Subgroups — C₇×#22550 #13199766

Order 1792.

1150 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3480	C₂	1	1	yes	maximal, characteristic
2	C₇×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1980	C₂	1	3	yes	maximal, complemented
5	C₇×#1962	C₂	1	3	yes	maximal, complemented
6	C₇×#1806	C₂	1	3	yes	maximal, complemented
7	C₄×C₇×#104	C₂	1	3	yes	maximal, complemented
8	C₇×#559	C₄	1	3	yes	complemented
9	C₇×#557	C₄	1	1	yes	characteristic, complemented
10	C₇×#556	C₄	1	3	yes	complemented
11	C₇×#553	—	2	3	no	—
12	C₇×#550	C₄	1	1	yes	characteristic, complemented
13	C₇×#548	—	2	1	no	—
14	C₇×#532	C₂²	1	3	yes	—
15	C₇×#529	—	2	3	no	—
16	C₄×C₇×#41	—	2	1	no	—
17	C₄×C₇×#41	C₂²	1	3	yes	—
18	C₂×C₄×C₇×Q₈	—	2	1	no	—
19	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
20	C₇×#446	—	2	3	no	—
21	C₇×C₈×Q₈	—	2	1	no	—
22	C₇×#423	C₂²	1	3	yes	—
23	C₂×C₇×#104	C₂²	1	3	yes	—
24	C₂×C₇×#104	C₂²	1	3	yes	—
25	C₂×C₇×#104	C₂²	1	6	yes	—
26	C₄×C₇×M₁₆	C₂²	1	3	yes	—
27	C₄×C₇×C₄⋊C₄	—	2	3	no	—
28	C₄×C₇×C₄⋊C₄	C₂²	1	3	yes	—
29	C₄³×C₇	C₂²	1	3	yes	—
30	C₇×#339	C₂²	1	1	yes	characteristic
31	C₇×#339	C₂²	1	3	yes	—
32	#22550	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂×C₇×#41	—	2	1	no	—
34	C₂×C₇×#41	C₂³	1	3	yes	—
35	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
36	C₂×C₇×M₁₆	C₂³	1	3	yes	—
37	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
38	C₇×C₄⋊Q₈	C₂×C₄	1	3	yes	—
39	C₇×#127	C₂×C₄	1	3	yes	—
40	C₇×#126	—	2	6	no	—
41	C₇×#125	—	2	3	no	—
42	C₇×#124	—	2	3	no	—
43	C₇×#124	C₂×C₄	1	6	yes	—
44	C₇×#123	—	2	6	no	—
45	C₇×C₂²⋊Q₈	—	2	3	no	—
46	C₇×#121	—	2	3	no	—
47	C₇×#121	—	2	3	no	—
48	C₇×#121	—	2	3	no	—
49	C₄×C₇×Q₈	—	2	8	no	—
50	C₄×C₇×Q₈	—	2	1	no	—
51	C₄×C₇×Q₈	C₂×C₄	1	3	yes	—
52	C₄×C₇×Q₈	C₂×C₄	1	3	yes	—
53	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
54	C₄×C₇×Q₈	C₂×C₄	1	3	yes	—
55	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
56	C₄×C₇×Q₈	D₄	1	3	yes	—
57	C₄×C₇×D₄	—	2	3	no	—
58	C₄×C₇×D₄	—	2	3	no	—
59	C₄×C₇×D₄	—	2	3	no	—
60	C₄×C₇×D₄	—	2	3	no	—
61	C₄×C₇×D₄	—	2	3	no	—
62	C₄×C₇×D₄	C₂×C₄	1	3	yes	—
63	C₄×C₇×D₄	C₂×C₄	1	3	yes	—
64	C₇×#117	—	2	3	no	—
65	C₇×#117	—	2	3	no	—
66	C₇×#117	C₂³	1	1	yes	characteristic
67	C₂×C₇×C₄⋊C₄	—	2	3	no	—
68	C₂×C₇×C₄⋊C₄	D₄	1	3	yes	—
69	C₂×C₄²×C₇	—	2	3	no	—
70	C₂×C₄²×C₇	—	2	3	no	—
71	C₂×C₄²×C₇	—	2	3	no	—
72	C₂×C₄²×C₇	C₂³	1	3	yes	—
73	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₇	C₂³	1	3	yes	—
75	C₇×C₄⋊C₈	—	2	3	no	—
76	C₇×C₄⋊C₈	—	2	3	no	—
77	C₇×#104	—	2	6	no	—
78	C₇×#104	—	2	6	no	—
79	C₇×#104	—	4	6	no	—
80	C₇×#97	—	2	3	no	—
81	C₄×C₇×C₈	—	2	3	no	—
82	C₇×#95	—	2	3	no	—
83	#3480	C₂×C₇	1	1	yes	characteristic
