Finite Group Databasebeta

← C2×#13082533 #15662274

Subgroups — C2×#13082533 #15662274

Order 2816.

7238 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082533C2132yesmaximal, direct product factor
2C2×#10623071C214yesmaximal, complemented
3C2×#10623045C212yesmaximal, complemented
4C2×#10623096C214yesmaximal, complemented
5C2×#10623061C212yesmaximal, complemented
6C2×#10623060C212yesmaximal, complemented
7C2×#10623044C212yesmaximal, complemented
8C2×#10623114C212yesmaximal, complemented
9C2×#10623093C212yesmaximal, complemented
10C2×#10623041C211yesmaximal, characteristic, complemented
11C2×#10623364C211yesmaximal, characteristic, complemented
12C2×#10623363C211yesmaximal, characteristic, complemented
13C2×#10623111C212yesmaximal, complemented
14C2×#10623088C212yesmaximal, complemented
15C22×#66943C211yesmaximal, characteristic, complemented
16C2×#10623054C211yesmaximal, characteristic, complemented
17C2×#10623053C211yesmaximal, characteristic, complemented
18C2×C11×#520C211yesmaximal, characteristic, complemented
19C22×C11×#41C2211yescharacteristic
20C22×#4339C2211yescharacteristic
21C22×#4339C2211yescharacteristic
22C11×#520C22116yescomplemented
23C2×C4×Q8×C11C2212yes—
24C2×C4×D4×C11C2214yes—
25C2×C4×D4×C11C2212yes—
26C2×C11×#117C2212yes—
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2212yes—
29C22×C11×C4⋊C4C2211yescharacteristic
30#10623364C22116yescomplemented
31#10623363C22116yescomplemented
32C2×#67000C2211yescharacteristic
33C2×#66999C2212yes—
34C2×#66997C2211yescharacteristic
35C2×#66993C2211yescharacteristic
36C2×#66992C2212yes—
37C2×#66992C2214yes—
38C2×#66992C2212yes—
39C2×#66991C2212yes—
40C2×#66989C2211yescharacteristic
41C2×#66983C2212yes—
42C2×#66983C2214yes—
43C2×#66983C2214yes—
44C2×#66982C2214yes—
45C2×C4×C22⋊D11C2212yes—
46C2×C4×C22⋊D11C2212yes—
47C2×C4×C22⋊D11C2214yes—
48C2×#66979C2214yes—
49C22×C4⋊Dic11C2212yes—
50C22×C4⋊Dic11C2211yescharacteristic
51C2×#66977C2212yes—
52C22×Dic11⋊C4C2212yes—
53C22×C4×Dic11C2211yescharacteristic
54#10623114C22132yescomplemented
55#10623111C22132yescomplemented
56#10623096C22164yescomplemented
57#10623093C22132yescomplemented
58#10623088C22132yescomplemented
59#10623071C22164yescomplemented
60#10623061C22132yescomplemented
61#10623060C22132yescomplemented
62#10623054C22116yescomplemented
63#10623053C22116yescomplemented
64#10623045C22132yescomplemented
65#10623044C22132yescomplemented
66C2×#66951C2214yes—
67C2×#66951C2214yes—
68#10623041C22116yescomplemented
69C2×#66950C2212yes—
70C2×#66950C2212yes—
71C2×#66948C2212yes—
72C2×#66948C2212yes—
73C2×#66947C2214yes—
