Finite Group Databasebeta

← C2×#13082524 #15662145

Subgroups — C2×#13082524 #15662145

Order 2816.

7758 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082524C2132yesmaximal, direct product factor
2C2×#10623172C212yesmaximal, complemented
3C2×#10623265C211yesmaximal, characteristic, complemented
4C2×#10623094C211yesmaximal, characteristic, complemented
5C2×#10623110C211yesmaximal, characteristic, complemented
6C2×#10623226C212yesmaximal, complemented
7C2×#10623089C212yesmaximal, complemented
8C2×#10623164C214yesmaximal, complemented
9C2×#10623038C212yesmaximal, complemented
10C2×#10623171C214yesmaximal, complemented
11C2×#10623160C212yesmaximal, complemented
12C2×#10623219C212yesmaximal, complemented
13C2×#10623079C211yesmaximal, characteristic, complemented
14C2×#10623079C212yesmaximal, complemented
15C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
16C2×#10623035C212yesmaximal, complemented
17C2×C4×#4343C211yesmaximal, characteristic, complemented
18C2×C11×#554C211yesmaximal, characteristic, complemented
19C22×#4343C2211yescharacteristic
20C22×Q8×D11C2212yes—
21C22×#4339C2212yes—
22C22×#4339C2214yes—
23C11×#554C22116yescomplemented
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#125C2212yes—
26C2×C11×C22⋊Q8C2212yes—
27C2×C11×C22⋊Q8C2214yes—
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11C2212yes—
30C2×C4×D4×C11C2211yescharacteristic
31C22×C11×C4⋊C4C2212yes—
32C2×#67000C2214yes—
33C2×#66999C2212yes—
34C2×Q8×Dic11C2211yescharacteristic
35C2×#66997C2212yes—
36C2×#66993C2211yescharacteristic
37C2×#66991C2211yescharacteristic
38C2×#66991C2212yes—
39C2×#66983C2212yes—
40C2×#66982C2214yes—
41C2×C4×C22⋊D11C2214yes—
42C2×C4×C22⋊D11C2212yes—
43C2×C4×C22⋊D11C2214yes—
44C2×#66979C2212yes—
45#10623265C22116yescomplemented
46D11×C4⋊Q8C22116yescomplemented
47#10623226C22132yescomplemented
48#10623219C22132yescomplemented
49#10623172C22132yescomplemented
50#10623171C22164yescomplemented
51#10623164C22164yescomplemented
52#10623160C22132yescomplemented
53#10623110C22116yescomplemented
54C4×#4343C22116yescomplemented
55#10623094C22116yescomplemented
56#10623089C22132yescomplemented
57#10623079C22116yescomplemented
58#10623079C22132yescomplemented
59C2×#66951C2214yes—
60C2×#66949C2214yes—
61C2×#66949C2214yes—
62C2×#66949C2214yes—
63#10623038C22132yescomplemented
64C2×#66948C2211yescharacteristic
65C2×#66948C2212yes—
66C2×#66948C2214yes—
67C2×#66948C2212yes—
68C2×#66947C2214yes—
69#10623035C22132yescomplemented
70C2×#66946C2214yes—
71C2×#66946C2211yescharacteristic
72C2×#66946C2212yes—
73C2×#66945C2212yes—
74C2×#66945C2212yes—
75C2×#66945C2212yes—
