Subgroups — #25250955

Order 11008.

694 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583340	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14583329	C₂	1	1	yes	maximal, characteristic
3	#19143472	C₂	1	1	yes	maximal, characteristic, complemented
4	#19136654	C₂	1	2	yes	maximal, complemented
5	#19136647	C₂	1	2	yes	maximal, complemented
6	#19136642	C₂	1	2	yes	maximal, complemented
7	#19136637	C₂	1	2	yes	maximal, complemented
8	#19136354	C₂	1	1	yes	maximal, characteristic, complemented
9	#19136307	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14582703	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	C₂²	1	1	yes	characteristic
13	#14583379	—	2	1	no	—
14	#14583340	—	2	4	no	—
15	#14583329	—	2	4	no	—
16	C₂×#13063271	C₂²	1	1	yes	characteristic
17	C₂×#13063271	C₂²	1	2	yes	—
18	C₂×#13063269	C₂²	1	1	yes	characteristic
19	C₂×#13063268	C₂²	1	1	yes	characteristic
20	C₂×#13063268	C₂²	1	2	yes	—
21	C₂×#13063266	C₂²	1	1	yes	characteristic
22	C₂×#13063265	C₂²	1	1	yes	characteristic
23	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
24	#14583001	—	2	2	no	—
25	C₄×Dic₁₇₂	C₂²	1	2	yes	—
26	C₄×D₃₄₄	C₂²	1	2	yes	—
27	C₂×#13063259	C₂²	1	1	yes	characteristic
28	#14582901	—	2	1	no	—
29	C₄⋊(C₄₃⋊C₁₆)	C₂²	1	2	yes	—
30	C₄⋊(C₄₃⋊C₁₆)	C₂²	1	2	yes	—
31	#14582703	C₂²	1	2	yes	—
32	#14582703	C₂²	1	2	yes	—
33	#14582703	C₂²	1	2	yes	—
34	#14582700	C₂²	1	2	yes	—
35	C₂×#137×C₄₃	—	2	1	no	—
36	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
37	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
38	C₄₃×#536	—	2	1	no	—
39	C₄₃×#497	—	2	2	no	—
40	C₄₃×#495	C₂²	1	2	yes	—
41	C₄₃×#494	C₂²	1	2	yes	—
42	C₄₃×#405	C₂²	1	1	yes	characteristic
43	C₂×#10621898	—	2	1	no	—
44	#13063347	—	2	2	no	—
45	#13063347	D₄	1	4	yes	—
46	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
47	C₂×#10621873	—	2	1	no	—
48	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
49	C₄×Dic₈₆	—	2	2	no	—
50	C₄×D₁₇₂	—	2	2	no	—
51	(C₂²⋊D₄₃)⋊C₄	—	4	2	no	—
52	#13063283	—	4	1	no	—
53	C₂×C₄⋊Dic₄₃	—	2	1	no	—
54	C₄⋊C₄×D₄₃	—	4	1	no	—
55	#13063271	—	2	2	no	—
56	#13063271	—	2	4	no	—
57	#13063269	—	2	2	no	—
58	#13063268	—	2	2	no	—
59	#13063268	—	2	4	no	—
60	#13063266	—	2	2	no	—
61	#13063265	—	2	2	no	—
62	C₂×C₄₃⋊C₁₆	—	2	2	no	—
63	C₂×C₄₃⋊C₁₆	C₂³	1	1	yes	characteristic
64	C₂×C₄₃⋊C₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₄₃⋊C₁₆	C₂³	1	2	yes	—
66	#13063259	—	2	1	no	—
67	#13063259	C₂³	1	2	yes	—
68	#13063250	—	2	2	no	—
69	#13063247	—	2	2	no	—
70	C₂×#41×C₄₃	—	2	1	no	—
71	C₂²×Q₈×C₄₃	—	2	1	no	—
