Subgroups — C₁₀₇×#18525 #41044489

Order 27392.

1048 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₇×#3152	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₇×#3109	C₂	1	1	yes	maximal, characteristic
5	C₁₀₇×#1632	C₂	1	4	yes	maximal, complemented
6	C₁₀₇×#1622	C₂	1	4	yes	maximal, complemented
7	C₁₀₇×#1558	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₇×#1491	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₇×#1490	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#137×C₁₀₇	—	2	2	no	—
11	#554×C₁₀₇	—	2	2	no	—
12	#554×C₁₀₇	—	2	2	no	—
13	#554×C₁₀₇	—	2	2	no	—
14	#554×C₁₀₇	C₂²	1	4	yes	—
15	#532×C₁₀₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
17	C₂×#125×C₁₀₇	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₁₀₇	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₁₀₇	—	2	2	no	—
20	C₂×C₄×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₀₇	—	2	1	no	—
22	C₂×C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₀₇	—	2	1	no	—
24	#497×C₁₀₇	—	2	2	no	—
25	#494×C₁₀₇	C₂²	1	2	yes	complemented
26	#492×C₁₀₇	C₂²	1	2	yes	complemented
27	#481×C₁₀₇	—	2	1	no	—
28	#480×C₁₀₇	—	2	1	no	—
29	#477×C₁₀₇	C₂²	1	2	yes	complemented
30	#476×C₁₀₇	C₂²	1	2	yes	—
31	#460×C₁₀₇	C₂²	1	2	yes	complemented
32	#459×C₁₀₇	C₂²	1	2	yes	—
33	#448×C₁₀₇	—	2	1	no	—
34	#447×C₁₀₇	—	2	1	no	—
35	#442×C₁₀₇	—	2	2	no	—
36	#440×C₁₀₇	—	2	2	no	—
37	#432×C₁₀₇	C₂²	1	1	yes	characteristic
38	#432×C₁₀₇	C₂²	1	1	yes	characteristic
39	C₄×M₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
40	#333×C₁₀₇	C₂²	1	4	yes	complemented
41	Q₈⋊C₈×C₁₀₇	C₂²	1	4	yes	complemented
42	D₄⋊C₈×C₁₀₇	C₂²	1	4	yes	—
43	C₂×#41×C₁₀₇	—	2	1	no	—
44	C₂²×Q₈×C₁₀₇	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₁₀₇	D₄	1	2	yes	—
46	C₂²×D₄×C₁₀₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₀₇	—	2	2	no	—
48	C₂³×C₄×C₁₀₇	—	2	1	no	—
49	#137×C₁₀₇	—	4	8	no	—
50	C₂×Q₁₆×C₁₀₇	—	2	4	no	—
51	C₂×SD₁₆×C₁₀₇	—	2	2	no	—
52	C₂×SD₁₆×C₁₀₇	—	2	4	no	—
53	C₂×D₈×C₁₀₇	—	2	2	no	—
54	C₂×M₁₆×C₁₀₇	—	2	1	no	—
55	C₄⋊Q₈×C₁₀₇	—	2	1	no	—
56	C₄⋊Q₈×C₁₀₇	—	2	1	no	—
57	C₄⋊Q₈×C₁₀₇	D₄	1	2	yes	—
58	C₄⋊Q₈×C₁₀₇	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₁₀₇	C₂³	1	2	yes	—
60	#127×C₁₀₇	C₂³	1	1	yes	characteristic
61	#125×C₁₀₇	—	2	4	no	—
62	#125×C₁₀₇	—	2	4	no	—
63	#124×C₁₀₇	—	2	1	no	—
64	C₂²⋊Q₈×C₁₀₇	—	2	4	no	—
65	C₂²⋊Q₈×C₁₀₇	—	2	8	no	—
