Finite Group Databasebeta

← C22×#10623151 #15660640

Subgroups — C22×#10623151 #15660640

Order 2816.

9606 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623151C2148yesmaximal, direct product factor
2C22×#66993C211yesmaximal, characteristic, complemented
3C22×#66951C211yesmaximal, characteristic, complemented
4C22×#66932C211yesmaximal, characteristic, complemented
5C22×#66947C211yesmaximal, characteristic, complemented
6C22×#66939C211yesmaximal, characteristic, complemented
7C22×#66982C211yesmaximal, characteristic, complemented
8C22×#66983C211yesmaximal, characteristic, complemented
9C22×#66937C211yesmaximal, characteristic, complemented
10C22×#66992C211yesmaximal, characteristic, complemented
11C22×#66992C211yesmaximal, characteristic, complemented
12C22×#66991C211yesmaximal, characteristic, complemented
13C22×#66935C211yesmaximal, characteristic, complemented
14C22×#66990C211yesmaximal, characteristic, complemented
15C22×#66990C211yesmaximal, characteristic, complemented
16C22×C11×#121C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×D4×C11C2211yescharacteristic, complemented
21C24×C4×C11C2211yescharacteristic, complemented
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic
24C23×C22⋊D11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C23×C22⋊D11C2211yescharacteristic
27C23×C22⋊D11C2211yescharacteristic, complemented
28C23×C22⋊D11C2211yescharacteristic, complemented
29C24×Dic11C2211yescharacteristic, complemented
30C23×D44C2211yescharacteristic
31C23×D44C2211yescharacteristic
32C23×C4×D11C2211yescharacteristic, complemented
33C2×C11×#121C22124yescomplemented
34C22×C11×C4⋊C4C2211yescharacteristic, complemented
35C22×C11×C22⋊C4C2211yescharacteristic
36C22×C11×C22⋊C4C2211yescharacteristic, complemented
37C22×C22⋊Dic11C2211yescharacteristic
38C22×C22⋊Dic11C2211yescharacteristic
39C22×C22⋊Dic11C2211yescharacteristic, complemented
40C2×#66993C22124yescomplemented
41C2×#66992C22124yescomplemented
42C2×#66992C22124yescomplemented
43C2×#66991C22124yescomplemented
44C2×#66990C22124yescomplemented
45C2×#66990C22124yescomplemented
46C2×#66983C22124yescomplemented
47C2×#66982C22124yescomplemented
48C22×(C2×D11)⋊C4C2211yescharacteristic
49C22×(C2×D11)⋊C4C2211yescharacteristic
50C22×(C2×D11)⋊C4C2211yescharacteristic
51C22×(C2×D11)⋊C4C2211yescharacteristic
52C22×(C2×D11)⋊C4C2211yescharacteristic
53C22×(C2×D11)⋊C4C2211yescharacteristic
54C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
55C22×C4⋊Dic11C2211yescharacteristic, complemented
56C22×C4⋊Dic11C2211yescharacteristic, complemented
57C22×Dic11⋊C4C2211yescharacteristic, complemented
58C22×Dic11⋊C4C2211yescharacteristic, complemented
59C22×Dic11⋊C4C2211yescharacteristic, complemented
60C22×C4×Dic11C2211yescharacteristic, complemented
61#10623151C221256yesdirect product factor
62C2×#66951C22124yescomplemented
63C2×#66947C22124yescomplemented
64C2×#66939C22124yescomplemented
