Subgroups — C₁₀₇×#33631 #41059595

Order 27392.

556 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₇×#3164	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₇×#2948	C₂	1	1	yes	maximal, characteristic
3	C₁₀₇×#2228	C₂	1	2	yes	maximal, complemented
4	C₁₀₇×#2228	C₂	1	2	yes	maximal, complemented
5	C₁₀₇×#2226	C₂	1	2	yes	maximal, complemented
6	C₁₀₇×#2224	C₂	1	2	yes	maximal, complemented
7	C₁₀₇×#2159	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₇×#2158	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₇×#2151	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₇×#2140	C₂	1	1	yes	maximal, characteristic
11	C₂×#357×C₁₀₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×D₈×C₁₀₇	C₂²	1	1	yes	characteristic
13	#544×C₁₀₇	—	2	1	no	—
14	#518×C₁₀₇	—	2	1	no	—
15	C₂×M₃₂×C₁₀₇	C₂²	1	1	yes	characteristic
16	C₂²×C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
17	#501×C₁₀₇	—	2	2	no	—
18	#500×C₁₀₇	C₂²	1	2	yes	complemented
19	#499×C₁₀₇	C₂²	1	2	yes	complemented
20	#442×C₁₀₇	—	2	2	no	—
21	C₄×D₈×C₁₀₇	C₂²	1	2	yes	—
22	C₄×D₈×C₁₀₇	C₂²	1	2	yes	—
23	#428×C₁₀₇	—	2	1	no	—
24	#427×C₁₀₇	C₂²	1	1	yes	characteristic
25	#427×C₁₀₇	C₂²	1	1	yes	characteristic
26	C₂×#107×C₁₀₇	C₂²	1	1	yes	characteristic
27	#418×C₁₀₇	—	2	1	no	—
28	#405×C₁₀₇	C₂²	1	1	yes	characteristic
29	#367×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
30	#367×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
31	#367×C₁₀₇	C₂²	1	2	yes	complemented
32	#366×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
33	#366×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
34	#366×C₁₀₇	C₂²	1	2	yes	complemented
35	C₄⋊C₁₆×C₁₀₇	C₂²	1	2	yes	complemented
36	C₄⋊C₁₆×C₁₀₇	C₂²	1	2	yes	complemented
37	#357×C₁₀₇	C₂²	1	2	yes	—
38	#357×C₁₀₇	C₂²	1	2	yes	—
39	#357×C₁₀₇	C₂²	1	2	yes	—
40	#357×C₁₀₇	C₂²	1	2	yes	—
41	C₂²×D₄×C₁₀₇	—	2	1	no	—
42	C₂×D₈×C₁₀₇	—	2	1	no	—
43	C₂×D₈×C₁₀₇	—	2	2	no	—
44	C₂×D₈×C₁₀₇	Q₈	1	4	yes	complemented
45	C₂×D₈×C₁₀₇	C₂³	1	2	yes	—
46	C₂×M₁₆×C₁₀₇	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
48	C₄⋊Q₈×C₁₀₇	—	2	2	no	—
49	C₄⋊Q₈×C₁₀₇	—	4	1	no	—
50	#125×C₁₀₇	—	2	2	no	—
51	#125×C₁₀₇	—	4	1	no	—
