂³	1	2	yes	—
84	C₂×#1136	—	2	2	no	—
85	C₂×#1136	C₂³	1	2	yes	—
86	C₂×#1136	C₂³	1	2	yes	—
87	C₂²×C₇⋊C₈	—	2	2	no	—
88	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
89	C₇×#103	C₂×C₄	1	1	yes	characteristic
90	C₇×#103	C₂×C₄	1	1	yes	characteristic
91	C₇×#103	C₂×C₄	1	1	yes	characteristic
92	C₇×#103	C₂×C₄	1	1	yes	characteristic
93	C₇×#103	C₂×C₄	1	1	yes	characteristic
94	C₇×#103	C₂×C₄	1	1	yes	characteristic
95	C₇×#103	C₂×C₄	1	1	yes	characteristic
96	C₇×#103	C₂×C₄	1	1	yes	characteristic
97	C₇×#102	C₂×C₄	1	1	yes	characteristic
98	C₇×#102	C₂×C₄	1	1	yes	characteristic
99	C₇×#102	C₂×C₄	1	1	yes	characteristic
100	C₇×#102	C₂×C₄	1	1	yes	characteristic
101	C₇×#102	C₂×C₄	1	1	yes	characteristic
102	C₇×#102	C₂×C₄	1	1	yes	characteristic
103	C₇×#102	C₂×C₄	1	1	yes	characteristic
104	C₇×#102	C₂×C₄	1	1	yes	characteristic
105	#6411	—	2	4	no	—
106	#6411	—	4	2	no	—
107	C₇⋊#95	—	2	1	no	—
108	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
109	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
110	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
111	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
112	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
113	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
114	C₂²⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
115	C₂²⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
116	C₂²⋊(C₇⋊C₈)	D₄	1	2	yes	—
117	#6393	—	4	2	no	—
118	#6389	—	4	2	no	—
119	C₄⋊(C₇⋊C₈)	—	2	2	no	—
120	C₄⋊(C₇⋊C₈)	—	2	2	no	—
121	#6377	—	2	2	no	—
122	C₄×C₇⋊C₈	—	2	2	no	—
123	#2924	—	7	1	no	—
124	C₂×#416	D₇	1	1	yes	characteristic
125	#2880	—	7	1	no	—
126	#1938	—	7	2	no	—
127	#1929	—	7	2	no	—
128	#1866	—	7	2	no	—
129	#1826	—	7	1	no	—
130	#1810	—	7	1	no	—
131	#1789	—	7	1	no	—
132	#1765	—	7	2	no	—
133	#1752	—	7	1	no	—
134	C₂⁴×C₇	—	2	1	no	—
135	C₂⁴×C₇	#41	1	1	yes	characteristic
136	C₇×#41	—	2	2	no	—
137	C₇×#41	—	2	2	no	—
138	C₇×#41	—	2	2	no	—
139	C₇×#41	—	2	2	no	—
140	C₇×#41	—	2	2	no	—
141	C₇×#41	—	4	4	no	—
142	C₇×#41	—	4	1	no	—
143	C₇×#41	—	4	1	no	—
144	C₇×#41	—	4	4	no	—
145	C₇×#41	#41	1	4	yes	—
146	C₂×C₇×Q₈	—	2	1	no	—
147	C₂×C₇×Q₈	—	2	2	no	—
148	C₂×C₇×Q₈	—	4	1	no	—
149	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₇×D₄	—	2	1	no	—
152	C₂×C₇×D₄	—	2	2	no	—
153	C₂×C₇×D₄	—	2	1	no	—
154	C₂×C₇×D₄	—	2	1	no	—
155	C₂×C₇×D₄	—	2	1	no	—
156	C₂×C₇×D₄	—	2	1	no	—
157	C₂×C₇×D₄	—	4	1	no	—
158	C₂×C₇×D₄	—	4	4	no	—
159	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₇	—	2	1	no	—
162	C₂²×C₄×C₇	—	2	2	no	—
163	C₂²×C₄×C₇	—	2	2	no	—
164	C₂²×C₄×C₇	—	2	1	no	—
165	C₂²×C₄×C₇	—	2	1	no	—
166	C₂²×C₄×C₇	—	2	1	no	—
167	C₂²×C₄×C₇	—	2	1	no	—
168	C₂²×C₄×C₇	—	2	1	no	—
169	C₂²×C₄×C₇	—	2	1	no	—
170	C₂²×C₄×C₇	—	4	4	no	—
171	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₇	#41	1	1	yes	characteristic
176	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
177	C₂²×Dic₇	—	2	2	no	—
178	C₂×C₇×C₈	—	2	2	no	—
179	C₂×C₇×C₈	—	2	2	no	—
