Subgroups — #11743711

Order 896.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 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	#90518	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	#90489	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	#90356	C₂	1	2	yes	maximal, complemented
9	#90341	C₂	1	2	yes	maximal, complemented
10	#90332	C₂	1	1	yes	maximal, characteristic, complemented
11	#90316	C₂	1	1	yes	maximal, characteristic, complemented
12	#90309	C₂	1	1	yes	maximal, characteristic, complemented
13	#90294	C₂	1	1	yes	maximal, characteristic, complemented
14	#90292	C₂	1	2	yes	maximal, complemented
15	#90291	C₂	1	2	yes	maximal, complemented
16	#90284	C₂	1	2	yes	maximal, complemented
17	#90278	C₂	1	2	yes	maximal, complemented
18	#90248	C₂	1	1	yes	maximal, characteristic, complemented
19	#90232	C₂	1	1	yes	maximal, characteristic, complemented
20	#90230	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×#6442	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	C₂×#1159	C₂²	1	1	yes	characteristic
27	C₇×#124	C₂²	1	1	yes	characteristic
28	C₇×#123	C₂²	1	2	yes	—
29	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₇×#121	C₂²	1	2	yes	—
31	C₇×#121	C₂²	1	1	yes	characteristic
32	C₇×#120	C₂²	1	2	yes	—
33	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
34	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
36	#6516	C₂²	1	2	yes	—
37	C₂×C₂²⋊Dic₇	C₂²	1	2	yes	—
38	C₂×C₂²⋊Dic₇	C₂²	1	2	yes	—
39	C₂×C₂²⋊Dic₇	C₂²	1	2	yes	—
40	#6509	C₂²	1	1	yes	characteristic, complemented
41	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
43	#6507	C₂²	1	1	yes	characteristic, complemented
44	#6502	C₂²	1	2	yes	—
45	#6502	C₂²	1	2	yes	complemented
46	#6502	C₂²	1	2	yes	complemented
47	#6501	C₂²	1	1	yes	characteristic
48	#6501	C₂²	1	1	yes	characteristic
49	#6499	C₂²	1	1	yes	characteristic
50	#6499	C₂²	1	1	yes	characteristic
51	#6499	C₂²	1	2	yes	complemented
52	#6498	C₂²	1	2	yes	—
53	#6498	C₂²	1	2	yes	—
54	#6498	C₂²	1	2	yes	complemented
55	#6498	C₂²	1	2	yes	complemented
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	1	yes	characteristic
71	#6489	C₂²	1	1	yes	characteristic
72	#6489	C₂²	1	2	yes	complemented
73	#6489	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₄⋊Dic₇	C₂²	1	2	yes	complemented
75	C₂×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
76	#6487	C₂²	1	1	yes	characteristic
77	#6487	C₂²	1	2	yes	complemented
78	#6487	C₂²	1	1	yes	characteristic, complemented
79	C₂×Dic₇⋊C₄	C₂²	1	2	yes	complemented
80	C₂×Dic₇⋊C₄	C₂²	1	2	yes	complemented
81	C₂×C₄×Dic₇	C₂²	1	2	yes	complemented
82	#6461	C₂²	1	2	yes	complemented
83	#6460	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	1	yes	characteristic, complemented
87	#6453	C₂²	1	2	yes	complemented
88	#6452	C₂²	1	2	yes	complemented
89	#6452	C₂²	1	2	yes	complemented