52	C₂²⋊Q₈×C₁₀₇	—	4	2	no	—
53	C₄×D₄×C₁₀₇	—	2	2	no	—
54	C₄×D₄×C₁₀₇	—	2	2	no	—
55	C₄×D₄×C₁₀₇	—	4	1	no	—
56	C₄×D₄×C₁₀₇	—	4	1	no	—
57	#117×C₁₀₇	—	2	1	no	—
58	#117×C₁₀₇	—	2	1	no	—
59	#117×C₁₀₇	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₀₇	—	4	2	no	—
62	M₃₂×C₁₀₇	—	2	2	no	—
63	C₂×C₁₆×C₁₀₇	—	2	2	no	—
64	C₂×C₁₆×C₁₀₇	C₂³	1	1	yes	characteristic
65	C₂×C₁₆×C₁₀₇	C₂³	1	2	yes	—
66	C₂×C₁₆×C₁₀₇	C₂³	1	1	yes	characteristic
67	#107×C₁₀₇	—	2	1	no	—
68	#107×C₁₀₇	—	2	2	no	—
69	#107×C₁₀₇	C₂³	1	2	yes	—
70	#107×C₁₀₇	C₂³	1	1	yes	characteristic
71	#107×C₁₀₇	C₂³	1	1	yes	characteristic
72	#107×C₁₀₇	C₂³	1	1	yes	characteristic
73	#107×C₁₀₇	C₂³	1	1	yes	characteristic
74	#106×C₁₀₇	—	2	1	no	—
75	#106×C₁₀₇	—	2	1	no	—
76	#106×C₁₀₇	—	2	2	no	—
77	#102×C₁₀₇	—	2	2	no	—
78	#102×C₁₀₇	—	2	2	no	—
79	#97×C₁₀₇	D₄	1	2	yes	—
80	C₄×C₈×C₁₀₇	C₂³	1	2	yes	—
81	C₂⁴×C₁₀₇	—	4	1	no	—
82	C₂×Q₈×C₁₀₇	—	4	2	no	—
83	C₂×D₄×C₁₀₇	—	2	4	no	—
84	C₂×D₄×C₁₀₇	—	2	2	no	—
85	C₂×D₄×C₁₀₇	—	4	1	no	—
86	C₂×D₄×C₁₀₇	—	4	2	no	—
87	C₂²×C₄×C₁₀₇	—	4	1	no	—
88	C₂²×C₄×C₁₀₇	—	4	2	no	—
89	C₂²×C₄×C₁₀₇	—	4	2	no	—
90	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
91	D₈×C₁₀₇	—	2	4	no	—
92	D₈×C₁₀₇	—	2	2	no	—
93	D₈×C₁₀₇	C₂×Q₈	1	4	yes	—
94	M₁₆×C₁₀₇	—	2	2	no	—
95	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
96	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
97	C₂×C₈×C₁₀₇	C₂×Q₈	1	2	yes	—
98	C₂×C₈×C₁₀₇	#41	1	2	yes	—
99	C₂×C₈×C₁₀₇	C₂⁴	1	1	yes	characteristic
100	C₄⋊C₄×C₁₀₇	—	2	1	no	—
101	C₄⋊C₄×C₁₀₇	—	2	1	no	—
102	C₄⋊C₄×C₁₀₇	—	2	1	no	—
103	C₄⋊C₄×C₁₀₇	—	2	2	no	—
104	C₄⋊C₄×C₁₀₇	—	2	1	no	—
105	C₄⋊C₄×C₁₀₇	—	4	1	no	—
106	C₄⋊C₄×C₁₀₇	—	4	2	no	—
107	C₄⋊C₄×C₁₀₇	—	4	2	no	—
108	C₄⋊C₄×C₁₀₇	—	4	2	no	—
109	C₄⋊C₄×C₁₀₇	D₈	1	1	yes	characteristic
110	C₄⋊C₄×C₁₀₇	D₈	1	1	yes	characteristic
111	C₂²⋊C₄×C₁₀₇	—	4	1	no	—
112	C₂²⋊C₄×C₁₀₇	—	4	1	no	—
113	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
114	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
115	C₂²⋊C₄×C₁₀₇	D₈	1	2	yes	—
116	C₄²×C₁₀₇	—	4	1	no	—
117	C₄²×C₁₀₇	—	4	1	no	—
118	C₄²×C₁₀₇	C₂×D₄	1	2	yes	—
119	C₁₆×C₁₀₇	—	2	1	no	—
120	C₁₆×C₁₀₇	—	2	1	no	—
121	C₁₆×C₁₀₇	—	2	2	no	—
