Finite Group Databasebeta

← C2×#13082957 #15661456

Subgroups — C2×#13082957 #15661456

Order 2816.

7086 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082957C2132yesmaximal, direct product factor
2C2×#10623177C214yesmaximal, complemented
3C2×Q8×Dic22C211yesmaximal, characteristic, complemented
4C2×#10623094C211yesmaximal, characteristic, complemented
5C2×#10623261C211yesmaximal, characteristic, complemented
6C2×#10623225C212yesmaximal, complemented
7C2×#10623170C212yesmaximal, complemented
8C2×#10623082C212yesmaximal, complemented
9C2×#10623038C212yesmaximal, complemented
10C2×#10623031C212yesmaximal, complemented
11C2×#10623220C212yesmaximal, complemented
12C2×#10623174C212yesmaximal, complemented
13C2×#10623092C212yesmaximal, complemented
14C2×#10623159C214yesmaximal, complemented
15C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
16C2×#10623111C211yesmaximal, characteristic, complemented
17C2×#10623088C211yesmaximal, characteristic, complemented
18C2×C11×#554C211yesmaximal, characteristic, complemented
19C22×Q8×D11C2212yes—
20C22×#4339C2214yes—
21C11×#554C22116yescomplemented
22C2×C11×C4⋊Q8C2211yescharacteristic
23C2×C11×#125C2212yes—
24C2×C11×C22⋊Q8C2212yes—
25C2×C11×C22⋊Q8C2214yes—
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2212yes—
29C22×C11×C4⋊C4C2212yes—
30C2×#67000C2211yescharacteristic
31C2×#66999C2211yescharacteristic
32C2×#66999C2214yes—
33C2×Q8×Dic11C2212yes—
34C2×#66997C2212yes—
35C2×#66991C2211yescharacteristic
36C2×#66991C2212yes—
37C2×#66989C2211yescharacteristic
38C2×#66983C2212yes—
39C2×#66982C2214yes—
40C2×C4×C22⋊D11C2212yes—
41C2×#66979C2212yes—
42C2×#66979C2212yes—
43C2×#66977C2214yes—
44C2×#66977C2214yes—
45#10623261C22116yescomplemented
46D11×C4⋊Q8C22116yescomplemented
47#10623225C22132yescomplemented
48#10623220C22132yescomplemented
49#10623177C22164yescomplemented
50#10623174C22132yescomplemented
51#10623170C22132yescomplemented
52#10623159C22164yescomplemented
53#10623111C22116yescomplemented
54Q8×Dic22C22116yescomplemented
55#10623094C22116yescomplemented
56#10623092C22132yescomplemented
57#10623088C22116yescomplemented
58#10623082C22132yescomplemented
59C2×#66951C2214yes—
60C2×#66951C2212yes—
61C2×#66950C2211yescharacteristic
62C2×#66950C2212yes—
63C2×#66950C2214yes—
64C2×#66949C2214yes—
65#10623038C22132yescomplemented
66C2×#66948C2211yescharacteristic
67C2×#66947C2214yes—
68C2×#66947C2212yes—
69C2×#66946C2212yes—
70C2×#66945C2214yes—
71C2×#66945C2212yes—
72C2×C4⋊C4×D11C2212yes—
