Subgroups — C₁₀₇×#2428 #28333111

Order 13696.

832 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#127×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#121×C₁₀₇	C₂	1	2	yes	maximal, complemented
3	C₂×#121×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#121×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×D₄×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#394×C₁₀₇	C₂	1	2	yes	maximal, complemented
7	#392×C₁₀₇	C₂	1	2	yes	maximal, complemented
8	#390×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#389×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#386×C₁₀₇	C₂	1	2	yes	maximal, complemented
11	C₄×C₂²⋊C₄×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₁₀₇	C₂²	1	2	yes	—
14	C₂²×D₄×C₁₀₇	C₂²	1	2	yes	—
15	C₂²×D₄×C₁₀₇	C₂²	1	2	yes	—
16	C₂²×D₄×C₁₀₇	C₂²	1	2	yes	—
17	C₂²×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₁₀₇	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₁₀₇	C₂²	1	2	yes	—
20	#127×C₁₀₇	—	2	4	no	—
21	#121×C₁₀₇	—	2	4	no	—
22	#121×C₁₀₇	—	2	4	no	—
23	#121×C₁₀₇	—	2	8	no	—
24	C₄×D₄×C₁₀₇	—	2	4	no	—
25	C₂×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	—
27	C₂×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₁₀₇	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₄×C₁₀₇	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₄×C₁₀₇	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₄×C₁₀₇	C₂²	1	2	yes	—
33	C₂×C₂²⋊C₄×C₁₀₇	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
35	C₂×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
36	C₂×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
37	#95×C₁₀₇	C₂²	1	1	yes	characteristic
38	#95×C₁₀₇	C₂²	1	1	yes	characteristic
39	#95×C₁₀₇	C₂²	1	2	yes	—
40	C₂⁴×C₁₀₇	C₂³	1	2	yes	—
41	C₂⁴×C₁₀₇	C₂³	1	2	yes	—
42	C₂⁴×C₁₀₇	C₂³	1	1	yes	characteristic
43	C₂×D₄×C₁₀₇	—	2	4	no	—
44	C₂×D₄×C₁₀₇	—	2	4	no	—
45	C₂×D₄×C₁₀₇	—	2	4	no	—
46	C₂×D₄×C₁₀₇	—	2	4	no	—
47	C₂×D₄×C₁₀₇	—	2	4	no	—
48	C₂×D₄×C₁₀₇	—	2	2	no	—
49	C₂×D₄×C₁₀₇	—	2	4	no	—
50	C₂×D₄×C₁₀₇	—	2	4	no	—
51	C₂×D₄×C₁₀₇	—	2	2	no	—
52	C₂×D₄×C₁₀₇	—	2	2	no	—
53	C₂×D₄×C₁₀₇	—	2	2	no	—
54	C₂×D₄×C₁₀₇	—	2	4	no	—
55	C₂×D₄×C₁₀₇	—	2	2	no	—
56	C₂×D₄×C₁₀₇	—	4	2	no	—
57	C₂×D₄×C₁₀₇	—	4	2	no	—
58	C₂×D₄×C₁₀₇	—	4	2	no	—
59	C₂×D₄×C₁₀₇	—	4	2	no	—
60	C₂×D₄×C₁₀₇	D₄	1	4	yes	complemented
61	C₂²×C₄×C₁₀₇	—	2	4	no	—
62	C₂²×C₄×C₁₀₇	—	2	4	no	—
63	C₂²×C₄×C₁₀₇	—	2	2	no	—
64	C₂²×C₄×C₁₀₇	—	2	2	no	—
65	C₂²×C₄×C₁₀₇	—	2	2	no	—
66	C₂²×C₄×C₁₀₇	—	4	2	no	—
67	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₁₀₇	C₂³	1	2	yes	—
