Subgroups — C₁₀₇×#18686 #41044650

Order 27392.

1082 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₇×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₇×#3253	C₂	1	2	yes	maximal, complemented
3	C₁₀₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₇×#1634	C₂	1	2	yes	maximal, complemented
5	C₁₀₇×#1629	C₂	1	2	yes	maximal, complemented
6	C₁₀₇×#1624	C₂	1	2	yes	maximal, complemented
7	C₁₀₇×#1619	C₂	1	2	yes	maximal, complemented
8	C₁₀₇×#1560	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₇×#1492	C₂	1	2	yes	maximal, complemented
10	C₂×#135×C₁₀₇	—	2	2	no	—
11	H(3,𝔽₄)×C₁₀₇	—	2	2	no	—
12	#555×C₁₀₇	—	2	2	no	—
13	#555×C₁₀₇	C₂²	1	2	yes	—
14	D₄²×C₁₀₇	—	2	2	no	—
15	D₄²×C₁₀₇	C₂²	1	2	yes	—
16	#535×C₁₀₇	—	2	2	no	—
17	#535×C₁₀₇	—	2	4	no	—
18	#532×C₁₀₇	C₂²	1	1	yes	characteristic
19	#532×C₁₀₇	C₂²	1	2	yes	—
20	#532×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
21	#495×C₁₀₇	—	2	2	no	—
22	#494×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
23	#493×C₁₀₇	C₂²	1	1	yes	characteristic
24	#492×C₁₀₇	C₂²	1	1	yes	characteristic
25	#492×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
26	#476×C₁₀₇	—	2	2	no	—
27	#476×C₁₀₇	C₂²	1	4	yes	complemented
28	#469×C₁₀₇	—	2	4	no	—
29	#459×C₁₀₇	—	2	2	no	—
30	#459×C₁₀₇	C₂²	1	4	yes	complemented
31	#423×C₁₀₇	C₂²	1	2	yes	complemented
32	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
33	#333×C₁₀₇	C₂²	1	2	yes	complemented
34	#331×C₁₀₇	C₂²	1	2	yes	—
35	D₄⋊C₈×C₁₀₇	C₂²	1	4	yes	complemented
36	D₄⋊C₈×C₁₀₇	C₂²	1	4	yes	complemented
37	C₂×#41×C₁₀₇	—	2	2	no	—
38	C₂×#41×C₁₀₇	—	2	1	no	—
39	C₂×#41×C₁₀₇	D₄	1	2	yes	—
40	C₂²×D₄×C₁₀₇	—	2	2	no	—
41	C₂²×D₄×C₁₀₇	—	2	4	no	—
42	#135×C₁₀₇	—	4	8	no	—
43	C₂×Q₁₆×C₁₀₇	—	2	2	no	—
44	C₂×SD₁₆×C₁₀₇	—	2	2	no	—
45	C₂×SD₁₆×C₁₀₇	—	2	2	no	—
46	C₂×D₈×C₁₀₇	—	2	2	no	—
47	C₂×D₈×C₁₀₇	—	2	4	no	—
48	C₂×M₁₆×C₁₀₇	—	2	2	no	—
49	C₂²×C₈×C₁₀₇	—	2	1	no	—
50	C₄⋊Q₈×C₁₀₇	D₄	1	2	yes	—
51	C₄⋊Q₈×C₁₀₇	C₂³	1	1	yes	characteristic
52	C₄⋊Q₈×C₁₀₇	C₂³	1	1	yes	characteristic
53	#127×C₁₀₇	—	2	4	no	—
54	#127×C₁₀₇	D₄	1	2	yes	—
55	#127×C₁₀₇	C₂³	1	1	yes	characteristic
56	#127×C₁₀₇	C₂³	1	1	yes	characteristic
57	#124×C₁₀₇	—	2	8	no	—
58	#124×C₁₀₇	—	2	4	no	—
59	#124×C₁₀₇	—	2	2	no	—
60	#124×C₁₀₇	—	2	1	no	—
61	#124×C₁₀₇	D₄	1	2	yes	—
62	#121×C₁₀₇	—	2	4	no	—
63	#121×C₁₀₇	—	2	4	no	—
64	#121×C₁₀₇	—	2	2	no	—
65	#121×C₁₀₇	—	2	2	no	—
66	#121×C₁₀₇	—	2	4	no	—
67	#121×C₁₀₇	—	2	2	no	—
68	#121×C₁₀₇	D₄	1	4	yes	—
69	#120×C₁₀₇	—	2	4	no	—
70	#120×C₁₀₇	—	2	8	no	—
71	#120×C₁₀₇	—	2	4	no	—
72	C₄×D₄×C₁₀₇	—	2	2	no	—
73	C₄×D₄×C₁₀₇	—	2	2	no	—
