Subgroups — #13322994

Order 1792.

616 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11736776	C₂	1	1	yes	maximal, characteristic
2	#11736483	C₂	1	1	yes	maximal, characteristic
3	#11735962	C₂	1	1	yes	maximal, characteristic
4	C₇×#1569	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728549	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728246	C₂	1	1	yes	maximal, characteristic, complemented
7	#11727605	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726329	C₂	1	2	yes	maximal, complemented
9	#11726327	C₂	1	2	yes	maximal, complemented
10	#11726289	C₂	1	2	yes	maximal, complemented
11	#11726287	C₂	1	2	yes	maximal, complemented
12	C₂×C₄²×D₇	C₂²	1	1	yes	characteristic
13	C₇×#432	C₂²	1	1	yes	characteristic
14	C₇×#423	C₂²	1	1	yes	characteristic
15	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
16	#89898	—	2	1	no	—
17	#89898	C₄	1	2	yes	—
18	#89890	C₄	1	2	yes	—
19	M₁₆×Dic₇	—	2	1	no	—
20	#89698	C₂²	1	1	yes	characteristic
21	#89696	C₂²	1	1	yes	characteristic
22	C₄×#1136	C₂²	1	1	yes	characteristic
23	#89609	C₂²	1	1	yes	characteristic
24	#89609	C₂²	1	1	yes	characteristic
25	#89607	—	2	1	no	—
26	#89607	C₂²	1	2	yes	—
27	#89605	—	2	1	no	—
28	#89605	C₂²	1	2	yes	—
29	#89605	C₂²	1	1	yes	characteristic
30	#89605	C₂²	1	1	yes	characteristic
31	#89498	—	2	1	no	—
32	#89490	—	2	1	no	—
33	#89479	—	2	1	no	—
34	#89477	—	2	1	no	—
35	#89477	C₄	1	2	yes	—
36	#89477	C₄	1	2	yes	—
37	#89457	C₂²	1	2	yes	—
38	#89457	C₂²	1	2	yes	—
39	C₇×#335	C₂²	1	2	yes	complemented
40	C₇×#334	C₂²	1	2	yes	complemented
41	#89275	C₂²	1	2	yes	complemented
42	#89275	C₂²	1	2	yes	complemented
43	#89274	C₂²	1	2	yes	complemented
44	#89274	C₂²	1	2	yes	complemented
45	#89253	C₂²	1	2	yes	complemented
46	#89252	C₂²	1	2	yes	complemented
47	#17823	—	7	1	no	maximal, Sylow
48	C₂²×C₄×D₇	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₇	D₄	1	1	yes	characteristic
50	C₂²×C₄×D₇	Q₈	1	1	yes	characteristic
51	C₂×C₇×M₁₆	—	2	1	no	—
52	C₂×C₇×M₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
54	C₂×C₄×Dic₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₇	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₇	Q₈	1	1	yes	characteristic
57	C₂×#1136	—	2	1	no	—
58	C₂×#1136	C₂×C₄	1	2	yes	—
59	C₂×#1131	—	2	1	no	—
60	C₂×#1131	—	2	1	no	—
61	C₄²×D₇	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₇	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₇	D₄	1	1	yes	characteristic
64	C₄²×D₇	D₄	1	1	yes	characteristic
65	C₄²×D₇	Q₈	1	1	yes	characteristic
66	C₄²×D₇	Q₈	1	1	yes	characteristic
67	C₄²×D₇	C₂³	1	1	yes	characteristic
68	C₄²×D₇	C₂³	1	1	yes	characteristic
69	C₇×C₄⋊C₈	—	2	1	no	—
70	C₇×C₄⋊C₈	C₂³	1	2	yes	—
71	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
