Subgroups — C₇×#3513 #11744465

Order 896.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#553	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#553	C₂	1	2	yes	maximal, complemented
5	C₇×#552	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#551	C₂	1	2	yes	maximal, complemented
7	C₇×#551	C₂	1	2	yes	maximal, complemented
8	C₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#546	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#546	C₂	1	2	yes	maximal, complemented
12	C₇×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#540	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#539	C₂	1	2	yes	maximal, complemented
16	C₇×#538	C₂	1	2	yes	maximal, complemented
17	C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#525	C₂	1	2	yes	maximal, complemented
20	C₂×C₇×#123	C₂	1	2	yes	maximal, complemented
21	C₇×#520	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#518	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#41	C₂²	1	1	yes	characteristic
25	C₂×C₇×#41	C₂²	1	2	yes	complemented
26	C₂²×C₇×D₄	C₂²	1	1	yes	characteristic
27	C₂²×C₇×D₄	C₂²	1	1	yes	characteristic
28	C₂²×C₇×D₄	C₂²	1	2	yes	—
29	C₂³×C₄×C₇	C₂²	1	2	yes	complemented
30	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₇×#127	C₂²	1	1	yes	characteristic
32	C₇×#126	C₂²	1	2	yes	complemented
33	C₇×#126	C₂²	1	1	yes	characteristic, complemented
34	C₇×#126	C₂²	1	1	yes	characteristic, complemented
35	C₇×#126	C₂²	1	2	yes	complemented
36	C₇×#126	C₂²	1	2	yes	complemented
37	C₇×#126	C₂²	1	2	yes	complemented
38	C₇×#125	C₂²	1	1	yes	characteristic, complemented
39	C₇×#125	C₂²	1	1	yes	characteristic, complemented
40	C₇×#125	C₂²	1	2	yes	complemented
41	C₇×#125	C₂²	1	1	yes	characteristic, complemented
42	C₇×#124	C₂²	1	1	yes	characteristic, complemented
43	C₇×#124	C₂²	1	1	yes	characteristic, complemented
44	C₇×#124	C₂²	1	2	yes	complemented
45	C₇×#124	C₂²	1	2	yes	complemented
46	C₇×#124	C₂²	1	1	yes	characteristic, complemented
47	C₇×#123	C₂²	1	1	yes	characteristic
48	C₇×#123	C₂²	1	2	yes	—
49	C₇×#123	C₂²	1	2	yes	complemented
50	C₇×#123	C₂²	1	2	yes	complemented
51	C₇×#123	C₂²	1	2	yes	complemented
52	C₇×#123	C₂²	1	2	yes	complemented
53	C₇×#123	C₂²	1	2	yes	complemented
54	C₇×#123	C₂²	1	2	yes	complemented
55	C₇×#123	C₂²	1	1	yes	characteristic, complemented
56	C₇×#123	C₂²	1	2	yes	complemented
57	C₇×#123	C₂²	1	2	yes	complemented
58	C₇×#123	C₂²	1	2	yes	complemented
59	C₇×#123	C₂²	1	2	yes	complemented
60	C₇×#123	C₂²	1	2	yes	complemented
61	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
64	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
65	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
66	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
67	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
68	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
69	C₇×#121	C₂²	1	1	yes	characteristic
70	C₇×#121	C₂²	1	1	yes	characteristic
71	C₇×#121	C₂²	1	2	yes	—
72	C₇×#121	C₂²	1	1	yes	characteristic
73	C₇×#121	C₂²	1	2	yes	complemented
74	C₇×#121	C₂²	1	2	yes	complemented
75	C₇×#121	C₂²	1	2	yes	complemented
76	C₇×#121	C₂²	1	2	yes	complemented
77	C₇×#121	C₂²	1	1	yes	characteristic, complemented
78	C₇×#121	C₂²	1	2	yes	complemented
79	C₇×#121	C₂²	1	1	yes	characteristic, complemented
80	C₇×#120	C₂²	1	2	yes	—
81	C₇×#120	C₂²	1	2	yes	—
82	C₇×#120	C₂²	1	2	yes	complemented
83	C₇×#120	C₂²	1	2	yes	complemented
84	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
87	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
88	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
89	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
90	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
91	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
