Subgroups — #25155502

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144453	C₂	1	2	yes	maximal
2	#19143192	C₂	1	1	yes	maximal, characteristic
3	#19136108	C₂	1	2	yes	maximal, complemented
4	#19135942	C₂	1	2	yes	maximal, complemented
5	#19135380	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135344	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134825	C₂	1	2	yes	maximal
8	#19134758	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134660	C₂	1	1	yes	maximal, characteristic
10	#19134434	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063331	C₂²	1	1	yes	characteristic
13	#14583379	C₂²	1	2	yes	—
14	#14583203	—	2	2	no	—
15	#14583196	—	2	2	no	—
16	#14583186	—	2	2	no	—
17	#14583181	—	2	2	no	—
18	C₂×#13063261	C₂²	1	1	yes	characteristic
19	#14582942	C₂²	1	2	yes	—
20	#14582942	C₂²	1	2	yes	—
21	#14582938	—	2	2	no	—
22	#14582936	—	2	1	no	—
23	C₂×#13063259	C₂²	1	1	yes	characteristic
24	#107×D₄₃	—	2	1	no	—
25	C₂×#13063256	C₂²	1	2	yes	—
26	#14582926	C₂²	1	2	yes	—
27	C₂×#13063251	C₂²	1	1	yes	characteristic
28	#14582898	C₂²	1	2	yes	—
29	#14582893	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
31	#14582764	C₂²	1	2	yes	—
32	#14582668	C₂²	1	2	yes	—
33	#14582667	C₂²	1	2	yes	—
34	#14582663	C₂²	1	1	yes	characteristic
35	#14582658	C₂²	1	2	yes	—
36	#14582658	C₂²	1	1	yes	characteristic
37	C₄₃×#544	C₂²	1	2	yes	—
38	C₄₃×#501	—	2	2	no	—
39	C₄₃×#500	—	2	1	no	—
40	C₄₃×#499	—	2	1	no	—
41	C₄₃×#428	C₂²	1	2	yes	—
42	C₄₃×#427	C₂²	1	1	yes	characteristic
43	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#405	C₂²	1	1	yes	characteristic
45	C₂×#10621898	C₂³	1	1	yes	characteristic
46	#13063331	—	2	2	no	—
47	#13063331	Q₈	1	4	yes	complemented
48	C₂×#10621877	C₂³	1	2	yes	—
49	C₂×#10621877	C₂³	1	1	yes	characteristic
50	C₂×#10621872	—	2	1	no	—
51	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
52	C₂×C₈×D₄₃	—	2	1	no	—
53	C₄×Dic₈₆	—	2	2	no	—
54	C₄×D₁₇₂	—	2	2	no	—
55	(C₂²⋊D₄₃)⋊C₄	—	4	2	no	—
56	#13063283	—	2	2	no	—
57	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
58	C₄⋊C₄×D₄₃	—	2	2	no	—
59	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
60	#13063261	—	2	2	no	—
61	#13063259	—	2	1	no	—
62	#13063259	—	2	1	no	—
63	#13063258	—	2	2	no	—
64	#13063258	—	2	2	no	—
65	#13063256	—	2	2	no	—
66	#13063256	—	2	2	no	—
67	#13063256	—	2	2	no	—
68	#13063256	—	2	2	no	—
69	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
70	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
71	#13063251	Q₈	1	4	yes	complemented
72	#13063248	—	2	2	no	—
73	#13063248	D₄	1	1	yes	characteristic
74	#13063248	D₄	1	1	yes	characteristic
75	#13063245	—	2	2	no	—
76	#13063245	D₄	1	1	yes	characteristic
77	#13063245	D₄	1	1	yes	characteristic
78	C₈×Dic₄₃	—	2	2	no	—
79	C₄₃⋊#95	—	4	2	no	—
80	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₄₃	—	2	2	no	—
83	C₄⋊Q₈×C₄₃	—	2	2	no	—
84	#125×C₄₃	—	2	2	no	—
85	#125×C₄₃	—	2	2	no	—
86	C₂²⋊Q₈×C₄₃	—	4	2	no	—
87	#117×C₄₃	C₂³	1	1	yes	characteristic
88	#117×C₄₃	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
90	#107×C₄₃	—	2	1	no	—
91	#107×C₄₃	—	2	1	no	—
92	#107×C₄₃	—	2	2	no	—
93	#107×C₄₃	D₄	1	1	yes	characteristic
94	#107×C₄₃	D₄	1	1	yes	characteristic
