Finite Group Databasebeta

← C2×#13082370 #15662204

Subgroups — C2×#13082370 #15662204

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#13082370C2132yesmaximal, direct product factor
2C2×#10623073C212yesmaximal, complemented
3C2×#10623074C212yesmaximal, complemented
4C2×#10623072C212yesmaximal, complemented
5C2×#10623072C212yesmaximal, complemented
6C2×#10623181C214yesmaximal, complemented
7C2×#10623118C214yesmaximal, complemented
8C2×#10623050C211yesmaximal, characteristic, complemented
9C2×#10623134C212yesmaximal, complemented
10C2×#10623156C212yesmaximal, complemented
11C2×#10623356C211yesmaximal, characteristic, complemented
12C2×#10623153C212yesmaximal, complemented
13C2×#10623131C212yesmaximal, complemented
14C22×#66977C211yesmaximal, characteristic, complemented
15C2×#10623358C211yesmaximal, characteristic, complemented
16C2×#10623047C211yesmaximal, characteristic, complemented
17C22×#66979C211yesmaximal, characteristic, complemented
18C2×C11×#525C211yesmaximal, characteristic
19C22×C11×#41C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic
21C23×Dic22C2211yescharacteristic
22C11×#525C22116yes—
23C2×C11×#123C2212yes—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C11×#120C2212yes—
29C2×C4×D4×C11C2212yes—
30C2×C4×D4×C11C2212yes—
31C2×C11×#117C2211yescharacteristic
32C22×C22⋊Dic11C2212yes—
33C22×C22⋊Dic11C2212yes—
34#10623358C22116yescomplemented
35#10623356C22116yescomplemented
36C2×Q8×Dic11C2212yescomplemented
37C2×#66997C2212yescomplemented
38C2×#66989C2214yes—
39C2×#66989C2212yescomplemented
40C2×#66988C2214yes—
41C2×#66988C2214yes—
42C2×#66988C2214yes—
43C2×D4×Dic11C2214yes—
44C2×D4×Dic11C2214yes—
45C2×D4×Dic11C2212yescomplemented
46C2×#66979C2212yes—
47C2×#66979C2211yescharacteristic
48C2×#66979C2211yescharacteristic
49C2×#66979C2211yescharacteristic
50C2×#66979C2212yes—
51C2×#66979C2211yescharacteristic
52C2×#66979C22116yescomplemented
53C2×#66979C2212yescomplemented
54C22×C4⋊Dic11C2211yescharacteristic
55C22×C4⋊Dic11C2211yescharacteristic
56C22×C4⋊Dic11C2211yescharacteristic
57C22×C4⋊Dic11C2212yescomplemented
58C2×#66977C2212yes—
59C2×#66977C2212yes—
60C2×#66977C2212yes—
61C2×#66977C2212yes—
62C2×#66977C22116yescomplemented
63C2×#66977C2212yescomplemented
64C2×#66977C2212yescomplemented
65C22×Dic11⋊C4C2212yes—
66C22×C4×Dic11C2212yes—
67#10623181C22164yescomplemented
68#10623156C22132yescomplemented
69#10623153C22132yescomplemented
70#10623134C22132yescomplemented
71#10623131C22132yescomplemented
72#10623118C22164yescomplemented
73#10623074C22132yescomplemented
74#10623073C22132yescomplemented
75#10623072C22132yescomplemented
76#10623072C22132yescomplemented
77#10623050C22116yescomplemented
78#10623047C22116yescomplemented
