Subgroups — #11742975

Order 896.

1124 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#520	C₂	1	1	yes	maximal, characteristic, complemented
2	#90520	C₂	1	1	yes	maximal, characteristic, complemented
3	#90515	C₂	1	1	yes	maximal, characteristic, complemented
4	#90273	C₂	1	1	yes	maximal, characteristic, complemented
5	#90270	C₂	1	1	yes	maximal, characteristic, complemented
6	#90269	C₂	1	1	yes	maximal, characteristic, complemented
7	#90259	C₂	1	1	yes	maximal, characteristic, complemented
8	#90255	C₂	1	2	yes	maximal, complemented
9	#90247	C₂	1	2	yes	maximal, complemented
10	#90245	C₂	1	1	yes	maximal, characteristic, complemented
11	#90243	C₂	1	2	yes	maximal, complemented
12	#90238	C₂	1	2	yes	maximal, complemented
13	#90237	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×D₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×Dic₁₄	C₂	1	1	yes	maximal, characteristic, complemented
16	#90225	C₂	1	1	yes	maximal, characteristic, complemented
17	#90222	C₂	1	2	yes	maximal, complemented
18	#90219	C₂	1	1	yes	maximal, characteristic, complemented
19	#90218	C₂	1	2	yes	maximal, complemented
20	#90206	C₂	1	2	yes	maximal, complemented
21	#90202	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#6459	C₂	1	2	yes	maximal, complemented
23	#90198	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#41	C₂²	1	1	yes	characteristic
25	C₂×#1159	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
27	C₂×#1157	C₂²	1	2	yes	complemented
28	C₂²×C₄×D₇	C₂²	1	2	yes	—
29	C₂²×Dic₁₄	C₂²	1	2	yes	complemented
30	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
33	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
34	C₄×C₇×D₄	C₂²	1	2	yes	complemented
35	C₄×C₇×D₄	C₂²	1	2	yes	complemented
36	C₇×#117	C₂²	1	2	yes	complemented
37	C₇×#117	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
40	#6510	C₂²	1	1	yes	characteristic
41	#6509	C₂²	1	1	yes	characteristic
42	#6509	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	#6500	C₂²	1	2	yes	—
47	#6498	C₂²	1	2	yes	complemented
48	D₄×Dic₇	C₂²	1	1	yes	characteristic
49	D₄×Dic₇	C₂²	1	1	yes	characteristic
50	#6493	C₂²	1	1	yes	characteristic
51	#6493	C₂²	1	2	yes	—
52	#6492	C₂²	1	2	yes	—
53	#6492	C₂²	1	2	yes	complemented
54	#6492	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊D₇	C₂²	1	2	yes	—
57	C₄×C₂²⋊D₇	C₂²	1	2	yes	—
58	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
60	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
61	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