74C2×#66946C2211yescharacteristic
75C2×#66946C2211yescharacteristic
76C2×#66945C2212yes—
77C2×C4⋊C4×D11C2212yes—
78C2×#66943C2212yes—
79C2×#66943C2212yes—
80C2×#66943C2212yes—
81C2×#66943C2212yes—
82C2×#66943C22116yescomplemented
83C2×#66942C2214yes—
84C2×#66940C2211yescharacteristic
85C2×#66940C2211yescharacteristic
86C2×#66937C2214yes—
87C2×#66936C2214yes—
88C2×#66936C2214yes—
89C2×(C22⋊D11)⋊C4C2212yes—
90C2×(C22⋊D11)⋊C4C2214yes—
91C2×(C22⋊D11)⋊C4C2212yes—
92C2×#66932C2214yes—
93C2×#66929C2214yes—
94C2×C4×D44C2214yes—
95C2×C4×D44C2212yes—
96C2×#66925C2214yes—
97C2×#66925C2212yes—
98C2×C42×D11C2212yes—
99C2×#66923C2214yes—
100C2×C4×Dic22C2212yes—
101C2×C11×#41—28no—
102C2×C11×#41C2318yes—
103C22×Q8×C11C2311yescharacteristic
104C22×D4×C11C2311yescharacteristic
105C22×D4×C11C2312yes—
106C23×C4×C11C2312yes—
107C23×C4×C11C2312yes—
108C23×C4×C11C2314yes—
109C23×C4×C11C2311yescharacteristic
110C22×C22⋊D11C2312yes—
111C22×C22⋊D11C2312yes—
112C22×C22⋊D11C2312yes—
113C22×C22⋊D11C2314yes—
114C22×C22⋊D11C2312yes—
115C23×Dic11C2311yescharacteristic
116C23×Dic11C2311yescharacteristic
117C23×Dic11C2312yes—
118C2×#4339—28no—
119C2×#4339—28no—
120C2×#4339C2318yes—
121C2×#4339C2318yes—
122C22×D44C2311yescharacteristic
123C22×D44C2311yescharacteristic
124C22×D44C2314yes—
125C22×C4×D11C2312yes—
126C22×C4×D11C2312yes—
127C22×C4×D11C2312yes—
128C22×C4×D11C2312yes—
129C22×C4×D11C2314yes—
130C22×Dic22C2311yescharacteristic
131C22×Dic22C2311yescharacteristic
132C4×Q8×C11C23116yes—
133C4×D4×C11C23132yes—
134C4×D4×C11C23116yes—
135C11×#117C2318yes—
136C11×#117C23116yes—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2314yes—
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2318yes—
143C2×C11×C4⋊C4C23116yes—
144C2×C11×C22⋊C4C2314yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C42×C11C2312yes—
147C2×C42×C11C2314yes—
148C2×C22⋊Dic11C2312yes—
149C2×C22⋊Dic11C2314yes—
150C2×C22⋊Dic11C2312yes—
151#67000C2318yes—
152#66999C23116yes—
153#66997C2318yes—
154#66993C2318yes—
155#66992C23116yes—
156#66992C23132yes—
157#66992C23116yes—
158#66991C23116yes—
159#66989C2318yes—
160#66983C23132yes—
161#66983C23116yes—
162#66983C23132yes—
163#66982C23132yes—
164C4×C22⋊D11C23116yes—
165C4×C22⋊D11C23116yes—
166C4×C22⋊D11C23132yes—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2314yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2314yes—
173C2×(C2×D11)⋊C4C2314yes—
174C2×(C2×D11)⋊C4C2314yes—
175#66979C23132yes—
176C2×C4⋊Dic11C2312yes—
177C2×C4⋊Dic11C2314yes—
178C2×C4⋊Dic11C2314yes—
179C2×C4⋊Dic11C2314yes—
180C2×C4⋊Dic11C2312yes—
181C2×C4⋊Dic11C2318yes—
182C2×C4⋊Dic11C23116yes—