72	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
73	C₇×C₂²⋊C₈	—	2	1	no	—
74	C₇×#97	—	2	1	no	—
75	C₇×#97	C₂×C₄	1	2	yes	—
76	C₄×C₇×C₈	C₂³	1	2	yes	—
77	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
78	(C₂×D₇)⋊C₈	—	2	2	no	—
79	(C₂×D₇)⋊C₈	—	2	2	no	—
80	(C₂×D₇)⋊C₈	—	2	1	no	—
81	(C₂×D₇)⋊C₈	—	2	1	no	—
82	(C₂×D₇)⋊C₈	C₂×C₄	1	4	yes	—
83	(C₂×D₇)⋊C₈	C₂×C₄	1	4	yes	—
84	#6389	—	2	2	no	—
85	Dic₇⋊C₈	—	2	1	no	—
86	Dic₇⋊C₈	—	2	1	no	—
87	Dic₇⋊C₈	C₂×C₄	1	4	yes	—
88	Dic₇⋊C₈	C₂×C₄	1	4	yes	—
89	C₈×Dic₇	—	2	2	no	—
90	C₈×Dic₇	—	2	1	no	—
91	C₈×Dic₇	—	2	1	no	—
92	C₄⋊(C₇⋊C₈)	—	2	1	no	—
93	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
94	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
95	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
96	#6377	—	2	1	no	—
97	#6377	C₂×C₄	1	2	yes	—
98	C₄×C₇⋊C₈	C₂³	1	2	yes	—
99	#2920	—	7	1	no	—
100	#2920	—	7	1	no	—
101	#2920	—	7	1	no	—
102	#1574	—	7	2	no	—
103	#1574	—	7	2	no	—
104	#1572	—	7	2	no	—
105	#1572	—	7	2	no	—
106	#1569	—	7	1	no	—
107	#1569	—	7	1	no	—
108	#1569	—	7	1	no	—
109	#1569	D₇	1	1	yes	characteristic, complemented
110	C₂³×D₇	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
114	C₂²×Dic₇	C₄⋊C₄	1	1	yes	characteristic
115	C₂²×Dic₇	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×Dic₇	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₄×D₇	—	4	2	no	—
118	C₂×C₄×D₇	—	4	2	no	—
119	C₂×C₄×D₇	—	4	1	no	—
120	C₂×C₄×D₇	—	4	1	no	—
121	C₂×C₄×D₇	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×D₇	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×D₇	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×D₇	C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×D₇	C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×D₇	C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×D₇	C₂×Q₈	1	1	yes	characteristic
132	C₂×C₄×D₇	C₂×Q₈	1	1	yes	characteristic
133	C₇×M₁₆	—	4	2	no	—
134	C₇×M₁₆	—	4	2	no	—
135	C₂×C₇×C₈	—	2	1	no	—
136	C₂×C₇×C₈	—	2	1	no	—
137	C₂×C₇×C₈	—	2	2	no	—
138	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
139	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₇	C₂×Q₈	1	1	yes	characteristic
142	C₄²×C₇	C₂⁴	1	1	yes	characteristic
143	C₄×Dic₇	C₄⋊C₄	1	1	yes	characteristic
144	C₄×Dic₇	C₄⋊C₄	1	1	yes	characteristic
145	C₄×Dic₇	C₄⋊C₄	1	1	yes	characteristic
146	C₄×Dic₇	C₄⋊C₄	1	1	yes	characteristic
147	C₄×Dic₇	C₄⋊C₄	1	1	yes	characteristic
148	C₄×Dic₇	C₄⋊C₄	1	1	yes	characteristic
149	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
152	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
153	C₄×Dic₇	C₂×Q₈	1	1	yes	characteristic
154	C₄×Dic₇	C₂×Q₈	1	1	yes	characteristic
155	#1136	—	4	2	no	—
156	#1136	—	4	2	no	—
157	C₂×C₇⋊C₈	—	2	1	no	—
158	C₂×C₇⋊C₈	—	2	1	no	—
