Finite Group Databasebeta

← C2×#13082596 #15661888

Subgroups — C2×#13082596 #15661888

Order 2816.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082596C2132yesmaximal, direct product factor
2C2×#10623101C211yesmaximal, characteristic, complemented
3C2×#10623110C211yesmaximal, characteristic, complemented
4C2×#10623074C211yesmaximal, characteristic, complemented
5C2×#10623145C212yesmaximal, complemented
6C2×#10623072C212yesmaximal, complemented
7C2×#10623239C214yesmaximal, complemented
8C2×#10623170C212yesmaximal, complemented
9C2×#10623082C211yesmaximal, characteristic, complemented
10C2×#10623082C212yesmaximal, complemented
11C2×#10623049C212yesmaximal, complemented
12C2×#10623191C214yesmaximal, complemented
13C2×#10623001C211yesmaximal, characteristic, complemented
14C2×#10623211C212yesmaximal, complemented
15C2×D11×#125C212yesmaximal, complemented
16C2×#10623054C212yesmaximal, complemented
17C2×C4×#4339C211yesmaximal, characteristic, complemented
18C2×C11×#529C211yesmaximal, characteristic, complemented
19C22×#4339C2211yescharacteristic
20C22×#4339C2212yes—
21C11×#529C22116yescomplemented
22C2×C11×#126C2212yes—
23C2×C11×#125C2211yescharacteristic
24C2×C11×#124C2211yescharacteristic
25C2×C11×#123C2212yes—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11C2212yes—
30C2×C4×D4×C11C2211yescharacteristic
31C2×C11×#117C2212yes—
32C22×C42×C11C2211yescharacteristic
33C2×#66999C2212yes—
34C2×Q8×Dic11C2212yes—
35C2×#66991C2212yes—
36C2×#66991C2214yes—
37C2×#66988C2214yes—
38C2×D4×Dic11C2212yes—
39C2×C4×C22⋊D11C2212yes—
40C2×C4×C22⋊D11C2212yes—
41C2×#66979C2212yes—
42C2×#66979C2211yescharacteristic
43C22×C4⋊Dic11C2212yes—
44C2×#66977C2212yes—
45C2×#66977C2212yes—
46C2×#66977C2212yes—
47C2×#66977C2212yes—
48#10623239C22164yescomplemented
49D11×#125C22132yescomplemented
50#10623211C22132yescomplemented
51#10623191C22164yescomplemented
52#10623170C22132yescomplemented
53#10623145C22132yescomplemented
54#10623110C22116yescomplemented
55#10623101C22116yescomplemented
56#10623082C22116yescomplemented
57#10623082C22132yescomplemented
58#10623074C22116yescomplemented
59#10623072C22132yescomplemented
60#10623054C22132yescomplemented
61#10623049C22132yescomplemented
62C2×#66949C2214yes—
63C2×#66945C2214yes—
64C2×C4⋊C4×D11C2212yes—
65C2×C4⋊C4×D11C2214yes—
66C2×C4⋊C4×D11C2212yes—
67C2×C4⋊C4×D11C2214yes—
68C2×#66943C2212yes—
69C2×#66943C2212yes—
70C2×#66943C2214yes—
71C2×#66942C2214yes—
72C2×#66942C2214yes—
73C2×#66942C2214yes—
74C2×#66936C2214yes—
75C2×#66936C2214yes—
76C2×#66936C2214yes—
77C2×(C22⋊D11)⋊C4C2214yes—
78C2×(C22⋊D11)⋊C4C2214yes—
79C2×#66932C2214yes—
80C2×#66932C2214yes—
81C2×#66932C2214yes—
82C2×#66931C2214yes—
83C2×#66930C2214yes—
84C4×#4339C22116yescomplemented
85C2×C4×D44C2211yescharacteristic
86C2×C4×D44C2212yes—
87C2×C4×D44C2211yescharacteristic
88C2×#66925C2212yes—
89C2×C42×D11C2212yes—
90#10623001C22116yescomplemented