66	C₂²⋊Q₈×C₁₀₇	—	2	4	no	—
67	C₂²⋊Q₈×C₁₀₇	—	2	8	no	—
68	#121×C₁₀₇	—	2	1	no	—
69	#121×C₁₀₇	—	2	1	no	—
70	C₄×Q₈×C₁₀₇	—	2	1	no	—
71	C₄×Q₈×C₁₀₇	—	2	1	no	—
72	C₄×Q₈×C₁₀₇	D₄	1	2	yes	—
73	C₄×Q₈×C₁₀₇	C₂³	1	2	yes	—
74	C₄×D₄×C₁₀₇	—	2	4	no	—
75	C₄×D₄×C₁₀₇	—	2	4	no	—
76	C₄×D₄×C₁₀₇	—	2	1	no	—
77	C₄×D₄×C₁₀₇	—	2	1	no	—
78	C₄×D₄×C₁₀₇	—	2	1	no	—
79	C₄×D₄×C₁₀₇	—	2	1	no	—
80	C₄×D₄×C₁₀₇	D₄	1	2	yes	—
81	C₄×D₄×C₁₀₇	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₀₇	—	2	4	no	—
84	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₀₇	—	2	4	no	—
89	C₂×C₄⋊C₄×C₁₀₇	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₀₇	D₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
93	C₂×C₄²×C₁₀₇	—	2	1	no	—
94	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
95	#107×C₁₀₇	—	2	2	no	—
96	#106×C₁₀₇	—	2	2	no	—
97	C₄⋊C₈×C₁₀₇	C₂³	1	2	yes	—
98	C₄⋊C₈×C₁₀₇	C₂³	1	2	yes	—
99	#103×C₁₀₇	—	2	2	no	—
100	#102×C₁₀₇	—	2	2	no	—
101	#102×C₁₀₇	—	2	2	no	—
102	#102×C₁₀₇	—	2	2	no	—
103	C₂²⋊C₈×C₁₀₇	—	2	1	no	—
104	C₂²⋊C₈×C₁₀₇	—	2	1	no	—
105	#97×C₁₀₇	—	2	1	no	—
106	#97×C₁₀₇	—	2	1	no	—
107	#97×C₁₀₇	—	2	1	no	—
108	C₄×C₈×C₁₀₇	C₂³	1	2	yes	—
109	C₂⁴×C₁₀₇	—	2	1	no	—
110	#41×C₁₀₇	—	4	4	no	—
111	C₂×Q₈×C₁₀₇	—	2	1	no	—
112	C₂×Q₈×C₁₀₇	—	2	2	no	—
113	C₂×Q₈×C₁₀₇	—	2	1	no	—
114	C₂×Q₈×C₁₀₇	—	4	2	no	—
115	C₂×Q₈×C₁₀₇	—	4	4	no	—
116	C₂×Q₈×C₁₀₇	C₂×D₄	1	2	yes	—
117	C₂×Q₈×C₁₀₇	C₂×D₄	1	4	yes	—
118	C₂×D₄×C₁₀₇	—	2	4	no	—
119	C₂×D₄×C₁₀₇	—	2	1	no	—
120	C₂×D₄×C₁₀₇	—	2	1	no	—
121	C₂×D₄×C₁₀₇	—	2	1	no	—
122	C₂×D₄×C₁₀₇	—	2	1	no	—
123	C₂×D₄×C₁₀₇	—	4	1	no	—
124	C₂×D₄×C₁₀₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₀₇	—	2	1	no	—
126	C₂²×C₄×C₁₀₇	—	2	1	no	—
127	C₂²×C₄×C₁₀₇	—	2	1	no	—
128	C₂²×C₄×C₁₀₇	—	2	2	no	—
129	C₂²×C₄×C₁₀₇	—	2	8	no	—
130	C₂²×C₄×C₁₀₇	—	2	2	no	—
131	C₂²×C₄×C₁₀₇	—	2	2	no	—
132	C₂²×C₄×C₁₀₇	—	4	4	no	—
133	C₂²×C₄×C₁₀₇	—	4	1	no	—
134	C₂²×C₄×C₁₀₇	—	8	4	no	—
135	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
138	Q₁₆×C₁₀₇	—	4	8	no	—
139	SD₁₆×C₁₀₇	—	4	8	no	—
140	SD₁₆×C₁₀₇	—	4	4	no	—
141	D₈×C₁₀₇	—	4	4	no	—
142	M₁₆×C₁₀₇	—	2	4	no	—
143	C₂×C₈×C₁₀₇	—	2	2	no	—
144	C₂×C₈×C₁₀₇	—	2	2	no	—
145	C₂×C₈×C₁₀₇	—	2	2	no	—
146	C₄⋊C₄×C₁₀₇	—	2	8	no	—
147	C₄⋊C₄×C₁₀₇	—	2	8	no	—
148	C₄⋊C₄×C₁₀₇	—	2	1	no	—
149	C₄⋊C₄×C₁₀₇	—	2	2	no	—
150	C₄⋊C₄×C₁₀₇	—	2	2	no	—
151	C₄⋊C₄×C₁₀₇	—	2	2	no	—
152	C₄⋊C₄×C₁₀₇	—	2	1	no	—
153	C₄⋊C₄×C₁₀₇	—	2	2	no	—
