Finite Group Databasebeta

← C2×#13082519 #15662142

Subgroups — C2×#13082519 #15662142

Order 2816.

7758 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082519C2132yesmaximal, direct product factor
2C2×#10623064C212yesmaximal, complemented
3C2×#10623063C212yesmaximal, complemented
4C2×#10623042C212yesmaximal, complemented
5C2×#10623071C214yesmaximal, complemented
6C2×#10623083C214yesmaximal, complemented
7C2×#10623038C212yesmaximal, complemented
8C2×#10623113C212yesmaximal, complemented
9C2×#10623092C212yesmaximal, complemented
10C2×#10623041C211yesmaximal, characteristic, complemented
11C2×#10623364C211yesmaximal, characteristic, complemented
12C2×#10623109C212yesmaximal, complemented
13C2×#10623079C212yesmaximal, complemented
14C2×#10623363C211yesmaximal, characteristic, complemented
15C22×#66941C211yesmaximal, characteristic, complemented
16C2×#10623054C211yesmaximal, characteristic, complemented
17C2×#10623053C211yesmaximal, characteristic, complemented
18C2×C11×#520C211yesmaximal, characteristic, complemented
19C22×C11×#41C2211yescharacteristic
20C22×#4339C2211yescharacteristic
21C22×#4339C2211yescharacteristic
22C22×#4339C2214yes—
23C23×Dic22C2212yes—
24C11×#520C22116yescomplemented
25C2×C4×Q8×C11C2212yes—
26C2×C4×D4×C11C2214yes—
27C2×C4×D4×C11C2212yes—
28C2×C11×#117C2212yes—
29C2×C11×#117C2211yescharacteristic
30C22×C11×C4⋊C4C2212yes—
31C22×C11×C4⋊C4C2211yescharacteristic
32#10623364C22116yescomplemented
33#10623363C22116yescomplemented
34C2×#67000C2211yescharacteristic
35C2×#66999C2212yes—
36C2×#66997C2211yescharacteristic
37C2×#66993C2211yescharacteristic
38C2×#66992C2212yes—
39C2×#66992C2214yes—
40C2×#66992C2212yes—
41C2×#66991C2212yes—
42C2×#66989C2211yescharacteristic
43C2×#66983C2214yes—
44C2×#66983C2212yes—
45C2×#66982C2214yes—
46C2×C4×C22⋊D11C2214yes—
47C2×C4×C22⋊D11C2212yes—
48C2×C4×C22⋊D11C2212yes—
49C22×C4⋊Dic11C2211yescharacteristic
50C2×#66977C2212yes—
51C2×#66977C2214yes—
52C22×Dic11⋊C4C2212yes—
53C22×C4×Dic11C2211yescharacteristic
54#10623113C22132yescomplemented
55#10623109C22132yescomplemented
56#10623092C22132yescomplemented
57#10623083C22164yescomplemented
58#10623079C22132yescomplemented
59#10623071C22164yescomplemented
60#10623064C22132yescomplemented
61#10623063C22132yescomplemented
62#10623054C22116yescomplemented
63#10623053C22116yescomplemented
64#10623042C22132yescomplemented
65#10623041C22116yescomplemented
66C2×#66950C2212yes—
67C2×#66950C2212yes—
68C2×#66949C2214yes—
69C2×#66949C2214yes—
70#10623038C22132yescomplemented
71C2×#66948C2212yes—
72C2×#66948C2212yes—
73C2×#66947C2214yes—
74C2×#66946C2211yescharacteristic
75C2×#66946C2211yescharacteristic
