Subgroups — #11743211

Order 896.

930 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#90399	C₂	1	2	yes	maximal, complemented
3	#90393	C₂	1	2	yes	maximal, complemented
4	#90387	C₂	1	2	yes	maximal, complemented
5	#90360	C₂	1	2	yes	maximal, complemented
6	#90353	C₂	1	2	yes	maximal, complemented
7	#90351	C₂	1	2	yes	maximal, complemented
8	#90337	C₂	1	2	yes	maximal, complemented
9	#90312	C₂	1	2	yes	maximal, complemented
10	#90270	C₂	1	1	yes	maximal, characteristic, complemented
11	#90258	C₂	1	1	yes	maximal, characteristic, complemented
12	#90256	C₂	1	1	yes	maximal, characteristic, complemented
13	#90256	C₂	1	1	yes	maximal, characteristic, complemented
14	#90254	C₂	1	1	yes	maximal, characteristic, complemented
15	#90233	C₂	1	1	yes	maximal, characteristic, complemented
16	#90232	C₂	1	1	yes	maximal, characteristic, complemented
17	#90232	C₂	1	1	yes	maximal, characteristic, complemented
18	#90225	C₂	1	1	yes	maximal, characteristic, complemented
19	#90225	C₂	1	1	yes	maximal, characteristic, complemented
20	#90210	C₂	1	1	yes	maximal, characteristic, complemented
21	#90210	C₂	1	1	yes	maximal, characteristic, complemented
22	#90170	C₂	1	1	yes	maximal, characteristic, complemented
23	#90161	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#126	C₂²	1	1	yes	characteristic
25	C₇×#126	C₂²	1	1	yes	characteristic
26	C₇×#125	C₂²	1	1	yes	characteristic
27	C₇×#124	C₂²	1	1	yes	characteristic
28	C₇×#123	C₂²	1	1	yes	characteristic
29	C₇×#123	C₂²	1	1	yes	characteristic
30	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₇×#121	C₂²	1	1	yes	characteristic
32	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
33	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
34	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
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
38	C₂×C₄²×C₇	C₂²	1	1	yes	characteristic
39	#6509	C₂²	1	2	yes	—
40	#6507	C₂²	1	2	yes	—
41	#6502	C₂²	1	2	yes	—
42	#6502	C₂²	1	2	yes	—
43	#6501	C₂²	1	2	yes	—
44	#6499	C₂²	1	2	yes	—
45	#6498	C₂²	1	2	yes	—
46	#6498	C₂²	1	2	yes	—
47	#6493	C₂²	1	1	yes	characteristic
48	#6493	C₂²	1	1	yes	characteristic
49	#6493	C₂²	1	1	yes	characteristic
50	#6492	C₂²	1	2	yes	—
51	C₄×C₂²⋊D₇	C₂²	1	2	yes	—
52	#6489	C₂²	1	1	yes	characteristic
53	#6489	C₂²	1	1	yes	characteristic
54	#6489	C₂²	1	1	yes	characteristic
55	#6489	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
57	C₂×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
58	#6487	C₂²	1	2	yes	—
59	#6487	C₂²	1	2	yes	—
60	#6487	C₂²	1	1	yes	characteristic
61	#6487	C₂²	1	1	yes	characteristic
62	#6487	C₂²	1	1	yes	characteristic
63	#6461	C₂²	1	2	yes	—
64	#6461	C₂²	1	2	yes	—
65	#6461	C₂²	1	2	yes	—
66	#6461	C₂²	1	2	yes	—
67	#6459	C₂²	1	2	yes	—
