Subgroups — C₂×C₁₀₇×#2324 #41060028

Order 27392.

3934 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#117×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₇×#2324	C₂	1	16	yes	maximal, direct product factor
5	C₂×#390×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#390×C₁₀₇	C₂	1	2	yes	maximal, complemented
7	C₂×#389×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#388×C₁₀₇	C₂	1	2	yes	maximal, complemented
9	C₂×#386×C₁₀₇	C₂	1	2	yes	maximal, complemented
10	C₂×#385×C₁₀₇	C₂	1	2	yes	maximal, complemented
11	C₂×#380×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₄⋊C₄×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₀₇	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₁₀₇	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₀₇	C₂²	1	2	yes	—
17	C₂×#121×C₁₀₇	C₄	1	16	yes	complemented
18	C₂×#121×C₁₀₇	C₂²	1	8	yes	—
19	C₂×C₄×D₄×C₁₀₇	—	2	8	no	—
20	C₂×C₄×D₄×C₁₀₇	C₂²	1	8	yes	complemented
21	C₂×#117×C₁₀₇	—	2	8	no	—
22	C₂×#117×C₁₀₇	C₂²	1	8	yes	complemented
23	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	—
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	C₂²×C₂²⋊C₄×C₁₀₇	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₁₀₇	C₂²	1	2	yes	—
33	C₂²×C₂²⋊C₄×C₁₀₇	C₂²	1	2	yes	—
34	C₂²×C₂²⋊C₄×C₁₀₇	C₂²	1	2	yes	—
35	C₂²×C₂²⋊C₄×C₁₀₇	C₂²	1	2	yes	—
36	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₁₀₇	C₂²	1	2	yes	—
38	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
39	#390×C₁₀₇	C₂²	1	8	yes	complemented
40	#390×C₁₀₇	C₂²	1	16	yes	complemented
41	#389×C₁₀₇	C₂²	1	8	yes	complemented
42	#388×C₁₀₇	C₂²	1	16	yes	complemented
43	#386×C₁₀₇	C₂²	1	16	yes	complemented
44	#385×C₁₀₇	C₂²	1	16	yes	complemented
45	#380×C₁₀₇	C₂²	1	8	yes	complemented
46	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	8	yes	complemented
47	C₂×#95×C₁₀₇	C₂²	1	2	yes	—
48	C₂×#95×C₁₀₇	C₂²	1	2	yes	—
49	C₂×#95×C₁₀₇	C₂²	1	2	yes	—
50	C₂⁵×C₁₀₇	C₂³	1	1	yes	characteristic
51	C₂⁵×C₁₀₇	C₂³	1	2	yes	—
52	C₂²×D₄×C₁₀₇	—	2	4	no	—
53	C₂²×D₄×C₁₀₇	—	2	4	no	—
54	C₂²×D₄×C₁₀₇	—	4	4	no	—
55	C₂²×D₄×C₁₀₇	—	4	4	no	—
56	C₂²×D₄×C₁₀₇	C₂×C₄	1	8	yes	—
57	C₂²×D₄×C₁₀₇	C₂×C₄	1	16	yes	complemented
58	C₂²×D₄×C₁₀₇	C₂³	1	4	yes	—
59	C₂²×D₄×C₁₀₇	C₂³	1	8	yes	—
60	C₂³×C₄×C₁₀₇	—	2	4	no	—
61	C₂³×C₄×C₁₀₇	—	2	4	no	—
62	C₂³×C₄×C₁₀₇	—	2	8	no	—
63	C₂³×C₄×C₁₀₇	—	4	4	no	—
64	C₂³×C₄×C₁₀₇	—	4	4	no	—
65	C₂³×C₄×C₁₀₇	C₂×C₄	1	8	yes	complemented
66	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₀₇	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₀₇	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₀₇	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₀₇	C₂³	1	4	yes	—
73	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₀₇	C₂³	1	8	yes	—
76	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