76C2×#66945C2212yes—
77C2×C4⋊C4×D11C2212yes—
78C2×#66942C2214yes—
79C2×#66941C2212yes—
80C2×#66941C2212yes—
81C2×#66941C2212yes—
82C2×#66941C2212yes—
83C2×#66941C22116yescomplemented
84C2×#66940C2211yescharacteristic
85C2×#66940C2211yescharacteristic
86C2×#66938C2214yes—
87C2×#66938C2214yes—
88C2×#66937C2214yes—
89C2×(C22⋊D11)⋊C4C2212yes—
90C2×(C22⋊D11)⋊C4C2214yes—
91C2×(C22⋊D11)⋊C4C2212yes—
92C2×#66932C2214yes—
93C2×#66929C2214yes—
94C2×#66928C2214yes—
95C2×C4×D44C2212yes—
96C2×#66925C2214yes—
97C2×#66925C2212yes—
98C2×C42×D11C2212yes—
99C2×C4×Dic22C2214yes—
100C2×C4×Dic22C2212yes—
101C2×C11×#41—28no—
102C2×C11×#41C2318yes—
103C22×Q8×C11C2311yescharacteristic
104C22×D4×C11C2311yescharacteristic
105C22×D4×C11C2312yes—
106C23×C4×C11C2312yes—
107C23×C4×C11C2312yes—
108C23×C4×C11C2314yes—
109C23×C4×C11C2311yescharacteristic
110C22×C22⋊D11C2312yes—
111C22×C22⋊D11C2312yes—
112C22×C22⋊D11C2312yes—
113C22×C22⋊D11C2312yes—
114C22×C22⋊D11C2314yes—
115C23×Dic11C2311yescharacteristic
116C23×Dic11C2311yescharacteristic
117C23×Dic11C2312yes—
118C2×#4339—28no—
119C2×#4339—28no—
120C2×#4339—416no—
121C2×#4339C2318yes—
122C2×#4339C2318yes—
123C2×#4339C23132yes—
124C22×D44C2311yescharacteristic
125C22×D44C2311yescharacteristic
126C22×D44C2314yes—
127C22×C4×D11C2312yes—
128C22×C4×D11C2312yes—
129C22×C4×D11C2312yes—
130C22×C4×D11C2312yes—
131C22×C4×D11C2314yes—
132C22×Dic22—48no—
133C22×Dic22C2311yescharacteristic
134C22×Dic22C2314yes—
135C22×Dic22C2311yescharacteristic
136C22×Dic22C2314yes—
137C22×Dic22C23116yes—
138C4×Q8×C11C23116yes—
139C4×D4×C11C23132yes—
140C4×D4×C11C23116yes—
141C11×#117C2318yes—
142C11×#117C23116yes—
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2312yes—
147C2×C11×C4⋊C4C2318yes—
148C2×C11×C4⋊C4C2314yes—
149C2×C11×C4⋊C4C23116yes—
150C2×C11×C22⋊C4C2314yes—
151C2×C11×C22⋊C4C2312yes—
152C2×C42×C11C2312yes—
153C2×C42×C11C2314yes—
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2314yes—
156C2×C22⋊Dic11C2312yes—
157#67000C2318yes—
158#66999C23116yes—
159#66997C2318yes—
160#66993C2318yes—
161#66992C23116yes—
162#66992C23132yes—
163#66992C23116yes—
164#66991C23116yes—
165#66989C2318yes—
166#66983C23116yes—
167#66983C23132yes—
168#66982C23132yes—
169C4×C22⋊D11C23116yes—
170C4×C22⋊D11C23116yes—
171C4×C22⋊D11C23132yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2314yes—
174C2×(C2×D11)⋊C4C2312yes—
175C2×(C2×D11)⋊C4C2314yes—
176C2×(C2×D11)⋊C4C2314yes—
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2314yes—
180C2×C4⋊Dic11C2312yes—
181C2×C4⋊Dic11C2314yes—
182C2×C4⋊Dic11C2312yes—
183C2×C4⋊Dic11C2318yes—
184#66977C23116yes—
185#66977C23132yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2314yes—