92	C₄×C₇×D₄	C₂²	1	2	yes	complemented
93	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₇×D₄	C₂²	1	2	yes	complemented
95	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₇×D₄	C₂²	1	2	yes	complemented
97	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₇×D₄	C₂²	1	2	yes	complemented
100	C₄×C₇×D₄	C₂²	1	2	yes	complemented
101	C₄×C₇×D₄	C₂²	1	2	yes	complemented
102	C₄×C₇×D₄	C₂²	1	2	yes	complemented
103	C₄×C₇×D₄	C₂²	1	2	yes	complemented
104	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₇×D₄	C₂²	1	2	yes	complemented
106	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
107	C₇×#117	C₂²	1	1	yes	characteristic, complemented
108	C₇×#117	C₂²	1	1	yes	characteristic, complemented
109	C₇×#117	C₂²	1	1	yes	characteristic, complemented
110	C₇×#117	C₂²	1	2	yes	complemented
111	C₇×#117	C₂²	1	2	yes	complemented
112	C₇×#117	C₂²	1	2	yes	complemented
113	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
115	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
117	C₂×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
118	C₂×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
119	C₂×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
120	C₂×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₂×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
123	#3513	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂⁴×C₇	C₂³	1	2	yes	—
125	C₂⁴×C₇	C₂³	1	2	yes	—
126	C₇×#41	—	2	4	no	—
127	C₇×#41	—	4	4	no	—
128	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
129	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
130	C₂×C₇×Q₈	C₂³	1	2	yes	—
131	C₂×C₇×D₄	—	2	4	no	—
132	C₂×C₇×D₄	—	2	4	no	—
133	C₂×C₇×D₄	—	4	4	no	—
134	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
135	C₂×C₇×D₄	C₂³	1	2	yes	—
136	C₂×C₇×D₄	C₂³	1	2	yes	—
137	C₂×C₇×D₄	C₂³	1	2	yes	—
138	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
139	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
140	C₂×C₇×D₄	C₂³	1	2	yes	—
141	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
142	C₂×C₇×D₄	C₂³	1	2	yes	—
143	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
144	C₂×C₇×D₄	C₂³	1	2	yes	—
145	C₂×C₇×D₄	C₂³	1	2	yes	—
146	C₂×C₇×D₄	C₂³	1	2	yes	—
147	C₂×C₇×D₄	C₂³	1	2	yes	—
148	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
149	C₂²×C₄×C₇	—	4	4	no	—
150	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
151	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
152	C₂²×C₄×C₇	C₂³	1	2	yes	—
153	C₂²×C₄×C₇	C₂³	1	2	yes	—
154	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
155	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
156	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
157	C₂²×C₄×C₇	C₂³	1	2	yes	—
158	C₂²×C₄×C₇	C₂³	1	2	yes	—
159	C₂²×C₄×C₇	C₂³	1	2	yes	—
160	C₂²×C₄×C₇	C₂³	1	2	yes	—
161	C₂²×C₄×C₇	C₂³	1	2	yes	—
162	C₂²×C₄×C₇	C₂³	1	2	yes	—
163	C₂²×C₄×C₇	C₂³	1	2	yes	—
164	C₂²×C₄×C₇	C₂³	1	2	yes	—
165	C₂²×C₄×C₇	C₂³	1	2	yes	—
166	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₇×C₄⋊C₄	C₂³	1	2	yes	—
168	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₇×C₄⋊C₄	C₂³	1	2	yes	—
171	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₇×C₄⋊C₄	C₂³	1	2	yes	—
175	C₇×C₄⋊C₄	C₂³	1	2	yes	—
176	C₇×C₄⋊C₄	C₂³	1	2	yes	—
177	C₇×C₄⋊C₄	C₂³	1	2	yes	—
178	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₇×C₄⋊C₄	C₂³	1	2	yes	—
183	C₇×C₄⋊C₄	C₂³	1	2	yes	—
184	C₇×C₄⋊C₄	C₂³	1	2	yes	—
185	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₇×C₄⋊C₄	C₂³	1	2	yes	—
188	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
210	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
212	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
215	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
