Subgroups — #11743619

Order 896.

1022 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#90420	C₂	1	1	yes	maximal, characteristic, complemented
3	#90419	C₂	1	1	yes	maximal, characteristic, complemented
4	#90399	C₂	1	2	yes	maximal, complemented
5	#90399	C₂	1	2	yes	maximal, complemented
6	#90371	C₂	1	1	yes	maximal, characteristic, complemented
7	#90370	C₂	1	2	yes	maximal, complemented
8	#90366	C₂	1	1	yes	maximal, characteristic, complemented
9	#90362	C₂	1	2	yes	maximal, complemented
10	#90350	C₂	1	2	yes	maximal, complemented
11	#90341	C₂	1	2	yes	maximal, complemented
12	#90330	C₂	1	2	yes	maximal, complemented
13	#90327	C₂	1	2	yes	maximal, complemented
14	D₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	#90316	C₂	1	1	yes	maximal, characteristic, complemented
16	#90297	C₂	1	1	yes	maximal, characteristic
17	#90294	C₂	1	1	yes	maximal, characteristic, complemented
18	#90269	C₂	1	1	yes	maximal, characteristic, complemented
19	#90263	C₂	1	1	yes	maximal, characteristic, complemented
20	#90248	C₂	1	1	yes	maximal, characteristic, complemented
21	#90237	C₂	1	1	yes	maximal, characteristic, complemented
22	D₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
23	#90209	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₇	C₂²	1	1	yes	characteristic
25	C₂×#1159	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	complemented
29	C₇×#124	C₂²	1	2	yes	—
30	C₇×#124	C₂²	1	1	yes	characteristic, complemented
31	C₇×#123	C₂²	1	2	yes	—
32	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₇×#121	C₂²	1	1	yes	characteristic
35	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
37	C₇×#117	C₂²	1	1	yes	characteristic
38	#6509	C₂²	1	2	yes	—
39	#6509	C₂²	1	2	yes	—
40	#6509	C₂²	1	1	yes	characteristic
41	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₇	C₂²	1	2	yes	complemented
43	#6507	C₂²	1	2	yes	complemented
44	#6507	C₂²	1	1	yes	characteristic, complemented
45	#6501	C₂²	1	1	yes	characteristic
46	#6500	C₂²	1	2	yes	—
47	#6499	C₂²	1	2	yes	—
48	#6499	C₂²	1	1	yes	characteristic, complemented
49	#6498	C₂²	1	2	yes	—
50	D₄×Dic₇	C₂²	1	2	yes	—
51	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₂²⋊D₇	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₇	C₂²	1	2	yes	—
54	#6489	C₂²	1	1	yes	characteristic
55	#6489	C₂²	1	2	yes	complemented
56	#6487	C₂²	1	1	yes	characteristic
57	#6487	C₂²	1	1	yes	characteristic
58	C₂×Dic₇⋊C₄	C₂²	1	2	yes	complemented
59	#6460	C₂²	1	1	yes	characteristic
60	#6460	C₂²	1	1	yes	characteristic
61	#6459	C₂²	1	2	yes	—
62	#6459	C₂²	1	2	yes	—
63	#6459	C₂²	1	2	yes	—
64	#6455	C₂²	1	1	yes	characteristic
65	#6455	C₂²	1	2	yes	—
66	#6455	C₂²	1	1	yes	characteristic
67	#6455	C₂²	1	1	yes	characteristic
68	#6455	C₂²	1	2	yes	—
69	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	D₇×C₄⋊C₄	C₂²	1	2	yes	—
71	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
73	#6453	C₂²	1	2	yes	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	1	yes	characteristic, complemented