72	#137×C₄₃	—	4	4	no	—
73	#135×C₄₃	—	2	2	no	—
74	#135×C₄₃	—	2	2	no	—
75	C₂×Q₁₆×C₄₃	—	2	2	no	—
76	C₂×Q₁₆×C₄₃	—	2	1	no	—
77	C₂×Q₁₆×C₄₃	—	2	2	no	—
78	C₂×Q₁₆×C₄₃	—	2	2	no	—
79	C₂×Q₁₆×C₄₃	C₂³	1	2	yes	—
80	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
81	C₂×SD₁₆×C₄₃	—	2	1	no	—
82	C₂×SD₁₆×C₄₃	—	2	2	no	—
83	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
86	C₄⋊Q₈×C₄₃	—	2	2	no	—
87	#124×C₄₃	—	2	2	no	—
88	#123×C₄₃	—	4	2	no	—
89	C₂²⋊Q₈×C₄₃	—	4	1	no	—
90	C₂²⋊Q₈×C₄₃	—	4	1	no	—
91	#117×C₄₃	D₄	1	1	yes	characteristic
92	#97×C₄₃	D₄	1	2	yes	—
93	C₄×C₈×C₄₃	C₂³	1	2	yes	—
94	#41×C₄₃	—	4	2	no	—
95	#41×C₄₃	—	4	2	no	—
96	C₂×Q₈×C₄₃	—	2	2	no	—
97	C₂×Q₈×C₄₃	—	2	1	no	—
98	C₂×Q₈×C₄₃	—	4	1	no	—
99	C₂×Q₈×C₄₃	—	4	2	no	—
100	C₂×Q₈×C₄₃	—	4	2	no	—
101	C₂×D₄×C₄₃	—	2	1	no	—
102	C₂×D₄×C₄₃	—	4	1	no	—
103	C₂²×C₄×C₄₃	—	4	1	no	—
104	C₂²×C₄×C₄₃	—	4	1	no	—
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂×C₂²⋊D₄₃	—	4	1	no	—
107	C₂²×Dic₄₃	—	4	1	no	—
108	#10621898	—	2	4	no	—
109	#10621898	—	4	2	no	—
110	C₂×D₁₇₂	—	2	1	no	—
111	C₂×C₄×D₄₃	—	4	1	no	—
112	C₂×C₄×D₄₃	—	4	2	no	—
113	C₂×Dic₈₆	—	2	1	no	—
114	Q₁₆×C₄₃	—	2	2	no	—
115	Q₁₆×C₄₃	—	2	1	no	—
116	Q₁₆×C₄₃	—	2	2	no	—
117	Q₁₆×C₄₃	—	2	1	no	—
118	Q₁₆×C₄₃	—	4	4	no	—
119	Q₁₆×C₄₃	—	4	2	no	—
120	SD₁₆×C₄₃	—	4	4	no	—
121	SD₁₆×C₄₃	—	4	2	no	—
122	D₈×C₄₃	—	2	1	no	—
123	D₈×C₄₃	—	2	1	no	—
124	M₁₆×C₄₃	—	2	2	no	—
125	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₃	#41	1	2	yes	—
129	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
130	C₄⋊C₄×C₄₃	—	4	2	no	—
131	C₄⋊C₄×C₄₃	—	4	2	no	—
132	C₄⋊C₄×C₄₃	D₈	1	1	yes	characteristic
133	C₄⋊C₄×C₄₃	D₈	1	1	yes	characteristic
134	C₂²⋊C₄×C₄₃	—	4	2	no	—
135	C₂²⋊C₄×C₄₃	—	4	2	no	—
136	C₂²⋊C₄×C₄₃	D₈	1	2	yes	—
137	C₄²×C₄₃	C₂×D₄	1	2	yes	—
138	(C₂×D₄₃)⋊C₄	—	4	2	no	—
139	C₄⋊Dic₄₃	—	2	2	no	—
140	C₄⋊Dic₄₃	—	4	1	no	—
141	Dic₄₃⋊C₄	—	4	2	no	—
142	C₄×Dic₄₃	—	4	2	no	—
143	Dic₁₇₂	—	2	1	no	—
144	Dic₁₇₂	C₂×D₄	1	2	yes	—
145	D₃₄₄	—	2	1	no	—
146	D₃₄₄	C₂×D₄	1	2	yes	—
147	#10621873	—	2	4	no	—
148	C₄₃⋊C₁₆	—	2	1	no	—
149	C₄₃⋊C₁₆	—	2	1	no	—
150	C₄₃⋊C₁₆	—	2	2	no	—
151	C₂³×C₄₃	—	4	1	no	—
152	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
153	C₂²×D₄₃	—	4	1	no	—
154	Q₈×C₄₃	—	4	1	no	—
155	Q₈×C₄₃	—	4	2	no	—
156	Q₈×C₄₃	—	4	2	no	—
157	Q₈×C₄₃	—	4	1	no	—
158	Q₈×C₄₃	—	8	2	no	—
159	D₄×C₄₃	—	4	1	no	—
160	D₄×C₄₃	—	4	1	no	—
161	D₄×C₄₃	—	8	2	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	—	8	2	no	—
165	C₂×C₄×C₄₃	—	8	2	no	—
166	C₂×C₄×C₄₃	#121	1	2	yes	—
167	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
