Subgroups — C₁₀₇×#10275 #41036239

Order 27392.

562 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#487×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#476×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#474×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₁₀₇×#1954	C₂	1	1	yes	maximal, characteristic
5	C₂×#333×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#332×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₇×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
11	#487×C₁₀₇	—	2	2	no	—
12	#487×C₁₀₇	—	2	2	no	—
13	#476×C₁₀₇	—	2	2	no	—
14	#476×C₁₀₇	—	2	2	no	—
15	#474×C₁₀₇	—	2	2	no	—
16	#474×C₁₀₇	—	2	2	no	—
17	C₂×#107×C₁₀₇	—	2	1	no	—
18	C₂×#106×C₁₀₇	—	2	1	no	—
19	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	1	yes	characteristic
22	C₂×#103×C₁₀₇	—	2	2	no	—
23	C₂×#102×C₁₀₇	—	2	1	no	—
24	C₂×#102×C₁₀₇	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₁₀₇	—	2	2	no	—
26	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
27	#333×C₁₀₇	—	2	2	no	—
28	#332×C₁₀₇	—	2	2	no	—
29	C₂²×Q₈×C₁₀₇	—	2	1	no	—
30	C₂²×Q₈×C₁₀₇	—	2	1	no	—
31	C₂²×D₄×C₁₀₇	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₀₇	—	2	1	no	—
33	C₂²×C₈×C₁₀₇	—	2	1	no	—
34	C₂²×C₈×C₁₀₇	—	2	1	no	—
35	C₂²×C₈×C₁₀₇	—	2	1	no	—
36	C₂²×C₈×C₁₀₇	D₄	1	2	yes	—
37	C₄⋊Q₈×C₁₀₇	—	2	1	no	—
38	C₄⋊Q₈×C₁₀₇	—	2	1	no	—
39	C₄⋊Q₈×C₁₀₇	—	2	1	no	—
40	C₄⋊Q₈×C₁₀₇	—	2	1	no	—
41	C₄⋊Q₈×C₁₀₇	—	2	1	no	—
42	C₄⋊Q₈×C₁₀₇	—	2	1	no	—
43	C₄⋊Q₈×C₁₀₇	D₄	1	2	yes	—
44	C₄⋊Q₈×C₁₀₇	D₄	1	2	yes	—
45	C₄×D₄×C₁₀₇	—	2	1	no	—
46	C₄×D₄×C₁₀₇	—	2	1	no	—
47	C₄×D₄×C₁₀₇	—	2	1	no	—
48	C₄×D₄×C₁₀₇	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₀₇	D₄	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
55	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
56	#107×C₁₀₇	—	2	4	no	—
57	#106×C₁₀₇	—	2	4	no	—
58	C₄⋊C₈×C₁₀₇	—	2	1	no	—
59	C₄⋊C₈×C₁₀₇	—	2	1	no	—
60	C₄⋊C₈×C₁₀₇	—	2	1	no	—
61	C₄⋊C₈×C₁₀₇	—	2	1	no	—
62	C₄⋊C₈×C₁₀₇	D₄	1	2	yes	—
63	C₄⋊C₈×C₁₀₇	D₄	1	2	yes	—
64	#103×C₁₀₇	—	2	8	no	—
65	#102×C₁₀₇	—	2	4	no	—
66	#102×C₁₀₇	—	2	4	no	—
67	C₂²⋊C₈×C₁₀₇	—	4	4	no	—
68	C₄×C₈×C₁₀₇	—	2	1	no	—
69	C₄×C₈×C₁₀₇	—	2	1	no	—
70	C₂⁴×C₁₀₇	—	2	1	no	—
71	C₂×Q₈×C₁₀₇	—	2	2	no	—
72	C₂×Q₈×C₁₀₇	—	2	2	no	—
73	C₂×Q₈×C₁₀₇	—	4	1	no	—
74	C₂×Q₈×C₁₀₇	—	4	1	no	—
75	C₂×Q₈×C₁₀₇	—	4	2	no	—
76	C₂×Q₈×C₁₀₇	—	4	2	no	—
77	C₂×Q₈×C₁₀₇	—	8	2	no	—
78	C₂×D₄×C₁₀₇	—	2	1	no	—
79	C₂×D₄×C₁₀₇	—	2	1	no	—
80	C₂×D₄×C₁₀₇	—	2	1	no	—
81	C₂×D₄×C₁₀₇	—	2	1	no	—
82	C₂×D₄×C₁₀₇	—	2	1	no	—
83	C₂×D₄×C₁₀₇	Q₁₆	1	2	yes	—
84	C₂²×C₄×C₁₀₇	—	2	1	no	—
85	C₂²×C₄×C₁₀₇	—	4	1	no	—
86	C₂²×C₄×C₁₀₇	—	4	1	no	—
87	C₂²×C₄×C₁₀₇	—	4	1	no	—
88	C₂²×C₄×C₁₀₇	—	4	1	no	—
89	C₂²×C₄×C₁₀₇	—	4	2	no	—
90	C₂²×C₄×C₁₀₇	—	4	2	no	—
91	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₀₇	#41	1	1	yes	characteristic
