Finite Group Databasebeta

← C2×#13082358 #15662196

Subgroups — C2×#13082358 #15662196

Order 2816.

7206 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#13082358C2132yesmaximal, direct product factor
2C2×#10623115C212yesmaximal, complemented
3C2×#10623110C212yesmaximal, complemented
4C2×#10623112C212yesmaximal, complemented
5C2×#10623112C212yesmaximal, complemented
6C2×#10623062C214yesmaximal, complemented
7C2×#10623058C214yesmaximal, complemented
8C2×#10623050C211yesmaximal, characteristic, complemented
9C2×#10623113C212yesmaximal, complemented
10C2×#10623114C212yesmaximal, complemented
11C2×#10623347C211yesmaximal, characteristic, complemented
12C2×#10623109C212yesmaximal, complemented
13C2×#10623111C212yesmaximal, complemented
14C2×#10623055C211yesmaximal, characteristic
15C22×#66999C211yesmaximal, characteristic, complemented
16C2×#10623054C211yesmaximal, characteristic, complemented
17C2×D11×#117C211yesmaximal, characteristic, complemented
18C2×C11×#519C211yesmaximal, characteristic, complemented
19C23×Q8×C11C2211yescharacteristic
20C22×#4339C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C11×#519C22116yescomplemented
23C2×C4×Q8×C11C2212yescomplemented
24C2×C4×Q8×C11C2212yescomplemented
25C2×C4×Q8×C11C2212yescomplemented
26C2×C4×Q8×C11C2212yescomplemented
27C2×C11×#117C2211yescharacteristic
28C2×C11×#117C2214yes—
29C2×C11×#117C2211yescharacteristic
30#10623347C22116yescomplemented
31C2×#67000C2212yescomplemented
32C2×#66999C2212yes—
33C2×#66999C2212yes—
34C2×#66999C2212yes—
35C2×#66999C2212yes—
36C2×#66999C22116yescomplemented
37C2×#66999C2212yescomplemented
38C2×#66999C2212yescomplemented
39C2×#66997C2212yescomplemented
40C2×#66982C2214yes—
41C22×(C2×D11)⋊C4C2212yes—
42C2×#66979C2211yescharacteristic
43C22×C4⋊Dic11C2211yescharacteristic
44C22×Dic11⋊C4C2212yes—
45#10623115C22132yescomplemented
46#10623114C22132yescomplemented
47#10623113C22132yescomplemented
48#10623112C22132yescomplemented
49#10623112C22132yescomplemented
50#10623111C22132yescomplemented
51#10623110C22132yescomplemented
52#10623109C22132yescomplemented
53#10623062C22164yescomplemented
54#10623058C22164yescomplemented
55#10623055C22116yes—
56#10623054C22116yescomplemented
57D11×#117C22116yescomplemented
58#10623050C22116yescomplemented
59C2×#66951C2214yes—
60C2×#66951C2214yescomplemented
61C2×#66950C2211yescharacteristic
62C2×#66950C2211yescharacteristic
63C2×#66949C2214yes—
64C2×#66949C2214yescomplemented
65C2×#66948C2211yescharacteristic
66C2×#66948C2211yescharacteristic
67C2×#66947C2214yes—
68C2×#66947C2214yes—
69C2×#66945C2211yescharacteristic
70C2×#66945C2211yescharacteristic
71C2×#66945C2212yescomplemented
72C2×C4⋊C4×D11C2211yescharacteristic
73C2×C4⋊C4×D11C2211yescharacteristic
74C2×C4⋊C4×D11C2212yescomplemented
75C2×#66943C2212yescomplemented
76C2×#66942C2214yescomplemented
77C2×#66942C2214yescomplemented
