Finite Group Databasebeta

← C2×#13083007 #15661467

Subgroups — C2×#13083007 #15661467

Order 2816.

7182 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13083007C2132yesmaximal, direct product factor
2C2×#10623198C214yesmaximal, complemented
3C2×#10623094C211yesmaximal, characteristic, complemented
4C2×#10623094C212yesmaximal, complemented
5C2×#10623110C211yesmaximal, characteristic, complemented
6C2×#10623096C212yesmaximal, complemented
7C2×#10623225C212yesmaximal, complemented
8C2×Q8×D44C211yesmaximal, characteristic, complemented
9C2×#10623208C212yesmaximal, complemented
10C2×#10623086C211yesmaximal, characteristic, complemented
11C2×#10623050C212yesmaximal, complemented
12C2×#10623241C214yesmaximal, complemented
13C2×#10623066C212yesmaximal, complemented
14C2×#10623139C212yesmaximal, complemented
15C2×#10623159C212yesmaximal, complemented
16C2×#10623001C211yesmaximal, characteristic, complemented
17C2×#10623008C211yesmaximal, characteristic, complemented
18C2×C11×#529C211yesmaximal, characteristic, complemented
19C22×Q8×D11C2212yes—
20C22×#4341C2212yes—
21C22×#4339C2212yes—
22C11×#529C22116yescomplemented
23C2×C11×#126C2212yes—
24C2×C11×#125C2211yescharacteristic
25C2×C11×#124C2211yescharacteristic
26C2×C11×#123C2212yes—
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×D4×C11C2212yes—
31C2×C4×D4×C11C2211yescharacteristic
32C2×C11×#117C2212yes—
33C22×C42×C11C2211yescharacteristic
34C2×#66999C2212yes—
35C2×#66992C2214yes—
36C2×#66991C2214yes—
37C2×#66991C2212yes—
38C2×#66983C2211yescharacteristic
39C2×#66983C2212yes—
40C2×#66983C2211yescharacteristic
41C2×#66983C2212yes—
42C2×#66983C2212yes—
43C2×#66979C2212yes—
44C2×#66979C2212yes—
45C22×C4⋊Dic11C2212yes—
46C2×#66977C2212yes—
47C2×#66977C2212yes—
48#10623241C22164yescomplemented
49#10623225C22132yescomplemented
50#10623208C22132yescomplemented
51#10623198C22164yescomplemented
52#10623159C22132yescomplemented
53#10623139C22132yescomplemented
54#10623110C22116yescomplemented
55Q8×D44C22116yescomplemented
56#10623096C22132yescomplemented
57#10623094C22116yescomplemented
58#10623094C22132yescomplemented
59#10623086C22116yescomplemented
60#10623066C22132yescomplemented
61#10623050C22132yescomplemented
62C2×#66951C2214yes—
63C2×#66950C2212yes—
64C2×#66950C2212yes—
65C2×#66950C2214yes—
66C2×#66949C2214yes—
67C2×#66947C2214yes—
68C2×#66947C2214yes—
69C2×#66945C2212yes—
70C2×#66945C2214yes—
71C2×C4⋊C4×D11C2212yes—
72C2×#66943C2214yes—
73C2×#66941C2214yes—
74C2×#66939C2214yes—
75C2×#66938C2214yes—
76C2×#66938C2214yes—
77C2×#66938C2214yes—