79C2×#66943C2214yescomplemented
80C2×#66943C2212yescomplemented
81C2×#66942C2214yescomplemented
82C2×#66942C2214yescomplemented
83C2×#66941C2212yescomplemented
84C2×#66940C2214yescomplemented
85C2×#66940C2212yescomplemented
86C2×#66940C2212yescomplemented
87C2×#66932C2214yes—
88C2×#66932C2214yes—
89C2×#66932C2214yescomplemented
90C2×#66932C2214yescomplemented
91C2×#66931C2214yes—
92C2×#66931C2214yes—
93C2×#66931C2214yescomplemented
94C2×#66930C2214yes—
95C2×#66930C2214yes—
96C2×#66930C2214yescomplemented
97C2×#66923C2212yescomplemented
98C2×#66922C2212yescomplemented
99C2×C4×Dic22C2212yescomplemented
100C2×C4×Dic22C2212yescomplemented
101C25×C11C2311yescharacteristic
102C2×C11×#41—28no—
103C2×C11×#41C2318yes—
104C22×Q8×C11C2311yescharacteristic
105C22×D4×C11C2312yes—
106C22×D4×C11C2312yes—
107C22×D4×C11C2311yescharacteristic
108C22×D4×C11C2312yes—
109C23×C4×C11—28no—
110C23×C4×C11C2311yescharacteristic
111C23×C4×C11C2311yescharacteristic
112C23×C4×C11C2311yescharacteristic
113C23×C4×C11C2311yescharacteristic
114C23×C4×C11C2311yescharacteristic
115C23×C4×C11C2312yes—
116C23×C4×C11C2318yes—
117C23×C4×C11C2311yescharacteristic
118C23×Dic11C2312yes—
119C23×Dic11C2312yes—
120C23×Dic11C2314yes—
121C23×Dic11C2312yes—
122C23×Dic11C2312yes—
123C22×Dic22—28no—
124C22×Dic22C2312yes—
125C22×Dic22C2312yes—
126C22×Dic22C2318yes—
127C22×Dic22C2314yes—
128C11×#123C23116yes—
129C11×C22⋊Q8C2318yes—
130C11×C22⋊Q8C2318yes—
131C11×#121C2318yes—
132C11×#121C2318yes—
133C11×#120C23116yes—
134C4×D4×C11C23116yes—
135C4×D4×C11C23116yes—
136C11×#117C2318yes—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2312yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C42×C11C2312yes—
147C2×C22⋊Dic11C2312yes—
148C2×C22⋊Dic11C2314yes—
149C2×C22⋊Dic11C2314yes—
150C2×C22⋊Dic11C2312yes—
151C2×C22⋊Dic11C2314yes—
152C2×C22⋊Dic11C2314yes—
153C2×C22⋊Dic11C2312yes—
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2314yes—
156C2×C22⋊Dic11C23116yes—
157C2×C22⋊Dic11C23116yes—
158Q8×Dic11C23116yescomplemented
159#66997C23116yescomplemented
160#66989C23132yes—
161#66989C23116yescomplemented
162#66988C23132yes—
163#66988C23132yes—
164#66988C23132yes—
165D4×Dic11C23132yes—
166D4×Dic11C23132yes—
167D4×Dic11C23116yescomplemented
168#66979C2318yes—
169#66979C2318yes—
170#66979C2318yes—
171#66979C2318yes—
172#66979C23116yes—
173#66979C23116yes—
174#66979C23116yescomplemented
175C2×C4⋊Dic11C2311yescharacteristic
176C2×C4⋊Dic11C2311yescharacteristic
177C2×C4⋊Dic11C2311yescharacteristic
178C2×C4⋊Dic11C2312yes—
179C2×C4⋊Dic11C2314yes—
180C2×C4⋊Dic11C2311yescharacteristic
181C2×C4⋊Dic11C2314yes—
182C2×C4⋊Dic11C2312yes—
183C2×C4⋊Dic11C2312yes—
184C2×C4⋊Dic11C2312yes—