78C2×#66941C2212yescomplemented
79C2×#66939C2212yes—
80C2×#66935C2212yes—
81C2×(C22⋊D11)⋊C4C2214yes—
82C2×C22⋊C4×D11C2212yes—
83C2×#66931C2214yes—
84C2×#66930C2212yes—
85C2×#66929C2214yes—
86C2×#66929C2214yescomplemented
87C2×#66928C2214yes—
88C2×C4×D44C2212yes—
89C2×C4×D44C2212yes—
90C2×C4×D44C2214yes—
91C2×C4×D44C2212yescomplemented
92C2×#66925C2214yes—
93C2×#66925C2212yes—
94C2×#66925C2214yescomplemented
95C2×C42×D11C2212yes—
96C2×#66923C2214yescomplemented
97C2×#66923C2212yescomplemented
98C2×#66922C2212yescomplemented
99C2×C4×Dic22C2214yescomplemented
100C2×C4×Dic22C2212yescomplemented
101C24×D11C2311yescharacteristic
102C22×Q8×C11—28no—
103C22×Q8×C11C2312yes—
104C22×Q8×C11C2312yes—
105C22×Q8×C11C2318yes—
106C23×C4×C11C2312yes—
107C23×C4×C11C2311yescharacteristic
108C22×C22⋊D11C2312yes—
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2312yes—
111C2×#4339—28no—
112C2×#4339C2318yes—
113C22×D44C2312yes—
114C22×D44C2311yescharacteristic
115C22×D44C2312yes—
116C22×C4×D11—28no—
117C22×C4×D11C2311yescharacteristic
118C22×C4×D11C2312yes—
119C22×C4×D11C2311yescharacteristic
120C22×C4×D11C2311yescharacteristic
121C22×C4×D11C2312yes—
122C22×C4×D11C2311yescharacteristic
123C22×C4×D11C2318yes—
124C22×C4×D11C2312yes—
125C22×C4×D11C2314yes—
126C22×Dic22C2311yescharacteristic
127C22×Dic22C2314yes—
128C4×Q8×C11C23116yescomplemented
129C4×Q8×C11C23116yescomplemented
130C4×Q8×C11C23116yescomplemented
131C4×Q8×C11C23116yescomplemented
132C11×#117C2318yes—
133C11×#117C2318yes—
134C11×#117C23132yes—
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2314yes—
137C2×C11×C4⋊C4C2314yes—
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2312yes—
143C2×C42×C11C2312yes—
144C2×C42×C11C2314yes—
145C2×C42×C11C2312yes—
146C2×C42×C11C2314yes—
147C2×C22⋊Dic11C2312yes—
148#67000C23116yescomplemented
149#66999C23116yes—
150#66999C23116yes—
151#66999C23116yes—
152#66999C23116yes—
153#66999C23116yescomplemented
154#66999C23116yescomplemented
155#66997C23116yescomplemented
156#66982C23132yes—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2314yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2312yes—
162C2×(C2×D11)⋊C4C2314yes—
163C2×(C2×D11)⋊C4C2314yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2314yes—
167C2×(C2×D11)⋊C4C2314yes—
168C2×(C2×D11)⋊C4C23116yes—
169#66979C2318yes—
170C2×C4⋊Dic11C2312yes—
171C2×C4⋊Dic11C2312yes—
172C2×C4⋊Dic11C2311yescharacteristic
173C2×C4⋊Dic11C2314yes—
174C2×C4⋊Dic11C2312yes—
175C2×C4⋊Dic11C2312yes—
176C2×C4⋊Dic11C2311yescharacteristic
177C2×C4⋊Dic11C2318yes—
178C2×Dic11⋊C4C2314yes—
179C2×Dic11⋊C4C2314yes—
180C2×Dic11⋊C4C2314yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2314yes—
183C2×Dic11⋊C4C2314yes—
184C2×Dic11⋊C4C2314yes—
185C2×Dic11⋊C4C2314yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C23116yes—
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2314yes—
