Subgroups — #11744050

Order 896.

1022 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#90421	C₂	1	1	yes	maximal, characteristic, complemented
3	#90420	C₂	1	1	yes	maximal, characteristic, complemented
4	#90399	C₂	1	2	yes	maximal, complemented
5	#90397	C₂	1	2	yes	maximal, complemented
6	#90396	C₂	1	2	yes	maximal, complemented
7	#90392	C₂	1	2	yes	maximal, complemented
8	#90370	C₂	1	2	yes	maximal, complemented
9	#90360	C₂	1	2	yes	maximal, complemented
10	#90330	C₂	1	1	yes	maximal, characteristic, complemented
11	#90326	C₂	1	1	yes	maximal, characteristic, complemented
12	#90319	C₂	1	1	yes	maximal, characteristic, complemented
13	D₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#90272	C₂	1	2	yes	maximal, complemented
15	#90272	C₂	1	1	yes	maximal, characteristic, complemented
16	#90269	C₂	1	2	yes	maximal, complemented
17	#90263	C₂	1	1	yes	maximal, characteristic, complemented
18	#90238	C₂	1	1	yes	maximal, characteristic
19	#90232	C₂	1	1	yes	maximal, characteristic, complemented
20	#90224	C₂	1	1	yes	maximal, characteristic, complemented
21	#90220	C₂	1	1	yes	maximal, characteristic, complemented
22	#90214	C₂	1	1	yes	maximal, characteristic, complemented
23	D₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₇	C₂²	1	1	yes	characteristic
25	C₂×#1157	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₇	C₂²	1	1	yes	characteristic
27	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₇×#126	C₂²	1	2	yes	—
29	C₇×#126	C₂²	1	2	yes	complemented
30	C₇×#124	C₂²	1	2	yes	—
31	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₄×C₇×Q₈	C₂²	1	2	yes	complemented
35	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
36	C₇×#117	C₂²	1	1	yes	characteristic
37	C₇×#117	C₂²	1	1	yes	characteristic, complemented
38	#6509	C₂²	1	2	yes	—
39	#6509	C₂²	1	2	yes	—
40	#6509	C₂²	1	1	yes	characteristic
41	#6509	C₂²	1	2	yes	complemented
42	#6509	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
44	#6507	C₂²	1	2	yes	complemented
45	#6502	C₂²	1	1	yes	characteristic
46	#6500	C₂²	1	1	yes	characteristic
47	#6498	C₂²	1	2	yes	—
48	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
50	#6489	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
52	#6487	C₂²	1	1	yes	characteristic
53	#6487	C₂²	1	1	yes	characteristic, complemented
54	#6460	C₂²	1	2	yes	—
55	#6460	C₂²	1	1	yes	characteristic
56	#6460	C₂²	1	1	yes	characteristic, complemented
57	#6459	C₂²	1	2	yes	—
58	#6459	C₂²	1	2	yes	—
59	#6459	C₂²	1	1	yes	characteristic
60	#6457	C₂²	1	2	yes	—
61	#6457	C₂²	1	2	yes	—
62	#6457	C₂²	1	1	yes	characteristic
63	#6456	C₂²	1	2	yes	—
64	#6455	C₂²	1	2	yes	—
65	#6455	C₂²	1	1	yes	characteristic