159	C₂×C₇⋊C₈	—	2	2	no	—
160	C₂×C₇⋊C₈	C₂²×C₄	1	4	yes	—
161	#1131	—	4	2	no	—
162	#1131	—	4	2	no	—
163	C₂²×C₄²	—	7	1	no	—
164	#432	—	7	2	no	—
165	#432	—	7	2	no	—
166	#432	—	7	1	no	—
167	#432	—	7	2	no	—
168	#432	—	14	1	no	—
169	#432	—	14	1	no	—
170	#432	C₂×D₇	1	1	yes	characteristic
171	#431	—	7	2	no	—
172	#431	—	7	2	no	—
173	#431	—	7	1	no	—
174	#431	—	7	1	no	—
175	#431	—	7	2	no	—
176	#431	—	14	1	no	—
177	#431	—	14	1	no	—
178	#423	—	7	2	no	—
179	#423	—	7	1	no	—
180	#423	—	7	1	no	—
181	#423	—	7	1	no	—
182	#423	C₂×D₇	1	1	yes	characteristic
183	#407	—	7	2	no	—
184	#407	—	14	1	no	—
185	#407	—	14	1	no	—
186	C₄×M₁₆	—	7	1	no	—
187	C₄×M₁₆	—	14	1	no	—
188	C₄×M₁₆	—	14	1	no	—
189	C₄×M₁₆	C₂×D₇	1	1	yes	characteristic
190	#335	—	7	2	no	—
191	#335	—	7	2	no	—
192	#335	—	7	2	no	—
193	#335	C₂×D₇	1	2	yes	complemented
194	#334	—	7	2	no	—
195	#334	—	7	2	no	—
196	#334	—	7	2	no	—
197	#334	C₂×D₇	1	2	yes	complemented
198	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂²×D₇	—	4	1	no	—
200	C₂²×D₇	—	4	1	no	—
201	C₂²×D₇	—	4	1	no	—
202	C₂²×D₇	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂²×D₇	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₇	—	2	2	no	—
205	C₂×C₄×C₇	—	2	1	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	4	1	no	—
208	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
214	C₂×Dic₇	—	2	2	no	—
215	C₂×Dic₇	—	4	1	no	—
216	C₂×Dic₇	—	4	1	no	—
217	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
221	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
223	C₄×D₇	—	2	2	no	—
224	C₄×D₇	—	2	2	no	—
225	C₄×D₇	—	2	1	no	—
226	C₄×D₇	—	2	1	no	—
227	C₄×D₇	—	2	1	no	—
228	C₄×D₇	—	2	1	no	—
229	C₄×D₇	—	2	2	no	—
230	C₄×D₇	—	2	2	no	—
231	C₄×D₇	—	4	1	no	—
232	C₄×D₇	—	4	1	no	—
233	C₄×D₇	—	4	1	no	—
234	C₄×D₇	—	4	1	no	—
235	C₄×D₇	—	4	1	no	—
236	C₄×D₇	—	4	1	no	—
237	C₇×C₈	—	2	4	no	—
238	C₇×C₈	—	4	1	no	—
239	C₇×C₈	—	4	1	no	—
240	C₇×C₈	—	4	2	no	—
241	C₇⋊C₈	—	2	4	no	—
242	C₇⋊C₈	—	4	1	no	—
243	C₇⋊C₈	—	4	1	no	—
244	C₇⋊C₈	—	4	2	no	—
245	C₂³×C₄	—	7	1	no	—
246	C₂³×C₄	—	7	1	no	—
247	C₂³×C₄	—	7	1	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	7	2	no	—
250	C₂×M₁₆	—	14	1	no	—
251	C₂×M₁₆	—	14	1	no	—
252	C₂×M₁₆	—	14	1	no	—
253	C₂×M₁₆	C₄×D₇	1	2	yes	—
254	C₂×C₄²	—	7	1	no	—
255	C₂×C₄²	—	7	1	no	—
256	C₂×C₄²	—	7	1	no	—
257	C₂×C₄²	—	7	1	no	—
258	C₂×C₄²	—	7	1	no	—
259	C₂×C₄²	—	7	1	no	—
260	C₂×C₄²	—	7	1	no	—
261	C₂×C₄²	—	7	1	no	—
262	C₂×C₄²	—	7	1	no	—
263	C₂×C₄²	—	7	1	no	—
264	C₂×C₄²	—	7	1	no	—
265	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	7	4	no	—
268	C₄⋊C₈	—	7	4	no	—
269	C₄⋊C₈	—	7	1	no	—
270	C₄⋊C₈	—	7	2	no	—
271	C₄⋊C₈	—	7	1	no	—
272	C₄⋊C₈	—	14	1	no	—
273	C₄⋊C₈	—	14	1	no	—
274	C₄⋊C₈	—	14	1	no	—
275	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
