Subgroups — C₁₀₇×#33606 #41059570

Order 27392.

686 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#510×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×M₃₂×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₇×#3050	C₂	1	1	yes	maximal, characteristic
4	C₂×#467×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₇×#2220	C₂	1	2	yes	maximal, complemented
6	C₁₀₇×#2219	C₂	1	2	yes	maximal, complemented
7	C₁₀₇×#2217	C₂	1	2	yes	maximal, complemented
8	C₁₀₇×#2216	C₂	1	2	yes	maximal, complemented
9	C₁₀₇×#2159	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₇×#2141	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₀₇×#2139	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₀₇	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
15	#525×C₁₀₇	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₁₀₇	—	2	1	no	—
17	#510×C₁₀₇	—	2	4	no	—
18	C₂×Q₃₂×C₁₀₇	C₂²	1	2	yes	complemented
19	C₂×SD₃₂×C₁₀₇	C₂²	1	2	yes	complemented
20	C₂×M₃₂×C₁₀₇	—	2	4	no	—
21	C₂×M₃₂×C₁₀₇	C₂²	1	1	yes	characteristic
22	C₂×M₃₂×C₁₀₇	C₂²	1	2	yes	—
23	C₂×M₃₂×C₁₀₇	C₂²	1	1	yes	characteristic
24	C₂²×C₁₆×C₁₀₇	C₂²	1	2	yes	—
25	#467×C₁₀₇	—	2	1	no	—
26	#467×C₁₀₇	—	2	1	no	—
27	#467×C₁₀₇	C₂²	1	1	yes	characteristic
28	#467×C₁₀₇	C₂²	1	2	yes	—
29	#467×C₁₀₇	C₂²	1	1	yes	characteristic
30	#467×C₁₀₇	C₂²	1	2	yes	—
31	#466×C₁₀₇	C₂²	1	1	yes	characteristic
32	#466×C₁₀₇	C₂²	1	1	yes	characteristic
33	#465×C₁₀₇	—	2	1	no	—
34	#465×C₁₀₇	—	2	1	no	—
35	#427×C₁₀₇	C₂²	1	1	yes	characteristic
36	C₂×#107×C₁₀₇	C₂²	1	1	yes	characteristic
37	#416×C₁₀₇	—	2	1	no	—
38	C₂×#103×C₁₀₇	—	2	1	no	—
39	#367×C₁₀₇	C₂²	1	2	yes	complemented
40	#366×C₁₀₇	C₂²	1	2	yes	complemented
41	#358×C₁₀₇	C₂²	1	2	yes	complemented
42	#358×C₁₀₇	C₂²	1	2	yes	complemented
43	#358×C₁₀₇	C₂²	1	2	yes	complemented
44	#357×C₁₀₇	C₂²	1	2	yes	complemented
45	C₂×#41×C₁₀₇	—	2	1	no	—
46	C₂²×Q₈×C₁₀₇	—	2	1	no	—
47	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
48	#135×C₁₀₇	—	2	2	no	—
49	#135×C₁₀₇	—	2	2	no	—
50	C₂×Q₁₆×C₁₀₇	—	2	2	no	—
51	C₂×Q₁₆×C₁₀₇	—	2	1	no	—
52	C₂×Q₁₆×C₁₀₇	—	2	2	no	—
53	C₂×Q₁₆×C₁₀₇	C₂³	1	2	yes	—
54	C₂×Q₁₆×C₁₀₇	C₂³	1	1	yes	characteristic
55	C₂×SD₁₆×C₁₀₇	—	2	1	no	—
56	C₂×D₈×C₁₀₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₀₇	—	2	2	no	—
58	C₂²×C₈×C₁₀₇	—	2	2	no	—
59	C₂²×C₈×C₁₀₇	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₁₀₇	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₀₇	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