188C2×Dic11⋊C4C2314yes—
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2312yes—
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2314yes—
193C2×Dic11⋊C4C2314yes—
194C2×Dic11⋊C4C23116yes—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2314yes—
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2318yes—
203#66950C23116yes—
204#66950C23116yes—
205#66949C23132yes—
206#66949C23132yes—
207#66948C23116yes—
208#66948C23116yes—
209#66947C23132yes—
210#66946C2318yes—
211#66946C2318yes—
212#66945C23116yes—
213C4⋊C4×D11C23116yes—
214#66942C23132yes—
215#66941C23116yes—
216#66941C23116yes—
217#66941C23116yes—
218#66941C23116yes—
219#66940C2318yes—
220#66940C2318yes—
221#66938C23132yes—
222#66938C23132yes—
223#66937C23132yes—
224(C22⋊D11)⋊C4C23116yes—
225(C22⋊D11)⋊C4C23116yes—
226(C22⋊D11)⋊C4C23132yes—
227#66932C23132yes—
228#66929C23132yes—
229#66928C23132yes—
230C4×D44C23116yes—
231#66925C23116yes—
232#66925C23132yes—
233C42×D11C23116yes—
234C4×Dic22C23116yes—
235C4×Dic22C23132yes—
236C2×#3511—111nomaximal, Sylow
237C24×C11C2412yes—
238C24×C11C2411yescharacteristic
239C23×D11C2412yes—
240C23×D11C2412yes—
241C11×#41—232no—
242C2×Q8×C11—24no—
243C2×Q8×C11C2414yes—
244C2×D4×C11—28no—
245C2×D4×C11—24no—
246C2×D4×C11C2414yes—
247C2×D4×C11C2418yes—
248C22×C4×C11—28no—
249C22×C4×C11—44no—
250C22×C4×C11—48no—
251C22×C4×C11#4118yescomplemented
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2414yes—
256C22×C4×C11C2418yes—
257C22×C4×C11C2418yes—
258C22×C4×C11C24116yes—
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2414yes—
262C2×C22⋊D11—28no—
263C2×C22⋊D11—28no—
264C2×C22⋊D11—28no—
265C2×C22⋊D11—28no—
266C2×C22⋊D11—48no—
267C2×C22⋊D11C2418yes—
268C2×C22⋊D11C2418yes—
269C2×C22⋊D11C2418yes—
270C2×C22⋊D11C2418yes—
271C2×C22⋊D11C24116yes—
272C22×Dic11—24no—
273C22×Dic11—24no—
274C22×Dic11—44no—
275C22×Dic11C2414yes—
276C22×Dic11C2414yes—
277C22×Dic11C2411yescharacteristic
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
280C22×Dic11C2411yescharacteristic
281C22×Dic11C2414yes—
282C22×Dic11C2418yes—
283C22×Dic11C2411yescharacteristic
284C22×Dic11C2411yescharacteristic
285#4339—232no—
286#4339—232no—
287#4339—464no—
288C2×D44—24no—
289C2×D44—24no—
290C2×D44—48no—
291C2×D44C2414yes—
292C2×D44C2414yes—
293C2×D44C24116yes—
294C2×C4×D11—28no—
295C2×C4×D11—28no—
296C2×C4×D11—28no—
297C2×C4×D11—28no—
298C2×C4×D11—48no—
299C2×C4×D11C2418yes—
300C2×C4×D11C2418yes—
301C2×C4×D11C2418yes—
302C2×C4×D11C2418yes—
303C2×C4×D11C24116yes—
304C2×Dic22—216no—
305C2×Dic22—24no—
306C2×Dic22—24no—
307C2×Dic22—48no—
308C2×Dic22—432no—
309C2×Dic22C2414yes—
310C2×Dic22C24116yes—
311C2×Dic22C2414yes—
312C2×Dic22C24116yes—
