Subgroups — C₁₀₇×#33524 #41059488

Order 27392.

1118 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#578×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#509×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×SD₃₂×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₇×#3058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₇×#2186	C₂	1	4	yes	maximal, complemented
6	C₁₀₇×#2185	C₂	1	4	yes	maximal, complemented
7	C₁₀₇×#2141	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₇×#2138	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₇×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×2₋¹⁺⁴×C₁₀₇	—	2	1	no	—
11	#578×C₁₀₇	—	2	4	no	—
12	#578×C₁₀₇	—	2	4	no	—
13	C₂×#137×C₁₀₇	—	2	1	no	—
14	C₂×#137×C₁₀₇	—	2	2	no	—
15	C₂×#135×C₁₀₇	C₂²	1	1	yes	characteristic
16	C₂×#135×C₁₀₇	C₂²	1	2	yes	complemented
17	C₂²×Q₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₁₀₇	C₂²	1	2	yes	complemented
19	C₂²×D₈×C₁₀₇	C₂²	1	1	yes	characteristic
20	C₂×#131×C₁₀₇	C₂²	1	1	yes	characteristic
21	#535×C₁₀₇	—	2	1	no	—
22	#509×C₁₀₇	—	2	4	no	—
23	C₂×SD₃₂×C₁₀₇	—	2	4	no	—
24	C₂×SD₃₂×C₁₀₇	C₂²	1	4	yes	—
25	C₂×SD₃₂×C₁₀₇	C₂²	1	2	yes	—
26	C₂×D₁₆×C₁₀₇	C₂²	1	2	yes	—
27	C₂×M₃₂×C₁₀₇	C₂²	1	1	yes	characteristic
28	C₂²×C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
29	#469×C₁₀₇	—	2	2	no	—
30	#466×C₁₀₇	C₂²	1	4	yes	—
31	#427×C₁₀₇	C₂²	1	1	yes	characteristic
32	#418×C₁₀₇	—	2	1	no	—
33	#358×C₁₀₇	C₂²	1	2	yes	complemented
34	#358×C₁₀₇	C₂²	1	4	yes	complemented
35	#357×C₁₀₇	C₂²	1	2	yes	complemented
36	C₂²⋊C₁₆×C₁₀₇	C₂²	1	4	yes	complemented
37	2₋¹⁺⁴×C₁₀₇	—	2	8	no	—
38	2₋¹⁺⁴×C₁₀₇	—	4	4	no	—
39	C₂×#41×C₁₀₇	—	2	1	no	—
40	C₂×#41×C₁₀₇	—	2	2	no	—
41	C₂×#41×C₁₀₇	—	4	2	no	—
42	C₂×#41×C₁₀₇	—	4	1	no	—
43	C₂×#41×C₁₀₇	D₄	1	1	yes	characteristic
44	C₂²×Q₈×C₁₀₇	—	2	1	no	—
45	C₂²×Q₈×C₁₀₇	—	2	2	no	—
46	C₂²×Q₈×C₁₀₇	—	4	1	no	—
47	C₂²×D₄×C₁₀₇	—	2	1	no	—
48	#137×C₁₀₇	—	2	8	no	—
49	#137×C₁₀₇	—	2	16	no	—
50	#135×C₁₀₇	—	2	4	no	—
51	#135×C₁₀₇	—	2	4	no	—
52	#135×C₁₀₇	—	2	2	no	—
53	#135×C₁₀₇	D₄	1	4	yes	complemented
54	C₂×Q₁₆×C₁₀₇	—	2	4	no	—
55	C₂×Q₁₆×C₁₀₇	—	2	4	no	—
56	C₂×Q₁₆×C₁₀₇	—	2	1	no	—
57	C₂×Q₁₆×C₁₀₇	—	2	2	no	—
58	C₂×Q₁₆×C₁₀₇	—	2	2	no	—
59	C₂×Q₁₆×C₁₀₇	D₄	1	4	yes	complemented
60	C₂×Q₁₆×C₁₀₇	C₂³	1	2	yes	—
61	C₂×Q₁₆×C₁₀₇	C₂³	1	1	yes	characteristic
62	C₂×SD₁₆×C₁₀₇	—	2	1	no	—
63	C₂×SD₁₆×C₁₀₇	—	2	2	no	—
