Finite Group Databasebeta

← C2×#13082439 #15662253

Subgroups — C2×#13082439 #15662253

Order 2816.

6958 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082439C2132yesmaximal, direct product factor
2C2×#10623216C212yesmaximal, complemented
3C2×#10623252C212yesmaximal, complemented
4C2×#10623261C212yesmaximal, complemented
5C2×#10623166C214yesmaximal, complemented
6C2×#10623221C212yesmaximal, complemented
7C2×#10623167C214yesmaximal, complemented
8C2×#10623220C212yesmaximal, complemented
9C2×#10623050C211yesmaximal, characteristic, complemented
10C2×#10623260C212yesmaximal, complemented
11C2×#10623259C212yesmaximal, complemented
12C2×#10623048C211yesmaximal, characteristic, complemented
13C22×#66943C211yesmaximal, characteristic, complemented
14C2×D11×#125C212yesmaximal, complemented
15C2×#10623035C211yesmaximal, characteristic
16C2×#10623054C211yesmaximal, characteristic
17C2×#10623053C211yesmaximal, characteristic
18C2×C11×#544C211yesmaximal, characteristic, complemented
19C22×#4339C2211yescharacteristic
20C11×#544C22116yescomplemented
21C2×C11×C4⋊Q8C2212yes—
22C2×C11×C4⋊Q8C2212yes—
23C2×C11×#125C2212yes—
24C2×C11×#125C2212yes—
25C2×C11×C22⋊Q8C2214yes—
26C2×C11×#117C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C2×#66999C2214yes—
30C2×#66999C2214yes—
31C2×Q8×Dic11C2214yes—
32C2×#66997C2214yes—
33C2×C4×C22⋊D11C2214yes—
34C2×#66979C2211yescharacteristic
35C22×C4⋊Dic11C2212yes—
36C22×C4⋊Dic11C2211yescharacteristic
37C22×Dic11⋊C4C2212yes—
38C22×C4×Dic11C2211yescharacteristic
39#10623261C22132yescomplemented
40#10623260C22132yescomplemented
41#10623259C22132yescomplemented
42#10623252C22132yescomplemented
43#10623221C22132yescomplemented
44#10623220C22132yescomplemented
45D11×#125C22132yescomplemented
46#10623216C22132yescomplemented
47#10623167C22164yescomplemented
48#10623166C22164yescomplemented
49#10623054C22116yes—
50#10623053C22116yes—
51#10623050C22116yescomplemented
52#10623048C22116yescomplemented
53C2×#66950C2214yes—
54C2×#66950C2214yes—
55C2×#66949C2214yes—
56C2×#66949C2214yes—
57#10623035C22116yes—
58C2×#66946C2211yescharacteristic
59C2×#66946C2212yes—
60C2×#66946C2211yescharacteristic
61C2×#66945C2212yes—
62C2×#66945C2212yes—
63C2×C4⋊C4×D11C2214yes—
64C2×C4⋊C4×D11C2214yes—
65C2×C4⋊C4×D11C2212yes—
66C2×C4⋊C4×D11C2212yes—
67C2×#66943C2211yescharacteristic
68C2×#66943C2212yes—
69C2×#66943C2212yes—
70C2×#66943C2212yes—
71C2×#66943C2212yes—
72C2×#66943C2212yes—
73C2×#66943C2211yescharacteristic
