Subgroups — #11743695

Order 896.

1132 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	#41×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#90515	C₂	1	1	yes	maximal, characteristic, complemented
4	#90497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#90371	C₂	1	1	yes	maximal, characteristic, complemented
7	#90362	C₂	1	1	yes	maximal, characteristic, complemented
8	#90341	C₂	1	2	yes	maximal, complemented
9	#90340	C₂	1	2	yes	maximal, complemented
10	#90333	C₂	1	1	yes	maximal, characteristic, complemented
11	#90313	C₂	1	1	yes	maximal, characteristic, complemented
12	#90307	C₂	1	1	yes	maximal, characteristic, complemented
13	#90292	C₂	1	2	yes	maximal, complemented
14	#90291	C₂	1	2	yes	maximal, complemented
15	#90291	C₂	1	1	yes	maximal, characteristic, complemented
16	#90278	C₂	1	2	yes	maximal, complemented
17	#90277	C₂	1	2	yes	maximal, complemented
18	#90232	C₂	1	1	yes	maximal, characteristic, complemented
19	#90230	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#1159	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#1159	C₂	1	1	yes	maximal, characteristic, complemented
22	#90186	C₂	1	2	yes	maximal, complemented
23	C₂×#6440	C₂	1	2	yes	maximal, complemented
24	C₂×C₇×#41	C₂²	1	1	yes	characteristic
25	C₂²×C₇×D₄	C₂²	1	1	yes	characteristic
26	C₂³×Dic₇	C₂²	1	2	yes	—
27	C₂×#1159	C₂²	1	1	yes	characteristic
28	C₂×#1159	C₂²	1	1	yes	characteristic
29	C₇×#124	C₂²	1	1	yes	characteristic
30	C₇×#123	C₂²	1	2	yes	—
31	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₇×#121	C₂²	1	2	yes	—
33	C₇×#121	C₂²	1	1	yes	characteristic
34	C₇×#120	C₂²	1	2	yes	—
35	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
36	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
38	#6516	C₂²	1	2	yes	—
39	C₂×C₂²⋊Dic₇	C₂²	1	2	yes	—
40	C₂×C₂²⋊Dic₇	C₂²	1	2	yes	—
41	#6509	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
44	#6507	C₂²	1	1	yes	characteristic, complemented
45	#6502	C₂²	1	2	yes	—
46	#6502	C₂²	1	2	yes	complemented
47	#6502	C₂²	1	2	yes	complemented
48	#6501	C₂²	1	1	yes	characteristic
49	#6499	C₂²	1	1	yes	characteristic
50	#6499	C₂²	1	2	yes	complemented
51	#6498	C₂²	1	2	yes	—
52	#6498	C₂²	1	2	yes	—
53	#6498	C₂²	1	2	yes	complemented
54	#6498	C₂²	1	2	yes	complemented
55	D₄×Dic₇	C₂²	1	1	yes	characteristic
56	D₄×Dic₇	C₂²	1	1	yes	characteristic
57	D₄×Dic₇	C₂²	1	1	yes	characteristic
58	D₄×Dic₇	C₂²	1	1	yes	characteristic
59	D₄×Dic₇	C₂²	1	1	yes	characteristic
60	D₄×Dic₇	C₂²	1	2	yes	—
61	D₄×Dic₇	C₂²	1	2	yes	—
62	D₄×Dic₇	C₂²	1	1	yes	characteristic
63	D₄×Dic₇	C₂²	1	2	yes	complemented