91C2×#66923C2212yes—
92C2×#66923C2212yes—
93C2×#66922C2211yescharacteristic
94C2×#66922C2211yescharacteristic
95C2×#66922C2212yes—
96C2×C4×Dic22C2212yes—
97C2×C4×Dic22C2212yes—
98C2×C4×Dic22C2211yescharacteristic
99C2×C4×Dic22C2212yes—
100C2×C4×Dic22C2211yescharacteristic
101C22×Q8×C11C2311yescharacteristic
102C22×D4×C11C2311yescharacteristic
103C22×D4×C11C2312yes—
104C23×C4×C11C2312yes—
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2311yescharacteristic
108C22×C22⋊D11C2314yes—
109C22×C22⋊D11C2312yes—
110C23×Dic11C2314yes—
111C2×#4339—28no—
112C2×#4339—216no—
113C2×#4339C2318yes—
114C2×#4339C23116yes—
115C22×D44C2311yescharacteristic
116C22×C4×D11C2312yes—
117C22×C4×D11C2312yes—
118C22×C4×D11C2314yes—
119C22×C4×D11C2312yes—
120C22×C4×D11C2314yes—
121C22×Dic22C2312yes—
122C22×Dic22C2311yescharacteristic
123C22×Dic22C2312yes—
124C11×#126C23116yes—
125C11×#125C2318yes—
126C11×#124C2318yes—
127C11×#123C23116yes—
128C11×C22⋊Q8C2318yes—
129C11×#121C2318yes—
130C4×Q8×C11C2318yes—
131C4×D4×C11C23116yes—
132C4×D4×C11C2318yes—
133C11×#117C23116yes—
134C2×C11×C4⋊C4C2312yes—
135C2×C11×C4⋊C4C2312yes—
136C2×C11×C4⋊C4C2312yes—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C22⋊C4C2312yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2312yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2312yes—
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2318yes—
151C2×C22⋊Dic11C2314yes—
152C2×C22⋊Dic11C2314yes—
153C2×C22⋊Dic11C2312yes—
154C2×C22⋊Dic11C2314yes—
155#66999C23116yes—
156Q8×Dic11C23116yes—
157#66991C23132yes—
158#66991C23116yes—
159#66988C23132yes—
160D4×Dic11C23116yes—
161C4×C22⋊D11C23116yes—
162C4×C22⋊D11C23116yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2314yes—
166#66979C23116yes—
167#66979C2318yes—
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2312yes—
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2312yes—
173C2×C4⋊Dic11C2312yes—
174C2×C4⋊Dic11C2314yes—
175C2×C4⋊Dic11C2314yes—
176C2×C4⋊Dic11C2314yes—
177C2×C4⋊Dic11C23116yes—
178#66977C23116yes—
179#66977C23116yes—
180#66977C23116yes—
181#66977C23116yes—
182C2×Dic11⋊C4C2314yes—
183C2×Dic11⋊C4C2314yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2314yes—
187C2×Dic11⋊C4C2314yes—
188C2×Dic11⋊C4C2314yes—
189C2×Dic11⋊C4C2314yes—
190C2×Dic11⋊C4C2314yes—
191C2×C4×Dic11C2314yes—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2312yes—
194C2×C4×Dic11C2314yes—
195C2×C4×Dic11C2312yes—
196#66949C23132yes—
197#66945C23132yes—
198C4⋊C4×D11C23132yes—
199C4⋊C4×D11C23132yes—
200C4⋊C4×D11C23116yes—
201C4⋊C4×D11C23116yes—
202#66943C23132yes—
203#66943C23116yes—
204#66943C23116yes—
205#66942C23132yes—
206#66942C23132yes—
207#66942C23132yes—
208#66936C23132yes—
209#66936C23132yes—
210#66936C23132yes—
211(C22⋊D11)⋊C4C23132yes—
212(C22⋊D11)⋊C4C23132yes—
213#66932C23132yes—
214#66932C23132yes—
215#66932C23132yes—
216#66931C23132yes—
