Subgroups — C₇×#19883 #13197099

Order 1792.

798 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3334	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3272	C₂	1	2	yes	maximal, complemented
4	C₇×#1706	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1685	C₂	1	2	yes	maximal, complemented
6	C₇×#1673	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1667	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1639	C₂	1	2	yes	maximal, complemented
9	C₇×#1625	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	C₂×C₇×AGL(1,ℤ/8)	—	2	2	no	—
13	C₂²×C₇×D₈	—	2	1	no	—
14	C₇×#547	C₂²	1	2	yes	complemented
15	C₇×D₄²	C₂²	1	2	yes	—
16	C₇×#500	C₂²	1	1	yes	characteristic, complemented
17	C₇×#493	C₂²	1	1	yes	characteristic
18	C₇×#492	C₂²	1	2	yes	complemented
19	C₇×#486	C₂²	1	2	yes	complemented
20	C₇×#480	—	2	2	no	—
21	C₇×#474	C₂²	1	2	yes	complemented
22	C₇×#468	—	2	2	no	—
23	C₇×#466	—	2	1	no	—
24	C₇×#466	—	2	1	no	—
25	C₇×#461	C₂²	1	2	yes	—
26	C₇×#459	C₂²	1	2	yes	—
27	C₇×#459	C₂²	1	2	yes	complemented
28	C₇×#450	—	2	2	no	—
29	C₇×#449	—	2	2	no	—
30	C₇×#447	—	2	2	no	—
31	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
32	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
33	C₇×#436	C₂²	1	2	yes	complemented
34	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
35	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₇×#107	—	2	1	no	—
37	C₇×#335	C₂²	1	1	yes	characteristic, complemented
38	C₇×#335	C₂²	1	1	yes	characteristic, complemented
39	C₇×#332	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	#19883	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₇×#41	—	2	2	no	—
47	C₂²×C₇×D₄	—	2	2	no	—
48	C₂²×C₇×D₄	—	2	2	no	—
49	C₇×AGL(1,ℤ/8)	—	4	8	no	—
50	C₂×C₇×SD₁₆	—	2	2	no	—
51	C₂×C₇×SD₁₆	—	2	2	no	—
52	C₂×C₇×SD₁₆	—	2	2	no	—
53	C₂×C₇×D₈	—	2	2	no	—
54	C₂×C₇×D₈	—	2	2	no	—
55	C₂×C₇×D₈	—	2	1	no	—
56	C₂×C₇×D₈	—	2	1	no	—
57	C₂×C₇×D₈	—	4	4	no	—
58	C₂×C₇×D₈	D₄	1	1	yes	characteristic
59	C₂×C₇×D₈	D₄	1	1	yes	characteristic
60	C₂×C₇×M₁₆	—	2	2	no	—
61	C₂²×C₇×C₈	—	2	1	no	—
62	C₂²×C₇×C₈	—	2	1	no	—
63	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₇×#127	C₂³	1	2	yes	—
65	C₇×#123	—	4	2	no	—
66	C₇×C₂²⋊Q₈	—	2	2	no	—
67	C₇×#121	—	2	2	no	—
68	C₇×#121	—	2	2	no	—
69	C₇×#121	—	2	2	no	—
70	C₇×#120	—	4	2	no	—
71	C₄×C₇×D₄	C₂³	1	2	yes	—
72	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
73	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
74	C₂×C₇×C₄⋊C₄	—	2	2	no	—
75	C₇×#107	—	2	1	no	—
76	C₇×#107	—	2	1	no	—
77	C₇×#107	—	2	2	no	—
78	C₇×#107	D₄	1	1	yes	characteristic
79	C₇×#107	D₄	1	1	yes	characteristic
80	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
81	C₇×C₄⋊C₈	C₂³	1	2	yes	—
82	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₇×#103	—	2	2	no	—
84	C₇×#102	—	2	2	no	—
85	C₇×#102	—	2	2	no	—
86	C₇×#102	—	2	2	no	—
87	C₇×#102	—	4	2	no	—