65	#123×C₁₀₇	—	4	1	no	—
66	C₂²⋊Q₈×C₁₀₇	—	2	1	no	—
67	C₂²⋊Q₈×C₁₀₇	—	2	1	no	—
68	C₂²⋊Q₈×C₁₀₇	—	2	2	no	—
69	C₂²⋊Q₈×C₁₀₇	—	2	2	no	—
70	C₂²⋊Q₈×C₁₀₇	—	4	1	no	—
71	C₂²⋊Q₈×C₁₀₇	—	4	1	no	—
72	#121×C₁₀₇	—	2	1	no	—
73	#121×C₁₀₇	—	2	1	no	—
74	#120×C₁₀₇	—	4	1	no	—
75	C₄×D₄×C₁₀₇	—	4	1	no	—
76	C₄×D₄×C₁₀₇	—	4	1	no	—
77	#117×C₁₀₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₀₇	—	4	1	no	—
80	C₂×C₂²⋊C₄×C₁₀₇	—	4	1	no	—
81	Q₃₂×C₁₀₇	—	2	4	no	—
82	SD₃₂×C₁₀₇	—	2	4	no	—
83	M₃₂×C₁₀₇	—	2	2	no	—
84	M₃₂×C₁₀₇	—	2	4	no	—
85	M₃₂×C₁₀₇	D₄	1	4	yes	complemented
86	C₂×C₁₆×C₁₀₇	—	2	4	no	—
87	C₂×C₁₆×C₁₀₇	C₂³	1	2	yes	—
88	C₂×C₁₆×C₁₀₇	C₂³	1	2	yes	—
89	#107×C₁₀₇	—	2	1	no	—
90	#107×C₁₀₇	C₂³	1	2	yes	—
91	#107×C₁₀₇	C₂³	1	1	yes	characteristic
92	#107×C₁₀₇	C₂³	1	1	yes	characteristic
93	#106×C₁₀₇	—	2	1	no	—
94	#103×C₁₀₇	—	2	2	no	—
95	#103×C₁₀₇	—	2	2	no	—
96	#103×C₁₀₇	—	2	1	no	—
97	#103×C₁₀₇	—	2	1	no	—
98	#102×C₁₀₇	—	2	1	no	—
99	#102×C₁₀₇	—	2	1	no	—
100	C₂⁴×C₁₀₇	D₈	1	1	yes	characteristic
101	#41×C₁₀₇	—	4	2	no	—
102	#41×C₁₀₇	—	4	2	no	—
103	C₂×Q₈×C₁₀₇	—	2	1	no	—
104	C₂×Q₈×C₁₀₇	—	2	2	no	—
105	C₂×Q₈×C₁₀₇	—	4	1	no	—
106	C₂×Q₈×C₁₀₇	—	4	2	no	—
107	C₂×Q₈×C₁₀₇	—	4	2	no	—
108	C₂×D₄×C₁₀₇	—	2	1	no	—
109	C₂×D₄×C₁₀₇	—	4	1	no	—
110	C₂×D₄×C₁₀₇	—	4	1	no	—
111	C₂×D₄×C₁₀₇	—	4	1	no	—
112	C₂²×C₄×C₁₀₇	—	2	2	no	—
113	C₂²×C₄×C₁₀₇	—	2	2	no	—
114	C₂²×C₄×C₁₀₇	—	4	1	no	—
115	C₂²×C₄×C₁₀₇	—	4	1	no	—
116	C₂²×C₄×C₁₀₇	—	4	1	no	—
117	C₂²×C₄×C₁₀₇	D₈	1	1	yes	characteristic
118	C₂²×C₄×C₁₀₇	D₈	1	1	yes	characteristic
119	C₂²×C₄×C₁₀₇	D₈	1	1	yes	characteristic
120	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
123	Q₁₆×C₁₀₇	—	2	2	no	—
124	Q₁₆×C₁₀₇	—	2	1	no	—
125	Q₁₆×C₁₀₇	—	2	2	no	—
126	Q₁₆×C₁₀₇	—	2	1	no	—
127	Q₁₆×C₁₀₇	—	4	2	no	—
128	SD₁₆×C₁₀₇	—	4	2	no	—
129	D₈×C₁₀₇	—	2	1	no	—
130	D₈×C₁₀₇	—	2	1	no	—
131	C₂×C₈×C₁₀₇	—	2	2	no	—
132	C₂×C₈×C₁₀₇	—	2	2	no	—
133	C₂×C₈×C₁₀₇	—	2	2	no	—
134	C₂×C₈×C₁₀₇	—	2	1	no	—
135	C₂×C₈×C₁₀₇	—	2	1	no	—
136	C₂×C₈×C₁₀₇	—	2	1	no	—
137	C₂×C₈×C₁₀₇	—	2	1	no	—
138	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₁₀₇	#41	1	2	yes	—
143	C₂×C₈×C₁₀₇	C₂⁴	1	1	yes	characteristic
144	C₄⋊C₄×C₁₀₇	—	2	1	no	—
145	C₄⋊C₄×C₁₀₇	—	2	1	no	—
146	C₄⋊C₄×C₁₀₇	—	2	2	no	—
147	C₄⋊C₄×C₁₀₇	—	4	1	no	—
148	C₄⋊C₄×C₁₀₇	—	4	2	no	—
149	C₄⋊C₄×C₁₀₇	—	4	2	no	—
150	C₄⋊C₄×C₁₀₇	—	4	1	no	—
151	C₄⋊C₄×C₁₀₇	—	4	1	no	—
152	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
153	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
154	C₂²⋊C₄×C₁₀₇	—	4	1	no	—