73C2×C4⋊C4×D11C2212yes—
74C2×C4⋊C4×D11C2212yes—
75#10623031C22132yescomplemented
76C2×#66943C2212yes—
77C2×#66943C2214yes—
78C2×#66943C2211yescharacteristic
79C2×#66943C2211yescharacteristic
80C2×#66942C2214yes—
81C2×#66941C2212yes—
82C2×#66941C2212yes—
83C2×#66941C2214yes—
84C2×#66941C2214yes—
85C2×#66941C2212yes—
86C2×#66938C2214yes—
87C2×#66938C2214yes—
88C2×#66936C2214yes—
89C2×#66936C2212yes—
90C2×#66936C2214yes—
91C2×#66932C2214yes—
92C2×#66932C2212yes—
93C2×C4×D44C2212yes—
94C2×C4×D44C2211yescharacteristic
95C2×#66925C2212yes—
96C2×C42×D11C2211yescharacteristic
97C2×#66922C2211yescharacteristic
98C2×#66922C2212yes—
99C2×C4×Dic22C2212yes—
100C2×C4×Dic22C2211yescharacteristic
101C22×Q8×C11C2311yescharacteristic
102C22×Q8×C11C2312yes—
103C22×D4×C11C2311yescharacteristic
104C23×C4×C11C2312yes—
105C23×C4×C11C2314yes—
106C22×C22⋊D11C2312yes—
107C22×C22⋊D11C2314yes—
108C2×Q8×D11—48no—
109C2×Q8×D11C23116yes—
110C2×#4339—416no—
111C2×#4339C23132yes—
112C22×D44C2311yescharacteristic
113C22×D44C2312yes—
114C22×C4×D11C2311yescharacteristic
115C22×C4×D11C2311yescharacteristic
116C22×C4×D11C2311yescharacteristic
117C22×C4×D11C2312yes—
118C22×C4×D11C2314yes—
119C22×C4×D11C2314yes—
120C22×Dic22C2311yescharacteristic
121C22×Dic22C2312yes—
122C22×Dic22C2314yes—
123C22×Dic22C2314yes—
124C11×C4⋊Q8C2318yes—
125C11×#125C23116yes—
126C11×C22⋊Q8C23132yes—
127C11×C22⋊Q8C23116yes—
128C4×Q8×C11C2318yes—
129C4×D4×C11C23116yes—
130C4×D4×C11C2318yes—
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C4⋊C4C2312yes—
133C2×C11×C4⋊C4C2312yes—
134C2×C11×C4⋊C4C2314yes—
135C2×C11×C4⋊C4C2312yes—
136C2×C11×C4⋊C4C2314yes—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C23116yes—
139C2×C11×C22⋊C4C2314yes—
140C2×C11×C22⋊C4C2312yes—
141C2×C42×C11C2311yescharacteristic
142C2×C42×C11C2312yes—
143C2×C22⋊Dic11C2312yes—
144C2×C22⋊Dic11C2312yes—
145C2×C22⋊Dic11C2314yes—
146C2×C22⋊Dic11C2312yes—
147#67000C2318yes—
148#66999C23132yes—
149#66999C2318yes—
150Q8×Dic11C23116yes—
151#66997C23116yes—
152#66991C2318yes—
153#66991C23116yes—
154#66989C2318yes—
155#66983C23116yes—
156#66982C23132yes—
157C4×C22⋊D11C23116yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2312yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2314yes—
165C2×(C2×D11)⋊C4C2314yes—
166#66979C23116yes—
167#66979C23116yes—
168C2×C4⋊Dic11C2312yes—
169C2×C4⋊Dic11C2311yescharacteristic
170C2×C4⋊Dic11C2314yes—
171C2×C4⋊Dic11C2312yes—
172C2×C4⋊Dic11C2312yes—
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2314yes—