78C2×#66937C2214yes—
79C2×#66937C2214yes—
80C2×#66936C2214yes—
81C2×(C22⋊D11)⋊C4C2214yes—
82C2×#66931C2214yes—
83C2×#66931C2214yes—
84#10623008C22116yescomplemented
85C2×#66928C2212yes—
86C2×#66927C2211yescharacteristic
87C2×C4×D44C2212yes—
88C2×C4×D44C2212yes—
89C2×C4×D44C2211yescharacteristic
90C2×C4×D44C2212yes—
91C2×C4×D44C2211yescharacteristic
92#10623001C22116yescomplemented
93C2×#66923C2212yes—
94C2×#66923C2212yes—
95C2×#66922C2211yescharacteristic
96C2×#66922C2211yescharacteristic
97C2×#66922C2212yes—
98C2×#66922C2211yescharacteristic
99C2×C4×Dic22C2212yes—
100C2×C4×Dic22C2212yes—
101C22×Q8×C11C2311yescharacteristic
102C22×D4×C11C2311yescharacteristic
103C22×D4×C11C2312yes—
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2312yes—
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2311yescharacteristic
108C22×C22⋊D11C2314yes—
109C22×C22⋊D11C2312yes—
110C22×C22⋊D11C2314yes—
111C22×C22⋊D11C2312yes—
112C23×Dic11C2314yes—
113C2×Q8×D11—48no—
114C2×Q8×D11C23116yes—
115C2×#4341—48no—
116C2×#4341C23116yes—
117C2×#4339—48no—
118C2×#4339C23116yes—
119C22×D44C2311yescharacteristic
120C22×D44C2311yescharacteristic
121C22×D44C2312yes—
122C22×D44C2312yes—
123C22×C4×D11C2312yes—
124C22×C4×D11C2312yes—
125C22×C4×D11C2314yes—
126C22×C4×D11C2314yes—
127C22×Dic22C2312yes—
128C22×Dic22C2312yes—
129C22×Dic22C2312yes—
130C22×Dic22C2314yes—
131C11×#126C23116yes—
132C11×#125C2318yes—
133C11×#124C2318yes—
134C11×#123C23116yes—
135C11×C22⋊Q8C2318yes—
136C11×#121C2318yes—
137C4×Q8×C11C2318yes—
138C4×D4×C11C2318yes—
139C4×D4×C11C23116yes—
140C11×#117C23116yes—
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2312yes—
147C2×C11×C22⋊C4C2312yes—
148C2×C11×C22⋊C4C2312yes—
149C2×C11×C22⋊C4C2312yes—
150C2×C11×C22⋊C4C2312yes—
151C2×C11×C22⋊C4C2312yes—
152C2×C42×C11C2311yescharacteristic
153C2×C42×C11C2311yescharacteristic
154C2×C42×C11C2311yescharacteristic
155C2×C42×C11C2311yescharacteristic
156C2×C42×C11C2312yes—
157C2×C42×C11C2318yes—
158C2×C22⋊Dic11C2314yes—
159C2×C22⋊Dic11C2314yes—
160#66999C23116yes—
161#66992C23132yes—
162#66991C23132yes—
163#66991C23116yes—
164#66983C2318yes—
165#66983C2318yes—
166#66983C23116yes—
167#66983C23116yes—
168#66983C23116yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2314yes—
174C2×(C2×D11)⋊C4C2314yes—
175C2×(C2×D11)⋊C4C2314yes—
176C2×(C2×D11)⋊C4C2314yes—
177#66979C23116yes—
178#66979C23116yes—
179C2×C4⋊Dic11C2312yes—
180C2×C4⋊Dic11C2312yes—
181C2×C4⋊Dic11C2311yescharacteristic
182C2×C4⋊Dic11C2312yes—
183C2×C4⋊Dic11C2311yescharacteristic
184C2×C4⋊Dic11C2312yes—
185C2×C4⋊Dic11C2312yes—