217#66930C23132yes—
218C4×D44C2318yes—
219C4×D44C2318yes—
220C4×D44C23116yes—
221#66925C23116yes—
222C42×D11C23116yes—
223#66923C23116yes—
224#66923C23116yes—
225#66922C2318yes—
226#66922C2318yes—
227#66922C23116yes—
228C4×Dic22C23116yes—
229C4×Dic22C23116yes—
230C4×Dic22C2318yes—
231C4×Dic22C2318yes—
232C4×Dic22C23116yes—
233C2×#3515—111nomaximal, Sylow
234C24×C11C2411yescharacteristic
235C24×C11C2412yes—
236C23×D11C2412yes—
237C2×Q8×C11—24no—
238C2×Q8×C11C2414yes—
239C2×D4×C11—24no—
240C2×D4×C11—44no—
241C2×D4×C11C2414yes—
242C2×D4×C11C2418yes—
243C22×C4×C11—28no—
244C22×C4×C11—24no—
245C22×C4×C11—24no—
246C22×C4×C11—42no—
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2412yes—
251C22×C4×C11C2412yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2418yes—
255C22×C4×C11C2414yes—
256C22×C4×C11C2414yes—
257C22×C4×C11C2414yes—
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C2×C22⋊D11—216no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11C24116yes—
263C2×C22⋊D11C2418yes—
264C22×Dic11—48no—
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267C22×Dic11C2414yes—
268C22×Dic11C2412yes—
269C22×Dic11C2414yes—
270C22×Dic11C24116yes—
271#4339—232no—
272#4339—264no—
273C2×D44#4118yes—
274C2×D44C2414yes—
275C2×C4×D11—28no—
276C2×C4×D11—216no—
277C2×C4×D11—28no—
278C2×C4×D11—44no—
279C2×C4×D11—48no—
280C2×C4×D11C2418yes—
281C2×C4×D11C2418yes—
282C2×C4×D11C24116yes—
283C2×C4×D11C2418yes—
284C2×C4×D11C24116yes—
285C2×Dic22—28no—
286C2×Dic22—24no—
287C2×Dic22—44no—
288C2×Dic22C2418yes—
289C2×Dic22C2414yes—
290C2×Dic22C2418yes—
291C11×C4⋊C4C2418yes—
292C11×C4⋊C4C2418yes—
293C11×C4⋊C4C2418yes—
294C11×C4⋊C4C2414yes—
295C11×C4⋊C4C2414yes—
296C11×C4⋊C4C2418yes—
297C11×C22⋊C4C2418yes—
298C11×C22⋊C4C2418yes—
299C11×C22⋊C4C2418yes—
300C11×C22⋊C4C2418yes—
301C11×C22⋊C4C2418yes—
302C42×C11C2414yes—
303C42×C11C2414yes—
304C42×C11C2414yes—
305C42×C11C2418yes—
306C42×C11C2414yes—
307C22⋊Dic11C24116yes—
308C22⋊Dic11C24116yes—
309C22⋊Dic11C2418yes—
310C22⋊Dic11C24116yes—
311(C2×D11)⋊C4C2418yes—
312(C2×D11)⋊C4C2418yes—
313(C2×D11)⋊C4C24116yes—
314C4⋊Dic11C2414yes—
315C4⋊Dic11C2418yes—
316C4⋊Dic11C2418yes—
317C4⋊Dic11C2414yes—
318C4⋊Dic11C2418yes—
319C4⋊Dic11C2418yes—
320C4⋊Dic11C24116yes—
321C4⋊Dic11C24116yes—
322C4⋊Dic11C24116yes—
323Dic11⋊C4C24116yes—
324Dic11⋊C4C24116yes—
325Dic11⋊C4C2418yes—
326Dic11⋊C4C2418yes—
327Dic11⋊C4C24116yes—
328Dic11⋊C4C24116yes—
329Dic11⋊C4C24116yes—
330Dic11⋊C4C24116yes—
331Dic11⋊C4C24116yes—
332C4×Dic11C24116yes—
333C4×Dic11C2418yes—
334C4×Dic11C2418yes—
335C4×Dic11C24116yes—
336C4×Dic11C2418yes—
337#3515—1132no—
338C2×#557—111no—
339C2×#554—111no—
340C2×#554—111no—
341C2×#553—112no—
342C2×#552—114no—
343C2×#552—112no—
344C2×#552—112no—
345C2×#547—111no—
346C2×#547—112no—
347C2×#541—112no—
348C2×#539—114no—
349C2×#533—111no—
350C2×#529—112no—
351C2×#529D1111yescharacteristic, complemented