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2312yes—
192#66951C23132yes—
193#66951C23132yescomplemented
194#66950C2318yes—
195#66950C2318yes—
196#66949C23132yes—
197#66949C23132yescomplemented
198#66948C2318yes—
199#66948C2318yes—
200#66947C23132yes—
201#66947C23132yes—
202#66945C2318yes—
203#66945C2318yes—
204#66945C23116yescomplemented
205C4⋊C4×D11C2318yes—
206C4⋊C4×D11C2318yes—
207C4⋊C4×D11C23116yescomplemented
208#66943C23116yescomplemented
209#66942C23132yescomplemented
210#66942C23132yescomplemented
211#66941C23116yescomplemented
212#66939C23116yes—
213#66935C23116yes—
214(C22⋊D11)⋊C4C23132yes—
215C22⋊C4×D11C23116yes—
216#66931C23132yes—
217#66930C23116yes—
218#66929C23132yes—
219#66929C23132yescomplemented
220#66928C23132yes—
221C4×D44C23116yes—
222C4×D44C23116yes—
223C4×D44C23132yes—
224C4×D44C23116yescomplemented
225#66925C23116yes—
226#66925C23132yes—
227#66925C23132yescomplemented
228C42×D11C23116yes—
229#66923C23116yescomplemented
230#66923C23132yescomplemented
231#66922C23116yescomplemented
232C4×Dic22C23116yescomplemented
233C4×Dic22C23132yescomplemented
234C2×#3495—111nomaximal, Sylow
235C24×C11C2411yescharacteristic
236C23×D11—24no—
237C23×D11—24no—
238C23×D11—42no—
239C23×D11C2411yescharacteristic
240C23×D11C2412yes—
241C23×D11C2414yes—
242C23×D11C2411yescharacteristic
243C2×Q8×C11—28no—
244C2×Q8×C11—28no—
245C2×Q8×C11—232no—
246C2×Q8×C11C2418yes—
247C2×Q8×C11C2418yes—
248C22×C4×C11—28no—
249C22×C4×C11#4118yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2412yes—
252C22×C4×C11C2414yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2418yes—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2414yes—
259C2×C22⋊D11—28no—
260C2×C22⋊D11C2418yes—
261C22×Dic11—24no—
262C22×Dic11—44no—
263C22×Dic11C2414yes—
264C22×Dic11C2411yescharacteristic
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267C22×Dic11C2412yes—
268C22×Dic11C2414yes—
269C22×Dic11C2411yescharacteristic
270C22×Dic11C2418yes—
271#4339—232no—
272C2×D44—28no—
273C2×D44—24no—
274C2×D44—44no—
275C2×D44C2418yes—
276C2×D44C2414yes—
277C2×D44C2418yes—
278C2×C4×D11—28no—
279C2×C4×D11—24no—
280C2×C4×D11—24no—
281C2×C4×D11—24no—
282C2×C4×D11—24no—
283C2×C4×D11—232no—
284C2×C4×D11—28no—
285C2×C4×D11—44no—
286C2×C4×D11—48no—
287C2×C4×D11C2414yes—
288C2×C4×D11C2418yes—
289C2×C4×D11C2414yes—
290C2×C4×D11C2414yes—
291C2×C4×D11C2418yes—
292C2×C4×D11C2414yes—
293C2×C4×D11C2418yes—
294C2×C4×D11C24116yes—
295C2×Dic22—24no—
296C2×Dic22—48no—
297C2×Dic22C2414yes—
298C2×Dic22C24116yes—
299C11×C4⋊C4C2414yes—
300C11×C4⋊C4C24116yes—
301C11×C4⋊C4C24116yes—
302C11×C4⋊C4C2414yes—
303C11×C4⋊C4C2414yes—
304C11×C4⋊C4C2414yes—
305C11×C22⋊C4C2418yes—
306C11×C22⋊C4C2418yes—
307C42×C11C2418yes—
308C42×C11C24116yes—
309C42×C11C2418yes—
310C42×C11C24116yes—
311C22⋊Dic11C2418yes—
312(C2×D11)⋊C4C2418yes—
313(C2×D11)⋊C4C24116yes—
314(C2×D11)⋊C4C2418yes—