186C2×C4⋊Dic11C2314yes—
187C2×C4⋊Dic11C2314yes—
188C2×C4⋊Dic11C23116yes—
189#66977C23116yes—
190#66977C23116yes—
191C2×Dic11⋊C4C2314yes—
192C2×Dic11⋊C4C2314yes—
193C2×Dic11⋊C4C2314yes—
194C2×Dic11⋊C4C2314yes—
195C2×C4×Dic11C2314yes—
196C2×C4×Dic11C2314yes—
197#66951C23132yes—
198#66950C23132yes—
199#66950C23116yes—
200#66950C23116yes—
201#66949C23132yes—
202#66947C23132yes—
203#66947C23132yes—
204#66945C23132yes—
205#66945C23116yes—
206C4⋊C4×D11C23116yes—
207#66943C23132yes—
208#66941C23132yes—
209#66939C23132yes—
210#66938C23132yes—
211#66938C23132yes—
212#66938C23132yes—
213#66937C23132yes—
214#66937C23132yes—
215#66936C23132yes—
216(C22⋊D11)⋊C4C23132yes—
217#66931C23132yes—
218#66931C23132yes—
219#66928C23116yes—
220#66927C2318yes—
221C4×D44C2318yes—
222C4×D44C2318yes—
223C4×D44C23116yes—
224C4×D44C23116yes—
225C4×D44C23116yes—
226#66923C23116yes—
227#66923C23116yes—
228#66922C2318yes—
229#66922C2318yes—
230#66922C2318yes—
231#66922C23116yes—
232C4×Dic22C23116yes—
233C4×Dic22C23116yes—
234C2×#3547—111nomaximal, Sylow
235C24×C11C2411yescharacteristic
236C24×C11C2412yes—
237C23×D11C2412yes—
238C23×D11C2412yes—
239C2×Q8×C11—24no—
240C2×Q8×C11C2414yes—
241C2×D4×C11—24no—
242C2×D4×C11—44no—
243C2×D4×C11C2414yes—
244C2×D4×C11C2418yes—
245C22×C4×C11—24no—
246C22×C4×C11—28no—
247C22×C4×C11—24no—
248C22×C4×C11—42no—
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2412yes—
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2414yes—
256C22×C4×C11C2418yes—
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2414yes—
259C22×C4×C11C2414yes—
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C2×C22⋊D11—44no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—48no—
265C2×C22⋊D11—48no—
266C2×C22⋊D11C24116yes—
267C2×C22⋊D11C2418yes—
268C2×C22⋊D11C24116yes—
269C2×C22⋊D11C2418yes—
270C22×Dic11—48no—
271C22×Dic11C2414yes—
272C22×Dic11C2412yes—
273C22×Dic11C2414yes—
274C22×Dic11C2412yes—
275C22×Dic11C24116yes—
276Q8×D11—432no—
277#4341—432no—
278#4339—432no—
279C2×D44—24no—
280C2×D44—24no—
281C2×D44—44no—
282C2×D44—44no—
283C2×D44C2414yes—
284C2×D44C2414yes—
285C2×D44C2418yes—
286C2×D44C2418yes—
287C2×C4×D11—28no—
288C2×C4×D11—28no—
289C2×C4×D11—48no—
290C2×C4×D11—48no—
291C2×C4×D11C2418yes—
292C2×C4×D11C2418yes—
293C2×C4×D11C24116yes—
294C2×C4×D11C24116yes—
295C2×Dic22—28no—
296C2×Dic22—44no—
297C2×Dic22—44no—
298C2×Dic22—48no—
299C2×Dic22C2418yes—
300C2×Dic22C2418yes—
301C2×Dic22C2418yes—
302C2×Dic22C24116yes—
303C11×C4⋊C4C2418yes—
304C11×C4⋊C4C2418yes—
305C11×C4⋊C4C2414yes—
306C11×C4⋊C4C2414yes—
307C11×C4⋊C4C2418yes—