175C2×C4⋊Dic11C2312yes—
176C2×C4⋊Dic11C2312yes—
177#66977C23132yes—
178#66977C23132yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2314yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2314yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2314yes—
186C2×Dic11⋊C4C2314yes—
187C2×C4×Dic11C2314yes—
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2314yes—
193#66951C23116yes—
194#66951C23132yes—
195#66950C23116yes—
196#66950C2318yes—
197#66950C23132yes—
198#66949C23132yes—
199#66948C2318yes—
200#66947C23132yes—
201#66947C23116yes—
202#66946C23116yes—
203#66945C23116yes—
204#66945C23132yes—
205C4⋊C4×D11C23116yes—
206C4⋊C4×D11C23116yes—
207C4⋊C4×D11C23116yes—
208#66943C23116yes—
209#66943C2318yes—
210#66943C23132yes—
211#66943C2318yes—
212#66942C23132yes—
213#66941C23116yes—
214#66941C23116yes—
215#66941C23116yes—
216#66941C23132yes—
217#66941C23132yes—
218#66938C23132yes—
219#66938C23132yes—
220#66936C23132yes—
221#66936C23132yes—
222#66936C23116yes—
223#66932C23116yes—
224#66932C23132yes—
225C4×D44C2318yes—
226C4×D44C23116yes—
227#66925C23116yes—
228C42×D11C2318yes—
229#66922C2318yes—
230#66922C23116yes—
231C4×Dic22C2318yes—
232C4×Dic22C23116yes—
233C2×#3544—111nomaximal, Sylow
234C24×C11C2412yes—
235C23×D11C2412yes—
236C23×D11C2411yescharacteristic
237C2×Q8×C11—24no—
238C2×Q8×C11—44no—
239C2×Q8×C11C2414yes—
240C2×Q8×C11C2418yes—
241C2×D4×C11—24no—
242C2×D4×C11C2414yes—
243C22×C4×C11—28no—
244C22×C4×C11—48no—
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2412yes—
249C22×C4×C11C2414yes—
250C22×C4×C11C2418yes—
251C22×C4×C11C24116yes—
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C2×C22⋊D11—28no—
255C2×C22⋊D11—48no—
256C2×C22⋊D11C2418yes—
257C2×C22⋊D11C24116yes—
258C22×Dic11C2412yes—
259C22×Dic11C2411yescharacteristic
260C22×Dic11C2411yescharacteristic
261C22×Dic11C2412yes—
262C22×Dic11C2414yes—
263C22×Dic11C2411yescharacteristic
264C22×Dic11C2412yes—
265Q8×D11—432no—
266#4339—464no—
267C2×D44—28no—
268C2×D44—24no—
269C2×D44C2414yes—
270C2×D44C2418yes—
271C2×C4×D11—216no—
272C2×C4×D11—24no—
273C2×C4×D11—24no—
274C2×C4×D11—28no—
275C2×C4×D11—24no—
276C2×C4×D11—48no—
277C2×C4×D11C2414yes—
278C2×C4×D11C2414yes—
279C2×C4×D11C2414yes—
280C2×C4×D11C2418yes—
281C2×C4×D11C24116yes—
282C2×C4×D11C24116yes—
283C2×Dic22—24no—
284C2×Dic22—48no—
285C2×Dic22—44no—
286C2×Dic22—48no—
287C2×Dic22C2414yes—
288C2×Dic22C2418yes—
289C2×Dic22C24116yes—
290C2×Dic22C24116yes—
291C11×C4⋊C4C2414yes—
292C11×C4⋊C4C2418yes—
293C11×C4⋊C4C2418yes—