62	#6487	C₂²	1	1	yes	characteristic, complemented
63	#6487	C₂²	1	2	yes	complemented
64	#6487	C₂²	1	2	yes	complemented
65	C₂×Dic₇⋊C₄	C₂²	1	2	yes	complemented
66	C₂×Dic₇⋊C₄	C₂²	1	2	yes	complemented
67	#6461	C₂²	1	1	yes	characteristic, complemented
68	#6461	C₂²	1	2	yes	complemented
69	#6461	C₂²	1	2	yes	complemented
70	#6460	C₂²	1	1	yes	characteristic
71	#6459	C₂²	1	1	yes	characteristic
72	#6459	C₂²	1	2	yes	—
73	#6459	C₂²	1	2	yes	—
74	#6459	C₂²	1	2	yes	—
75	#6459	C₂²	1	2	yes	complemented
76	#6459	C₂²	1	2	yes	complemented
77	#6459	C₂²	1	2	yes	complemented
78	#6459	C₂²	1	2	yes	complemented
79	#6459	C₂²	1	2	yes	complemented
80	#6458	C₂²	1	1	yes	characteristic
81	#6457	C₂²	1	1	yes	characteristic
82	#6457	C₂²	1	2	yes	complemented
83	#6457	C₂²	1	2	yes	complemented
84	#6456	C₂²	1	1	yes	characteristic
85	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
86	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
87	#6452	C₂²	1	2	yes	complemented
88	#6452	C₂²	1	2	yes	complemented
89	#6452	C₂²	1	1	yes	characteristic, complemented
90	#6451	C₂²	1	1	yes	characteristic, complemented
91	#6451	C₂²	1	1	yes	characteristic, complemented
92	#6450	C₂²	1	1	yes	characteristic, complemented
93	#6449	C₂²	1	2	yes	—
94	#6448	C₂²	1	1	yes	characteristic, complemented
95	#6448	C₂²	1	2	yes	complemented
96	#6447	C₂²	1	1	yes	characteristic
97	#6446	C₂²	1	1	yes	characteristic
98	#6446	C₂²	1	2	yes	complemented
99	#6445	C₂²	1	2	yes	—
100	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	—
101	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
102	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
103	#6442	C₂²	1	1	yes	characteristic, complemented
104	#6441	C₂²	1	2	yes	complemented
105	#6441	C₂²	1	2	yes	complemented
106	#6440	C₂²	1	2	yes	complemented
107	#6439	C₂²	1	2	yes	complemented
108	#6439	C₂²	1	2	yes	complemented
109	#6438	C₂²	1	1	yes	characteristic
110	#6438	C₂²	1	2	yes	complemented
111	C₄×D₂₈	C₂²	1	2	yes	—
112	C₄×D₂₈	C₂²	1	1	yes	characteristic
113	C₄×D₂₈	C₂²	1	1	yes	characteristic
114	#6435	C₂²	1	2	yes	—
115	#6435	C₂²	1	1	yes	characteristic, complemented
116	#6435	C₂²	1	2	yes	complemented
117	C₄²×D₇	C₂²	1	1	yes	characteristic
118	#6433	C₂²	1	2	yes	complemented
119	#6432	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₄	C₂²	1	2	yes	complemented
122	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
123	#3520	—	7	1	no	maximal, Sylow
124	C₂³×D₇	C₂³	1	2	yes	—
125	C₇×#41	—	2	4	no	—
126	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