308C11×C4⋊C4C2418yes—
309C11×C22⋊C4C2418yes—
310C11×C22⋊C4C2418yes—
311C11×C22⋊C4C2418yes—
312C11×C22⋊C4C2418yes—
313C11×C22⋊C4C2418yes—
314C42×C11C2414yes—
315C42×C11C2414yes—
316C42×C11C2414yes—
317C42×C11C2414yes—
318C42×C11C2418yes—
319C22⋊Dic11C24116yes—
320C22⋊Dic11C24116yes—
321(C2×D11)⋊C4C2418yes—
322(C2×D11)⋊C4C2418yes—
323(C2×D11)⋊C4C2418yes—
324(C2×D11)⋊C4C2418yes—
325(C2×D11)⋊C4C24116yes—
326(C2×D11)⋊C4C24116yes—
327(C2×D11)⋊C4C24116yes—
328(C2×D11)⋊C4C24116yes—
329C4⋊Dic11C2418yes—
330C4⋊Dic11C2418yes—
331C4⋊Dic11C2414yes—
332C4⋊Dic11C2418yes—
333C4⋊Dic11C2414yes—
334C4⋊Dic11C2418yes—
335C4⋊Dic11C2418yes—
336C4⋊Dic11C24116yes—
337C4⋊Dic11C24116yes—
338Dic11⋊C4C24116yes—
339Dic11⋊C4C24116yes—
340Dic11⋊C4C24116yes—
341Dic11⋊C4C24116yes—
342C4×Dic11C24116yes—
343C4×Dic11C24116yes—
344#3547—1132no—
345C2×#562—114no—
346C2×#555—112no—
347C2×#555—111no—
348C2×#554—111no—
349C2×#553—112no—
350C2×#552—112no—
351C2×D4×Q8—111no—
352C2×#548—112no—
353C2×#547—111no—
354C2×#544—112no—
355C2×#542—114no—
356C2×#540—112no—
357C2×#537—112no—
358C2×#536—112no—
359C2×#533—111no—
360C2×#532—111no—
361C2×#529D1111yescharacteristic, complemented
362C23×C11—24no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—24no—
366C23×C11—24no—
367C23×C11—22no—
368C23×C11C2512yes—
369C23×C11C2514yes—
370C23×C11C2511yescharacteristic
371C22×D11—24no—
372C22×D11—24no—
373C22×D11—24no—
374C22×D11—24no—
375C22×D11—24no—
376C22×D11—24no—
377C22×D11C2514yes—
378C22×D11C2514yes—
379Q8×C11—28no—
380D4×C11—28no—
381D4×C11—48no—
382C2×C4×C11—24no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—24no—
386C2×C4×C11—22no—
387C2×C4×C11—24no—
388C2×C4×C11—22no—
389C2×C4×C11—28no—
390C2×C4×C11—216no—
391C2×C4×C11—28no—
392C2×C4×C11—44no—
393C2×C4×C11H(5,𝔽2)14yes—
394C2×C4×C112−1+414yes—
395C2×C4×C11C2512yes—
396C2×C4×C11C2514yes—
397C2×C4×C11C2512yes—
398C2×C4×C11C2512yes—
399C2×C4×C11C2514yes—
400C2×C4×C11C2514yes—
401C2×C4×C11C2512yes—
402C2×C4×C11C2512yes—
403C2×C4×C11C2512yes—
404C22⋊D11—48no—
405C22⋊D11—48no—
406C22⋊D11—416no—
407C22⋊D11—416no—
408C2×Dic11—28no—
409C2×Dic11—24no—
410C2×Dic11—24no—
411C2×Dic11—28no—
412C2×Dic11—416no—
413C2×Dic11C2518yes—
414C2×Dic11C2514yes—
415C2×Dic11C2518yes—
416C2×Dic11C2514yes—
417D44—28no—
418D44—28no—
419D44—48no—
420D44—48no—
421C4×D11—216no—
422C4×D11—216no—
423C4×D11—416no—
424C4×D11—416no—
425Dic22—216no—
426Dic22—48no—
427Dic22—48no—
428Dic22—416no—
429C22×#41—112no—
430C22×#41—112no—
431C23×Q8—112no—
432#562—1164no—
433#555—1132no—
434#555—1116no—
435#554—1116no—
436#553—1132no—
