Subgroups — C₁₀₇×#18684 #41044648

Order 27392.

1006 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₇×#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₇×#3217	C₂	1	2	yes	maximal, complemented
3	C₂×#492×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₇×#1624	C₂	1	2	yes	maximal, complemented
5	C₁₀₇×#1623	C₂	1	2	yes	maximal, complemented
6	C₁₀₇×#1622	C₂	1	4	yes	maximal, complemented
7	C₁₀₇×#1558	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₇×#1494	C₂	1	2	yes	maximal, complemented
9	C₂²×SD₁₆×C₁₀₇	—	2	2	no	—
10	#563×C₁₀₇	—	2	2	no	—
11	Q₈²×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
12	#555×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
13	#554×C₁₀₇	C₂²	1	2	yes	complemented
14	#552×C₁₀₇	—	2	2	no	—
15	#547×C₁₀₇	—	2	2	no	—
16	#544×C₁₀₇	—	2	2	no	—
17	#542×C₁₀₇	—	2	2	no	—
18	#536×C₁₀₇	—	2	2	no	—
19	C₂×C₄⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
20	C₂×#127×C₁₀₇	C₂²	1	1	yes	characteristic
21	#529×C₁₀₇	C₂²	1	2	yes	—
22	#496×C₁₀₇	—	2	2	no	—
23	#492×C₁₀₇	—	2	2	no	—
24	#492×C₁₀₇	C₂²	1	2	yes	—
25	#492×C₁₀₇	C₂²	1	2	yes	—
26	#490×C₁₀₇	—	2	2	no	—
27	#460×C₁₀₇	C₂²	1	4	yes	—
28	#459×C₁₀₇	C₂²	1	4	yes	—
29	#450×C₁₀₇	—	2	2	no	—
30	#447×C₁₀₇	—	2	2	no	—
31	#432×C₁₀₇	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
33	#333×C₁₀₇	C₂²	1	2	yes	complemented
34	#333×C₁₀₇	C₂²	1	2	yes	complemented
35	Q₈⋊C₈×C₁₀₇	C₂²	1	4	yes	complemented
36	D₄⋊C₈×C₁₀₇	C₂²	1	4	yes	complemented
37	C₂×#41×C₁₀₇	—	2	2	no	—
38	C₂²×Q₈×C₁₀₇	D₄	1	2	yes	—
39	C₂²×D₄×C₁₀₇	—	2	1	no	—
40	C₂²×D₄×C₁₀₇	—	2	2	no	—
41	C₂×SD₁₆×C₁₀₇	—	2	4	no	—
42	C₂×SD₁₆×C₁₀₇	—	2	4	no	—
43	C₂×SD₁₆×C₁₀₇	—	2	4	no	—
44	C₂×SD₁₆×C₁₀₇	—	4	8	no	—
45	C₂×D₈×C₁₀₇	—	2	4	no	—
46	C₂²×C₈×C₁₀₇	—	2	1	no	—
47	C₄⋊Q₈×C₁₀₇	—	2	2	no	—
48	C₄⋊Q₈×C₁₀₇	—	2	2	no	—
49	C₄⋊Q₈×C₁₀₇	—	2	2	no	—
50	C₄⋊Q₈×C₁₀₇	—	2	2	no	—
51	C₄⋊Q₈×C₁₀₇	D₄	1	2	yes	—
52	C₄⋊Q₈×C₁₀₇	C₂³	1	1	yes	characteristic
53	C₄⋊Q₈×C₁₀₇	C₂³	1	1	yes	characteristic
54	#127×C₁₀₇	—	2	2	no	—
55	#127×C₁₀₇	—	2	1	no	—
56	#127×C₁₀₇	C₂³	1	2	yes	—
57	#126×C₁₀₇	—	2	4	no	—
58	#126×C₁₀₇	—	2	2	no	—
59	#125×C₁₀₇	—	2	4	no	—
60	#125×C₁₀₇	—	2	2	no	—
61	#125×C₁₀₇	D₄	1	2	yes	—
62	#124×C₁₀₇	—	2	2	no	—
63	#124×C₁₀₇	—	2	2	no	—
64	#124×C₁₀₇	D₄	1	2	yes	—
65	#123×C₁₀₇	—	2	4	no	—
66	#123×C₁₀₇	—	2	4	no	—
67	#123×C₁₀₇	—	2	2	no	—
68	C₂²⋊Q₈×C₁₀₇	—	2	4	no	—
69	C₂²⋊Q₈×C₁₀₇	—	2	4	no	—
70	C₂²⋊Q₈×C₁₀₇	—	2	4	no	—