185C2×C4⋊Dic11C2318yes—
186C2×C4⋊Dic11C2318yes—
187C2×C4⋊Dic11C2318yes—
188C2×C4⋊Dic11C23116yescomplemented
189#66977C23116yes—
190#66977C23116yes—
191#66977C23116yes—
192#66977C23116yes—
193#66977C23116yescomplemented
194#66977C23116yescomplemented
195C2×Dic11⋊C4C2314yes—
196C2×Dic11⋊C4C2314yes—
197C2×Dic11⋊C4C2314yes—
198C2×Dic11⋊C4C2314yes—
199C2×Dic11⋊C4C2314yes—
200C2×Dic11⋊C4C2314yes—
201C2×Dic11⋊C4C2314yes—
202C2×Dic11⋊C4C2314yes—
203C2×Dic11⋊C4C23116yes—
204C2×C4×Dic11C2314yes—
205C2×C4×Dic11C2314yes—
206C2×C4×Dic11C2314yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C23116yes—
212#66943C23116yescomplemented
213#66943C23132yescomplemented
214#66942C23132yescomplemented
215#66942C23132yescomplemented
216#66941C23116yescomplemented
217#66940C23116yescomplemented
218#66940C23116yescomplemented
219#66940C23132yescomplemented
220#66932C23132yes—
221#66932C23132yes—
222#66932C23132yescomplemented
223#66932C23132yescomplemented
224#66931C23132yes—
225#66931C23132yes—
226#66931C23132yescomplemented
227#66930C23132yes—
228#66930C23132yes—
229#66930C23132yescomplemented
230#66923C23116yescomplemented
231#66922C23116yescomplemented
232C4×Dic22C23116yescomplemented
233C4×Dic22C23116yescomplemented
234C2×#3495—111nomaximal, Sylow
235C24×C11—24no—
236C24×C11—24no—
237C24×C11—42no—
238C24×C11C2411yescharacteristic
239C24×C11C2412yes—
240C24×C11C2414yes—
241C24×C11C2411yescharacteristic
242C24×C11C2411yescharacteristic
243C11×#41—232no—
244C2×Q8×C11—24no—
245C2×Q8×C11C2414yes—
246C2×D4×C11—28no—
247C2×D4×C11—28no—
248C2×D4×C11—24no—
249C2×D4×C11—44no—
250C2×D4×C11C2418yes—
251C2×D4×C11C2418yes—
252C2×D4×C11C2414yes—
253C2×D4×C11C2418yes—
254C22×C4×C11—24no—
255C22×C4×C11—24no—
256C22×C4×C11—24no—
257C22×C4×C11—24no—
258C22×C4×C11—24no—
259C22×C4×C11—232no—
260C22×C4×C11—28no—
261C22×C4×C11#4118yes—
262C22×C4×C11C2411yescharacteristic
263C22×C4×C11C2414yes—
264C22×C4×C11C2412yes—
265C22×C4×C11C2412yes—
266C22×C4×C11C2412yes—
267C22×C4×C11C2411yescharacteristic
268C22×C4×C11C2414yes—
269C22×C4×C11C2414yes—
270C22×C4×C11C2414yes—
271C22×C4×C11C2414yes—
272C22×C4×C11C2418yes—
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2414yes—
276C22×Dic11—28no—
277C22×Dic11—28no—
278C22×Dic11—44no—
279C22×Dic11—44no—
280C22×Dic11—48no—
281C22×Dic11C2418yes—
282C22×Dic11C2418yes—
283C22×Dic11C2412yes—
284C22×Dic11C2412yes—
285C22×Dic11C2412yes—
286C22×Dic11C2414yes—
287C22×Dic11C2412yes—
288C22×Dic11C2414yes—
289C22×Dic11C24116yes—
290C22×Dic11C2418yes—
291C22×Dic11C2418yes—
292C2×Dic22—28no—
293C2×Dic22—28no—
294C2×Dic22—232no—
295C2×Dic22—48no—
296C2×Dic22C2418yes—
297C2×Dic22C2418yes—
298C2×Dic22C24116yes—
299C11×C4⋊C4C2414yes—
300C11×C4⋊C4C2418yes—
