Subgroups — C₁₀₇×#36707 #41062671

Order 27392.

2782 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#537×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₇×#2847	C₂	1	2	yes	maximal, complemented
4	C₁₀₇×#2692	C₂	1	8	yes	maximal, complemented
5	C₁₀₇×#2676	C₂	1	8	yes	maximal, complemented
6	C₁₀₇×#2618	C₂	1	2	yes	maximal, complemented
7	C₁₀₇×#2539	C₂	1	2	yes	maximal, complemented
8	C₁₀₇×#2436	C₂	1	2	yes	maximal, complemented
9	C₁₀₇×#2406	C₂	1	2	yes	maximal, complemented
10	C₁₀₇×#2404	C₂	1	2	yes	maximal, complemented
11	C₁₀₇×#2313	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₀₇	C₂²	1	2	yes	—
13	C₂³×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₀₇	C₂²	1	1	yes	characteristic
15	#537×C₁₀₇	—	2	8	no	—
16	C₂×#124×C₁₀₇	C₂²	1	4	yes	complemented
17	C₂×#123×C₁₀₇	C₂²	1	4	yes	—
18	C₂×C₂²⋊Q₈×C₁₀₇	—	2	8	no	—
19	C₂×C₂²⋊Q₈×C₁₀₇	C₂²	1	8	yes	—
20	C₂×C₂²⋊Q₈×C₁₀₇	C₂²	1	4	yes	complemented
21	C₂×#121×C₁₀₇	C₂²	1	2	yes	—
22	C₂×#121×C₁₀₇	C₂²	1	2	yes	—
23	C₂×#121×C₁₀₇	C₂²	1	4	yes	—
24	C₂×#121×C₁₀₇	C₂²	1	4	yes	complemented
25	C₂×#120×C₁₀₇	C₂²	1	4	yes	—
26	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
31	#399×C₁₀₇	C₂²	1	4	yes	—
32	#398×C₁₀₇	C₂²	1	4	yes	complemented
33	#396×C₁₀₇	C₂²	1	8	yes	complemented
34	#395×C₁₀₇	C₂²	1	4	yes	complemented
35	#394×C₁₀₇	C₂²	1	4	yes	complemented
36	#394×C₁₀₇	C₂²	1	4	yes	complemented
37	#393×C₁₀₇	C₂²	1	4	yes	—
38	#393×C₁₀₇	C₂²	1	8	yes	complemented
39	#392×C₁₀₇	C₂²	1	4	yes	—
40	#392×C₁₀₇	C₂²	1	4	yes	—
41	#391×C₁₀₇	C₂²	1	4	yes	complemented
42	#390×C₁₀₇	C₂²	1	8	yes	—
43	#387×C₁₀₇	C₂²	1	8	yes	complemented
44	#386×C₁₀₇	C₂²	1	8	yes	—
45	#386×C₁₀₇	C₂²	1	4	yes	—
46	#386×C₁₀₇	C₂²	1	4	yes	—
47	#386×C₁₀₇	C₂²	1	8	yes	—
48	#385×C₁₀₇	C₂²	1	8	yes	complemented
49	#381×C₁₀₇	C₂²	1	2	yes	—
50	#380×C₁₀₇	C₂²	1	4	yes	—
51	#380×C₁₀₇	C₂²	1	2	yes	—
52	C₄×C₂²⋊C₄×C₁₀₇	C₂²	1	2	yes	—
53	C₂⁵×C₁₀₇	C₂³	1	1	yes	characteristic
54	C₂×#41×C₁₀₇	—	2	8	no	—
55	C₂×#41×C₁₀₇	—	4	8	no	—
56	C₂²×Q₈×C₁₀₇	—	2	4	no	—
57	C₂²×Q₈×C₁₀₇	—	4	4	no	—
58	C₂²×Q₈×C₁₀₇	C₂³	1	4	yes	—
59	C₂²×Q₈×C₁₀₇	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₀₇	C₂³	1	4	yes	—
61	C₂²×D₄×C₁₀₇	C₂³	1	8	yes	—
62	C₂²×D₄×C₁₀₇	C₂³	1	2	yes	—
63	C₂²×D₄×C₁₀₇	C₂³	1	2	yes	—
64	C₂²×D₄×C₁₀₇	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₀₇	—	2	4	no	—
66	C₂³×C₄×C₁₀₇	—	4	4	no	—
67	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₀₇	C₂³	1	4	yes	—
70	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₀₇	C₂³	1	4	yes	—