94	C₂×C₈×C₁₀₇	—	2	2	no	—
95	C₂×C₈×C₁₀₇	—	2	2	no	—
96	C₂×C₈×C₁₀₇	—	2	2	no	—
97	C₂×C₈×C₁₀₇	—	2	2	no	—
98	C₂×C₈×C₁₀₇	—	2	2	no	—
99	C₂×C₈×C₁₀₇	—	4	1	no	—
100	C₂×C₈×C₁₀₇	—	4	1	no	—
101	C₂×C₈×C₁₀₇	—	4	1	no	—
102	C₂×C₈×C₁₀₇	—	4	1	no	—
103	C₂×C₈×C₁₀₇	—	4	1	no	—
104	C₂×C₈×C₁₀₇	—	4	2	no	—
105	C₄⋊C₄×C₁₀₇	—	2	2	no	—
106	C₄⋊C₄×C₁₀₇	—	2	2	no	—
107	C₄⋊C₄×C₁₀₇	—	2	2	no	—
108	C₄⋊C₄×C₁₀₇	—	2	1	no	—
109	C₄⋊C₄×C₁₀₇	—	2	1	no	—
110	C₄⋊C₄×C₁₀₇	—	2	2	no	—
111	C₄⋊C₄×C₁₀₇	—	4	1	no	—
112	C₄⋊C₄×C₁₀₇	—	4	1	no	—
113	C₄⋊C₄×C₁₀₇	—	4	1	no	—
114	C₄⋊C₄×C₁₀₇	—	4	1	no	—
115	C₂²⋊C₄×C₁₀₇	—	4	1	no	—
116	C₂²⋊C₄×C₁₀₇	—	4	1	no	—
117	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
121	C₂³×C₁₀₇	—	2	2	no	—
122	C₂³×C₁₀₇	—	4	1	no	—
123	C₂³×C₁₀₇	—	4	2	no	—
124	C₂³×C₁₀₇	—	4	1	no	—
125	C₂³×C₁₀₇	—	4	2	no	—
126	C₂³×C₁₀₇	#121	1	1	yes	characteristic
127	Q₈×C₁₀₇	—	4	4	no	—
128	Q₈×C₁₀₇	—	8	2	no	—
129	Q₈×C₁₀₇	—	8	2	no	—
130	Q₈×C₁₀₇	—	8	1	no	—
131	Q₈×C₁₀₇	—	8	1	no	—
132	D₄×C₁₀₇	—	2	2	no	—
133	D₄×C₁₀₇	—	2	2	no	—
134	D₄×C₁₀₇	—	4	1	no	—
135	D₄×C₁₀₇	—	4	1	no	—
136	C₂×C₄×C₁₀₇	—	2	2	no	—
137	C₂×C₄×C₁₀₇	—	4	1	no	—
138	C₂×C₄×C₁₀₇	—	4	2	no	—
139	C₂×C₄×C₁₀₇	—	4	2	no	—
140	C₂×C₄×C₁₀₇	—	4	2	no	—
141	C₂×C₄×C₁₀₇	—	8	2	no	—
142	C₂×C₄×C₁₀₇	—	8	2	no	—
143	C₂×C₄×C₁₀₇	—	8	2	no	—
144	C₂×C₄×C₁₀₇	—	8	1	no	—
145	C₂×C₄×C₁₀₇	—	8	1	no	—
146	C₂×C₄×C₁₀₇	#120	1	1	yes	characteristic
147	C₂×C₄×C₁₀₇	#120	1	1	yes	characteristic
148	C₂×C₄×C₁₀₇	#120	1	1	yes	characteristic
149	C₂×C₄×C₁₀₇	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₀₇	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₀₇	#127	1	1	yes	characteristic
152	C₂×C₄×C₁₀₇	C₂×Q₁₆	1	1	yes	characteristic
153	C₂×C₄×C₁₀₇	#135	1	2	yes	—
154	C₂×C₄×C₁₀₇	#135	1	1	yes	characteristic
155	C₂×C₄×C₁₀₇	AGL(1,ℤ/8)	1	2	yes	—
156	C₂×C₄×C₁₀₇	#137	1	1	yes	characteristic
157	C₂×C₄×C₁₀₇	#137	1	1	yes	characteristic
158	C₈×C₁₀₇	—	4	2	no	—
159	C₈×C₁₀₇	—	4	2	no	—
160	C₈×C₁₀₇	—	4	2	no	—
161	C₈×C₁₀₇	—	8	1	no	—
162	C₂²×C₁₀₇	—	4	4	no	—
163	C₂²×C₁₀₇	—	4	2	no	—
164	C₂²×C₁₀₇	—	8	2	no	—
165	C₂²×C₁₀₇	—	8	1	no	—
166	C₂²×C₁₀₇	—	8	1	no	—
167	C₂²×C₁₀₇	#392	1	1	yes	characteristic
168	C₂²×C₁₀₇	#463	1	2	yes	—
169	C₂²×C₁₀₇	#467	1	1	yes	characteristic
170	C₂²×C₁₀₇	#470	1	1	yes	characteristic
171	C₂²×C₁₀₇	#471	1	2	yes	—
172	C₄×C₁₀₇	—	2	1	no	—
173	C₄×C₁₀₇	—	2	1	no	—
174	C₄×C₁₀₇	—	8	1	no	—
175	C₄×C₁₀₇	—	8	2	no	—
176	C₄×C₁₀₇	—	8	2	no	—
177	C₄×C₁₀₇	#449	1	2	yes	—
178	C₄×C₁₀₇	#451	1	1	yes	characteristic
179	C₄×C₁₀₇	#451	1	1	yes	characteristic
180	C₄×C₁₀₇	#452	1	1	yes	characteristic
181	C₄×C₁₀₇	#452	1	1	yes	characteristic
182	C₄×C₁₀₇	#495	1	1	yes	characteristic
183	C₄×C₁₀₇	#496	1	1	yes	characteristic
184	#10275	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂×C₁₀₇	—	8	2	no	—
186	C₂×C₁₀₇	#1683	1	2	yes	—
187	C₂×C₁₀₇	#1703	1	2	yes	—