127	C₂×C₇×D₄	C₂³	1	2	yes	—
128	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₇	C₂³	1	2	yes	—
130	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₇	C₂³	1	2	yes	—
132	C₂²×C₄×C₇	C₂³	1	2	yes	—
133	C₂²×C₄×C₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
139	C₂²×Dic₇	C₂³	1	2	yes	—
140	C₂²×Dic₇	C₂³	1	2	yes	—
141	C₂²×Dic₇	C₂³	1	2	yes	—
142	#1159	—	2	4	no	—
143	D₄×D₇	—	2	4	no	—
144	#1157	—	4	4	no	—
145	C₂×D₂₈	C₂³	1	1	yes	characteristic
146	C₂×D₂₈	C₂³	1	1	yes	characteristic
147	C₂×D₂₈	C₂³	1	2	yes	—
148	C₂×C₄×D₇	—	4	4	no	—
149	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
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×C₄×D₇	C₂³	1	2	yes	—
154	C₂×C₄×D₇	C₂³	1	2	yes	—
155	C₂×C₄×D₇	C₂³	1	2	yes	—
156	C₂×C₄×D₇	C₂³	1	2	yes	—
157	C₂×Dic₁₄	—	4	4	no	—
158	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
159	C₂×Dic₁₄	C₂³	1	2	yes	—
160	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
161	C₂×Dic₁₄	C₂³	1	2	yes	—
162	C₂×Dic₁₄	C₂³	1	2	yes	—
163	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₇×C₄⋊C₄	C₂³	1	2	yes	—
167	C₇×C₄⋊C₄	C₂³	1	2	yes	—
168	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₇×C₄⋊C₄	C₂³	1	2	yes	—
170	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₄²×C₇	C₂³	1	1	yes	characteristic
175	C₄²×C₇	C₂³	1	1	yes	characteristic
176	C₄²×C₇	C₂³	1	2	yes	—
177	C₄²×C₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₇	C₂³	1	2	yes	—
183	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
188	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
200	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₇	C₂³	1	2	yes	—
203	C₄⋊Dic₇	C₂³	1	2	yes	—
204	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
206	Dic₇⋊C₄	C₂³	1	2	yes	—
207	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₇⋊C₄	C₂³	1	2	yes	—
209	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
214	Dic₇⋊C₄	C₂³	1	2	yes	—
215	Dic₇⋊C₄	C₂³	1	2	yes	—
216	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
217	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₇⋊C₄	C₂³	1	2	yes	—
219	Dic₇⋊C₄	C₂³	1	2	yes	—
220	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
221	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
222	Dic₇⋊C₄	C₂³	1	2	yes	—
223	C₄×Dic₇	C₂³	1	1	yes	characteristic
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	C₄×Dic₇	C₂³	1	2	yes	—
229	#556	—	7	1	no	—
230	#554	—	7	1	no	—
231	#554	—	7	1	no	—
232	#552	—	7	2	no	—
233	#551	—	7	2	no	—
234	#551	—	7	2	no	—
235	D₄×Q₈	—	7	1	no	—
236	#548	—	7	2	no	—
237	#547	—	7	1	no	—