74	C₄×D₄×C₁₀₇	—	2	2	no	—
75	C₄×D₄×C₁₀₇	C₂³	1	4	yes	—
76	#117×C₁₀₇	—	2	2	no	—
77	#117×C₁₀₇	—	2	4	no	—
78	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
79	#106×C₁₀₇	—	2	4	no	—
80	C₄⋊C₈×C₁₀₇	—	2	2	no	—
81	C₄⋊C₈×C₁₀₇	C₂³	1	4	yes	—
82	#102×C₁₀₇	—	2	4	no	—
83	#102×C₁₀₇	—	2	4	no	—
84	C₄×C₈×C₁₀₇	—	2	1	no	—
85	C₄×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
87	C₂⁴×C₁₀₇	—	2	4	no	—
88	#41×C₁₀₇	—	4	4	no	—
89	#41×C₁₀₇	—	4	4	no	—
90	#41×C₁₀₇	—	8	2	no	—
91	#41×C₁₀₇	—	8	2	no	—
92	C₂×Q₈×C₁₀₇	—	2	2	no	—
93	C₂×Q₈×C₁₀₇	—	2	1	no	—
94	C₂×Q₈×C₁₀₇	C₂×D₄	1	2	yes	—
95	C₂×D₄×C₁₀₇	—	2	4	no	—
96	C₂×D₄×C₁₀₇	—	2	8	no	—
97	C₂×D₄×C₁₀₇	—	2	2	no	—
98	C₂×D₄×C₁₀₇	—	2	4	no	—
99	C₂×D₄×C₁₀₇	—	2	2	no	—
100	C₂×D₄×C₁₀₇	—	2	2	no	—
101	C₂×D₄×C₁₀₇	—	2	2	no	—
102	C₂×D₄×C₁₀₇	—	2	2	no	—
103	C₂×D₄×C₁₀₇	—	2	1	no	—
104	C₂×D₄×C₁₀₇	—	4	1	no	—
105	C₂×D₄×C₁₀₇	—	8	4	no	—
106	C₂×D₄×C₁₀₇	—	8	4	no	—
107	C₂×D₄×C₁₀₇	—	8	4	no	—
108	C₂×D₄×C₁₀₇	C₂×D₄	1	4	yes	—
109	C₂×D₄×C₁₀₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₀₇	—	2	2	no	—
111	C₂²×C₄×C₁₀₇	—	2	4	no	—
112	C₂²×C₄×C₁₀₇	—	4	1	no	—
113	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
115	Q₁₆×C₁₀₇	—	4	4	no	—
116	SD₁₆×C₁₀₇	—	4	4	no	—
117	SD₁₆×C₁₀₇	—	4	4	no	—
118	D₈×C₁₀₇	—	4	4	no	—
119	D₈×C₁₀₇	—	8	4	no	—
120	M₁₆×C₁₀₇	—	8	2	no	—
121	C₂×C₈×C₁₀₇	—	2	4	no	—
122	C₂×C₈×C₁₀₇	—	2	1	no	—
123	C₂×C₈×C₁₀₇	—	2	1	no	—
124	C₂×C₈×C₁₀₇	—	2	4	no	—
125	C₄⋊C₄×C₁₀₇	—	2	2	no	—
126	C₄⋊C₄×C₁₀₇	—	2	2	no	—
127	C₄⋊C₄×C₁₀₇	—	2	2	no	—
128	C₄⋊C₄×C₁₀₇	C₂×D₄	1	4	yes	—
129	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
130	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
131	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
132	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
133	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
134	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
135	C₄²×C₁₀₇	—	2	4	no	—
136	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₀₇	C₂×D₄	1	2	yes	—
138	C₄²×C₁₀₇	C₂⁴	1	1	yes	characteristic
139	C₂³×C₁₀₇	—	2	4	no	—
140	C₂³×C₁₀₇	—	2	2	no	—
141	C₂³×C₁₀₇	—	4	1	no	—
142	C₂³×C₁₀₇	—	8	8	no	—
143	C₂³×C₁₀₇	—	8	4	no	—
144	C₂³×C₁₀₇	#120	1	1	yes	characteristic
145	Q₈×C₁₀₇	—	4	2	no	—
146	Q₈×C₁₀₇	—	4	2	no	—
147	Q₈×C₁₀₇	—	8	2	no	—
148	D₄×C₁₀₇	—	2	4	no	—
149	D₄×C₁₀₇	—	2	4	no	—
150	D₄×C₁₀₇	—	4	2	no	—
151	D₄×C₁₀₇	—	4	2	no	—
152	D₄×C₁₀₇	—	4	2	no	—
153	D₄×C₁₀₇	—	4	2	no	—
154	D₄×C₁₀₇	—	4	2	no	—
155	D₄×C₁₀₇	—	4	2	no	—
156	D₄×C₁₀₇	—	4	4	no	—
157	D₄×C₁₀₇	—	8	2	no	—
158	D₄×C₁₀₇	—	8	2	no	—
159	D₄×C₁₀₇	—	8	4	no	—