188	C₂×C₁₀₇	#2001	1	1	yes	characteristic
189	C₂×C₁₀₇	#2012	1	1	yes	characteristic
190	C₂×C₁₀₇	#2019	1	1	yes	characteristic
191	C₂×#487	C₂×C₁₀₇	1	1	yes	characteristic, complemented
192	C₂×#476	C₂×C₁₀₇	1	1	yes	characteristic
193	C₂×#474	C₂×C₁₀₇	1	1	yes	characteristic
194	#1954	C₂×C₁₀₇	1	1	yes	characteristic
195	C₂×#333	C₂×C₁₀₇	1	1	yes	characteristic, complemented
196	C₂×#332	C₂×C₁₀₇	1	1	yes	characteristic, complemented
197	#1277	C₂×C₁₀₇	1	1	yes	characteristic, complemented
198	C₁₀₇	#10275	1	1	yes	characteristic, direct product factor, Sylow
199	C₂×C₄⋊Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
200	C₂×C₄⋊Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
201	C₂×C₄×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
202	#487	—	2	2	no	—
203	#487	—	2	2	no	—
204	#476	—	2	2	no	—
205	#476	—	2	2	no	—
206	#474	—	2	2	no	—
207	#474	—	2	2	no	—
208	C₂×#107	—	2	1	no	—
209	C₂×#106	—	2	1	no	—
210	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	1	yes	characteristic
213	C₂×#103	—	2	2	no	—
214	C₂×#102	—	2	1	no	—
215	C₂×#102	—	2	1	no	—
216	C₂×C₂²⋊C₈	—	2	2	no	—
217	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
218	#333	—	2	2	no	—
219	#332	—	2	2	no	—
220	C₂²×Q₈	—	2	1	no	—
221	C₂²×Q₈	—	2	1	no	—
222	C₂²×D₄	D₄×C₁₀₇	1	1	yes	characteristic
223	C₂³×C₄	—	2	1	no	—
224	C₂²×C₈	—	2	1	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₂²×C₈	—	2	1	no	—
227	C₂²×C₈	D₄×C₁₀₇	1	2	yes	—
228	C₄⋊Q₈	—	2	1	no	—
229	C₄⋊Q₈	—	2	1	no	—
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	D₄×C₁₀₇	1	2	yes	—
235	C₄⋊Q₈	D₄×C₁₀₇	1	2	yes	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	D₄×C₁₀₇	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	—	2	1	no	—
246	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
247	#107	—	2	4	no	—
248	#106	—	2	4	no	—
249	C₄⋊C₈	—	2	1	no	—
250	C₄⋊C₈	—	2	1	no	—
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	D₄×C₁₀₇	1	2	yes	—
254	C₄⋊C₈	D₄×C₁₀₇	1	2	yes	—
255	#103	—	2	8	no	—
256	#102	—	2	4	no	—
257	#102	—	2	4	no	—
258	C₂²⋊C₈	—	4	4	no	—
259	C₄×C₈	—	2	1	no	—
260	C₄×C₈	—	2	1	no	—
261	C₂⁴	—	2	1	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	4	1	no	—
265	C₂×Q₈	—	4	1	no	—
266	C₂×Q₈	—	4	2	no	—
267	C₂×Q₈	—	4	2	no	—
268	C₂×Q₈	—	8	2	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	Q₁₆×C₁₀₇	1	2	yes	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
284	C₂²×C₄	#41×C₁₀₇	1	1	yes	characteristic
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	4	1	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	4	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	—	4	1	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
309	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
310	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