301C11×C4⋊C4C2414yes—
302C11×C4⋊C4C2418yes—
303C11×C22⋊C4C2418yes—
304C11×C22⋊C4C2418yes—
305C11×C22⋊C4C2418yes—
306C11×C22⋊C4C2418yes—
307C11×C22⋊C4C2418yes—
308C42×C11C2418yes—
309C22⋊Dic11C2418yes—
310C22⋊Dic11C24116yes—
311C22⋊Dic11C24116yes—
312C22⋊Dic11C2418yes—
313C22⋊Dic11C24116yes—
314C22⋊Dic11C24116yes—
315C22⋊Dic11C2418yes—
316C22⋊Dic11C2418yes—
317C22⋊Dic11C24116yes—
318C4⋊Dic11C2414yes—
319C4⋊Dic11C2414yes—
320C4⋊Dic11C2414yes—
321C4⋊Dic11C2418yes—
322C4⋊Dic11C24116yes—
323C4⋊Dic11C2414yes—
324C4⋊Dic11C24116yes—
325C4⋊Dic11C2418yes—
326C4⋊Dic11C2418yes—
327C4⋊Dic11C2418yes—
328Dic11⋊C4C24116yes—
329Dic11⋊C4C24116yes—
330Dic11⋊C4C24116yes—
331Dic11⋊C4C24116yes—
332Dic11⋊C4C24116yes—
333Dic11⋊C4C24116yes—
334Dic11⋊C4C24116yes—
335Dic11⋊C4C24116yes—
336C4×Dic11C24116yes—
337C4×Dic11C24116yes—
338C4×Dic11C24116yes—
339C4×Dic11C2418yes—
340C4×Dic11C2418yes—
341C4×Dic11C2418yes—
342C4×Dic11C2418yes—
343#3495—1132no—
344C2×#556—112no—
345C2×#554—112no—
346C2×#552—114no—
347C2×#552—112no—
348C2×#552—112no—
349C2×#551—114no—
350C2×#544—111no—
351C2×#542—112no—
352C2×#541—112no—
353C2×#536—111no—
354C2×#533—112no—
355C2×#529—112no—
356C2×#525D1111yescharacteristic
357C22×C22⋊Q8—111no—
358C2×#520—111no—
359C2×#519—111no—
360C22×#117—111no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—28no—
366C23×C11—22no—
367C23×C11—24no—
368C23×C11—24no—
369C23×C11—28no—
370C23×C11—22no—
371C23×C11—24no—
372C23×C11—22no—
373C23×C11—44no—
374C23×C11—416no—
375C23×C11C2×#4114yes—
376C23×C112−1+414yes—
377C23×C11C2512yes—
378C23×C11C2514yes—
379C23×C11C2512yes—
380C23×C11C2512yes—
381C23×C11C2511yescharacteristic
382Q8×C11—28no—
383D4×C11—216no—
384D4×C11—216no—
385D4×C11—28no—
386D4×C11—48no—
387C2×C4×C11—28no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—24no—
391C2×C4×C11—24no—
392C2×C4×C11—24no—
393C2×C4×C11—28no—
394C2×C4×C11—28no—
395C2×C4×C11—28no—
396C2×C4×C11—28no—
397C2×C4×C11—216no—
398C2×C4×C11C2×#4114yes—
399C2×C4×C11C2×#4114yes—
400C2×C4×C11C2×#41116yes—
401C2×C4×C11C2512yes—
402C2×C4×C11C2514yes—
403C2×C4×C11C2514yes—
404C2×C4×C11C2514yes—
405C2×C4×C11C2512yes—
406C2×C4×C11C2512yes—
407C2×C4×C11C2512yes—
408C2×Dic11—216no—
409C2×Dic11—28no—
410C2×Dic11—216no—
411C2×Dic11—24no—
412C2×Dic11—24no—
413C2×Dic11—24no—
414C2×Dic11—28no—
415C2×Dic11—24no—
416C2×Dic11—48no—
417C2×Dic11—48no—
418C2×Dic11—416no—
419C2×Dic11C2514yes—
420C2×Dic11C2514yes—
421C2×Dic11C2514yes—
422C2×Dic11C2518yes—
423C2×Dic11C2514yes—
424C2×Dic11C2518yes—
425Dic22—216no—
426Dic22—216no—
427Dic22—416no—
428C22×#41C2×D1111yescharacteristic
429C23×Q8—111no—
430C24×C4C2×D1111yescharacteristic
431#556—1132no—
432#554—1132no—
433#552—1164no—
434#552—1132no—
435#552—1132no—