313C11×C4⋊C4C2414yes—
314C11×C4⋊C4C2414yes—
315C11×C4⋊C4C2418yes—
316C11×C4⋊C4C2418yes—
317C11×C4⋊C4C24116yes—
318C11×C22⋊C4C24116yes—
319C11×C22⋊C4C2418yes—
320C42×C11C2418yes—
321C42×C11C24116yes—
322C22⋊Dic11C2418yes—
323C22⋊Dic11C24116yes—
324C22⋊Dic11C2418yes—
325(C2×D11)⋊C4C2418yes—
326(C2×D11)⋊C4C24116yes—
327(C2×D11)⋊C4C2418yes—
328(C2×D11)⋊C4C24116yes—
329(C2×D11)⋊C4C24116yes—
330(C2×D11)⋊C4C2418yes—
331(C2×D11)⋊C4C2418yes—
332(C2×D11)⋊C4C24116yes—
333C4⋊Dic11C2418yes—
334C4⋊Dic11C24116yes—
335C4⋊Dic11C2418yes—
336Dic11⋊C4C2418yes—
337Dic11⋊C4C24116yes—
338Dic11⋊C4C24116yes—
339Dic11⋊C4C2418yes—
340Dic11⋊C4C2418yes—
341Dic11⋊C4C2418yes—
342Dic11⋊C4C24116yes—
343Dic11⋊C4C24116yes—
344C4×Dic11C2418yes—
345C4×Dic11C24116yes—
346C4×Dic11C2414yes—
347C4×Dic11C2418yes—
348C4×Dic11C2414yes—
349C4×Dic11C2414yes—
350C4×Dic11C2414yes—
351#3511—1132no—
352C2×#556—112no—
353C2×#555—112no—
354C2×#554—112no—
355C2×#553—114no—
356C2×#548—114no—
357C2×#547—112no—
358C2×#542—112no—
359C2×#542—112no—
360C2×#537—111no—
361C2×#537—111no—
362C2×#533—112no—
363C2×#532—111no—
364C2×#532—112no—
365C22×C4⋊Q8—111no—
366C2×#520—111no—
367C2×#520D1111yescharacteristic, complemented
368C2×C4×#41—111no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—24no—
372C23×C11—24no—
373C23×C11—24no—
374C23×C11C2×#4114yes—
375C23×C11C2514yes—
376C23×C11C2512yes—
377C23×C11C2511yescharacteristic
378C22×D11—24no—
379C22×D11—24no—
380C22×D11—24no—
381C22×D11—24no—
382C22×D11—24no—
383C22×D11—24no—
384C22×D11C2514yes—
385C22×D11C2514yes—
386Q8×C11—28no—
387D4×C11—216no—
388D4×C11—28no—
389C2×C4×C11—24no—
390C2×C4×C11—28no—
391C2×C4×C11—24no—
392C2×C4×C11—24no—
393C2×C4×C11—216no—
394C2×C4×C11—48no—
395C2×C4×C11—416no—
396C2×C4×C11C2×#4114yes—
397C2×C4×C11C2×#4114yes—
398C2×C4×C11C2×#41116yescomplemented
399C2×C4×C11C2514yes—
400C2×C4×C11C2514yes—
401C2×C4×C11C2514yes—
402C2×C4×C11C2518yes—
403C2×C4×C11C2512yes—
404C2×C4×C11C2512yes—
405C22⋊D11—216no—
406C22⋊D11—216no—
407C22⋊D11—216no—
408C22⋊D11—216no—
409C22⋊D11—416no—
410C2×Dic11—24no—
411C2×Dic11—24no—
412C2×Dic11—28no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—28no—
416C2×Dic11—28no—
417C2×Dic11—48no—
418C2×Dic11H(5,𝔽2)14yes—
419C2×Dic112−1+414yes—
420C2×Dic11C2512yes—
421C2×Dic11C2514yes—
422C2×Dic11C2514yes—
423C2×Dic11C2512yes—
424C2×Dic11C2518yes—
425C2×Dic11C2512yes—
426C2×Dic11C2512yes—
427D44—28no—
428D44—28no—
429D44—416no—
430C4×D11—216no—
431C4×D11—216no—
432C4×D11—216no—
433C4×D11—216no—
434C4×D11—416no—
435Dic22—28no—
436Dic22—28no—
437Dic22—232no—
438Dic22—416no—
439C22×#41—111no—
440C22×#41—111no—
441C22×#41—114no—
442C22×#41C2×D1111yescharacteristic