90	#6451	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	complemented
94	#6448	C₂²	1	2	yes	—
95	#6446	C₂²	1	1	yes	characteristic
96	#6446	C₂²	1	2	yes	complemented
97	#6446	C₂²	1	1	yes	characteristic, complemented
98	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
100	#6442	C₂²	1	1	yes	characteristic
101	#6442	C₂²	1	2	yes	—
102	#6442	C₂²	1	2	yes	—
103	#6442	C₂²	1	2	yes	—
104	#6442	C₂²	1	2	yes	—
105	#6442	C₂²	1	2	yes	complemented
106	#6442	C₂²	1	2	yes	complemented
107	#6442	C₂²	1	2	yes	complemented
108	#6442	C₂²	1	2	yes	complemented
109	#6442	C₂²	1	1	yes	characteristic, complemented
110	#6442	C₂²	1	2	yes	complemented
111	#6441	C₂²	1	2	yes	complemented
112	#6441	C₂²	1	2	yes	complemented
113	#6441	C₂²	1	2	yes	complemented
114	#6441	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	2	yes	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	#3521	—	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	2	yes	—
131	C₂×C₇×D₄	C₂³	1	2	yes	—
132	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
133	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₇	C₂³	1	2	yes	—
135	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
142	C₂²×Dic₇	C₂³	1	2	yes	—
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	2	yes	—
148	C₂²×Dic₇	C₂³	1	2	yes	—
149	#1159	—	2	4	no	—
150	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
153	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
154	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
155	C₂×Dic₁₄	C₂³	1	2	yes	—
156	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₇×C₄⋊C₄	C₂³	1	2	yes	—
158	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
160	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₄²×C₇	C₂³	1	1	yes	characteristic
167	C₂²⋊Dic₇	C₂³	1	2	yes	—
168	C₂²⋊Dic₇	C₂³	1	2	yes	—
169	C₂²⋊Dic₇	C₂³	1	2	yes	—
170	C₂²⋊Dic₇	C₂³	1	2	yes	—
171	C₂²⋊Dic₇	C₂³	1	2	yes	—
172	C₂²⋊Dic₇	C₂³	1	2	yes	—
173	C₂²⋊Dic₇	C₂³	1	2	yes	—
174	C₂²⋊Dic₇	C₂³	1	2	yes	—
175	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
184	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
188	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₇	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	2	yes	—
194	C₄⋊Dic₇	C₂³	1	2	yes	—
195	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₇	C₂³	1	2	yes	—
197	C₄⋊Dic₇	C₂³	1	2	yes	—
198	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
200	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
201	Dic₇⋊C₄	C₂³	1	2	yes	—
202	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
203	Dic₇⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
211	Dic₇⋊C₄	C₂³	1	2	yes	—
212	Dic₇⋊C₄	C₂³	1	2	yes	—
213	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
215	C₄×Dic₇	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
226	#556	—	7	1	no	—
227	#556	—	7	1	no	—
228	#554	—	7	1	no	—
229	#553	—	7	2	no	—
230	#553	—	7	1	no	—
231	#552	—	7	2	no	—
