Subgroups — C₁₀₇×#23081 #41049045

Order 27392.

662 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₇×#3076	C₂	1	1	yes	maximal, characteristic
2	C₁₀₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₇×#2925	C₂	1	1	yes	maximal, characteristic
4	C₁₀₇×#1994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₇×#1950	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₇×#1938	C₂	1	2	yes	maximal
7	C₁₀₇×#1929	C₂	1	2	yes	maximal
8	C₁₀₇×#1922	C₂	1	2	yes	maximal, complemented
9	C₁₀₇×#1773	C₂	1	2	yes	maximal, complemented
10	C₁₀₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#104×C₁₀₇	C₂	1	1	yes	maximal, characteristic
12	#533×C₁₀₇	C₂²	1	1	yes	characteristic
13	C₄×#41×C₁₀₇	C₂²	1	1	yes	characteristic
14	#479×C₁₀₇	C₄	1	2	yes	complemented
15	#478×C₁₀₇	C₄	1	2	yes	complemented
16	#477×C₁₀₇	C₄	1	1	yes	characteristic, complemented
17	#476×C₁₀₇	C₄	1	1	yes	characteristic, complemented
18	#475×C₁₀₇	C₄	1	1	yes	characteristic, complemented
19	#474×C₁₀₇	C₄	1	1	yes	characteristic, complemented
20	#446×C₁₀₇	—	2	2	no	—
21	#446×C₁₀₇	—	2	1	no	—
22	C₈×Q₈×C₁₀₇	—	2	1	no	—
23	#433×C₁₀₇	—	2	2	no	—
24	#432×C₁₀₇	—	2	1	no	—
25	#431×C₁₀₇	—	2	1	no	—
26	C₂×#108×C₁₀₇	C₂²	1	2	yes	—
27	#427×C₁₀₇	C₂²	1	2	yes	—
28	#424×C₁₀₇	C₂²	1	2	yes	—
29	#423×C₁₀₇	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	1	yes	characteristic
32	C₂×#104×C₁₀₇	C₂²	1	1	yes	characteristic
33	C₂×#104×C₁₀₇	C₂²	1	1	yes	characteristic
34	#416×C₁₀₇	C₂²	1	2	yes	—
35	#408×C₁₀₇	C₂²	1	2	yes	—
36	#405×C₁₀₇	C₂²	1	2	yes	—
37	#405×C₁₀₇	C₂²	1	2	yes	—
38	C₄×M₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
39	C₂×#97×C₁₀₇	C₂²	1	2	yes	—
40	C₄³×C₁₀₇	C₂²	1	1	yes	characteristic
41	#341×C₁₀₇	C₂²	1	2	yes	—
42	#339×C₁₀₇	C₂²	1	1	yes	characteristic
43	#339×C₁₀₇	C₂²	1	2	yes	—
44	#339×C₁₀₇	C₂²	1	2	yes	—
45	#339×C₁₀₇	C₂²	1	1	yes	characteristic
46	#336×C₁₀₇	C₂²	1	2	yes	—
47	C₂×#41×C₁₀₇	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₁₀₇	C₂³	1	2	yes	—
49	C₂×M₁₆×C₁₀₇	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₁₀₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
54	C₄⋊Q₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
55	#125×C₁₀₇	C₂×C₄	1	2	yes	—
56	C₂²⋊Q₈×C₁₀₇	—	2	1	no	—
57	C₂²⋊Q₈×C₁₀₇	—	2	1	no	—
58	C₄×Q₈×C₁₀₇	—	2	1	no	—
59	C₄×Q₈×C₁₀₇	—	2	1	no	—
60	C₄×Q₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
62	C₄×D₄×C₁₀₇	—	2	1	no	—
63	C₄×D₄×C₁₀₇	—	2	1	no	—
64	C₄×D₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
