Subgroups — C₇×Q₈×#104 #13199744

Order 1792.

1096 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₈×#41	C₂	1	1	yes	maximal, characteristic
2	C₇×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1994	C₂	1	3	yes	maximal, complemented
5	C₇×#1986	C₂	1	3	yes	maximal, complemented
6	C₇×#1806	C₂	1	3	yes	maximal
7	C₄×C₇×#104	C₂	1	3	yes	maximal
8	C₇×Q₈²	C₄	1	1	yes	characteristic, complemented
9	C₇×#557	C₄	1	3	yes	complemented
10	C₇×#554	—	2	3	no	—
11	C₇×#554	C₄	1	3	yes	complemented
12	C₇×D₄×Q₈	—	2	1	no	—
13	C₇×D₄×Q₈	C₄	1	1	yes	characteristic, complemented
14	C₇×#533	—	2	3	no	—
15	C₇×#533	C₂²	1	3	yes	—
16	C₄×C₇×#41	C₂²	1	3	yes	—
17	C₂×C₄×C₇×Q₈	—	2	1	no	—
18	C₂×C₄×C₇×Q₈	—	2	1	no	—
19	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
20	C₇×#446	—	2	3	no	—
21	C₇×C₈×Q₈	—	2	1	no	—
22	C₇×#423	C₂²	1	3	yes	—
23	C₂×C₇×#104	C₂²	1	3	yes	—
24	C₂×C₇×#104	C₂²	1	1	yes	characteristic
25	C₄×C₇×M₁₆	C₂²	1	3	yes	—
26	C₄×C₇×C₄⋊C₄	—	2	3	no	—
27	C₄×C₇×C₄⋊C₄	C₂²	1	3	yes	—
28	C₄³×C₇	C₂²	1	3	yes	—
29	C₇×#339	C₂²	1	3	yes	—
30	C₇×#339	C₂²	1	6	yes	—
31	C₇×#339	C₂²	1	3	yes	—
32	Q₈×#104	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂×C₇×#41	C₂³	1	1	yes	characteristic
34	C₂²×C₇×Q₈	—	2	1	no	—
35	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
36	C₂×C₇×M₁₆	C₂³	1	3	yes	—
37	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
38	C₇×C₄⋊Q₈	—	2	3	no	—
39	C₇×C₄⋊Q₈	—	2	3	no	—
40	C₇×C₄⋊Q₈	C₂×C₄	1	3	yes	—
41	C₇×C₄⋊Q₈	C₂×C₄	1	3	yes	—
42	C₇×#125	—	2	6	no	—
43	C₇×#125	C₂×C₄	1	6	yes	—
44	C₇×C₂²⋊Q₈	—	2	3	no	—
45	C₇×C₂²⋊Q₈	—	2	3	no	—
46	C₇×C₂²⋊Q₈	—	2	3	no	—
47	C₇×C₂²⋊Q₈	—	2	3	no	—
48	C₇×C₂²⋊Q₈	—	2	6	no	—
49	C₄×C₇×Q₈	—	2	8	no	—
50	C₄×C₇×Q₈	—	2	1	no	—
51	C₄×C₇×Q₈	—	2	3	no	—
52	C₄×C₇×Q₈	—	2	3	no	—
53	C₄×C₇×Q₈	—	2	3	no	—
54	C₄×C₇×Q₈	C₂×C₄	1	3	yes	—
55	C₄×C₇×Q₈	C₂×C₄	1	3	yes	—
56	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
57	C₄×C₇×Q₈	C₂×C₄	1	3	yes	—
58	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
59	C₄×C₇×Q₈	D₄	1	3	yes	—
60	C₄×C₇×D₄	—	2	3	no	—
61	C₄×C₇×D₄	—	2	3	no	—
62	C₄×C₇×D₄	C₂×C₄	1	3	yes	—
63	C₄×C₇×D₄	C₂×C₄	1	3	yes	—
64	C₇×#117	—	2	3	no	—
65	C₇×#117	C₂³	1	3	yes	—
66	C₂×C₇×C₄⋊C₄	—	2	3	no	—
67	C₂×C₇×C₄⋊C₄	—	2	3	no	—
68	C₂×C₇×C₄⋊C₄	D₄	1	3	yes	—
69	C₂×C₄²×C₇	—	2	3	no	—
70	C₂×C₄²×C₇	—	2	3	no	—
71	C₂×C₄²×C₇	—	2	3	no	—
72	C₂×C₄²×C₇	C₂³	1	3	yes	—
73	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₇	C₂³	1	3	yes	—
75	C₇×C₄⋊C₈	—	2	3	no	—
76	C₇×C₄⋊C₈	—	2	3	no	—
77	C₇×#104	—	2	6	no	—
78	C₇×#104	Q₈	1	4	yes	direct product factor
79	C₇×#97	—	2	3	no	—
80	C₄×C₇×C₈	—	2	3	no	—
81	C₇×#95	—	2	3	no	—
82	Q₈×#41	C₂×C₇	1	1	yes	characteristic
