Finite Group Databasebeta

← C22×#10623078 #15660428

Subgroups — C22×#10623078 #15660428

Order 2816.

14334 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
1C23×#4339C211yesmaximal, characteristic, complemented
2C24×C4×D11C211yesmaximal, characteristic, complemented
3C2×#10623078C2148yesmaximal, direct product factor
4C22×#66947C211yesmaximal, characteristic, complemented
5C22×#66936C211yesmaximal, characteristic, complemented
6C22×#66949C211yesmaximal, characteristic, complemented
7C22×#66931C211yesmaximal, characteristic, complemented
8C22×#66937C211yesmaximal, characteristic, complemented
9C22×#66992C211yesmaximal, characteristic, complemented
10C22×#66935C211yesmaximal, characteristic, complemented
11C22×#66990C211yesmaximal, characteristic, complemented
12C22×C4×D44C211yesmaximal, characteristic, complemented
13C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
14C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
15C22×#66925C211yesmaximal, characteristic, complemented
16C22×C4×D4×C11C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic, complemented
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic
24C23×C22⋊D11C2211yescharacteristic, complemented
25C24×Dic11C2211yescharacteristic
26C22×#4339—216no—
27C22×#4339C22124yescomplemented
28C23×D44C2211yescharacteristic
29C23×D44C2211yescharacteristic
30C23×C4×D11—216no—
31C23×C4×D11C2211yescharacteristic
32C23×C4×D11C2211yescharacteristic
33C23×C4×D11C2211yescharacteristic
34C23×C4×D11C2211yescharacteristic
35C23×C4×D11C22124yescomplemented
36C23×C4×D11C2211yescharacteristic, complemented
37C23×Dic22C2211yescharacteristic, complemented
38C2×C4×D4×C11C22124yescomplemented
39C22×C11×C4⋊C4C2211yescharacteristic, complemented
40C22×C11×C22⋊C4C2211yescharacteristic
41C22×C11×C22⋊C4C2211yescharacteristic, complemented
42C22×C42×C11C2211yescharacteristic, complemented
43C22×C22⋊Dic11C2211yescharacteristic
44C22×C22⋊Dic11C2211yescharacteristic, complemented
45C2×#66992C22124yescomplemented
46C2×#66990C22124yescomplemented
47C2×C4×C22⋊D11C22124yescomplemented
48C2×C4×C22⋊D11C22124yescomplemented
49C22×(C2×D11)⋊C4C2211yescharacteristic
50C22×(C2×D11)⋊C4C2211yescharacteristic
51C22×(C2×D11)⋊C4C2211yescharacteristic
52C22×(C2×D11)⋊C4C2211yescharacteristic
53C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
54C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
55C22×C4⋊Dic11C2211yescharacteristic, complemented
56C22×Dic11⋊C4C2211yescharacteristic, complemented
57C22×Dic11⋊C4C2211yescharacteristic, complemented
58C22×Dic11⋊C4C2211yescharacteristic, complemented
59C22×Dic11⋊C4C2211yescharacteristic, complemented