352C22×#125—112no—
353C2×#520—112no—
354C2×C4×#41—111no—
355C23×C11—22no—
356C23×C11—24no—
357C23×C11—22no—
358C23×C11—24no—
359C23×C11—24no—
360C23×C11—22no—
361C23×C11C2512yes—
362C23×C11C2514yes—
363C23×C11C2511yescharacteristic
364C22×D11—24no—
365C22×D11—24no—
366C22×D11C2×#4118yes—
367C22×D11C2514yes—
368Q8×C11—28no—
369D4×C11—28no—
370D4×C11—48no—
371C2×C4×C11—22no—
372C2×C4×C11—24no—
373C2×C4×C11—22no—
374C2×C4×C11—24no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—24no—
378C2×C4×C11—216no—
379C2×C4×C11—28no—
380C2×C4×C11—28no—
381C2×C4×C11—44no—
382C2×C4×C11C2×#4114yes—
383C2×C4×C112−1+414yes—
384C2×C4×C11C2512yes—
385C2×C4×C11C2512yes—
386C2×C4×C11C2512yes—
387C2×C4×C11C2514yes—
388C2×C4×C11C2514yes—
389C2×C4×C11C2514yes—
390C2×C4×C11C2512yes—
391C2×C4×C11C2512yes—
392C2×C4×C11C2512yes—
393C22⋊D11—232no—
394C22⋊D11—216no—
395C2×Dic11—24no—
396C2×Dic11—28no—
397C2×Dic11—24no—
398C2×Dic11—28no—
399C2×Dic11—24no—
400C2×Dic11—416no—
401C2×Dic11C2514yes—
402C2×Dic11C2514yes—
403C2×Dic11C2518yes—
404C2×Dic11C2514yes—
405C2×Dic11C2518yes—
406D44C2×#41116yes—
407C4×D11—216no—
408C4×D11—232no—
409C4×D11—216no—
410C4×D11—416no—
411C4×D11—48no—
412Dic22—216no—
413Dic22—28no—
414Dic22—48no—
415C22×#41—111no—
416C22×#41—112no—
417#557—1116no—
418#554—1116no—
419#554—1116no—
420#553—1132no—
421#552—1164no—
422#552—1132no—
423#552—1132no—
424#547—1116no—
425#547—1132no—
426#541—1132no—
427#539—1164no—
428#533—1116no—
429C2×C4⋊Q8—111no—
430C2×C4⋊Q8—111no—
431C2×C4⋊Q8—112no—
432#529—1132no—
433#529C2×D11116yescomplemented
434C2×#126—114no—
435C2×#126—114no—
436C2×#126—114no—
437C2×#126C2×D1112yes—
438C2×#125—1132no—
439C2×#125—114no—
440C2×#125—114no—
441C2×#125—114no—
442C2×#125—112no—
443C2×#125—112no—
444C2×#125—114no—
445C2×#125—112no—
446C2×#125—112no—
447C2×#125C2×D1111yescharacteristic
448C2×#124C2×D1111yescharacteristic
449C2×#123—114no—
450C2×#123—114no—
451C2×#123—114no—
452C2×#123—114no—
453C2×#123C2×D1112yes—
454C2×C22⋊Q8—112no—
455C2×C22⋊Q8—112no—
456C2×C22⋊Q8—112no—
457C2×C22⋊Q8—112no—
458C2×C22⋊Q8—112no—
459C2×C22⋊Q8—114no—
460C2×C22⋊Q8—114no—
461C2×C22⋊Q8C2×D1111yescharacteristic
462C2×#121—112no—
463C2×#121—114no—
464C2×#121C2×D1111yescharacteristic
465#520—1132no—
466C4×#41—1116no—
467C2×C4×Q8—112no—
468C2×C4×Q8—111no—
469C2×C4×Q8—111no—
470C2×C4×Q8—112no—
471C2×C4×Q8—112no—
472C2×C4×Q8—112no—
473C2×C4×Q8C2×D1111yescharacteristic
474C2×C4×D4—112no—
475C2×C4×D4—112no—
476C2×C4×D4—112no—
477C2×C4×D4—114no—
478C2×C4×D4—114no—
479C2×C4×D4—111no—
480C2×C4×D4—111no—
481C2×C4×D4—112no—
482C2×C4×D4C2×D1112yes—
483C2×C4×D4C2×D1111yescharacteristic
484C2×#117—111no—
485C2×#117—112no—
486C2×#117—114no—
487C2×#117—114no—
488C2×#117—112no—
489C2×#117C2×D1112yes—
490C22×C4⋊C4—112no—
491C22×C4⋊C4—114no—
492C22×C4⋊C4—112no—
493C22×C4⋊C4—114no—
494C22×C4⋊C4—112no—
495C22×C42—112no—
496C22×C42C2×D1111yescharacteristic