71	C₂²⋊Q₈×C₁₀₇	—	2	2	no	—
72	C₂²⋊Q₈×C₁₀₇	D₄	1	2	yes	—
73	#121×C₁₀₇	—	2	2	no	—
74	#121×C₁₀₇	D₄	1	2	yes	—
75	C₄×Q₈×C₁₀₇	—	2	2	no	—
76	C₄×Q₈×C₁₀₇	C₂³	1	2	yes	—
77	C₄×D₄×C₁₀₇	—	2	2	no	—
78	C₄×D₄×C₁₀₇	—	2	2	no	—
79	C₄×D₄×C₁₀₇	C₂³	1	2	yes	—
80	#117×C₁₀₇	—	2	2	no	—
81	#117×C₁₀₇	—	2	2	no	—
82	#117×C₁₀₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
85	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₁₀₇	C₂³	1	4	yes	—
87	#102×C₁₀₇	—	2	4	no	—
88	#102×C₁₀₇	—	2	4	no	—
89	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
90	#97×C₁₀₇	—	2	2	no	—
91	C₄×C₈×C₁₀₇	—	2	1	no	—
92	C₄×C₈×C₁₀₇	C₂³	1	2	yes	—
93	C₂⁴×C₁₀₇	—	4	1	no	—
94	#41×C₁₀₇	—	8	4	no	—
95	C₂×Q₈×C₁₀₇	—	2	2	no	—
96	C₂×Q₈×C₁₀₇	—	2	2	no	—
97	C₂×Q₈×C₁₀₇	—	4	4	no	—
98	C₂×Q₈×C₁₀₇	C₂×D₄	1	2	yes	—
99	C₂×Q₈×C₁₀₇	C₂×D₄	1	2	yes	—
100	C₂×Q₈×C₁₀₇	C₂×D₄	1	2	yes	—
101	C₂×D₄×C₁₀₇	—	2	2	no	—
102	C₂×D₄×C₁₀₇	—	2	2	no	—
103	C₂×D₄×C₁₀₇	—	2	4	no	—
104	C₂×D₄×C₁₀₇	—	2	2	no	—
105	C₂×D₄×C₁₀₇	—	4	4	no	—
106	C₂×D₄×C₁₀₇	—	4	2	no	—
107	C₂×D₄×C₁₀₇	—	4	1	no	—
108	C₂×D₄×C₁₀₇	—	8	4	no	—
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	—	2	2	no	—
113	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
115	SD₁₆×C₁₀₇	—	4	8	no	—
116	SD₁₆×C₁₀₇	—	4	8	no	—
117	SD₁₆×C₁₀₇	—	8	4	no	—
118	D₈×C₁₀₇	—	8	4	no	—
119	C₂×C₈×C₁₀₇	—	2	4	no	—
120	C₂×C₈×C₁₀₇	—	2	2	no	—
121	C₂×C₈×C₁₀₇	—	2	4	no	—
122	C₄⋊C₄×C₁₀₇	—	2	4	no	—
123	C₄⋊C₄×C₁₀₇	—	2	4	no	—
124	C₄⋊C₄×C₁₀₇	—	2	4	no	—
125	C₄⋊C₄×C₁₀₇	—	2	4	no	—
126	C₄⋊C₄×C₁₀₇	—	2	2	no	—
127	C₄⋊C₄×C₁₀₇	—	2	2	no	—
128	C₄⋊C₄×C₁₀₇	—	2	2	no	—
129	C₄⋊C₄×C₁₀₇	—	2	2	no	—
130	C₄⋊C₄×C₁₀₇	—	2	2	no	—
131	C₄⋊C₄×C₁₀₇	—	2	2	no	—
132	C₄⋊C₄×C₁₀₇	C₂×D₄	1	2	yes	—
133	C₄⋊C₄×C₁₀₇	C₂×D₄	1	2	yes	—
134	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
135	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
136	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
137	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
138	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
139	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
140	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
141	C₄²×C₁₀₇	—	2	2	no	—
142	C₄²×C₁₀₇	—	2	2	no	—
143	C₄²×C₁₀₇	—	2	2	no	—
144	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₀₇	C₂×D₄	1	2	yes	—
146	C₄²×C₁₀₇	C₂⁴	1	1	yes	characteristic
147	C₂³×C₁₀₇	—	2	2	no	—
148	C₂³×C₁₀₇	—	4	2	no	—
149	C₂³×C₁₀₇	—	8	4	no	—