168	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
169	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
171	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
172	C₂²⋊D₄₃	—	4	4	no	—
173	C₂×Dic₄₃	—	4	1	no	—
174	C₂×Dic₄₃	—	4	2	no	—
175	C₂×Dic₄₃	—	16	1	no	—
176	D₁₇₂	—	2	2	no	—
177	D₁₇₂	—	4	1	no	—
178	C₄×D₄₃	—	4	4	no	—
179	C₄×D₄₃	—	16	2	no	—
180	Dic₈₆	—	2	2	no	—
181	Dic₈₆	—	4	1	no	—
182	C₈×C₄₃	—	2	2	no	—
183	C₈×C₄₃	#121	1	2	yes	—
184	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
185	C₈×C₄₃	C₂×#41	1	1	yes	characteristic
186	#33590	—	43	1	no	maximal, Sylow
187	C₂²×C₄₃	—	2	1	no	—
188	C₂²×C₄₃	—	2	1	no	—
189	C₂²×C₄₃	—	8	1	no	—
190	C₂²×C₄₃	—	8	1	no	—
191	C₂²×C₄₃	—	8	1	no	—
192	C₂²×C₄₃	#459	1	2	yes	—
193	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
194	C₂×D₄₃	—	4	2	no	—
195	C₂×D₄₃	—	8	1	no	—
196	C₂×D₄₃	—	8	1	no	—
197	C₄×C₄₃	—	2	2	no	—
198	C₄×C₄₃	—	2	2	no	—
199	C₄×C₄₃	—	8	1	no	—
200	C₄×C₄₃	—	8	2	no	—
201	C₄×C₄₃	#459	1	2	yes	—
202	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
203	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	Dic₄₃	—	4	2	no	—
205	Dic₄₃	—	8	2	no	—
206	C₂×#510	—	43	1	no	—
207	C₂×#508	—	43	1	no	—
208	#3156	D₄₃	1	1	yes	characteristic, complemented
209	#2951	—	43	1	no	—
210	#2211	—	43	2	no	—
211	#2210	—	43	2	no	—
212	#2209	—	43	2	no	—
213	#2208	—	43	2	no	—
214	#2151	—	43	1	no	—
215	#2139	—	43	1	no	—
216	C₂×#358	—	43	1	no	—
217	C₂×C₄₃	—	2	2	no	—
218	C₂×C₄₃	—	16	1	no	—
219	C₂×C₄₃	C₂×#459	1	1	yes	characteristic
220	C₂×C₄₃	#3416	1	1	yes	characteristic
221	C₂×C₄₃	#3417	1	1	yes	characteristic
222	D₄₃	—	8	2	no	—
223	C₂×#137	—	2	1	no	—
224	C₂×#135	—	43	1	no	—
225	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
226	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
227	#536	—	2	1	no	—
228	#520	—	86	1	no	—
229	#510	—	86	4	no	—
230	#508	—	86	4	no	—
231	C₂×Q₃₂	—	43	1	no	—
232	C₂×Q₃₂	—	43	2	no	—
233	C₂×SD₃₂	—	43	1	no	—
234	C₂×SD₃₂	—	43	2	no	—
235	C₂×SD₃₂	—	43	1	no	—
236	C₂×D₁₆	—	43	1	no	—
237	C₂×M₃₂	—	43	1	no	—
238	C₂²×C₁₆	—	43	1	no	—
239	#497	—	2	2	no	—
240	#495	C₂×D₄₃	1	2	yes	—
241	#494	C₂×D₄₃	1	2	yes	—
242	#440	—	86	2	no	—
243	C₄×Q₁₆	—	43	2	no	—
244	C₄×D₈	—	43	2	no	—
245	C₂×#107	—	43	1	no	—
246	#417	—	86	1	no	—
247	#405	C₂×D₄₃	1	1	yes	characteristic
248	C₄⋊C₁₆	—	43	2	no	—
249	C₄⋊C₁₆	—	43	2	no	—
250	#358	—	43	2	no	—
251	#358	—	43	2	no	—
252	#358	—	43	2	no	—
253	#357	—	43	2	no	—
254	C₄₃	#33590	1	1	yes	characteristic, complemented, Sylow
255	C₂×#41	—	2	1	no	—
256	C₂×#41	—	86	1	no	—