88	C₇×#102	D₄	1	2	yes	—
89	C₇×#102	D₄	1	1	yes	characteristic
90	C₇×#102	D₄	1	1	yes	characteristic
91	C₇×C₂²⋊C₈	—	2	1	no	—
92	C₇×C₂²⋊C₈	—	2	1	no	—
93	C₇×C₂²⋊C₈	—	2	2	no	—
94	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
95	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
96	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
97	#3334	C₂×C₇	1	1	yes	characteristic, complemented
98	D₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
99	#3272	C₂×C₇	1	2	yes	complemented
100	#1706	C₂×C₇	1	1	yes	characteristic, complemented
101	#1685	C₂×C₇	1	2	yes	complemented
102	#1673	C₂×C₇	1	1	yes	characteristic, complemented
103	#1667	C₂×C₇	1	1	yes	characteristic, complemented
104	#1639	C₂×C₇	1	2	yes	complemented
105	#1625	C₂×C₇	1	2	yes	complemented
106	#1589	C₂×C₇	1	1	yes	characteristic, complemented
107	C₈×D₈	C₂×C₇	1	1	yes	characteristic, complemented
108	C₂⁴×C₇	—	4	2	no	—
109	C₇×#41	—	4	4	no	—
110	C₇×#41	—	8	2	no	—
111	C₂×C₇×Q₈	—	2	2	no	—
112	C₂×C₇×D₄	—	2	2	no	—
113	C₂×C₇×D₄	—	2	2	no	—
114	C₂×C₇×D₄	—	2	2	no	—
115	C₂×C₇×D₄	—	4	2	no	—
116	C₂×C₇×D₄	—	4	2	no	—
117	C₂×C₇×D₄	—	4	4	no	—
118	C₂×C₇×D₄	—	4	4	no	—
119	C₂×C₇×D₄	—	4	2	no	—
120	C₂×C₇×D₄	—	8	2	no	—
121	C₂×C₇×D₄	—	8	2	no	—
122	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
123	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
124	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇	—	2	1	no	—
126	C₂²×C₄×C₇	—	2	1	no	—
127	C₂²×C₄×C₇	—	2	2	no	—
128	C₂²×C₄×C₇	—	4	2	no	—
129	C₇×SD₁₆	—	4	4	no	—
130	C₇×SD₁₆	—	4	4	no	—
131	C₇×SD₁₆	—	8	2	no	—
132	C₇×D₈	—	2	2	no	—
133	C₇×D₈	—	4	4	no	—
134	C₇×D₈	—	4	4	no	—
135	C₇×D₈	—	4	2	no	—
136	C₇×D₈	—	8	1	no	—
137	C₇×D₈	D₈	1	4	yes	complemented
138	C₇×M₁₆	—	4	4	no	—
139	C₂×C₇×C₈	—	2	1	no	—
140	C₂×C₇×C₈	—	2	1	no	—
141	C₂×C₇×C₈	—	2	2	no	—
142	C₂×C₇×C₈	—	2	1	no	—
143	C₂×C₇×C₈	—	4	2	no	—
144	C₂×C₇×C₈	—	4	2	no	—
145	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
146	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
148	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
149	C₇×C₄⋊C₄	—	2	2	no	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	4	2	no	—
152	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
153	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
154	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
155	C₇×C₂²⋊C₄	—	2	1	no	—
156	C₇×C₂²⋊C₄	—	2	2	no	—
157	C₇×C₂²⋊C₄	—	2	1	no	—
158	C₇×C₂²⋊C₄	—	4	2	no	—
159	C₇×C₂²⋊C₄	—	4	2	no	—
160	C₄²×C₇	C₂⁴	1	1	yes	characteristic
161	C₂×AGL(1,ℤ/8)	—	2	2	no	—
162	C₂²×D₈	—	2	1	no	—
163	#547	C₂²×C₇	1	2	yes	complemented
164	D₄²	C₂²×C₇	1	2	yes	—
165	#500	C₂²×C₇	1	1	yes	characteristic, complemented
166	#493	C₂²×C₇	1	1	yes	characteristic
167	#492	C₂²×C₇	1	2	yes	complemented
168	#486	C₂²×C₇	1	2	yes	complemented
169	#480	—	2	2	no	—
170	#474	C₂²×C₇	1	2	yes	complemented
171	#468	—	2	2	no	—
