Subgroups — #107×D₁₈₈ #26234397

Order 12032.

1126 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#107×D₄₇	C₂	1	2	yes	maximal, complemented
3	C₄⋊C₄×D₁₈₈	C₂	1	2	yes	maximal
4	#20244146	C₂	1	2	yes	maximal, complemented
5	#20243577	C₂	1	4	yes	maximal, complemented
6	#20243548	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243414	C₂	1	2	yes	maximal, complemented
8	C₄×#107×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
10	C₂×C₄×D₁₈₈	—	2	2	no	—
11	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×D₄₇	C₂²	1	4	yes	—
13	C₈×D₁₈₈	C₄	1	8	yes	complemented
14	C₂×#13093958	C₂²	1	2	yes	—
15	C₂×#13093958	C₂²	1	2	yes	—
16	C₂×#13093957	C₂²	1	4	yes	—
17	#107×D₄₇	—	2	8	no	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
20	#15689021	—	2	2	no	—
21	#15688997	—	2	4	no	—
22	#15688993	C₂²	1	2	yes	—
23	#15688980	C₂²	1	4	yes	—
24	#15688885	C₂²	1	4	yes	—
25	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
29	C₄₇×#340	C₂²	1	2	yes	—
30	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₄₇	—	2	4	no	—
32	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
33	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
34	C₂×C₈×D₄₇	—	2	4	no	—
35	C₂×C₈×D₄₇	—	2	4	no	—
36	C₂×C₈×D₄₇	C₂×C₄	1	8	yes	complemented
37	C₄×D₁₈₈	—	4	8	no	—
38	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
39	C₄×D₁₈₈	Q₈	1	4	yes	—
40	C₂×C₄⋊Dic₄₇	—	2	2	no	—
41	C₂×C₄⋊Dic₄₇	—	2	2	no	—
42	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
43	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
44	C₂×Dic₄₇⋊C₄	—	2	4	no	—
45	C₄⋊C₄×D₄₇	—	2	8	no	—
46	C₄⋊C₄×D₄₇	—	4	4	no	—
47	C₂×(C₂×D₄₇)⋊C₄	—	2	4	no	—
48	C₂×(C₂×D₄₇)⋊C₄	D₄	1	2	yes	—
49	#13093958	—	2	4	no	—
50	#13093958	—	4	2	no	—
51	#13093957	—	2	8	no	—
52	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
53	(C₂×D₄₇)⋊C₈	C₂×C₄	1	8	yes	complemented
54	C₄₇⋊#95	—	2	4	no	—
55	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
59	C₂×C₄²×C₄₇	—	2	2	no	—
60	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
61	#107×C₄₇	—	2	2	no	—
62	#107×C₄₇	D₄	1	4	yes	complemented
63	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
64	#95×C₄₇	—	2	2	no	—
65	C₂³×D₄₇	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
71	C₂²×Dic₄₇	—	2	4	no	—
72	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
73	C₂×D₁₈₈	C₄⋊C₄	1	4	yes	—
74	C₂×D₁₈₈	D₈	1	4	yes	—
75	C₂×D₁₈₈	Q₁₆	1	4	yes	—
76	C₂×C₄×D₄₇	—	2	2	no	—
77	C₂×C₄×D₄₇	—	2	2	no	—
78	C₂×C₄×D₄₇	—	2	2	no	—
79	C₂×C₄×D₄₇	—	2	2	no	—
80	C₂×C₄×D₄₇	—	4	8	no	—
81	C₂×C₄×D₄₇	—	4	8	no	—
82	C₂×C₄×D₄₇	—	8	4	no	—
83	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
84	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
85	C₂×C₈×C₄₇	—	2	1	no	—
86	C₂×C₈×C₄₇	—	2	1	no	—
87	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
88	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
89	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
90	C₂×C₈×C₄₇	#41	1	2	yes	—
91	C₄⋊C₄×C₄₇	—	2	2	no	—
92	C₄⋊C₄×C₄₇	—	2	2	no	—
93	C₄⋊C₄×C₄₇	—	2	2	no	—
94	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
95	C₄²×C₄₇	—	4	4	no	—
96	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
97	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