65	C₄×D₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
66	#117×C₁₀₇	—	2	1	no	—
67	#117×C₁₀₇	C₂³	1	1	yes	characteristic
68	#117×C₁₀₇	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₀₇	—	2	1	no	—
70	C₂×C₄²×C₁₀₇	—	2	1	no	—
71	C₂×C₄²×C₁₀₇	—	2	1	no	—
72	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
75	#108×C₁₀₇	—	2	4	no	—
76	#107×C₁₀₇	C₂×C₄	1	2	yes	—
77	#107×C₁₀₇	C₂×C₄	1	2	yes	—
78	#106×C₁₀₇	C₂×C₄	1	2	yes	—
79	#106×C₁₀₇	C₂×C₄	1	2	yes	—
80	C₄⋊C₈×C₁₀₇	—	2	2	no	—
81	C₄⋊C₈×C₁₀₇	—	2	2	no	—
82	C₄⋊C₈×C₁₀₇	—	2	1	no	—
83	C₄⋊C₈×C₁₀₇	—	2	1	no	—
84	C₄⋊C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
85	C₄⋊C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
86	C₄⋊C₈×C₁₀₇	C₂×C₄	1	2	yes	—
87	C₄⋊C₈×C₁₀₇	D₄	1	1	yes	characteristic
88	C₄⋊C₈×C₁₀₇	D₄	1	1	yes	characteristic
89	C₄⋊C₈×C₁₀₇	D₄	1	2	yes	—
90	#104×C₁₀₇	—	2	2	no	—
91	#104×C₁₀₇	—	2	2	no	—
92	#103×C₁₀₇	C₂×C₄	1	2	yes	—
93	#103×C₁₀₇	C₂×C₄	1	2	yes	—
94	#102×C₁₀₇	C₂×C₄	1	2	yes	—
95	#102×C₁₀₇	C₂×C₄	1	2	yes	—
96	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
97	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
98	#97×C₁₀₇	—	2	2	no	—
99	#97×C₁₀₇	—	2	2	no	—
100	#97×C₁₀₇	—	2	1	no	—
101	#97×C₁₀₇	—	2	4	no	—
102	C₄×C₈×C₁₀₇	—	2	2	no	—
103	C₄×C₈×C₁₀₇	—	2	2	no	—
104	C₄×C₈×C₁₀₇	—	2	1	no	—
105	#41×C₁₀₇	—	2	1	no	—
106	#41×C₁₀₇	—	2	1	no	—
107	#41×C₁₀₇	—	2	1	no	—
108	#41×C₁₀₇	—	2	1	no	—
109	C₂×Q₈×C₁₀₇	—	2	1	no	—
110	C₂×Q₈×C₁₀₇	—	2	1	no	—
111	C₂×Q₈×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₄×C₁₀₇	—	2	1	no	—
113	C₂×D₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₀₇	—	2	1	no	—
115	C₂²×C₄×C₁₀₇	—	2	1	no	—
116	C₂²×C₄×C₁₀₇	—	2	1	no	—
117	C₂²×C₄×C₁₀₇	—	2	1	no	—
118	C₂²×C₄×C₁₀₇	—	2	1	no	—
119	C₂²×C₄×C₁₀₇	#41	1	1	yes	characteristic
120	C₂²×C₄×C₁₀₇	#41	1	1	yes	characteristic
121	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
122	M₁₆×C₁₀₇	—	2	1	no	—
123	M₁₆×C₁₀₇	—	2	1	no	—
124	M₁₆×C₁₀₇	—	2	2	no	—
125	M₁₆×C₁₀₇	—	2	1	no	—
126	M₁₆×C₁₀₇	—	2	2	no	—
127	M₁₆×C₁₀₇	#41	1	2	yes	—
128	C₂×C₈×C₁₀₇	—	2	1	no	—
129	C₂×C₈×C₁₀₇	—	2	2	no	—
130	C₂×C₈×C₁₀₇	—	2	2	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	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₁₀₇	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₁₀₇	—	2	1	no	—
140	C₄⋊C₄×C₁₀₇	—	2	1	no	—
141	C₄⋊C₄×C₁₀₇	—	2	2	no	—
142	C₄⋊C₄×C₁₀₇	—	2	2	no	—
143	C₄⋊C₄×C₁₀₇	—	2	1	no	—
144	C₄⋊C₄×C₁₀₇	—	2	1	no	—
145	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