154	C₄⋊C₄×C₁₀₇	—	2	2	no	—
155	C₄⋊C₄×C₁₀₇	—	2	2	no	—
156	C₄⋊C₄×C₁₀₇	—	2	1	no	—
157	C₄⋊C₄×C₁₀₇	—	2	1	no	—
158	C₄⋊C₄×C₁₀₇	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₁₀₇	C₂×D₄	1	2	yes	—
160	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
161	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
162	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
163	C₂²⋊C₄×C₁₀₇	—	4	1	no	—
164	C₂²⋊C₄×C₁₀₇	—	4	1	no	—
165	C₄²×C₁₀₇	—	2	2	no	—
166	C₄²×C₁₀₇	—	2	2	no	—
167	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₀₇	C₂⁴	1	1	yes	characteristic
171	C₂³×C₁₀₇	—	2	4	no	—
172	C₂³×C₁₀₇	—	2	2	no	—
173	C₂³×C₁₀₇	—	4	2	no	—
174	C₂³×C₁₀₇	—	4	2	no	—
175	C₂³×C₁₀₇	—	4	1	no	—
176	C₂³×C₁₀₇	#120	1	1	yes	characteristic
177	Q₈×C₁₀₇	—	2	2	no	—
178	Q₈×C₁₀₇	—	2	2	no	—
179	Q₈×C₁₀₇	—	4	4	no	—
180	Q₈×C₁₀₇	—	4	2	no	—
181	Q₈×C₁₀₇	—	4	2	no	—
182	Q₈×C₁₀₇	—	8	2	no	—
183	D₄×C₁₀₇	—	2	4	no	—
184	D₄×C₁₀₇	—	2	2	no	—
185	D₄×C₁₀₇	—	4	2	no	—
186	D₄×C₁₀₇	—	4	2	no	—
187	D₄×C₁₀₇	—	4	2	no	—
188	D₄×C₁₀₇	—	8	2	no	—
189	D₄×C₁₀₇	#137	1	4	yes	complemented
190	C₂×C₄×C₁₀₇	—	2	2	no	—
191	C₂×C₄×C₁₀₇	—	2	2	no	—
192	C₂×C₄×C₁₀₇	—	2	2	no	—
193	C₂×C₄×C₁₀₇	—	2	2	no	—
194	C₂×C₄×C₁₀₇	—	2	2	no	—
195	C₂×C₄×C₁₀₇	—	2	2	no	—
196	C₂×C₄×C₁₀₇	—	2	4	no	—
197	C₂×C₄×C₁₀₇	—	4	4	no	—
198	C₂×C₄×C₁₀₇	—	4	2	no	—
199	C₂×C₄×C₁₀₇	—	4	2	no	—
200	C₂×C₄×C₁₀₇	—	4	2	no	—
201	C₂×C₄×C₁₀₇	—	4	4	no	—
202	C₂×C₄×C₁₀₇	—	4	4	no	—
203	C₂×C₄×C₁₀₇	—	4	1	no	—
204	C₂×C₄×C₁₀₇	—	8	2	no	—
205	C₂×C₄×C₁₀₇	—	8	8	no	—
206	C₂×C₄×C₁₀₇	#120	1	1	yes	characteristic
207	C₂×C₄×C₁₀₇	#120	1	1	yes	characteristic
208	C₂×C₄×C₁₀₇	#120	1	1	yes	characteristic
209	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
212	C₈×C₁₀₇	—	2	4	no	—
213	C₈×C₁₀₇	—	4	2	no	—
214	C₈×C₁₀₇	—	4	2	no	—
215	C₂²×C₁₀₇	—	2	1	no	—
216	C₂²×C₁₀₇	—	2	1	no	—
217	C₂²×C₁₀₇	—	2	4	no	—
218	C₂²×C₁₀₇	—	4	8	no	—
219	C₂²×C₁₀₇	—	4	2	no	—
220	C₂²×C₁₀₇	—	4	2	no	—
221	C₂²×C₁₀₇	—	8	1	no	—
222	C₂²×C₁₀₇	—	8	1	no	—
223	C₂²×C₁₀₇	—	8	1	no	—
224	C₂²×C₁₀₇	#453	1	2	yes	—
225	C₂²×C₁₀₇	C₂×#120	1	1	yes	characteristic
226	C₄×C₁₀₇	—	2	1	no	—
227	C₄×C₁₀₇	—	2	1	no	—
228	C₄×C₁₀₇	—	2	1	no	—
229	C₄×C₁₀₇	—	2	1	no	—
230	C₄×C₁₀₇	—	4	2	no	—
231	C₄×C₁₀₇	—	4	2	no	—
232	C₄×C₁₀₇	—	4	2	no	—
233	C₄×C₁₀₇	—	4	4	no	—
234	C₄×C₁₀₇	—	8	1	no	—
235	C₄×C₁₀₇	C₂×#137	1	2	yes	—
236	C₄×C₁₀₇	#575	1	2	yes	—
237	#18525	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂×C₁₀₇	—	2	2	no	—