180	C₂×C₇×C₈	—	4	1	no	—
181	C₂×C₇×C₈	—	4	1	no	—
182	C₂×C₇×C₈	—	4	1	no	—
183	C₂×C₇×C₈	—	4	1	no	—
184	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
188	C₇×C₄⋊C₄	—	2	1	no	—
189	C₇×C₄⋊C₄	—	2	1	no	—
190	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
191	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
192	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
193	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
194	C₇×C₂²⋊C₄	—	2	1	no	—
195	C₇×C₂²⋊C₄	—	2	1	no	—
196	C₇×C₂²⋊C₄	—	2	1	no	—
197	C₇×C₂²⋊C₄	—	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	C₂²⋊Dic₇	—	4	2	no	—
203	C₄×Dic₇	—	2	2	no	—
204	C₄×Dic₇	—	2	2	no	—
205	#1136	—	2	2	no	—
206	#1136	—	2	2	no	—
207	#1136	—	2	2	no	—
208	#1136	—	2	2	no	—
209	#1136	—	4	4	no	—
210	C₂×C₇⋊C₈	—	2	2	no	—
211	C₂×C₇⋊C₈	—	2	2	no	—
212	C₂×C₇⋊C₈	—	2	2	no	—
213	C₂×C₇⋊C₈	—	2	2	no	—
214	C₂×C₇⋊C₈	—	4	4	no	—
215	C₂×C₇⋊C₈	C₂×D₄	1	2	yes	—
216	C₂×C₇⋊C₈	C₂×D₄	1	2	yes	—
217	C₂²×#41	C₂×D₇	1	1	yes	characteristic
218	C₂×#131	—	7	2	no	—
219	C₂³×C₈	C₂×D₇	1	1	yes	characteristic
220	C₂×#117	C₂×D₇	1	1	yes	characteristic
221	#433	—	14	2	no	—
222	#432	—	14	1	no	—
223	#431	—	14	1	no	—
224	C₂×#108	—	7	2	no	—
225	#424	—	7	2	no	—
226	C₂×#104	—	7	2	no	—
227	C₂×#104	—	7	2	no	—
228	#416	Dic₇	1	1	yes	characteristic, complemented
229	#416	Dic₇	1	1	yes	characteristic, complemented
230	#416	Dic₇	1	1	yes	characteristic, complemented
231	#416	Dic₇	1	1	yes	characteristic, complemented
232	#416	C₂×D₇	1	1	yes	characteristic
233	#416	C₂×D₇	1	1	yes	characteristic
234	#416	C₂×D₇	1	1	yes	characteristic
235	#416	C₂×D₇	1	1	yes	characteristic
236	C₂×#103	Dic₇	1	1	yes	characteristic, complemented
237	C₂×#103	Dic₇	1	1	yes	characteristic, complemented
238	C₂×#102	Dic₇	1	1	yes	characteristic, complemented
239	C₂×#102	Dic₇	1	1	yes	characteristic, complemented
240	#408	—	7	2	no	—
241	#408	—	14	2	no	—
242	#407	—	7	1	no	—
243	#407	—	7	1	no	—
244	#407	—	14	1	no	—
245	C₂×C₂²⋊C₈	—	7	1	no	—
246	C₂×C₂²⋊C₈	—	14	1	no	—
247	#405	—	7	2	no	—
248	C₂×#97	—	7	2	no	—
249	C₄×C₂²⋊C₄	—	7	1	no	—
250	#341	—	7	2	no	—
251	#339	—	7	2	no	—
252	#339	—	7	2	no	—
253	#336	—	7	2	no	—
254	C₂³×C₇	—	2	1	no	—
255	C₂³×C₇	—	2	2	no	—
256	C₂³×C₇	—	2	2	no	—
257	C₂³×C₇	—	2	1	no	—
258	C₂³×C₇	—	4	1	no	—
259	C₂³×C₇	—	4	2	no	—
260	C₂³×C₇	—	4	2	no	—
261	C₂³×C₇	—	8	1	no	—
262	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
263	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
264	C₂³×C₇	C₂×#41	1	1	yes	characteristic
265	C₇×Q₈	—	2	1	no	—
266	C₇×Q₈	—	2	1	no	—
267	C₇×Q₈	—	2	1	no	—
268	C₇×Q₈	—	4	2	no	—
269	C₇×Q₈	#117	1	2	yes	—
270	C₇×D₄	—	2	4	no	—
271	C₇×D₄	—	2	1	no	—
272	C₇×D₄	—	2	1	no	—
273	C₇×D₄	—	2	1	no	—
274	C₇×D₄	—	4	2	no	—
275	C₇×D₄	—	4	2	no	—
276	C₇×D₄	—	4	2	no	—
277	C₇×D₄	—	4	2	no	—
278	C₇×D₄	#117	1	2	yes	—
279	C₂×C₄×C₇	—	2	1	no	—
280	C₂×C₄×C₇	—	2	2	no	—
281	C₂×C₄×C₇	—	2	1	no	—
282	C₂×C₄×C₇	—	2	1	no	—
283	C₂×C₄×C₇	—	2	1	no	—
284	C₂×C₄×C₇	—	2	1	no	—
