Subgroups — #26234760

Order 12032.

846 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689239	C₂	1	1	yes	maximal, characteristic
2	#20252265	C₂	1	1	yes	maximal, characteristic
3	#20252262	C₂	1	1	yes	maximal, characteristic
4	#20251982	C₂	1	2	yes	maximal, complemented
5	#20244174	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243624	C₂	1	2	yes	maximal, complemented
7	#20243618	C₂	1	2	yes	maximal, complemented
8	#20243551	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243446	C₂	1	2	yes	maximal, complemented
10	#20243268	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1952	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₂²	1	1	yes	characteristic
13	C₂×#13094032	C₂²	1	2	yes	—
14	#15689604	C₂²	1	2	yes	—
15	#15689603	C₂²	1	2	yes	—
16	#15689239	C₄	1	8	yes	complemented
17	#15689225	—	2	2	no	—
18	#15689222	—	2	2	no	—
19	C₄×Dic₁₈₈	—	2	1	no	—
20	#15689217	—	2	1	no	—
21	C₄×D₃₇₆	—	2	1	no	—
22	#15689205	—	2	1	no	—
23	C₂×#13093959	C₂²	1	1	yes	characteristic
24	#15689165	C₂²	1	2	yes	—
25	#15689164	—	2	2	no	—
26	#15689162	—	2	2	no	—
27	#15689160	—	2	2	no	—
28	#15689159	C₂²	1	1	yes	characteristic
29	C₂×#13093958	C₂²	1	1	yes	characteristic
30	C₂×#13093955	C₂²	1	2	yes	—
31	#106×D₄₇	—	2	2	no	—
32	C₂×#13093950	C₂²	1	2	yes	—
33	#15689125	C₂²	1	2	yes	—
34	#15689122	C₂²	1	2	yes	—
35	#15689078	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
37	#15688988	C₂²	1	2	yes	—
38	#15688891	C₂²	1	2	yes	—
39	#15688884	C₂²	1	1	yes	characteristic
40	#15688882	C₂²	1	1	yes	characteristic
41	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#428	C₂²	1	2	yes	—
43	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#405	C₂²	1	1	yes	characteristic
45	C₄₇×#343	C₂²	1	2	yes	—
46	C₂×#10625350	C₂³	1	2	yes	—
47	#13094046	C₂×C₄	1	4	yes	—
48	#13094046	Q₈	1	4	yes	—
49	C₂×Dic₁₈₈	D₄	1	1	yes	characteristic
50	C₂×#10625325	D₄	1	2	yes	—
51	C₂×D₃₇₆	D₄	1	1	yes	characteristic
52	#13094032	—	2	4	no	—
53	#13094032	C₂×C₄	1	8	yes	complemented
54	C₂×#10625329	C₂³	1	1	yes	characteristic
55	C₂×#10625324	—	2	2	no	—
56	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₄₇	—	2	2	no	—
58	C₄×Dic₉₄	—	2	2	no	—
59	#13093989	—	2	2	no	—
60	C₄×D₁₈₈	—	2	2	no	—
61	#13093986	—	2	2	no	—
62	C₄×C₂²⋊D₄₇	—	4	2	no	—
63	(C₂²⋊D₄₇)⋊C₄	—	4	2	no	—
64	#13093983	C₂³	1	1	yes	characteristic
65	#13093982	—	2	2	no	—
66	#13093982	—	2	2	no	—
67	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
68	C₄⋊C₄×D₄₇	—	2	2	no	—
69	C₄⋊C₄×D₄₇	—	2	2	no	—
70	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
71	#13093959	—	2	2	no	—
72	#13093958	—	2	1	no	—
73	#13093958	—	2	1	no	—
74	#13093958	—	2	2	no	—
75	#13093957	D₄	1	1	yes	characteristic
76	#13093957	D₄	1	1	yes	characteristic
77	#13093956	—	2	2	no	—
78	#13093955	—	2	2	no	—
79	#13093955	—	2	2	no	—
80	#13093955	D₄	1	1	yes	characteristic
81	#13093955	D₄	1	1	yes	characteristic
82	#13093950	C₂×C₄	1	8	yes	complemented
83	#13093949	—	2	2	no	—
84	#13093947	—	2	2	no	—
85	#13093946	—	2	2	no	—
86	#13093944	—	2	2	no	—
87	#13093934	—	2	1	no	—
88	C₈×Dic₄₇	—	2	1	no	—
89	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
90	C₄₇⋊#95	—	4	2	no	—
91	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
93	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	#117×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
96	#108×C₄₇	C₂×C₄	1	4	yes	complemented
97	#107×C₄₇	—	2	1	no	—
