Finite Group Databasebeta

← C2×#13082520 #15662141

Subgroups — C2×#13082520 #15662141

Order 2816.

7758 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082520C2132yesmaximal, direct product factor
2C2×#10623115C211yesmaximal, characteristic, complemented
3C2×#10623063C212yesmaximal, complemented
4C2×#10623166C212yesmaximal, complemented
5C2×#10623240C214yesmaximal, complemented
6C2×#10623107C212yesmaximal, complemented
7C2×#10623208C212yesmaximal, complemented
8C2×#10623086C211yesmaximal, characteristic, complemented
9C2×#10623257C211yesmaximal, characteristic, complemented
10C2×#10623241C214yesmaximal, complemented
11C2×#10623160C212yesmaximal, complemented
12C2×#10623109C212yesmaximal, complemented
13C2×#10623199C212yesmaximal, complemented
14C2×#10623079C211yesmaximal, characteristic, complemented
15C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
16C2×#10623054C212yesmaximal, complemented
17C2×C4×#4343C211yesmaximal, characteristic, complemented
18C2×C11×#556C211yesmaximal, characteristic, complemented
19C22×#4343C2211yescharacteristic
20C22×#4343C2212yes—
21C22×Q8×D11C2212yes—
22C22×#4341C2212yes—
23C22×#4339C2212yes—
24C11×#556C22116yescomplemented
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×#126C2214yes—
27C2×C11×#124C2212yes—
28C2×C11×C22⋊Q8C2212yes—
29C2×C4×Q8×C11C2212yes—
30C2×C4×Q8×C11C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C11×#117C2212yes—
33C2×#66999C2212yes—
34C2×#66999C2212yes—
35C2×Q8×Dic11C2211yescharacteristic
36C2×#66997C2212yes—
37C2×#66993C2211yescharacteristic
38C2×#66991C2211yescharacteristic
39C2×#66983C2212yes—
40C2×C4×C22⋊D11C2212yes—
41C22×C4⋊Dic11C2212yes—
42#10623257C22116yescomplemented
43D11×C4⋊Q8C22116yescomplemented
44#10623241C22164yescomplemented
45#10623240C22164yescomplemented
46#10623208C22132yescomplemented
47#10623199C22132yescomplemented
48#10623166C22132yescomplemented
49#10623160C22132yescomplemented
50#10623115C22116yescomplemented
51#10623109C22132yescomplemented
52#10623107C22132yescomplemented
53C4×#4343C22116yescomplemented
54#10623086C22116yescomplemented
55#10623079C22116yescomplemented
56#10623063C22132yescomplemented
57#10623054C22132yescomplemented
58C2×#66951C2214yes—
59C2×#66950C2214yes—
60C2×#66950C2212yes—
61C2×#66949C2214yes—
62C2×#66948C2214yes—
63C2×#66948C2211yescharacteristic
64C2×#66948C2212yes—
65C2×#66947C2214yes—
66C2×#66946C2212yes—
67C2×#66946C2211yescharacteristic
68C2×#66945C2212yes—
69C2×#66945C2212yes—
70C2×#66945C2211yescharacteristic
71C2×C4⋊C4×D11C2212yes—
72C2×C4⋊C4×D11C2212yes—
73C2×C4⋊C4×D11C2212yes—
74C2×#66942C2214yes—
75C2×#66941C2212yes—
76C2×#66941C2212yes—