74C2×#66943C22116yescomplemented
75C2×#66942C2214yes—
76C2×#66942C2214yes—
77C2×#66942C2214yes—
78C2×#66942C2214yes—
79C2×#66941C2212yes—
80C2×#66941C2214yes—
81C2×#66941C2211yescharacteristic
82C2×#66941C2211yescharacteristic
83C2×#66940C2214yes—
84C2×#66940C2211yescharacteristic
85C2×#66940C2212yes—
86C2×#66940C2211yescharacteristic
87C2×(C22⋊D11)⋊C4C2212yes—
88C2×(C22⋊D11)⋊C4C2214yes—
89C2×(C22⋊D11)⋊C4C2212yes—
90C2×#66931C2212yes—
91C2×#66931C2214yes—
92C2×#66931C2212yes—
93C2×C4×D44C2212yes—
94C2×#66925C2212yes—
95C2×C42×D11C2212yes—
96C2×#66923C2212yes—
97C2×#66922C2212yes—
98C2×C4×Dic22C2212yes—
99C2×C4×Dic22C2212yes—
100C2×C4×Dic22C2212yes—
101C22×Q8×C11C2314yes—
102C23×C4×C11C2312yes—
103C23×C4×C11C2311yescharacteristic
104C22×C22⋊D11C2312yes—
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2312yes—
108C2×#4339Q8116yescomplemented
109C2×#4339C2318yes—
110C22×D44C2311yescharacteristic
111C22×C4×D11C2312yes—
112C22×C4×D11C2312yes—
113C22×C4×D11C2314yes—
114C22×C4×D11C2314yes—
115C22×C4×D11C2312yes—
116C22×Dic22C2312yes—
117C22×Dic22C2312yes—
118C22×Dic22C2314yes—
119C22×Dic22C2311yescharacteristic
120C11×C4⋊Q8C23116yes—
121C11×C4⋊Q8C23116yes—
122C11×#125C23116yes—
123C11×#125C23116yes—
124C11×C22⋊Q8C23132yes—
125C11×#117C2318yes—
126C11×#117C2318yes—
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C4⋊C4C2314yes—
129C2×C11×C4⋊C4C2312yes—
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C4⋊C4C2314yes—
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2314yes—
135C2×C11×C4⋊C4C2312yes—
136C2×C11×C4⋊C4C2318yes—
137C2×C11×C22⋊C4C2312yes—
138C2×C11×C22⋊C4C2312yes—
139C2×C42×C11C2312yes—
140C2×C42×C11C2312yes—
141C2×C22⋊Dic11C2312yes—
142#66999C23132yes—
143#66999C23132yes—
144Q8×Dic11C23132yes—
145#66997C23132yes—
146C4×C22⋊D11C23132yes—
147C2×(C2×D11)⋊C4C2312yes—
148C2×(C2×D11)⋊C4C2312yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151#66979C2318yes—
152C2×C4⋊Dic11C2312yes—
153C2×C4⋊Dic11C2312yes—
154C2×C4⋊Dic11C2312yes—
155C2×C4⋊Dic11C2311yescharacteristic
156C2×C4⋊Dic11C2312yes—
157C2×C4⋊Dic11C2314yes—
158C2×C4⋊Dic11C2311yescharacteristic
159C2×C4⋊Dic11C2314yes—
160C2×C4⋊Dic11C2314yes—
161C2×C4⋊Dic11C2318yes—
162C2×C4⋊Dic11C23116yes—
163C2×Dic11⋊C4C2312yes—
164C2×Dic11⋊C4C2312yes—
165C2×Dic11⋊C4C2312yes—
166C2×Dic11⋊C4C2312yes—
167C2×Dic11⋊C4C2314yes—
168C2×Dic11⋊C4C2314yes—
169C2×Dic11⋊C4C2314yes—
170C2×Dic11⋊C4C2312yes—
171C2×Dic11⋊C4C2312yes—
172C2×Dic11⋊C4C2314yes—
173C2×Dic11⋊C4C2314yes—
