Subgroups — C₇×#22688 #13199904

Order 1792.

870 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	C₂×C₇×#443	C₂	1	2	yes	maximal
2	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic
3	C₇×#2906	C₂	1	2	yes	maximal, complemented
4	C₇×#1945	C₂	1	2	yes	maximal, complemented
5	C₇×#1866	C₂	1	4	yes	maximal, complemented
6	C₇×#1848	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1806	C₂	1	2	yes	maximal, complemented
8	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#135	C₂²	1	1	yes	characteristic
10	C₂×C₇×#131	C₂²	1	4	yes	—
11	C₄×C₇×#41	C₂²	1	2	yes	—
12	C₇×#443	—	2	8	no	—
13	C₄×C₇×Q₁₆	C₄	1	1	yes	characteristic, complemented
14	C₄×C₇×Q₁₆	C₄	1	1	yes	characteristic, complemented
15	C₄×C₇×SD₁₆	C₄	1	2	yes	complemented
16	C₄×C₇×SD₁₆	C₄	1	2	yes	complemented
17	C₄×C₇×D₈	C₄	1	1	yes	characteristic, complemented
18	C₄×C₇×D₈	C₄	1	1	yes	characteristic, complemented
19	C₂×C₇×#108	C₂²	1	2	yes	—
20	C₂×C₇×#108	C₂²	1	2	yes	—
21	C₇×#427	C₂²	1	1	yes	characteristic
22	C₇×#424	—	2	4	no	—
23	C₇×#424	C₂²	1	4	yes	—
24	C₇×#423	—	2	2	no	—
25	C₇×#423	C₂²	1	2	yes	—
26	C₂×C₇×C₄⋊C₈	—	2	2	no	—
27	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×#104	C₂²	1	4	yes	—
29	C₇×#416	C₂²	1	2	yes	—
30	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
31	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
32	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₇×#339	C₂²	1	4	yes	—
34	C₇×#336	C₂²	1	2	yes	—
35	#22688	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂×C₇×#41	C₂³	1	2	yes	—
37	C₇×#135	D₄	1	4	yes	—
38	C₇×#135	Q₈	1	4	yes	—
39	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
40	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
41	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
42	C₇×#131	—	2	8	no	—
43	C₇×#131	—	4	4	no	—
44	C₂×C₇×M₁₆	—	2	4	no	—
45	C₂×C₇×M₁₆	C₂³	1	4	yes	—
46	C₂²×C₇×C₈	—	2	4	no	—
47	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₇×C₈	C₂³	1	2	yes	—
49	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
50	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
51	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
52	C₄×C₇×D₄	—	2	2	no	—
53	C₄×C₇×D₄	—	2	2	no	—
54	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
55	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
56	C₇×#117	—	2	2	no	—
57	C₇×#117	C₂³	1	2	yes	—
58	C₂×C₇×C₄⋊C₄	—	2	1	no	—
59	C₂×C₄²×C₇	—	2	2	no	—
60	C₂×C₄²×C₇	C₂³	1	2	yes	—
61	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
62	C₇×#108	—	2	4	no	—
63	C₇×#108	—	4	2	no	—
64	C₇×#107	C₂×C₄	1	1	yes	characteristic
65	C₇×#107	C₂×C₄	1	1	yes	characteristic
66	C₇×#106	C₂×C₄	1	2	yes	—
67	C₇×C₄⋊C₈	—	2	4	no	—
68	C₇×C₄⋊C₈	—	2	4	no	—
69	C₇×C₄⋊C₈	—	2	2	no	—
70	C₇×C₄⋊C₈	—	2	2	no	—
71	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
72	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
73	C₇×C₄⋊C₈	D₄	1	2	yes	—
74	C₇×#104	—	2	8	no	—
75	C₇×#103	C₂×C₄	1	2	yes	—
76	C₇×#103	C₂×C₄	1	2	yes	—
77	C₇×#102	C₂×C₄	1	2	yes	—
78	C₇×#102	C₂×C₄	1	2	yes	—
79	C₄×C₇×C₈	—	2	4	no	—
80	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
81	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
82	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
83	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
84	C₇×#95	—	2	1	no	—
85	C₂×#443	C₂×C₇	1	2	yes	—