146	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
147	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²⋊C₄×C₁₀₇	—	2	1	no	—
150	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
151	C₂²⋊C₄×C₁₀₇	—	2	1	no	—
152	C₂²⋊C₄×C₁₀₇	—	2	1	no	—
153	C₄²×C₁₀₇	—	2	1	no	—
154	C₄²×C₁₀₇	—	2	1	no	—
155	C₄²×C₁₀₇	—	2	1	no	—
156	C₄²×C₁₀₇	—	2	2	no	—
157	C₄²×C₁₀₇	—	2	1	no	—
158	C₄²×C₁₀₇	—	2	1	no	—
159	C₄²×C₁₀₇	—	2	1	no	—
160	C₄²×C₁₀₇	—	4	2	no	—
161	C₄²×C₁₀₇	—	4	2	no	—
162	C₄²×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₀₇	#41	1	2	yes	—
167	C₂³×C₁₀₇	—	2	1	no	—
168	C₂³×C₁₀₇	C₂×#41	1	1	yes	characteristic
169	Q₈×C₁₀₇	—	2	1	no	—
170	Q₈×C₁₀₇	—	2	1	no	—
171	Q₈×C₁₀₇	—	4	2	no	—
172	Q₈×C₁₀₇	—	8	1	no	—
173	D₄×C₁₀₇	—	2	1	no	—
174	D₄×C₁₀₇	—	2	1	no	—
175	D₄×C₁₀₇	—	4	1	no	—
176	D₄×C₁₀₇	—	4	1	no	—
177	C₂×C₄×C₁₀₇	—	2	2	no	—
178	C₂×C₄×C₁₀₇	—	2	2	no	—
179	C₂×C₄×C₁₀₇	—	2	1	no	—
180	C₂×C₄×C₁₀₇	—	2	1	no	—
181	C₂×C₄×C₁₀₇	—	2	1	no	—
182	C₂×C₄×C₁₀₇	—	2	2	no	—
183	C₂×C₄×C₁₀₇	—	2	2	no	—
184	C₂×C₄×C₁₀₇	—	2	2	no	—
185	C₂×C₄×C₁₀₇	—	4	1	no	—
186	C₂×C₄×C₁₀₇	—	4	1	no	—
187	C₂×C₄×C₁₀₇	—	4	1	no	—
188	C₂×C₄×C₁₀₇	—	4	1	no	—
189	C₂×C₄×C₁₀₇	—	4	1	no	—
190	C₂×C₄×C₁₀₇	—	4	1	no	—
191	C₂×C₄×C₁₀₇	—	4	1	no	—
192	C₂×C₄×C₁₀₇	—	4	2	no	—
193	C₂×C₄×C₁₀₇	—	8	1	no	—
194	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₀₇	2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₄×C₁₀₇	2₋¹⁺⁴	1	1	yes	characteristic
204	C₈×C₁₀₇	—	2	2	no	—
205	C₈×C₁₀₇	—	2	2	no	—
206	C₈×C₁₀₇	—	2	2	no	—
207	C₈×C₁₀₇	—	2	2	no	—
208	C₈×C₁₀₇	—	2	2	no	—
209	C₈×C₁₀₇	—	4	1	no	—
210	C₈×C₁₀₇	—	4	2	no	—
211	C₂²×C₁₀₇	—	2	1	no	—
212	C₂²×C₁₀₇	—	2	1	no	—
213	C₂²×C₁₀₇	—	4	1	no	—
214	C₂²×C₁₀₇	—	4	1	no	—
215	C₂²×C₁₀₇	—	4	1	no	—
216	C₂²×C₁₀₇	C₂×C₄×D₄	1	1	yes	characteristic
217	C₂²×C₁₀₇	#552	1	1	yes	characteristic
218	C₂²×C₁₀₇	#556	1	1	yes	characteristic
219	C₄×C₁₀₇	—	2	1	no	—
220	C₄×C₁₀₇	—	2	1	no	—
221	C₄×C₁₀₇	—	2	1	no	—
222	C₄×C₁₀₇	—	4	2	no	—
223	C₄×C₁₀₇	—	4	2	no	—
224	C₄×C₁₀₇	—	4	1	no	—
225	C₄×C₁₀₇	—	4	1	no	—
226	C₄×C₁₀₇	—	4	2	no	—
227	C₄×C₁₀₇	—	4	1	no	—
228	C₄×C₁₀₇	—	4	2	no	—
229	C₄×C₁₀₇	#444	1	2	yes	—
230	C₄×C₁₀₇	C₄×#41	1	1	yes	characteristic
231	C₄×C₁₀₇	#519	1	1	yes	characteristic
232	C₄×C₁₀₇	#547	1	1	yes	characteristic
233	C₄×C₁₀₇	#548	1	1	yes	characteristic
234	#23081	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂×C₁₀₇	—	2	1	no	—
236	C₂×C₁₀₇	—	2	1	no	—
237	C₂×C₁₀₇	—	8	1	no	—
238	C₂×C₁₀₇	#2362	1	1	yes	characteristic