122	C₂³×C₁₀₇	—	4	2	no	—
123	C₂³×C₁₀₇	—	4	4	no	—
124	C₂³×C₁₀₇	—	16	1	no	—
125	C₂³×C₁₀₇	—	16	1	no	—
126	C₂³×C₁₀₇	C₂×D₈	1	1	yes	characteristic
127	Q₈×C₁₀₇	—	16	2	no	—
128	D₄×C₁₀₇	—	2	4	no	—
129	D₄×C₁₀₇	—	4	2	no	—
130	D₄×C₁₀₇	—	4	4	no	—
131	C₂×C₄×C₁₀₇	—	4	1	no	—
132	C₂×C₄×C₁₀₇	—	4	1	no	—
133	C₂×C₄×C₁₀₇	—	4	1	no	—
134	C₂×C₄×C₁₀₇	—	4	1	no	—
135	C₂×C₄×C₁₀₇	—	4	2	no	—
136	C₂×C₄×C₁₀₇	—	16	2	no	—
137	C₂×C₄×C₁₀₇	—	16	2	no	—
138	C₂×C₄×C₁₀₇	—	16	1	no	—
139	C₂×C₄×C₁₀₇	C₂²⋊Q₈	1	2	yes	—
140	C₂×C₄×C₁₀₇	C₂×D₈	1	2	yes	—
141	C₂×C₄×C₁₀₇	C₂×D₈	1	2	yes	—
142	C₂×C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
143	C₂×C₄×C₁₀₇	#137	1	2	yes	—
144	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
145	C₈×C₁₀₇	—	2	2	no	—
146	C₈×C₁₀₇	C₂²⋊Q₈	1	2	yes	—
147	C₈×C₁₀₇	C₂²×Q₈	1	1	yes	characteristic
148	C₈×C₁₀₇	C₂×#41	1	1	yes	characteristic
149	C₂²×C₁₀₇	—	2	1	no	—
150	C₂²×C₁₀₇	—	2	1	no	—
151	C₂²×C₁₀₇	—	4	4	no	—
152	C₂²×C₁₀₇	—	8	2	no	—
153	C₂²×C₁₀₇	—	8	2	no	—
154	C₂²×C₁₀₇	—	16	4	no	—
155	C₂²×C₁₀₇	#474	1	2	yes	—
156	C₂²×C₁₀₇	C₂²×D₈	1	1	yes	characteristic
157	C₄×C₁₀₇	—	2	2	no	—
158	C₄×C₁₀₇	—	2	2	no	—
159	C₄×C₁₀₇	—	8	1	no	—
160	C₄×C₁₀₇	—	8	2	no	—
161	C₄×C₁₀₇	—	8	1	no	—
162	C₄×C₁₀₇	—	8	1	no	—
163	C₄×C₁₀₇	—	8	1	no	—
164	C₄×C₁₀₇	#474	1	2	yes	—
165	C₄×C₁₀₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
166	C₄×C₁₀₇	C₂×#137	1	1	yes	characteristic
167	#33631	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂×C₁₀₇	—	2	2	no	—
169	C₂×C₁₀₇	—	8	4	no	—
170	C₂×C₁₀₇	C₂×#474	1	1	yes	characteristic
171	C₂×C₁₀₇	#3415	1	1	yes	characteristic
172	C₂×C₁₀₇	#3416	1	1	yes	characteristic
173	#3164	C₂×C₁₀₇	1	1	yes	characteristic, complemented
174	#2948	C₂×C₁₀₇	1	1	yes	characteristic
175	#2228	C₂×C₁₀₇	1	2	yes	complemented
176	#2228	C₂×C₁₀₇	1	2	yes	complemented
177	#2226	C₂×C₁₀₇	1	2	yes	complemented
178	#2224	C₂×C₁₀₇	1	2	yes	complemented
179	#2159	C₂×C₁₀₇	1	1	yes	characteristic, complemented
180	#2158	C₂×C₁₀₇	1	1	yes	characteristic, complemented
181	#2151	C₂×C₁₀₇	1	1	yes	characteristic, complemented
182	#2140	C₂×C₁₀₇	1	1	yes	characteristic
183	C₂×#357	C₂×C₁₀₇	1	1	yes	characteristic