76C2×#66945C2212yes—
77C2×#66945C2211yescharacteristic
78C2×C4⋊C4×D11C2212yes—
79C2×C4⋊C4×D11C2212yes—
80C2×C4⋊C4×D11C2212yes—
81C2×#66941C2212yes—
82C2×#66941C2212yes—
83C2×#66941C2211yescharacteristic
84C2×#66940C2214yes—
85C2×#66940C2214yes—
86C2×#66938C2214yes—
87C2×#66938C2212yes—
88C2×#66938C2214yes—
89C2×#66937C2214yes—
90C2×#66937C2214yes—
91C2×#66937C2212yes—
92C2×#66932C2214yes—
93C2×C4×D44C2212yes—
94C2×C4×D44C2212yes—
95C2×C4×D44C2211yescharacteristic
96C2×C4×D44C2211yescharacteristic
97C2×C42×D11C2211yescharacteristic
98C2×C42×D11C2212yes—
99C2×#66923C2212yes—
100C2×#66922C2211yescharacteristic
101C22×Q8×C11C2311yescharacteristic
102C22×Q8×C11C2312yes—
103C22×D4×C11C2311yescharacteristic
104C23×C4×C11C2312yes—
105C23×C4×C11C2314yes—
106C22×C22⋊D11C2312yes—
107C22×C22⋊D11C2312yes—
108C22×C22⋊D11C2312yes—
109C22×C22⋊D11C2314yes—
110C2×#4343—28no—
111C2×#4343C2318yes—
112C2×Q8×D11—48no—
113C2×Q8×D11C23116yes—
114C2×#4339—216no—
115C2×#4339—416no—
116C2×#4339C23116yes—
117C2×#4339C23132yes—
118C22×D44C2311yescharacteristic
119C22×D44C2312yes—
120C22×D44C2311yescharacteristic
121C22×D44C2312yes—
122C22×D44C2314yes—
123C22×C4×D11C2311yescharacteristic
124C22×C4×D11C2312yes—
125C22×C4×D11C2312yes—
126C22×C4×D11C2311yescharacteristic
127C22×C4×D11C2312yes—
128C22×C4×D11C2312yes—
129C22×C4×D11C2314yes—
130C22×C4×D11C2314yes—
131C22×C4×D11C2311yescharacteristic
132C22×Dic22C2312yes—
133C22×Dic22C2314yes—
134C22×Dic22C2312yes—
135C11×C4⋊Q8C2318yes—
136C11×#125C23116yes—
137C11×C22⋊Q8C23116yes—
138C11×C22⋊Q8C23132yes—
139C4×Q8×C11C2318yes—
140C4×D4×C11C23116yes—
141C4×D4×C11C2318yes—
142C2×C11×C4⋊C4C2314yes—
143C2×C11×C4⋊C4C2314yes—
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C4⋊C4C2311yescharacteristic
148C2×C11×C4⋊C4C2312yes—
149C2×C11×C4⋊C4C23116yes—
150C2×C11×C22⋊C4C2314yes—
151C2×C11×C22⋊C4C2312yes—
152C2×C42×C11C2311yescharacteristic
153C2×C42×C11C2312yes—
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2314yes—
156#67000C23132yes—
157#66999C23116yes—
158Q8×Dic11C2318yes—
159#66997C23116yes—
160#66993C2318yes—
161#66991C2318yes—
162#66991C23116yes—
163#66983C23116yes—
164#66982C23132yes—
165C4×C22⋊D11C23132yes—
166C4×C22⋊D11C23132yes—
167C4×C22⋊D11C23116yes—
168C2×(C2×D11)⋊C4C2314yes—
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)⋊C4C2312yes—
177#66979C23116yes—
178C2×C4⋊Dic11C2312yes—
179C2×C4⋊Dic11C2312yes—
180C2×C4⋊Dic11C2311yescharacteristic
181C2×C4⋊Dic11C2312yes—
182C2×C4⋊Dic11C2311yescharacteristic
183C2×Dic11⋊C4C2314yes—
184C2×Dic11⋊C4C2314yes—
185C2×Dic11⋊C4C2314yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2314yes—
