Subgroups — C₂×#11725537 #13268707

Order 1792.

554 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#108	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6393	C₂	1	1	yes	maximal, characteristic
3	C₂²×#6386	C₂	1	1	yes	maximal, characteristic
4	#11725537	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₇×M₁₆	—	2	1	no	—
6	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
7	C₂²×#1136	—	2	1	no	—
8	C₂×C₇×#108	—	2	1	no	—
9	C₂×C₇×#108	—	2	1	no	—
10	C₂×C₇×#108	—	2	1	no	—
11	C₂×C₇×#108	C₄	1	2	yes	—
12	C₂×C₇×#108	C₄	1	2	yes	—
13	C₂×C₇×#108	C₂²	1	2	yes	—
14	C₂×#6393	—	2	1	no	—
15	C₂×#6393	—	2	1	no	—
16	C₂×#6393	—	2	1	no	—
17	C₂×#6393	C₄	1	2	yes	—
18	C₂×#6393	C₄	1	2	yes	—
19	C₂×#6393	C₂²	1	2	yes	—
20	C₂×#6386	—	2	1	no	—
21	C₂×#6386	—	2	1	no	—
22	C₂×#6386	—	2	1	no	—
23	C₂×#6386	—	2	1	no	—
24	C₂×#6386	C₄	1	2	yes	—
25	C₂×#6386	C₂²	1	2	yes	—
26	C₂²×C₇⋊C₁₆	C₄	1	2	yes	—
27	C₂×#1385	—	7	1	no	maximal, Sylow
28	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
29	C₂×C₇×M₁₆	—	2	2	no	—
30	C₂×C₇×M₁₆	—	2	2	no	—
31	C₂×C₇×M₁₆	—	2	2	no	—
32	C₂×C₇×M₁₆	—	4	1	no	—
33	C₂×C₇×M₁₆	—	4	1	no	—
34	C₂×C₇×M₁₆	—	4	1	no	—
35	C₂²×C₇×C₈	—	4	1	no	—
36	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
43	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
44	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
45	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
46	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
47	C₂²×C₇×C₈	Q₈	1	1	yes	characteristic
48	C₂²×C₇×C₈	Q₈	1	1	yes	characteristic
49	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
50	C₂×#1136	—	2	2	no	—
51	C₂×#1136	—	2	2	no	—
52	C₂×#1136	—	2	2	no	—
53	C₂×#1136	—	4	1	no	—
54	C₂×#1136	—	4	1	no	—
55	C₂×#1136	—	4	1	no	—
56	C₂²×C₇⋊C₈	—	4	1	no	—
57	C₇×#108	—	2	2	no	—
58	C₇×#108	—	2	2	no	—
59	C₇×#108	—	2	2	no	—
60	C₇×#108	C₂×C₄	1	4	yes	—
61	#6393	—	2	2	no	—
62	#6393	—	2	2	no	—
63	#6393	—	2	2	no	—
64	#6393	C₂×C₄	1	4	yes	—
65	#6386	—	2	2	no	—
66	#6386	—	2	2	no	—
67	#6386	—	2	2	no	—
68	#6386	—	2	2	no	—
69	C₂×C₇⋊C₁₆	—	2	2	no	—
70	C₂×C₇⋊C₁₆	—	2	2	no	—
71	C₂×C₇⋊C₁₆	C₂×C₄	1	4	yes	—
72	C₂²×M₃₂	—	7	1	no	—
73	C₂²×#108	—	7	1	no	—
74	C₂²×#108	D₇	1	1	yes	characteristic
75	#1385	—	7	4	no	—
76	C₂⁴×C₇	Q₁₆	1	1	yes	characteristic
77	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇	D₈	1	1	yes	characteristic
84	C₂²×C₄×C₇	D₈	1	1	yes	characteristic
85	C₂²×C₄×C₇	SD₁₆	1	1	yes	characteristic
86	C₂²×C₄×C₇	SD₁₆	1	1	yes	characteristic
87	C₂²×C₄×C₇	SD₁₆	1	1	yes	characteristic
88	C₂²×C₄×C₇	SD₁₆	1	1	yes	characteristic
89	C₂²×C₄×C₇	Q₁₆	1	1	yes	characteristic
90	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
91	C₇×M₁₆	—	2	4	no	—
92	C₇×M₁₆	—	4	2	no	—
93	C₇×M₁₆	—	4	2	no	—
94	C₇×M₁₆	—	4	2	no	—
95	C₂×C₇×C₈	—	4	2	no	—
96	C₂×C₇×C₈	—	4	2	no	—
97	C₂×C₇×C₈	—	4	2	no	—
98	C₂×C₇×C₈	C₄²	1	1	yes	characteristic
99	C₂×C₇×C₈	C₄²	1	1	yes	characteristic
100	C₂×C₇×C₈	C₄²	1	1	yes	characteristic