65C2×#66937C22124yescomplemented
66C2×#66935C22124yescomplemented
67C2×#66932C22124yescomplemented
68C25×C11C2311yescharacteristic
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11—44no—
72C24×D11—44no—
73C24×D11—44no—
74C24×D11C2311yescharacteristic
75C24×D11C2311yescharacteristic
76C24×D11C2311yescharacteristic
77C24×D11C23112yes—
78C22×D4×C11—44no—
79C22×D4×C11—44no—
80C22×D4×C11—44no—
81C22×D4×C11C23112yes—
82C22×D4×C11C23112yes—
83C22×D4×C11C23112yescomplemented
84C23×C4×C11—44no—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C23112yescomplemented
90C22×C22⋊D11—44no—
91C22×C22⋊D11—44no—
92C22×C22⋊D11—44no—
93C22×C22⋊D11—44no—
94C22×C22⋊D11—44no—
95C22×C22⋊D11—44no—
96C22×C22⋊D11—44no—
97C22×C22⋊D11C23112yes—
98C22×C22⋊D11C23112yes—
99C22×C22⋊D11C23112yes—
100C22×C22⋊D11C23112yes—
101C22×C22⋊D11C23112yes—
102C22×C22⋊D11C23112yescomplemented
103C22×C22⋊D11C23112yescomplemented
104C23×Dic11—44no—
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C23112yescomplemented
111C22×D44—44no—
112C22×D44—44no—
113C22×D44C23112yes—
114C22×D44C23112yes—
115C22×C4×D11—44no—
116C22×C4×D11C23112yescomplemented
117C11×#121C23164yescomplemented
118C2×C11×C4⋊C4C23112yescomplemented
119C2×C11×C22⋊C4C23112yes—
120C2×C11×C22⋊C4C23112yescomplemented
121C2×C22⋊Dic11C23112yes—
122C2×C22⋊Dic11C23112yes—
123C2×C22⋊Dic11C23112yescomplemented
124#66993C23164yescomplemented
125#66992C23164yescomplemented
126#66992C23164yescomplemented
127#66991C23164yescomplemented
128#66990C23164yescomplemented
129#66990C23164yescomplemented
130#66983C23164yescomplemented
131#66982C23164yescomplemented
132C2×(C2×D11)⋊C4C23112yes—
133C2×(C2×D11)⋊C4C23112yes—
134C2×(C2×D11)⋊C4C23112yes—
135C2×(C2×D11)⋊C4C23112yes—
136C2×(C2×D11)⋊C4C23112yes—
137C2×(C2×D11)⋊C4C23112yes—
138C2×(C2×D11)⋊C4C23112yescomplemented
139C2×C4⋊Dic11C23112yescomplemented
140C2×C4⋊Dic11C23112yescomplemented
141C2×Dic11⋊C4C23112yescomplemented
142C2×Dic11⋊C4C23112yescomplemented
143C2×Dic11⋊C4C23112yescomplemented
144C2×C4×Dic11C23112yescomplemented
145#66951C23164yescomplemented
146#66947C23164yescomplemented
147#66939C23164yescomplemented
148#66937C23164yescomplemented
149#66935C23164yescomplemented
150#66932C23164yescomplemented
151C22×#560—111nomaximal, Sylow
152C24×C11—24no—
153C24×C11—24no—
154C24×C11—24no—
155C24×C11—24no—
156C24×C11—24no—
157C24×C11—24no—
158C24×C11—24no—
159C24×C11—24no—
160C24×C11—24no—
161C24×C11C2416yes—
162C24×C11C2416yes—
163C24×C11C2416yes—
164C24×C11C2411yescharacteristic
165C23×D11—24no—
166C23×D11—24no—
167C23×D11—24no—
168C23×D11—24no—
169C23×D11—24no—
170C23×D11—24no—
171C23×D11—24no—
172C23×D11—24no—
173C23×D11—24no—
174C23×D11—424no—
175C23×D11—424no—
176C23×D11—424no—
177C23×D11—464no—
178C23×D11C2416yes—
179C23×D11C2416yes—
180C23×D11C2416yes—
181C23×D11C24116yes—
182C2×D4×C11—424no—
183C2×D4×C11—424no—
184C2×D4×C11—424no—