66	#6455	C₂²	1	1	yes	characteristic
67	#6455	C₂²	1	2	yes	complemented
68	#6455	C₂²	1	1	yes	characteristic, complemented
69	D₇×C₄⋊C₄	C₂²	1	2	yes	—
70	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
73	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
74	#6453	C₂²	1	2	yes	complemented
75	#6453	C₂²	1	1	yes	characteristic, complemented
76	#6452	C₂²	1	2	yes	complemented
77	#6452	C₂²	1	2	yes	complemented
78	#6452	C₂²	1	2	yes	complemented
79	#6452	C₂²	1	2	yes	complemented
80	#6452	C₂²	1	2	yes	complemented
81	#6451	C₂²	1	2	yes	complemented
82	#6451	C₂²	1	1	yes	characteristic, complemented
83	#6450	C₂²	1	2	yes	complemented
84	#6450	C₂²	1	1	yes	characteristic, complemented
85	#6448	C₂²	1	2	yes	—
86	#6448	C₂²	1	2	yes	complemented
87	#6447	C₂²	1	1	yes	characteristic
88	#6446	C₂²	1	2	yes	—
89	#6446	C₂²	1	2	yes	—
90	#6446	C₂²	1	2	yes	—
91	#6446	C₂²	1	1	yes	characteristic
92	#6445	C₂²	1	1	yes	characteristic
93	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	—
94	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	—
95	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
96	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
97	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
98	#6442	C₂²	1	2	yes	—
99	#6442	C₂²	1	2	yes	—
100	#6442	C₂²	1	2	yes	—
101	#6442	C₂²	1	2	yes	complemented
102	#6441	C₂²	1	1	yes	characteristic
103	#6441	C₂²	1	2	yes	—
104	#6441	C₂²	1	2	yes	complemented
105	#6440	C₂²	1	2	yes	—
106	#6440	C₂²	1	2	yes	complemented
107	#6439	C₂²	1	2	yes	complemented
108	#6439	C₂²	1	2	yes	complemented
109	C₄×D₂₈	C₂²	1	2	yes	—
110	C₄×D₂₈	C₂²	1	1	yes	characteristic
111	#6435	C₂²	1	2	yes	—
112	#6435	C₂²	1	2	yes	—
113	#6435	C₂²	1	2	yes	—
114	#6435	C₂²	1	2	yes	—
115	#6435	C₂²	1	1	yes	characteristic
116	C₄²×D₇	C₂²	1	2	yes	—
117	#6433	C₂²	1	2	yes	complemented
118	#6433	C₂²	1	1	yes	characteristic, complemented
119	C₄×Dic₁₄	C₂²	1	2	yes	complemented
120	C₄×Dic₁₄	C₂²	1	2	yes	complemented
121	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₄	C₂²	1	2	yes	complemented
123	#3495	—	7	1	no	maximal, Sylow
124	C₂³×D₇	C₂³	1	1	yes	characteristic
125	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
126	C₂×C₇×Q₈	C₂³	1	2	yes	—
127	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
134	C₂²×Dic₇	C₂³	1	1	yes	characteristic
135	C₂²×Dic₇	C₂³	1	2	yes	—
136	Q₈×D₇	—	2	4	no	—
137	#1157	—	2	4	no	—
138	C₂×D₂₈	C₂³	1	1	yes	characteristic
139	C₂×D₂₈	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₇	—	2	4	no	—
141	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₇	C₂³	1	2	yes	—
143	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₇	C₂³	1	2	yes	—