68	#6459	C₂²	1	2	yes	—
69	#6459	C₂²	1	2	yes	—
70	#6459	C₂²	1	2	yes	—
71	#6455	C₂²	1	2	yes	—
72	D₇×C₄⋊C₄	C₂²	1	2	yes	—
73	#6453	C₂²	1	2	yes	—
74	#6453	C₂²	1	2	yes	—
75	#6452	C₂²	1	2	yes	—
76	#6452	C₂²	1	2	yes	—
77	#6452	C₂²	1	2	yes	—
78	#6452	C₂²	1	2	yes	—
79	#6451	C₂²	1	2	yes	—
80	#6451	C₂²	1	2	yes	—
81	#6450	C₂²	1	2	yes	—
82	#6450	C₂²	1	2	yes	—
83	#6448	C₂²	1	2	yes	—
84	#6448	C₂²	1	2	yes	—
85	#6448	C₂²	1	2	yes	—
86	#6448	C₂²	1	2	yes	—
87	#6446	C₂²	1	2	yes	—
88	#6446	C₂²	1	2	yes	—
89	#6446	C₂²	1	2	yes	—
90	#6446	C₂²	1	2	yes	—
91	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	—
92	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	—
93	#6442	C₂²	1	2	yes	—
94	#6442	C₂²	1	2	yes	—
95	#6442	C₂²	1	2	yes	—
96	#6442	C₂²	1	2	yes	—
97	#6441	C₂²	1	2	yes	—
98	#6441	C₂²	1	2	yes	—
99	#6441	C₂²	1	2	yes	—
100	#6441	C₂²	1	2	yes	—
101	#6440	C₂²	1	2	yes	—
102	#6440	C₂²	1	2	yes	—
103	#6439	C₂²	1	2	yes	—
104	#6438	C₂²	1	1	yes	characteristic
105	C₄×D₂₈	C₂²	1	1	yes	characteristic
106	C₄×D₂₈	C₂²	1	1	yes	characteristic
107	C₄×D₂₈	C₂²	1	1	yes	characteristic
108	#6435	C₂²	1	2	yes	—
109	#6433	C₂²	1	1	yes	characteristic
110	#6433	C₂²	1	1	yes	characteristic
111	#6433	C₂²	1	1	yes	characteristic
112	#6433	C₂²	1	1	yes	characteristic
113	#6433	C₂²	1	1	yes	characteristic
114	#6432	C₂²	1	1	yes	characteristic
115	#6432	C₂²	1	1	yes	characteristic
116	#6432	C₂²	1	1	yes	characteristic
117	#6432	C₂²	1	1	yes	characteristic
118	C₄×Dic₁₄	C₂²	1	2	yes	—
119	C₄×Dic₁₄	C₂²	1	2	yes	—
120	C₄×Dic₁₄	C₂²	1	1	yes	characteristic
121	C₄×Dic₁₄	C₂²	1	1	yes	characteristic
122	C₄×Dic₁₄	C₂²	1	1	yes	characteristic
123	#3565	—	7	1	no	maximal, Sylow
124	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
125	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
126	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
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	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
136	C₂²×Dic₇	C₂³	1	2	yes	—
137	C₂²×Dic₇	C₂³	1	2	yes	—
138	C₂×D₂₈	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₇	C₂³	1	2	yes	—
140	C₂×C₄×D₇	C₂³	1	2	yes	—
141	C₂×C₄×D₇	C₂³	1	2	yes	—
142	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
143	C₂×Dic₁₄	C₂³	1	2	yes	—
144	C₂×Dic₁₄	C₂³	1	2	yes	—
145	C₂×Dic₁₄	C₂³	1	2	yes	—
146	C₂×Dic₁₄	C₂³	1	2	yes	—
147	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
158	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
159	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
160	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
161	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
162	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
163	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