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—114no—
456C2×#124—112no—
457#525C2×D11116yes—
458C2×#123—114no—
459C2×#123—114no—
460C2×#123—114no—
461C2×#123C2×D1112yes—
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—114no—
472C2×C22⋊Q8C2×D1111yescharacteristic
473C2×C22⋊Q8C2×D1111yescharacteristic
474C2×#121C2×D1111yescharacteristic
475C2×#121C2×D1111yescharacteristic
476C2×#120C2×D1112yes—
477#520—1116no—
478#519—1116no—
479C2×C4×Q8—112no—
480C2×C4×Q8—112no—
481C2×C4×Q8—112no—
482C2×C4×Q8—114no—
483C2×C4×Q8—112no—
484C2×C4×Q8—112no—
485C2×C4×D4—114no—
486C2×C4×D4—114no—
487C2×C4×D4—112no—
488C2×C4×D4C2×D1112yes—
489C2×C4×D4C2×D1112yes—
490C2×#117—111no—
491C2×#117—111no—
492C2×#117—112no—
493C2×#117—111no—
494C2×#117—112no—
495C2×#117—111no—
496C2×#117—1116no—
497C2×#117—112no—
498C2×#117—114no—
499C2×#117—114no—
500C2×#117—114no—
501C2×#117C2×D1111yescharacteristic
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—22no—
513C22×C11—22no—
514C22×C11—28no—
515C22×C11—28no—
516C22×C11—22no—
517C22×C11—24no—
518C22×C11—24no—
519C22×C11—22no—
520C22×C11—22no—
521C22×C11—24no—
522C22×C11—416no—
523C22×C11—48no—
524C22×C11—44no—
525C22×C11C22×#4114yes—
526C22×C11C22×#4112yes—
527C22×C11C2×2−1+414yes—
528C22×C11C2×2−1+412yes—
529C22×C11#58512yes—
530C22×C11C2611yescharacteristic
531C4×C11—22no—
532C4×C11—22no—
533C4×C11—24no—
534C4×C11—24no—
535C4×C11—24no—
536C4×C11C22×#4114yes—
537C4×C11C22×#4114yes—
538Dic11—28no—
539Dic11—24no—
540Dic11—24no—
541Dic11—24no—
542Dic11—28no—
543Dic11—24no—
544C25C22×D1111yescharacteristic
545C2×#41—28no—
546C2×#41C22×D1118yes—
547C22×Q8—112no—
548C22×Q8—112no—
549C22×Q8—118no—
550C22×Q8—114no—
551C22×Q8—228no—
552C22×Q8C22×D1111yescharacteristic
553C22×D4C22×D1112yes—
554C22×D4C22×D1112yes—
555C22×D4C22×D1111yescharacteristic
556C22×D4C22×D1112yes—
557C23×C4—28no—
558C23×C4—112no—
559C23×C4—112no—
560C23×C4—112no—
561C23×C4—112no—
562C23×C4—114no—
563C23×C4C22×D1111yescharacteristic
564C23×C4C22×D1111yescharacteristic
565C23×C4C22×D1112yes—
566C23×C4C22×D1111yescharacteristic
567C23×C4C22×D1111yescharacteristic
568C23×C4C22×D1118yes—
569C23×C4C22×D1111yescharacteristic
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#123C22×D11116yes—
589C22⋊Q8—1116no—
590C22⋊Q8—1116no—
591C22⋊Q8—1116no—
592C22⋊Q8—1116no—
593C22⋊Q8—1116no—
594C22⋊Q8—1116no—
595C22⋊Q8—1132no—
596C22⋊Q8—1132no—
597C22⋊Q8—1132no—
598C22⋊Q8C22×D1118yes—
599C22⋊Q8C22×D1118yes—
600#121C22×D1118yes—
601#121C22×D1118yes—
602#120C22×D11116yes—
603C4×Q8—1116no—
604C4×Q8—1116no—
605C4×Q8—1116no—
606C4×Q8—1132no—
607C4×Q8—1116no—
608C4×Q8—1116no—
609C4×D4—1116no—
610C4×D4—1132no—
611C4×D4—1132no—
612C4×D4C22×D11116yes—
613C4×D4C22×D11116yes—
