Subgroups — C₇×#33690 #13210906

Order 1792.

526 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3183	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#2956	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2239	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2238	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2231	C₂	1	2	yes	maximal, complemented
6	C₇×#2212	C₂	1	2	yes	maximal, complemented
7	C₇×#2191	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2190	C₂	1	1	yes	maximal, characteristic
9	C₇×AGL(1,ℤ/16)	C₂	1	2	yes	maximal, complemented
10	C₇×#2180	C₂	1	2	yes	maximal, complemented
11	C₇×#2165	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#575	C₂²	1	1	yes	characteristic
13	C₇×#568	—	2	1	no	—
14	C₇×#529	—	2	1	no	—
15	C₇×#510	C₂²	1	2	yes	—
16	C₇×#509	C₂²	1	2	yes	—
17	C₇×#499	C₂²	1	1	yes	characteristic, complemented
18	C₇×#495	C₂²	1	1	yes	characteristic, complemented
19	C₇×#488	—	2	1	no	—
20	C₇×#470	C₂²	1	1	yes	characteristic
21	C₇×#469	C₂²	1	1	yes	characteristic
22	C₇×#468	—	2	1	no	—
23	C₇×#444	—	2	1	no	—
24	C₇×#444	C₂²	1	2	yes	—
25	C₇×#443	—	2	1	no	—
26	C₇×#443	C₂²	1	2	yes	—
27	C₇×#442	C₂²	1	1	yes	characteristic, complemented
28	C₇×#441	C₂²	1	1	yes	characteristic, complemented
29	C₇×#440	—	2	1	no	—
30	C₇×#430	C₂²	1	1	yes	characteristic
31	C₂×C₇×#104	—	2	1	no	—
32	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
33	C₇×#365	C₂²	1	2	yes	complemented
34	C₇×#365	C₂²	1	2	yes	complemented
35	C₇×#364	C₂²	1	2	yes	complemented
36	C₇×#362	C₂²	1	2	yes	complemented
37	C₇×#361	C₂²	1	2	yes	complemented
38	C₇×#360	C₂²	1	2	yes	—
39	C₇×#360	C₂²	1	2	yes	—
40	C₇×#349	C₂²	1	1	yes	characteristic
41	C₇×#349	C₂²	1	1	yes	characteristic
42	C₇×#347	C₂²	1	2	yes	complemented
43	#33690	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₇×#41	—	2	1	no	—
45	C₇×#137	—	2	2	no	—
46	C₇×AGL(1,ℤ/8)	—	2	2	no	—
47	C₇×#135	—	2	1	no	—
48	C₇×#135	C₂³	1	2	yes	—
49	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₇×SD₁₆	—	2	1	no	—
51	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
52	C₇×#131	—	2	2	no	—
53	C₇×#131	—	2	2	no	—
54	C₇×#131	—	4	2	no	—
55	C₂×C₇×M₁₆	—	2	1	no	—
56	C₂×C₇×M₁₆	—	4	2	no	—
57	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
58	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
59	C₇×#126	—	4	1	no	—
60	C₇×#125	—	2	1	no	—
61	C₇×#124	—	2	1	no	—
62	C₇×#123	—	4	1	no	—
63	C₇×C₂²⋊Q₈	—	2	1	no	—
64	C₇×#121	—	2	1	no	—
65	C₄×C₇×Q₈	—	2	1	no	—
66	C₄×C₇×D₄	—	2	1	no	—
67	C₄×C₇×D₄	—	4	1	no	—
