Subgroups — C₇×#19898 #13197114

Order 1792.

724 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3341	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3325	C₂	1	2	yes	maximal, complemented
3	C₇×D₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1706	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1697	C₂	1	2	yes	maximal, complemented
6	C₇×#1675	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1667	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1629	C₂	1	2	yes	maximal, complemented
9	C₇×#1624	C₂	1	2	yes	maximal, complemented
10	C₇×#1589	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×C₈×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×D₈	—	2	1	no	—
13	C₇×#555	C₂²	1	2	yes	complemented
14	C₇×D₄²	C₂²	1	2	yes	—
15	C₇×#500	C₂²	1	1	yes	characteristic, complemented
16	C₇×#493	C₂²	1	1	yes	characteristic
17	C₇×#492	C₂²	1	2	yes	complemented
18	C₇×#486	C₂²	1	2	yes	complemented
19	C₇×#482	—	2	2	no	—
20	C₇×#482	—	2	2	no	—
21	C₇×#476	C₂²	1	2	yes	—
22	C₇×#476	C₂²	1	2	yes	complemented
23	C₇×#469	—	2	2	no	—
24	C₇×#466	—	2	1	no	—
25	C₇×#466	—	2	1	no	—
26	C₇×#459	C₂²	1	2	yes	—
27	C₇×#459	C₂²	1	2	yes	complemented
28	C₇×#447	—	2	2	no	—
29	C₇×#447	—	2	2	no	—
30	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
31	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
32	C₇×#436	C₂²	1	2	yes	complemented
33	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
34	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
35	C₇×#427	—	2	1	no	—
36	C₇×#418	—	2	2	no	—
37	C₇×#335	C₂²	1	1	yes	characteristic, complemented
38	C₇×#335	C₂²	1	1	yes	characteristic, complemented
39	C₇×#333	C₂²	1	2	yes	complemented
40	C₇×#331	C₂²	1	2	yes	complemented
41	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
43	C₇×D₄⋊C₈	C₂²	1	2	yes	complemented
44	C₇×C₈²	C₂²	1	1	yes	characteristic, complemented
45	#19898	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂²×C₇×D₄	—	2	2	no	—
47	C₂²×C₇×D₄	—	2	2	no	—
48	C₂×C₇×SD₁₆	—	4	2	no	—
49	C₂×C₇×D₈	—	2	2	no	—
50	C₂×C₇×D₈	—	2	2	no	—
51	C₂×C₇×D₈	—	2	1	no	—
52	C₂×C₇×D₈	—	2	1	no	—
53	C₂×C₇×D₈	—	4	4	no	—
54	C₂×C₇×D₈	D₄	1	1	yes	characteristic
55	C₂×C₇×D₈	D₄	1	1	yes	characteristic
56	C₂×C₇×M₁₆	—	2	2	no	—
57	C₂²×C₇×C₈	—	2	1	no	—
58	C₂²×C₇×C₈	—	2	1	no	—
59	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₇×#127	C₂³	1	2	yes	—
61	C₇×#124	—	4	2	no	—
62	C₇×#121	—	2	2	no	—
63	C₇×#121	—	2	2	no	—
64	C₇×#121	—	2	2	no	—
65	C₇×#121	—	2	2	no	—
66	C₇×#120	—	4	2	no	—
67	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
68	C₄×C₇×D₄	C₂³	1	2	yes	—
69	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
70	C₇×#117	—	2	2	no	—
71	C₇×#117	—	2	2	no	—
72	C₇×#107	—	2	1	no	—
73	C₇×#107	—	2	1	no	—
74	C₇×#107	D₄	1	1	yes	characteristic
75	C₇×#107	D₄	1	1	yes	characteristic