60C22×C4×Dic11C2211yescharacteristic, complemented
61#10623078C221256yesdirect product factor
62C2×#66949C22124yescomplemented
63C2×#66947C22124yescomplemented
64C2×#66937C22124yescomplemented
65C2×#66936C22124yescomplemented
66C2×#66935C22124yescomplemented
67C2×#66931C22124yescomplemented
68C2×C4×D44C22124yescomplemented
69C2×#66925C22124yescomplemented
70C25×C11C2311yescharacteristic
71C25×C11C2311yescharacteristic
72C24×D11—28no—
73C24×D11—28no—
74C24×D11—28no—
75C24×D11C23112yes—
76C24×D11C2311yescharacteristic
77C24×D11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C22×D4×C11—28no—
80C22×D4×C11C23112yes—
81C23×C4×C11—28no—
82C23×C4×C11—28no—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C23112yes—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C23112yescomplemented
90C22×C22⋊D11—28no—
91C22×C22⋊D11—28no—
92C22×C22⋊D11—28no—
93C22×C22⋊D11—28no—
94C22×C22⋊D11C23112yes—
95C22×C22⋊D11C23112yes—
96C22×C22⋊D11C23112yes—
97C22×C22⋊D11C23112yescomplemented
98C23×Dic11—28no—
99C23×Dic11C23112yes—
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C2×#4339—2192no—
106C2×#4339C23164yescomplemented
107C22×D44—28no—
108C22×D44—28no—
109C22×D44C23112yes—
110C22×D44C23112yes—
111C22×C4×D11—28no—
112C22×C4×D11—28no—
113C22×C4×D11—28no—
114C22×C4×D11—28no—
115C22×C4×D11—2192no—
116C22×C4×D11D4116yescomplemented
117C22×C4×D11C23112yes—
118C22×C4×D11C23112yes—
119C22×C4×D11C23112yes—
120C22×C4×D11C23112yes—
121C22×C4×D11C23164yescomplemented
122C22×C4×D11C23112yescomplemented
123C22×Dic22—28no—
124C22×Dic22C23112yescomplemented
125C4×D4×C11C23164yescomplemented
126C2×C11×C4⋊C4C23112yescomplemented
127C2×C11×C22⋊C4C23112yes—
128C2×C11×C22⋊C4C23112yescomplemented
129C2×C42×C11C23112yescomplemented
130C2×C22⋊Dic11C23112yes—
131C2×C22⋊Dic11C23112yescomplemented
132#66992C23164yescomplemented
133#66990C23164yescomplemented
134C4×C22⋊D11C23164yescomplemented
135C4×C22⋊D11C23164yescomplemented
136C2×(C2×D11)⋊C4C23112yes—
137C2×(C2×D11)⋊C4C23112yes—
138C2×(C2×D11)⋊C4C23112yes—
139C2×(C2×D11)⋊C4C23112yes—
140C2×(C2×D11)⋊C4C23112yescomplemented
141C2×(C2×D11)⋊C4C23112yescomplemented
142C2×C4⋊Dic11C23112yescomplemented
143C2×Dic11⋊C4C23112yescomplemented
144C2×Dic11⋊C4C23112yescomplemented
145C2×Dic11⋊C4C23112yescomplemented
146C2×Dic11⋊C4C23112yescomplemented
147C2×C4×Dic11C23112yescomplemented
148#66949C23164yescomplemented
149#66947C23164yescomplemented
150#66937C23164yescomplemented
151#66936C23164yescomplemented
152#66935C23164yescomplemented
153#66931C23164yescomplemented
154C4×D44C23164yescomplemented
155#66925C23164yescomplemented