64	C₂×D₈×C₁₀₇	—	2	2	no	—
65	C₂×D₈×C₁₀₇	—	2	2	no	—
66	C₂×D₈×C₁₀₇	—	2	1	no	—
67	C₂×D₈×C₁₀₇	C₂³	1	2	yes	—
68	C₂×D₈×C₁₀₇	C₂³	1	1	yes	characteristic
69	#131×C₁₀₇	—	2	2	no	—
70	#131×C₁₀₇	—	2	2	no	—
71	C₂×M₁₆×C₁₀₇	D₄	1	1	yes	characteristic
72	C₂×M₁₆×C₁₀₇	D₄	1	2	yes	—
73	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
74	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
75	#127×C₁₀₇	—	4	1	no	—
76	#124×C₁₀₇	—	4	1	no	—
77	#121×C₁₀₇	—	2	4	no	—
78	#120×C₁₀₇	—	4	2	no	—
79	#117×C₁₀₇	—	2	1	no	—
80	SD₃₂×C₁₀₇	—	2	8	no	—
81	SD₃₂×C₁₀₇	—	2	4	no	—
82	D₁₆×C₁₀₇	—	2	4	no	—
83	M₃₂×C₁₀₇	—	2	2	no	—
84	C₂×C₁₆×C₁₀₇	—	2	2	no	—
85	C₂×C₁₆×C₁₀₇	C₂³	1	2	yes	—
86	C₂×C₁₆×C₁₀₇	C₂³	1	2	yes	—
87	#107×C₁₀₇	C₂³	1	2	yes	—
88	#106×C₁₀₇	—	2	1	no	—
89	#102×C₁₀₇	—	2	4	no	—
90	C₂⁴×C₁₀₇	—	4	1	no	—
91	#41×C₁₀₇	—	2	2	no	—
92	#41×C₁₀₇	—	2	2	no	—
93	#41×C₁₀₇	—	2	8	no	—
94	#41×C₁₀₇	—	2	4	no	—
95	#41×C₁₀₇	—	4	4	no	—
96	#41×C₁₀₇	—	4	16	no	—
97	#41×C₁₀₇	—	4	8	no	—
98	#41×C₁₀₇	—	4	2	no	—
99	C₂×Q₈×C₁₀₇	—	2	8	no	—
100	C₂×Q₈×C₁₀₇	—	2	4	no	—
101	C₂×Q₈×C₁₀₇	—	2	1	no	—
102	C₂×Q₈×C₁₀₇	—	2	2	no	—
103	C₂×Q₈×C₁₀₇	—	4	4	no	—
104	C₂×Q₈×C₁₀₇	—	4	8	no	—
105	C₂×Q₈×C₁₀₇	—	4	2	no	—
106	C₂×Q₈×C₁₀₇	—	4	1	no	—
107	C₂×Q₈×C₁₀₇	—	4	2	no	—
108	C₂×Q₈×C₁₀₇	D₈	1	1	yes	characteristic
109	C₂×D₄×C₁₀₇	—	2	1	no	—
110	C₂×D₄×C₁₀₇	—	2	2	no	—
111	C₂×D₄×C₁₀₇	—	4	2	no	—
112	C₂×D₄×C₁₀₇	—	4	1	no	—
113	C₂×D₄×C₁₀₇	—	4	4	no	—
114	C₂×D₄×C₁₀₇	—	4	2	no	—
115	C₂×D₄×C₁₀₇	—	4	1	no	—
116	C₂×D₄×C₁₀₇	—	4	2	no	—
117	C₂×D₄×C₁₀₇	D₈	1	2	yes	—
118	C₂×D₄×C₁₀₇	D₈	1	1	yes	characteristic
119	C₂²×C₄×C₁₀₇	—	4	2	no	—
120	C₂²×C₄×C₁₀₇	—	4	1	no	—
121	C₂²×C₄×C₁₀₇	—	4	2	no	—
122	C₂²×C₄×C₁₀₇	—	4	1	no	—
123	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
125	Q₁₆×C₁₀₇	—	2	8	no	—
126	Q₁₆×C₁₀₇	—	2	4	no	—
127	Q₁₆×C₁₀₇	—	2	1	no	—
128	Q₁₆×C₁₀₇	—	2	2	no	—
129	Q₁₆×C₁₀₇	C₂×D₄	1	2	yes	—
130	Q₁₆×C₁₀₇	C₂×D₄	1	4	yes	—
131	SD₁₆×C₁₀₇	—	2	8	no	—
132	SD₁₆×C₁₀₇	—	2	4	no	—
133	D₈×C₁₀₇	—	2	1	no	—
134	D₈×C₁₀₇	—	2	2	no	—
135	D₈×C₁₀₇	—	2	2	no	—
136	D₈×C₁₀₇	—	4	2	no	—
137	D₈×C₁₀₇	C₂×D₄	1	2	yes	—
138	M₁₆×C₁₀₇	—	2	2	no	—
139	M₁₆×C₁₀₇	—	2	4	no	—
140	C₂×C₈×C₁₀₇	—	2	2	no	—
141	C₂×C₈×C₁₀₇	—	2	2	no	—
142	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₁₀₇	C₂⁴	1	1	yes	characteristic
147	C₄⋊C₄×C₁₀₇	—	2	2	no	—
148	C₂²⋊C₄×C₁₀₇	—	4	1	no	—
149	C₂²⋊C₄×C₁₀₇	—	4	4	no	—
150	C₄²×C₁₀₇	—	4	1	no	—