174C2×Dic11⋊C4C2314yes—
175C2×Dic11⋊C4C23116yes—
176C2×C4×Dic11C2312yes—
177C2×C4×Dic11C2311yescharacteristic
178C2×C4×Dic11C2311yescharacteristic
179C2×C4×Dic11C2314yes—
180C2×C4×Dic11C2311yescharacteristic
181C2×C4×Dic11C2312yes—
182C2×C4×Dic11C2312yes—
183C2×C4×Dic11C2311yescharacteristic
184C2×C4×Dic11C2314yes—
185C2×C4×Dic11C2318yes—
186#66950C23132yes—
187#66950C23132yes—
188#66949C23132yes—
189#66949C23132yes—
190#66946C2318yes—
191#66946C23116yes—
192#66946C2318yes—
193#66945C23116yes—
194#66945C23116yes—
195C4⋊C4×D11C23116yes—
196C4⋊C4×D11C23132yes—
197C4⋊C4×D11C23116yes—
198C4⋊C4×D11C23132yes—
199#66943C23116yes—
200#66943C23116yes—
201#66943C2318yes—
202#66943C23116yes—
203#66943C23116yes—
204#66943C23116yes—
205#66943C2318yes—
206#66942C23132yes—
207#66942C23132yes—
208#66942C23132yes—
209#66942C23132yes—
210#66941C2318yes—
211#66941C2318yes—
212#66941C23116yes—
213#66941C23132yes—
214#66940C2318yes—
215#66940C23116yes—
216#66940C23132yes—
217#66940C2318yes—
218(C22⋊D11)⋊C4C23116yes—
219(C22⋊D11)⋊C4C23116yes—
220(C22⋊D11)⋊C4C23132yes—
221#66931C23116yes—
222#66931C23116yes—
223#66931C23132yes—
224C4×D44C23116yes—
225#66925C23116yes—
226C42×D11C23116yes—
227#66923C23116yes—
228#66922C23116yes—
229C4×Dic22C23116yes—
230C4×Dic22C23116yes—
231C4×Dic22C23116yes—
232C2×#3504—111nomaximal, Sylow
233C24×C11C2411yescharacteristic
234C23×D11C2412yes—
235C2×Q8×C11—48no—
236C2×Q8×C11C24116yes—
237C22×C4×C11—44no—
238C22×C4×C11C2×Q818yes—
239C22×C4×C11C2412yes—
240C22×C4×C11C2412yes—
241C22×C4×C11C2414yes—
242C22×C4×C11C2412yes—
243C22×C4×C11C2412yes—
244C22×C4×C11C2418yes—
245C22×C4×C11C2411yescharacteristic
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2414yes—
248C2×C22⋊D11C2×Q8116yes—
249C2×C22⋊D11C2418yes—
250C22×Dic11—42no—
251C22×Dic11—44no—
252C22×Dic11—42no—
253C22×Dic11C2411yescharacteristic
254C22×Dic11C2411yescharacteristic
255C22×Dic11C2412yes—
256C22×Dic11C2411yescharacteristic
257C22×Dic11C2411yescharacteristic
258C22×Dic11C2412yes—
259C22×Dic11C2414yes—
260C22×Dic11C2414yes—
261C22×Dic11C2414yes—
262C22×Dic11C2418yes—
263C22×Dic11C2412yes—
264#4339C2×Q8164yescomplemented
265C2×D44C2×Q818yes—
266C2×D44C2414yes—
267C2×C4×D11—44no—
268C2×C4×D11—48no—
269C2×C4×D11—48no—
270C2×C4×D11—44no—
271C2×C4×D11C2×Q8116yes—
272C2×C4×D11C2418yes—
273C2×C4×D11C2418yes—
274C2×C4×D11C24116yes—
275C2×C4×D11C24116yes—
276C2×C4×D11C2418yes—
277C2×Dic22—48no—
278C2×Dic22—44no—
279C2×Dic22—44no—
280C2×Dic22C2×Q818yes—
281C2×Dic22C2418yes—