145	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₇	C₂³	1	2	yes	—
148	C₂×C₄×D₇	C₂³	1	2	yes	—
149	C₂×C₄×D₇	C₂³	1	2	yes	—
150	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
151	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
152	C₂×Dic₁₄	C₂³	1	2	yes	—
153	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
154	C₂×Dic₁₄	C₂³	1	2	yes	—
155	C₇×C₄⋊C₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₇×C₄⋊C₄	C₂³	1	2	yes	—
161	C₇×C₄⋊C₄	C₂³	1	2	yes	—
162	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	C₄²×C₇	C₂³	1	2	yes	—
170	C₄²×C₇	C₂³	1	1	yes	characteristic
171	C₄²×C₇	C₂³	1	2	yes	—
172	C₄²×C₇	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	2	yes	—
177	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
178	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
181	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
182	(C₂×D₇)⋊C₄	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	1	yes	characteristic
186	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₇	C₂³	1	2	yes	—
192	C₄⋊Dic₇	C₂³	1	2	yes	—
193	C₄⋊Dic₇	C₂³	1	2	yes	—
194	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₇	C₂³	1	2	yes	—
196	C₄⋊Dic₇	C₂³	1	2	yes	—
197	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
200	Dic₇⋊C₄	C₂³	1	2	yes	—
201	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
215	Dic₇⋊C₄	C₂³	1	2	yes	—
216	Dic₇⋊C₄	C₂³	1	2	yes	—
217	Dic₇⋊C₄	C₂³	1	2	yes	—
218	C₄×Dic₇	C₂³	1	2	yes	—
219	C₄×Dic₇	C₂³	1	2	yes	—
220	C₄×Dic₇	C₂³	1	2	yes	—
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	#556	—	7	1	no	—
227	#556	D₇	1	1	yes	characteristic, complemented
228	#554	—	7	1	no	—
229	#554	—	7	1	no	—
230	#552	—	7	2	no	—
231	#552	—	7	1	no	—
232	#552	—	7	1	no	—
233	#552	—	7	2	no	—
234	#552	—	7	1	no	—
235	#552	—	7	1	no	—
236	#551	—	7	2	no	—
237	#551	—	7	2	no	—
238	#544	—	7	1	no	—
239	#542	—	7	2	no	—
240	#541	—	7	2	no	—
241	#536	—	7	1	no	—
242	#533	—	7	2	no	—
243	#529	—	7	2	no	—
244	#525	—	7	1	no	—
245	C₂×C₂²⋊Q₈	—	7	1	no	—
246	#520	—	7	1	no	—
247	#519	—	7	1	no	—
248	C₂×#117	—	7	1	no	—
249	C₂³×C₇	C₂⁴	1	1	yes	characteristic
250	C₂³×C₇	C₂⁴	1	1	yes	characteristic
251	C₂²×D₇	—	2	2	no	—
252	C₂²×D₇	—	2	2	no	—
253	C₂²×D₇	—	4	1	no	—
254	C₂²×D₇	C₂⁴	1	1	yes	characteristic
255	C₂²×D₇	C₂⁴	1	1	yes	characteristic
256	C₂²×D₇	C₂⁴	1	1	yes	characteristic
257	C₇×Q₈	—	2	2	no	—
258	C₇×Q₈	—	4	2	no	—
259	C₇×D₄	—	4	1	no	—
260	C₂×C₄×C₇	—	2	2	no	—
261	C₂×C₄×C₇	—	2	2	no	—
262	C₂×C₄×C₇	C₂⁴	1	2	yes	—
263	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₇	C₂⁴	1	2	yes	—
266	C₂×C₄×C₇	C₂⁴	1	2	yes	—
267	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₇	—	2	2	no	—