164	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
167	C₄²×C₇	C₂³	1	1	yes	characteristic
168	C₄²×C₇	C₂³	1	1	yes	characteristic
169	C₄²×C₇	C₂³	1	1	yes	characteristic
170	C₄²×C₇	C₂³	1	1	yes	characteristic
171	C₄²×C₇	C₂³	1	1	yes	characteristic
172	C₄²×C₇	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₇	C₂³	1	2	yes	—
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	2	yes	—
179	C₂²⋊Dic₇	C₂³	1	2	yes	—
180	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
186	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
192	C₄⋊Dic₇	C₂³	1	2	yes	—
193	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
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	2	yes	—
199	C₄⋊Dic₇	C₂³	1	2	yes	—
200	Dic₇⋊C₄	C₂³	1	2	yes	—
201	Dic₇⋊C₄	C₂³	1	2	yes	—
202	Dic₇⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
214	Dic₇⋊C₄	C₂³	1	2	yes	—
215	Dic₇⋊C₄	C₂³	1	2	yes	—
216	C₄×Dic₇	C₂³	1	2	yes	—
217	C₄×Dic₇	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	#563	—	7	2	no	—
224	#562	—	7	2	no	—
225	#557	—	7	1	no	—
226	#556	—	7	2	no	—
227	#556	—	7	1	no	—
228	#555	—	7	1	no	—
229	#554	—	7	1	no	—
230	#553	—	7	1	no	—
231	#553	—	7	1	no	—
232	#552	—	7	2	no	—
233	#552	—	7	1	no	—
234	#552	—	7	1	no	—
235	#544	—	7	1	no	—
236	#544	—	7	1	no	—
237	#542	—	7	2	no	—
238	#542	—	7	2	no	—
239	#542	—	7	1	no	—
240	#542	—	7	1	no	—
241	#541	—	7	2	no	—
242	#539	—	7	2	no	—
243	#533	—	7	1	no	—
244	#529	—	7	1	no	—
245	#529	D₇	1	1	yes	characteristic, complemented
246	C₂³×C₇	C₂⁴	1	1	yes	characteristic
247	C₂³×C₇	C₂⁴	1	1	yes	characteristic
248	C₂³×C₇	C₂⁴	1	1	yes	characteristic
249	C₂²×D₇	C₂⁴	1	2	yes	—
250	C₇×Q₈	—	4	1	no	—
251	C₇×D₄	—	4	1	no	—
252	C₇×D₄	—	4	1	no	—
253	C₇×D₄	—	4	1	no	—
254	C₂×C₄×C₇	—	2	2	no	—
255	C₂×C₄×C₇	—	2	2	no	—
256	C₂×C₄×C₇	—	2	2	no	—
257	C₂×C₄×C₇	—	4	1	no	—
258	C₂×C₄×C₇	—	4	1	no	—
259	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
271	C₂²⋊D₇	—	4	2	no	—
272	C₂²⋊D₇	—	4	2	no	—
273	C₂²⋊D₇	—	4	2	no	—
274	C₂×Dic₇	—	4	2	no	—
275	C₂×Dic₇	—	4	2	no	—
276	C₂×Dic₇	C₂⁴	1	2	yes	—
277	C₂×Dic₇	C₂⁴	1	2	yes	—
278	C₂×Dic₇	C₂⁴	1	2	yes	—
279	C₂×Dic₇	C₂⁴	1	2	yes	—
280	C₂×Dic₇	C₂⁴	1	2	yes	—
281	C₂×Dic₇	C₂⁴	1	2	yes	—
282	C₂×Dic₇	C₂⁴	1	2	yes	—
283	D₂₈	—	2	2	no	—
284	C₄×D₇	—	4	2	no	—
285	C₄×D₇	—	4	2	no	—
286	C₄×D₇	—	4	2	no	—
287	Dic₁₄	—	2	2	no	—
288	Dic₁₄	—	4	2	no	—
289	Dic₁₄	—	4	2	no	—
290	Dic₁₄	—	4	2	no	—
291	Dic₁₄	—	4	2	no	—
292	C₄⋊Q₈	—	7	2	no	—
293	C₄⋊Q₈	—	7	2	no	—
294	C₄⋊Q₈	—	7	2	no	—
295	C₄⋊Q₈	—	7	1	no	—
296	C₄⋊Q₈	—	7	1	no	—
297	C₄⋊Q₈	—	7	1	no	—
298	C₄⋊Q₈	—	7	1	no	—
299	#126	—	7	2	no	—
300	#126	—	7	2	no	—
301	#126	—	7	2	no	—
302	#126	—	7	2	no	—
303	#126	—	7	2	no	—
304	#126	—	7	2	no	—
305	#126	—	7	2	no	—
306	#126	—	7	2	no	—
307	#126	—	7	2	no	—