150	C₂³×C₁₀₇	—	8	2	no	—
151	C₂³×C₁₀₇	#120	1	1	yes	characteristic
152	Q₈×C₁₀₇	—	2	4	no	—
153	Q₈×C₁₀₇	—	4	2	no	—
154	Q₈×C₁₀₇	—	4	2	no	—
155	Q₈×C₁₀₇	—	8	2	no	—
156	Q₈×C₁₀₇	—	8	2	no	—
157	D₄×C₁₀₇	—	2	4	no	—
158	D₄×C₁₀₇	—	4	4	no	—
159	D₄×C₁₀₇	—	4	4	no	—
160	D₄×C₁₀₇	—	4	4	no	—
161	D₄×C₁₀₇	—	4	4	no	—
162	D₄×C₁₀₇	—	8	2	no	—
163	D₄×C₁₀₇	—	8	4	no	—
164	D₄×C₁₀₇	—	8	2	no	—
165	C₂×C₄×C₁₀₇	—	2	2	no	—
166	C₂×C₄×C₁₀₇	—	2	4	no	—
167	C₂×C₄×C₁₀₇	—	2	2	no	—
168	C₂×C₄×C₁₀₇	—	2	2	no	—
169	C₂×C₄×C₁₀₇	—	2	2	no	—
170	C₂×C₄×C₁₀₇	—	2	2	no	—
171	C₂×C₄×C₁₀₇	—	2	2	no	—
172	C₂×C₄×C₁₀₇	—	4	4	no	—
173	C₂×C₄×C₁₀₇	—	4	4	no	—
174	C₂×C₄×C₁₀₇	—	8	4	no	—
175	C₂×C₄×C₁₀₇	#120	1	2	yes	—
176	C₂×C₄×C₁₀₇	#120	1	1	yes	characteristic
177	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₀₇	C₂²×D₄	1	2	yes	—
179	C₈×C₁₀₇	—	2	4	no	—
180	C₈×C₁₀₇	—	4	4	no	—
181	C₂²×C₁₀₇	—	2	2	no	—
182	C₂²×C₁₀₇	—	4	2	no	—
183	C₂²×C₁₀₇	—	4	2	no	—
184	C₂²×C₁₀₇	—	4	2	no	—
185	C₂²×C₁₀₇	—	8	4	no	—
186	C₂²×C₁₀₇	—	8	2	no	—
187	C₂²×C₁₀₇	—	16	4	no	—
188	C₂²×C₁₀₇	#453	1	2	yes	—
189	C₂²×C₁₀₇	C₂×#120	1	1	yes	characteristic
190	C₄×C₁₀₇	—	2	2	no	—
191	C₄×C₁₀₇	—	2	1	no	—
192	C₄×C₁₀₇	—	2	1	no	—
193	C₄×C₁₀₇	—	4	2	no	—
194	C₄×C₁₀₇	—	4	2	no	—
195	C₄×C₁₀₇	—	4	2	no	—
196	C₄×C₁₀₇	—	4	2	no	—
197	C₄×C₁₀₇	—	4	2	no	—
198	C₄×C₁₀₇	#577	1	4	yes	—
199	#18684	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂×C₁₀₇	—	2	2	no	—
201	C₂×C₁₀₇	—	8	2	no	—
202	C₂×C₁₀₇	—	16	2	no	—
203	C₂×C₁₀₇	#3010	1	2	yes	—
204	C₂×C₁₀₇	C₂×#453	1	1	yes	characteristic
205	#3544	C₂×C₁₀₇	1	1	yes	characteristic, complemented
206	#3217	C₂×C₁₀₇	1	2	yes	complemented
207	C₂×#492	C₂×C₁₀₇	1	1	yes	characteristic, complemented
208	#1624	C₂×C₁₀₇	1	2	yes	complemented
209	#1623	C₂×C₁₀₇	1	2	yes	complemented
210	#1622	C₂×C₁₀₇	1	4	yes	complemented
211	#1558	C₂×C₁₀₇	1	1	yes	characteristic, complemented
212	#1494	C₂×C₁₀₇	1	2	yes	complemented
213	C₁₀₇	#18684	1	1	yes	characteristic, direct product factor, Sylow
214	C₂²×SD₁₆	—	2	2	no	—
215	#563	—	2	2	no	—
216	Q₈²	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
217	#555	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
218	#554	C₂²×C₁₀₇	1	2	yes	complemented
219	#552	—	2	2	no	—
220	#547	—	2	2	no	—
221	#544	—	2	2	no	—
222	#542	—	2	2	no	—
223	#536	—	2	2	no	—
224	C₂×C₄⋊Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
225	C₂×#127	C₂²×C₁₀₇	1	1	yes	characteristic