184	C₁₀₇	#33631	1	1	yes	characteristic, direct product factor, Sylow
185	C₂²×D₈	C₂²×C₁₀₇	1	1	yes	characteristic
186	#544	—	2	1	no	—
187	#518	—	2	1	no	—
188	C₂×M₃₂	C₂²×C₁₀₇	1	1	yes	characteristic
189	C₂²×C₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
190	#501	—	2	2	no	—
191	#500	C₂²×C₁₀₇	1	2	yes	complemented
192	#499	C₂²×C₁₀₇	1	2	yes	complemented
193	#442	—	2	2	no	—
194	C₄×D₈	C₂²×C₁₀₇	1	2	yes	—
195	C₄×D₈	C₂²×C₁₀₇	1	2	yes	—
196	#428	—	2	1	no	—
197	#427	C₂²×C₁₀₇	1	1	yes	characteristic
198	#427	C₂²×C₁₀₇	1	1	yes	characteristic
199	C₂×#107	C₂²×C₁₀₇	1	1	yes	characteristic
200	#418	—	2	1	no	—
201	#405	C₂²×C₁₀₇	1	1	yes	characteristic
202	#367	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
203	#367	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
204	#367	C₂²×C₁₀₇	1	2	yes	complemented
205	#366	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
206	#366	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
207	#366	C₂²×C₁₀₇	1	2	yes	complemented
208	C₄⋊C₁₆	C₂²×C₁₀₇	1	2	yes	complemented
209	C₄⋊C₁₆	C₂²×C₁₀₇	1	2	yes	complemented
210	#357	C₂²×C₁₀₇	1	2	yes	—
211	#357	C₂²×C₁₀₇	1	2	yes	—
212	#357	C₂²×C₁₀₇	1	2	yes	—
213	#357	C₂²×C₁₀₇	1	2	yes	—
214	C₂²×D₄	—	2	1	no	—
215	C₂×D₈	—	2	1	no	—
216	C₂×D₈	—	2	2	no	—
217	C₂×D₈	Q₈×C₁₀₇	1	4	yes	complemented
218	C₂×D₈	C₂³×C₁₀₇	1	2	yes	—
219	C₂×M₁₆	D₄×C₁₀₇	1	1	yes	characteristic
220	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
221	C₄⋊Q₈	—	2	2	no	—
222	C₄⋊Q₈	—	4	1	no	—
223	#125	—	2	2	no	—
224	#125	—	4	1	no	—
225	C₂²⋊Q₈	—	4	2	no	—
226	C₄×D₄	—	2	2	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	—	4	1	no	—
229	C₄×D₄	—	4	1	no	—
230	#117	—	2	1	no	—
231	#117	—	2	1	no	—
232	#117	D₄×C₁₀₇	1	1	yes	characteristic
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₂²⋊C₄	—	4	2	no	—
235	M₃₂	—	2	2	no	—
236	C₂×C₁₆	—	2	2	no	—
237	C₂×C₁₆	C₂³×C₁₀₇	1	1	yes	characteristic
238	C₂×C₁₆	C₂³×C₁₀₇	1	2	yes	—
239	C₂×C₁₆	C₂³×C₁₀₇	1	1	yes	characteristic
240	#107	—	2	1	no	—
241	#107	—	2	2	no	—
242	#107	C₂³×C₁₀₇	1	2	yes	—
243	#107	C₂³×C₁₀₇	1	1	yes	characteristic
244	#107	C₂³×C₁₀₇	1	1	yes	characteristic
245	#107	C₂³×C₁₀₇	1	1	yes	characteristic