285	C₂×C₄×C₇	—	2	4	no	—
286	C₂×C₄×C₇	—	2	2	no	—
287	C₂×C₄×C₇	—	2	2	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	—	4	2	no	—
294	C₂×C₄×C₇	—	4	2	no	—
295	C₂×C₄×C₇	—	4	2	no	—
296	C₂×C₄×C₇	—	4	2	no	—
297	C₂×C₄×C₇	—	4	2	no	—
298	C₂×C₄×C₇	—	8	1	no	—
299	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
300	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
301	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
302	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₇	C₂×#41	1	2	yes	—
304	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
305	C₂×Dic₇	—	4	2	no	—
306	C₂×Dic₇	—	4	2	no	—
307	C₂×Dic₇	—	4	2	no	—
308	C₇×C₈	—	2	1	no	—
309	C₇×C₈	—	2	1	no	—
310	C₇×C₈	—	2	1	no	—
311	C₇×C₈	—	2	1	no	—
312	C₇⋊C₈	—	2	2	no	—
313	C₇⋊C₈	—	2	2	no	—
314	C₇⋊C₈	—	4	2	no	—
315	C₇⋊C₈	—	4	2	no	—
316	C₂×#41	—	2	1	no	—
317	C₂×#41	—	2	1	no	—
318	C₂×#41	—	2	4	no	—
319	C₂×#41	—	4	2	no	—
320	C₂×#41	C₂×Dic₇	1	1	yes	characteristic
321	C₂×#41	C₂×Dic₇	1	1	yes	characteristic
322	C₂×#41	C₂²×D₇	1	1	yes	characteristic
323	C₂×#41	C₂²×D₇	1	1	yes	characteristic
324	C₂²×Q₈	C₂×Dic₇	1	1	yes	characteristic
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	C₂×Dic₇	1	1	yes	characteristic
327	C₂³×C₄	—	2	1	no	—
328	C₂³×C₄	C₂²×D₇	1	1	yes	characteristic
329	#131	—	14	4	no	—
330	#131	—	28	2	no	—
331	C₂×M₁₆	—	7	2	no	—
332	C₂×M₁₆	—	7	2	no	—
333	C₂×M₁₆	—	14	2	no	—
334	C₂²×C₈	—	4	2	no	—
335	C₂²×C₈	—	7	2	no	—
336	C₂²×C₈	—	14	2	no	—
337	C₂²×C₈	C₂×Dic₇	1	1	yes	characteristic
338	C₂²×C₈	C₂×Dic₇	1	1	yes	characteristic
339	C₂²×C₈	C₂×Dic₇	1	1	yes	characteristic
340	C₂²×C₈	C₂×Dic₇	1	1	yes	characteristic
341	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
342	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
343	#117	—	2	1	no	—
344	#117	—	2	1	no	—
345	#117	C₂×Dic₇	1	1	yes	characteristic
346	#117	C₂×Dic₇	1	1	yes	characteristic
347	#117	C₂²×D₇	1	1	yes	characteristic
348	#117	C₂²×D₇	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	14	1	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	—	7	2	no	—
355	#108	—	28	2	no	—
356	C₄⋊C₈	—	14	2	no	—
357	C₄⋊C₈	—	14	2	no	—
358	#104	—	14	4	no	—
359	#104	—	28	2	no	—
360	#103	C₂×Dic₇	1	1	yes	characteristic
361	#103	C₂×Dic₇	1	1	yes	characteristic
362	#103	C₂×Dic₇	1	1	yes	characteristic
363	#103	C₂×Dic₇	1	1	yes	characteristic
364	#103	C₂×Dic₇	1	1	yes	characteristic
365	#103	C₂×Dic₇	1	1	yes	characteristic
366	#103	C₂×Dic₇	1	1	yes	characteristic
367	#103	C₂×Dic₇	1	1	yes	characteristic
368	#102	C₂×Dic₇	1	1	yes	characteristic
369	#102	C₂×Dic₇	1	1	yes	characteristic
370	#102	C₂×Dic₇	1	1	yes	characteristic
371	#102	C₂×Dic₇	1	1	yes	characteristic
372	#102	C₂×Dic₇	1	1	yes	characteristic
373	#102	C₂×Dic₇	1	1	yes	characteristic
374	#102	C₂×Dic₇	1	1	yes	characteristic
375	#102	C₂×Dic₇	1	1	yes	characteristic
376	C₂²⋊C₈	—	7	1	no	—
377	C₂²⋊C₈	—	7	1	no	—
378	C₂²⋊C₈	—	7	2	no	—
379	C₂²⋊C₈	—	14	2	no	—
380	C₂²⋊C₈	—	14	2	no	—
381	C₂²⋊C₈	—	14	1	no	—
