Subgroups — C₇×#61234 #13238450

Order 1792.

1874 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3475	C₂	1	2	yes	maximal, complemented
2	C₇×#3342	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3341	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3340	C₂	1	2	yes	maximal, complemented
5	C₇×#3339	C₂	1	2	yes	maximal, complemented
6	C₇×#3338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3337	C₂	1	4	yes	maximal, complemented
8	C₇×#3336	C₂	1	2	yes	maximal, complemented
9	C₇×#3335	C₂	1	2	yes	maximal, complemented
10	C₇×#3334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3091	C₂	1	4	yes	maximal, complemented
13	C₇×#3076	C₂	1	2	yes	maximal, complemented
14	C₇×#3050	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#427	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×#135	C₂²	1	1	yes	characteristic
19	C₂³×C₇×C₈	C₂²	1	2	yes	—
20	C₇×#556	C₂²	1	2	yes	—
21	C₇×#555	C₂²	1	2	yes	—
22	C₇×#554	C₂²	1	2	yes	—
23	C₇×#553	C₂²	1	4	yes	—
24	C₇×#552	—	2	2	no	—
25	C₇×#552	C₂²	1	4	yes	—
26	C₇×#551	—	2	4	no	—
27	C₇×#547	C₂²	1	2	yes	—
28	C₇×#546	—	2	2	no	—
29	C₇×#533	C₂²	1	2	yes	—
30	C₇×#529	—	2	4	no	—
31	C₇×#529	—	2	2	no	—
32	C₇×#525	C₂²	1	4	yes	—
33	C₄×C₇×#41	—	2	2	no	—
34	C₄×C₇×#41	C₂²	1	2	yes	—
35	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₇×#117	C₂²	1	4	yes	—
37	C₇×#500	C₂²	1	1	yes	characteristic, complemented
38	C₇×#500	C₂²	1	1	yes	characteristic, complemented
39	C₇×#499	C₂²	1	2	yes	complemented
40	C₇×#499	C₂²	1	2	yes	complemented
41	C₇×#498	C₂²	1	2	yes	complemented
42	C₇×#485	C₂²	1	4	yes	complemented
43	C₇×#485	C₂²	1	4	yes	complemented
44	C₇×#484	C₂²	1	4	yes	complemented
45	C₇×#483	C₂²	1	4	yes	complemented
46	C₇×#482	C₂²	1	4	yes	complemented
47	C₇×#482	C₂²	1	4	yes	complemented
48	C₇×#481	C₂²	1	4	yes	complemented
49	C₇×#480	C₂²	1	4	yes	complemented
50	C₇×#479	C₂²	1	4	yes	complemented
51	C₇×#478	C₂²	1	4	yes	complemented
52	C₇×#477	C₂²	1	2	yes	complemented
53	C₇×#476	C₂²	1	2	yes	complemented
54	C₇×#475	C₂²	1	2	yes	complemented
55	C₇×#474	C₂²	1	2	yes	complemented
56	C₇×#467	C₂²	1	2	yes	complemented
57	C₇×#467	C₂²	1	2	yes	complemented
58	C₇×#466	C₂²	1	2	yes	complemented
59	C₇×#466	C₂²	1	2	yes	complemented
60	C₇×#465	C₂²	1	4	yes	complemented
61	C₇×#465	C₂²	1	4	yes	complemented
62	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
63	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
64	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
65	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
66	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
67	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
68	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
69	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
70	C₇×C₈×D₄	C₂²	1	2	yes	—
71	C₇×C₈×D₄	C₂²	1	2	yes	—
72	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
73	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
74	C₇×#427	C₂²	1	2	yes	—
75	C₇×#427	C₂²	1	2	yes	—
76	C₇×#427	C₂²	1	1	yes	characteristic
77	C₇×#427	C₂²	1	4	yes	—
78	C₇×#427	C₂²	1	2	yes	complemented
79	C₇×#427	C₂²	1	4	yes	complemented
80	C₇×#427	C₂²	1	2	yes	complemented
81	C₂×C₇×#107	C₂²	1	2	yes	complemented
82	C₂×C₇×#107	C₂²	1	2	yes	complemented
83	C₂×C₇×#106	C₂²	1	4	yes	complemented
84	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