156C22×#525—111nomaximal, Sylow
157C24×C11—24no—
158C24×C11—24no—
159C24×C11—24no—
160C24×C11—24no—
161C24×C11—24no—
162C24×C11#4118yescomplemented
163C24×C11C2416yes—
164C24×C11C2416yes—
165C24×C11C2411yescharacteristic
166C23×D11—2128no—
167C23×D11—24no—
168C23×D11—24no—
169C23×D11—24no—
170C23×D11—24no—
171C23×D11—248no—
172C23×D11—248no—
173C23×D11—248no—
174C23×D11—24no—
175C23×D11—24no—
176C23×D11—24no—
177C23×D11C2×D418yes—
178C23×D11#4118yescomplemented
179C23×D11C24116yes—
180C23×D11C2416yes—
181C23×D11C2416yes—
182C23×D11C2416yes—
183C2×D4×C11—248no—
184C2×D4×C11C24116yes—
185C22×C4×C11—24no—
186C22×C4×C11—24no—
187C22×C4×C11—24no—
188C22×C4×C11—24no—
189C22×C4×C11—248no—
190C22×C4×C11—248no—
191C22×C4×C11C2×D418yes—
192C22×C4×C11C2416yes—
193C22×C4×C11C2416yes—
194C22×C4×C11C2416yes—
195C22×C4×C11C2416yes—
196C22×C4×C11C24116yes—
197C22×C4×C11C2416yes—
198C22×C4×C11C24116yescomplemented
199C2×C22⋊D11—248no—
200C2×C22⋊D11—248no—
201C2×C22⋊D11—248no—
202C2×C22⋊D11—248no—
203C2×C22⋊D11C24116yes—
204C2×C22⋊D11C24116yes—
205C2×C22⋊D11C24116yes—
206C2×C22⋊D11C24116yescomplemented
207C22×Dic11—248no—
208C22×Dic11—24no—
209C22×Dic11—24no—
210C22×Dic11—24no—
211C22×Dic11—24no—
212C22×Dic11C2×D418yes—
213C22×Dic11C24116yes—
214C22×Dic11C2416yes—
215C22×Dic11C2416yes—
216C22×Dic11C2416yes—
217C22×Dic11C2416yes—
218C22×Dic11C2416yes—
219#4339—2256no—
220C2×D44—248no—
221C2×D44—248no—
222C2×D44C24116yes—
223C2×D44C24116yes—
224C2×C4×D11—248no—
225C2×C4×D11—2256no—
226C2×C4×D11—248no—
227C2×C4×D11—248no—
228C2×C4×D11—248no—
229C2×C4×D11C2×D4196yescomplemented
230C2×C4×D11C24116yes—
231C2×C4×D11C24116yes—
232C2×C4×D11C24116yes—
233C2×C4×D11C24116yes—
234C2×C4×D11C24116yescomplemented
235C2×Dic22—248no—
236C2×Dic22C24116yescomplemented
237C11×C4⋊C4C24116yescomplemented
238C11×C22⋊C4C24116yes—
239C11×C22⋊C4C24116yescomplemented
240C42×C11C24116yescomplemented
241C22⋊Dic11C24116yes—
242C22⋊Dic11C24116yescomplemented
243(C2×D11)⋊C4C24116yes—
244(C2×D11)⋊C4C24116yes—
245(C2×D11)⋊C4C24116yes—
246(C2×D11)⋊C4C24116yes—
247(C2×D11)⋊C4C24116yescomplemented
248(C2×D11)⋊C4C24116yescomplemented
249C4⋊Dic11C24116yescomplemented
250Dic11⋊C4C24116yescomplemented
251Dic11⋊C4C24116yescomplemented
252Dic11⋊C4C24116yescomplemented
253Dic11⋊C4C24116yescomplemented
254C4×Dic11C24116yescomplemented
255C23×#41—111no—
256C25×C4—111no—
257C2×#525—1148no—
258C22×#123—111no—
259C22×#123—111no—
260C22×C22⋊Q8—111no—
261C22×C22⋊Q8—111no—
262C22×#121—111no—
263C22×#121—111no—
264C22×#120—111no—
265C22×#120—111no—
266C22×C4×D4—111no—
267C22×C4×D4—111no—
268C22×C4×D4—111no—
269C22×C4×D4D1111yescharacteristic, complemented