185C2×D4×C11C24116yes—
186C2×D4×C11C24116yes—
187C2×D4×C11C24116yescomplemented
188C22×C4×C11—24no—
189C22×C4×C11—24no—
190C22×C4×C11—24no—
191C22×C4×C11—24no—
192C22×C4×C11—424no—
193C22×C4×C11C2416yes—
194C22×C4×C11C2416yes—
195C22×C4×C11C2416yes—
196C22×C4×C11C2416yes—
197C22×C4×C11C24116yescomplemented
198C2×C22⋊D11—424no—
199C2×C22⋊D11—424no—
200C2×C22⋊D11—424no—
201C2×C22⋊D11—424no—
202C2×C22⋊D11—424no—
203C2×C22⋊D11—424no—
204C2×C22⋊D11—424no—
205C2×C22⋊D11C24116yes—
206C2×C22⋊D11C24116yes—
207C2×C22⋊D11C24116yes—
208C2×C22⋊D11C24116yes—
209C2×C22⋊D11C24116yes—
210C2×C22⋊D11C24116yescomplemented
211C2×C22⋊D11C24116yescomplemented
212C22×Dic11—24no—
213C22×Dic11—24no—
214C22×Dic11—24no—
215C22×Dic11—24no—
216C22×Dic11—24no—
217C22×Dic11—424no—
218C22×Dic11C2416yes—
219C22×Dic11C2416yes—
220C22×Dic11C2416yes—
221C22×Dic11C2416yes—
222C22×Dic11C2416yes—
223C22×Dic11C24116yescomplemented
224C2×D44—424no—
225C2×D44—424no—
226C2×D44C24116yes—
227C2×D44C24116yes—
228C2×C4×D11—424no—
229C2×C4×D11C24116yescomplemented
230C11×C4⋊C4C24116yescomplemented
231C11×C22⋊C4C24116yes—
232C11×C22⋊C4C24116yescomplemented
233C22⋊Dic11C24116yes—
234C22⋊Dic11C24116yes—
235C22⋊Dic11C24116yescomplemented
236(C2×D11)⋊C4C24116yes—
237(C2×D11)⋊C4C24116yes—
238(C2×D11)⋊C4C24116yes—
239(C2×D11)⋊C4C24116yes—
240(C2×D11)⋊C4C24116yes—
241(C2×D11)⋊C4C24116yes—
242(C2×D11)⋊C4C24116yescomplemented
243C4⋊Dic11C24116yescomplemented
244C4⋊Dic11C24116yescomplemented
245Dic11⋊C4C24116yescomplemented
246Dic11⋊C4C24116yescomplemented
247Dic11⋊C4C24116yescomplemented
248C4×Dic11C24116yescomplemented
249C2×#560—1148no—
250C22×#127—111no—
251C22×#126—111no—
252C22×#126—111no—
253C22×#123—111no—
254C22×#123—111no—
255C22×#123—111no—
256C22×#121—111no—
257C22×#121—111no—
258C22×#121—111no—
259C22×#121—111no—
260C22×#121—111no—
261C22×#121D1111yescharacteristic, complemented
262C22×#120—111no—
263C22×#120—111no—
264C22×#120—111no—
265C23×C11—212no—
266C23×C11—212no—
267C23×C11—212no—
268C23×C11—212no—
269C23×C11—212no—
270C23×C11—212no—
271C23×C11—212no—
272C23×C11—212no—
273C23×C11—212no—
274C23×C11—416no—
275C23×C11—416no—
276C23×C11—416no—
277C23×C11H(5,𝔽2)14yes—
278C23×C11H(5,𝔽2)14yes—
279C23×C11H(5,𝔽2)14yes—
280C23×C11C2514yes—
281C23×C11C2514yes—
282C23×C11C2514yes—
283C23×C11C2513yes—
284C22×D11—212no—
285C22×D11—212no—
286C22×D11—212no—
287C22×D11—212no—
288C22×D11—212no—
289C22×D11—212no—
290C22×D11—212no—
291C22×D11—212no—
292C22×D11—212no—
293C22×D11—416no—
294C22×D11—416no—
295C22×D11—416no—
296C22×D11—4192no—
297C22×D11—416no—
298C22×D11—416no—
299C22×D11—416no—
300C22×D11C2514yes—
301C22×D11C2514yes—
302C22×D11C2514yes—
303D4×C11—416no—
304D4×C11—416no—
305D4×C11—416no—
306C2×C4×C11—212no—
307C2×C4×C11—212no—
308C2×C4×C11—212no—
309C2×C4×C11—212no—
310C2×C4×C11—416no—
311C2×C4×C11C2514yes—
312C2×C4×C11C2514yes—
313C2×C4×C11C2514yes—
314C2×C4×C11C2514yes—