220	C₄²×C₇	C₂³	1	1	yes	characteristic
221	C₄²×C₇	C₂³	1	1	yes	characteristic
222	C₄²×C₇	C₂³	1	1	yes	characteristic
223	C₄²×C₇	C₂³	1	1	yes	characteristic
224	C₄²×C₇	C₂³	1	2	yes	—
225	C₄²×C₇	C₂³	1	2	yes	—
226	C₄²×C₇	C₂³	1	2	yes	—
227	C₄²×C₇	C₂³	1	1	yes	characteristic
228	C₄²×C₇	C₂³	1	1	yes	characteristic
229	#559	C₂×C₇	1	1	yes	characteristic, complemented
230	#554	C₂×C₇	1	1	yes	characteristic, complemented
231	#553	C₂×C₇	1	1	yes	characteristic, complemented
232	#553	C₂×C₇	1	2	yes	complemented
233	#552	C₂×C₇	1	1	yes	characteristic, complemented
234	#551	C₂×C₇	1	2	yes	complemented
235	#551	C₂×C₇	1	2	yes	complemented
236	#547	C₂×C₇	1	1	yes	characteristic, complemented
237	#546	C₂×C₇	1	1	yes	characteristic, complemented
238	#546	C₂×C₇	1	1	yes	characteristic, complemented
239	#546	C₂×C₇	1	2	yes	complemented
240	D₄²	C₂×C₇	1	1	yes	characteristic, complemented
241	#542	C₂×C₇	1	1	yes	characteristic, complemented
242	#540	C₂×C₇	1	1	yes	characteristic, complemented
243	#539	C₂×C₇	1	2	yes	complemented
244	#538	C₂×C₇	1	2	yes	complemented
245	#529	C₂×C₇	1	1	yes	characteristic, complemented
246	#529	C₂×C₇	1	1	yes	characteristic, complemented
247	#525	C₂×C₇	1	2	yes	complemented
248	C₂×#123	C₂×C₇	1	2	yes	complemented
249	#520	C₂×C₇	1	1	yes	characteristic, complemented
250	#518	C₂×C₇	1	1	yes	characteristic, complemented
251	C₂×C₄×D₄	C₂×C₇	1	1	yes	characteristic, complemented
252	C₂³×C₇	—	2	4	no	—
253	C₂³×C₇	—	2	4	no	—
254	C₂³×C₇	—	2	4	no	—
255	C₂³×C₇	—	4	2	no	—
256	C₂³×C₇	—	4	2	no	—
257	C₂³×C₇	—	4	2	no	—
258	C₂³×C₇	C₂⁴	1	1	yes	characteristic
259	C₂³×C₇	C₂⁴	1	2	yes	—
260	C₂³×C₇	C₂⁴	1	2	yes	—
261	C₂³×C₇	C₂⁴	1	1	yes	characteristic
262	C₂³×C₇	C₂⁴	1	2	yes	—
263	C₂³×C₇	C₂⁴	1	1	yes	characteristic
264	C₇×Q₈	—	2	2	no	—
265	C₇×Q₈	—	4	1	no	—
266	C₇×Q₈	—	4	2	no	—
267	C₇×D₄	—	2	4	no	—
268	C₇×D₄	—	2	4	no	—
269	C₇×D₄	—	2	4	no	—
270	C₇×D₄	—	2	2	no	—
271	C₇×D₄	—	2	4	no	—
272	C₇×D₄	—	2	2	no	—
273	C₇×D₄	—	2	2	no	—
274	C₇×D₄	—	2	2	no	—
275	C₇×D₄	—	4	2	no	—
276	C₇×D₄	—	4	2	no	—
277	C₇×D₄	—	4	2	no	—
278	C₇×D₄	—	4	1	no	—
279	C₇×D₄	—	4	2	no	—
280	C₇×D₄	—	4	2	no	—
281	C₇×D₄	#41	1	4	yes	complemented
282	C₂×C₄×C₇	—	2	4	no	—
283	C₂×C₄×C₇	—	2	2	no	—
284	C₂×C₄×C₇	—	2	4	no	—
285	C₂×C₄×C₇	—	2	2	no	—
286	C₂×C₄×C₇	—	2	2	no	—
287	C₂×C₄×C₇	—	2	2	no	—
288	C₂×C₄×C₇	—	4	2	no	—
289	C₂×C₄×C₇	—	4	2	no	—
290	C₂×C₄×C₇	—	4	2	no	—
291	C₂×C₄×C₇	—	4	2	no	—
292	C₂×C₄×C₇	—	4	2	no	—
293	C₂×C₄×C₇	—	4	1	no	—
294	C₂×C₄×C₇	—	4	2	no	—
295	C₂×C₄×C₇	—	4	2	no	—
296	C₂×C₄×C₇	—	4	2	no	—
297	C₂×C₄×C₇	—	4	2	no	—
298	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
299	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
300	C₂×C₄×C₇	C₂⁴	1	2	yes	—
301	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
302	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
303	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
304	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
305	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
306	C₂×C₄×C₇	C₂⁴	1	2	yes	—
307	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
308	C₂×C₄×C₇	C₂⁴	1	2	yes	—
309	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
310	C₂×C₄×C₇	C₂⁴	1	2	yes	—
311	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
312	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
313	C₂×C₄×C₇	C₂⁴	1	2	yes	—
314	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
315	C₂×#41	C₂²×C₇	1	1	yes	characteristic
316	C₂×#41	C₂²×C₇	1	2	yes	complemented
317	C₂²×D₄	C₂²×C₇	1	1	yes	characteristic
318	C₂²×D₄	C₂²×C₇	1	1	yes	characteristic
319	C₂²×D₄	C₂²×C₇	1	2	yes	—
320	C₂³×C₄	C₂²×C₇	1	2	yes	complemented
321	C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
322	#127	C₂²×C₇	1	1	yes	characteristic
323	#126	C₂²×C₇	1	2	yes	complemented
