Subgroups — #25079996

Order 11008.

584 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145932	C₂	1	2	yes	maximal
2	#19145181	C₂	1	1	yes	maximal, characteristic, complemented
3	#19134149	C₂	1	2	yes	maximal, complemented
4	#19134142	C₂	1	2	yes	maximal, complemented
5	#19133989	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133984	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133965	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133960	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14582652	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133296	C₂	1	2	yes	maximal, complemented
11	C₄₃×#2966	C₂	1	1	yes	maximal, characteristic
12	#14583456	C₂²	1	2	yes	—
13	#14583304	C₂²	1	1	yes	characteristic
14	#14583279	C₂²	1	1	yes	characteristic
15	#14583250	C₂²	1	2	yes	—
16	#14583203	—	2	2	no	—
17	#14583184	C₂²	1	2	yes	—
18	#14583179	C₂²	1	2	yes	—
19	#14583140	—	2	1	no	—
20	#14583140	—	2	1	no	—
21	#14583138	—	2	2	no	—
22	#14583126	—	2	2	no	—
23	#14583118	—	2	2	no	—
24	#14583109	C₂²	1	2	yes	—
25	#14583104	C₂²	1	2	yes	—
26	C₄×Dic₁₇₂	—	2	1	no	—
27	C₄×Dic₁₇₂	—	2	1	no	—
28	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
29	#14582652	C₂²	1	1	yes	characteristic
30	#14582652	C₂²	1	1	yes	characteristic
31	#14582652	C₂²	1	2	yes	—
32	#14582646	C₂²	1	2	yes	—
33	#14582646	C₂²	1	2	yes	—
34	#14582644	C₂²	1	2	yes	—
35	#14582644	C₂²	1	2	yes	—
36	C₄₃×#529	C₂²	1	1	yes	characteristic
37	C₄₃×#446	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#436	C₂²	1	1	yes	characteristic
40	C₄₃×#435	—	2	1	no	—
41	C₈×D₄×C₄₃	—	2	1	no	—
42	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#433	—	2	1	no	—
44	C₄₃×#432	C₂²	1	1	yes	characteristic
45	C₄₃×#405	—	2	1	no	—
46	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×Dic₁₇₂	—	2	1	no	—
48	C₂×Dic₁₇₂	—	2	1	no	—
49	C₂×#10621885	—	2	2	no	—
50	C₂×#10621883	—	2	2	no	—
51	C₂²×C₄₃⋊C₈	—	2	2	no	—
52	#13063325	C₂³	1	2	yes	—
53	#13063325	C₂³	1	2	yes	—
54	#13063317	—	2	2	no	—
55	#13063304	—	2	2	no	—
56	#13063304	—	2	2	no	—
57	C₄×Dic₈₆	—	2	2	no	—
58	C₄×Dic₈₆	—	2	2	no	—
59	#13063284	—	2	2	no	—
60	#13063259	—	2	1	no	—
61	#13063259	—	2	1	no	—
62	#13063258	—	2	2	no	—
63	#13063256	—	2	2	no	—
64	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
65	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
66	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
67	#13063250	—	2	2	no	—
68	#13063250	—	2	2	no	—
69	#13063249	—	2	2	no	—
70	#13063248	—	2	2	no	—
71	#13063248	—	2	2	no	—
72	#13063246	—	2	2	no	—
73	C₂×M₁₆×C₄₃	—	2	1	no	—
74	C₂²×C₈×C₄₃	—	2	1	no	—
75	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
77	#126×C₄₃	—	2	1	no	—
78	#125×C₄₃	D₄	1	1	yes	characteristic
79	#124×C₄₃	D₄	1	1	yes	characteristic
80	#123×C₄₃	—	2	1	no	—
81	C₂²⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
82	#121×C₄₃	D₄	1	1	yes	characteristic
83	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₄₃	—	2	1	no	—
85	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
86	#117×C₄₃	—	2	1	no	—
87	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₃	—	2	1	no	—
89	C₄⋊C₈×C₄₃	—	2	1	no	—