270C22×#117—111no—
271C23×C11—232no—
272C23×C11—212no—
273C23×C11—212no—
274C23×C11—212no—
275C23×C11—212no—
276C23×C11—212no—
277C23×C11—416no—
278C23×C11C22×D414yes—
279C23×C11C2×#4114yes—
280C23×C11C2×#4114yes—
281C23×C11C2×#41124yescomplemented
282C23×C11C2514yes—
283C23×C11C2514yes—
284C23×C11C2513yes—
285C22×D11—2384no—
286C22×D11—232no—
287C22×D11—232no—
288C22×D11—212no—
289C22×D11—212no—
290C22×D11—212no—
291C22×D11—212no—
292C22×D11—232no—
293C22×D11—232no—
294C22×D11—232no—
295C22×D11—212no—
296C22×D11—212no—
297C22×D11—212no—
298C22×D11—416no—
299C22×D11C22×D4124yes—
300C22×D11C2×#41124yescomplemented
301C22×D11C2514yes—
302C22×D11C2514yes—
303C22×D11C2514yes—
304D4×C11—232no—
305C2×C4×C11—212no—
306C2×C4×C11—212no—
307C2×C4×C11—212no—
308C2×C4×C11—212no—
309C2×C4×C11—232no—
310C2×C4×C11—232no—
311C2×C4×C11C22×D4124yes—
312C2×C4×C11C2514yes—
313C2×C4×C11C2514yes—
314C2×C4×C11C2514yes—
315C2×C4×C11C2514yes—
316C2×C4×C11C2514yes—
317C22⋊D11—232no—
318C22⋊D11—232no—
319C22⋊D11—232no—
320C22⋊D11—232no—
321C2×Dic11—212no—
322C2×Dic11—212no—
323C2×Dic11—212no—
324C2×Dic11—212no—
325C2×Dic11—232no—
326C2×Dic11C22×D4124yes—
327C2×Dic11C2514yes—
328C2×Dic11C2514yes—
329C2×Dic11C2514yes—
330C2×Dic11C2514yes—
331C2×Dic11C2514yes—
332D44—232no—
333D44—232no—
334C4×D11—232no—
335C4×D11—232no—
336C4×D11—232no—
337C4×D11—232no—
338C4×D11C22×D4164yescomplemented
339Dic22—232no—
340C26—111no—
341C22×#41—1124no—
342C22×#41—2216no—
343C23×Q8—111no—
344C23×D4—111no—
345C23×D4—111no—
346C23×D4—111no—
347C23×D4—111no—
348C23×D4—111no—
349C23×D4—111no—
350C23×D4C2×D1111yescharacteristic
351C24×C4—111no—
352C24×C4—111no—
353C24×C4—111no—
354C24×C4—111no—
355C24×C4—1124no—
356C24×C4—111no—
357C24×C4—111no—
358C24×C4—2216no—
359C24×C4C2×D1111yescharacteristic
360C24×C4C2×D1111yescharacteristic, complemented
361#525—11256no—
362C2×#123—1124no—
363C2×#123—1124no—
364C2×C22⋊Q8—1124no—
365C2×C22⋊Q8—1124no—
366C2×#121—1124no—
367C2×#121—1124no—
368C2×#120—1124no—
369C2×#120—1124no—
370C2×C4×D4—1124no—
371C2×C4×D4—1124no—
372C2×C4×D4—1124no—
373C2×C4×D4C2×D11124yescomplemented
374C2×#117—1124no—
375C22×C4⋊C4—111no—
376C22×C4⋊C4—111no—
377C22×C4⋊C4—111no—
378C22×C4⋊C4—111no—
379C22×C4⋊C4—111no—
380C22×C4⋊C4C2×D1111yescharacteristic, complemented
381C22×C22⋊C4—111no—
382C22×C22⋊C4—111no—
383C22×C22⋊C4—111no—
384C22×C22⋊C4—111no—
385C22×C22⋊C4—111no—
386C22×C22⋊C4—111no—
387C22×C22⋊C4—111no—
388C22×C22⋊C4—111no—
389C22×C22⋊C4C2×D1111yescharacteristic
390C22×C22⋊C4C2×D1111yescharacteristic, complemented
391C22×C42—111no—
392C22×C42C2×D1111yescharacteristic, complemented
