Finite Group Databasebeta

← C2×#13127186 #16741335

Subgroups — C2×#13127186 #16741335

Order 3328.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719340C211yesmaximal, characteristic, complemented
2C2×#11719212C211yesmaximal, characteristic
3#13127186C2116yesmaximal, direct product factor
4C2×#11718516C211yesmaximal, characteristic, complemented
5C2×#11718524C211yesmaximal, characteristic, complemented
6C2×#11718396C211yesmaximal, characteristic, complemented
7C2×#11718466C211yesmaximal, characteristic, complemented
8C2×#11718452C211yesmaximal, characteristic, complemented
9C2×#11718531C211yesmaximal, characteristic, complemented
10C2×#11718468C211yesmaximal, characteristic, complemented
11C2×#11718709C211yesmaximal, characteristic, complemented
12C2×#11718449C211yesmaximal, characteristic, complemented
13C2×#11718386C211yesmaximal, characteristic, complemented
14C22×#88048C211yesmaximal, characteristic, complemented
15C2×D13×#106C211yesmaximal, characteristic, complemented
16C2×C13×#483C211yesmaximal, characteristic, complemented
17C22×#6127—21no—
18C2×C13×C22⋊Q8C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C2×#88200C2211yescharacteristic
21C2×Q8×Dic13C2211yescharacteristic
22C22×#6106C2211yescharacteristic
23C2×#88184C2211yescharacteristic
24C2×#88183—21no—
25C2×C4×C22⋊D13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C23×#1055C2211yescharacteristic
28C22×C8×D13C2211yescharacteristic
29#11719340—24no—
30#11719340C2218yescomplemented
31C2×#88151—21no—
32C2×#88150—21no—
33#11719212—24no—
34#11719212C2218yes—
35C2×#88149C2211yescharacteristic
36C2×#88148—21no—
37C2×#88147C2211yescharacteristic
38C2×C4⋊C4×D13C2211yescharacteristic
39C2×C4⋊C4×D13C2211yescharacteristic
40C2×#88143—21no—
41C2×#88142C2211yescharacteristic
42C2×#88142C2211yescharacteristic
43C2×#88135—21no—
44C2×#88132—21no—
45C13×#483C2218yescomplemented
46C2×C13×#106C2211yescharacteristic
47C2×C13×#106C2211yescharacteristic
48C2×C13×#103C2211yescharacteristic
49C2×C13×#103C2211yescharacteristic
50C2×C13×C22⋊C8C2211yescharacteristic
51C2×#88075C2211yescharacteristic
52C2×#88061C2211yescharacteristic
53C2×#88061C2211yescharacteristic
54C2×#88060C2211yescharacteristic
55C2×#88057C2211yescharacteristic
56C2×#88057C2211yescharacteristic
57C2×#88054C2211yescharacteristic
58C2×C8×Dic13C2211yescharacteristic
59#11718709C2218yescomplemented
60C2×#88049C2211yescharacteristic
61C2×#88048C2211yescharacteristic
62C2×#88048C2211yescharacteristic
63C2×#88048C2211yescharacteristic
64C2×#88048C2211yescharacteristic
65C2×#88048C2211yescharacteristic
66C2×#88048C2218yescomplemented
67#11718531C2218yescomplemented
68#11718524C2218yescomplemented
69D13×#106C2218yescomplemented
70#11718516C2218yescomplemented
71#11718468C2218yescomplemented
72#11718466C2218yescomplemented
73#11718452C2218yescomplemented
74#11718449C2218yescomplemented
75#11718396C2218yescomplemented
76#11718386C2218yescomplemented
77C22×Q8×C13C2311yescharacteristic
78C23×C4×C13—21no—
79C23×C4×C13C2311yescharacteristic
80C22×C22⋊D13—21no—
81C22×C22⋊D13D411yescharacteristic
82C23×Dic13—21no—
83C2×#6127—28no—
84C2×#6127—48no—
85C22×D52—21no—
86C22×D52C2311yescharacteristic
87C22×C4×D13—21no—
88C22×C4×D13—21no—
89C22×C4×D13—21no—
90C22×C4×D13C2311yescharacteristic
91C22×Dic26—21no—
92C22×Dic26—21no—
