Subgroups — #13358741

Order 1792.

714 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11741192	C₂	1	1	yes	maximal, characteristic
2	#11736065	C₂	1	1	yes	maximal, characteristic
3	C₂×#89492	C₂	1	1	yes	maximal, characteristic
4	C₇×#1855	C₂	1	1	yes	maximal, characteristic
5	#11729755	C₂	1	1	yes	maximal, characteristic
6	#11728449	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728449	C₂	1	1	yes	maximal, characteristic, complemented
8	#11728446	C₂	1	1	yes	maximal, characteristic, complemented
9	Dic₇×#108	C₂	1	1	yes	maximal, characteristic, complemented
10	#11727738	C₂	1	1	yes	maximal, characteristic
11	#11727708	C₂	1	1	yes	maximal, characteristic
12	#11726674	C₂	1	1	yes	maximal, characteristic, complemented
13	#11726674	C₂	1	1	yes	maximal, characteristic, complemented
14	#11726671	C₂	1	1	yes	maximal, characteristic, complemented
15	#11726670	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×#6489	C₂²	1	1	yes	characteristic
18	C₂²×#1136	C₂²	1	1	yes	characteristic
19	C₂×C₇×#108	C₂²	1	1	yes	characteristic
20	C₂×C₇×#108	C₂²	1	1	yes	characteristic
21	C₇×#407	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	#89979	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×#6396	C₂²	1	1	yes	characteristic
26	C₂×#6396	C₂²	1	1	yes	characteristic
27	C₂×#6396	C₂²	1	1	yes	characteristic
28	C₂×#6396	C₂²	1	1	yes	characteristic
29	#89894	—	2	1	no	—
30	#89894	—	2	1	no	—
31	#89890	C₂²	1	1	yes	characteristic
32	#89890	C₂²	1	1	yes	characteristic
33	M₁₆×Dic₇	C₂²	1	1	yes	characteristic
34	M₁₆×Dic₇	C₂²	1	1	yes	characteristic
35	M₁₆×Dic₇	C₂²	1	1	yes	characteristic
36	M₁₆×Dic₇	C₂²	1	1	yes	characteristic
37	M₁₆×Dic₇	C₂²	1	1	yes	characteristic
38	M₁₆×Dic₇	C₂²	1	1	yes	characteristic
39	C₂×#6393	C₂²	1	1	yes	characteristic
40	C₂×#6393	C₂²	1	1	yes	characteristic
41	#89873	—	2	1	no	—
42	#89873	—	2	1	no	—
43	C₂×#6389	C₂²	1	1	yes	characteristic
44	C₂×Dic₇⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×Dic₇⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₈×Dic₇	C₂²	1	1	yes	characteristic
47	#89492	—	2	1	no	—
48	#89492	—	2	1	no	—
49	#89492	—	2	1	no	—
50	#89492	—	2	1	no	—
51	#89492	C₄	1	2	yes	—
52	#89492	C₄	1	2	yes	—
53	#89492	C₄	1	2	yes	—
54	#89492	C₄	1	2	yes	—
55	C₇×#341	C₂²	1	1	yes	characteristic
56	C₇×#341	C₂²	1	1	yes	characteristic
57	#89353	C₂²	1	1	yes	characteristic
58	#89353	C₂²	1	1	yes	characteristic
59	#89353	C₂²	1	1	yes	characteristic
60	#89353	C₂²	1	1	yes	characteristic
61	#89347	C₂²	1	1	yes	characteristic
62	#89347	C₂²	1	1	yes	characteristic
63	#21372	—	7	1	no	maximal, Sylow
64	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
65	C₂×C₇×M₁₆	—	2	1	no	—
66	C₂×C₇×M₁₆	—	2	2	no	—
67	C₂×C₇×M₁₆	—	2	2	no	—
68	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
69	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
70	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
71	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
72	C₂²×C₇×C₈	—	2	1	no	—
73	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊Dic₇	Q₈	1	1	yes	characteristic