83	Q₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
84	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
85	#1994	C₂×C₇	1	3	yes	complemented
86	#1986	C₂×C₇	1	3	yes	complemented
87	#1806	C₂×C₇	1	3	yes	—
88	C₄×#104	C₂×C₇	1	3	yes	—
89	C₇×#41	—	2	1	no	—
90	C₇×#41	—	2	1	no	—
91	C₇×#41	C₂×Q₈	1	2	yes	—
92	C₇×#41	#41	1	2	yes	—
93	C₂×C₇×Q₈	—	2	4	no	—
94	C₂×C₇×Q₈	—	2	3	no	—
95	C₂×C₇×Q₈	—	2	3	no	—
96	C₂×C₇×Q₈	—	4	4	no	—
97	C₂×C₇×Q₈	C₂²⋊C₄	1	3	yes	—
98	C₂×C₇×Q₈	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₇×D₄	—	2	1	no	—
101	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₇	—	2	1	no	—
103	C₂²×C₄×C₇	—	2	1	no	—
104	C₂²×C₄×C₇	—	2	3	no	—
105	C₂²×C₄×C₇	—	2	3	no	—
106	C₂²×C₄×C₇	—	2	3	no	—
107	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
108	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
109	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
110	C₇×M₁₆	—	2	1	no	—
111	C₇×M₁₆	—	2	3	no	—
112	C₇×M₁₆	—	2	3	no	—
113	C₇×M₁₆	C₂×Q₈	1	2	yes	complemented
114	C₂×C₇×C₈	—	2	1	no	—
115	C₂×C₇×C₈	—	2	3	no	—
116	C₇×C₄⋊C₄	—	2	12	no	—
117	C₇×C₄⋊C₄	—	2	6	no	—
118	C₇×C₄⋊C₄	—	2	3	no	—
119	C₇×C₄⋊C₄	—	2	3	no	—
120	C₇×C₄⋊C₄	—	2	3	no	—
121	C₇×C₄⋊C₄	—	2	3	no	—
122	C₇×C₄⋊C₄	—	2	6	no	—
123	C₇×C₄⋊C₄	C₂²⋊C₄	1	3	yes	—
124	C₇×C₄⋊C₄	C₂²⋊C₄	1	6	yes	—
125	C₇×C₄⋊C₄	C₂²⋊C₄	1	3	yes	—
126	C₇×C₄⋊C₄	C₂²×C₄	1	3	yes	—
127	C₇×C₄⋊C₄	C₂²×C₄	1	3	yes	—
128	C₇×C₂²⋊C₄	—	2	3	no	—
129	C₇×C₂²⋊C₄	—	2	3	no	—
130	C₇×C₂²⋊C₄	—	2	3	no	—
131	C₄²×C₇	—	2	12	no	—
132	C₄²×C₇	—	2	3	no	—
133	C₄²×C₇	—	2	3	no	—
134	C₄²×C₇	—	2	3	no	—
135	C₄²×C₇	—	2	1	no	—
136	C₄²×C₇	—	2	3	no	—
137	C₄²×C₇	—	2	3	no	—
138	C₄²×C₇	—	4	6	no	—
139	C₄²×C₇	C₂²×C₄	1	3	yes	—
140	C₄²×C₇	C₂²×C₄	1	3	yes	—
141	C₄²×C₇	C₂×D₄	1	3	yes	—
142	C₄²×C₇	C₂×D₄	1	3	yes	—
143	C₄²×C₇	C₂×Q₈	1	2	yes	complemented
144	Q₈²	C₄×C₇	1	1	yes	characteristic, complemented
145	#557	C₄×C₇	1	3	yes	complemented
146	#554	—	2	3	no	—
147	#554	C₄×C₇	1	3	yes	complemented
148	D₄×Q₈	—	2	1	no	—
149	D₄×Q₈	C₄×C₇	1	1	yes	characteristic, complemented
150	#533	—	2	3	no	—
151	#533	C₂²×C₇	1	3	yes	—
152	C₄×#41	C₂²×C₇	1	3	yes	—
153	C₂×C₄×Q₈	—	2	1	no	—
154	C₂×C₄×Q₈	—	2	1	no	—
155	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
156	#446	—	2	3	no	—
157	C₈×Q₈	—	2	1	no	—
158	#423	C₂²×C₇	1	3	yes	—
159	C₂×#104	C₂²×C₇	1	3	yes	—
160	C₂×#104	C₂²×C₇	1	1	yes	characteristic
161	C₄×M₁₆	C₂²×C₇	1	3	yes	—
162	C₄×C₄⋊C₄	—	2	3	no	—
163	C₄×C₄⋊C₄	C₂²×C₇	1	3	yes	—
164	C₄³	C₂²×C₇	1	3	yes	—
165	#339	C₂²×C₇	1	6	yes	—
166	#339	C₂²×C₇	1	3	yes	—
167	#339	C₂²×C₇	1	3	yes	—
168	C₂³×C₇	—	2	1	no	—
169	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