308	#126	C₂×D₇	1	1	yes	characteristic
309	#126	C₂×D₇	1	1	yes	characteristic
310	#125	—	7	2	no	—
311	#125	—	7	2	no	—
312	#125	—	7	2	no	—
313	#125	—	7	2	no	—
314	#125	—	7	2	no	—
315	#125	—	7	2	no	—
316	#125	—	7	1	no	—
317	#125	—	7	1	no	—
318	#125	—	7	1	no	—
319	#125	—	7	1	no	—
320	#125	—	7	1	no	—
321	#125	C₂×D₇	1	1	yes	characteristic
322	#124	—	7	2	no	—
323	#124	—	7	2	no	—
324	#124	—	7	2	no	—
325	#124	—	7	2	no	—
326	#124	—	7	2	no	—
327	#124	—	7	1	no	—
328	#124	C₂×D₇	1	1	yes	characteristic
329	#123	—	7	2	no	—
330	#123	—	7	2	no	—
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	C₂×D₇	1	1	yes	characteristic
337	#123	C₂×D₇	1	1	yes	characteristic
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	2	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	—	7	2	no	—
351	C₂²⋊Q₈	—	7	2	no	—
352	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
353	#121	—	7	2	no	—
354	#121	—	7	2	no	—
355	#121	—	7	2	no	—
356	#121	—	7	1	no	—
357	#121	—	7	1	no	—
358	#121	—	7	1	no	—
359	#121	C₂×D₇	1	1	yes	characteristic
360	C₄×Q₈	—	7	2	no	—
361	C₄×Q₈	—	7	2	no	—
362	C₄×Q₈	—	7	1	no	—
363	C₄×Q₈	—	7	2	no	—
364	C₄×Q₈	—	7	2	no	—
365	C₄×Q₈	—	7	1	no	—
366	C₄×Q₈	—	7	1	no	—
367	C₄×Q₈	C₂×D₇	1	1	yes	characteristic
368	C₄×D₄	—	7	2	no	—
369	C₄×D₄	—	7	2	no	—
370	C₄×D₄	—	7	2	no	—
371	C₄×D₄	—	7	1	no	—
372	C₄×D₄	—	7	1	no	—
373	C₄×D₄	—	7	1	no	—
374	C₄×D₄	C₂×D₇	1	1	yes	characteristic
375	C₄×D₄	C₂×D₇	1	1	yes	characteristic
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	1	no	—
381	#117	—	7	2	no	—
382	#117	—	7	2	no	—
383	#117	—	7	2	no	—
384	#117	—	7	2	no	—
385	#117	C₂×D₇	1	1	yes	characteristic
386	#117	C₂×D₇	1	1	yes	characteristic
387	C₂×C₄⋊C₄	—	7	1	no	—
388	C₂×C₄⋊C₄	—	7	1	no	—
389	C₂×C₄⋊C₄	—	7	2	no	—
390	C₂×C₄²	C₂×D₇	1	1	yes	characteristic
391	C₂²×C₇	—	2	1	no	—
392	C₂²×C₇	—	2	1	no	—
393	C₂²×C₇	—	2	1	no	—
394	C₂²×C₇	—	2	1	no	—
395	C₂²×C₇	—	2	1	no	—
396	C₂²×C₇	—	2	1	no	—
397	C₂²×C₇	—	2	1	no	—
398	C₂²×C₇	—	2	1	no	—
399	C₂²×C₇	—	2	1	no	—
400	C₂²×C₇	C₂⁵	1	1	yes	characteristic
401	C₂×D₇	—	2	2	no	—
402	C₂×D₇	—	2	2	no	—
403	C₂×D₇	—	2	2	no	—
404	C₄×C₇	—	2	1	no	—
405	C₄×C₇	—	2	1	no	—
406	C₄×C₇	—	2	1	no	—
407	C₄×C₇	—	2	1	no	—
408	C₄×C₇	—	2	1	no	—
409	C₄×C₇	—	2	1	no	—
410	C₄×C₇	—	2	1	no	—
411	C₄×C₇	—	2	1	no	—
412	C₄×C₇	—	2	1	no	—
413	C₄×C₇	—	2	1	no	—
414	C₄×C₇	—	2	1	no	—
415	C₄×C₇	2₋¹⁺⁴	1	2	yes	—
416	Dic₇	—	2	2	no	—
417	Dic₇	—	2	2	no	—
418	Dic₇	—	2	2	no	—
419	Dic₇	—	2	2	no	—
420	Dic₇	—	2	2	no	—
421	Dic₇	—	2	2	no	—
422	Dic₇	—	2	2	no	—
423	C₂×Q₈	—	7	1	no	—
424	C₂×Q₈	—	7	2	no	—
425	C₂×Q₈	—	7	2	no	—
426	C₂×Q₈	—	7	2	no	—
427	C₂×Q₈	—	7	2	no	—
428	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
429	C₂×D₄	—	7	2	no	—
430	C₂×D₄	—	7	2	no	—
431	C₂×D₄	—	7	2	no	—
432	C₂×D₄	—	7	1	no	—