77C2×#66941C2211yescharacteristic
78C2×#66939C2214yes—
79C2×#66938C2212yes—
80C2×#66938C2214yes—
81C2×#66937C2212yes—
82C2×#66937C2214yes—
83C2×#66937C2214yes—
84C2×#66937C2214yes—
85C2×(C22⋊D11)⋊C4C2214yes—
86C2×(C22⋊D11)⋊C4C2214yes—
87C2×(C22⋊D11)⋊C4C2214yes—
88C2×#66931C2214yes—
89C2×#66928C2212yes—
90C2×#66928C2214yes—
91C2×C4×D44C2214yes—
92C2×C4×D44C2211yescharacteristic
93C2×C4×D44C2211yescharacteristic
94C2×C4×D44C2212yes—
95C2×#66925C2214yes—
96C2×C42×D11C2211yescharacteristic
97C2×C42×D11C2212yes—
98C2×#66922C2211yescharacteristic
99C2×C4×Dic22C2212yes—
100C2×C4×Dic22C2214yes—
101C22×Q8×C11C2312yes—
102C22×Q8×C11C2311yescharacteristic
103C22×D4×C11C2311yescharacteristic
104C23×C4×C11C2312yes—
105C22×C22⋊D11C2312yes—
106C22×C22⋊D11C2312yes—
107C22×C22⋊D11C2312yes—
108C22×C22⋊D11C2314yes—
109C23×Dic11C2314yes—
110C2×#4343—28no—
111C2×#4343—48no—
112C2×#4343C2318yes—
113C2×#4343C23116yes—
114C2×Q8×D11—48no—
115C2×Q8×D11C23116yes—
116C2×#4341—48no—
117C2×#4341C23116yes—
118C2×#4339—216no—
119C2×#4339C23116yes—
120C22×D44C2312yes—
121C22×D44C2311yescharacteristic
122C22×D44C2312yes—
123C22×D44C2311yescharacteristic
124C22×D44C2314yes—
125C22×C4×D11C2312yes—
126C22×C4×D11C2311yescharacteristic
127C22×C4×D11C2312yes—
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2312yes—
130C22×C4×D11C2312yes—
131C22×C4×D11C2314yes—
132C22×C4×D11C2314yes—
133C22×C4×D11C2311yescharacteristic
134C22×Dic22C2312yes—
135C22×Dic22C2312yes—
136C22×Dic22C2314yes—
137C11×C4⋊Q8C2318yes—
138C11×#126C23132yes—
139C11×#124C23116yes—
140C11×C22⋊Q8C23116yes—
141C4×Q8×C11C2318yes—
142C4×Q8×C11C23116yes—
143C4×D4×C11C2318yes—
144C11×#117C23116yes—
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2312yes—
147C2×C11×C4⋊C4C2311yescharacteristic
148C2×C11×C4⋊C4C2314yes—
149C2×C11×C4⋊C4C2311yescharacteristic
150C2×C11×C4⋊C4C2312yes—
151C2×C11×C22⋊C4C2314yes—
152C2×C11×C22⋊C4C2314yes—
153C2×C11×C22⋊C4C2312yes—
154C2×C42×C11C2312yes—
155C2×C42×C11C2314yes—
156C2×C42×C11C2311yescharacteristic
157C2×C22⋊Dic11C2312yes—
158#66999C23116yes—
159#66999C23116yes—
160Q8×Dic11C2318yes—
161#66997C23116yes—
162#66993C2318yes—
163#66991C2318yes—
164#66983C23116yes—
165C4×C22⋊D11C23116yes—
166C2×(C2×D11)⋊C4C2314yes—
167C2×(C2×D11)⋊C4C2314yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2314yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2314yes—
175C2×C4⋊Dic11C2311yescharacteristic
176C2×C4⋊Dic11C2314yes—
177C2×C4⋊Dic11C2312yes—
178C2×C4⋊Dic11C2312yes—
179C2×C4⋊Dic11C2312yes—
180C2×C4⋊Dic11C2311yescharacteristic
181C2×C4⋊Dic11C23116yes—
182C2×Dic11⋊C4C2314yes—
183C2×Dic11⋊C4C2314yes—