82	#6450	C₂²	1	1	yes	characteristic, complemented
83	#6450	C₂²	1	1	yes	characteristic, complemented
84	#6450	C₂²	1	2	yes	complemented
85	#6446	C₂²	1	2	yes	—
86	#6446	C₂²	1	2	yes	—
87	#6446	C₂²	1	2	yes	—
88	#6446	C₂²	1	2	yes	—
89	#6446	C₂²	1	2	yes	—
90	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	—
91	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	—
92	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	—
93	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
94	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
95	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
96	#6442	C₂²	1	2	yes	—
97	#6442	C₂²	1	2	yes	—
98	#6442	C₂²	1	2	yes	—
99	#6442	C₂²	1	2	yes	—
100	#6442	C₂²	1	2	yes	complemented
101	#6442	C₂²	1	2	yes	complemented
102	#6442	C₂²	1	2	yes	complemented
103	#6441	C₂²	1	2	yes	—
104	#6441	C₂²	1	2	yes	complemented
105	#6441	C₂²	1	2	yes	complemented
106	#6441	C₂²	1	2	yes	complemented
107	#6440	C₂²	1	1	yes	characteristic
108	#6440	C₂²	1	1	yes	characteristic
109	#6440	C₂²	1	2	yes	complemented
110	#6440	C₂²	1	2	yes	complemented
111	#6435	C₂²	1	2	yes	—
112	#6435	C₂²	1	2	yes	—
113	#6435	C₂²	1	1	yes	characteristic
114	#6435	C₂²	1	1	yes	characteristic
115	C₄²×D₇	C₂²	1	1	yes	characteristic
116	C₄²×D₇	C₂²	1	1	yes	characteristic
117	#6433	C₂²	1	1	yes	characteristic, complemented
118	#6432	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	1	yes	characteristic, 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	C₂×C₇×D₄	C₂³	1	2	yes	—
129	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
133	C₂²×Dic₇	C₂³	1	1	yes	characteristic
134	C₂²×Dic₇	C₂³	1	2	yes	—
135	C₂²×Dic₇	C₂³	1	2	yes	—
136	Q₈×D₇	—	2	4	no	—
137	#1159	—	2	4	no	—
138	C₂×C₄×D₇	—	2	4	no	—
139	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
149	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
150	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
151	C₂×Dic₁₄	C₂³	1	2	yes	—
152	C₂×Dic₁₄	C₂³	1	2	yes	—
153	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₇×C₄⋊C₄	C₂³	1	2	yes	—
155	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₇×C₄⋊C₄	C₂³	1	2	yes	—
159	C₇×C₄⋊C₄	C₂³	1	2	yes	—
160	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
161	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
162	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₄²×C₇	C₂³	1	1	yes	characteristic
168	C₄²×C₇	C₂³	1	2	yes	—
169	C₄²×C₇	C₂³	1	1	yes	characteristic
170	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
171	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
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	2	yes	—
176	C₂²⋊Dic₇	C₂³	1	2	yes	—
177	C₂²⋊Dic₇	C₂³	1	2	yes	—
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	1	yes	characteristic
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	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
188	C₄⋊Dic₇	C₂³	1	2	yes	—