272	C₂²⋊D₇	—	2	2	no	—
273	C₂²⋊D₇	—	2	2	no	—
274	C₂²⋊D₇	—	4	1	no	—
275	C₂×Dic₇	—	2	2	no	—
276	C₂×Dic₇	—	4	2	no	—
277	C₂×Dic₇	C₂⁴	1	2	yes	—
278	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₇	C₂⁴	1	2	yes	—
281	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₇	C₂⁴	1	2	yes	—
283	C₂×Dic₇	C₂⁴	1	2	yes	—
284	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
286	D₂₈	—	2	2	no	—
287	D₂₈	—	2	2	no	—
288	C₄×D₇	—	2	2	no	—
289	C₄×D₇	—	2	4	no	—
290	C₄×D₇	—	2	4	no	—
291	C₄×D₇	—	2	2	no	—
292	C₄×D₇	—	2	2	no	—
293	C₄×D₇	—	2	2	no	—
294	C₄×D₇	—	4	2	no	—
295	C₄×D₇	—	4	2	no	—
296	C₄×D₇	—	4	2	no	—
297	C₄×D₇	#41	1	4	yes	—
298	Dic₁₄	—	2	2	no	—
299	Dic₁₄	—	2	2	no	—
300	Dic₁₄	—	2	4	no	—
301	Dic₁₄	—	4	2	no	—
302	C₂×#41	—	7	1	no	—
303	C₂²×Q₈	—	7	1	no	—
304	C₂³×C₄	—	7	1	no	—
305	C₄⋊Q₈	—	7	2	no	—
306	C₄⋊Q₈	—	7	2	no	—
307	C₄⋊Q₈	—	7	1	no	—
308	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
309	#126	—	7	2	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	C₂×D₇	1	2	yes	—
316	#126	C₂×D₇	1	2	yes	complemented
317	#125	—	7	2	no	—
318	#125	—	7	2	no	—
319	#125	—	7	2	no	—
320	#125	—	7	2	no	—
321	#125	—	7	2	no	—
322	#125	—	7	2	no	—
323	#125	—	7	1	no	—
324	#125	—	7	2	no	—
325	#125	—	7	1	no	—
326	#124	—	7	2	no	—
327	#124	—	7	2	no	—
328	#124	C₂×D₇	1	2	yes	—
329	#123	—	7	2	no	—
330	#123	—	7	1	no	—
331	#123	—	7	2	no	—
332	#123	—	7	2	no	—
333	#123	—	7	1	no	—
334	#123	—	7	2	no	—
335	#123	—	7	2	no	—
336	#123	—	7	2	no	—
337	C₂²⋊Q₈	—	7	1	no	—
338	C₂²⋊Q₈	—	7	2	no	—
339	C₂²⋊Q₈	—	7	1	no	—
340	C₂²⋊Q₈	—	7	2	no	—
341	C₂²⋊Q₈	—	7	2	no	—
342	C₂²⋊Q₈	—	7	1	no	—
343	C₂²⋊Q₈	—	7	1	no	—
344	C₂²⋊Q₈	—	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	1	no	—
349	C₂²⋊Q₈	—	7	2	no	—
350	C₂²⋊Q₈	—	7	2	no	—
351	C₂²⋊Q₈	—	7	1	no	—
352	C₂²⋊Q₈	—	7	2	no	—
353	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
354	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
355	#121	—	7	1	no	—
356	#121	—	7	1	no	—
357	#120	—	7	1	no	—
358	#120	—	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	2	no	—
363	C₄×Q₈	—	7	1	no	—
364	C₄×Q₈	—	7	2	no	—
365	C₄×Q₈	—	7	2	no	—
366	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
367	C₄×Q₈	C₂×D₇	1	2	yes	complemented
368	C₄×D₄	—	7	1	no	—
369	C₄×D₄	—	7	1	no	—
370	C₄×D₄	—	7	2	no	—
371	C₄×D₄	—	7	2	no	—
372	C₄×D₄	—	7	2	no	—
373	C₄×D₄	—	7	2	no	—
374	C₄×D₄	—	7	2	no	—
375	C₄×D₄	—	7	1	no	—
376	C₄×D₄	C₂×D₇	1	1	yes	characteristic
377	#117	—	7	1	no	—
378	#117	—	7	1	no	—
379	#117	—	7	1	no	—
380	#117	—	7	2	no	—
381	#117	—	7	1	no	—
382	#117	—	7	2	no	—
383	#117	—	7	2	no	—
384	#117	—	7	2	no	—
385	#117	—	7	2	no	—
386	#117	—	7	1	no	—
387	#117	—	7	2	no	—
388	#117	—	7	2	no	—