282C2×Dic22C2418yes—
283C2×Dic22C24116yes—
284C2×Dic22C2414yes—
285C11×C4⋊C4C2414yes—
286C11×C4⋊C4C24116yes—
287C11×C4⋊C4C2418yes—
288C11×C4⋊C4C2414yes—
289C11×C4⋊C4C24116yes—
290C11×C4⋊C4C2414yes—
291C11×C4⋊C4C2414yes—
292C11×C4⋊C4C24116yes—
293C11×C4⋊C4C2418yes—
294C11×C22⋊C4C2418yes—
295C11×C22⋊C4C2418yes—
296C42×C11C2418yes—
297C42×C11C2418yes—
298C22⋊Dic11C2418yes—
299(C2×D11)⋊C4C2418yes—
300(C2×D11)⋊C4C2418yes—
301(C2×D11)⋊C4C24116yes—
302(C2×D11)⋊C4C24116yes—
303C4⋊Dic11C2418yes—
304C4⋊Dic11C2418yes—
305C4⋊Dic11C2418yes—
306C4⋊Dic11C2414yes—
307C4⋊Dic11C2418yes—
308C4⋊Dic11C24116yes—
309C4⋊Dic11C2414yes—
310C4⋊Dic11C24116yes—
311C4⋊Dic11C24116yes—
312Dic11⋊C4C2418yes—
313Dic11⋊C4C2418yes—
314Dic11⋊C4C2418yes—
315Dic11⋊C4C2418yes—
316Dic11⋊C4C24116yes—
317Dic11⋊C4C24116yes—
318Dic11⋊C4C24116yes—
319Dic11⋊C4C2418yes—
320Dic11⋊C4C2418yes—
321Dic11⋊C4C24116yes—
322Dic11⋊C4C24116yes—
323Dic11⋊C4C24116yes—
324C4×Dic11C2418yes—
325C4×Dic11C2414yes—
326C4×Dic11C2414yes—
327C4×Dic11C24116yes—
328C4×Dic11C2414yes—
329C4×Dic11C2418yes—
330C4×Dic11C2418yes—
331C4×Dic11C2414yes—
332C4×Dic11C24116yes—
333#3504—1132no—
334C2×#557—112no—
335C2×#557—112no—
336C2×#554—112no—
337C2×#554—112no—
338C2×#554—114no—
339C2×#554—114no—
340C2×#544—112no—
341C2×#544—112no—
342C2×#544—111no—
343C2×#544D1111yescharacteristic, complemented
344C2×#533—112no—
345C2×#533—111no—
346C22×#125—112no—
347C22×#125—111no—
348C2×#520—111no—
349C2×#520—111no—
350C2×C4×#41—111no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11C22×Q814yes—
354C23×C11C2512yes—
355C23×C11C2511yescharacteristic
356C22×D11—24no—
357C22×D11—24no—
358C22×D11C22×Q818yes—
359C22×D11C2514yes—
360Q8×C11—416no—
361C2×C4×C11—24no—
362C2×C4×C11—24no—
363C2×C4×C11—24no—
364C2×C4×C11—28no—
365C2×C4×C11—24no—
366C2×C4×C11—48no—
367C2×C4×C11C22×Q814yes—
368C2×C4×C11C22×Q814yes—
369C2×C4×C11C22×Q8116yes—
370C2×C4×C11C2514yes—
371C2×C4×C11C2514yes—
372C2×C4×C11C2518yes—
373C2×C4×C11C2514yes—
374C2×C4×C11C2514yes—
375C2×C4×C11C2512yes—
376C2×C4×C11C2512yes—
377C22⋊D11C22×Q8132yes—
378C2×Dic11—24no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—24no—
382C2×Dic11—28no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387C2×Dic11—48no—
388C2×Dic11C22×Q818yes—
389C2×Dic11C2512yes—
390C2×Dic11C2512yes—
391C2×Dic11C2514yes—
392C2×Dic11C2512yes—
393C2×Dic11C2512yes—
394C2×Dic11C2514yes—
395C2×Dic11C2518yes—
396C2×Dic11C2514yes—
397D44C22×Q8116yes—
398C4×D11—416no—
399C4×D11—416no—