170	C₇×Q₈	—	2	1	no	—
171	C₇×Q₈	—	2	6	no	—
172	C₇×Q₈	—	4	6	no	—
173	C₇×Q₈	—	8	3	no	—
174	C₇×Q₈	#104	1	4	yes	direct product factor
175	C₇×Q₈	C₄×Q₈	1	2	yes	complemented
176	C₇×D₄	—	2	2	no	—
177	C₇×D₄	—	2	2	no	—
178	C₇×D₄	—	2	1	no	—
179	C₇×D₄	C₄×Q₈	1	2	yes	complemented
180	C₂×C₄×C₇	—	2	2	no	—
181	C₂×C₄×C₇	—	2	2	no	—
182	C₂×C₄×C₇	—	2	1	no	—
183	C₂×C₄×C₇	—	2	2	no	—
184	C₂×C₄×C₇	—	2	2	no	—
185	C₂×C₄×C₇	—	2	2	no	—
186	C₂×C₄×C₇	—	2	6	no	—
187	C₂×C₄×C₇	—	2	6	no	—
188	C₂×C₄×C₇	—	2	3	no	—
189	C₂×C₄×C₇	—	2	3	no	—
190	C₂×C₄×C₇	—	4	3	no	—
191	C₂×C₄×C₇	—	4	3	no	—
192	C₂×C₄×C₇	—	4	3	no	—
193	C₂×C₄×C₇	—	4	6	no	—
194	C₂×C₄×C₇	—	8	3	no	—
195	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	3	yes	—
196	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	3	yes	—
197	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	3	yes	—
198	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	3	yes	—
199	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
202	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
204	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
205	C₇×C₈	—	2	2	no	—
206	C₇×C₈	—	4	3	no	—
207	C₂×#41	C₂³×C₇	1	1	yes	characteristic
208	C₂²×Q₈	—	2	1	no	—
209	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
210	C₂×M₁₆	C₂³×C₇	1	3	yes	—
211	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
212	C₄⋊Q₈	—	2	3	no	—
213	C₄⋊Q₈	—	2	3	no	—
214	C₄⋊Q₈	C₂×C₄×C₇	1	3	yes	—
215	C₄⋊Q₈	C₂×C₄×C₇	1	3	yes	—
216	#125	—	2	6	no	—
217	#125	C₂×C₄×C₇	1	6	yes	—
218	C₂²⋊Q₈	—	2	3	no	—
219	C₂²⋊Q₈	—	2	3	no	—
220	C₂²⋊Q₈	—	2	3	no	—
221	C₂²⋊Q₈	—	2	3	no	—
222	C₂²⋊Q₈	—	2	6	no	—
223	C₄×Q₈	—	2	8	no	—
224	C₄×Q₈	—	2	1	no	—
225	C₄×Q₈	—	2	3	no	—
226	C₄×Q₈	—	2	3	no	—
227	C₄×Q₈	—	2	3	no	—
228	C₄×Q₈	C₂×C₄×C₇	1	3	yes	—
229	C₄×Q₈	C₂×C₄×C₇	1	3	yes	—
230	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
231	C₄×Q₈	C₂×C₄×C₇	1	3	yes	—
232	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
233	C₄×Q₈	C₇×D₄	1	3	yes	—
234	C₄×D₄	—	2	3	no	—
235	C₄×D₄	—	2	3	no	—
236	C₄×D₄	C₂×C₄×C₇	1	3	yes	—
237	C₄×D₄	C₂×C₄×C₇	1	3	yes	—
238	#117	—	2	3	no	—
239	#117	C₂³×C₇	1	3	yes	—
240	C₂×C₄⋊C₄	—	2	3	no	—
241	C₂×C₄⋊C₄	—	2	3	no	—
242	C₂×C₄⋊C₄	C₇×D₄	1	3	yes	—
243	C₂×C₄²	—	2	3	no	—
244	C₂×C₄²	—	2	3	no	—
245	C₂×C₄²	—	2	3	no	—
246	C₂×C₄²	C₂³×C₇	1	3	yes	—
247	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₇	1	3	yes	—
249	C₄⋊C₈	—	2	3	no	—
250	C₄⋊C₈	—	2	3	no	—
251	#104	—	2	6	no	—
252	#104	C₇×Q₈	1	4	yes	direct product factor
253	#97	—	2	3	no	—
254	C₄×C₈	—	2	3	no	—
255	#95	—	2	3	no	—
256	C₂²×C₇	—	2	1	no	—
257	C₂²×C₇	—	2	1	no	—
258	C₂²×C₇	—	2	2	no	—
