Subgroups — C₇×#33702 #13210918

Order 1792.

602 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3164	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3155	C₂	1	1	yes	maximal, characteristic
3	C₇×#2244	C₂	1	2	yes	maximal, complemented
4	C₇×#2243	C₂	1	2	yes	maximal, complemented
5	C₇×#2242	C₂	1	2	yes	maximal, complemented
6	C₇×#2240	C₂	1	2	yes	maximal, complemented
7	C₇×#2140	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#357	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2108	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×AGL(1,ℤ/8)	—	2	1	no	—
13	C₂×C₇×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
15	C₇×#544	—	2	1	no	—
16	C₇×#535	—	2	1	no	—
17	C₂×C₇×M₃₂	C₂²	1	1	yes	characteristic
18	C₂²×C₇×C₁₆	C₂²	1	1	yes	characteristic
19	C₇×#501	—	2	2	no	—
20	C₇×#500	C₂²	1	2	yes	complemented
21	C₇×#499	C₂²	1	2	yes	complemented
22	C₇×#496	—	2	2	no	—
23	C₇×#495	C₂²	1	2	yes	—
24	C₇×#493	C₂²	1	2	yes	—
25	C₇×#428	—	2	1	no	—
26	C₇×#427	C₂²	1	1	yes	characteristic
27	C₂×C₇×#107	C₂²	1	1	yes	characteristic
28	C₇×#405	C₂²	1	1	yes	characteristic
29	C₇×#358	C₂²	1	1	yes	characteristic, complemented
30	C₇×#358	C₂²	1	2	yes	complemented
31	C₇×#358	C₂²	1	1	yes	characteristic, complemented
32	C₇×#357	C₂²	1	2	yes	—
33	C₇×#357	C₂²	1	2	yes	—
34	C₇×#357	C₂²	1	2	yes	—
35	C₇×#357	C₂²	1	2	yes	—
36	C₇×#357	C₂²	1	1	yes	characteristic, complemented
37	C₇×#357	C₂²	1	2	yes	complemented
38	C₇×#357	C₂²	1	1	yes	characteristic, complemented
39	C₇×#346	C₂²	1	2	yes	complemented
40	C₄×C₇×C₁₆	C₂²	1	2	yes	complemented
41	#33702	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₇×#41	—	2	1	no	—
43	C₂²×C₇×D₄	—	2	1	no	—
44	C₇×AGL(1,ℤ/8)	—	4	4	no	—
45	C₇×#135	—	2	2	no	—
46	C₇×#135	—	2	2	no	—
47	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
48	C₂×C₇×SD₁₆	—	2	2	no	—
49	C₂×C₇×SD₁₆	—	2	1	no	—
50	C₂×C₇×D₈	—	2	2	no	—
51	C₂×C₇×D₈	—	2	1	no	—
52	C₂×C₇×D₈	—	2	2	no	—
53	C₂×C₇×D₈	—	2	2	no	—
54	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
55	C₂×C₇×D₈	C₂³	1	2	yes	—
56	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₇×C₄⋊Q₈	—	2	2	no	—
59	C₇×C₄⋊Q₈	—	4	1	no	—
60	C₇×#127	—	2	2	no	—
61	C₇×#125	—	2	2	no	—
62	C₇×#125	—	4	1	no	—
63	C₇×#124	—	2	2	no	—
64	C₇×C₂²⋊Q₈	—	4	2	no	—
65	C₇×#121	—	4	1	no	—
66	C₇×#121	—	4	1	no	—
67	C₇×#120	—	4	2	no	—
68	C₇×#117	—	2	1	no	—
69	C₇×#117	D₄	1	1	yes	characteristic
70	C₂×C₇×C₄⋊C₄	—	2	1	no	—
71	C₇×M₃₂	—	2	2	no	—
72	C₂×C₇×C₁₆	—	2	2	no	—
73	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₇×C₁₆	C₂³	1	2	yes	—