183#66977C23116yes—
184C2×Dic11⋊C4C2314yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2314yes—
188C2×Dic11⋊C4C2314yes—
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2312yes—
191C2×Dic11⋊C4C2314yes—
192C2×Dic11⋊C4C23116yes—
193C2×C4×Dic11C2314yes—
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2318yes—
201#66951C23132yes—
202#66951C23132yes—
203#66950C23116yes—
204#66950C23116yes—
205#66948C23116yes—
206#66948C23116yes—
207#66947C23132yes—
208#66946C2318yes—
209#66946C2318yes—
210#66945C23116yes—
211C4⋊C4×D11C23116yes—
212#66943C23116yes—
213#66943C23116yes—
214#66943C23116yes—
215#66943C23116yes—
216#66942C23132yes—
217#66940C2318yes—
218#66940C2318yes—
219#66937C23132yes—
220#66936C23132yes—
221#66936C23132yes—
222(C22⋊D11)⋊C4C23116yes—
223(C22⋊D11)⋊C4C23116yes—
224(C22⋊D11)⋊C4C23132yes—
225#66932C23132yes—
226#66929C23132yes—
227C4×D44C23116yes—
228C4×D44C23132yes—
229#66925C23116yes—
230#66925C23132yes—
231C42×D11C23116yes—
232#66923C23132yes—
233C4×Dic22C23116yes—
234C2×#3512—111nomaximal, Sylow
235C24×C11C2412yes—
236C24×C11C2411yescharacteristic
237C23×D11C2412yes—
238C23×D11C2412yes—
239C11×#41—232no—
240C2×Q8×C11—24no—
241C2×Q8×C11C2414yes—
242C2×D4×C11—28no—
243C2×D4×C11—24no—
244C2×D4×C11C2414yes—
245C2×D4×C11C2418yes—
246C22×C4×C11—28no—
247C22×C4×C11—48no—
248C22×C4×C11—44no—
249C22×C4×C11#4118yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2412yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2414yes—
254C22×C4×C11C2418yes—
255C22×C4×C11C2418yes—
256C22×C4×C11C24116yes—
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2414yes—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11—44no—
263C2×C22⋊D11—48no—
264C2×C22⋊D11—44no—
265C2×C22⋊D11C2418yes—
266C2×C22⋊D11C2418yes—
267C2×C22⋊D11C2418yes—
268C2×C22⋊D11C24116yes—
269C2×C22⋊D11C2418yes—
270C22×Dic11—42no—
271C22×Dic11—44no—
272C22×Dic11—42no—
273C22×Dic11C2411yescharacteristic
274C22×Dic11C2411yescharacteristic
275C22×Dic11C2411yescharacteristic
276C22×Dic11C2411yescharacteristic
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2414yes—
280C22×Dic11C2414yes—
281C22×Dic11C2414yes—
282C22×Dic11C2418yes—
283#4339—232no—
284#4339—232no—
285C2×D44—24no—
286C2×D44—24no—
287C2×D44—48no—
288C2×D44C2414yes—
289C2×D44C2414yes—
290C2×D44C24116yes—
291C2×C4×D11—28no—
292C2×C4×D11—28no—
293C2×C4×D11—48no—
294C2×C4×D11—44no—
295C2×C4×D11—44no—
296C2×C4×D11C2418yes—
297C2×C4×D11C2418yes—
298C2×C4×D11C2418yes—
299C2×C4×D11C2418yes—
300C2×C4×D11C24116yes—
301C2×Dic22—24no—
302C2×Dic22—24no—
303C2×Dic22C2414yes—
304C2×Dic22C2414yes—
305C11×C4⋊C4C2414yes—