90	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
92	C₂²⋊C₈×C₄₃	—	2	1	no	—
93	C₂²⋊C₈×C₄₃	—	2	1	no	—
94	C₂²⋊C₈×C₄₃	—	2	1	no	—
95	#97×C₄₃	—	2	1	no	—
96	#97×C₄₃	—	2	1	no	—
97	C₄×C₈×C₄₃	—	2	1	no	—
98	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₄₃	—	2	1	no	—
104	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	—	2	1	no	—
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
109	C₂×Dic₈₆	—	2	2	no	—
110	C₂×Dic₈₆	—	2	2	no	—
111	M₁₆×C₄₃	—	4	2	no	—
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	2	1	no	—
114	C₂×C₈×C₄₃	—	2	1	no	—
115	C₂×C₈×C₄₃	—	4	1	no	—
116	C₂×C₈×C₄₃	—	4	2	no	—
117	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₄⋊C₄×C₄₃	—	2	1	no	—
122	C₄⋊C₄×C₄₃	—	2	1	no	—
123	C₄⋊C₄×C₄₃	—	2	1	no	—
124	C₄⋊C₄×C₄₃	—	2	1	no	—
125	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂²⋊C₄×C₄₃	—	2	1	no	—
128	C₂²⋊C₄×C₄₃	—	2	1	no	—
129	C₂²⋊C₄×C₄₃	—	2	1	no	—
130	C₂²⋊C₄×C₄₃	—	2	1	no	—
131	C₂²⋊C₄×C₄₃	—	2	1	no	—
132	C₄²×C₄₃	—	2	1	no	—
133	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₃	#41	1	1	yes	characteristic
136	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
137	C₂²⋊Dic₄₃	—	4	2	no	—
138	#10621885	—	8	2	no	—
139	#10621883	—	8	2	no	—
140	C₄⋊Dic₄₃	—	2	2	no	—
141	C₄⋊Dic₄₃	—	2	2	no	—
142	C₄⋊Dic₄₃	—	2	2	no	—
143	C₄⋊Dic₄₃	—	2	2	no	—
144	Dic₄₃⋊C₄	—	4	2	no	—
145	Dic₄₃⋊C₄	—	4	2	no	—
146	C₄×Dic₄₃	—	4	2	no	—
147	C₂×C₄₃⋊C₈	—	2	2	no	—
148	C₂×C₄₃⋊C₈	—	2	2	no	—
149	C₂×C₄₃⋊C₈	—	8	2	no	—
150	Dic₁₇₂	—	4	2	no	—
151	Dic₁₇₂	—	4	2	no	—
152	C₂³×C₄₃	—	2	1	no	—
153	C₂³×C₄₃	#121	1	1	yes	characteristic
154	Q₈×C₄₃	—	2	1	no	—
155	Q₈×C₄₃	—	2	1	no	—
156	D₄×C₄₃	—	2	1	no	—
157	D₄×C₄₃	—	2	1	no	—
158	D₄×C₄₃	—	4	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	1	no	—
161	C₂×C₄×C₄₃	—	2	1	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	1	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
170	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
171	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₂×Dic₄₃	—	4	2	no	—
176	C₂×Dic₄₃	—	4	2	no	—
177	Dic₈₆	—	4	2	no	—
178	Dic₈₆	—	4	2	no	—
179	Dic₈₆	—	4	2	no	—
180	Dic₈₆	—	4	2	no	—
181	C₈×C₄₃	—	2	1	no	—
182	C₈×C₄₃	—	2	1	no	—
183	C₈×C₄₃	—	2	1	no	—
184	C₈×C₄₃	—	4	1	no	—
185	C₈×C₄₃	—	4	1	no	—
186	C₈×C₄₃	#135	1	2	yes	—
187	C₄₃⋊C₈	—	4	2	no	—
188	C₄₃⋊C₈	—	4	2	no	—
189	#19223	—	43	1	no	maximal, Sylow
190	C₂²×C₄₃	—	2	1	no	—
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	—	4	1	no	—
193	C₂²×C₄₃	—	4	1	no	—
194	C₂²×C₄₃	—	4	1	no	—
195	C₂²×C₄₃	#473	1	2	yes	—
196	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
197	C₄×C₄₃	—	2	1	no	—
198	C₄×C₄₃	—	2	1	no	—
199	C₄×C₄₃	—	2	1	no	—
200	C₄×C₄₃	—	2	1	no	—
201	C₄×C₄₃	—	4	1	no	—
202	C₄×C₄₃	—	4	1	no	—
203	C₄×C₄₃	—	4	1	no	—
204	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
205	C₄×C₄₃	#575	1	1	yes	characteristic
206	C₄×C₄₃	#576	1	1	yes	characteristic
207	C₄×C₄₃	#578	1	1	yes	characteristic
208	Dic₄₃	—	8	2	no	—
209	Dic₄₃	—	8	2	no	—
210	#3248	—	43	2	no	—
211	#3170	—	43	1	no	—
212	#2966	D₄₃	1	1	yes	characteristic
213	#1700	—	43	2	no	—
214	#1699	—	43	2	no	—
215	#1674	—	43	1	no	—
216	#1673	—	43	1	no	—