259	C₂²×C₇	—	4	1	no	—
260	C₂²×C₇	—	4	1	no	—
261	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
262	C₂²×C₇	#548	1	1	yes	characteristic
263	C₂²×C₇	D₄×Q₈	1	1	yes	characteristic
264	C₄×C₇	—	2	4	no	—
265	C₄×C₇	—	2	2	no	—
266	C₄×C₇	—	2	3	no	—
267	C₄×C₇	—	2	3	no	—
268	C₄×C₇	—	2	3	no	—
269	C₄×C₇	—	4	6	no	—
270	C₄×C₇	—	4	3	no	—
271	C₄×C₇	—	4	3	no	—
272	C₄×C₇	C₂×#104	1	6	yes	—
273	C₄×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
274	C₄×C₇	#519	1	1	yes	characteristic
275	C₄×C₇	#548	1	1	yes	characteristic
276	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
277	#41	—	2	1	no	—
278	#41	—	2	1	no	—
279	#41	C₂×C₇×Q₈	1	2	yes	—
280	#41	C₇×#41	1	2	yes	—
281	C₂×Q₈	—	2	4	no	—
282	C₂×Q₈	—	2	3	no	—
283	C₂×Q₈	—	2	3	no	—
284	C₂×Q₈	—	4	4	no	—
285	C₂×Q₈	C₇×C₂²⋊C₄	1	3	yes	—
286	C₂×Q₈	C₇×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	3	no	—
293	C₂²×C₄	—	2	3	no	—
294	C₂²×C₄	—	2	3	no	—
295	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
296	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
297	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
298	M₁₆	—	2	1	no	—
299	M₁₆	—	2	3	no	—
300	M₁₆	—	2	3	no	—
301	M₁₆	C₂×C₇×Q₈	1	2	yes	complemented
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	3	no	—
304	C₄⋊C₄	—	2	12	no	—
305	C₄⋊C₄	—	2	6	no	—
306	C₄⋊C₄	—	2	3	no	—
307	C₄⋊C₄	—	2	3	no	—
308	C₄⋊C₄	—	2	3	no	—
309	C₄⋊C₄	—	2	3	no	—
310	C₄⋊C₄	—	2	6	no	—
311	C₄⋊C₄	C₇×C₂²⋊C₄	1	3	yes	—
312	C₄⋊C₄	C₇×C₂²⋊C₄	1	6	yes	—
313	C₄⋊C₄	C₇×C₂²⋊C₄	1	3	yes	—
314	C₄⋊C₄	C₂²×C₄×C₇	1	3	yes	—
315	C₄⋊C₄	C₂²×C₄×C₇	1	3	yes	—
316	C₂²⋊C₄	—	2	3	no	—
317	C₂²⋊C₄	—	2	3	no	—
318	C₂²⋊C₄	—	2	3	no	—
319	C₄²	—	2	12	no	—
320	C₄²	—	2	3	no	—
321	C₄²	—	2	3	no	—
322	C₄²	—	2	3	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	3	no	—
325	C₄²	—	2	3	no	—
326	C₄²	—	4	6	no	—
327	C₄²	C₂²×C₄×C₇	1	3	yes	—
328	C₄²	C₂²×C₄×C₇	1	3	yes	—
329	C₄²	C₂×C₇×D₄	1	3	yes	—
330	C₄²	C₂×C₇×D₄	1	3	yes	—
331	C₄²	C₂×C₇×Q₈	1	2	yes	complemented
332	C₂×C₇	—	2	1	no	—
333	C₂×C₇	—	2	1	no	—
334	C₂×C₇	—	4	2	no	—
335	C₂×C₇	Q₈×C₂²⋊C₄	1	1	yes	characteristic
336	C₂×C₇	C₂²×#104	1	1	yes	characteristic
337	C₂×C₇	#2901	1	1	yes	characteristic
338	C₂³	—	2	1	no	—
339	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
340	Q₈	—	2	1	no	—
341	Q₈	—	2	6	no	—
342	Q₈	—	4	6	no	—
343	Q₈	—	8	3	no	—
344	Q₈	C₇×#104	1	4	yes	direct product factor
345	Q₈	C₄×C₇×Q₈	1	2	yes	complemented
346	D₄	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	2	1	no	—
349	D₄	C₄×C₇×Q₈	1	2	yes	complemented
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	6	no	—
357	C₂×C₄	—	2	6	no	—
358	C₂×C₄	—	2	3	no	—
359	C₂×C₄	—	2	3	no	—
