Subgroups — #32097417

Order 18176.

608 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22598863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17986119	C₂	1	1	yes	maximal, characteristic
3	#22589515	C₂	1	2	yes	maximal, complemented
4	#22589510	C₂	1	2	yes	maximal, complemented
5	#22589237	C₂	1	2	yes	maximal
6	#22588461	C₂	1	2	yes	maximal, complemented
7	#22588395	C₂	1	1	yes	maximal, characteristic, complemented
8	#22588386	C₂	1	1	yes	maximal, characteristic, complemented
9	#22588383	C₂	1	1	yes	maximal, characteristic, complemented
10	#22588227	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#1814	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556148	C₂²	1	1	yes	characteristic
13	C₂×#14556134	C₂²	1	1	yes	characteristic
14	#17986552	C₂²	1	2	yes	—
15	#17986407	—	2	2	no	—
16	#17986406	—	2	2	no	—
17	#17986119	—	2	2	no	—
18	#17986119	—	2	2	no	—
19	C₂×#14556063	C₂²	1	1	yes	characteristic
20	#17986037	C₂²	1	1	yes	characteristic
21	#17986037	C₂²	1	1	yes	characteristic
22	#17986035	C₂²	1	2	yes	—
23	#17986015	C₂²	1	2	yes	—
24	C₂×#14556055	C₂²	1	1	yes	characteristic
25	C₂×#14556054	C₂²	1	1	yes	characteristic
26	#17985973	C₂²	1	2	yes	—
27	#17985972	C₂²	1	2	yes	—
28	#17985957	C₂²	1	2	yes	—
29	C₂×#14556038	C₂²	1	1	yes	characteristic
30	#17985770	C₂²	1	2	yes	—
31	#17985760	C₂²	1	2	yes	—
32	#17985756	C₂²	1	2	yes	—
33	#17985755	C₂²	1	2	yes	—
34	C₂×#131×C₇₁	C₂²	1	1	yes	characteristic
35	C₂×#108×C₇₁	C₂²	1	1	yes	characteristic
36	#427×C₇₁	C₂²	1	1	yes	characteristic
37	#421×C₇₁	C₂²	1	2	yes	—
38	#344×C₇₁	C₂²	1	2	yes	—
39	C₂×#11765865	C₂³	1	1	yes	characteristic
40	#14556148	—	2	2	no	—
41	#14556148	—	2	2	no	—
42	C₂×#11765855	Q₈	1	1	yes	characteristic, complemented
43	C₂×#11765853	Q₈	1	1	yes	characteristic, complemented
44	C₂×#11765852	Q₈	1	1	yes	characteristic, complemented
45	C₂×#11765850	Q₈	1	1	yes	characteristic, complemented
46	#14556134	—	2	1	no	—
47	#14556134	—	2	1	no	—
48	#14556134	—	2	1	no	—
49	#14556134	—	2	1	no	—
50	C₂×#11765849	C₂³	1	1	yes	characteristic
51	C₂×#11765848	—	2	1	no	—
52	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
53	C₂×C₈×D₇₁	—	2	1	no	—
54	#14556127	—	2	2	no	—
55	#14556119	—	2	2	no	—
56	#14556105	—	4	2	no	—
57	C₄×Dic₁₄₂	—	4	2	no	—
58	#14556087	C₂³	1	2	yes	—
59	#14556087	C₂³	1	2	yes	—
60	C₂×C₄×Dic₇₁	C₂³	1	1	yes	characteristic
61	#14556063	—	2	2	no	—
62	#14556062	—	2	1	no	—
63	#14556062	—	2	1	no	—
64	#14556061	—	2	2	no	—
65	#14556060	—	2	1	no	—
66	#14556060	—	2	1	no	—
67	#14556059	—	2	2	no	—
68	#14556055	—	2	2	no	—
69	#14556054	—	2	2	no	—
70	#14556054	—	4	2	no	—
71	#14556043	—	4	2	no	—
72	#14556042	—	4	2	no	—
73	#14556038	—	2	2	no	—
74	#14556038	D₄	1	2	yes	—
75	#14556038	D₄	1	2	yes	—
76	C₈×Dic₇₁	—	2	2	no	—