437#552—1132no—
438D4×Q8—1116no—
439#548—1132no—
440#547—1116no—
441#544—1132no—
442#542—1164no—
443#540—1132no—
444#537—1132no—
445#536—1132no—
446#533—1116no—
447#532—1116no—
448C2×C4⋊Q8—114no—
449C2×C4⋊Q8—111no—
450C2×C4⋊Q8—111no—
451C2×C4⋊Q8—111no—
452C2×C4⋊Q8—112no—
453C2×#127—111no—
454#529C2×D11116yescomplemented
455C2×#126—114no—
456C2×#126C2×D1112yes—
457C2×#125—114no—
458C2×#125—112no—
459C2×#125—112no—
460C2×#125C2×D1111yescharacteristic
461C2×#124—114no—
462C2×#124—114no—
463C2×#124—114no—
464C2×#124—112no—
465C2×#124C2×D1111yescharacteristic
466C2×#123—114no—
467C2×#123—114no—
468C2×#123—114no—
469C2×#123—114no—
470C2×#123C2×D1112yes—
471C2×C22⋊Q8—112no—
472C2×C22⋊Q8—112no—
473C2×C22⋊Q8—112no—
474C2×C22⋊Q8—114no—
475C2×C22⋊Q8—112no—
476C2×C22⋊Q8—112no—
477C2×C22⋊Q8—114no—
478C2×C22⋊Q8—114no—
479C2×C22⋊Q8—114no—
480C2×C22⋊Q8C2×D1111yescharacteristic
481C2×#121—112no—
482C2×#121—114no—
483C2×#121—114no—
484C2×#121—111no—
485C2×#121—111no—
486C2×#121—112no—
487C2×#121—112no—
488C2×#121—112no—
489C2×#121—114no—
490C2×#121—114no—
491C2×#121C2×D1111yescharacteristic
492C2×C4×Q8—112no—
493C2×C4×Q8—112no—
494C2×C4×Q8C2×D1111yescharacteristic
495C2×C4×D4—114no—
496C2×C4×D4—111no—
497C2×C4×D4—112no—
498C2×C4×D4—111no—
499C2×C4×D4—112no—
500C2×C4×D4—112no—
501C2×C4×D4C2×D1111yescharacteristic
502C2×C4×D4C2×D1112yes—
503C2×#117—112no—
504C2×#117—112no—
505C2×#117—112no—
506C2×#117—114no—
507C2×#117C2×D1112yes—
508C22×C4⋊C4—112no—
509C22×C4⋊C4—112no—
510C22×C42C2×D1111yescharacteristic
511C22×C11—22no—
512C22×C11—24no—
513C22×C11—22no—
514C22×C11—24no—
515C22×C11—22no—
516C22×C11—24no—
517C22×C11—48no—
518C22×C11—44no—
519C22×C11C2×H(5,𝔽2)12yes—
520C22×C11C2×2−1+412yes—
521C22×C11#58512yes—
522C22×C11C2611yescharacteristic
523C2×D11—24no—
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—48no—
530C2×D11—48no—
531C4×C11—22no—
532C4×C11—24no—
533C4×C11—22no—
534C4×C11—24no—
535C4×C11—22no—
536C4×C11—22no—
537C4×C11—24no—
538C4×C11C2×H(5,𝔽2)14yes—
539C4×C11C2×2−1+414yes—
540Dic11—28no—
541Dic11—24no—
542Dic11—24no—
543Dic11—28no—
544C2×#41—1116no—
545C2×#41—1116no—
546C2×#41—448no—
547C2×#41—448no—
548C22×Q8—1116no—
549C22×Q8—112no—
550C22×Q8—112no—
551C22×Q8—114no—
552C22×Q8—112no—
553C22×Q8—448no—
554C22×Q8C22×D1111yescharacteristic
555C22×D4—114no—
556C22×D4—112no—
557C22×D4—114no—
558C22×D4—112no—
559C22×D4—111no—
560C22×D4—111no—
561C22×D4—112no—
562C22×D4—112no—
563C22×D4C22×D1111yescharacteristic
564C22×D4C22×D1112yes—
565C23×C4—114no—
566C23×C4—112no—
567C23×C4—112no—
568C23×C4—114no—
569C23×C4—114no—
