Subgroups — D₇×#3549 #14261594

Order 1792.

8802 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇×H(3,𝔽₄)	C₂	1	4	yes	maximal, complemented
3	#11744155	C₂	1	4	yes	maximal, complemented
4	D₇×#555	C₂	1	6	yes	maximal, complemented
5	#11744036	C₂	1	6	yes	maximal, complemented
6	D₄²×D₇	C₂	1	6	yes	maximal, complemented
7	#11743685	C₂	1	6	yes	maximal, complemented
8	D₇×#535	C₂	1	12	yes	maximal, complemented
9	#11743394	C₂	1	12	yes	maximal, complemented
10	#11743320	C₂	1	3	yes	maximal, complemented
11	D₇×#532	C₂	1	3	yes	maximal, complemented
12	C₂×D₇×#41	C₂²	1	6	yes	complemented
13	C₂²×D₄×D₇	C₂²	1	12	yes	complemented
14	C₇×H(3,𝔽₄)	C₂²	1	4	yes	complemented
15	C₇×#555	C₂²	1	6	yes	complemented
16	C₇×D₄²	C₂²	1	6	yes	complemented
17	C₇×#535	C₂²	1	12	yes	complemented
18	C₇×#532	C₂²	1	3	yes	complemented
19	#90523	C₂²	1	6	yes	complemented
20	#90521	C₂²	1	12	yes	complemented
21	#90496	C₂²	1	12	yes	complemented
22	D₄×C₂²⋊D₇	C₂²	1	24	yes	complemented
23	#90425	C₂²	1	6	yes	complemented
24	#90416	C₂²	1	3	yes	complemented
25	D₇×C₄⋊Q₈	C₂²	1	3	yes	complemented
26	#90408	C₂²	1	6	yes	complemented
27	#90407	C₂²	1	3	yes	complemented
28	#90406	C₂²	1	24	yes	complemented
29	D₇×#127	C₂²	1	3	yes	—
30	D₇×#127	C₂²	1	8	yes	complemented
31	#90374	C₂²	1	24	yes	complemented
32	#90374	C₂²	1	12	yes	complemented
33	#90365	C₂²	1	24	yes	complemented
34	D₇×#124	C₂²	1	24	yes	complemented
35	D₇×#124	C₂²	1	6	yes	complemented
36	#90361	C₂²	1	24	yes	complemented
37	#90359	C₂²	1	6	yes	complemented
38	#90307	C₂²	1	24	yes	complemented
39	#90300	C₂²	1	24	yes	complemented
40	#90298	C₂²	1	24	yes	complemented
41	#90298	C₂²	1	24	yes	complemented
42	D₇×#121	C₂²	1	24	yes	complemented
43	D₇×#121	C₂²	1	12	yes	complemented
44	#90287	C₂²	1	12	yes	complemented
45	#90285	C₂²	1	24	yes	complemented
46	#90283	C₂²	1	24	yes	complemented
47	#90283	C₂²	1	24	yes	complemented
48	#90281	C₂²	1	24	yes	complemented
49	D₇×#120	C₂²	1	24	yes	complemented
50	D₇×#120	C₂²	1	8	yes	complemented
51	#90254	C₂²	1	12	yes	complemented
52	D₄×D₂₈	C₂²	1	12	yes	complemented
53	#90239	C₂²	1	12	yes	complemented
54	C₄×D₄×D₇	C₂²	1	12	yes	complemented
55	#90223	C₂²	1	24	yes	complemented
56	#90216	C₂²	1	12	yes	complemented
57	D₇×#117	C₂²	1	12	yes	complemented
58	#90168	C₂²	1	3	yes	complemented
59	C₂×C₄²×D₇	C₂²	1	1	yes	characteristic, complemented
60	C₂×#3549	—	7	1	no	maximal, Sylow
61	C₂⁴×D₇	C₂³	1	8	yes	—
62	C₂×C₇×#41	C₂³	1	6	yes	complemented
63	C₂²×C₇×D₄	C₂³	1	12	yes	complemented
64	C₂²×C₂²⋊D₇	C₂³	1	24	yes	complemented
65	D₇×#41	—	4	24	no	—
66	C₂×#1161	C₂³	1	6	yes	complemented