72	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
75	#124×C₁₀₇	—	4	8	no	—
76	#123×C₁₀₇	—	4	8	no	—
77	C₂²⋊Q₈×C₁₀₇	—	2	32	no	—
78	C₂²⋊Q₈×C₁₀₇	—	2	16	no	—
79	#121×C₁₀₇	—	2	8	no	—
80	#121×C₁₀₇	—	2	8	no	—
81	#121×C₁₀₇	—	2	16	no	—
82	#121×C₁₀₇	—	4	8	no	—
83	#120×C₁₀₇	—	4	8	no	—
84	C₂×C₄⋊C₄×C₁₀₇	—	2	4	no	—
85	C₂×C₄⋊C₄×C₁₀₇	—	2	4	no	—
86	C₂×C₄⋊C₄×C₁₀₇	D₄	1	8	yes	complemented
87	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	8	yes	—
93	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₁₀₇	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₁₀₇	—	2	4	no	—
96	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	8	yes	—
103	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	8	yes	—
104	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	8	yes	—
105	C₂×C₄²×C₁₀₇	C₂³	1	4	yes	—
106	#95×C₁₀₇	C₂³	1	4	yes	—
107	#95×C₁₀₇	C₂³	1	8	yes	—
108	#95×C₁₀₇	C₂³	1	4	yes	—
109	#95×C₁₀₇	C₂³	1	4	yes	—
110	#95×C₁₀₇	C₂³	1	4	yes	—
111	#95×C₁₀₇	C₂³	1	8	yes	—
112	C₂⁴×C₁₀₇	—	2	2	no	—
113	C₂⁴×C₁₀₇	—	2	4	no	—
114	C₂⁴×C₁₀₇	—	2	4	no	—
115	C₂⁴×C₁₀₇	—	4	2	no	—
116	C₂⁴×C₁₀₇	C₂⁴	1	4	yes	—
117	C₂⁴×C₁₀₇	C₂⁴	1	2	yes	—
118	C₂⁴×C₁₀₇	C₂⁴	1	1	yes	characteristic
119	#41×C₁₀₇	—	4	32	no	—
120	C₂×Q₈×C₁₀₇	—	2	8	no	—
121	C₂×Q₈×C₁₀₇	—	2	4	no	—
122	C₂×Q₈×C₁₀₇	—	2	8	no	—
123	C₂×Q₈×C₁₀₇	—	4	4	no	—
124	C₂×Q₈×C₁₀₇	—	4	4	no	—
125	C₂×Q₈×C₁₀₇	—	4	16	no	—
126	C₂×D₄×C₁₀₇	—	2	8	no	—
127	C₂×D₄×C₁₀₇	—	2	8	no	—
128	C₂×D₄×C₁₀₇	—	2	8	no	—
129	C₂×D₄×C₁₀₇	—	2	16	no	—
130	C₂×D₄×C₁₀₇	—	2	4	no	—
131	C₂×D₄×C₁₀₇	—	2	4	no	—
132	C₂×D₄×C₁₀₇	—	2	4	no	—
133	C₂×D₄×C₁₀₇	—	4	4	no	—
134	C₂×D₄×C₁₀₇	—	4	8	no	—
135	C₂×D₄×C₁₀₇	—	4	4	no	—
136	C₂×D₄×C₁₀₇	—	4	8	no	—
137	C₂×D₄×C₁₀₇	—	4	4	no	—
138	C₂²×C₄×C₁₀₇	—	2	2	no	—
139	C₂²×C₄×C₁₀₇	—	2	4	no	—
140	C₂²×C₄×C₁₀₇	—	2	4	no	—
141	C₂²×C₄×C₁₀₇	—	2	2	no	—
142	C₂²×C₄×C₁₀₇	—	2	2	no	—
143	C₂²×C₄×C₁₀₇	—	2	4	no	—
144	C₂²×C₄×C₁₀₇	—	2	8	no	—
145	C₂²×C₄×C₁₀₇	—	2	8	no	—
146	C₂²×C₄×C₁₀₇	—	2	8	no	—
147	C₂²×C₄×C₁₀₇	—	4	2	no	—
148	C₂²×C₄×C₁₀₇	—	4	4	no	—
149	C₂²×C₄×C₁₀₇	—	4	2	no	—
150	C₂²×C₄×C₁₀₇	—	4	2	no	—
151	C₂²×C₄×C₁₀₇	—	4	4	no	—
152	C₂²×C₄×C₁₀₇	—	4	4	no	—
153	C₂²×C₄×C₁₀₇	—	4	16	no	—
154	C₂²×C₄×C₁₀₇	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₁₀₇	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₁₀₇	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₁₀₇	C₂⁴	1	8	yes	—
158	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₁₀₇	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