570C23×C4C22×D1112yes—
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573C23×C4C22×D1111yescharacteristic
574C4⋊Q8—1132no—
575C4⋊Q8—118no—
576C4⋊Q8—118no—
577C4⋊Q8—118no—
578C4⋊Q8—1116no—
579#127—118no—
580#126—1132no—
581#126C22×D11116yes—
582#125—1132no—
583#125—1116no—
584#125—1116no—
585#125C22×D1118yes—
586#124—1132no—
587#124—1132no—
588#124—1132no—
589#124—1116no—
590#124C22×D1118yes—
591#123—1132no—
592#123—1132no—
593#123—1132no—
594#123—1132no—
595#123C22×D11116yes—
596C22⋊Q8—1116no—
597C22⋊Q8—1116no—
598C22⋊Q8—1116no—
599C22⋊Q8—1116no—
600C22⋊Q8—1116no—
601C22⋊Q8—1132no—
602C22⋊Q8—1132no—
603C22⋊Q8—1132no—
604C22⋊Q8—1132no—
605C22⋊Q8C22×D1118yes—
606#121—1116no—
607#121—1132no—
608#121—1132no—
609#121—118no—
610#121—118no—
611#121—1116no—
612#121—1116no—
613#121—1116no—
614#121—1132no—
615#121—1132no—
616#121C22×D1118yes—
617C4×Q8—1116no—
618C4×Q8—1116no—
619C4×Q8C22×D1118yes—
620C4×D4—1132no—
621C4×D4—118no—
622C4×D4—1116no—
623C4×D4—118no—
624C4×D4—1116no—
625C4×D4—1116no—
626C4×D4C22×D1118yes—
627C4×D4C22×D11116yes—
628#117—1116no—
629#117—1116no—
630#117—1116no—
631#117—1132no—
632#117C22×D11116yes—
633C2×C4⋊C4—111no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—112no—
636C2×C4⋊C4—114no—
637C2×C4⋊C4—114no—
638C2×C4⋊C4—1116no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—111no—
641C2×C4⋊C4—114no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—114no—
644C2×C4⋊C4—114no—
645C2×C4⋊C4—114no—
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×D1112yes—
653C2×C4⋊C4C22×D1112yes—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—112no—
657C2×C22⋊C4—114no—
658C2×C22⋊C4—114no—
659C2×C22⋊C4—112no—
660C2×C22⋊C4—114no—
661C2×C22⋊C4—112no—
662C2×C22⋊C4—114no—
663C2×C22⋊C4—112no—
664C2×C22⋊C4C22×D1112yes—
665C2×C22⋊C4C22×D1112yes—
666C2×C22⋊C4C22×D1112yes—
667C2×C22⋊C4C22×D1112yes—
668C2×C22⋊C4C22×D1112yes—
669C2×C42—114no—
670C2×C42—114no—
671C2×C42C22×D1111yescharacteristic
672C2×C42C22×D1112yes—
673C2×C42C22×D1111yescharacteristic
674C2×C42C22×D1111yescharacteristic
675C2×C42C22×D1111yescharacteristic
676C2×C42C22×D1118yes—
677C2×C11—42no—
678C2×C11—44no—
679C2×C11#354714yescomplemented
680C2×C11C22×H(5,𝔽2)11yescharacteristic
681C2×C11C22×2−1+411yescharacteristic
682C2×C11C2×#58511yescharacteristic
683D11—44no—
684D11—44no—
685C24—112no—
686C24—112no—
687C24C23×D1111yescharacteristic
688C24C23×D1112yes—
689#41—4432no—
690#41—4432no—
691C2×Q8—24no—
692C2×Q8—118no—
693C2×Q8—118no—
694C2×Q8—1116no—
695C2×Q8—118no—
696C2×Q8—228no—
697C2×Q8—448no—
698C2×Q8—444no—
