Finite Group Databasebeta

← C2×#13082496 #15662210

Subgroups — C2×#13082496 #15662210

Order 2816.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082496C2132yesmaximal, direct product factor
2C2×#10623101C211yesmaximal, characteristic, complemented
3C2×#10623098C212yesmaximal, complemented
4C2×#10623252C211yesmaximal, characteristic, complemented
5C2×#10623073C211yesmaximal, characteristic, complemented
6C2×#10623202C212yesmaximal, complemented
7C2×#10623060C212yesmaximal, complemented
8C2×#10623239C214yesmaximal, complemented
9C2×#10623170C212yesmaximal, complemented
10C2×#10623232C214yesmaximal, complemented
11C2×#10623206C212yesmaximal
12C2×#10623109C211yesmaximal, characteristic, complemented
13C2×#10623048C212yesmaximal, complemented
14C2×#10623153C212yesmaximal, complemented
15C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
16C2×#10623103C212yesmaximal, complemented
17C2×C4×#4341C211yesmaximal, characteristic
18C2×C11×#556C211yesmaximal, characteristic, complemented
19C22×Q8×D11C2212yes—
20C22×#4341C2211yescharacteristic
21C11×#556C22116yescomplemented
22C2×C11×C4⋊Q8C2211yescharacteristic
23C2×C11×#126C2214yes—
24C2×C11×#124C2212yes—
25C2×C11×C22⋊Q8C2212yes—
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×Q8×C11C2212yes—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117C2212yes—
30C2×#66999C2211yescharacteristic
31C2×Q8×Dic11C2212yes—
32C2×Q8×Dic11C2212yes—
33C2×#66997C2212yes—
34C2×#66997C2211yescharacteristic
35C2×#66997C2212yes—
36C2×#66989C2212yes—
37C2×D4×Dic11C2211yescharacteristic
38C2×C4×C22⋊D11C2212yes—
39C2×#66979C2212yes—
40C2×#66977C2212yes—
41C22×C4×Dic11C2212yes—
42D11×C4⋊Q8C22116yescomplemented
43#10623252C22116yescomplemented
44#10623239C22164yescomplemented
45#10623232C22164yescomplemented
46#10623206C22132yes—
47#10623202C22132yescomplemented
48#10623170C22132yescomplemented
49#10623153C22132yescomplemented
50#10623109C22116yescomplemented
51#10623103C22132yescomplemented
52#10623101C22116yescomplemented
53#10623098C22132yescomplemented
54#10623073C22116yescomplemented
55C4×#4341C22116yes—
56#10623060C22132yescomplemented
57#10623048C22132yescomplemented
58C2×#66950C2211yescharacteristic
59C2×#66949C2212yes—
60C2×#66945C2214yes—
61C2×#66945C2211yescharacteristic
62C2×C4⋊C4×D11C2212yes—
63C2×C4⋊C4×D11C2212yes—
64C2×#66943C2212yes—
65C2×#66943C2214yes—
66C2×#66943C2212yes—
67C2×#66942C2214yes—
68C2×#66942C2214yes—
69C2×#66942C2214yes—
70C2×#66942C2212yes—
71C2×#66941C2212yes—
