Subgroups — C₇×D₄×#108 #13199883

Order 1792.

894 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₄×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₇×#108	C₂	1	2	yes	maximal, complemented
4	C₇×#1950	C₂	1	2	yes	maximal, complemented
5	C₇×#1855	C₂	1	4	yes	maximal, complemented
6	C₇×#1848	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1810	C₂	1	2	yes	maximal, complemented
8	C₄×C₇×#108	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×M₁₆	C₂²	1	4	yes	—
10	C₂³×C₇×C₈	C₂²	1	2	yes	—
11	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
12	C₇×#436	—	2	2	no	—
13	C₇×#435	—	2	4	no	—
14	C₇×C₈×D₄	—	2	2	no	—
15	C₇×C₈×D₄	C₄	1	4	yes	—
16	C₇×C₈×D₄	C₄	1	2	yes	—
17	C₇×C₈×D₄	C₄	1	2	yes	—
18	C₂×C₇×#108	—	2	8	no	—
19	C₂×C₇×#108	C₂²	1	2	yes	—
20	C₂×C₇×#108	C₂²	1	4	yes	—
21	C₂×C₇×#108	C₂²	1	1	yes	characteristic
22	C₂×C₇×#108	C₂²	1	2	yes	—
23	C₂×C₇×#108	C₂²	1	1	yes	characteristic
24	C₇×#423	C₂²	1	2	yes	—
25	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₇×#407	C₂²	1	4	yes	—
27	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₄×C₇×M₁₆	C₂²	1	2	yes	—
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₇×#341	C₂²	1	2	yes	—
31	C₇×#341	C₂²	1	4	yes	—
32	D₄×#108	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂²×C₇×D₄	Q₈	1	1	yes	characteristic
34	C₂³×C₄×C₇	C₂³	1	2	yes	—
35	C₂×C₇×M₁₆	—	2	4	no	—
36	C₂×C₇×M₁₆	—	2	8	no	—
37	C₂×C₇×M₁₆	—	4	4	no	—
38	C₂×C₇×M₁₆	C₂³	1	2	yes	—
39	C₂×C₇×M₁₆	C₂³	1	4	yes	—
40	C₂×C₇×M₁₆	C₂³	1	2	yes	—
41	C₂²×C₇×C₈	—	2	4	no	—
42	C₂²×C₇×C₈	—	2	4	no	—
43	C₂²×C₇×C₈	—	2	4	no	—
44	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
45	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
46	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₇×C₈	C₂³	1	2	yes	—
48	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
49	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
50	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
51	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
52	C₄×C₇×D₄	D₄	1	1	yes	characteristic
53	C₄×C₇×D₄	D₄	1	2	yes	—
54	C₄×C₇×D₄	D₄	1	1	yes	characteristic
55	C₂×C₇×C₄⋊C₄	Q₈	1	1	yes	characteristic
56	C₂×C₇×C₂²⋊C₄	Q₈	1	2	yes	—
57	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
58	C₇×#108	—	2	8	no	—
59	C₇×#108	—	2	4	no	—
60	C₇×#108	—	2	2	no	—
61	C₇×#108	—	4	2	no	—
62	C₇×#108	D₄	1	4	yes	direct product factor
63	C₇×C₄⋊C₈	—	2	2	no	—
64	C₇×C₄⋊C₈	—	2	2	no	—
65	C₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
66	C₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
67	C₇×C₂²⋊C₈	—	2	4	no	—
68	C₇×C₂²⋊C₈	—	2	4	no	—
69	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
70	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
71	C₇×#97	—	2	2	no	—
72	C₄×C₇×C₈	—	2	2	no	—
73	C₄×C₇×C₈	C₂×C₄	1	2	yes	—
74	C₄×C₇×C₈	C₂×C₄	1	2	yes	—
75	D₄×M₁₆	C₂×C₇	1	2	yes	—
76	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic
77	C₂²×#108	C₂×C₇	1	2	yes	complemented
78	#1950	C₂×C₇	1	2	yes	complemented
79	#1855	C₂×C₇	1	4	yes	complemented
80	#1848	C₂×C₇	1	1	yes	characteristic, complemented
81	#1810	C₂×C₇	1	2	yes	complemented
82	C₄×#108	C₂×C₇	1	1	yes	characteristic, complemented
83	C₂⁴×C₇	C₂×Q₈	1	2	yes	—
84	C₂×C₇×D₄	—	2	4	no	—
85	C₂×C₇×D₄	C₄⋊C₄	1	2	yes	—
86	C₂×C₇×D₄	C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₇×D₄	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₇	—	2	2	no	—