68	C₇×#117	—	4	1	no	—
69	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
70	C₇×Q₃₂	—	2	2	no	—
71	C₇×SD₃₂	—	2	2	no	—
72	C₇×SD₃₂	—	2	2	no	—
73	C₇×D₁₆	—	2	2	no	—
74	C₇×M₃₂	C₂³	1	2	yes	—
75	C₇×M₃₂	C₂³	1	2	yes	—
76	C₇×#108	—	2	1	no	—
77	C₇×#108	C₂³	1	2	yes	—
78	C₇×#107	—	2	1	no	—
79	C₇×#106	C₂³	1	1	yes	characteristic
80	C₇×#106	C₂³	1	1	yes	characteristic
81	C₇×#104	—	2	2	no	—
82	C₇×#104	—	2	2	no	—
83	C₇×#103	—	2	1	no	—
84	C₇×#103	—	2	1	no	—
85	C₇×#102	—	2	1	no	—
86	C₇×#102	—	2	1	no	—
87	C₇×#97	D₄	1	1	yes	characteristic
88	C₇×#97	C₂³	1	1	yes	characteristic
89	C₄×C₇×C₈	D₄	1	1	yes	characteristic
90	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
91	#3183	C₂×C₇	1	1	yes	characteristic, complemented
92	#2956	C₂×C₇	1	1	yes	characteristic, complemented
93	#2239	C₂×C₇	1	1	yes	characteristic, complemented
94	#2238	C₂×C₇	1	1	yes	characteristic, complemented
95	#2231	C₂×C₇	1	2	yes	complemented
96	#2212	C₂×C₇	1	2	yes	complemented
97	#2191	C₂×C₇	1	1	yes	characteristic, complemented
98	#2190	C₂×C₇	1	1	yes	characteristic
99	AGL(1,ℤ/16)	C₂×C₇	1	2	yes	complemented
100	#2180	C₂×C₇	1	2	yes	complemented
101	#2165	C₂×C₇	1	1	yes	characteristic, complemented
102	C₇×#41	—	2	2	no	—
103	C₇×#41	—	2	2	no	—
104	C₇×#41	—	4	1	no	—
105	C₇×#41	—	4	1	no	—
106	C₂×C₇×Q₈	—	2	1	no	—
107	C₂×C₇×Q₈	—	2	1	no	—
108	C₂×C₇×D₄	—	2	1	no	—
109	C₂×C₇×D₄	—	2	1	no	—
110	C₂×C₇×D₄	—	4	1	no	—
111	C₂×C₇×D₄	—	4	1	no	—
112	C₂²×C₄×C₇	—	2	1	no	—
113	C₂²×C₄×C₇	—	4	1	no	—
114	C₂²×C₄×C₇	—	4	1	no	—
115	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
116	C₇×Q₁₆	—	2	1	no	—
117	C₇×Q₁₆	—	2	2	no	—
118	C₇×Q₁₆	#41	1	2	yes	—
119	C₇×SD₁₆	—	2	2	no	—
120	C₇×SD₁₆	—	2	2	no	—
121	C₇×SD₁₆	—	4	2	no	—
122	C₇×D₈	—	2	1	no	—
123	C₇×D₈	—	2	2	no	—
124	C₇×D₈	#41	1	2	yes	—
125	C₇×M₁₆	—	2	2	no	—
126	C₇×M₁₆	—	2	2	no	—
127	C₇×M₁₆	—	2	2	no	—
128	C₇×M₁₆	—	4	2	no	—
129	C₇×M₁₆	—	4	1	no	—
130	C₇×M₁₆	—	4	2	no	—
131	C₂×C₇×C₈	—	4	2	no	—
132	C₂×C₇×C₈	—	4	1	no	—
133	C₂×C₇×C₈	—	4	2	no	—
134	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
136	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
138	C₇×C₄⋊C₄	—	2	1	no	—
139	C₇×C₄⋊C₄	—	2	1	no	—
140	C₇×C₄⋊C₄	—	4	1	no	—
141	C₇×C₄⋊C₄	—	4	1	no	—
142	C₇×C₄⋊C₄	—	4	1	no	—
143	C₇×C₄⋊C₄	—	4	1	no	—
144	C₇×C₂²⋊C₄	—	4	1	no	—
145	C₇×C₂²⋊C₄	—	4	1	no	—
146	C₇×C₂²⋊C₄	—	4	1	no	—
147	C₇×C₂²⋊C₄	—	4	1	no	—
148	C₇×C₂²⋊C₄	—	4	1	no	—
149	C₄²×C₇	—	2	1	no	—
150	C₄²×C₇	—	4	1	no	—
151	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
153	C₇×C₁₆	—	2	2	no	—