393C22×C11—24no—
394C22×C11—24no—
395C22×C11—248no—
396C22×C11—24no—
397C22×C11—24no—
398C22×C11—24no—
399C22×C11—424no—
400C22×C11#525116yescomplemented
401C22×C11C23×D416yes—
402C22×C11C22×#4116yes—
403C22×C11C22×#4116yes—
404C22×C11C22×#4118yescomplemented
405C22×C11C2611yescharacteristic
406C2×D11—2128no—
407C2×D11—24no—
408C2×D11—24no—
409C2×D11—24no—
410C2×D11—24no—
411C2×D11—248no—
412C2×D11—248no—
413C2×D11—24no—
414C2×D11—24no—
415C2×D11—24no—
416C2×D11—424no—
417C2×D11C23×D418yes—
418C2×D11C22×#4118yescomplemented
419C4×C11—24no—
420C4×C11—24no—
421C4×C11—24no—
422C4×C11—24no—
423C4×C11C23×D418yes—
424Dic11—24no—
425Dic11—24no—
426Dic11—24no—
427Dic11—24no—
428Dic11C23×D418yes—
429C25—111no—
430C25—111no—
431C25—111no—
432C25—1112no—
433C25—228no—
434C25—228no—
435C25—228no—
436C25C22×D1111yescharacteristic
437C25C22×D1111yescharacteristic
438C2×#41—1164no—
439C2×#41—22192no—
440C22×Q8—1112no—
441C22×Q8—228no—
442C22×D4—28no—
443C22×D4—1112no—
444C22×D4—1112no—
445C22×D4—1112no—
446C22×D4—1112no—
447C22×D4—1112no—
448C22×D4—1112no—
449C22×D4—228no—
450C22×D4—228no—
451C22×D4—228no—
452C22×D4—228no—
453C22×D4—228no—
454C22×D4—228no—
455C22×D4C22×D11112yes—
456C23×C4—28no—
457C23×C4—28no—
458C23×C4—111no—
459C23×C4—1116no—
460C23×C4—1112no—
461C23×C4—111no—
462C23×C4—111no—
463C23×C4—111no—
464C23×C4—111no—
465C23×C4—1112no—
466C23×C4—1112no—
467C23×C4—1112no—
468C23×C4—1112no—
469C23×C4—1112no—
470C23×C4—1164no—
471C23×C4—228no—
472C23×C4—22192no—
473C23×C4—228no—
474C23×C4—228no—
475C23×C4—228no—
476C23×C4—228no—
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1111yescharacteristic
479C23×C4C22×D1111yescharacteristic
480C23×C4C22×D1111yescharacteristic
481C23×C4C22×D11112yes—
482C23×C4C22×D1111yescharacteristic
483C23×C4C22×D11112yescomplemented
484#123—1164no—
485#123—1164no—
486C22⋊Q8—1164no—
487C22⋊Q8—1164no—
488#121—1164no—
489#121—1164no—
490#120—1164no—
491#120—1164no—
492C4×D4—1164no—
493C4×D4—1164no—
494C4×D4—1164no—
495C4×D4C22×D11164yescomplemented
496#117—1164no—
497C2×C4⋊C4—1112no—
498C2×C4⋊C4—1112no—
499C2×C4⋊C4—1112no—
500C2×C4⋊C4—1112no—
501C2×C4⋊C4—1112no—
502C2×C4⋊C4C22×D11112yescomplemented
503C2×C22⋊C4—1112no—
504C2×C22⋊C4—1112no—
505C2×C22⋊C4—1112no—
506C2×C22⋊C4—1112no—
507C2×C22⋊C4—1112no—
508C2×C22⋊C4—1112no—
509C2×C22⋊C4—1112no—
510C2×C22⋊C4—1112no—
511C2×C22⋊C4C22×D11112yes—
512C2×C22⋊C4C22×D11112yescomplemented
513C2×C42—1112no—
514C2×C42C22×D11112yescomplemented
515C2×C11—28no—
516C2×C11—44no—
517C2×C11C2×#525112yescomplemented
518C2×C11C24×D411yescharacteristic
519C2×C11C23×#4111yescharacteristic
520C2×C11C23×#4111yescharacteristic