232	#552	—	7	1	no	—
233	#551	—	7	2	no	—
234	#551	—	7	2	no	—
235	#547	—	7	1	no	—
236	#546	—	7	1	no	—
237	#546	D₇	1	1	yes	characteristic, complemented
238	#542	—	7	1	no	—
239	#541	—	7	1	no	—
240	#539	—	7	2	no	—
241	#538	—	7	2	no	—
242	#529	—	7	1	no	—
243	#529	—	7	2	no	—
244	#529	—	7	1	no	—
245	C₂×#126	—	7	2	no	—
246	#520	—	7	1	no	—
247	#518	—	7	1	no	—
248	C₄×#41	—	7	1	no	—
249	C₂³×C₇	—	2	4	no	—
250	C₂³×C₇	—	4	2	no	—
251	C₂³×C₇	—	4	2	no	—
252	C₂³×C₇	C₂⁴	1	1	yes	characteristic
253	C₂³×C₇	C₂⁴	1	2	yes	—
254	C₂³×C₇	C₂⁴	1	1	yes	characteristic
255	C₂³×C₇	C₂⁴	1	2	yes	—
256	C₂²×D₇	C₂⁴	1	1	yes	characteristic
257	C₇×Q₈	—	2	2	no	—
258	C₇×D₄	—	2	4	no	—
259	C₇×D₄	—	2	4	no	—
260	C₇×D₄	—	2	2	no	—
261	C₇×D₄	—	4	1	no	—
262	C₇×D₄	—	4	2	no	—
263	C₇×D₄	#41	1	4	yes	—
264	C₂×C₄×C₇	—	2	4	no	—
265	C₂×C₄×C₇	—	2	2	no	—
266	C₂×C₄×C₇	—	2	2	no	—
267	C₂×C₄×C₇	—	4	2	no	—
268	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₇	C₂⁴	1	2	yes	—
270	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₇	C₂⁴	1	2	yes	—
272	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
275	C₂²⋊D₇	—	2	4	no	—
276	C₂²⋊D₇	—	4	1	no	—
277	C₂²⋊D₇	—	4	2	no	—
278	C₂²⋊D₇	—	4	1	no	—
279	C₂×Dic₇	—	2	4	no	—
280	C₂×Dic₇	—	4	2	no	—
281	C₂×Dic₇	—	4	2	no	—
282	C₂×Dic₇	—	4	2	no	—
283	C₂×Dic₇	—	4	2	no	—
284	C₂×Dic₇	—	4	2	no	—
285	C₂×Dic₇	—	4	2	no	—
286	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₇	C₂⁴	1	2	yes	—
289	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
290	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₇	C₂⁴	1	2	yes	—
292	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
293	C₂×Dic₇	C₂⁴	1	2	yes	—
294	C₂×Dic₇	C₂⁴	1	2	yes	—
295	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
297	C₄×D₇	—	2	2	no	—
298	C₄×D₇	—	4	1	no	—
299	C₄×D₇	—	4	1	no	—
300	Dic₁₄	—	2	2	no	—
301	Dic₁₄	—	4	2	no	—
302	Dic₁₄	—	4	1	no	—
303	C₂×#41	—	7	1	no	—
304	C₂×#41	C₂×D₇	1	1	yes	characteristic
305	C₂²×D₄	C₂×D₇	1	1	yes	characteristic
306	C₄⋊Q₈	—	7	1	no	—
307	C₄⋊Q₈	—	7	1	no	—
308	#126	—	7	2	no	—
309	#126	—	7	1	no	—
310	#126	—	7	2	no	—
311	#126	—	7	2	no	—
312	#126	—	7	2	no	—
313	#126	—	7	2	no	—
314	#126	—	7	2	no	—
315	#126	—	7	2	no	—
316	#126	—	7	2	no	—
317	#126	—	7	1	no	—
318	#126	—	7	2	no	—
319	#126	—	7	2	no	—
320	#125	—	7	2	no	—
321	#125	—	7	1	no	—
322	#125	—	7	2	no	—
323	#125	—	7	2	no	—
324	#125	—	7	1	no	—
325	#125	—	7	1	no	—
326	#124	—	7	2	no	—
327	#124	—	7	1	no	—
328	#124	—	7	1	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	1	no	—
338	#123	—	7	1	no	—
339	#123	—	7	2	no	—
340	#123	C₂×D₇	1	2	yes	—
341	C₂²⋊Q₈	—	7	1	no	—
342	C₂²⋊Q₈	—	7	2	no	—
343	C₂²⋊Q₈	—	7	1	no	—
344	C₂²⋊Q₈	—	7	1	no	—
345	C₂²⋊Q₈	—	7	1	no	—
346	C₂²⋊Q₈	—	7	2	no	—
347	C₂²⋊Q₈	—	7	2	no	—
348	C₂²⋊Q₈	—	7	2	no	—
349	C₂²⋊Q₈	—	7	2	no	—
350	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
351	#121	—	7	1	no	—
352	#121	—	7	1	no	—
353	#121	—	7	2	no	—