315C22⋊D11—416no—
316C22⋊D11—416no—
317C22⋊D11—416no—
318C22⋊D11—416no—
319C22⋊D11—416no—
320C22⋊D11—416no—
321C22⋊D11—416no—
322C2×Dic11—212no—
323C2×Dic11—212no—
324C2×Dic11—212no—
325C2×Dic11—212no—
326C2×Dic11—212no—
327C2×Dic11—416no—
328C2×Dic11C2514yes—
329C2×Dic11C2514yes—
330C2×Dic11C2514yes—
331C2×Dic11C2514yes—
332C2×Dic11C2514yes—
333D44—416no—
334D44—416no—
335C4×D11—416no—
336C26—111no—
337C23×D4—111no—
338C23×D4—111no—
339C23×D4—111no—
340C23×D4—111no—
341C23×D4—111no—
342C23×D4—111no—
343C23×D4—111no—
344C23×D4—111no—
345C23×D4—111no—
346C23×D4C2×D1111yescharacteristic
347C23×D4C2×D1111yescharacteristic
348C23×D4C2×D1111yescharacteristic, complemented
349C24×C4—111no—
350C24×C4—111no—
351C24×C4C2×D1111yescharacteristic, complemented
352#560—11256no—
353C2×#127—1124no—
354C2×#126—1124no—
355C2×#126—1124no—
356C2×#123—1124no—
357C2×#123—1124no—
358C2×#123—1124no—
359C2×#121—1124no—
360C2×#121—1124no—
361C2×#121—1124no—
362C2×#121—1124no—
363C2×#121—1124no—
364C2×#121C2×D11124yescomplemented
365C2×#120—1124no—
366C2×#120—1124no—
367C2×#120—1124no—
368C22×C4⋊C4—111no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4—111no—
371C22×C4⋊C4—111no—
372C22×C4⋊C4—111no—
373C22×C4⋊C4C2×D1111yescharacteristic, complemented
374C22×C22⋊C4—111no—
375C22×C22⋊C4—111no—
376C22×C22⋊C4—111no—
377C22×C22⋊C4—111no—
378C22×C22⋊C4—111no—
379C22×C22⋊C4—111no—
380C22×C22⋊C4—111no—
381C22×C22⋊C4—111no—
382C22×C22⋊C4—111no—
383C22×C22⋊C4—111no—
384C22×C22⋊C4C2×D1111yescharacteristic
385C22×C22⋊C4C2×D1111yescharacteristic, complemented
386C22×C42—111no—
387C22×C11—24no—
388C22×C11—24no—
389C22×C11—24no—
390C22×C11—24no—
391C22×C11—24no—
392C22×C11—24no—
393C22×C11—24no—
394C22×C11—24no—
395C22×C11—24no—
396C22×C11—424no—
397C22×C11—424no—
398C22×C11—424no—
399C22×C11#560116yescomplemented
400C22×C11C2×H(5,𝔽2)16yes—
401C22×C11C2×H(5,𝔽2)16yes—
402C22×C11C2×H(5,𝔽2)16yes—
403C22×C11C2611yescharacteristic
404C2×D11—24no—
405C2×D11—24no—
406C2×D11—24no—
407C2×D11—24no—
408C2×D11—24no—
409C2×D11—24no—
410C2×D11—24no—
411C2×D11—24no—
412C2×D11—24no—
413C2×D11—464no—
414C2×D11—424no—
415C2×D11—424no—
416C2×D11—424no—
417C4×C11—24no—
418C4×C11—24no—
419C4×C11—24no—
420C4×C11—24no—
421Dic11—24no—
422Dic11—24no—
423Dic11—24no—
424Dic11—24no—
425Dic11—24no—
426C25—111no—
427C25—111no—
428C25—111no—
429C25—1112no—
430C25—444no—
431C25—444no—
432C25—444no—
433C25C22×D1111yescharacteristic
434C25C22×D1111yescharacteristic
435C25C22×D1111yescharacteristic
436C22×D4—44no—
437C22×D4—44no—
438C22×D4—44no—
439C22×D4—1112no—
440C22×D4—1112no—
441C22×D4—1112no—
442C22×D4—1112no—
443C22×D4—1112no—
444C22×D4—1112no—
445C22×D4—1112no—
446C22×D4—1112no—
447C22×D4—1112no—
448C22×D4—444no—
449C22×D4—444no—
450C22×D4—444no—
451C22×D4—444no—
452C22×D4—444no—
453C22×D4—444no—
454C22×D4—444no—
455C22×D4—444no—
456C22×D4—444no—
457C22×D4C22×D11112yes—
458C22×D4C22×D11112yes—