98	#107×C₄₇	—	2	1	no	—
99	#107×C₄₇	—	2	2	no	—
100	#106×C₄₇	—	2	2	no	—
101	#97×C₄₇	—	2	1	no	—
102	C₄×C₈×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂×C₂²⋊D₄₇	—	2	2	no	—
106	C₂²×Dic₄₇	—	2	1	no	—
107	C₂²×Dic₄₇	—	2	2	no	—
108	#10625350	—	2	2	no	—
109	#10625350	—	2	2	no	—
110	#10625350	C₂²×C₄	1	4	yes	—
111	#10625350	C₂×Q₈	1	4	yes	—
112	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
113	C₂×C₄×D₄₇	—	2	2	no	—
114	C₂×C₄×D₄₇	—	4	2	no	—
115	C₂×C₄×D₄₇	—	4	2	no	—
116	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
117	M₁₆×C₄₇	—	2	2	no	—
118	M₁₆×C₄₇	—	2	1	no	—
119	M₁₆×C₄₇	—	2	1	no	—
120	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
127	C₄⋊C₄×C₄₇	—	2	2	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²⋊C₄×C₄₇	—	2	1	no	—
132	C₄²×C₄₇	—	2	1	no	—
133	C₂²⋊Dic₄₇	—	2	1	no	—
134	(C₂×D₄₇)⋊C₄	—	4	2	no	—
135	(C₂×D₄₇)⋊C₄	—	4	2	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
139	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
140	Dic₄₇⋊C₄	—	4	2	no	—
141	Dic₄₇⋊C₄	—	4	2	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	4	2	no	—
145	C₄×Dic₄₇	—	4	2	no	—
146	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
147	#10625329	—	2	1	no	—
148	#10625329	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
151	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄₇⋊C₈	#41	1	2	yes	—
154	Dic₁₈₈	C₄⋊C₄	1	4	yes	—
155	D₃₇₆	C₄⋊C₄	1	4	yes	—
156	#10625325	C₄⋊C₄	1	8	yes	—
157	#10625324	—	2	8	no	—
158	C₈×D₄₇	—	2	8	no	—
159	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
160	C₂²×D₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	8	2	no	—
165	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
171	C₂²⋊D₄₇	—	2	4	no	—
172	C₂²⋊D₄₇	—	2	4	no	—
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	2	1	no	—
176	C₂×Dic₄₇	—	2	1	no	—
177	C₂×Dic₄₇	—	4	1	no	—
178	C₂×Dic₄₇	—	4	1	no	—
179	C₂×Dic₄₇	—	4	2	no	—
180	C₂×Dic₄₇	—	8	2	no	—
181	D₁₈₈	—	2	2	no	—
182	D₁₈₈	C₂×C₄⋊C₄	1	4	yes	—
183	C₄×D₄₇	—	2	4	no	—
184	C₄×D₄₇	—	2	4	no	—
185	C₄×D₄₇	—	16	2	no	—
186	C₄×D₄₇	—	16	2	no	—
187	Dic₉₄	—	2	2	no	—
188	Dic₉₄	C₂×C₄⋊C₄	1	4	yes	—
189	C₈×C₄₇	—	2	4	no	—
190	C₈×C₄₇	—	4	1	no	—
191	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
192	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
193	C₄₇⋊C₈	—	4	1	no	—
194	C₄₇⋊C₈	C₄×D₄	1	2	yes	—
195	C₄₇⋊C₈	C₄×D₄	1	2	yes	—
196	#22690	—	47	1	no	maximal, Sylow
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	—	2	1	no	—
199	C₂²×C₄₇	#520	1	1	yes	characteristic
200	C₂²×C₄₇	D₄²	1	1	yes	characteristic
201	C₂²×C₄₇	#554	1	1	yes	characteristic
202	C₂×D₄₇	—	2	4	no	—
203	C₂×D₄₇	—	4	2	no	—
204	C₂×D₄₇	—	4	2	no	—
205	C₄×C₄₇	—	4	1	no	—
206	C₄×C₄₇	—	4	1	no	—
207	C₄×C₄₇	—	8	2	no	—
208	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
209	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
210	C₄×C₄₇	#547	1	1	yes	characteristic
211	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
212	Dic₄₇	—	2	4	no	—
213	Dic₄₇	—	4	2	no	—
214	Dic₄₇	—	4	1	no	—
215	Dic₄₇	—	4	1	no	—
216	Dic₄₇	—	8	2	no	—
217	C₂×#443	—	47	1	no	—
218	#2951	—	47	1	no	—
219	#2951	—	47	1	no	—
220	#2912	—	47	2	no	—
221	#1952	—	47	1	no	—
222	#1952	D₄₇	1	1	yes	characteristic, complemented
223	#1860	—	47	2	no	—
224	#1860	—	47	2	no	—
225	#1846	—	47	1	no	—
226	#1815	—	47	2	no	—
227	#1772	—	47	1	no	—
228	C₂×C₄₇	—	2	1	no	—
229	C₂×C₄₇	—	2	1	no	—
230	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