184C2×Dic11⋊C4C2314yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2314yes—
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2314yes—
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193#66951C23132yes—
194#66950C23132yes—
195#66950C23116yes—
196#66949C23132yes—
197#66948C23132yes—
198#66948C23116yes—
199#66948C2318yes—
200#66947C23132yes—
201#66946C23116yes—
202#66946C2318yes—
203#66945C23116yes—
204#66945C2318yes—
205#66945C23116yes—
206C4⋊C4×D11C23116yes—
207C4⋊C4×D11C23116yes—
208C4⋊C4×D11C23116yes—
209#66942C23132yes—
210#66941C23116yes—
211#66941C23116yes—
212#66941C2318yes—
213#66939C23132yes—
214#66938C23116yes—
215#66938C23132yes—
216#66937C23116yes—
217#66937C23132yes—
218#66937C23132yes—
219#66937C23132yes—
220(C22⋊D11)⋊C4C23132yes—
221(C22⋊D11)⋊C4C23132yes—
222(C22⋊D11)⋊C4C23132yes—
223#66931C23132yes—
224#66928C23132yes—
225#66928C23116yes—
226C4×D44C23132yes—
227C4×D44C2318yes—
228C4×D44C2318yes—
229C4×D44C23116yes—
230#66925C23132yes—
231C42×D11C2318yes—
232C42×D11C23116yes—
233#66922C2318yes—
234C4×Dic22C23132yes—
235C4×Dic22C23116yes—
236C2×#3511—111nomaximal, Sylow
237C24×C11C2412yes—
238C23×D11C2412yes—
239C23×D11C2412yes—
240C23×D11C2411yescharacteristic
241C2×Q8×C11—24no—
242C2×Q8×C11—28no—
243C2×Q8×C11C2418yes—
244C2×Q8×C11C2414yes—
245C2×D4×C11—24no—
246C2×D4×C11C2414yes—
247C22×C4×C11—28no—
248C22×C4×C11C2412yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2414yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2418yes—
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C2×C22⋊D11—28no—
257C2×C22⋊D11—28no—
258C2×C22⋊D11—28no—
259C2×C22⋊D11—48no—
260C2×C22⋊D11C2418yes—
261C2×C22⋊D11C2418yes—
262C2×C22⋊D11C2418yes—
263C2×C22⋊D11C24116yes—
264C22×Dic11—48no—
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267C22×Dic11C2411yescharacteristic
268C22×Dic11C2414yes—
269C22×Dic11C24116yes—
270C22×Dic11C2411yescharacteristic
271C22×Dic11C2411yescharacteristic
272#4343—232no—
273#4343—432no—
274Q8×D11—432no—
275#4341—432no—
276#4339—264no—
277C2×D44—28no—
278C2×D44—28no—
279C2×D44—24no—
280C2×D44—24no—
281C2×D44—48no—
282C2×D44C2418yes—
283C2×D44C2414yes—
284C2×D44C2418yes—
285C2×D44C2414yes—
286C2×D44C24116yes—
287C2×C4×D11—28no—
288C2×C4×D11—24no—
289C2×C4×D11—28no—
290C2×C4×D11—28no—
291C2×C4×D11—28no—
292C2×C4×D11—24no—
293C2×C4×D11—48no—
294C2×C4×D11—48no—
295C2×C4×D11#4118yescomplemented
296C2×C4×D11C2418yes—
297C2×C4×D11C2414yes—
298C2×C4×D11C2418yes—
299C2×C4×D11C2414yes—
300C2×C4×D11C2418yes—
301C2×C4×D11C2418yes—
302C2×C4×D11C24116yes—
303C2×C4×D11C24116yes—
304C2×C4×D11C2414yes—
305C2×Dic22—28no—
306C2×Dic22—28no—
307C2×Dic22—48no—
308C2×Dic22C2418yes—