306C11×C4⋊C4C2414yes—
307C11×C4⋊C4C24116yes—
308C11×C4⋊C4C2418yes—
309C11×C4⋊C4C2418yes—
310C11×C22⋊C4C24116yes—
311C11×C22⋊C4C2418yes—
312C42×C11C2418yes—
313C42×C11C24116yes—
314C22⋊Dic11C2418yes—
315C22⋊Dic11C24116yes—
316C22⋊Dic11C2418yes—
317(C2×D11)⋊C4C2418yes—
318(C2×D11)⋊C4C2418yes—
319(C2×D11)⋊C4C2418yes—
320(C2×D11)⋊C4C24116yes—
321(C2×D11)⋊C4C2418yes—
322(C2×D11)⋊C4C24116yes—
323(C2×D11)⋊C4C24116yes—
324(C2×D11)⋊C4C24116yes—
325C4⋊Dic11C2418yes—
326C4⋊Dic11C24116yes—
327C4⋊Dic11C24116yes—
328C4⋊Dic11C24116yes—
329C4⋊Dic11C2418yes—
330Dic11⋊C4C24116yes—
331Dic11⋊C4C2418yes—
332Dic11⋊C4C2418yes—
333Dic11⋊C4C24116yes—
334Dic11⋊C4C24116yes—
335Dic11⋊C4C2418yes—
336Dic11⋊C4C2418yes—
337Dic11⋊C4C24116yes—
338C4×Dic11C24116yes—
339C4×Dic11C2414yes—
340C4×Dic11C2418yes—
341C4×Dic11C2418yes—
342C4×Dic11C2414yes—
343C4×Dic11C2414yes—
344C4×Dic11C2414yes—
345#3512—1132no—
346C2×#553—114no—
347C2×#553—114no—
348C2×#553—112no—
349C2×#553—112no—
350C2×#552—112no—
351C2×#552—112no—
352C2×#541—112no—
353C2×#540—112no—
354C2×#537—111no—
355C2×#537—111no—
356C2×#532—111no—
357C2×#529—112no—
358C2×#529—112no—
359C22×#125—111no—
360C2×#520—111no—
361C2×#520D1111yescharacteristic, complemented
362C2×C4×#41—111no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—24no—
366C23×C11—24no—
367C23×C11—24no—
368C23×C11C2×#4114yes—
369C23×C11C2514yes—
370C23×C11C2512yes—
371C23×C11C2511yescharacteristic
372C22×D11—24no—
373C22×D11—24no—
374C22×D11—24no—
375C22×D11—24no—
376C22×D11—24no—
377C22×D11—24no—
378C22×D11C2514yes—
379C22×D11C2514yes—
380Q8×C11—28no—
381D4×C11—216no—
382D4×C11—28no—
383C2×C4×C11—24no—
384C2×C4×C11—24no—
385C2×C4×C11—24no—
386C2×C4×C11—28no—
387C2×C4×C11—216no—
388C2×C4×C11—416no—
389C2×C4×C11—48no—
390C2×C4×C11C2×#4114yes—
391C2×C4×C11C2×#4114yes—
392C2×C4×C11C2×#41116yes—
393C2×C4×C11C2514yes—
394C2×C4×C11C2514yes—
395C2×C4×C11C2514yes—
396C2×C4×C11C2518yes—
397C2×C4×C11C2512yes—
398C2×C4×C11C2512yes—
399C22⋊D11—216no—
400C22⋊D11—216no—
401C22⋊D11—416no—
402C22⋊D11—48no—
403C22⋊D11—48no—
404C2×Dic11—24no—
405C2×Dic11—24no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—28no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—44no—
412C2×Dic11—44no—
413C2×Dic11—48no—
414C2×Dic11C2512yes—
415C2×Dic11C2512yes—
416C2×Dic11C2512yes—
417C2×Dic11C2512yes—
418C2×Dic11C2514yes—
419C2×Dic11C2514yes—
420C2×Dic11C2518yes—
421D44—28no—
422D44—28no—
423D44—416no—
424C4×D11—216no—
425C4×D11—216no—
426C4×D11—48no—
427C4×D11—48no—
428C4×D11—416no—
429Dic22—28no—
430Dic22—28no—
431C22×#41—111no—
432C22×#41—111no—
433C22×#41C2×D1111yescharacteristic