64	D₄×Dic₇	C₂²	1	2	yes	complemented
65	D₄×Dic₇	C₂²	1	2	yes	complemented
66	#6492	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
70	#6489	C₂²	1	2	yes	complemented
71	#6489	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
73	#6487	C₂²	1	1	yes	characteristic
74	#6487	C₂²	1	2	yes	complemented
75	#6487	C₂²	1	1	yes	characteristic, complemented
76	C₂×Dic₇⋊C₄	C₂²	1	2	yes	complemented
77	C₂×Dic₇⋊C₄	C₂²	1	2	yes	complemented
78	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic
79	C₂×C₄×Dic₇	C₂²	1	2	yes	complemented
80	C₂×C₄×Dic₇	C₂²	1	2	yes	complemented
81	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
82	#6461	C₂²	1	2	yes	complemented
83	#6455	C₂²	1	1	yes	characteristic, complemented
84	#6455	C₂²	1	1	yes	characteristic, complemented
85	#6453	C₂²	1	1	yes	characteristic, complemented
86	#6453	C₂²	1	2	yes	complemented
87	#6452	C₂²	1	2	yes	complemented
88	#6452	C₂²	1	2	yes	complemented
89	#6451	C₂²	1	1	yes	characteristic, complemented
90	#6450	C₂²	1	1	yes	characteristic, complemented
91	#6450	C₂²	1	1	yes	characteristic, complemented
92	#6450	C₂²	1	2	yes	complemented
93	#6449	C₂²	1	2	yes	—
94	#6448	C₂²	1	2	yes	complemented
95	#6446	C₂²	1	2	yes	complemented
96	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
97	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
98	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
100	#6442	C₂²	1	2	yes	complemented
101	#6442	C₂²	1	2	yes	complemented
102	#6442	C₂²	1	2	yes	complemented
103	#6442	C₂²	1	2	yes	complemented
104	#6442	C₂²	1	2	yes	complemented
105	#6441	C₂²	1	2	yes	—
106	#6441	C₂²	1	2	yes	complemented
107	#6441	C₂²	1	2	yes	complemented
108	#6441	C₂²	1	2	yes	complemented
109	#6440	C₂²	1	1	yes	characteristic
110	#6440	C₂²	1	2	yes	—
111	#6440	C₂²	1	2	yes	—
112	#6440	C₂²	1	2	yes	—
113	#6440	C₂²	1	2	yes	complemented
114	#6440	C₂²	1	2	yes	complemented
115	#6440	C₂²	1	2	yes	complemented
116	#6440	C₂²	1	2	yes	complemented
117	#6440	C₂²	1	2	yes	complemented
118	#6440	C₂²	1	1	yes	characteristic, complemented
119	C₄²×D₇	C₂²	1	1	yes	characteristic, complemented
120	#6433	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
123	#3475	—	7	1	no	maximal, Sylow
124	C₂⁴×C₇	C₂³	1	2	yes	—
125	C₇×#41	—	2	4	no	—
126	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
127	C₂×C₇×D₄	—	2	4	no	—
128	C₂×C₇×D₄	C₂³	1	2	yes	—
129	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
130	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
131	C₂×C₇×D₄	C₂³	1	2	yes	—
132	C₂×C₇×D₄	C₂³	1	2	yes	—