101	C₂×C₇×C₈	C₄²	1	1	yes	characteristic
102	C₂×C₇×C₈	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₇×C₈	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₇×C₈	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₇×C₈	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₇×C₈	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₇×C₈	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₇×C₈	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₇×C₈	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₇×C₈	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₇×C₈	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₇×C₈	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₇×C₈	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₇×C₈	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₇×C₈	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₇×C₈	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₇×C₈	C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₇×C₈	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₇×C₈	C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
124	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
125	C₂×C₇×C₈	C₂×Q₈	1	1	yes	characteristic
126	#1136	—	2	4	no	—
127	#1136	—	4	2	no	—
128	#1136	—	4	2	no	—
129	#1136	—	4	2	no	—
130	C₂×C₇⋊C₈	—	4	2	no	—
131	C₂×C₇⋊C₈	—	4	2	no	—
132	C₂×C₇⋊C₈	—	4	2	no	—
133	C₇⋊C₁₆	—	2	4	no	—
134	C₂²×M₁₆	—	2	1	no	—
135	C₂²×M₁₆	—	14	1	no	—
136	C₂³×C₈	C₂×D₇	1	1	yes	characteristic
137	C₂×M₃₂	—	7	2	no	—
138	C₂×M₃₂	—	7	2	no	—
139	C₂×M₃₂	—	14	1	no	—
140	C₂×M₃₂	—	14	1	no	—
141	C₂×M₃₂	—	14	1	no	—
142	C₂×M₃₂	—	14	1	no	—
143	C₂²×C₁₆	—	7	2	no	—
144	C₂×#108	—	2	1	no	—
145	C₂×#108	—	2	1	no	—
146	C₂×#108	—	2	1	no	—
147	C₂×#108	—	7	2	no	—
148	C₂×#108	—	7	2	no	—
149	C₂×#108	—	7	2	no	—
150	C₂×#108	—	14	1	no	—
151	C₂×#108	—	14	1	no	—
152	C₂×#108	—	14	1	no	—
153	C₂×#108	Dic₇	1	2	yes	—
154	C₂×#108	Dic₇	1	2	yes	—
155	C₂×#108	C₂×D₇	1	2	yes	—
156	C₂³×C₇	—	4	2	no	—
157	C₂³×C₇	#103	1	1	yes	characteristic
158	C₂³×C₇	#103	1	1	yes	characteristic
159	C₂³×C₇	#103	1	1	yes	characteristic
160	C₂³×C₇	#103	1	1	yes	characteristic
161	C₂³×C₇	#107	1	1	yes	characteristic
162	C₂³×C₇	#107	1	1	yes	characteristic
163	C₂³×C₇	C₂×Q₁₆	1	1	yes	characteristic
164	C₂×C₄×C₇	#95	1	1	yes	characteristic
165	C₂×C₄×C₇	#95	1	1	yes	characteristic
166	C₂×C₄×C₇	#95	1	1	yes	characteristic
167	C₂×C₄×C₇	#95	1	1	yes	characteristic
168	C₂×C₄×C₇	#102	1	1	yes	characteristic
169	C₂×C₄×C₇	#102	1	1	yes	characteristic
170	C₂×C₄×C₇	#102	1	1	yes	characteristic
171	C₂×C₄×C₇	#102	1	1	yes	characteristic
172	C₂×C₄×C₇	#102	1	1	yes	characteristic
173	C₂×C₄×C₇	#102	1	1	yes	characteristic
174	C₂×C₄×C₇	#102	1	1	yes	characteristic
175	C₂×C₄×C₇	#102	1	1	yes	characteristic
176	C₂×C₄×C₇	#103	1	1	yes	characteristic
177	C₂×C₄×C₇	#103	1	1	yes	characteristic
178	C₂×C₄×C₇	#103	1	1	yes	characteristic
179	C₂×C₄×C₇	#103	1	1	yes	characteristic