257	C₂²×Q₈	—	2	1	no	—
258	#137	—	4	4	no	—
259	#135	—	2	2	no	—
260	#135	—	2	2	no	—
261	#135	—	43	4	no	—
262	#135	—	86	2	no	—
263	C₂×Q₁₆	—	2	2	no	—
264	C₂×Q₁₆	—	2	2	no	—
265	C₂×Q₁₆	—	2	1	no	—
266	C₂×Q₁₆	—	2	2	no	—
267	C₂×Q₁₆	—	43	1	no	—
268	C₂×Q₁₆	C₂²×D₄₃	1	2	yes	—
269	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
270	C₂×SD₁₆	—	2	1	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂×SD₁₆	—	86	1	no	—
273	C₂×D₈	—	43	1	no	—
274	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
275	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
276	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
277	C₄⋊Q₈	—	2	2	no	—
278	#124	—	2	2	no	—
279	#123	—	4	2	no	—
280	C₂²⋊Q₈	—	4	1	no	—
281	C₂²⋊Q₈	—	4	1	no	—
282	C₄×Q₈	—	86	2	no	—
283	C₄×D₄	—	86	2	no	—
284	C₄×D₄	—	172	2	no	—
285	#117	—	172	1	no	—
286	#117	C₂²⋊D₄₃	1	1	yes	characteristic
287	C₂×C₄⋊C₄	—	86	1	no	—
288	C₂×C₄⋊C₄	—	172	1	no	—
289	Q₃₂	—	86	2	no	—
290	Q₃₂	—	86	4	no	—
291	SD₃₂	—	86	2	no	—
292	SD₃₂	—	86	2	no	—
293	SD₃₂	—	86	4	no	—
294	D₁₆	—	86	2	no	—
295	M₃₂	—	86	2	no	—
296	C₂×C₁₆	—	43	2	no	—
297	C₂×C₁₆	—	43	1	no	—
298	C₂×C₁₆	—	43	1	no	—
299	C₂×C₁₆	—	86	2	no	—
300	#107	—	43	2	no	—
301	#107	—	86	1	no	—
302	#103	—	86	2	no	—
303	#102	—	86	2	no	—
304	#97	C₂²⋊D₄₃	1	2	yes	—
305	C₄×C₈	C₂²×D₄₃	1	2	yes	—
306	#41	—	4	2	no	—
307	#41	—	4	2	no	—
308	#41	—	86	4	no	—
309	#41	—	172	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	—	86	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	86	1	no	—
319	C₂×D₄	—	172	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	172	1	no	—
323	C₂²×C₄	—	172	1	no	—
324	C₂²×C₄	—	172	2	no	—
325	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
326	Q₁₆	—	2	2	no	—
327	Q₁₆	—	2	1	no	—
328	Q₁₆	—	2	2	no	—
329	Q₁₆	—	2	1	no	—
330	Q₁₆	—	4	4	no	—
331	Q₁₆	—	4	2	no	—
332	Q₁₆	—	43	2	no	—
333	Q₁₆	—	86	1	no	—
334	SD₁₆	—	4	4	no	—
335	SD₁₆	—	4	2	no	—
336	SD₁₆	—	86	4	no	—
337	D₈	—	2	1	no	—
338	D₈	—	2	1	no	—
339	D₈	—	43	2	no	—
340	D₈	—	86	1	no	—
341	M₁₆	—	2	2	no	—
342	C₂×C₈	D₄×D₄₃	1	2	yes	—
343	C₂×C₈	#10621900	1	2	yes	—
344	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
345	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
346	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	86	2	no	—
350	C₄⋊C₄	—	172	1	no	—
351	C₄⋊C₄	—	172	2	no	—
352	C₄⋊C₄	#10621882	1	1	yes	characteristic
353	C₄⋊C₄	#10621882	1	1	yes	characteristic
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	172	2	no	—
357	C₂²⋊C₄	#10621882	1	2	yes	—
358	C₄²	—	172	2	no	—