72C2×#66941C2212yes—
73C2×#66941C2211yescharacteristic
74C2×#66940C2212yes—
75C2×#66940C2214yes—
76C2×#66940C2212yes—
77C2×#66940C2211yescharacteristic
78C2×#66936C2214yes—
79C2×#66936C2214yes—
80C2×(C22⋊D11)⋊C4C2212yes—
81C2×#66932C2214yes—
82C2×#66932C2214yes—
83C2×#66932C2214yes—
84C2×#66931C2214yes—
85C2×#66931C2214yes—
86C2×#66931C2214yes—
87C2×#66930C2214yes—
88C2×#66930C2212yes—
89C2×#66925C2214yes—
90C2×#66925C2212yes—
91C2×C42×D11C2211yescharacteristic
92C2×#66923C2214yes—
93C2×#66922C2211yescharacteristic
94C2×#66922C2212yes—
95C2×C4×Dic22C2214yes—
96C2×C4×Dic22C2214yes—
97C2×C4×Dic22C2212yes—
98C2×C4×Dic22C2211yescharacteristic
99C2×C4×Dic22C2212yes—
100C2×C4×Dic22C2211yescharacteristic
101C22×Q8×C11C2312yes—
102C22×Q8×C11C2311yescharacteristic
103C22×D4×C11C2311yescharacteristic
104C23×C4×C11C2312yes—
105C22×C22⋊D11C2312yes—
106C23×Dic11C2312yes—
107C23×Dic11C2312yes—
108C2×Q8×D11—216no—
109C2×Q8×D11C23116yes—
110C2×#4341—28no—
111C2×#4341C2318yes—
112C22×C4×D11C2311yescharacteristic
113C22×C4×D11C2311yescharacteristic
114C22×C4×D11C2314yes—
115C22×C4×D11C2311yescharacteristic
116C22×Dic22C2312yes—
117C22×Dic22C2312yes—
118C22×Dic22C2311yescharacteristic
119C22×Dic22C2314yes—
120C22×Dic22C2311yescharacteristic
121C11×C4⋊Q8C2318yes—
122C11×#126C23132yes—
123C11×#124C23116yes—
124C11×C22⋊Q8C23116yes—
125C4×Q8×C11C23116yes—
126C4×Q8×C11C2318yes—
127C4×D4×C11C2318yes—
128C11×#117C23116yes—
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2312yes—
131C2×C11×C4⋊C4C2314yes—
132C2×C11×C4⋊C4C2312yes—
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2312yes—
135C2×C11×C22⋊C4C2314yes—
136C2×C11×C22⋊C4C2312yes—
137C2×C11×C22⋊C4C2314yes—
138C2×C42×C11C2311yescharacteristic
139C2×C42×C11C2312yes—
140C2×C42×C11C2314yes—
141C2×C22⋊Dic11C2314yes—
142C2×C22⋊Dic11C2312yes—
143C2×C22⋊Dic11C2314yes—
144#66999C2318yes—
145Q8×Dic11C23116yes—
146Q8×Dic11C23116yes—
147#66997C23116yes—
148#66997C23116yes—
149#66997C2318yes—
150#66989C23116yes—
151D4×Dic11C2318yes—
152C4×C22⋊D11C23116yes—
153C2×(C2×D11)⋊C4C2312yes—
154C2×(C2×D11)⋊C4C2312yes—
155C2×(C2×D11)⋊C4C2312yes—
156#66979C23116yes—
157C2×C4⋊Dic11C2311yescharacteristic
158C2×C4⋊Dic11C2314yes—
159C2×C4⋊Dic11C2312yes—
160C2×C4⋊Dic11C2314yes—
161C2×C4⋊Dic11C2311yescharacteristic
162C2×C4⋊Dic11C2314yes—
163C2×C4⋊Dic11C2312yes—
164C2×C4⋊Dic11C2312yes—
165#66977C23116yes—
166C2×Dic11⋊C4C2312yes—
167C2×Dic11⋊C4C2314yes—
168C2×Dic11⋊C4C2312yes—
169C2×Dic11⋊C4C2314yes—