84	Q₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
85	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
86	#1980	C₂×C₇	1	3	yes	complemented
87	#1962	C₂×C₇	1	3	yes	complemented
88	#1806	C₂×C₇	1	3	yes	complemented
89	C₄×#104	C₂×C₇	1	3	yes	complemented
90	C₇×#41	—	2	3	no	—
91	C₇×#41	—	2	3	no	—
92	C₇×#41	—	2	3	no	—
93	C₇×#41	—	2	3	no	—
94	C₇×#41	—	4	4	no	—
95	C₂×C₇×Q₈	—	2	4	no	—
96	C₂×C₇×Q₈	C₂²⋊C₄	1	3	yes	—
97	C₂×C₇×Q₈	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₇×Q₈	C₂²×C₄	1	3	yes	—
99	C₂×C₇×D₄	—	2	3	no	—
100	C₂×C₇×D₄	—	2	3	no	—
101	C₂×C₇×D₄	—	2	3	no	—
102	C₂×C₇×D₄	C₂²×C₄	1	3	yes	—
103	C₂²×C₄×C₇	—	2	1	no	—
104	C₂²×C₄×C₇	—	2	3	no	—
105	C₂²×C₄×C₇	—	2	3	no	—
106	C₂²×C₄×C₇	—	2	3	no	—
107	C₂²×C₄×C₇	—	2	3	no	—
108	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
109	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
110	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
111	C₇×M₁₆	—	2	1	no	—
112	C₇×M₁₆	—	2	3	no	—
113	C₇×M₁₆	—	2	3	no	—
114	C₇×M₁₆	#41	1	2	yes	complemented
115	C₂×C₇×C₈	—	2	1	no	—
116	C₂×C₇×C₈	—	2	3	no	—
117	C₇×C₄⋊C₄	—	2	12	no	—
118	C₇×C₄⋊C₄	—	2	3	no	—
119	C₇×C₄⋊C₄	—	2	3	no	—
120	C₇×C₄⋊C₄	—	2	3	no	—
121	C₇×C₄⋊C₄	—	2	3	no	—
122	C₇×C₄⋊C₄	C₂²⋊C₄	1	3	yes	—
123	C₇×C₄⋊C₄	C₂²⋊C₄	1	3	yes	—
124	C₇×C₄⋊C₄	C₂²⋊C₄	1	6	yes	—
125	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
126	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
127	C₇×C₂²⋊C₄	—	2	1	no	—
128	C₇×C₂²⋊C₄	—	2	6	no	—
129	C₇×C₂²⋊C₄	—	2	3	no	—
130	C₇×C₂²⋊C₄	—	2	3	no	—
131	C₇×C₂²⋊C₄	—	2	6	no	—
132	C₄²×C₇	—	2	12	no	—
133	C₄²×C₇	—	2	3	no	—
134	C₄²×C₇	—	2	3	no	—
135	C₄²×C₇	—	2	1	no	—
136	C₄²×C₇	—	2	1	no	—
137	C₄²×C₇	—	2	3	no	—
138	C₄²×C₇	—	2	3	no	—
139	C₄²×C₇	—	4	6	no	—
140	C₄²×C₇	C₂²×C₄	1	3	yes	—
141	C₄²×C₇	C₂²×C₄	1	3	yes	—
142	C₄²×C₇	C₂×D₄	1	3	yes	—
143	C₄²×C₇	C₂×D₄	1	3	yes	—
144	C₄²×C₇	#41	1	2	yes	complemented
145	#559	C₄×C₇	1	3	yes	complemented
146	#557	C₄×C₇	1	1	yes	characteristic, complemented
147	#556	C₄×C₇	1	3	yes	complemented
148	#553	—	2	3	no	—
149	#550	C₄×C₇	1	1	yes	characteristic, complemented
150	#548	—	2	1	no	—
151	#532	C₂²×C₇	1	3	yes	—
152	#529	—	2	3	no	—
153	C₄×#41	—	2	1	no	—
154	C₄×#41	C₂²×C₇	1	3	yes	—
155	C₂×C₄×Q₈	—	2	1	no	—
156	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
157	#446	—	2	3	no	—
158	C₈×Q₈	—	2	1	no	—
159	#423	C₂²×C₇	1	3	yes	—
160	C₂×#104	C₂²×C₇	1	3	yes	—
161	C₂×#104	C₂²×C₇	1	3	yes	—
162	C₂×#104	C₂²×C₇	1	6	yes	—
163	C₄×M₁₆	C₂²×C₇	1	3	yes	—
164	C₄×C₄⋊C₄	—	2	3	no	—
165	C₄×C₄⋊C₄	C₂²×C₇	1	3	yes	—
166	C₄³	C₂²×C₇	1	3	yes	—
167	#339	C₂²×C₇	1	3	yes	—
168	#339	C₂²×C₇	1	1	yes	characteristic