76	C₇×#107	—	2	2	no	—
77	C₇×#107	—	2	1	no	—
78	C₇×#107	C₂³	1	1	yes	characteristic
79	C₇×#107	C₂³	1	2	yes	—
80	C₇×#107	C₂³	1	1	yes	characteristic
81	C₇×#106	—	2	2	no	—
82	C₇×#106	—	2	1	no	—
83	C₇×#97	D₄	1	2	yes	—
84	C₄×C₇×C₈	C₂³	1	2	yes	—
85	#3164	C₂×C₇	1	1	yes	characteristic, complemented
86	#3155	C₂×C₇	1	1	yes	characteristic
87	#2244	C₂×C₇	1	2	yes	complemented
88	#2243	C₂×C₇	1	2	yes	complemented
89	#2242	C₂×C₇	1	2	yes	complemented
90	#2240	C₂×C₇	1	2	yes	complemented
91	#2140	C₂×C₇	1	1	yes	characteristic, complemented
92	#2139	C₂×C₇	1	1	yes	characteristic, complemented
93	#2138	C₂×C₇	1	1	yes	characteristic, complemented
94	C₂×#357	C₂×C₇	1	1	yes	characteristic, complemented
95	#2108	C₂×C₇	1	1	yes	characteristic, complemented
96	C₂⁴×C₇	—	4	1	no	—
97	C₇×#41	—	4	2	no	—
98	C₇×#41	—	4	2	no	—
99	C₂×C₇×Q₈	—	2	1	no	—
100	C₂×C₇×Q₈	—	4	2	no	—
101	C₂×C₇×D₄	—	2	2	no	—
102	C₂×C₇×D₄	—	2	1	no	—
103	C₂×C₇×D₄	—	4	1	no	—
104	C₂×C₇×D₄	—	4	2	no	—
105	C₂×C₇×D₄	—	4	1	no	—
106	C₂×C₇×D₄	—	4	2	no	—
107	C₂×C₇×D₄	—	4	2	no	—
108	C₂×C₇×D₄	—	4	2	no	—
109	C₂²×C₄×C₇	—	4	1	no	—
110	C₂²×C₄×C₇	—	4	1	no	—
111	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
112	C₇×Q₁₆	—	2	1	no	—
113	C₇×Q₁₆	—	2	1	no	—
114	C₇×SD₁₆	—	4	2	no	—
115	C₇×SD₁₆	—	4	4	no	—
116	C₇×D₈	—	2	2	no	—
117	C₇×D₈	—	2	2	no	—
118	C₇×D₈	—	2	1	no	—
119	C₇×D₈	—	2	1	no	—
120	C₇×D₈	—	4	2	no	—
121	C₇×D₈	—	4	4	no	—
122	C₇×M₁₆	SD₁₆	1	4	yes	—
123	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
124	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
125	C₂×C₇×C₈	#41	1	2	yes	—
126	C₂×C₇×C₈	#41	1	2	yes	—
127	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
128	C₇×C₄⋊C₄	—	2	1	no	—
129	C₇×C₄⋊C₄	—	2	2	no	—
130	C₇×C₄⋊C₄	—	2	1	no	—
131	C₇×C₄⋊C₄	—	4	1	no	—
132	C₇×C₄⋊C₄	—	4	2	no	—
133	C₇×C₄⋊C₄	—	4	2	no	—
134	C₇×C₄⋊C₄	—	4	2	no	—
135	C₇×C₄⋊C₄	D₈	1	1	yes	characteristic
136	C₇×C₄⋊C₄	D₈	1	1	yes	characteristic
137	C₇×C₂²⋊C₄	—	4	1	no	—
138	C₇×C₂²⋊C₄	—	4	2	no	—
139	C₇×C₂²⋊C₄	—	4	2	no	—
140	C₇×C₂²⋊C₄	D₈	1	2	yes	—
141	C₄²×C₇	—	4	1	no	—
142	C₄²×C₇	C₂×D₄	1	2	yes	—
143	C₇×C₁₆	—	2	1	no	—
144	C₇×C₁₆	—	2	1	no	—
145	C₇×C₁₆	—	2	2	no	—
146	C₂×AGL(1,ℤ/8)	—	2	1	no	—
147	C₂×#135	C₂²×C₇	1	1	yes	characteristic
148	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
149	#544	—	2	1	no	—
150	#535	—	2	1	no	—
151	C₂×M₃₂	C₂²×C₇	1	1	yes	characteristic
152	C₂²×C₁₆	C₂²×C₇	1	1	yes	characteristic
153	#501	—	2	2	no	—
154	#500	C₂²×C₇	1	2	yes	complemented
155	#499	C₂²×C₇	1	2	yes	complemented
156	#496	—	2	2	no	—
157	#495	C₂²×C₇	1	2	yes	—