172	#466	—	2	1	no	—
173	#466	—	2	1	no	—
174	#461	C₂²×C₇	1	2	yes	—
175	#459	C₂²×C₇	1	2	yes	—
176	#459	C₂²×C₇	1	2	yes	complemented
177	#450	—	2	2	no	—
178	#449	—	2	2	no	—
179	#447	—	2	2	no	—
180	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
181	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
182	#436	C₂²×C₇	1	2	yes	complemented
183	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
184	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
185	C₂×#107	—	2	1	no	—
186	#335	C₂²×C₇	1	1	yes	characteristic, complemented
187	#335	C₂²×C₇	1	1	yes	characteristic, complemented
188	#332	C₂²×C₇	1	2	yes	complemented
189	#331	C₂²×C₇	1	2	yes	complemented
190	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
191	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
192	D₄⋊C₈	C₂²×C₇	1	2	yes	complemented
193	C₈²	C₂²×C₇	1	1	yes	characteristic, complemented
194	C₂³×C₇	—	2	1	no	—
195	C₂³×C₇	—	2	1	no	—
196	C₂³×C₇	—	2	2	no	—
197	C₂³×C₇	—	4	2	no	—
198	C₂³×C₇	—	8	4	no	—
199	C₂³×C₇	—	8	4	no	—
200	C₂³×C₇	—	16	2	no	—
201	C₇×Q₈	—	4	2	no	—
202	C₇×Q₈	—	4	2	no	—
203	C₇×D₄	—	2	2	no	—
204	C₇×D₄	—	2	1	no	—
205	C₇×D₄	—	2	1	no	—
206	C₇×D₄	—	2	2	no	—
207	C₇×D₄	—	4	2	no	—
208	C₇×D₄	—	4	2	no	—
209	C₇×D₄	—	4	2	no	—
210	C₇×D₄	—	4	2	no	—
211	C₇×D₄	—	8	2	no	—
212	C₇×D₄	—	8	4	no	—
213	C₇×D₄	—	8	4	no	—
214	C₇×D₄	—	8	4	no	—
215	C₇×D₄	C₂×D₈	1	2	yes	—
216	C₇×D₄	C₂×D₈	1	2	yes	complemented
217	C₂×C₄×C₇	—	2	1	no	—
218	C₂×C₄×C₇	—	2	1	no	—
219	C₂×C₄×C₇	—	2	2	no	—
220	C₂×C₄×C₇	—	4	2	no	—
221	C₂×C₄×C₇	—	4	1	no	—
222	C₂×C₄×C₇	—	4	1	no	—
223	C₂×C₄×C₇	—	4	2	no	—
224	C₂×C₄×C₇	—	4	1	no	—
225	C₂×C₄×C₇	—	4	1	no	—
226	C₂×C₄×C₇	—	4	2	no	—
227	C₂×C₄×C₇	—	8	4	no	—
228	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
231	C₇×C₈	—	2	1	no	—
232	C₇×C₈	—	2	1	no	—
233	C₇×C₈	—	4	1	no	—
234	C₇×C₈	—	4	2	no	—
235	C₇×C₈	—	4	1	no	—
236	C₇×C₈	—	4	1	no	—
237	C₇×C₈	C₂×D₈	1	2	yes	complemented
238	C₇×C₈	AGL(1,ℤ/8)	1	2	yes	complemented
239	C₂×#41	—	2	2	no	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	—	2	2	no	—
242	AGL(1,ℤ/8)	—	4	8	no	—
243	C₂×SD₁₆	—	2	2	no	—
244	C₂×SD₁₆	—	2	2	no	—
245	C₂×SD₁₆	—	2	2	no	—
246	C₂×D₈	—	2	2	no	—
247	C₂×D₈	—	2	2	no	—
248	C₂×D₈	—	2	1	no	—
249	C₂×D₈	—	2	1	no	—
250	C₂×D₈	—	4	4	no	—
251	C₂×D₈	C₇×D₄	1	1	yes	characteristic
252	C₂×D₈	C₇×D₄	1	1	yes	characteristic
253	C₂×M₁₆	—	2	2	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	2	1	no	—
256	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
257	#127	C₂³×C₇	1	2	yes	—
258	#123	—	4	2	no	—
259	C₂²⋊Q₈	—	2	2	no	—
260	#121	—	2	2	no	—
261	#121	—	2	2	no	—
262	#121	—	2	2	no	—
263	#120	—	4	2	no	—
264	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
265	C₄×D₄	C₂³×C₇	1	2	yes	—
266	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
267	C₂×C₄⋊C₄	—	2	2	no	—
268	#107	—	2	1	no	—
269	#107	—	2	1	no	—
270	#107	—	2	2	no	—