239	C₂×C₁₀₇	—	4	4	no	—
240	C₂×C₁₀₇	—	16	1	no	—
241	C₂×C₁₀₇	#3004	1	1	yes	characteristic
242	C₂×C₁₀₇	#3005	1	1	yes	characteristic
243	C₂×C₁₀₇	C₂×#453	1	1	yes	characteristic
244	C₂×#554	C₂×C₁₀₇	1	1	yes	characteristic, complemented
245	#3152	C₂×C₁₀₇	1	1	yes	characteristic, complemented
246	#3112	C₂×C₁₀₇	1	1	yes	characteristic, complemented
247	#3109	C₂×C₁₀₇	1	1	yes	characteristic
248	#1632	C₂×C₁₀₇	1	4	yes	complemented
249	#1622	C₂×C₁₀₇	1	4	yes	complemented
250	#1558	C₂×C₁₀₇	1	1	yes	characteristic, complemented
251	#1491	C₂×C₁₀₇	1	1	yes	characteristic, complemented
252	#1490	C₂×C₁₀₇	1	1	yes	characteristic, complemented
253	C₁₀₇	#18525	1	1	yes	characteristic, direct product factor, Sylow
254	C₂×#137	—	2	2	no	—
255	#554	—	2	2	no	—
256	#554	—	2	2	no	—
257	#554	—	2	2	no	—
258	#554	C₂²×C₁₀₇	1	4	yes	—
259	#532	C₂²×C₁₀₇	1	1	yes	characteristic
260	C₂×C₄⋊Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
261	C₂×#125	—	2	1	no	—
262	C₂×C₂²⋊Q₈	—	2	1	no	—
263	C₂×C₂²⋊Q₈	—	2	2	no	—
264	C₂×C₄×Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
265	C₂×C₄×D₄	—	2	1	no	—
266	C₂×C₄×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	—	2	1	no	—
268	#497	—	2	2	no	—
269	#494	C₂²×C₁₀₇	1	2	yes	complemented
270	#492	C₂²×C₁₀₇	1	2	yes	complemented
271	#481	—	2	1	no	—
272	#480	—	2	1	no	—
273	#477	C₂²×C₁₀₇	1	2	yes	complemented
274	#476	C₂²×C₁₀₇	1	2	yes	—
275	#460	C₂²×C₁₀₇	1	2	yes	complemented
276	#459	C₂²×C₁₀₇	1	2	yes	—
277	#448	—	2	1	no	—
278	#447	—	2	1	no	—
279	#442	—	2	2	no	—
280	#440	—	2	2	no	—
281	#432	C₂²×C₁₀₇	1	1	yes	characteristic
282	#432	C₂²×C₁₀₇	1	1	yes	characteristic
283	C₄×M₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
284	#333	C₂²×C₁₀₇	1	4	yes	complemented
285	Q₈⋊C₈	C₂²×C₁₀₇	1	4	yes	complemented
286	D₄⋊C₈	C₂²×C₁₀₇	1	4	yes	—
287	C₂×#41	—	2	1	no	—
288	C₂²×Q₈	D₄×C₁₀₇	1	1	yes	characteristic
289	C₂²×Q₈	D₄×C₁₀₇	1	2	yes	—
290	C₂²×D₄	D₄×C₁₀₇	1	1	yes	characteristic
291	C₂³×C₄	—	2	2	no	—
292	C₂³×C₄	—	2	1	no	—
293	#137	—	4	8	no	—
294	C₂×Q₁₆	—	2	4	no	—
295	C₂×SD₁₆	—	2	4	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×D₈	—	2	2	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₄⋊Q₈	—	2	1	no	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	D₄×C₁₀₇	1	2	yes	—
302	C₄⋊Q₈	C₂³×C₁₀₇	1	1	yes	characteristic
303	C₄⋊Q₈	C₂³×C₁₀₇	1	2	yes	—
