Subgroups — C₇×#19228 #13196444

Order 1792.

584 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3248	C₂	1	2	yes	maximal
2	C₇×#3170	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2966	C₂	1	1	yes	maximal, characteristic
4	C₇×#1694	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1693	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1690	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1689	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1680	C₂	1	2	yes	maximal, complemented
9	C₇×#1679	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1552	C₂	1	2	yes	maximal, complemented
12	C₇×#533	C₂²	1	2	yes	—
13	C₇×#529	C₂²	1	1	yes	characteristic
14	C₇×#500	C₂²	1	1	yes	characteristic
15	C₇×#494	C₂²	1	1	yes	characteristic
16	C₇×#487	C₂²	1	2	yes	—
17	C₇×#479	—	2	2	no	—
18	C₇×#475	C₂²	1	2	yes	—
19	C₇×#474	C₂²	1	2	yes	—
20	C₇×#467	—	2	1	no	—
21	C₇×#467	—	2	1	no	—
22	C₇×#467	—	2	2	no	—
23	C₇×#465	—	2	2	no	—
24	C₇×#464	—	2	2	no	—
25	C₇×#462	C₂²	1	2	yes	—
26	C₇×#461	C₂²	1	2	yes	—
27	C₇×#446	C₂²	1	1	yes	characteristic
28	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
29	C₄×C₇×Q₁₆	—	2	1	no	—
30	C₄×C₇×Q₁₆	—	2	1	no	—
31	C₇×#436	C₂²	1	1	yes	characteristic
32	C₇×#435	—	2	1	no	—
33	C₇×C₈×D₄	—	2	1	no	—
34	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
35	C₇×#433	—	2	1	no	—
36	C₇×#432	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
38	C₇×#405	—	2	1	no	—
39	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
40	C₇×#334	C₂²	1	2	yes	—
41	C₇×#334	C₂²	1	1	yes	characteristic
42	C₇×#334	C₂²	1	1	yes	characteristic
43	C₇×#332	C₂²	1	2	yes	—
44	C₇×#332	C₂²	1	2	yes	—
45	C₇×#332	C₂²	1	2	yes	—
46	C₇×#332	C₂²	1	2	yes	—
47	#19228	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×Q₁₆	—	2	2	no	—
49	C₂×C₇×Q₁₆	—	2	1	no	—
50	C₂×C₇×Q₁₆	—	2	1	no	—
51	C₂×C₇×SD₁₆	—	2	2	no	—
52	C₂×C₇×M₁₆	—	2	1	no	—
53	C₂²×C₇×C₈	—	2	2	no	—
54	C₂²×C₇×C₈	—	2	1	no	—
55	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
56	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
57	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₇×#126	—	2	1	no	—
60	C₇×#125	—	2	2	no	—
61	C₇×#125	D₄	1	1	yes	characteristic
62	C₇×#124	D₄	1	1	yes	characteristic
63	C₇×#123	—	2	1	no	—
64	C₇×C₂²⋊Q₈	—	2	2	no	—
65	C₇×C₂²⋊Q₈	—	2	2	no	—
66	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
67	C₇×#121	D₄	1	1	yes	characteristic
68	C₄×C₇×Q₈	—	2	2	no	—
69	C₄×C₇×Q₈	—	2	2	no	—
70	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
71	C₄×C₇×D₄	—	2	1	no	—
72	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
73	C₇×#117	—	2	1	no	—
74	C₇×#117	—	2	2	no	—
75	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
76	C₇×#107	—	2	1	no	—
77	C₇×#107	—	2	1	no	—
78	C₇×#107	—	2	2	no	—
79	C₇×#106	—	2	2	no	—
80	C₇×C₄⋊C₈	—	2	1	no	—
81	C₇×C₄⋊C₈	—	2	1	no	—
82	C₇×C₄⋊C₈	—	2	2	no	—
83	C₇×C₄⋊C₈	C₂³	1	2	yes	—
84	C₇×C₄⋊C₈	C₂³	1	2	yes	—
85	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₇×#103	—	2	2	no	—
88	C₇×#103	—	2	2	no	—
89	C₇×#103	—	2	2	no	—
90	C₇×#103	—	2	2	no	—
91	C₇×#103	—	2	2	no	—
92	C₇×#102	—	2	2	no	—
93	C₇×C₂²⋊C₈	—	2	1	no	—