188C2×C4×Dic11C2311yescharacteristic
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2314yes—
194C2×C4×Dic11C2314yes—
195#66951C23132yes—
196#66949C23132yes—
197#66949C23132yes—
198#66949C23132yes—
199#66948C23116yes—
200#66948C23116yes—
201#66948C2318yes—
202#66948C23132yes—
203#66947C23132yes—
204#66946C23132yes—
205#66946C2318yes—
206#66946C23116yes—
207#66945C23116yes—
208#66945C23116yes—
209#66945C2318yes—
210#66945C23116yes—
211#66945C23116yes—
212C4⋊C4×D11C23116yes—
213C4⋊C4×D11C23116yes—
214C4⋊C4×D11C23116yes—
215#66941C23116yes—
216#66941C23116yes—
217#66941C2318yes—
218#66940C23132yes—
219#66940C23132yes—
220#66938C23132yes—
221#66938C23116yes—
222#66938C23132yes—
223#66937C23132yes—
224#66937C23116yes—
225#66937C23132yes—
226#66932C23132yes—
227C4×D44C2318yes—
228C4×D44C2318yes—
229C4×D44C23116yes—
230C4×D44C23116yes—
231C42×D11C2318yes—
232C42×D11C23116yes—
233#66923C23116yes—
234#66922C2318yes—
235C2×#3511—111nomaximal, Sylow
236C24×C11C2412yes—
237C23×D11C2412yes—
238C23×D11C2412yes—
239C23×D11C2411yescharacteristic
240C2×Q8×C11—24no—
241C2×Q8×C11—44no—
242C2×Q8×C11C2414yes—
243C2×Q8×C11C2418yes—
244C2×D4×C11—24no—
245C2×D4×C11C2414yes—
246C22×C4×C11—28no—
247C22×C4×C11—48no—
248C22×C4×C11C2412yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2414yes—
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2418yes—
254C22×C4×C11C24116yes—
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2411yescharacteristic
257C2×C22⋊D11—28no—
258C2×C22⋊D11—28no—
259C2×C22⋊D11—28no—
260C2×C22⋊D11—48no—
261C2×C22⋊D11C2418yes—
262C2×C22⋊D11C2418yes—
263C2×C22⋊D11C2418yes—
264C2×C22⋊D11C24116yes—
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267C22×Dic11C2411yescharacteristic
268C22×Dic11C2414yes—
269C22×Dic11C2411yescharacteristic
270C22×Dic11C2411yescharacteristic
271#4343—232no—
272Q8×D11—432no—
273#4339—264no—
274#4339—464no—
275C2×D44—28no—
276C2×D44—28no—
277C2×D44—24no—
278C2×D44—24no—
279C2×D44—48no—
280C2×D44C2414yes—
281C2×D44C2418yes—
282C2×D44C2414yes—
283C2×D44C2418yes—
284C2×D44C24116yes—
285C2×C4×D11—28no—
286C2×C4×D11—28no—
287C2×C4×D11—24no—
288C2×C4×D11—28no—
289C2×C4×D11—24no—
290C2×C4×D11—28no—
291C2×C4×D11—48no—
292C2×C4×D11—48no—
293C2×C4×D11#4118yescomplemented
294C2×C4×D11C2414yes—
295C2×C4×D11C2418yes—
296C2×C4×D11C2418yes—
297C2×C4×D11C2414yes—
298C2×C4×D11C2418yes—
299C2×C4×D11C2418yes—
300C2×C4×D11C24116yes—
301C2×C4×D11C24116yes—
302C2×C4×D11C2414yes—
303C2×Dic22—28no—
304C2×Dic22—216no—
305C2×Dic22—44no—
306C2×Dic22C2418yes—
307C2×Dic22C24116yes—
308C2×Dic22C2418yes—
309C11×C4⋊C4C24116yes—
310C11×C4⋊C4C24116yes—