389	#117	—	7	2	no	—
390	#117	C₂×D₇	1	1	yes	characteristic
391	#117	C₂×D₇	1	1	yes	characteristic, complemented
392	C₂×C₄⋊C₄	—	7	1	no	—
393	C₂×C₄⋊C₄	—	7	1	no	—
394	C₂×C₄⋊C₄	—	7	1	no	—
395	C₂×C₄⋊C₄	—	7	1	no	—
396	C₂×C₄⋊C₄	—	7	1	no	—
397	C₂×C₄⋊C₄	—	7	2	no	—
398	C₂×C₂²⋊C₄	—	7	2	no	—
399	C₂×C₂²⋊C₄	—	7	2	no	—
400	C₂×C₄²	—	7	2	no	—
401	C₂²×C₇	—	2	1	no	—
402	C₂²×C₇	—	2	1	no	—
403	C₂²×C₇	—	2	1	no	—
404	C₂²×C₇	—	2	1	no	—
405	C₂²×C₇	—	2	1	no	—
406	C₂²×C₇	—	2	1	no	—
407	C₂²×C₇	C₂⁵	1	1	yes	characteristic
408	C₂×D₇	—	2	1	no	—
409	C₂×D₇	—	2	1	no	—
410	C₂×D₇	—	2	1	no	—
411	C₂×D₇	—	2	1	no	—
412	C₂×D₇	—	2	1	no	—
413	C₂×D₇	—	2	1	no	—
414	C₂×D₇	—	2	1	no	—
415	C₂×D₇	—	4	4	no	—
416	C₂×D₇	C₂×#41	1	2	yes	—
417	C₂×D₇	2₋¹⁺⁴	1	2	yes	—
418	C₄×C₇	—	2	2	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	2	no	—
425	C₄×C₇	—	2	1	no	—
426	C₄×C₇	C₂×#41	1	2	yes	—
427	Dic₇	—	2	2	no	—
428	Dic₇	—	2	1	no	—
429	Dic₇	—	2	1	no	—
430	Dic₇	—	2	2	no	—
431	Dic₇	—	2	1	no	—
432	Dic₇	—	2	1	no	—
433	Dic₇	—	2	2	no	—
434	Dic₇	—	2	2	no	—
435	Dic₇	C₂×#41	1	2	yes	—
436	C₂⁴	—	7	1	no	—
437	#41	—	14	4	no	—
438	C₂×Q₈	—	7	1	no	—
439	C₂×Q₈	—	7	2	no	—
440	C₂×Q₈	—	7	1	no	—
441	C₂×Q₈	—	7	2	no	—
442	C₂×Q₈	—	14	4	no	—
443	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
444	C₂×Q₈	C₂²×D₇	1	2	yes	—
445	C₂×D₄	—	7	1	no	—
446	C₂×D₄	—	7	1	no	—
447	C₂×D₄	—	7	1	no	—
448	C₂×D₄	—	7	1	no	—
449	C₂×D₄	—	7	1	no	—
450	C₂×D₄	—	7	1	no	—
451	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
452	C₂²×C₄	—	7	1	no	—
453	C₂²×C₄	—	7	1	no	—
454	C₂²×C₄	—	7	2	no	—
455	C₂²×C₄	—	7	1	no	—
456	C₂²×C₄	—	7	2	no	—
457	C₂²×C₄	—	7	2	no	—
458	C₂²×C₄	—	7	1	no	—
459	C₂²×C₄	—	7	1	no	—
460	C₂²×C₄	—	7	1	no	—
461	C₂²×C₄	—	7	2	no	—
462	C₂²×C₄	—	7	2	no	—
463	C₂²×C₄	—	7	2	no	—
464	C₂²×C₄	—	14	4	no	—
465	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
466	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
467	C₄⋊C₄	—	7	2	no	—
468	C₄⋊C₄	—	7	2	no	—
469	C₄⋊C₄	—	7	2	no	—
470	C₄⋊C₄	—	7	2	no	—
471	C₄⋊C₄	—	7	2	no	—
472	C₄⋊C₄	—	7	2	no	—
473	C₄⋊C₄	—	7	1	no	—
474	C₄⋊C₄	—	7	1	no	—
475	C₄⋊C₄	—	7	2	no	—
476	C₄⋊C₄	—	7	2	no	—
477	C₄⋊C₄	—	7	2	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	1	no	—
483	C₄⋊C₄	—	7	1	no	—
484	C₄⋊C₄	—	7	2	no	—
485	C₄⋊C₄	—	7	1	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	2	no	—
491	C₄⋊C₄	—	7	2	no	—
492	C₄⋊C₄	—	7	1	no	—
493	C₄⋊C₄	—	7	2	no	—
494	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₇	1	2	yes	—
498	C₄⋊C₄	C₂²×D₇	1	2	yes	—
499	C₄⋊C₄	C₂²×D₇	1	2	yes	—
500	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₇	1	2	yes	—
502	C₂²⋊C₄	—	7	2	no	—
503	C₂²⋊C₄	—	7	2	no	—
504	C₂²⋊C₄	—	7	2	no	—
505	C₂²⋊C₄	—	7	1	no	—