85	C₇×#416	C₂²	1	2	yes	—
86	C₇×#416	C₂²	1	4	yes	—
87	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
88	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
89	#61234	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×C₇×#41	—	2	2	no	—
91	C₂×C₇×#41	C₂³	1	2	yes	—
92	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
93	C₂³×C₄×C₇	C₂³	1	2	yes	—
94	C₇×#135	—	2	4	no	—
95	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
97	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
98	C₂²×C₇×C₈	—	2	8	no	—
99	C₂²×C₇×C₈	C₂³	1	2	yes	—
100	C₂²×C₇×C₈	C₂³	1	2	yes	—
101	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
102	C₂²×C₇×C₈	C₂³	1	2	yes	—
103	C₂²×C₇×C₈	C₂³	1	2	yes	—
104	C₂²×C₇×C₈	C₂³	1	2	yes	—
105	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
106	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₇×#126	—	2	4	no	—
109	C₇×#126	—	2	4	no	—
110	C₇×#126	—	2	4	no	—
111	C₇×#125	—	2	4	no	—
112	C₇×#125	—	2	2	no	—
113	C₇×#125	C₂³	1	4	yes	—
114	C₇×#124	—	2	2	no	—
115	C₇×#124	—	2	4	no	—
116	C₇×#123	—	2	4	no	—
117	C₇×#123	—	2	4	no	—
118	C₇×#123	—	2	4	no	—
119	C₇×#123	—	2	4	no	—
120	C₇×C₂²⋊Q₈	—	2	2	no	—
121	C₇×C₂²⋊Q₈	—	2	2	no	—
122	C₇×C₂²⋊Q₈	—	2	2	no	—
123	C₇×C₂²⋊Q₈	—	2	4	no	—
124	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₇×#121	—	2	4	no	—
127	C₇×#121	—	2	2	no	—
128	C₇×#121	C₂³	1	4	yes	—
129	C₇×#121	C₂³	1	4	yes	—
130	C₇×#120	—	2	4	no	—
131	C₄×C₇×Q₈	—	2	2	no	—
132	C₄×C₇×Q₈	—	2	2	no	—
133	C₄×C₇×Q₈	—	2	2	no	—
134	C₄×C₇×Q₈	C₂³	1	2	yes	—
135	C₄×C₇×Q₈	C₂³	1	2	yes	—
136	C₄×C₇×D₄	—	2	2	no	—
137	C₄×C₇×D₄	—	2	4	no	—
138	C₄×C₇×D₄	—	2	2	no	—
139	C₄×C₇×D₄	—	2	2	no	—
140	C₄×C₇×D₄	—	2	4	no	—
141	C₄×C₇×D₄	—	2	4	no	—
142	C₄×C₇×D₄	D₄	1	1	yes	characteristic
143	C₄×C₇×D₄	D₄	1	1	yes	characteristic
144	C₄×C₇×D₄	D₄	1	2	yes	—
145	C₄×C₇×D₄	C₂³	1	2	yes	—
146	C₄×C₇×D₄	C₂³	1	2	yes	—
147	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
148	C₄×C₇×D₄	C₂³	1	2	yes	—
149	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
150	C₇×#117	—	2	4	no	—
151	C₇×#117	—	2	4	no	—
152	C₇×#117	—	2	2	no	—
153	C₇×#117	—	2	4	no	—
154	C₇×#117	—	2	2	no	—
155	C₇×#117	C₂³	1	4	yes	—
156	C₇×#117	C₂³	1	4	yes	—
157	C₇×#117	C₂³	1	2	yes	—
158	C₇×#117	C₂³	1	4	yes	—
159	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
160	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
161	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
162	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
163	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
164	C₂×C₄²×C₇	—	2	4	no	—
165	C₂×C₄²×C₇	—	2	2	no	—
166	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
167	C₇×#107	C₂³	1	2	yes	—
168	C₇×#107	C₂³	1	2	yes	—
169	C₇×#107	C₂³	1	4	yes	—
170	C₇×#107	C₂³	1	4	yes	—
171	C₇×#107	C₂³	1	2	yes	—
172	C₇×#107	C₂³	1	2	yes	—
173	C₇×#107	C₂³	1	1	yes	characteristic
174	C₇×#107	C₂³	1	1	yes	characteristic
175	C₇×#106	C₂³	1	4	yes	—
176	C₇×#106	C₂³	1	4	yes	—
177	C₇×#106	C₂³	1	4	yes	—
178	C₇×#106	C₂³	1	4	yes	—
179	C₇×#106	C₂³	1	2	yes	—
180	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
181	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
182	C₇×C₄⋊C₈	C₂³	1	2	yes	—
183	C₇×#103	C₂³	1	4	yes	—
184	C₇×#103	C₂³	1	4	yes	—
185	C₇×#103	C₂³	1	2	yes	—
186	C₇×#103	C₂³	1	2	yes	—
187	C₇×#102	C₂³	1	4	yes	—
188	C₇×#102	C₂³	1	4	yes	—
189	C₇×#102	C₂³	1	2	yes	—