89	C₂²×C₄×C₇	—	2	2	no	—
90	C₂²×C₄×C₇	—	2	2	no	—
91	C₂²×C₄×C₇	—	2	2	no	—
92	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
97	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
98	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
100	C₇×M₁₆	—	2	2	no	—
101	C₇×M₁₆	—	2	4	no	—
102	C₇×M₁₆	—	2	2	no	—
103	C₇×M₁₆	—	2	4	no	—
104	C₇×M₁₆	—	2	2	no	—
105	C₇×M₁₆	—	4	8	no	—
106	C₇×M₁₆	C₂×D₄	1	4	yes	—
107	C₂×C₇×C₈	—	2	2	no	—
108	C₂×C₇×C₈	—	2	2	no	—
109	C₂×C₇×C₈	—	2	2	no	—
110	C₂×C₇×C₈	—	2	1	no	—
111	C₂×C₇×C₈	—	2	1	no	—
112	C₂×C₇×C₈	—	2	8	no	—
113	C₂×C₇×C₈	—	2	8	no	—
114	C₂×C₇×C₈	—	2	2	no	—
115	C₂×C₇×C₈	—	2	4	no	—
116	C₂×C₇×C₈	—	4	8	no	—
117	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
118	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
119	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
120	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
121	C₂×C₇×C₈	#41	1	2	yes	—
122	C₇×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
123	C₇×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
124	C₇×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
125	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
126	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
127	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
128	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
129	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×M₁₆	C₂²×C₇	1	4	yes	—
134	C₂³×C₈	C₂²×C₇	1	2	yes	—
135	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
136	#436	—	2	2	no	—
137	#435	—	2	4	no	—
138	C₈×D₄	—	2	2	no	—
139	C₈×D₄	C₄×C₇	1	4	yes	—
140	C₈×D₄	C₄×C₇	1	2	yes	—
141	C₈×D₄	C₄×C₇	1	2	yes	—
142	C₂×#108	—	2	8	no	—
143	C₂×#108	C₂²×C₇	1	1	yes	characteristic
144	C₂×#108	C₂²×C₇	1	2	yes	—
145	C₂×#108	C₂²×C₇	1	4	yes	—
146	C₂×#108	C₂²×C₇	1	2	yes	—
147	C₂×#108	C₂²×C₇	1	1	yes	characteristic
148	#423	C₂²×C₇	1	2	yes	—
149	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
150	#407	C₂²×C₇	1	4	yes	—
151	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
152	C₄×M₁₆	C₂²×C₇	1	2	yes	—
153	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
154	#341	C₂²×C₇	1	4	yes	—
155	#341	C₂²×C₇	1	2	yes	—
156	C₂³×C₇	—	2	2	no	—
157	C₂³×C₇	—	2	2	no	—
158	C₂³×C₇	—	2	4	no	—
159	C₂³×C₇	—	4	2	no	—
160	C₂³×C₇	C₂×C₄⋊C₄	1	2	yes	—
161	C₂³×C₇	C₂×C₄⋊C₄	1	2	yes	—
162	C₂³×C₇	C₂²×Q₈	1	1	yes	characteristic
163	C₇×D₄	—	2	4	no	—
164	C₇×D₄	—	2	2	no	—
165	C₇×D₄	#108	1	4	yes	direct product factor
166	C₂×C₄×C₇	—	2	2	no	—
167	C₂×C₄×C₇	—	2	2	no	—
168	C₂×C₄×C₇	—	2	2	no	—
169	C₂×C₄×C₇	—	2	2	no	—
170	C₂×C₄×C₇	—	2	2	no	—
171	C₂×C₄×C₇	—	2	2	no	—
172	C₂×C₄×C₇	—	2	2	no	—
173	C₂×C₄×C₇	—	2	2	no	—
174	C₂×C₄×C₇	—	2	2	no	—
175	C₂×C₄×C₇	—	2	2	no	—
176	C₂×C₄×C₇	—	2	2	no	—
177	C₂×C₄×C₇	—	4	1	no	—
178	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
182	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
183	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
189	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
190	C₇×C₈	—	2	4	no	—
191	C₇×C₈	—	2	2	no	—
192	C₇×C₈	—	2	4	no	—
193	C₇×C₈	—	4	4	no	—
194	C₇×C₈	—	4	2	no	—
195	C₇×C₈	C₄×D₄	1	4	yes	—
196	C₂²×D₄	C₇×Q₈	1	1	yes	characteristic
197	C₂³×C₄	C₂³×C₇	1	2	yes	—
198	C₂×M₁₆	—	2	4	no	—
199	C₂×M₁₆	—	2	8	no	—
200	C₂×M₁₆	—	4	4	no	—