133	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₇	C₂³	1	2	yes	—
136	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
142	C₂²×Dic₇	—	2	8	no	—
143	C₂²×Dic₇	C₂³	1	2	yes	—
144	C₂²×Dic₇	C₂³	1	2	yes	—
145	C₂²×Dic₇	C₂³	1	2	yes	—
146	C₂²×Dic₇	C₂³	1	2	yes	—
147	C₂²×Dic₇	C₂³	1	1	yes	characteristic
148	C₂²×Dic₇	C₂³	1	2	yes	—
149	C₂²×Dic₇	C₂³	1	2	yes	—
150	C₂²×Dic₇	C₂³	1	1	yes	characteristic
151	C₂²×Dic₇	C₂³	1	2	yes	—
152	C₂²×Dic₇	C₂³	1	1	yes	characteristic
153	C₂²×Dic₇	C₂³	1	1	yes	characteristic
154	#1159	—	2	4	no	—
155	#1159	—	2	4	no	—
156	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
159	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
160	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
161	C₂×Dic₁₄	C₂³	1	2	yes	—
162	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₇×C₄⋊C₄	C₂³	1	2	yes	—
165	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₄²×C₇	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₇	C₂³	1	2	yes	—
175	C₂²⋊Dic₇	C₂³	1	2	yes	—
176	C₂²⋊Dic₇	C₂³	1	2	yes	—
177	C₂²⋊Dic₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₇	C₂³	1	2	yes	—
182	C₂²⋊Dic₇	C₂³	1	2	yes	—
183	C₂²⋊Dic₇	C₂³	1	2	yes	—
184	C₂²⋊Dic₇	C₂³	1	2	yes	—
185	C₂²⋊Dic₇	C₂³	1	2	yes	—
186	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₇	C₂³	1	2	yes	—
195	C₄⋊Dic₇	C₂³	1	2	yes	—
196	C₄⋊Dic₇	C₂³	1	2	yes	—
197	C₄⋊Dic₇	C₂³	1	2	yes	—
198	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
199	Dic₇⋊C₄	C₂³	1	2	yes	—
200	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
201	Dic₇⋊C₄	C₂³	1	2	yes	—
202	Dic₇⋊C₄	C₂³	1	2	yes	—
203	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
204	Dic₇⋊C₄	C₂³	1	2	yes	—
205	Dic₇⋊C₄	C₂³	1	2	yes	—
206	Dic₇⋊C₄	C₂³	1	2	yes	—
207	Dic₇⋊C₄	C₂³	1	2	yes	—
208	Dic₇⋊C₄	C₂³	1	2	yes	—
209	Dic₇⋊C₄	C₂³	1	2	yes	—
210	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₇⋊C₄	C₂³	1	2	yes	—
212	Dic₇⋊C₄	C₂³	1	2	yes	—
213	C₄×Dic₇	C₂³	1	2	yes	—
214	C₄×Dic₇	C₂³	1	1	yes	characteristic
215	C₄×Dic₇	C₂³	1	1	yes	characteristic
216	C₄×Dic₇	C₂³	1	1	yes	characteristic
217	C₄×Dic₇	C₂³	1	1	yes	characteristic
218	C₄×Dic₇	C₂³	1	1	yes	characteristic
219	C₄×Dic₇	C₂³	1	2	yes	—
220	C₄×Dic₇	C₂³	1	1	yes	characteristic
221	C₄×Dic₇	C₂³	1	2	yes	—
222	C₄×Dic₇	C₂³	1	2	yes	—
223	C₄×Dic₇	C₂³	1	2	yes	—
224	C₄×Dic₇	C₂³	1	2	yes	—
225	C₄×Dic₇	C₂³	1	1	yes	characteristic
226	C₄×Dic₇	C₂³	1	1	yes	characteristic
227	C₄×Dic₇	C₂³	1	1	yes	characteristic
228	#556	—	7	1	no	—
229	#555	—	7	1	no	—
230	#554	—	7	1	no	—
231	#553	—	7	2	no	—
232	#552	—	7	2	no	—
233	#552	—	7	1	no	—
234	#552	—	7	1	no	—