354	#121	—	7	2	no	—
355	#121	—	7	2	no	—
356	#121	C₂×D₇	1	2	yes	—
357	#121	C₂×D₇	1	1	yes	characteristic
358	#120	—	7	2	no	—
359	#120	C₂×D₇	1	2	yes	—
360	C₄×Q₈	—	7	1	no	—
361	C₄×Q₈	—	7	1	no	—
362	C₄×Q₈	—	7	1	no	—
363	C₄×Q₈	—	7	2	no	—
364	C₄×Q₈	—	7	1	no	—
365	C₄×Q₈	—	7	1	no	—
366	C₄×D₄	—	7	1	no	—
367	C₄×D₄	—	7	2	no	—
368	C₄×D₄	—	7	1	no	—
369	C₄×D₄	—	7	1	no	—
370	C₄×D₄	—	7	2	no	—
371	C₄×D₄	—	7	1	no	—
372	C₄×D₄	—	7	2	no	—
373	C₄×D₄	—	7	1	no	—
374	C₄×D₄	—	7	2	no	—
375	C₄×D₄	—	7	2	no	—
376	C₄×D₄	—	7	2	no	—
377	C₄×D₄	—	7	1	no	—
378	C₄×D₄	—	7	1	no	—
379	C₄×D₄	—	7	2	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	1	no	—
384	#117	—	7	1	no	—
385	#117	—	7	1	no	—
386	#117	—	7	2	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	C₂×C₄⋊C₄	—	7	2	no	—
393	C₂×C₄⋊C₄	—	7	1	no	—
394	C₂×C₄⋊C₄	—	7	2	no	—
395	C₂×C₄⋊C₄	—	7	2	no	—
396	C₂×C₂²⋊C₄	—	7	2	no	—
397	C₂×C₂²⋊C₄	—	7	2	no	—
398	C₂×C₂²⋊C₄	—	7	2	no	—
399	C₂×C₂²⋊C₄	C₂×D₇	1	2	yes	—
400	C₂×C₄²	—	7	2	no	—
401	C₂×C₄²	—	7	1	no	—
402	C₂²×C₇	—	2	2	no	—
403	C₂²×C₇	—	2	2	no	—
404	C₂²×C₇	—	2	1	no	—
405	C₂²×C₇	—	2	1	no	—
406	C₂²×C₇	—	2	2	no	—
407	C₂²×C₇	—	2	1	no	—
408	C₂²×C₇	—	2	2	no	—
409	C₂²×C₇	—	2	2	no	—
410	C₂²×C₇	—	2	1	no	—
411	C₂²×C₇	—	2	1	no	—
412	C₂²×C₇	—	2	1	no	—
413	C₂²×C₇	—	8	4	no	—
414	C₂²×C₇	C₂×#41	1	4	yes	—
415	C₂²×C₇	C₂⁵	1	1	yes	characteristic
416	C₂×D₇	—	2	1	no	—
417	C₂×D₇	—	2	1	no	—
418	C₂×D₇	—	2	1	no	—
419	C₄×C₇	—	2	1	no	—
420	C₄×C₇	—	2	1	no	—
421	C₄×C₇	—	2	2	no	—
422	C₄×C₇	—	2	1	no	—
423	C₄×C₇	—	2	2	no	—
424	C₄×C₇	—	2	1	no	—
425	C₄×C₇	C₂×#41	1	2	yes	—
426	Dic₇	—	2	2	no	—
427	Dic₇	—	2	1	no	—
428	Dic₇	—	2	1	no	—
429	Dic₇	—	2	1	no	—
430	Dic₇	—	2	1	no	—
431	Dic₇	—	2	2	no	—
432	Dic₇	—	2	1	no	—
433	Dic₇	—	2	1	no	—
434	Dic₇	—	2	2	no	—
435	Dic₇	—	2	2	no	—
436	Dic₇	—	2	1	no	—
437	C₂⁴	C₂²×D₇	1	2	yes	—
438	#41	—	2	4	no	—
439	#41	—	14	4	no	—
440	C₂×Q₈	—	7	1	no	—
441	C₂×Q₈	—	7	1	no	—
442	C₂×Q₈	—	7	2	no	—
443	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	7	2	no	—
446	C₂×D₄	—	7	1	no	—
447	C₂×D₄	—	7	2	no	—
448	C₂×D₄	—	7	1	no	—
449	C₂×D₄	C₂²×D₇	1	2	yes	—
450	C₂×D₄	C₂²×D₇	1	2	yes	—
451	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
452	C₂×D₄	C₂²×D₇	1	2	yes	—
453	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
454	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
455	C₂²×C₄	—	7	2	no	—
456	C₂²×C₄	—	7	2	no	—
457	C₂²×C₄	—	7	2	no	—
458	C₂²×C₄	—	7	2	no	—
459	C₂²×C₄	—	7	2	no	—
460	C₂²×C₄	—	7	2	no	—
461	C₂²×C₄	—	7	2	no	—
462	C₂²×C₄	—	7	1	no	—
463	C₂²×C₄	—	7	1	no	—
464	C₂²×C₄	—	7	1	no	—
465	C₂²×C₄	C₂²×D₇	1	2	yes	—
466	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
467	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
468	C₂²×C₄	C₂²×D₇	1	2	yes	—
469	C₄⋊C₄	—	7	1	no	—
470	C₄⋊C₄	—	7	1	no	—
471	C₄⋊C₄	—	7	2	no	—
472	C₄⋊C₄	—	7	2	no	—
473	C₄⋊C₄	—	7	2	no	—
474	C₄⋊C₄	—	7	2	no	—
475	C₄⋊C₄	—	7	2	no	—