294C11×C4⋊C4C24116yes—
295C11×C4⋊C4C2418yes—
296C11×C4⋊C4C24116yes—
297C11×C4⋊C4C2414yes—
298C11×C22⋊C4C24116yes—
299C11×C22⋊C4C2418yes—
300C42×C11C2414yes—
301C42×C11C2418yes—
302C22⋊Dic11C2418yes—
303C22⋊Dic11C2418yes—
304C22⋊Dic11C24116yes—
305C22⋊Dic11C2418yes—
306(C2×D11)⋊C4C2418yes—
307(C2×D11)⋊C4C2418yes—
308(C2×D11)⋊C4C2418yes—
309(C2×D11)⋊C4C2418yes—
310(C2×D11)⋊C4C2418yes—
311(C2×D11)⋊C4C2418yes—
312(C2×D11)⋊C4C24116yes—
313(C2×D11)⋊C4C24116yes—
314C4⋊Dic11C2418yes—
315C4⋊Dic11C2414yes—
316C4⋊Dic11C24116yes—
317C4⋊Dic11C2418yes—
318C4⋊Dic11C2418yes—
319C4⋊Dic11C2414yes—
320C4⋊Dic11C24116yes—
321C4⋊Dic11C2418yes—
322C4⋊Dic11C2418yes—
323Dic11⋊C4C2418yes—
324Dic11⋊C4C24116yes—
325Dic11⋊C4C2418yes—
326Dic11⋊C4C2418yes—
327Dic11⋊C4C24116yes—
328Dic11⋊C4C2418yes—
329Dic11⋊C4C24116yes—
330Dic11⋊C4C24116yes—
331C4×Dic11C24116yes—
332C4×Dic11C2418yes—
333C4×Dic11C2414yes—
334C4×Dic11C2414yes—
335C4×Dic11C2414yes—
336C4×Dic11C24116yes—
337#3544—1132no—
338C2×#563—114no—
339C2×Q82—111no—
340C2×#555—111no—
341C2×#554—111no—
342C2×#554D1111yescharacteristic, complemented
343C2×#552—112no—
344C2×#552—112no—
345C2×#547—112no—
346C2×#547—112no—
347C2×#544—112no—
348C2×#544—112no—
349C2×#542—112no—
350C2×#542—112no—
351C2×#536—114no—
352C22×C4⋊Q8—111no—
353C2×#529—111no—
354C2×#529—111no—
355C23×C11—24no—
356C23×C11—24no—
357C23×C11—24no—
358C23×C11C2514yes—
359C23×C11C2511yescharacteristic
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—24no—
363C22×D11—24no—
364C22×D11—24no—
365C22×D11H(5,𝔽2)14yes—
366C22×D11C2514yes—
367C22×D11C2512yes—
368Q8×C11—28no—
369Q8×C11—48no—
370D4×C11—28no—
371C2×C4×C11—22no—
372C2×C4×C11—24no—
373C2×C4×C11—28no—
374C2×C4×C11—24no—
375C2×C4×C11—24no—
376C2×C4×C11—216no—
377C2×C4×C11—416no—
378C2×C4×C112−1+414yes—
379C2×C4×C112−1+414yes—
380C2×C4×C11C2514yes—
381C2×C4×C11C2514yes—
382C2×C4×C11C2512yes—
383C2×C4×C11C2514yes—
384C2×C4×C11C2518yes—
385C2×C4×C11C2512yes—
386C2×C4×C11C2512yes—
387C22⋊D11—216no—
388C22⋊D11—416no—
389C2×Dic11—22no—
390C2×Dic11—28no—
391C2×Dic11—24no—
392C2×Dic11—24no—
393C2×Dic11—22no—
394C2×Dic11—24no—
395C2×Dic11—22no—
396C2×Dic11C2514yes—
397C2×Dic11C2512yes—
398C2×Dic11C2512yes—
399C2×Dic11C2514yes—
400C2×Dic11C2518yes—
401C2×Dic11C2512yes—
402C2×Dic11C2514yes—
403D44—216no—
404D44—28no—
405C4×D11—232no—
406C4×D11—28no—
407C4×D11—28no—
408C4×D11—216no—
409C4×D11—28no—
410C4×D11—416no—
411Dic22—28no—
412Dic22—416no—
413Dic22—416no—
414Dic22—48no—
415C22×#41—114no—
416C23×Q8—112no—
417#563—1164no—