235	#551	—	7	2	no	—
236	#551	—	7	2	no	—
237	#547	—	7	1	no	—
238	#546	—	7	1	no	—
239	#546	D₇	1	1	yes	characteristic, complemented
240	#533	—	7	1	no	—
241	#529	—	7	1	no	—
242	#529	—	7	2	no	—
243	#529	—	7	2	no	—
244	#529	—	7	1	no	—
245	#525	—	7	2	no	—
246	C₄×#41	—	7	1	no	—
247	C₄×#41	—	7	1	no	—
248	C₄×#41	—	7	1	no	—
249	C₂×C₄×D₄	—	7	1	no	—
250	C₂×#117	—	7	2	no	—
251	C₂³×C₇	—	2	4	no	—
252	C₂³×C₇	—	2	4	no	—
253	C₂³×C₇	—	4	2	no	—
254	C₂³×C₇	C₂⁴	1	2	yes	—
255	C₂³×C₇	C₂⁴	1	1	yes	characteristic
256	C₂³×C₇	C₂⁴	1	1	yes	characteristic
257	C₂³×C₇	C₂⁴	1	2	yes	—
258	C₂²×D₇	C₂⁴	1	1	yes	characteristic
259	C₇×Q₈	—	2	2	no	—
260	C₇×D₄	—	2	2	no	—
261	C₇×D₄	—	2	4	no	—
262	C₇×D₄	—	2	4	no	—
263	C₇×D₄	—	2	2	no	—
264	C₇×D₄	—	4	2	no	—
265	C₇×D₄	#41	1	4	yes	complemented
266	C₂×C₄×C₇	—	2	4	no	—
267	C₂×C₄×C₇	—	2	2	no	—
268	C₂×C₄×C₇	—	2	2	no	—
269	C₂×C₄×C₇	—	4	2	no	—
270	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₇	C₂⁴	1	2	yes	—
273	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₇	C₂⁴	1	2	yes	—
275	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
277	C₂²⋊D₇	—	2	4	no	—
278	C₂²⋊D₇	—	2	2	no	—
279	C₂²⋊D₇	—	2	2	no	—
280	C₂²⋊D₇	—	4	2	no	—
281	C₂×Dic₇	—	2	4	no	—
282	C₂×Dic₇	—	2	4	no	—
283	C₂×Dic₇	—	2	2	no	—
284	C₂×Dic₇	—	2	4	no	—
285	C₂×Dic₇	—	2	4	no	—
286	C₂×Dic₇	—	2	4	no	—
287	C₂×Dic₇	—	2	4	no	—
288	C₂×Dic₇	—	4	1	no	—
289	C₂×Dic₇	—	4	2	no	—
290	C₂×Dic₇	—	4	1	no	—
291	C₂×Dic₇	#41	1	4	yes	complemented
292	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
293	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
294	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
295	C₂×Dic₇	C₂⁴	1	2	yes	—
296	C₂×Dic₇	C₂⁴	1	2	yes	—
297	C₂×Dic₇	C₂⁴	1	2	yes	—
298	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
299	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₇	C₂⁴	1	2	yes	—
301	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
302	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
303	C₄×D₇	—	2	2	no	—
304	C₄×D₇	—	2	2	no	—
305	C₄×D₇	—	4	1	no	—
306	Dic₁₄	—	2	2	no	—
307	Dic₁₄	—	2	2	no	—
308	Dic₁₄	—	4	2	no	—
309	C₂×#41	—	7	1	no	—
310	C₂×#41	—	7	1	no	—
311	C₂×#41	C₂×D₇	1	1	yes	characteristic
312	C₂²×D₄	C₂×D₇	1	1	yes	characteristic
313	C₂³×C₄	—	7	2	no	—
314	C₄⋊Q₈	—	7	1	no	—
315	C₄⋊Q₈	—	7	1	no	—
316	#126	—	7	2	no	—
317	#126	—	7	2	no	—
318	#126	—	7	2	no	—
319	#126	—	7	2	no	—
320	#126	—	7	2	no	—
321	#126	—	7	2	no	—
322	#125	—	7	2	no	—
323	#125	—	7	2	no	—
324	#125	—	7	1	no	—
325	#125	—	7	2	no	—
326	#125	—	7	1	no	—
327	#124	—	7	1	no	—
328	#124	—	7	2	no	—
329	#124	—	7	2	no	—