324	#126	C₂²×C₇	1	1	yes	characteristic, complemented
325	#126	C₂²×C₇	1	1	yes	characteristic, complemented
326	#126	C₂²×C₇	1	2	yes	complemented
327	#126	C₂²×C₇	1	2	yes	complemented
328	#126	C₂²×C₇	1	2	yes	complemented
329	#125	C₂²×C₇	1	1	yes	characteristic, complemented
330	#125	C₂²×C₇	1	1	yes	characteristic, complemented
331	#125	C₂²×C₇	1	2	yes	complemented
332	#125	C₂²×C₇	1	1	yes	characteristic, complemented
333	#124	C₂²×C₇	1	1	yes	characteristic, complemented
334	#124	C₂²×C₇	1	1	yes	characteristic, complemented
335	#124	C₂²×C₇	1	2	yes	complemented
336	#124	C₂²×C₇	1	2	yes	complemented
337	#124	C₂²×C₇	1	1	yes	characteristic, complemented
338	#123	C₂²×C₇	1	1	yes	characteristic
339	#123	C₂²×C₇	1	2	yes	—
340	#123	C₂²×C₇	1	2	yes	complemented
341	#123	C₂²×C₇	1	2	yes	complemented
342	#123	C₂²×C₇	1	2	yes	complemented
343	#123	C₂²×C₇	1	2	yes	complemented
344	#123	C₂²×C₇	1	2	yes	complemented
345	#123	C₂²×C₇	1	2	yes	complemented
346	#123	C₂²×C₇	1	1	yes	characteristic, complemented
347	#123	C₂²×C₇	1	2	yes	complemented
348	#123	C₂²×C₇	1	2	yes	complemented
349	#123	C₂²×C₇	1	2	yes	complemented
350	#123	C₂²×C₇	1	2	yes	complemented
351	#123	C₂²×C₇	1	2	yes	complemented
352	C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
353	C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
354	C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
355	C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
356	C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
357	C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
358	C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
359	C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
360	#121	C₂²×C₇	1	1	yes	characteristic
361	#121	C₂²×C₇	1	1	yes	characteristic
362	#121	C₂²×C₇	1	2	yes	—
363	#121	C₂²×C₇	1	1	yes	characteristic
364	#121	C₂²×C₇	1	2	yes	complemented
365	#121	C₂²×C₇	1	2	yes	complemented
366	#121	C₂²×C₇	1	2	yes	complemented
367	#121	C₂²×C₇	1	2	yes	complemented
368	#121	C₂²×C₇	1	1	yes	characteristic, complemented
369	#121	C₂²×C₇	1	2	yes	complemented
370	#121	C₂²×C₇	1	1	yes	characteristic, complemented
371	#120	C₂²×C₇	1	2	yes	—
372	#120	C₂²×C₇	1	2	yes	—
373	#120	C₂²×C₇	1	2	yes	complemented
374	#120	C₂²×C₇	1	2	yes	complemented
375	C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
376	C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
377	C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
378	C₄×D₄	C₂²×C₇	1	1	yes	characteristic
379	C₄×D₄	C₂²×C₇	1	1	yes	characteristic
380	C₄×D₄	C₂²×C₇	1	1	yes	characteristic
381	C₄×D₄	C₂²×C₇	1	1	yes	characteristic
382	C₄×D₄	C₂²×C₇	1	1	yes	characteristic
383	C₄×D₄	C₂²×C₇	1	2	yes	complemented
384	C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
385	C₄×D₄	C₂²×C₇	1	2	yes	complemented
386	C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
387	C₄×D₄	C₂²×C₇	1	2	yes	complemented
388	C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
389	C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
390	C₄×D₄	C₂²×C₇	1	2	yes	complemented
391	C₄×D₄	C₂²×C₇	1	2	yes	complemented
392	C₄×D₄	C₂²×C₇	1	2	yes	complemented
393	C₄×D₄	C₂²×C₇	1	2	yes	complemented
394	C₄×D₄	C₂²×C₇	1	2	yes	complemented
395	C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
396	C₄×D₄	C₂²×C₇	1	2	yes	complemented
397	C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
398	#117	C₂²×C₇	1	1	yes	characteristic, complemented
399	#117	C₂²×C₇	1	1	yes	characteristic, complemented
400	#117	C₂²×C₇	1	1	yes	characteristic, complemented
401	#117	C₂²×C₇	1	2	yes	complemented
402	#117	C₂²×C₇	1	2	yes	complemented
403	#117	C₂²×C₇	1	2	yes	complemented
404	C₂×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
405	C₂×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