77	#121×C₁₀₇	C₂×C₄	1	64	yes	complemented
78	C₄×D₄×C₁₀₇	—	2	32	no	—
79	#117×C₁₀₇	—	2	32	no	—
80	C₂×C₄⋊C₄×C₁₀₇	—	2	4	no	—
81	C₂×C₄⋊C₄×C₁₀₇	—	2	4	no	—
82	C₂×C₄⋊C₄×C₁₀₇	—	2	4	no	—
83	C₂×C₄⋊C₄×C₁₀₇	—	2	4	no	—
84	C₂×C₄⋊C₄×C₁₀₇	—	4	4	no	—
85	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	8	yes	complemented
86	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	8	yes	—
91	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₁₀₇	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₁₀₇	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₁₀₇	—	2	8	no	—
95	C₂×C₂²⋊C₄×C₁₀₇	—	4	4	no	—
96	C₂×C₂²⋊C₄×C₁₀₇	—	4	4	no	—
97	C₂×C₂²⋊C₄×C₁₀₇	—	4	4	no	—
98	C₂×C₂²⋊C₄×C₁₀₇	C₂×C₄	1	16	yes	complemented
99	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	8	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×C₂²⋊C₄×C₁₀₇	C₂³	1	8	yes	—
106	C₂×C₄²×C₁₀₇	—	2	4	no	—
107	C₂×C₄²×C₁₀₇	—	4	4	no	—
108	C₂×C₄²×C₁₀₇	D₄	1	8	yes	complemented
109	C₂×C₄²×C₁₀₇	C₂³	1	4	yes	—
110	C₂×C₄²×C₁₀₇	C₂³	1	8	yes	—
111	C₂×C₄²×C₁₀₇	C₂³	1	4	yes	—
112	#95×C₁₀₇	C₂³	1	8	yes	—
113	#95×C₁₀₇	C₂³	1	8	yes	—
114	#95×C₁₀₇	C₂³	1	8	yes	—
115	C₂⁴×C₁₀₇	—	2	2	no	—
116	C₂⁴×C₁₀₇	—	2	4	no	—
117	C₂⁴×C₁₀₇	—	2	2	no	—
118	C₂⁴×C₁₀₇	—	2	4	no	—
119	C₂⁴×C₁₀₇	—	2	2	no	—
120	C₂⁴×C₁₀₇	—	2	4	no	—
121	C₂⁴×C₁₀₇	—	2	4	no	—
122	C₂⁴×C₁₀₇	—	2	4	no	—
123	C₂⁴×C₁₀₇	—	2	2	no	—
124	C₂⁴×C₁₀₇	—	2	2	no	—
125	C₂⁴×C₁₀₇	—	2	2	no	—
126	C₂⁴×C₁₀₇	—	2	4	no	—
127	C₂⁴×C₁₀₇	C₂²×C₄	1	8	yes	—
128	C₂⁴×C₁₀₇	C₂²×C₄	1	4	yes	—
129	C₂⁴×C₁₀₇	C₂⁴	1	2	yes	—
130	C₂⁴×C₁₀₇	C₂⁴	1	4	yes	—
131	C₂⁴×C₁₀₇	C₂⁴	1	1	yes	characteristic
132	C₂×D₄×C₁₀₇	—	2	32	no	—
133	C₂×D₄×C₁₀₇	—	2	8	no	—
134	C₂×D₄×C₁₀₇	—	2	8	no	—
135	C₂×D₄×C₁₀₇	—	4	32	no	—
136	C₂×D₄×C₁₀₇	—	4	8	no	—
137	C₂×D₄×C₁₀₇	—	4	8	no	—
138	C₂×D₄×C₁₀₇	C₂²×C₄	1	16	yes	—
139	C₂×D₄×C₁₀₇	C₂²×C₄	1	32	yes	complemented
140	C₂²×C₄×C₁₀₇	—	2	2	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	4	no	—
145	C₂²×C₄×C₁₀₇	—	2	2	no	—
146	C₂²×C₄×C₁₀₇	—	2	2	no	—
147	C₂²×C₄×C₁₀₇	—	2	2	no	—
148	C₂²×C₄×C₁₀₇	—	2	32	no	—
149	C₂²×C₄×C₁₀₇	—	2	8	no	—
150	C₂²×C₄×C₁₀₇	—	2	8	no	—
151	C₂²×C₄×C₁₀₇	—	2	2	no	—
152	C₂²×C₄×C₁₀₇	—	2	2	no	—
153	C₂²×C₄×C₁₀₇	—	2	4	no	—
154	C₂²×C₄×C₁₀₇	—	2	4	no	—
155	C₂²×C₄×C₁₀₇	—	2	4	no	—
156	C₂²×C₄×C₁₀₇	—	2	2	no	—
157	C₂²×C₄×C₁₀₇	—	2	2	no	—
158	C₂²×C₄×C₁₀₇	—	2	4	no	—
159	C₂²×C₄×C₁₀₇	—	2	4	no	—
160	C₂²×C₄×C₁₀₇	—	2	2	no	—
161	C₂²×C₄×C₁₀₇	—	2	4	no	—
162	C₂²×C₄×C₁₀₇	—	2	2	no	—
163	C₂²×C₄×C₁₀₇	—	2	16	no	—
164	C₂²×C₄×C₁₀₇	—	4	8	no	—
165	C₂²×C₄×C₁₀₇	—	4	8	no	—
166	C₂²×C₄×C₁₀₇	—	4	32	no	—
167	C₂²×C₄×C₁₀₇	C₂²×C₄	1	4	yes	—
168	C₂²×C₄×C₁₀₇	C₂²×C₄	1	8	yes	—
169	C₂²×C₄×C₁₀₇	C₂²×C₄	1	4	yes	—
170	C₂²×C₄×C₁₀₇	C₂²×C₄	1	16	yes	complemented
171	C₂²×C₄×C₁₀₇	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₁₀₇	C₂×D₄	1	4	yes	—