93C22×C8×C13C2311yescharacteristic
94C22×C8×C13C2311yescharacteristic
95C13×C22⋊Q8—22no—
96C13×C22⋊Q8C2314yes—
97C2×C13×C4⋊C4—21no—
98C2×C13×C4⋊C4—21no—
99C2×C13×C4⋊C4—22no—
100C2×C13×C4⋊C4C2311yescharacteristic
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C4⋊C4C2311yescharacteristic
103C2×C13×C4⋊C4C2314yes—
104C2×C13×C22⋊C4—21no—
105C2×C22⋊Dic13D411yescharacteristic
106#88200—22no—
107#88200C2314yes—
108Q8×Dic13—22no—
109Q8×Dic13C2314yes—
110C2×#6106—24no—
111C2×#6106C2314yes—
112#88184—22no—
113#88184C2314yes—
114#88183—28no—
115C4×C22⋊D13D414yes—
116C4×C22⋊D13C2314yes—
117C2×#6103—21no—
118C2×#6103—21no—
119C2×#6103—21no—
120C2×#6103—21no—
121C2×#6103D411yescharacteristic
122C2×C4⋊Dic13—21no—
123C2×C4⋊Dic13—22no—
124C2×C4⋊Dic13—21no—
125C2×C4⋊Dic13C2311yescharacteristic
126C2×C4⋊Dic13C2311yescharacteristic
127C2×C4⋊Dic13C2311yescharacteristic
128C2×C4⋊Dic13C2314yes—
129C2×#6101—21no—
130C2×#6101—21no—
131C2×#6101—21no—
132C2×#6101—21no—
133C2×#6101—21no—
134C2×#6101D411yescharacteristic
135C2×C4×Dic13—21no—
136C2×C4×Dic13C2311yescharacteristic
137C22×#1055—24no—
138C22×#1055C2314yes—
139C22×#1055C2311yescharacteristic
140C22×#1055C2311yescharacteristic
141C2×C8×D13—24no—
142C2×C8×D13C2314yes—
143#88151—28no—
144#88150—28no—
145#88149—22no—
146#88149C2314yes—
147#88148—28no—
148#88147—22no—
149#88147C2314yes—
150C4⋊C4×D13—22no—
151C4⋊C4×D13—22no—
152C4⋊C4×D13C2314yes—
153C4⋊C4×D13C2314yes—
154#88143—28no—
155#88142—22no—
156#88142—22no—
157#88142C2314yes—
158#88142C2314yes—
159#88135—28no—
160#88132—28no—
161C13×#106C2314yes—
162C13×#106C2314yes—
163C13×#103C2314yes—
164C13×#103C2314yes—
165C13×C22⋊C8C2314yes—
166#88075C2314yes—
167#88061C2314yes—
168#88061C2314yes—
169#88060C2314yes—
170#88057C2314yes—
171#88057C2314yes—
172#88054C2314yes—
173C8×Dic13C2314yes—
174#88049C2314yes—
175#88048C2314yes—
176#88048C2314yes—
177#88048C2314yes—
178#88048C2314yes—
179#88048C2314yes—
180C2×#3335—131nomaximal, Sylow
181C24×C13C2×D411yescharacteristic
182C23×D13—21no—
183C23×D13C2×D411yescharacteristic
184C2×Q8×C13—21no—
185C2×Q8×C13—22no—
186C2×Q8×C13—22no—
187C2×Q8×C13C2412yes—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—24no—
195C22×C4×C13—44no—
196C22×C4×C13C2×D411yescharacteristic
197C22×C4×C13C2×D412yes—
198C22×C4×C13C2412yes—
199C22×C4×C13C2411yescharacteristic
200C2×C22⋊D13—24no—
201C2×C22⋊D13—44no—
202C2×C22⋊D13SD1618yescomplemented
203C2×C22⋊D13C2×D414yes—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—24no—
208C22×Dic13—82no—
209C22×Dic13C2×D411yescharacteristic
210C22×Dic13C2×D411yescharacteristic
211C22×Dic13C2×D411yescharacteristic
212#6127—432no—
213C2×D52—22no—
214C2×D52—22no—
215C2×D52—24no—
216C2×D52—21no—
217C2×D52—44no—
218C2×D52C2412yes—
219C2×C4×D13—22no—
220C2×C4×D13—22no—
221C2×C4×D13—24no—
222C2×C4×D13—24no—
223C2×C4×D13—24no—
224C2×C4×D13—44no—
225C2×C4×D13—44no—
226C2×C4×D13—82no—
227C2×C4×D13C2×D412yes—
228C2×C4×D13C2412yes—
229C2×Dic26—24no—
230C2×Dic26—24no—
231C2×Dic26—44no—
232C2×Dic26—82no—
233C2×C8×C13—22no—
234C2×C8×C13—22no—
235C2×C8×C13C2412yes—
236C2×C8×C13C2412yes—
237C13×C4⋊C4—21no—
238C13×C4⋊C4—21no—
239C13×C4⋊C4—24no—
240C13×C4⋊C4—21no—
241C13×C4⋊C4—24no—
242C13×C4⋊C4C2412yes—
243C13×C4⋊C4C2412yes—
244C13×C4⋊C4C2412yes—
245C13×C22⋊C4—24no—
246C22⋊Dic13C2×D414yes—
247#6106—28no—
248#6103—24no—
249#6103—24no—