304	#127	C₂³×C₁₀₇	1	1	yes	characteristic
305	#125	—	2	4	no	—
306	#125	—	2	4	no	—
307	#124	—	2	1	no	—
308	C₂²⋊Q₈	—	2	4	no	—
309	C₂²⋊Q₈	—	2	8	no	—
310	C₂²⋊Q₈	—	2	4	no	—
311	C₂²⋊Q₈	—	2	8	no	—
312	#121	—	2	1	no	—
313	#121	—	2	1	no	—
314	C₄×Q₈	—	2	1	no	—
315	C₄×Q₈	—	2	1	no	—
316	C₄×Q₈	D₄×C₁₀₇	1	2	yes	—
317	C₄×Q₈	C₂³×C₁₀₇	1	2	yes	—
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	—	2	4	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	—	2	1	no	—
324	C₄×D₄	D₄×C₁₀₇	1	2	yes	—
325	C₄×D₄	C₂³×C₁₀₇	1	2	yes	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	4	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	4	no	—
333	C₂×C₄⋊C₄	D₄×C₁₀₇	1	1	yes	characteristic
334	C₂×C₄⋊C₄	D₄×C₁₀₇	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
339	#107	—	2	2	no	—
340	#106	—	2	2	no	—
341	C₄⋊C₈	C₂³×C₁₀₇	1	2	yes	—
342	C₄⋊C₈	C₂³×C₁₀₇	1	2	yes	—
343	#103	—	2	2	no	—
344	#102	—	2	2	no	—
345	#102	—	2	2	no	—
346	#102	—	2	2	no	—
347	C₂²⋊C₈	—	2	1	no	—
348	C₂²⋊C₈	—	2	1	no	—
349	#97	—	2	1	no	—
350	#97	—	2	1	no	—
351	#97	—	2	1	no	—
352	C₄×C₈	C₂³×C₁₀₇	1	2	yes	—
353	C₂⁴	—	2	1	no	—
354	#41	—	4	4	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	—	4	4	no	—
360	C₂×Q₈	C₂×D₄×C₁₀₇	1	2	yes	—
361	C₂×Q₈	C₂×D₄×C₁₀₇	1	4	yes	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂×D₄	C₂×D₄×C₁₀₇	1	2	yes	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	8	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	—	8	4	no	—
379	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
382	Q₁₆	—	4	8	no	—
383	SD₁₆	—	4	8	no	—
384	SD₁₆	—	4	4	no	—
385	D₈	—	4	4	no	—
386	M₁₆	—	2	4	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	C₂×D₄×C₁₀₇	1	2	yes	—
403	C₄⋊C₄	C₂×D₄×C₁₀₇	1	2	yes	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	4	1	no	—
408	C₂²⋊C₄	—	4	1	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
412	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
413	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
414	C₄²	C₂⁴×C₁₀₇	1	1	yes	characteristic
415	C₂³	—	2	4	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	1	no	—
420	C₂³	#120×C₁₀₇	1	1	yes	characteristic
421	Q₈	—	2	2	no	—
422	Q₈	—	2	2	no	—
423	Q₈	—	4	4	no	—
424	Q₈	—	4	2	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	8	2	no	—
427	D₄	—	2	4	no	—
428	D₄	—	2	2	no	—
429	D₄	—	4	2	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	8	2	no	—