76	C₇×#106	—	2	2	no	—
77	C₇×#106	—	2	2	no	—
78	C₇×C₄⋊C₈	C₂³	1	2	yes	—
79	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
81	C₇×#102	—	2	2	no	—
82	C₇×#102	—	2	2	no	—
83	C₇×#102	—	2	2	no	—
84	C₇×#102	—	2	2	no	—
85	C₇×#102	—	2	2	no	—
86	C₇×#102	—	2	2	no	—
87	C₇×#102	D₄	1	1	yes	characteristic
88	C₇×#102	D₄	1	2	yes	—
89	C₇×#102	D₄	1	1	yes	characteristic
90	C₇×C₂²⋊C₈	—	2	1	no	—
91	C₇×C₂²⋊C₈	—	2	2	no	—
92	C₇×C₂²⋊C₈	—	2	1	no	—
93	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
94	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
95	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
96	#3341	C₂×C₇	1	1	yes	characteristic, complemented
97	#3325	C₂×C₇	1	2	yes	complemented
98	D₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
99	#1706	C₂×C₇	1	1	yes	characteristic, complemented
100	#1697	C₂×C₇	1	2	yes	complemented
101	#1675	C₂×C₇	1	1	yes	characteristic, complemented
102	#1667	C₂×C₇	1	1	yes	characteristic, complemented
103	#1629	C₂×C₇	1	2	yes	complemented
104	#1624	C₂×C₇	1	2	yes	complemented
105	#1589	C₂×C₇	1	1	yes	characteristic, complemented
106	C₈×D₈	C₂×C₇	1	1	yes	characteristic, complemented
107	C₂⁴×C₇	—	4	2	no	—
108	C₂×C₇×Q₈	—	2	2	no	—
109	C₂×C₇×D₄	—	2	2	no	—
110	C₂×C₇×D₄	—	2	2	no	—
111	C₂×C₇×D₄	—	2	2	no	—
112	C₂×C₇×D₄	—	4	2	no	—
113	C₂×C₇×D₄	—	4	2	no	—
114	C₂×C₇×D₄	—	4	4	no	—
115	C₂×C₇×D₄	—	4	4	no	—
116	C₂×C₇×D₄	—	4	2	no	—
117	C₂×C₇×D₄	—	8	2	no	—
118	C₂×C₇×D₄	—	8	2	no	—
119	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
120	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
121	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇	—	2	1	no	—
123	C₂²×C₄×C₇	—	2	2	no	—
124	C₂²×C₄×C₇	—	2	1	no	—
125	C₇×SD₁₆	—	8	4	no	—
126	C₇×D₈	—	2	2	no	—
127	C₇×D₈	—	2	2	no	—
128	C₇×D₈	—	4	4	no	—
129	C₇×D₈	—	4	2	no	—
130	C₇×D₈	—	8	1	no	—
131	C₇×D₈	—	8	2	no	—
132	C₇×M₁₆	—	8	2	no	—
133	C₂×C₇×C₈	—	2	1	no	—
134	C₂×C₇×C₈	—	2	1	no	—
135	C₂×C₇×C₈	—	2	2	no	—
136	C₂×C₇×C₈	—	2	1	no	—
137	C₂×C₇×C₈	—	4	2	no	—
138	C₂×C₇×C₈	—	4	2	no	—
139	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
140	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
141	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
142	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
143	C₇×C₄⋊C₄	—	2	2	no	—
144	C₇×C₄⋊C₄	—	2	2	no	—
145	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
146	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
147	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
148	C₇×C₂²⋊C₄	—	2	1	no	—
149	C₇×C₂²⋊C₄	—	2	2	no	—
150	C₇×C₂²⋊C₄	—	2	1	no	—
151	C₇×C₂²⋊C₄	—	4	2	no	—
152	C₇×C₂²⋊C₄	—	4	2	no	—
153	C₇×C₂²⋊C₄	—	4	2	no	—
154	C₄²×C₇	—	4	2	no	—
155	C₄²×C₇	C₂⁴	1	1	yes	characteristic
156	C₂²×D₈	—	2	1	no	—
157	#555	C₂²×C₇	1	2	yes	complemented
158	D₄²	C₂²×C₇	1	2	yes	—