67	C₂×Q₈×D₇	C₂³	1	6	yes	—
68	C₂×#1159	C₂³	1	12	yes	complemented
69	C₂×#1159	C₂³	1	6	yes	complemented
70	C₂×D₄×D₇	—	4	48	no	—
71	C₂×D₄×D₇	C₂³	1	12	yes	—
72	C₂×D₄×D₇	C₂³	1	6	yes	—
73	C₂×D₄×D₇	C₂³	1	12	yes	—
74	C₂×D₄×D₇	C₂³	1	24	yes	—
75	C₂×D₄×D₇	C₂³	1	24	yes	complemented
76	C₂×D₄×D₇	C₂³	1	24	yes	complemented
77	C₂×#1157	C₂³	1	6	yes	complemented
78	C₂×#1157	C₂³	1	12	yes	complemented
79	C₂²×D₂₈	C₂³	1	12	yes	complemented
80	C₂²×C₄×D₇	C₂³	1	3	yes	—
81	C₂²×C₄×D₇	C₂³	1	12	yes	—
82	C₇×C₄⋊Q₈	C₂³	1	3	yes	complemented
83	C₇×#127	C₂³	1	3	yes	—
84	C₇×#127	C₂³	1	8	yes	complemented
85	C₇×#124	C₂³	1	6	yes	complemented
86	C₇×#124	C₂³	1	24	yes	complemented
87	C₇×#121	C₂³	1	12	yes	complemented
88	C₇×#121	C₂³	1	24	yes	complemented
89	C₇×#120	C₂³	1	24	yes	complemented
90	C₇×#120	C₂³	1	8	yes	complemented
91	C₄×C₇×D₄	C₂³	1	12	yes	complemented
92	C₇×#117	C₂³	1	12	yes	complemented
93	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic, complemented
94	#6516	C₂³	1	24	yes	complemented
95	#6516	C₂³	1	8	yes	complemented
96	#6510	C₂³	1	6	yes	complemented
97	#6510	C₂³	1	24	yes	complemented
98	#6507	C₂³	1	6	yes	complemented
99	#6503	C₂³	1	12	yes	—
100	#6503	C₂³	1	6	yes	—
101	#6503	C₂³	1	24	yes	complemented
102	#6503	C₂³	1	24	yes	complemented
103	#6502	C₂³	1	24	yes	complemented
104	#6502	C₂³	1	48	yes	complemented
105	#6501	C₂³	1	12	yes	complemented
106	#6501	C₂³	1	24	yes	complemented
107	#6500	C₂³	1	48	yes	complemented
108	#6500	C₂³	1	24	yes	complemented
109	#6500	C₂³	1	24	yes	complemented
110	#6499	C₂³	1	24	yes	complemented
111	#6499	C₂³	1	6	yes	complemented
112	D₄×Dic₇	C₂³	1	12	yes	complemented
113	#6493	C₂³	1	12	yes	complemented
114	#6493	C₂³	1	24	yes	complemented
115	C₄×C₂²⋊D₇	C₂³	1	24	yes	complemented
116	#6489	C₂³	1	12	yes	complemented
117	C₂×C₄×Dic₇	C₂³	1	3	yes	complemented
118	#6458	C₂³	1	12	yes	complemented
119	#6458	C₂³	1	24	yes	complemented
120	#6456	C₂³	1	12	yes	complemented
121	#6455	C₂³	1	24	yes	complemented
122	D₇×C₄⋊C₄	C₂³	1	12	yes	—
123	#6451	C₂³	1	12	yes	complemented
124	#6448	C₂³	1	24	yes	complemented
125	#6448	C₂³	1	48	yes	complemented
126	#6448	C₂³	1	48	yes	complemented
127	#6447	C₂³	1	48	yes	complemented
128	#6447	C₂³	1	24	yes	complemented
129	#6445	C₂³	1	24	yes	complemented
130	#6445	C₂³	1	48	yes	complemented
131	#6445	C₂³	1	24	yes	complemented
132	(C₂²⋊D₇)⋊C₄	C₂³	1	24	yes	complemented
133	D₇×C₂²⋊C₄	C₂³	1	24	yes	—
134	D₇×C₂²⋊C₄	C₂³	1	24	yes	—
135	#6440	C₂³	1	24	yes	complemented
136	#6438	C₂³	1	6	yes	complemented
137	#6438	C₂³	1	24	yes	complemented