173	C₂²×C₄×C₁₀₇	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₁₀₇	#41	1	4	yes	—
175	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₀₇	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₀₇	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₀₇	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
184	C₄⋊C₄×C₁₀₇	—	2	8	no	—
185	C₄⋊C₄×C₁₀₇	—	2	8	no	—
186	C₄⋊C₄×C₁₀₇	—	2	8	no	—
187	C₄⋊C₄×C₁₀₇	—	2	8	no	—
188	C₄⋊C₄×C₁₀₇	—	4	8	no	—
189	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	16	yes	complemented
190	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
191	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
192	C₂²⋊C₄×C₁₀₇	—	2	16	no	—
193	C₂²⋊C₄×C₁₀₇	—	4	8	no	—
194	C₂²⋊C₄×C₁₀₇	—	4	8	no	—
195	C₂²⋊C₄×C₁₀₇	—	4	8	no	—
196	C₂²⋊C₄×C₁₀₇	C₂²×C₄	1	32	yes	complemented
197	C₄²×C₁₀₇	—	2	8	no	—
198	C₄²×C₁₀₇	—	4	8	no	—
199	C₄²×C₁₀₇	C₂×D₄	1	16	yes	complemented
200	C₂³×C₁₀₇	—	2	8	no	—
201	C₂³×C₁₀₇	—	2	16	no	—
202	C₂³×C₁₀₇	—	2	8	no	—
203	C₂³×C₁₀₇	—	2	16	no	—
204	C₂³×C₁₀₇	—	2	8	no	—
205	C₂³×C₁₀₇	—	2	16	no	—
206	C₂³×C₁₀₇	—	2	2	no	—
207	C₂³×C₁₀₇	—	2	4	no	—
208	C₂³×C₁₀₇	—	2	2	no	—
209	C₂³×C₁₀₇	—	2	4	no	—
210	C₂³×C₁₀₇	—	2	2	no	—
211	C₂³×C₁₀₇	—	2	4	no	—
212	C₂³×C₁₀₇	—	2	4	no	—
213	C₂³×C₁₀₇	—	2	4	no	—
214	C₂³×C₁₀₇	—	2	2	no	—
215	C₂³×C₁₀₇	—	2	2	no	—
216	C₂³×C₁₀₇	—	2	2	no	—
217	C₂³×C₁₀₇	—	2	4	no	—
218	C₂³×C₁₀₇	—	4	8	no	—
219	C₂³×C₁₀₇	—	4	4	no	—
220	C₂³×C₁₀₇	—	4	4	no	—
221	C₂³×C₁₀₇	—	4	8	no	—
222	C₂³×C₁₀₇	—	4	4	no	—
223	C₂³×C₁₀₇	—	4	8	no	—
224	C₂³×C₁₀₇	—	4	4	no	—
225	C₂³×C₁₀₇	—	4	8	no	—
226	C₂³×C₁₀₇	C₂³×C₄	1	8	yes	—
227	C₂³×C₁₀₇	C₂³×C₄	1	4	yes	—
228	C₂³×C₁₀₇	C₂³×C₄	1	2	yes	—
229	C₂³×C₁₀₇	C₂²×D₄	1	2	yes	—
230	C₂³×C₁₀₇	C₂×#41	1	2	yes	—
231	C₂³×C₁₀₇	H(5,𝔽₂)	1	2	yes	—
232	C₂³×C₁₀₇	H(5,𝔽₂)	1	2	yes	—
233	C₂³×C₁₀₇	H(5,𝔽₂)	1	2	yes	—
234	C₂³×C₁₀₇	2₋¹⁺⁴	1	2	yes	—
235	C₂³×C₁₀₇	C₂⁵	1	1	yes	characteristic
236	D₄×C₁₀₇	—	2	32	no	—
237	D₄×C₁₀₇	—	4	32	no	—
238	C₂×C₄×C₁₀₇	—	2	8	no	—
239	C₂×C₄×C₁₀₇	—	2	16	no	—
240	C₂×C₄×C₁₀₇	—	2	8	no	—
241	C₂×C₄×C₁₀₇	—	2	8	no	—
242	C₂×C₄×C₁₀₇	—	2	2	no	—
243	C₂×C₄×C₁₀₇	—	2	2	no	—
244	C₂×C₄×C₁₀₇	—	2	2	no	—
245	C₂×C₄×C₁₀₇	—	2	4	no	—
246	C₂×C₄×C₁₀₇	—	2	4	no	—
247	C₂×C₄×C₁₀₇	—	2	2	no	—
248	C₂×C₄×C₁₀₇	—	2	2	no	—
249	C₂×C₄×C₁₀₇	—	2	2	no	—
250	C₂×C₄×C₁₀₇	—	2	32	no	—
251	C₂×C₄×C₁₀₇	—	2	2	no	—
252	C₂×C₄×C₁₀₇	—	2	2	no	—
253	C₂×C₄×C₁₀₇	—	2	4	no	—
254	C₂×C₄×C₁₀₇	—	2	4	no	—
255	C₂×C₄×C₁₀₇	—	2	4	no	—
256	C₂×C₄×C₁₀₇	—	2	2	no	—
257	C₂×C₄×C₁₀₇	—	2	2	no	—
258	C₂×C₄×C₁₀₇	—	2	4	no	—
259	C₂×C₄×C₁₀₇	—	2	4	no	—
260	C₂×C₄×C₁₀₇	—	2	2	no	—
261	C₂×C₄×C₁₀₇	—	2	4	no	—
262	C₂×C₄×C₁₀₇	—	2	2	no	—
263	C₂×C₄×C₁₀₇	—	4	32	no	—
264	C₂×C₄×C₁₀₇	—	4	4	no	—
265	C₂×C₄×C₁₀₇	—	4	8	no	—
266	C₂×C₄×C₁₀₇	—	4	4	no	—
267	C₂×C₄×C₁₀₇	—	4	8	no	—
268	C₂×C₄×C₁₀₇	C₄×D₄	1	16	yes	—
269	C₂×C₄×C₁₀₇	C₂³×C₄	1	4	yes	—
270	C₂×C₄×C₁₀₇	C₂³×C₄	1	8	yes	—