159	#500	C₂²×C₇	1	1	yes	characteristic, complemented
160	#493	C₂²×C₇	1	1	yes	characteristic
161	#492	C₂²×C₇	1	2	yes	complemented
162	#486	C₂²×C₇	1	2	yes	complemented
163	#482	—	2	2	no	—
164	#482	—	2	2	no	—
165	#476	C₂²×C₇	1	2	yes	—
166	#476	C₂²×C₇	1	2	yes	complemented
167	#469	—	2	2	no	—
168	#466	—	2	1	no	—
169	#466	—	2	1	no	—
170	#459	C₂²×C₇	1	2	yes	—
171	#459	C₂²×C₇	1	2	yes	complemented
172	#447	—	2	2	no	—
173	#447	—	2	2	no	—
174	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
175	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
176	#436	C₂²×C₇	1	2	yes	complemented
177	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
178	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
179	#427	—	2	1	no	—
180	#418	—	2	2	no	—
181	#335	C₂²×C₇	1	1	yes	characteristic, complemented
182	#335	C₂²×C₇	1	1	yes	characteristic, complemented
183	#333	C₂²×C₇	1	2	yes	complemented
184	#331	C₂²×C₇	1	2	yes	complemented
185	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
186	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
187	D₄⋊C₈	C₂²×C₇	1	2	yes	complemented
188	C₈²	C₂²×C₇	1	1	yes	characteristic, complemented
189	C₂³×C₇	—	2	1	no	—
190	C₂³×C₇	—	2	1	no	—
191	C₂³×C₇	—	2	2	no	—
192	C₂³×C₇	—	4	2	no	—
193	C₂³×C₇	—	8	4	no	—
194	C₂³×C₇	—	8	4	no	—
195	C₂³×C₇	—	16	2	no	—
196	C₇×Q₈	—	8	2	no	—
197	C₇×D₄	—	2	1	no	—
198	C₇×D₄	—	2	2	no	—
199	C₇×D₄	—	2	1	no	—
200	C₇×D₄	—	2	1	no	—
201	C₇×D₄	—	2	2	no	—
202	C₇×D₄	—	4	2	no	—
203	C₇×D₄	—	4	2	no	—
204	C₇×D₄	—	4	2	no	—
205	C₇×D₄	—	4	2	no	—
206	C₇×D₄	—	8	2	no	—
207	C₇×D₄	—	8	4	no	—
208	C₇×D₄	—	8	4	no	—
209	C₇×D₄	—	16	2	no	—
210	C₇×D₄	#135	1	2	yes	—
211	C₂×C₄×C₇	—	2	1	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	1	no	—
214	C₂×C₄×C₇	—	4	2	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	1	no	—
219	C₂×C₄×C₇	—	4	1	no	—
220	C₂×C₄×C₇	—	4	2	no	—
221	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
224	C₇×C₈	—	2	2	no	—
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	AGL(1,ℤ/8)	1	2	yes	—
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	—	2	2	no	—
234	C₂×SD₁₆	—	4	2	no	—
235	C₂×D₈	—	2	2	no	—
236	C₂×D₈	—	2	2	no	—
237	C₂×D₈	—	2	1	no	—
238	C₂×D₈	—	2	1	no	—
239	C₂×D₈	—	4	4	no	—
240	C₂×D₈	C₇×D₄	1	1	yes	characteristic
241	C₂×D₈	C₇×D₄	1	1	yes	characteristic
242	C₂×M₁₆	—	2	2	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
246	#127	C₂³×C₇	1	2	yes	—
247	#124	—	4	2	no	—
248	#121	—	2	2	no	—
249	#121	—	2	2	no	—
250	#121	—	2	2	no	—
251	#121	—	2	2	no	—
252	#120	—	4	2	no	—
253	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
254	C₄×D₄	C₂³×C₇	1	2	yes	—
255	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
256	#117	—	2	2	no	—
257	#117	—	2	2	no	—
258	#107	—	2	1	no	—
259	#107	—	2	1	no	—
260	#107	C₇×D₄	1	1	yes	characteristic