138	#6437	C₂³	1	3	yes	—
139	#6437	C₂³	1	8	yes	complemented
140	C₄×D₂₈	C₂³	1	12	yes	complemented
141	#6435	C₂³	1	24	yes	complemented
142	C₄²×D₇	C₂³	1	3	yes	—
143	C₄²×D₇	C₂³	1	8	yes	—
144	C₄²×D₇	C₂³	1	1	yes	characteristic
145	C₄²×D₇	C₂³	1	3	yes	complemented
146	C₄²×D₇	C₂³	1	1	yes	characteristic, complemented
147	#6432	C₂³	1	3	yes	complemented
148	#3549	—	7	4	no	—
149	#3549	—	7	6	no	—
150	#3549	—	7	6	no	—
151	#3549	—	7	12	no	—
152	#3549	—	7	3	no	—
153	#3549	D₇	1	1	yes	characteristic, direct product factor
154	C₂×H(3,𝔽₄)	—	7	4	no	—
155	C₂×#555	—	7	6	no	—
156	C₂×D₄²	—	7	6	no	—
157	C₂×#535	—	7	12	no	—
158	C₂×#532	—	7	3	no	—
159	C₂⁴×C₇	C₂⁴	1	8	yes	—
160	C₂³×D₇	—	4	48	no	—
161	C₂³×D₇	C₂⁴	1	12	yes	—
162	C₂³×D₇	C₂⁴	1	1	yes	characteristic
163	C₂³×D₇	C₂⁴	1	24	yes	—
164	C₇×#41	—	4	12	no	—
165	C₂×C₇×Q₈	C₂⁴	1	6	yes	—
166	C₂×C₇×D₄	—	4	24	no	—
167	C₂×C₇×D₄	C₂⁴	1	12	yes	—
168	C₂×C₇×D₄	C₂⁴	1	6	yes	—
169	C₂×C₇×D₄	C₂⁴	1	24	yes	—
170	C₂×C₇×D₄	C₂⁴	1	12	yes	—
171	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
172	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
173	C₂×C₂²⋊D₇	—	4	48	no	—
174	C₂×C₂²⋊D₇	C₂⁴	1	24	yes	—
175	C₂×C₂²⋊D₇	C₂⁴	1	12	yes	—
176	C₂×C₂²⋊D₇	C₂⁴	1	12	yes	—
177	C₂×C₂²⋊D₇	C₂⁴	1	48	yes	—
178	C₂×C₂²⋊D₇	C₂⁴	1	12	yes	—
179	C₂²×Dic₇	C₂⁴	1	12	yes	—
180	C₂²×Dic₇	C₂⁴	1	3	yes	—
181	#1161	—	4	12	no	—
182	Q₈×D₇	—	4	12	no	—
183	#1159	—	4	24	no	—
184	#1159	—	4	12	no	—
185	D₄×D₇	—	2	48	no	—
186	D₄×D₇	—	4	48	no	—
187	D₄×D₇	—	4	48	no	—
188	D₄×D₇	—	4	48	no	—
189	D₄×D₇	—	4	24	no	—
190	D₄×D₇	—	4	12	no	—
191	#1157	—	4	24	no	—
192	#1157	—	4	12	no	—
193	C₂×D₂₈	—	4	24	no	—
194	C₂×D₂₈	C₂⁴	1	12	yes	—
195	C₂×D₂₈	C₂⁴	1	6	yes	—
196	C₂×D₂₈	C₂⁴	1	12	yes	—
197	C₂×D₂₈	C₂⁴	1	24	yes	—
198	C₂×C₄×D₇	—	2	48	no	—
199	C₂×C₄×D₇	—	2	12	no	—
200	C₂×C₄×D₇	C₂⁴	1	3	yes	—
201	C₂×C₄×D₇	C₂⁴	1	12	yes	—
202	C₂×C₄×D₇	C₂⁴	1	3	yes	—
203	C₂×C₄×D₇	C₂⁴	1	3	yes	—
204	C₂×C₄×D₇	C₂⁴	1	12	yes	—
205	C₂×C₄×D₇	C₂⁴	1	12	yes	—
206	C₂×C₄×D₇	C₂⁴	1	3	yes	—
207	C₂×Dic₁₄	C₂⁴	1	6	yes	—
208	C₂×Dic₁₄	C₂⁴	1	12	yes	—
209	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
210	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
211	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
212	C₄²×C₇	C₂⁴	1	3	yes	—
213	C₄²×C₇	C₂⁴	1	1	yes	characteristic
214	C₄²×C₇	C₂⁴	1	8	yes	—
215	C₂²⋊Dic₇	C₂⁴	1	24	yes	—
216	C₂²⋊Dic₇	C₂⁴	1	24	yes	—
217	(C₂×D₇)⋊C₄	C₂⁴	1	48	yes	—
218	(C₂×D₇)⋊C₄	C₂⁴	1	24	yes	—
219	(C₂×D₇)⋊C₄	C₂⁴	1	24	yes	—
220	C₄⋊Dic₇	C₂⁴	1	12	yes	—
221	Dic₇⋊C₄	C₂⁴	1	24	yes	—
222	C₄×Dic₇	C₂⁴	1	3	yes	—
223	C₄×Dic₇	C₂⁴	1	3	yes	—
224	C₄×Dic₇	C₂⁴	1	6	yes	—