311C11×C4⋊C4C2418yes—
312C11×C4⋊C4C2418yes—
313C11×C4⋊C4C2414yes—
314C11×C4⋊C4C2414yes—
315C11×C4⋊C4C2418yes—
316C11×C22⋊C4C24116yes—
317C11×C22⋊C4C2418yes—
318C42×C11C2414yes—
319C42×C11C2418yes—
320C22⋊Dic11C2418yes—
321C22⋊Dic11C24116yes—
322(C2×D11)⋊C4C24116yes—
323(C2×D11)⋊C4C2418yes—
324(C2×D11)⋊C4C2418yes—
325(C2×D11)⋊C4C2418yes—
326(C2×D11)⋊C4C2418yes—
327(C2×D11)⋊C4C24116yes—
328(C2×D11)⋊C4C24116yes—
329(C2×D11)⋊C4C24116yes—
330(C2×D11)⋊C4C2418yes—
331C4⋊Dic11C2418yes—
332C4⋊Dic11C2418yes—
333C4⋊Dic11C2414yes—
334C4⋊Dic11C2418yes—
335C4⋊Dic11C2414yes—
336Dic11⋊C4C24116yes—
337Dic11⋊C4C24116yes—
338Dic11⋊C4C24116yes—
339Dic11⋊C4C2418yes—
340Dic11⋊C4C24116yes—
341C4×Dic11C2414yes—
342C4×Dic11C2418yes—
343C4×Dic11C2414yes—
344C4×Dic11C2418yes—
345C4×Dic11C2414yes—
346C4×Dic11C24116yes—
347C4×Dic11C24116yes—
348#3511—1132no—
349C2×#556—112no—
350C2×#555—111no—
351C2×#555—111no—
352C2×#554—111no—
353C2×#554D1111yescharacteristic, complemented
354C2×#553—112no—
355C2×#553—112no—
356C2×#548—114no—
357C2×#547—112no—
358C2×#542—114no—
359C2×#537—112no—
360C2×#533—112no—
361C2×#532—112no—
362C2×#532—111no—
363C22×C4⋊Q8—111no—
364C2×#520—112no—
365C2×C4×#41—111no—
366C23×C11—24no—
367C23×C11—24no—
368C23×C11—24no—
369C23×C11C2514yes—
370C23×C11C2511yescharacteristic
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—24no—
374C22×D11—24no—
375C22×D11—24no—
376C22×D11—24no—
377C22×D11—24no—
378C22×D11—24no—
379C22×D11C2×#4114yes—
380C22×D11C2514yes—
381C22×D11C2514yes—
382C22×D11C2512yes—
383Q8×C11—28no—
384Q8×C11—48no—
385D4×C11—28no—
386C2×C4×C11—24no—
387C2×C4×C11—24no—
388C2×C4×C11—28no—
389C2×C4×C11—22no—
390C2×C4×C11—24no—
391C2×C4×C11—216no—
392C2×C4×C11—416no—
393C2×C4×C11C2×#4114yes—
394C2×C4×C112−1+414yes—
395C2×C4×C11C2514yes—
396C2×C4×C11C2514yes—
397C2×C4×C11C2514yes—
398C2×C4×C11C2518yes—
399C2×C4×C11C2512yes—
400C2×C4×C11C2512yes—
401C2×C4×C11C2512yes—
402C22⋊D11—216no—
403C22⋊D11—216no—
404C22⋊D11—216no—
405C22⋊D11—416no—
406C2×Dic11—24no—
407C2×Dic11—28no—
408C2×Dic11—24no—
409C2×Dic11—22no—
410C2×Dic11C2×#4114yes—
411C2×Dic11H(5,𝔽2)14yes—
412C2×Dic11C2514yes—
413C2×Dic11C2514yes—
414C2×Dic11C2512yes—
415C2×Dic11C2518yes—
416C2×Dic11C2512yes—
417C2×Dic11C2512yes—
418D44—216no—
419D44—216no—
420D44—28no—
421D44—28no—
422D44—416no—
423C4×D11—216no—
424C4×D11—28no—
425C4×D11—216no—
426C4×D11—216no—
427C4×D11—216no—
428C4×D11—28no—
429C4×D11—416no—
430C4×D11—416no—
431C4×D11C2×#41116yescomplemented
432Dic22—216no—
433Dic22—232no—
434Dic22—48no—
435C22×#41—111no—
436C22×#41—112no—
437C22×#41—114no—
438C23×Q8—112no—
439#556—1132no—