165	C₄⋊C₄×C₁₀₇	—	2	8	no	—
166	C₄⋊C₄×C₁₀₇	—	2	8	no	—
167	C₄⋊C₄×C₁₀₇	—	2	4	no	—
168	C₄⋊C₄×C₁₀₇	—	2	4	no	—
169	C₄⋊C₄×C₁₀₇	—	4	4	no	—
170	C₄⋊C₄×C₁₀₇	—	4	8	no	—
171	C₄⋊C₄×C₁₀₇	C₂×D₄	1	16	yes	—
172	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
173	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
174	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
175	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
176	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
177	C₂²⋊C₄×C₁₀₇	—	2	16	no	—
178	C₂²⋊C₄×C₁₀₇	—	4	8	no	—
179	C₂²⋊C₄×C₁₀₇	—	4	8	no	—
180	C₂²⋊C₄×C₁₀₇	—	4	8	no	—
181	C₄²×C₁₀₇	—	4	4	no	—
182	C₂³×C₁₀₇	—	2	2	no	—
183	C₂³×C₁₀₇	—	2	2	no	—
184	C₂³×C₁₀₇	—	2	8	no	—
185	C₂³×C₁₀₇	—	2	2	no	—
186	C₂³×C₁₀₇	—	2	4	no	—
187	C₂³×C₁₀₇	—	2	4	no	—
188	C₂³×C₁₀₇	—	2	2	no	—
189	C₂³×C₁₀₇	—	2	4	no	—
190	C₂³×C₁₀₇	—	2	8	no	—
191	C₂³×C₁₀₇	—	2	4	no	—
192	C₂³×C₁₀₇	—	2	4	no	—
193	C₂³×C₁₀₇	—	2	8	no	—
194	C₂³×C₁₀₇	—	4	16	no	—
195	C₂³×C₁₀₇	—	4	4	no	—
196	C₂³×C₁₀₇	—	4	4	no	—
197	C₂³×C₁₀₇	C₂²×D₄	1	2	yes	—
198	C₂³×C₁₀₇	H(5,𝔽₂)	1	4	yes	—
199	C₂³×C₁₀₇	2₋¹⁺⁴	1	4	yes	—
200	C₂³×C₁₀₇	C₂⁵	1	1	yes	characteristic
201	Q₈×C₁₀₇	—	4	16	no	—
202	Q₈×C₁₀₇	—	4	8	no	—
203	D₄×C₁₀₇	—	4	8	no	—
204	D₄×C₁₀₇	—	4	16	no	—
205	D₄×C₁₀₇	—	8	4	no	—
206	D₄×C₁₀₇	—	8	4	no	—
207	D₄×C₁₀₇	—	8	16	no	—
208	C₂×C₄×C₁₀₇	—	2	8	no	—
209	C₂×C₄×C₁₀₇	—	2	8	no	—
210	C₂×C₄×C₁₀₇	—	2	2	no	—
211	C₂×C₄×C₁₀₇	—	2	4	no	—
212	C₂×C₄×C₁₀₇	—	2	4	no	—
213	C₂×C₄×C₁₀₇	—	2	4	no	—
214	C₂×C₄×C₁₀₇	—	2	2	no	—
215	C₂×C₄×C₁₀₇	—	2	2	no	—
216	C₂×C₄×C₁₀₇	—	2	4	no	—
217	C₂×C₄×C₁₀₇	—	2	2	no	—
218	C₂×C₄×C₁₀₇	—	2	8	no	—
219	C₂×C₄×C₁₀₇	—	2	8	no	—
220	C₂×C₄×C₁₀₇	—	2	4	no	—
221	C₂×C₄×C₁₀₇	—	2	4	no	—
222	C₂×C₄×C₁₀₇	—	2	4	no	—
223	C₂×C₄×C₁₀₇	—	2	4	no	—
224	C₂×C₄×C₁₀₇	—	2	8	no	—
225	C₂×C₄×C₁₀₇	—	4	4	no	—
226	C₂×C₄×C₁₀₇	—	4	4	no	—
227	C₂×C₄×C₁₀₇	—	4	16	no	—
228	C₂×C₄×C₁₀₇	—	4	16	no	—
229	C₂×C₄×C₁₀₇	—	4	4	no	—
230	C₂×C₄×C₁₀₇	—	4	4	no	—
231	C₂×C₄×C₁₀₇	C₂²×D₄	1	4	yes	—
232	C₂×C₄×C₁₀₇	C₂²×D₄	1	4	yes	—
233	C₂×C₄×C₁₀₇	C₂²×D₄	1	4	yes	—
234	C₂×C₄×C₁₀₇	H(5,𝔽₂)	1	4	yes	—
235	C₂²×C₁₀₇	—	2	2	no	—
236	C₂²×C₁₀₇	—	2	2	no	—
237	C₂²×C₁₀₇	—	2	8	no	—
238	C₂²×C₁₀₇	—	2	4	no	—
239	C₂²×C₁₀₇	—	2	8	no	—
240	C₂²×C₁₀₇	—	4	16	no	—
241	C₂²×C₁₀₇	—	4	2	no	—
242	C₂²×C₁₀₇	—	4	2	no	—
243	C₂²×C₁₀₇	—	4	4	no	—
244	C₂²×C₁₀₇	—	4	4	no	—
245	C₂²×C₁₀₇	—	4	4	no	—
246	C₂²×C₁₀₇	—	4	4	no	—
247	C₂²×C₁₀₇	—	4	8	no	—
248	C₂²×C₁₀₇	—	4	8	no	—
249	C₂²×C₁₀₇	#535	1	4	yes	—
250	C₂²×C₁₀₇	C₂³×D₄	1	1	yes	characteristic