330	#124	C₂×D₇	1	1	yes	characteristic
331	#123	—	7	2	no	—
332	#123	—	7	2	no	—
333	#123	—	7	2	no	—
334	#123	—	7	2	no	—
335	#123	—	7	2	no	—
336	#123	—	7	2	no	—
337	#123	—	7	2	no	—
338	#123	C₂×D₇	1	2	yes	—
339	C₂²⋊Q₈	—	7	1	no	—
340	C₂²⋊Q₈	—	7	1	no	—
341	C₂²⋊Q₈	—	7	2	no	—
342	C₂²⋊Q₈	—	7	1	no	—
343	C₂²⋊Q₈	—	7	2	no	—
344	C₂²⋊Q₈	—	7	2	no	—
345	C₂²⋊Q₈	—	7	2	no	—
346	C₂²⋊Q₈	—	7	2	no	—
347	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
348	#121	—	7	2	no	—
349	#121	—	7	2	no	—
350	#121	—	7	2	no	—
351	#121	—	7	1	no	—
352	#121	C₂×D₇	1	2	yes	—
353	#121	C₂×D₇	1	1	yes	characteristic
354	#120	—	7	2	no	—
355	#120	C₂×D₇	1	2	yes	—
356	C₄×Q₈	—	7	1	no	—
357	C₄×Q₈	—	7	1	no	—
358	C₄×Q₈	—	7	1	no	—
359	C₄×Q₈	—	7	1	no	—
360	C₄×Q₈	—	7	2	no	—
361	C₄×Q₈	—	7	1	no	—
362	C₄×Q₈	—	7	1	no	—
363	C₄×D₄	—	7	1	no	—
364	C₄×D₄	—	7	1	no	—
365	C₄×D₄	—	7	2	no	—
366	C₄×D₄	—	7	1	no	—
367	C₄×D₄	—	7	2	no	—
368	C₄×D₄	—	7	1	no	—
369	C₄×D₄	—	7	2	no	—
370	C₄×D₄	—	7	1	no	—
371	C₄×D₄	—	7	1	no	—
372	C₄×D₄	—	7	2	no	—
373	C₄×D₄	—	7	2	no	—
374	C₄×D₄	—	7	1	no	—
375	C₄×D₄	—	7	1	no	—
376	C₄×D₄	—	7	2	no	—
377	C₄×D₄	—	7	2	no	—
378	C₄×D₄	—	7	1	no	—
379	C₄×D₄	—	7	1	no	—
380	C₄×D₄	—	7	2	no	—
381	C₄×D₄	C₂×D₇	1	1	yes	characteristic
382	C₄×D₄	C₂×D₇	1	1	yes	characteristic
383	#117	—	7	2	no	—
384	#117	—	7	1	no	—
385	#117	—	7	1	no	—
386	#117	—	7	1	no	—
387	#117	—	7	1	no	—
388	#117	—	7	2	no	—
389	#117	—	7	2	no	—
390	#117	—	7	2	no	—
391	#117	—	7	2	no	—
392	#117	—	7	2	no	—
393	#117	—	7	2	no	—
394	#117	—	7	2	no	—
395	#117	—	7	1	no	—
396	#117	—	7	2	no	—
397	C₂×C₄⋊C₄	—	7	2	no	—
398	C₂×C₄⋊C₄	—	7	2	no	—
399	C₂×C₄⋊C₄	—	7	1	no	—
400	C₂×C₂²⋊C₄	—	7	2	no	—
401	C₂×C₂²⋊C₄	—	7	2	no	—
402	C₂×C₂²⋊C₄	C₂×D₇	1	2	yes	—
403	C₂×C₄²	—	7	2	no	—
404	C₂×C₄²	—	7	2	no	—
405	C₂×C₄²	—	7	1	no	—
406	C₂×C₄²	—	7	1	no	—
407	C₂×C₄²	—	7	1	no	—
408	C₂²×C₇	—	2	2	no	—
409	C₂²×C₇	—	2	1	no	—
410	C₂²×C₇	—	2	2	no	—
411	C₂²×C₇	—	2	1	no	—
412	C₂²×C₇	—	2	2	no	—
413	C₂²×C₇	—	2	1	no	—
414	C₂²×C₇	—	2	1	no	—
415	C₂²×C₇	—	2	2	no	—
416	C₂²×C₇	—	2	1	no	—
417	C₂²×C₇	—	2	2	no	—
418	C₂²×C₇	—	4	8	no	—
419	C₂²×C₇	C₂×#41	1	4	yes	—
420	C₂²×C₇	C₂×#41	1	2	yes	—
421	C₂²×C₇	C₂⁵	1	1	yes	characteristic
422	C₂×D₇	—	2	1	no	—
423	C₂×D₇	—	2	1	no	—
424	C₂×D₇	—	2	1	no	—
425	C₄×C₇	—	2	1	no	—
426	C₄×C₇	—	2	1	no	—
427	C₄×C₇	—	2	1	no	—
428	C₄×C₇	—	2	2	no	—
429	C₄×C₇	—	2	2	no	—
430	C₄×C₇	—	2	1	no	—
431	C₄×C₇	C₂×#41	1	2	yes	—
432	Dic₇	—	2	2	no	—
433	Dic₇	—	2	1	no	—
434	Dic₇	—	2	1	no	—
435	Dic₇	—	2	2	no	—
436	Dic₇	—	2	2	no	—
437	Dic₇	—	2	1	no	—
438	Dic₇	—	2	2	no	—
439	Dic₇	—	2	1	no	—
440	Dic₇	—	2	1	no	—