434#553—1164no—
435#553—1164no—
436#553—1132no—
437#553—1132no—
438#552—1132no—
439#552—1132no—
440#541—1132no—
441#540—1132no—
442#537—1116no—
443#537—1116no—
444#532—1116no—
445C2×C4⋊Q8—111no—
446C2×#127—111no—
447#529—1132no—
448#529—1132no—
449C2×#126—114no—
450C2×#126—114no—
451C2×#126—114no—
452C2×#126—114no—
453C2×#125—114no—
454C2×#125—112no—
455C2×#125—112no—
456C2×#125—112no—
457C2×#125—112no—
458C2×#125—1116no—
459C2×#125—114no—
460C2×#124—111no—
461C2×#124—111no—
462C2×#123—114no—
463C2×#123—114no—
464C2×#123—114no—
465C2×#123—114no—
466C2×C22⋊Q8—112no—
467C2×C22⋊Q8—112no—
468C2×C22⋊Q8—112no—
469C2×C22⋊Q8—112no—
470C2×#121—112no—
471C2×#121—112no—
472C2×#121—112no—
473C2×#121—114no—
474C2×#121—114no—
475C2×#121—112no—
476C2×#121—114no—
477C2×#121—112no—
478C2×#121—112no—
479C2×#121—114no—
480#520—1116no—
481#520C2×D11116yescomplemented
482C4×#41—1116no—
483C2×C4×Q8—111no—
484C2×C4×Q8—111no—
485C2×C4×Q8—112no—
486C2×C4×Q8C2×D1112yes—
487C2×C4×D4—114no—
488C2×C4×D4—112no—
489C2×C4×D4—112no—
490C2×C4×D4—111no—
491C2×C4×D4—111no—
492C2×C4×D4—112no—
493C2×C4×D4—112no—
494C2×C4×D4—114no—
495C2×C4×D4—112no—
496C2×C4×D4—114no—
497C2×C4×D4C2×D1112yes—
498C2×C4×D4C2×D1114yes—
499C2×#117—114no—
500C2×#117—112no—
501C2×#117—112no—
502C2×#117—114no—
503C2×#117C2×D1111yescharacteristic
504C2×#117C2×D1112yes—
505C22×C4⋊C4—112no—
506C22×C4⋊C4—111no—
507C22×C4⋊C4—112no—
508C22×C4⋊C4—112no—
509C22×C4⋊C4C2×D1111yescharacteristic
510C22×C4⋊C4C2×D1112yes—
511C22×C42—111no—
512C22×C42—112no—
513C22×C11—22no—
514C22×C11—22no—
515C22×C11—28no—
516C22×C11—24no—
517C22×C11—24no—
518C22×C11—24no—
519C22×C11—48no—
520C22×C11C22×#4114yes—
521C22×C11C22×#4112yes—
522C22×C11#58512yes—
523C22×C11#58512yes—
524C22×C11C2611yescharacteristic
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—24no—
530C2×D11—24no—
531C2×D11—48no—
532C2×D11—48no—
533C4×C11—24no—
534C4×C11—24no—
535C4×C11—28no—
536C4×C11—24no—
537C4×C11C22×#4114yes—
538C4×C11C22×#4114yes—
539Dic11—24no—
540Dic11—24no—
541Dic11—22no—
542Dic11—22no—
543Dic11—28no—
544Dic11—22no—
545Dic11—22no—
546C2×#41—28no—
547C2×#41—118no—
548C2×#41—118no—
549C2×#41—228no—
550C2×#41—228no—
551C2×#41C22×D1118yes—
552C22×Q8—111no—
553C22×Q8—111no—
554C22×Q8C22×D1111yescharacteristic
555C22×D4—112no—
556C22×D4—112no—
557C22×D4—114no—
558C22×D4—112no—
559C22×D4—112no—
560C22×D4—111no—
561C22×D4—111no—
562C22×D4—114no—
563C22×D4C22×D1112yes—
564C22×D4C22×D1111yescharacteristic
565C23×C4—112no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—112no—
569C23×C4—112no—
570C23×C4—114no—
571C23×C4—112no—
572C23×C4—112no—
