Subgroups — C₇×C₄⋊C₄×D₈ #13199896

Order 1792.

1134 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×D₈	C₂	1	2	yes	maximal
2	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic
3	C₇×D₄×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
4	C₇×#1942	C₂	1	2	yes	maximal, complemented
5	C₇×#1862	C₂	1	4	yes	maximal, complemented
6	C₇×#1845	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1802	C₂	1	2	yes	maximal, complemented
8	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
11	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
12	C₂²×C₇×C₄⋊C₄	—	2	2	no	—
13	C₄×C₇×D₈	—	2	8	no	—
14	C₄×C₇×D₈	C₄	1	8	yes	complemented
15	C₂×C₇×#107	C₂²	1	2	yes	—
16	C₂×C₇×#107	C₂²	1	2	yes	—
17	C₂×C₇×#107	C₂²	1	1	yes	characteristic
18	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×#102	C₂²	1	4	yes	—
20	C₂×C₇×#102	C₂²	1	2	yes	—
21	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
23	C₇×#389	C₂²	1	4	yes	—
24	C₇×#385	—	2	4	no	—
25	C₇×#384	C₂²	1	2	yes	—
26	C₇×#380	—	2	2	no	—
27	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₇×#340	C₂²	1	4	yes	—
29	C₇×#336	C₂²	1	2	yes	—
30	C₄⋊C₄×D₈	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂²×C₇×D₄	C₂³	1	2	yes	—
32	C₂³×C₄×C₇	—	2	2	no	—
33	C₂³×C₄×C₇	—	2	4	no	—
34	C₂×C₇×D₈	C₂×C₄	1	4	yes	—
35	C₂×C₇×D₈	D₄	1	4	yes	—
36	C₂×C₇×D₈	Q₈	1	4	yes	—
37	C₂²×C₇×C₈	C₂³	1	2	yes	—
38	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
39	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
40	C₄×C₇×D₄	—	2	8	no	—
41	C₄×C₇×D₄	—	2	4	no	—
42	C₄×C₇×D₄	—	4	4	no	—
43	C₄×C₇×D₄	C₂×C₄	1	8	yes	complemented
44	C₂×C₇×C₄⋊C₄	—	2	2	no	—
45	C₂×C₇×C₄⋊C₄	—	2	4	no	—
46	C₂×C₇×C₄⋊C₄	—	2	2	no	—
47	C₂×C₇×C₄⋊C₄	—	4	8	no	—
48	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
49	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
50	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
51	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
52	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
53	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
54	C₂×C₄²×C₇	C₂³	1	2	yes	—
55	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
56	C₇×#107	—	2	4	no	—
57	C₇×#107	—	4	2	no	—
58	C₇×#107	C₂×C₄	1	4	yes	complemented
59	C₇×C₄⋊C₈	—	2	2	no	—
60	C₇×#102	—	2	8	no	—
61	C₇×#102	C₂×C₄	1	8	yes	complemented
62	C₄×C₇×C₈	—	2	4	no	—
63	C₄×C₇×C₈	C₂×C₄	1	4	yes	complemented
64	C₇×#95	—	2	4	no	—
65	C₇×#95	D₄	1	2	yes	—
66	C₂×C₄×D₈	C₂×C₇	1	2	yes	—
67	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic
68	D₄×C₄⋊C₄	C₂×C₇	1	2	yes	complemented
69	#1942	C₂×C₇	1	2	yes	complemented
70	#1862	C₂×C₇	1	4	yes	complemented
71	#1845	C₂×C₇	1	1	yes	characteristic, complemented
72	#1802	C₂×C₇	1	2	yes	complemented
73	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
74	C₂⁴×C₇	—	2	2	no	—
75	C₂×C₇×D₄	—	2	2	no	—
76	C₂×C₇×D₄	—	2	2	no	—
77	C₂×C₇×D₄	—	2	2	no	—
78	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
79	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
80	C₂×C₇×D₄	C₂×Q₈	1	4	yes	—
81	C₂²×C₄×C₇	—	2	2	no	—
82	C₂²×C₄×C₇	—	2	8	no	—
83	C₂²×C₄×C₇	—	2	4	no	—
84	C₂²×C₄×C₇	—	4	8	no	—
85	C₂²×C₄×C₇	—	4	4	no	—
86	C₂²×C₄×C₇	—	4	4	no	—
87	C₂²×C₄×C₇	—	4	8	no	—
88	C₂²×C₄×C₇	—	8	4	no	—
89	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