315(C2×D11)⋊C4C2418yes—
316(C2×D11)⋊C4C2418yes—
317(C2×D11)⋊C4C24116yes—
318(C2×D11)⋊C4C24116yes—
319(C2×D11)⋊C4C2418yes—
320(C2×D11)⋊C4C2418yes—
321(C2×D11)⋊C4C24116yes—
322(C2×D11)⋊C4C24116yes—
323C4⋊Dic11C2418yes—
324C4⋊Dic11C2418yes—
325C4⋊Dic11C2414yes—
326C4⋊Dic11C24116yes—
327C4⋊Dic11C2418yes—
328C4⋊Dic11C2418yes—
329C4⋊Dic11C2414yes—
330Dic11⋊C4C24116yes—
331Dic11⋊C4C24116yes—
332Dic11⋊C4C24116yes—
333Dic11⋊C4C2418yes—
334Dic11⋊C4C24116yes—
335Dic11⋊C4C24116yes—
336Dic11⋊C4C24116yes—
337Dic11⋊C4C24116yes—
338Dic11⋊C4C2418yes—
339C4×Dic11C2418yes—
340C4×Dic11C24116yes—
341C4×Dic11C2418yes—
342C4×Dic11C2418yes—
343#3495—1132no—
344C2×#556—112no—
345C2×#554—112no—
346C2×#552—112no—
347C2×#552—112no—
348C2×#552—114no—
349C2×#551—114no—
350C2×#544—111no—
351C2×#542—112no—
352C2×#541—112no—
353C2×#536—111no—
354C2×#533—112no—
355C2×#529—112no—
356C2×#525—111no—
357C22×C22⋊Q8—111no—
358C2×#520—111no—
359C2×#519D1111yescharacteristic, complemented
360C22×#117—111no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11C2×#4114yes—
364C23×C11C2512yes—
365C23×C11C2511yescharacteristic
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—28no—
369C22×D11—22no—
370C22×D11—24no—
371C22×D11—24no—
372C22×D11—22no—
373C22×D11—24no—
374C22×D11—22no—
375C22×D11—28no—
376C22×D11—44no—
377C22×D11—416no—
378C22×D112−1+414yes—
379C22×D11C2512yes—
380C22×D11C2514yes—
381C22×D11C2512yes—
382Q8×C11—216no—
383Q8×C11—216no—
384C2×C4×C11—216no—
385C2×C4×C11—28no—
386C2×C4×C11—24no—
387C2×C4×C11—24no—
388C2×C4×C11—24no—
389C2×C4×C11—24no—
390C2×C4×C11C2×#4114yes—
391C2×C4×C11C2×#4114yes—
392C2×C4×C11C2×#41116yes—
393C2×C4×C11C2514yes—
394C2×C4×C11C2514yes—
395C2×C4×C11C2518yes—
396C2×C4×C11C2514yes—
397C2×C4×C11C2514yes—
398C2×C4×C11C2512yes—
399C2×C4×C11C2512yes—
400C22⋊D11—216no—
401C2×Dic11—24no—
402C2×Dic11—28no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—24no—
406C2×Dic11—24no—
407C2×Dic11—28no—
408C2×Dic11—48no—
409C2×Dic11C2512yes—
410C2×Dic11C2514yes—
411C2×Dic11C2514yes—
412C2×Dic11C2514yes—
413C2×Dic11C2518yes—
414C2×Dic11C2512yes—
415D44—216no—
416D44—28no—
417D44—48no—
418C4×D11—216no—
419C4×D11—28no—
420C4×D11—28no—
421C4×D11—28no—
422C4×D11—28no—
423C4×D11—216no—
424C4×D11—48no—
425C4×D11—416no—
426Dic22—28no—
427Dic22—416no—
428C22×#41—111no—
429C23×Q8C2×D1111yescharacteristic
430C24×C4—111no—
431#556—1132no—
432#554—1132no—
433#552—1132no—
434#552—1132no—
435#552—1164no—
436#551—1164no—
437#544—1116no—
438#542—1132no—
439#541—1132no—
440#536—1116no—
441#533—1132no—
442C2×C4⋊Q8—112no—
443C2×C4⋊Q8—112no—
444C2×C4⋊Q8—112no—
445#529—1132no—
446C2×#126—114no—
447C2×#126—114no—
448C2×#126—114no—
449C2×#126—114no—
450C2×#125—114no—
451C2×#125—114no—
452C2×#125—112no—
453C2×#125—114no—
454C2×#125—112no—
455C2×#124—112no—
456C2×#124—114no—
457#525—1116no—
458C2×#123—114no—
459C2×#123—114no—