251	C₂²×C₁₀₇	C₂×H(5,𝔽₂)	1	2	yes	—
252	C₂²×C₁₀₇	C₂×H(5,𝔽₂)	1	2	yes	—
253	C₂²×C₁₀₇	C₂×2₋¹⁺⁴	1	2	yes	—
254	C₄×C₁₀₇	—	2	4	no	—
255	C₄×C₁₀₇	—	2	4	no	—
256	C₄×C₁₀₇	—	2	4	no	—
257	C₄×C₁₀₇	—	2	4	no	—
258	C₄×C₁₀₇	—	4	2	no	—
259	C₄×C₁₀₇	—	4	4	no	—
260	C₄×C₁₀₇	—	4	2	no	—
261	C₄×C₁₀₇	—	4	8	no	—
262	#36707	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂×C₁₀₇	—	2	4	no	—
264	C₂×C₁₀₇	—	4	4	no	—
265	C₂×C₁₀₇	—	8	4	no	—
266	C₂×C₁₀₇	C₂×#535	1	1	yes	characteristic
267	C₂×C₁₀₇	#3484	1	1	yes	characteristic
268	C₂×C₁₀₇	#3486	1	1	yes	characteristic
269	C₂×C₁₀₇	#3536	1	4	yes	—
270	C₂×#537	C₂×C₁₀₇	1	1	yes	characteristic, complemented
271	C₂²×C₂²⋊Q₈	C₂×C₁₀₇	1	1	yes	characteristic, complemented
272	#2847	C₂×C₁₀₇	1	2	yes	complemented
273	#2692	C₂×C₁₀₇	1	8	yes	complemented
274	#2676	C₂×C₁₀₇	1	8	yes	complemented
275	#2618	C₂×C₁₀₇	1	2	yes	complemented
276	#2539	C₂×C₁₀₇	1	2	yes	complemented
277	#2436	C₂×C₁₀₇	1	2	yes	complemented
278	#2406	C₂×C₁₀₇	1	2	yes	complemented
279	#2404	C₂×C₁₀₇	1	2	yes	complemented
280	#2313	C₂×C₁₀₇	1	1	yes	characteristic, complemented
281	C₁₀₇	#36707	1	1	yes	characteristic, direct product factor, Sylow
282	C₂²×#41	C₂²×C₁₀₇	1	2	yes	—
283	C₂³×Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
284	C₂⁴×C₄	C₂²×C₁₀₇	1	1	yes	characteristic
285	#537	—	2	8	no	—
286	C₂×#124	C₂²×C₁₀₇	1	4	yes	complemented
287	C₂×#123	C₂²×C₁₀₇	1	4	yes	—
288	C₂×C₂²⋊Q₈	—	2	8	no	—
289	C₂×C₂²⋊Q₈	C₂²×C₁₀₇	1	8	yes	—
290	C₂×C₂²⋊Q₈	C₂²×C₁₀₇	1	4	yes	complemented
291	C₂×#121	C₂²×C₁₀₇	1	2	yes	—
292	C₂×#121	C₂²×C₁₀₇	1	2	yes	—
293	C₂×#121	C₂²×C₁₀₇	1	4	yes	—
294	C₂×#121	C₂²×C₁₀₇	1	4	yes	complemented
295	C₂×#120	C₂²×C₁₀₇	1	4	yes	—
296	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
297	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
298	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
299	C₂²×C₂²⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
300	C₂²×C₂²⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
301	#399	C₂²×C₁₀₇	1	4	yes	—
302	#398	C₂²×C₁₀₇	1	4	yes	complemented
303	#396	C₂²×C₁₀₇	1	8	yes	complemented
304	#395	C₂²×C₁₀₇	1	4	yes	complemented
305	#394	C₂²×C₁₀₇	1	4	yes	complemented
306	#394	C₂²×C₁₀₇	1	4	yes	complemented
307	#393	C₂²×C₁₀₇	1	4	yes	—
308	#393	C₂²×C₁₀₇	1	8	yes	complemented
309	#392	C₂²×C₁₀₇	1	4	yes	—
310	#392	C₂²×C₁₀₇	1	4	yes	—
311	#391	C₂²×C₁₀₇	1	4	yes	complemented
312	#390	C₂²×C₁₀₇	1	8	yes	—
313	#387	C₂²×C₁₀₇	1	8	yes	complemented