170C2×Dic11⋊C4C2312yes—
171C2×Dic11⋊C4C2314yes—
172C2×Dic11⋊C4C2312yes—
173C2×Dic11⋊C4C2312yes—
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2314yes—
176C2×Dic11⋊C4C2314yes—
177C2×Dic11⋊C4C2314yes—
178C2×Dic11⋊C4C2312yes—
179C2×C4×Dic11C2311yescharacteristic
180C2×C4×Dic11C2312yes—
181C2×C4×Dic11C2312yes—
182C2×C4×Dic11C2314yes—
183C2×C4×Dic11C2312yes—
184C2×C4×Dic11C2314yes—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2311yescharacteristic
187C2×C4×Dic11C2311yescharacteristic
188C2×C4×Dic11C2314yes—
189C2×C4×Dic11C23116yes—
190#66950C2318yes—
191#66949C23116yes—
192#66945C23132yes—
193#66945C2318yes—
194C4⋊C4×D11C23116yes—
195C4⋊C4×D11C23116yes—
196#66943C23132yes—
197#66943C23116yes—
198#66943C23116yes—
199#66942C23116yes—
200#66942C23132yes—
201#66942C23132yes—
202#66942C23132yes—
203#66941C23116yes—
204#66941C23116yes—
205#66941C2318yes—
206#66940C23132yes—
207#66940C23116yes—
208#66940C2318yes—
209#66940C23116yes—
210#66936C23132yes—
211#66936C23132yes—
212(C22⋊D11)⋊C4C23116yes—
213#66932C23132yes—
214#66932C23132yes—
215#66932C23132yes—
216#66931C23132yes—
217#66931C23132yes—
218#66931C23132yes—
219#66930C23116yes—
220#66930C23132yes—
221#66925C23132yes—
222#66925C23116yes—
223C42×D11C2318yes—
224#66923C23132yes—
225#66922C2318yes—
226#66922C23116yes—
227C4×Dic22C23132yes—
228C4×Dic22C23132yes—
229C4×Dic22C2318yes—
230C4×Dic22C2318yes—
231C4×Dic22C23116yes—
232C4×Dic22C23116yes—
233C2×#3509—111nomaximal, Sylow
234C24×C11C2412yes—
235C23×D11C2411yescharacteristic
236C2×Q8×C11—28no—
237C2×Q8×C11—24no—
238C2×Q8×C11C2418yes—
239C2×Q8×C11C2414yes—
240C2×D4×C11—24no—
241C2×D4×C11C2414yes—
242C22×C4×C11—28no—
243C22×C4×C11C2412yes—
244C22×C4×C11C2412yes—
245C22×C4×C11C2418yes—
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2414yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C2×C22⋊D11—28no—
252C2×C22⋊D11C2418yes—
253C22×Dic11—28no—
254C22×Dic11—28no—
255C22×Dic11C2418yes—
256C22×Dic11C2418yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C22×Dic11C2411yescharacteristic
261C22×Dic11C2412yes—
262C22×Dic11C2414yes—
263C22×Dic11C2411yescharacteristic
264C22×Dic11C2411yescharacteristic
265Q8×D11—264no—
266#4341—232no—
267C2×C4×D11—24no—
268C2×C4×D11—216no—
269C2×C4×D11—24no—
270C2×C4×D11#4118yes—
271C2×C4×D11C2414yes—
272C2×C4×D11C2414yes—
273C2×C4×D11C24116yes—
274C2×C4×D11C2414yes—
275C2×Dic22—216no—
276C2×Dic22—28no—
277C2×Dic22—24no—
278C2×Dic22—28no—
279C2×Dic22—24no—