158	#493	C₂²×C₇	1	2	yes	—
159	#428	—	2	1	no	—
160	#427	C₂²×C₇	1	1	yes	characteristic
161	C₂×#107	C₂²×C₇	1	1	yes	characteristic
162	#405	C₂²×C₇	1	1	yes	characteristic
163	#358	C₂²×C₇	1	1	yes	characteristic, complemented
164	#358	C₂²×C₇	1	1	yes	characteristic, complemented
165	#358	C₂²×C₇	1	2	yes	complemented
166	#357	C₂²×C₇	1	2	yes	—
167	#357	C₂²×C₇	1	2	yes	—
168	#357	C₂²×C₇	1	2	yes	—
169	#357	C₂²×C₇	1	2	yes	—
170	#357	C₂²×C₇	1	1	yes	characteristic, complemented
171	#357	C₂²×C₇	1	1	yes	characteristic, complemented
172	#357	C₂²×C₇	1	2	yes	complemented
173	#346	C₂²×C₇	1	2	yes	complemented
174	C₄×C₁₆	C₂²×C₇	1	2	yes	complemented
175	C₂³×C₇	—	4	2	no	—
176	C₂³×C₇	—	4	1	no	—
177	C₂³×C₇	—	8	2	no	—
178	C₂³×C₇	—	16	1	no	—
179	C₂³×C₇	—	16	1	no	—
180	C₂³×C₇	C₂×D₈	1	1	yes	characteristic
181	C₇×Q₈	—	4	1	no	—
182	C₇×Q₈	—	4	1	no	—
183	C₇×Q₈	—	16	2	no	—
184	C₇×D₄	—	4	2	no	—
185	C₇×D₄	—	4	1	no	—
186	C₇×D₄	—	4	1	no	—
187	C₇×D₄	—	4	2	no	—
188	C₇×D₄	—	8	2	no	—
189	C₇×D₄	—	8	2	no	—
190	C₇×D₄	—	16	2	no	—
191	C₇×D₄	—	16	2	no	—
192	C₂×C₄×C₇	—	4	1	no	—
193	C₂×C₄×C₇	—	4	1	no	—
194	C₂×C₄×C₇	—	4	1	no	—
195	C₂×C₄×C₇	—	4	2	no	—
196	C₂×C₄×C₇	—	8	2	no	—
197	C₂×C₄×C₇	—	16	1	no	—
198	C₂×C₄×C₇	#124	1	2	yes	—
199	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
200	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
201	C₂×C₄×C₇	C₂×D₈	1	1	yes	characteristic
202	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
203	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
204	C₇×C₈	#124	1	2	yes	—
205	C₇×C₈	C₂×SD₁₆	1	4	yes	—
206	C₇×C₈	C₂×#41	1	1	yes	characteristic
207	C₇×C₈	C₂×#41	1	1	yes	characteristic
208	C₂×#41	—	2	1	no	—
209	C₂²×D₄	—	2	1	no	—
210	AGL(1,ℤ/8)	—	4	4	no	—
211	#135	—	2	2	no	—
212	#135	—	2	2	no	—
213	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
214	C₂×SD₁₆	—	2	1	no	—
215	C₂×SD₁₆	—	2	2	no	—
216	C₂×D₈	—	2	1	no	—
217	C₂×D₈	—	2	2	no	—
218	C₂×D₈	—	2	2	no	—
219	C₂×D₈	—	2	2	no	—
220	C₂×D₈	C₂³×C₇	1	2	yes	—
221	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
222	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
224	C₄⋊Q₈	—	2	2	no	—
225	C₄⋊Q₈	—	4	1	no	—
226	#127	—	2	2	no	—
227	#125	—	2	2	no	—
228	#125	—	4	1	no	—
229	#124	—	2	2	no	—
230	C₂²⋊Q₈	—	4	2	no	—
231	#121	—	4	1	no	—
232	#121	—	4	1	no	—
233	#120	—	4	2	no	—
234	#117	—	2	1	no	—
235	#117	C₇×D₄	1	1	yes	characteristic
236	C₂×C₄⋊C₄	—	2	1	no	—
237	M₃₂	—	2	2	no	—
238	C₂×C₁₆	—	2	2	no	—
239	C₂×C₁₆	C₂³×C₇	1	1	yes	characteristic
240	C₂×C₁₆	C₂³×C₇	1	2	yes	—