460C2×#123—114no—
461C2×#123—112no—
462C2×C22⋊Q8—112no—
463C2×C22⋊Q8—112no—
464C2×C22⋊Q8—112no—
465C2×C22⋊Q8—112no—
466C2×C22⋊Q8—1116no—
467C2×C22⋊Q8—112no—
468C2×C22⋊Q8—112no—
469C2×C22⋊Q8—114no—
470C2×C22⋊Q8—114no—
471C2×C22⋊Q8—111no—
472C2×C22⋊Q8—111no—
473C2×C22⋊Q8—114no—
474C2×#121—111no—
475C2×#121—111no—
476C2×#120—112no—
477#520—1116no—
478#519C2×D11116yescomplemented
479C2×C4×Q8—112no—
480C2×C4×Q8—114no—
481C2×C4×Q8C2×D1112yescomplemented
482C2×C4×Q8C2×D1112yescomplemented
483C2×C4×Q8C2×D1112yescomplemented
484C2×C4×Q8C2×D1112yescomplemented
485C2×C4×D4—114no—
486C2×C4×D4—112no—
487C2×C4×D4—112no—
488C2×C4×D4—114no—
489C2×C4×D4—112no—
490C2×#117—111no—
491C2×#117—1116no—
492C2×#117—111no—
493C2×#117—111no—
494C2×#117—112no—
495C2×#117—112no—
496C2×#117—112no—
497C2×#117—114no—
498C2×#117—114no—
499C2×#117C2×D1111yescharacteristic
500C2×#117C2×D1111yescharacteristic
501C2×#117C2×D1114yes—
502C22×C4⋊C4—112no—
503C22×C4⋊C4—111no—
504C22×C4⋊C4—111no—
505C22×C4⋊C4—111no—
506C22×C4⋊C4—112no—
507C22×C22⋊C4—112no—
508C22×C22⋊C4—112no—
509C22×C42—112no—
510C22×C11—22no—
511C22×C11—22no—
512C22×C11—28no—
513C22×C11C22×#4114yes—
514C22×C11C22×#4112yes—
515C22×C11C2×2−1+412yes—
516C22×C11#58512yes—
517C22×C11C2611yescharacteristic
518C2×D11—22no—
519C2×D11—22no—
520C2×D11—28no—
521C2×D11—22no—
522C2×D11—24no—
523C2×D11—22no—
524C2×D11—24no—
525C2×D11—22no—
526C2×D11—24no—
527C2×D11—416no—
528C2×D11—48no—
529C2×D11—44no—
530C2×D11C2×2−1+414yes—
531C4×C11—28no—
532C4×C11—24no—
533C4×C11—24no—
534C4×C11—24no—
535C4×C11—24no—
536C4×C11C22×#4114yes—
537C4×C11C22×#4114yes—
538Dic11—24no—
539Dic11—22no—
540Dic11—22no—
541Dic11—24no—
542Dic11—24no—
543Dic11—28no—
544C25—111no—
545C2×#41—118no—
546C2×#41—228no—
547C22×Q8—28no—
548C22×Q8—111no—
549C22×Q8—114no—
550C22×Q8C22×D1112yes—
551C22×Q8C22×D1112yes—
552C22×Q8C22×D1118yes—
553C22×D4—112no—
554C22×D4—112no—
555C22×D4—111no—
556C22×D4—112no—
557C23×C4—111no—
558C23×C4—112no—
559C23×C4—112no—
560C23×C4—111no—
561C23×C4—112no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—118no—
565C23×C4—111no—
566C23×C4—112no—
567C23×C4—114no—
568C23×C4—228no—
569C23×C4C22×D1112yes—
570C23×C4C22×D1111yescharacteristic
571C4⋊Q8—1116no—
572C4⋊Q8—1116no—
573C4⋊Q8—1116no—
574#126—1132no—
575#126—1132no—
576#126—1132no—
577#126—1132no—
578#125—1116no—
579#125—1132no—
580#125—1132no—
581#125—1132no—
582#125—1116no—
583#124—1116no—
584#124—1132no—
585#123—1132no—
586#123—1132no—
587#123—1132no—
588#123—1116no—
589C22⋊Q8—1116no—
590C22⋊Q8—1116no—
591C22⋊Q8—1116no—
592C22⋊Q8—1116no—
593C22⋊Q8—1116no—
594C22⋊Q8—1116no—
595C22⋊Q8—118no—
596C22⋊Q8—118no—
597C22⋊Q8—1132no—
598C22⋊Q8—1132no—
599C22⋊Q8—1132no—
600#121—118no—
601#121—118no—
602#120—1116no—
603C4×Q8—1116no—
604C4×Q8—1132no—
605C4×Q8C22×D11116yescomplemented
606C4×Q8C22×D11116yescomplemented
607C4×Q8C22×D11116yescomplemented