443C23×Q8—112no—
444#556—1132no—
445#555—1132no—
446#554—1132no—
447#553—1164no—
448#548—1164no—
449#547—1132no—
450#542—1132no—
451#542—1132no—
452#537—1116no—
453#537—1116no—
454#533—1132no—
455#532—1116no—
456#532—1132no—
457C2×C4⋊Q8—111no—
458C2×C4⋊Q8—112no—
459C2×C4⋊Q8—112no—
460C2×C4⋊Q8—112no—
461C2×C4⋊Q8—112no—
462C2×C4⋊Q8—1116no—
463C2×#127—111no—
464C2×#126—114no—
465C2×#126—114no—
466C2×#125—114no—
467C2×#124—111no—
468C2×#124—111no—
469C2×#124—114no—
470C2×#124—114no—
471C2×#124—114no—
472C2×#123—114no—
473C2×#123—114no—
474C2×C22⋊Q8—112no—
475C2×C22⋊Q8—112no—
476C2×C22⋊Q8—114no—
477C2×C22⋊Q8—114no—
478C2×C22⋊Q8—114no—
479C2×C22⋊Q8—112no—
480C2×C22⋊Q8—112no—
481C2×#121—112no—
482C2×#121—112no—
483C2×#121—112no—
484C2×#121—114no—
485C2×#121—112no—
486C2×#121—114no—
487C2×#121—112no—
488C2×#121—112no—
489C2×#121—114no—
490#520—1116no—
491#520C2×D11116yescomplemented
492C4×#41—1116no—
493C2×C4×Q8—111no—
494C2×C4×Q8—111no—
495C2×C4×Q8—112no—
496C2×C4×Q8—114no—
497C2×C4×Q8C2×D1112yes—
498C2×C4×D4—112no—
499C2×C4×D4—114no—
500C2×C4×D4—112no—
501C2×C4×D4—111no—
502C2×C4×D4—111no—
503C2×C4×D4—112no—
504C2×C4×D4—112no—
505C2×C4×D4—114no—
506C2×C4×D4—112no—
507C2×C4×D4C2×D1112yes—
508C2×C4×D4C2×D1114yes—
509C2×#117—112no—
510C2×#117—112no—
511C2×#117—114no—
512C2×#117C2×D1111yescharacteristic
513C2×#117C2×D1112yes—
514C22×C4⋊C4—112no—
515C22×C4⋊C4—111no—
516C22×C4⋊C4—112no—
517C22×C4⋊C4C2×D1111yescharacteristic
518C22×C4⋊C4C2×D1112yes—
519C22×C42—111no—
520C22×C42—112no—
521C22×C11—22no—
522C22×C11—22no—
523C22×C11—28no—
524C22×C11—24no—
525C22×C11—24no—
526C22×C11—24no—
527C22×C11—48no—
528C22×C11C22×#4114yes—
529C22×C11C22×#4112yes—
530C22×C11C2×H(5,𝔽2)12yes—
531C22×C11C2×2−1+412yes—
532C22×C11C2611yescharacteristic
533C2×D11—24no—
534C2×D11—24no—
535C2×D11—24no—
536C2×D11—24no—
537C2×D11—24no—
538C2×D11—24no—
539C2×D11—48no—
540C2×D11—48no—
541C4×C11—24no—
542C4×C11—28no—
543C4×C11—24no—
544C4×C11—24no—
545C4×C11C22×#4114yes—
546C4×C11C22×#4114yes—
547Dic11—24no—
548Dic11—24no—
549Dic11—28no—
550Dic11—22no—
551Dic11—22no—
552Dic11C2×H(5,𝔽2)14yes—
553Dic11C2×2−1+414yes—
554C2×#41—28no—
555C2×#41—118no—
556C2×#41—118no—
557C2×#41—1132no—
558C2×#41—228no—
559C2×#41—228no—
560C2×#41—4416no—
561C2×#41C22×D1118yes—
562C22×Q8—111no—
563C22×Q8—111no—
564C22×Q8—114no—
565C22×Q8—114no—
566C22×Q8—1116no—
567C22×Q8—448no—
568C22×Q8C22×D1111yescharacteristic
569C22×D4—112no—
570C22×D4—112no—
571C22×D4—112no—
572C22×D4—112no—
573C22×D4—114no—
574C22×D4—111no—
575C22×D4—111no—
576C22×D4—114no—
577C22×D4C22×D1112yes—
578C22×D4C22×D1111yescharacteristic
579C23×C4—111no—
580C23×C4—111no—
581C23×C4—112no—