155	C₂²⋊C₄×C₁₀₇	—	4	1	no	—
156	C₂²⋊C₄×C₁₀₇	—	4	1	no	—
157	C₂²⋊C₄×C₁₀₇	—	4	1	no	—
158	C₂²⋊C₄×C₁₀₇	—	4	1	no	—
159	C₄²×C₁₀₇	—	4	1	no	—
160	C₁₆×C₁₀₇	—	2	2	no	—
161	C₁₆×C₁₀₇	C₂×D₄	1	4	yes	—
162	C₂³×C₁₀₇	—	2	2	no	—
163	C₂³×C₁₀₇	—	2	2	no	—
164	C₂³×C₁₀₇	—	4	1	no	—
165	C₂³×C₁₀₇	—	4	1	no	—
166	C₂³×C₁₀₇	C₂×D₈	1	1	yes	characteristic
167	C₂³×C₁₀₇	C₂×D₈	1	1	yes	characteristic
168	C₂³×C₁₀₇	C₂×D₈	1	1	yes	characteristic
169	Q₈×C₁₀₇	—	4	1	no	—
170	Q₈×C₁₀₇	—	4	2	no	—
171	Q₈×C₁₀₇	—	4	2	no	—
172	Q₈×C₁₀₇	—	4	1	no	—
173	Q₈×C₁₀₇	—	8	2	no	—
174	D₄×C₁₀₇	—	4	1	no	—
175	D₄×C₁₀₇	—	4	1	no	—
176	D₄×C₁₀₇	—	8	2	no	—
177	D₄×C₁₀₇	—	8	2	no	—
178	D₄×C₁₀₇	—	8	2	no	—
179	C₂×C₄×C₁₀₇	—	2	2	no	—
180	C₂×C₄×C₁₀₇	—	2	1	no	—
181	C₂×C₄×C₁₀₇	—	2	1	no	—
182	C₂×C₄×C₁₀₇	—	2	1	no	—
183	C₂×C₄×C₁₀₇	—	2	1	no	—
184	C₂×C₄×C₁₀₇	—	2	2	no	—
185	C₂×C₄×C₁₀₇	—	2	2	no	—
186	C₂×C₄×C₁₀₇	—	4	1	no	—
187	C₂×C₄×C₁₀₇	—	4	1	no	—
188	C₂×C₄×C₁₀₇	—	4	2	no	—
189	C₂×C₄×C₁₀₇	—	4	1	no	—
190	C₂×C₄×C₁₀₇	—	4	2	no	—
191	C₂×C₄×C₁₀₇	—	8	2	no	—
192	C₂×C₄×C₁₀₇	—	8	2	no	—
193	C₂×C₄×C₁₀₇	—	8	2	no	—
194	C₂×C₄×C₁₀₇	#121	1	2	yes	—
195	C₂×C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
197	C₂×C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
198	C₂×C₄×C₁₀₇	#135	1	2	yes	—
199	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
200	C₈×C₁₀₇	—	2	1	no	—
201	C₈×C₁₀₇	—	2	1	no	—
202	C₈×C₁₀₇	#121	1	2	yes	—
203	C₈×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
204	C₈×C₁₀₇	C₂×#41	1	1	yes	characteristic
205	C₂²×C₁₀₇	—	2	1	no	—
206	C₂²×C₁₀₇	—	2	1	no	—
207	C₂²×C₁₀₇	—	2	1	no	—
208	C₂²×C₁₀₇	—	2	1	no	—
209	C₂²×C₁₀₇	—	2	1	no	—
210	C₂²×C₁₀₇	—	2	1	no	—
211	C₂²×C₁₀₇	—	2	1	no	—
212	C₂²×C₁₀₇	—	4	4	no	—
213	C₂²×C₁₀₇	—	8	1	no	—
214	C₂²×C₁₀₇	—	8	1	no	—
215	C₂²×C₁₀₇	—	8	1	no	—
216	C₂²×C₁₀₇	#466	1	2	yes	—
217	C₂²×C₁₀₇	#510	1	2	yes	complemented
218	C₂²×C₁₀₇	C₂²×D₈	1	1	yes	characteristic
219	C₄×C₁₀₇	—	2	1	no	—
220	C₄×C₁₀₇	—	2	1	no	—
221	C₄×C₁₀₇	—	8	1	no	—
222	C₄×C₁₀₇	—	8	2	no	—
223	C₄×C₁₀₇	—	8	1	no	—
224	C₄×C₁₀₇	—	8	1	no	—
225	C₄×C₁₀₇	—	8	2	no	—
226	C₄×C₁₀₇	#466	1	2	yes	—
227	C₄×C₁₀₇	C₂×#121	1	1	yes	characteristic
228	C₄×C₁₀₇	C₂×#135	1	1	yes	characteristic
229	#33606	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂×C₁₀₇	—	2	2	no	—
231	C₂×C₁₀₇	—	2	2	no	—
232	C₂×C₁₀₇	—	4	1	no	—
233	C₂×C₁₀₇	—	16	1	no	—
234	C₂×C₁₀₇	C₂×#466	1	1	yes	characteristic
235	C₂×C₁₀₇	C₂×#510	1	1	yes	characteristic
236	C₂×C₁₀₇	#3414	1	1	yes	characteristic