151	C₁₆×C₁₀₇	—	2	2	no	—
152	C₁₆×C₁₀₇	—	2	2	no	—
153	C₂³×C₁₀₇	—	4	1	no	—
154	C₂³×C₁₀₇	—	4	2	no	—
155	C₂³×C₁₀₇	—	8	2	no	—
156	C₂³×C₁₀₇	—	16	2	no	—
157	C₂³×C₁₀₇	C₂×D₈	1	2	yes	—
158	C₂³×C₁₀₇	C₂×D₈	1	1	yes	characteristic
159	Q₈×C₁₀₇	—	2	2	no	—
160	Q₈×C₁₀₇	—	2	4	no	—
161	Q₈×C₁₀₇	—	2	2	no	—
162	Q₈×C₁₀₇	—	4	8	no	—
163	Q₈×C₁₀₇	—	4	1	no	—
164	Q₈×C₁₀₇	—	4	2	no	—
165	Q₈×C₁₀₇	—	4	4	no	—
166	D₄×C₁₀₇	—	2	4	no	—
167	D₄×C₁₀₇	—	2	2	no	—
168	D₄×C₁₀₇	—	2	2	no	—
169	D₄×C₁₀₇	—	4	8	no	—
170	D₄×C₁₀₇	—	4	4	no	—
171	D₄×C₁₀₇	—	4	2	no	—
172	D₄×C₁₀₇	—	4	1	no	—
173	D₄×C₁₀₇	—	4	2	no	—
174	D₄×C₁₀₇	—	8	2	no	—
175	D₄×C₁₀₇	—	16	4	no	—
176	C₂×C₄×C₁₀₇	—	2	2	no	—
177	C₂×C₄×C₁₀₇	—	2	2	no	—
178	C₂×C₄×C₁₀₇	—	4	8	no	—
179	C₂×C₄×C₁₀₇	—	4	8	no	—
180	C₂×C₄×C₁₀₇	—	4	2	no	—
181	C₂×C₄×C₁₀₇	—	4	1	no	—
182	C₂×C₄×C₁₀₇	—	4	4	no	—
183	C₂×C₄×C₁₀₇	—	4	4	no	—
184	C₂×C₄×C₁₀₇	—	4	2	no	—
185	C₂×C₄×C₁₀₇	#120	1	2	yes	—
186	C₂×C₄×C₁₀₇	C₂×D₈	1	2	yes	—
187	C₂×C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
188	C₂×C₄×C₁₀₇	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₁₀₇	—	2	2	no	—
191	C₈×C₁₀₇	#120	1	2	yes	—
192	C₈×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
194	C₂²×C₁₀₇	—	2	2	no	—
195	C₂²×C₁₀₇	—	2	4	no	—
196	C₂²×C₁₀₇	—	2	2	no	—
197	C₂²×C₁₀₇	—	4	2	no	—
198	C₂²×C₁₀₇	—	8	2	no	—
199	C₂²×C₁₀₇	—	8	4	no	—
200	C₂²×C₁₀₇	—	8	2	no	—
201	C₂²×C₁₀₇	—	16	4	no	—
202	C₂²×C₁₀₇	#447	1	2	yes	—
203	C₂²×C₁₀₇	C₂²×D₈	1	1	yes	characteristic
204	C₄×C₁₀₇	—	2	2	no	—
205	C₄×C₁₀₇	—	4	4	no	—
206	C₄×C₁₀₇	—	4	2	no	—
207	C₄×C₁₀₇	—	8	2	no	—
208	C₄×C₁₀₇	#447	1	2	yes	—
209	C₄×C₁₀₇	C₂×#120	1	1	yes	characteristic
210	C₄×C₁₀₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
211	#33524	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂×C₁₀₇	—	2	2	no	—
213	C₂×C₁₀₇	—	4	2	no	—
214	C₂×C₁₀₇	—	8	2	no	—
215	C₂×C₁₀₇	—	16	2	no	—
216	C₂×C₁₀₇	C₂×#447	1	1	yes	characteristic
217	C₂×C₁₀₇	#3416	1	2	yes	—
218	C₂×#578	C₂×C₁₀₇	1	1	yes	characteristic, complemented
219	C₂×#509	C₂×C₁₀₇	1	1	yes	characteristic, complemented
220	C₂²×SD₃₂	C₂×C₁₀₇	1	1	yes	characteristic, complemented
221	#3058	C₂×C₁₀₇	1	1	yes	characteristic, complemented
222	#2186	C₂×C₁₀₇	1	4	yes	complemented
223	#2185	C₂×C₁₀₇	1	4	yes	complemented
224	#2141	C₂×C₁₀₇	1	1	yes	characteristic, complemented
225	#2138	C₂×C₁₀₇	1	1	yes	characteristic, complemented