608C4×Q8C22×D11116yescomplemented
609C4×D4—1132no—
610C4×D4—1116no—
611C4×D4—1116no—
612C4×D4—1116no—
613C4×D4—1132no—
614#117—118no—
615#117—118no—
616#117—118no—
617#117—1116no—
618#117—1116no—
619#117—1116no—
620#117—1132no—
621#117—1132no—
622#117C22×D1118yes—
623#117C22×D1118yes—
624#117C22×D11132yes—
625C2×C4⋊C4—112no—
626C2×C4⋊C4—112no—
627C2×C4⋊C4—111no—
628C2×C4⋊C4—111no—
629C2×C4⋊C4—112no—
630C2×C4⋊C4—114no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—114no—
633C2×C4⋊C4—118no—
634C2×C4⋊C4—114no—
635C2×C4⋊C4—1116no—
636C2×C4⋊C4—114no—
637C2×C4⋊C4—114no—
638C2×C4⋊C4—114no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—114no—
642C2×C4⋊C4—114no—
643C2×C4⋊C4—118no—
644C2×C4⋊C4—118no—
645C2×C4⋊C4—1116no—
646C2×C4⋊C4C22×D1111yescharacteristic
647C2×C4⋊C4C22×D1111yescharacteristic
648C2×C4⋊C4C22×D1111yescharacteristic
649C2×C4⋊C4C22×D1111yescharacteristic
650C2×C4⋊C4C22×D1114yes—
651C2×C4⋊C4C22×D1114yes—
652C2×C22⋊C4—112no—
653C2×C22⋊C4—112no—
654C2×C22⋊C4—112no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—114no—
657C2×C22⋊C4—1116no—
658C2×C22⋊C4—112no—
659C2×C22⋊C4—112no—
660C2×C22⋊C4—114no—
661C2×C22⋊C4—114no—
662C2×C22⋊C4—112no—
663C2×C22⋊C4—112no—
664C2×C22⋊C4—114no—
665C2×C22⋊C4—1116no—
666C2×C22⋊C4C22×D1112yes—
667C2×C22⋊C4C22×D1112yes—
668C2×C42—112no—
669C2×C42—114no—
670C2×C42—112no—
671C2×C42—112no—
672C2×C42—1116no—
673C2×C42C22×D1112yes—
674C2×C42C22×D1114yes—
675C2×C42C22×D1114yes—
676C2×C42C22×D1112yes—
677C2×C11—24no—
678C2×C11#349514yescomplemented
679C2×C11C23×#4111yescharacteristic
680C2×C11C22×2−1+411yescharacteristic
681C2×C11C2×#58511yescharacteristic
682D11—24no—
683D11—44no—
684D11—42no—
685C24—111no—
686C24—111no—
687C24—112no—
688C24—114no—
689C24—224no—
690C24—224no—
691C24—442no—
692C24C23×D1111yescharacteristic
693#41—2232no—
694C2×Q8—28no—
695C2×Q8—28no—
696C2×Q8—232no—
697C2×Q8—114no—
698C2×Q8—1116no—
699C2×Q8—224no—
700C2×Q8—448no—
701C2×Q8C23×D1118yes—
702C2×Q8C23×D1118yes—
703C2×D4—118no—
704C2×D4—118no—
705C2×D4—114no—
706C2×D4—118no—
707C2×D4—228no—
708C2×D4—228no—
709C2×D4—224no—
710C2×D4—444no—
711C22×C4—28no—
712C22×C4—114no—
713C22×C4—111no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—114no—
718C22×C4—111no—
719C22×C4—118no—
720C22×C4—114no—
721C22×C4—118no—
722C22×C4—114no—
723C22×C4—118no—
724C22×C4—114no—
725C22×C4—114no—
726C22×C4—118no—
727C22×C4—1116no—
728C22×C4—228no—
729C22×C4—224no—
730C22×C4—224no—
731C22×C4—224no—
732C22×C4—224no—
733C22×C4—224no—
734C22×C4—2232no—
735C22×C4—228no—
736C22×C4—448no—
737C22×C4—444no—
738C22×C4—444no—
739C22×C4#433918yes—
740C22×C4C23×D1118yes—
741C22×C4C23×D1112yes—
742C22×C4C23×D1112yes—
743C22×C4C23×D1112yes—
744C22×C4C23×D1112yes—
745C22×C4C23×D1114yes—
746C22×C4C23×D1114yes—
747C22×C4C23×D1111yescharacteristic
748C22×C4C23×D1111yescharacteristic
749C4⋊C4—118no—
750C4⋊C4—118no—