241	C₂×C₁₆	C₂³×C₇	1	1	yes	characteristic
242	#107	—	2	1	no	—
243	#107	—	2	2	no	—
244	#107	C₂³×C₇	1	2	yes	—
245	#107	C₂³×C₇	1	1	yes	characteristic
246	#107	C₂³×C₇	1	1	yes	characteristic
247	#106	—	2	1	no	—
248	#106	—	2	2	no	—
249	#97	C₇×D₄	1	2	yes	—
250	C₄×C₈	C₂³×C₇	1	2	yes	—
251	C₂²×C₇	—	2	1	no	—
252	C₂²×C₇	—	2	1	no	—
253	C₂²×C₇	—	8	1	no	—
254	C₂²×C₇	—	8	2	no	—
255	C₂²×C₇	—	8	1	no	—
256	C₂²×C₇	—	8	2	no	—
257	C₂²×C₇	—	8	1	no	—
258	C₂²×C₇	—	8	2	no	—
259	C₂²×C₇	—	16	4	no	—
260	C₂²×C₇	#486	1	2	yes	—
261	C₂²×C₇	C₂²×D₈	1	1	yes	characteristic
262	C₄×C₇	—	2	2	no	—
263	C₄×C₇	—	2	2	no	—
264	C₄×C₇	—	8	1	no	—
265	C₄×C₇	—	8	2	no	—
266	C₄×C₇	—	8	1	no	—
267	C₄×C₇	—	8	1	no	—
268	C₄×C₇	#486	1	2	yes	—
269	C₄×C₇	C₂×#124	1	1	yes	characteristic
270	C₄×C₇	C₂²×SD₁₆	1	1	yes	characteristic
271	C₂⁴	—	4	1	no	—
272	#41	—	4	2	no	—
273	#41	—	4	2	no	—
274	C₂×Q₈	—	2	1	no	—
275	C₂×Q₈	—	4	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	—	4	2	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	4	2	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
287	Q₁₆	—	2	1	no	—
288	Q₁₆	—	2	1	no	—
289	SD₁₆	—	4	2	no	—
290	SD₁₆	—	4	4	no	—
291	D₈	—	2	2	no	—
292	D₈	—	2	2	no	—
293	D₈	—	2	1	no	—
294	D₈	—	2	1	no	—
295	D₈	—	4	2	no	—
296	D₈	—	4	4	no	—
297	M₁₆	C₇×SD₁₆	1	4	yes	—
298	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
299	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
300	C₂×C₈	C₇×#41	1	2	yes	—
301	C₂×C₈	C₇×#41	1	2	yes	—
302	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	C₇×D₈	1	1	yes	characteristic
311	C₄⋊C₄	C₇×D₈	1	1	yes	characteristic
312	C₂²⋊C₄	—	4	1	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	C₇×D₈	1	2	yes	—
316	C₄²	—	4	1	no	—
317	C₄²	C₂×C₇×D₄	1	2	yes	—
318	C₁₆	—	2	1	no	—
319	C₁₆	—	2	1	no	—
320	C₁₆	—	2	2	no	—
321	C₂×C₇	—	2	2	no	—
322	C₂×C₇	—	16	1	no	—
323	C₂×C₇	—	16	2	no	—
324	C₂×C₇	C₂×#486	1	1	yes	characteristic
325	C₂×C₇	#3415	1	1	yes	characteristic
326	C₂×C₇	#3416	1	1	yes	characteristic
327	C₂³	—	4	2	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	8	2	no	—
330	C₂³	—	16	1	no	—
331	C₂³	—	16	1	no	—
332	C₂³	C₂×C₇×D₈	1	1	yes	characteristic
333	Q₈	—	4	1	no	—
334	Q₈	—	4	1	no	—
335	Q₈	—	16	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	1	no	—
338	D₄	—	4	1	no	—
339	D₄	—	4	2	no	—
340	D₄	—	8	2	no	—
341	D₄	—	8	2	no	—
342	D₄	—	16	2	no	—
343	D₄	—	16	2	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	16	1	no	—
350	C₂×C₄	C₇×#124	1	2	yes	—
351	C₂×C₄	C₂×C₇×D₈	1	2	yes	—
352	C₂×C₄	C₂×C₇×D₈	1	2	yes	—
353	C₂×C₄	C₂×C₇×D₈	1	1	yes	characteristic