441	Dic₇	C₂×#41	1	2	yes	—
442	Dic₇	C₂×#41	1	2	yes	—
443	C₂⁴	C₂²×D₇	1	2	yes	—
444	#41	—	2	4	no	—
445	#41	—	14	4	no	—
446	#41	—	14	4	no	—
447	C₂×Q₈	—	7	1	no	—
448	C₂×Q₈	—	7	1	no	—
449	C₂×Q₈	—	7	2	no	—
450	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	7	1	no	—
453	C₂×D₄	—	7	2	no	—
454	C₂×D₄	—	7	1	no	—
455	C₂×D₄	—	7	2	no	—
456	C₂×D₄	C₂²×D₇	1	2	yes	—
457	C₂×D₄	C₂²×D₇	1	2	yes	—
458	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
459	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
460	C₂×D₄	C₂²×D₇	1	2	yes	—
461	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
462	C₂²×C₄	—	7	1	no	—
463	C₂²×C₄	—	7	2	no	—
464	C₂²×C₄	—	7	2	no	—
465	C₂²×C₄	—	7	1	no	—
466	C₂²×C₄	—	7	2	no	—
467	C₂²×C₄	—	7	2	no	—
468	C₂²×C₄	—	7	2	no	—
469	C₂²×C₄	—	7	2	no	—
470	C₂²×C₄	—	7	1	no	—
471	C₂²×C₄	—	7	2	no	—
472	C₂²×C₄	—	7	1	no	—
473	C₂²×C₄	—	7	1	no	—
474	C₂²×C₄	—	7	1	no	—
475	C₂²×C₄	—	7	1	no	—
476	C₂²×C₄	—	14	8	no	—
477	C₂²×C₄	C₂²×D₇	1	2	yes	—
478	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
479	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
480	C₂²×C₄	C₂²×D₇	1	2	yes	—
481	C₄⋊C₄	—	7	1	no	—
482	C₄⋊C₄	—	7	1	no	—
483	C₄⋊C₄	—	7	2	no	—
484	C₄⋊C₄	—	7	2	no	—
485	C₄⋊C₄	—	7	2	no	—
486	C₄⋊C₄	—	7	2	no	—
487	C₄⋊C₄	—	7	2	no	—
488	C₄⋊C₄	—	7	2	no	—
489	C₄⋊C₄	—	7	1	no	—
490	C₄⋊C₄	—	7	2	no	—
491	C₄⋊C₄	—	7	2	no	—
492	C₄⋊C₄	—	7	1	no	—
493	C₄⋊C₄	—	7	2	no	—
494	C₄⋊C₄	—	7	2	no	—
495	C₄⋊C₄	—	7	2	no	—
496	C₄⋊C₄	—	7	1	no	—
497	C₄⋊C₄	—	7	1	no	—
498	C₄⋊C₄	—	7	2	no	—
499	C₄⋊C₄	—	7	1	no	—
500	C₄⋊C₄	—	7	1	no	—
501	C₄⋊C₄	—	7	2	no	—
502	C₄⋊C₄	—	7	2	no	—
503	C₄⋊C₄	—	7	2	no	—
504	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₇	1	2	yes	—
507	C₂²⋊C₄	—	7	1	no	—
508	C₂²⋊C₄	—	7	2	no	—
509	C₂²⋊C₄	—	7	2	no	—
510	C₂²⋊C₄	—	7	2	no	—
511	C₂²⋊C₄	—	7	2	no	—
512	C₂²⋊C₄	—	7	2	no	—
513	C₂²⋊C₄	—	7	2	no	—
514	C₂²⋊C₄	—	7	2	no	—
515	C₂²⋊C₄	—	7	2	no	—
516	C₂²⋊C₄	—	7	2	no	—
517	C₂²⋊C₄	—	7	1	no	—
518	C₂²⋊C₄	—	7	2	no	—
519	C₂²⋊C₄	—	7	2	no	—
520	C₂²⋊C₄	—	7	1	no	—
521	C₂²⋊C₄	—	7	2	no	—
522	C₂²⋊C₄	—	7	1	no	—
523	C₂²⋊C₄	—	7	2	no	—
524	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
525	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
529	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
530	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
531	C₄²	—	7	1	no	—
532	C₄²	—	7	1	no	—
533	C₄²	—	7	1	no	—
534	C₄²	—	7	2	no	—
535	C₄²	—	7	2	no	—
536	C₄²	—	7	1	no	—
537	C₄²	—	7	2	no	—
538	C₄²	—	7	2	no	—
539	C₄²	—	7	2	no	—
540	C₄²	—	7	1	no	—
541	C₄²	—	7	1	no	—
542	C₄²	—	7	2	no	—
543	C₄²	—	7	1	no	—
544	C₄²	—	7	1	no	—