180	C₂×C₄×C₇	#106	1	1	yes	characteristic
181	C₂×C₄×C₇	#106	1	1	yes	characteristic
182	C₂×C₄×C₇	#106	1	1	yes	characteristic
183	C₂×C₄×C₇	#106	1	1	yes	characteristic
184	C₂×C₄×C₇	#107	1	1	yes	characteristic
185	C₂×C₄×C₇	#107	1	1	yes	characteristic
186	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₇	C₂×D₈	1	1	yes	characteristic
190	C₂×C₄×C₇	C₂×SD₁₆	1	1	yes	characteristic
191	C₂×C₄×C₇	C₂×SD₁₆	1	1	yes	characteristic
192	C₇×C₈	—	4	4	no	—
193	C₇×C₈	#95	1	1	yes	characteristic
194	C₇×C₈	#95	1	1	yes	characteristic
195	C₇×C₈	#95	1	1	yes	characteristic
196	C₇×C₈	#95	1	1	yes	characteristic
197	C₇×C₈	C₂×C₄²	1	1	yes	characteristic
198	C₇×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₇×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₇×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₇⋊C₈	—	4	4	no	—
202	C₂³×C₄	C₂²⋊D₇	1	1	yes	characteristic
203	C₂×M₁₆	—	2	2	no	—
204	C₂×M₁₆	—	2	2	no	—
205	C₂×M₁₆	—	2	2	no	—
206	C₂×M₁₆	—	4	1	no	—
207	C₂×M₁₆	—	4	1	no	—
208	C₂×M₁₆	—	4	1	no	—
209	C₂×M₁₆	—	14	2	no	—
210	C₂×M₁₆	—	14	2	no	—
211	C₂×M₁₆	—	14	2	no	—
212	C₂×M₁₆	—	28	1	no	—
213	C₂×M₁₆	—	28	1	no	—
214	C₂×M₁₆	—	28	1	no	—
215	C₂²×C₈	—	4	1	no	—
216	C₂²×C₈	—	28	1	no	—
217	C₂²×C₈	Dic₁₄	1	1	yes	characteristic
218	C₂²×C₈	Dic₁₄	1	1	yes	characteristic
219	C₂²×C₈	C₄×D₇	1	1	yes	characteristic
220	C₂²×C₈	C₄×D₇	1	1	yes	characteristic
221	C₂²×C₈	C₄×D₇	1	1	yes	characteristic
222	C₂²×C₈	C₄×D₇	1	1	yes	characteristic
223	C₂²×C₈	D₂₈	1	1	yes	characteristic
224	C₂²×C₈	D₂₈	1	1	yes	characteristic
225	C₂²×C₈	C₂×Dic₇	1	1	yes	characteristic
226	C₂²×C₈	C₂×Dic₇	1	1	yes	characteristic
227	C₂²×C₈	C₂²⋊D₇	1	1	yes	characteristic
228	C₂²×C₈	C₂²⋊D₇	1	1	yes	characteristic
229	C₂²×C₈	C₂²⋊D₇	1	1	yes	characteristic
230	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
231	M₃₂	—	14	2	no	—
232	M₃₂	—	14	2	no	—
233	M₃₂	—	14	2	no	—
234	M₃₂	—	14	2	no	—
235	C₂×C₁₆	—	7	4	no	—
236	C₂×C₁₆	—	14	2	no	—
237	C₂×C₁₆	—	14	2	no	—
238	#108	—	2	2	no	—
239	#108	—	2	2	no	—
240	#108	—	2	2	no	—
241	#108	—	7	4	no	—
242	#108	—	14	2	no	—
243	#108	—	14	2	no	—
244	#108	—	14	2	no	—
245	#108	C₂×Dic₇	1	4	yes	—
246	C₂²×C₇	—	2	2	no	—
247	C₂²×C₇	—	2	2	no	—
248	C₂²×C₇	—	2	2	no	—
249	C₂²×C₇	—	4	1	no	—
250	C₂²×C₇	—	4	1	no	—
251	C₂²×C₇	—	4	1	no	—
252	C₂²×C₇	—	4	1	no	—
253	C₂²×C₇	#340	1	1	yes	characteristic
254	C₂²×C₇	#340	1	1	yes	characteristic
255	C₂²×C₇	#340	1	1	yes	characteristic
256	C₂²×C₇	#340	1	1	yes	characteristic
257	C₂²×C₇	C₂×#103	1	1	yes	characteristic
258	C₂²×C₇	C₂×#103	1	1	yes	characteristic
259	C₂²×C₇	C₂×#107	1	1	yes	characteristic
260	C₄×C₇	#340	1	1	yes	characteristic
261	C₄×C₇	#340	1	1	yes	characteristic
262	C₄×C₇	#340	1	1	yes	characteristic
263	C₄×C₇	#340	1	1	yes	characteristic
264	C₄×C₇	C₂×#95	1	1	yes	characteristic
265	C₄×C₇	C₂×#102	1	1	yes	characteristic
266	C₄×C₇	C₂×#102	1	1	yes	characteristic
267	C₄×C₇	C₂×#106	1	1	yes	characteristic
268	C₂⁴	#1144	1	1	yes	characteristic