459C22×D4C22×D11112yescomplemented
460C23×C4—44no—
461C23×C4—111no—
462C23×C4—111no—
463C23×C4—111no—
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—1112no—
467C23×C4—1112no—
468C23×C4—444no—
469C23×C4—444no—
470C23×C4C22×D1111yescharacteristic
471C23×C4C22×D1111yescharacteristic
472C23×C4C22×D1111yescharacteristic
473C23×C4C22×D1111yescharacteristic
474C23×C4C22×D11112yescomplemented
475#127—1164no—
476#126—1164no—
477#126—1164no—
478#123—1164no—
479#123—1164no—
480#123—1164no—
481#121—1164no—
482#121—1164no—
483#121—1164no—
484#121—1164no—
485#121—1164no—
486#121C22×D11164yescomplemented
487#120—1164no—
488#120—1164no—
489#120—1164no—
490C2×C4⋊C4—1112no—
491C2×C4⋊C4—1112no—
492C2×C4⋊C4—1112no—
493C2×C4⋊C4—1112no—
494C2×C4⋊C4—1112no—
495C2×C4⋊C4C22×D11112yescomplemented
496C2×C22⋊C4—1112no—
497C2×C22⋊C4—1112no—
498C2×C22⋊C4—1112no—
499C2×C22⋊C4—1112no—
500C2×C22⋊C4—1112no—
501C2×C22⋊C4—1112no—
502C2×C22⋊C4—1112no—
503C2×C22⋊C4—1112no—
504C2×C22⋊C4—1112no—
505C2×C22⋊C4—1112no—
506C2×C22⋊C4C22×D11112yes—
507C2×C22⋊C4C22×D11112yescomplemented
508C2×C42—1112no—
509C2×C11—44no—
510C2×C11—44no—
511C2×C11—44no—
512C2×C11C2×#560112yescomplemented
513C2×C11C22×H(5,𝔽2)11yescharacteristic
514C2×C11C22×H(5,𝔽2)11yescharacteristic
515C2×C11C22×H(5,𝔽2)11yescharacteristic
516D11—44no—
517D11—44no—
518D11—44no—
519C24—24no—
520C24—24no—
521C24—24no—
522C24—24no—
523C24—24no—
524C24—24no—
525C24—24no—
526C24—24no—
527C24—24no—
528C24—116no—
529C24—116no—
530C24—116no—
531C24—1116no—
532C24—224no—
533C24—224no—
534C24—224no—
535C24—224no—
536C24—224no—
537C24—224no—
538C24—224no—
539C24—224no—
540C24—224no—
541C24—4424no—
542C24—4424no—
543C24—4424no—
544C24—4464no—
545C24C23×D1116yes—
546C24C23×D1116yes—
547C24C23×D1116yes—
548C24C23×D1111yescharacteristic
549C2×D4—424no—
550C2×D4—424no—
551C2×D4—424no—
552C2×D4—1116no—
553C2×D4—1116no—
554C2×D4—1116no—
555C2×D4—1116no—
556C2×D4—1116no—
557C2×D4—1116no—
558C2×D4—1116no—
559C2×D4—1116no—
560C2×D4—1116no—
561C2×D4—4424no—
562C2×D4—4424no—
563C2×D4—4424no—
564C2×D4—4424no—
565C2×D4—4424no—
566C2×D4—4424no—
567C2×D4—4424no—
568C2×D4—4424no—
569C2×D4—4424no—
570C2×D4C23×D11116yes—
571C2×D4C23×D11116yes—
572C2×D4C23×D11116yescomplemented
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—424no—
578C22×C4—116no—
579C22×C4—116no—
580C22×C4—116no—
581C22×C4—116no—
582C22×C4—116no—
583C22×C4—1116no—
584C22×C4—1116no—
585C22×C4—224no—
586C22×C4—224no—
587C22×C4—224no—
588C22×C4—224no—
589C22×C4—224no—
590C22×C4—4424no—
591C22×C4—4424no—
592C22×C4C23×D1116yes—
593C22×C4C23×D1116yes—
594C22×C4C23×D1116yes—
595C22×C4C23×D1116yes—
596C22×C4C23×D11116yescomplemented
597C4⋊C4—1116no—
598C4⋊C4—1116no—
599C4⋊C4—1116no—
600C4⋊C4—1116no—
601C4⋊C4—1116no—
602C4⋊C4C23×D11116yescomplemented
603C22⋊C4—1116no—
604C22⋊C4—1116no—
605C22⋊C4—1116no—
606C22⋊C4—1116no—
607C22⋊C4—1116no—
608C22⋊C4—1116no—