70	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₁₀₇	C₂³	1	2	yes	—
73	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
75	C₄⋊C₄×C₁₀₇	—	2	4	no	—
76	C₄⋊C₄×C₁₀₇	—	2	2	no	—
77	C₄⋊C₄×C₁₀₇	D₄	1	4	yes	complemented
78	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
79	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
80	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
81	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
82	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
83	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
84	C₂²⋊C₄×C₁₀₇	D₄	1	4	yes	complemented
85	C₄²×C₁₀₇	—	2	2	no	—
86	C₄²×C₁₀₇	—	2	2	no	—
87	C₂³×C₁₀₇	—	2	2	no	—
88	C₂³×C₁₀₇	—	2	1	no	—
89	C₂³×C₁₀₇	—	2	1	no	—
90	C₂³×C₁₀₇	—	2	2	no	—
91	C₂³×C₁₀₇	—	2	1	no	—
92	C₂³×C₁₀₇	—	2	1	no	—
93	C₂³×C₁₀₇	—	2	2	no	—
94	C₂³×C₁₀₇	—	2	2	no	—
95	C₂³×C₁₀₇	—	2	2	no	—
96	C₂³×C₁₀₇	—	2	1	no	—
97	C₂³×C₁₀₇	—	2	2	no	—
98	C₂³×C₁₀₇	—	2	1	no	—
99	C₂³×C₁₀₇	—	2	2	no	—
100	C₂³×C₁₀₇	—	2	2	no	—
101	C₂³×C₁₀₇	—	2	2	no	—
102	C₂³×C₁₀₇	—	2	2	no	—
103	C₂³×C₁₀₇	—	2	2	no	—
104	C₂³×C₁₀₇	—	2	2	no	—
105	C₂³×C₁₀₇	—	2	2	no	—
106	C₂³×C₁₀₇	C₂×D₄	1	4	yes	—
107	C₂³×C₁₀₇	C₂×D₄	1	2	yes	—
108	C₂³×C₁₀₇	C₂⁴	1	1	yes	characteristic
109	D₄×C₁₀₇	—	2	8	no	—
110	D₄×C₁₀₇	—	4	8	no	—
111	D₄×C₁₀₇	—	4	8	no	—
112	D₄×C₁₀₇	—	4	8	no	—
113	D₄×C₁₀₇	—	4	8	no	—
114	D₄×C₁₀₇	—	4	4	no	—
115	C₂×C₄×C₁₀₇	—	2	1	no	—
116	C₂×C₄×C₁₀₇	—	2	1	no	—
117	C₂×C₄×C₁₀₇	—	2	1	no	—
118	C₂×C₄×C₁₀₇	—	2	2	no	—
119	C₂×C₄×C₁₀₇	—	2	1	no	—
120	C₂×C₄×C₁₀₇	—	2	2	no	—
121	C₂×C₄×C₁₀₇	—	2	1	no	—
122	C₂×C₄×C₁₀₇	—	2	1	no	—
123	C₂×C₄×C₁₀₇	—	2	1	no	—
124	C₂×C₄×C₁₀₇	—	2	1	no	—
125	C₂×C₄×C₁₀₇	—	2	1	no	—
126	C₂×C₄×C₁₀₇	—	2	2	no	—
127	C₂×C₄×C₁₀₇	—	2	2	no	—
128	C₂×C₄×C₁₀₇	—	2	1	no	—
129	C₂×C₄×C₁₀₇	—	2	1	no	—
130	C₂×C₄×C₁₀₇	—	2	1	no	—
131	C₂×C₄×C₁₀₇	—	2	2	no	—
132	C₂×C₄×C₁₀₇	—	4	8	no	—
133	C₂×C₄×C₁₀₇	—	4	4	no	—
134	C₂×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
135	C₂×C₄×C₁₀₇	C₂×D₄	1	4	yes	—
136	C₂×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
137	C₂×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
138	C₂×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
139	C₂×C₄×C₁₀₇	#41	1	2	yes	—
140	C₂×C₄×C₁₀₇	#41	1	2	yes	—
141	C₂²×C₁₀₇	—	2	4	no	—
142	C₂²×C₁₀₇	—	2	2	no	—
143	C₂²×C₁₀₇	—	2	2	no	—
144	C₂²×C₁₀₇	—	2	4	no	—
145	C₂²×C₁₀₇	—	2	2	no	—
146	C₂²×C₁₀₇	—	2	4	no	—
147	C₂²×C₁₀₇	—	4	1	no	—
148	C₂²×C₁₀₇	—	4	2	no	—
149	C₂²×C₁₀₇	—	4	1	no	—
150	C₂²×C₁₀₇	—	4	2	no	—
151	C₂²×C₁₀₇	—	4	2	no	—
152	C₂²×C₁₀₇	—	4	1	no	—
153	C₂²×C₁₀₇	—	4	2	no	—
154	C₂²×C₁₀₇	—	4	1	no	—
155	C₂²×C₁₀₇	—	4	2	no	—