226	#2113	C₂×C₁₀₇	1	1	yes	characteristic, complemented
227	C₁₀₇	#33524	1	1	yes	characteristic, direct product factor, Sylow
228	C₂×2₋¹⁺⁴	—	2	1	no	—
229	#578	—	2	4	no	—
230	#578	—	2	4	no	—
231	C₂×#137	—	2	1	no	—
232	C₂×#137	—	2	2	no	—
233	C₂×#135	C₂²×C₁₀₇	1	1	yes	characteristic
234	C₂×#135	C₂²×C₁₀₇	1	2	yes	complemented
235	C₂²×Q₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
236	C₂²×Q₁₆	C₂²×C₁₀₇	1	2	yes	complemented
237	C₂²×D₈	C₂²×C₁₀₇	1	1	yes	characteristic
238	C₂×#131	C₂²×C₁₀₇	1	1	yes	characteristic
239	#535	—	2	1	no	—
240	#509	—	2	4	no	—
241	C₂×SD₃₂	—	2	4	no	—
242	C₂×SD₃₂	C₂²×C₁₀₇	1	4	yes	—
243	C₂×SD₃₂	C₂²×C₁₀₇	1	2	yes	—
244	C₂×D₁₆	C₂²×C₁₀₇	1	2	yes	—
245	C₂×M₃₂	C₂²×C₁₀₇	1	1	yes	characteristic
246	C₂²×C₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
247	#469	—	2	2	no	—
248	#466	C₂²×C₁₀₇	1	4	yes	—
249	#427	C₂²×C₁₀₇	1	1	yes	characteristic
250	#418	—	2	1	no	—
251	#358	C₂²×C₁₀₇	1	2	yes	complemented
252	#358	C₂²×C₁₀₇	1	4	yes	complemented
253	#357	C₂²×C₁₀₇	1	2	yes	complemented
254	C₂²⋊C₁₆	C₂²×C₁₀₇	1	4	yes	complemented
255	2₋¹⁺⁴	—	2	8	no	—
256	2₋¹⁺⁴	—	4	4	no	—
257	C₂×#41	—	2	1	no	—
258	C₂×#41	—	2	2	no	—
259	C₂×#41	—	4	2	no	—
260	C₂×#41	—	4	1	no	—
261	C₂×#41	D₄×C₁₀₇	1	1	yes	characteristic
262	C₂²×Q₈	—	2	1	no	—
263	C₂²×Q₈	—	2	2	no	—
264	C₂²×Q₈	—	4	1	no	—
265	C₂²×D₄	—	2	1	no	—
266	#137	—	2	8	no	—
267	#137	—	2	16	no	—
268	#135	—	2	4	no	—
269	#135	—	2	4	no	—
270	#135	—	2	2	no	—
271	#135	D₄×C₁₀₇	1	4	yes	complemented
272	C₂×Q₁₆	—	2	4	no	—
273	C₂×Q₁₆	—	2	4	no	—
274	C₂×Q₁₆	—	2	1	no	—
275	C₂×Q₁₆	—	2	2	no	—
276	C₂×Q₁₆	—	2	2	no	—
277	C₂×Q₁₆	D₄×C₁₀₇	1	4	yes	complemented
278	C₂×Q₁₆	C₂³×C₁₀₇	1	2	yes	—
279	C₂×Q₁₆	C₂³×C₁₀₇	1	1	yes	characteristic
280	C₂×SD₁₆	—	2	1	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×D₈	—	2	2	no	—
283	C₂×D₈	—	2	2	no	—
284	C₂×D₈	—	2	1	no	—
285	C₂×D₈	C₂³×C₁₀₇	1	2	yes	—
286	C₂×D₈	C₂³×C₁₀₇	1	1	yes	characteristic
287	#131	—	2	2	no	—
288	#131	—	2	2	no	—
289	C₂×M₁₆	D₄×C₁₀₇	1	1	yes	characteristic
290	C₂×M₁₆	D₄×C₁₀₇	1	2	yes	—
291	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
292	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
293	#127	—	4	1	no	—
294	#124	—	4	1	no	—
295	#121	—	2	4	no	—
296	#120	—	4	2	no	—
297	#117	—	2	1	no	—
298	SD₃₂	—	2	8	no	—
299	SD₃₂	—	2	4	no	—
300	D₁₆	—	2	4	no	—
301	M₃₂	—	2	2	no	—
302	C₂×C₁₆	—	2	2	no	—