238	#547	—	7	1	no	—
239	#546	—	7	1	no	—
240	#546	—	7	1	no	—
241	#542	—	7	1	no	—
242	#542	—	7	1	no	—
243	#539	—	7	2	no	—
244	#539	—	7	2	no	—
245	#533	—	7	1	no	—
246	#529	—	7	1	no	—
247	#525	—	7	2	no	—
248	C₂×C₂²⋊Q₈	—	7	2	no	—
249	#520	—	7	1	no	—
250	#520	D₇	1	1	yes	characteristic, complemented
251	C₂×C₄×D₄	—	7	1	no	—
252	C₂³×C₇	C₂⁴	1	1	yes	characteristic
253	C₂³×C₇	C₂⁴	1	2	yes	—
254	C₂²×D₇	—	2	4	no	—
255	C₂²×D₇	—	2	4	no	—
256	C₂²×D₇	—	4	2	no	—
257	C₂²×D₇	C₂⁴	1	2	yes	—
258	C₂²×D₇	C₂⁴	1	1	yes	characteristic
259	C₂²×D₇	C₂⁴	1	1	yes	characteristic
260	C₇×Q₈	—	2	2	no	—
261	C₇×D₄	—	2	4	no	—
262	C₇×D₄	#41	1	4	yes	complemented
263	C₂×C₄×C₇	—	2	4	no	—
264	C₂×C₄×C₇	—	2	2	no	—
265	C₂×C₄×C₇	—	4	2	no	—
266	C₂×C₄×C₇	—	4	2	no	—
267	C₂×C₄×C₇	—	4	2	no	—
268	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₇	C₂⁴	1	2	yes	—
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	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	4	no	—
279	C₂²⋊D₇	—	2	2	no	—
280	C₂²⋊D₇	—	2	2	no	—
281	C₂²⋊D₇	—	4	2	no	—
282	C₂×Dic₇	—	2	4	no	—
283	C₂×Dic₇	—	2	4	no	—
284	C₂×Dic₇	—	4	2	no	—
285	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
290	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
292	C₂×Dic₇	C₂⁴	1	2	yes	—
293	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
294	D₂₈	—	2	2	no	—
295	D₂₈	—	2	2	no	—
296	D₂₈	—	4	2	no	—
297	C₄×D₇	—	2	2	no	—
298	C₄×D₇	—	2	2	no	—
299	C₄×D₇	—	2	2	no	—
300	C₄×D₇	—	2	2	no	—
301	C₄×D₇	—	2	4	no	—
302	C₄×D₇	—	4	2	no	—
303	C₄×D₇	—	4	2	no	—
304	C₄×D₇	—	4	2	no	—
305	Dic₁₄	—	2	2	no	—
306	Dic₁₄	—	2	2	no	—
307	Dic₁₄	—	2	4	no	—
308	Dic₁₄	—	4	2	no	—
309	Dic₁₄	—	4	2	no	—
310	C₂×#41	—	7	1	no	—
311	C₂×#41	—	7	2	no	—
312	C₂×#41	C₂×D₇	1	1	yes	characteristic
313	C₂²×Q₈	—	7	2	no	—
314	C₂²×D₄	—	7	1	no	—
315	C₂³×C₄	—	7	2	no	—
316	C₄⋊Q₈	—	7	1	no	—
317	C₄⋊Q₈	—	7	1	no	—
318	C₄⋊Q₈	—	7	1	no	—
319	C₄⋊Q₈	—	7	1	no	—
320	#126	—	7	1	no	—
321	#126	—	7	2	no	—
322	#126	—	7	2	no	—
323	#126	—	7	1	no	—
324	#126	—	7	2	no	—
325	#126	—	7	2	no	—
326	#125	—	7	1	no	—
327	#125	—	7	2	no	—
328	#125	—	7	2	no	—
329	#125	—	7	2	no	—
330	#124	—	7	1	no	—
331	#124	—	7	1	no	—
332	#124	—	7	2	no	—
333	#124	—	7	1	no	—
334	#124	—	7	2	no	—
335	#123	—	7	2	no	—
336	#123	—	7	2	no	—
337	#123	—	7	2	no	—
338	#123	—	7	2	no	—
339	#123	—	7	2	no	—
340	#123	—	7	1	no	—
341	#123	—	7	2	no	—
342	#123	—	7	2	no	—
343	#123	—	7	1	no	—
344	#123	—	7	2	no	—
345	C₂²⋊Q₈	—	7	1	no	—
346	C₂²⋊Q₈	—	7	1	no	—
347	C₂²⋊Q₈	—	7	2	no	—
348	C₂²⋊Q₈	—	7	2	no	—
349	C₂²⋊Q₈	—	7	1	no	—
350	C₂²⋊Q₈	—	7	1	no	—