76	C₂×C₂²⋊Dic₇	Q₈	1	1	yes	characteristic
77	#6489	C₂×C₄	1	1	yes	characteristic
78	#6489	C₂×C₄	1	1	yes	characteristic
79	#6489	C₂×C₄	1	1	yes	characteristic
80	#6489	C₂×C₄	1	1	yes	characteristic
81	#6489	D₄	1	1	yes	characteristic
82	#6489	D₄	1	1	yes	characteristic
83	#6489	D₄	1	1	yes	characteristic
84	#6489	D₄	1	1	yes	characteristic
85	C₂×C₄⋊Dic₇	Q₈	1	1	yes	characteristic
86	C₂×C₄⋊Dic₇	Q₈	1	1	yes	characteristic
87	C₂×C₄×Dic₇	C₂³	1	1	yes	characteristic
88	C₂×C₄×Dic₇	C₂³	1	1	yes	characteristic
89	C₂×#1136	—	2	1	no	—
90	C₂×#1136	—	2	2	no	—
91	C₂×#1136	—	2	2	no	—
92	C₂×#1136	C₂³	1	1	yes	characteristic
93	C₂×#1136	C₂³	1	1	yes	characteristic
94	C₂×#1136	C₂³	1	1	yes	characteristic
95	C₂×#1136	C₂³	1	1	yes	characteristic
96	C₂²×C₇⋊C₈	—	2	1	no	—
97	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
98	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
99	C₇×#108	—	2	2	no	—
100	C₇×#108	—	2	2	no	—
101	C₇×C₂²⋊C₈	—	2	1	no	—
102	C₇×C₂²⋊C₈	—	2	1	no	—
103	C₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
104	C₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
105	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
106	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
107	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	2	yes	—
108	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	2	yes	—
109	#6396	—	2	2	no	—
110	#6396	—	2	2	no	—
111	#6396	—	2	2	no	—
112	#6396	—	2	2	no	—
113	#6393	—	2	2	no	—
114	#6393	—	2	2	no	—
115	#6389	—	2	1	no	—
116	#6389	—	2	1	no	—
117	#6389	—	2	1	no	—
118	#6389	—	2	1	no	—
119	#6389	—	2	1	no	—
120	#6389	—	2	1	no	—
121	#6389	C₂×C₄	1	2	yes	—
122	#6389	C₂×C₄	1	2	yes	—
123	Dic₇⋊C₈	—	2	1	no	—
124	Dic₇⋊C₈	—	2	1	no	—
125	Dic₇⋊C₈	—	2	1	no	—
126	Dic₇⋊C₈	—	2	1	no	—
127	Dic₇⋊C₈	C₂×C₄	1	2	yes	—
128	Dic₇⋊C₈	C₂×C₄	1	2	yes	—
129	Dic₇⋊C₈	C₂×C₄	1	2	yes	—
130	Dic₇⋊C₈	C₂×C₄	1	2	yes	—
131	C₈×Dic₇	—	2	1	no	—
132	C₈×Dic₇	—	2	1	no	—
133	C₈×Dic₇	—	2	1	no	—
134	C₈×Dic₇	—	2	1	no	—
135	C₈×Dic₇	—	2	1	no	—
136	C₈×Dic₇	—	2	1	no	—
137	C₈×Dic₇	C₂×C₄	1	2	yes	—
138	C₈×Dic₇	C₂×C₄	1	2	yes	—
139	#2921	—	7	1	no	—
140	C₂×#433	—	7	1	no	—
141	#2873	—	7	1	no	—
142	#1950	—	7	1	no	—
143	#1950	—	7	1	no	—
144	#1950	—	7	1	no	—
145	#1950	—	7	1	no	—
146	#1855	—	7	1	no	—
147	#1855	—	7	1	no	—
148	#1855	—	7	1	no	—
149	#1855	D₇	1	1	yes	characteristic
150	#1778	—	7	1	no	—
151	#1778	—	7	1	no	—
152	C₄×#108	—	7	1	no	—
153	C₄×#108	—	7	1	no	—
154	C₂⁴×C₇	C₂×Q₈	1	1	yes	characteristic
155	C₂²×C₄×C₇	—	2	1	no	—
156	C₂²×C₄×C₇	—	2	1	no	—
157	C₂²×C₄×C₇	—	2	1	no	—
158	C₂²×C₄×C₇	—	2	1	no	—
159	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
164	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
165	C₂²×Dic₇	C₂×Q₈	1	1	yes	characteristic
166	C₂²×Dic₇	C₂×Q₈	1	1	yes	characteristic
167	C₂²×Dic₇	C₂×Q₈	1	1	yes	characteristic
168	C₂²×Dic₇	C₂×Q₈	1	1	yes	characteristic
169	C₇×M₁₆	—	2	4	no	—
170	C₇×M₁₆	—	2	1	no	—
171	C₇×M₁₆	—	2	1	no	—
172	C₇×M₁₆	—	2	1	no	—
173	C₇×M₁₆	—	2	1	no	—
174	C₇×M₁₆	—	2	1	no	—
175	C₇×M₁₆	—	2	1	no	—
176	C₇×M₁₆	#41	1	2	yes	—