169	C₂³×C₇	—	2	3	no	—
170	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
171	C₇×Q₈	—	2	6	no	—
172	C₇×Q₈	—	2	3	no	—
173	C₇×Q₈	—	2	3	no	—
174	C₇×Q₈	#104	1	4	yes	complemented
175	C₇×D₄	—	2	3	no	—
176	C₇×D₄	—	2	3	no	—
177	C₇×D₄	—	4	3	no	—
178	C₇×D₄	—	4	3	no	—
179	C₇×D₄	—	4	6	no	—
180	C₇×D₄	—	8	3	no	—
181	C₂×C₄×C₇	—	2	2	no	—
182	C₂×C₄×C₇	—	2	2	no	—
183	C₂×C₄×C₇	—	2	2	no	—
184	C₂×C₄×C₇	—	2	6	no	—
185	C₂×C₄×C₇	—	2	6	no	—
186	C₂×C₄×C₇	—	2	1	no	—
187	C₂×C₄×C₇	—	2	1	no	—
188	C₂×C₄×C₇	—	2	3	no	—
189	C₂×C₄×C₇	—	4	3	no	—
190	C₂×C₄×C₇	—	4	3	no	—
191	C₂×C₄×C₇	—	4	3	no	—
192	C₂×C₄×C₇	—	4	3	no	—
193	C₂×C₄×C₇	—	4	3	no	—
194	C₂×C₄×C₇	—	4	6	no	—
195	C₂×C₄×C₇	—	8	3	no	—
196	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	3	yes	—
197	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	3	yes	—
198	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	3	yes	—
199	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	3	yes	—
200	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
206	C₇×C₈	—	2	2	no	—
207	C₇×C₈	—	4	3	no	—
208	C₂×#41	—	2	1	no	—
209	C₂×#41	C₂³×C₇	1	3	yes	—
210	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
211	C₂×M₁₆	C₂³×C₇	1	3	yes	—
212	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
213	C₄⋊Q₈	C₂×C₄×C₇	1	3	yes	—
214	#127	C₂×C₄×C₇	1	3	yes	—
215	#126	—	2	6	no	—
216	#125	—	2	3	no	—
217	#124	—	2	3	no	—
218	#124	C₂×C₄×C₇	1	6	yes	—
219	#123	—	2	6	no	—
220	C₂²⋊Q₈	—	2	3	no	—
221	#121	—	2	3	no	—
222	#121	—	2	3	no	—
223	#121	—	2	3	no	—
224	C₄×Q₈	—	2	8	no	—
225	C₄×Q₈	—	2	1	no	—
226	C₄×Q₈	C₂×C₄×C₇	1	3	yes	—
227	C₄×Q₈	C₂×C₄×C₇	1	3	yes	—
228	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
229	C₄×Q₈	C₂×C₄×C₇	1	3	yes	—
230	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
231	C₄×Q₈	C₇×D₄	1	3	yes	—
232	C₄×D₄	—	2	3	no	—
233	C₄×D₄	—	2	3	no	—
234	C₄×D₄	—	2	3	no	—
235	C₄×D₄	—	2	3	no	—
236	C₄×D₄	—	2	3	no	—
237	C₄×D₄	C₂×C₄×C₇	1	3	yes	—
238	C₄×D₄	C₂×C₄×C₇	1	3	yes	—
239	#117	—	2	3	no	—
240	#117	—	2	3	no	—
241	#117	C₂³×C₇	1	1	yes	characteristic
242	C₂×C₄⋊C₄	—	2	3	no	—
243	C₂×C₄⋊C₄	C₇×D₄	1	3	yes	—
244	C₂×C₄²	—	2	3	no	—
245	C₂×C₄²	—	2	3	no	—
246	C₂×C₄²	—	2	3	no	—
247	C₂×C₄²	C₂³×C₇	1	3	yes	—
248	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₇	1	3	yes	—
250	C₄⋊C₈	—	2	3	no	—
251	C₄⋊C₈	—	2	3	no	—
252	#104	—	2	6	no	—
253	#104	—	2	6	no	—
254	#104	—	4	6	no	—
255	#97	—	2	3	no	—
256	C₄×C₈	—	2	3	no	—
257	#95	—	2	3	no	—
258	C₂²×C₇	—	2	1	no	—
259	C₂²×C₇	—	2	1	no	—
260	C₂²×C₇	—	4	3	no	—
261	C₂²×C₇	—	4	3	no	—
262	C₂²×C₇	—	4	3	no	—
263	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