354	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
355	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
356	C₈	C₇×#124	1	2	yes	—
357	C₈	C₂×C₇×SD₁₆	1	4	yes	—
358	C₈	C₂×C₇×#41	1	1	yes	characteristic
359	C₈	C₂×C₇×#41	1	1	yes	characteristic
360	C₇	#33702	1	1	yes	characteristic, direct product factor, Sylow
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	1	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	16	4	no	—
370	C₂²	C₇×#486	1	2	yes	—
371	C₂²	C₂²×C₇×D₈	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	8	2	no	—
375	C₄	—	8	1	no	—
376	C₄	—	8	1	no	—
377	C₄	—	8	1	no	—
378	C₄	C₇×#486	1	2	yes	—
379	C₄	C₂×C₇×#124	1	1	yes	characteristic
380	C₄	C₂²×C₇×SD₁₆	1	1	yes	characteristic
381	C₂	—	2	2	no	—
382	C₂	—	16	2	no	—
383	C₂	—	16	1	no	—
384	C₂	C₂×C₇×#486	1	1	yes	characteristic
385	C₂	C₇×#3415	1	1	yes	characteristic
386	C₂	C₇×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₇
prime radical	C₇×#3155	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#117 ◁ C₇×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3164	C₂	semidirect
3. C₇×#2244	C₂	semidirect
4. C₇×#2243	C₂	semidirect
5. C₇×#2242	C₂	semidirect
6. C₇×#2240	C₂	semidirect
7. C₇×#2140	C₂	semidirect
8. C₇×#2139	C₂	semidirect
9. C₇×#2138	C₂	semidirect
10. C₂×C₇×#357	C₂	semidirect
11. C₇×#2108	C₂	semidirect
20. C₇×#500	C₂²	semidirect
21. C₇×#499	C₂²	semidirect
29. C₇×#358	C₂²	semidirect
30. C₇×#358	C₂²	semidirect
31. C₇×#358	C₂²	semidirect
36. C₇×#357	C₂²	semidirect
37. C₇×#357	C₂²	semidirect
38. C₇×#357	C₂²	semidirect
39. C₇×#346	C₂²	semidirect
40. C₄×C₇×C₁₆	C₂²	semidirect
41. #33702	C₇	direct (N × H)
85. #3164	C₂×C₇	semidirect
87. #2244	C₂×C₇	semidirect
88. #2243	C₂×C₇	semidirect
89. #2242	C₂×C₇	semidirect
90. #2240	C₂×C₇	semidirect
91. #2140	C₂×C₇	semidirect
92. #2139	C₂×C₇	semidirect
93. #2138	C₂×C₇	semidirect
94. C₂×#357	C₂×C₇	semidirect
95. #2108	C₂×C₇	semidirect
154. #500	C₂²×C₇	semidirect
155. #499	C₂²×C₇	semidirect
163. #358	C₂²×C₇	semidirect
164. #358	C₂²×C₇	semidirect
165. #358	C₂²×C₇	semidirect
170. #357	C₂²×C₇	semidirect
171. #357	C₂²×C₇	semidirect
172. #357	C₂²×C₇	semidirect
173. #346	C₂²×C₇	semidirect
174. C₄×C₁₆	C₂²×C₇	semidirect
360. C₇	#33702	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×#3164	2
C₇×#3155	2
C₇×#2244	2
C₇×#2243	2
C₇×#2242	2
C₇×#2240	2
C₇×#2140	2
C₇×#2139	2
C₇×#2138	2
C₂×C₇×#357	2
C₇×#2108	2
#33702	7

Subgroups — C7×#33702 #13210918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#33702 #13210918