177	C₇×M₁₆	#41	1	2	yes	—
178	C₂×C₇×C₈	—	2	4	no	—
179	C₂×C₇×C₈	—	2	1	no	—
180	C₂×C₇×C₈	—	2	1	no	—
181	C₂×C₇×C₈	—	2	1	no	—
182	C₂×C₇×C₈	—	2	1	no	—
183	C₂×C₇×C₈	—	2	1	no	—
184	C₂×C₇×C₈	—	2	1	no	—
185	C₂×C₇×C₈	—	2	1	no	—
186	C₂×C₇×C₈	—	2	1	no	—
187	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
188	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
189	C₂²⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
190	C₂²⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
191	C₂²⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
192	C₂²⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
193	C₂²⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
194	C₂²⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
195	C₂²⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
196	C₂²⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
197	C₄⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
198	C₄⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
199	C₄⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
200	C₄⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
201	C₄⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
202	C₄⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
203	C₄⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
204	C₄⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
205	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
206	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
207	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
208	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
209	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
210	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
211	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
212	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
213	#1136	—	2	4	no	—
214	#1136	—	2	1	no	—
215	#1136	—	2	1	no	—
216	#1136	—	2	1	no	—
217	#1136	—	2	1	no	—
218	#1136	—	2	1	no	—
219	#1136	—	2	1	no	—
220	#1136	#41	1	2	yes	—
221	#1136	#41	1	2	yes	—
222	C₂×C₇⋊C₈	—	2	4	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	—	2	1	no	—
227	C₂×C₇⋊C₈	—	2	1	no	—
228	C₂×C₇⋊C₈	—	2	1	no	—
229	C₂×C₇⋊C₈	—	2	1	no	—
230	C₂×C₇⋊C₈	—	2	1	no	—
231	C₂×C₇⋊C₈	C₂²×C₄	1	2	yes	—
232	C₂×C₇⋊C₈	C₂²×C₄	1	2	yes	—
233	C₂²×M₁₆	—	7	1	no	—
234	C₂²×M₁₆	C₂×D₇	1	1	yes	characteristic
235	C₂×#117	—	7	1	no	—
236	#433	—	7	2	no	—
237	#433	—	7	2	no	—
238	#433	—	7	2	no	—
239	#433	—	7	2	no	—
240	#433	—	14	1	no	—
241	#433	—	14	1	no	—
242	#433	—	14	1	no	—
243	#433	—	14	1	no	—
244	C₂×#108	—	7	1	no	—
245	C₂×#108	—	7	1	no	—
246	C₂×#108	—	7	1	no	—
247	C₂×#108	—	7	1	no	—
248	C₂×#108	—	7	1	no	—
249	C₂×#108	—	7	1	no	—
250	C₂×#108	C₂×D₇	1	1	yes	characteristic
251	C₂×#108	C₂×D₇	1	1	yes	characteristic
252	#423	—	7	1	no	—
253	#423	—	7	1	no	—
254	C₂×C₄⋊C₈	—	7	1	no	—
255	C₂×C₄⋊C₈	—	7	1	no	—
256	#407	—	7	1	no	—
257	#407	C₂×D₇	1	1	yes	characteristic
258	C₂×C₂²⋊C₈	—	7	1	no	—
259	C₂×C₂²⋊C₈	C₂×D₇	1	1	yes	characteristic
260	#405	—	14	1	no	—
261	#405	—	14	1	no	—
262	#405	—	14	1	no	—