225	C₄×Dic₇	C₂⁴	1	24	yes	—
226	C₂²×#41	—	7	6	no	—
227	C₂³×D₄	—	7	12	no	—
228	H(3,𝔽₄)	—	7	24	no	—
229	H(3,𝔽₄)	—	7	12	no	—
230	H(3,𝔽₄)	—	7	24	no	—
231	H(3,𝔽₄)	C₂×D₇	1	4	yes	complemented
232	#555	—	7	6	no	—
233	#555	—	7	24	no	—
234	#555	—	7	24	no	—
235	#555	—	7	12	no	—
236	#555	—	7	24	no	—
237	#555	C₂×D₇	1	6	yes	complemented
238	D₄²	—	7	24	no	—
239	D₄²	—	7	6	no	—
240	D₄²	—	7	24	no	—
241	D₄²	—	7	24	no	—
242	D₄²	—	7	12	no	—
243	D₄²	C₂×D₇	1	6	yes	complemented
244	#535	—	7	12	no	—
245	#535	—	7	12	no	—
246	#535	—	7	24	no	—
247	#535	—	7	24	no	—
248	#535	—	7	24	no	—
249	#535	—	7	24	no	—
250	#535	—	7	24	no	—
251	#535	—	7	24	no	—
252	#535	—	7	12	no	—
253	#535	C₂×D₇	1	12	yes	complemented
254	#532	—	7	6	no	—
255	#532	—	7	3	no	—
256	#532	—	7	3	no	—
257	#532	—	7	6	no	—
258	#532	—	7	12	no	—
259	#532	—	7	12	no	—
260	#532	—	7	3	no	—
261	#532	C₂×D₇	1	3	yes	complemented
262	C₂×C₄⋊Q₈	—	7	3	no	—
263	C₂×#127	—	7	3	no	—
264	C₂×#127	—	7	8	no	—
265	C₂×#124	—	7	6	no	—
266	C₂×#124	—	7	24	no	—
267	C₂×#121	—	7	12	no	—
268	C₂×#121	—	7	24	no	—
269	C₂×#120	—	7	8	no	—
270	C₂×#120	—	7	24	no	—
271	C₂×C₄×D₄	—	7	12	no	—
272	C₂×#117	—	7	12	no	—
273	C₂²×C₄²	—	7	1	no	—
274	C₂³×C₇	—	4	24	no	—
275	C₂³×C₇	C₂⁵	1	12	yes	—
276	C₂³×C₇	C₂⁵	1	1	yes	characteristic
277	C₂²×D₇	—	2	6	no	—
278	C₂²×D₇	—	2	24	no	—
279	C₂²×D₇	—	2	48	no	—
280	C₂²×D₇	—	4	24	no	—
281	C₂²×D₇	—	4	48	no	—
282	C₂²×D₇	—	8	64	no	—
283	C₂²×D₇	C₂⁵	1	12	yes	—
284	C₂²×D₇	C₂⁵	1	1	yes	characteristic
285	C₂²×D₇	C₂⁵	1	1	yes	characteristic
286	C₇×Q₈	—	4	6	no	—
287	C₇×D₄	—	2	24	no	—
288	C₇×D₄	—	4	24	no	—
289	C₇×D₄	—	4	6	no	—
290	C₇×D₄	—	4	12	no	—
291	C₂×C₄×C₇	—	2	24	no	—
292	C₂×C₄×C₇	—	2	6	no	—
293	C₂×C₄×C₇	C₂⁵	1	12	yes	—
294	C₂×C₄×C₇	C₂⁵	1	3	yes	—
295	C₂×C₄×C₇	C₂⁵	1	3	yes	—
296	C₂²⋊D₇	—	2	48	no	—
297	C₂²⋊D₇	—	4	12	no	—
298	C₂²⋊D₇	—	4	12	no	—
299	C₂²⋊D₇	—	4	12	no	—
300	C₂²⋊D₇	—	4	48	no	—
301	C₂×Dic₇	—	2	6	no	—
302	C₂×Dic₇	—	2	24	no	—
303	C₂×Dic₇	C₂⁵	1	12	yes	—
304	C₂×Dic₇	C₂⁵	1	3	yes	—
305	C₂×Dic₇	C₂⁵	1	3	yes	—
306	D₂₈	—	2	24	no	—
307	D₂₈	—	4	24	no	—
308	D₂₈	—	4	6	no	—
309	D₂₈	—	4	12	no	—
310	C₄×D₇	—	2	24	no	—
311	C₄×D₇	—	2	6	no	—
312	C₄×D₇	—	2	6	no	—
313	C₄×D₇	—	2	24	no	—
314	C₄×D₇	—	2	24	no	—
315	C₄×D₇	—	2	6	no	—
316	C₄×D₇	H(5,𝔽₂)	1	12	yes	—
317	Dic₁₄	—	4	12	no	—
318	Dic₁₄	—	4	6	no	—
319	C₂⁵	—	7	8	no	—
320	C₂×#41	—	7	6	no	—
321	C₂×#41	—	7	12	no	—
322	C₂×#41	—	7	6	no	—
323	C₂×#41	—	7	12	no	—
324	C₂×#41	—	7	6	no	—
325	C₂×#41	—	28	24	no	—
326	C₂×#41	C₂²×D₇	1	6	yes	complemented
327	C₂²×Q₈	—	7	6	no	—
328	C₂²×D₄	—	7	24	no	—
329	C₂²×D₄	—	7	12	no	—
330	C₂²×D₄	—	7	6	no	—
