Subgroups — #13322944

Order 1792.

730 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#423	C₂	1	1	yes	maximal, characteristic
2	C₂×#89697	C₂	1	1	yes	maximal, characteristic
3	C₂×#89696	C₂	1	1	yes	maximal, characteristic
4	#11728248	C₂	1	4	yes	maximal, complemented
5	#11728245	C₂	1	4	yes	maximal, complemented
6	#11728176	C₂	1	4	yes	maximal, complemented
7	C₂²×C₇×M₁₆	—	2	1	no	—
8	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
9	C₂²×#1136	—	2	1	no	—
10	C₇×#423	—	2	1	no	—
11	C₇×#423	—	2	1	no	—
12	C₇×#423	C₂²	1	2	yes	—
13	C₇×#423	C₂²	1	2	yes	—
14	C₂×C₇×C₄⋊C₈	—	2	1	no	—
15	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₇⋊C₈)	C₄	1	2	yes	—
17	#89697	C₄	1	2	yes	—
18	#89697	C₄	1	2	yes	—
19	#89697	C₂²	1	2	yes	—
20	#89697	C₂²	1	2	yes	—
21	#89696	—	2	1	no	—
22	#89696	—	2	1	no	—
23	#89696	C₂²	1	2	yes	—
24	#89696	C₂²	1	2	yes	—
25	C₂×C₄⋊(C₇⋊C₈)	—	2	1	no	—
26	C₂×C₄⋊(C₇⋊C₈)	C₄	1	2	yes	—
27	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	2	yes	—
28	C₂×C₄×C₇⋊C₈	C₂²	1	2	yes	—
29	#89274	C₂²	1	16	yes	complemented
30	#17814	—	7	1	no	maximal, Sylow
31	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₇	Q₈	1	1	yes	characteristic
34	C₂×C₇×M₁₆	—	2	2	no	—
35	C₂×C₇×M₁₆	—	2	2	no	—
36	C₂×C₇×M₁₆	—	4	4	no	—
37	C₂²×C₇×C₈	—	2	2	no	—
38	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₇	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₇	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₇	Q₈	1	1	yes	characteristic
47	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
49	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
50	C₂×#1136	—	2	2	no	—
51	C₂×#1136	—	2	2	no	—
52	C₂×#1136	—	4	4	no	—
53	C₂²×C₇⋊C₈	—	2	2	no	—
54	C₂²×C₇⋊C₈	C₂×C₄	1	4	yes	—
55	C₇×C₄⋊C₈	—	2	2	no	—
56	C₇×C₄⋊C₈	—	2	2	no	—
57	C₇×C₄⋊C₈	—	2	2	no	—
58	C₇×C₄⋊C₈	C₂³	1	4	yes	—
59	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	4	yes	—
60	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	4	yes	—
61	C₄⋊(C₇⋊C₈)	—	2	2	no	—
62	C₄⋊(C₇⋊C₈)	—	2	2	no	—
63	C₄⋊(C₇⋊C₈)	—	2	2	no	—
64	C₄⋊(C₇⋊C₈)	C₂×C₄	1	4	yes	—
65	C₄⋊(C₇⋊C₈)	C₂×C₄	1	4	yes	—
66	C₄⋊(C₇⋊C₈)	C₂³	1	4	yes	—
67	C₄×C₇⋊C₈	C₂×C₄	1	4	yes	—
68	C₄×C₇⋊C₈	C₂³	1	4	yes	—
69	C₂×#431	—	7	1	no	—
70	C₂×#423	—	7	1	no	—
71	C₂×#423	D₇	1	1	yes	characteristic
72	#1571	—	7	4	no	—
73	#1571	—	7	4	no	—
74	#1567	—	7	4	no	—
75	C₂⁴×C₇	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₇	—	4	2	no	—
77	C₂²×C₄×C₇	—	4	2	no	—
78	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₇	C₄⋊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	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₇	D₈	1	4	yes	—
88	C₂²×C₄×C₇	Q₁₆	1	4	yes	—
89	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