264	C₂²×C₇	#548	1	1	yes	characteristic
265	C₂²×C₇	#550	1	1	yes	characteristic
266	C₄×C₇	—	2	4	no	—
267	C₄×C₇	—	2	3	no	—
268	C₄×C₇	—	2	3	no	—
269	C₄×C₇	—	2	3	no	—
270	C₄×C₇	—	4	6	no	—
271	C₄×C₇	—	4	3	no	—
272	C₄×C₇	—	4	1	no	—
273	C₄×C₇	—	4	1	no	—
274	C₄×C₇	C₂×#104	1	6	yes	—
275	C₄×C₇	C₄×#41	1	1	yes	characteristic
276	C₄×C₇	#520	1	1	yes	characteristic
277	C₄×C₇	#548	1	1	yes	characteristic
278	C₄×C₇	#550	1	1	yes	characteristic
279	#41	—	2	3	no	—
280	#41	—	2	3	no	—
281	#41	—	2	3	no	—
282	#41	—	2	3	no	—
283	#41	—	4	4	no	—
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	C₇×C₂²⋊C₄	1	3	yes	—
286	C₂×Q₈	C₇×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×Q₈	C₂²×C₄×C₇	1	3	yes	—
288	C₂×D₄	—	2	3	no	—
289	C₂×D₄	—	2	3	no	—
290	C₂×D₄	—	2	3	no	—
291	C₂×D₄	C₂²×C₄×C₇	1	3	yes	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	3	no	—
294	C₂²×C₄	—	2	3	no	—
295	C₂²×C₄	—	2	3	no	—
296	C₂²×C₄	—	2	3	no	—
297	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
298	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
299	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
300	M₁₆	—	2	1	no	—
301	M₁₆	—	2	3	no	—
302	M₁₆	—	2	3	no	—
303	M₁₆	C₇×#41	1	2	yes	complemented
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	3	no	—
306	C₄⋊C₄	—	2	12	no	—
307	C₄⋊C₄	—	2	3	no	—
308	C₄⋊C₄	—	2	3	no	—
309	C₄⋊C₄	—	2	3	no	—
310	C₄⋊C₄	—	2	3	no	—
311	C₄⋊C₄	C₇×C₂²⋊C₄	1	3	yes	—
312	C₄⋊C₄	C₇×C₂²⋊C₄	1	3	yes	—
313	C₄⋊C₄	C₇×C₂²⋊C₄	1	6	yes	—
314	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
315	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	2	6	no	—
318	C₂²⋊C₄	—	2	3	no	—
319	C₂²⋊C₄	—	2	3	no	—
320	C₂²⋊C₄	—	2	6	no	—
321	C₄²	—	2	12	no	—
322	C₄²	—	2	3	no	—
323	C₄²	—	2	3	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	3	no	—
327	C₄²	—	2	3	no	—
328	C₄²	—	4	6	no	—
329	C₄²	C₂²×C₄×C₇	1	3	yes	—
330	C₄²	C₂²×C₄×C₇	1	3	yes	—
331	C₄²	C₂×C₇×D₄	1	3	yes	—
332	C₄²	C₂×C₇×D₄	1	3	yes	—
333	C₄²	C₇×#41	1	2	yes	complemented
334	C₂×C₇	—	2	1	no	—
335	C₂×C₇	—	2	1	no	—
336	C₂×C₇	—	8	3	no	—
337	C₂×C₇	#2341	1	1	yes	characteristic
338	C₂×C₇	C₂²×#104	1	1	yes	characteristic
339	C₂×C₇	#2901	1	1	yes	characteristic
340	C₂³	—	2	3	no	—
341	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
342	Q₈	—	2	6	no	—
343	Q₈	—	2	3	no	—
344	Q₈	—	2	3	no	—
345	Q₈	C₇×#104	1	4	yes	complemented
346	D₄	—	2	3	no	—
347	D₄	—	2	3	no	—
348	D₄	—	4	3	no	—
349	D₄	—	4	3	no	—
350	D₄	—	4	6	no	—
351	D₄	—	8	3	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	6	no	—
356	C₂×C₄	—	2	6	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	3	no	—
360	C₂×C₄	—	4	3	no	—
361	C₂×C₄	—	4	3	no	—
362	C₂×C₄	—	4	3	no	—