476	C₄⋊C₄	—	7	2	no	—
477	C₄⋊C₄	—	7	1	no	—
478	C₄⋊C₄	—	7	2	no	—
479	C₄⋊C₄	—	7	2	no	—
480	C₄⋊C₄	—	7	2	no	—
481	C₄⋊C₄	—	7	2	no	—
482	C₄⋊C₄	—	7	2	no	—
483	C₄⋊C₄	—	7	1	no	—
484	C₄⋊C₄	—	7	1	no	—
485	C₄⋊C₄	—	7	2	no	—
486	C₄⋊C₄	—	7	1	no	—
487	C₄⋊C₄	—	7	1	no	—
488	C₄⋊C₄	—	7	2	no	—
489	C₄⋊C₄	—	7	2	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	C₄⋊C₄	—	7	2	no	—
495	C₄⋊C₄	—	7	1	no	—
496	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₇	1	2	yes	—
499	C₂²⋊C₄	—	7	1	no	—
500	C₂²⋊C₄	—	7	2	no	—
501	C₂²⋊C₄	—	7	1	no	—
502	C₂²⋊C₄	—	7	1	no	—
503	C₂²⋊C₄	—	7	2	no	—
504	C₂²⋊C₄	—	7	2	no	—
505	C₂²⋊C₄	—	7	2	no	—
506	C₂²⋊C₄	—	7	2	no	—
507	C₂²⋊C₄	—	7	2	no	—
508	C₂²⋊C₄	—	7	2	no	—
509	C₂²⋊C₄	—	7	2	no	—
510	C₂²⋊C₄	—	7	2	no	—
511	C₂²⋊C₄	—	7	1	no	—
512	C₂²⋊C₄	—	7	1	no	—
513	C₂²⋊C₄	—	7	2	no	—
514	C₂²⋊C₄	—	7	2	no	—
515	C₂²⋊C₄	—	7	1	no	—
516	C₂²⋊C₄	—	7	2	no	—
517	C₂²⋊C₄	—	7	1	no	—
518	C₂²⋊C₄	—	7	2	no	—
519	C₂²⋊C₄	—	7	1	no	—
520	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
521	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
522	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
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	C₄²	—	7	1	no	—
528	C₄²	—	7	1	no	—
529	C₄²	—	7	1	no	—
530	C₄²	—	7	2	no	—
531	C₄²	—	7	2	no	—
532	C₄²	—	7	2	no	—
533	C₄²	—	7	2	no	—
534	C₄²	—	7	2	no	—
535	C₄²	—	7	2	no	—
536	C₄²	—	7	1	no	—
537	C₄²	—	7	1	no	—
538	C₄²	C₂²×D₇	1	1	yes	characteristic
539	C₂×C₇	—	2	4	no	—
540	C₂×C₇	—	4	1	no	—
541	C₂×C₇	—	4	2	no	—
542	C₂×C₇	—	4	1	no	—
543	C₂×C₇	C₂²×#41	1	1	yes	characteristic
544	C₂×C₇	#585	1	1	yes	characteristic
545	C₂×C₇	#585	1	1	yes	characteristic
546	D₇	—	4	1	no	—
547	C₂³	—	2	4	no	—
548	C₂³	—	4	2	no	—
549	C₂³	—	4	2	no	—
550	C₂³	—	7	1	no	—
551	C₂³	C₂³×D₇	1	1	yes	characteristic
552	C₂³	C₂³×D₇	1	2	yes	—
553	C₂³	C₂³×D₇	1	1	yes	characteristic
554	C₂³	C₂³×D₇	1	2	yes	—
555	Q₈	—	2	2	no	—
556	Q₈	—	14	2	no	—
557	Q₈	—	28	1	no	—
558	Q₈	—	28	2	no	—
559	D₄	—	2	4	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	2	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	2	no	—
564	D₄	—	14	4	no	—
565	D₄	—	28	2	no	—
566	D₄	—	28	1	no	—
567	D₄	—	28	1	no	—
568	D₄	#1159	1	4	yes	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	7	1	no	—
574	C₂×C₄	—	7	1	no	—
575	C₂×C₄	—	7	2	no	—
576	C₂×C₄	—	7	1	no	—
577	C₂×C₄	—	7	1	no	—
578	C₂×C₄	—	7	2	no	—
579	C₂×C₄	—	7	1	no	—
580	C₂×C₄	—	7	1	no	—
581	C₂×C₄	—	7	2	no	—
582	C₂×C₄	—	7	2	no	—
583	C₂×C₄	—	7	1	no	—
584	C₂×C₄	—	14	4	no	—
585	C₂×C₄	—	14	2	no	—
586	C₂×C₄	—	28	1	no	—
587	C₂×C₄	—	28	1	no	—
588	C₂×C₄	—	28	2	no	—
589	C₂×C₄	—	28	2	no	—
590	C₂×C₄	—	28	2	no	—
591	C₂×C₄	—	28	2	no	—
592	C₂×C₄	—	28	2	no	—
593	C₂×C₄	—	28	2	no	—
594	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₇	1	2	yes	—
596	C₂×C₄	C₂³×D₇	1	2	yes	—
597	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
601	C₇	#3521	1	1	yes	characteristic, complemented, Sylow