303	C₂×C₁₆	C₂³×C₁₀₇	1	2	yes	—
304	C₂×C₁₆	C₂³×C₁₀₇	1	2	yes	—
305	#107	C₂³×C₁₀₇	1	2	yes	—
306	#106	—	2	1	no	—
307	#102	—	2	4	no	—
308	C₂⁴	—	4	1	no	—
309	#41	—	2	2	no	—
310	#41	—	2	2	no	—
311	#41	—	2	8	no	—
312	#41	—	2	4	no	—
313	#41	—	4	4	no	—
314	#41	—	4	16	no	—
315	#41	—	4	8	no	—
316	#41	—	4	2	no	—
317	C₂×Q₈	—	2	8	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	4	4	no	—
322	C₂×Q₈	—	4	8	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	—	4	1	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	D₈×C₁₀₇	1	1	yes	characteristic
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	4	2	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	4	4	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	D₈×C₁₀₇	1	2	yes	—
336	C₂×D₄	D₈×C₁₀₇	1	1	yes	characteristic
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
343	Q₁₆	—	2	8	no	—
344	Q₁₆	—	2	4	no	—
345	Q₁₆	—	2	1	no	—
346	Q₁₆	—	2	2	no	—
347	Q₁₆	C₂×D₄×C₁₀₇	1	2	yes	—
348	Q₁₆	C₂×D₄×C₁₀₇	1	4	yes	—
349	SD₁₆	—	2	8	no	—
350	SD₁₆	—	2	4	no	—
351	D₈	—	2	1	no	—
352	D₈	—	2	2	no	—
353	D₈	—	2	2	no	—
354	D₈	—	4	2	no	—
355	D₈	C₂×D₄×C₁₀₇	1	2	yes	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	4	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
361	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
362	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
363	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
364	C₂×C₈	C₂⁴×C₁₀₇	1	1	yes	characteristic
365	C₄⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	4	4	no	—
368	C₄²	—	4	1	no	—
369	C₁₆	—	2	2	no	—
370	C₁₆	—	2	2	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	—	16	2	no	—
375	C₂³	C₂×D₈×C₁₀₇	1	2	yes	—
376	C₂³	C₂×D₈×C₁₀₇	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	2	4	no	—
379	Q₈	—	2	2	no	—
380	Q₈	—	4	8	no	—
381	Q₈	—	4	4	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	4	2	no	—
384	D₄	—	2	4	no	—
385	D₄	—	2	2	no	—
386	D₄	—	2	2	no	—
387	D₄	—	4	8	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	1	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	16	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	8	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	#120×C₁₀₇	1	2	yes	—
404	C₂×C₄	C₂×D₈×C₁₀₇	1	2	yes	—
405	C₂×C₄	C₂×D₈×C₁₀₇	1	1	yes	characteristic
406	C₂×C₄	AGL(1,ℤ/8)×C₁₀₇	1	2	yes	—