154	C₇×C₁₆	—	2	2	no	—
155	#575	C₂²×C₇	1	1	yes	characteristic
156	#568	—	2	1	no	—
157	#529	—	2	1	no	—
158	#510	C₂²×C₇	1	2	yes	—
159	#509	C₂²×C₇	1	2	yes	—
160	#499	C₂²×C₇	1	1	yes	characteristic, complemented
161	#495	C₂²×C₇	1	1	yes	characteristic, complemented
162	#488	—	2	1	no	—
163	#470	C₂²×C₇	1	1	yes	characteristic
164	#469	C₂²×C₇	1	1	yes	characteristic
165	#468	—	2	1	no	—
166	#444	—	2	1	no	—
167	#444	C₂²×C₇	1	2	yes	—
168	#443	—	2	1	no	—
169	#443	C₂²×C₇	1	2	yes	—
170	#442	C₂²×C₇	1	1	yes	characteristic, complemented
171	#441	C₂²×C₇	1	1	yes	characteristic, complemented
172	#440	—	2	1	no	—
173	#430	C₂²×C₇	1	1	yes	characteristic
174	C₂×#104	—	2	1	no	—
175	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
176	#365	C₂²×C₇	1	2	yes	complemented
177	#365	C₂²×C₇	1	2	yes	complemented
178	#364	C₂²×C₇	1	2	yes	complemented
179	#362	C₂²×C₇	1	2	yes	complemented
180	#361	C₂²×C₇	1	2	yes	complemented
181	#360	C₂²×C₇	1	2	yes	—
182	#360	C₂²×C₇	1	2	yes	—
183	#349	C₂²×C₇	1	1	yes	characteristic
184	#349	C₂²×C₇	1	1	yes	characteristic
185	#347	C₂²×C₇	1	2	yes	complemented
186	C₂³×C₇	—	4	1	no	—
187	C₂³×C₇	—	4	1	no	—
188	C₂³×C₇	AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₇×Q₈	—	2	2	no	—
190	C₇×Q₈	—	4	1	no	—
191	C₇×Q₈	—	4	1	no	—
192	C₇×Q₈	—	4	1	no	—
193	C₇×D₄	—	2	2	no	—
194	C₇×D₄	—	4	1	no	—
195	C₇×D₄	—	4	2	no	—
196	C₇×D₄	—	4	2	no	—
197	C₇×D₄	—	4	1	no	—
198	C₇×D₄	—	4	1	no	—
199	C₇×D₄	—	8	2	no	—
200	C₂×C₄×C₇	—	2	1	no	—
201	C₂×C₄×C₇	—	2	1	no	—
202	C₂×C₄×C₇	—	2	1	no	—
203	C₂×C₄×C₇	—	2	1	no	—
204	C₂×C₄×C₇	—	4	2	no	—
205	C₂×C₄×C₇	—	4	1	no	—
206	C₂×C₄×C₇	—	4	2	no	—
207	C₂×C₄×C₇	—	4	1	no	—
208	C₂×C₄×C₇	—	4	1	no	—
209	C₂×C₄×C₇	—	4	1	no	—
210	C₂×C₄×C₇	—	8	1	no	—
211	C₂×C₄×C₇	—	8	2	no	—
212	C₂×C₄×C₇	AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
214	C₇×C₈	—	2	1	no	—
215	C₇×C₈	—	2	1	no	—
216	C₇×C₈	—	4	2	no	—
217	C₇×C₈	AGL(1,ℤ/8)	1	2	yes	—
218	C₇×C₈	C₂×#41	1	2	yes	—
219	C₂×#41	—	2	1	no	—
220	#137	—	2	2	no	—
221	AGL(1,ℤ/8)	—	2	2	no	—
222	#135	—	2	1	no	—
223	#135	C₂³×C₇	1	2	yes	—
224	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
225	C₂×SD₁₆	—	2	1	no	—
226	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
227	#131	—	2	2	no	—
228	#131	—	2	2	no	—
229	#131	—	4	2	no	—
230	C₂×M₁₆	—	2	1	no	—
231	C₂×M₁₆	—	4	2	no	—
232	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
233	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
234	#126	—	4	1	no	—
235	#125	—	2	1	no	—
236	#124	—	2	1	no	—
237	#123	—	4	1	no	—
238	C₂²⋊Q₈	—	2	1	no	—