351	C₂²⋊Q₈	—	7	2	no	—
352	C₂²⋊Q₈	—	7	2	no	—
353	C₂²⋊Q₈	—	7	2	no	—
354	C₂²⋊Q₈	—	7	2	no	—
355	C₂²⋊Q₈	—	7	2	no	—
356	C₂²⋊Q₈	—	7	2	no	—
357	C₂²⋊Q₈	—	7	2	no	—
358	C₂²⋊Q₈	—	7	1	no	—
359	C₂²⋊Q₈	—	7	2	no	—
360	C₂²⋊Q₈	—	7	2	no	—
361	C₂²⋊Q₈	—	7	2	no	—
362	#121	—	7	2	no	—
363	#121	—	7	2	no	—
364	#121	—	7	2	no	—
365	#121	—	7	1	no	—
366	#121	—	7	1	no	—
367	#121	—	7	1	no	—
368	#120	—	7	2	no	—
369	#120	—	7	2	no	—
370	C₄×Q₈	—	7	1	no	—
371	C₄×Q₈	—	7	1	no	—
372	C₄×Q₈	—	7	1	no	—
373	C₄×Q₈	—	7	2	no	—
374	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
375	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
376	C₄×D₄	—	7	1	no	—
377	C₄×D₄	—	7	1	no	—
378	C₄×D₄	—	7	2	no	—
379	C₄×D₄	—	7	2	no	—
380	C₄×D₄	—	7	2	no	—
381	C₄×D₄	—	7	1	no	—
382	C₄×D₄	—	7	1	no	—
383	C₄×D₄	—	7	1	no	—
384	C₄×D₄	—	7	2	no	—
385	C₄×D₄	—	7	2	no	—
386	C₄×D₄	—	7	1	no	—
387	C₄×D₄	—	7	2	no	—
388	C₄×D₄	—	7	1	no	—
389	C₄×D₄	C₂×D₇	1	1	yes	characteristic
390	C₄×D₄	C₂×D₇	1	1	yes	characteristic
391	C₄×D₄	C₂×D₇	1	2	yes	complemented
392	C₄×D₄	C₂×D₇	1	2	yes	complemented
393	#117	—	7	2	no	—
394	#117	—	7	1	no	—
395	#117	—	7	2	no	—
396	#117	—	7	2	no	—
397	#117	C₂×D₇	1	1	yes	characteristic, complemented
398	#117	C₂×D₇	1	2	yes	complemented
399	C₂×C₄⋊C₄	—	7	2	no	—
400	C₂×C₄⋊C₄	—	7	2	no	—
401	C₂×C₄⋊C₄	—	7	1	no	—
402	C₂×C₄⋊C₄	—	7	1	no	—
403	C₂×C₄⋊C₄	C₂×D₇	1	2	yes	complemented
404	C₂×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
405	C₂×C₂²⋊C₄	—	7	2	no	—
406	C₂×C₂²⋊C₄	—	7	2	no	—
407	C₂×C₂²⋊C₄	—	7	2	no	—
408	C₂×C₄²	—	7	1	no	—
409	C₂²×C₇	—	2	2	no	—
410	C₂²×C₇	—	2	2	no	—
411	C₂²×C₇	—	2	1	no	—
412	C₂²×C₇	—	2	1	no	—
413	C₂²×C₇	—	2	1	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	C₂×D₇	—	2	2	no	—
420	C₂×D₇	—	2	2	no	—
421	C₂×D₇	—	2	1	no	—
422	C₂×D₇	—	2	1	no	—
423	C₂×D₇	—	2	2	no	—
424	C₂×D₇	—	4	8	no	—
425	C₂×D₇	2₋¹⁺⁴	1	2	yes	—
426	C₄×C₇	—	2	1	no	—
427	C₄×C₇	—	2	2	no	—
428	C₄×C₇	—	2	1	no	—
429	C₄×C₇	—	2	2	no	—
430	C₄×C₇	—	2	1	no	—
431	C₄×C₇	—	2	2	no	—
432	C₄×C₇	—	2	1	no	—
433	C₄×C₇	—	2	1	no	—
434	C₄×C₇	C₂×#41	1	2	yes	—
435	Dic₇	—	2	2	no	—
436	Dic₇	—	2	1	no	—
437	Dic₇	—	2	1	no	—
438	Dic₇	—	2	1	no	—
439	Dic₇	—	2	2	no	—
440	Dic₇	—	2	2	no	—
441	Dic₇	—	2	1	no	—
442	Dic₇	—	2	1	no	—
443	Dic₇	H(5,𝔽₂)	1	2	yes	—
444	C₂⁴	—	7	2	no	—
445	#41	—	2	4	no	—
446	#41	—	14	4	no	—
447	#41	—	28	4	no	—
448	C₂×Q₈	—	7	1	no	—
449	C₂×Q₈	—	7	1	no	—
450	C₂×Q₈	—	7	2	no	—
451	C₂×Q₈	—	7	2	no	—
452	C₂×Q₈	—	7	2	no	—
453	C₂×Q₈	—	28	4	no	—
454	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
455	C₂×D₄	—	7	1	no	—