433	D₄	#137×C₁₀₇	1	4	yes	complemented
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	8	2	no	—
449	C₂×C₄	—	8	8	no	—
450	C₂×C₄	#120×C₁₀₇	1	1	yes	characteristic
451	C₂×C₄	#120×C₁₀₇	1	1	yes	characteristic
452	C₂×C₄	#120×C₁₀₇	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
454	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
456	C₈	—	2	4	no	—
457	C₈	—	4	2	no	—
458	C₈	—	4	2	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	4	8	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	8	1	no	—
466	C₂²	—	8	1	no	—
467	C₂²	—	8	1	no	—
468	C₂²	#453×C₁₀₇	1	2	yes	—
469	C₂²	C₂×#120×C₁₀₇	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	4	no	—
478	C₄	—	8	1	no	—
479	C₄	C₂×#137×C₁₀₇	1	2	yes	—
480	C₄	#575×C₁₀₇	1	2	yes	—
481	C₂	—	2	2	no	—
482	C₂	—	4	4	no	—
483	C₂	—	16	1	no	—
484	C₂	C₁₀₇×#3004	1	1	yes	characteristic
485	C₂	C₁₀₇×#3005	1	1	yes	characteristic
486	C₂	C₂×#453×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₇
prime radical	C₁₀₇×#3109	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ C₂×C₄²×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#554×C₁₀₇	C₂	semidirect
2. C₁₀₇×#3152	C₂	semidirect
3. C₁₀₇×#3112	C₂	semidirect
5. C₁₀₇×#1632	C₂	semidirect
6. C₁₀₇×#1622	C₂	semidirect
7. C₁₀₇×#1558	C₂	semidirect
8. C₁₀₇×#1491	C₂	semidirect
9. C₁₀₇×#1490	C₂	semidirect
25. #494×C₁₀₇	C₂²	semidirect
26. #492×C₁₀₇	C₂²	semidirect
29. #477×C₁₀₇	C₂²	semidirect
31. #460×C₁₀₇	C₂²	semidirect
40. #333×C₁₀₇	C₂²	semidirect
41. Q₈⋊C₈×C₁₀₇	C₂²	semidirect
189. D₄×C₁₀₇	#137	semidirect
237. #18525	C₁₀₇	direct (N × H)
244. C₂×#554	C₂×C₁₀₇	semidirect
245. #3152	C₂×C₁₀₇	semidirect
246. #3112	C₂×C₁₀₇	semidirect
248. #1632	C₂×C₁₀₇	semidirect
249. #1622	C₂×C₁₀₇	semidirect
250. #1558	C₂×C₁₀₇	semidirect
251. #1491	C₂×C₁₀₇	semidirect
252. #1490	C₂×C₁₀₇	semidirect
253. C₁₀₇	#18525	direct (N × H)
269. #494	C₂²×C₁₀₇	semidirect
270. #492	C₂²×C₁₀₇	semidirect
273. #477	C₂²×C₁₀₇	semidirect
275. #460	C₂²×C₁₀₇	semidirect
284. #333	C₂²×C₁₀₇	semidirect
285. Q₈⋊C₈	C₂²×C₁₀₇	semidirect
433. D₄	#137×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₁₀₇	2
C₁₀₇×#3152	2
C₁₀₇×#3112	2
C₁₀₇×#3109	2
C₁₀₇×#1632	2
C₁₀₇×#1622	2
C₁₀₇×#1558	2
C₁₀₇×#1491	2
C₁₀₇×#1490	2
#18525	107

Subgroups — C107×#18525 #41044489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#18525 #41044489