406	C₂×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
407	C₂×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
408	C₂×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
409	C₂×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
410	C₂×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
411	C₂×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
412	C₂×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
413	C₂×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
414	C₂²×C₇	—	2	1	no	—
415	C₂²×C₇	—	2	2	no	—
416	C₂²×C₇	—	2	1	no	—
417	C₂²×C₇	—	2	2	no	—
418	C₂²×C₇	—	2	1	no	—
419	C₂²×C₇	—	2	1	no	—
420	C₂²×C₇	—	2	2	no	—
421	C₂²×C₇	—	2	2	no	—
422	C₂²×C₇	—	2	1	no	—
423	C₂²×C₇	—	2	2	no	—
424	C₂²×C₇	—	2	2	no	—
425	C₂²×C₇	—	2	1	no	—
426	C₂²×C₇	—	2	2	no	—
427	C₂²×C₇	—	2	1	no	—
428	C₂²×C₇	—	2	2	no	—
429	C₂²×C₇	—	2	1	no	—
430	C₂²×C₇	—	4	8	no	—
431	C₂²×C₇	—	8	4	no	—
432	C₂²×C₇	C₂×#41	1	4	yes	—
433	C₂²×C₇	H(5,𝔽₂)	1	2	yes	—
434	C₂²×C₇	C₂⁵	1	1	yes	characteristic
435	C₄×C₇	—	2	1	no	—
436	C₄×C₇	—	2	1	no	—
437	C₄×C₇	—	2	1	no	—
438	C₄×C₇	—	2	2	no	—
439	C₄×C₇	—	2	1	no	—
440	C₄×C₇	—	2	1	no	—
441	C₄×C₇	—	2	2	no	—
442	C₄×C₇	—	2	2	no	—
443	C₄×C₇	—	2	1	no	—
444	C₄×C₇	—	2	2	no	—
445	C₄×C₇	—	2	1	no	—
446	C₄×C₇	—	2	1	no	—
447	C₄×C₇	—	2	2	no	—
448	C₄×C₇	—	2	1	no	—
449	C₄×C₇	—	2	1	no	—
450	C₄×C₇	—	2	1	no	—
451	C₄×C₇	C₂×#41	1	2	yes	—
452	C₂⁴	C₂³×C₇	1	2	yes	—
453	C₂⁴	C₂³×C₇	1	2	yes	—
454	#41	—	2	4	no	—
455	#41	—	4	4	no	—
456	C₂×Q₈	C₂³×C₇	1	1	yes	characteristic
457	C₂×Q₈	C₂³×C₇	1	1	yes	characteristic
458	C₂×Q₈	C₂³×C₇	1	2	yes	—
459	C₂×D₄	—	2	4	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	4	4	no	—
462	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
463	C₂×D₄	C₂³×C₇	1	2	yes	—
464	C₂×D₄	C₂³×C₇	1	2	yes	—
465	C₂×D₄	C₂³×C₇	1	2	yes	—
466	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
467	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
468	C₂×D₄	C₂³×C₇	1	2	yes	—
469	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
470	C₂×D₄	C₂³×C₇	1	2	yes	—
471	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
472	C₂×D₄	C₂³×C₇	1	2	yes	—
473	C₂×D₄	C₂³×C₇	1	2	yes	—
474	C₂×D₄	C₂³×C₇	1	2	yes	—
475	C₂×D₄	C₂³×C₇	1	2	yes	—
476	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
477	C₂²×C₄	—	4	4	no	—
478	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
479	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
480	C₂²×C₄	C₂³×C₇	1	2	yes	—
481	C₂²×C₄	C₂³×C₇	1	2	yes	—
482	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
483	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
484	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
485	C₂²×C₄	C₂³×C₇	1	2	yes	—
486	C₂²×C₄	C₂³×C₇	1	2	yes	—
487	C₂²×C₄	C₂³×C₇	1	2	yes	—
488	C₂²×C₄	C₂³×C₇	1	2	yes	—
489	C₂²×C₄	C₂³×C₇	1	2	yes	—
490	C₂²×C₄	C₂³×C₇	1	2	yes	—
491	C₂²×C₄	C₂³×C₇	1	2	yes	—
492	C₂²×C₄	C₂³×C₇	1	2	yes	—
493	C₂²×C₄	C₂³×C₇	1	2	yes	—
494	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
495	C₄⋊C₄	C₂³×C₇	1	2	yes	—
496	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
497	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
498	C₄⋊C₄	C₂³×C₇	1	2	yes	—
499	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
500	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
501	C₄⋊C₄	C₂³×C₇	1	2	yes	—
502	C₄⋊C₄	C₂³×C₇	1	2	yes	—
503	C₄⋊C₄	C₂³×C₇	1	2	yes	—
504	C₄⋊C₄	C₂³×C₇	1	2	yes	—
505	C₄⋊C₄	C₂³×C₇	1	2	yes	—
506	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
507	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
508	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
509	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
510	C₄⋊C₄	C₂³×C₇	1	2	yes	—
511	C₄⋊C₄	C₂³×C₇	1	2	yes	—
512	C₄⋊C₄	C₂³×C₇	1	2	yes	—