311	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
312	C₂³	—	2	2	no	—
313	C₂³	—	4	1	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	4	2	no	—
317	C₂³	#121×C₁₀₇	1	1	yes	characteristic
318	Q₈	—	4	4	no	—
319	Q₈	—	8	2	no	—
320	Q₈	—	8	2	no	—
321	Q₈	—	8	1	no	—
322	Q₈	—	8	1	no	—
323	D₄	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	4	1	no	—
326	D₄	—	4	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	8	2	no	—
333	C₂×C₄	—	8	2	no	—
334	C₂×C₄	—	8	2	no	—
335	C₂×C₄	—	8	1	no	—
336	C₂×C₄	—	8	1	no	—
337	C₂×C₄	#120×C₁₀₇	1	1	yes	characteristic
338	C₂×C₄	#120×C₁₀₇	1	1	yes	characteristic
339	C₂×C₄	#120×C₁₀₇	1	1	yes	characteristic
340	C₂×C₄	#121×C₁₀₇	1	1	yes	characteristic
341	C₂×C₄	#121×C₁₀₇	1	1	yes	characteristic
342	C₂×C₄	#127×C₁₀₇	1	1	yes	characteristic
343	C₂×C₄	C₂×Q₁₆×C₁₀₇	1	1	yes	characteristic
344	C₂×C₄	#135×C₁₀₇	1	2	yes	—
345	C₂×C₄	#135×C₁₀₇	1	1	yes	characteristic
346	C₂×C₄	AGL(1,ℤ/8)×C₁₀₇	1	2	yes	—
347	C₂×C₄	#137×C₁₀₇	1	1	yes	characteristic
348	C₂×C₄	#137×C₁₀₇	1	1	yes	characteristic
349	C₈	—	4	2	no	—
350	C₈	—	4	2	no	—
351	C₈	—	4	2	no	—
352	C₈	—	8	1	no	—
353	C₂²	—	4	4	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	1	no	—
357	C₂²	—	8	1	no	—
358	C₂²	#392×C₁₀₇	1	1	yes	characteristic
359	C₂²	#463×C₁₀₇	1	2	yes	—
360	C₂²	#467×C₁₀₇	1	1	yes	characteristic
361	C₂²	#470×C₁₀₇	1	1	yes	characteristic
362	C₂²	#471×C₁₀₇	1	2	yes	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	8	1	no	—
366	C₄	—	8	2	no	—
367	C₄	—	8	2	no	—
368	C₄	#449×C₁₀₇	1	2	yes	—
369	C₄	#451×C₁₀₇	1	1	yes	characteristic
370	C₄	#451×C₁₀₇	1	1	yes	characteristic
371	C₄	#452×C₁₀₇	1	1	yes	characteristic
372	C₄	#452×C₁₀₇	1	1	yes	characteristic
373	C₄	#495×C₁₀₇	1	1	yes	characteristic
374	C₄	#496×C₁₀₇	1	1	yes	characteristic
375	C₂	—	8	2	no	—
376	C₂	C₁₀₇×#1683	1	2	yes	—
377	C₂	C₁₀₇×#1703	1	2	yes	—
378	C₂	C₁₀₇×#2001	1	1	yes	characteristic
379	C₂	C₁₀₇×#2012	1	1	yes	characteristic
380	C₂	C₁₀₇×#2019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₇	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₀₇
prime radical	C₂²×D₄×C₁₀₇	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₇ ◁ C₂×C₄²×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#487×C₁₀₇	C₂	semidirect
5. C₂×#333×C₁₀₇	C₂	semidirect
6. C₂×#332×C₁₀₇	C₂	semidirect
7. C₁₀₇×#1277	C₂	semidirect
184. #10275	C₁₀₇	direct (N × H)
191. C₂×#487	C₂×C₁₀₇	semidirect
195. C₂×#333	C₂×C₁₀₇	semidirect
196. C₂×#332	C₂×C₁₀₇	semidirect
197. #1277	C₂×C₁₀₇	semidirect
198. C₁₀₇	#10275	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#487×C₁₀₇	2
C₂×#476×C₁₀₇	2
C₂×#474×C₁₀₇	2
C₁₀₇×#1954	2
C₂×#333×C₁₀₇	2
C₂×#332×C₁₀₇	2
C₁₀₇×#1277	2
#10275	107

Subgroups — C107×#10275 #41036239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#10275 #41036239