237	C₂×#510	C₂×C₁₀₇	1	1	yes	characteristic, complemented
238	C₂²×M₃₂	C₂×C₁₀₇	1	1	yes	characteristic, complemented
239	#3050	C₂×C₁₀₇	1	1	yes	characteristic
240	C₂×#467	C₂×C₁₀₇	1	1	yes	characteristic, complemented
241	#2220	C₂×C₁₀₇	1	2	yes	complemented
242	#2219	C₂×C₁₀₇	1	2	yes	complemented
243	#2217	C₂×C₁₀₇	1	2	yes	complemented
244	#2216	C₂×C₁₀₇	1	2	yes	complemented
245	#2159	C₂×C₁₀₇	1	1	yes	characteristic, complemented
246	#2141	C₂×C₁₀₇	1	1	yes	characteristic, complemented
247	#2139	C₂×C₁₀₇	1	1	yes	characteristic, complemented
248	C₁₀₇	#33606	1	1	yes	characteristic, direct product factor, Sylow
249	C₂×#135	C₂²×C₁₀₇	1	1	yes	characteristic
250	C₂²×Q₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
251	C₂³×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
252	#525	—	2	1	no	—
253	C₂×C₂²⋊Q₈	—	2	1	no	—
254	#510	—	2	4	no	—
255	C₂×Q₃₂	C₂²×C₁₀₇	1	2	yes	complemented
256	C₂×SD₃₂	C₂²×C₁₀₇	1	2	yes	complemented
257	C₂×M₃₂	—	2	4	no	—
258	C₂×M₃₂	C₂²×C₁₀₇	1	1	yes	characteristic
259	C₂×M₃₂	C₂²×C₁₀₇	1	2	yes	—
260	C₂×M₃₂	C₂²×C₁₀₇	1	1	yes	characteristic
261	C₂²×C₁₆	C₂²×C₁₀₇	1	2	yes	—
262	#467	—	2	1	no	—
263	#467	—	2	1	no	—
264	#467	C₂²×C₁₀₇	1	1	yes	characteristic
265	#467	C₂²×C₁₀₇	1	2	yes	—
266	#467	C₂²×C₁₀₇	1	1	yes	characteristic
267	#467	C₂²×C₁₀₇	1	2	yes	—
268	#466	C₂²×C₁₀₇	1	1	yes	characteristic
269	#466	C₂²×C₁₀₇	1	1	yes	characteristic
270	#465	—	2	1	no	—
271	#465	—	2	1	no	—
272	#427	C₂²×C₁₀₇	1	1	yes	characteristic
273	C₂×#107	C₂²×C₁₀₇	1	1	yes	characteristic
274	#416	—	2	1	no	—
275	C₂×#103	—	2	1	no	—
276	#367	C₂²×C₁₀₇	1	2	yes	complemented
277	#366	C₂²×C₁₀₇	1	2	yes	complemented
278	#358	C₂²×C₁₀₇	1	2	yes	complemented
279	#358	C₂²×C₁₀₇	1	2	yes	complemented
280	#358	C₂²×C₁₀₇	1	2	yes	complemented
281	#357	C₂²×C₁₀₇	1	2	yes	complemented
282	C₂×#41	—	2	1	no	—
283	C₂²×Q₈	—	2	1	no	—
284	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
285	#135	—	2	2	no	—
286	#135	—	2	2	no	—
287	C₂×Q₁₆	—	2	2	no	—
288	C₂×Q₁₆	—	2	1	no	—
289	C₂×Q₁₆	—	2	2	no	—
290	C₂×Q₁₆	C₂³×C₁₀₇	1	2	yes	—
291	C₂×Q₁₆	C₂³×C₁₀₇	1	1	yes	characteristic
292	C₂×SD₁₆	—	2	1	no	—
293	C₂×D₈	C₂³×C₁₀₇	1	1	yes	characteristic
294	C₂²×C₈	—	2	2	no	—
295	C₂²×C₈	—	2	2	no	—
296	C₂²×C₈	D₄×C₁₀₇	1	1	yes	characteristic
297	C₂²×C₈	D₄×C₁₀₇	1	1	yes	characteristic
298	C₂²×C₈	D₄×C₁₀₇	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
302	#123	—	4	1	no	—
303	C₂²⋊Q₈	—	2	2	no	—
304	C₂²⋊Q₈	—	2	2	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	C₂²⋊Q₈	—	4	1	no	—