280C2×Dic22C2418yes—
281C2×Dic22C2418yes—
282C2×Dic22C2414yes—
283C2×Dic22C24116yes—
284C2×Dic22C2414yes—
285C11×C4⋊C4C2414yes—
286C11×C4⋊C4C2418yes—
287C11×C4⋊C4C24116yes—
288C11×C4⋊C4C2418yes—
289C11×C4⋊C4C2414yes—
290C11×C4⋊C4C2418yes—
291C11×C22⋊C4C24116yes—
292C11×C22⋊C4C2418yes—
293C11×C22⋊C4C24116yes—
294C42×C11C2414yes—
295C42×C11C2418yes—
296C42×C11C24116yes—
297C22⋊Dic11C24116yes—
298C22⋊Dic11C2418yes—
299C22⋊Dic11C24116yes—
300(C2×D11)⋊C4C2418yes—
301(C2×D11)⋊C4C2418yes—
302(C2×D11)⋊C4C2418yes—
303C4⋊Dic11C2414yes—
304C4⋊Dic11C24116yes—
305C4⋊Dic11C2418yes—
306C4⋊Dic11C24116yes—
307C4⋊Dic11C2414yes—
308C4⋊Dic11C24116yes—
309C4⋊Dic11C2418yes—
310C4⋊Dic11C2418yes—
311Dic11⋊C4C2418yes—
312Dic11⋊C4C24116yes—
313Dic11⋊C4C2418yes—
314Dic11⋊C4C24116yes—
315Dic11⋊C4C2418yes—
316Dic11⋊C4C24116yes—
317Dic11⋊C4C2418yes—
318Dic11⋊C4C2418yes—
319Dic11⋊C4C2418yes—
320Dic11⋊C4C24116yes—
321Dic11⋊C4C24116yes—
322Dic11⋊C4C24116yes—
323Dic11⋊C4C2418yes—
324C4×Dic11C2414yes—
325C4×Dic11C2418yes—
326C4×Dic11C2418yes—
327C4×Dic11C24116yes—
328C4×Dic11C2418yes—
329C4×Dic11C24116yes—
330C4×Dic11C2418yes—
331C4×Dic11C2414yes—
332C4×Dic11C2414yes—
333C4×Dic11C24116yes—
334#3509—1132no—
335C2×#557—111no—
336C2×#557—112no—
337C2×#557—111no—
338C2×#556—112no—
339C2×#556—111no—
340C2×#556D1111yescharacteristic, complemented
341C2×#552—114no—
342C2×#552—112no—
343C2×#552—112no—
344C2×#541—114no—
345C2×#536—112no—
346C2×#533—112no—
347C2×#533—111no—
348C2×#533—112no—
349C22×C4⋊Q8—111no—
350C2×#519—112no—
351C2×C4×#41—111no—
352C23×C11—24no—
353C23×C11—24no—
354C23×C11—24no—
355C23×C11C2514yes—
356C23×C11C2511yescharacteristic
357C22×D11—22no—
358C22×D11—22no—
359C22×D11C2×#4114yes—
360C22×D11C2512yes—
361Q8×C11—216no—
362Q8×C11—28no—
363D4×C11—28no—
364C2×C4×C11—28no—
365C2×C4×C11—24no—
366C2×C4×C11—22no—
367C2×C4×C11—24no—
368C2×C4×C11—24no—
369C2×C4×C11—216no—
370C2×C4×C11C2×#4114yes—
371C2×C4×C112−1+414yes—
372C2×C4×C11C2514yes—
373C2×C4×C11C2514yes—
374C2×C4×C11C2512yes—
375C2×C4×C11C2518yes—
376C2×C4×C11C2514yes—
377C2×C4×C11C2512yes—
378C2×C4×C11C2512yes—
379C22⋊D11—216no—
380C2×Dic11—28no—
381C2×Dic11—24no—
382C2×Dic11—24no—
383C2×Dic11—24no—
384C2×Dic11—22no—
385C2×Dic11—24no—
386C2×Dic11—216no—
387C2×Dic11—216no—
388C2×Dic11C2×#4114yes—
389C2×Dic112−1+414yes—
390C2×Dic11C2514yes—
391C2×Dic11C2514yes—
392C2×Dic11C2514yes—
393C2×Dic11C2512yes—
394C2×Dic11C2514yes—
395C2×Dic11C2518yes—
396C2×Dic11C2512yes—
397C2×Dic11C2512yes—
398C4×D11—232no—