309C2×Dic22C2418yes—
310C2×Dic22C24116yes—
311C11×C4⋊C4C2418yes—
312C11×C4⋊C4C2418yes—
313C11×C4⋊C4C2414yes—
314C11×C4⋊C4C24116yes—
315C11×C4⋊C4C2414yes—
316C11×C4⋊C4C2418yes—
317C11×C22⋊C4C24116yes—
318C11×C22⋊C4C24116yes—
319C11×C22⋊C4C2418yes—
320C42×C11C2418yes—
321C42×C11C24116yes—
322C42×C11C2414yes—
323C22⋊Dic11C2418yes—
324(C2×D11)⋊C4C24116yes—
325(C2×D11)⋊C4C24116yes—
326(C2×D11)⋊C4C2418yes—
327(C2×D11)⋊C4C24116yes—
328(C2×D11)⋊C4C2418yes—
329(C2×D11)⋊C4C2418yes—
330(C2×D11)⋊C4C2418yes—
331(C2×D11)⋊C4C2418yes—
332(C2×D11)⋊C4C24116yes—
333C4⋊Dic11C2414yes—
334C4⋊Dic11C24116yes—
335C4⋊Dic11C2418yes—
336C4⋊Dic11C2418yes—
337C4⋊Dic11C2418yes—
338C4⋊Dic11C2414yes—
339Dic11⋊C4C24116yes—
340Dic11⋊C4C24116yes—
341Dic11⋊C4C24116yes—
342Dic11⋊C4C2418yes—
343Dic11⋊C4C24116yes—
344C4×Dic11C2418yes—
345C4×Dic11C24116yes—
346C4×Dic11C2414yes—
347C4×Dic11C2418yes—
348C4×Dic11C2414yes—
349C4×Dic11C2414yes—
350#3511—1132no—
351C2×#556—111no—
352C2×#556D1111yescharacteristic, complemented
353C2×#555—112no—
354C2×#554—112no—
355C2×#553—114no—
356C2×#548—112no—
357C2×#548—112no—
358C2×#547—111no—
359C2×#547—111no—
360C2×#542—114no—
361C2×#537—112no—
362C2×#533—112no—
363C2×#532—112no—
364C2×#532—111no—
365C22×C4⋊Q8—111no—
366C2×#520—112no—
367C2×C4×#41—111no—
368C23×C11—24no—
369C23×C11—24no—
370C23×C11—24no—
371C23×C11C2514yes—
372C23×C11C2511yescharacteristic
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—24no—
376C22×D11—24no—
377C22×D11—24no—
378C22×D11—24no—
379C22×D11—24no—
380C22×D11—24no—
381C22×D11C2×#4114yes—
382C22×D11C2514yes—
383C22×D11C2514yes—
384C22×D11C2512yes—
385Q8×C11—28no—
386Q8×C11—216no—
387D4×C11—28no—
388C2×C4×C11—24no—
389C2×C4×C11—24no—
390C2×C4×C11—28no—
391C2×C4×C11—24no—
392C2×C4×C11—22no—
393C2×C4×C11—216no—
394C2×C4×C11C2×#4114yes—
395C2×C4×C11H(5,𝔽2)14yes—
396C2×C4×C11C2514yes—
397C2×C4×C11C2514yes—
398C2×C4×C11C2512yes—
399C2×C4×C11C2518yes—
400C2×C4×C11C2514yes—
401C2×C4×C11C2512yes—
402C2×C4×C11C2512yes—
403C22⋊D11—216no—
404C22⋊D11—216no—
405C22⋊D11—216no—
406C22⋊D11—416no—
407C2×Dic11—24no—
408C2×Dic11—28no—
409C2×Dic11—22no—
410C2×Dic11—24no—
411C2×Dic11—416no—
412C2×Dic11C2×#4114yes—
413C2×Dic112−1+414yes—
414C2×Dic11C2514yes—
415C2×Dic11C2514yes—
416C2×Dic11C2512yes—
417C2×Dic11C2518yes—
418C2×Dic11C2512yes—
419C2×Dic11C2512yes—
420D44—216no—
421D44—216no—
422D44—28no—
423D44—28no—
424D44—416no—
425C4×D11—216no—
426C4×D11—216no—
427C4×D11—28no—
428C4×D11—216no—
429C4×D11—28no—
430C4×D11—216no—
431C4×D11—416no—
432C4×D11—416no—
433C4×D11C2×#41116yescomplemented
434Dic22—216no—
435Dic22—216no—
436Dic22—416no—
437C22×#41—111no—
438C22×#41—112no—