699C2×Q8—444no—
700C2×Q8—4432no—
701C2×Q8C23×D1114yes—
702C2×D4—24no—
703C2×D4—44no—
704C2×D4—1116no—
705C2×D4—118no—
706C2×D4—1116no—
707C2×D4—118no—
708C2×D4—114no—
709C2×D4—114no—
710C2×D4—118no—
711C2×D4—118no—
712C2×D4—224no—
713C2×D4—224no—
714C2×D4—444no—
715C2×D4—444no—
716C2×D4—444no—
717C2×D4—444no—
718C2×D4—448no—
719C2×D4—448no—
720C2×D4C23×D1114yes—
721C2×D4C23×D1118yes—
722C22×C4—24no—
723C22×C4—28no—
724C22×C4—24no—
725C22×C4—42no—
726C22×C4—114no—
727C22×C4—112no—
728C22×C4—114no—
729C22×C4—112no—
730C22×C4—1116no—
731C22×C4—118no—
732C22×C4—118no—
733C22×C4—1116no—
734C22×C4—1116no—
735C22×C4—228no—
736C22×C4—228no—
737C22×C4—448no—
738C22×C4—448no—
739C22×C4—448no—
740C22×C4C23×D1114yes—
741C22×C4C23×D1114yes—
742C22×C4C23×D1118yes—
743C22×C4C23×D1111yescharacteristic
744C22×C4C23×D1112yes—
745C22×C4C23×D1111yescharacteristic
746C22×C4C23×D1111yescharacteristic
747C22×C4C23×D1111yescharacteristic
748C22×C4C23×D1112yes—
749C22×C4C23×D1112yes—
750C22×C4C23×D1114yes—
751C22×C4C23×D1111yescharacteristic
752C22×C4C23×D1111yescharacteristic
753C4⋊C4—114no—
754C4⋊C4—118no—
755C4⋊C4—118no—
756C4⋊C4—1116no—
757C4⋊C4—1116no—
758C4⋊C4—118no—
759C4⋊C4—114no—
760C4⋊C4—1116no—
761C4⋊C4—118no—
762C4⋊C4—1116no—
763C4⋊C4—1116no—
764C4⋊C4—1116no—
765C4⋊C4—118no—
766C4⋊C4C23×D1114yes—
767C4⋊C4C23×D1114yes—
768C4⋊C4C23×D1118yes—
769C4⋊C4C23×D1118yes—
770C4⋊C4C23×D1118yes—
771C4⋊C4C23×D1118yes—
772C22⋊C4—1116no—
773C22⋊C4—1116no—
774C22⋊C4—118no—
775C22⋊C4—1116no—
776C22⋊C4—1116no—
777C22⋊C4—118no—
778C22⋊C4—1116no—
779C22⋊C4—118no—
780C22⋊C4—1116no—
781C22⋊C4—118no—
782C22⋊C4C23×D1118yes—
783C22⋊C4C23×D1118yes—
784C22⋊C4C23×D1118yes—
785C22⋊C4C23×D1118yes—
786C22⋊C4C23×D1118yes—
787C42—1116no—
788C42—1116no—
789C42C23×D1114yes—
790C42C23×D1114yes—
791C42C23×D1114yes—
792C42C23×D1114yes—
793C42C23×D1118yes—
794C11C2×#354711yescharacteristic, complemented, Sylow
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—114no—
802C23—114no—
803C23—224no—
804C23—224no—
805C23—224no—
806C23—224no—
807C23—224no—
808C23—224no—
809C23C24×D1112yes—
810C23C24×D1114yes—
811C23C24×D1111yescharacteristic
812Q8—28no—
813Q8—2216no—
814Q8—4416no—
815Q8—448no—
816Q8—448no—
817D4—28no—
818D4—48no—
819D4—228no—
820D4—228no—
821D4—448no—
822D4—448no—
823D4—448no—
824D4—448no—
825D4—4416no—
826D4—4416no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—216no—
837C2×C4—44no—
838C2×C4—118no—
839C2×C4—114no—
840C2×C4—118no—
841C2×C4—114no—
842C2×C4—224no—
843C2×C4—224no—
844C2×C4—228no—
845C2×C4—228no—
846C2×C4—2216no—
847C2×C4—2216no—