314	#386	C₂²×C₁₀₇	1	4	yes	—
315	#386	C₂²×C₁₀₇	1	8	yes	—
316	#386	C₂²×C₁₀₇	1	4	yes	—
317	#386	C₂²×C₁₀₇	1	8	yes	—
318	#385	C₂²×C₁₀₇	1	8	yes	complemented
319	#381	C₂²×C₁₀₇	1	2	yes	—
320	#380	C₂²×C₁₀₇	1	2	yes	—
321	#380	C₂²×C₁₀₇	1	4	yes	—
322	C₄×C₂²⋊C₄	C₂²×C₁₀₇	1	2	yes	—
323	C₂⁵	C₂³×C₁₀₇	1	1	yes	characteristic
324	C₂×#41	—	2	8	no	—
325	C₂×#41	—	4	8	no	—
326	C₂²×Q₈	—	2	4	no	—
327	C₂²×Q₈	—	4	4	no	—
328	C₂²×Q₈	C₂³×C₁₀₇	1	4	yes	—
329	C₂²×Q₈	C₂³×C₁₀₇	1	2	yes	—
330	C₂²×D₄	C₂³×C₁₀₇	1	4	yes	—
331	C₂²×D₄	C₂³×C₁₀₇	1	8	yes	—
332	C₂²×D₄	C₂³×C₁₀₇	1	2	yes	—
333	C₂²×D₄	C₂³×C₁₀₇	1	2	yes	—
334	C₂²×D₄	C₂³×C₁₀₇	1	2	yes	—
335	C₂³×C₄	—	2	4	no	—
336	C₂³×C₄	—	4	4	no	—
337	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
338	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₁₀₇	1	4	yes	—
340	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
342	C₂³×C₄	C₂³×C₁₀₇	1	4	yes	—
343	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
344	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
345	#124	—	4	8	no	—
346	#123	—	4	8	no	—
347	C₂²⋊Q₈	—	2	32	no	—
348	C₂²⋊Q₈	—	2	16	no	—
349	#121	—	2	8	no	—
350	#121	—	2	8	no	—
351	#121	—	2	16	no	—
352	#121	—	4	8	no	—
353	#120	—	4	8	no	—
354	C₂×C₄⋊C₄	—	2	4	no	—
355	C₂×C₄⋊C₄	—	2	4	no	—
356	C₂×C₄⋊C₄	D₄×C₁₀₇	1	8	yes	complemented
357	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	4	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	4	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	8	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	4	yes	—
364	C₂×C₂²⋊C₄	—	2	4	no	—
365	C₂×C₂²⋊C₄	—	2	4	no	—
366	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	4	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	4	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	4	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	4	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	4	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	8	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	8	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	8	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	8	yes	—
375	C₂×C₄²	C₂³×C₁₀₇	1	4	yes	—
376	#95	C₂³×C₁₀₇	1	4	yes	—
377	#95	C₂³×C₁₀₇	1	8	yes	—
378	#95	C₂³×C₁₀₇	1	4	yes	—
379	#95	C₂³×C₁₀₇	1	4	yes	—
380	#95	C₂³×C₁₀₇	1	4	yes	—
381	#95	C₂³×C₁₀₇	1	8	yes	—
382	C₂⁴	—	2	2	no	—
383	C₂⁴	—	2	4	no	—
384	C₂⁴	—	2	4	no	—
385	C₂⁴	—	4	2	no	—
386	C₂⁴	C₂⁴×C₁₀₇	1	4	yes	—
387	C₂⁴	C₂⁴×C₁₀₇	1	2	yes	—
388	C₂⁴	C₂⁴×C₁₀₇	1	1	yes	characteristic