521D11—28no—
522D11—28no—
523D11—44no—
524C24—24no—
525C24—24no—
526C24—24no—
527C24—24no—
528C24—24no—
529C24—118no—
530C24—118no—
531C24—116no—
532C24—116no—
533C24—116no—
534C24—1116no—
535C24—2248no—
536C24—2248no—
537C24—22128no—
538C24—224no—
539C24—224no—
540C24—2248no—
541C24—224no—
542C24—224no—
543C24—224no—
544C24—224no—
545C24—224no—
546C24#433918yescomplemented
547C24C23×D1116yes—
548C24C23×D1116yes—
549C24C23×D1111yescharacteristic
550#41—22256no—
551C2×Q8—1116no—
552C2×Q8—2248no—
553C2×D4—248no—
554C2×D4—1116no—
555C2×D4—1116no—
556C2×D4—1116no—
557C2×D4—1116no—
558C2×D4—1116no—
559C2×D4—1116no—
560C2×D4—2248no—
561C2×D4—2248no—
562C2×D4—2248no—
563C2×D4—2248no—
564C2×D4—2248no—
565C2×D4—2248no—
566C2×D4C23×D11116yes—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—248no—
572C22×C4—248no—
573C22×C4—118no—
574C22×C4—116no—
575C22×C4—1196no—
576C22×C4—1116no—
577C22×C4—116no—
578C22×C4—116no—
579C22×C4—116no—
580C22×C4—116no—
581C22×C4—1116no—
582C22×C4—1116no—
583C22×C4—1116no—
584C22×C4—1116no—
585C22×C4—1116no—
586C22×C4—2248no—
587C22×C4—22256no—
588C22×C4—2248no—
589C22×C4—2248no—
590C22×C4—224no—
591C22×C4—224no—
592C22×C4—224no—
593C22×C4—224no—
594C22×C4—2248no—
595C22×C4—2248no—
596C22×C4D4×D1118yes—
597C22×C4C23×D1116yes—
598C22×C4C23×D1116yes—
599C22×C4C23×D1116yes—
600C22×C4C23×D1116yes—
601C22×C4C23×D11116yes—
602C22×C4C23×D1116yes—
603C22×C4C23×D11116yescomplemented
604C4⋊C4—1116no—
605C4⋊C4—1116no—
606C4⋊C4—1116no—
607C4⋊C4—1116no—
608C4⋊C4—1116no—
609C4⋊C4C23×D11116yescomplemented
610C22⋊C4—1116no—
611C22⋊C4—1116no—
612C22⋊C4—1116no—
613C22⋊C4—1116no—
614C22⋊C4—1116no—
615C22⋊C4—1116no—
616C22⋊C4—1116no—
617C22⋊C4—1116no—
618C22⋊C4C23×D11116yes—
619C22⋊C4C23×D11116yescomplemented
620C42—1116no—
621C42C23×D11116yescomplemented
622C11C22×#52511yescharacteristic, complemented, Sylow
623C23—232no—
624C23—212no—
625C23—212no—
626C23—212no—
627C23—212no—
628C23—212no—
629C23—416no—
630C23—1124no—
631C23—1124no—
632C23—114no—
633C23—114no—
634C23—114no—
635C23—2232no—
636C23—2232no—
637C23—22384no—
638C23—2232no—
639C23—2232no—
640C23—2212no—
641C23—2212no—
642C23—2232no—
643C23—2212no—
644C23—2212no—
645C23—2212no—
646C23—2212no—
647C23—2212no—
648C23—4416no—
649C23C2×#433914yes—
650C23C2×#4339124yescomplemented
651C23C2×D4×D1114yes—
652C23#41×D1114yes—
653C23C24×D1114yes—
654C23C24×D1114yes—
655C23C24×D1113yes—
656Q8—2232no—
657D4—232no—
658D4—2232no—
659D4—2232no—
660D4—2232no—
661D4—2232no—
662D4—2232no—
663D4—2232no—
664C2×C4—212no—
665C2×C4—212no—
666C2×C4—212no—
667C2×C4—212no—
668C2×C4—232no—
669C2×C4—232no—
670C2×C4—1124no—