269	C₂²×C₄	Dic₇⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	Dic₇⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	(C₂×D₇)⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	(C₂×D₇)⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	#1141	1	1	yes	characteristic
274	C₂²×C₄	#1141	1	1	yes	characteristic
275	C₂²×C₄	#1142	1	1	yes	characteristic
276	C₂²×C₄	#1142	1	1	yes	characteristic
277	C₂²×C₄	#1143	1	1	yes	characteristic
278	C₂²×C₄	#1143	1	1	yes	characteristic
279	C₂²×C₄	#1144	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊Dic₇	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊Dic₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
283	M₁₆	—	2	4	no	—
284	M₁₆	—	4	2	no	—
285	M₁₆	—	4	2	no	—
286	M₁₆	—	4	2	no	—
287	M₁₆	—	14	4	no	—
288	M₁₆	—	28	2	no	—
289	M₁₆	—	28	2	no	—
290	M₁₆	—	28	2	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	—	4	2	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	—	28	2	no	—
295	C₂×C₈	—	28	2	no	—
296	C₂×C₈	—	28	2	no	—
297	C₂×C₈	C₄×Dic₇	1	1	yes	characteristic
298	C₂×C₈	C₄×Dic₇	1	1	yes	characteristic
299	C₂×C₈	C₄×Dic₇	1	1	yes	characteristic
300	C₂×C₈	C₄×Dic₇	1	1	yes	characteristic
301	C₂×C₈	Dic₇⋊C₄	1	1	yes	characteristic
302	C₂×C₈	Dic₇⋊C₄	1	1	yes	characteristic
303	C₂×C₈	Dic₇⋊C₄	1	1	yes	characteristic
304	C₂×C₈	Dic₇⋊C₄	1	1	yes	characteristic
305	C₂×C₈	Dic₇⋊C₄	1	1	yes	characteristic
306	C₂×C₈	Dic₇⋊C₄	1	1	yes	characteristic
307	C₂×C₈	C₄⋊Dic₇	1	1	yes	characteristic
308	C₂×C₈	C₄⋊Dic₇	1	1	yes	characteristic
309	C₂×C₈	C₄⋊Dic₇	1	1	yes	characteristic
310	C₂×C₈	C₄⋊Dic₇	1	1	yes	characteristic
311	C₂×C₈	(C₂×D₇)⋊C₄	1	1	yes	characteristic
312	C₂×C₈	(C₂×D₇)⋊C₄	1	1	yes	characteristic
313	C₂×C₈	(C₂×D₇)⋊C₄	1	1	yes	characteristic
314	C₂×C₈	(C₂×D₇)⋊C₄	1	1	yes	characteristic
315	C₂×C₈	(C₂×D₇)⋊C₄	1	1	yes	characteristic
316	C₂×C₈	(C₂×D₇)⋊C₄	1	1	yes	characteristic
317	C₂×C₈	C₂²⋊Dic₇	1	1	yes	characteristic
318	C₂×C₈	C₂²⋊Dic₇	1	1	yes	characteristic
319	C₂×C₈	C₂×Dic₁₄	1	1	yes	characteristic
320	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
321	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
322	C₂×C₈	C₂×D₂₈	1	1	yes	characteristic
323	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
324	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
325	C₁₆	—	14	4	no	—
326	C₂×C₇	—	2	1	no	—
327	C₂×C₇	—	2	1	no	—
328	C₂×C₇	—	2	1	no	—
329	C₂×C₇	—	2	1	no	—
330	C₂×C₇	—	2	1	no	—
331	C₂×C₇	—	2	1	no	—
332	C₂×C₇	#1385	1	2	yes	complemented
333	C₂×C₇	C₂×#340	1	1	yes	characteristic
334	C₂³	—	4	2	no	—
335	C₂³	#6381	1	1	yes	characteristic
336	C₂³	#6381	1	1	yes	characteristic
337	C₂³	#6384	1	1	yes	characteristic
338	C₂³	#6384	1	1	yes	characteristic
339	C₂³	#6409	1	1	yes	characteristic
340	C₂³	#6409	1	1	yes	characteristic
341	C₂³	C₂×#1144	1	1	yes	characteristic
342	C₂×C₄	#6381	1	1	yes	characteristic
343	C₂×C₄	#6381	1	1	yes	characteristic
344	C₂×C₄	#6382	1	1	yes	characteristic