456	C₂×D₄	—	7	2	no	—
457	C₂×D₄	—	7	2	no	—
458	C₂×D₄	—	7	1	no	—
459	C₂×D₄	—	7	2	no	—
460	C₂×D₄	—	7	1	no	—
461	C₂×D₄	—	7	1	no	—
462	C₂×D₄	—	7	2	no	—
463	C₂×D₄	—	14	4	no	—
464	C₂×D₄	C₂²×D₇	1	2	yes	—
465	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
466	C₂²×C₄	—	7	2	no	—
467	C₂²×C₄	—	7	2	no	—
468	C₂²×C₄	—	7	2	no	—
469	C₂²×C₄	—	7	1	no	—
470	C₂²×C₄	—	7	1	no	—
471	C₂²×C₄	—	7	1	no	—
472	C₂²×C₄	—	7	1	no	—
473	C₂²×C₄	—	7	2	no	—
474	C₂²×C₄	—	7	2	no	—
475	C₂²×C₄	—	7	2	no	—
476	C₂²×C₄	—	7	2	no	—
477	C₂²×C₄	—	28	4	no	—
478	C₂²×C₄	C₂²×D₇	1	2	yes	—
479	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
480	C₂²×C₄	C₂²×D₇	1	2	yes	—
481	C₂²×C₄	C₂²×D₇	1	2	yes	—
482	C₂²×C₄	C₂²×D₇	1	2	yes	—
483	C₄⋊C₄	—	7	1	no	—
484	C₄⋊C₄	—	7	2	no	—
485	C₄⋊C₄	—	7	1	no	—
486	C₄⋊C₄	—	7	2	no	—
487	C₄⋊C₄	—	7	2	no	—
488	C₄⋊C₄	—	7	2	no	—
489	C₄⋊C₄	—	7	2	no	—
490	C₄⋊C₄	—	7	2	no	—
491	C₄⋊C₄	—	7	2	no	—
492	C₄⋊C₄	—	7	1	no	—
493	C₄⋊C₄	—	7	1	no	—
494	C₄⋊C₄	—	7	2	no	—
495	C₄⋊C₄	—	7	2	no	—
496	C₄⋊C₄	—	7	2	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	1	no	—
502	C₄⋊C₄	—	7	2	no	—
503	C₄⋊C₄	—	7	1	no	—
504	C₄⋊C₄	—	7	2	no	—
505	C₄⋊C₄	—	7	1	no	—
506	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×D₇	1	2	yes	—
509	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₇	1	2	yes	—
511	C₄⋊C₄	C₂²×D₇	1	2	yes	—
512	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
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	1	no	—
519	C₂²⋊C₄	—	7	1	no	—
520	C₂²⋊C₄	—	7	2	no	—
521	C₂²⋊C₄	—	7	2	no	—
522	C₂²⋊C₄	—	7	2	no	—
523	C₂²⋊C₄	—	7	2	no	—
524	C₂²⋊C₄	—	7	2	no	—
525	C₂²⋊C₄	—	7	2	no	—
526	C₂²⋊C₄	—	7	2	no	—
527	C₂²⋊C₄	—	7	2	no	—
528	C₂²⋊C₄	—	7	1	no	—
529	C₂²⋊C₄	—	7	1	no	—
530	C₂²⋊C₄	—	7	2	no	—
531	C₂²⋊C₄	—	7	2	no	—
532	C₂²⋊C₄	—	7	1	no	—
533	C₂²⋊C₄	—	7	2	no	—
534	C₂²⋊C₄	—	7	1	no	—
535	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
537	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
538	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
539	C₄²	—	7	1	no	—
540	C₄²	—	7	1	no	—
541	C₄²	—	7	1	no	—
542	C₄²	—	7	2	no	—
543	C₄²	—	7	2	no	—
544	C₄²	—	7	1	no	—
545	C₄²	C₂²×D₇	1	1	yes	characteristic
546	C₄²	C₂²×D₇	1	2	yes	—
547	C₄²	C₂²×D₇	1	2	yes	—
548	C₄²	C₂²×D₇	1	1	yes	characteristic
549	C₂×C₇	—	2	4	no	—
550	C₂×C₇	—	4	1	no	—
551	C₂×C₇	C₂²×#41	1	1	yes	characteristic
552	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
553	C₂×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
554	D₇	—	2	2	no	—
555	D₇	—	4	1	no	—
556	D₇	—	4	2	no	—
557	C₂³	—	7	1	no	—