418Q82—1116no—
419#555—1116no—
420#554—1116no—
421#554C2×D11116yescomplemented
422#552—1132no—
423#552—1132no—
424#547—1132no—
425#547—1132no—
426#544—1132no—
427#544—1132no—
428#542—1132no—
429#542—1132no—
430#536—1164no—
431C2×C4⋊Q8—112no—
432C2×C4⋊Q8—1116no—
433C2×C4⋊Q8—112no—
434C2×C4⋊Q8—112no—
435C2×C4⋊Q8—114no—
436C2×C4⋊Q8—114no—
437C2×C4⋊Q8—112no—
438C2×C4⋊Q8—111no—
439C2×C4⋊Q8—112no—
440C2×C4⋊Q8C2×D1111yescharacteristic
441#529—1116no—
442#529—1116no—
443C2×#126—112no—
444C2×#126—114no—
445C2×#126—112no—
446C2×#126—114no—
447C2×#125—114no—
448C2×#125—111no—
449C2×#125—111no—
450C2×#125—112no—
451C2×#125—114no—
452C2×#125C2×D1112yes—
453C2×#124—111no—
454C2×#124—111no—
455C2×#124—114no—
456C2×#124—114no—
457C2×#123—114no—
458C2×#123—112no—
459C2×#123—114no—
460C2×#123—112no—
461C2×#123—114no—
462C2×#123—114no—
463C2×C22⋊Q8—111no—
464C2×C22⋊Q8—114no—
465C2×C22⋊Q8—114no—
466C2×C22⋊Q8—114no—
467C2×C22⋊Q8—114no—
468C2×C22⋊Q8—111no—
469C2×C22⋊Q8—114no—
470C2×C22⋊Q8—112no—
471C2×C22⋊Q8C2×D1114yes—
472C2×C22⋊Q8C2×D1112yes—
473C2×#121—111no—
474C2×#121—112no—
475C2×#121—112no—
476C2×#121—111no—
477C2×C4×Q8—112no—
478C2×C4×Q8—111no—
479C2×C4×Q8—112no—
480C2×C4×Q8C2×D1111yescharacteristic
481C2×C4×D4—112no—
482C2×C4×D4—112no—
483C2×C4×D4—112no—
484C2×C4×D4—111no—
485C2×C4×D4C2×D1111yescharacteristic
486C2×C4×D4C2×D1112yes—
487C2×#117—112no—
488C2×#117—112no—
489C2×#117—114no—
490C2×#117—112no—
491C2×#117—112no—
492C22×C4⋊C4—112no—
493C22×C4⋊C4—112no—
494C22×C4⋊C4—112no—
495C22×C4⋊C4C2×D1112yes—
496C22×C42—111no—
497C22×C11—24no—
498C22×C11—24no—
499C22×C11—24no—
500C22×C11—48no—
501C22×C11C2×H(5,𝔽2)12yes—
502C22×C11C2×2−1+412yes—
503C22×C11C2×2−1+412yes—
504C22×C11C2611yescharacteristic
505C2×D11—22no—
506C2×D11—22no—
507C2×D11—28no—
508C2×D11—24no—
509C2×D11—24no—
510C2×D11—24no—
511C2×D11—48no—
512C2×D11C2×H(5,𝔽2)14yes—
513C4×C11—24no—
514C4×C11—28no—
515C4×C11—22no—
516C4×C11—24no—
517C4×C11—24no—
518C4×C11C2×2−1+414yes—
519C4×C11C2×2−1+414yes—
520Dic11—22no—
521Dic11—28no—
522Dic11—24no—
523Dic11—24no—
524Dic11—22no—
525Dic11—22no—
526Dic11—24no—
527C2×#41—1132no—
528C2×#41—4416no—
529C22×Q8—1116no—
530C22×Q8—111no—
531C22×Q8—114no—
532C22×Q8—114no—
533C22×Q8—112no—
534C22×Q8—448no—
535C22×Q8C22×D1111yescharacteristic
536C22×Q8C22×D1112yes—
537C22×D4—112no—
538C22×D4—114no—
539C22×D4—111no—
540C22×D4—112no—
541C22×D4C22×D1111yescharacteristic
542C23×C4—114no—
543C23×C4—111no—
544C23×C4—111no—
545C23×C4—112no—
546C23×C4—111no—
547C23×C4—114no—