439C22×#41—112no—
440C22×#41—112no—
441C23×Q8—112no—
442#556—1116no—
443#556C2×D11116yescomplemented
444#555—1132no—
445#554—1132no—
446#553—1164no—
447#548—1132no—
448#548—1132no—
449#547—1116no—
450#547—1116no—
451#542—1164no—
452#537—1132no—
453#533—1132no—
454#532—1132no—
455#532—1116no—
456C2×C4⋊Q8—112no—
457C2×C4⋊Q8—1116no—
458C2×C4⋊Q8—112no—
459C2×C4⋊Q8—112no—
460C2×C4⋊Q8—111no—
461C2×C4⋊Q8—111no—
462C2×C4⋊Q8C2×D1111yescharacteristic
463C2×#127—111no—
464C2×#126—114no—
465C2×#126C2×D1114yes—
466C2×#125—114no—
467C2×#124—112no—
468C2×#124—114no—
469C2×#124—112no—
470C2×#124—114no—
471C2×#124C2×D1112yes—
472C2×#123—114no—
473C2×#123—114no—
474C2×C22⋊Q8—112no—
475C2×C22⋊Q8—112no—
476C2×C22⋊Q8—114no—
477C2×C22⋊Q8—112no—
478C2×C22⋊Q8—114no—
479C2×C22⋊Q8—114no—
480C2×C22⋊Q8C2×D1112yes—
481C2×#121—111no—
482C2×#121—112no—
483C2×#121—111no—
484C2×#121—112no—
485C2×#121—114no—
486C2×#121—114no—
487C2×#121—112no—
488C2×#121—114no—
489C2×#121—114no—
490#520—1132no—
491C4×#41—1116no—
492C2×C4×Q8—111no—
493C2×C4×Q8—114no—
494C2×C4×Q8—112no—
495C2×C4×Q8C2×D1111yescharacteristic
496C2×C4×Q8C2×D1112yes—
497C2×C4×D4—112no—
498C2×C4×D4—112no—
499C2×C4×D4—111no—
500C2×C4×D4—114no—
501C2×C4×D4—114no—
502C2×C4×D4—114no—
503C2×C4×D4—111no—
504C2×C4×D4—112no—
505C2×C4×D4—114no—
506C2×C4×D4—111no—
507C2×C4×D4C2×D1111yescharacteristic
508C2×#117—111no—
509C2×#117—112no—
510C2×#117—112no—
511C2×#117—114no—
512C2×#117C2×D1112yes—
513C22×C4⋊C4—112no—
514C22×C4⋊C4—112no—
515C22×C4⋊C4—112no—
516C22×C4⋊C4—112no—
517C22×C42—111no—
518C22×C42—112no—
519C22×C11—24no—
520C22×C11—24no—
521C22×C11—24no—
522C22×C11—48no—
523C22×C11C22×#4112yes—
524C22×C11C2×H(5,𝔽2)12yes—
525C22×C11C2×2−1+412yes—
526C22×C11C2611yescharacteristic
527C2×D11—22no—
528C2×D11—22no—
529C2×D11—28no—
530C2×D11—24no—
531C2×D11—24no—
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—24no—
535C2×D11—24no—
536C2×D11—48no—
537C2×D11—48no—
538C2×D11C22×#4114yes—
539C4×C11—24no—
540C4×C11—24no—
541C4×C11—28no—
542C4×C11—24no—
543C4×C11—22no—
544C4×C11C22×#4114yes—
545C4×C11C2×H(5,𝔽2)14yes—
546Dic11—24no—
547Dic11—28no—
548Dic11—22no—
549Dic11—24no—
550Dic11C22×#4114yes—
551Dic11C2×2−1+414yes—
552C2×#41—118no—
553C2×#41—1116no—
554C2×#41—1116no—
555C2×#41—1116no—
556C2×#41—2216no—
557C2×#41—228no—
558C2×#41—448no—
559C2×#41—448no—
560C22×Q8—1116no—
561C22×Q8—112no—
562C22×Q8—112no—
563C22×Q8—114no—
564C22×Q8—448no—
565C22×Q8C22×D1111yescharacteristic
566C22×Q8C22×D1112yes—
567C22×D4—112no—
568C22×D4—112no—
569C22×D4—112no—
570C22×D4—114no—
571C22×D4—112no—
572C22×D4—112no—
573C22×D4—111no—
574C22×D4—111no—
575C22×D4—114no—