614#117—118no—
615#117—118no—
616#117—1116no—
617#117—118no—
618#117—1116no—
619#117—118no—
620#117—1116no—
621#117—1132no—
622#117—1132no—
623#117—1132no—
624#117C22×D1118yes—
625C2×C4⋊C4—111no—
626C2×C4⋊C4—112no—
627C2×C4⋊C4—111no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—111no—
630C2×C4⋊C4—111no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—118no—
633C2×C4⋊C4—118no—
634C2×C4⋊C4—114no—
635C2×C4⋊C4—112no—
636C2×C4⋊C4—114no—
637C2×C4⋊C4—118no—
638C2×C4⋊C4—1116no—
639C2×C4⋊C4—114no—
640C2×C4⋊C4—1116no—
641C2×C4⋊C4—114no—
642C2×C4⋊C4—114no—
643C2×C4⋊C4—114no—
644C2×C4⋊C4—114no—
645C2×C4⋊C4—114no—
646C2×C4⋊C4—114no—
647C2×C4⋊C4—114no—
648C2×C4⋊C4C22×D1111yescharacteristic
649C2×C4⋊C4C22×D1111yescharacteristic
650C2×C4⋊C4C22×D1112yes—
651C2×C4⋊C4C22×D1112yes—
652C2×C22⋊C4—112no—
653C2×C22⋊C4—112no—
654C2×C22⋊C4—112no—
655C2×C22⋊C4—112no—
656C2×C22⋊C4—1116no—
657C2×C22⋊C4—114no—
658C2×C22⋊C4—114no—
659C2×C22⋊C4—1116no—
660C2×C22⋊C4—114no—
661C2×C22⋊C4—114no—
662C2×C22⋊C4—114no—
663C2×C22⋊C4C22×D1112yes—
664C2×C22⋊C4C22×D1112yes—
665C2×C22⋊C4C22×D1112yes—
666C2×C22⋊C4C22×D1112yes—
667C2×C22⋊C4C22×D1112yes—
668C2×C42—112no—
669C2×C42—112no—
670C2×C42—114no—
671C2×C42—114no—
672C2×C42—114no—
673C2×C42—112no—
674C2×C42—112no—
675C2×C42—1116no—
676C2×C42C22×D1112yes—
677C2×C11—24no—
678C2×C11—24no—
679C2×C11—44no—
680C2×C11—42no—
681C2×C11#349514yescomplemented
682C2×C11C23×#4111yescharacteristic
683C2×C11C22×2−1+411yescharacteristic
684C2×C11C2×#58511yescharacteristic
685C24—24no—
686C24—24no—
687C24—42no—
688C24C23×D1111yescharacteristic
689C24C23×D1112yes—
690C24C23×D1114yes—
691C24C23×D1111yescharacteristic
692C24C23×D1111yescharacteristic
693#41—232no—
694C2×Q8—24no—
695C2×Q8—118no—
696C2×Q8—118no—
697C2×Q8—1116no—
698C2×Q8—228no—
699C2×Q8—228no—
700C2×Q8—2232no—
701C2×Q8—448no—
702C2×Q8C23×D1114yes—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—44no—
707C2×D4C23×D1118yes—
708C2×D4C23×D1118yes—
709C2×D4C23×D1114yes—
710C2×D4C23×D1118yes—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—232no—
717C22×C4—28no—
718C22×C4—118no—
719C22×C4—118no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—112no—
723C22×C4—114no—
724C22×C4—112no—
725C22×C4—114no—
726C22×C4—118no—
727C22×C4—118no—
728C22×C4—1116no—
729C22×C4—228no—
730C22×C4—228no—
731C22×C4—448no—
732C22×C4—444no—
733C22×C4—444no—
734C22×C4#434118yes—
735C22×C4C23×D1114yes—
736C22×C4C23×D1114yes—
737C22×C4C23×D1114yes—
738C22×C4C23×D1118yes—
739C22×C4C23×D1114yes—
740C22×C4C23×D1114yes—
741C22×C4C23×D1111yescharacteristic
742C22×C4C23×D1112yes—
743C22×C4C23×D1112yes—
744C22×C4C23×D1112yes—
745C22×C4C23×D1111yescharacteristic
746C22×C4C23×D1114yes—