231	C₂×C₄₇	#3290	1	1	yes	characteristic
232	C₂×C₄₇	#3290	1	1	yes	characteristic
233	D₄₇	—	4	4	no	—
234	C₂×#135	—	47	1	no	—
235	C₂×#131	—	47	2	no	—
236	#520	—	47	2	no	—
237	#520	—	47	2	no	—
238	#443	—	47	8	no	—
239	#440	—	94	2	no	—
240	#440	—	94	2	no	—
241	C₄×Q₁₆	—	94	1	no	—
242	C₄×Q₁₆	—	94	1	no	—
243	C₄×D₈	—	94	1	no	—
244	C₄×D₈	—	94	1	no	—
245	C₂×#108	—	47	1	no	—
246	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
247	#428	—	47	2	no	—
248	#428	—	94	2	no	—
249	#428	—	94	2	no	—
250	#428	C₂×D₄₇	1	2	yes	—
251	#427	—	47	1	no	—
252	#427	—	94	2	no	—
253	C₂×#107	—	47	1	no	—
254	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
255	C₂×#106	—	47	2	no	—
256	C₂×#106	—	94	2	no	—
257	C₂×#104	—	47	2	no	—
258	#417	—	47	2	no	—
259	#417	—	47	2	no	—
260	#405	—	47	1	no	—
261	#405	C₂×D₄₇	1	1	yes	characteristic
262	C₂×C₄×C₈	—	47	1	no	—
263	#382	—	47	2	no	—
264	#343	—	47	2	no	—
265	#343	C₂×D₄₇	1	2	yes	—
266	#339	—	47	1	no	—
267	#339	—	47	1	no	—
268	C₄₇	#22690	1	1	yes	characteristic, complemented, Sylow
269	C₂×#41	—	47	2	no	—
270	#135	—	47	4	no	—
271	#135	—	47	4	no	—
272	C₂×Q₁₆	—	47	1	no	—
273	C₂×SD₁₆	—	47	2	no	—
274	C₂×D₈	—	47	1	no	—
275	#131	—	47	8	no	—
276	#131	—	94	4	no	—
277	C₂×M₁₆	—	47	1	no	—
278	C₂×M₁₆	—	94	2	no	—
279	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
280	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
281	C₂²×C₈	—	47	1	no	—
282	C₂²×C₈	—	94	2	no	—
283	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
284	C₄×Q₈	—	94	2	no	—
285	C₄×Q₈	—	94	2	no	—
286	C₄×D₄	—	94	2	no	—
287	C₄×D₄	—	94	2	no	—
288	C₄×D₄	—	188	2	no	—
289	C₄×D₄	—	188	2	no	—
290	#117	—	47	1	no	—
291	#117	—	94	2	no	—
292	#117	—	94	2	no	—
293	#117	C₂²×D₄₇	1	1	yes	characteristic
294	C₂×C₄⋊C₄	—	47	2	no	—
295	C₂×C₄⋊C₄	—	94	2	no	—
296	C₂×C₄⋊C₄	—	94	2	no	—
297	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
298	C₂×C₄²	—	47	1	no	—
299	#108	—	94	2	no	—
300	#108	C₄×D₄₇	1	4	yes	complemented
301	#107	—	2	1	no	—
302	#107	—	2	1	no	—
303	#107	—	2	2	no	—
304	#107	—	47	1	no	—
305	#107	—	47	1	no	—
306	#107	—	94	2	no	—
307	#107	—	94	1	no	—
308	#107	—	94	1	no	—
309	#106	—	2	2	no	—
310	#106	—	47	1	no	—
311	#106	—	47	1	no	—
312	#106	—	94	2	no	—
313	#106	—	94	2	no	—
314	#106	—	94	2	no	—
315	#104	—	47	8	no	—
316	#103	—	94	2	no	—
317	#103	—	94	2	no	—
318	#102	—	94	2	no	—
319	#102	—	94	2	no	—
320	#97	—	2	1	no	—
321	#97	—	94	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	47	4	no	—
324	C₄×C₈	—	94	1	no	—
325	#95	—	188	2	no	—
326	#41	—	47	4	no	—
327	#41	—	47	4	no	—
328	#41	—	94	2	no	—
329	#41	—	94	2	no	—
330	C₂×Q₈	—	47	2	no	—
331	C₂×D₄	—	47	2	no	—
332	C₂×D₄	—	94	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	94	2	no	—
335	C₂²×C₄	—	94	1	no	—
336	C₂²×C₄	—	94	2	no	—
337	C₂²×C₄	—	188	2	no	—
338	C₂²×C₄	—	188	2	no	—
339	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
340	Q₁₆	—	47	4	no	—
341	SD₁₆	—	47	8	no	—
342	D₈	—	47	4	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	2	1	no	—
345	M₁₆	—	2	1	no	—
346	M₁₆	—	94	8	no	—
347	M₁₆	—	94	1	no	—
348	M₁₆	—	94	1	no	—
349	M₁₆	C₂×C₄×D₄₇	1	4	yes	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	47	2	no	—
353	C₂×C₈	—	47	1	no	—
354	C₂×C₈	—	47	1	no	—
355	C₂×C₈	—	47	2	no	—
356	C₂×C₈	—	94	8	no	—
357	C₂×C₈	—	94	1	no	—
358	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
359	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