77	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
78	#131×C₇₁	—	2	1	no	—
79	#131×C₇₁	—	2	1	no	—
80	#131×C₇₁	—	2	1	no	—
81	#131×C₇₁	—	2	1	no	—
82	C₂×M₁₆×C₇₁	—	2	1	no	—
83	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
84	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₇₁	—	2	1	no	—
86	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
87	#117×C₇₁	C₂³	1	2	yes	—
88	#108×C₇₁	—	2	1	no	—
89	#108×C₇₁	—	2	1	no	—
90	#107×C₇₁	—	2	1	no	—
91	#106×C₇₁	—	2	1	no	—
92	#104×C₇₁	—	4	2	no	—
93	#11765865	—	2	1	no	—
94	#11765865	—	2	1	no	—
95	#11765865	—	2	1	no	—
96	#11765865	—	2	1	no	—
97	C₂×Dic₁₄₂	—	4	2	no	—
98	C₂×Dic₁₄₂	C₂×Q₈	1	1	yes	characteristic
99	C₂×D₂₈₄	C₂×Q₈	1	1	yes	characteristic
100	C₂×C₂²⋊D₇₁	—	2	1	no	—
101	C₂²×Dic₇₁	—	2	1	no	—
102	C₂×C₄×D₇₁	—	2	1	no	—
103	#11765855	—	2	2	no	—
104	#11765853	—	2	2	no	—
105	#11765852	—	2	2	no	—
106	#11765850	—	2	2	no	—
107	#11765849	—	2	1	no	—
108	#11765849	—	2	1	no	—
109	#11765848	—	4	1	no	—
110	#11765848	—	4	1	no	—
111	C₂×C₇₁⋊C₈	—	2	1	no	—
112	C₂×C₇₁⋊C₈	C₂×D₄	1	2	yes	—
113	C₂×C₇₁⋊C₈	C₂×Q₈	1	1	yes	characteristic
114	C₂×C₇₁⋊C₈	C₂×Q₈	1	1	yes	characteristic
115	C₂×C₇₁⋊C₈	#41	1	2	yes	—
116	C₈×D₇₁	—	4	1	no	—
117	C₈×D₇₁	—	4	1	no	—
118	C₄⋊Dic₇₁	—	2	2	no	—
119	C₄⋊Dic₇₁	—	2	2	no	—
120	C₄⋊Dic₇₁	—	4	2	no	—
121	Dic₇₁⋊C₄	—	4	2	no	—
122	Dic₇₁⋊C₄	—	4	2	no	—
123	C₂²⋊Dic₇₁	—	2	2	no	—
124	C₂²⋊Dic₇₁	—	2	2	no	—
125	C₄×Dic₇₁	—	2	1	no	—
126	C₄×Dic₇₁	—	2	2	no	—
127	C₄×Dic₇₁	—	2	2	no	—
128	C₄×Dic₇₁	C₂×D₄	1	2	yes	—
129	#41×C₇₁	—	2	1	no	—
130	#41×C₇₁	—	2	1	no	—
131	#41×C₇₁	—	2	1	no	—
132	#41×C₇₁	—	2	1	no	—
133	C₂×Q₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
134	C₂×D₄×C₇₁	—	2	1	no	—
135	C₂×D₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
136	C₂²×C₄×C₇₁	—	2	1	no	—
137	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
138	M₁₆×C₇₁	—	2	1	no	—
139	M₁₆×C₇₁	—	2	2	no	—
140	M₁₆×C₇₁	—	2	1	no	—
141	M₁₆×C₇₁	—	2	2	no	—
142	M₁₆×C₇₁	—	4	1	no	—
143	M₁₆×C₇₁	—	4	1	no	—
144	C₂×C₈×C₇₁	—	2	1	no	—
145	C₂×C₈×C₇₁	—	2	2	no	—
146	C₂×C₈×C₇₁	—	4	1	no	—
147	C₂×C₈×C₇₁	—	4	1	no	—
148	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
151	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
152	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
153	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
154	C₄⋊C₄×C₇₁	—	2	2	no	—
155	C₂²⋊C₄×C₇₁	—	2	2	no	—
156	C₄²×C₇₁	—	2	2	no	—
157	C₂³×C₇₁	—	2	1	no	—
158	C₂³×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
159	C₂²×D₇₁	—	2	1	no	—
160	Q₈×C₇₁	—	2	1	no	—
161	Q₈×C₇₁	—	2	1	no	—
162	D₄×C₇₁	—	2	1	no	—
163	D₄×C₇₁	—	2	1	no	—
164	D₄×C₇₁	—	4	1	no	—
165	D₄×C₇₁	—	4	1	no	—
166	C₂×C₄×C₇₁	—	2	1	no	—
167	C₂×C₄×C₇₁	—	4	1	no	—
168	C₂×C₄×C₇₁	—	4	1	no	—
169	C₂×C₄×C₇₁	—	4	2	no	—