190	C₇×#102	C₂³	1	2	yes	—
191	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
193	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
196	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
197	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
198	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
199	#3475	C₂×C₇	1	2	yes	complemented
200	#3342	C₂×C₇	1	1	yes	characteristic, complemented
201	#3341	C₂×C₇	1	1	yes	characteristic, complemented
202	#3340	C₂×C₇	1	2	yes	complemented
203	#3339	C₂×C₇	1	2	yes	complemented
204	#3338	C₂×C₇	1	1	yes	characteristic, complemented
205	#3337	C₂×C₇	1	4	yes	complemented
206	#3336	C₂×C₇	1	2	yes	complemented
207	#3335	C₂×C₇	1	2	yes	complemented
208	#3334	C₂×C₇	1	1	yes	characteristic, complemented
209	#3160	C₂×C₇	1	1	yes	characteristic, complemented
210	#3091	C₂×C₇	1	4	yes	complemented
211	#3076	C₂×C₇	1	2	yes	complemented
212	#3050	C₂×C₇	1	2	yes	complemented
213	C₄×#135	C₂×C₇	1	1	yes	characteristic, complemented
214	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
215	C₂×#427	C₂×C₇	1	2	yes	complemented
216	C₂⁴×C₇	C₂×D₄	1	2	yes	—
217	C₇×#41	—	2	4	no	—
218	C₇×#41	—	2	4	no	—
219	C₇×#41	—	4	8	no	—
220	C₂×C₇×Q₈	—	2	2	no	—
221	C₂×C₇×Q₈	—	2	2	no	—
222	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
223	C₂×C₇×D₄	—	2	4	no	—
224	C₂×C₇×D₄	—	2	2	no	—
225	C₂×C₇×D₄	—	2	4	no	—
226	C₂×C₇×D₄	—	2	4	no	—
227	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
228	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
229	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
230	C₂×C₇×D₄	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₇	—	2	4	no	—
232	C₂²×C₄×C₇	—	2	4	no	—
233	C₂²×C₄×C₇	—	2	4	no	—
234	C₂²×C₄×C₇	—	2	4	no	—
235	C₂²×C₄×C₇	—	2	2	no	—
236	C₂²×C₄×C₇	—	2	2	no	—
237	C₂²×C₄×C₇	—	2	2	no	—
238	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
241	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
242	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
246	C₇×Q₁₆	—	2	2	no	—
247	C₇×SD₁₆	—	2	4	no	—
248	C₇×D₈	—	2	2	no	—
249	C₂×C₇×C₈	—	2	4	no	—
250	C₂×C₇×C₈	—	2	2	no	—
251	C₂×C₇×C₈	—	2	4	no	—
252	C₂×C₇×C₈	—	2	4	no	—
253	C₂×C₇×C₈	—	2	4	no	—
254	C₂×C₇×C₈	—	2	4	no	—
255	C₂×C₇×C₈	#41	1	4	yes	complemented
256	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
257	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
258	C₂×C₇×C₈	C₂⁴	1	2	yes	—
259	C₂×C₇×C₈	C₂⁴	1	2	yes	—
260	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
261	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
262	C₇×C₄⋊C₄	—	2	4	no	—
263	C₇×C₄⋊C₄	—	2	4	no	—
264	C₇×C₄⋊C₄	—	2	2	no	—
265	C₇×C₄⋊C₄	—	2	4	no	—
266	C₇×C₄⋊C₄	—	2	4	no	—
267	C₇×C₄⋊C₄	—	2	2	no	—
268	C₇×C₄⋊C₄	—	2	2	no	—
269	C₇×C₄⋊C₄	—	2	4	no	—
270	C₇×C₄⋊C₄	—	2	4	no	—
271	C₇×C₄⋊C₄	—	2	2	no	—
272	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
273	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
274	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
275	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
276	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
277	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
278	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
279	C₇×C₂²⋊C₄	—	2	2	no	—
280	C₇×C₂²⋊C₄	—	2	4	no	—
281	C₇×C₂²⋊C₄	—	2	4	no	—
282	C₇×C₂²⋊C₄	—	2	4	no	—
283	C₇×C₂²⋊C₄	—	2	4	no	—
284	C₇×C₂²⋊C₄	—	2	4	no	—