389	#41	—	4	32	no	—
390	C₂×Q₈	—	2	8	no	—
391	C₂×Q₈	—	2	4	no	—
392	C₂×Q₈	—	2	8	no	—
393	C₂×Q₈	—	4	4	no	—
394	C₂×Q₈	—	4	4	no	—
395	C₂×Q₈	—	4	16	no	—
396	C₂×D₄	—	2	8	no	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	—	2	8	no	—
399	C₂×D₄	—	2	16	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	4	4	no	—
404	C₂×D₄	—	4	8	no	—
405	C₂×D₄	—	4	4	no	—
406	C₂×D₄	—	4	8	no	—
407	C₂×D₄	—	4	4	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	2	8	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	4	4	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	4	no	—
422	C₂²×C₄	—	4	4	no	—
423	C₂²×C₄	—	4	16	no	—
424	C₂²×C₄	C₂×D₄×C₁₀₇	1	4	yes	—
425	C₂²×C₄	C₂×D₄×C₁₀₇	1	4	yes	—
426	C₂²×C₄	C₂×D₄×C₁₀₇	1	4	yes	—
427	C₂²×C₄	C₂⁴×C₁₀₇	1	8	yes	—
428	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
429	C₂²×C₄	C₂⁴×C₁₀₇	1	4	yes	—
430	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	2	8	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	4	4	no	—
440	C₄⋊C₄	—	4	8	no	—
441	C₄⋊C₄	C₂×D₄×C₁₀₇	1	16	yes	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₂²⋊C₄	—	2	8	no	—
444	C₂²⋊C₄	—	2	8	no	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	8	no	—
447	C₂²⋊C₄	—	2	16	no	—
448	C₂²⋊C₄	—	4	8	no	—
449	C₂²⋊C₄	—	4	8	no	—
450	C₂²⋊C₄	—	4	8	no	—
451	C₄²	—	4	4	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	8	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	2	8	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	4	no	—
463	C₂³	—	2	8	no	—
464	C₂³	—	4	16	no	—
465	C₂³	—	4	4	no	—
466	C₂³	—	4	4	no	—
467	C₂³	C₂²×D₄×C₁₀₇	1	2	yes	—
468	C₂³	H(5,𝔽₂)×C₁₀₇	1	4	yes	—
469	C₂³	2₋¹⁺⁴×C₁₀₇	1	4	yes	—
470	C₂³	C₂⁵×C₁₀₇	1	1	yes	characteristic
471	Q₈	—	4	16	no	—
472	Q₈	—	4	8	no	—
473	D₄	—	4	8	no	—
474	D₄	—	4	16	no	—
475	D₄	—	8	4	no	—
476	D₄	—	8	4	no	—
477	D₄	—	8	16	no	—
478	C₂×C₄	—	2	8	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	2	8	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	8	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	16	no	—
498	C₂×C₄	—	4	16	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	C₂²×D₄×C₁₀₇	1	4	yes	—
502	C₂×C₄	C₂²×D₄×C₁₀₇	1	4	yes	—
503	C₂×C₄	C₂²×D₄×C₁₀₇	1	4	yes	—
504	C₂×C₄	H(5,𝔽₂)×C₁₀₇	1	4	yes	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	8	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	8	no	—
510	C₂²	—	4	16	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	8	no	—
518	C₂²	—	4	8	no	—
519	C₂²	#535×C₁₀₇	1	4	yes	—