170	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂²⋊D₇₁	—	4	1	no	—
177	C₂²⋊D₇₁	—	4	1	no	—
178	C₂×Dic₇₁	—	2	2	no	—
179	C₂×Dic₇₁	—	2	1	no	—
180	C₂×Dic₇₁	—	4	2	no	—
181	C₂×Dic₇₁	—	4	2	no	—
182	C₂×Dic₇₁	—	8	1	no	—
183	D₂₈₄	—	2	1	no	—
184	D₂₈₄	—	2	1	no	—
185	C₄×D₇₁	—	4	1	no	—
186	C₄×D₇₁	—	4	1	no	—
187	Dic₁₄₂	—	2	1	no	—
188	Dic₁₄₂	—	2	1	no	—
189	Dic₁₄₂	—	8	4	no	—
190	C₈×C₇₁	—	4	1	no	—
191	C₈×C₇₁	—	4	2	no	—
192	C₈×C₇₁	#124	1	1	yes	characteristic
193	C₈×C₇₁	#124	1	1	yes	characteristic
194	C₈×C₇₁	#124	1	1	yes	characteristic
195	C₈×C₇₁	#124	1	1	yes	characteristic
196	C₇₁⋊C₈	—	4	1	no	—
197	C₇₁⋊C₈	C₂²⋊Q₈	1	2	yes	—
198	C₇₁⋊C₈	C₂²⋊Q₈	1	2	yes	—
199	C₂²×C₇₁	—	4	1	no	—
200	C₂²×C₇₁	—	4	1	no	—
201	C₂²×C₇₁	—	8	1	no	—
202	C₂²×C₇₁	#535	1	1	yes	characteristic
203	C₂²×C₇₁	#554	1	1	yes	characteristic
204	C₂²×C₇₁	#555	1	1	yes	characteristic
205	C₂×D₇₁	—	4	1	no	—
206	C₂×D₇₁	—	8	1	no	—
207	C₄×C₇₁	—	4	1	no	—
208	C₄×C₇₁	—	8	2	no	—
209	C₄×C₇₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
210	C₄×C₇₁	C₂×#124	1	1	yes	characteristic
211	C₄×C₇₁	#554	1	1	yes	characteristic
212	C₄×C₇₁	#555	1	1	yes	characteristic
213	Dic₇₁	—	4	2	no	—
214	Dic₇₁	—	4	1	no	—
215	Dic₇₁	—	8	2	no	—
216	Dic₇₁	—	8	2	no	—
217	#29155	—	71	1	no	maximal, Sylow
218	C₂×C₇₁	—	2	1	no	—
219	C₂×C₇₁	—	2	1	no	—
220	C₂×C₇₁	—	2	1	no	—
221	C₂×C₇₁	—	8	1	no	—
222	C₂×C₇₁	#2563	1	1	yes	characteristic
223	D₇₁	—	8	1	no	—
224	#3162	—	71	1	no	—
225	C₂×#444	—	71	1	no	—
226	#2031	—	71	2	no	—
227	#2031	—	71	2	no	—
228	#1976	—	71	2	no	—
229	#1833	—	71	2	no	—
230	#1814	—	71	1	no	—
231	#1814	D₇₁	1	1	yes	characteristic, complemented
232	#1812	—	71	1	no	—
233	#1812	—	71	1	no	—
234	#1773	—	71	1	no	—
235	C₇₁	#29155	1	1	yes	characteristic, complemented, Sylow
236	C₂×#135	—	71	1	no	—
237	C₂×#131	—	71	1	no	—
238	C₂×#131	C₂×D₇₁	1	1	yes	characteristic
239	#533	—	71	2	no	—
240	#501	—	142	2	no	—
241	#501	—	142	2	no	—
242	#444	—	142	2	no	—
243	#444	—	142	2	no	—
244	C₂×#108	—	71	1	no	—
245	C₂×#108	C₂×D₇₁	1	1	yes	characteristic
246	#427	—	71	1	no	—
247	#427	—	71	1	no	—
248	#427	—	71	2	no	—
249	#427	C₂×D₇₁	1	1	yes	characteristic
250	#421	—	71	2	no	—
251	#421	C₂×D₇₁	1	2	yes	—
252	C₂×#104	—	71	1	no	—
253	C₂×#104	—	71	1	no	—
254	#410	—	71	2	no	—
255	#410	—	71	2	no	—
256	#405	—	71	2	no	—
257	C₂×#97	—	71	1	no	—
258	#344	—	71	2	no	—
259	#344	C₂×D₇₁	1	2	yes	—
260	#339	—	71	2	no	—
261	H(3,ℤ/4)	—	71	2	no	—
262	H(3,ℤ/4)	—	71	2	no	—
263	C₂×#41	—	71	1	no	—
264	C₂×#41	C₂²×D₇₁	1	1	yes	characteristic
265	#135	—	142	2	no	—
266	#135	—	142	2	no	—
267	C₂×Q₁₆	—	71	1	no	—
268	C₂×SD₁₆	—	71	1	no	—
269	C₂×SD₁₆	—	71	1	no	—
270	C₂×D₈	—	71	1	no	—
271	#131	—	2	1	no	—
272	#131	—	2	1	no	—
273	#131	—	2	1	no	—
274	#131	—	2	1	no	—
275	#131	—	142	1	no	—
276	#131	—	142	1	no	—