751C4⋊C4—114no—
752C4⋊C4—114no—
753C4⋊C4—118no—
754C4⋊C4—1116no—
755C4⋊C4—118no—
756C4⋊C4—1116no—
757C4⋊C4—1116no—
758C4⋊C4—1116no—
759C4⋊C4—1116no—
760C4⋊C4—1116no—
761C4⋊C4—118no—
762C4⋊C4—118no—
763C4⋊C4—1116no—
764C4⋊C4—1116no—
765C4⋊C4C23×D1114yes—
766C4⋊C4C23×D1114yes—
767C4⋊C4C23×D1114yes—
768C4⋊C4C23×D1114yes—
769C4⋊C4C23×D11116yes—
770C4⋊C4C23×D11116yes—
771C22⋊C4—118no—
772C22⋊C4—118no—
773C22⋊C4—118no—
774C22⋊C4—1116no—
775C22⋊C4—1116no—
776C22⋊C4—118no—
777C22⋊C4—118no—
778C22⋊C4—1116no—
779C22⋊C4—1116no—
780C22⋊C4—118no—
781C22⋊C4—118no—
782C22⋊C4—1116no—
783C22⋊C4C23×D1118yes—
784C22⋊C4C23×D1118yes—
785C42—118no—
786C42—118no—
787C42—118no—
788C42—1116no—
789C42C23×D1118yes—
790C42C23×D11116yes—
791C42C23×D11116yes—
792C42C23×D1118yes—
793C11C2×#349511yescharacteristic, complemented, Sylow
794C23—22no—
795C23—22no—
796C23—114no—
797C23—112no—
798C23—112no—
799C23—114no—
800C23—228no—
801C23—222no—
802C23—222no—
803C23—228no—
804C23—222no—
805C23—224no—
806C23—224no—
807C23—222no—
808C23—224no—
809C23—222no—
810C23—444no—
811C23—4416no—
812C23C2×#433914yes—
813C23C24×D1112yes—
814C23C24×D1111yescharacteristic
815Q8—216no—
816Q8—216no—
817Q8—228no—
818Q8—4416no—
819D4—2216no—
820D4—2216no—
821D4—228no—
822D4—448no—
823C2×C4—216no—
824C2×C4—28no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—112no—
830C2×C4—114no—
831C2×C4—114no—
832C2×C4—114no—
833C2×C4—118no—
834C2×C4—112no—
835C2×C4—2216no—
836C2×C4—228no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—224no—
840C2×C4—224no—
841C2×C4—228no—
842C2×C4—224no—
843C2×C4—228no—
844C2×C4—228no—
845C2×C4—228no—
846C2×C4—228no—
847C2×C4—2216no—
848C2×C4—4416no—
849C2×C4—448no—
850C2×C4—448no—
851C2×C4C2×#433914yes—
852C2×C4C2×#433914yes—
853C2×C4C2×#4339116yes—
854C2×C4C24×D1114yes—
855C2×C4C24×D1114yes—
856C2×C4C24×D1114yes—
857C2×C4C24×D1114yes—
858C2×C4C24×D1118yes—
859C2×C4C24×D1112yes—
860C2×C4C24×D1112yes—
861C22—22no—
862C22—22no—
863C22—28no—
864C22—114no—
865C22—222no—
866C22—222no—
867C22—228no—
868C22—222no—
869C22—224no—
870C22—224no—
871C22—222no—
872C22—224no—
873C22—222no—
874C22—4416no—
875C22—444no—
876C22—448no—
877C22C22×#433914yes—
878C22C22×#433912yes—
879C22D11×2−1+412yes—
880C22#1062345712yes—
881C22C25×D1111yescharacteristic
882C4—28no—
883C4—24no—
884C4—24no—
885C4—24no—
886C4—24no—
887C4—222no—
888C4—222no—
889C4—224no—
890C4—224no—
891C4—228no—
892C4—224no—
893C4C22×#433914yes—
894C4C22×#433914yes—
895C2—24no—
896C2—224no—
897C2—442no—
898C2—444no—
899C2#1308235814yesdirect product factor
900C2C23×#433911yescharacteristic
901C2C2×D11×2−1+411yescharacteristic
902C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#519C2
socleC23×C11C25
prime radicalC2×#10623055C2
hypercenterC2×#519D11
hypocenterC11C2×#3495
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
1. #13082358C2direct (N × H)
2. C2×#10623115C2semidirect