276	C₄⋊C₈	C₂²×D₇	1	2	yes	—
277	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
278	C₂²⋊C₈	—	2	1	no	—
279	C₂²⋊C₈	—	7	4	no	—
280	C₂²⋊C₈	—	7	4	no	—
281	C₂²⋊C₈	—	14	1	no	—
282	C₂²⋊C₈	—	14	1	no	—
283	C₂²⋊C₈	—	14	2	no	—
284	C₂²⋊C₈	—	14	2	no	—
285	C₂²⋊C₈	—	14	1	no	—
286	#97	—	2	1	no	—
287	#97	—	7	2	no	—
288	#97	—	14	2	no	—
289	#97	—	14	1	no	—
290	#97	C₄×D₇	1	2	yes	—
291	C₄×C₈	—	7	2	no	—
292	C₄×C₈	—	14	1	no	—
293	C₄×C₈	—	14	1	no	—
294	C₄×C₈	—	14	2	no	—
295	C₄×C₈	C₂²×D₇	1	2	yes	—
296	C₂²×C₇	—	2	1	no	—
297	C₂²×C₇	—	2	1	no	—
298	C₂²×C₇	—	2	1	no	—
299	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
300	C₂×D₇	—	2	1	no	—
301	C₂×D₇	—	2	1	no	—
302	C₂×D₇	—	2	1	no	—
303	C₂×D₇	—	2	1	no	—
304	C₂×D₇	—	2	1	no	—
305	C₂×D₇	—	2	1	no	—
306	C₂×D₇	—	4	4	no	—
307	C₄×C₇	—	2	1	no	—
308	C₄×C₇	—	2	1	no	—
309	C₄×C₇	—	2	1	no	—
310	C₄×C₇	—	2	1	no	—
311	C₄×C₇	#568	1	2	yes	—
312	C₄×C₇	#575	1	1	yes	characteristic
313	C₄×C₇	#575	1	1	yes	characteristic
314	Dic₇	—	2	1	no	—
315	Dic₇	—	2	1	no	—
316	Dic₇	—	2	1	no	—
317	Dic₇	—	2	1	no	—
318	Dic₇	—	2	1	no	—
319	Dic₇	#430	1	2	yes	—
320	C₂⁴	—	7	1	no	—
321	C₂²×C₄	—	7	1	no	—
322	C₂²×C₄	—	7	1	no	—
323	C₂²×C₄	—	7	1	no	—
324	C₂²×C₄	—	7	1	no	—
325	C₂²×C₄	—	7	1	no	—
326	C₂²×C₄	—	7	1	no	—
327	C₂²×C₄	—	7	1	no	—
328	C₂²×C₄	—	7	1	no	—
329	C₂²×C₄	—	7	1	no	—
330	C₂²×C₄	—	7	1	no	—
331	C₂²×C₄	—	7	1	no	—
332	C₂²×C₄	—	7	1	no	—
333	C₂²×C₄	—	7	1	no	—
334	C₂²×C₄	—	7	1	no	—
335	C₂²×C₄	—	7	1	no	—
336	C₂²×C₄	—	28	2	no	—
337	C₂²×C₄	—	28	1	no	—
338	C₂²×C₄	—	28	1	no	—
339	C₂²×C₄	—	28	2	no	—
340	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
341	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
342	C₂²×C₄	Q₈×D₇	1	1	yes	characteristic
343	M₁₆	—	4	2	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	28	2	no	—
346	M₁₆	—	28	2	no	—
347	M₁₆	—	28	2	no	—
348	M₁₆	—	28	2	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	7	4	no	—
353	C₂×C₈	—	14	1	no	—
354	C₂×C₈	—	14	2	no	—
355	C₂×C₈	—	14	1	no	—
356	C₂×C₈	C₂×C₄×D₇	1	4	yes	—
357	C₄²	—	7	1	no	—
358	C₄²	—	7	1	no	—
359	C₄²	—	7	1	no	—
360	C₄²	—	7	1	no	—
361	C₄²	—	7	1	no	—
362	C₄²	—	7	1	no	—
363	C₄²	—	7	1	no	—
364	C₄²	—	7	1	no	—
365	C₄²	—	7	1	no	—
366	C₄²	—	7	1	no	—
367	C₄²	—	7	1	no	—
368	C₄²	—	7	1	no	—
369	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
370	C₄²	D₄×D₇	1	1	yes	characteristic
371	C₄²	Q₈×D₇	1	1	yes	characteristic
372	C₄²	C₂³×D₇	1	1	yes	characteristic
373	C₂×C₇	—	4	1	no	—
374	C₂×C₇	#2905	1	1	yes	characteristic
375	C₂×C₇	#2911	1	1	yes	characteristic
376	C₂×C₇	C₂×#430	1	1	yes	characteristic
377	D₇	—	4	1	no	—
378	D₇	—	4	1	no	—
379	C₂³	—	7	1	no	—
380	C₂³	—	7	1	no	—
381	C₂³	—	28	1	no	—
382	C₂³	—	28	1	no	—
383	C₂³	—	28	1	no	—
384	C₂³	D₇×C₄⋊C₄	1	1	yes	characteristic