86	C₄×#135	C₂×C₇	1	1	yes	characteristic
87	#2906	C₂×C₇	1	2	yes	complemented
88	#1945	C₂×C₇	1	2	yes	complemented
89	#1866	C₂×C₇	1	4	yes	complemented
90	#1848	C₂×C₇	1	1	yes	characteristic, complemented
91	#1806	C₂×C₇	1	2	yes	complemented
92	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
93	C₇×#41	—	2	2	no	—
94	C₇×#41	—	2	2	no	—
95	C₇×#41	C₂×D₄	1	4	yes	—
96	C₇×#41	C₂×Q₈	1	4	yes	—
97	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
98	C₂×C₇×D₄	—	2	2	no	—
99	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₇	—	2	2	no	—
101	C₂²×C₄×C₇	—	2	2	no	—
102	C₂²×C₄×C₇	—	2	2	no	—
103	C₂²×C₄×C₇	—	2	2	no	—
104	C₂²×C₄×C₇	#41	1	1	yes	characteristic
105	C₂²×C₄×C₇	#41	1	1	yes	characteristic
106	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
107	C₇×Q₁₆	C₄⋊C₄	1	4	yes	complemented
108	C₇×SD₁₆	C₄⋊C₄	1	8	yes	complemented
109	C₇×D₈	C₄⋊C₄	1	4	yes	complemented
110	C₇×M₁₆	—	2	4	no	—
111	C₇×M₁₆	—	2	4	no	—
112	C₇×M₁₆	—	4	8	no	—
113	C₂×C₇×C₈	—	2	2	no	—
114	C₂×C₇×C₈	—	2	1	no	—
115	C₂×C₇×C₈	—	2	2	no	—
116	C₂×C₇×C₈	—	2	1	no	—
117	C₂×C₇×C₈	—	2	4	no	—
118	C₂×C₇×C₈	—	4	8	no	—
119	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
124	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
125	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
126	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
127	C₇×C₄⋊C₄	—	2	4	no	—
128	C₇×C₄⋊C₄	—	2	2	no	—
129	C₇×C₄⋊C₄	—	2	2	no	—
130	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
131	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
132	C₇×C₂²⋊C₄	—	2	2	no	—
133	C₇×C₂²⋊C₄	—	2	2	no	—
134	C₇×C₂²⋊C₄	—	2	2	no	—
135	C₄²×C₇	—	2	2	no	—
136	C₄²×C₇	—	2	2	no	—
137	C₄²×C₇	—	2	2	no	—
138	C₄²×C₇	—	2	2	no	—
139	C₄²×C₇	—	2	2	no	—
140	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
144	C₂×#135	C₂²×C₇	1	1	yes	characteristic
145	C₂×#131	C₂²×C₇	1	4	yes	—
146	C₄×#41	C₂²×C₇	1	2	yes	—
147	#443	—	2	8	no	—
148	C₄×Q₁₆	C₄×C₇	1	1	yes	characteristic, complemented
149	C₄×Q₁₆	C₄×C₇	1	1	yes	characteristic, complemented
150	C₄×SD₁₆	C₄×C₇	1	2	yes	complemented
151	C₄×SD₁₆	C₄×C₇	1	2	yes	complemented
152	C₄×D₈	C₄×C₇	1	1	yes	characteristic, complemented
153	C₄×D₈	C₄×C₇	1	1	yes	characteristic, complemented
154	C₂×#108	C₂²×C₇	1	2	yes	—
155	C₂×#108	C₂²×C₇	1	2	yes	—
156	#427	C₂²×C₇	1	1	yes	characteristic
157	#424	—	2	4	no	—
158	#424	C₂²×C₇	1	4	yes	—
159	#423	—	2	2	no	—
160	#423	C₂²×C₇	1	2	yes	—
161	C₂×C₄⋊C₈	—	2	2	no	—
162	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
163	C₂×#104	C₂²×C₇	1	4	yes	—
164	#416	C₂²×C₇	1	2	yes	—
165	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
166	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
167	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
168	#339	C₂²×C₇	1	4	yes	—
169	#336	C₂²×C₇	1	2	yes	—
170	C₂³×C₇	—	2	2	no	—
171	C₂³×C₇	C₂×#41	1	1	yes	characteristic
172	C₇×Q₈	—	2	2	no	—
173	C₇×Q₈	C₂×C₄⋊C₄	1	4	yes	—
174	C₇×D₄	—	2	4	no	—
175	C₇×D₄	—	2	4	no	—
176	C₇×D₄	—	2	2	no	—
177	C₇×D₄	C₂×C₄⋊C₄	1	4	yes	—
178	C₂×C₄×C₇	—	2	2	no	—
179	C₂×C₄×C₇	—	2	4	no	—
180	C₂×C₄×C₇	—	2	4	no	—
181	C₂×C₄×C₇	—	2	2	no	—
182	C₂×C₄×C₇	—	2	4	no	—
183	C₂×C₄×C₇	—	2	2	no	—
184	C₂×C₄×C₇	—	2	2	no	—
185	C₂×C₄×C₇	—	4	1	no	—
186	C₂×C₄×C₇	—	4	2	no	—
187	C₂×C₄×C₇	—	4	2	no	—
188	C₂×C₄×C₇	—	4	4	no	—
189	C₂×C₄×C₇	—	8	2	no	—
190	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