263	#405	—	14	1	no	—
264	C₄×M₁₆	—	7	1	no	—
265	C₄×M₁₆	—	7	1	no	—
266	C₄×M₁₆	—	7	1	no	—
267	C₄×M₁₆	—	7	1	no	—
268	C₄×M₁₆	—	7	1	no	—
269	C₄×M₁₆	—	7	1	no	—
270	C₂×#97	—	7	1	no	—
271	C₂×C₄×C₈	—	7	1	no	—
272	#341	—	7	1	no	—
273	#341	—	7	1	no	—
274	#341	—	7	1	no	—
275	#341	—	7	1	no	—
276	#341	—	7	1	no	—
277	#341	—	7	1	no	—
278	#341	C₂×D₇	1	1	yes	characteristic
279	#341	C₂×D₇	1	1	yes	characteristic
280	C₂³×C₇	—	2	1	no	—
281	C₂³×C₇	—	2	1	no	—
282	C₂³×C₇	—	4	1	no	—
283	C₂³×C₇	—	4	1	no	—
284	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
285	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
286	C₂³×C₇	C₂²×Q₈	1	1	yes	characteristic
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	1	no	—
297	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
298	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
299	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
300	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
303	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
305	C₂×Dic₇	—	4	1	no	—
306	C₂×Dic₇	—	4	1	no	—
307	C₂×Dic₇	—	4	1	no	—
308	C₂×Dic₇	—	4	1	no	—
309	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
310	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
311	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
312	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
313	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
314	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
315	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
316	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
317	C₇×C₈	—	2	2	no	—
318	C₇×C₈	—	2	2	no	—
319	C₇×C₈	—	2	2	no	—
320	C₇×C₈	—	2	2	no	—
321	C₇×C₈	—	4	1	no	—
322	C₇×C₈	—	4	1	no	—
323	C₇⋊C₈	—	2	2	no	—
324	C₇⋊C₈	—	2	2	no	—
325	C₇⋊C₈	—	2	2	no	—
326	C₇⋊C₈	—	2	2	no	—
327	C₇⋊C₈	—	4	1	no	—
328	C₇⋊C₈	—	4	1	no	—
329	C₂³×C₄	C₂²×D₇	1	1	yes	characteristic
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	—	2	2	no	—
333	C₂×M₁₆	—	7	1	no	—
334	C₂×M₁₆	—	7	1	no	—
335	C₂×M₁₆	—	7	1	no	—
336	C₂×M₁₆	—	7	1	no	—
337	C₂×M₁₆	—	14	2	no	—
338	C₂×M₁₆	—	14	2	no	—
339	C₂×M₁₆	—	14	1	no	—
340	C₂×M₁₆	C₂²×D₇	1	1	yes	characteristic
341	C₂×M₁₆	C₂²×D₇	1	1	yes	characteristic
342	C₂×M₁₆	C₂²×D₇	1	1	yes	characteristic
343	C₂×M₁₆	C₂²×D₇	1	1	yes	characteristic
344	C₂²×C₈	—	2	1	no	—
345	C₂²×C₈	—	7	1	no	—
346	C₂²×C₈	—	7	1	no	—
347	C₂²×C₈	—	14	1	no	—
348	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
349	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
350	#117	—	7	1	no	—
351	#117	—	7	1	no	—
352	#117	—	7	1	no	—
353	#117	—	7	1	no	—
354	#117	—	7	1	no	—
355	#117	—	7	1	no	—
356	#117	—	7	1	no	—
357	#117	—	7	1	no	—
358	C₂×C₄⋊C₄	—	7	1	no	—
359	C₂×C₄⋊C₄	—	7	1	no	—
360	C₂×C₂²⋊C₄	—	7	1	no	—
361	C₂×C₂²⋊C₄	—	7	1	no	—
362	C₂×C₄²	—	7	1	no	—
363	C₂×C₄²	—	7	1	no	—
364	#108	—	2	2	no	—
365	#108	—	2	2	no	—
366	#108	—	14	2	no	—
367	#108	—	14	2	no	—
368	#108	—	14	2	no	—
369	#108	—	14	2	no	—
370	#108	—	14	2	no	—
371	#108	—	14	2	no	—
372	C₄⋊C₈	—	7	2	no	—
373	C₄⋊C₈	—	7	2	no	—
374	C₄⋊C₈	—	7	2	no	—