239	C₂×C₁₀₇	C₂×#444	1	1	yes	characteristic
240	C₂×C₁₀₇	#2956	1	1	yes	characteristic
241	#3076	C₂×C₁₀₇	1	1	yes	characteristic
242	#2962	C₂×C₁₀₇	1	1	yes	characteristic, complemented
243	#2925	C₂×C₁₀₇	1	1	yes	characteristic
244	#1994	C₂×C₁₀₇	1	1	yes	characteristic, complemented
245	#1950	C₂×C₁₀₇	1	1	yes	characteristic, complemented
246	#1938	C₂×C₁₀₇	1	2	yes	—
247	#1929	C₂×C₁₀₇	1	2	yes	—
248	#1922	C₂×C₁₀₇	1	2	yes	complemented
249	#1773	C₂×C₁₀₇	1	2	yes	complemented
250	#1767	C₂×C₁₀₇	1	1	yes	characteristic, complemented
251	C₄×#104	C₂×C₁₀₇	1	1	yes	characteristic
252	C₁₀₇	#23081	1	1	yes	characteristic, direct product factor, Sylow
253	#533	C₂²×C₁₀₇	1	1	yes	characteristic
254	C₄×#41	C₂²×C₁₀₇	1	1	yes	characteristic
255	#479	C₄×C₁₀₇	1	2	yes	complemented
256	#478	C₄×C₁₀₇	1	2	yes	complemented
257	#477	C₄×C₁₀₇	1	1	yes	characteristic, complemented
258	#476	C₄×C₁₀₇	1	1	yes	characteristic, complemented
259	#475	C₄×C₁₀₇	1	1	yes	characteristic, complemented
260	#474	C₄×C₁₀₇	1	1	yes	characteristic, complemented
261	#446	—	2	2	no	—
262	#446	—	2	1	no	—
263	C₈×Q₈	—	2	1	no	—
264	#433	—	2	2	no	—
265	#432	—	2	1	no	—
266	#431	—	2	1	no	—
267	C₂×#108	C₂²×C₁₀₇	1	2	yes	—
268	#427	C₂²×C₁₀₇	1	2	yes	—
269	#424	C₂²×C₁₀₇	1	2	yes	—
270	#423	C₂²×C₁₀₇	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	1	yes	characteristic
273	C₂×#104	C₂²×C₁₀₇	1	1	yes	characteristic
274	C₂×#104	C₂²×C₁₀₇	1	1	yes	characteristic
275	#416	C₂²×C₁₀₇	1	2	yes	—
276	#408	C₂²×C₁₀₇	1	2	yes	—
277	#405	C₂²×C₁₀₇	1	2	yes	—
278	#405	C₂²×C₁₀₇	1	2	yes	—
279	C₄×M₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
280	C₂×#97	C₂²×C₁₀₇	1	2	yes	—
281	C₄³	C₂²×C₁₀₇	1	1	yes	characteristic
282	#341	C₂²×C₁₀₇	1	2	yes	—
283	#339	C₂²×C₁₀₇	1	1	yes	characteristic
284	#339	C₂²×C₁₀₇	1	2	yes	—
285	#339	C₂²×C₁₀₇	1	2	yes	—
286	#339	C₂²×C₁₀₇	1	1	yes	characteristic
287	#336	C₂²×C₁₀₇	1	2	yes	—
288	C₂×#41	C₂³×C₁₀₇	1	1	yes	characteristic
289	C₂×M₁₆	C₂³×C₁₀₇	1	2	yes	—
290	C₂×M₁₆	C₂³×C₁₀₇	1	1	yes	characteristic
291	C₂×M₁₆	C₂³×C₁₀₇	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
293	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
294	C₄⋊Q₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
295	C₄⋊Q₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
296	#125	C₂×C₄×C₁₀₇	1	2	yes	—
297	C₂²⋊Q₈	—	2	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×Q₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