382	C₂²⋊C₈	—	14	1	no	—
383	C₂²⋊C₈	—	14	1	no	—
384	C₂²⋊C₈	—	14	1	no	—
385	#97	—	14	2	no	—
386	#97	—	28	2	no	—
387	C₄×C₈	—	14	2	no	—
388	#95	—	14	1	no	—
389	C₂²×C₇	—	2	1	no	—
390	C₂²×C₇	—	2	1	no	—
391	C₂²×C₇	—	2	1	no	—
392	C₂²×C₇	—	2	1	no	—
393	C₂²×C₇	—	2	1	no	—
394	C₂²×C₇	—	2	2	no	—
395	C₂²×C₇	—	2	1	no	—
396	C₂²×C₇	—	2	1	no	—
397	C₂²×C₇	—	4	4	no	—
398	C₂²×C₇	—	4	1	no	—
399	C₂²×C₇	—	4	1	no	—
400	C₂²×C₇	—	4	1	no	—
401	C₂²×C₇	—	4	1	no	—
402	C₂²×C₇	—	4	1	no	—
403	C₂²×C₇	—	8	4	no	—
404	C₂²×C₇	#444	1	2	yes	—
405	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
406	C₂²×C₇	#551	1	2	yes	—
407	C₄×C₇	—	2	1	no	—
408	C₄×C₇	—	2	1	no	—
409	C₄×C₇	—	2	2	no	—
410	C₄×C₇	—	4	1	no	—
411	C₄×C₇	—	4	1	no	—
412	C₄×C₇	—	4	1	no	—
413	C₄×C₇	—	4	1	no	—
414	C₄×C₇	—	4	1	no	—
415	C₄×C₇	C₂×#117	1	1	yes	characteristic
416	C₄×C₇	#518	1	1	yes	characteristic
417	C₄×C₇	#546	1	2	yes	—
418	Dic₇	—	8	2	no	—
419	C₂⁴	—	2	1	no	—
420	C₂⁴	#1159	1	1	yes	characteristic
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	4	4	no	—
427	#41	—	4	1	no	—
428	#41	—	4	1	no	—
429	#41	—	4	4	no	—
430	#41	#1157	1	4	yes	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	4	1	no	—
434	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
435	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂×D₄	—	4	4	no	—
444	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
445	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	4	4	no	—
456	C₂²×C₄	—	14	2	no	—
457	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
458	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
459	C₂²×C₄	#1159	1	1	yes	characteristic
460	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
461	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
462	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
463	M₁₆	—	14	2	no	—
464	M₁₆	—	14	2	no	—
465	M₁₆	—	14	2	no	—
466	M₁₆	—	14	2	no	—
467	M₁₆	—	28	4	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	4	1	no	—
471	C₂×C₈	—	4	1	no	—
472	C₂×C₈	—	4	1	no	—
473	C₂×C₈	—	4	1	no	—
474	C₂×C₈	—	7	2	no	—
475	C₂×C₈	—	7	2	no	—
476	C₂×C₈	—	14	2	no	—
477	C₂×C₈	—	14	2	no	—
478	C₂×C₈	—	14	2	no	—
479	C₂×C₈	—	14	2	no	—
480	C₂×C₈	—	28	4	no	—
481	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
482	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
483	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
484	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	28	2	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	14	2	no	—
501	C₄²	—	14	2	no	—
502	C₂×C₇	—	2	2	no	—
503	C₂×C₇	—	2	2	no	—
504	C₂×C₇	—	4	1	no	—
505	C₂×C₇	—	4	2	no	—
506	C₂×C₇	—	8	1	no	—
507	C₂×C₇	#2342	1	1	yes	characteristic
508	C₂×C₇	C₂×#444	1	1	yes	characteristic
509	C₂×C₇	#2957	1	1	yes	characteristic
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	—	4	2	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	8	1	no	—
518	C₂³	D₄×Dic₇	1	1	yes	characteristic
519	C₂³	D₄×Dic₇	1	1	yes	characteristic