375	C₄⋊C₈	—	7	2	no	—
376	C₄⋊C₈	—	14	1	no	—
377	C₄⋊C₈	—	14	1	no	—
378	C₄⋊C₈	—	14	1	no	—
379	C₄⋊C₈	—	14	1	no	—
380	C₂²⋊C₈	—	2	1	no	—
381	C₂²⋊C₈	—	2	1	no	—
382	C₂²⋊C₈	—	7	2	no	—
383	C₂²⋊C₈	—	7	2	no	—
384	C₂²⋊C₈	—	14	1	no	—
385	C₂²⋊C₈	—	14	1	no	—
386	C₂²⋊C₈	C₄×D₇	1	2	yes	—
387	C₂²⋊C₈	C₄×D₇	1	2	yes	—
388	#97	—	7	2	no	—
389	#97	—	7	2	no	—
390	#97	—	14	1	no	—
391	#97	—	14	1	no	—
392	#97	—	14	1	no	—
393	#97	—	14	1	no	—
394	#97	—	14	1	no	—
395	#97	—	14	1	no	—
396	C₄×C₈	—	7	2	no	—
397	C₄×C₈	—	7	2	no	—
398	C₄×C₈	—	14	1	no	—
399	C₄×C₈	—	14	1	no	—
400	C₄×C₈	—	14	1	no	—
401	C₄×C₈	—	14	1	no	—
402	C₄×C₈	—	14	1	no	—
403	C₄×C₈	—	14	1	no	—
404	C₂²×C₇	—	2	1	no	—
405	C₂²×C₇	—	2	1	no	—
406	C₂²×C₇	—	2	1	no	—
407	C₂²×C₇	—	2	1	no	—
408	C₂²×C₇	—	2	1	no	—
409	C₂²×C₇	—	2	1	no	—
410	C₂²×C₇	—	2	1	no	—
411	C₂²×C₇	—	2	1	no	—
412	C₂²×C₇	—	8	1	no	—
413	C₂²×C₇	—	8	1	no	—
414	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
415	C₂²×C₇	#533	1	1	yes	characteristic
416	C₂²×C₇	#533	1	1	yes	characteristic
417	C₄×C₇	—	2	1	no	—
418	C₄×C₇	—	2	1	no	—
419	C₄×C₇	C₄×#41	1	1	yes	characteristic
420	C₄×C₇	C₄×#41	1	1	yes	characteristic
421	C₄×C₇	#525	1	1	yes	characteristic
422	C₄×C₇	#525	1	1	yes	characteristic
423	Dic₇	—	2	1	no	—
424	Dic₇	—	2	1	no	—
425	Dic₇	—	2	1	no	—
426	Dic₇	—	2	1	no	—
427	Dic₇	—	2	1	no	—
428	Dic₇	—	2	1	no	—
429	Dic₇	—	2	1	no	—
430	Dic₇	—	2	1	no	—
431	C₂⁴	Q₈×D₇	1	1	yes	characteristic
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	7	1	no	—
437	C₂²×C₄	—	7	1	no	—
438	C₂²×C₄	—	7	1	no	—
439	C₂²×C₄	—	7	1	no	—
440	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
441	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
442	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
443	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
444	C₂²×C₄	Q₈×D₇	1	1	yes	characteristic
445	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
446	M₁₆	—	2	4	no	—
447	M₁₆	—	2	1	no	—
448	M₁₆	—	2	1	no	—
449	M₁₆	—	2	1	no	—
450	M₁₆	—	2	1	no	—
451	M₁₆	—	2	1	no	—
452	M₁₆	—	2	1	no	—
453	M₁₆	—	7	2	no	—
454	M₁₆	—	7	2	no	—
455	M₁₆	—	14	4	no	—
456	M₁₆	—	14	1	no	—
457	M₁₆	—	14	1	no	—
458	M₁₆	—	14	1	no	—
459	M₁₆	—	14	1	no	—
460	M₁₆	—	14	1	no	—
461	M₁₆	—	14	1	no	—
462	M₁₆	#1159	1	2	yes	—
463	M₁₆	#1159	1	2	yes	—
464	C₂×C₈	—	2	4	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	7	2	no	—
474	C₂×C₈	—	7	2	no	—
475	C₂×C₈	—	14	4	no	—
476	C₂×C₈	—	14	1	no	—
477	C₂×C₈	—	14	1	no	—
478	C₂×C₈	—	14	1	no	—
479	C₂×C₈	—	14	1	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	C₂×C₄×D₇	1	2	yes	—
485	C₂×C₈	C₂×C₄×D₇	1	2	yes	—
486	C₄⋊C₄	—	7	1	no	—
487	C₄⋊C₄	—	7	1	no	—
488	C₄⋊C₄	—	7	1	no	—
489	C₄⋊C₄	—	7	1	no	—
490	C₄⋊C₄	—	7	1	no	—
491	C₄⋊C₄	—	7	1	no	—
492	C₄⋊C₄	—	7	1	no	—
493	C₄⋊C₄	—	7	1	no	—
494	C₂²⋊C₄	—	7	1	no	—
495	C₂²⋊C₄	—	7	1	no	—
496	C₂²⋊C₄	—	7	1	no	—
497	C₂²⋊C₄	—	7	1	no	—
498	C₂²⋊C₄	—	7	1	no	—
499	C₂²⋊C₄	—	7	1	no	—
500	C₂²⋊C₄	—	7	1	no	—
501	C₂²⋊C₄	—	7	1	no	—
502	C₄²	—	7	1	no	—
503	C₄²	—	7	1	no	—
504	C₄²	—	7	1	no	—
505	C₄²	—	7	1	no	—
506	C₄²	—	7	1	no	—
507	C₄²	—	7	1	no	—
508	C₄²	—	7	1	no	—