189	C₄⋊Dic₇	C₂³	1	2	yes	—
190	C₄⋊Dic₇	C₂³	1	2	yes	—
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	2	yes	—
195	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
196	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
197	Dic₇⋊C₄	C₂³	1	2	yes	—
198	Dic₇⋊C₄	C₂³	1	2	yes	—
199	Dic₇⋊C₄	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	1	yes	characteristic
204	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
205	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
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	C₄×Dic₇	C₂³	1	1	yes	characteristic
215	C₄×Dic₇	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	1	yes	characteristic
220	C₄×Dic₇	C₂³	1	1	yes	characteristic
221	C₄×Dic₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₇	C₂³	1	1	yes	characteristic
223	C₄×Dic₇	C₂³	1	1	yes	characteristic
224	C₄×Dic₇	C₂³	1	2	yes	—
225	C₄×Dic₇	C₂³	1	2	yes	—
226	#556	—	7	2	no	—
227	#554	—	7	2	no	—
228	#552	—	7	2	no	—
229	#552	—	7	2	no	—
230	#552	—	7	2	no	—
231	#552	—	7	2	no	—
232	#551	—	7	2	no	—
233	#551	—	7	2	no	—
234	#544	—	7	1	no	—
235	#542	—	7	1	no	—
236	#542	D₇	1	1	yes	characteristic, complemented
237	#541	—	7	1	no	—
238	#541	—	7	1	no	—
239	#536	—	7	1	no	—
240	#533	—	7	1	no	—
241	#533	—	7	1	no	—
242	#529	—	7	1	no	—
243	#529	—	7	1	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	2	yes	—
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	C₇×Q₈	—	2	2	no	—
257	C₇×Q₈	—	4	2	no	—
258	C₇×D₄	—	2	2	no	—
259	C₇×D₄	—	4	2	no	—
260	C₂×C₄×C₇	—	2	2	no	—
261	C₂×C₄×C₇	—	4	2	no	—
262	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₇	C₂⁴	1	2	yes	—
265	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₇	C₂⁴	1	2	yes	—
268	C₂×C₄×C₇	C₂⁴	1	2	yes	—
269	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
271	C₂²⋊D₇	—	2	4	no	—
272	C₂²⋊D₇	—	2	4	no	—
273	C₂×Dic₇	—	2	2	no	—
274	C₂×Dic₇	—	2	4	no	—
275	C₂×Dic₇	—	4	2	no	—
276	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₇	C₂⁴	1	2	yes	—
280	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₇	C₂⁴	1	2	yes	—
282	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₇	C₂⁴	1	2	yes	—
284	C₂×Dic₇	C₂⁴	1	2	yes	—
285	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
286	C₄×D₇	—	2	2	no	—
287	C₄×D₇	—	2	4	no	—
288	C₄×D₇	—	2	2	no	—
289	C₄×D₇	—	2	2	no	—
290	C₄×D₇	—	2	2	no	—
291	C₄×D₇	—	2	2	no	—
292	C₄×D₇	—	4	1	no	—
293	C₄×D₇	—	4	2	no	—
294	C₄×D₇	—	4	1	no	—
295	C₄×D₇	#41	1	4	yes	—
296	Dic₁₄	—	2	2	no	—
297	Dic₁₄	—	2	2	no	—
298	Dic₁₄	—	2	4	no	—
299	Dic₁₄	—	4	2	no	—
300	C₂×#41	—	7	1	no	—
301	C₂²×Q₈	—	7	1	no	—
302	C₂³×C₄	—	7	1	no	—
303	C₄⋊Q₈	—	7	1	no	—
304	C₄⋊Q₈	—	7	2	no	—
305	C₄⋊Q₈	—	7	1	no	—
306	C₄⋊Q₈	—	7	1	no	—
307	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
308	#126	—	7	2	no	—
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	complemented
316	#125	—	7	1	no	—
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	2	no	—
324	#125	—	7	1	no	—
325	#124	—	7	1	no	—
326	#124	—	7	2	no	—