399C4×D11—28no—
400C4×D11—28no—
401C4×D11C2×#41116yes—
402Dic22—28no—
403Dic22—216no—
404Dic22—28no—
405Dic22—232no—
406Dic22—216no—
407C22×#41—111no—
408C23×Q8—112no—
409#557—1116no—
410#557—1132no—
411#557—1116no—
412#556—1132no—
413#556—1116no—
414#556C2×D11116yescomplemented
415#552—1164no—
416#552—1132no—
417#552—1132no—
418#541—1164no—
419#536—1132no—
420#533—1132no—
421#533—1116no—
422#533—1132no—
423C2×C4⋊Q8—112no—
424C2×C4⋊Q8—111no—
425C2×C4⋊Q8—112no—
426C2×C4⋊Q8—1116no—
427C2×C4⋊Q8—112no—
428C2×C4⋊Q8—112no—
429C2×C4⋊Q8—111no—
430C2×C4⋊Q8—111no—
431C2×C4⋊Q8—112no—
432C2×C4⋊Q8C2×D1111yescharacteristic
433C2×#126—114no—
434C2×#126—114no—
435C2×#126—114no—
436C2×#126C2×D1114yes—
437C2×#125—112no—
438C2×#125—114no—
439C2×#125—114no—
440C2×#125—114no—
441C2×#125—112no—
442C2×#125—112no—
443C2×#125—114no—
444C2×#125—114no—
445C2×#124—112no—
446C2×#124C2×D1112yes—
447C2×#123—114no—
448C2×#123—114no—
449C2×C22⋊Q8—111no—
450C2×C22⋊Q8—112no—
451C2×C22⋊Q8—112no—
452C2×C22⋊Q8—111no—
453C2×C22⋊Q8—114no—
454C2×C22⋊Q8—114no—
455C2×C22⋊Q8—114no—
456C2×C22⋊Q8C2×D1112yes—
457#519—1132no—
458C4×#41—1116no—
459C2×C4×Q8—112no—
460C2×C4×Q8—112no—
461C2×C4×Q8—111no—
462C2×C4×Q8—114no—
463C2×C4×Q8—112no—
464C2×C4×Q8—112no—
465C2×C4×Q8—111no—
466C2×C4×Q8—114no—
467C2×C4×Q8—112no—
468C2×C4×Q8—114no—
469C2×C4×Q8—111no—
470C2×C4×Q8—112no—
471C2×C4×Q8C2×D1112yes—
472C2×C4×Q8C2×D1111yescharacteristic
473C2×C4×D4—111no—
474C2×C4×D4—112no—
475C2×C4×D4—112no—
476C2×C4×D4C2×D1111yescharacteristic
477C2×#117—112no—
478C2×#117—111no—
479C2×#117—114no—
480C2×#117—112no—
481C2×#117—114no—
482C2×#117—112no—
483C2×#117—114no—
484C2×#117C2×D1112yes—
485C22×C4⋊C4—112no—
486C22×C4⋊C4—112no—
487C22×C42—112no—
488C22×C42—111no—
489C22×C11—24no—
490C22×C11—24no—
491C22×C11—24no—
492C22×C11—48no—
493C22×C11C22×#4112yes—
494C22×C11C2×2−1+412yes—
495C22×C11C2×2−1+412yes—
496C22×C11C2611yescharacteristic
497C2×D11—22no—
498C2×D11—22no—
499C2×D11—28no—
500C2×D11C22×#4114yes—
501C4×C11—28no—
502C4×C11—24no—
503C4×C11—24no—
504C4×C11—24no—
505C4×C11—22no—
506C4×C11C22×#4114yes—
507C4×C11C2×2−1+414yes—
508Dic11—28no—
509Dic11—24no—
510Dic11—24no—
511Dic11—24no—
512Dic11—22no—
513Dic11—24no—
514Dic11C22×#4114yes—
515Dic11C2×2−1+414yes—
516C2×#41—118no—
517C2×#41—228no—
518C22×Q8—1116no—
519C22×Q8—112no—
520C22×Q8—111no—
521C22×Q8—114no—
522C22×Q8—112no—
523C22×Q8—111no—
524C22×Q8—2216no—
525C22×Q8C22×D1111yescharacteristic
526C22×Q8C22×D1112yes—