97	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
98	C₇×M₁₆	—	4	4	no	—
99	C₇×M₁₆	—	4	4	no	—
100	C₂×C₇×C₈	—	2	4	no	—
101	C₂×C₇×C₈	—	4	4	no	—
102	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₇	C₂×Q₈	1	1	yes	characteristic
115	C₄²×C₇	C₂×Q₈	1	1	yes	characteristic
116	C₄²×C₇	C₂×Q₈	1	1	yes	characteristic
117	C₄²×C₇	C₂⁴	1	1	yes	characteristic
118	#1136	—	4	4	no	—
119	#1136	—	4	4	no	—
120	C₂×C₇⋊C₈	—	2	4	no	—
121	C₂×C₇⋊C₈	—	4	4	no	—
122	C₂×C₇⋊C₈	—	4	4	no	—
123	C₂×C₇⋊C₈	C₂²×C₄	1	8	yes	—
124	C₂²×M₁₆	—	2	1	no	—
125	C₂²×M₁₆	—	14	1	no	—
126	C₂²×C₄²	C₂×D₇	1	1	yes	characteristic
127	#431	—	7	2	no	—
128	#431	—	7	2	no	—
129	#431	—	7	2	no	—
130	#431	—	7	2	no	—
131	#423	—	2	1	no	—
132	#423	—	2	1	no	—
133	#423	—	7	2	no	—
134	#423	—	7	2	no	—
135	#423	—	14	1	no	—
136	#423	—	14	1	no	—
137	#423	C₂×D₇	1	2	yes	—
138	#423	C₂×D₇	1	2	yes	—
139	C₂×C₄⋊C₈	—	2	1	no	—
140	C₂×C₄⋊C₈	—	7	2	no	—
141	C₂×C₄⋊C₈	—	7	2	no	—
142	C₂×C₄⋊C₈	—	14	1	no	—
143	C₂×C₄⋊C₈	C₂×D₇	1	2	yes	—
144	C₂×C₂²⋊C₈	—	7	2	no	—
145	C₂×C₄×C₈	—	7	2	no	—
146	#335	—	7	16	no	—
147	C₂³×C₇	—	4	1	no	—
148	C₂³×C₇	—	4	1	no	—
149	C₂³×C₇	#107	1	4	yes	—
150	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₇	—	2	2	no	—
154	C₂×C₄×C₇	—	2	2	no	—
155	C₂×C₄×C₇	—	2	2	no	—
156	C₂×C₄×C₇	—	2	2	no	—
157	C₂×C₄×C₇	—	2	2	no	—
158	C₂×C₄×C₇	—	2	2	no	—
159	C₂×C₄×C₇	—	4	1	no	—
160	C₂×C₄×C₇	—	4	1	no	—
161	C₂×C₄×C₇	—	4	1	no	—
162	C₂×C₄×C₇	—	4	1	no	—
163	C₂×C₄×C₇	—	4	1	no	—
164	C₂×C₄×C₇	—	4	1	no	—
165	C₂×C₄×C₇	#107	1	4	yes	—
166	C₂×C₄×C₇	#107	1	4	yes	—
167	C₂×C₄×C₇	#107	1	4	yes	—
168	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
178	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
179	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
180	C₂×C₄×C₇	C₂×Q₁₆	1	2	yes	—
181	C₂×C₄×C₇	C₂×Q₁₆	1	2	yes	—
182	C₂×C₄×C₇	C₂×Q₁₆	1	2	yes	—
183	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
186	C₇×C₈	—	4	4	no	—
187	C₇⋊C₈	—	2	8	no	—
188	C₇⋊C₈	—	4	4	no	—
189	C₂³×C₄	Dic₁₄	1	1	yes	characteristic
190	C₂³×C₄	C₄×D₇	1	1	yes	characteristic
191	C₂³×C₄	C₂²⋊D₇	1	1	yes	characteristic
192	C₂×M₁₆	—	2	2	no	—
193	C₂×M₁₆	—	2	2	no	—
194	C₂×M₁₆	—	4	4	no	—
195	C₂×M₁₆	—	14	2	no	—
196	C₂×M₁₆	—	14	2	no	—
197	C₂×M₁₆	—	28	4	no	—
198	C₂²×C₈	—	2	2	no	—
199	C₂²×C₈	—	7	4	no	—
200	C₂²×C₈	—	14	2	no	—
201	C₂×C₄²	Dic₁₄	1	1	yes	characteristic
202	C₂×C₄²	Dic₁₄	1	1	yes	characteristic
203	C₂×C₄²	Dic₁₄	1	1	yes	characteristic
204	C₂×C₄²	C₄×D₇	1	1	yes	characteristic
205	C₂×C₄²	C₄×D₇	1	1	yes	characteristic
206	C₂×C₄²	C₄×D₇	1	1	yes	characteristic
207	C₂×C₄²	C₂²⋊D₇	1	1	yes	characteristic
208	C₂×C₄²	C₂²⋊D₇	1	1	yes	characteristic
209	C₂×C₄²	C₂²⋊D₇	1	1	yes	characteristic
210	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