94	C₇×D₈	C₄⋊C₄	1	16	yes	direct product factor
95	C₂×C₇×C₈	—	2	1	no	—
96	C₂×C₇×C₈	—	2	1	no	—
97	C₂×C₇×C₈	—	2	2	no	—
98	C₂×C₇×C₈	—	2	2	no	—
99	C₂×C₇×C₈	—	2	2	no	—
100	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
101	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
102	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
103	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
104	C₇×C₄⋊C₄	—	2	2	no	—
105	C₇×C₄⋊C₄	—	2	2	no	—
106	C₇×C₄⋊C₄	—	2	4	no	—
107	C₇×C₄⋊C₄	—	2	4	no	—
108	C₇×C₄⋊C₄	—	4	8	no	—
109	C₇×C₄⋊C₄	—	4	4	no	—
110	C₇×C₄⋊C₄	—	8	2	no	—
111	C₇×C₄⋊C₄	D₈	1	4	yes	direct product factor
112	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
113	C₇×C₂²⋊C₄	—	2	8	no	—
114	C₇×C₂²⋊C₄	—	4	8	no	—
115	C₄²×C₇	—	2	2	no	—
116	C₄²×C₇	—	2	2	no	—
117	C₄²×C₇	C₂²×C₄	1	2	yes	—
118	C₄²×C₇	#41	1	2	yes	—
119	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
120	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
121	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
122	C₂²×C₄⋊C₄	—	2	2	no	—
123	C₄×D₈	—	2	8	no	—
124	C₄×D₈	C₄×C₇	1	8	yes	complemented
125	C₂×#107	C₂²×C₇	1	2	yes	—
126	C₂×#107	C₂²×C₇	1	2	yes	—
127	C₂×#107	C₂²×C₇	1	1	yes	characteristic
128	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
129	C₂×#102	C₂²×C₇	1	4	yes	—
130	C₂×#102	C₂²×C₇	1	2	yes	—
131	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
132	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
133	#389	C₂²×C₇	1	4	yes	—
134	#385	—	2	4	no	—
135	#384	C₂²×C₇	1	2	yes	—
136	#380	—	2	2	no	—
137	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
138	#340	C₂²×C₇	1	4	yes	—
139	#336	C₂²×C₇	1	2	yes	—
140	C₂³×C₇	—	2	4	no	—
141	C₂³×C₇	—	2	4	no	—
142	C₂³×C₇	—	2	4	no	—
143	C₂³×C₇	—	4	2	no	—
144	C₂³×C₇	—	4	2	no	—
145	C₂³×C₇	—	4	2	no	—
146	C₂³×C₇	—	4	2	no	—
147	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
148	C₇×D₄	—	2	4	no	—
149	C₇×D₄	—	2	4	no	—
150	C₇×D₄	—	2	4	no	—
151	C₇×D₄	C₂×C₄⋊C₄	1	8	yes	complemented
152	C₂×C₄×C₇	—	2	2	no	—
153	C₂×C₄×C₇	—	2	1	no	—
154	C₂×C₄×C₇	—	2	2	no	—
155	C₂×C₄×C₇	—	2	1	no	—
156	C₂×C₄×C₇	—	2	4	no	—
157	C₂×C₄×C₇	—	2	2	no	—
158	C₂×C₄×C₇	—	2	2	no	—
159	C₂×C₄×C₇	—	2	2	no	—
160	C₂×C₄×C₇	—	4	2	no	—
161	C₂×C₄×C₇	—	4	2	no	—
162	C₂×C₄×C₇	—	4	16	no	—
163	C₂×C₄×C₇	—	4	4	no	—
164	C₂×C₄×C₇	—	4	4	no	—
165	C₂×C₄×C₇	—	4	4	no	—
166	C₂×C₄×C₇	—	8	16	no	—
167	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₇	C₂×D₈	1	4	yes	—
170	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
171	C₂×C₄×C₇	#135	1	2	yes	—
172	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
178	C₇×C₈	—	2	2	no	—
179	C₇×C₈	—	4	2	no	—
180	C₇×C₈	C₂×C₄⋊C₄	1	4	yes	complemented
181	C₂²×D₄	C₂³×C₇	1	2	yes	—
182	C₂³×C₄	—	2	2	no	—
183	C₂³×C₄	—	2	4	no	—
184	C₂×D₈	C₂×C₄×C₇	1	4	yes	—
185	C₂×D₈	C₇×D₄	1	4	yes	—
186	C₂×D₈	C₇×Q₈	1	4	yes	—
187	C₂²×C₈	C₂³×C₇	1	2	yes	—
188	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
189	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
190	C₄×D₄	—	2	8	no	—
191	C₄×D₄	—	2	4	no	—
192	C₄×D₄	—	4	4	no	—
193	C₄×D₄	C₂×C₄×C₇	1	8	yes	complemented
194	C₂×C₄⋊C₄	—	2	2	no	—
195	C₂×C₄⋊C₄	—	2	4	no	—
196	C₂×C₄⋊C₄	—	2	2	no	—
197	C₂×C₄⋊C₄	—	4	8	no	—
198	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