527C22×D4—112no—
528C22×D4C22×D1111yescharacteristic
529C23×C4—111no—
530C23×C4—112no—
531C23×C4—112no—
532C23×C4—114no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4C22×D1112yes—
536C4⋊Q8—1116no—
537C4⋊Q8—118no—
538C4⋊Q8—1116no—
539C4⋊Q8—1116no—
540C4⋊Q8—1116no—
541C4⋊Q8—118no—
542C4⋊Q8—118no—
543C4⋊Q8—1116no—
544C4⋊Q8C22×D1118yes—
545#126—1132no—
546#126—1132no—
547#126—1132no—
548#126C22×D11132yes—
549#125—1116no—
550#125—1132no—
551#125—1116no—
552#125—1116no—
553#125—1132no—
554#125—1132no—
555#125—1132no—
556#125—1132no—
557#124—1116no—
558#124C22×D11116yes—
559#123—1132no—
560#123—1132no—
561C22⋊Q8—118no—
562C22⋊Q8—1116no—
563C22⋊Q8—1116no—
564C22⋊Q8—118no—
565C22⋊Q8—1132no—
566C22⋊Q8—1132no—
567C22⋊Q8—1132no—
568C22⋊Q8C22×D11116yes—
569C4×Q8—1116no—
570C4×Q8—1116no—
571C4×Q8—118no—
572C4×Q8—1132no—
573C4×Q8—1116no—
574C4×Q8—1116no—
575C4×Q8—118no—
576C4×Q8—1132no—
577C4×Q8—1116no—
578C4×Q8—1132no—
579C4×Q8—1116no—
580C4×Q8—118no—
581C4×Q8C22×D11116yes—
582C4×Q8C22×D1118yes—
583C4×D4—118no—
584C4×D4—1116no—
585C4×D4—1116no—
586C4×D4C22×D1118yes—
587#117—1116no—
588#117—118no—
589#117—1132no—
590#117—1116no—
591#117—1132no—
592#117—1116no—
593#117—1132no—
594#117C22×D11116yes—
595C2×C4⋊C4—114no—
596C2×C4⋊C4—112no—
597C2×C4⋊C4—114no—
598C2×C4⋊C4—112no—
599C2×C4⋊C4—112no—
600C2×C4⋊C4—111no—
601C2×C4⋊C4—111no—
602C2×C4⋊C4—112no—
603C2×C4⋊C4—112no—
604C2×C4⋊C4—112no—
605C2×C4⋊C4—112no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—114no—
609C2×C4⋊C4—114no—
610C2×C4⋊C4—114no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—112no—
614C2×C4⋊C4—112no—
615C2×C4⋊C4—112no—
616C2×C4⋊C4—1116no—
617C2×C4⋊C4—1116no—
618C2×C4⋊C4C22×D1112yes—
619C2×C4⋊C4C22×D1112yes—
620C2×C4⋊C4C22×D1111yescharacteristic
621C2×C4⋊C4C22×D1114yes—
622C2×C4⋊C4C22×D1111yescharacteristic
623C2×C4⋊C4C22×D1112yes—
624C2×C22⋊C4—112no—
625C2×C22⋊C4—114no—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—112no—
628C2×C22⋊C4—112no—
629C2×C22⋊C4—112no—
630C2×C22⋊C4C22×D1112yes—
631C2×C22⋊C4C22×D1114yes—
632C2×C22⋊C4C22×D1114yes—
633C2×C42—112no—
634C2×C42—114no—
635C2×C42—114no—
636C2×C42—114no—
637C2×C42—111no—
638C2×C42—112no—
639C2×C42—112no—
640C2×C42—112no—
641C2×C42—111no—
642C2×C42—1116no—
643C2×C42—111no—
644C2×C42—118no—
645C2×C42C22×D1114yes—
646C2×C42C22×D1112yes—
647C2×C42C22×D1111yescharacteristic
648C2×C11—44no—
649C2×C11#350914yescomplemented
650C2×C11C23×#4111yescharacteristic
651C2×C11C22×2−1+411yescharacteristic