331	C₂²×D₄	—	7	24	no	—
332	C₂²×D₄	—	7	12	no	—
333	C₂²×D₄	—	7	24	no	—
334	C₂²×D₄	—	7	24	no	—
335	C₂²×D₄	—	7	12	no	—
336	C₂²×D₄	—	28	48	no	—
337	C₂²×D₄	C₂²×D₇	1	12	yes	complemented
338	C₂³×C₄	—	7	12	no	—
339	C₂³×C₄	—	7	3	no	—
340	C₄⋊Q₈	—	7	6	no	—
341	C₄⋊Q₈	—	7	12	no	—
342	C₄⋊Q₈	—	7	3	no	—
343	C₄⋊Q₈	C₂²×D₇	1	3	yes	complemented
344	#127	—	7	6	no	—
345	#127	—	7	12	no	—
346	#127	—	7	24	no	—
347	#127	—	7	24	no	—
348	#127	—	7	3	no	—
349	#127	—	7	8	no	—
350	#127	C₂²×D₇	1	3	yes	—
351	#127	C₂²×D₇	1	8	yes	complemented
352	#124	—	7	6	no	—
353	#124	—	7	24	no	—
354	#124	—	7	6	no	—
355	#124	—	7	24	no	—
356	#124	—	7	24	no	—
357	#124	—	7	48	no	—
358	#124	—	7	48	no	—
359	#124	—	7	6	no	—
360	#124	—	7	24	no	—
361	#124	C₂²×D₇	1	6	yes	complemented
362	#124	C₂²×D₇	1	24	yes	complemented
363	#121	—	7	12	no	—
364	#121	—	7	24	no	—
365	#121	—	7	24	no	—
366	#121	—	7	48	no	—
367	#121	—	7	12	no	—
368	#121	—	7	24	no	—
369	#121	—	7	12	no	—
370	#121	—	7	24	no	—
371	#121	—	7	24	no	—
372	#121	—	7	48	no	—
373	#121	C₂²×D₇	1	12	yes	complemented
374	#121	C₂²×D₇	1	24	yes	complemented
375	#120	—	7	8	no	—
376	#120	—	7	24	no	—
377	#120	—	7	24	no	—
378	#120	—	7	24	no	—
379	#120	—	7	48	no	—
380	#120	—	7	24	no	—
381	#120	—	7	48	no	—
382	#120	—	7	24	no	—
383	#120	C₂²×D₇	1	8	yes	complemented
384	#120	C₂²×D₇	1	24	yes	complemented
385	C₄×D₄	—	7	12	no	—
386	C₄×D₄	—	7	24	no	—
387	C₄×D₄	—	7	12	no	—
388	C₄×D₄	—	7	24	no	—
389	C₄×D₄	—	7	12	no	—
390	C₄×D₄	C₂²×D₇	1	12	yes	complemented
391	#117	—	7	12	no	—
392	#117	—	7	24	no	—
393	#117	—	7	24	no	—
394	#117	—	7	24	no	—
395	#117	C₂²×D₇	1	12	yes	complemented
396	C₂×C₄⋊C₄	—	7	12	no	—
397	C₂×C₂²⋊C₄	—	7	24	no	—
398	C₂×C₂²⋊C₄	—	7	24	no	—
399	C₂×C₄²	—	7	3	no	—
400	C₂×C₄²	—	7	8	no	—
401	C₂×C₄²	—	7	3	no	—
402	C₂×C₄²	—	7	1	no	—
403	C₂×C₄²	—	7	1	no	—
404	C₂×C₄²	—	7	3	no	—
405	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic, complemented
406	C₂²×C₇	—	2	3	no	—
407	C₂²×C₇	—	2	12	no	—
408	C₂²×C₇	—	2	24	no	—
409	C₂²×C₇	—	8	16	no	—
410	C₂²×C₇	C₂⁶	1	1	yes	characteristic
411	C₂×D₇	—	2	3	no	—
412	C₂×D₇	—	2	12	no	—
413	C₂×D₇	—	2	24	no	—
414	C₂×D₇	—	4	4	no	—
415	C₂×D₇	—	4	48	no	—
416	C₂×D₇	—	8	48	no	—
417	C₂×D₇	C₂×H(5,𝔽₂)	1	6	yes	—
418	C₄×C₇	—	2	3	no	—
419	C₄×C₇	—	2	12	no	—
420	C₄×C₇	C₂×H(5,𝔽₂)	1	6	yes	—
421	Dic₇	—	2	3	no	—
422	Dic₇	—	2	12	no	—
423	Dic₇	C₂×H(5,𝔽₂)	1	6	yes	—
424	C₂⁴	—	7	12	no	—
425	C₂⁴	—	7	1	no	—
426	C₂⁴	—	7	24	no	—
427	C₂⁴	—	28	48	no	—
428	C₂⁴	C₂³×D₇	1	8	yes	—
429	#41	—	4	12	no	—
430	#41	—	28	24	no	—
431	#41	—	28	12	no	—
432	#41	—	28	24	no	—
433	#41	—	28	12	no	—
434	#41	—	28	12	no	—