440#555—1116no—
441#555—1116no—
442#554—1116no—
443#554C2×D11116yescomplemented
444#553—1132no—
445#553—1132no—
446#548—1164no—
447#547—1132no—
448#542—1164no—
449#537—1132no—
450#533—1132no—
451#532—1116no—
452#532—1132no—
453C2×C4⋊Q8—112no—
454C2×C4⋊Q8—1116no—
455C2×C4⋊Q8—112no—
456C2×C4⋊Q8—112no—
457C2×C4⋊Q8—111no—
458C2×C4⋊Q8—111no—
459C2×C4⋊Q8C2×D1111yescharacteristic
460C2×#127—111no—
461C2×#126—114no—
462C2×#126—114no—
463C2×#125—112no—
464C2×#125C2×D1112yes—
465C2×#124—114no—
466C2×#124—112no—
467C2×#124—114no—
468C2×#124—114no—
469C2×#123—114no—
470C2×#123—114no—
471C2×C22⋊Q8—112no—
472C2×C22⋊Q8—114no—
473C2×C22⋊Q8—114no—
474C2×C22⋊Q8—114no—
475C2×C22⋊Q8C2×D1112yes—
476C2×C22⋊Q8C2×D1114yes—
477C2×#121—111no—
478C2×#121—112no—
479C2×#121—112no—
480C2×#121—111no—
481C2×#121—112no—
482C2×#121—112no—
483C2×#121—114no—
484C2×#121—114no—
485C2×#121—112no—
486C2×#121—114no—
487#520—1132no—
488C4×#41—1116no—
489C2×C4×Q8—111no—
490C2×C4×Q8—114no—
491C2×C4×Q8—114no—
492C2×C4×Q8C2×D1111yescharacteristic
493C2×C4×D4—114no—
494C2×C4×D4—114no—
495C2×C4×D4—112no—
496C2×C4×D4—111no—
497C2×C4×D4—112no—
498C2×C4×D4—114no—
499C2×C4×D4—112no—
500C2×C4×D4—111no—
501C2×C4×D4—112no—
502C2×C4×D4—111no—
503C2×C4×D4C2×D1112yes—
504C2×C4×D4C2×D1111yescharacteristic
505C2×#117—112no—
506C2×#117—111no—
507C2×#117—112no—
508C2×#117—112no—
509C2×#117—112no—
510C2×#117—112no—
511C22×C4⋊C4—112no—
512C22×C4⋊C4—112no—
513C22×C4⋊C4—112no—
514C22×C4⋊C4C2×D1112yes—
515C22×C42—111no—
516C22×C42—112no—
517C22×C11—24no—
518C22×C11—24no—
519C22×C11—24no—
520C22×C11—48no—
521C22×C11C22×#4112yes—
522C22×C11C2×H(5,𝔽2)12yes—
523C22×C11C2×2−1+412yes—
524C22×C11C2611yescharacteristic
525C2×D11—22no—
526C2×D11—22no—
527C2×D11—28no—
528C2×D11—24no—
529C2×D11—24no—
530C2×D11—24no—
531C2×D11—24no—
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—48no—
535C2×D11—48no—
536C2×D11C22×#4114yes—
537C4×C11—24no—
538C4×C11—24no—
539C4×C11—24no—
540C4×C11—28no—
541C4×C11—22no—
542C4×C11C22×#4114yes—
543C4×C11C2×2−1+414yes—
544Dic11—24no—
545Dic11—28no—
546Dic11—24no—
547Dic11—22no—
548Dic11C22×#4114yes—
549Dic11C2×H(5,𝔽2)14yes—
550C2×#41—118no—
551C2×#41—1116no—
552C2×#41—1132no—
553C2×#41—2216no—
554C2×#41—228no—
555C2×#41—4416no—
556C22×Q8—1116no—
557C22×Q8—112no—
558C22×Q8—114no—
559C22×Q8—112no—
560C22×Q8—448no—
561C22×Q8C22×D1111yescharacteristic
562C22×Q8C22×D1112yes—
563C22×D4—112no—
564C22×D4—112no—
565C22×D4—112no—
566C22×D4—114no—
567C22×D4—111no—
568C22×D4—112no—
569C22×D4—112no—
570C22×D4—111no—
571C22×D4—114no—
572C22×D4C22×D1111yescharacteristic
573C23×C4—111no—
574C23×C4—111no—
575C23×C4—112no—