285	C₇×C₂²⋊C₄	—	2	4	no	—
286	C₇×C₂²⋊C₄	—	2	2	no	—
287	C₇×C₂²⋊C₄	—	2	2	no	—
288	C₇×C₂²⋊C₄	—	2	4	no	—
289	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
290	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
291	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
292	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
293	C₄²×C₇	—	2	4	no	—
294	C₄²×C₇	—	2	2	no	—
295	C₄²×C₇	—	2	4	no	—
296	C₄²×C₇	—	2	2	no	—
297	C₄²×C₇	—	2	2	no	—
298	C₄²×C₇	—	2	4	no	—
299	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₇	C₂⁴	1	1	yes	characteristic
302	C₄²×C₇	C₂⁴	1	1	yes	characteristic
303	C₂×#135	C₂²×C₇	1	1	yes	characteristic
304	C₂³×C₈	C₂²×C₇	1	2	yes	—
305	#556	C₂²×C₇	1	2	yes	—
306	#555	C₂²×C₇	1	2	yes	—
307	#554	C₂²×C₇	1	2	yes	—
308	#553	C₂²×C₇	1	4	yes	—
309	#552	—	2	2	no	—
310	#552	C₂²×C₇	1	4	yes	—
311	#551	—	2	4	no	—
312	#547	C₂²×C₇	1	2	yes	—
313	#546	—	2	2	no	—
314	#533	C₂²×C₇	1	2	yes	—
315	#529	—	2	4	no	—
316	#529	—	2	2	no	—
317	#525	C₂²×C₇	1	4	yes	—
318	C₄×#41	—	2	2	no	—
319	C₄×#41	C₂²×C₇	1	2	yes	—
320	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
321	C₂×#117	C₂²×C₇	1	4	yes	—
322	#500	C₂²×C₇	1	1	yes	characteristic, complemented
323	#500	C₂²×C₇	1	1	yes	characteristic, complemented
324	#499	C₂²×C₇	1	2	yes	complemented
325	#499	C₂²×C₇	1	2	yes	complemented
326	#498	C₂²×C₇	1	2	yes	complemented
327	#485	C₂²×C₇	1	4	yes	complemented
328	#485	C₂²×C₇	1	4	yes	complemented
329	#484	C₂²×C₇	1	4	yes	complemented
330	#483	C₂²×C₇	1	4	yes	complemented
331	#482	C₂²×C₇	1	4	yes	complemented
332	#482	C₂²×C₇	1	4	yes	complemented
333	#481	C₂²×C₇	1	4	yes	complemented
334	#480	C₂²×C₇	1	4	yes	complemented
335	#479	C₂²×C₇	1	4	yes	complemented
336	#478	C₂²×C₇	1	4	yes	complemented
337	#477	C₂²×C₇	1	2	yes	complemented
338	#476	C₂²×C₇	1	2	yes	complemented
339	#475	C₂²×C₇	1	2	yes	complemented
340	#474	C₂²×C₇	1	2	yes	complemented
341	#467	C₂²×C₇	1	2	yes	complemented
342	#467	C₂²×C₇	1	2	yes	complemented
343	#466	C₂²×C₇	1	2	yes	complemented
344	#466	C₂²×C₇	1	2	yes	complemented
345	#465	C₂²×C₇	1	4	yes	complemented
346	#465	C₂²×C₇	1	4	yes	complemented
347	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
348	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
349	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
350	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
351	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
352	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
353	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
354	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
355	C₈×D₄	C₂²×C₇	1	2	yes	—
356	C₈×D₄	C₂²×C₇	1	2	yes	—
357	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
358	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
359	#427	C₂²×C₇	1	4	yes	—
360	#427	C₂²×C₇	1	2	yes	—
361	#427	C₂²×C₇	1	2	yes	—
362	#427	C₂²×C₇	1	1	yes	characteristic
363	#427	C₂²×C₇	1	2	yes	complemented
364	#427	C₂²×C₇	1	4	yes	complemented
365	#427	C₂²×C₇	1	2	yes	complemented
366	C₂×#107	C₂²×C₇	1	2	yes	complemented
367	C₂×#107	C₂²×C₇	1	2	yes	complemented
368	C₂×#106	C₂²×C₇	1	4	yes	complemented
369	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
370	#416	C₂²×C₇	1	4	yes	—
371	#416	C₂²×C₇	1	2	yes	—
372	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
373	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