545	C₄²	—	7	1	no	—
546	C₄²	C₂²×D₇	1	1	yes	characteristic
547	C₂×C₇	—	2	2	no	—
548	C₂×C₇	—	2	4	no	—
549	C₂×C₇	—	4	1	no	—
550	C₂×C₇	—	4	2	no	—
551	C₂×C₇	C₂²×#41	1	1	yes	characteristic
552	C₂×C₇	C₂²×#41	1	1	yes	characteristic
553	C₂×C₇	#585	1	1	yes	characteristic
554	D₇	—	4	1	no	—
555	C₂³	—	2	4	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	4	2	no	—
558	C₂³	—	7	1	no	—
559	C₂³	C₂³×D₇	1	2	yes	—
560	C₂³	C₂³×D₇	1	1	yes	characteristic
561	C₂³	C₂³×D₇	1	2	yes	—
562	C₂³	C₂³×D₇	1	1	yes	characteristic
563	Q₈	—	2	2	no	—
564	Q₈	—	14	2	no	—
565	Q₈	—	14	2	no	—
566	Q₈	—	28	2	no	—
567	D₄	—	2	4	no	—
568	D₄	—	2	4	no	—
569	D₄	—	2	2	no	—
570	D₄	—	2	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	14	2	no	—
573	D₄	—	14	4	no	—
574	D₄	—	14	2	no	—
575	D₄	—	28	2	no	—
576	D₄	#1159	1	4	yes	complemented
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	7	4	no	—
582	C₂×C₄	—	7	1	no	—
583	C₂×C₄	—	7	1	no	—
584	C₂×C₄	—	7	1	no	—
585	C₂×C₄	—	7	2	no	—
586	C₂×C₄	—	7	1	no	—
587	C₂×C₄	—	7	1	no	—
588	C₂×C₄	—	7	1	no	—
589	C₂×C₄	—	7	2	no	—
590	C₂×C₄	—	7	1	no	—
591	C₂×C₄	—	7	2	no	—
592	C₂×C₄	—	7	2	no	—
593	C₂×C₄	—	14	2	no	—
594	C₂×C₄	—	14	4	no	—
595	C₂×C₄	—	14	4	no	—
596	C₂×C₄	—	14	4	no	—
597	C₂×C₄	—	14	4	no	—
598	C₂×C₄	—	14	2	no	—
599	C₂×C₄	—	14	4	no	—
600	C₂×C₄	—	14	4	no	—
601	C₂×C₄	—	14	2	no	—
602	C₂×C₄	—	28	1	no	—
603	C₂×C₄	—	28	1	no	—
604	C₂×C₄	—	28	2	no	—
605	C₂×C₄	—	28	1	no	—
606	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₇	1	2	yes	—
609	C₂×C₄	C₂³×D₇	1	2	yes	—
610	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
613	C₇	#3475	1	1	yes	characteristic, complemented, Sylow
614	C₂²	—	2	1	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	4	8	no	—
625	C₂²	—	14	1	no	—
626	C₂²	—	14	1	no	—
627	C₂²	—	14	1	no	—
628	C₂²	C₂×#1159	1	4	yes	—
629	C₂²	D₇×#41	1	2	yes	—
630	C₂²	C₂⁴×D₇	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	7	2	no	—
638	C₄	—	7	2	no	—
639	C₄	—	14	1	no	—
640	C₄	—	14	2	no	—
641	C₄	—	14	2	no	—
642	C₄	—	14	2	no	—
643	C₄	—	14	1	no	—
644	C₄	—	14	1	no	—
645	C₄	—	14	1	no	—
646	C₄	—	14	2	no	—
647	C₄	—	14	1	no	—
648	C₄	C₂×#1159	1	2	yes	—
649	C₂	—	2	2	no	—
650	C₂	—	2	4	no	—
651	C₂	—	4	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	28	1	no	—
654	C₂	C₂²×#1159	1	1	yes	characteristic
655	C₂	C₂×D₇×#41	1	1	yes	characteristic
656	C₂	#90618	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#546	C₂
hypercenter	#546	D₇
hypocenter	C₇	#3475
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₇×#546	C₂	semidirect
2. #41×Dic₇	C₂	semidirect
3. #90515	C₂	semidirect