513	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
514	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
515	C₄⋊C₄	C₂³×C₇	1	2	yes	—
516	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
517	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
518	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
519	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
520	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
521	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
522	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
523	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
524	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
525	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
526	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
527	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
528	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
529	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
530	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
531	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
532	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
533	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
534	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
535	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
536	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
537	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
538	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
539	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
540	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
541	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
542	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
543	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
544	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
545	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
546	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
547	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
548	C₄²	C₂³×C₇	1	1	yes	characteristic
549	C₄²	C₂³×C₇	1	1	yes	characteristic
550	C₄²	C₂³×C₇	1	1	yes	characteristic
551	C₄²	C₂³×C₇	1	1	yes	characteristic
552	C₄²	C₂³×C₇	1	2	yes	—
553	C₄²	C₂³×C₇	1	2	yes	—
554	C₄²	C₂³×C₇	1	2	yes	—
555	C₄²	C₂³×C₇	1	1	yes	characteristic
556	C₄²	C₂³×C₇	1	1	yes	characteristic
557	C₂×C₇	—	2	2	no	—
558	C₂×C₇	—	2	4	no	—
559	C₂×C₇	—	4	1	no	—
560	C₂×C₇	—	4	2	no	—
561	C₂×C₇	—	4	2	no	—
562	C₂×C₇	—	4	1	no	—
563	C₂×C₇	C₂²×#41	1	1	yes	characteristic
564	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
565	C₂×C₇	#585	1	1	yes	characteristic
566	C₂³	—	2	4	no	—
567	C₂³	—	2	4	no	—
568	C₂³	—	2	4	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	4	2	no	—
571	C₂³	—	4	2	no	—
572	C₂³	C₂⁴×C₇	1	1	yes	characteristic
573	C₂³	C₂⁴×C₇	1	2	yes	—
574	C₂³	C₂⁴×C₇	1	2	yes	—
575	C₂³	C₂⁴×C₇	1	1	yes	characteristic
576	C₂³	C₂⁴×C₇	1	2	yes	—
577	C₂³	C₂⁴×C₇	1	1	yes	characteristic
578	Q₈	—	2	2	no	—
579	Q₈	—	4	1	no	—
580	Q₈	—	4	2	no	—
581	D₄	—	2	4	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	4	no	—
584	D₄	—	2	2	no	—
585	D₄	—	2	4	no	—
586	D₄	—	2	2	no	—
587	D₄	—	2	2	no	—
588	D₄	—	2	2	no	—
589	D₄	—	4	2	no	—
590	D₄	—	4	2	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	1	no	—
593	D₄	—	4	2	no	—
594	D₄	—	4	2	no	—
595	D₄	C₇×#41	1	4	yes	complemented
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
613	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
614	C₂×C₄	C₂⁴×C₇	1	2	yes	—
615	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
616	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
617	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
618	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