360	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
361	C₂×C₈	Q₈×D₄₇	1	2	yes	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	47	1	no	—
365	C₄⋊C₄	—	47	1	no	—
366	C₄⋊C₄	—	94	2	no	—
367	C₄⋊C₄	—	94	2	no	—
368	C₄⋊C₄	—	188	2	no	—
369	C₄⋊C₄	—	188	2	no	—
370	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
371	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	94	1	no	—
374	C₂²⋊C₄	—	188	2	no	—
375	C₂²⋊C₄	—	188	2	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	47	2	no	—
378	C₄²	—	94	1	no	—
379	C₄²	—	94	1	no	—
380	C₄²	—	188	2	no	—
381	C₄²	—	188	2	no	—
382	C₂³	—	94	2	no	—
383	C₂³	#13094070	1	1	yes	characteristic
384	Q₈	—	47	4	no	—
385	Q₈	—	94	2	no	—
386	D₄	—	47	4	no	—
387	D₄	—	94	4	no	—
388	D₄	—	94	4	no	—
389	D₄	—	94	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	8	2	no	—
394	C₂×C₄	—	94	2	no	—
395	C₂×C₄	—	94	4	no	—
396	C₂×C₄	—	94	4	no	—
397	C₂×C₄	—	94	1	no	—
398	C₂×C₄	—	94	1	no	—
399	C₂×C₄	—	94	2	no	—
400	C₂×C₄	—	376	2	no	—
401	C₂×C₄	—	188	2	no	—
402	C₂×C₄	—	188	1	no	—
403	C₂×C₄	—	188	1	no	—
404	C₂×C₄	—	752	2	no	—
405	C₂×C₄	—	752	2	no	—
406	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
407	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
408	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
409	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
410	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
411	C₂×C₄	#13094072	1	1	yes	characteristic
412	C₈	—	2	4	no	—
413	C₈	—	4	1	no	—
414	C₈	—	47	2	no	—
415	C₈	—	47	2	no	—
416	C₈	—	188	1	no	—
417	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
418	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	94	4	no	—
422	C₂²	—	188	2	no	—
423	C₂²	—	188	2	no	—
424	C₂²	#15689605	1	1	yes	characteristic
425	C₂²	#15689757	1	1	yes	characteristic
426	C₂²	#15689829	1	1	yes	characteristic
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	94	4	no	—
431	C₄	—	376	2	no	—
432	C₄	—	188	2	no	—
433	C₄	—	188	1	no	—
434	C₄	—	188	1	no	—
435	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
436	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
437	C₄	#15689775	1	1	yes	characteristic
438	C₄	#15689788	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	188	4	no	—
442	C₂	#20246289	1	1	yes	characteristic
443	C₂	#20255169	1	1	yes	characteristic
444	C₂	#20255177	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15689757
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1952	C₂
socle	C₂²×C₄₇	D₄²
prime radical	C₂×#13094046	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1952	D₄₇
hypocenter	C₄₇	#22690
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1952

Complements

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

N	H ≅ G/N	type
4. #20251982	C₂	semidirect
5. #20244174	C₂	semidirect
6. #20243624	C₂	semidirect
7. #20243618	C₂	semidirect
8. #20243551	C₂	semidirect
9. #20243446	C₂	semidirect
10. #20243268	C₂	semidirect
11. C₄₇×#1952	C₂	semidirect
16. #15689239	C₄	semidirect
53. #13094032	C₂×C₄	semidirect
82. #13093950	C₂×C₄	semidirect
89. C₈×Dic₄₇	C₂×C₄	semidirect
96. #108×C₄₇	C₂×C₄	semidirect
222. #1952	D₄₇	semidirect
268. C₄₇	#22690	semidirect
300. #108	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689239	2
#20252265	2
#20252262	2
#20251982	2
#20244174	2
#20243624	2
#20243618	2
#20243551	2
#20243446	2
#20243268	2
C₄₇×#1952	2
#22690	47