400C4×D11—48no—
401C4×D11—48no—
402C4×D11C22×Q8132yes—
403Dic22—48no—
404Dic22—416no—
405Dic22—48no—
406Dic22C22×Q8116yes—
407C22×#41—111no—
408#557—1132no—
409#557—1132no—
410#554—1132no—
411#554—1132no—
412#554—1164no—
413#554—1164no—
414#544—1132no—
415#544—1132no—
416#544—1116no—
417#544C2×D11116yescomplemented
418#533—1132no—
419#533—1116no—
420C2×C4⋊Q8—114no—
421C2×C4⋊Q8—111no—
422C2×C4⋊Q8—111no—
423C2×C4⋊Q8—114no—
424C2×C4⋊Q8—112no—
425C2×C4⋊Q8—112no—
426C2×C4⋊Q8C2×D1112yes—
427C2×C4⋊Q8C2×D1112yes—
428C2×#125—1132no—
429C2×#125—114no—
430C2×#125—114no—
431C2×#125—114no—
432C2×#125—114no—
433C2×#125—111no—
434C2×#125—112no—
435C2×#125—112no—
436C2×#125—112no—
437C2×#125—112no—
438C2×#125—111no—
439C2×#125—112no—
440C2×#125—1116no—
441C2×#125—112no—
442C2×#125C2×D1112yes—
443C2×#125C2×D1112yes—
444C2×C22⋊Q8—114no—
445C2×C22⋊Q8—114no—
446C2×C22⋊Q8—114no—
447C2×C22⋊Q8—114no—
448C2×C22⋊Q8—114no—
449C2×C22⋊Q8—114no—
450C2×C22⋊Q8—112no—
451C2×C22⋊Q8—112no—
452C2×C22⋊Q8—114no—
453C2×C22⋊Q8C2×D1114yes—
454#520—1116no—
455#520—1116no—
456C4×#41—1116no—
457C2×C4×Q8—114no—
458C2×C4×Q8—111no—
459C2×C4×Q8—111no—
460C2×C4×Q8—112no—
461C2×C4×Q8—114no—
462C2×C4×Q8—112no—
463C2×C4×Q8—112no—
464C2×C4×Q8—112no—
465C2×C4×D4—114no—
466C2×C4×D4—111no—
467C2×C4×D4—111no—
468C2×C4×D4—112no—
469C2×C4×D4—112no—
470C2×C4×D4—112no—
471C2×C4×D4—114no—
472C2×C4×D4—112no—
473C2×#117—111no—
474C2×#117—112no—
475C2×#117—112no—
476C2×#117—112no—
477C2×#117C2×D1111yescharacteristic
478C2×#117C2×D1111yescharacteristic
479C22×C4⋊C4—112no—
480C22×C4⋊C4—111no—
481C22×C4⋊C4—112no—
482C22×C4⋊C4—112no—
483C22×C4⋊C4—112no—
484C22×C4⋊C4—114no—
485C22×C4⋊C4—114no—
486C22×C4⋊C4C2×D1111yescharacteristic
487C22×C42—111no—
488C22×C42—112no—
489C22×C11—22no—
490C22×C11—22no—
491C22×C11—28no—
492C22×C11C23×Q814yes—
493C22×C11C23×Q812yes—
494C22×C11#58512yes—
495C22×C11#58512yes—
496C22×C11C2611yescharacteristic
497C2×D11—24no—
498C2×D11—24no—
499C2×D11—216no—
500C2×D11C23×Q818yes—
501C4×C11—28no—
502C4×C11—24no—
503C4×C11—24no—
504C4×C11—24no—
505C4×C11—24no—
506C4×C11C23×Q814yes—
507C4×C11C23×Q814yes—
508Dic11—24no—
509Dic11—22no—
510Dic11—22no—
511Dic11—24no—
512Dic11—28no—
513Dic11—22no—
514Dic11—22no—
515Dic11C23×Q818yes—
516C2×#41—1116no—
517C2×#41—118no—
518C22×Q8—111no—
519C22×Q8—112no—
520C22×Q8—114no—
521C22×Q8—112no—
522C22×Q8C22×D1114yes—
523C22×D4—112no—
524C22×D4—111no—
525C23×C4—112no—
526C23×C4—112no—
527C23×C4—111no—
528C23×C4—111no—
529C23×C4—114no—