520	C₂²	C₂³×D₄×C₁₀₇	1	1	yes	characteristic
521	C₂²	C₂×H(5,𝔽₂)×C₁₀₇	1	2	yes	—
522	C₂²	C₂×H(5,𝔽₂)×C₁₀₇	1	2	yes	—
523	C₂²	C₂×2₋¹⁺⁴×C₁₀₇	1	2	yes	—
524	C₄	—	2	4	no	—
525	C₄	—	2	4	no	—
526	C₄	—	2	4	no	—
527	C₄	—	2	4	no	—
528	C₄	—	4	4	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	8	no	—
532	C₂	—	2	4	no	—
533	C₂	—	4	4	no	—
534	C₂	—	8	4	no	—
535	C₂	C₂×#535×C₁₀₇	1	1	yes	characteristic
536	C₂	C₁₀₇×#3484	1	1	yes	characteristic
537	C₂	C₁₀₇×#3486	1	1	yes	characteristic
538	C₂	C₁₀₇×#3536	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×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×#537×C₁₀₇	C₂	semidirect
2. C₂²×C₂²⋊Q₈×C₁₀₇	C₂	semidirect
3. C₁₀₇×#2847	C₂	semidirect
4. C₁₀₇×#2692	C₂	semidirect
5. C₁₀₇×#2676	C₂	semidirect
6. C₁₀₇×#2618	C₂	semidirect
7. C₁₀₇×#2539	C₂	semidirect
8. C₁₀₇×#2436	C₂	semidirect
9. C₁₀₇×#2406	C₂	semidirect
10. C₁₀₇×#2404	C₂	semidirect
11. C₁₀₇×#2313	C₂	semidirect
16. C₂×#124×C₁₀₇	C₂²	semidirect
20. C₂×C₂²⋊Q₈×C₁₀₇	C₂²	semidirect
24. C₂×#121×C₁₀₇	C₂²	semidirect
32. #398×C₁₀₇	C₂²	semidirect
33. #396×C₁₀₇	C₂²	semidirect
34. #395×C₁₀₇	C₂²	semidirect
35. #394×C₁₀₇	C₂²	semidirect
36. #394×C₁₀₇	C₂²	semidirect
38. #393×C₁₀₇	C₂²	semidirect
41. #391×C₁₀₇	C₂²	semidirect
43. #387×C₁₀₇	C₂²	semidirect
48. #385×C₁₀₇	C₂²	semidirect
86. C₂×C₄⋊C₄×C₁₀₇	D₄	semidirect
262. #36707	C₁₀₇	direct (N × H)
270. C₂×#537	C₂×C₁₀₇	semidirect
271. C₂²×C₂²⋊Q₈	C₂×C₁₀₇	semidirect
272. #2847	C₂×C₁₀₇	semidirect
273. #2692	C₂×C₁₀₇	semidirect
274. #2676	C₂×C₁₀₇	semidirect
275. #2618	C₂×C₁₀₇	semidirect
276. #2539	C₂×C₁₀₇	semidirect
277. #2436	C₂×C₁₀₇	semidirect
278. #2406	C₂×C₁₀₇	semidirect
279. #2404	C₂×C₁₀₇	semidirect
280. #2313	C₂×C₁₀₇	semidirect
281. C₁₀₇	#36707	direct (N × H)
286. C₂×#124	C₂²×C₁₀₇	semidirect
290. C₂×C₂²⋊Q₈	C₂²×C₁₀₇	semidirect
294. C₂×#121	C₂²×C₁₀₇	semidirect
302. #398	C₂²×C₁₀₇	semidirect
303. #396	C₂²×C₁₀₇	semidirect
304. #395	C₂²×C₁₀₇	semidirect
305. #394	C₂²×C₁₀₇	semidirect
306. #394	C₂²×C₁₀₇	semidirect
308. #393	C₂²×C₁₀₇	semidirect
311. #391	C₂²×C₁₀₇	semidirect
313. #387	C₂²×C₁₀₇	semidirect
318. #385	C₂²×C₁₀₇	semidirect
356. C₂×C₄⋊C₄	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×#537×C₁₀₇	2
C₂²×C₂²⋊Q₈×C₁₀₇	2
C₁₀₇×#2847	2
C₁₀₇×#2692	2
C₁₀₇×#2676	2
C₁₀₇×#2618	2
C₁₀₇×#2539	2
C₁₀₇×#2436	2
C₁₀₇×#2406	2
C₁₀₇×#2404	2
C₁₀₇×#2313	2
#36707	107

Subgroups — C107×#36707 #41062671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#36707 #41062671