548C23×C4C22×D1112yes—
549C23×C4C22×D1114yes—
550C4⋊Q8—1116no—
551C4⋊Q8—1116no—
552C4⋊Q8—1116no—
553C4⋊Q8—1132no—
554C4⋊Q8—1132no—
555C4⋊Q8—1116no—
556C4⋊Q8—118no—
557C4⋊Q8—1116no—
558C4⋊Q8C22×D1118yes—
559#126—1116no—
560#126—1132no—
561#126—1116no—
562#126—1132no—
563#125—118no—
564#125—118no—
565#125—1116no—
566#125—1132no—
567#125—1132no—
568#125C22×D11116yes—
569#124—118no—
570#124—118no—
571#124—1132no—
572#124—1132no—
573#123—1132no—
574#123—1116no—
575#123—1132no—
576#123—1116no—
577#123—1132no—
578#123—1132no—
579C22⋊Q8—118no—
580C22⋊Q8—1132no—
581C22⋊Q8—1132no—
582C22⋊Q8—1132no—
583C22⋊Q8—118no—
584C22⋊Q8—1132no—
585C22⋊Q8—1116no—
586C22⋊Q8—1132no—
587C22⋊Q8C22×D11132yes—
588C22⋊Q8C22×D11116yes—
589#121—118no—
590#121—1116no—
591#121—1116no—
592#121—118no—
593C4×Q8—1116no—
594C4×Q8—118no—
595C4×Q8—1116no—
596C4×Q8C22×D1118yes—
597C4×D4—1116no—
598C4×D4—1116no—
599C4×D4—1116no—
600C4×D4—118no—
601C4×D4C22×D1118yes—
602C4×D4C22×D11116yes—
603#117—1116no—
604#117—1116no—
605#117—1132no—
606#117—1116no—
607#117—1116no—
608C2×C4⋊C4—111no—
609C2×C4⋊C4—112no—
610C2×C4⋊C4—112no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—114no—
614C2×C4⋊C4—111no—
615C2×C4⋊C4—114no—
616C2×C4⋊C4—112no—
617C2×C4⋊C4—112no—
618C2×C4⋊C4—112no—
619C2×C4⋊C4—112no—
620C2×C4⋊C4—112no—
621C2×C4⋊C4—112no—
622C2×C4⋊C4—112no—
623C2×C4⋊C4—114no—
624C2×C4⋊C4—114no—
625C2×C4⋊C4—1116no—
626C2×C4⋊C4—1116no—
627C2×C4⋊C4—1116no—
628C2×C4⋊C4C22×D1112yes—
629C2×C4⋊C4C22×D1112yes—
630C2×C4⋊C4C22×D1111yescharacteristic
631C2×C4⋊C4C22×D1114yes—
632C2×C4⋊C4C22×D11116yes—
633C2×C4⋊C4C22×D1111yescharacteristic
634C2×C4⋊C4C22×D1114yes—
635C2×C4⋊C4C22×D1112yes—
636C2×C22⋊C4—112no—
637C2×C22⋊C4—114no—
638C2×C22⋊C4—112no—
639C2×C22⋊C4—112no—
640C2×C22⋊C4—112no—
641C2×C22⋊C4—112no—
642C2×C22⋊C4—112no—
643C2×C22⋊C4—114no—
644C2×C22⋊C4—112no—
645C2×C22⋊C4—114no—
646C2×C22⋊C4—112no—
647C2×C22⋊C4—112no—
648C2×C22⋊C4C22×D1114yes—
649C2×C22⋊C4C22×D1112yes—
650C2×C42—114no—
651C2×C42—111no—
652C2×C42—111no—
653C2×C42—112no—
654C2×C42—114no—
655C2×C42—111no—
656C2×C42—118no—
657C2×C42C22×D1112yes—
658C2×C42C22×D1111yescharacteristic
659C2×C11—44no—
660C2×C11#354414yescomplemented
661C2×C11C22×H(5,𝔽2)11yescharacteristic
662C2×C11C22×2−1+411yescharacteristic
663C2×C11C22×2−1+411yescharacteristic
664D11—24no—
665D11—44no—
666C24—111no—
667C24—112no—
668C24C23×D1112yes—
669#41—4464no—
670C2×Q8—24no—
671C2×Q8—44no—
672C2×Q8—114no—
673C2×Q8—1116no—
674C2×Q8—1116no—
675C2×Q8—118no—
676C2×Q8—224no—