160	D₄×C₁₀₇	—	8	8	no	—
161	D₄×C₁₀₇	—	8	4	no	—
162	D₄×C₁₀₇	—	8	2	no	—
163	C₂×C₄×C₁₀₇	—	2	2	no	—
164	C₂×C₄×C₁₀₇	—	2	2	no	—
165	C₂×C₄×C₁₀₇	—	2	2	no	—
166	C₂×C₄×C₁₀₇	—	2	2	no	—
167	C₂×C₄×C₁₀₇	—	2	4	no	—
168	C₂×C₄×C₁₀₇	—	4	4	no	—
169	C₂×C₄×C₁₀₇	—	4	4	no	—
170	C₂×C₄×C₁₀₇	—	4	4	no	—
171	C₂×C₄×C₁₀₇	—	4	1	no	—
172	C₂×C₄×C₁₀₇	—	8	2	no	—
173	C₂×C₄×C₁₀₇	#120	1	2	yes	—
174	C₂×C₄×C₁₀₇	#120	1	1	yes	characteristic
175	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₀₇	C₂²×D₄	1	2	yes	—
177	C₈×C₁₀₇	—	2	2	no	—
178	C₈×C₁₀₇	—	2	2	no	—
179	C₈×C₁₀₇	—	4	4	no	—
180	C₂²×C₁₀₇	—	2	2	no	—
181	C₂²×C₁₀₇	—	2	1	no	—
182	C₂²×C₁₀₇	—	4	4	no	—
183	C₂²×C₁₀₇	—	4	4	no	—
184	C₂²×C₁₀₇	—	4	4	no	—
185	C₂²×C₁₀₇	—	4	2	no	—
186	C₂²×C₁₀₇	—	4	4	no	—
187	C₂²×C₁₀₇	—	8	2	no	—
188	C₂²×C₁₀₇	—	8	1	no	—
189	C₂²×C₁₀₇	—	16	8	no	—
190	C₂²×C₁₀₇	C₂×#120	1	1	yes	characteristic
191	C₄×C₁₀₇	—	2	2	no	—
192	C₄×C₁₀₇	—	2	1	no	—
193	C₄×C₁₀₇	—	4	4	no	—
194	C₄×C₁₀₇	—	4	2	no	—
195	C₄×C₁₀₇	—	8	1	no	—
196	C₄×C₁₀₇	#453	1	2	yes	—
197	C₄×C₁₀₇	#576	1	2	yes	—
198	C₄×C₁₀₇	#577	1	2	yes	—
199	#18686	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂×C₁₀₇	—	4	1	no	—
201	C₂×C₁₀₇	—	8	4	no	—
202	C₂×C₁₀₇	—	8	2	no	—
203	C₂×C₁₀₇	—	16	1	no	—
204	C₂×C₁₀₇	#3012	1	2	yes	—
205	C₂×C₁₀₇	C₂×#453	1	1	yes	characteristic
206	#3549	C₂×C₁₀₇	1	1	yes	characteristic, complemented
207	#3253	C₂×C₁₀₇	1	2	yes	complemented
208	#3147	C₂×C₁₀₇	1	1	yes	characteristic, complemented
209	#1634	C₂×C₁₀₇	1	2	yes	complemented
210	#1629	C₂×C₁₀₇	1	2	yes	complemented
211	#1624	C₂×C₁₀₇	1	2	yes	complemented
212	#1619	C₂×C₁₀₇	1	2	yes	complemented
213	#1560	C₂×C₁₀₇	1	1	yes	characteristic, complemented
214	#1492	C₂×C₁₀₇	1	2	yes	complemented
215	C₁₀₇	#18686	1	1	yes	characteristic, direct product factor, Sylow
216	C₂×#135	—	2	2	no	—
217	H(3,𝔽₄)	—	2	2	no	—
218	#555	—	2	2	no	—
219	#555	C₂²×C₁₀₇	1	2	yes	—
220	D₄²	—	2	2	no	—
221	D₄²	C₂²×C₁₀₇	1	2	yes	—
222	#535	—	2	2	no	—
223	#535	—	2	4	no	—
224	#532	C₂²×C₁₀₇	1	1	yes	characteristic
225	#532	C₂²×C₁₀₇	1	2	yes	—
226	#532	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
227	#495	—	2	2	no	—
228	#494	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
229	#493	C₂²×C₁₀₇	1	1	yes	characteristic
230	#492	C₂²×C₁₀₇	1	1	yes	characteristic
231	#492	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
232	#476	—	2	2	no	—
233	#476	C₂²×C₁₀₇	1	4	yes	complemented
234	#469	—	2	4	no	—
235	#459	—	2	2	no	—
236	#459	C₂²×C₁₀₇	1	4	yes	complemented
237	#423	C₂²×C₁₀₇	1	2	yes	complemented
238	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