345	C₂×C₄	#6382	1	1	yes	characteristic
346	C₂×C₄	#6382	1	1	yes	characteristic
347	C₂×C₄	#6382	1	1	yes	characteristic
348	C₂×C₄	#6383	1	1	yes	characteristic
349	C₂×C₄	#6383	1	1	yes	characteristic
350	C₂×C₄	#6383	1	1	yes	characteristic
351	C₂×C₄	#6383	1	1	yes	characteristic
352	C₂×C₄	#6384	1	1	yes	characteristic
353	C₂×C₄	#6384	1	1	yes	characteristic
354	C₂×C₄	C₇⋊#95	1	1	yes	characteristic
355	C₂×C₄	C₇⋊#95	1	1	yes	characteristic
356	C₂×C₄	C₇⋊#95	1	1	yes	characteristic
357	C₂×C₄	C₇⋊#95	1	1	yes	characteristic
358	C₂×C₄	#6406	1	1	yes	characteristic
359	C₂×C₄	#6406	1	1	yes	characteristic
360	C₂×C₄	#6406	1	1	yes	characteristic
361	C₂×C₄	#6406	1	1	yes	characteristic
362	C₂×C₄	#6409	1	1	yes	characteristic
363	C₂×C₄	#6409	1	1	yes	characteristic
364	C₂×C₄	C₂×Dic₇⋊C₄	1	1	yes	characteristic
365	C₂×C₄	C₂×(C₂×D₇)⋊C₄	1	1	yes	characteristic
366	C₂×C₄	C₂×#1141	1	1	yes	characteristic
367	C₂×C₄	C₂×#1142	1	1	yes	characteristic
368	C₂×C₄	C₂×#1143	1	1	yes	characteristic
369	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
370	C₈	—	4	4	no	—
371	C₈	—	28	4	no	—
372	C₈	C₇⋊#95	1	1	yes	characteristic
373	C₈	C₇⋊#95	1	1	yes	characteristic
374	C₈	C₇⋊#95	1	1	yes	characteristic
375	C₈	C₇⋊#95	1	1	yes	characteristic
376	C₈	C₂×C₄×Dic₇	1	1	yes	characteristic
377	C₈	C₂×Dic₇⋊C₄	1	1	yes	characteristic
378	C₈	C₂×C₄⋊Dic₇	1	1	yes	characteristic
379	C₈	C₂×(C₂×D₇)⋊C₄	1	1	yes	characteristic
380	C₇	C₂×#1385	1	1	yes	characteristic, complemented, Sylow
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	#89324	1	1	yes	characteristic
389	C₂²	#89324	1	1	yes	characteristic
390	C₂²	#89324	1	1	yes	characteristic
391	C₂²	#89324	1	1	yes	characteristic
392	C₂²	C₂×#6381	1	1	yes	characteristic
393	C₂²	C₂×#6384	1	1	yes	characteristic
394	C₂²	C₂×#6409	1	1	yes	characteristic
395	C₄	#89324	1	1	yes	characteristic
396	C₄	#89324	1	1	yes	characteristic
397	C₄	#89324	1	1	yes	characteristic
398	C₄	#89324	1	1	yes	characteristic
399	C₄	C₂×#6382	1	1	yes	characteristic
400	C₄	C₂×#6383	1	1	yes	characteristic
401	C₄	C₂×C₇⋊#95	1	1	yes	characteristic
402	C₄	C₂×#6406	1	1	yes	characteristic
403	C₂	—	2	1	no	—
404	C₂	—	2	1	no	—
405	C₂	—	2	1	no	—
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	#11725537	1	2	yes	direct product factor
410	C₂	C₂×#89324	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#6382
commutator	C₇×C₈	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₇
Fitting	C₂²×C₇×#108	C₂
socle	C₂²×C₇	#340
prime radical	C₂⁴×C₇	Q₁₆
cosocle	C₂²×C₇×C₈	C₂³
hypercenter	C₂²×#108	D₇
hypocenter	C₇	C₂×#1385
LCS	G ▷ C₇×C₈ ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
4. #11725537	C₂	direct (N × H)
332. C₂×C₇	#1385	semidirect
380. C₇	C₂×#1385	semidirect
409. C₂	#11725537	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇×#108	2
C₂²×#6393	2
C₂²×#6386	2
#11725537	2
C₂×#1385	7

Subgroups — C2×#11725537 #13268707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11725537 #13268707