506	C₂²⋊C₄	—	7	1	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	1	no	—
514	C₂²⋊C₄	—	7	1	no	—
515	C₂²⋊C₄	—	7	1	no	—
516	C₂²⋊C₄	—	7	2	no	—
517	C₂²⋊C₄	—	7	2	no	—
518	C₂²⋊C₄	—	7	1	no	—
519	C₂²⋊C₄	—	7	2	no	—
520	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
521	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
522	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
523	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
526	C₄²	—	7	2	no	—
527	C₄²	—	7	2	no	—
528	C₄²	—	7	2	no	—
529	C₄²	—	7	2	no	—
530	C₄²	—	7	2	no	—
531	C₄²	—	7	2	no	—
532	C₄²	—	7	2	no	—
533	C₄²	—	7	1	no	—
534	C₄²	C₂²×D₇	1	2	yes	—
535	C₄²	C₂²×D₇	1	2	yes	—
536	C₄²	C₂²×D₇	1	2	yes	—
537	C₄²	C₂²×D₇	1	1	yes	characteristic
538	C₂×C₇	—	4	1	no	—
539	C₂×C₇	—	4	1	no	—
540	C₂×C₇	C₂²×#41	1	1	yes	characteristic
541	C₂×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
542	C₂×C₇	#585	1	1	yes	characteristic
543	D₇	—	2	2	no	—
544	D₇	—	2	2	no	—
545	D₇	—	4	1	no	—
546	C₂³	—	7	1	no	—
547	C₂³	—	7	1	no	—
548	C₂³	—	7	1	no	—
549	C₂³	—	14	2	no	—
550	C₂³	—	14	2	no	—
551	C₂³	—	28	1	no	—
552	C₂³	C₂³×D₇	1	1	yes	characteristic
553	C₂³	C₂³×D₇	1	1	yes	characteristic
554	Q₈	—	2	2	no	—
555	Q₈	—	4	2	no	—
556	Q₈	—	14	4	no	—
557	Q₈	—	14	2	no	—
558	Q₈	—	14	2	no	—
559	Q₈	—	28	2	no	—
560	D₄	—	4	1	no	—
561	D₄	—	14	2	no	—
562	D₄	—	14	2	no	—
563	D₄	—	14	2	no	—
564	D₄	—	14	2	no	—
565	D₄	—	14	2	no	—
566	D₄	—	28	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	7	1	no	—
570	C₂×C₄	—	7	4	no	—
571	C₂×C₄	—	7	2	no	—
572	C₂×C₄	—	7	1	no	—
573	C₂×C₄	—	7	1	no	—
574	C₂×C₄	—	7	2	no	—
575	C₂×C₄	—	7	2	no	—
576	C₂×C₄	—	7	1	no	—
577	C₂×C₄	—	7	2	no	—
578	C₂×C₄	—	7	1	no	—
579	C₂×C₄	—	14	2	no	—
580	C₂×C₄	—	14	4	no	—
581	C₂×C₄	—	14	2	no	—
582	C₂×C₄	—	14	4	no	—
583	C₂×C₄	—	14	2	no	—
584	C₂×C₄	—	14	2	no	—
585	C₂×C₄	—	14	2	no	—
586	C₂×C₄	—	28	2	no	—
587	C₂×C₄	—	28	2	no	—
588	C₂×C₄	—	28	2	no	—
589	C₂×C₄	—	28	2	no	—
590	C₂×C₄	C₂³×D₇	1	2	yes	—
591	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₇	1	2	yes	—
594	C₂×C₄	C₂³×D₇	1	2	yes	—
595	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₇	1	2	yes	—
598	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
599	C₇	#3495	1	1	yes	characteristic, complemented, Sylow
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	7	2	no	—
607	C₂²	—	7	2	no	—
608	C₂²	—	14	1	no	—
609	C₂²	—	14	1	no	—
610	C₂²	—	14	1	no	—
611	C₂²	—	14	1	no	—
612	C₂²	—	14	1	no	—
613	C₂²	—	14	1	no	—
614	C₂²	—	14	1	no	—
615	C₂²	—	28	4	no	—
616	C₂²	C₂⁴×D₇	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	7	2	no	—
626	C₄	—	14	1	no	—
627	C₄	—	14	1	no	—
628	C₄	—	14	2	no	—
629	C₄	—	14	2	no	—
630	C₄	—	14	2	no	—