497C22×C11—22no—
498C22×C11—24no—
499C22×C11—22no—
500C22×C11—24no—
501C22×C11—22no—
502C22×C11—24no—
503C22×C11—44no—
504C22×C11—48no—
505C22×C11C22×#4112yes—
506C22×C11C2×2−1+412yes—
507C22×C11#58512yes—
508C22×C11C2611yescharacteristic
509C2×D11—24no—
510C2×D11—24no—
511C2×D11—216no—
512C2×D11C22×#4118yes—
513C4×C11—22no—
514C4×C11—24no—
515C4×C11—22no—
516C4×C11—24no—
517C4×C11—22no—
518C4×C11—22no—
519C4×C11—24no—
520C4×C11C22×#4114yes—
521C4×C11C2×2−1+414yes—
522Dic11—24no—
523Dic11—28no—
524Dic11—24no—
525Dic11—28no—
526Dic11—24no—
527C2×#41—118no—
528C2×#41—1116no—
529C2×#41—228no—
530C2×#41—2216no—
531C22×Q8—111no—
532C22×Q8—112no—
533C22×Q8—112no—
534C22×Q8C22×D1111yescharacteristic
535C22×D4—112no—
536C22×D4—114no—
537C22×D4—111no—
538C22×D4C22×D1111yescharacteristic
539C22×D4C22×D1112yes—
540C23×C4—114no—
541C23×C4—114no—
542C23×C4—112no—
543C23×C4—112no—
544C23×C4—114no—
545C23×C4—112no—
546C23×C4C22×D1112yes—
547C23×C4C22×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550C4⋊Q8—118no—
551C4⋊Q8—118no—
552C4⋊Q8—1116no—
553#126—1132no—
554#126—1132no—
555#126—1132no—
556#126C22×D11116yes—
557#125—1132no—
558#125—1132no—
559#125—1116no—
560#125—1116no—
561#125—1132no—
562#125—1132no—
563#125—1116no—
564#125—1116no—
565#125C22×D1118yes—
566#124C22×D1118yes—
567#123—1132no—
568#123—1132no—
569#123—1132no—
570#123—1132no—
571#123C22×D11116yes—
572C22⋊Q8—1116no—
573C22⋊Q8—1116no—
574C22⋊Q8—1116no—
575C22⋊Q8—1116no—
576C22⋊Q8—1116no—
577C22⋊Q8—1132no—
578C22⋊Q8—1132no—
579C22⋊Q8C22×D1118yes—
580#121—1116no—
581#121—1132no—
582#121C22×D1118yes—
583C4×Q8—1116no—
584C4×Q8—118no—
585C4×Q8—118no—
586C4×Q8—1116no—
587C4×Q8—1116no—
588C4×Q8—1116no—
589C4×Q8C22×D1118yes—
590C4×D4—1116no—
591C4×D4—1116no—
592C4×D4—1116no—
593C4×D4—1132no—
594C4×D4—1132no—
595C4×D4—118no—
596C4×D4—118no—
597C4×D4—1116no—
598C4×D4C22×D11116yes—
599C4×D4C22×D1118yes—
600#117—118no—
601#117—1116no—
602#117—1132no—
603#117—1132no—
604#117—1116no—
605#117C22×D11116yes—
606C2×C4⋊C4—111no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—112no—
609C2×C4⋊C4—112no—
610C2×C4⋊C4—114no—
611C2×C4⋊C4—112no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—114no—
614C2×C4⋊C4—1116no—
615C2×C4⋊C4—114no—
616C2×C4⋊C4—114no—
617C2×C4⋊C4—114no—
618C2×C4⋊C4—114no—
619C2×C4⋊C4—112no—
620C2×C4⋊C4—111no—
621C2×C4⋊C4—112no—
622C2×C4⋊C4—114no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—114no—
625C2×C4⋊C4—1132no—
626C2×C4⋊C4—1116no—
627C2×C4⋊C4—1132no—
628C2×C4⋊C4—1116no—
629C2×C4⋊C4C22×D1112yes—
630C2×C4⋊C4C22×D1111yescharacteristic
631C2×C4⋊C4C22×D1112yes—
632C2×C4⋊C4C22×D1111yescharacteristic
633C2×C4⋊C4C22×D1112yes—
634C2×C4⋊C4C22×D1112yes—
635C2×C22⋊C4—112no—
636C2×C22⋊C4—114no—
637C2×C22⋊C4—114no—
638C2×C22⋊C4—114no—
639C2×C22⋊C4—112no—
640C2×C22⋊C4—112no—
641C2×C22⋊C4—114no—
642C2×C22⋊C4C22×D1112yes—
643C2×C22⋊C4C22×D1112yes—