671C2×C4—114no—
672C2×C4—1164no—
673C2×C4—114no—
674C2×C4—114no—
675C2×C4—114no—
676C2×C4—114no—
677C2×C4—2232no—
678C2×C4—2232no—
679C2×C4—2232no—
680C2×C4—2212no—
681C2×C4—2212no—
682C2×C4—2212no—
683C2×C4—2212no—
684C2×C4—2232no—
685C2×C4—2232no—
686C2×C4C2×D4×D11124yes—
687C2×C4C24×D1114yes—
688C2×C4C24×D1114yes—
689C2×C4C24×D1114yes—
690C2×C4C24×D1114yes—
691C2×C4C24×D1114yes—
692C22—248no—
693C22—24no—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—24no—
698C22—424no—
699C22—118no—
700C22—118no—
701C22—22128no—
702C22—2248no—
703C22—2248no—
704C22—224no—
705C22—224no—
706C22—224no—
707C22—224no—
708C22—224no—
709C22—224no—
710C22—224no—
711C22—4424no—
712C22#10623078116yesdirect product factor
713C22C22×#433916yes—
714C22C22×#433918yescomplemented
715C22C22×D4×D1116yes—
716C22C2×#41×D1116yes—
717C22C25×D1111yescharacteristic
718C4—24no—
719C4—24no—
720C4—24no—
721C4—24no—
722C4—118no—
723C4—224no—
724C4—224no—
725C4—224no—
726C4—224no—
727C4C22×D4×D1118yes—
728C2—28no—
729C2—44no—
730C2—228no—
731C2—228no—
732C2—444no—
733C2C2×#10623078112yesdirect product factor
734C2C23×D4×D1111yescharacteristic
735C2C22×#41×D1111yescharacteristic
736C2C23×#433911yescharacteristic
subgroupG/H
centerC23×C4C22×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
hypercenterC22×C4×D4D11
hypocenterC11C22×#525
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C23×#4339C2semidirect
2. C24×C4×D11C2semidirect
3. C2×#10623078C2direct (N × H)
4. C22×#66947C2semidirect
5. C22×#66936C2semidirect
6. C22×#66949C2semidirect
7. C22×#66931C2semidirect
8. C22×#66937C2semidirect
9. C22×#66992C2semidirect
10. C22×#66935C2semidirect
11. C22×#66990C2semidirect
12. C22×C4×D44C2semidirect
13. C22×C4×C22⋊D11C2semidirect
14. C22×C4×C22⋊D11C2semidirect
15. C22×#66925C2semidirect
16. C22×C4×D4×C11C2semidirect
20. C24×C4×C11C22semidirect
24. C23×C22⋊D11C22semidirect
27. C22×#4339C22semidirect
35. C23×C4×D11C22semidirect
36. C23×C4×D11C22semidirect
37. C23×Dic22C22semidirect
38. C2×C4×D4×C11C22semidirect
39. C22×C11×C4⋊C4C22semidirect
41. C22×C11×C22⋊C4C22semidirect
42. C22×C42×C11C22semidirect
44. C22×C22⋊Dic11C22semidirect
45. C2×#66992C22semidirect
46. C2×#66990C22semidirect
47. C2×C4×C22⋊D11C22semidirect
48. C2×C4×C22⋊D11C22semidirect
53. C22×(C2×D11)⋊C4C22semidirect
54. C22×(C2×D11)⋊C4C22semidirect
55. C22×C4⋊Dic11C22semidirect
56. C22×Dic11⋊C4C22semidirect
57. C22×Dic11⋊C4C22semidirect
58. C22×Dic11⋊C4C22semidirect
59. C22×Dic11⋊C4C22semidirect
60. C22×C4×Dic11C22semidirect
61. #10623078C22direct (N × H)
62. C2×#66949C22semidirect
63. C2×#66947C22semidirect
64. C2×#66937C22semidirect