156	C₂²×C₁₀₇	—	4	2	no	—
157	C₂²×C₁₀₇	—	4	2	no	—
158	C₂²×C₁₀₇	—	4	2	no	—
159	C₂²×C₁₀₇	—	4	2	no	—
160	C₂²×C₁₀₇	—	4	2	no	—
161	C₂²×C₁₀₇	—	4	2	no	—
162	C₂²×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
163	C₂²×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
164	C₂²×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
165	C₂²×C₁₀₇	C₂×#41	1	1	yes	characteristic
166	C₂²×C₁₀₇	C₂×#41	1	1	yes	characteristic
167	C₂²×C₁₀₇	H(5,𝔽₂)	1	1	yes	characteristic
168	C₂²×C₁₀₇	H(5,𝔽₂)	1	1	yes	characteristic
169	C₄×C₁₀₇	—	2	2	no	—
170	C₄×C₁₀₇	—	2	4	no	—
171	C₄×C₁₀₇	—	2	2	no	—
172	C₄×C₁₀₇	—	2	2	no	—
173	C₄×C₁₀₇	—	4	1	no	—
174	C₄×C₁₀₇	—	4	2	no	—
175	C₄×C₁₀₇	—	4	1	no	—
176	C₄×C₁₀₇	#121	1	4	yes	complemented
177	C₂×C₁₀₇	—	4	4	no	—
178	C₂×C₁₀₇	—	4	2	no	—
179	C₂×C₁₀₇	—	8	2	no	—
180	C₂×C₁₀₇	C₂×#121	1	1	yes	characteristic
181	C₂×C₁₀₇	#532	1	1	yes	characteristic
182	C₂×C₁₀₇	#540	1	1	yes	characteristic
183	C₂×C₁₀₇	D₄²	1	1	yes	characteristic
184	C₂×C₁₀₇	D₄²	1	1	yes	characteristic
185	C₂×C₁₀₇	#546	1	1	yes	characteristic
186	C₂×C₁₀₇	#550	1	1	yes	characteristic
187	#2428	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₁₀₇	#2428	1	1	yes	characteristic, direct product factor, Sylow
189	C₂×#127	C₂×C₁₀₇	1	1	yes	characteristic, complemented
190	C₂×#121	C₂×C₁₀₇	1	2	yes	complemented
191	C₂×#121	C₂×C₁₀₇	1	1	yes	characteristic, complemented
192	C₂×#121	C₂×C₁₀₇	1	1	yes	characteristic, complemented
193	C₂×C₄×D₄	C₂×C₁₀₇	1	1	yes	characteristic, complemented
194	#394	C₂×C₁₀₇	1	2	yes	complemented
195	#392	C₂×C₁₀₇	1	2	yes	complemented
196	#390	C₂×C₁₀₇	1	1	yes	characteristic, complemented
197	#389	C₂×C₁₀₇	1	1	yes	characteristic, complemented
198	#386	C₂×C₁₀₇	1	2	yes	complemented
199	C₄×C₂²⋊C₄	C₂×C₁₀₇	1	1	yes	characteristic, complemented
200	C₂²×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
201	C₂²×D₄	C₂²×C₁₀₇	1	2	yes	—
202	C₂²×D₄	C₂²×C₁₀₇	1	2	yes	—
203	C₂²×D₄	C₂²×C₁₀₇	1	2	yes	—
204	C₂²×D₄	C₂²×C₁₀₇	1	2	yes	—
205	C₂²×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
206	C₂³×C₄	C₂²×C₁₀₇	1	1	yes	characteristic
207	C₂³×C₄	C₂²×C₁₀₇	1	2	yes	—
208	#127	—	2	4	no	—
209	#121	—	2	4	no	—
210	#121	—	2	4	no	—
211	#121	—	2	8	no	—
212	C₄×D₄	—	2	4	no	—
213	C₂×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂²×C₁₀₇	1	2	yes	—
215	C₂×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
216	C₂×C₂²⋊C₄	C₂²×C₁₀₇	1	2	yes	—
217	C₂×C₂²⋊C₄	C₂²×C₁₀₇	1	2	yes	—
218	C₂×C₂²⋊C₄	C₂²×C₁₀₇	1	2	yes	—
219	C₂×C₂²⋊C₄	C₂²×C₁₀₇	1	2	yes	—
220	C₂×C₂²⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	C₂²×C₁₀₇	1	2	yes	—