435	C₂×Q₈	—	7	12	no	—
436	C₂×Q₈	—	7	6	no	—
437	C₂×Q₈	—	28	12	no	—
438	C₂×Q₈	C₂³×D₇	1	6	yes	—
439	C₂×D₄	—	4	24	no	—
440	C₂×D₄	—	7	24	no	—
441	C₂×D₄	—	7	12	no	—
442	C₂×D₄	—	7	48	no	—
443	C₂×D₄	—	7	12	no	—
444	C₂×D₄	—	7	12	no	—
445	C₂×D₄	—	7	12	no	—
446	C₂×D₄	—	7	6	no	—
447	C₂×D₄	—	7	24	no	—
448	C₂×D₄	—	7	12	no	—
449	C₂×D₄	—	14	48	no	—
450	C₂×D₄	—	28	24	no	—
451	C₂×D₄	—	28	48	no	—
452	C₂×D₄	—	28	48	no	—
453	C₂×D₄	—	28	48	no	—
454	C₂×D₄	—	28	24	no	—
455	C₂×D₄	—	28	12	no	—
456	C₂×D₄	—	28	48	no	—
457	C₂×D₄	C₂³×D₇	1	12	yes	—
458	C₂×D₄	C₂³×D₇	1	6	yes	—
459	C₂×D₄	C₂³×D₇	1	24	yes	—
460	C₂×D₄	C₂³×D₇	1	12	yes	—
461	C₂²×C₄	—	7	3	no	—
462	C₂²×C₄	—	7	3	no	—
463	C₂²×C₄	—	7	12	no	—
464	C₂²×C₄	—	7	3	no	—
465	C₂²×C₄	—	7	12	no	—
466	C₂²×C₄	—	7	3	no	—
467	C₂²×C₄	—	7	3	no	—
468	C₂²×C₄	—	7	12	no	—
469	C₂²×C₄	—	7	12	no	—
470	C₂²×C₄	—	14	48	no	—
471	C₂²×C₄	—	14	12	no	—
472	C₂²×C₄	C₂³×D₇	1	3	yes	—
473	C₂²×C₄	C₂³×D₇	1	12	yes	—
474	C₄⋊C₄	—	7	24	no	—
475	C₄⋊C₄	—	7	12	no	—
476	C₄⋊C₄	C₂³×D₇	1	12	yes	—
477	C₂²⋊C₄	—	7	24	no	—
478	C₂²⋊C₄	—	7	24	no	—
479	C₂²⋊C₄	—	7	48	no	—
480	C₂²⋊C₄	—	7	24	no	—
481	C₂²⋊C₄	—	7	24	no	—
482	C₂²⋊C₄	C₂³×D₇	1	24	yes	—
483	C₂²⋊C₄	C₂³×D₇	1	24	yes	—
484	C₄²	—	7	3	no	—
485	C₄²	—	7	6	no	—
486	C₄²	—	7	3	no	—
487	C₄²	—	7	24	no	—
488	C₄²	C₂³×D₇	1	3	yes	—
489	C₄²	C₂³×D₇	1	1	yes	characteristic
490	C₄²	C₂³×D₇	1	8	yes	—
491	C₂×C₇	—	4	12	no	—
492	C₂×C₇	—	4	1	no	—
493	C₂×C₇	C₂²×H(5,𝔽₂)	1	3	yes	—
494	D₇	—	4	1	no	—
495	D₇	—	4	12	no	—
496	D₇	#3549	1	4	yes	direct product factor
497	C₂³	—	4	24	no	—
498	C₂³	—	7	1	no	—
499	C₂³	—	7	12	no	—
500	C₂³	—	7	1	no	—
501	C₂³	—	14	6	no	—
502	C₂³	—	14	24	no	—
503	C₂³	—	14	48	no	—
504	C₂³	—	28	24	no	—
505	C₂³	—	28	48	no	—
506	C₂³	—	56	64	no	—
507	C₂³	C₂⁴×D₇	1	12	yes	—
508	C₂³	C₂⁴×D₇	1	1	yes	characteristic
509	Q₈	—	4	6	no	—
510	Q₈	—	28	12	no	—
511	Q₈	—	28	6	no	—
512	D₄	—	2	24	no	—
513	D₄	—	4	24	no	—
514	D₄	—	4	12	no	—
515	D₄	—	4	6	no	—
516	D₄	—	14	48	no	—
517	D₄	—	14	24	no	—
518	D₄	—	28	24	no	—
519	D₄	—	28	12	no	—
520	D₄	—	28	6	no	—
521	D₄	—	28	48	no	—
522	D₄	—	28	12	no	—
523	D₄	—	28	12	no	—
524	D₄	—	28	12	no	—
525	C₂×C₄	—	2	24	no	—
526	C₂×C₄	—	2	6	no	—
527	C₂×C₄	—	7	3	no	—
528	C₂×C₄	—	7	12	no	—
529	C₂×C₄	—	7	3	no	—
530	C₂×C₄	—	7	12	no	—
531	C₂×C₄	—	14	24	no	—
532	C₂×C₄	—	14	6	no	—
533	C₂×C₄	—	14	24	no	—
534	C₂×C₄	—	14	6	no	—
535	C₂×C₄	—	14	24	no	—
536	C₂×C₄	—	14	6	no	—
537	C₂×C₄	—	14	24	no	—
538	C₂×C₄	—	14	6	no	—
539	C₂×C₄	C₂⁴×D₇	1	3	yes	—
540	C₂×C₄	C₂⁴×D₇	1	12	yes	—
541	C₂×C₄	C₂⁴×D₇	1	3	yes	—
542	C₇	C₂×#3549	1	1	yes	characteristic, complemented, Sylow