226	#529	C₂²×C₁₀₇	1	2	yes	—
227	#496	—	2	2	no	—
228	#492	—	2	2	no	—
229	#492	C₂²×C₁₀₇	1	2	yes	—
230	#492	C₂²×C₁₀₇	1	2	yes	—
231	#490	—	2	2	no	—
232	#460	C₂²×C₁₀₇	1	4	yes	—
233	#459	C₂²×C₁₀₇	1	4	yes	—
234	#450	—	2	2	no	—
235	#447	—	2	2	no	—
236	#432	C₂²×C₁₀₇	1	2	yes	—
237	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
238	#333	C₂²×C₁₀₇	1	2	yes	complemented
239	#333	C₂²×C₁₀₇	1	2	yes	complemented
240	Q₈⋊C₈	C₂²×C₁₀₇	1	4	yes	complemented
241	D₄⋊C₈	C₂²×C₁₀₇	1	4	yes	complemented
242	C₂×#41	—	2	2	no	—
243	C₂²×Q₈	D₄×C₁₀₇	1	2	yes	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	2	no	—
246	C₂×SD₁₆	—	2	4	no	—
247	C₂×SD₁₆	—	2	4	no	—
248	C₂×SD₁₆	—	2	4	no	—
249	C₂×SD₁₆	—	4	8	no	—
250	C₂×D₈	—	2	4	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	—	2	2	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	2	no	—
260	#127	—	2	1	no	—
261	#127	C₂³×C₁₀₇	1	2	yes	—
262	#126	—	2	4	no	—
263	#126	—	2	2	no	—
264	#125	—	2	4	no	—
265	#125	—	2	2	no	—
266	#125	D₄×C₁₀₇	1	2	yes	—
267	#124	—	2	2	no	—
268	#124	—	2	2	no	—
269	#124	D₄×C₁₀₇	1	2	yes	—
270	#123	—	2	4	no	—
271	#123	—	2	4	no	—
272	#123	—	2	2	no	—
273	C₂²⋊Q₈	—	2	4	no	—
274	C₂²⋊Q₈	—	2	4	no	—
275	C₂²⋊Q₈	—	2	4	no	—
276	C₂²⋊Q₈	—	2	2	no	—
277	C₂²⋊Q₈	D₄×C₁₀₇	1	2	yes	—
278	#121	—	2	2	no	—
279	#121	D₄×C₁₀₇	1	2	yes	—
280	C₄×Q₈	—	2	2	no	—
281	C₄×Q₈	C₂³×C₁₀₇	1	2	yes	—
282	C₄×D₄	—	2	2	no	—
283	C₄×D₄	—	2	2	no	—
284	C₄×D₄	C₂³×C₁₀₇	1	2	yes	—
285	#117	—	2	2	no	—
286	#117	—	2	2	no	—
287	#117	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
291	C₄⋊C₈	C₂³×C₁₀₇	1	4	yes	—
292	#102	—	2	4	no	—
293	#102	—	2	4	no	—
294	C₂²⋊C₈	—	2	2	no	—
295	#97	—	2	2	no	—
296	C₄×C₈	—	2	1	no	—
297	C₄×C₈	C₂³×C₁₀₇	1	2	yes	—
298	C₂⁴	—	4	1	no	—
299	#41	—	8	4	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	4	4	no	—
303	C₂×Q₈	C₂×D₄×C₁₀₇	1	2	yes	—
304	C₂×Q₈	C₂×D₄×C₁₀₇	1	2	yes	—
305	C₂×Q₈	C₂×D₄×C₁₀₇	1	2	yes	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	4	4	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	8	4	no	—
314	C₂×D₄	C₂×D₄×C₁₀₇	1	2	yes	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
320	SD₁₆	—	4	8	no	—
321	SD₁₆	—	4	8	no	—
322	SD₁₆	—	8	4	no	—
323	D₈	—	8	4	no	—
324	C₂×C₈	—	2	4	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	4	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	C₂×D₄×C₁₀₇	1	2	yes	—
338	C₄⋊C₄	C₂×D₄×C₁₀₇	1	2	yes	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