201	C₂×M₁₆	C₂³×C₇	1	4	yes	—
202	C₂×M₁₆	C₂³×C₇	1	2	yes	—
203	C₂×M₁₆	C₂³×C₇	1	2	yes	—
204	C₂²×C₈	—	2	4	no	—
205	C₂²×C₈	—	2	4	no	—
206	C₂²×C₈	—	2	4	no	—
207	C₂²×C₈	C₂×C₄×C₇	1	4	yes	—
208	C₂²×C₈	C₂×C₄×C₇	1	4	yes	—
209	C₂²×C₈	C₂³×C₇	1	2	yes	—
210	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
211	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
212	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
213	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
214	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
215	C₄×D₄	C₇×D₄	1	1	yes	characteristic
216	C₄×D₄	C₇×D₄	1	2	yes	—
217	C₄×D₄	C₇×D₄	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₇×Q₈	1	1	yes	characteristic
219	C₂×C₂²⋊C₄	C₇×Q₈	1	2	yes	—
220	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
221	#108	—	2	8	no	—
222	#108	—	2	4	no	—
223	#108	—	2	2	no	—
224	#108	—	4	2	no	—
225	#108	C₇×D₄	1	4	yes	direct product factor
226	C₄⋊C₈	—	2	2	no	—
227	C₄⋊C₈	—	2	2	no	—
228	C₄⋊C₈	C₂×C₄×C₇	1	2	yes	—
229	C₄⋊C₈	C₂×C₄×C₇	1	2	yes	—
230	C₂²⋊C₈	—	2	4	no	—
231	C₂²⋊C₈	—	2	4	no	—
232	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	—
233	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	—
234	#97	—	2	2	no	—
235	C₄×C₈	—	2	2	no	—
236	C₄×C₈	C₂×C₄×C₇	1	2	yes	—
237	C₄×C₈	C₂×C₄×C₇	1	2	yes	—
238	C₂²×C₇	—	2	2	no	—
239	C₂²×C₇	—	2	1	no	—
240	C₂²×C₇	—	2	1	no	—
241	C₂²×C₇	—	2	2	no	—
242	C₂²×C₇	—	2	2	no	—
243	C₂²×C₇	—	2	2	no	—
244	C₂²×C₇	—	2	2	no	—
245	C₂²×C₇	—	4	4	no	—
246	C₂²×C₇	—	4	4	no	—
247	C₂²×C₇	C₂×#108	1	4	yes	complemented
248	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
249	C₂²×C₇	D₄×Q₈	1	1	yes	characteristic
250	C₂²×C₇	#554	1	1	yes	characteristic
251	C₄×C₇	—	2	2	no	—
252	C₄×C₇	—	2	2	no	—
253	C₄×C₇	—	2	1	no	—
254	C₄×C₇	—	2	1	no	—
255	C₄×C₇	—	2	1	no	—
256	C₄×C₇	C₂×#108	1	2	yes	complemented
257	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
258	C₄×C₇	#520	1	1	yes	characteristic
259	C₄×C₇	D₄²	1	1	yes	characteristic
260	C₄×C₇	#547	1	1	yes	characteristic
261	C₂⁴	C₂×C₇×Q₈	1	2	yes	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	C₇×C₄⋊C₄	1	2	yes	—
264	C₂×D₄	C₇×C₄⋊C₄	1	1	yes	characteristic
265	C₂×D₄	C₇×C₄⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
272	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
273	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
274	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
276	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
277	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
278	M₁₆	—	2	2	no	—
279	M₁₆	—	2	4	no	—
280	M₁₆	—	2	2	no	—
281	M₁₆	—	2	4	no	—
282	M₁₆	—	2	2	no	—
283	M₁₆	—	4	8	no	—
284	M₁₆	C₂×C₇×D₄	1	4	yes	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	8	no	—
291	C₂×C₈	—	2	8	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	4	8	no	—
295	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
296	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
297	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
298	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
299	C₂×C₈	C₇×#41	1	2	yes	—
300	C₄⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
301	C₄⋊C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
302	C₄⋊C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
303	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