211	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
212	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
213	C₄⋊C₈	—	2	2	no	—
214	C₄⋊C₈	—	2	2	no	—
215	C₄⋊C₈	—	2	2	no	—
216	C₄⋊C₈	—	7	4	no	—
217	C₄⋊C₈	—	7	4	no	—
218	C₄⋊C₈	—	7	4	no	—
219	C₄⋊C₈	—	14	2	no	—
220	C₄⋊C₈	—	14	2	no	—
221	C₄⋊C₈	—	14	2	no	—
222	C₄⋊C₈	C₂²×D₇	1	4	yes	—
223	C₂²⋊C₈	—	7	4	no	—
224	C₂²⋊C₈	—	7	4	no	—
225	C₄×C₈	—	7	4	no	—
226	C₄×C₈	—	7	4	no	—
227	C₂²×C₇	—	2	1	no	—
228	C₂²×C₇	—	2	1	no	—
229	C₂²×C₇	—	2	1	no	—
230	C₂²×C₇	—	2	1	no	—
231	C₂²×C₇	—	2	1	no	—
232	C₂²×C₇	—	2	1	no	—
233	C₂²×C₇	—	4	4	no	—
234	C₂²×C₇	C₂×#107	1	2	yes	—
235	C₂²×C₇	C₂×#107	1	2	yes	—
236	C₂²×C₇	C₂×#107	1	2	yes	—
237	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
238	C₄×C₇	—	2	1	no	—
239	C₄×C₇	—	2	1	no	—
240	C₄×C₇	—	2	1	no	—
241	C₄×C₇	—	2	1	no	—
242	C₄×C₇	—	2	1	no	—
243	C₄×C₇	—	2	1	no	—
244	C₄×C₇	C₂×#107	1	2	yes	—
245	C₄×C₇	C₂×#107	1	2	yes	—
246	C₄×C₇	C₂×#107	1	2	yes	—
247	C₄×C₇	#430	1	2	yes	—
248	C₄×C₇	#568	1	2	yes	—
249	C₄×C₇	C₂²×D₈	1	1	yes	characteristic
250	C₄×C₇	C₂²×Q₁₆	1	1	yes	characteristic
251	C₂⁴	Dic₇⋊C₄	1	1	yes	characteristic
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	Dic₇⋊C₄	1	1	yes	characteristic
255	C₂²×C₄	Dic₇⋊C₄	1	1	yes	characteristic
256	C₂²×C₄	Dic₇⋊C₄	1	1	yes	characteristic
257	C₂²×C₄	Dic₇⋊C₄	1	1	yes	characteristic
258	C₂²×C₄	Dic₇⋊C₄	1	1	yes	characteristic
259	C₂²×C₄	Dic₇⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	Dic₇⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	Dic₇⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	Dic₇⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	#1141	1	4	yes	—
264	C₂²×C₄	#1144	1	4	yes	—
265	C₂²×C₄	C₂×Dic₁₄	1	1	yes	characteristic
266	C₂²×C₄	C₂×Dic₁₄	1	1	yes	characteristic
267	C₂²×C₄	C₂×Dic₁₄	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
274	M₁₆	—	4	4	no	—
275	M₁₆	—	4	4	no	—
276	M₁₆	—	28	4	no	—
277	M₁₆	—	28	4	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	4	4	no	—
280	C₂×C₈	—	7	8	no	—
281	C₂×C₈	—	14	4	no	—
282	C₂×C₈	—	28	4	no	—
283	C₂×C₈	—	28	4	no	—
284	C₄²	Dic₇⋊C₄	1	1	yes	characteristic
285	C₄²	Dic₇⋊C₄	1	1	yes	characteristic
286	C₄²	Dic₇⋊C₄	1	1	yes	characteristic
287	C₄²	Dic₇⋊C₄	1	1	yes	characteristic
288	C₄²	Dic₇⋊C₄	1	1	yes	characteristic
289	C₄²	Dic₇⋊C₄	1	1	yes	characteristic
290	C₄²	C₂×Dic₁₄	1	1	yes	characteristic
291	C₄²	C₂×Dic₁₄	1	1	yes	characteristic
292	C₄²	C₂×Dic₁₄	1	1	yes	characteristic
293	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
294	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
295	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
296	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