433	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
434	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
435	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
436	C₂²×C₄	—	7	2	no	—
437	C₂²×C₄	—	7	2	no	—
438	C₂²×C₄	—	7	2	no	—
439	C₂²×C₄	—	7	2	no	—
440	C₂²×C₄	—	7	2	no	—
441	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
442	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
443	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
444	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
445	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
446	C₄⋊C₄	—	7	2	no	—
447	C₄⋊C₄	—	7	2	no	—
448	C₄⋊C₄	—	7	2	no	—
449	C₄⋊C₄	—	7	2	no	—
450	C₄⋊C₄	—	7	2	no	—
451	C₄⋊C₄	—	7	2	no	—
452	C₄⋊C₄	—	7	2	no	—
453	C₄⋊C₄	—	7	2	no	—
454	C₄⋊C₄	—	7	2	no	—
455	C₄⋊C₄	—	7	2	no	—
456	C₄⋊C₄	—	7	2	no	—
457	C₄⋊C₄	—	7	2	no	—
458	C₄⋊C₄	—	7	2	no	—
459	C₄⋊C₄	—	7	2	no	—
460	C₄⋊C₄	—	7	2	no	—
461	C₄⋊C₄	—	7	2	no	—
462	C₄⋊C₄	—	7	1	no	—
463	C₄⋊C₄	—	7	1	no	—
464	C₄⋊C₄	—	7	1	no	—
465	C₄⋊C₄	—	7	1	no	—
466	C₄⋊C₄	—	7	2	no	—
467	C₄⋊C₄	—	7	2	no	—
468	C₄⋊C₄	—	7	2	no	—
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	C₂²×D₇	1	1	yes	characteristic
475	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
476	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
484	C₂²⋊C₄	—	7	2	no	—
485	C₂²⋊C₄	—	7	2	no	—
486	C₂²⋊C₄	—	7	2	no	—
487	C₂²⋊C₄	—	7	2	no	—
488	C₂²⋊C₄	—	7	2	no	—
489	C₂²⋊C₄	—	7	2	no	—
490	C₂²⋊C₄	—	7	2	no	—
491	C₂²⋊C₄	—	7	2	no	—
492	C₂²⋊C₄	—	7	2	no	—
493	C₂²⋊C₄	—	7	2	no	—
494	C₂²⋊C₄	—	7	2	no	—
495	C₂²⋊C₄	—	7	2	no	—
496	C₂²⋊C₄	—	7	2	no	—
497	C₂²⋊C₄	—	7	2	no	—
498	C₂²⋊C₄	—	7	2	no	—
499	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
500	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
501	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
502	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
503	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
504	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
505	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
506	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
507	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
508	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
509	C₄²	—	7	2	no	—
510	C₄²	—	7	2	no	—
511	C₄²	—	7	2	no	—
512	C₄²	—	7	2	no	—
513	C₄²	—	7	2	no	—
514	C₄²	—	7	2	no	—
515	C₄²	—	7	2	no	—
516	C₄²	C₂²×D₇	1	1	yes	characteristic
517	C₄²	C₂²×D₇	1	1	yes	characteristic
518	C₄²	C₂²×D₇	1	1	yes	characteristic
519	C₄²	C₂²×D₇	1	1	yes	characteristic
520	C₄²	C₂²×D₇	1	1	yes	characteristic
521	C₄²	C₂²×D₇	1	1	yes	characteristic
522	C₂×C₇	—	4	1	no	—
523	C₂×C₇	—	4	1	no	—
524	C₂×C₇	—	4	1	no	—
525	C₂×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