246	#107	C₂³×C₁₀₇	1	1	yes	characteristic
247	#106	—	2	1	no	—
248	#106	—	2	1	no	—
249	#106	—	2	2	no	—
250	#102	—	2	2	no	—
251	#102	—	2	2	no	—
252	#97	D₄×C₁₀₇	1	2	yes	—
253	C₄×C₈	C₂³×C₁₀₇	1	2	yes	—
254	C₂⁴	—	4	1	no	—
255	C₂×Q₈	—	4	2	no	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	4	1	no	—
259	C₂×D₄	—	4	2	no	—
260	C₂²×C₄	—	4	1	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
264	D₈	—	2	4	no	—
265	D₈	—	2	2	no	—
266	D₈	C₂×Q₈×C₁₀₇	1	4	yes	—
267	M₁₆	—	2	2	no	—
268	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
269	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
270	C₂×C₈	C₂×Q₈×C₁₀₇	1	2	yes	—
271	C₂×C₈	#41×C₁₀₇	1	2	yes	—
272	C₂×C₈	C₂⁴×C₁₀₇	1	1	yes	characteristic
273	C₄⋊C₄	—	2	1	no	—
274	C₄⋊C₄	—	2	1	no	—
275	C₄⋊C₄	—	2	1	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	1	no	—
278	C₄⋊C₄	—	4	1	no	—
279	C₄⋊C₄	—	4	2	no	—
280	C₄⋊C₄	—	4	2	no	—
281	C₄⋊C₄	—	4	2	no	—
282	C₄⋊C₄	D₈×C₁₀₇	1	1	yes	characteristic
283	C₄⋊C₄	D₈×C₁₀₇	1	1	yes	characteristic
284	C₂²⋊C₄	—	4	1	no	—
285	C₂²⋊C₄	—	4	1	no	—
286	C₂²⋊C₄	—	4	2	no	—
287	C₂²⋊C₄	—	4	2	no	—
288	C₂²⋊C₄	D₈×C₁₀₇	1	2	yes	—
289	C₄²	—	4	1	no	—
290	C₄²	—	4	1	no	—
291	C₄²	C₂×D₄×C₁₀₇	1	2	yes	—
292	C₁₆	—	2	1	no	—
293	C₁₆	—	2	1	no	—
294	C₁₆	—	2	2	no	—
295	C₂³	—	4	2	no	—
296	C₂³	—	4	4	no	—
297	C₂³	—	16	1	no	—
298	C₂³	—	16	1	no	—
299	C₂³	C₂×D₈×C₁₀₇	1	1	yes	characteristic
300	Q₈	—	16	2	no	—
301	D₄	—	2	4	no	—
302	D₄	—	4	4	no	—
303	D₄	—	4	2	no	—
304	C₂×C₄	—	4	1	no	—
305	C₂×C₄	—	4	1	no	—
306	C₂×C₄	—	4	1	no	—
307	C₂×C₄	—	4	1	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	16	2	no	—
310	C₂×C₄	—	16	2	no	—
311	C₂×C₄	—	16	1	no	—
312	C₂×C₄	C₂²⋊Q₈×C₁₀₇	1	2	yes	—
313	C₂×C₄	C₂×D₈×C₁₀₇	1	2	yes	—
314	C₂×C₄	C₂×D₈×C₁₀₇	1	2	yes	—
315	C₂×C₄	C₂×D₈×C₁₀₇	1	1	yes	characteristic
316	C₂×C₄	#137×C₁₀₇	1	2	yes	—
317	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
318	C₈	—	2	2	no	—
319	C₈	C₂²⋊Q₈×C₁₀₇	1	2	yes	—
320	C₈	C₂²×Q₈×C₁₀₇	1	1	yes	characteristic
321	C₈	C₂×#41×C₁₀₇	1	1	yes	characteristic
322	C₂²	—	2	1	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	4	4	no	—
325	C₂²	—	8	2	no	—
326	C₂²	—	8	2	no	—
327	C₂²	—	16	4	no	—
328	C₂²	#474×C₁₀₇	1	2	yes	—