359	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
360	C₁₆	—	86	1	no	—
361	C₁₆	—	86	1	no	—
362	C₁₆	—	86	2	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	172	1	no	—
365	C₂³	C₂×#10621882	1	1	yes	characteristic
366	Q₈	—	4	1	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	1	no	—
370	Q₈	—	8	2	no	—
371	Q₈	—	86	2	no	—
372	Q₈	—	172	1	no	—
373	D₄	—	4	1	no	—
374	D₄	—	4	1	no	—
375	D₄	—	8	2	no	—
376	D₄	—	86	2	no	—
377	D₄	—	172	4	no	—
378	D₄	—	172	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	8	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	—	172	2	no	—
384	C₂×C₄	—	172	1	no	—
385	C₂×C₄	—	172	4	no	—
386	C₂×C₄	—	688	2	no	—
387	C₂×C₄	—	688	1	no	—
388	C₂×C₄	#13063296	1	2	yes	—
389	C₂×C₄	C₂×#10621882	1	2	yes	—
390	C₂×C₄	C₂×#10621882	1	2	yes	—
391	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
392	C₂×C₄	#13063351	1	2	yes	—
393	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	#13063296	1	2	yes	—
396	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
397	C₈	C₂×#10621900	1	1	yes	characteristic
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	344	1	no	—
404	C₂²	—	344	1	no	—
405	C₂²	—	172	2	no	—
406	C₂²	#14583091	1	2	yes	—
407	C₂²	C₂²×#10621882	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	2	no	—
412	C₄	—	344	2	no	—
413	C₄	—	172	2	no	—
414	C₄	#14583091	1	2	yes	—
415	C₄	C₂×#13063296	1	1	yes	characteristic
416	C₄	C₂×#13063351	1	1	yes	characteristic
417	C₂	—	2	2	no	—
418	C₂	—	16	1	no	—
419	C₂	—	344	2	no	—
420	C₂	C₂×#14583091	1	1	yes	characteristic
421	C₂	#19147739	1	1	yes	characteristic
422	C₂	#19147746	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#10621882
commutator, cosocle	C₂×C₈×C₄₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₄₃×#3156	C₂
socle	C₂²×C₄₃	C₂²×D₈
prime radical	C₂×#14583329	C₂
hypercenter	#3156	D₄₃
hypocenter	C₄₃	#33590
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405 ◁ #3156

Complements

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

N	H ≅ G/N	type
1. C₂×#14583340	C₂	semidirect
3. #19143472	C₂	semidirect
4. #19136654	C₂	semidirect
5. #19136647	C₂	semidirect
6. #19136642	C₂	semidirect
7. #19136637	C₂	semidirect
8. #19136354	C₂	semidirect
9. #19136307	C₂	semidirect
10. C₂×#14582703	C₂	semidirect
11. C₄₃×#3156	C₂	semidirect
208. #3156	D₄₃	semidirect
254. C₄₃	#33590	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583340	2
C₂×#14583329	2
#19143472	2
#19136654	2
#19136647	2
#19136642	2
#19136637	2
#19136354	2
#19136307	2
C₂×#14582703	2
C₄₃×#3156	2
#33590	43