576C23×C4—112no—
577C23×C4—112no—
578C23×C4—111no—
579C23×C4—112no—
580C23×C4—114no—
581C23×C4—114no—
582C23×C4C22×D1112yes—
583C23×C4C22×D1114yes—
584C4⋊Q8—1116no—
585C4⋊Q8—1116no—
586C4⋊Q8—1116no—
587C4⋊Q8—118no—
588C4⋊Q8—118no—
589C4⋊Q8C22×D1118yes—
590#127—118no—
591#126—1132no—
592#126—1132no—
593#125—1116no—
594#125C22×D11116yes—
595#124—1132no—
596#124—1116no—
597#124—1132no—
598#124—1132no—
599#123—1132no—
600#123—1132no—
601C22⋊Q8—1116no—
602C22⋊Q8—1132no—
603C22⋊Q8—1132no—
604C22⋊Q8—1132no—
605C22⋊Q8C22×D11116yes—
606C22⋊Q8C22×D11132yes—
607#121—118no—
608#121—1116no—
609#121—1116no—
610#121—118no—
611#121—1116no—
612#121—1116no—
613#121—1132no—
614#121—1132no—
615#121—1116no—
616#121—1132no—
617C4×Q8—118no—
618C4×Q8—1132no—
619C4×Q8—1132no—
620C4×Q8C22×D1118yes—
621C4×D4—1132no—
622C4×D4—1132no—
623C4×D4—1116no—
624C4×D4—118no—
625C4×D4—1116no—
626C4×D4—1132no—
627C4×D4—1116no—
628C4×D4—118no—
629C4×D4—1116no—
630C4×D4—118no—
631C4×D4C22×D11116yes—
632C4×D4C22×D1118yes—
633#117—1116no—
634#117—118no—
635#117—1116no—
636#117—1116no—
637#117—1116no—
638#117—1116no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—114no—
642C2×C4⋊C4—114no—
643C2×C4⋊C4—114no—
644C2×C4⋊C4—111no—
645C2×C4⋊C4—111no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4—112no—
648C2×C4⋊C4—114no—
649C2×C4⋊C4—1116no—
650C2×C4⋊C4—1116no—
651C2×C4⋊C4—1116no—
652C2×C4⋊C4C22×D1111yescharacteristic
653C2×C4⋊C4C22×D1112yes—
654C2×C4⋊C4C22×D1112yes—
655C2×C4⋊C4C22×D1114yes—
656C2×C4⋊C4C22×D11116yes—
657C2×C4⋊C4C22×D1111yescharacteristic
658C2×C4⋊C4C22×D1112yes—
659C2×C4⋊C4C22×D1114yes—
660C2×C22⋊C4—114no—
661C2×C22⋊C4—112no—
662C2×C22⋊C4—112no—
663C2×C22⋊C4—114no—
664C2×C22⋊C4—112no—
665C2×C22⋊C4—112no—
666C2×C22⋊C4—114no—
667C2×C22⋊C4—114no—
668C2×C22⋊C4—114no—
669C2×C22⋊C4—112no—
670C2×C22⋊C4—112no—
671C2×C22⋊C4C22×D1114yes—
672C2×C22⋊C4C22×D1112yes—
673C2×C42—112no—
674C2×C42—114no—
675C2×C42—114no—
676C2×C42—111no—
677C2×C42—111no—
678C2×C42—112no—
679C2×C42—111no—
680C2×C42—118no—
681C2×C42—1116no—
682C2×C42C22×D1112yes—
683C2×C42C22×D1111yescharacteristic
684C2×C11—44no—
685C2×C11#351114yescomplemented
686C2×C11C23×#4111yescharacteristic
687C2×C11C22×H(5,𝔽2)11yescharacteristic
688C2×C11C22×2−1+411yescharacteristic
689D11—24no—
690D11—44no—
691D11—44no—
692C24—111no—
693C24—112no—
694C24—112no—
695C24C23×D1112yes—
696#41—2264no—
697#41—2232no—
698#41—4464no—
699C2×Q8—24no—
700C2×Q8—44no—
701C2×Q8—118no—
702C2×Q8—1116no—
703C2×Q8—118no—
704C2×Q8—2216no—
705C2×Q8—228no—
706C2×Q8—444no—
707C2×Q8—4432no—
708C2×Q8C23×D1114yes—
709C2×Q8C23×D1118yes—
710C2×D4—24no—
711C2×D4—118no—