374	C₂³×C₇	—	2	4	no	—
375	C₂³×C₇	—	2	4	no	—
376	C₂³×C₇	—	2	2	no	—
377	C₂³×C₇	—	4	2	no	—
378	C₂³×C₇	C₂²×D₄	1	2	yes	—
379	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
380	C₂³×C₇	C₂²×D₄	1	2	yes	—
381	C₇×Q₈	—	2	2	no	—
382	C₇×Q₈	—	2	2	no	—
383	C₇×Q₈	—	4	4	no	—
384	C₇×Q₈	—	8	2	no	—
385	C₇×D₄	—	2	4	no	—
386	C₇×D₄	—	2	2	no	—
387	C₇×D₄	—	2	2	no	—
388	C₇×D₄	—	2	2	no	—
389	C₇×D₄	—	4	4	no	—
390	C₇×D₄	—	4	8	no	—
391	C₇×D₄	—	8	4	no	—
392	C₇×D₄	#135	1	4	yes	complemented
393	C₂×C₄×C₇	—	2	4	no	—
394	C₂×C₄×C₇	—	2	4	no	—
395	C₂×C₄×C₇	—	2	4	no	—
396	C₂×C₄×C₇	—	2	2	no	—
397	C₂×C₄×C₇	—	2	2	no	—
398	C₂×C₄×C₇	—	2	2	no	—
399	C₂×C₄×C₇	—	2	2	no	—
400	C₂×C₄×C₇	—	2	2	no	—
401	C₂×C₄×C₇	—	2	2	no	—
402	C₂×C₄×C₇	—	2	2	no	—
403	C₂×C₄×C₇	—	2	2	no	—
404	C₂×C₄×C₇	—	2	4	no	—
405	C₂×C₄×C₇	—	2	4	no	—
406	C₂×C₄×C₇	—	4	1	no	—
407	C₂×C₄×C₇	—	4	8	no	—
408	C₂×C₄×C₇	—	4	4	no	—
409	C₂×C₄×C₇	—	4	4	no	—
410	C₂×C₄×C₇	—	8	2	no	—
411	C₂×C₄×C₇	—	8	4	no	—
412	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₇	C₂×#41	1	2	yes	—
420	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
421	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
422	C₇×C₈	—	2	2	no	—
423	C₇×C₈	—	2	2	no	—
424	C₇×C₈	—	2	1	no	—
425	C₇×C₈	—	2	1	no	—
426	C₇×C₈	C₂×#41	1	2	yes	—
427	C₇×C₈	C₂×#41	1	2	yes	—
428	C₂×#41	—	2	2	no	—
429	C₂×#41	C₂³×C₇	1	2	yes	—
430	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₇	1	2	yes	—
432	#135	—	2	4	no	—
433	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
434	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
435	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
436	C₂²×C₈	—	2	8	no	—
437	C₂²×C₈	C₂³×C₇	1	2	yes	—
438	C₂²×C₈	C₂³×C₇	1	2	yes	—
439	C₂²×C₈	C₂³×C₇	1	2	yes	—
440	C₂²×C₈	C₂³×C₇	1	2	yes	—
441	C₂²×C₈	C₂³×C₇	1	2	yes	—
442	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
443	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
444	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
445	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
446	#126	—	2	4	no	—
447	#126	—	2	4	no	—
448	#126	—	2	4	no	—
449	#125	—	2	4	no	—
450	#125	—	2	2	no	—
451	#125	C₂³×C₇	1	4	yes	—
452	#124	—	2	2	no	—
453	#124	—	2	4	no	—
454	#123	—	2	4	no	—
455	#123	—	2	4	no	—
456	#123	—	2	4	no	—
457	#123	—	2	4	no	—
458	C₂²⋊Q₈	—	2	2	no	—
459	C₂²⋊Q₈	—	2	2	no	—
460	C₂²⋊Q₈	—	2	2	no	—
461	C₂²⋊Q₈	—	2	4	no	—
462	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
463	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
464	#121	—	2	4	no	—
465	#121	—	2	2	no	—
466	#121	C₂³×C₇	1	4	yes	—
467	#121	C₂³×C₇	1	4	yes	—
468	#120	—	2	4	no	—
469	C₄×Q₈	—	2	2	no	—
470	C₄×Q₈	—	2	2	no	—
471	C₄×Q₈	—	2	2	no	—
472	C₄×Q₈	C₂³×C₇	1	2	yes	—
473	C₄×Q₈	C₂³×C₇	1	2	yes	—
474	C₄×D₄	—	2	2	no	—
475	C₄×D₄	—	2	4	no	—
476	C₄×D₄	—	2	2	no	—
477	C₄×D₄	—	2	2	no	—
478	C₄×D₄	—	2	4	no	—
479	C₄×D₄	—	2	4	no	—
480	C₄×D₄	C₇×D₄	1	1	yes	characteristic
481	C₄×D₄	C₇×D₄	1	1	yes	characteristic
482	C₄×D₄	C₇×D₄	1	2	yes	—
483	C₄×D₄	C₂³×C₇	1	2	yes	—
484	C₄×D₄	C₂³×C₇	1	2	yes	—
485	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
486	C₄×D₄	C₂³×C₇	1	2	yes	—
487	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
488	#117	—	2	4	no	—
489	#117	—	2	4	no	—
490	#117	—	2	2	no	—
491	#117	—	2	4	no	—
492	#117	—	2	2	no	—
493	#117	C₂³×C₇	1	2	yes	—
494	#117	C₂³×C₇	1	4	yes	—