543	C₂²	—	2	3	no	—
544	C₂²	—	2	12	no	—
545	C₂²	—	2	24	no	—
546	C₂²	—	7	6	no	—
547	C₂²	—	8	16	no	—
548	C₂²	—	14	3	no	—
549	C₂²	—	14	12	no	—
550	C₂²	—	14	24	no	—
551	C₂²	—	28	48	no	—
552	C₂²	—	28	4	no	—
553	C₂²	—	56	48	no	—
554	C₂²	C₂⁵×D₇	1	1	yes	characteristic
555	C₄	—	2	12	no	—
556	C₄	—	2	3	no	—
557	C₄	—	7	6	no	—
558	C₄	—	14	12	no	—
559	C₄	—	14	3	no	—
560	C₄	D₇×H(5,𝔽₂)	1	6	yes	—
561	C₂	—	4	12	no	—
562	C₂	—	4	1	no	—
563	C₂	—	7	4	no	—
564	C₂	—	28	12	no	—
565	C₂	—	28	1	no	—
566	C₂	C₂×D₇×H(5,𝔽₂)	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁶
Fitting	C₇×#3549	C₂
hypercenter	#3549	D₇
hypocenter	C₇	C₂×#3549
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #3549

Complements

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

N	H ≅ G/N	type
1. C₇×#3549	C₂	semidirect
2. D₇×H(3,𝔽₄)	C₂	semidirect
3. #11744155	C₂	semidirect
4. D₇×#555	C₂	semidirect
5. #11744036	C₂	semidirect
6. D₄²×D₇	C₂	semidirect
7. #11743685	C₂	semidirect
8. D₇×#535	C₂	semidirect
9. #11743394	C₂	semidirect
10. #11743320	C₂	semidirect
11. D₇×#532	C₂	semidirect
12. C₂×D₇×#41	C₂²	semidirect
13. C₂²×D₄×D₇	C₂²	semidirect
14. C₇×H(3,𝔽₄)	C₂²	semidirect
15. C₇×#555	C₂²	semidirect
16. C₇×D₄²	C₂²	semidirect
17. C₇×#535	C₂²	semidirect
18. C₇×#532	C₂²	semidirect
19. #90523	C₂²	semidirect
20. #90521	C₂²	semidirect
21. #90496	C₂²	semidirect
22. D₄×C₂²⋊D₇	C₂²	semidirect
23. #90425	C₂²	semidirect
24. #90416	C₂²	semidirect
25. D₇×C₄⋊Q₈	C₂²	semidirect
26. #90408	C₂²	semidirect
27. #90407	C₂²	semidirect
28. #90406	C₂²	semidirect
30. D₇×#127	C₂²	semidirect
31. #90374	C₂²	semidirect
32. #90374	C₂²	semidirect
33. #90365	C₂²	semidirect
34. D₇×#124	C₂²	semidirect
35. D₇×#124	C₂²	semidirect
36. #90361	C₂²	semidirect
37. #90359	C₂²	semidirect
38. #90307	C₂²	semidirect
39. #90300	C₂²	semidirect
40. #90298	C₂²	semidirect
41. #90298	C₂²	semidirect
42. D₇×#121	C₂²	semidirect
43. D₇×#121	C₂²	semidirect
44. #90287	C₂²	semidirect
45. #90285	C₂²	semidirect
46. #90283	C₂²	semidirect
47. #90283	C₂²	semidirect
48. #90281	C₂²	semidirect
49. D₇×#120	C₂²	semidirect
50. D₇×#120	C₂²	semidirect
51. #90254	C₂²	semidirect
52. D₄×D₂₈	C₂²	semidirect
53. #90239	C₂²	semidirect
54. C₄×D₄×D₇	C₂²	semidirect
55. #90223	C₂²	semidirect
56. #90216	C₂²	semidirect
57. D₇×#117	C₂²	semidirect
58. #90168	C₂²	semidirect
59. C₂×C₄²×D₇	C₂²	semidirect
62. C₂×C₇×#41	C₂³	semidirect
63. C₂²×C₇×D₄	C₂³	semidirect
64. C₂²×C₂²⋊D₇	C₂³	semidirect
66. C₂×#1161	C₂³	semidirect
68. C₂×#1159	C₂³	semidirect
69. C₂×#1159	C₂³	semidirect
75. C₂×D₄×D₇	C₂³	semidirect