308	C₂²⋊Q₈	—	4	1	no	—
309	#121	—	2	1	no	—
310	#121	—	2	1	no	—
311	#120	—	4	1	no	—
312	C₄×D₄	—	4	1	no	—
313	C₄×D₄	—	4	1	no	—
314	#117	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	4	1	no	—
317	C₂×C₂²⋊C₄	—	4	1	no	—
318	Q₃₂	—	2	4	no	—
319	SD₃₂	—	2	4	no	—
320	M₃₂	—	2	2	no	—
321	M₃₂	—	2	4	no	—
322	M₃₂	D₄×C₁₀₇	1	4	yes	complemented
323	C₂×C₁₆	—	2	4	no	—
324	C₂×C₁₆	C₂³×C₁₀₇	1	2	yes	—
325	C₂×C₁₆	C₂³×C₁₀₇	1	2	yes	—
326	#107	—	2	1	no	—
327	#107	C₂³×C₁₀₇	1	2	yes	—
328	#107	C₂³×C₁₀₇	1	1	yes	characteristic
329	#107	C₂³×C₁₀₇	1	1	yes	characteristic
330	#106	—	2	1	no	—
331	#103	—	2	2	no	—
332	#103	—	2	2	no	—
333	#103	—	2	1	no	—
334	#103	—	2	1	no	—
335	#102	—	2	1	no	—
336	#102	—	2	1	no	—
337	C₂⁴	D₈×C₁₀₇	1	1	yes	characteristic
338	#41	—	4	2	no	—
339	#41	—	4	2	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	4	1	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×Q₈	—	4	2	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	D₈×C₁₀₇	1	1	yes	characteristic
355	C₂²×C₄	D₈×C₁₀₇	1	1	yes	characteristic
356	C₂²×C₄	D₈×C₁₀₇	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
360	Q₁₆	—	2	2	no	—
361	Q₁₆	—	2	1	no	—
362	Q₁₆	—	2	2	no	—
363	Q₁₆	—	2	1	no	—
364	Q₁₆	—	4	2	no	—
365	SD₁₆	—	4	2	no	—
366	D₈	—	2	1	no	—
367	D₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
376	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
377	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
378	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
379	C₂×C₈	#41×C₁₀₇	1	2	yes	—
380	C₂×C₈	C₂⁴×C₁₀₇	1	1	yes	characteristic
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	4	1	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₂²⋊C₄	—	4	1	no	—
396	C₄²	—	4	1	no	—
397	C₁₆	—	2	2	no	—
398	C₁₆	C₂×D₄×C₁₀₇	1	4	yes	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	C₂×D₈×C₁₀₇	1	1	yes	characteristic
404	C₂³	C₂×D₈×C₁₀₇	1	1	yes	characteristic
405	C₂³	C₂×D₈×C₁₀₇	1	1	yes	characteristic
406	Q₈	—	4	1	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	1	no	—
410	Q₈	—	8	2	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	1	no	—
413	D₄	—	8	2	no	—
414	D₄	—	8	2	no	—
415	D₄	—	8	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	8	2	no	—
430	C₂×C₄	—	8	2	no	—
431	C₂×C₄	#121×C₁₀₇	1	2	yes	—
432	C₂×C₄	C₂×D₈×C₁₀₇	1	1	yes	characteristic
433	C₂×C₄	C₂×D₈×C₁₀₇	1	1	yes	characteristic
434	C₂×C₄	C₂×D₈×C₁₀₇	1	1	yes	characteristic
435	C₂×C₄	#135×C₁₀₇	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	#121×C₁₀₇	1	2	yes	—