573C23×C4C22×D1112yes—
574C23×C4C22×D1112yes—
575C23×C4C22×D1114yes—
576C23×C4C22×D1111yescharacteristic
577C4⋊Q8—118no—
578#127—118no—
579#126—1132no—
580#126—1132no—
581#126—1132no—
582#126—1132no—
583#125—1116no—
584#125—1116no—
585#125—1116no—
586#125—1116no—
587#125—1132no—
588#125—1132no—
589#124—118no—
590#124—118no—
591#123—1132no—
592#123—1132no—
593#123—1132no—
594#123—1132no—
595C22⋊Q8—1116no—
596C22⋊Q8—1116no—
597C22⋊Q8—1116no—
598C22⋊Q8—1116no—
599#121—1116no—
600#121—1116no—
601#121—1116no—
602#121—1132no—
603#121—1132no—
604#121—1116no—
605#121—1132no—
606#121—1116no—
607#121—1116no—
608#121—1132no—
609C4×Q8—118no—
610C4×Q8—118no—
611C4×Q8—1116no—
612C4×Q8C22×D11116yes—
613C4×D4—1132no—
614C4×D4—1116no—
615C4×D4—1116no—
616C4×D4—118no—
617C4×D4—118no—
618C4×D4—1116no—
619C4×D4—1116no—
620C4×D4—1132no—
621C4×D4—1116no—
622C4×D4—1132no—
623C4×D4C22×D11116yes—
624C4×D4C22×D11132yes—
625#117—1132no—
626#117—1116no—
627#117—1116no—
628#117—1132no—
629#117C22×D1118yes—
630#117C22×D11116yes—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—114no—
633C2×C4⋊C4—114no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—114no—
636C2×C4⋊C4—118no—
637C2×C4⋊C4—114no—
638C2×C4⋊C4—114no—
639C2×C4⋊C4—1116no—
640C2×C4⋊C4—1116no—
641C2×C4⋊C4—112no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—114no—
644C2×C4⋊C4—114no—
645C2×C4⋊C4—112no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4—1116no—
648C2×C4⋊C4C22×D1111yescharacteristic
649C2×C4⋊C4C22×D1111yescharacteristic
650C2×C4⋊C4C22×D1112yes—
651C2×C4⋊C4C22×D1112yes—
652C2×C4⋊C4C22×D1114yes—
653C2×C4⋊C4C22×D1118yes—
654C2×C4⋊C4C22×D11116yes—
655C2×C22⋊C4—112no—
656C2×C22⋊C4—114no—
657C2×C22⋊C4—112no—
658C2×C22⋊C4—112no—
659C2×C22⋊C4—112no—
660C2×C22⋊C4—112no—
661C2×C22⋊C4—114no—
662C2×C22⋊C4—114no—
663C2×C22⋊C4—112no—
664C2×C22⋊C4—114no—
665C2×C22⋊C4—114no—
666C2×C22⋊C4C22×D1112yes—
667C2×C22⋊C4C22×D1114yes—
668C2×C42—114no—
669C2×C42—112no—
670C2×C42—112no—
671C2×C42—111no—
672C2×C42—111no—
673C2×C42—111no—
674C2×C42—118no—
675C2×C42—111no—
676C2×C42—1116no—
677C2×C42C22×D1112yes—
678C2×C42C22×D1114yes—
679C2×C11—24no—
680C2×C11—44no—
681C2×C11#351214yescomplemented
682C2×C11C23×#4111yescharacteristic
683C2×C11C2×#58511yescharacteristic
684C2×C11C2×#58511yescharacteristic
685D11—44no—
686D11—44no—
687C24—112no—
688C24—112no—
689C24C23×D1112yes—
690C24C23×D1111yescharacteristic
691#41—232no—
692#41—2232no—
693#41—2232no—
694C2×Q8—24no—
695C2×Q8—114no—
696C2×Q8—114no—
697C2×Q8—224no—
698C2×Q8—224no—
699C2×Q8C23×D1114yes—
700C2×D4—28no—
701C2×D4—24no—
702C2×D4—118no—
703C2×D4—118no—