198	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
200	C₇×C₈	—	2	1	no	—
201	C₇×C₈	—	2	1	no	—
202	C₇×C₈	—	2	2	no	—
203	C₇×C₈	—	2	2	no	—
204	C₇×C₈	—	4	4	no	—
205	C₇×C₈	C₂×C₄⋊C₄	1	2	yes	—
206	C₇×C₈	C₂×C₄⋊C₄	1	2	yes	—
207	C₂×#41	C₂³×C₇	1	2	yes	—
208	#135	C₇×D₄	1	4	yes	—
209	#135	C₇×Q₈	1	4	yes	—
210	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
211	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
212	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
213	#131	—	2	8	no	—
214	#131	—	4	4	no	—
215	C₂×M₁₆	—	2	4	no	—
216	C₂×M₁₆	C₂³×C₇	1	4	yes	—
217	C₂²×C₈	—	2	4	no	—
218	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
219	C₂²×C₈	C₂³×C₇	1	2	yes	—
220	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
221	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
222	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
226	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
227	#117	—	2	2	no	—
228	#117	C₂³×C₇	1	2	yes	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄²	—	2	2	no	—
231	C₂×C₄²	C₂³×C₇	1	2	yes	—
232	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
233	#108	—	2	4	no	—
234	#108	—	4	2	no	—
235	#107	C₂×C₄×C₇	1	1	yes	characteristic
236	#107	C₂×C₄×C₇	1	1	yes	characteristic
237	#106	C₂×C₄×C₇	1	2	yes	—
238	C₄⋊C₈	—	2	4	no	—
239	C₄⋊C₈	—	2	4	no	—
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
243	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
244	C₄⋊C₈	C₇×D₄	1	2	yes	—
245	#104	—	2	8	no	—
246	#103	C₂×C₄×C₇	1	2	yes	—
247	#103	C₂×C₄×C₇	1	2	yes	—
248	#102	C₂×C₄×C₇	1	2	yes	—
249	#102	C₂×C₄×C₇	1	2	yes	—
250	C₄×C₈	—	2	4	no	—
251	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
252	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
253	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
254	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
255	#95	—	2	1	no	—
256	C₂²×C₇	—	2	1	no	—
257	C₂²×C₇	—	2	1	no	—
258	C₂²×C₇	—	2	4	no	—
259	C₂²×C₇	—	4	2	no	—
260	C₂²×C₇	—	4	2	no	—
261	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
262	C₂²×C₇	#547	1	1	yes	characteristic
263	C₂²×C₇	#554	1	1	yes	characteristic
264	C₄×C₇	—	2	4	no	—
265	C₄×C₇	—	2	1	no	—
266	C₄×C₇	—	2	1	no	—
267	C₄×C₇	—	2	1	no	—
268	C₄×C₇	—	4	4	no	—
269	C₄×C₇	—	4	2	no	—
270	C₄×C₇	—	4	2	no	—
271	C₄×C₇	#443	1	2	yes	complemented
272	C₄×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
273	C₄×C₇	#520	1	1	yes	characteristic
274	C₄×C₇	D₄²	1	1	yes	characteristic
275	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
276	#41	—	2	2	no	—
277	#41	—	2	2	no	—
278	#41	C₂×C₇×D₄	1	4	yes	—
279	#41	C₂×C₇×Q₈	1	4	yes	—
280	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	C₇×#41	1	1	yes	characteristic
288	C₂²×C₄	C₇×#41	1	1	yes	characteristic
289	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
290	Q₁₆	C₇×C₄⋊C₄	1	4	yes	complemented
291	SD₁₆	C₇×C₄⋊C₄	1	8	yes	complemented
292	D₈	C₇×C₄⋊C₄	1	4	yes	complemented
293	M₁₆	—	2	4	no	—
294	M₁₆	—	2	4	no	—
295	M₁₆	—	4	8	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	4	8	no	—
302	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
303	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
304	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
305	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
306	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