652C2×C11C22×2−1+411yescharacteristic
653D11—24no—
654C24—111no—
655C24C23×D1112yes—
656#41—2232no—
657C2×Q8—28no—
658C2×Q8—24no—
659C2×Q8—118no—
660C2×Q8—114no—
661C2×Q8—1116no—
662C2×Q8—118no—
663C2×Q8—114no—
664C2×Q8—2216no—
665C2×Q8—228no—
666C2×Q8—2264no—
667C2×Q8—228no—
668C2×Q8—224no—
669C2×Q8—224no—
670C2×Q8C23×D1114yes—
671C2×Q8C23×D1118yes—
672C2×D4—24no—
673C2×D4—118no—
674C2×D4—228no—
675C2×D4C23×D1114yes—
676C22×C4—28no—
677C22×C4—111no—
678C22×C4—111no—
679C22×C4—118no—
680C22×C4—114no—
681C22×C4—118no—
682C22×C4—118no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—111no—
687C22×C4—114no—
688C22×C4—112no—
689C22×C4—114no—
690C22×C4—114no—
691C22×C4—1116no—
692C22×C4—224no—
693C22×C4—2216no—
694C22×C4—228no—
695C22×C4—228no—
696C22×C4—224no—
697C22×C4C23×D1118yes—
698C22×C4C23×D1112yes—
699C22×C4C23×D1112yes—
700C22×C4C23×D1111yescharacteristic
701C22×C4C23×D1114yes—
702C22×C4C23×D1112yes—
703C22×C4C23×D1111yescharacteristic
704C22×C4C23×D1111yescharacteristic
705C4⋊C4—1116no—
706C4⋊C4—118no—
707C4⋊C4—1116no—
708C4⋊C4—118no—
709C4⋊C4—118no—
710C4⋊C4—114no—
711C4⋊C4—114no—
712C4⋊C4—118no—
713C4⋊C4—118no—
714C4⋊C4—118no—
715C4⋊C4—118no—
716C4⋊C4—1116no—
717C4⋊C4—1116no—
718C4⋊C4—1116no—
719C4⋊C4—1116no—
720C4⋊C4—1116no—
721C4⋊C4—1116no—
722C4⋊C4—1116no—
723C4⋊C4—118no—
724C4⋊C4—118no—
725C4⋊C4—118no—
726C4⋊C4C23×D1118yes—
727C4⋊C4C23×D1118yes—
728C4⋊C4C23×D1114yes—
729C4⋊C4C23×D11116yes—
730C4⋊C4C23×D1114yes—
731C4⋊C4C23×D1118yes—
732C22⋊C4—118no—
733C22⋊C4—1116no—
734C22⋊C4—1116no—
735C22⋊C4—118no—
736C22⋊C4—118no—
737C22⋊C4—118no—
738C22⋊C4C23×D1118yes—
739C22⋊C4C23×D11116yes—
740C22⋊C4C23×D11116yes—
741C42—114no—
742C42—118no—
743C42—114no—
744C42—118no—
745C42—118no—
746C42—114no—
747C42—1116no—
748C42—1116no—
749C42—1116no—
750C42—118no—
751C42C23×D1114yes—
752C42C23×D11116yes—
753C42C23×D1118yes—
754C11C2×#350911yescharacteristic, complemented, Sylow
755C23—24no—
756C23—24no—
757C23—24no—
758C23—114no—
759C23—112no—
760C23—222no—
761C23—222no—
762C23C24×D1114yes—
763C23C24×D1111yescharacteristic
764Q8—216no—
765Q8—28no—
766Q8—2232no—
767Q8—2216no—
768Q8—2216no—
769Q8—228no—
770Q8—228no—
771D4—28no—
772D4—2216no—
773C2×C4—28no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—216no—
779C2×C4—114no—
780C2×C4—114no—
781C2×C4—112no—
782C2×C4—112no—
783C2×C4—1116no—
784C2×C4—114no—
785C2×C4—114no—
786C2×C4—114no—
787C2×C4—112no—
788C2×C4—118no—
789C2×C4—114no—
790C2×C4—228no—
791C2×C4—2232no—
792C2×C4—2216no—