526	C₂×C₇	#585	1	1	yes	characteristic
527	C₂×C₇	#585	1	1	yes	characteristic
528	D₇	—	4	2	no	—
529	C₂³	—	7	2	no	—
530	C₂³	C₂³×D₇	1	1	yes	characteristic
531	C₂³	C₂³×D₇	1	1	yes	characteristic
532	C₂³	C₂³×D₇	1	1	yes	characteristic
533	Q₈	—	4	1	no	—
534	Q₈	—	14	2	no	—
535	Q₈	—	28	2	no	—
536	Q₈	—	28	2	no	—
537	Q₈	—	28	2	no	—
538	Q₈	—	28	2	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	1	no	—
542	D₄	—	14	2	no	—
543	D₄	—	28	2	no	—
544	D₄	—	28	2	no	—
545	D₄	—	28	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	7	2	no	—
552	C₂×C₄	—	7	2	no	—
553	C₂×C₄	—	7	2	no	—
554	C₂×C₄	—	7	2	no	—
555	C₂×C₄	—	7	2	no	—
556	C₂×C₄	—	7	2	no	—
557	C₂×C₄	—	7	2	no	—
558	C₂×C₄	—	28	2	no	—
559	C₂×C₄	—	28	2	no	—
560	C₂×C₄	—	28	2	no	—
561	C₂×C₄	—	28	2	no	—
562	C₂×C₄	—	28	2	no	—
563	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
564	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
568	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
572	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
573	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
574	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
575	C₇	#3565	1	1	yes	characteristic, complemented, Sylow
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	14	2	no	—
586	C₂²	—	14	2	no	—
587	C₂²	—	14	2	no	—
588	C₂²	C₂⁴×D₇	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	14	2	no	—
601	C₄	—	14	2	no	—
602	C₄	—	14	2	no	—
603	C₄	—	14	2	no	—
604	C₄	—	14	2	no	—
605	C₄	—	14	2	no	—
606	C₄	—	14	2	no	—
607	C₄	#6554	1	2	yes	—
608	C₂	—	4	1	no	—
609	C₂	—	4	1	no	—
610	C₂	—	4	1	no	—
611	C₂	—	28	2	no	—
612	C₂	C₂×#6554	1	1	yes	characteristic
613	C₂	#90616	1	1	yes	characteristic
614	C₂	#90616	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#529	C₂
hypercenter	#529	D₇
hypocenter	C₇	#3565
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₇×#529	C₂	semidirect
2. #90399	C₂	semidirect
3. #90393	C₂	semidirect
4. #90387	C₂	semidirect
5. #90360	C₂	semidirect
6. #90353	C₂	semidirect
7. #90351	C₂	semidirect
8. #90337	C₂	semidirect
9. #90312	C₂	semidirect
10. #90270	C₂	semidirect
11. #90258	C₂	semidirect
12. #90256	C₂	semidirect
13. #90256	C₂	semidirect
14. #90254	C₂	semidirect
15. #90233	C₂	semidirect
16. #90232	C₂	semidirect
17. #90232	C₂	semidirect
18. #90225	C₂	semidirect
19. #90225	C₂	semidirect
20. #90210	C₂	semidirect
21. #90210	C₂	semidirect
22. #90170	C₂	semidirect
23. #90161	C₂	semidirect
245. #529	D₇	semidirect
575. C₇	#3565	semidirect

Maximal subgroups

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

subgroup	index
C₇×#529	2
#90399	2
#90393	2
#90387	2
#90360	2
#90353	2
#90351	2
#90337	2
#90312	2
#90270	2
#90258	2
#90256	2
#90254	2
#90233	2
#90232	2
#90225	2
#90210	2
#90170	2
#90161	2
#3565	7