277	#131	—	142	1	no	—
278	#131	—	142	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	71	1	no	—
281	C₂×M₁₆	—	142	1	no	—
282	C₂×M₁₆	C₂²×D₇₁	1	1	yes	characteristic
283	C₂×M₁₆	C₂²×D₇₁	1	2	yes	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	71	1	no	—
286	C₂²×C₈	—	142	1	no	—
287	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
288	C₄⋊Q₈	—	142	2	no	—
289	#125	—	142	2	no	—
290	C₂²⋊Q₈	—	284	2	no	—
291	C₄×Q₈	—	284	2	no	—
292	#117	—	71	2	no	—
293	#117	—	71	2	no	—
294	#117	C₂²×D₇₁	1	2	yes	—
295	C₂×C₄²	—	71	1	no	—
296	#108	—	2	1	no	—
297	#108	—	2	1	no	—
298	#108	—	142	2	no	—
299	#107	—	2	1	no	—
300	#107	—	142	2	no	—
301	#107	—	142	1	no	—
302	#107	—	142	1	no	—
303	#106	—	2	1	no	—
304	#106	—	142	2	no	—
305	#106	—	142	1	no	—
306	#106	—	142	1	no	—
307	#104	—	4	2	no	—
308	#104	—	284	2	no	—
309	#104	—	142	2	no	—
310	#104	—	142	2	no	—
311	#99	—	284	2	no	—
312	#99	—	284	2	no	—
313	#97	—	71	2	no	—
314	#97	—	71	2	no	—
315	#97	—	142	2	no	—
316	C₄×C₈	—	142	2	no	—
317	#41	—	2	1	no	—
318	#41	—	2	1	no	—
319	#41	—	2	1	no	—
320	#41	—	2	1	no	—
321	#41	—	142	1	no	—
322	#41	—	142	1	no	—
323	#41	—	142	1	no	—
324	#41	—	142	1	no	—
325	C₂×Q₈	—	284	2	no	—
326	C₂×Q₈	—	71	1	no	—
327	C₂×Q₈	Q₈×D₇₁	1	1	yes	characteristic
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	71	1	no	—
330	C₂×D₄	—	142	1	no	—
331	C₂×D₄	Q₈×D₇₁	1	1	yes	characteristic
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	142	1	no	—
334	C₂²×C₄	—	142	1	no	—
335	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
336	Q₁₆	—	142	2	no	—
337	SD₁₆	—	142	2	no	—
338	SD₁₆	—	142	2	no	—
339	D₈	—	142	2	no	—
340	M₁₆	—	2	1	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	2	1	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	4	1	no	—
345	M₁₆	—	4	1	no	—
346	M₁₆	—	284	1	no	—
347	M₁₆	—	284	1	no	—
348	M₁₆	—	142	1	no	—
349	M₁₆	—	142	1	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	284	1	no	—
355	C₂×C₈	—	284	1	no	—
356	C₂×C₈	—	71	2	no	—
357	C₂×C₈	—	71	1	no	—
358	C₂×C₈	—	71	1	no	—
359	C₂×C₈	—	71	2	no	—
360	C₂×C₈	—	142	1	no	—
361	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
362	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
363	C₂×C₈	#11765864	1	1	yes	characteristic
364	C₂×C₈	#11765864	1	1	yes	characteristic
365	C₂×C₈	#11765865	1	1	yes	characteristic
366	C₂×C₈	#11765865	1	1	yes	characteristic
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	284	2	no	—
369	C₄⋊C₄	—	284	2	no	—
370	C₄⋊C₄	—	284	2	no	—
371	C₄⋊C₄	—	142	2	no	—
372	C₄⋊C₄	—	142	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	142	2	no	—
375	C₂²⋊C₄	—	142	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	71	2	no	—
378	C₄²	—	142	2	no	—
379	C₄²	—	142	2	no	—
380	C₄²	—	142	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	142	1	no	—