271	C₂×C₄×C₁₀₇	C₂³×C₄	1	4	yes	—
272	C₂×C₄×C₁₀₇	C₂²×D₄	1	4	yes	—
273	C₂×C₄×C₁₀₇	C₂²×D₄	1	4	yes	—
274	C₂×C₄×C₁₀₇	C₂²×D₄	1	4	yes	—
275	C₂×C₄×C₁₀₇	C₂×#41	1	4	yes	—
276	C₂²×C₁₀₇	—	2	4	no	—
277	C₂²×C₁₀₇	—	2	8	no	—
278	C₂²×C₁₀₇	—	2	4	no	—
279	C₂²×C₁₀₇	—	2	8	no	—
280	C₂²×C₁₀₇	—	2	4	no	—
281	C₂²×C₁₀₇	—	2	8	no	—
282	C₂²×C₁₀₇	—	4	16	no	—
283	C₂²×C₁₀₇	—	4	32	no	—
284	C₂²×C₁₀₇	—	4	4	no	—
285	C₂²×C₁₀₇	—	4	2	no	—
286	C₂²×C₁₀₇	—	4	2	no	—
287	C₂²×C₁₀₇	—	4	4	no	—
288	C₂²×C₁₀₇	—	4	2	no	—
289	C₂²×C₁₀₇	—	4	4	no	—
290	C₂²×C₁₀₇	—	4	2	no	—
291	C₂²×C₁₀₇	—	4	4	no	—
292	C₂²×C₁₀₇	C₂×C₄×D₄	1	4	yes	—
293	C₂²×C₁₀₇	#518	1	4	yes	—
294	C₂²×C₁₀₇	#520	1	4	yes	—
295	C₂²×C₁₀₇	#535	1	4	yes	—
296	C₂²×C₁₀₇	#537	1	4	yes	—
297	C₂²×C₁₀₇	#540	1	4	yes	—
298	C₂²×C₁₀₇	#542	1	4	yes	—
299	C₂²×C₁₀₇	C₂⁴×C₄	1	1	yes	characteristic
300	C₂²×C₁₀₇	C₂³×D₄	1	1	yes	characteristic
301	C₂²×C₁₀₇	C₂²×#41	1	1	yes	characteristic
302	C₂²×C₁₀₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
303	C₂²×C₁₀₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
304	C₂²×C₁₀₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
305	C₂²×C₁₀₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
306	C₄×C₁₀₇	—	2	4	no	—
307	C₄×C₁₀₇	—	2	8	no	—
308	C₄×C₁₀₇	—	2	4	no	—
309	C₄×C₁₀₇	—	2	4	no	—
310	C₄×C₁₀₇	—	4	2	no	—
311	C₄×C₁₀₇	—	4	4	no	—
312	C₄×C₁₀₇	—	4	2	no	—
313	C₄×C₁₀₇	—	4	4	no	—
314	C₄×C₁₀₇	C₂×C₄×D₄	1	8	yes	—
315	C₂×#2324	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂×C₁₀₇	—	4	4	no	—
317	C₂×C₁₀₇	—	4	8	no	—
318	C₂×C₁₀₇	#2324	1	8	yes	direct product factor
319	C₂×C₁₀₇	C₂²×C₄×D₄	1	1	yes	characteristic
320	C₂×C₁₀₇	C₂×#518	1	1	yes	characteristic
321	C₂×C₁₀₇	C₂×#520	1	1	yes	characteristic
322	C₂×C₁₀₇	C₂×#535	1	1	yes	characteristic
323	C₂×C₁₀₇	C₂×#537	1	1	yes	characteristic
324	C₂×C₁₀₇	C₂×#540	1	1	yes	characteristic
325	C₂×C₁₀₇	C₂×#542	1	1	yes	characteristic
326	C₂²×#121	C₂×C₁₀₇	1	1	yes	characteristic
327	C₂²×C₄×D₄	C₂×C₁₀₇	1	1	yes	characteristic, complemented
328	C₂²×#117	C₂×C₁₀₇	1	1	yes	characteristic, complemented
329	#2324	C₂×C₁₀₇	1	16	yes	direct product factor
330	C₂×#390	C₂×C₁₀₇	1	2	yes	complemented
331	C₂×#390	C₂×C₁₀₇	1	1	yes	characteristic, complemented
332	C₂×#389	C₂×C₁₀₇	1	1	yes	characteristic, complemented
333	C₂×#388	C₂×C₁₀₇	1	2	yes	complemented
334	C₂×#386	C₂×C₁₀₇	1	2	yes	complemented
335	C₂×#385	C₂×C₁₀₇	1	2	yes	complemented
336	C₂×#380	C₂×C₁₀₇	1	1	yes	characteristic, complemented
337	C₂×C₄×C₄⋊C₄	C₂×C₁₀₇	1	1	yes	characteristic, complemented
338	C₁₀₇	C₂×#2324	1	1	yes	characteristic, direct product factor, Sylow
339	C₂³×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
340	C₂³×D₄	C₂²×C₁₀₇	1	2	yes	—
341	C₂⁴×C₄	C₂²×C₁₀₇	1	1	yes	characteristic
342	C₂⁴×C₄	C₂²×C₁₀₇	1	2	yes	—
343	C₂×#121	C₄×C₁₀₇	1	16	yes	complemented