94	C₇×C₂²⋊C₈	—	2	1	no	—
95	C₇×C₂²⋊C₈	—	2	1	no	—
96	C₇×#97	—	2	1	no	—
97	C₇×#97	—	2	1	no	—
98	C₄×C₇×C₈	—	2	1	no	—
99	C₄×C₇×C₈	D₄	1	1	yes	characteristic
100	C₄×C₇×C₈	D₄	1	1	yes	characteristic
101	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
102	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
103	#3248	C₂×C₇	1	2	yes	—
104	#3170	C₂×C₇	1	1	yes	characteristic, complemented
105	#2966	C₂×C₇	1	1	yes	characteristic
106	#1694	C₂×C₇	1	1	yes	characteristic, complemented
107	#1693	C₂×C₇	1	1	yes	characteristic, complemented
108	#1690	C₂×C₇	1	1	yes	characteristic, complemented
109	#1689	C₂×C₇	1	1	yes	characteristic, complemented
110	#1680	C₂×C₇	1	2	yes	complemented
111	#1679	C₂×C₇	1	2	yes	complemented
112	C₂×#334	C₂×C₇	1	1	yes	characteristic, complemented
113	#1552	C₂×C₇	1	2	yes	complemented
114	C₂×C₇×Q₈	—	2	2	no	—
115	C₂×C₇×Q₈	—	2	2	no	—
116	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
117	C₂×C₇×D₄	—	2	1	no	—
118	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₇	—	2	1	no	—
120	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇	#41	1	1	yes	characteristic
123	C₇×Q₁₆	—	4	2	no	—
124	C₇×Q₁₆	—	4	2	no	—
125	C₇×Q₁₆	—	8	2	no	—
126	C₇×SD₁₆	—	8	2	no	—
127	C₇×M₁₆	—	4	2	no	—
128	C₂×C₇×C₈	—	2	2	no	—
129	C₂×C₇×C₈	—	2	1	no	—
130	C₂×C₇×C₈	—	2	1	no	—
131	C₂×C₇×C₈	—	2	2	no	—
132	C₂×C₇×C₈	—	2	2	no	—
133	C₂×C₇×C₈	—	4	1	no	—
134	C₂×C₇×C₈	—	4	2	no	—
135	C₂×C₇×C₈	—	8	2	no	—
136	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
139	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
140	C₇×C₄⋊C₄	—	2	1	no	—
141	C₇×C₄⋊C₄	—	2	1	no	—
142	C₇×C₄⋊C₄	—	2	1	no	—
143	C₇×C₄⋊C₄	—	2	1	no	—
144	C₇×C₄⋊C₄	—	2	2	no	—
145	C₇×C₄⋊C₄	—	2	2	no	—
146	C₇×C₄⋊C₄	—	2	2	no	—
147	C₇×C₄⋊C₄	—	2	2	no	—
148	C₇×C₄⋊C₄	—	4	2	no	—
149	C₇×C₄⋊C₄	—	4	2	no	—
150	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
151	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
152	C₇×C₂²⋊C₄	—	2	1	no	—
153	C₇×C₂²⋊C₄	—	2	1	no	—
154	C₇×C₂²⋊C₄	—	2	1	no	—
155	C₇×C₂²⋊C₄	—	2	1	no	—
156	C₇×C₂²⋊C₄	—	2	1	no	—
157	C₇×C₂²⋊C₄	—	4	2	no	—
158	C₄²×C₇	—	2	1	no	—
159	C₄²×C₇	—	4	2	no	—
160	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₇	#41	1	1	yes	characteristic
163	C₄²×C₇	C₂⁴	1	1	yes	characteristic
164	#533	C₂²×C₇	1	2	yes	—
165	#529	C₂²×C₇	1	1	yes	characteristic
166	#500	C₂²×C₇	1	1	yes	characteristic
167	#494	C₂²×C₇	1	1	yes	characteristic
168	#487	C₂²×C₇	1	2	yes	—
169	#479	—	2	2	no	—
170	#475	C₂²×C₇	1	2	yes	—
171	#474	C₂²×C₇	1	2	yes	—
172	#467	—	2	1	no	—
173	#467	—	2	1	no	—
174	#467	—	2	2	no	—
175	#465	—	2	2	no	—
176	#464	—	2	2	no	—
177	#462	C₂²×C₇	1	2	yes	—
178	#461	C₂²×C₇	1	2	yes	—
179	#446	C₂²×C₇	1	1	yes	characteristic
180	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
181	C₄×Q₁₆	—	2	1	no	—
182	C₄×Q₁₆	—	2	1	no	—
183	#436	C₂²×C₇	1	1	yes	characteristic
184	#435	—	2	1	no	—
185	C₈×D₄	—	2	1	no	—
186	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
187	#433	—	2	1	no	—
188	#432	C₂²×C₇	1	1	yes	characteristic
189	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
190	#405	—	2	1	no	—
191	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