98	(C₂×D₄₇)⋊C₄	—	4	8	no	—
99	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	8	yes	—
100	C₄⋊Dic₄₇	—	2	4	no	—
101	C₄⋊Dic₄₇	—	2	4	no	—
102	C₄⋊Dic₄₇	—	4	4	no	—
103	C₄⋊Dic₄₇	—	8	2	no	—
104	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
105	Dic₄₇⋊C₄	—	4	8	no	—
106	C₂×C₄₇⋊C₈	—	2	2	no	—
107	C₂×C₄₇⋊C₈	—	2	2	no	—
108	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
109	C₈×D₄₇	—	2	16	no	—
110	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
111	C₂²×D₄₇	—	2	2	no	—
112	C₂²×D₄₇	—	2	2	no	—
113	C₂²×D₄₇	—	2	2	no	—
114	C₂²×D₄₇	—	2	2	no	—
115	C₂²×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
116	C₂²×D₄₇	C₂×D₈	1	4	yes	—
117	C₂²×D₄₇	C₂×Q₁₆	1	4	yes	—
118	C₂×C₄×C₄₇	—	2	1	no	—
119	C₂×C₄×C₄₇	—	2	1	no	—
120	C₂×C₄×C₄₇	—	2	4	no	—
121	C₂×C₄×C₄₇	—	4	2	no	—
122	C₂×C₄×C₄₇	—	4	2	no	—
123	C₂×C₄×C₄₇	—	4	2	no	—
124	C₂×C₄×C₄₇	—	4	2	no	—
125	C₂×C₄×C₄₇	—	4	2	no	—
126	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
129	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
130	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
131	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
133	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
134	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
135	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
136	C₂×Dic₄₇	—	2	2	no	—
137	C₂×Dic₄₇	—	2	2	no	—
138	C₂×Dic₄₇	—	4	4	no	—
139	C₂×Dic₄₇	—	4	4	no	—
140	C₂×Dic₄₇	—	4	4	no	—
141	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
142	D₁₈₈	#107	1	16	yes	direct product factor
143	C₄×D₄₇	—	2	4	no	—
144	C₄×D₄₇	—	2	4	no	—
145	C₄×D₄₇	—	2	4	no	—
146	C₄×D₄₇	—	2	4	no	—
147	C₄×D₄₇	—	8	16	no	—
148	C₈×C₄₇	—	2	2	no	—
149	C₈×C₄₇	C₄×D₄	1	4	yes	complemented
150	C₄₇⋊C₈	—	2	4	no	—
151	D₄×#107	—	47	1	no	maximal, Sylow
152	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
153	C₂²×C₄₇	D₄²	1	1	yes	characteristic
154	C₂²×C₄₇	#547	1	1	yes	characteristic
155	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
156	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
157	C₂²×C₄₇	#576	1	1	yes	characteristic
158	C₂²×C₄₇	#578	1	1	yes	characteristic
159	C₂×D₄₇	—	2	4	no	—
160	C₂×D₄₇	—	2	4	no	—
161	C₂×D₄₇	—	2	4	no	—
162	C₂×D₄₇	—	2	4	no	—
163	C₂×D₄₇	—	2	4	no	—
164	C₂×D₄₇	—	2	4	no	—
165	C₂×D₄₇	C₂×#107	1	8	yes	complemented
166	C₄×C₄₇	—	2	2	no	—
167	C₄×C₄₇	—	4	4	no	—
168	C₄×C₄₇	—	8	2	no	—
169	C₄×C₄₇	C₂×#107	1	4	yes	complemented
170	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
171	C₄×C₄₇	#520	1	1	yes	characteristic
172	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
173	C₄×C₄₇	#554	1	1	yes	characteristic
174	Dic₄₇	—	2	4	no	—
175	Dic₄₇	—	8	4	no	—
176	C₂×C₈×D₄	—	47	1	no	—
177	C₂²×#107	—	47	2	no	—
178	D₄×C₄⋊C₄	—	47	2	no	—
179	#1947	—	47	2	no	—
180	#1852	—	47	4	no	—
181	#1845	—	47	1	no	—
182	#1808	—	47	2	no	—
183	C₄×#107	D₄₇	1	1	yes	characteristic, complemented
184	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄₇	C₂²×#107	1	1	yes	characteristic
186	C₂×C₄₇	#2913	1	1	yes	characteristic
187	C₂×C₄₇	D₄×D₈	1	1	yes	characteristic
188	C₂×C₄₇	D₄×Q₁₆	1	1	yes	characteristic
189	C₂×C₄₇	#3334	1	1	yes	characteristic
190	C₂×C₄₇	#3338	1	1	yes	characteristic
191	D₄₇	—	2	8	no	—