344	C₂×#121	C₂²×C₁₀₇	1	8	yes	—
345	C₂×C₄×D₄	—	2	8	no	—
346	C₂×C₄×D₄	C₂²×C₁₀₇	1	8	yes	complemented
347	C₂×#117	—	2	8	no	—
348	C₂×#117	C₂²×C₁₀₇	1	8	yes	complemented
349	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
350	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
351	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
352	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
353	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	2	yes	—
354	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
355	C₂²×C₂²⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
356	C₂²×C₂²⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
357	C₂²×C₂²⋊C₄	C₂²×C₁₀₇	1	2	yes	—
358	C₂²×C₂²⋊C₄	C₂²×C₁₀₇	1	2	yes	—
359	C₂²×C₂²⋊C₄	C₂²×C₁₀₇	1	2	yes	—
360	C₂²×C₂²⋊C₄	C₂²×C₁₀₇	1	2	yes	—
361	C₂²×C₂²⋊C₄	C₂²×C₁₀₇	1	2	yes	—
362	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
363	C₂²×C₄²	C₂²×C₁₀₇	1	2	yes	—
364	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
365	#390	C₂²×C₁₀₇	1	8	yes	complemented
366	#390	C₂²×C₁₀₇	1	16	yes	complemented
367	#389	C₂²×C₁₀₇	1	8	yes	complemented
368	#388	C₂²×C₁₀₇	1	16	yes	complemented
369	#386	C₂²×C₁₀₇	1	16	yes	complemented
370	#385	C₂²×C₁₀₇	1	16	yes	complemented
371	#380	C₂²×C₁₀₇	1	8	yes	complemented
372	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	8	yes	complemented
373	C₂×#95	C₂²×C₁₀₇	1	2	yes	—
374	C₂×#95	C₂²×C₁₀₇	1	2	yes	—
375	C₂×#95	C₂²×C₁₀₇	1	2	yes	—
376	C₂⁵	C₂³×C₁₀₇	1	1	yes	characteristic
377	C₂⁵	C₂³×C₁₀₇	1	2	yes	—
378	C₂²×D₄	—	2	4	no	—
379	C₂²×D₄	—	2	4	no	—
380	C₂²×D₄	—	4	4	no	—
381	C₂²×D₄	—	4	4	no	—
382	C₂²×D₄	C₂×C₄×C₁₀₇	1	8	yes	—
383	C₂²×D₄	C₂×C₄×C₁₀₇	1	16	yes	complemented
384	C₂²×D₄	C₂³×C₁₀₇	1	4	yes	—
385	C₂²×D₄	C₂³×C₁₀₇	1	8	yes	—
386	C₂³×C₄	—	2	4	no	—
387	C₂³×C₄	—	2	4	no	—
388	C₂³×C₄	—	2	8	no	—
389	C₂³×C₄	—	4	4	no	—
390	C₂³×C₄	—	4	4	no	—
391	C₂³×C₄	C₂×C₄×C₁₀₇	1	8	yes	complemented
392	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₁₀₇	1	2	yes	—
395	C₂³×C₄	C₂³×C₁₀₇	1	2	yes	—
396	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₁₀₇	1	2	yes	—
398	C₂³×C₄	C₂³×C₁₀₇	1	4	yes	—
399	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
400	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₁₀₇	1	8	yes	—
402	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
403	#121	C₂×C₄×C₁₀₇	1	64	yes	complemented
404	C₄×D₄	—	2	32	no	—
405	#117	—	2	32	no	—
406	C₂×C₄⋊C₄	—	2	4	no	—
407	C₂×C₄⋊C₄	—	2	4	no	—
408	C₂×C₄⋊C₄	—	2	4	no	—
409	C₂×C₄⋊C₄	—	2	4	no	—
410	C₂×C₄⋊C₄	—	4	4	no	—
411	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	8	yes	complemented
412	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	4	yes	—
415	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	4	yes	—