192	#334	C₂²×C₇	1	2	yes	—
193	#334	C₂²×C₇	1	1	yes	characteristic
194	#334	C₂²×C₇	1	1	yes	characteristic
195	#332	C₂²×C₇	1	2	yes	—
196	#332	C₂²×C₇	1	2	yes	—
197	#332	C₂²×C₇	1	2	yes	—
198	#332	C₂²×C₇	1	2	yes	—
199	C₂³×C₇	—	2	1	no	—
200	C₂³×C₇	#121	1	1	yes	characteristic
201	C₇×Q₈	—	2	2	no	—
202	C₇×Q₈	—	4	2	no	—
203	C₇×Q₈	—	4	2	no	—
204	C₇×Q₈	—	4	2	no	—
205	C₇×Q₈	—	4	2	no	—
206	C₇×D₄	—	2	2	no	—
207	C₇×D₄	—	4	2	no	—
208	C₂×C₄×C₇	—	2	2	no	—
209	C₂×C₄×C₇	—	2	1	no	—
210	C₂×C₄×C₇	—	2	1	no	—
211	C₂×C₄×C₇	—	2	2	no	—
212	C₂×C₄×C₇	—	2	1	no	—
213	C₂×C₄×C₇	—	2	1	no	—
214	C₂×C₄×C₇	—	2	1	no	—
215	C₂×C₄×C₇	—	4	1	no	—
216	C₂×C₄×C₇	—	4	1	no	—
217	C₂×C₄×C₇	—	4	2	no	—
218	C₂×C₄×C₇	—	4	2	no	—
219	C₂×C₄×C₇	#121	1	1	yes	characteristic
220	C₂×C₄×C₇	#121	1	1	yes	characteristic
221	C₂×C₄×C₇	#121	1	1	yes	characteristic
222	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
225	C₇×C₈	—	2	1	no	—
226	C₇×C₈	—	2	1	no	—
227	C₇×C₈	—	2	1	no	—
228	C₇×C₈	—	4	1	no	—
229	C₇×C₈	—	4	1	no	—
230	C₇×C₈	—	4	2	no	—
231	C₇×C₈	—	4	2	no	—
232	C₇×C₈	#135	1	2	yes	—
233	C₂×Q₁₆	—	2	2	no	—
234	C₂×Q₁₆	—	2	1	no	—
235	C₂×Q₁₆	—	2	1	no	—
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	1	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
241	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
242	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
243	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
244	#126	—	2	1	no	—
245	#125	—	2	2	no	—
246	#125	C₇×D₄	1	1	yes	characteristic
247	#124	C₇×D₄	1	1	yes	characteristic
248	#123	—	2	1	no	—
249	C₂²⋊Q₈	—	2	2	no	—
250	C₂²⋊Q₈	—	2	2	no	—
251	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
252	#121	C₇×D₄	1	1	yes	characteristic
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
258	#117	—	2	1	no	—
259	#117	—	2	2	no	—
260	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
261	#107	—	2	1	no	—
262	#107	—	2	1	no	—
263	#107	—	2	2	no	—
264	#106	—	2	2	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
269	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
270	C₄⋊C₈	C₂³×C₇	1	2	yes	—
271	C₄⋊C₈	C₂³×C₇	1	2	yes	—
272	#103	—	2	2	no	—
273	#103	—	2	2	no	—
274	#103	—	2	2	no	—
275	#103	—	2	2	no	—
276	#103	—	2	2	no	—
277	#102	—	2	2	no	—
278	C₂²⋊C₈	—	2	1	no	—
279	C₂²⋊C₈	—	2	1	no	—
280	C₂²⋊C₈	—	2	1	no	—
281	#97	—	2	1	no	—
282	#97	—	2	1	no	—
283	C₄×C₈	—	2	1	no	—
284	C₄×C₈	C₇×D₄	1	1	yes	characteristic
285	C₄×C₈	C₇×D₄	1	1	yes	characteristic
286	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
287	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
288	C₂²×C₇	—	2	1	no	—
289	C₂²×C₇	—	2	1	no	—
290	C₂²×C₇	—	4	1	no	—
291	C₂²×C₇	—	4	1	no	—
292	C₂²×C₇	—	4	1	no	—
293	C₂²×C₇	#473	1	2	yes	—
294	C₂²×C₇	C₂×#121	1	1	yes	characteristic
295	C₄×C₇	—	2	1	no	—
296	C₄×C₇	—	2	1	no	—
297	C₄×C₇	—	2	1	no	—
298	C₄×C₇	—	2	1	no	—
299	C₄×C₇	—	4	1	no	—
300	C₄×C₇	—	4	1	no	—
301	C₄×C₇	—	4	1	no	—
302	C₄×C₇	—	8	2	no	—
303	C₄×C₇	—	8	2	no	—
304	C₄×C₇	C₂×#135	1	1	yes	characteristic
305	C₄×C₇	#575	1	1	yes	characteristic
306	C₄×C₇	#577	1	2	yes	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