192	C₂³×C₈	—	47	2	no	—
193	C₂×C₄×D₄	—	47	1	no	—
194	C₂×C₄×D₄	—	94	2	no	—
195	C₂²×C₄⋊C₄	—	47	4	no	—
196	C₈×D₄	—	47	8	no	—
197	C₂×#107	—	47	2	no	—
198	C₂×#107	—	47	4	no	—
199	C₂×#107	—	47	2	no	—
200	C₂×#107	—	94	8	no	—
201	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
202	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
203	C₂×C₄⋊C₈	—	47	1	no	—
204	C₂×C₂²⋊C₈	—	47	2	no	—
205	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
206	#389	—	94	2	no	—
207	#385	—	94	4	no	—
208	#384	—	47	2	no	—
209	#380	—	47	4	no	—
210	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
211	#340	—	47	4	no	—
212	#340	C₂×D₄₇	1	2	yes	—
213	C₄₇	D₄×#107	1	1	yes	characteristic, complemented, Sylow
214	C₂²×D₄	—	47	1	no	—
215	C₂³×C₄	—	47	2	no	—
216	C₂³×C₄	—	94	4	no	—
217	C₂²×C₈	—	47	2	no	—
218	C₂²×C₈	—	47	8	no	—
219	C₂²×C₈	—	94	4	no	—
220	C₂²×C₈	—	94	4	no	—
221	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
222	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
223	C₄×D₄	—	47	4	no	—
224	C₄×D₄	—	47	4	no	—
225	C₄×D₄	—	188	8	no	—
226	C₂×C₄⋊C₄	—	47	1	no	—
227	C₂×C₄⋊C₄	—	47	4	no	—
228	C₂×C₄⋊C₄	—	94	8	no	—
229	C₂×C₄⋊C₄	—	94	2	no	—
230	C₂×C₄⋊C₄	—	94	4	no	—
231	C₂×C₄⋊C₄	—	94	2	no	—
232	C₂×C₄⋊C₄	—	188	4	no	—
233	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
234	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
235	C₂×C₂²⋊C₄	—	47	2	no	—
236	C₂×C₂²⋊C₄	—	94	4	no	—
237	C₂×C₄²	—	2	2	no	—
238	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
239	#107	—	2	2	no	—
240	#107	—	94	4	no	—
241	#107	—	94	8	no	—
242	#107	—	188	2	no	—
243	#107	D₁₈₈	1	4	yes	direct product factor
244	C₄⋊C₈	—	47	4	no	—
245	C₂²⋊C₈	—	47	8	no	—
246	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
247	#95	—	2	2	no	—
248	#95	—	94	4	no	—
249	C₂⁴	—	47	2	no	—
250	C₂×D₄	—	47	4	no	—
251	C₂×D₄	—	47	4	no	—
252	C₂×D₄	—	47	4	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	47	2	no	—
256	C₂²×C₄	—	47	4	no	—
257	C₂²×C₄	—	47	4	no	—
258	C₂²×C₄	—	94	2	no	—
259	C₂²×C₄	—	94	2	no	—
260	C₂²×C₄	—	94	2	no	—
261	C₂²×C₄	—	94	2	no	—
262	C₂²×C₄	—	94	4	no	—
263	C₂²×C₄	—	376	4	no	—
264	C₂²×C₄	—	188	8	no	—
265	C₂²×C₄	—	188	8	no	—
266	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
267	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
268	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
269	C₂×C₈	—	2	1	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	47	4	no	—
272	C₂×C₈	—	94	2	no	—
273	C₂×C₈	—	94	2	no	—
274	C₂×C₈	—	94	16	no	—
275	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
276	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
277	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
278	C₂×C₈	#10625350	1	2	yes	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	47	4	no	—
283	C₄⋊C₄	—	94	4	no	—
284	C₄⋊C₄	—	94	4	no	—
285	C₄⋊C₄	—	376	2	no	—
286	C₄⋊C₄	—	188	8	no	—
287	C₄⋊C₄	—	188	4	no	—
288	C₄⋊C₄	C₂×D₁₈₈	1	4	yes	—
289	C₂²⋊C₄	—	47	8	no	—
290	C₂²⋊C₄	—	188	8	no	—
291	C₄²	—	4	4	no	—
292	C₄²	C₂×C₄×D₄₇	1	2	yes	—
293	C₄²	Q₈×D₄₇	1	2	yes	—
294	C₂³	—	47	4	no	—
295	C₂³	—	47	4	no	—
296	C₂³	—	47	4	no	—
297	C₂³	—	94	2	no	—
298	C₂³	—	94	2	no	—
299	C₂³	—	94	2	no	—
300	C₂³	—	94	2	no	—