327	#124	C₂×D₇	1	2	yes	—
328	#124	C₂×D₇	1	1	yes	characteristic, complemented
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	C₂×D₇	1	2	yes	—
336	C₂²⋊Q₈	—	7	1	no	—
337	C₂²⋊Q₈	—	7	2	no	—
338	C₂²⋊Q₈	—	7	2	no	—
339	C₂²⋊Q₈	—	7	1	no	—
340	C₂²⋊Q₈	—	7	1	no	—
341	C₂²⋊Q₈	—	7	1	no	—
342	C₂²⋊Q₈	—	7	2	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	C₂×D₇	1	1	yes	characteristic
351	C₂²⋊Q₈	C₂×D₇	1	2	yes	complemented
352	#121	—	7	1	no	—
353	#121	C₂×D₇	1	1	yes	characteristic
354	#120	—	7	2	no	—
355	C₄×Q₈	—	7	1	no	—
356	C₄×Q₈	—	7	2	no	—
357	C₄×Q₈	—	7	1	no	—
358	C₄×Q₈	—	7	2	no	—
359	C₄×Q₈	—	7	1	no	—
360	C₄×Q₈	—	7	1	no	—
361	C₄×Q₈	—	7	2	no	—
362	C₄×Q₈	—	7	1	no	—
363	C₄×Q₈	—	7	2	no	—
364	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
365	C₄×D₄	—	7	1	no	—
366	C₄×D₄	—	7	2	no	—
367	C₄×D₄	—	7	2	no	—
368	C₄×D₄	—	7	2	no	—
369	C₄×D₄	—	7	2	no	—
370	C₄×D₄	—	7	2	no	—
371	C₄×D₄	—	7	2	no	—
372	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
373	#117	—	7	1	no	—
374	#117	—	7	2	no	—
375	#117	—	7	1	no	—
376	#117	—	7	1	no	—
377	#117	—	7	1	no	—
378	#117	—	7	2	no	—
379	#117	—	7	2	no	—
380	#117	—	7	1	no	—
381	#117	—	7	1	no	—
382	#117	—	7	2	no	—
383	#117	—	7	2	no	—
384	#117	—	7	1	no	—
385	#117	—	7	1	no	—
386	#117	—	7	2	no	—
387	#117	—	7	2	no	—
388	#117	C₂×D₇	1	1	yes	characteristic
389	C₂×C₄⋊C₄	—	7	2	no	—
390	C₂×C₄⋊C₄	—	7	1	no	—
391	C₂×C₄⋊C₄	—	7	1	no	—
392	C₂×C₄⋊C₄	—	7	1	no	—
393	C₂×C₄⋊C₄	—	7	2	no	—
394	C₂×C₂²⋊C₄	—	7	1	no	—
395	C₂×C₂²⋊C₄	—	7	1	no	—
396	C₂×C₂²⋊C₄	—	7	2	no	—
397	C₂×C₄²	—	7	1	no	—
398	C₂×C₄²	—	7	1	no	—
399	C₂²×C₇	—	2	2	no	—
400	C₂²×C₇	—	2	1	no	—
401	C₂²×C₇	—	2	2	no	—
402	C₂²×C₇	—	2	1	no	—
403	C₂²×C₇	—	2	2	no	—
404	C₂²×C₇	—	2	1	no	—
405	C₂²×C₇	C₂⁵	1	1	yes	characteristic
406	C₂×D₇	—	2	1	no	—
407	C₂×D₇	—	2	1	no	—
408	C₂×D₇	—	2	1	no	—
409	C₂×D₇	—	2	1	no	—
410	C₂×D₇	—	4	4	no	—
411	C₂×D₇	C₂×#41	1	2	yes	—
412	C₂×D₇	2₋¹⁺⁴	1	2	yes	—
413	C₄×C₇	—	2	2	no	—
414	C₄×C₇	—	2	1	no	—
415	C₄×C₇	—	2	1	no	—
416	C₄×C₇	—	2	1	no	—
417	C₄×C₇	—	2	2	no	—
418	C₄×C₇	—	2	1	no	—
419	C₄×C₇	—	2	2	no	—
420	C₄×C₇	—	2	1	no	—
421	C₄×C₇	C₂×#41	1	2	yes	—
422	Dic₇	—	2	2	no	—
423	Dic₇	—	2	2	no	—
424	Dic₇	—	2	1	no	—
425	Dic₇	—	2	1	no	—
426	Dic₇	—	2	1	no	—
427	Dic₇	—	2	2	no	—
428	Dic₇	—	2	1	no	—
429	Dic₇	—	2	2	no	—
430	Dic₇	—	2	1	no	—
431	Dic₇	C₂×#41	1	2	yes	—
432	C₂⁴	—	7	1	no	—
433	#41	—	14	4	no	—
434	C₂×Q₈	—	7	2	no	—
435	C₂×Q₈	—	7	1	no	—
436	C₂×Q₈	—	7	1	no	—
437	C₂×Q₈	—	7	2	no	—
438	C₂×Q₈	—	14	4	no	—
439	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
440	C₂×Q₈	C₂²×D₇	1	2	yes	—
441	C₂×D₄	—	7	2	no	—
442	C₂×D₄	—	7	2	no	—
443	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
444	C₂×D₄	C₂²×D₇	1	2	yes	—
445	C₂²×C₄	—	7	1	no	—
446	C₂²×C₄	—	7	2	no	—
447	C₂²×C₄	—	7	1	no	—
448	C₂²×C₄	—	7	2	no	—
449	C₂²×C₄	—	7	1	no	—
450	C₂²×C₄	—	7	1	no	—
451	C₂²×C₄	—	7	1	no	—
452	C₂²×C₄	—	7	2	no	—
453	C₂²×C₄	—	7	1	no	—
454	C₂²×C₄	—	7	1	no	—
455	C₂²×C₄	—	7	1	no	—
456	C₂²×C₄	—	7	1	no	—