793C2×C4—2216no—
794C2×C4—224no—
795C2×C4—228no—
796C2×C4—222no—
797C2×C4—224no—
798C2×C4—224no—
799C2×C4—224no—
800C2×C4—228no—
801C2×C4#41×D1114yes—
802C2×C4#6704314yes—
803C2×C4C24×D1114yes—
804C2×C4C24×D1114yes—
805C2×C4C24×D1112yes—
806C2×C4C24×D1118yes—
807C2×C4C24×D1114yes—
808C2×C4C24×D1112yes—
809C2×C4C24×D1112yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—48no—
814C22—114no—
815C22—222no—
816C22—222no—
817C22—228no—
818C22C2×#41×D1112yes—
819C22C2×#6704312yes—
820C22D11×2−1+412yes—
821C22C25×D1111yescharacteristic
822C4—28no—
823C4—22no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—114no—
828C4—114no—
829C4—224no—
830C4—228no—
831C4—224no—
832C4—224no—
833C4—222no—
834C4—224no—
835C4C2×#41×D1114yes—
836C4C2×#6704314yes—
837C2—44no—
838C2—224no—
839C2#1308249614yesdirect product factor
840C2C22×#41×D1111yescharacteristic
841C2C2×D11×2−1+411yescharacteristic
842C2C22×#6704311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#556C2
socleC23×C11C25
prime radicalC22×#4341C22
hypercenterC2×#556D11
hypocenterC11C2×#3509
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #13082496C2direct (N × H)
2. C2×#10623101C2semidirect
3. C2×#10623098C2semidirect
4. C2×#10623252C2semidirect
5. C2×#10623073C2semidirect
6. C2×#10623202C2semidirect
7. C2×#10623060C2semidirect
8. C2×#10623239C2semidirect
9. C2×#10623170C2semidirect
10. C2×#10623232C2semidirect
12. C2×#10623109C2semidirect
13. C2×#10623048C2semidirect
14. C2×#10623153C2semidirect
15. C2×D11×C4⋊Q8C2semidirect
16. C2×#10623103C2semidirect
18. C2×C11×#556C2semidirect
21. C11×#556C22semidirect
42. D11×C4⋊Q8C22semidirect
43. #10623252C22semidirect
44. #10623239C22semidirect
45. #10623232C22semidirect
47. #10623202C22semidirect
48. #10623170C22semidirect
49. #10623153C22semidirect
50. #10623109C22semidirect
51. #10623103C22semidirect
52. #10623101C22semidirect
53. #10623098C22semidirect
54. #10623073C22semidirect
56. #10623060C22semidirect
57. #10623048C22semidirect
340. C2×#556D11semidirect
414. #556C2×D11semidirect
649. C2×C11#3509semidirect
754. C11C2×#3509semidirect
839. C2#13082496direct (N × H)

Maximal subgroups

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

subgroupindex
#130824962
C2×#106231012
C2×#106230982
C2×#106232522
C2×#106230732
C2×#106232022
C2×#106230602
C2×#106232392
C2×#106231702
C2×#106232322
C2×#106232062
C2×#106231092
C2×#106230482
C2×#106231532
C2×D11×C4⋊Q82
C2×#106231032
C2×C4×#43412
C2×C11×#5562
C2×#350911