271	#107	C₇×D₄	1	1	yes	characteristic
272	#107	C₇×D₄	1	1	yes	characteristic
273	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
274	C₄⋊C₈	C₂³×C₇	1	2	yes	—
275	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
276	#103	—	2	2	no	—
277	#102	—	2	2	no	—
278	#102	—	2	2	no	—
279	#102	—	2	2	no	—
280	#102	—	4	2	no	—
281	#102	C₇×D₄	1	2	yes	—
282	#102	C₇×D₄	1	1	yes	characteristic
283	#102	C₇×D₄	1	1	yes	characteristic
284	C₂²⋊C₈	—	2	1	no	—
285	C₂²⋊C₈	—	2	1	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
290	C₂²×C₇	—	2	2	no	—
291	C₂²×C₇	—	2	2	no	—
292	C₂²×C₇	—	4	1	no	—
293	C₂²×C₇	—	4	1	no	—
294	C₂²×C₇	—	4	1	no	—
295	C₂²×C₇	—	4	1	no	—
296	C₂²×C₇	—	4	2	no	—
297	C₂²×C₇	—	4	2	no	—
298	C₂²×C₇	—	4	2	no	—
299	C₂²×C₇	—	8	2	no	—
300	C₂²×C₇	—	8	2	no	—
301	C₂²×C₇	—	8	2	no	—
302	C₂²×C₇	—	16	8	no	—
303	C₂²×C₇	D₄²	1	1	yes	characteristic
304	C₄×C₇	—	2	1	no	—
305	C₄×C₇	—	4	1	no	—
306	C₄×C₇	—	4	1	no	—
307	C₄×C₇	—	4	2	no	—
308	C₄×C₇	—	8	2	no	—
309	C₄×C₇	C₂²×D₈	1	1	yes	characteristic
310	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
311	C₄×C₇	#576	1	1	yes	characteristic
312	C₄×C₇	#577	1	1	yes	characteristic
313	C₂⁴	—	4	2	no	—
314	#41	—	4	4	no	—
315	#41	—	8	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	4	4	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	8	2	no	—
326	C₂×D₄	—	8	2	no	—
327	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
328	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
329	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	SD₁₆	—	4	4	no	—
335	SD₁₆	—	4	4	no	—
336	SD₁₆	—	8	2	no	—
337	D₈	—	2	2	no	—
338	D₈	—	4	4	no	—
339	D₈	—	4	4	no	—
340	D₈	—	4	2	no	—
341	D₈	—	8	1	no	—
342	D₈	C₇×D₈	1	4	yes	complemented
343	M₁₆	—	4	4	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	4	2	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
351	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
352	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
353	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
358	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
359	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₄²	C₂⁴×C₇	1	1	yes	characteristic
366	C₂×C₇	—	4	2	no	—
367	C₂×C₇	—	4	2	no	—
368	C₂×C₇	—	8	2	no	—
369	C₂×C₇	—	16	2	no	—
370	C₂×C₇	#3272	1	1	yes	characteristic
371	C₂×C₇	D₄×D₈	1	1	yes	characteristic
372	C₂×C₇	#3290	1	1	yes	characteristic
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	8	4	no	—
378	C₂³	—	8	4	no	—
379	C₂³	—	16	2	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	1	no	—
384	D₄	—	2	1	no	—
385	D₄	—	2	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	8	2	no	—
391	D₄	—	8	4	no	—
392	D₄	—	8	4	no	—
393	D₄	—	8	4	no	—
394	D₄	C₂×C₇×D₈	1	2	yes	—
395	D₄	C₂×C₇×D₈	1	2	yes	complemented
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	4	no	—
407	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