530C23×C4—114no—
531C23×C4—112no—
532C23×C4—112no—
533C23×C4C22×D1112yes—
534C23×C4C22×D1111yescharacteristic
535C4⋊Q8—1132no—
536C4⋊Q8—118no—
537C4⋊Q8—118no—
538C4⋊Q8—1132no—
539C4⋊Q8—1116no—
540C4⋊Q8—1116no—
541C4⋊Q8C22×D11116yes—
542C4⋊Q8C22×D11116yes—
543#125—118no—
544#125—1116no—
545#125—1116no—
546#125—1132no—
547#125—1132no—
548#125—1116no—
549#125—1116no—
550#125—118no—
551#125—1132no—
552#125—1132no—
553#125—1116no—
554#125—1116no—
555#125C22×D11116yes—
556#125C22×D11116yes—
557C22⋊Q8—1132no—
558C22⋊Q8—1132no—
559C22⋊Q8—1132no—
560C22⋊Q8—1132no—
561C22⋊Q8—1132no—
562C22⋊Q8—1132no—
563C22⋊Q8—1116no—
564C22⋊Q8—1116no—
565C22⋊Q8—1132no—
566C22⋊Q8C22×D11132yes—
567C4×Q8—1132no—
568C4×Q8—118no—
569C4×Q8—118no—
570C4×Q8—1116no—
571C4×Q8—1132no—
572C4×Q8—1116no—
573C4×Q8—1116no—
574C4×Q8—1116no—
575C4×D4—1132no—
576C4×D4—118no—
577C4×D4—118no—
578C4×D4—1116no—
579C4×D4—1116no—
580C4×D4—1116no—
581C4×D4—1132no—
582C4×D4—1116no—
583#117—118no—
584#117—1116no—
585#117—1116no—
586#117—1116no—
587#117C22×D1118yes—
588#117C22×D1118yes—
589C2×C4⋊C4—112no—
590C2×C4⋊C4—111no—
591C2×C4⋊C4—114no—
592C2×C4⋊C4—112no—
593C2×C4⋊C4—114no—
594C2×C4⋊C4—112no—
595C2×C4⋊C4—114no—
596C2×C4⋊C4—114no—
597C2×C4⋊C4—112no—
598C2×C4⋊C4—118no—
599C2×C4⋊C4—114no—
600C2×C4⋊C4—114no—
601C2×C4⋊C4—114no—
602C2×C4⋊C4—114no—
603C2×C4⋊C4—1116no—
604C2×C4⋊C4—1116no—
605C2×C4⋊C4—111no—
606C2×C4⋊C4—112no—
607C2×C4⋊C4—112no—
608C2×C4⋊C4—112no—
609C2×C4⋊C4—112no—
610C2×C4⋊C4—112no—
611C2×C4⋊C4—112no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—1116no—
614C2×C4⋊C4—1116no—
615C2×C4⋊C4—1132no—
616C2×C4⋊C4—1132no—
617C2×C4⋊C4C22×D1111yescharacteristic
618C2×C4⋊C4C22×D1112yes—
619C2×C4⋊C4C22×D1114yes—
620C2×C4⋊C4C22×D1114yes—
621C2×C4⋊C4C22×D1112yes—
622C2×C4⋊C4C22×D1118yes—
623C2×C4⋊C4C22×D1111yescharacteristic
624C2×C4⋊C4C22×D1111yescharacteristic
625C2×C4⋊C4C22×D1111yescharacteristic
626C2×C4⋊C4C22×D1114yes—
627C2×C22⋊C4—112no—
628C2×C22⋊C4—114no—
629C2×C22⋊C4—112no—
630C2×C22⋊C4—112no—
631C2×C22⋊C4—114no—
632C2×C22⋊C4C22×D1112yes—
633C2×C22⋊C4C22×D1112yes—
634C2×C42—111no—
635C2×C42—114no—
636C2×C42—114no—
637C2×C42—112no—
638C2×C42—112no—
639C2×C42—112no—
640C2×C42—111no—
641C2×C42—111no—
642C2×C42—118no—
643C2×C42—111no—
644C2×C42—1116no—
645C2×C42C22×D1112yes—
646C2×C42C22×D1112yes—
647C2×C11—24no—
648C2×C11#350414yescomplemented
649C2×C11C24×Q811yescharacteristic
650C2×C11C2×#58511yescharacteristic
651C2×C11C2×#58511yescharacteristic