712C2×D4—118no—
713C2×D4—118no—
714C2×D4—1116no—
715C2×D4—114no—
716C2×D4—118no—
717C2×D4—118no—
718C2×D4—114no—
719C2×D4—1116no—
720C2×D4—228no—
721C2×D4—228no—
722C2×D4—228no—
723C2×D4—228no—
724C2×D4—228no—
725C2×D4—224no—
726C2×D4—224no—
727C2×D4—448no—
728C2×D4—448no—
729C2×D4C23×D1114yes—
730C22×C4—28no—
731C22×C4—48no—
732C22×C4—111no—
733C22×C4—111no—
734C22×C4—118no—
735C22×C4—114no—
736C22×C4—112no—
737C22×C4—111no—
738C22×C4—112no—
739C22×C4—114no—
740C22×C4—114no—
741C22×C4—118no—
742C22×C4—118no—
743C22×C4—114no—
744C22×C4—118no—
745C22×C4—118no—
746C22×C4—1116no—
747C22×C4—1116no—
748C22×C4—224no—
749C22×C4—228no—
750C22×C4—228no—
751C22×C4—224no—
752C22×C4—228no—
753C22×C4—228no—
754C22×C4—448no—
755C22×C4—448no—
756C22×C4C23×D1118yes—
757C22×C4C23×D1112yes—
758C22×C4C23×D1111yescharacteristic
759C22×C4C23×D1112yes—
760C22×C4C23×D1112yes—
761C22×C4C23×D1114yes—
762C22×C4C23×D11116yes—
763C22×C4C23×D1111yescharacteristic
764C22×C4C23×D1111yescharacteristic
765C4⋊C4—118no—
766C4⋊C4—118no—
767C4⋊C4—1116no—
768C4⋊C4—1116no—
769C4⋊C4—1116no—
770C4⋊C4—114no—
771C4⋊C4—114no—
772C4⋊C4—118no—
773C4⋊C4—118no—
774C4⋊C4—1116no—
775C4⋊C4C23×D1114yes—
776C4⋊C4C23×D1118yes—
777C4⋊C4C23×D1118yes—
778C4⋊C4C23×D11116yes—
779C4⋊C4C23×D1114yes—
780C4⋊C4C23×D1118yes—
781C4⋊C4C23×D11116yes—
782C22⋊C4—1116no—
783C22⋊C4—118no—
784C22⋊C4—118no—
785C22⋊C4—1116no—
786C22⋊C4—118no—
787C22⋊C4—118no—
788C22⋊C4—1116no—
789C22⋊C4—1116no—
790C22⋊C4—1116no—
791C22⋊C4—118no—
792C22⋊C4—118no—
793C22⋊C4C23×D11116yes—
794C22⋊C4C23×D1118yes—
795C42—114no—
796C42—118no—
797C42—114no—
798C42—114no—
799C42—118no—
800C42—1116no—
801C42—1116no—
802C42C23×D1118yes—
803C42C23×D1114yes—
804C11C2×#351111yescharacteristic, complemented, Sylow
805C23—24no—
806C23—24no—
807C23—24no—
808C23—114no—
809C23—112no—
810C23—114no—
811C23—114no—
812C23—222no—
813C23—222no—
814C23—224no—
815C23—224no—
816C23—224no—
817C23—224no—
818C23—224no—
819C23—224no—
820C23C24×D1114yes—
821C23C24×D1111yescharacteristic
822Q8—28no—
823Q8—48no—
824Q8—2232no—
825Q8—2216no—
826Q8—448no—
827D4—28no—
828D4—2216no—
829D4—2216no—
830D4—2216no—
831D4—2216no—
832D4—2216no—
833D4—228no—
834D4—228no—
835D4—4416no—
836D4—4416no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—28no—
841C2×C4—22no—
842C2×C4—216no—
843C2×C4—416no—
844C2×C4—114no—
845C2×C4—114no—
846C2×C4—112no—
847C2×C4—112no—
848C2×C4—1116no—
849C2×C4—114no—
850C2×C4—112no—
851C2×C4—114no—
852C2×C4—118no—
853C2×C4—228no—
854C2×C4—2216no—
855C2×C4—2216no—
856C2×C4—224no—
857C2×C4—222no—
858C2×C4—224no—
859C2×C4—228no—
860C2×C4—228no—
861C2×C4—2216no—