199	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
200	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
201	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
202	C₂×C₂²⋊C₄	—	2	2	no	—
203	C₂×C₂²⋊C₄	—	2	4	no	—
204	C₂×C₄²	C₂³×C₇	1	2	yes	—
205	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
206	#107	—	2	4	no	—
207	#107	—	4	2	no	—
208	#107	C₂×C₄×C₇	1	4	yes	complemented
209	C₄⋊C₈	—	2	2	no	—
210	#102	—	2	8	no	—
211	#102	C₂×C₄×C₇	1	8	yes	complemented
212	C₄×C₈	—	2	4	no	—
213	C₄×C₈	C₂×C₄×C₇	1	4	yes	complemented
214	#95	—	2	4	no	—
215	#95	C₇×D₄	1	2	yes	—
216	C₂²×C₇	—	2	8	no	—
217	C₂²×C₇	—	4	4	no	—
218	C₂²×C₇	—	4	4	no	—
219	C₂²×C₇	—	4	4	no	—
220	C₂²×C₇	—	4	4	no	—
221	C₂²×C₇	—	4	4	no	—
222	C₂²×C₇	—	4	4	no	—
223	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
224	C₂²×C₇	D₄²	1	1	yes	characteristic
225	C₂²×C₇	D₄×Q₈	1	1	yes	characteristic
226	C₂²×C₇	C₂²×D₈	1	1	yes	characteristic
227	C₂²×C₇	C₂×#135	1	1	yes	characteristic
228	C₂²×C₇	#576	1	1	yes	characteristic
229	C₂²×C₇	#578	1	1	yes	characteristic
230	C₄×C₇	—	2	2	no	—
231	C₄×C₇	—	2	4	no	—
232	C₄×C₇	—	4	4	no	—
233	C₄×C₇	—	4	2	no	—
234	C₄×C₇	—	8	4	no	—
235	C₄×C₇	C₄×D₈	1	4	yes	complemented
236	C₄×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
237	C₄×C₇	#520	1	1	yes	characteristic
238	C₄×C₇	#547	1	1	yes	characteristic
239	C₄×C₇	#554	1	1	yes	characteristic
240	C₂⁴	—	2	2	no	—
241	C₂×D₄	—	2	2	no	—
242	C₂×D₄	—	2	2	no	—
243	C₂×D₄	—	2	2	no	—
244	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
245	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
246	C₂×D₄	C₂×C₇×Q₈	1	4	yes	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	8	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	4	8	no	—
251	C₂²×C₄	—	4	4	no	—
252	C₂²×C₄	—	4	4	no	—
253	C₂²×C₄	—	4	8	no	—
254	C₂²×C₄	—	8	4	no	—
255	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
256	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
258	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
259	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
260	D₈	C₇×C₄⋊C₄	1	16	yes	direct product factor
261	C₂×C₈	—	2	1	no	—
262	C₂×C₈	—	2	1	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
267	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
268	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
269	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	2	4	no	—
273	C₄⋊C₄	—	2	4	no	—
274	C₄⋊C₄	—	4	8	no	—
275	C₄⋊C₄	—	4	4	no	—
276	C₄⋊C₄	—	8	2	no	—
277	C₄⋊C₄	C₇×D₈	1	4	yes	direct product factor
278	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
279	C₂²⋊C₄	—	2	8	no	—
280	C₂²⋊C₄	—	4	8	no	—
281	C₄²	—	2	2	no	—
282	C₄²	—	2	2	no	—
283	C₄²	C₂²×C₄×C₇	1	2	yes	—
284	C₄²	C₇×#41	1	2	yes	—
285	C₂×C₇	—	4	8	no	—
286	C₂×C₇	D₄×C₄⋊C₄	1	1	yes	characteristic
287	C₂×C₇	C₂×C₄×D₈	1	1	yes	characteristic
288	C₂×C₇	#2951	1	1	yes	characteristic
289	C₂×C₇	D₄×D₈	1	1	yes	characteristic
290	C₂×C₇	#3283	1	1	yes	characteristic
291	C₂×C₇	Q₈×D₈	1	1	yes	characteristic
292	C₂×C₇	#3380	1	1	yes	characteristic
293	C₂³	—	2	4	no	—
294	C₂³	—	2	4	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	4	2	no	—
297	C₂³	—	4	2	no	—
298	C₂³	—	4	2	no	—
299	C₂³	—	4	2	no	—
300	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
301	D₄	—	2	4	no	—
302	D₄	—	2	4	no	—