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	8	4	no	—
614	C₂²	—	14	1	no	—
615	C₂²	—	14	1	no	—
616	C₂²	—	14	1	no	—
617	C₂²	C₂×#1159	1	4	yes	—
618	C₂²	C₂⁴×D₇	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	2	no	—
625	C₄	—	14	1	no	—
626	C₄	—	14	2	no	—
627	C₄	—	14	1	no	—
628	C₄	—	14	2	no	—
629	C₄	—	14	2	no	—
630	C₄	—	14	1	no	—
631	C₄	—	14	1	no	—
632	C₄	—	14	1	no	—
633	C₄	—	14	1	no	—
634	C₄	—	14	2	no	—
635	C₄	—	14	1	no	—
636	C₄	C₂×#1159	1	2	yes	—
637	C₂	—	2	4	no	—
638	C₂	—	4	1	no	—
639	C₂	—	4	2	no	—
640	C₂	—	4	1	no	—
641	C₂	—	28	1	no	—
642	C₂	C₂²×#1159	1	1	yes	characteristic
643	C₂	#90616	1	1	yes	characteristic
644	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	#3521
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. #90518	C₂	semidirect
3. #90515	C₂	semidirect
4. #90497	C₂	semidirect
5. #90489	C₂	semidirect
6. #90371	C₂	semidirect
7. #90362	C₂	semidirect
8. #90356	C₂	semidirect
9. #90341	C₂	semidirect
10. #90332	C₂	semidirect
11. #90316	C₂	semidirect
12. #90309	C₂	semidirect
13. #90294	C₂	semidirect
14. #90292	C₂	semidirect
15. #90291	C₂	semidirect
16. #90284	C₂	semidirect
17. #90278	C₂	semidirect
18. #90248	C₂	semidirect
19. #90232	C₂	semidirect
20. #90230	C₂	semidirect
21. C₄×#1159	C₂	semidirect
22. #90186	C₂	semidirect
23. C₂×#6442	C₂	semidirect
40. #6509	C₂²	semidirect
41. Q₈×Dic₇	C₂²	semidirect
42. Q₈×Dic₇	C₂²	semidirect
43. #6507	C₂²	semidirect
45. #6502	C₂²	semidirect
46. #6502	C₂²	semidirect
51. #6499	C₂²	semidirect
54. #6498	C₂²	semidirect
55. #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
72. #6489	C₂²	semidirect
73. #6489	C₂²	semidirect
74. C₂×C₄⋊Dic₇	C₂²	semidirect
75. C₂×C₄⋊Dic₇	C₂²	semidirect
77. #6487	C₂²	semidirect
78. #6487	C₂²	semidirect
79. C₂×Dic₇⋊C₄	C₂²	semidirect
80. C₂×Dic₇⋊C₄	C₂²	semidirect
81. C₂×C₄×Dic₇	C₂²	semidirect
82. #6461	C₂²	semidirect
83. #6460	C₂²	semidirect
84. #6455	C₂²	semidirect
85. #6453	C₂²	semidirect
86. #6453	C₂²	semidirect
87. #6453	C₂²	semidirect
88. #6452	C₂²	semidirect
89. #6452	C₂²	semidirect
90. #6451	C₂²	semidirect
91. #6450	C₂²	semidirect
92. #6450	C₂²	semidirect
93. #6449	C₂²	semidirect
96. #6446	C₂²	semidirect
97. #6446	C₂²	semidirect
98. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
105. #6442	C₂²	semidirect
106. #6442	C₂²	semidirect
107. #6442	C₂²	semidirect
108. #6442	C₂²	semidirect
109. #6442	C₂²	semidirect
110. #6442	C₂²	semidirect
111. #6441	C₂²	semidirect
112. #6441	C₂²	semidirect
113. #6441	C₂²	semidirect
114. #6441	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
237. #546	D₇	semidirect
601. C₇	#3521	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
#90518	2
#90515	2
#90497	2
#90489	2
#90371	2
#90362	2
#90356	2
#90341	2
#90332	2
#90316	2
#90309	2
#90294	2
#90292	2
#90291	2
#90284	2
#90278	2
#90248	2
#90232	2
#90230	2
C₄×#1159	2
#90186	2
C₂×#6442	2
#3521	7