239	#333	C₂²×C₁₀₇	1	2	yes	complemented
240	#331	C₂²×C₁₀₇	1	2	yes	—
241	D₄⋊C₈	C₂²×C₁₀₇	1	4	yes	complemented
242	D₄⋊C₈	C₂²×C₁₀₇	1	4	yes	complemented
243	C₂×#41	—	2	2	no	—
244	C₂×#41	—	2	1	no	—
245	C₂×#41	D₄×C₁₀₇	1	2	yes	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	—	2	4	no	—
248	#135	—	4	8	no	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×SD₁₆	—	2	2	no	—
251	C₂×SD₁₆	—	2	2	no	—
252	C₂×D₈	—	2	2	no	—
253	C₂×D₈	—	2	4	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂²×C₈	—	2	1	no	—
256	C₄⋊Q₈	D₄×C₁₀₇	1	2	yes	—
257	C₄⋊Q₈	C₂³×C₁₀₇	1	1	yes	characteristic
258	C₄⋊Q₈	C₂³×C₁₀₇	1	1	yes	characteristic
259	#127	—	2	4	no	—
260	#127	D₄×C₁₀₇	1	2	yes	—
261	#127	C₂³×C₁₀₇	1	1	yes	characteristic
262	#127	C₂³×C₁₀₇	1	1	yes	characteristic
263	#124	—	2	8	no	—
264	#124	—	2	4	no	—
265	#124	—	2	2	no	—
266	#124	—	2	1	no	—
267	#124	D₄×C₁₀₇	1	2	yes	—
268	#121	—	2	4	no	—
269	#121	—	2	4	no	—
270	#121	—	2	2	no	—
271	#121	—	2	2	no	—
272	#121	—	2	4	no	—
273	#121	—	2	2	no	—
274	#121	D₄×C₁₀₇	1	4	yes	—
275	#120	—	2	4	no	—
276	#120	—	2	8	no	—
277	#120	—	2	4	no	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	—	2	2	no	—
281	C₄×D₄	C₂³×C₁₀₇	1	4	yes	—
282	#117	—	2	2	no	—
283	#117	—	2	4	no	—
284	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
285	#106	—	2	4	no	—
286	C₄⋊C₈	—	2	2	no	—
287	C₄⋊C₈	C₂³×C₁₀₇	1	4	yes	—
288	#102	—	2	4	no	—
289	#102	—	2	4	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
292	C₄×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
293	C₂⁴	—	2	4	no	—
294	#41	—	4	4	no	—
295	#41	—	4	4	no	—
296	#41	—	8	2	no	—
297	#41	—	8	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	C₂×D₄×C₁₀₇	1	2	yes	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	8	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	8	4	no	—
312	C₂×D₄	—	8	4	no	—
313	C₂×D₄	—	8	4	no	—
314	C₂×D₄	C₂×D₄×C₁₀₇	1	4	yes	—
315	C₂×D₄	C₂×D₄×C₁₀₇	1	2	yes	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
321	Q₁₆	—	4	4	no	—
322	SD₁₆	—	4	4	no	—
323	SD₁₆	—	4	4	no	—
324	D₈	—	4	4	no	—
325	D₈	—	8	4	no	—
326	M₁₆	—	8	2	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	C₂×D₄×C₁₀₇	1	4	yes	—
335	C₂²⋊C₄	—	2	8	no	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₄²	—	2	4	no	—
342	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
343	C₄²	C₂×D₄×C₁₀₇	1	2	yes	—
344	C₄²	C₂⁴×C₁₀₇	1	1	yes	characteristic
345	C₂³	—	2	4	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	8	8	no	—
349	C₂³	—	8	4	no	—
350	C₂³	#120×C₁₀₇	1	1	yes	characteristic