217	#1670	—	43	1	no	—
218	#1669	—	43	1	no	—
219	C₂×#335	—	43	1	no	—
220	#1552	—	43	2	no	—
221	C₂×C₄₃	—	2	2	no	—
222	C₂×C₄₃	—	8	1	no	—
223	C₂×C₄₃	#3035	1	1	yes	characteristic
224	C₂×C₄₃	#3061	1	1	yes	characteristic
225	C₂×C₄₃	C₂×#473	1	1	yes	characteristic
226	#533	—	43	2	no	—
227	#529	C₂×D₄₃	1	1	yes	characteristic
228	#500	—	43	1	no	—
229	#494	—	43	1	no	—
230	#487	—	43	2	no	—
231	#479	—	86	2	no	—
232	#475	—	43	2	no	—
233	#474	—	43	2	no	—
234	#467	—	86	1	no	—
235	#467	—	86	1	no	—
236	#467	—	86	2	no	—
237	#465	—	86	2	no	—
238	#464	—	86	2	no	—
239	#462	—	43	2	no	—
240	#461	—	43	2	no	—
241	#446	C₂×D₄₃	1	1	yes	characteristic
242	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic
243	C₄×Q₁₆	—	86	1	no	—
244	C₄×Q₁₆	—	86	1	no	—
245	#436	C₂×D₄₃	1	1	yes	characteristic
246	#435	—	2	1	no	—
247	C₈×D₄	—	2	1	no	—
248	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic
249	#433	—	2	1	no	—
250	#432	C₂×D₄₃	1	1	yes	characteristic
251	C₂×C₄⋊C₈	—	43	2	no	—
252	#405	—	2	1	no	—
253	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
254	#335	—	43	1	no	—
255	#335	—	43	1	no	—
256	#335	—	43	2	no	—
257	#332	—	43	2	no	—
258	#332	—	43	2	no	—
259	#332	—	43	2	no	—
260	#332	—	43	2	no	—
261	C₄₃	#19223	1	1	yes	characteristic, complemented, Sylow
262	C₂×Q₁₆	—	86	2	no	—
263	C₂×Q₁₆	—	86	1	no	—
264	C₂×Q₁₆	—	86	1	no	—
265	C₂×SD₁₆	—	86	2	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	86	2	no	—
269	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
270	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
271	C₄⋊Q₈	—	43	2	no	—
272	C₄⋊Q₈	—	43	2	no	—
273	#126	—	2	1	no	—
274	#125	—	86	2	no	—
275	#125	D₁₇₂	1	1	yes	characteristic
276	#124	D₁₇₂	1	1	yes	characteristic
277	#123	—	2	1	no	—
278	C₂²⋊Q₈	—	86	2	no	—
279	C₂²⋊Q₈	—	86	2	no	—
280	C₂²⋊Q₈	D₁₇₂	1	1	yes	characteristic
281	#121	D₁₇₂	1	1	yes	characteristic
282	C₄×Q₈	—	86	2	no	—
283	C₄×Q₈	—	86	2	no	—
284	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
287	#117	—	2	1	no	—
288	#117	—	86	2	no	—
289	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
290	#107	—	86	1	no	—
291	#107	—	86	1	no	—
292	#107	—	86	2	no	—
293	#106	—	86	2	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	43	2	no	—
297	C₄⋊C₈	—	43	2	no	—
298	C₄⋊C₈	—	86	2	no	—
299	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
300	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
301	#103	—	86	2	no	—
302	#103	—	86	2	no	—
303	#103	—	86	2	no	—
304	#103	—	86	2	no	—
305	#103	—	86	2	no	—
306	#102	—	86	2	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	2	1	no	—
310	#97	—	2	1	no	—
311	#97	—	2	1	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
314	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
316	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
317	C₂×Q₈	—	86	2	no	—
318	C₂×Q₈	—	86	2	no	—
319	C₂×Q₈	C₂×D₁₇₂	1	1	yes	characteristic
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	C₂×D₁₇₂	1	1	yes	characteristic
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
324	C₂²×C₄	#10621898	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
326	Q₁₆	—	344	2	no	—
327	Q₁₆	—	172	2	no	—