644C2×C22⋊C4C22×D1112yes—
645C2×C22⋊C4C22×D1112yes—
646C2×C22⋊C4C22×D1112yes—
647C2×C42—112no—
648C2×C42—114no—
649C2×C42—114no—
650C2×C42—112no—
651C2×C42—112no—
652C2×C42—1116no—
653C2×C42C22×D1111yescharacteristic
654C2×C42C22×D1111yescharacteristic
655C2×C42C22×D1112yes—
656C2×C42C22×D1111yescharacteristic
657C2×C42C22×D1118yes—
658C2×C42C22×D1111yescharacteristic
659C2×C11—42no—
660C2×C11—44no—
661C2×C11#351514yescomplemented
662C2×C11C23×#4111yescharacteristic
663C2×C11C22×2−1+411yescharacteristic
664C2×C11C2×#58511yescharacteristic
665D11—28no—
666C24—112no—
667C24C23×D1111yescharacteristic
668C24C23×D1112yes—
669#41—2232no—
670#41—2264no—
671C2×Q8—24no—
672C2×Q8—114no—
673C2×Q8—118no—
674C2×Q8—118no—
675C2×Q8—224no—
676C2×Q8—228no—
677C2×Q8—444no—
678C2×Q8C23×D1114yes—
679C2×D4—24no—
680C2×D4—44no—
681C2×D4—118no—
682C2×D4—1116no—
683C2×D4—118no—
684C2×D4—114no—
685C2×D4—228no—
686C2×D4—2216no—
687C2×D4C23×D1114yes—
688C2×D4C23×D1118yes—
689C22×C4—28no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—42no—
693C22×C4—112no—
694C22×C4—112no—
695C22×C4—114no—
696C22×C4—112no—
697C22×C4—114no—
698C22×C4—1116no—
699C22×C4—118no—
700C22×C4—118no—
701C22×C4—1116no—
702C22×C4—118no—
703C22×C4—1116no—
704C22×C4—2216no—
705C22×C4—228no—
706C22×C4—228no—
707C22×C4—444no—
708C22×C4—448no—
709C22×C4—448no—
710C22×C4C23×D1114yes—
711C22×C4C23×D1114yes—
712C22×C4C23×D1118yes—
713C22×C4C23×D1111yescharacteristic
714C22×C4C23×D1111yescharacteristic
715C22×C4C23×D1111yescharacteristic
716C22×C4C23×D1112yes—
717C22×C4C23×D1111yescharacteristic
718C22×C4C23×D1112yes—
719C22×C4C23×D1112yes—
720C22×C4C23×D1114yes—
721C22×C4C23×D1111yescharacteristic
722C22×C4C23×D1111yescharacteristic
723C4⋊C4—114no—
724C4⋊C4—1116no—
725C4⋊C4—118no—
726C4⋊C4—118no—
727C4⋊C4—1116no—
728C4⋊C4—118no—
729C4⋊C4—1116no—
730C4⋊C4—1116no—
731C4⋊C4—1116no—
732C4⋊C4—1116no—
733C4⋊C4—1116no—
734C4⋊C4—1116no—
735C4⋊C4—118no—
736C4⋊C4—114no—
737C4⋊C4—118no—
738C4⋊C4—1116no—
739C4⋊C4—118no—
740C4⋊C4—1116no—
741C4⋊C4C23×D1118yes—
742C4⋊C4C23×D1114yes—
743C4⋊C4C23×D1118yes—
744C4⋊C4C23×D1114yes—
745C4⋊C4C23×D1118yes—
746C4⋊C4C23×D1118yes—
747C22⋊C4—118no—
748C22⋊C4—1116no—
749C22⋊C4—1116no—
750C22⋊C4—1116no—
751C22⋊C4—118no—
752C22⋊C4—118no—
753C22⋊C4—1116no—
754C22⋊C4C23×D1118yes—
755C22⋊C4C23×D1118yes—
756C22⋊C4C23×D1118yes—
757C22⋊C4C23×D1118yes—
758C22⋊C4C23×D1118yes—
759C42—118no—
760C42—118no—
761C42—118no—
762C42—1116no—
763C42—1116no—
764C42C23×D1114yes—
765C42C23×D1114yes—
766C42C23×D1114yes—
767C42C23×D1114yes—
768C42C23×D1118yes—
769C11C2×#351511yescharacteristic, complemented, Sylow
770C23—22no—
771C23—24no—
772C23—22no—
773C23—24no—
774C23—22no—
775C23—24no—
776C23—118no—
777C23—114no—
778C23—224no—
779C23—224no—
780C23C24×D1112yes—
781C23C24×D1114yes—
782C23C24×D1111yescharacteristic
783Q8—28no—
784Q8—228no—
785Q8—2216no—
786Q8—448no—
787D4—28no—