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	8	2	no	—
354	D₄	—	2	4	no	—
355	D₄	—	2	4	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	4	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	8	2	no	—
364	D₄	—	8	2	no	—
365	D₄	—	8	4	no	—
366	D₄	—	8	8	no	—
367	D₄	—	8	4	no	—
368	D₄	—	8	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	#120×C₁₀₇	1	2	yes	—
380	C₂×C₄	#120×C₁₀₇	1	1	yes	characteristic
381	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
382	C₂×C₄	C₂²×D₄×C₁₀₇	1	2	yes	—
383	C₈	—	2	2	no	—
384	C₈	—	2	2	no	—
385	C₈	—	4	4	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	1	no	—
395	C₂²	—	16	8	no	—
396	C₂²	C₂×#120×C₁₀₇	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	4	4	no	—
400	C₄	—	4	2	no	—
401	C₄	—	8	1	no	—
402	C₄	#453×C₁₀₇	1	2	yes	—
403	C₄	#576×C₁₀₇	1	2	yes	—
404	C₄	#577×C₁₀₇	1	2	yes	—
405	C₂	—	4	1	no	—
406	C₂	—	8	4	no	—
407	C₂	—	8	2	no	—
408	C₂	—	16	1	no	—
409	C₂	C₁₀₇×#3012	1	2	yes	—
410	C₂	C₂×#453×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₇
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. C₁₀₇×#3549	C₂	semidirect
2. C₁₀₇×#3253	C₂	semidirect
3. C₁₀₇×#3147	C₂	semidirect
4. C₁₀₇×#1634	C₂	semidirect
5. C₁₀₇×#1629	C₂	semidirect
6. C₁₀₇×#1624	C₂	semidirect
7. C₁₀₇×#1619	C₂	semidirect
8. C₁₀₇×#1560	C₂	semidirect
9. C₁₀₇×#1492	C₂	semidirect
20. #532×C₁₀₇	C₂²	semidirect
22. #494×C₁₀₇	C₂²	semidirect
25. #492×C₁₀₇	C₂²	semidirect
27. #476×C₁₀₇	C₂²	semidirect
30. #459×C₁₀₇	C₂²	semidirect
31. #423×C₁₀₇	C₂²	semidirect
32. C₂×C₄×C₈×C₁₀₇	C₂²	semidirect
33. #333×C₁₀₇	C₂²	semidirect
35. D₄⋊C₈×C₁₀₇	C₂²	semidirect
36. D₄⋊C₈×C₁₀₇	C₂²	semidirect
199. #18686	C₁₀₇	direct (N × H)
206. #3549	C₂×C₁₀₇	semidirect
207. #3253	C₂×C₁₀₇	semidirect
208. #3147	C₂×C₁₀₇	semidirect
209. #1634	C₂×C₁₀₇	semidirect
210. #1629	C₂×C₁₀₇	semidirect
211. #1624	C₂×C₁₀₇	semidirect
212. #1619	C₂×C₁₀₇	semidirect
213. #1560	C₂×C₁₀₇	semidirect
214. #1492	C₂×C₁₀₇	semidirect
215. C₁₀₇	#18686	direct (N × H)
226. #532	C₂²×C₁₀₇	semidirect
228. #494	C₂²×C₁₀₇	semidirect
231. #492	C₂²×C₁₀₇	semidirect
233. #476	C₂²×C₁₀₇	semidirect
236. #459	C₂²×C₁₀₇	semidirect
237. #423	C₂²×C₁₀₇	semidirect
238. C₂×C₄×C₈	C₂²×C₁₀₇	semidirect
239. #333	C₂²×C₁₀₇	semidirect
241. D₄⋊C₈	C₂²×C₁₀₇	semidirect
242. D₄⋊C₈	C₂²×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₇×#3549	2
C₁₀₇×#3253	2
C₁₀₇×#3147	2
C₁₀₇×#1634	2
C₁₀₇×#1629	2
C₁₀₇×#1624	2
C₁₀₇×#1619	2
C₁₀₇×#1560	2
C₁₀₇×#1492	2
#18686	107

Subgroups — C107×#18686 #41044650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#18686 #41044650