416	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	8	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	4	yes	—
418	C₂×C₂²⋊C₄	—	2	4	no	—
419	C₂×C₂²⋊C₄	—	2	4	no	—
420	C₂×C₂²⋊C₄	—	2	8	no	—
421	C₂×C₂²⋊C₄	—	4	4	no	—
422	C₂×C₂²⋊C₄	—	4	4	no	—
423	C₂×C₂²⋊C₄	—	4	4	no	—
424	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₇	1	16	yes	complemented
425	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	8	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	8	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	8	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	8	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	8	yes	—
432	C₂×C₄²	—	2	4	no	—
433	C₂×C₄²	—	4	4	no	—
434	C₂×C₄²	D₄×C₁₀₇	1	8	yes	complemented
435	C₂×C₄²	C₂³×C₁₀₇	1	4	yes	—
436	C₂×C₄²	C₂³×C₁₀₇	1	8	yes	—
437	C₂×C₄²	C₂³×C₁₀₇	1	4	yes	—
438	#95	C₂³×C₁₀₇	1	8	yes	—
439	#95	C₂³×C₁₀₇	1	8	yes	—
440	#95	C₂³×C₁₀₇	1	8	yes	—
441	C₂⁴	—	2	2	no	—
442	C₂⁴	—	2	4	no	—
443	C₂⁴	—	2	2	no	—
444	C₂⁴	—	2	4	no	—
445	C₂⁴	—	2	2	no	—
446	C₂⁴	—	2	4	no	—
447	C₂⁴	—	2	4	no	—
448	C₂⁴	—	2	4	no	—
449	C₂⁴	—	2	2	no	—
450	C₂⁴	—	2	2	no	—
451	C₂⁴	—	2	2	no	—
452	C₂⁴	—	2	4	no	—
453	C₂⁴	C₂²×C₄×C₁₀₇	1	8	yes	—
454	C₂⁴	C₂²×C₄×C₁₀₇	1	4	yes	—
455	C₂⁴	C₂⁴×C₁₀₇	1	2	yes	—
456	C₂⁴	C₂⁴×C₁₀₇	1	4	yes	—
457	C₂⁴	C₂⁴×C₁₀₇	1	1	yes	characteristic
458	C₂×D₄	—	2	32	no	—
459	C₂×D₄	—	2	8	no	—
460	C₂×D₄	—	2	8	no	—
461	C₂×D₄	—	4	32	no	—
462	C₂×D₄	—	4	8	no	—
463	C₂×D₄	—	4	8	no	—
464	C₂×D₄	C₂²×C₄×C₁₀₇	1	16	yes	—
465	C₂×D₄	C₂²×C₄×C₁₀₇	1	32	yes	complemented
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	32	no	—
475	C₂²×C₄	—	2	8	no	—
476	C₂²×C₄	—	2	8	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	16	no	—
490	C₂²×C₄	—	4	8	no	—
491	C₂²×C₄	—	4	8	no	—
492	C₂²×C₄	—	4	32	no	—
493	C₂²×C₄	C₂²×C₄×C₁₀₇	1	4	yes	—
494	C₂²×C₄	C₂²×C₄×C₁₀₇	1	8	yes	—
495	C₂²×C₄	C₂²×C₄×C₁₀₇	1	4	yes	—
496	C₂²×C₄	C₂²×C₄×C₁₀₇	1	16	yes	complemented
497	C₂²×C₄	C₂×D₄×C₁₀₇	1	4	yes	—
498	C₂²×C₄	C₂×D₄×C₁₀₇	1	4	yes	—
499	C₂²×C₄	C₂×D₄×C₁₀₇	1	4	yes	—
500	C₂²×C₄	#41×C₁₀₇	1	4	yes	—
501	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
502	C₂²×C₄	C₂⁴×C₁₀₇	1	4	yes	—
503	C₂²×C₄	C₂⁴×C₁₀₇	1	4	yes	—
504	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₁₀₇	1	4	yes	—
506	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
508	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
510	C₄⋊C₄	—	2	8	no	—
511	C₄⋊C₄	—	2	8	no	—
512	C₄⋊C₄	—	2	8	no	—
513	C₄⋊C₄	—	2	8	no	—
514	C₄⋊C₄	—	4	8	no	—
515	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	16	yes	complemented
516	C₂²⋊C₄	—	2	8	no	—
517	C₂²⋊C₄	—	2	8	no	—
518	C₂²⋊C₄	—	2	16	no	—
519	C₂²⋊C₄	—	4	8	no	—
520	C₂²⋊C₄	—	4	8	no	—
521	C₂²⋊C₄	—	4	8	no	—
522	C₂²⋊C₄	C₂²×C₄×C₁₀₇	1	32	yes	complemented
523	C₄²	—	2	8	no	—
524	C₄²	—	4	8	no	—
525	C₄²	C₂×D₄×C₁₀₇	1	16	yes	complemented
526	C₂³	—	2	8	no	—