95	#106×C₄₃	—	2	2	no	—
96	#106×C₄₃	D₄	1	2	yes	—
97	#97×C₄₃	—	2	1	no	—
98	C₄×C₈×C₄₃	—	2	1	no	—
99	C₂×Q₈×C₄₃	—	4	2	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
102	C₂×C₂²⋊D₄₃	—	2	1	no	—
103	C₂²×Dic₄₃	—	2	1	no	—
104	C₂²×Dic₄₃	—	2	2	no	—
105	#10621898	—	2	1	no	—
106	#10621898	—	2	1	no	—
107	#10621898	C₂×Q₈	1	2	yes	—
108	#10621898	C₂×Q₈	1	2	yes	—
109	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×D₄₃	—	2	1	no	—
111	C₂×C₄×D₄₃	—	4	2	no	—
112	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
113	M₁₆×C₄₃	—	2	1	no	—
114	M₁₆×C₄₃	C₂×Q₈	1	2	yes	—
115	C₂×C₈×C₄₃	—	2	1	no	—
116	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
119	C₂×C₈×C₄₃	#41	1	2	yes	—
120	C₄⋊C₄×C₄₃	—	2	2	no	—
121	C₄⋊C₄×C₄₃	—	2	2	no	—
122	C₄⋊C₄×C₄₃	—	4	2	no	—
123	C₄⋊C₄×C₄₃	—	4	2	no	—
124	C₄⋊C₄×C₄₃	—	4	2	no	—
125	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
129	C₂²⋊C₄×C₄₃	—	2	1	no	—
130	C₂²⋊C₄×C₄₃	—	2	2	no	—
131	C₄²×C₄₃	—	2	1	no	—
132	C₄²×C₄₃	—	2	2	no	—
133	(C₂×D₄₃)⋊C₄	—	4	2	no	—
134	C₄⋊Dic₄₃	—	2	2	no	—
135	C₄⋊Dic₄₃	—	2	2	no	—
136	Dic₄₃⋊C₄	—	4	2	no	—
137	C₄×Dic₄₃	—	2	1	no	—
138	C₄×Dic₄₃	—	4	2	no	—
139	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
140	#10621877	—	2	1	no	—
141	#10621877	—	2	2	no	—
142	#10621877	—	2	2	no	—
143	#10621877	C₂×Q₈	1	2	yes	—
144	C₂×C₄₃⋊C₈	—	2	1	no	—
145	C₂×C₄₃⋊C₈	—	2	1	no	—
146	C₂×C₄₃⋊C₈	—	2	1	no	—
147	C₂×C₄₃⋊C₈	—	2	2	no	—
148	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
150	#10621872	—	2	4	no	—
151	C₈×D₄₃	—	2	4	no	—
152	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
153	C₂²×D₄₃	—	2	1	no	—
154	Q₈×C₄₃	—	16	2	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	4	2	no	—
160	C₂×C₄×C₄₃	—	8	2	no	—
161	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
167	C₂²⋊D₄₃	—	2	2	no	—
168	C₂²⋊D₄₃	—	2	2	no	—
169	C₂×Dic₄₃	—	2	1	no	—
170	C₂×Dic₄₃	—	2	2	no	—
171	C₂×Dic₄₃	—	4	1	no	—
172	C₂×Dic₄₃	—	4	1	no	—
173	C₂×Dic₄₃	—	4	2	no	—
174	C₂×Dic₄₃	—	8	2	no	—
175	D₁₇₂	—	2	1	no	—
176	D₁₇₂	C₄⋊Q₈	1	2	yes	—
177	C₄×D₄₃	—	2	2	no	—
178	C₄×D₄₃	—	2	2	no	—
179	C₄×D₄₃	—	16	2	no	—
180	Dic₈₆	—	2	1	no	—
181	Dic₈₆	C₄⋊Q₈	1	2	yes	—
182	C₈×C₄₃	—	2	2	no	—
183	C₈×C₄₃	C₂²⋊Q₈	1	2	yes	—
184	C₈×C₄₃	C₂²⋊Q₈	1	2	yes	—
185	C₄₃⋊C₈	—	2	2	no	—
186	C₄₃⋊C₈	—	2	1	no	—
187	C₄₃⋊C₈	—	2	1	no	—
188	C₄₃⋊C₈	—	4	2	no	—
189	#26082	—	43	1	no	maximal, Sylow
190	C₂²×C₄₃	—	2	1	no	—
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	#544	1	1	yes	characteristic
193	C₂²×C₄₃	D₄²	1	1	yes	characteristic
194	C₂²×C₄₃	#554	1	1	yes	characteristic
195	C₂×D₄₃	—	2	2	no	—
196	C₂×D₄₃	—	4	1	no	—
197	C₂×D₄₃	—	4	1	no	—
198	C₄×C₄₃	—	4	2	no	—
199	C₄×C₄₃	—	4	1	no	—
200	C₄×C₄₃	—	4	2	no	—
201	C₄×C₄₃	—	4	1	no	—
202	C₄×C₄₃	—	8	2	no	—
203	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
204	C₄×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
205	C₄×C₄₃	#547	1	1	yes	characteristic
206	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
207	Dic₄₃	—	2	2	no	—
208	Dic₄₃	—	4	2	no	—
209	Dic₄₃	—	8	2	no	—
210	#3164	D₄₃	1	1	yes	characteristic, complemented
211	#3084	—	43	2	no	—
212	#2913	—	43	1	no	—
213	#2090	—	43	2	no	—
214	#2061	—	43	2	no	—
215	#1952	—	43	1	no	—
216	#1945	—	43	1	no	—