222	C₂×C₂²⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
223	C₂×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
224	C₂×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
225	#95	C₂²×C₁₀₇	1	1	yes	characteristic
226	#95	C₂²×C₁₀₇	1	1	yes	characteristic
227	#95	C₂²×C₁₀₇	1	2	yes	—
228	C₂⁴	C₂³×C₁₀₇	1	2	yes	—
229	C₂⁴	C₂³×C₁₀₇	1	2	yes	—
230	C₂⁴	C₂³×C₁₀₇	1	1	yes	characteristic
231	C₂×D₄	—	2	4	no	—
232	C₂×D₄	—	2	4	no	—
233	C₂×D₄	—	2	4	no	—
234	C₂×D₄	—	2	4	no	—
235	C₂×D₄	—	2	4	no	—
236	C₂×D₄	—	2	2	no	—
237	C₂×D₄	—	2	4	no	—
238	C₂×D₄	—	2	4	no	—
239	C₂×D₄	—	2	2	no	—
240	C₂×D₄	—	2	2	no	—
241	C₂×D₄	—	2	2	no	—
242	C₂×D₄	—	2	4	no	—
243	C₂×D₄	—	2	2	no	—
244	C₂×D₄	—	4	2	no	—
245	C₂×D₄	—	4	2	no	—
246	C₂×D₄	—	4	2	no	—
247	C₂×D₄	—	4	2	no	—
248	C₂×D₄	D₄×C₁₀₇	1	4	yes	complemented
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	4	2	no	—
255	C₂²×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
256	C₂²×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
257	C₂²×C₄	C₂³×C₁₀₇	1	2	yes	—
258	C₂²×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
259	C₂²×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
260	C₂²×C₄	C₂³×C₁₀₇	1	2	yes	—
261	C₂²×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
262	C₂²×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
263	C₄⋊C₄	—	2	4	no	—
264	C₄⋊C₄	—	2	2	no	—
265	C₄⋊C₄	D₄×C₁₀₇	1	4	yes	complemented
266	C₂²⋊C₄	—	2	4	no	—
267	C₂²⋊C₄	—	2	4	no	—
268	C₂²⋊C₄	—	2	4	no	—
269	C₂²⋊C₄	—	2	4	no	—
270	C₂²⋊C₄	—	2	2	no	—
271	C₂²⋊C₄	—	4	2	no	—
272	C₂²⋊C₄	D₄×C₁₀₇	1	4	yes	complemented
273	C₄²	—	2	2	no	—
274	C₄²	—	2	2	no	—
275	C₂³	—	2	2	no	—
276	C₂³	—	2	1	no	—
277	C₂³	—	2	1	no	—
278	C₂³	—	2	2	no	—
279	C₂³	—	2	1	no	—
280	C₂³	—	2	1	no	—
281	C₂³	—	2	2	no	—
282	C₂³	—	2	2	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	1	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	1	no	—
287	C₂³	—	2	2	no	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	2	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	C₂×D₄×C₁₀₇	1	4	yes	—
295	C₂³	C₂×D₄×C₁₀₇	1	2	yes	—
296	C₂³	C₂⁴×C₁₀₇	1	1	yes	characteristic
297	D₄	—	2	8	no	—
298	D₄	—	4	8	no	—
299	D₄	—	4	8	no	—
300	D₄	—	4	8	no	—
301	D₄	—	4	8	no	—
302	D₄	—	4	4	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	4	8	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
323	C₂×C₄	C₂×D₄×C₁₀₇	1	4	yes	—
324	C₂×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
325	C₂×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
326	C₂×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