3. C2×#10623110C2semidirect
4. C2×#10623112C2semidirect
5. C2×#10623112C2semidirect
6. C2×#10623062C2semidirect
7. C2×#10623058C2semidirect
8. C2×#10623050C2semidirect
9. C2×#10623113C2semidirect
10. C2×#10623114C2semidirect
11. C2×#10623347C2semidirect
12. C2×#10623109C2semidirect
13. C2×#10623111C2semidirect
15. C22×#66999C2semidirect
16. C2×#10623054C2semidirect
17. C2×D11×#117C2semidirect
18. C2×C11×#519C2semidirect
22. C11×#519C22semidirect
23. C2×C4×Q8×C11C22semidirect
24. C2×C4×Q8×C11C22semidirect
25. C2×C4×Q8×C11C22semidirect
26. C2×C4×Q8×C11C22semidirect
30. #10623347C22semidirect
31. C2×#67000C22semidirect
36. C2×#66999C22semidirect
37. C2×#66999C22semidirect
38. C2×#66999C22semidirect
39. C2×#66997C22semidirect
45. #10623115C22semidirect
46. #10623114C22semidirect
47. #10623113C22semidirect
48. #10623112C22semidirect
49. #10623112C22semidirect
50. #10623111C22semidirect
51. #10623110C22semidirect
52. #10623109C22semidirect
53. #10623062C22semidirect
54. #10623058C22semidirect
56. #10623054C22semidirect
57. D11×#117C22semidirect
58. #10623050C22semidirect
60. C2×#66951C22semidirect
64. C2×#66949C22semidirect
71. C2×#66945C22semidirect
74. C2×C4⋊C4×D11C22semidirect
75. C2×#66943C22semidirect
76. C2×#66942C22semidirect
77. C2×#66942C22semidirect
78. C2×#66941C22semidirect
86. C2×#66929C22semidirect
91. C2×C4×D44C22semidirect
94. C2×#66925C22semidirect
96. C2×#66923C22semidirect
97. C2×#66923C22semidirect
98. C2×#66922C22semidirect
99. C2×C4×Dic22C22semidirect
100. C2×C4×Dic22C22semidirect
128. C4×Q8×C11C23semidirect
129. C4×Q8×C11C23semidirect
130. C4×Q8×C11C23semidirect
131. C4×Q8×C11C23semidirect
148. #67000C23semidirect
153. #66999C23semidirect
154. #66999C23semidirect
155. #66997C23semidirect
193. #66951C23semidirect
197. #66949C23semidirect
204. #66945C23semidirect
207. C4⋊C4×D11C23semidirect
208. #66943C23semidirect
209. #66942C23semidirect
210. #66942C23semidirect
211. #66941C23semidirect
219. #66929C23semidirect
224. C4×D44C23semidirect
227. #66925C23semidirect
229. #66923C23semidirect
230. #66923C23semidirect
231. #66922C23semidirect
232. C4×Dic22C23semidirect
233. C4×Dic22C23semidirect
359. C2×#519D11semidirect
478. #519C2×D11semidirect
481. C2×C4×Q8C2×D11semidirect
482. C2×C4×Q8C2×D11semidirect
483. C2×C4×Q8C2×D11semidirect
484. C2×C4×Q8C2×D11semidirect
605. C4×Q8C22×D11semidirect
606. C4×Q8C22×D11semidirect
607. C4×Q8C22×D11semidirect
608. C4×Q8C22×D11semidirect
678. C2×C11#3495semidirect
793. C11C2×#3495semidirect
899. C2#13082358direct (N × H)

Maximal subgroups

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

subgroupindex
#130823582
C2×#106231152
C2×#106231102
C2×#106231122
C2×#106230622
C2×#106230582
C2×#106230502
C2×#106231132
C2×#106231142
C2×#106233472
C2×#106231092
C2×#106231112
C2×#106230552
C22×#669992
C2×#106230542
C2×D11×#1172
C2×C11×#5192
C2×#349511