440	C₈	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
441	C₈	C₂×#41×C₁₀₇	1	1	yes	characteristic
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	#466×C₁₀₇	1	2	yes	—
454	C₂²	#510×C₁₀₇	1	2	yes	complemented
455	C₂²	C₂²×D₈×C₁₀₇	1	1	yes	characteristic
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	1	no	—
462	C₄	—	8	2	no	—
463	C₄	#466×C₁₀₇	1	2	yes	—
464	C₄	C₂×#121×C₁₀₇	1	1	yes	characteristic
465	C₄	C₂×#135×C₁₀₇	1	1	yes	characteristic
466	C₂	—	2	2	no	—
467	C₂	—	2	2	no	—
468	C₂	—	4	1	no	—
469	C₂	—	16	1	no	—
470	C₂	C₂×#466×C₁₀₇	1	1	yes	characteristic
471	C₂	C₂×#510×C₁₀₇	1	1	yes	characteristic
472	C₂	C₁₀₇×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₀₇
prime radical	C₁₀₇×#3050	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ C₂³×C₄×C₁₀₇ ◁ C₂³×C₈×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#510×C₁₀₇	C₂	semidirect
2. C₂²×M₃₂×C₁₀₇	C₂	semidirect
4. C₂×#467×C₁₀₇	C₂	semidirect
5. C₁₀₇×#2220	C₂	semidirect
6. C₁₀₇×#2219	C₂	semidirect
7. C₁₀₇×#2217	C₂	semidirect
8. C₁₀₇×#2216	C₂	semidirect
9. C₁₀₇×#2159	C₂	semidirect
10. C₁₀₇×#2141	C₂	semidirect
11. C₁₀₇×#2139	C₂	semidirect
18. C₂×Q₃₂×C₁₀₇	C₂²	semidirect
19. C₂×SD₃₂×C₁₀₇	C₂²	semidirect
39. #367×C₁₀₇	C₂²	semidirect
40. #366×C₁₀₇	C₂²	semidirect
41. #358×C₁₀₇	C₂²	semidirect
42. #358×C₁₀₇	C₂²	semidirect
43. #358×C₁₀₇	C₂²	semidirect
44. #357×C₁₀₇	C₂²	semidirect
85. M₃₂×C₁₀₇	D₄	semidirect
217. C₂²×C₁₀₇	#510	semidirect
229. #33606	C₁₀₇	direct (N × H)
237. C₂×#510	C₂×C₁₀₇	semidirect
238. C₂²×M₃₂	C₂×C₁₀₇	semidirect
240. C₂×#467	C₂×C₁₀₇	semidirect
241. #2220	C₂×C₁₀₇	semidirect
242. #2219	C₂×C₁₀₇	semidirect
243. #2217	C₂×C₁₀₇	semidirect
244. #2216	C₂×C₁₀₇	semidirect
245. #2159	C₂×C₁₀₇	semidirect
246. #2141	C₂×C₁₀₇	semidirect
247. #2139	C₂×C₁₀₇	semidirect
248. C₁₀₇	#33606	direct (N × H)
255. C₂×Q₃₂	C₂²×C₁₀₇	semidirect
256. C₂×SD₃₂	C₂²×C₁₀₇	semidirect
276. #367	C₂²×C₁₀₇	semidirect
277. #366	C₂²×C₁₀₇	semidirect
278. #358	C₂²×C₁₀₇	semidirect
279. #358	C₂²×C₁₀₇	semidirect
280. #358	C₂²×C₁₀₇	semidirect
281. #357	C₂²×C₁₀₇	semidirect
322. M₃₂	D₄×C₁₀₇	semidirect
454. C₂²	#510×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#510×C₁₀₇	2
C₂²×M₃₂×C₁₀₇	2
C₁₀₇×#3050	2
C₂×#467×C₁₀₇	2
C₁₀₇×#2220	2
C₁₀₇×#2219	2
C₁₀₇×#2217	2
C₁₀₇×#2216	2
C₁₀₇×#2159	2
C₁₀₇×#2141	2
C₁₀₇×#2139	2
#33606	107

Subgroups — C107×#33606 #41059570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#33606 #41059570