558	C₂³	—	7	2	no	—
559	C₂³	—	7	1	no	—
560	C₂³	—	14	4	no	—
561	C₂³	—	14	4	no	—
562	C₂³	—	28	2	no	—
563	C₂³	C₂³×D₇	1	1	yes	characteristic
564	C₂³	C₂³×D₇	1	2	yes	—
565	Q₈	—	2	2	no	—
566	Q₈	—	14	2	no	—
567	Q₈	—	14	4	no	—
568	Q₈	—	14	2	no	—
569	Q₈	—	28	2	no	—
570	Q₈	—	28	2	no	—
571	D₄	—	2	4	no	—
572	D₄	—	14	2	no	—
573	D₄	—	14	2	no	—
574	D₄	—	14	2	no	—
575	D₄	—	14	4	no	—
576	D₄	—	14	4	no	—
577	D₄	—	14	2	no	—
578	D₄	—	28	2	no	—
579	D₄	—	28	2	no	—
580	D₄	#1157	1	4	yes	complemented
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	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	1	no	—
592	C₂×C₄	—	7	2	no	—
593	C₂×C₄	—	7	1	no	—
594	C₂×C₄	—	7	2	no	—
595	C₂×C₄	—	14	2	no	—
596	C₂×C₄	—	14	4	no	—
597	C₂×C₄	—	14	2	no	—
598	C₂×C₄	—	14	4	no	—
599	C₂×C₄	—	14	4	no	—
600	C₂×C₄	—	14	2	no	—
601	C₂×C₄	—	14	2	no	—
602	C₂×C₄	—	28	2	no	—
603	C₂×C₄	—	28	2	no	—
604	C₂×C₄	—	28	2	no	—
605	C₂×C₄	—	28	2	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	1	yes	characteristic
610	C₂×C₄	C₂³×D₇	1	2	yes	—
611	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₇	1	2	yes	—
613	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
615	C₇	#3520	1	1	yes	characteristic, complemented, Sylow
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	7	2	no	—
622	C₂²	—	14	1	no	—
623	C₂²	—	14	1	no	—
624	C₂²	—	14	1	no	—
625	C₂²	—	14	2	no	—
626	C₂²	—	14	2	no	—
627	C₂²	—	14	1	no	—
628	C₂²	—	14	1	no	—
629	C₂²	—	14	2	no	—
630	C₂²	—	28	8	no	—
631	C₂²	C₂×#1157	1	4	yes	—
632	C₂²	C₂⁴×D₇	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	1	no	—
641	C₄	—	7	2	no	—
642	C₄	—	14	1	no	—
643	C₄	—	14	1	no	—
644	C₄	—	14	2	no	—
645	C₄	—	14	2	no	—
646	C₄	—	14	2	no	—
647	C₄	—	14	1	no	—
648	C₄	—	14	1	no	—
649	C₄	—	14	1	no	—
650	C₄	C₂×#1157	1	2	yes	—
651	C₂	—	2	4	no	—
652	C₂	—	4	1	no	—
653	C₂	—	14	2	no	—
654	C₂	—	28	2	no	—
655	C₂	—	28	1	no	—
656	C₂	C₂²×#1157	1	1	yes	characteristic
657	C₂	D₇×H(5,𝔽₂)	1	1	yes	characteristic
658	C₂	D₇×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#520	C₂
hypercenter	#520	D₇
hypocenter	C₇	#3520
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #520

Complements

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

N	H ≅ G/N	type
1. C₇×#520	C₂	semidirect
2. #90520	C₂	semidirect
3. #90515	C₂	semidirect
4. #90273	C₂	semidirect
5. #90270	C₂	semidirect
6. #90269	C₂	semidirect
7. #90259	C₂	semidirect
8. #90255	C₂	semidirect
9. #90247	C₂	semidirect
10. #90245	C₂	semidirect
11. #90243	C₂	semidirect
12. #90238	C₂	semidirect
13. #90237	C₂	semidirect