457	C₂²×C₄	—	7	2	no	—
458	C₂²×C₄	—	14	4	no	—
459	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
460	C₂²×C₄	C₂²×D₇	1	2	yes	—
461	C₄⋊C₄	—	7	1	no	—
462	C₄⋊C₄	—	7	2	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	2	no	—
470	C₄⋊C₄	—	7	2	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	2	no	—
478	C₄⋊C₄	—	7	2	no	—
479	C₄⋊C₄	—	7	1	no	—
480	C₄⋊C₄	—	7	1	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	2	no	—
486	C₄⋊C₄	—	7	2	no	—
487	C₄⋊C₄	—	7	2	no	—
488	C₄⋊C₄	—	7	2	no	—
489	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₇	1	2	yes	—
493	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₇	1	2	yes	—
495	C₄⋊C₄	C₂²×D₇	1	2	yes	—
496	C₂²⋊C₄	—	7	1	no	—
497	C₂²⋊C₄	—	7	1	no	—
498	C₂²⋊C₄	—	7	2	no	—
499	C₂²⋊C₄	—	7	2	no	—
500	C₂²⋊C₄	—	7	2	no	—
501	C₂²⋊C₄	—	7	2	no	—
502	C₂²⋊C₄	—	7	2	no	—
503	C₂²⋊C₄	—	7	2	no	—
504	C₂²⋊C₄	—	7	1	no	—
505	C₂²⋊C₄	—	7	1	no	—
506	C₂²⋊C₄	—	7	1	no	—
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	C₂²×D₇	1	1	yes	characteristic
513	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
514	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
515	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
516	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
517	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
518	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
519	C₄²	—	7	1	no	—
520	C₄²	—	7	1	no	—
521	C₄²	—	7	1	no	—
522	C₄²	—	7	1	no	—
523	C₄²	—	7	1	no	—
524	C₄²	—	7	1	no	—
525	C₄²	—	7	2	no	—
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	C₂²×D₇	1	1	yes	characteristic
532	C₄²	C₂²×D₇	1	1	yes	characteristic
533	C₄²	C₂²×D₇	1	2	yes	—
534	C₂×C₇	—	4	1	no	—
535	C₂×C₇	—	4	2	no	—
536	C₂×C₇	C₂²×#41	1	1	yes	characteristic
537	C₂×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
538	C₂×C₇	#585	1	1	yes	characteristic
539	D₇	—	2	2	no	—
540	D₇	—	2	2	no	—
541	C₂³	—	7	1	no	—
542	C₂³	—	7	1	no	—
543	C₂³	—	14	2	no	—
544	C₂³	—	14	2	no	—
545	C₂³	—	28	1	no	—
546	C₂³	C₂³×D₇	1	1	yes	characteristic
547	C₂³	C₂³×D₇	1	2	yes	—
548	Q₈	—	2	2	no	—
549	Q₈	—	4	2	no	—
550	Q₈	—	14	4	no	—
551	Q₈	—	14	2	no	—
552	Q₈	—	14	2	no	—
553	Q₈	—	28	2	no	—
554	D₄	—	2	2	no	—
555	D₄	—	4	2	no	—
556	D₄	—	14	4	no	—
557	D₄	—	14	4	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	7	1	no	—
561	C₂×C₄	—	7	4	no	—
562	C₂×C₄	—	7	1	no	—
563	C₂×C₄	—	7	1	no	—
564	C₂×C₄	—	7	1	no	—
565	C₂×C₄	—	7	2	no	—
566	C₂×C₄	—	7	1	no	—
567	C₂×C₄	—	7	2	no	—
568	C₂×C₄	—	7	1	no	—
569	C₂×C₄	—	7	2	no	—
570	C₂×C₄	—	7	2	no	—
571	C₂×C₄	—	14	2	no	—
572	C₂×C₄	—	14	2	no	—
573	C₂×C₄	—	14	2	no	—
574	C₂×C₄	—	14	2	no	—
575	C₂×C₄	—	14	4	no	—
576	C₂×C₄	—	14	2	no	—
577	C₂×C₄	—	14	4	no	—
578	C₂×C₄	—	14	2	no	—
579	C₂×C₄	—	28	1	no	—
580	C₂×C₄	—	28	2	no	—
581	C₂×C₄	—	28	1	no	—
582	C₂×C₄	—	28	2	no	—
583	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₇	1	2	yes	—
586	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₇	1	2	yes	—
589	C₂×C₄	C₂³×D₇	1	2	yes	—