582C23×C4—112no—
583C23×C4—112no—
584C23×C4—112no—
585C23×C4—112no—
586C23×C4—114no—
587C23×C4C22×D1112yes—
588C23×C4C22×D1112yes—
589C23×C4C22×D1114yes—
590C23×C4C22×D1111yescharacteristic
591C4⋊Q8—118no—
592C4⋊Q8—1116no—
593C4⋊Q8—1116no—
594C4⋊Q8—1116no—
595C4⋊Q8—1116no—
596#127—118no—
597#126—1132no—
598#126—1132no—
599#125—1132no—
600#124—118no—
601#124—118no—
602#124—1132no—
603#124—1132no—
604#124—1132no—
605#123—1132no—
606#123—1132no—
607C22⋊Q8—1116no—
608C22⋊Q8—1116no—
609C22⋊Q8—1132no—
610C22⋊Q8—1116no—
611C22⋊Q8—1132no—
612C22⋊Q8—1116no—
613C22⋊Q8—1132no—
614#121—1116no—
615#121—1116no—
616#121—1116no—
617#121—1132no—
618#121—1116no—
619#121—1132no—
620#121—1116no—
621#121—1116no—
622#121—1132no—
623C4×Q8—118no—
624C4×Q8—118no—
625C4×Q8—1116no—
626C4×Q8—1132no—
627C4×Q8C22×D11116yes—
628C4×D4—1116no—
629C4×D4—1132no—
630C4×D4—1116no—
631C4×D4—118no—
632C4×D4—118no—
633C4×D4—1116no—
634C4×D4—1116no—
635C4×D4—1132no—
636C4×D4—1116no—
637C4×D4C22×D11116yes—
638C4×D4C22×D11132yes—
639#117—1116no—
640#117—1116no—
641#117—1132no—
642#117C22×D1118yes—
643#117C22×D11116yes—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—114no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4—114no—
648C2×C4⋊C4—118no—
649C2×C4⋊C4—114no—
650C2×C4⋊C4—1116no—
651C2×C4⋊C4—112no—
652C2×C4⋊C4—112no—
653C2×C4⋊C4—112no—
654C2×C4⋊C4—112no—
655C2×C4⋊C4—114no—
656C2×C4⋊C4—114no—
657C2×C4⋊C4—1116no—
658C2×C4⋊C4C22×D1111yescharacteristic
659C2×C4⋊C4C22×D1112yes—
660C2×C4⋊C4C22×D1112yes—
661C2×C4⋊C4C22×D1114yes—
662C2×C4⋊C4C22×D1118yes—
663C2×C4⋊C4C22×D11116yes—
664C2×C4⋊C4C22×D1111yescharacteristic
665C2×C22⋊C4—114no—
666C2×C22⋊C4—112no—
667C2×C22⋊C4—112no—
668C2×C22⋊C4—114no—
669C2×C22⋊C4—112no—
670C2×C22⋊C4—112no—
671C2×C22⋊C4—114no—
672C2×C22⋊C4—114no—
673C2×C22⋊C4—114no—
674C2×C22⋊C4—112no—
675C2×C22⋊C4—112no—
676C2×C22⋊C4C22×D1112yes—
677C2×C22⋊C4C22×D1114yes—
678C2×C42—114no—
679C2×C42—111no—
680C2×C42—112no—
681C2×C42—111no—
682C2×C42—111no—
683C2×C42—112no—
684C2×C42—118no—
685C2×C42—111no—
686C2×C42—1116no—
687C2×C42C22×D1112yes—
688C2×C42C22×D1114yes—
689C2×C11—24no—
690C2×C11—44no—
691C2×C11#351114yescomplemented
692C2×C11C23×#4111yescharacteristic
693C2×C11C22×H(5,𝔽2)11yescharacteristic
694C2×C11C22×2−1+411yescharacteristic
695D11—44no—
696D11—44no—
697C24—112no—
698C24—112no—
699C24C23×D1112yes—
700C24C23×D1111yescharacteristic
701#41—232no—
702#41—2232no—
703#41—2232no—
704#41—4464no—
705C2×Q8—24no—
706C2×Q8—114no—
707C2×Q8—114no—
708C2×Q8—1116no—
709C2×Q8—1116no—
710C2×Q8—2216no—
711C2×Q8—224no—
712C2×Q8—224no—
713C2×Q8—448no—
714C2×Q8—4432no—
715C2×Q8C23×D1114yes—
716C2×D4—28no—
717C2×D4—24no—
718C2×D4—118no—