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	7	1	no	—
390	C₂×C₄	—	7	1	no	—
391	C₂×C₄	—	7	1	no	—
392	C₂×C₄	—	7	1	no	—
393	C₂×C₄	—	7	1	no	—
394	C₂×C₄	—	7	1	no	—
395	C₂×C₄	—	14	2	no	—
396	C₂×C₄	—	14	2	no	—
397	C₂×C₄	—	14	2	no	—
398	C₂×C₄	—	14	2	no	—
399	C₂×C₄	—	14	2	no	—
400	C₂×C₄	—	14	1	no	—
401	C₂×C₄	—	14	1	no	—
402	C₂×C₄	—	14	1	no	—
403	C₂×C₄	—	14	1	no	—
404	C₂×C₄	—	28	1	no	—
405	C₂×C₄	—	28	1	no	—
406	C₂×C₄	—	28	1	no	—
407	C₂×C₄	—	28	1	no	—
408	C₂×C₄	—	28	1	no	—
409	C₂×C₄	—	28	1	no	—
410	C₂×C₄	—	28	1	no	—
411	C₂×C₄	—	28	1	no	—
412	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
413	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
414	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
417	C₂×C₄	C₂×Q₈×D₇	1	1	yes	characteristic
418	C₈	—	2	4	no	—
419	C₈	—	4	2	no	—
420	C₈	—	4	1	no	—
421	C₈	—	4	1	no	—
422	C₈	—	14	4	no	—
423	C₈	—	28	1	no	—
424	C₈	—	28	1	no	—
425	C₈	—	28	2	no	—
426	C₇	#17823	1	1	yes	characteristic, complemented, Sylow
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	14	1	no	—
431	C₂²	—	14	1	no	—
432	C₂²	—	14	1	no	—
433	C₂²	—	14	1	no	—
434	C₂²	—	14	1	no	—
435	C₂²	—	14	1	no	—
436	C₂²	—	28	4	no	—
437	C₂²	C₂×D₇×C₄⋊C₄	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	7	2	no	—
443	C₄	—	14	1	no	—
444	C₄	—	14	1	no	—
445	C₄	—	14	1	no	—
446	C₄	—	14	1	no	—
447	C₄	—	14	1	no	—
448	C₄	#90436	1	2	yes	—
449	C₄	#90464	1	1	yes	characteristic
450	C₄	#90468	1	1	yes	characteristic
451	C₂	—	4	1	no	—
452	C₂	—	28	1	no	—
453	C₂	—	28	1	no	—
454	C₂	#11736493	1	1	yes	characteristic
455	C₂	#11736653	1	1	yes	characteristic
456	C₂	D₇×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting	C₇×#1569	C₂
socle	C₂²×C₇	C₂²×C₄⋊C₄
prime radical	C₂³×D₇	C₄⋊C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1569	D₇
hypocenter	C₇	#17823
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1569

Complements

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

N	H ≅ G/N	type
4. C₇×#1569	C₂	semidirect
5. #11728549	C₂	semidirect
6. #11728246	C₂	semidirect
7. #11727605	C₂	semidirect
8. #11726329	C₂	semidirect
9. #11726327	C₂	semidirect
10. #11726289	C₂	semidirect
11. #11726287	C₂	semidirect
39. C₇×#335	C₂²	semidirect
40. C₇×#334	C₂²	semidirect
41. #89275	C₂²	semidirect
42. #89275	C₂²	semidirect
43. #89274	C₂²	semidirect
44. #89274	C₂²	semidirect
45. #89253	C₂²	semidirect
46. #89252	C₂²	semidirect
109. #1569	D₇	semidirect
193. #335	C₂×D₇	semidirect
197. #334	C₂×D₇	semidirect
426. C₇	#17823	semidirect

Maximal subgroups

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

subgroup	index
#11736776	2
#11736483	2
#11735962	2
C₇×#1569	2
#11728549	2
#11728246	2
#11727605	2
#11726329	2
#11726327	2
#11726289	2
#11726287	2
#17823	7