590	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
592	C₇	#3495	1	1	yes	characteristic, complemented, Sylow
593	C₂²	—	2	1	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	7	2	no	—
600	C₂²	—	7	2	no	—
601	C₂²	—	14	1	no	—
602	C₂²	—	14	1	no	—
603	C₂²	—	14	1	no	—
604	C₂²	—	14	1	no	—
605	C₂²	—	28	4	no	—
606	C₂²	C₂⁴×D₇	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	2	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	7	2	no	—
616	C₄	—	14	1	no	—
617	C₄	—	14	2	no	—
618	C₄	—	14	2	no	—
619	C₄	—	14	1	no	—
620	C₄	—	14	2	no	—
621	C₄	—	14	1	no	—
622	C₄	—	14	1	no	—
623	C₄	—	14	1	no	—
624	C₄	—	14	2	no	—
625	C₄	D₇×#41	1	2	yes	—
626	C₂	—	4	1	no	—
627	C₂	—	4	2	no	—
628	C₂	—	14	2	no	—
629	C₂	—	14	2	no	—
630	C₂	C₂×D₇×#41	1	1	yes	characteristic
631	C₂	#90618	1	1	yes	characteristic
632	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×#542	C₂
prime radical	#90297	C₂
hypercenter	#542	D₇
hypocenter	C₇	#3495
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₇×#542	C₂	semidirect
2. #90420	C₂	semidirect
3. #90419	C₂	semidirect
4. #90399	C₂	semidirect
5. #90399	C₂	semidirect
6. #90371	C₂	semidirect
7. #90370	C₂	semidirect
8. #90366	C₂	semidirect
9. #90362	C₂	semidirect
10. #90350	C₂	semidirect
11. #90341	C₂	semidirect
12. #90330	C₂	semidirect
13. #90327	C₂	semidirect
14. D₇×C₂²⋊Q₈	C₂	semidirect
15. #90316	C₂	semidirect
17. #90294	C₂	semidirect
18. #90269	C₂	semidirect
19. #90263	C₂	semidirect
20. #90248	C₂	semidirect
21. #90237	C₂	semidirect
22. D₇×#117	C₂	semidirect
23. #90209	C₂	semidirect
27. C₇×C₄⋊Q₈	C₂²	semidirect
28. C₇×#126	C₂²	semidirect
30. C₇×#124	C₂²	semidirect
33. C₇×C₂²⋊Q₈	C₂²	semidirect
35. C₄×C₇×Q₈	C₂²	semidirect
36. C₄×C₇×D₄	C₂²	semidirect
41. Q₈×Dic₇	C₂²	semidirect
42. Q₈×Dic₇	C₂²	semidirect
43. #6507	C₂²	semidirect
44. #6507	C₂²	semidirect
48. #6499	C₂²	semidirect
51. D₄×Dic₇	C₂²	semidirect
55. #6489	C₂²	semidirect
58. C₂×Dic₇⋊C₄	C₂²	semidirect
73. #6453	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. #6450	C₂²	semidirect
83. #6450	C₂²	semidirect
84. #6450	C₂²	semidirect
100. #6442	C₂²	semidirect
101. #6442	C₂²	semidirect
102. #6442	C₂²	semidirect
104. #6441	C₂²	semidirect
105. #6441	C₂²	semidirect
106. #6441	C₂²	semidirect
109. #6440	C₂²	semidirect
110. #6440	C₂²	semidirect
117. #6433	C₂²	semidirect
118. #6432	C₂²	semidirect
119. C₄×Dic₁₄	C₂²	semidirect
120. C₄×Dic₁₄	C₂²	semidirect
121. C₄×Dic₁₄	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
236. #542	D₇	semidirect
307. C₄⋊Q₈	C₂×D₇	semidirect
315. #126	C₂×D₇	semidirect
328. #124	C₂×D₇	semidirect
351. C₂²⋊Q₈	C₂×D₇	semidirect
364. C₄×Q₈	C₂×D₇	semidirect
372. C₄×D₄	C₂×D₇	semidirect
592. 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×#542	2
#90420	2
#90419	2
#90399	2
#90371	2
#90370	2
#90366	2
#90362	2
#90350	2
#90341	2
#90330	2
#90327	2
D₇×C₂²⋊Q₈	2
#90316	2
#90297	2
#90294	2
#90269	2
#90263	2
#90248	2
#90237	2
D₇×#117	2
#90209	2
#3495	7