14. C₄×D₄×D₇	C₂	semidirect
15. D₄×Dic₁₄	C₂	semidirect
16. #90225	C₂	semidirect
17. #90222	C₂	semidirect
18. #90219	C₂	semidirect
19. #90218	C₂	semidirect
20. #90206	C₂	semidirect
21. #90202	C₂	semidirect
22. C₂×#6459	C₂	semidirect
23. #90198	C₂	semidirect
27. C₂×#1157	C₂²	semidirect
29. C₂²×Dic₁₄	C₂²	semidirect
30. C₄×C₇×Q₈	C₂²	semidirect
31. C₄×C₇×Q₈	C₂²	semidirect
34. C₄×C₇×D₄	C₂²	semidirect
35. C₄×C₇×D₄	C₂²	semidirect
36. C₇×#117	C₂²	semidirect
37. C₇×#117	C₂²	semidirect
38. C₂×C₇×C₄⋊C₄	C₂²	semidirect
39. C₂×C₇×C₄⋊C₄	C₂²	semidirect
42. #6509	C₂²	semidirect
43. #6507	C₂²	semidirect
45. #6502	C₂²	semidirect
47. #6498	C₂²	semidirect
53. #6492	C₂²	semidirect
54. #6492	C₂²	semidirect
58. C₄×C₂²⋊D₇	C₂²	semidirect
59. C₄×C₂²⋊D₇	C₂²	semidirect
62. #6487	C₂²	semidirect
63. #6487	C₂²	semidirect
64. #6487	C₂²	semidirect
65. C₂×Dic₇⋊C₄	C₂²	semidirect
66. C₂×Dic₇⋊C₄	C₂²	semidirect
67. #6461	C₂²	semidirect
68. #6461	C₂²	semidirect
69. #6461	C₂²	semidirect
75. #6459	C₂²	semidirect
76. #6459	C₂²	semidirect
77. #6459	C₂²	semidirect
78. #6459	C₂²	semidirect
79. #6459	C₂²	semidirect
82. #6457	C₂²	semidirect
83. #6457	C₂²	semidirect
86. D₇×C₄⋊C₄	C₂²	semidirect
87. #6452	C₂²	semidirect
88. #6452	C₂²	semidirect
89. #6452	C₂²	semidirect
90. #6451	C₂²	semidirect
91. #6451	C₂²	semidirect
92. #6450	C₂²	semidirect
94. #6448	C₂²	semidirect
95. #6448	C₂²	semidirect
98. #6446	C₂²	semidirect
101. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
103. #6442	C₂²	semidirect
104. #6441	C₂²	semidirect
105. #6441	C₂²	semidirect
106. #6440	C₂²	semidirect
107. #6439	C₂²	semidirect
108. #6439	C₂²	semidirect
110. #6438	C₂²	semidirect
115. #6435	C₂²	semidirect
116. #6435	C₂²	semidirect
118. #6433	C₂²	semidirect
119. #6432	C₂²	semidirect
120. C₄×Dic₁₄	C₂²	semidirect
121. C₄×Dic₁₄	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
250. #520	D₇	semidirect
262. C₇×D₄	#41	semidirect
374. C₄×Q₈	C₂×D₇	semidirect
375. C₄×Q₈	C₂×D₇	semidirect
391. C₄×D₄	C₂×D₇	semidirect
392. C₄×D₄	C₂×D₇	semidirect
397. #117	C₂×D₇	semidirect
398. #117	C₂×D₇	semidirect
403. C₂×C₄⋊C₄	C₂×D₇	semidirect
404. C₂×C₄⋊C₄	C₂×D₇	semidirect
580. D₄	#1157	semidirect
615. C₇	#3520	semidirect

Maximal subgroups

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

subgroup	index
C₇×#520	2
#90520	2
#90515	2
#90273	2
#90270	2
#90269	2
#90259	2
#90255	2
#90247	2
#90245	2
#90243	2
#90238	2
#90237	2
C₄×D₄×D₇	2
D₄×Dic₁₄	2
#90225	2
#90222	2
#90219	2
#90218	2
#90206	2
#90202	2
C₂×#6459	2
#90198	2
#3520	7