303	D₄	—	2	4	no	—
304	D₄	C₂×C₇×C₄⋊C₄	1	8	yes	complemented
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	16	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	8	16	no	—
320	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
321	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
322	C₂×C₄	C₂×C₇×D₈	1	4	yes	—
323	C₂×C₄	C₂×C₇×D₈	1	2	yes	—
324	C₂×C₄	C₇×#135	1	2	yes	—
325	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
326	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
327	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
328	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
329	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
331	C₈	—	2	2	no	—
332	C₈	—	4	2	no	—
333	C₈	C₂×C₇×C₄⋊C₄	1	4	yes	complemented
334	C₇	C₄⋊C₄×D₈	1	1	yes	characteristic, direct product factor, Sylow
335	C₂²	—	2	8	no	—
336	C₂²	—	4	4	no	—
337	C₂²	—	4	4	no	—
338	C₂²	—	4	4	no	—
339	C₂²	—	4	4	no	—
340	C₂²	—	4	4	no	—
341	C₂²	—	4	4	no	—
342	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
343	C₂²	C₇×D₄²	1	1	yes	characteristic
344	C₂²	C₇×D₄×Q₈	1	1	yes	characteristic
345	C₂²	C₂²×C₇×D₈	1	1	yes	characteristic
346	C₂²	C₂×C₇×#135	1	1	yes	characteristic
347	C₂²	C₇×#576	1	1	yes	characteristic
348	C₂²	C₇×#578	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	2	4	no	—
351	C₄	—	4	4	no	—
352	C₄	—	4	2	no	—
353	C₄	—	8	4	no	—
354	C₄	C₄×C₇×D₈	1	4	yes	complemented
355	C₄	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
356	C₄	C₇×#520	1	1	yes	characteristic
357	C₄	C₇×#547	1	1	yes	characteristic
358	C₄	C₇×#554	1	1	yes	characteristic
359	C₂	—	4	8	no	—
360	C₂	C₇×D₄×C₄⋊C₄	1	1	yes	characteristic
361	C₂	C₂×C₄×C₇×D₈	1	1	yes	characteristic
362	C₂	C₇×#2951	1	1	yes	characteristic
363	C₂	C₇×D₄×D₈	1	1	yes	characteristic
364	C₂	C₇×#3283	1	1	yes	characteristic
365	C₂	C₇×Q₈×D₈	1	1	yes	characteristic
366	C₂	C₇×#3380	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄×C₇×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×D₄×C₄⋊C₄	C₂	semidirect
4. C₇×#1942	C₂	semidirect
5. C₇×#1862	C₂	semidirect
6. C₇×#1845	C₂	semidirect
7. C₇×#1802	C₂	semidirect
8. C₇×C₈×C₄⋊C₄	C₂	semidirect
14. C₄×C₇×D₈	C₄	semidirect
30. C₄⋊C₄×D₈	C₇	direct (N × H)
43. C₄×C₇×D₄	C₂×C₄	semidirect
58. C₇×#107	C₂×C₄	semidirect
61. C₇×#102	C₂×C₄	semidirect
63. C₄×C₇×C₈	C₂×C₄	semidirect
68. D₄×C₄⋊C₄	C₂×C₇	semidirect
69. #1942	C₂×C₇	semidirect
70. #1862	C₂×C₇	semidirect
71. #1845	C₂×C₇	semidirect
72. #1802	C₂×C₇	semidirect
73. C₈×C₄⋊C₄	C₂×C₇	semidirect
94. C₇×D₈	C₄⋊C₄	direct (N × H)
111. C₇×C₄⋊C₄	D₈	direct (N × H)
124. C₄×D₈	C₄×C₇	semidirect
151. C₇×D₄	C₂×C₄⋊C₄	semidirect
180. C₇×C₈	C₂×C₄⋊C₄	semidirect
193. C₄×D₄	C₂×C₄×C₇	semidirect
208. #107	C₂×C₄×C₇	semidirect
211. #102	C₂×C₄×C₇	semidirect
213. C₄×C₈	C₂×C₄×C₇	semidirect
235. C₄×C₇	C₄×D₈	semidirect
260. D₈	C₇×C₄⋊C₄	direct (N × H)
277. C₄⋊C₄	C₇×D₈	direct (N × H)
304. D₄	C₂×C₇×C₄⋊C₄	semidirect
333. C₈	C₂×C₇×C₄⋊C₄	semidirect
334. C₇	C₄⋊C₄×D₈	direct (N × H)
354. C₄	C₄×C₇×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₇×D₈	2
C₇×D₄×C₄⋊C₄	2
C₇×#1942	2
C₇×#1862	2
C₇×#1845	2
C₇×#1802	2
C₇×C₈×C₄⋊C₄	2
C₄⋊C₄×D₈	7

Subgroups — C7×C4⋊C4×D8 #13199896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₄⋊C₄×D₈ #13199896