261	#107	C₇×D₄	1	1	yes	characteristic
262	#106	—	2	2	no	—
263	#106	—	2	2	no	—
264	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
265	C₄⋊C₈	C₂³×C₇	1	2	yes	—
266	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
267	#102	—	2	2	no	—
268	#102	—	2	2	no	—
269	#102	—	2	2	no	—
270	#102	—	2	2	no	—
271	#102	—	2	2	no	—
272	#102	—	2	2	no	—
273	#102	C₇×D₄	1	1	yes	characteristic
274	#102	C₇×D₄	1	2	yes	—
275	#102	C₇×D₄	1	1	yes	characteristic
276	C₂²⋊C₈	—	2	1	no	—
277	C₂²⋊C₈	—	2	1	no	—
278	C₂²⋊C₈	—	2	2	no	—
279	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
281	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
282	C₂²×C₇	—	2	2	no	—
283	C₂²×C₇	—	4	1	no	—
284	C₂²×C₇	—	4	1	no	—
285	C₂²×C₇	—	4	1	no	—
286	C₂²×C₇	—	4	2	no	—
287	C₂²×C₇	—	4	2	no	—
288	C₂²×C₇	—	4	1	no	—
289	C₂²×C₇	—	4	1	no	—
290	C₂²×C₇	—	4	2	no	—
291	C₂²×C₇	—	8	2	no	—
292	C₂²×C₇	—	8	2	no	—
293	C₂²×C₇	—	8	2	no	—
294	C₂²×C₇	—	16	8	no	—
295	C₂²×C₇	D₄²	1	1	yes	characteristic
296	C₄×C₇	—	2	1	no	—
297	C₄×C₇	—	4	1	no	—
298	C₄×C₇	—	4	1	no	—
299	C₄×C₇	—	4	2	no	—
300	C₄×C₇	—	8	2	no	—
301	C₄×C₇	C₂×#135	1	1	yes	characteristic
302	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
303	C₄×C₇	#576	1	1	yes	characteristic
304	C₄×C₇	#577	1	1	yes	characteristic
305	C₂⁴	—	4	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	4	no	—
313	C₂×D₄	—	4	4	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	8	2	no	—
316	C₂×D₄	—	8	2	no	—
317	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
318	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
319	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	1	no	—
323	SD₁₆	—	8	4	no	—
324	D₈	—	2	2	no	—
325	D₈	—	2	2	no	—
326	D₈	—	4	4	no	—
327	D₈	—	4	2	no	—
328	D₈	—	8	1	no	—
329	D₈	—	8	2	no	—
330	M₁₆	—	8	2	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	4	2	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
338	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
339	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
340	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
344	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
345	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	2	1	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₄²	—	4	2	no	—
353	C₄²	C₂⁴×C₇	1	1	yes	characteristic
354	C₂×C₇	—	4	2	no	—
355	C₂×C₇	—	8	1	no	—
356	C₂×C₇	—	8	2	no	—
357	C₂×C₇	—	16	2	no	—
358	C₂×C₇	#3272	1	1	yes	characteristic
359	C₂×C₇	#3280	1	1	yes	characteristic
360	C₂×C₇	#3292	1	1	yes	characteristic
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	8	4	no	—
366	C₂³	—	8	4	no	—
367	C₂³	—	16	2	no	—
368	Q₈	—	8	2	no	—
369	D₄	—	2	1	no	—
370	D₄	—	2	2	no	—
371	D₄	—	2	1	no	—
372	D₄	—	2	1	no	—
373	D₄	—	2	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	8	2	no	—
379	D₄	—	8	4	no	—