360	C₂×C₄	—	4	3	no	—
361	C₂×C₄	—	4	3	no	—
362	C₂×C₄	—	4	3	no	—
363	C₂×C₄	—	4	6	no	—
364	C₂×C₄	—	8	3	no	—
365	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	3	yes	—
366	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	3	yes	—
367	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	3	yes	—
368	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	3	yes	—
369	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
372	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
373	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
374	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	4	3	no	—
377	C₇	Q₈×#104	1	1	yes	characteristic, direct product factor, Sylow
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
384	C₂²	C₇×#548	1	1	yes	characteristic
385	C₂²	C₇×D₄×Q₈	1	1	yes	characteristic
386	C₄	—	2	4	no	—
387	C₄	—	2	3	no	—
388	C₄	—	2	3	no	—
389	C₄	—	2	3	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	6	no	—
392	C₄	—	4	3	no	—
393	C₄	—	4	3	no	—
394	C₄	C₂×C₇×#104	1	6	yes	—
395	C₄	C₂×C₄×C₇×Q₈	1	1	yes	characteristic
396	C₄	C₇×#519	1	1	yes	characteristic
397	C₄	C₇×#548	1	1	yes	characteristic
398	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
399	C₂	—	2	1	no	—
400	C₂	—	2	1	no	—
401	C₂	—	4	2	no	—
402	C₂	C₇×Q₈×C₂²⋊C₄	1	1	yes	characteristic
403	C₂	C₂²×C₇×#104	1	1	yes	characteristic
404	C₂	C₇×#2901	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×C₂²⋊C₄
prime radical	C₂×C₇×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×Q₈×M₁₆	C₂	semidirect
3. C₄²×C₇×Q₈	C₂	semidirect
4. C₇×#1994	C₂	semidirect
5. C₇×#1986	C₂	semidirect
8. C₇×Q₈²	C₄	semidirect
9. C₇×#557	C₄	semidirect
11. C₇×#554	C₄	semidirect
13. C₇×D₄×Q₈	C₄	semidirect
32. Q₈×#104	C₇	direct (N × H)
78. C₇×#104	Q₈	direct (N × H)
83. Q₈×M₁₆	C₂×C₇	semidirect
84. C₄²×Q₈	C₂×C₇	semidirect
85. #1994	C₂×C₇	semidirect
86. #1986	C₂×C₇	semidirect
113. C₇×M₁₆	C₂×Q₈	semidirect
143. C₄²×C₇	C₂×Q₈	semidirect
144. Q₈²	C₄×C₇	semidirect
145. #557	C₄×C₇	semidirect
147. #554	C₄×C₇	semidirect
149. D₄×Q₈	C₄×C₇	semidirect
174. C₇×Q₈	#104	direct (N × H)
175. C₇×Q₈	C₄×Q₈	semidirect
179. C₇×D₄	C₄×Q₈	semidirect
252. #104	C₇×Q₈	direct (N × H)
301. M₁₆	C₂×C₇×Q₈	semidirect
331. C₄²	C₂×C₇×Q₈	semidirect
344. Q₈	C₇×#104	direct (N × H)
345. Q₈	C₄×C₇×Q₈	semidirect
349. D₄	C₄×C₇×Q₈	semidirect
377. C₇	Q₈×#104	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×Q₈×#41	2
C₇×Q₈×M₁₆	2
C₄²×C₇×Q₈	2
C₇×#1994	2
C₇×#1986	2
C₇×#1806	2
C₄×C₇×#104	2
Q₈×#104	7

Subgroups — C7×Q8×#104 #13199744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×Q₈×#104 #13199744