704C2×D4—1116no—
705C2×D4—118no—
706C2×D4—118no—
707C2×D4—114no—
708C2×D4—114no—
709C2×D4—1116no—
710C2×D4—228no—
711C2×D4—228no—
712C2×D4—224no—
713C2×D4—224no—
714C2×D4—448no—
715C2×D4—444no—
716C2×D4—448no—
717C2×D4—444no—
718C2×D4C23×D1118yes—
719C2×D4C23×D1114yes—
720C22×C4—28no—
721C22×C4—48no—
722C22×C4—44no—
723C22×C4—111no—
724C22×C4—111no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—111no—
728C22×C4—111no—
729C22×C4—114no—
730C22×C4—114no—
731C22×C4—114no—
732C22×C4—118no—
733C22×C4—118no—
734C22×C4—118no—
735C22×C4—118no—
736C22×C4—118no—
737C22×C4—1116no—
738C22×C4—228no—
739C22×C4—228no—
740C22×C4—444no—
741C22×C4—444no—
742C22×C4—448no—
743C22×C4—442no—
744C22×C4—442no—
745C22×C4—444no—
746C22×C4#433918yes—
747C22×C4C23×D1118yes—
748C22×C4C23×D1112yes—
749C22×C4C23×D1112yes—
750C22×C4C23×D1112yes—
751C22×C4C23×D1114yes—
752C22×C4C23×D1118yes—
753C22×C4C23×D11116yes—
754C22×C4C23×D1114yes—
755C22×C4C23×D1111yescharacteristic
756C22×C4C23×D1111yescharacteristic
757C4⋊C4—118no—
758C4⋊C4—1116no—
759C4⋊C4—1116no—
760C4⋊C4—118no—
761C4⋊C4—1116no—
762C4⋊C4—1116no—
763C4⋊C4—1116no—
764C4⋊C4—118no—
765C4⋊C4—118no—
766C4⋊C4—1116no—
767C4⋊C4—1116no—
768C4⋊C4—118no—
769C4⋊C4—118no—
770C4⋊C4C23×D1114yes—
771C4⋊C4C23×D1114yes—
772C4⋊C4C23×D1118yes—
773C4⋊C4C23×D1118yes—
774C4⋊C4C23×D11116yes—
775C22⋊C4—118no—
776C22⋊C4—1116no—
777C22⋊C4—118no—
778C22⋊C4—118no—
779C22⋊C4—118no—
780C22⋊C4—118no—
781C22⋊C4—1116no—
782C22⋊C4—1116no—
783C22⋊C4—118no—
784C22⋊C4—1116no—
785C22⋊C4—1116no—
786C22⋊C4C23×D1118yes—
787C22⋊C4C23×D11116yes—
788C42—114no—
789C42—118no—
790C42—118no—
791C42—114no—
792C42—114no—
793C42—114no—
794C42—1116no—
795C42C23×D1118yes—
796C42C23×D11116yes—
797C11C2×#351211yescharacteristic, complemented, Sylow
798C23—22no—
799C23—22no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—114no—
804C23—114no—
805C23—224no—
806C23—224no—
807C23—224no—
808C23—224no—
809C23—224no—
810C23—224no—
811C23C2×#433914yes—
812C23C24×D1114yes—
813C23C24×D1112yes—
814C23C24×D1111yescharacteristic
815Q8—28no—
816Q8—228no—
817Q8—228no—
818D4—216no—
819D4—28no—
820D4—2216no—
821D4—2216no—
822D4—228no—
823D4—228no—
824D4—4416no—
825D4—448no—
826D4—4416no—
827D4—448no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—28no—
831C2×C4—24no—
832C2×C4—216no—
833C2×C4—416no—
834C2×C4—48no—
835C2×C4—112no—
836C2×C4—112no—
837C2×C4—114no—
838C2×C4—114no—
839C2×C4—112no—
840C2×C4—112no—
841C2×C4—118no—
842C2×C4—224no—
843C2×C4—224no—
844C2×C4—222no—
845C2×C4—222no—
846C2×C4—222no—
847C2×C4—228no—
848C2×C4—222no—
849C2×C4—2216no—
850C2×C4—2216no—
851C2×C4—448no—