495	#117	C₂³×C₇	1	4	yes	—
496	#117	C₂³×C₇	1	4	yes	—
497	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
500	C₂×C₂²⋊C₄	—	2	4	no	—
501	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
502	C₂×C₄²	—	2	4	no	—
503	C₂×C₄²	—	2	2	no	—
504	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
505	#107	C₂³×C₇	1	1	yes	characteristic
506	#107	C₂³×C₇	1	1	yes	characteristic
507	#107	C₂³×C₇	1	2	yes	—
508	#107	C₂³×C₇	1	2	yes	—
509	#107	C₂³×C₇	1	4	yes	—
510	#107	C₂³×C₇	1	4	yes	—
511	#107	C₂³×C₇	1	2	yes	—
512	#107	C₂³×C₇	1	2	yes	—
513	#106	C₂³×C₇	1	2	yes	—
514	#106	C₂³×C₇	1	4	yes	—
515	#106	C₂³×C₇	1	4	yes	—
516	#106	C₂³×C₇	1	4	yes	—
517	#106	C₂³×C₇	1	4	yes	—
518	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
519	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
520	C₄⋊C₈	C₂³×C₇	1	2	yes	—
521	#103	C₂³×C₇	1	2	yes	—
522	#103	C₂³×C₇	1	2	yes	—
523	#103	C₂³×C₇	1	4	yes	—
524	#103	C₂³×C₇	1	4	yes	—
525	#102	C₂³×C₇	1	2	yes	—
526	#102	C₂³×C₇	1	2	yes	—
527	#102	C₂³×C₇	1	4	yes	—
528	#102	C₂³×C₇	1	4	yes	—
529	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
530	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
531	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
532	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
533	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
534	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
535	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
536	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
537	C₂²×C₇	—	2	1	no	—
538	C₂²×C₇	—	2	2	no	—
539	C₂²×C₇	—	2	2	no	—
540	C₂²×C₇	—	2	1	no	—
541	C₂²×C₇	—	2	2	no	—
542	C₂²×C₇	—	2	2	no	—
543	C₂²×C₇	—	2	2	no	—
544	C₂²×C₇	—	4	8	no	—
545	C₂²×C₇	—	4	2	no	—
546	C₂²×C₇	—	4	2	no	—
547	C₂²×C₇	—	4	2	no	—
548	C₂²×C₇	#547	1	2	yes	—
549	C₂²×C₇	C₂×#135	1	4	yes	—
550	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
551	C₄×C₇	—	2	1	no	—
552	C₄×C₇	—	2	1	no	—
553	C₄×C₇	—	2	2	no	—
554	C₄×C₇	—	2	2	no	—
555	C₄×C₇	—	2	1	no	—
556	C₄×C₇	—	4	2	no	—
557	C₄×C₇	—	4	4	no	—
558	C₄×C₇	—	4	2	no	—
559	C₄×C₇	—	4	2	no	—
560	C₄×C₇	—	4	4	no	—
561	C₄×C₇	#547	1	2	yes	—
562	C₄×C₇	C₂×#135	1	2	yes	—
563	C₄×C₇	C₂²×#41	1	1	yes	characteristic
564	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
565	C₂⁴	C₂×C₇×D₄	1	2	yes	—
566	#41	—	2	4	no	—
567	#41	—	2	4	no	—
568	#41	—	4	8	no	—
569	C₂×Q₈	—	2	2	no	—
570	C₂×Q₈	—	2	2	no	—
571	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
577	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
578	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
579	C₂×D₄	C₂⁴×C₇	1	2	yes	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
588	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
589	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
590	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
591	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
595	Q₁₆	—	2	2	no	—
596	SD₁₆	—	2	4	no	—
597	D₈	—	2	2	no	—
598	C₂×C₈	—	2	4	no	—
599	C₂×C₈	—	2	2	no	—
600	C₂×C₈	—	2	4	no	—
601	C₂×C₈	—	2	4	no	—
602	C₂×C₈	—	2	4	no	—
603	C₂×C₈	—	2	4	no	—
604	C₂×C₈	C₇×#41	1	4	yes	complemented
605	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
606	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
607	C₂×C₈	C₂⁴×C₇	1	2	yes	—
608	C₂×C₈	C₂⁴×C₇	1	2	yes	—
609	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