747C22×C4C23×D1111yescharacteristic
748C22×C4C23×D1111yescharacteristic
749C4⋊C4—114no—
750C4⋊C4—118no—
751C4⋊C4—114no—
752C4⋊C4—118no—
753C4⋊C4—114no—
754C4⋊C4—114no—
755C4⋊C4—118no—
756C4⋊C4—1116no—
757C4⋊C4—118no—
758C4⋊C4—1116no—
759C4⋊C4—1116no—
760C4⋊C4—1116no—
761C4⋊C4—1116no—
762C4⋊C4—1116no—
763C4⋊C4—1116no—
764C4⋊C4—1116no—
765C4⋊C4—1116no—
766C4⋊C4—1116no—
767C4⋊C4C23×D1114yes—
768C4⋊C4C23×D1114yes—
769C4⋊C4C23×D1118yes—
770C4⋊C4C23×D1118yes—
771C22⋊C4—118no—
772C22⋊C4—118no—
773C22⋊C4—118no—
774C22⋊C4—118no—
775C22⋊C4—1116no—
776C22⋊C4—1116no—
777C22⋊C4—1116no—
778C22⋊C4—1116no—
779C22⋊C4—1116no—
780C22⋊C4C23×D1118yes—
781C22⋊C4C23×D1118yes—
782C22⋊C4C23×D1118yes—
783C22⋊C4C23×D1118yes—
784C22⋊C4C23×D1118yes—
785C42—118no—
786C42—118no—
787C42—118no—
788C42—118no—
789C42—1116no—
790C42—1116no—
791C42—1116no—
792C42C23×D1118yes—
793C11C2×#349511yescharacteristic, complemented, Sylow
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—28no—
799C23—22no—
800C23—24no—
801C23—24no—
802C23—28no—
803C23—22no—
804C23—24no—
805C23—22no—
806C23—44no—
807C23—416no—
808C23C2×#434114yes—
809C23#6704314yes—
810C23C24×D1112yes—
811C23C24×D1114yes—
812C23C24×D1112yes—
813C23C24×D1112yes—
814C23C24×D1111yescharacteristic
815Q8—28no—
816Q8—2216no—
817Q8—2216no—
818Q8—4416no—
819D4—216no—
820D4—216no—
821D4—28no—
822D4—48no—
823C2×C4—28no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—216no—
834C2×C4—114no—
835C2×C4—114no—
836C2×C4—114no—
837C2×C4—118no—
838C2×C4—114no—
839C2×C4—118no—
840C2×C4—2216no—
841C2×C4—228no—
842C2×C4—2216no—
843C2×C4—224no—
844C2×C4—224no—
845C2×C4—224no—
846C2×C4—228no—
847C2×C4—224no—
848C2×C4—4416no—
849C2×C4—448no—
850C2×C4—448no—
851C2×C4C2×#434114yes—
852C2×C4C2×#434114yes—
853C2×C4C2×#4341116yes—
854C2×C4C24×D1112yes—
855C2×C4C24×D1114yes—
856C2×C4C24×D1114yes—
857C2×C4C24×D1114yes—
858C2×C4C24×D1112yes—
859C2×C4C24×D1112yes—
860C2×C4C24×D1112yes—
861C22—28no—
862C22—28no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—24no—
869C22—24no—
870C22—22no—
871C22—24no—
872C22—22no—
873C22—416no—
874C22—44no—
875C22—48no—
876C22C22×#434114yes—
877C22C22×#434112yes—
878C22C2×#6704314yes—
879C22C2×#6704312yes—
880C22#1062345312yes—
881C22C25×D1111yescharacteristic
882C4—22no—
883C4—22no—
884C4—24no—
885C4—24no—
886C4—24no—
887C4—228no—
888C4—224no—
889C4—224no—
890C4—224no—
891C4—228no—
892C4—224no—
893C4C22×#434114yes—
894C4C22×#434114yes—
895C2—24no—
896C2—24no—
897C2—42no—
898C2—44no—
899C2#1308237014yesdirect product factor
900C2C23×#434111yescharacteristic
901C2C22×#6704311yescharacteristic
902C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
Fitting, prime radicalC2×C11×#525C2
socleC23×C11C25