301	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
302	D₄	—	47	16	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	47	4	no	—
312	C₂×C₄	—	94	2	no	—
313	C₂×C₄	—	94	2	no	—
314	C₂×C₄	—	94	4	no	—
315	C₂×C₄	—	94	4	no	—
316	C₂×C₄	—	94	4	no	—
317	C₂×C₄	—	94	4	no	—
318	C₂×C₄	—	376	16	no	—
319	C₂×C₄	—	188	4	no	—
320	C₂×C₄	—	188	4	no	—
321	C₂×C₄	—	188	4	no	—
322	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
323	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
324	C₂×C₄	D₈×D₄₇	1	2	yes	—
325	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
326	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
327	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
328	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
329	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
330	C₂×C₄	#13094070	1	1	yes	characteristic
331	C₂×C₄	#13094071	1	1	yes	characteristic
332	C₈	—	2	2	no	—
333	C₈	—	94	4	no	—
334	C₈	C₄×D₁₈₈	1	4	yes	complemented
335	C₂²	—	47	8	no	—
336	C₂²	—	94	4	no	—
337	C₂²	—	94	4	no	—
338	C₂²	—	94	4	no	—
339	C₂²	—	94	4	no	—
340	C₂²	—	94	4	no	—
341	C₂²	—	94	4	no	—
342	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
343	C₂²	D₄×D₁₈₈	1	1	yes	characteristic
344	C₂²	#15689778	1	1	yes	characteristic
345	C₂²	C₂×D₈×D₄₇	1	1	yes	characteristic
346	C₂²	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
347	C₂²	#15689925	1	1	yes	characteristic
348	C₂²	#15689937	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	4	4	no	—
351	C₄	—	8	2	no	—
352	C₄	—	94	4	no	—
353	C₄	—	376	4	no	—
354	C₄	#107×D₄₇	1	4	yes	complemented
355	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
356	C₄	#15689603	1	1	yes	characteristic
357	C₄	Q₈×D₁₈₈	1	1	yes	characteristic
358	C₄	#15689833	1	1	yes	characteristic
359	C₂	—	94	8	no	—
360	C₂	C₄⋊C₄×D₁₈₈	1	1	yes	characteristic
361	C₂	C₂×#107×D₄₇	1	1	yes	characteristic
362	C₂	#20251985	1	1	yes	characteristic
363	C₂	D₈×D₁₈₈	1	1	yes	characteristic
364	C₂	Q₁₆×D₁₈₈	1	1	yes	characteristic
365	C₂	#20255737	1	1	yes	characteristic
366	C₂	#20255782	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×#107×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#107	D₄₇
hypocenter	C₄₇	D₄×#107
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
2. C₂×#107×D₄₇	C₂	semidirect
4. #20244146	C₂	semidirect
5. #20243577	C₂	semidirect
6. #20243548	C₂	semidirect
7. #20243414	C₂	semidirect
8. C₄×#107×C₄₇	C₂	semidirect
13. C₈×D₁₈₈	C₄	semidirect
36. C₂×C₈×D₄₇	C₂×C₄	semidirect
52. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
53. (C₂×D₄₇)⋊C₈	C₂×C₄	semidirect
62. #107×C₄₇	D₄	semidirect
63. C₄×C₈×C₄₇	C₂×C₄	semidirect
142. D₁₈₈	#107	direct (N × H)
149. C₈×C₄₇	C₄×D₄	semidirect
165. C₂×D₄₇	C₂×#107	semidirect
169. C₄×C₄₇	C₂×#107	semidirect
183. C₄×#107	D₄₇	semidirect
213. C₄₇	D₄×#107	semidirect
243. #107	D₁₈₈	direct (N × H)
246. C₄×C₈	C₄×D₄₇	semidirect
334. C₈	C₄×D₁₈₈	semidirect
354. C₄	#107×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₁₈₈	2
C₂×#107×D₄₇	2
C₄⋊C₄×D₁₈₈	2
#20244146	2
#20243577	2
#20243548	2
#20243414	2
C₄×#107×C₄₇	2
D₄×#107	47

Subgroups — #107×D188 #26234397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #107×D₁₈₈ #26234397