297	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
298	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
299	C₄²	C₂³×D₇	1	1	yes	characteristic
300	C₂×C₇	—	2	2	no	—
301	C₂×C₇	—	2	2	no	—
302	C₂×C₇	—	2	2	no	—
303	C₂×C₇	#2905	1	1	yes	characteristic
304	C₂×C₇	C₂²×#107	1	1	yes	characteristic
305	C₂×C₇	C₂×#430	1	1	yes	characteristic
306	C₂³	—	4	1	no	—
307	C₂³	—	4	1	no	—
308	C₂³	#6381	1	4	yes	—
309	C₂³	C₂×Dic₇⋊C₄	1	1	yes	characteristic
310	C₂³	C₂×Dic₇⋊C₄	1	1	yes	characteristic
311	C₂³	C₂×Dic₇⋊C₄	1	1	yes	characteristic
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	#6381	1	4	yes	—
325	C₂×C₄	#6381	1	4	yes	—
326	C₂×C₄	#6381	1	4	yes	—
327	C₂×C₄	C₂×Dic₇⋊C₄	1	1	yes	characteristic
328	C₂×C₄	C₂×Dic₇⋊C₄	1	1	yes	characteristic
329	C₂×C₄	C₂×Dic₇⋊C₄	1	1	yes	characteristic
330	C₂×C₄	C₂×Dic₇⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₂×Dic₇⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂×Dic₇⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×Dic₇⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₂×Dic₇⋊C₄	1	1	yes	characteristic
335	C₂×C₄	C₂×Dic₇⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂×#1141	1	2	yes	—
337	C₂×C₄	C₂×#1141	1	2	yes	—
338	C₂×C₄	C₂×#1141	1	2	yes	—
339	C₂×C₄	C₂×#1144	1	2	yes	—
340	C₂×C₄	C₂×#1144	1	2	yes	—
341	C₂×C₄	C₂×#1144	1	2	yes	—
342	C₂×C₄	C₂²×Dic₁₄	1	1	yes	characteristic
343	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₂²⋊D₇	1	1	yes	characteristic
345	C₈	—	4	4	no	—
346	C₈	—	14	8	no	—
347	C₈	—	28	4	no	—
348	C₇	#17814	1	1	yes	characteristic, complemented, Sylow
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	4	4	no	—
356	C₂²	C₂×#6381	1	2	yes	—
357	C₂²	C₂×#6381	1	2	yes	—
358	C₂²	C₂×#6381	1	2	yes	—
359	C₂²	C₂²×Dic₇⋊C₄	1	1	yes	characteristic
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	C₂×#6381	1	2	yes	—
367	C₄	C₂×#6381	1	2	yes	—
368	C₄	C₂×#6381	1	2	yes	—
369	C₄	#89896	1	2	yes	—
370	C₄	#90436	1	2	yes	—
371	C₄	C₂²×#1141	1	1	yes	characteristic
372	C₄	C₂²×#1144	1	1	yes	characteristic
373	C₂	—	2	2	no	—
374	C₂	—	2	2	no	—
375	C₂	—	2	2	no	—
376	C₂	C₂²×#6381	1	1	yes	characteristic
377	C₂	#11741195	1	1	yes	characteristic
378	C₂	C₂×#89896	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting	C₂×C₇×#423	C₂
socle	C₂²×C₇	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₇	C₄⋊C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	C₂×#423	D₇
hypocenter	C₇	#17814
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
4. #11728248	C₂	semidirect
5. #11728245	C₂	semidirect
6. #11728176	C₂	semidirect
29. #89274	C₂²	semidirect
348. C₇	#17814	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#423	2
C₂×#89697	2
C₂×#89696	2
#11728248	2
#11728245	2
#11728176	2
#17814	7