520	C₂³	C₂×#1159	1	1	yes	characteristic
521	Q₈	—	2	1	no	—
522	Q₈	—	2	1	no	—
523	Q₈	—	2	1	no	—
524	Q₈	—	4	2	no	—
525	Q₈	#6489	1	2	yes	—
526	D₄	—	2	4	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	#6489	1	2	yes	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	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	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	8	1	no	—
555	C₂×C₄	—	28	2	no	—
556	C₂×C₄	—	28	2	no	—
557	C₂×C₄	—	28	2	no	—
558	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
559	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
560	C₂×C₄	C₂×#1157	1	2	yes	—
561	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
562	C₂×C₄	#6548	1	2	yes	—
563	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
564	C₈	—	2	1	no	—
565	C₈	—	2	1	no	—
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	—	14	2	no	—
569	C₈	—	14	2	no	—
570	C₈	—	28	2	no	—
571	C₈	—	28	2	no	—
572	C₇	#22586	1	1	yes	characteristic, complemented, Sylow
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	8	4	no	—
588	C₂²	#89969	1	2	yes	—
589	C₂²	#90186	1	2	yes	—
590	C₂²	C₂×D₄×Dic₇	1	1	yes	characteristic
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	56	2	no	—
600	C₄	#90181	1	2	yes	—
601	C₄	C₂×#6489	1	1	yes	characteristic
602	C₄	#90489	1	1	yes	characteristic
603	C₂	—	2	2	no	—
604	C₂	—	2	2	no	—
605	C₂	—	4	1	no	—
606	C₂	—	4	2	no	—
607	C₂	—	8	1	no	—
608	C₂	#11739542	1	1	yes	characteristic
609	C₂	C₂×#89969	1	1	yes	characteristic
610	C₂	#11741355	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇
Fitting	C₂×C₇×#416	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂²×C₇×#41	C₂²
cosocle	C₂²×C₄×C₇	C₂⁴
hypercenter	C₂×#416	D₇
hypocenter	C₇	#22586
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#416

Complements

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

N	H ≅ G/N	type
3. #11739655	C₂	semidirect
5. #11729731	C₂	semidirect
6. #11729721	C₂	semidirect
7. #11729344	C₂	semidirect
8. #11728046	C₂	semidirect
9. #11728045	C₂	semidirect
10. #11728044	C₂	semidirect
11. #11728042	C₂	semidirect
16. C₇×#416	C₄	semidirect
17. C₇×#416	C₄	semidirect
18. C₇×#416	C₄	semidirect
19. C₇×#416	C₄	semidirect
24. C₂×C₇×#103	C₄	semidirect
25. C₂×C₇×#103	C₄	semidirect
26. C₂×C₇×#102	C₄	semidirect
27. C₂×C₇×#102	C₄	semidirect
38. C₂×#6393	C₂²	semidirect
39. C₂×#6389	C₂²	semidirect
41. #89771	C₂²	semidirect
42. #89769	C₂²	semidirect
45. #89347	C₂²	semidirect
46. #89345	C₂²	semidirect
47. #89327	C₂²	semidirect
48. #89327	C₂²	semidirect
228. #416	Dic₇	semidirect
229. #416	Dic₇	semidirect
230. #416	Dic₇	semidirect
231. #416	Dic₇	semidirect
236. C₂×#103	Dic₇	semidirect
237. C₂×#103	Dic₇	semidirect
238. C₂×#102	Dic₇	semidirect
239. C₂×#102	Dic₇	semidirect
572. C₇	#22586	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#416	2
#11741520	2
#11739655	2
#11729892	2
#11729731	2
#11729721	2
#11729344	2
#11728046	2
#11728045	2
#11728044	2
#11728042	2
#22586	7