509	C₄²	—	7	1	no	—
510	C₂×C₇	—	2	1	no	—
511	C₂×C₇	—	2	1	no	—
512	C₂×C₇	—	4	1	no	—
513	C₂×C₇	—	4	1	no	—
514	C₂×C₇	#2296	1	1	yes	characteristic
515	C₂×C₇	#2916	1	1	yes	characteristic
516	C₂×C₇	#2916	1	1	yes	characteristic
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	4	1	no	—
520	C₂³	—	4	1	no	—
521	C₂³	D₇×C₄⋊C₄	1	1	yes	characteristic
522	C₂³	D₇×C₄⋊C₄	1	1	yes	characteristic
523	C₂³	C₂×Q₈×D₇	1	1	yes	characteristic
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	7	1	no	—
535	C₂×C₄	—	7	1	no	—
536	C₂×C₄	—	7	1	no	—
537	C₂×C₄	—	7	1	no	—
538	C₂×C₄	—	7	1	no	—
539	C₂×C₄	—	7	1	no	—
540	C₂×C₄	—	7	1	no	—
541	C₂×C₄	—	7	1	no	—
542	C₂×C₄	—	28	1	no	—
543	C₂×C₄	—	28	1	no	—
544	C₂×C₄	—	28	1	no	—
545	C₂×C₄	—	28	1	no	—
546	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
547	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
548	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
549	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
550	C₂×C₄	C₂×#1159	1	1	yes	characteristic
551	C₂×C₄	C₂×#1159	1	1	yes	characteristic
552	C₂×C₄	D₇×#41	1	1	yes	characteristic
553	C₂×C₄	D₇×#41	1	1	yes	characteristic
554	C₈	—	2	2	no	—
555	C₈	—	2	2	no	—
556	C₈	—	2	2	no	—
557	C₈	—	2	2	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	14	2	no	—
561	C₈	—	14	2	no	—
562	C₈	—	14	2	no	—
563	C₈	—	14	2	no	—
564	C₈	—	28	1	no	—
565	C₈	—	28	1	no	—
566	C₇	#21372	1	1	yes	characteristic, complemented, Sylow
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	8	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	C₂×D₇×C₄⋊C₄	1	1	yes	characteristic
578	C₂²	#90313	1	1	yes	characteristic
579	C₂²	#90313	1	1	yes	characteristic
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	14	1	no	—
583	C₄	—	14	1	no	—
584	C₄	—	14	1	no	—
585	C₄	—	14	1	no	—
586	C₄	—	14	1	no	—
587	C₄	—	14	1	no	—
588	C₄	—	14	1	no	—
589	C₄	—	14	1	no	—
590	C₄	C₄×#1159	1	1	yes	characteristic
591	C₄	C₄×#1159	1	1	yes	characteristic
592	C₄	#90277	1	1	yes	characteristic
593	C₄	#90347	1	1	yes	characteristic
594	C₂	—	2	1	no	—
595	C₂	—	2	1	no	—
596	C₂	—	4	1	no	—
597	C₂	—	4	1	no	—
598	C₂	#11731823	1	1	yes	characteristic
599	C₂	#11736697	1	1	yes	characteristic
600	C₂	#11736705	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	C₇×#1855	C₂
socle	C₂²×C₇	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₇	C₂×Q₈
cosocle	C₂²×C₄×C₇	C₂⁴
hypercenter	#1855	D₇
hypocenter	C₇	#21372
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1855

Complements

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

N	H ≅ G/N	type
6. #11728449	C₂	semidirect
7. #11728449	C₂	semidirect
8. #11728446	C₂	semidirect
9. Dic₇×#108	C₂	semidirect
12. #11726674	C₂	semidirect
13. #11726674	C₂	semidirect
14. #11726671	C₂	semidirect
15. #11726670	C₂	semidirect
566. C₇	#21372	semidirect

Maximal subgroups

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

subgroup	index
#11741192	2
#11736065	2
C₂×#89492	2
C₇×#1855	2
#11729755	2
#11728449	2
#11728446	2
Dic₇×#108	2
#11727738	2
#11727708	2
#11726674	2
#11726671	2
#11726670	2
#21372	7