239	#121	—	2	1	no	—
240	C₄×Q₈	—	2	1	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	4	1	no	—
243	#117	—	4	1	no	—
244	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
245	Q₃₂	—	2	2	no	—
246	SD₃₂	—	2	2	no	—
247	SD₃₂	—	2	2	no	—
248	D₁₆	—	2	2	no	—
249	M₃₂	C₂³×C₇	1	2	yes	—
250	M₃₂	C₂³×C₇	1	2	yes	—
251	#108	—	2	1	no	—
252	#108	C₂³×C₇	1	2	yes	—
253	#107	—	2	1	no	—
254	#106	C₂³×C₇	1	1	yes	characteristic
255	#106	C₂³×C₇	1	1	yes	characteristic
256	#104	—	2	2	no	—
257	#104	—	2	2	no	—
258	#103	—	2	1	no	—
259	#103	—	2	1	no	—
260	#102	—	2	1	no	—
261	#102	—	2	1	no	—
262	#97	C₇×D₄	1	1	yes	characteristic
263	#97	C₂³×C₇	1	1	yes	characteristic
264	C₄×C₈	C₇×D₄	1	1	yes	characteristic
265	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
266	C₂²×C₇	—	2	1	no	—
267	C₂²×C₇	—	4	1	no	—
268	C₂²×C₇	—	4	2	no	—
269	C₂²×C₇	—	8	1	no	—
270	C₂²×C₇	—	8	1	no	—
271	C₂²×C₇	—	8	1	no	—
272	C₂²×C₇	—	16	1	no	—
273	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
274	C₄×C₇	—	2	1	no	—
275	C₄×C₇	—	4	1	no	—
276	C₄×C₇	—	4	1	no	—
277	C₄×C₇	—	4	2	no	—
278	C₄×C₇	—	8	1	no	—
279	C₄×C₇	—	8	1	no	—
280	C₄×C₇	—	8	1	no	—
281	C₄×C₇	#525	1	1	yes	characteristic
282	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	#41	—	4	1	no	—
286	#41	—	4	1	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
297	Q₁₆	—	2	1	no	—
298	Q₁₆	—	2	2	no	—
299	Q₁₆	C₇×#41	1	2	yes	—
300	SD₁₆	—	2	2	no	—
301	SD₁₆	—	2	2	no	—
302	SD₁₆	—	4	2	no	—
303	D₈	—	2	1	no	—
304	D₈	—	2	2	no	—
305	D₈	C₇×#41	1	2	yes	—
306	M₁₆	—	2	2	no	—
307	M₁₆	—	2	2	no	—
308	M₁₆	—	2	2	no	—
309	M₁₆	—	4	2	no	—
310	M₁₆	—	4	1	no	—
311	M₁₆	—	4	2	no	—
312	C₂×C₈	—	4	2	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
316	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
317	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
318	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₂²⋊C₄	—	4	1	no	—
326	C₂²⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	4	1	no	—
329	C₂²⋊C₄	—	4	1	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	4	1	no	—
332	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
333	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
334	C₁₆	—	2	2	no	—
335	C₁₆	—	2	2	no	—
336	C₂×C₇	—	2	1	no	—
337	C₂×C₇	—	4	1	no	—
338	C₂×C₇	—	8	2	no	—
339	C₂×C₇	—	16	1	no	—
340	C₂×C₇	#3109	1	1	yes	characteristic
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
344	Q₈	—	2	2	no	—
345	Q₈	—	4	1	no	—
346	Q₈	—	4	1	no	—
347	Q₈	—	4	1	no	—
348	D₄	—	2	2	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	1	no	—