848C2×C4—4416no—
849C2×C4—4416no—
850C2×C4—4416no—
851C2×C4#6704214yes—
852C2×C4#6704314yes—
853C2×C4C24×D1112yes—
854C2×C4C24×D1114yes—
855C2×C4C24×D1112yes—
856C2×C4C24×D1112yes—
857C2×C4C24×D1112yes—
858C2×C4C24×D1114yes—
859C2×C4C24×D1114yes—
860C2×C4C24×D1112yes—
861C2×C4C24×D1112yes—
862C22—22no—
863C22—24no—
864C22—22no—
865C22—24no—
866C22—22no—
867C22—24no—
868C22—44no—
869C22—48no—
870C22—224no—
871C22—224no—
872C22—224no—
873C22—224no—
874C22—224no—
875C22—224no—
876C22—448no—
877C22—448no—
878C22C2×#6704212yes—
879C22C2×#6704312yes—
880C22#1062345312yes—
881C22C25×D1111yescharacteristic
882C4—22no—
883C4—24no—
884C4—22no—
885C4—24no—
886C4—22no—
887C4—22no—
888C4—24no—
889C4—224no—
890C4—224no—
891C4—228no—
892C4—228no—
893C4C2×#6704214yes—
894C4C2×#6704314yes—
895C2—42no—
896C2—44no—
897C2—444no—
898C2—444no—
899C2#1308300714yesdirect product factor
900C2C22×#6704211yescharacteristic
901C2C22×#6704311yescharacteristic
902C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#529C2
socleC23×C11C25
hypercenterC2×#529D11
hypocenterC11C2×#3547
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #13083007C2direct (N × H)
2. C2×#10623198C2semidirect
3. C2×#10623094C2semidirect
4. C2×#10623094C2semidirect
5. C2×#10623110C2semidirect
6. C2×#10623096C2semidirect
7. C2×#10623225C2semidirect
8. C2×Q8×D44C2semidirect
9. C2×#10623208C2semidirect
10. C2×#10623086C2semidirect
11. C2×#10623050C2semidirect
12. C2×#10623241C2semidirect
13. C2×#10623066C2semidirect
14. C2×#10623139C2semidirect
15. C2×#10623159C2semidirect
16. C2×#10623001C2semidirect
17. C2×#10623008C2semidirect
18. C2×C11×#529C2semidirect
22. C11×#529C22semidirect
48. #10623241C22semidirect
49. #10623225C22semidirect
50. #10623208C22semidirect
51. #10623198C22semidirect
52. #10623159C22semidirect
53. #10623139C22semidirect
54. #10623110C22semidirect
55. Q8×D44C22semidirect
56. #10623096C22semidirect
57. #10623094C22semidirect
58. #10623094C22semidirect
59. #10623086C22semidirect
60. #10623066C22semidirect
61. #10623050C22semidirect
84. #10623008C22semidirect
92. #10623001C22semidirect
361. C2×#529D11semidirect
454. #529C2×D11semidirect
679. C2×C11#3547semidirect
794. C11C2×#3547semidirect
899. C2#13083007direct (N × H)

Maximal subgroups

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

subgroupindex
#130830072
C2×#106231982
C2×#106230942
C2×#106231102
C2×#106230962
C2×#106232252
C2×Q8×D442
C2×#106232082
C2×#106230862
C2×#106230502
C2×#106232412
C2×#106230662
C2×#106231392
C2×#106231592
C2×#106230012
C2×#106230082
C2×C11×#5292
C2×#354711