788D4—48no—
789D4—1116no—
790D4—2216no—
791D4—2232no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—28no—
800C2×C4—216no—
801C2×C4—28no—
802C2×C4—44no—
803C2×C4—114no—
804C2×C4—114no—
805C2×C4—114no—
806C2×C4—118no—
807C2×C4—118no—
808C2×C4—2216no—
809C2×C4—2232no—
810C2×C4—228no—
811C2×C4—224no—
812C2×C4—224no—
813C2×C4—224no—
814C2×C4—228no—
815C2×C4—2216no—
816C2×C4—448no—
817C2×C4—4416no—
818C2×C4—4416no—
819C2×C4#41×D1114yes—
820C2×C4#6704314yes—
821C2×C4C24×D1112yes—
822C2×C4C24×D1112yes—
823C2×C4C24×D1112yes—
824C2×C4C24×D1114yes—
825C2×C4C24×D1112yes—
826C2×C4C24×D1114yes—
827C2×C4C24×D1114yes—
828C2×C4C24×D1112yes—
829C2×C4C24×D1112yes—
830C22—22no—
831C22—24no—
832C22—22no—
833C22—24no—
834C22—22no—
835C22—24no—
836C22—44no—
837C22—48no—
838C22—118no—
839C22—224no—
840C22—224no—
841C22—2216no—
842C22C2×#41×D1112yes—
843C22C2×#6704312yes—
844C22#1062345312yes—
845C22C25×D1111yescharacteristic
846C4—22no—
847C4—24no—
848C4—22no—
849C4—24no—
850C4—22no—
851C4—22no—
852C4—24no—
853C4—224no—
854C4—228no—
855C4—224no—
856C4—224no—
857C4—228no—
858C4C2×#41×D1114yes—
859C4C2×#6704314yes—
860C2—42no—
861C2—44no—
862C2—228no—
863C2#1308259614yesdirect product factor
864C2C22×#41×D1111yescharacteristic
865C2C22×#6704311yescharacteristic
866C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#529C2
socleC23×C11C25
hypercenterC2×#529D11
hypocenterC11C2×#3515
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #13082596C2direct (N × H)
2. C2×#10623101C2semidirect
3. C2×#10623110C2semidirect
4. C2×#10623074C2semidirect
5. C2×#10623145C2semidirect
6. C2×#10623072C2semidirect
7. C2×#10623239C2semidirect
8. C2×#10623170C2semidirect
9. C2×#10623082C2semidirect
10. C2×#10623082C2semidirect
11. C2×#10623049C2semidirect
12. C2×#10623191C2semidirect
13. C2×#10623001C2semidirect
14. C2×#10623211C2semidirect
15. C2×D11×#125C2semidirect
16. C2×#10623054C2semidirect
17. C2×C4×#4339C2semidirect
18. C2×C11×#529C2semidirect
21. C11×#529C22semidirect
48. #10623239C22semidirect
49. D11×#125C22semidirect
50. #10623211C22semidirect
51. #10623191C22semidirect
52. #10623170C22semidirect
53. #10623145C22semidirect
54. #10623110C22semidirect
55. #10623101C22semidirect
56. #10623082C22semidirect
57. #10623082C22semidirect
58. #10623074C22semidirect
59. #10623072C22semidirect
60. #10623054C22semidirect
61. #10623049C22semidirect
84. C4×#4339C22semidirect
90. #10623001C22semidirect
351. C2×#529D11semidirect
433. #529C2×D11semidirect
661. C2×C11#3515semidirect
769. C11C2×#3515semidirect
863. C2#13082596direct (N × H)

Maximal subgroups

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

subgroupindex
#130825962
C2×#106231012
C2×#106231102
C2×#106230742
C2×#106231452
C2×#106230722
C2×#106232392
C2×#106231702
C2×#106230822
C2×#106230492
C2×#106231912
C2×#106230012
C2×#106232112
C2×D11×#1252
C2×#106230542
C2×C4×#43392
C2×C11×#5292
C2×#351511