304	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
305	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
306	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
307	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
308	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
309	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
310	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
311	C₂×C₇	—	2	1	no	—
312	C₂×C₇	—	2	1	no	—
313	C₂×C₇	—	2	4	no	—
314	C₂×C₇	—	4	2	no	—
315	C₂×C₇	D₄×C₄⋊C₄	1	1	yes	characteristic
316	C₂×C₇	C₂²×#108	1	1	yes	characteristic
317	C₂×C₇	#2916	1	1	yes	characteristic
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	4	2	no	—
322	C₂³	C₂×C₇×C₄⋊C₄	1	2	yes	—
323	C₂³	C₂×C₇×C₄⋊C₄	1	2	yes	—
324	C₂³	C₂²×C₇×Q₈	1	1	yes	characteristic
325	D₄	—	2	4	no	—
326	D₄	—	2	2	no	—
327	D₄	C₇×#108	1	4	yes	direct product factor
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
341	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
342	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
344	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
345	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
346	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
347	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
348	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
349	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
350	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
352	C₈	—	2	4	no	—
353	C₈	—	2	2	no	—
354	C₈	—	2	4	no	—
355	C₈	—	4	4	no	—
356	C₈	—	4	2	no	—
357	C₈	C₄×C₇×D₄	1	4	yes	—
358	C₇	D₄×#108	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	C₂×C₇×#108	1	4	yes	complemented
369	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
370	C₂²	C₇×D₄×Q₈	1	1	yes	characteristic
371	C₂²	C₇×#554	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	C₂×C₇×#108	1	2	yes	complemented
378	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
379	C₄	C₇×#520	1	1	yes	characteristic
380	C₄	C₇×D₄²	1	1	yes	characteristic
381	C₄	C₇×#547	1	1	yes	characteristic
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	2	4	no	—
385	C₂	—	4	2	no	—
386	C₂	C₇×D₄×C₄⋊C₄	1	1	yes	characteristic
387	C₂	C₂²×C₇×#108	1	1	yes	characteristic
388	C₂	C₇×#2916	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	C₂²×C₄⋊C₄
prime radical	C₂²×C₇×D₄	Q₈
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
3. C₂²×C₇×#108	C₂	semidirect
4. C₇×#1950	C₂	semidirect
5. C₇×#1855	C₂	semidirect
6. C₇×#1848	C₂	semidirect
7. C₇×#1810	C₂	semidirect
8. C₄×C₇×#108	C₂	semidirect
32. D₄×#108	C₇	direct (N × H)
62. C₇×#108	D₄	direct (N × H)
77. C₂²×#108	C₂×C₇	semidirect
78. #1950	C₂×C₇	semidirect
79. #1855	C₂×C₇	semidirect
80. #1848	C₂×C₇	semidirect
81. #1810	C₂×C₇	semidirect
82. C₄×#108	C₂×C₇	semidirect
165. C₇×D₄	#108	direct (N × H)
225. #108	C₇×D₄	direct (N × H)
247. C₂²×C₇	C₂×#108	semidirect
256. C₄×C₇	C₂×#108	semidirect
327. D₄	C₇×#108	direct (N × H)
358. C₇	D₄×#108	direct (N × H)
368. C₂²	C₂×C₇×#108	semidirect
377. C₄	C₂×C₇×#108	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₄×M₁₆	2
C₂×C₇×C₈×D₄	2
C₂²×C₇×#108	2
C₇×#1950	2
C₇×#1855	2
C₇×#1848	2
C₇×#1810	2
C₄×C₇×#108	2
D₄×#108	7

Subgroups — C7×D4×#108 #13199883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₄×#108 #13199883