576C22×D4C22×D1111yescharacteristic
577C23×C4—111no—
578C23×C4—114no—
579C23×C4—111no—
580C23×C4—112no—
581C23×C4—112no—
582C23×C4—112no—
583C23×C4—111no—
584C23×C4—112no—
585C23×C4—114no—
586C23×C4—114no—
587C23×C4C22×D1112yes—
588C4⋊Q8—1116no—
589C4⋊Q8—1116no—
590C4⋊Q8—1116no—
591C4⋊Q8—118no—
592C4⋊Q8—118no—
593C4⋊Q8C22×D1118yes—
594#127—118no—
595#126—1132no—
596#126C22×D11132yes—
597#125—1132no—
598#124—1116no—
599#124—1132no—
600#124—1116no—
601#124—1132no—
602#124C22×D11116yes—
603#123—1132no—
604#123—1132no—
605C22⋊Q8—1116no—
606C22⋊Q8—1116no—
607C22⋊Q8—1132no—
608C22⋊Q8—1116no—
609C22⋊Q8—1132no—
610C22⋊Q8—1132no—
611C22⋊Q8C22×D11116yes—
612#121—118no—
613#121—1116no—
614#121—118no—
615#121—1116no—
616#121—1132no—
617#121—1132no—
618#121—1116no—
619#121—1132no—
620#121—1132no—
621C4×Q8—118no—
622C4×Q8—1132no—
623C4×Q8—1116no—
624C4×Q8C22×D1118yes—
625C4×Q8C22×D11116yes—
626C4×D4—1116no—
627C4×D4—1116no—
628C4×D4—118no—
629C4×D4—1132no—
630C4×D4—1132no—
631C4×D4—1132no—
632C4×D4—118no—
633C4×D4—1116no—
634C4×D4—1132no—
635C4×D4—118no—
636C4×D4C22×D1118yes—
637#117—118no—
638#117—1116no—
639#117—1116no—
640#117—1132no—
641#117C22×D11116yes—
642C2×C4⋊C4—111no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—114no—
645C2×C4⋊C4—114no—
646C2×C4⋊C4—114no—
647C2×C4⋊C4—114no—
648C2×C4⋊C4—1116no—
649C2×C4⋊C4—112no—
650C2×C4⋊C4—112no—
651C2×C4⋊C4—112no—
652C2×C4⋊C4—111no—
653C2×C4⋊C4—114no—
654C2×C4⋊C4—1116no—
655C2×C4⋊C4—1116no—
656C2×C4⋊C4—1116no—
657C2×C4⋊C4C22×D1112yes—
658C2×C4⋊C4C22×D1112yes—
659C2×C4⋊C4C22×D1111yescharacteristic
660C2×C4⋊C4C22×D1112yes—
661C2×C4⋊C4C22×D1111yescharacteristic
662C2×C4⋊C4C22×D1114yes—
663C2×C22⋊C4—112no—
664C2×C22⋊C4—112no—
665C2×C22⋊C4—114no—
666C2×C22⋊C4—112no—
667C2×C22⋊C4—112no—
668C2×C22⋊C4—114no—
669C2×C22⋊C4—114no—
670C2×C22⋊C4—114no—
671C2×C22⋊C4—112no—
672C2×C22⋊C4—112no—
673C2×C22⋊C4C22×D1114yes—
674C2×C22⋊C4C22×D1114yes—
675C2×C22⋊C4C22×D1112yes—
676C2×C42—112no—
677C2×C42—114no—
678C2×C42—111no—
679C2×C42—112no—
680C2×C42—111no—
681C2×C42—111no—
682C2×C42—118no—
683C2×C42—1116no—
684C2×C42C22×D1114yes—
685C2×C42C22×D1111yescharacteristic
686C2×C42C22×D1112yes—
687C2×C11—44no—
688C2×C11#351114yescomplemented
689C2×C11C23×#4111yescharacteristic
690C2×C11C22×H(5,𝔽2)11yescharacteristic
691C2×C11C22×2−1+411yescharacteristic
692D11—24no—
693D11—44no—
694D11—44no—
695C24—111no—
696C24—112no—
697C24—112no—
698C24C23×D1112yes—
699#41—2264no—
700#41—2232no—
701#41—4432no—
702#41—4432no—
703C2×Q8—24no—
704C2×Q8—28no—
705C2×Q8—118no—
706C2×Q8—118no—
707C2×Q8—1116no—
708C2×Q8—228no—
709C2×Q8—228no—
710C2×Q8—448no—
711C2×Q8—4432no—
712C2×Q8C23×D1114yes—