610	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
622	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
623	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
624	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
625	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
627	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
639	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
640	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
641	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
642	C₄²	—	2	2	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	4	no	—
646	C₄²	—	2	4	no	—
647	C₄²	—	2	2	no	—
648	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
649	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
650	C₄²	C₂⁴×C₇	1	1	yes	characteristic
651	C₄²	C₂⁴×C₇	1	1	yes	characteristic
652	C₂×C₇	—	2	2	no	—
653	C₂×C₇	—	2	4	no	—
654	C₂×C₇	—	4	2	no	—
655	C₂×C₇	—	8	2	no	—
656	C₂×C₇	C₂×#547	1	1	yes	characteristic
657	C₂×C₇	C₂²×#135	1	1	yes	characteristic
658	C₂×C₇	#3584	1	1	yes	characteristic
659	C₂³	—	2	4	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	4	2	no	—
663	C₂³	C₂²×C₇×D₄	1	2	yes	—
664	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
665	C₂³	C₂²×C₇×D₄	1	2	yes	—
666	Q₈	—	2	2	no	—
667	Q₈	—	2	2	no	—
668	Q₈	—	4	4	no	—
669	Q₈	—	8	2	no	—
670	D₄	—	2	4	no	—
671	D₄	—	2	2	no	—
672	D₄	—	2	2	no	—
673	D₄	—	2	2	no	—
674	D₄	—	4	4	no	—
675	D₄	—	4	8	no	—
676	D₄	—	8	4	no	—
677	D₄	C₇×#135	1	4	yes	complemented
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	8	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	8	2	no	—
696	C₂×C₄	—	8	4	no	—
697	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
698	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
699	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
700	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
701	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
702	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
703	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
704	C₂×C₄	C₂×C₇×#41	1	2	yes	—
705	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
706	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
707	C₈	—	2	2	no	—
708	C₈	—	2	2	no	—
709	C₈	—	2	1	no	—
710	C₈	—	2	1	no	—
711	C₈	C₂×C₇×#41	1	2	yes	—
712	C₈	C₂×C₇×#41	1	2	yes	—
713	C₇	#61234	1	1	yes	characteristic, direct product factor, Sylow
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	4	8	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	C₇×#547	1	2	yes	—
726	C₂²	C₂×C₇×#135	1	4	yes	—
727	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	4	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	4	no	—
737	C₄	—	4	2	no	—
738	C₄	C₇×#547	1	2	yes	—
739	C₄	C₂×C₇×#135	1	2	yes	—
740	C₄	C₂²×C₇×#41	1	1	yes	characteristic
741	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
742	C₂	—	2	2	no	—
743	C₂	—	2	4	no	—
744	C₂	—	4	2	no	—
745	C₂	—	8	2	no	—
746	C₂	C₂×C₇×#547	1	1	yes	characteristic
747	C₂	C₂²×C₇×#135	1	1	yes	characteristic
748	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3475	C₂	semidirect
2. C₇×#3342	C₂	semidirect
3. C₇×#3341	C₂	semidirect
4. C₇×#3340	C₂	semidirect
5. C₇×#3339	C₂	semidirect
6. C₇×#3338	C₂	semidirect
7. C₇×#3337	C₂	semidirect
8. C₇×#3336	C₂	semidirect
9. C₇×#3335	C₂	semidirect
10. C₇×#3334	C₂	semidirect