329	C₂²	C₂²×D₈×C₁₀₇	1	1	yes	characteristic
330	C₄	—	2	2	no	—
331	C₄	—	2	2	no	—
332	C₄	—	8	1	no	—
333	C₄	—	8	2	no	—
334	C₄	—	8	1	no	—
335	C₄	—	8	1	no	—
336	C₄	—	8	1	no	—
337	C₄	#474×C₁₀₇	1	2	yes	—
338	C₄	C₂×C₂²⋊Q₈×C₁₀₇	1	1	yes	characteristic
339	C₄	C₂×#137×C₁₀₇	1	1	yes	characteristic
340	C₂	—	2	2	no	—
341	C₂	—	8	4	no	—
342	C₂	C₂×#474×C₁₀₇	1	1	yes	characteristic
343	C₂	C₁₀₇×#3415	1	1	yes	characteristic
344	C₂	C₁₀₇×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₀₇
prime radical	C₂²×D₈×C₁₀₇	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ #117×C₁₀₇ ◁ #405×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₀₇×#3164	C₂	semidirect
3. C₁₀₇×#2228	C₂	semidirect
4. C₁₀₇×#2228	C₂	semidirect
5. C₁₀₇×#2226	C₂	semidirect
6. C₁₀₇×#2224	C₂	semidirect
7. C₁₀₇×#2159	C₂	semidirect
8. C₁₀₇×#2158	C₂	semidirect
9. C₁₀₇×#2151	C₂	semidirect
18. #500×C₁₀₇	C₂²	semidirect
19. #499×C₁₀₇	C₂²	semidirect
29. #367×C₁₀₇	C₂²	semidirect
30. #367×C₁₀₇	C₂²	semidirect
31. #367×C₁₀₇	C₂²	semidirect
32. #366×C₁₀₇	C₂²	semidirect
33. #366×C₁₀₇	C₂²	semidirect
34. #366×C₁₀₇	C₂²	semidirect
35. C₄⋊C₁₆×C₁₀₇	C₂²	semidirect
36. C₄⋊C₁₆×C₁₀₇	C₂²	semidirect
44. C₂×D₈×C₁₀₇	Q₈	semidirect
167. #33631	C₁₀₇	direct (N × H)
173. #3164	C₂×C₁₀₇	semidirect
175. #2228	C₂×C₁₀₇	semidirect
176. #2228	C₂×C₁₀₇	semidirect
177. #2226	C₂×C₁₀₇	semidirect
178. #2224	C₂×C₁₀₇	semidirect
179. #2159	C₂×C₁₀₇	semidirect
180. #2158	C₂×C₁₀₇	semidirect
181. #2151	C₂×C₁₀₇	semidirect
184. C₁₀₇	#33631	direct (N × H)
191. #500	C₂²×C₁₀₇	semidirect
192. #499	C₂²×C₁₀₇	semidirect
202. #367	C₂²×C₁₀₇	semidirect
203. #367	C₂²×C₁₀₇	semidirect
204. #367	C₂²×C₁₀₇	semidirect
205. #366	C₂²×C₁₀₇	semidirect
206. #366	C₂²×C₁₀₇	semidirect
207. #366	C₂²×C₁₀₇	semidirect
208. C₄⋊C₁₆	C₂²×C₁₀₇	semidirect
209. C₄⋊C₁₆	C₂²×C₁₀₇	semidirect
217. C₂×D₈	Q₈×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₇×#3164	2
C₁₀₇×#2948	2
C₁₀₇×#2228	2
C₁₀₇×#2226	2
C₁₀₇×#2224	2
C₁₀₇×#2159	2
C₁₀₇×#2158	2
C₁₀₇×#2151	2
C₁₀₇×#2140	2
C₂×#357×C₁₀₇	2
#33631	107

Subgroups — C107×#33631 #41059595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#33631 #41059595