652D11—28no—
653C24—112no—
654C24C23×D1111yescharacteristic
655#41—1164no—
656C2×Q8—48no—
657C2×Q8—118no—
658C2×Q8—114no—
659C2×Q8—118no—
660C2×Q8—1116no—
661C2×Q8—118no—
662C2×Q8—444no—
663C2×Q8—444no—
664C2×Q8—448no—
665C2×Q8C23×D11116yes—
666C2×D4—1116no—
667C2×D4—118no—
668C2×D4—118no—
669C2×D4—114no—
670C22×C4—44no—
671C22×C4—112no—
672C22×C4—1116no—
673C22×C4—118no—
674C22×C4—111no—
675C22×C4—111no—
676C22×C4—112no—
677C22×C4—111no—
678C22×C4—111no—
679C22×C4—112no—
680C22×C4—114no—
681C22×C4—114no—
682C22×C4—114no—
683C22×C4—118no—
684C22×C4—118no—
685C22×C4—118no—
686C22×C4—1116no—
687C22×C4—1116no—
688C22×C4—448no—
689C22×C4—444no—
690C22×C4—448no—
691C22×C4—444no—
692C22×C4—442no—
693C22×C4—442no—
694C22×C4—444no—
695C22×C4Q8×D1118yes—
696C22×C4C23×D1112yes—
697C22×C4C23×D1112yes—
698C22×C4C23×D1112yes—
699C22×C4C23×D1114yes—
700C22×C4C23×D1112yes—
701C22×C4C23×D1118yes—
702C22×C4C23×D1114yes—
703C22×C4C23×D1111yescharacteristic
704C22×C4C23×D1111yescharacteristic
705C4⋊C4—118no—
706C4⋊C4—114no—
707C4⋊C4—1116no—
708C4⋊C4—118no—
709C4⋊C4—1116no—
710C4⋊C4—118no—
711C4⋊C4—1116no—
712C4⋊C4—1116no—
713C4⋊C4—118no—
714C4⋊C4—1116no—
715C4⋊C4—1116no—
716C4⋊C4—1116no—
717C4⋊C4—1116no—
718C4⋊C4—114no—
719C4⋊C4—118no—
720C4⋊C4—118no—
721C4⋊C4—118no—
722C4⋊C4—118no—
723C4⋊C4—118no—
724C4⋊C4—118no—
725C4⋊C4—1116no—
726C4⋊C4C23×D1114yes—
727C4⋊C4C23×D1118yes—
728C4⋊C4C23×D11116yes—
729C4⋊C4C23×D11116yes—
730C4⋊C4C23×D1118yes—
731C4⋊C4C23×D1114yes—
732C4⋊C4C23×D1114yes—
733C4⋊C4C23×D1114yes—
734C4⋊C4C23×D11116yes—
735C22⋊C4—118no—
736C22⋊C4—1116no—
737C22⋊C4—118no—
738C22⋊C4—118no—
739C22⋊C4—1116no—
740C22⋊C4C23×D1118yes—
741C22⋊C4C23×D1118yes—
742C42—114no—
743C42—114no—
744C42—118no—
745C42—118no—
746C42—114no—
747C42—114no—
748C42—1116no—
749C42—1116no—
750C42—118no—
751C42C23×D1118yes—
752C42C23×D1118yes—
753C11C2×#350411yescharacteristic, complemented, Sylow
754C23—22no—
755C23—22no—
756C23—118no—
757C23—114no—
758C23—224no—
759C23—224no—
760C23C2×Q8×D1114yes—
761C23C24×D1112yes—
762C23C24×D1111yescharacteristic
763Q8—416no—
764Q8—1116no—
765Q8—448no—
766Q8—448no—
767Q8—4416no—
768D4—1132no—
769D4—1116no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—48no—
776C2×C4—118no—
777C2×C4—114no—
778C2×C4—1132no—
779C2×C4—112no—
780C2×C4—112no—
781C2×C4—114no—
782C2×C4—112no—
783C2×C4—112no—
784C2×C4—114no—
785C2×C4—118no—
786C2×C4—222no—
787C2×C4—224no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—228no—
791C2×C4—222no—