862C2×C4—2216no—
863C2×C4—4416no—
864C2×C4—4416no—
865C2×C4#6704014yes—
866C2×C4#41×D1114yes—
867C2×C4C24×D1114yes—
868C2×C4C24×D1112yes—
869C2×C4C24×D1114yes—
870C2×C4C24×D1114yes—
871C2×C4C24×D1118yes—
872C2×C4C24×D1112yes—
873C2×C4C24×D1112yes—
874C22—24no—
875C22—24no—
876C22—24no—
877C22—48no—
878C22—114no—
879C22—222no—
880C22—222no—
881C22—228no—
882C22—224no—
883C22—224no—
884C22—224no—
885C22—224no—
886C22—224no—
887C22—224no—
888C22—448no—
889C22—448no—
890C22C2×#6704012yes—
891C22C2×#41×D1112yes—
892C22D11×H(5,𝔽2)12yes—
893C22C25×D1111yescharacteristic
894C4—24no—
895C4—24no—
896C4—24no—
897C4—28no—
898C4—22no—
899C4—114no—
900C4—114no—
901C4—224no—
902C4—228no—
903C4—224no—
904C4—222no—
905C4C2×#6704014yes—
906C4C2×#41×D1114yes—
907C2—44no—
908C2—224no—
909C2—444no—
910C2—444no—
911C2#1308252414yesdirect product factor
912C2C22×#41×D1111yescharacteristic
913C2C2×D11×H(5,𝔽2)11yescharacteristic
914C2C22×#6704011yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#554C2
socleC23×C11C25
hypercenterC2×#554D11
hypocenterC11C2×#3511
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #13082524C2direct (N × H)
2. C2×#10623172C2semidirect
3. C2×#10623265C2semidirect
4. C2×#10623094C2semidirect
5. C2×#10623110C2semidirect
6. C2×#10623226C2semidirect
7. C2×#10623089C2semidirect
8. C2×#10623164C2semidirect
9. C2×#10623038C2semidirect
10. C2×#10623171C2semidirect
11. C2×#10623160C2semidirect
12. C2×#10623219C2semidirect
13. C2×#10623079C2semidirect
14. C2×#10623079C2semidirect
15. C2×D11×C4⋊Q8C2semidirect
16. C2×#10623035C2semidirect
17. C2×C4×#4343C2semidirect
18. C2×C11×#554C2semidirect
23. C11×#554C22semidirect
45. #10623265C22semidirect
46. D11×C4⋊Q8C22semidirect
47. #10623226C22semidirect
48. #10623219C22semidirect
49. #10623172C22semidirect
50. #10623171C22semidirect
51. #10623164C22semidirect
52. #10623160C22semidirect
53. #10623110C22semidirect
54. C4×#4343C22semidirect
55. #10623094C22semidirect
56. #10623089C22semidirect
57. #10623079C22semidirect
58. #10623079C22semidirect
63. #10623038C22semidirect
69. #10623035C22semidirect
293. C2×C4×D11#41semidirect
353. C2×#554D11semidirect
431. C4×D11C2×#41semidirect
443. #554C2×D11semidirect
685. C2×C11#3511semidirect
804. C11C2×#3511semidirect
911. C2#13082524direct (N × H)

Maximal subgroups

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

subgroupindex
#130825242
C2×#106231722
C2×#106232652
C2×#106230942
C2×#106231102
C2×#106232262
C2×#106230892
C2×#106231642
C2×#106230382
C2×#106231712
C2×#106231602
C2×#106232192
C2×#106230792
C2×D11×C4⋊Q82
C2×#106230352
C2×C4×#43432
C2×C11×#5542
C2×#351111