719C2×D4—118no—
720C2×D4—118no—
721C2×D4—118no—
722C2×D4—1116no—
723C2×D4—114no—
724C2×D4—114no—
725C2×D4—1116no—
726C2×D4—228no—
727C2×D4—228no—
728C2×D4—228no—
729C2×D4—228no—
730C2×D4—224no—
731C2×D4—224no—
732C2×D4—448no—
733C2×D4—448no—
734C2×D4C23×D1118yes—
735C2×D4C23×D1114yes—
736C22×C4—28no—
737C22×C4—44no—
738C22×C4—48no—
739C22×C4—111no—
740C22×C4—111no—
741C22×C4—114no—
742C22×C4—114no—
743C22×C4—111no—
744C22×C4—111no—
745C22×C4—112no—
746C22×C4—112no—
747C22×C4—114no—
748C22×C4—118no—
749C22×C4—118no—
750C22×C4—118no—
751C22×C4—118no—
752C22×C4—118no—
753C22×C4—1116no—
754C22×C4—228no—
755C22×C4—228no—
756C22×C4—224no—
757C22×C4—224no—
758C22×C4—228no—
759C22×C4—228no—
760C22×C4—448no—
761C22×C4—444no—
762C22×C4#433918yescomplemented
763C22×C4C23×D1118yes—
764C22×C4C23×D1112yes—
765C22×C4C23×D1112yes—
766C22×C4C23×D1112yes—
767C22×C4C23×D1114yes—
768C22×C4C23×D1118yes—
769C22×C4C23×D11116yes—
770C22×C4C23×D1111yescharacteristic
771C22×C4C23×D1111yescharacteristic
772C22×C4C23×D1114yes—
773C4⋊C4—118no—
774C4⋊C4—1116no—
775C4⋊C4—118no—
776C4⋊C4—1116no—
777C4⋊C4—1116no—
778C4⋊C4—118no—
779C4⋊C4—118no—
780C4⋊C4—118no—
781C4⋊C4—118no—
782C4⋊C4—1116no—
783C4⋊C4—1116no—
784C4⋊C4C23×D1114yes—
785C4⋊C4C23×D1118yes—
786C4⋊C4C23×D1118yes—
787C4⋊C4C23×D11116yes—
788C4⋊C4C23×D1114yes—
789C22⋊C4—1116no—
790C22⋊C4—118no—
791C22⋊C4—118no—
792C22⋊C4—1116no—
793C22⋊C4—118no—
794C22⋊C4—118no—
795C22⋊C4—1116no—
796C22⋊C4—1116no—
797C22⋊C4—1116no—
798C22⋊C4—118no—
799C22⋊C4—118no—
800C22⋊C4C23×D1118yes—
801C22⋊C4C23×D11116yes—
802C42—114no—
803C42—114no—
804C42—118no—
805C42—114no—
806C42—114no—
807C42—118no—
808C42—1116no—
809C42C23×D1118yes—
810C42C23×D11116yes—
811C11C2×#351111yescharacteristic, complemented, Sylow
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—114no—
818C23—114no—
819C23—224no—
820C23—224no—
821C23—224no—
822C23—224no—
823C23—224no—
824C23—224no—
825C23C2×#433914yes—
826C23C24×D1114yes—
827C23C24×D1112yes—
828C23C24×D1111yescharacteristic
829Q8—28no—
830Q8—2232no—
831Q8—228no—
832Q8—228no—
833Q8—4416no—
834D4—216no—
835D4—28no—
836D4—2216no—
837D4—2216no—
838D4—2216no—
839D4—2216no—
840D4—228no—
841D4—228no—
842D4—4416no—
843D4—4416no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—24no—
848C2×C4—216no—
849C2×C4—48no—
850C2×C4—416no—
851C2×C4—114no—
852C2×C4—114no—
853C2×C4—112no—
854C2×C4—112no—
855C2×C4—112no—
856C2×C4—112no—
857C2×C4—114no—
858C2×C4—114no—
859C2×C4—118no—
860C2×C4—2216no—
861C2×C4—2216no—
862C2×C4—228no—
863C2×C4—228no—
864C2×C4—224no—
865C2×C4—224no—
866C2×C4—222no—
867C2×C4—228no—
868C2×C4—222no—
869C2×C4—2216no—
870C2×C4—2216no—
871C2×C4—4416no—