217	#1860	—	43	2	no	—
218	#1846	—	43	1	no	—
219	#1816	—	43	1	no	—
220	#1764	—	43	1	no	—
221	C₂×C₄₃	—	2	1	no	—
222	C₂×C₄₃	—	2	1	no	—
223	C₂×C₄₃	#2440	1	1	yes	characteristic
224	C₂×C₄₃	#3290	1	1	yes	characteristic
225	C₂×C₄₃	#3290	1	1	yes	characteristic
226	D₄₃	—	4	2	no	—
227	C₂×#131	—	43	1	no	—
228	#544	C₂×D₄₃	1	2	yes	—
229	#520	—	43	2	no	—
230	#501	—	2	2	no	—
231	#500	—	2	1	no	—
232	#499	—	2	1	no	—
233	#479	—	86	2	no	—
234	#478	—	86	2	no	—
235	#476	—	86	2	no	—
236	#475	—	86	2	no	—
237	C₂×#108	—	43	1	no	—
238	#428	—	43	2	no	—
239	#428	—	43	2	no	—
240	#428	—	86	2	no	—
241	#428	C₂×D₄₃	1	2	yes	—
242	#427	—	86	1	no	—
243	#427	C₂×D₄₃	1	1	yes	characteristic
244	C₂×#107	—	43	1	no	—
245	C₂×#107	—	86	1	no	—
246	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
247	C₂×#106	—	43	2	no	—
248	#424	—	43	2	no	—
249	C₂×#104	—	43	1	no	—
250	#417	—	43	2	no	—
251	#416	—	43	1	no	—
252	#405	C₂×D₄₃	1	1	yes	characteristic
253	C₂×C₄×C₈	—	43	1	no	—
254	#382	—	43	2	no	—
255	#343	—	43	2	no	—
256	#343	—	43	2	no	—
257	#341	—	43	1	no	—
258	#339	—	43	1	no	—
259	#339	—	43	2	no	—
260	C₄₃	#26082	1	1	yes	characteristic, complemented, Sylow
261	C₂×#41	—	43	1	no	—
262	#131	—	43	4	no	—
263	#131	—	86	2	no	—
264	C₂×M₁₆	—	43	1	no	—
265	C₂×M₁₆	—	43	2	no	—
266	C₂×M₁₆	—	86	1	no	—
267	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
268	C₂²×C₈	—	43	1	no	—
269	C₂²×C₈	—	86	1	no	—
270	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
271	C₄⋊Q₈	—	2	2	no	—
272	C₄⋊Q₈	—	2	2	no	—
273	#125	—	2	2	no	—
274	#125	—	2	2	no	—
275	C₂²⋊Q₈	—	4	2	no	—
276	C₄×Q₈	—	86	2	no	—
277	C₄×D₄	—	86	2	no	—
278	C₄×D₄	—	172	2	no	—
279	#117	—	86	2	no	—
280	#117	C₂²×D₄₃	1	1	yes	characteristic
281	#117	C₂²×D₄₃	1	2	yes	—
282	C₂×C₄⋊C₄	—	43	2	no	—
283	C₂×C₄⋊C₄	—	86	2	no	—
284	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
285	C₂×C₄²	—	43	1	no	—
286	#108	—	86	2	no	—
287	#107	—	2	1	no	—
288	#107	—	2	1	no	—
289	#107	—	2	2	no	—
290	#107	—	86	1	no	—
291	#107	—	86	1	no	—
292	#107	—	86	2	no	—
293	#107	—	86	2	no	—
294	#107	C₂²⋊D₄₃	1	1	yes	characteristic
295	#107	C₂²⋊D₄₃	1	1	yes	characteristic
296	#106	—	2	2	no	—
297	#106	—	86	2	no	—
298	#106	—	86	2	no	—
299	#106	—	86	2	no	—
300	#106	—	86	2	no	—
301	#106	C₂²⋊D₄₃	1	2	yes	—
302	C₄⋊C₈	—	86	2	no	—
303	C₄⋊C₈	—	86	2	no	—
304	#104	—	43	4	no	—
305	#103	—	43	1	no	—
306	#103	—	43	1	no	—
307	#103	—	86	2	no	—
308	#102	—	43	1	no	—
309	#102	—	43	1	no	—
310	#102	—	86	2	no	—
311	#97	—	2	1	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	86	2	no	—
314	#95	—	172	2	no	—
315	#41	—	43	2	no	—
316	#41	—	43	2	no	—
317	#41	—	86	1	no	—
318	#41	—	86	1	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	—	43	1	no	—
321	C₂×D₄	—	43	1	no	—
322	C₂×D₄	—	86	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	86	1	no	—
325	C₂²×C₄	—	86	1	no	—
326	C₂²×C₄	—	86	2	no	—
327	C₂²×C₄	—	172	2	no	—
328	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
329	M₁₆	—	2	1	no	—
330	M₁₆	—	43	2	no	—
331	M₁₆	—	86	1	no	—
332	M₁₆	—	86	4	no	—
333	M₁₆	—	86	2	no	—
334	M₁₆	—	86	2	no	—
335	M₁₆	Q₈×D₄₃	1	2	yes	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	43	1	no	—
338	C₂×C₈	—	43	1	no	—
339	C₂×C₈	—	86	1	no	—