677C2×Q8—448no—
678C2×Q8—444no—
679C2×Q8—448no—
680C2×Q8—4432no—
681C2×Q8C23×D1114yes—
682C2×Q8C23×D1118yes—
683C2×D4—24no—
684C2×D4—118no—
685C2×D4—1116no—
686C2×D4—114no—
687C2×D4—118no—
688C2×D4—228no—
689C2×D4—228no—
690C2×D4—224no—
691C2×D4—448no—
692C2×D4C23×D1114yes—
693C22×C4—28no—
694C22×C4—48no—
695C22×C4—112no—
696C22×C4—112no—
697C22×C4—111no—
698C22×C4—111no—
699C22×C4—111no—
700C22×C4—114no—
701C22×C4—112no—
702C22×C4—114no—
703C22×C4—114no—
704C22×C4—114no—
705C22×C4—1116no—
706C22×C4—118no—
707C22×C4—1116no—
708C22×C4—224no—
709C22×C4—2216no—
710C22×C4—224no—
711C22×C4—228no—
712C22×C4—224no—
713C22×C4—448no—
714C22×C4C23×D1118yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1111yescharacteristic
718C22×C4C23×D1112yes—
719C22×C4C23×D1114yes—
720C22×C4C23×D11116yes—
721C22×C4C23×D1111yescharacteristic
722C22×C4C23×D1111yescharacteristic
723C4⋊C4—114no—
724C4⋊C4—118no—
725C4⋊C4—118no—
726C4⋊C4—1116no—
727C4⋊C4—1116no—
728C4⋊C4—1116no—
729C4⋊C4—114no—
730C4⋊C4—1116no—
731C4⋊C4—118no—
732C4⋊C4—118no—
733C4⋊C4—118no—
734C4⋊C4—118no—
735C4⋊C4—118no—
736C4⋊C4—118no—
737C4⋊C4—118no—
738C4⋊C4—1116no—
739C4⋊C4—1116no—
740C4⋊C4C23×D1118yes—
741C4⋊C4C23×D1118yes—
742C4⋊C4C23×D1114yes—
743C4⋊C4C23×D11116yes—
744C4⋊C4C23×D1114yes—
745C4⋊C4C23×D11116yes—
746C4⋊C4C23×D1118yes—
747C22⋊C4—118no—
748C22⋊C4—1116no—
749C22⋊C4—118no—
750C22⋊C4—118no—
751C22⋊C4—118no—
752C22⋊C4—118no—
753C22⋊C4—118no—
754C22⋊C4—1116no—
755C22⋊C4—118no—
756C22⋊C4—1116no—
757C22⋊C4—118no—
758C22⋊C4—118no—
759C22⋊C4C23×D11116yes—
760C22⋊C4C23×D1118yes—
761C42—114no—
762C42—114no—
763C42—114no—
764C42—1116no—
765C42—118no—
766C42—1116no—
767C42C23×D1114yes—
768C42C23×D1118yes—
769C11C2×#354411yescharacteristic, complemented, Sylow
770C23—24no—
771C23—24no—
772C23—24no—
773C23—114no—
774C23—112no—
775C23—114no—
776C23—222no—
777C23—222no—
778C23—224no—
779C23—224no—
780C23—224no—
781C23C24×D1114yes—
782C23C24×D1111yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—228no—
786Q8—4416no—
787Q8—448no—
788Q8—4416no—
789D4—28no—
790D4—2216no—
791D4—2216no—
792D4—228no—
793D4—4416no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—28no—
798C2×C4—22no—
799C2×C4—216no—
800C2×C4—416no—
801C2×C4—114no—
802C2×C4—112no—
803C2×C4—112no—
804C2×C4—114no—
805C2×C4—112no—
806C2×C4—118no—
807C2×C4—114no—
808C2×C4—228no—
809C2×C4—2232no—
810C2×C4—224no—
811C2×C4—222no—
812C2×C4—224no—
813C2×C4—222no—
814C2×C4—228no—
815C2×C4—222no—
816C2×C4—224no—
817C2×C4—228no—
818C2×C4—2216no—