408	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
409	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	4	2	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	1	no	—
416	C₈	C₂×C₇×D₈	1	2	yes	complemented
417	C₈	C₇×AGL(1,ℤ/8)	1	2	yes	complemented
418	C₇	#19883	1	1	yes	characteristic, direct product factor, Sylow
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	16	8	no	—
432	C₂²	C₇×D₄²	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	2	no	—
437	C₄	—	8	2	no	—
438	C₄	C₂²×C₇×D₈	1	1	yes	characteristic
439	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
440	C₄	C₇×#576	1	1	yes	characteristic
441	C₄	C₇×#577	1	1	yes	characteristic
442	C₂	—	4	2	no	—
443	C₂	—	4	2	no	—
444	C₂	—	8	2	no	—
445	C₂	—	16	2	no	—
446	C₂	C₇×#3272	1	1	yes	characteristic
447	C₂	C₇×D₄×D₈	1	1	yes	characteristic
448	C₂	C₇×#3290	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×#3334	C₂	semidirect
2. C₇×D₄×D₈	C₂	semidirect
3. C₇×#3272	C₂	semidirect
4. C₇×#1706	C₂	semidirect
5. C₇×#1685	C₂	semidirect
6. C₇×#1673	C₂	semidirect
7. C₇×#1667	C₂	semidirect
8. C₇×#1639	C₂	semidirect
9. C₇×#1625	C₂	semidirect
10. C₇×#1589	C₂	semidirect
11. C₇×C₈×D₈	C₂	semidirect
14. C₇×#547	C₂²	semidirect
16. C₇×#500	C₂²	semidirect
18. C₇×#492	C₂²	semidirect
19. C₇×#486	C₂²	semidirect
21. C₇×#474	C₂²	semidirect
27. C₇×#459	C₂²	semidirect
33. C₇×#436	C₂²	semidirect
35. C₇×C₈×D₄	C₂²	semidirect
37. C₇×#335	C₂²	semidirect
38. C₇×#335	C₂²	semidirect
39. C₇×#332	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. #19883	C₇	direct (N × H)
97. #3334	C₂×C₇	semidirect
98. D₄×D₈	C₂×C₇	semidirect
99. #3272	C₂×C₇	semidirect
100. #1706	C₂×C₇	semidirect
101. #1685	C₂×C₇	semidirect
102. #1673	C₂×C₇	semidirect
103. #1667	C₂×C₇	semidirect
104. #1639	C₂×C₇	semidirect
105. #1625	C₂×C₇	semidirect
106. #1589	C₂×C₇	semidirect
107. C₈×D₈	C₂×C₇	semidirect
137. C₇×D₈	D₈	semidirect
163. #547	C₂²×C₇	semidirect
165. #500	C₂²×C₇	semidirect
167. #492	C₂²×C₇	semidirect
168. #486	C₂²×C₇	semidirect
170. #474	C₂²×C₇	semidirect
176. #459	C₂²×C₇	semidirect
182. #436	C₂²×C₇	semidirect
184. C₈×D₄	C₂²×C₇	semidirect
186. #335	C₂²×C₇	semidirect
187. #335	C₂²×C₇	semidirect
188. #332	C₂²×C₇	semidirect
189. #331	C₂²×C₇	semidirect
191. D₄⋊C₈	C₂²×C₇	semidirect
192. D₄⋊C₈	C₂²×C₇	semidirect
193. C₈²	C₂²×C₇	semidirect
216. C₇×D₄	C₂×D₈	semidirect
237. C₇×C₈	C₂×D₈	semidirect
238. C₇×C₈	AGL(1,ℤ/8)	semidirect
342. D₈	C₇×D₈	semidirect
395. D₄	C₂×C₇×D₈	semidirect
416. C₈	C₂×C₇×D₈	semidirect
417. C₈	C₇×AGL(1,ℤ/8)	semidirect
418. C₇	#19883	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×#3334	2
C₇×D₄×D₈	2
C₇×#3272	2
C₇×#1706	2
C₇×#1685	2
C₇×#1673	2
C₇×#1667	2
C₇×#1639	2
C₇×#1625	2
C₇×#1589	2
C₇×C₈×D₈	2
#19883	7

Subgroups — C7×#19883 #13197099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19883 #13197099