609C22⋊C4—1116no—
610C22⋊C4—1116no—
611C22⋊C4—1116no—
612C22⋊C4—1116no—
613C22⋊C4C23×D11116yes—
614C22⋊C4C23×D11116yescomplemented
615C42—1116no—
616C11C22×#56011yescharacteristic, complemented, Sylow
617C23—212no—
618C23—212no—
619C23—212no—
620C23—212no—
621C23—212no—
622C23—212no—
623C23—212no—
624C23—212no—
625C23—212no—
626C23—416no—
627C23—416no—
628C23—416no—
629C23—114no—
630C23—114no—
631C23—114no—
632C23—2212no—
633C23—2212no—
634C23—2212no—
635C23—2212no—
636C23—2212no—
637C23—2212no—
638C23—2212no—
639C23—2212no—
640C23—2212no—
641C23—4416no—
642C23—4416no—
643C23—4416no—
644C23—44192no—
645C23—4416no—
646C23—4416no—
647C23—4416no—
648C23#6703714yes—
649C23#6703714yes—
650C23#6704214yes—
651C23C24×D1114yes—
652C23C24×D1114yes—
653C23C24×D1114yes—
654C23C24×D1113yes—
655D4—416no—
656D4—416no—
657D4—416no—
658D4—4416no—
659D4—4416no—
660D4—4416no—
661D4—4416no—
662D4—4416no—
663D4—4416no—
664D4—4416no—
665D4—4416no—
666D4—4416no—
667C2×C4—212no—
668C2×C4—212no—
669C2×C4—212no—
670C2×C4—212no—
671C2×C4—416no—
672C2×C4—114no—
673C2×C4—114no—
674C2×C4—114no—
675C2×C4—114no—
676C2×C4—114no—
677C2×C4—2212no—
678C2×C4—2212no—
679C2×C4—2212no—
680C2×C4—2212no—
681C2×C4—2212no—
682C2×C4—4416no—
683C2×C4—4416no—
684C2×C4C24×D1114yes—
685C2×C4C24×D1114yes—
686C2×C4C24×D1114yes—
687C2×C4C24×D1114yes—
688C22—24no—
689C22—24no—
690C22—24no—
691C22—24no—
692C22—24no—
693C22—24no—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—424no—
698C22—424no—
699C22—424no—
700C22—224no—
701C22—224no—
702C22—224no—
703C22—224no—
704C22—224no—
705C22—224no—
706C22—224no—
707C22—224no—
708C22—224no—
709C22—4464no—
710C22—4424no—
711C22—4424no—
712C22—4424no—
713C22#10623151116yesdirect product factor
714C22C2×#6703716yes—
715C22C2×#6703716yes—
716C22C2×#6704216yes—
717C22C25×D1111yescharacteristic
718C4—24no—
719C4—24no—
720C4—24no—
721C4—24no—
722C4—224no—
723C4—224no—
724C4—224no—
725C4—224no—
726C4—224no—
727C2—44no—
728C2—44no—
729C2—44no—
730C2—444no—
731C2—444no—
732C2—444no—
733C2C2×#10623151112yesdirect product factor
734C2C22×#6703711yescharacteristic
735C2C22×#6703711yescharacteristic
736C2C22×#6704211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×#121C2
socleC24×C11C24
hypercenterC22×#121D11
hypocenterC11C22×#560
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10623151C2direct (N × H)
2. C22×#66993C2semidirect
3. C22×#66951C2semidirect
4. C22×#66932C2semidirect
5. C22×#66947C2semidirect
6. C22×#66939C2semidirect
7. C22×#66982C2semidirect
8. C22×#66983C2semidirect
9. C22×#66937C2semidirect
10. C22×#66992C2semidirect
11. C22×#66992C2semidirect
12. C22×#66991C2semidirect
13. C22×#66935C2semidirect
14. C22×#66990C2semidirect
15. C22×#66990C2semidirect
16. C22×C11×#121C2semidirect
20. C23×D4×C11C22semidirect
21. C24×C4×C11C22semidirect
27. C23×C22⋊D11C22semidirect
28. C23×C22⋊D11C22semidirect
29. C24×Dic11C22semidirect