363	C₂×C₄	—	4	3	no	—
364	C₂×C₄	—	4	3	no	—
365	C₂×C₄	—	4	6	no	—
366	C₂×C₄	—	8	3	no	—
367	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	3	yes	—
368	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	3	yes	—
369	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	3	yes	—
370	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	3	yes	—
371	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
373	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
374	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
375	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
376	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	4	3	no	—
379	C₇	#22550	1	1	yes	characteristic, direct product factor, Sylow
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	4	3	no	—
383	C₂²	—	4	3	no	—
384	C₂²	—	4	3	no	—
385	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
386	C₂²	C₇×#548	1	1	yes	characteristic
387	C₂²	C₇×#550	1	1	yes	characteristic
388	C₄	—	2	4	no	—
389	C₄	—	2	3	no	—
390	C₄	—	2	3	no	—
391	C₄	—	2	3	no	—
392	C₄	—	4	6	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	3	no	—
396	C₄	C₂×C₇×#104	1	6	yes	—
397	C₄	C₄×C₇×#41	1	1	yes	characteristic
398	C₄	C₇×#520	1	1	yes	characteristic
399	C₄	C₇×#548	1	1	yes	characteristic
400	C₄	C₇×#550	1	1	yes	characteristic
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	8	3	no	—
404	C₂	C₇×#2341	1	1	yes	characteristic
405	C₂	C₂²×C₇×#104	1	1	yes	characteristic
406	C₂	C₇×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂²×C₂²⋊C₄
prime radical	C₇×#3480	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×Q₈×M₁₆	C₂	semidirect
3. C₄²×C₇×Q₈	C₂	semidirect
4. C₇×#1980	C₂	semidirect
5. C₇×#1962	C₂	semidirect
6. C₇×#1806	C₂	semidirect
7. C₄×C₇×#104	C₂	semidirect
8. C₇×#559	C₄	semidirect
9. C₇×#557	C₄	semidirect
10. C₇×#556	C₄	semidirect
12. C₇×#550	C₄	semidirect
32. #22550	C₇	direct (N × H)
84. Q₈×M₁₆	C₂×C₇	semidirect
85. C₄²×Q₈	C₂×C₇	semidirect
86. #1980	C₂×C₇	semidirect
87. #1962	C₂×C₇	semidirect
88. #1806	C₂×C₇	semidirect
89. C₄×#104	C₂×C₇	semidirect
114. C₇×M₁₆	#41	semidirect
144. C₄²×C₇	#41	semidirect
145. #559	C₄×C₇	semidirect
146. #557	C₄×C₇	semidirect
147. #556	C₄×C₇	semidirect
149. #550	C₄×C₇	semidirect
174. C₇×Q₈	#104	semidirect
303. M₁₆	C₇×#41	semidirect
333. C₄²	C₇×#41	semidirect
345. Q₈	C₇×#104	semidirect
379. C₇	#22550	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×#3480	2
C₇×Q₈×M₁₆	2
C₄²×C₇×Q₈	2
C₇×#1980	2
C₇×#1962	2
C₇×#1806	2
C₄×C₇×#104	2
#22550	7

Subgroups — C7×#22550 #13199766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22550 #13199766