383	C₂³	#14556174	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	568	4	no	—
387	Q₈	—	142	1	no	—
388	Q₈	—	142	1	no	—
389	D₄	—	2	1	no	—
390	D₄	—	2	1	no	—
391	D₄	—	4	1	no	—
392	D₄	—	4	1	no	—
393	D₄	—	284	1	no	—
394	D₄	—	284	1	no	—
395	D₄	—	142	1	no	—
396	D₄	—	142	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	284	1	no	—
402	C₂×C₄	—	284	1	no	—
403	C₂×C₄	—	284	2	no	—
404	C₂×C₄	—	284	2	no	—
405	C₂×C₄	—	568	1	no	—
406	C₂×C₄	—	142	2	no	—
407	C₂×C₄	—	142	1	no	—
408	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
409	C₂×C₄	C₂×Q₈×D₇₁	1	1	yes	characteristic
410	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
411	C₂×C₄	C₂×#11765864	1	1	yes	characteristic
412	C₂×C₄	C₂×#11765865	1	1	yes	characteristic
413	C₂×C₄	#14556173	1	1	yes	characteristic
414	C₈	—	4	2	no	—
415	C₈	—	4	1	no	—
416	C₈	—	284	1	no	—
417	C₈	—	71	2	no	—
418	C₈	—	71	2	no	—
419	C₈	#14556114	1	1	yes	characteristic
420	C₈	#14556114	1	1	yes	characteristic
421	C₈	#14556114	1	1	yes	characteristic
422	C₈	#14556114	1	1	yes	characteristic
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	284	1	no	—
427	C₂²	—	568	1	no	—
428	C₂²	#17986565	1	1	yes	characteristic
429	C₂²	#17986707	1	1	yes	characteristic
430	C₂²	#17986712	1	1	yes	characteristic
431	C₄	—	4	1	no	—
432	C₄	—	8	2	no	—
433	C₄	—	284	2	no	—
434	C₄	—	284	1	no	—
435	C₄	—	568	2	no	—
436	C₄	—	568	2	no	—
437	C₄	C₂²⋊Q₈×D₇₁	1	1	yes	characteristic
438	C₄	C₂×#14556114	1	1	yes	characteristic
439	C₄	#17986704	1	1	yes	characteristic
440	C₄	#17986713	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	2	1	no	—
444	C₂	—	8	1	no	—
445	C₂	—	568	1	no	—
446	C₂	#22593510	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#17986713
commutator, cosocle	C₂²×C₄×C₇₁	C₂⁴
Frattini	C₂²×C₄	C₂³×D₇₁
Fitting	C₇₁×#1814	C₂
socle	C₂×C₇₁	#2563
prime radical	C₂×#14556148	C₂²
hypercenter	#1814	D₇₁
hypocenter	C₇₁	#29155
LCS	G ▷ C₂²×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1814

Complements

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

N	H ≅ G/N	type
1. #22598863	C₂	semidirect
3. #22589515	C₂	semidirect
4. #22589510	C₂	semidirect
6. #22588461	C₂	semidirect
7. #22588395	C₂	semidirect
8. #22588386	C₂	semidirect
9. #22588383	C₂	semidirect
10. #22588227	C₂	semidirect
11. C₇₁×#1814	C₂	semidirect
42. C₂×#11765855	Q₈	semidirect
43. C₂×#11765853	Q₈	semidirect
44. C₂×#11765852	Q₈	semidirect
45. C₂×#11765850	Q₈	semidirect
231. #1814	D₇₁	semidirect
235. C₇₁	#29155	semidirect

Maximal subgroups

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

subgroup	index
#22598863	2
C₂×#17986119	2
#22589515	2
#22589510	2
#22589237	2
#22588461	2
#22588395	2
#22588386	2
#22588383	2
#22588227	2
C₇₁×#1814	2
#29155	71