619	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
620	C₂×C₄	C₂⁴×C₇	1	2	yes	—
621	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
622	C₂×C₄	C₂⁴×C₇	1	2	yes	—
623	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
624	C₂×C₄	C₂⁴×C₇	1	2	yes	—
625	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
626	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
627	C₂×C₄	C₂⁴×C₇	1	2	yes	—
628	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
629	C₇	#3513	1	1	yes	characteristic, direct product factor, Sylow
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	4	8	no	—
647	C₂²	—	8	4	no	—
648	C₂²	C₂×C₇×#41	1	4	yes	—
649	C₂²	C₇×H(5,𝔽₂)	1	2	yes	—
650	C₂²	C₂⁵×C₇	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	C₂×C₇×#41	1	2	yes	—
668	C₂	—	2	2	no	—
669	C₂	—	2	4	no	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	4	2	no	—
673	C₂	—	4	1	no	—
674	C₂	C₂²×C₇×#41	1	1	yes	characteristic
675	C₂	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂	C₇×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#559	C₂	semidirect
2. C₇×#554	C₂	semidirect
3. C₇×#553	C₂	semidirect
4. C₇×#553	C₂	semidirect
5. C₇×#552	C₂	semidirect
6. C₇×#551	C₂	semidirect
7. C₇×#551	C₂	semidirect
8. C₇×#547	C₂	semidirect
9. C₇×#546	C₂	semidirect
10. C₇×#546	C₂	semidirect
11. C₇×#546	C₂	semidirect
12. C₇×D₄²	C₂	semidirect
13. C₇×#542	C₂	semidirect
14. C₇×#540	C₂	semidirect
15. C₇×#539	C₂	semidirect
16. C₇×#538	C₂	semidirect
17. C₇×#529	C₂	semidirect
18. C₇×#529	C₂	semidirect
19. C₇×#525	C₂	semidirect
20. C₂×C₇×#123	C₂	semidirect
21. C₇×#520	C₂	semidirect
22. C₇×#518	C₂	semidirect
23. C₂×C₄×C₇×D₄	C₂	semidirect
25. C₂×C₇×#41	C₂²	semidirect
29. C₂³×C₄×C₇	C₂²	semidirect
30. C₇×C₄⋊Q₈	C₂²	semidirect
32. C₇×#126	C₂²	semidirect
33. C₇×#126	C₂²	semidirect
34. C₇×#126	C₂²	semidirect
35. C₇×#126	C₂²	semidirect
36. C₇×#126	C₂²	semidirect
37. C₇×#126	C₂²	semidirect
38. C₇×#125	C₂²	semidirect
39. C₇×#125	C₂²	semidirect
40. C₇×#125	C₂²	semidirect
41. C₇×#125	C₂²	semidirect
42. C₇×#124	C₂²	semidirect
43. C₇×#124	C₂²	semidirect
44. C₇×#124	C₂²	semidirect
45. C₇×#124	C₂²	semidirect
46. C₇×#124	C₂²	semidirect
49. C₇×#123	C₂²	semidirect
50. C₇×#123	C₂²	semidirect
51. C₇×#123	C₂²	semidirect
52. C₇×#123	C₂²	semidirect
53. C₇×#123	C₂²	semidirect
54. C₇×#123	C₂²	semidirect
55. C₇×#123	C₂²	semidirect
56. C₇×#123	C₂²	semidirect
57. C₇×#123	C₂²	semidirect
58. C₇×#123	C₂²	semidirect
59. C₇×#123	C₂²	semidirect
60. C₇×#123	C₂²	semidirect
61. C₇×C₂²⋊Q₈	C₂²	semidirect
62. C₇×C₂²⋊Q₈	C₂²	semidirect
63. C₇×C₂²⋊Q₈	C₂²	semidirect
64. C₇×C₂²⋊Q₈	C₂²	semidirect
65. C₇×C₂²⋊Q₈	C₂²	semidirect
66. C₇×C₂²⋊Q₈	C₂²	semidirect
67. C₇×C₂²⋊Q₈	C₂²	semidirect
68. C₇×C₂²⋊Q₈	C₂²	semidirect
73. C₇×#121	C₂²	semidirect
74. C₇×#121	C₂²	semidirect
75. C₇×#121	C₂²	semidirect
76. C₇×#121	C₂²	semidirect
77. C₇×#121	C₂²	semidirect
78. C₇×#121	C₂²	semidirect
79. C₇×#121	C₂²	semidirect
82. C₇×#120	C₂²	semidirect
83. C₇×#120	C₂²	semidirect
84. C₄×C₇×Q₈	C₂²	semidirect
85. C₄×C₇×Q₈	C₂²	semidirect
86. C₄×C₇×Q₈	C₂²	semidirect
92. C₄×C₇×D₄	C₂²	semidirect
93. C₄×C₇×D₄	C₂²	semidirect
94. C₄×C₇×D₄	C₂²	semidirect
95. C₄×C₇×D₄	C₂²	semidirect
96. C₄×C₇×D₄	C₂²	semidirect
97. C₄×C₇×D₄	C₂²	semidirect
98. C₄×C₇×D₄	C₂²	semidirect
99. C₄×C₇×D₄	C₂²	semidirect
100. C₄×C₇×D₄	C₂²	semidirect
101. C₄×C₇×D₄	C₂²	semidirect
102. C₄×C₇×D₄	C₂²	semidirect
103. C₄×C₇×D₄	C₂²	semidirect
104. C₄×C₇×D₄	C₂²	semidirect
105. C₄×C₇×D₄	C₂²	semidirect
106. C₄×C₇×D₄	C₂²	semidirect
107. C₇×#117	C₂²	semidirect
108. C₇×#117	C₂²	semidirect
109. C₇×#117	C₂²	semidirect
110. C₇×#117	C₂²	semidirect
111. C₇×#117	C₂²	semidirect
112. C₇×#117	C₂²	semidirect
113. C₂×C₇×C₄⋊C₄	C₂²	semidirect
114. C₂×C₇×C₄⋊C₄	C₂²	semidirect
115. C₂×C₇×C₄⋊C₄	C₂²	semidirect