527	C₂³	—	2	16	no	—
528	C₂³	—	2	8	no	—
529	C₂³	—	2	16	no	—
530	C₂³	—	2	8	no	—
531	C₂³	—	2	16	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	4	8	no	—
545	C₂³	—	4	4	no	—
546	C₂³	—	4	4	no	—
547	C₂³	—	4	8	no	—
548	C₂³	—	4	4	no	—
549	C₂³	—	4	8	no	—
550	C₂³	—	4	4	no	—
551	C₂³	—	4	8	no	—
552	C₂³	C₂³×C₄×C₁₀₇	1	8	yes	—
553	C₂³	C₂³×C₄×C₁₀₇	1	4	yes	—
554	C₂³	C₂³×C₄×C₁₀₇	1	2	yes	—
555	C₂³	C₂²×D₄×C₁₀₇	1	2	yes	—
556	C₂³	C₂×#41×C₁₀₇	1	2	yes	—
557	C₂³	H(5,𝔽₂)×C₁₀₇	1	2	yes	—
558	C₂³	H(5,𝔽₂)×C₁₀₇	1	2	yes	—
559	C₂³	H(5,𝔽₂)×C₁₀₇	1	2	yes	—
560	C₂³	2₋¹⁺⁴×C₁₀₇	1	2	yes	—
561	C₂³	C₂⁵×C₁₀₇	1	1	yes	characteristic
562	D₄	—	2	32	no	—
563	D₄	—	4	32	no	—
564	C₂×C₄	—	2	8	no	—
565	C₂×C₄	—	2	16	no	—
566	C₂×C₄	—	2	8	no	—
567	C₂×C₄	—	2	8	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	32	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	4	32	no	—
590	C₂×C₄	—	4	8	no	—
591	C₂×C₄	—	4	4	no	—
592	C₂×C₄	—	4	4	no	—
593	C₂×C₄	—	4	8	no	—
594	C₂×C₄	C₄×D₄×C₁₀₇	1	16	yes	—
595	C₂×C₄	C₂³×C₄×C₁₀₇	1	4	yes	—
596	C₂×C₄	C₂³×C₄×C₁₀₇	1	8	yes	—
597	C₂×C₄	C₂³×C₄×C₁₀₇	1	4	yes	—
598	C₂×C₄	C₂²×D₄×C₁₀₇	1	4	yes	—
599	C₂×C₄	C₂²×D₄×C₁₀₇	1	4	yes	—
600	C₂×C₄	C₂²×D₄×C₁₀₇	1	4	yes	—
601	C₂×C₄	C₂×#41×C₁₀₇	1	4	yes	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	8	no	—
604	C₂²	—	2	4	no	—
605	C₂²	—	2	8	no	—
606	C₂²	—	2	4	no	—
607	C₂²	—	2	8	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	4	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	4	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	4	16	no	—
617	C₂²	—	4	32	no	—
618	C₂²	C₂×C₄×D₄×C₁₀₇	1	4	yes	—
619	C₂²	#518×C₁₀₇	1	4	yes	—
620	C₂²	#520×C₁₀₇	1	4	yes	—
621	C₂²	#535×C₁₀₇	1	4	yes	—
622	C₂²	#537×C₁₀₇	1	4	yes	—
623	C₂²	#540×C₁₀₇	1	4	yes	—
624	C₂²	#542×C₁₀₇	1	4	yes	—
625	C₂²	C₂⁴×C₄×C₁₀₇	1	1	yes	characteristic
626	C₂²	C₂³×D₄×C₁₀₇	1	1	yes	characteristic
627	C₂²	C₂²×#41×C₁₀₇	1	1	yes	characteristic
628	C₂²	C₂×H(5,𝔽₂)×C₁₀₇	1	1	yes	characteristic
629	C₂²	C₂×H(5,𝔽₂)×C₁₀₇	1	1	yes	characteristic
630	C₂²	C₂×H(5,𝔽₂)×C₁₀₇	1	1	yes	characteristic
631	C₂²	C₂×2₋¹⁺⁴×C₁₀₇	1	1	yes	characteristic
632	C₄	—	2	4	no	—
633	C₄	—	2	8	no	—
634	C₄	—	2	4	no	—
635	C₄	—	2	4	no	—
636	C₄	—	4	4	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	4	no	—
640	C₄	C₂×C₄×D₄×C₁₀₇	1	8	yes	—
641	C₂	—	4	4	no	—
642	C₂	—	4	8	no	—
643	C₂	C₁₀₇×#2324	1	8	yes	direct product factor
644	C₂	C₂²×C₄×D₄×C₁₀₇	1	1	yes	characteristic
645	C₂	C₂×#518×C₁₀₇	1	1	yes	characteristic
646	C₂	C₂×#520×C₁₀₇	1	1	yes	characteristic
647	C₂	C₂×#535×C₁₀₇	1	1	yes	characteristic
648	C₂	C₂×#537×C₁₀₇	1	1	yes	characteristic
649	C₂	C₂×#540×C₁₀₇	1	1	yes	characteristic
650	C₂	C₂×#542×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₀₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₀₇
Frattini, cosocle	C₂³	C₂⁵×C₁₀₇