713C2×Q8C23×D1118yes—
714C2×D4—24no—
715C2×D4—118no—
716C2×D4—118no—
717C2×D4—118no—
718C2×D4—1116no—
719C2×D4—118no—
720C2×D4—118no—
721C2×D4—114no—
722C2×D4—114no—
723C2×D4—1116no—
724C2×D4—228no—
725C2×D4—228no—
726C2×D4—228no—
727C2×D4—228no—
728C2×D4—228no—
729C2×D4—224no—
730C2×D4—224no—
731C2×D4—448no—
732C2×D4—448no—
733C2×D4C23×D1114yes—
734C22×C4—28no—
735C22×C4—111no—
736C22×C4—111no—
737C22×C4—118no—
738C22×C4—114no—
739C22×C4—111no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—114no—
743C22×C4—1116no—
744C22×C4—114no—
745C22×C4—118no—
746C22×C4—118no—
747C22×C4—114no—
748C22×C4—118no—
749C22×C4—118no—
750C22×C4—1116no—
751C22×C4—1116no—
752C22×C4—228no—
753C22×C4—224no—
754C22×C4—228no—
755C22×C4—228no—
756C22×C4—224no—
757C22×C4—228no—
758C22×C4—448no—
759C22×C4—448no—
760C22×C4—448no—
761C22×C4C23×D1118yes—
762C22×C4C23×D1112yes—
763C22×C4C23×D1111yescharacteristic
764C22×C4C23×D1112yes—
765C22×C4C23×D1112yes—
766C22×C4C23×D1114yes—
767C22×C4C23×D1111yescharacteristic
768C22×C4C23×D1111yescharacteristic
769C4⋊C4—114no—
770C4⋊C4—118no—
771C4⋊C4—1116no—
772C4⋊C4—1116no—
773C4⋊C4—1116no—
774C4⋊C4—1116no—
775C4⋊C4—118no—
776C4⋊C4—118no—
777C4⋊C4—118no—
778C4⋊C4—114no—
779C4⋊C4—1116no—
780C4⋊C4C23×D1118yes—
781C4⋊C4C23×D1118yes—
782C4⋊C4C23×D1114yes—
783C4⋊C4C23×D1118yes—
784C4⋊C4C23×D1114yes—
785C4⋊C4C23×D11116yes—
786C22⋊C4—118no—
787C22⋊C4—118no—
788C22⋊C4—1116no—
789C22⋊C4—118no—
790C22⋊C4—118no—
791C22⋊C4—1116no—
792C22⋊C4—1116no—
793C22⋊C4—1116no—
794C22⋊C4—118no—
795C22⋊C4—118no—
796C22⋊C4C23×D11116yes—
797C22⋊C4C23×D11116yes—
798C22⋊C4C23×D1118yes—
799C42—114no—
800C42—118no—
801C42—114no—
802C42—118no—
803C42—114no—
804C42—1116no—
805C42C23×D1114yes—
806C42C23×D1118yes—
807C42C23×D11116yes—
808C11C2×#351111yescharacteristic, complemented, Sylow
809C23—24no—
810C23—24no—
811C23—24no—
812C23—114no—
813C23—112no—
814C23—114no—
815C23—114no—
816C23—222no—
817C23—222no—
818C23—224no—
819C23—224no—
820C23—224no—
821C23—224no—
822C23—224no—
823C23—224no—
824C23C24×D1114yes—
825C23C24×D1111yescharacteristic
826Q8—28no—
827Q8—216no—
828Q8—2216no—
829Q8—2216no—
830Q8—4416no—
831D4—28no—
832D4—2216no—
833D4—2216no—
834D4—2216no—
835D4—2216no—
836D4—2216no—
837D4—228no—
838D4—228no—
839D4—4416no—
840D4—4416no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—216no—
847C2×C4—114no—
848C2×C4—114no—
849C2×C4—112no—
850C2×C4—112no—
851C2×C4—1116no—
852C2×C4—112no—
853C2×C4—114no—
854C2×C4—114no—
855C2×C4—118no—
856C2×C4—2216no—
857C2×C4—228no—
858C2×C4—2216no—
859C2×C4—224no—
860C2×C4—224no—
861C2×C4—222no—
862C2×C4—228no—
863C2×C4—2216no—
864C2×C4—228no—