307	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
308	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
309	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
314	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
324	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
325	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
326	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
327	C₂×C₇	—	2	1	no	—
328	C₂×C₇	—	2	1	no	—
329	C₂×C₇	—	4	4	no	—
330	C₂×C₇	D₄×C₄⋊C₄	1	1	yes	characteristic
331	C₂×C₇	C₂×#443	1	1	yes	characteristic
332	C₂×C₇	#2957	1	1	yes	characteristic
333	C₂³	—	2	2	no	—
334	C₂³	C₂×C₇×#41	1	1	yes	characteristic
335	Q₈	—	2	2	no	—
336	Q₈	C₂×C₇×C₄⋊C₄	1	4	yes	—
337	D₄	—	2	4	no	—
338	D₄	—	2	4	no	—
339	D₄	—	2	2	no	—
340	D₄	C₂×C₇×C₄⋊C₄	1	4	yes	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	8	2	no	—
353	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
354	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
355	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
356	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
357	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
359	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
361	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	2	no	—
366	C₈	—	2	2	no	—
367	C₈	—	4	4	no	—
368	C₈	C₂×C₇×C₄⋊C₄	1	2	yes	—
369	C₈	C₂×C₇×C₄⋊C₄	1	2	yes	—
370	C₇	#22688	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
377	C₂²	C₇×#547	1	1	yes	characteristic
378	C₂²	C₇×#554	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	4	no	—
383	C₄	—	4	4	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	C₇×#443	1	2	yes	complemented
387	C₄	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
388	C₄	C₇×#520	1	1	yes	characteristic
389	C₄	C₇×D₄²	1	1	yes	characteristic
390	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	4	4	no	—
394	C₂	C₇×D₄×C₄⋊C₄	1	1	yes	characteristic
395	C₂	C₂×C₇×#443	1	1	yes	characteristic
396	C₂	C₇×#2957	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	C₂×C₄×D₄
prime radical	C₂×C₇×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#2906	C₂	semidirect
4. C₇×#1945	C₂	semidirect
5. C₇×#1866	C₂	semidirect
6. C₇×#1848	C₂	semidirect
7. C₇×#1806	C₂	semidirect
8. C₇×C₈×C₄⋊C₄	C₂	semidirect
13. C₄×C₇×Q₁₆	C₄	semidirect
14. C₄×C₇×Q₁₆	C₄	semidirect
15. C₄×C₇×SD₁₆	C₄	semidirect
16. C₄×C₇×SD₁₆	C₄	semidirect
17. C₄×C₇×D₈	C₄	semidirect
18. C₄×C₇×D₈	C₄	semidirect
35. #22688	C₇	direct (N × H)
87. #2906	C₂×C₇	semidirect
88. #1945	C₂×C₇	semidirect
89. #1866	C₂×C₇	semidirect
90. #1848	C₂×C₇	semidirect
91. #1806	C₂×C₇	semidirect
92. C₈×C₄⋊C₄	C₂×C₇	semidirect
107. C₇×Q₁₆	C₄⋊C₄	semidirect
108. C₇×SD₁₆	C₄⋊C₄	semidirect
109. C₇×D₈	C₄⋊C₄	semidirect
148. C₄×Q₁₆	C₄×C₇	semidirect
149. C₄×Q₁₆	C₄×C₇	semidirect
150. C₄×SD₁₆	C₄×C₇	semidirect
151. C₄×SD₁₆	C₄×C₇	semidirect
152. C₄×D₈	C₄×C₇	semidirect
153. C₄×D₈	C₄×C₇	semidirect
271. C₄×C₇	#443	semidirect
290. Q₁₆	C₇×C₄⋊C₄	semidirect
291. SD₁₆	C₇×C₄⋊C₄	semidirect
292. D₈	C₇×C₄⋊C₄	semidirect
370. C₇	#22688	direct (N × H)
386. C₄	C₇×#443	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#443	2
C₄×C₇×#135	2
C₇×#2906	2
C₇×#1945	2
C₇×#1866	2
C₇×#1848	2
C₇×#1806	2
C₇×C₈×C₄⋊C₄	2
#22688	7

Subgroups — C7×#22688 #13199904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22688 #13199904