4. #90497	C₂	semidirect
5. C₂×D₄×Dic₇	C₂	semidirect
6. #90371	C₂	semidirect
7. #90362	C₂	semidirect
8. #90341	C₂	semidirect
9. #90340	C₂	semidirect
10. #90333	C₂	semidirect
11. #90313	C₂	semidirect
12. #90307	C₂	semidirect
13. #90292	C₂	semidirect
14. #90291	C₂	semidirect
15. #90291	C₂	semidirect
16. #90278	C₂	semidirect
17. #90277	C₂	semidirect
18. #90232	C₂	semidirect
19. #90230	C₂	semidirect
20. C₄×#1159	C₂	semidirect
21. C₄×#1159	C₂	semidirect
22. #90186	C₂	semidirect
23. C₂×#6440	C₂	semidirect
41. #6509	C₂²	semidirect
42. Q₈×Dic₇	C₂²	semidirect
43. Q₈×Dic₇	C₂²	semidirect
44. #6507	C₂²	semidirect
46. #6502	C₂²	semidirect
47. #6502	C₂²	semidirect
50. #6499	C₂²	semidirect
53. #6498	C₂²	semidirect
54. #6498	C₂²	semidirect
63. D₄×Dic₇	C₂²	semidirect
64. D₄×Dic₇	C₂²	semidirect
65. D₄×Dic₇	C₂²	semidirect
66. #6492	C₂²	semidirect
68. C₄×C₂²⋊D₇	C₂²	semidirect
69. C₄×C₂²⋊D₇	C₂²	semidirect
70. #6489	C₂²	semidirect
71. #6489	C₂²	semidirect
74. #6487	C₂²	semidirect
75. #6487	C₂²	semidirect
76. C₂×Dic₇⋊C₄	C₂²	semidirect
77. C₂×Dic₇⋊C₄	C₂²	semidirect
79. C₂×C₄×Dic₇	C₂²	semidirect
80. C₂×C₄×Dic₇	C₂²	semidirect
81. C₂×C₄×Dic₇	C₂²	semidirect
82. #6461	C₂²	semidirect
83. #6455	C₂²	semidirect
84. #6455	C₂²	semidirect
85. #6453	C₂²	semidirect
86. #6453	C₂²	semidirect
87. #6452	C₂²	semidirect
88. #6452	C₂²	semidirect
89. #6451	C₂²	semidirect
90. #6450	C₂²	semidirect
91. #6450	C₂²	semidirect
92. #6450	C₂²	semidirect
94. #6448	C₂²	semidirect
95. #6446	C₂²	semidirect
97. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
98. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
100. #6442	C₂²	semidirect
101. #6442	C₂²	semidirect
102. #6442	C₂²	semidirect
103. #6442	C₂²	semidirect
104. #6442	C₂²	semidirect
106. #6441	C₂²	semidirect
107. #6441	C₂²	semidirect
108. #6441	C₂²	semidirect
113. #6440	C₂²	semidirect
114. #6440	C₂²	semidirect
115. #6440	C₂²	semidirect
116. #6440	C₂²	semidirect
117. #6440	C₂²	semidirect
118. #6440	C₂²	semidirect
119. C₄²×D₇	C₂²	semidirect
120. #6433	C₂²	semidirect
121. C₄×Dic₁₄	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
239. #546	D₇	semidirect
265. C₇×D₄	#41	semidirect
291. C₂×Dic₇	#41	semidirect
576. D₄	#1159	semidirect
613. C₇	#3475	semidirect

Maximal subgroups

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

subgroup	index
C₇×#546	2
#41×Dic₇	2
#90515	2
#90497	2
C₂×D₄×Dic₇	2
#90371	2
#90362	2
#90341	2
#90340	2
#90333	2
#90313	2
#90307	2
#90292	2
#90291	2
#90278	2
#90277	2
#90232	2
#90230	2
C₄×#1159	2
#90186	2
C₂×#6440	2
#3475	7