380	D₄	—	8	4	no	—
381	D₄	—	16	2	no	—
382	D₄	C₇×#135	1	2	yes	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
395	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
396	C₈	—	2	2	no	—
397	C₈	—	2	1	no	—
398	C₈	—	2	1	no	—
399	C₈	—	2	1	no	—
400	C₈	—	4	1	no	—
401	C₈	—	4	1	no	—
402	C₈	—	4	2	no	—
403	C₈	C₇×AGL(1,ℤ/8)	1	2	yes	—
404	C₇	#19898	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²	—	2	2	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	16	8	no	—
418	C₂²	C₇×D₄²	1	1	yes	characteristic
419	C₄	—	2	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	2	no	—
423	C₄	—	8	2	no	—
424	C₄	C₂×C₇×#135	1	1	yes	characteristic
425	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
426	C₄	C₇×#576	1	1	yes	characteristic
427	C₄	C₇×#577	1	1	yes	characteristic
428	C₂	—	4	2	no	—
429	C₂	—	8	2	no	—
430	C₂	—	8	1	no	—
431	C₂	—	16	2	no	—
432	C₂	C₇×#3272	1	1	yes	characteristic
433	C₂	C₇×#3280	1	1	yes	characteristic
434	C₂	C₇×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3341	C₂	semidirect
2. C₇×#3325	C₂	semidirect
3. C₇×D₄×D₈	C₂	semidirect
4. C₇×#1706	C₂	semidirect
5. C₇×#1697	C₂	semidirect
6. C₇×#1675	C₂	semidirect
7. C₇×#1667	C₂	semidirect
8. C₇×#1629	C₂	semidirect
9. C₇×#1624	C₂	semidirect
10. C₇×#1589	C₂	semidirect
11. C₇×C₈×D₈	C₂	semidirect
13. C₇×#555	C₂²	semidirect
15. C₇×#500	C₂²	semidirect
17. C₇×#492	C₂²	semidirect
18. C₇×#486	C₂²	semidirect
22. C₇×#476	C₂²	semidirect
27. C₇×#459	C₂²	semidirect
32. C₇×#436	C₂²	semidirect
34. C₇×C₈×D₄	C₂²	semidirect
37. C₇×#335	C₂²	semidirect
38. C₇×#335	C₂²	semidirect
39. C₇×#333	C₂²	semidirect
40. C₇×#331	C₂²	semidirect
42. C₇×D₄⋊C₈	C₂²	semidirect
43. C₇×D₄⋊C₈	C₂²	semidirect
44. C₇×C₈²	C₂²	semidirect
45. #19898	C₇	direct (N × H)
96. #3341	C₂×C₇	semidirect
97. #3325	C₂×C₇	semidirect
98. D₄×D₈	C₂×C₇	semidirect
99. #1706	C₂×C₇	semidirect
100. #1697	C₂×C₇	semidirect
101. #1675	C₂×C₇	semidirect
102. #1667	C₂×C₇	semidirect
103. #1629	C₂×C₇	semidirect
104. #1624	C₂×C₇	semidirect
105. #1589	C₂×C₇	semidirect
106. C₈×D₈	C₂×C₇	semidirect
157. #555	C₂²×C₇	semidirect
159. #500	C₂²×C₇	semidirect
161. #492	C₂²×C₇	semidirect
162. #486	C₂²×C₇	semidirect
166. #476	C₂²×C₇	semidirect
171. #459	C₂²×C₇	semidirect
176. #436	C₂²×C₇	semidirect
178. C₈×D₄	C₂²×C₇	semidirect
181. #335	C₂²×C₇	semidirect
182. #335	C₂²×C₇	semidirect
183. #333	C₂²×C₇	semidirect
184. #331	C₂²×C₇	semidirect
186. D₄⋊C₈	C₂²×C₇	semidirect
187. D₄⋊C₈	C₂²×C₇	semidirect
188. C₈²	C₂²×C₇	semidirect
404. C₇	#19898	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×#3341	2
C₇×#3325	2
C₇×D₄×D₈	2
C₇×#1706	2
C₇×#1697	2
C₇×#1675	2
C₇×#1667	2
C₇×#1629	2
C₇×#1624	2
C₇×#1589	2
C₇×C₈×D₈	2
#19898	7

Subgroups — C7×#19898 #13197114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19898 #13197114