65. C2×#66936C22semidirect
66. C2×#66935C22semidirect
67. C2×#66931C22semidirect
68. C2×C4×D44C22semidirect
69. C2×#66925C22semidirect
89. C23×C4×C11C23semidirect
97. C22×C22⋊D11C23semidirect
106. C2×#4339C23semidirect
116. C22×C4×D11D4semidirect
121. C22×C4×D11C23semidirect
122. C22×C4×D11C23semidirect
124. C22×Dic22C23semidirect
125. C4×D4×C11C23semidirect
126. C2×C11×C4⋊C4C23semidirect
128. C2×C11×C22⋊C4C23semidirect
129. C2×C42×C11C23semidirect
131. C2×C22⋊Dic11C23semidirect
132. #66992C23semidirect
133. #66990C23semidirect
134. C4×C22⋊D11C23semidirect
135. C4×C22⋊D11C23semidirect
140. C2×(C2×D11)⋊C4C23semidirect
141. C2×(C2×D11)⋊C4C23semidirect
142. C2×C4⋊Dic11C23semidirect
143. C2×Dic11⋊C4C23semidirect
144. C2×Dic11⋊C4C23semidirect
145. C2×Dic11⋊C4C23semidirect
146. C2×Dic11⋊C4C23semidirect
147. C2×C4×Dic11C23semidirect
148. #66949C23semidirect
149. #66947C23semidirect
150. #66937C23semidirect
151. #66936C23semidirect
152. #66935C23semidirect
153. #66931C23semidirect
154. C4×D44C23semidirect
155. #66925C23semidirect
162. C24×C11#41semidirect
178. C23×D11#41semidirect
198. C22×C4×C11C24semidirect
206. C2×C22⋊D11C24semidirect
229. C2×C4×D11C2×D4semidirect
234. C2×C4×D11C24semidirect
236. C2×Dic22C24semidirect
237. C11×C4⋊C4C24semidirect
239. C11×C22⋊C4C24semidirect
240. C42×C11C24semidirect
242. C22⋊Dic11C24semidirect
247. (C2×D11)⋊C4C24semidirect
248. (C2×D11)⋊C4C24semidirect
249. C4⋊Dic11C24semidirect
250. Dic11⋊C4C24semidirect
251. Dic11⋊C4C24semidirect
252. Dic11⋊C4C24semidirect
253. Dic11⋊C4C24semidirect
254. C4×Dic11C24semidirect
269. C22×C4×D4D11semidirect
281. C23×C11C2×#41semidirect
300. C22×D11C2×#41semidirect
338. C4×D11C22×D4semidirect
360. C24×C4C2×D11semidirect
373. C2×C4×D4C2×D11semidirect
380. C22×C4⋊C4C2×D11semidirect
390. C22×C22⋊C4C2×D11semidirect
392. C22×C42C2×D11semidirect
400. C22×C11#525semidirect
404. C22×C11C22×#41semidirect
418. C2×D11C22×#41semidirect
483. C23×C4C22×D11semidirect
495. C4×D4C22×D11semidirect
502. C2×C4⋊C4C22×D11semidirect
512. C2×C22⋊C4C22×D11semidirect
514. C2×C42C22×D11semidirect
517. C2×C11C2×#525semidirect
546. C24#4339semidirect
603. C22×C4C23×D11semidirect
609. C4⋊C4C23×D11semidirect
619. C22⋊C4C23×D11semidirect
621. C42C23×D11semidirect
622. C11C22×#525semidirect
650. C23C2×#4339semidirect
712. C22#10623078direct (N × H)
714. C22C22×#4339semidirect
733. C2C2×#10623078direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43392
C24×C4×D112
C2×#106230782
C22×#669472
C22×#669362
C22×#669492
C22×#669312
C22×#669372
C22×#669922
C22×#669352
C22×#669902
C22×C4×D442
C22×C4×C22⋊D112
C22×#669252
C22×C4×D4×C112
C22×#52511