852C2×C4—448no—
853C2×C4—4416no—
854C2×C4—444no—
855C2×C4—444no—
856C2×C4—448no—
857C2×C4C2×#433914yes—
858C2×C4C2×#433914yes—
859C2×C4C2×#4339116yes—
860C2×C4C24×D1114yes—
861C2×C4C24×D1114yes—
862C2×C4C24×D1114yes—
863C2×C4C24×D1118yes—
864C2×C4C24×D1112yes—
865C2×C4C24×D1112yes—
866C22—22no—
867C22—22no—
868C22—28no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—48no—
873C22—224no—
874C22—224no—
875C22—224no—
876C22—224no—
877C22—224no—
878C22—224no—
879C22—448no—
880C22—448no—
881C22C22×#433914yes—
882C22C22×#433912yes—
883C22#1062345512yes—
884C22#1062345712yes—
885C22C25×D1111yescharacteristic
886C4—24no—
887C4—24no—
888C4—28no—
889C4—24no—
890C4—224no—
891C4—224no—
892C4—222no—
893C4—222no—
894C4—222no—
895C4—228no—
896C4—222no—
897C4C22×#433914yes—
898C4C22×#433914yes—
899C2—24no—
900C2—44no—
901C2—444no—
902C2—444no—
903C2#1308253314yesdirect product factor
904C2C23×#433911yescharacteristic
905C2C2×#1062345511yescharacteristic
906C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#520C2
socleC23×C11C25
hypercenterC2×#520D11
hypocenterC11C2×#3512
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #13082533C2direct (N × H)
2. C2×#10623071C2semidirect
3. C2×#10623045C2semidirect
4. C2×#10623096C2semidirect
5. C2×#10623061C2semidirect
6. C2×#10623060C2semidirect
7. C2×#10623044C2semidirect
8. C2×#10623114C2semidirect
9. C2×#10623093C2semidirect
10. C2×#10623041C2semidirect
11. C2×#10623364C2semidirect
12. C2×#10623363C2semidirect
13. C2×#10623111C2semidirect
14. C2×#10623088C2semidirect
15. C22×#66943C2semidirect
16. C2×#10623054C2semidirect
17. C2×#10623053C2semidirect
18. C2×C11×#520C2semidirect
22. C11×#520C22semidirect
30. #10623364C22semidirect
31. #10623363C22semidirect
54. #10623114C22semidirect
55. #10623111C22semidirect
56. #10623096C22semidirect
57. #10623093C22semidirect
58. #10623088C22semidirect
59. #10623071C22semidirect
60. #10623061C22semidirect
61. #10623060C22semidirect
62. #10623054C22semidirect
63. #10623053C22semidirect
64. #10623045C22semidirect
65. #10623044C22semidirect
68. #10623041C22semidirect
82. C2×#66943C22semidirect
361. C2×#520D11semidirect
481. #520C2×D11semidirect
681. C2×C11#3512semidirect
797. C11C2×#3512semidirect
903. C2#13082533direct (N × H)

Maximal subgroups

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

subgroupindex
#130825332
C2×#106230712
C2×#106230452
C2×#106230962
C2×#106230612
C2×#106230602
C2×#106230442
C2×#106231142
C2×#106230932
C2×#106230412
C2×#106233642
C2×#106233632
C2×#106231112
C2×#106230882
C22×#669432
C2×#106230542
C2×#106230532
C2×C11×#5202
C2×#351211