865C2×C4—2216no—
866C2×C4—4416no—
867C2×C4—4416no—
868C2×C4—4416no—
869C2×C4#41×D1114yes—
870C2×C4#6704214yes—
871C2×C4C24×D1114yes—
872C2×C4C24×D1112yes—
873C2×C4C24×D1114yes—
874C2×C4C24×D1114yes—
875C2×C4C24×D1118yes—
876C2×C4C24×D1112yes—
877C2×C4C24×D1112yes—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—48no—
882C22—114no—
883C22—222no—
884C22—222no—
885C22—228no—
886C22—224no—
887C22—224no—
888C22—224no—
889C22—224no—
890C22—224no—
891C22—224no—
892C22—448no—
893C22—448no—
894C22C2×#41×D1112yes—
895C22C2×#6704212yes—
896C22D11×2−1+412yes—
897C22C25×D1111yescharacteristic
898C4—24no—
899C4—24no—
900C4—28no—
901C4—24no—
902C4—22no—
903C4—114no—
904C4—114no—
905C4—224no—
906C4—224no—
907C4—222no—
908C4—228no—
909C4C2×#41×D1114yes—
910C4C2×#6704214yes—
911C2—44no—
912C2—224no—
913C2—444no—
914C2—444no—
915C2#1308252014yesdirect product factor
916C2C22×#41×D1111yescharacteristic
917C2C22×#6704211yescharacteristic
918C2C2×D11×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#556C2
socleC23×C11C25
hypercenterC2×#556D11
hypocenterC11C2×#3511
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #13082520C2direct (N × H)
2. C2×#10623115C2semidirect
3. C2×#10623063C2semidirect
4. C2×#10623166C2semidirect
5. C2×#10623240C2semidirect
6. C2×#10623107C2semidirect
7. C2×#10623208C2semidirect
8. C2×#10623086C2semidirect
9. C2×#10623257C2semidirect
10. C2×#10623241C2semidirect
11. C2×#10623160C2semidirect
12. C2×#10623109C2semidirect
13. C2×#10623199C2semidirect
14. C2×#10623079C2semidirect
15. C2×D11×C4⋊Q8C2semidirect
16. C2×#10623054C2semidirect
17. C2×C4×#4343C2semidirect
18. C2×C11×#556C2semidirect
24. C11×#556C22semidirect
42. #10623257C22semidirect
43. D11×C4⋊Q8C22semidirect
44. #10623241C22semidirect
45. #10623240C22semidirect
46. #10623208C22semidirect
47. #10623199C22semidirect
48. #10623166C22semidirect
49. #10623160C22semidirect
50. #10623115C22semidirect
51. #10623109C22semidirect
52. #10623107C22semidirect
53. C4×#4343C22semidirect
54. #10623086C22semidirect
55. #10623079C22semidirect
56. #10623063C22semidirect
57. #10623054C22semidirect
295. C2×C4×D11#41semidirect
352. C2×#556D11semidirect
433. C4×D11C2×#41semidirect
443. #556C2×D11semidirect
688. C2×C11#3511semidirect
808. C11C2×#3511semidirect
915. C2#13082520direct (N × H)

Maximal subgroups

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

subgroupindex
#130825202
C2×#106231152
C2×#106230632
C2×#106231662
C2×#106232402
C2×#106231072
C2×#106232082
C2×#106230862
C2×#106232572
C2×#106232412
C2×#106231602
C2×#106231092
C2×#106231992
C2×#106230792
C2×D11×C4⋊Q82
C2×#106230542
C2×C4×#43432
C2×C11×#5562
C2×#351111