302	C₄×Q₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
306	C₄×D₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
307	#117	—	2	1	no	—
308	#117	C₂³×C₁₀₇	1	1	yes	characteristic
309	#117	C₂³×C₁₀₇	1	2	yes	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
316	#108	—	2	4	no	—
317	#107	C₂×C₄×C₁₀₇	1	2	yes	—
318	#107	C₂×C₄×C₁₀₇	1	2	yes	—
319	#106	C₂×C₄×C₁₀₇	1	2	yes	—
320	#106	C₂×C₄×C₁₀₇	1	2	yes	—
321	C₄⋊C₈	—	2	2	no	—
322	C₄⋊C₈	—	2	2	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
326	C₄⋊C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
327	C₄⋊C₈	C₂×C₄×C₁₀₇	1	2	yes	—
328	C₄⋊C₈	D₄×C₁₀₇	1	1	yes	characteristic
329	C₄⋊C₈	D₄×C₁₀₇	1	1	yes	characteristic
330	C₄⋊C₈	D₄×C₁₀₇	1	2	yes	—
331	#104	—	2	2	no	—
332	#104	—	2	2	no	—
333	#103	C₂×C₄×C₁₀₇	1	2	yes	—
334	#103	C₂×C₄×C₁₀₇	1	2	yes	—
335	#102	C₂×C₄×C₁₀₇	1	2	yes	—
336	#102	C₂×C₄×C₁₀₇	1	2	yes	—
337	C₂²⋊C₈	—	2	2	no	—
338	C₂²⋊C₈	—	2	2	no	—
339	#97	—	2	2	no	—
340	#97	—	2	2	no	—
341	#97	—	2	1	no	—
342	#97	—	2	4	no	—
343	C₄×C₈	—	2	2	no	—
344	C₄×C₈	—	2	2	no	—
345	C₄×C₈	—	2	1	no	—
346	#41	—	2	1	no	—
347	#41	—	2	1	no	—
348	#41	—	2	1	no	—
349	#41	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	#41×C₁₀₇	1	1	yes	characteristic
361	C₂²×C₄	#41×C₁₀₇	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
363	M₁₆	—	2	1	no	—
364	M₁₆	—	2	1	no	—
365	M₁₆	—	2	2	no	—
366	M₁₆	—	2	1	no	—
367	M₁₆	—	2	2	no	—
368	M₁₆	#41×C₁₀₇	1	2	yes	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	C₂²×C₄×C₁₀₇	1	2	yes	—
377	C₂×C₈	C₂²×C₄×C₁₀₇	1	2	yes	—
378	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
379	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
387	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
388	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
389	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	4	2	no	—
402	C₄²	—	4	2	no	—
403	C₄²	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
404	C₄²	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
405	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
406	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
407	C₄²	#41×C₁₀₇	1	2	yes	—
408	C₂³	—	2	1	no	—
409	C₂³	C₂×#41×C₁₀₇	1	1	yes	characteristic
410	Q₈	—	2	1	no	—
411	Q₈	—	2	1	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	8	1	no	—
414	D₄	—	2	1	no	—
415	D₄	—	2	1	no	—
416	D₄	—	4	1	no	—
417	D₄	—	4	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	8	1	no	—
435	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