353	D₄	—	4	1	no	—
354	D₄	—	8	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	8	1	no	—
366	C₂×C₄	—	8	2	no	—
367	C₂×C₄	C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	4	2	no	—
372	C₈	C₇×AGL(1,ℤ/8)	1	2	yes	—
373	C₈	C₂×C₇×#41	1	2	yes	—
374	C₇	#33690	1	1	yes	characteristic, direct product factor, Sylow
375	C₂²	—	2	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	16	1	no	—
382	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
383	C₄	—	2	1	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	8	1	no	—
388	C₄	—	8	1	no	—
389	C₄	—	8	1	no	—
390	C₄	C₇×#525	1	1	yes	characteristic
391	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
392	C₂	—	2	1	no	—
393	C₂	—	4	1	no	—
394	C₂	—	8	2	no	—
395	C₂	—	16	1	no	—
396	C₂	C₇×#3109	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₇	#3109
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₇
prime radical	C₇×#2190	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇ ◁ C₂×C₄×C₇ ◁ C₄×C₇×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3183	C₂	semidirect
2. C₇×#2956	C₂	semidirect
3. C₇×#2239	C₂	semidirect
4. C₇×#2238	C₂	semidirect
5. C₇×#2231	C₂	semidirect
6. C₇×#2212	C₂	semidirect
7. C₇×#2191	C₂	semidirect
9. C₇×AGL(1,ℤ/16)	C₂	semidirect
10. C₇×#2180	C₂	semidirect
11. C₇×#2165	C₂	semidirect
17. C₇×#499	C₂²	semidirect
18. C₇×#495	C₂²	semidirect
27. C₇×#442	C₂²	semidirect
28. C₇×#441	C₂²	semidirect
33. C₇×#365	C₂²	semidirect
34. C₇×#365	C₂²	semidirect
35. C₇×#364	C₂²	semidirect
36. C₇×#362	C₂²	semidirect
37. C₇×#361	C₂²	semidirect
42. C₇×#347	C₂²	semidirect
43. #33690	C₇	direct (N × H)
91. #3183	C₂×C₇	semidirect
92. #2956	C₂×C₇	semidirect
93. #2239	C₂×C₇	semidirect
94. #2238	C₂×C₇	semidirect
95. #2231	C₂×C₇	semidirect
96. #2212	C₂×C₇	semidirect
97. #2191	C₂×C₇	semidirect
99. AGL(1,ℤ/16)	C₂×C₇	semidirect
100. #2180	C₂×C₇	semidirect
101. #2165	C₂×C₇	semidirect
160. #499	C₂²×C₇	semidirect
161. #495	C₂²×C₇	semidirect
170. #442	C₂²×C₇	semidirect
171. #441	C₂²×C₇	semidirect
176. #365	C₂²×C₇	semidirect
177. #365	C₂²×C₇	semidirect
178. #364	C₂²×C₇	semidirect
179. #362	C₂²×C₇	semidirect
180. #361	C₂²×C₇	semidirect
185. #347	C₂²×C₇	semidirect
374. C₇	#33690	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×#3183	2
C₇×#2956	2
C₇×#2239	2
C₇×#2238	2
C₇×#2231	2
C₇×#2212	2
C₇×#2191	2
C₇×#2190	2
C₇×AGL(1,ℤ/16)	2
C₇×#2180	2
C₇×#2165	2
#33690	7

Subgroups — C7×#33690 #13210906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#33690 #13210906