32. C23×C4×D11C22semidirect
33. C2×C11×#121C22semidirect
34. C22×C11×C4⋊C4C22semidirect
36. C22×C11×C22⋊C4C22semidirect
39. C22×C22⋊Dic11C22semidirect
40. C2×#66993C22semidirect
41. C2×#66992C22semidirect
42. C2×#66992C22semidirect
43. C2×#66991C22semidirect
44. C2×#66990C22semidirect
45. C2×#66990C22semidirect
46. C2×#66983C22semidirect
47. C2×#66982C22semidirect
54. C22×(C2×D11)⋊C4C22semidirect
55. C22×C4⋊Dic11C22semidirect
56. C22×C4⋊Dic11C22semidirect
57. C22×Dic11⋊C4C22semidirect
58. C22×Dic11⋊C4C22semidirect
59. C22×Dic11⋊C4C22semidirect
60. C22×C4×Dic11C22semidirect
61. #10623151C22direct (N × H)
62. C2×#66951C22semidirect
63. C2×#66947C22semidirect
64. C2×#66939C22semidirect
65. C2×#66937C22semidirect
66. C2×#66935C22semidirect
67. C2×#66932C22semidirect
83. C22×D4×C11C23semidirect
89. C23×C4×C11C23semidirect
102. C22×C22⋊D11C23semidirect
103. C22×C22⋊D11C23semidirect
110. C23×Dic11C23semidirect
116. C22×C4×D11C23semidirect
117. C11×#121C23semidirect
118. C2×C11×C4⋊C4C23semidirect
120. C2×C11×C22⋊C4C23semidirect
123. C2×C22⋊Dic11C23semidirect
124. #66993C23semidirect
125. #66992C23semidirect
126. #66992C23semidirect
127. #66991C23semidirect
128. #66990C23semidirect
129. #66990C23semidirect
130. #66983C23semidirect
131. #66982C23semidirect
138. C2×(C2×D11)⋊C4C23semidirect
139. C2×C4⋊Dic11C23semidirect
140. C2×C4⋊Dic11C23semidirect
141. C2×Dic11⋊C4C23semidirect
142. C2×Dic11⋊C4C23semidirect
143. C2×Dic11⋊C4C23semidirect
144. C2×C4×Dic11C23semidirect
145. #66951C23semidirect
146. #66947C23semidirect
147. #66939C23semidirect
148. #66937C23semidirect
149. #66935C23semidirect
150. #66932C23semidirect
187. C2×D4×C11C24semidirect
197. C22×C4×C11C24semidirect
210. C2×C22⋊D11C24semidirect
211. C2×C22⋊D11C24semidirect
223. C22×Dic11C24semidirect
229. C2×C4×D11C24semidirect
230. C11×C4⋊C4C24semidirect
232. C11×C22⋊C4C24semidirect
235. C22⋊Dic11C24semidirect
242. (C2×D11)⋊C4C24semidirect
243. C4⋊Dic11C24semidirect
244. C4⋊Dic11C24semidirect
245. Dic11⋊C4C24semidirect
246. Dic11⋊C4C24semidirect
247. Dic11⋊C4C24semidirect
248. C4×Dic11C24semidirect
261. C22×#121D11semidirect
348. C23×D4C2×D11semidirect
351. C24×C4C2×D11semidirect
364. C2×#121C2×D11semidirect
373. C22×C4⋊C4C2×D11semidirect
385. C22×C22⋊C4C2×D11semidirect
399. C22×C11#560semidirect
459. C22×D4C22×D11semidirect
474. C23×C4C22×D11semidirect
486. #121C22×D11semidirect
495. C2×C4⋊C4C22×D11semidirect
507. C2×C22⋊C4C22×D11semidirect
512. C2×C11C2×#560semidirect
572. C2×D4C23×D11semidirect
596. C22×C4C23×D11semidirect
602. C4⋊C4C23×D11semidirect
614. C22⋊C4C23×D11semidirect
616. C11C22×#560semidirect
713. C22#10623151direct (N × H)
733. C2C2×#10623151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231512
C22×#669932
C22×#669512
C22×#669322
C22×#669472
C22×#669392
C22×#669822
C22×#669832
C22×#669372
C22×#669922
C22×#669912
C22×#669352
C22×#669902
C22×C11×#1212
C22×#56011