350	C₄²	C₂×D₄×C₁₀₇	1	2	yes	—
351	C₄²	C₂⁴×C₁₀₇	1	1	yes	characteristic
352	C₂³	—	2	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	8	4	no	—
355	C₂³	—	8	2	no	—
356	C₂³	#120×C₁₀₇	1	1	yes	characteristic
357	Q₈	—	2	4	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	8	2	no	—
361	Q₈	—	8	2	no	—
362	D₄	—	2	4	no	—
363	D₄	—	4	4	no	—
364	D₄	—	4	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	4	no	—
367	D₄	—	8	2	no	—
368	D₄	—	8	4	no	—
369	D₄	—	8	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	8	4	no	—
380	C₂×C₄	#120×C₁₀₇	1	2	yes	—
381	C₂×C₄	#120×C₁₀₇	1	1	yes	characteristic
382	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
383	C₂×C₄	C₂²×D₄×C₁₀₇	1	2	yes	—
384	C₈	—	2	4	no	—
385	C₈	—	4	4	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	8	4	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	16	4	no	—
393	C₂²	#453×C₁₀₇	1	2	yes	—
394	C₂²	C₂×#120×C₁₀₇	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	2	no	—
403	C₄	#577×C₁₀₇	1	4	yes	—
404	C₂	—	2	2	no	—
405	C₂	—	8	2	no	—
406	C₂	—	16	2	no	—
407	C₂	C₁₀₇×#3010	1	2	yes	—
408	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×#3544	C₂	semidirect
2. C₁₀₇×#3217	C₂	semidirect
3. C₂×#492×C₁₀₇	C₂	semidirect
4. C₁₀₇×#1624	C₂	semidirect
5. C₁₀₇×#1623	C₂	semidirect
6. C₁₀₇×#1622	C₂	semidirect
7. C₁₀₇×#1558	C₂	semidirect
8. C₁₀₇×#1494	C₂	semidirect
11. Q₈²×C₁₀₇	C₂²	semidirect
12. #555×C₁₀₇	C₂²	semidirect
13. #554×C₁₀₇	C₂²	semidirect
33. #333×C₁₀₇	C₂²	semidirect
34. #333×C₁₀₇	C₂²	semidirect
35. Q₈⋊C₈×C₁₀₇	C₂²	semidirect
36. D₄⋊C₈×C₁₀₇	C₂²	semidirect
199. #18684	C₁₀₇	direct (N × H)
205. #3544	C₂×C₁₀₇	semidirect
206. #3217	C₂×C₁₀₇	semidirect
207. C₂×#492	C₂×C₁₀₇	semidirect
208. #1624	C₂×C₁₀₇	semidirect
209. #1623	C₂×C₁₀₇	semidirect
210. #1622	C₂×C₁₀₇	semidirect
211. #1558	C₂×C₁₀₇	semidirect
212. #1494	C₂×C₁₀₇	semidirect
213. C₁₀₇	#18684	direct (N × H)
216. Q₈²	C₂²×C₁₀₇	semidirect
217. #555	C₂²×C₁₀₇	semidirect
218. #554	C₂²×C₁₀₇	semidirect
238. #333	C₂²×C₁₀₇	semidirect
239. #333	C₂²×C₁₀₇	semidirect
240. Q₈⋊C₈	C₂²×C₁₀₇	semidirect
241. 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×#3544	2
C₁₀₇×#3217	2
C₂×#492×C₁₀₇	2
C₁₀₇×#1624	2
C₁₀₇×#1623	2
C₁₀₇×#1622	2
C₁₀₇×#1558	2
C₁₀₇×#1494	2
#18684	107

Subgroups — C107×#18684 #41044648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#18684 #41044648