819C2×C4—228no—
820C2×C4—4416no—
821C2×C4#6704014yes—
822C2×C4#6704314yes—
823C2×C4C24×D1114yes—
824C2×C4C24×D1114yes—
825C2×C4C24×D1112yes—
826C2×C4C24×D1114yes—
827C2×C4C24×D1118yes—
828C2×C4C24×D1112yes—
829C2×C4C24×D1112yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—48no—
834C22—114no—
835C22—222no—
836C22—222no—
837C22—228no—
838C22—224no—
839C22—224no—
840C22—224no—
841C22—448no—
842C22C2×#6704012yes—
843C22C2×#6704312yes—
844C22D11×H(5,𝔽2)12yes—
845C22C25×D1111yescharacteristic
846C4—24no—
847C4—28no—
848C4—22no—
849C4—24no—
850C4—24no—
851C4—228no—
852C4—222no—
853C4—224no—
854C4—222no—
855C4—222no—
856C4—224no—
857C4—224no—
858C4C2×#6704014yes—
859C4C2×#6704314yes—
860C2—44no—
861C2—224no—
862C2—444no—
863C2#1308295714yesdirect product factor
864C2C2×D11×H(5,𝔽2)11yescharacteristic
865C2C22×#6704311yescharacteristic
866C2C22×#6704011yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#554C2
socleC23×C11C25
hypercenterC2×#554D11
hypocenterC11C2×#3544
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #13082957C2direct (N × H)
2. C2×#10623177C2semidirect
3. C2×Q8×Dic22C2semidirect
4. C2×#10623094C2semidirect
5. C2×#10623261C2semidirect
6. C2×#10623225C2semidirect
7. C2×#10623170C2semidirect
8. C2×#10623082C2semidirect
9. C2×#10623038C2semidirect
10. C2×#10623031C2semidirect
11. C2×#10623220C2semidirect
12. C2×#10623174C2semidirect
13. C2×#10623092C2semidirect
14. C2×#10623159C2semidirect
15. C2×D11×C4⋊Q8C2semidirect
16. C2×#10623111C2semidirect
17. C2×#10623088C2semidirect
18. C2×C11×#554C2semidirect
21. C11×#554C22semidirect
45. #10623261C22semidirect
46. D11×C4⋊Q8C22semidirect
47. #10623225C22semidirect
48. #10623220C22semidirect
49. #10623177C22semidirect
50. #10623174C22semidirect
51. #10623170C22semidirect
52. #10623159C22semidirect
53. #10623111C22semidirect
54. Q8×Dic22C22semidirect
55. #10623094C22semidirect
56. #10623092C22semidirect
57. #10623088C22semidirect
58. #10623082C22semidirect
65. #10623038C22semidirect
75. #10623031C22semidirect
342. C2×#554D11semidirect
421. #554C2×D11semidirect
660. C2×C11#3544semidirect
769. C11C2×#3544semidirect
863. C2#13082957direct (N × H)

Maximal subgroups

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

subgroupindex
#130829572
C2×#106231772
C2×Q8×Dic222
C2×#106230942
C2×#106232612
C2×#106232252
C2×#106231702
C2×#106230822
C2×#106230382
C2×#106230312
C2×#106232202
C2×#106231742
C2×#106230922
C2×#106231592
C2×D11×C4⋊Q82
C2×#106231112
C2×#106230882
C2×C11×#5542
C2×#354411