407	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	#120×C₁₀₇	1	2	yes	—
410	C₈	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
411	C₈	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
412	C₂²	—	2	2	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	4	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	16	4	no	—
420	C₂²	#447×C₁₀₇	1	2	yes	—
421	C₂²	C₂²×D₈×C₁₀₇	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	2	no	—
425	C₄	—	8	2	no	—
426	C₄	#447×C₁₀₇	1	2	yes	—
427	C₄	C₂×#120×C₁₀₇	1	1	yes	characteristic
428	C₄	C₂×AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
429	C₂	—	2	2	no	—
430	C₂	—	4	2	no	—
431	C₂	—	8	2	no	—
432	C₂	—	16	2	no	—
433	C₂	C₂×#447×C₁₀₇	1	1	yes	characteristic
434	C₂	C₁₀₇×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₀₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₀₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ C₂×#41×C₁₀₇ ◁ C₂×#131×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#578×C₁₀₇	C₂	semidirect
2. C₂×#509×C₁₀₇	C₂	semidirect
3. C₂²×SD₃₂×C₁₀₇	C₂	semidirect
4. C₁₀₇×#3058	C₂	semidirect
5. C₁₀₇×#2186	C₂	semidirect
6. C₁₀₇×#2185	C₂	semidirect
7. C₁₀₇×#2141	C₂	semidirect
8. C₁₀₇×#2138	C₂	semidirect
9. C₁₀₇×#2113	C₂	semidirect
16. C₂×#135×C₁₀₇	C₂²	semidirect
18. C₂²×Q₁₆×C₁₀₇	C₂²	semidirect
33. #358×C₁₀₇	C₂²	semidirect
34. #358×C₁₀₇	C₂²	semidirect
35. #357×C₁₀₇	C₂²	semidirect
36. C₂²⋊C₁₆×C₁₀₇	C₂²	semidirect
53. #135×C₁₀₇	D₄	semidirect
59. C₂×Q₁₆×C₁₀₇	D₄	semidirect
211. #33524	C₁₀₇	direct (N × H)
218. C₂×#578	C₂×C₁₀₇	semidirect
219. C₂×#509	C₂×C₁₀₇	semidirect
220. C₂²×SD₃₂	C₂×C₁₀₇	semidirect
221. #3058	C₂×C₁₀₇	semidirect
222. #2186	C₂×C₁₀₇	semidirect
223. #2185	C₂×C₁₀₇	semidirect
224. #2141	C₂×C₁₀₇	semidirect
225. #2138	C₂×C₁₀₇	semidirect
226. #2113	C₂×C₁₀₇	semidirect
227. C₁₀₇	#33524	direct (N × H)
234. C₂×#135	C₂²×C₁₀₇	semidirect
236. C₂²×Q₁₆	C₂²×C₁₀₇	semidirect
251. #358	C₂²×C₁₀₇	semidirect
252. #358	C₂²×C₁₀₇	semidirect
253. #357	C₂²×C₁₀₇	semidirect
254. C₂²⋊C₁₆	C₂²×C₁₀₇	semidirect
271. #135	D₄×C₁₀₇	semidirect
277. C₂×Q₁₆	D₄×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#578×C₁₀₇	2
C₂×#509×C₁₀₇	2
C₂²×SD₃₂×C₁₀₇	2
C₁₀₇×#3058	2
C₁₀₇×#2186	2
C₁₀₇×#2185	2
C₁₀₇×#2141	2
C₁₀₇×#2138	2
C₁₀₇×#2113	2
#33524	107

Subgroups — C107×#33524 #41059488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#33524 #41059488