872C2×C4—448no—
873C2×C4C2×#433914yes—
874C2×C4C2×#433914yes—
875C2×C4C2×#4339116yescomplemented
876C2×C4C24×D1114yes—
877C2×C4C24×D1114yes—
878C2×C4C24×D1114yes—
879C2×C4C24×D1118yes—
880C2×C4C24×D1112yes—
881C2×C4C24×D1112yes—
882C22—22no—
883C22—22no—
884C22—28no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—48no—
889C22—224no—
890C22—224no—
891C22—224no—
892C22—224no—
893C22—224no—
894C22—224no—
895C22—448no—
896C22—448no—
897C22C22×#433914yes—
898C22C22×#433912yes—
899C22D11×H(5,𝔽2)12yes—
900C22D11×2−1+412yes—
901C22C25×D1111yescharacteristic
902C4—24no—
903C4—24no—
904C4—28no—
905C4—24no—
906C4—114no—
907C4—114no—
908C4—224no—
909C4—224no—
910C4—222no—
911C4—228no—
912C4—222no—
913C4C22×#433914yes—
914C4C22×#433914yes—
915C2—24no—
916C2—44no—
917C2—444no—
918C2—444no—
919C2#1308251914yesdirect product factor
920C2C23×#433911yescharacteristic
921C2C2×D11×H(5,𝔽2)11yescharacteristic
922C2C2×D11×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#520C2
socleC23×C11C25
hypercenterC2×#520D11
hypocenterC11C2×#3511
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #13082519C2direct (N × H)
2. C2×#10623064C2semidirect
3. C2×#10623063C2semidirect
4. C2×#10623042C2semidirect
5. C2×#10623071C2semidirect
6. C2×#10623083C2semidirect
7. C2×#10623038C2semidirect
8. C2×#10623113C2semidirect
9. C2×#10623092C2semidirect
10. C2×#10623041C2semidirect
11. C2×#10623364C2semidirect
12. C2×#10623109C2semidirect
13. C2×#10623079C2semidirect
14. C2×#10623363C2semidirect
15. C22×#66941C2semidirect
16. C2×#10623054C2semidirect
17. C2×#10623053C2semidirect
18. C2×C11×#520C2semidirect
24. C11×#520C22semidirect
32. #10623364C22semidirect
33. #10623363C22semidirect
54. #10623113C22semidirect
55. #10623109C22semidirect
56. #10623092C22semidirect
57. #10623083C22semidirect
58. #10623079C22semidirect
59. #10623071C22semidirect
60. #10623064C22semidirect
61. #10623063C22semidirect
62. #10623054C22semidirect
63. #10623053C22semidirect
64. #10623042C22semidirect
65. #10623041C22semidirect
70. #10623038C22semidirect
83. C2×#66941C22semidirect
251. C22×C4×C11#41semidirect
367. C2×#520D11semidirect
398. C2×C4×C11C2×#41semidirect
491. #520C2×D11semidirect
691. C2×C11#3511semidirect
762. C22×C4#4339semidirect
811. C11C2×#3511semidirect
875. C2×C4C2×#4339semidirect
919. C2#13082519direct (N × H)

Maximal subgroups

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

subgroupindex
#130825192
C2×#106230642
C2×#106230632
C2×#106230422
C2×#106230712
C2×#106230832
C2×#106230382
C2×#106231132
C2×#106230922
C2×#106230412
C2×#106233642
C2×#106231092
C2×#106230792
C2×#106233632
C22×#669412
C2×#106230542
C2×#106230532
C2×C11×#5202
C2×#351111