792C2×C4—224no—
793C2×C4—4416no—
794C2×C4—448no—
795C2×C4—4416no—
796C2×C4—448no—
797C2×C4—444no—
798C2×C4—444no—
799C2×C4—448no—
800C2×C4C2×Q8×D1114yes—
801C2×C4C2×Q8×D1114yes—
802C2×C4C2×Q8×D11116yes—
803C2×C4C24×D1114yes—
804C2×C4C24×D1114yes—
805C2×C4C24×D1114yes—
806C2×C4C24×D1118yes—
807C2×C4C24×D1114yes—
808C2×C4C24×D1112yes—
809C2×C4C24×D1112yes—
810C22—22no—
811C22—22no—
812C22—28no—
813C22—118no—
814C22—224no—
815C22—224no—
816C22—2216no—
817C22C22×Q8×D1114yes—
818C22C22×Q8×D1112yes—
819C22#1062345512yes—
820C22#1062345712yes—
821C22C25×D1111yescharacteristic
822C4—28no—
823C4—24no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—118no—
828C4—222no—
829C4—224no—
830C4—222no—
831C4—222no—
832C4—228no—
833C4—222no—
834C4—224no—
835C4C22×Q8×D1114yes—
836C4C22×Q8×D1114yes—
837C2—24no—
838C2—228no—
839C2#1308243914yesdirect product factor
840C2C23×Q8×D1111yescharacteristic
841C2C2×#1062345511yescharacteristic
842C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#544C2
socleC23×C11C25
prime radicalC22×#4339C22
hypercenterC2×#544D11
hypocenterC11C2×#3504
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #13082439C2direct (N × H)
2. C2×#10623216C2semidirect
3. C2×#10623252C2semidirect
4. C2×#10623261C2semidirect
5. C2×#10623166C2semidirect
6. C2×#10623221C2semidirect
7. C2×#10623167C2semidirect
8. C2×#10623220C2semidirect
9. C2×#10623050C2semidirect
10. C2×#10623260C2semidirect
11. C2×#10623259C2semidirect
12. C2×#10623048C2semidirect
13. C22×#66943C2semidirect
14. C2×D11×#125C2semidirect
18. C2×C11×#544C2semidirect
20. C11×#544C22semidirect
39. #10623261C22semidirect
40. #10623260C22semidirect
41. #10623259C22semidirect
42. #10623252C22semidirect
43. #10623221C22semidirect
44. #10623220C22semidirect
45. D11×#125C22semidirect
46. #10623216C22semidirect
47. #10623167C22semidirect
48. #10623166C22semidirect
51. #10623050C22semidirect
52. #10623048C22semidirect
74. C2×#66943C22semidirect
108. C2×#4339Q8semidirect
264. #4339C2×Q8semidirect
343. C2×#544D11semidirect
417. #544C2×D11semidirect
648. C2×C11#3504semidirect
753. C11C2×#3504semidirect
839. C2#13082439direct (N × H)

Maximal subgroups

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

subgroupindex
#130824392
C2×#106232162
C2×#106232522
C2×#106232612
C2×#106231662
C2×#106232212
C2×#106231672
C2×#106232202
C2×#106230502
C2×#106232602
C2×#106232592
C2×#106230482
C22×#669432
C2×D11×#1252
C2×#106230352
C2×#106230542
C2×#106230532
C2×C11×#5442
C2×#350411