315	C₂²×C₄	C₇×#41	1	1	yes	characteristic
316	Q₁₆	—	4	2	no	—
317	Q₁₆	—	4	2	no	—
318	Q₁₆	—	8	2	no	—
319	SD₁₆	—	8	2	no	—
320	M₁₆	—	4	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	—	8	2	no	—
329	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
330	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
331	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
332	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
344	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
345	C₂²⋊C₄	—	2	1	no	—
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	2	1	no	—
348	C₂²⋊C₄	—	2	1	no	—
349	C₂²⋊C₄	—	2	1	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	4	2	no	—
353	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
354	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
355	C₄²	C₇×#41	1	1	yes	characteristic
356	C₄²	C₂⁴×C₇	1	1	yes	characteristic
357	C₂×C₇	—	2	2	no	—
358	C₂×C₇	—	8	1	no	—
359	C₂×C₇	#3035	1	1	yes	characteristic
360	C₂×C₇	#3060	1	1	yes	characteristic
361	C₂×C₇	C₂×#473	1	1	yes	characteristic
362	C₂³	—	2	1	no	—
363	C₂³	C₇×#121	1	1	yes	characteristic
364	Q₈	—	2	2	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	4	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	C₇×#121	1	1	yes	characteristic
383	C₂×C₄	C₇×#121	1	1	yes	characteristic
384	C₂×C₄	C₇×#121	1	1	yes	characteristic
385	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
386	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
387	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	—	2	1	no	—
391	C₈	—	4	1	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	2	no	—
394	C₈	—	4	2	no	—
395	C₈	C₇×#135	1	2	yes	—
396	C₇	#19228	1	1	yes	characteristic, direct product factor, Sylow
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	C₇×#473	1	2	yes	—
403	C₂²	C₂×C₇×#121	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	8	2	no	—
412	C₄	—	8	2	no	—
413	C₄	C₂×C₇×#135	1	1	yes	characteristic
414	C₄	C₇×#575	1	1	yes	characteristic
415	C₄	C₇×#577	1	2	yes	—
416	C₂	—	2	2	no	—
417	C₂	—	8	1	no	—
418	C₂	C₇×#3035	1	1	yes	characteristic
419	C₂	C₇×#3060	1	1	yes	characteristic
420	C₂	C₂×C₇×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#121	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3170	C₂	semidirect
4. C₇×#1694	C₂	semidirect
5. C₇×#1693	C₂	semidirect
6. C₇×#1690	C₂	semidirect
7. C₇×#1689	C₂	semidirect
8. C₇×#1680	C₂	semidirect
9. C₇×#1679	C₂	semidirect
10. C₂×C₇×#334	C₂	semidirect
11. C₇×#1552	C₂	semidirect
47. #19228	C₇	direct (N × H)
104. #3170	C₂×C₇	semidirect
106. #1694	C₂×C₇	semidirect
107. #1693	C₂×C₇	semidirect
108. #1690	C₂×C₇	semidirect
109. #1689	C₂×C₇	semidirect
110. #1680	C₂×C₇	semidirect
111. #1679	C₂×C₇	semidirect
112. C₂×#334	C₂×C₇	semidirect
113. #1552	C₂×C₇	semidirect
396. C₇	#19228	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3248	2
C₇×#3170	2
C₇×#2966	2
C₇×#1694	2
C₇×#1693	2
C₇×#1690	2
C₇×#1689	2
C₇×#1680	2
C₇×#1679	2
C₂×C₇×#334	2
C₇×#1552	2
#19228	7

Subgroups — C7×#19228 #13196444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19228 #13196444