436	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
437	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
438	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
439	C₂×C₄	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
442	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
443	C₂×C₄	2₋¹⁺⁴×C₁₀₇	1	1	yes	characteristic
444	C₂×C₄	2₋¹⁺⁴×C₁₀₇	1	1	yes	characteristic
445	C₈	—	2	2	no	—
446	C₈	—	2	2	no	—
447	C₈	—	2	2	no	—
448	C₈	—	2	2	no	—
449	C₈	—	2	2	no	—
450	C₈	—	4	1	no	—
451	C₈	—	4	2	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	C₂×C₄×D₄×C₁₀₇	1	1	yes	characteristic
458	C₂²	#552×C₁₀₇	1	1	yes	characteristic
459	C₂²	#556×C₁₀₇	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	1	no	—
470	C₄	#444×C₁₀₇	1	2	yes	—
471	C₄	C₄×#41×C₁₀₇	1	1	yes	characteristic
472	C₄	#519×C₁₀₇	1	1	yes	characteristic
473	C₄	#547×C₁₀₇	1	1	yes	characteristic
474	C₄	#548×C₁₀₇	1	1	yes	characteristic
475	C₂	—	2	1	no	—
476	C₂	—	2	1	no	—
477	C₂	—	8	1	no	—
478	C₂	C₁₀₇×#2362	1	1	yes	characteristic
479	C₂	C₂×#444×C₁₀₇	1	1	yes	characteristic
480	C₂	C₁₀₇×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₀₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₇
socle	C₂²×C₁₀₇	C₂×C₄×D₄
prime radical	C₂×#41×C₁₀₇	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₇ ◁ C₂×C₄⋊C₈×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₇×#2962	C₂	semidirect
4. C₁₀₇×#1994	C₂	semidirect
5. C₁₀₇×#1950	C₂	semidirect
8. C₁₀₇×#1922	C₂	semidirect
9. C₁₀₇×#1773	C₂	semidirect
10. C₁₀₇×#1767	C₂	semidirect
14. #479×C₁₀₇	C₄	semidirect
15. #478×C₁₀₇	C₄	semidirect
16. #477×C₁₀₇	C₄	semidirect
17. #476×C₁₀₇	C₄	semidirect
18. #475×C₁₀₇	C₄	semidirect
19. #474×C₁₀₇	C₄	semidirect
234. #23081	C₁₀₇	direct (N × H)
242. #2962	C₂×C₁₀₇	semidirect
244. #1994	C₂×C₁₀₇	semidirect
245. #1950	C₂×C₁₀₇	semidirect
248. #1922	C₂×C₁₀₇	semidirect
249. #1773	C₂×C₁₀₇	semidirect
250. #1767	C₂×C₁₀₇	semidirect
252. C₁₀₇	#23081	direct (N × H)
255. #479	C₄×C₁₀₇	semidirect
256. #478	C₄×C₁₀₇	semidirect
257. #477	C₄×C₁₀₇	semidirect
258. #476	C₄×C₁₀₇	semidirect
259. #475	C₄×C₁₀₇	semidirect
260. #474	C₄×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₇×#3076	2
C₁₀₇×#2962	2
C₁₀₇×#2925	2
C₁₀₇×#1994	2
C₁₀₇×#1950	2
C₁₀₇×#1938	2
C₁₀₇×#1929	2
C₁₀₇×#1922	2
C₁₀₇×#1773	2
C₁₀₇×#1767	2
C₄×#104×C₁₀₇	2
#23081	107

Subgroups — C107×#23081 #41049045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#23081 #41049045