11. C₇×#3160	C₂	semidirect
12. C₇×#3091	C₂	semidirect
13. C₇×#3076	C₂	semidirect
14. C₇×#3050	C₂	semidirect
15. C₄×C₇×#135	C₂	semidirect
16. C₂×C₇×C₈×D₄	C₂	semidirect
17. C₂×C₇×#427	C₂	semidirect
37. C₇×#500	C₂²	semidirect
38. C₇×#500	C₂²	semidirect
39. C₇×#499	C₂²	semidirect
40. C₇×#499	C₂²	semidirect
41. C₇×#498	C₂²	semidirect
42. C₇×#485	C₂²	semidirect
43. C₇×#485	C₂²	semidirect
44. C₇×#484	C₂²	semidirect
45. C₇×#483	C₂²	semidirect
46. C₇×#482	C₂²	semidirect
47. C₇×#482	C₂²	semidirect
48. C₇×#481	C₂²	semidirect
49. C₇×#480	C₂²	semidirect
50. C₇×#479	C₂²	semidirect
51. C₇×#478	C₂²	semidirect
52. C₇×#477	C₂²	semidirect
53. C₇×#476	C₂²	semidirect
54. C₇×#475	C₂²	semidirect
55. C₇×#474	C₂²	semidirect
56. C₇×#467	C₂²	semidirect
57. C₇×#467	C₂²	semidirect
58. C₇×#466	C₂²	semidirect
59. C₇×#466	C₂²	semidirect
60. C₇×#465	C₂²	semidirect
61. C₇×#465	C₂²	semidirect
62. C₄×C₇×Q₁₆	C₂²	semidirect
63. C₄×C₇×Q₁₆	C₂²	semidirect
64. C₄×C₇×SD₁₆	C₂²	semidirect
65. C₄×C₇×SD₁₆	C₂²	semidirect
66. C₄×C₇×D₈	C₂²	semidirect
67. C₄×C₇×D₈	C₂²	semidirect
78. C₇×#427	C₂²	semidirect
79. C₇×#427	C₂²	semidirect
80. C₇×#427	C₂²	semidirect
81. C₂×C₇×#107	C₂²	semidirect
82. C₂×C₇×#107	C₂²	semidirect
83. C₂×C₇×#106	C₂²	semidirect
89. #61234	C₇	direct (N × H)
199. #3475	C₂×C₇	semidirect
200. #3342	C₂×C₇	semidirect
201. #3341	C₂×C₇	semidirect
202. #3340	C₂×C₇	semidirect
203. #3339	C₂×C₇	semidirect
204. #3338	C₂×C₇	semidirect
205. #3337	C₂×C₇	semidirect
206. #3336	C₂×C₇	semidirect
207. #3335	C₂×C₇	semidirect
208. #3334	C₂×C₇	semidirect
209. #3160	C₂×C₇	semidirect
210. #3091	C₂×C₇	semidirect
211. #3076	C₂×C₇	semidirect
212. #3050	C₂×C₇	semidirect
213. C₄×#135	C₂×C₇	semidirect
214. C₂×C₈×D₄	C₂×C₇	semidirect
215. C₂×#427	C₂×C₇	semidirect
255. C₂×C₇×C₈	#41	semidirect
322. #500	C₂²×C₇	semidirect
323. #500	C₂²×C₇	semidirect
324. #499	C₂²×C₇	semidirect
325. #499	C₂²×C₇	semidirect
326. #498	C₂²×C₇	semidirect
327. #485	C₂²×C₇	semidirect
328. #485	C₂²×C₇	semidirect
329. #484	C₂²×C₇	semidirect
330. #483	C₂²×C₇	semidirect
331. #482	C₂²×C₇	semidirect
332. #482	C₂²×C₇	semidirect
333. #481	C₂²×C₇	semidirect
334. #480	C₂²×C₇	semidirect
335. #479	C₂²×C₇	semidirect
336. #478	C₂²×C₇	semidirect
337. #477	C₂²×C₇	semidirect
338. #476	C₂²×C₇	semidirect
339. #475	C₂²×C₇	semidirect
340. #474	C₂²×C₇	semidirect
341. #467	C₂²×C₇	semidirect
342. #467	C₂²×C₇	semidirect
343. #466	C₂²×C₇	semidirect
344. #466	C₂²×C₇	semidirect
345. #465	C₂²×C₇	semidirect
346. #465	C₂²×C₇	semidirect
347. C₄×Q₁₆	C₂²×C₇	semidirect
348. C₄×Q₁₆	C₂²×C₇	semidirect
349. C₄×SD₁₆	C₂²×C₇	semidirect
350. C₄×SD₁₆	C₂²×C₇	semidirect
351. C₄×D₈	C₂²×C₇	semidirect
352. C₄×D₈	C₂²×C₇	semidirect
363. #427	C₂²×C₇	semidirect
364. #427	C₂²×C₇	semidirect
365. #427	C₂²×C₇	semidirect
366. C₂×#107	C₂²×C₇	semidirect
367. C₂×#107	C₂²×C₇	semidirect
368. C₂×#106	C₂²×C₇	semidirect
392. C₇×D₄	#135	semidirect
604. C₂×C₈	C₇×#41	semidirect
677. D₄	C₇×#135	semidirect
713. C₇	#61234	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×#3475	2
C₇×#3342	2
C₇×#3341	2
C₇×#3340	2
C₇×#3339	2
C₇×#3338	2
C₇×#3337	2
C₇×#3336	2
C₇×#3335	2
C₇×#3334	2
C₇×#3160	2
C₇×#3091	2
C₇×#3076	2
C₇×#3050	2
C₄×C₇×#135	2
C₂×C₇×C₈×D₄	2
C₂×C₇×#427	2
#61234	7

Subgroups — C7×#61234 #13238450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61234 #13238450