340	C₂×C₈	—	86	1	no	—
341	C₂×C₈	—	86	1	no	—
342	C₂×C₈	—	86	4	no	—
343	C₂×C₈	—	86	2	no	—
344	C₂×C₈	Q₈×D₄₃	1	2	yes	—
345	C₂×C₈	#10621902	1	2	yes	—
346	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
347	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	86	2	no	—
354	C₄⋊C₄	—	86	2	no	—
355	C₄⋊C₄	—	172	2	no	—
356	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
357	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
358	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
359	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	172	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	43	2	no	—
366	C₄²	—	86	1	no	—
367	C₄²	—	172	2	no	—
368	C₂³	—	86	1	no	—
369	C₂³	#13063370	1	1	yes	characteristic
370	Q₈	—	16	2	no	—
371	Q₈	—	43	2	no	—
372	Q₈	—	86	1	no	—
373	D₄	—	43	2	no	—
374	D₄	—	86	2	no	—
375	D₄	—	86	2	no	—
376	D₄	—	86	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	—	86	1	no	—
384	C₂×C₄	—	86	2	no	—
385	C₂×C₄	—	86	2	no	—
386	C₂×C₄	—	86	2	no	—
387	C₂×C₄	—	344	2	no	—
388	C₂×C₄	—	172	2	no	—
389	C₂×C₄	—	172	1	no	—
390	C₂×C₄	—	172	1	no	—
391	C₂×C₄	—	688	2	no	—
392	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
394	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
395	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
396	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
397	C₂×C₄	#13063373	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	86	1	no	—
400	C₈	—	86	1	no	—
401	C₈	—	86	2	no	—
402	C₈	—	172	2	no	—
403	C₈	#13063301	1	2	yes	—
404	C₈	#13063301	1	2	yes	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	86	2	no	—
408	C₂²	—	172	1	no	—
409	C₂²	—	172	1	no	—
410	C₂²	#14583526	1	1	yes	characteristic
411	C₂²	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
412	C₂²	#14583610	1	1	yes	characteristic
413	C₄	—	4	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	1	no	—
417	C₄	—	8	2	no	—
418	C₄	—	86	2	no	—
419	C₄	—	344	2	no	—
420	C₄	—	172	2	no	—
421	C₄	C₂×#13063301	1	1	yes	characteristic
422	C₄	C₄⋊Q₈×D₄₃	1	1	yes	characteristic
423	C₄	#14583552	1	1	yes	characteristic
424	C₄	Q₈×C₂²⋊D₄₃	1	1	yes	characteristic
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	172	2	no	—
428	C₂	#19138293	1	1	yes	characteristic
429	C₂	#19146377	1	1	yes	characteristic
430	C₂	#19146381	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×C₂²⋊D₄₃
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#3164	C₂
socle	C₂²×C₄₃	D₄²
prime radical	C₂×#10621898	C₂³
hypercenter	#3164	D₄₃
hypocenter	C₄₃	#26082
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #3164

Complements

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

N	H ≅ G/N	type
3. #19136108	C₂	semidirect
4. #19135942	C₂	semidirect
5. #19135380	C₂	semidirect
6. #19135344	C₂	semidirect
8. #19134758	C₂	semidirect
11. C₄₃×#3164	C₂	semidirect
47. #13063331	Q₈	semidirect
71. #13063251	Q₈	semidirect
210. #3164	D₄₃	semidirect
260. C₄₃	#26082	semidirect

Maximal subgroups

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

subgroup	index
#19144453	2
#19143192	2
#19136108	2
#19135942	2
#19135380	2
#19135344	2
#19134825	2
#19134758	2
#19134660	2
#19134434	2
C₄₃×#3164	2
#26082	43