prime radical	C₂²×#121×C₁₀₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₄×C₁₀₇	C₂	semidirect
3. C₂²×#117×C₁₀₇	C₂	semidirect
4. C₁₀₇×#2324	C₂	direct (N × H)
5. C₂×#390×C₁₀₇	C₂	semidirect
6. C₂×#390×C₁₀₇	C₂	semidirect
7. C₂×#389×C₁₀₇	C₂	semidirect
8. C₂×#388×C₁₀₇	C₂	semidirect
9. C₂×#386×C₁₀₇	C₂	semidirect
10. C₂×#385×C₁₀₇	C₂	semidirect
11. C₂×#380×C₁₀₇	C₂	semidirect
12. C₂×C₄×C₄⋊C₄×C₁₀₇	C₂	semidirect
17. C₂×#121×C₁₀₇	C₄	semidirect
20. C₂×C₄×D₄×C₁₀₇	C₂²	semidirect
22. C₂×#117×C₁₀₇	C₂²	semidirect
39. #390×C₁₀₇	C₂²	semidirect
40. #390×C₁₀₇	C₂²	semidirect
41. #389×C₁₀₇	C₂²	semidirect
42. #388×C₁₀₇	C₂²	semidirect
43. #386×C₁₀₇	C₂²	semidirect
44. #385×C₁₀₇	C₂²	semidirect
45. #380×C₁₀₇	C₂²	semidirect
46. C₄×C₄⋊C₄×C₁₀₇	C₂²	semidirect
57. C₂²×D₄×C₁₀₇	C₂×C₄	semidirect
65. C₂³×C₄×C₁₀₇	C₂×C₄	semidirect
77. #121×C₁₀₇	C₂×C₄	semidirect
85. C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	semidirect
98. C₂×C₂²⋊C₄×C₁₀₇	C₂×C₄	semidirect
108. C₂×C₄²×C₁₀₇	D₄	semidirect
139. C₂×D₄×C₁₀₇	C₂²×C₄	semidirect
170. C₂²×C₄×C₁₀₇	C₂²×C₄	semidirect
189. C₄⋊C₄×C₁₀₇	C₂²×C₄	semidirect
196. C₂²⋊C₄×C₁₀₇	C₂²×C₄	semidirect
199. C₄²×C₁₀₇	C₂×D₄	semidirect
315. C₂×#2324	C₁₀₇	direct (N × H)
318. C₂×C₁₀₇	#2324	direct (N × H)
327. C₂²×C₄×D₄	C₂×C₁₀₇	semidirect
328. C₂²×#117	C₂×C₁₀₇	semidirect
329. #2324	C₂×C₁₀₇	direct (N × H)
330. C₂×#390	C₂×C₁₀₇	semidirect
331. C₂×#390	C₂×C₁₀₇	semidirect
332. C₂×#389	C₂×C₁₀₇	semidirect
333. C₂×#388	C₂×C₁₀₇	semidirect
334. C₂×#386	C₂×C₁₀₇	semidirect
335. C₂×#385	C₂×C₁₀₇	semidirect
336. C₂×#380	C₂×C₁₀₇	semidirect
337. C₂×C₄×C₄⋊C₄	C₂×C₁₀₇	semidirect
338. C₁₀₇	C₂×#2324	direct (N × H)
343. C₂×#121	C₄×C₁₀₇	semidirect
346. C₂×C₄×D₄	C₂²×C₁₀₇	semidirect
348. C₂×#117	C₂²×C₁₀₇	semidirect
365. #390	C₂²×C₁₀₇	semidirect
366. #390	C₂²×C₁₀₇	semidirect
367. #389	C₂²×C₁₀₇	semidirect
368. #388	C₂²×C₁₀₇	semidirect
369. #386	C₂²×C₁₀₇	semidirect
370. #385	C₂²×C₁₀₇	semidirect
371. #380	C₂²×C₁₀₇	semidirect
372. C₄×C₄⋊C₄	C₂²×C₁₀₇	semidirect
383. C₂²×D₄	C₂×C₄×C₁₀₇	semidirect
391. C₂³×C₄	C₂×C₄×C₁₀₇	semidirect
403. #121	C₂×C₄×C₁₀₇	semidirect
411. C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	semidirect
424. C₂×C₂²⋊C₄	C₂×C₄×C₁₀₇	semidirect
434. C₂×C₄²	D₄×C₁₀₇	semidirect
465. C₂×D₄	C₂²×C₄×C₁₀₇	semidirect
496. C₂²×C₄	C₂²×C₄×C₁₀₇	semidirect
515. C₄⋊C₄	C₂²×C₄×C₁₀₇	semidirect
522. C₂²⋊C₄	C₂²×C₄×C₁₀₇	semidirect
525. C₄²	C₂×D₄×C₁₀₇	semidirect
643. C₂	C₁₀₇×#2324	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#121×C₁₀₇	2
C₂²×C₄×D₄×C₁₀₇	2
C₂²×#117×C₁₀₇	2
C₁₀₇×#2324	2
C₂×#390×C₁₀₇	2
C₂×#389×C₁₀₇	2
C₂×#388×C₁₀₇	2
C₂×#386×C₁₀₇	2
C₂×#385×C₁₀₇	2
C₂×#380×C₁₀₇	2
C₂×C₄×C₄⋊C₄×C₁₀₇	2
C₂×#2324	107

Subgroups — C2×C107×#2324 #41060028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₇×#2324 #41060028