76. C₂×D₄×D₇	C₂³	semidirect
77. C₂×#1157	C₂³	semidirect
78. C₂×#1157	C₂³	semidirect
79. C₂²×D₂₈	C₂³	semidirect
82. C₇×C₄⋊Q₈	C₂³	semidirect
84. C₇×#127	C₂³	semidirect
85. C₇×#124	C₂³	semidirect
86. C₇×#124	C₂³	semidirect
87. C₇×#121	C₂³	semidirect
88. C₇×#121	C₂³	semidirect
89. C₇×#120	C₂³	semidirect
90. C₇×#120	C₂³	semidirect
91. C₄×C₇×D₄	C₂³	semidirect
92. C₇×#117	C₂³	semidirect
93. C₂×C₄²×C₇	C₂³	semidirect
94. #6516	C₂³	semidirect
95. #6516	C₂³	semidirect
96. #6510	C₂³	semidirect
97. #6510	C₂³	semidirect
98. #6507	C₂³	semidirect
101. #6503	C₂³	semidirect
102. #6503	C₂³	semidirect
103. #6502	C₂³	semidirect
104. #6502	C₂³	semidirect
105. #6501	C₂³	semidirect
106. #6501	C₂³	semidirect
107. #6500	C₂³	semidirect
108. #6500	C₂³	semidirect
109. #6500	C₂³	semidirect
110. #6499	C₂³	semidirect
111. #6499	C₂³	semidirect
112. D₄×Dic₇	C₂³	semidirect
113. #6493	C₂³	semidirect
114. #6493	C₂³	semidirect
115. C₄×C₂²⋊D₇	C₂³	semidirect
116. #6489	C₂³	semidirect
117. C₂×C₄×Dic₇	C₂³	semidirect
118. #6458	C₂³	semidirect
119. #6458	C₂³	semidirect
120. #6456	C₂³	semidirect
121. #6455	C₂³	semidirect
123. #6451	C₂³	semidirect
124. #6448	C₂³	semidirect
125. #6448	C₂³	semidirect
126. #6448	C₂³	semidirect
127. #6447	C₂³	semidirect
128. #6447	C₂³	semidirect
129. #6445	C₂³	semidirect
130. #6445	C₂³	semidirect
131. #6445	C₂³	semidirect
132. (C₂²⋊D₇)⋊C₄	C₂³	semidirect
135. #6440	C₂³	semidirect
136. #6438	C₂³	semidirect
137. #6438	C₂³	semidirect
139. #6437	C₂³	semidirect
140. C₄×D₂₈	C₂³	semidirect
141. #6435	C₂³	semidirect
145. C₄²×D₇	C₂³	semidirect
146. C₄²×D₇	C₂³	semidirect
147. #6432	C₂³	semidirect
153. #3549	D₇	direct (N × H)
231. H(3,𝔽₄)	C₂×D₇	semidirect
237. #555	C₂×D₇	semidirect
243. D₄²	C₂×D₇	semidirect
253. #535	C₂×D₇	semidirect
261. #532	C₂×D₇	semidirect
326. C₂×#41	C₂²×D₇	semidirect
337. C₂²×D₄	C₂²×D₇	semidirect
343. C₄⋊Q₈	C₂²×D₇	semidirect
351. #127	C₂²×D₇	semidirect
361. #124	C₂²×D₇	semidirect
362. #124	C₂²×D₇	semidirect
373. #121	C₂²×D₇	semidirect
374. #121	C₂²×D₇	semidirect
383. #120	C₂²×D₇	semidirect
384. #120	C₂²×D₇	semidirect
390. C₄×D₄	C₂²×D₇	semidirect
395. #117	C₂²×D₇	semidirect
405. C₂×C₄²	C₂²×D₇	semidirect
496. D₇	#3549	direct (N × H)
542. C₇	C₂×#3549	semidirect

Maximal subgroups

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

subgroup	index
C₇×#3549	2
D₇×H(3,𝔽₄)	2
#11744155	2
D₇×#555	2
#11744036	2
D₄²×D₇	2
#11743685	2
D₇×#535	2
#11743394	2
#11743320	2
D₇×#532	2
C₂×#3549	7

Subgroups — D7×#3549 #14261594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×#3549 #14261594