327	C₂×C₄	#41×C₁₀₇	1	2	yes	—
328	C₂×C₄	#41×C₁₀₇	1	2	yes	—
329	C₂²	—	2	4	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	4	2	no	—
339	C₂²	—	4	2	no	—
340	C₂²	—	4	1	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	1	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	4	2	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
351	C₂²	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
352	C₂²	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
353	C₂²	C₂×#41×C₁₀₇	1	1	yes	characteristic
354	C₂²	C₂×#41×C₁₀₇	1	1	yes	characteristic
355	C₂²	H(5,𝔽₂)×C₁₀₇	1	1	yes	characteristic
356	C₂²	H(5,𝔽₂)×C₁₀₇	1	1	yes	characteristic
357	C₄	—	2	2	no	—
358	C₄	—	2	4	no	—
359	C₄	—	2	2	no	—
360	C₄	—	2	2	no	—
361	C₄	—	4	1	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	1	no	—
364	C₄	#121×C₁₀₇	1	4	yes	complemented
365	C₂	—	4	4	no	—
366	C₂	—	4	2	no	—
367	C₂	—	8	2	no	—
368	C₂	C₂×#121×C₁₀₇	1	1	yes	characteristic
369	C₂	#532×C₁₀₇	1	1	yes	characteristic
370	C₂	#540×C₁₀₇	1	1	yes	characteristic
371	C₂	D₄²×C₁₀₇	1	1	yes	characteristic
372	C₂	D₄²×C₁₀₇	1	1	yes	characteristic
373	C₂	#546×C₁₀₇	1	1	yes	characteristic
374	C₂	#550×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₀₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#127×C₁₀₇	C₂	semidirect
2. C₂×#121×C₁₀₇	C₂	semidirect
3. C₂×#121×C₁₀₇	C₂	semidirect
4. C₂×#121×C₁₀₇	C₂	semidirect
5. C₂×C₄×D₄×C₁₀₇	C₂	semidirect
6. #394×C₁₀₇	C₂	semidirect
7. #392×C₁₀₇	C₂	semidirect
8. #390×C₁₀₇	C₂	semidirect
9. #389×C₁₀₇	C₂	semidirect
10. #386×C₁₀₇	C₂	semidirect
11. C₄×C₂²⋊C₄×C₁₀₇	C₂	semidirect
60. C₂×D₄×C₁₀₇	D₄	semidirect
77. C₄⋊C₄×C₁₀₇	D₄	semidirect
84. C₂²⋊C₄×C₁₀₇	D₄	semidirect
176. C₄×C₁₀₇	#121	semidirect
187. #2428	C₁₀₇	direct (N × H)
188. C₁₀₇	#2428	direct (N × H)
189. C₂×#127	C₂×C₁₀₇	semidirect
190. C₂×#121	C₂×C₁₀₇	semidirect
191. C₂×#121	C₂×C₁₀₇	semidirect
192. C₂×#121	C₂×C₁₀₇	semidirect
193. C₂×C₄×D₄	C₂×C₁₀₇	semidirect
194. #394	C₂×C₁₀₇	semidirect
195. #392	C₂×C₁₀₇	semidirect
196. #390	C₂×C₁₀₇	semidirect
197. #389	C₂×C₁₀₇	semidirect
198. #386	C₂×C₁₀₇	semidirect
199. C₄×C₂²⋊C₄	C₂×C₁₀₇	semidirect
248. C₂×D₄	D₄×C₁₀₇	semidirect
265. C₄⋊C₄	D₄×C₁₀₇	semidirect
272. C₂²⋊C₄	D₄×C₁₀₇	semidirect
364. C₄	#121×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#127×C₁₀₇	2
C₂×#121×C₁₀₇	2
C₂×C₄×D₄×C₁₀₇	2
#394×C₁₀₇	2
#392×C₁₀₇	2
#390×C₁₀₇	2
#389×C₁₀₇	2
#386×C₁₀₇	2
C₄×C₂²⋊C₄×C₁₀₇	2
#2428	107

Subgroups — C107×#2428 #28333111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#2428 #28333111