631	C₄	—	14	1	no	—
632	C₄	—	14	2	no	—
633	C₄	—	14	1	no	—
634	C₄	D₇×#41	1	2	yes	—
635	C₂	—	4	1	no	—
636	C₂	—	4	1	no	—
637	C₂	—	14	2	no	—
638	C₂	—	14	2	no	—
639	C₂	—	28	1	no	—
640	C₂	C₂×D₇×#41	1	1	yes	characteristic
641	C₂	#90616	1	1	yes	characteristic
642	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×#556	C₂
prime radical	#90238	C₂
hypercenter	#556	D₇
hypocenter	C₇	#3495
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. C₇×#556	C₂	semidirect
2. #90421	C₂	semidirect
3. #90420	C₂	semidirect
4. #90399	C₂	semidirect
5. #90397	C₂	semidirect
6. #90396	C₂	semidirect
7. #90392	C₂	semidirect
8. #90370	C₂	semidirect
9. #90360	C₂	semidirect
10. #90330	C₂	semidirect
11. #90326	C₂	semidirect
12. #90319	C₂	semidirect
13. D₇×C₂²⋊Q₈	C₂	semidirect
14. #90272	C₂	semidirect
15. #90272	C₂	semidirect
16. #90269	C₂	semidirect
17. #90263	C₂	semidirect
19. #90232	C₂	semidirect
20. #90224	C₂	semidirect
21. #90220	C₂	semidirect
22. #90214	C₂	semidirect
23. D₇×#117	C₂	semidirect
27. C₇×C₄⋊Q₈	C₂²	semidirect
29. C₇×#126	C₂²	semidirect
32. C₇×C₂²⋊Q₈	C₂²	semidirect
33. C₄×C₇×Q₈	C₂²	semidirect
34. C₄×C₇×Q₈	C₂²	semidirect
37. C₇×#117	C₂²	semidirect
41. #6509	C₂²	semidirect
42. #6509	C₂²	semidirect
43. Q₈×Dic₇	C₂²	semidirect
44. #6507	C₂²	semidirect
51. C₂×C₄⋊Dic₇	C₂²	semidirect
53. #6487	C₂²	semidirect
56. #6460	C₂²	semidirect
67. #6455	C₂²	semidirect
68. #6455	C₂²	semidirect
73. D₇×C₄⋊C₄	C₂²	semidirect
74. #6453	C₂²	semidirect
75. #6453	C₂²	semidirect
76. #6452	C₂²	semidirect
77. #6452	C₂²	semidirect
78. #6452	C₂²	semidirect
79. #6452	C₂²	semidirect
80. #6452	C₂²	semidirect
81. #6451	C₂²	semidirect
82. #6451	C₂²	semidirect
83. #6450	C₂²	semidirect
84. #6450	C₂²	semidirect
86. #6448	C₂²	semidirect
95. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
101. #6442	C₂²	semidirect
104. #6441	C₂²	semidirect
106. #6440	C₂²	semidirect
107. #6439	C₂²	semidirect
108. #6439	C₂²	semidirect
117. #6433	C₂²	semidirect
118. #6433	C₂²	semidirect
119. C₄×Dic₁₄	C₂²	semidirect
120. C₄×Dic₁₄	C₂²	semidirect
121. C₄×Dic₁₄	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
227. #556	D₇	semidirect
308. C₄⋊Q₈	C₂×D₇	semidirect
316. #126	C₂×D₇	semidirect
354. C₂²⋊Q₈	C₂×D₇	semidirect
366. C₄×Q₈	C₂×D₇	semidirect
367. C₄×Q₈	C₂×D₇	semidirect
391. #117	C₂×D₇	semidirect
599. C₇	#3495	semidirect

Maximal subgroups

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

subgroup	index
C₇×#556	2
#90421	2
#90420	2
#90399	2
#90397	2
#90396	2
#90392	2
#90370	2
#90360	2
#90330	2
#90326	2
#90319	2
D₇×C₂²⋊Q₈	2
#90272	2
#90269	2
#90263	2
#90238	2
#90232	2
#90224	2
#90220	2
#90214	2
D₇×#117	2
#3495	7