116. C₂×C₇×C₄⋊C₄	C₂²	semidirect
117. C₂×C₇×C₂²⋊C₄	C₂²	semidirect
118. C₂×C₇×C₂²⋊C₄	C₂²	semidirect
119. C₂×C₇×C₂²⋊C₄	C₂²	semidirect
120. C₂×C₇×C₂²⋊C₄	C₂²	semidirect
121. C₂×C₇×C₂²⋊C₄	C₂²	semidirect
122. C₂×C₄²×C₇	C₂²	semidirect
123. #3513	C₇	direct (N × H)
229. #559	C₂×C₇	semidirect
230. #554	C₂×C₇	semidirect
231. #553	C₂×C₇	semidirect
232. #553	C₂×C₇	semidirect
233. #552	C₂×C₇	semidirect
234. #551	C₂×C₇	semidirect
235. #551	C₂×C₇	semidirect
236. #547	C₂×C₇	semidirect
237. #546	C₂×C₇	semidirect
238. #546	C₂×C₇	semidirect
239. #546	C₂×C₇	semidirect
240. D₄²	C₂×C₇	semidirect
241. #542	C₂×C₇	semidirect
242. #540	C₂×C₇	semidirect
243. #539	C₂×C₇	semidirect
244. #538	C₂×C₇	semidirect
245. #529	C₂×C₇	semidirect
246. #529	C₂×C₇	semidirect
247. #525	C₂×C₇	semidirect
248. C₂×#123	C₂×C₇	semidirect
249. #520	C₂×C₇	semidirect
250. #518	C₂×C₇	semidirect
251. C₂×C₄×D₄	C₂×C₇	semidirect
281. C₇×D₄	#41	semidirect
316. C₂×#41	C₂²×C₇	semidirect
320. C₂³×C₄	C₂²×C₇	semidirect
321. C₄⋊Q₈	C₂²×C₇	semidirect
323. #126	C₂²×C₇	semidirect
324. #126	C₂²×C₇	semidirect
325. #126	C₂²×C₇	semidirect
326. #126	C₂²×C₇	semidirect
327. #126	C₂²×C₇	semidirect
328. #126	C₂²×C₇	semidirect
329. #125	C₂²×C₇	semidirect
330. #125	C₂²×C₇	semidirect
331. #125	C₂²×C₇	semidirect
332. #125	C₂²×C₇	semidirect
333. #124	C₂²×C₇	semidirect
334. #124	C₂²×C₇	semidirect
335. #124	C₂²×C₇	semidirect
336. #124	C₂²×C₇	semidirect
337. #124	C₂²×C₇	semidirect
340. #123	C₂²×C₇	semidirect
341. #123	C₂²×C₇	semidirect
342. #123	C₂²×C₇	semidirect
343. #123	C₂²×C₇	semidirect
344. #123	C₂²×C₇	semidirect
345. #123	C₂²×C₇	semidirect
346. #123	C₂²×C₇	semidirect
347. #123	C₂²×C₇	semidirect
348. #123	C₂²×C₇	semidirect
349. #123	C₂²×C₇	semidirect
350. #123	C₂²×C₇	semidirect
351. #123	C₂²×C₇	semidirect
352. C₂²⋊Q₈	C₂²×C₇	semidirect
353. C₂²⋊Q₈	C₂²×C₇	semidirect
354. C₂²⋊Q₈	C₂²×C₇	semidirect
355. C₂²⋊Q₈	C₂²×C₇	semidirect
356. C₂²⋊Q₈	C₂²×C₇	semidirect
357. C₂²⋊Q₈	C₂²×C₇	semidirect
358. C₂²⋊Q₈	C₂²×C₇	semidirect
359. C₂²⋊Q₈	C₂²×C₇	semidirect
364. #121	C₂²×C₇	semidirect
365. #121	C₂²×C₇	semidirect
366. #121	C₂²×C₇	semidirect
367. #121	C₂²×C₇	semidirect
368. #121	C₂²×C₇	semidirect
369. #121	C₂²×C₇	semidirect
370. #121	C₂²×C₇	semidirect
373. #120	C₂²×C₇	semidirect
374. #120	C₂²×C₇	semidirect
375. C₄×Q₈	C₂²×C₇	semidirect
376. C₄×Q₈	C₂²×C₇	semidirect
377. C₄×Q₈	C₂²×C₇	semidirect
383. C₄×D₄	C₂²×C₇	semidirect
384. C₄×D₄	C₂²×C₇	semidirect
385. C₄×D₄	C₂²×C₇	semidirect
386. C₄×D₄	C₂²×C₇	semidirect
387. C₄×D₄	C₂²×C₇	semidirect
388. C₄×D₄	C₂²×C₇	semidirect
389. C₄×D₄	C₂²×C₇	semidirect
390. C₄×D₄	C₂²×C₇	semidirect
391. C₄×D₄	C₂²×C₇	semidirect
392. C₄×D₄	C₂²×C₇	semidirect
393. C₄×D₄	C₂²×C₇	semidirect
394. C₄×D₄	C₂²×C₇	semidirect
395. C₄×D₄	C₂²×C₇	semidirect
396. C₄×D₄	C₂²×C₇	semidirect
397. C₄×D₄	C₂²×C₇	semidirect
398. #117	C₂²×C₇	semidirect
399. #117	C₂²×C₇	semidirect
400. #117	C₂²×C₇	semidirect
401. #117	C₂²×C₇	semidirect
402. #117	C₂²×C₇	semidirect
403. #117	C₂²×C₇	semidirect
404. C₂×C₄⋊C₄	C₂²×C₇	semidirect
405. C₂×C₄⋊C₄	C₂²×C₇	semidirect
406. C₂×C₄⋊C₄	C₂²×C₇	semidirect
407. C₂×C₄⋊C₄	C₂²×C₇	semidirect
408. C₂×C₂²⋊C₄	C₂²×C₇	semidirect
409. C₂×C₂²⋊C₄	C₂²×C₇	semidirect
410. C₂×C₂²⋊C₄	C₂²×C₇	semidirect
411. C₂×C₂²⋊C₄	C₂²×C₇	semidirect
412. C₂×C₂²⋊C₄	C₂²×C₇	semidirect
413. C₂×C₄²	C₂²×C₇	semidirect
595. D₄	C₇×#41	semidirect
629. C₇	#3513	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×#559	2
C₇×#554	2
C₇×#553	2
C₇×#552	2
C₇×#551	2
C₇×#547	2
C₇×#546	2
C₇×D₄²	2
C₇×#542	2
C₇×#540	2
C₇×#539	2
C₇×#538	2
C₇×#529	2
C₇×#525	2
C₂×C₇×#123	2
C₇×#520	2
C₇×#518	2
C₂×C₄×C₇×D₄	2
#3513	7

Subgroups — C7×#3513 #11744465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#3513 #11744465