328	Q₁₆	—	172	2	no	—
329	SD₁₆	—	344	2	no	—
330	M₁₆	—	4	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	2	no	—
336	C₂×C₈	—	86	2	no	—
337	C₂×C₈	—	86	2	no	—
338	C₂×C₈	—	344	2	no	—
339	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
340	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
341	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
342	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	86	2	no	—
348	C₄⋊C₄	—	86	2	no	—
349	C₄⋊C₄	—	86	2	no	—
350	C₄⋊C₄	—	86	2	no	—
351	C₄⋊C₄	—	172	2	no	—
352	C₄⋊C₄	—	172	2	no	—
353	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
354	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	2	1	no	—
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	2	1	no	—
359	C₂²⋊C₄	—	2	1	no	—
360	C₂²⋊C₄	—	172	2	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	172	2	no	—
363	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
364	C₄²	#10621898	1	1	yes	characteristic
365	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
366	C₄²	C₂³×D₄₃	1	1	yes	characteristic
367	C₂³	—	2	1	no	—
368	C₂³	#13063299	1	1	yes	characteristic
369	Q₈	—	2	1	no	—
370	Q₈	—	2	1	no	—
371	Q₈	—	172	2	no	—
372	Q₈	—	172	2	no	—
373	Q₈	—	172	2	no	—
374	Q₈	—	172	2	no	—
375	D₄	—	2	1	no	—
376	D₄	—	2	1	no	—
377	D₄	—	4	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	172	2	no	—
389	C₂×C₄	—	172	2	no	—
390	C₂×C₄	#13063299	1	1	yes	characteristic
391	C₂×C₄	#13063299	1	1	yes	characteristic
392	C₂×C₄	#13063299	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
395	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	2	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	4	1	no	—
401	C₈	—	172	2	no	—
402	C₈	—	172	2	no	—
403	C₈	#13063345	1	2	yes	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	#14583174	1	2	yes	—
410	C₂²	C₂×#13063299	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	344	2	no	—
419	C₄	—	344	2	no	—
420	C₄	C₂×#13063345	1	1	yes	characteristic
421	C₄	#14583697	1	1	yes	characteristic
422	C₄	#14583704	1	1	yes	characteristic
423	C₄	#14583716	1	1	yes	characteristic
424	C₂	—	2	2	no	—
425	C₂	—	8	1	no	—
426	C₂	#19144050	1	1	yes	characteristic
427	C₂	#19144265	1	1	yes	characteristic
428	C₂	C₂×#14583174	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063299
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2966	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#121×C₄₃	D₄
hypercenter	#2966	D₄₃
hypocenter	C₄₃	#19223
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2966

Complements

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

N	H ≅ G/N	type
2. #19145181	C₂	semidirect
3. #19134149	C₂	semidirect
4. #19134142	C₂	semidirect
5. #19133989	C₂	semidirect
6. #19133984	C₂	semidirect
7. #19133965	C₂	semidirect
8. #19133960	C₂	semidirect
9. C₂×#14582652	C₂	semidirect
10. #19133296	C₂	semidirect
261. C₄₃	#19223	semidirect

Maximal subgroups

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

subgroup	index
#19145932	2
#19145181	2
#19134149	2
#19134142	2
#19133989	2
#19133984	2
#19133965	2
#19133960	2
C₂×#14582652	2
#19133296	2
C₄₃×#2966	2
#19223	43