hypercenterC2×#525D11
hypocenterC11C2×#3495
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. #13082370C2direct (N × H)
2. C2×#10623073C2semidirect
3. C2×#10623074C2semidirect
4. C2×#10623072C2semidirect
5. C2×#10623072C2semidirect
6. C2×#10623181C2semidirect
7. C2×#10623118C2semidirect
8. C2×#10623050C2semidirect
9. C2×#10623134C2semidirect
10. C2×#10623156C2semidirect
11. C2×#10623356C2semidirect
12. C2×#10623153C2semidirect
13. C2×#10623131C2semidirect
14. C22×#66977C2semidirect
15. C2×#10623358C2semidirect
16. C2×#10623047C2semidirect
17. C22×#66979C2semidirect
34. #10623358C22semidirect
35. #10623356C22semidirect
36. C2×Q8×Dic11C22semidirect
37. C2×#66997C22semidirect
39. C2×#66989C22semidirect
45. C2×D4×Dic11C22semidirect
52. C2×#66979C22semidirect
53. C2×#66979C22semidirect
57. C22×C4⋊Dic11C22semidirect
62. C2×#66977C22semidirect
63. C2×#66977C22semidirect
64. C2×#66977C22semidirect
67. #10623181C22semidirect
68. #10623156C22semidirect
69. #10623153C22semidirect
70. #10623134C22semidirect
71. #10623131C22semidirect
72. #10623118C22semidirect
73. #10623074C22semidirect
74. #10623073C22semidirect
75. #10623072C22semidirect
76. #10623072C22semidirect
77. #10623050C22semidirect
78. #10623047C22semidirect
79. C2×#66943C22semidirect
80. C2×#66943C22semidirect
81. C2×#66942C22semidirect
82. C2×#66942C22semidirect
83. C2×#66941C22semidirect
84. C2×#66940C22semidirect
85. C2×#66940C22semidirect
86. C2×#66940C22semidirect
89. C2×#66932C22semidirect
90. C2×#66932C22semidirect
93. C2×#66931C22semidirect
96. C2×#66930C22semidirect
97. C2×#66923C22semidirect
98. C2×#66922C22semidirect
99. C2×C4×Dic22C22semidirect
100. C2×C4×Dic22C22semidirect
158. Q8×Dic11C23semidirect
159. #66997C23semidirect
161. #66989C23semidirect
167. D4×Dic11C23semidirect
174. #66979C23semidirect
188. C2×C4⋊Dic11C23semidirect
193. #66977C23semidirect
194. #66977C23semidirect
212. #66943C23semidirect
213. #66943C23semidirect
214. #66942C23semidirect
215. #66942C23semidirect
216. #66941C23semidirect
217. #66940C23semidirect
218. #66940C23semidirect
219. #66940C23semidirect
222. #66932C23semidirect
223. #66932C23semidirect
226. #66931C23semidirect
229. #66930C23semidirect
230. #66923C23semidirect
231. #66922C23semidirect
232. C4×Dic22C23semidirect
233. C4×Dic22C23semidirect
681. C2×C11#3495semidirect
793. C11C2×#3495semidirect
899. C2#13082370direct (N × H)

Maximal subgroups

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

subgroupindex
#130823702
C2×#106230732
C2×#106230742
C2×#106230722
C2×#106231812
C2×#106231182
C2×#106230502
C2×#106231342
C2×#106231562
C2×#106233562
C2×#106231532
C2×#106231312
C22×#669772
C2×#106233582
C2×#106230472
C22×#669792
C2×C11×#5252
C2×#349511