250#6103—24no—
251#6103—24no—
252#6103C2×D414yes—
253C4⋊Dic13—21no—
254C4⋊Dic13—21no—
255C4⋊Dic13—24no—
256C4⋊Dic13—21no—
257C4⋊Dic13—24no—
258C4⋊Dic13C2412yes—
259C4⋊Dic13C2412yes—
260C4⋊Dic13C2412yes—
261#6101—24no—
262#6101—24no—
263#6101—24no—
264#6101—24no—
265#6101—24no—
266#6101C2×D414yes—
267C4×Dic13—24no—
268C4×Dic13C2×D412yes—
269C4×Dic13C2412yes—
270C2×#1055—22no—
271C2×#1055—28no—
272C2×#1055#4114yescomplemented
273C2×#1055C2412yes—
274C2×#1055C2412yes—
275C8×D13—28no—
276C2×#554—131no—
277C2×#547—131no—
278#3335—1316no—
279C2×#498—131no—
280C2×#481—131no—
281C2×#481—131no—
282C2×#483—131no—
283C2×#483D1311yescharacteristic, complemented
284C2×#475—131no—
285C2×#476—131no—
286C2×#465—131no—
287C2×#465—131no—
288C2×C4×SD16—131no—
289C2×C8×D4—131no—
290C22×#106—131no—
291C22×#106—131no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13C2×SD1614yes—
295C23×C13C22×D412yes—
296C23×C13C22×D411yescharacteristic
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—42no—
301C22×D13—42no—
302C22×D13—42no—
303C22×D13C2×SD1614yes—
304C22×D13C22×D412yes—
305Q8×C13—22no—
306Q8×C13—22no—
307Q8×C13—42no—
308C2×C4×C13—22no—
309C2×C4×C13—24no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—42no—
317C2×C4×C13—42no—
318C2×C4×C13—42no—
319C2×C4×C13—48no—
320C2×C4×C13—42no—
321C2×C4×C13C22×D412yes—
322C2×C4×C13C22×D411yescharacteristic
323C2×C4×C13C2×#4112yes—
324C2×C4×C132−1+412yes—
325C2×C4×C13C2511yescharacteristic
326C22⋊D13—48no—
327C22⋊D13C2×SD16116yescomplemented
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13—84no—
337C2×Dic13C2×SD1614yes—
338C2×Dic13C22×D412yes—
339C2×Dic13C22×D412yes—
340C2×Dic13C22×D412yes—
341D52—22no—
342D52—22no—
343D52—48no—
344D52—42no—
345C4×D13—24no—
346C4×D13—22no—
347C4×D13—22no—
348C4×D13—48no—
349C4×D13—48no—
350C4×D13—84no—
351Dic26—48no—
352Dic26—84no—
353C8×C13—22no—
354C8×C13—22no—
355#1055—22no—
356#1055C2×#4114yescomplemented
357C22×#41—261no—
358C22×SD16—131no—
359C23×C8—131no—
360C23×C8—131no—
361#554—138no—
362#554—264no—
363#547—138no—
364#547—264no—
365C2×C4⋊Q8—131no—
366C2×C4⋊Q8—131no—
367C2×#125—261no—
368C2×#123—261no—
369C2×#123—261no—
370C2×C22⋊Q8—131no—
371C2×C22⋊Q8—261no—
372C2×C22⋊Q8—261no—
373C2×C22⋊Q8—261no—
374C2×C22⋊Q8C2×D1311yescharacteristic
375C2×#121—131no—
376C2×#121—131no—
377C2×C4×Q8—131no—
378C2×C4×D4—131no—
379C2×C4×D4—131no—
380C2×C4×D4—261no—
381C22×C4⋊C4—131no—
382C22×C4⋊C4—131no—
383C22×C4⋊C4—131no—
384C22×C4⋊C4C2×D1311yescharacteristic
385#498—138no—
386#483—138no—
387#483C2×D1318yescomplemented
388#481—138no—
389#481—138no—
390#476—138no—
391#475—138no—
392#465—138no—
393#465—138no—
394C4×SD16—138no—
395C8×D4—138no—
396C2×#106—131no—
397C2×#106—131no—
398C2×#106—131no—
399C2×#106—138no—
400C2×#106—131no—
401C2×#106—131no—
402C2×#106—131no—
403C2×#106—131no—
404C2×#106—138no—
405C2×#106C2×D1311yescharacteristic
406C2×#106C2×D1311yescharacteristic
407C2×C4⋊C8—131no—
408C2×#103—131no—
409C2×#103C2×D1311yescharacteristic
410C2×#103C2×D1311yescharacteristic
411C2×#102—131no—
412C2×#102—131no—
413C2×#102—131no—
414C2×C22⋊C8—131no—
415C2×C22⋊C8C2×D1311yescharacteristic
416C2×C4×C8—131no—
417C22×C13—28no—
418C22×C13—22no—
419C22×C13—22no—
420C22×C13#54712yes—
421C22×C13C22×SD1614yes—
422C22×C13C22×SD1612yes—
423C22×C13#57712yes—
424C22×C13C23×D411yescharacteristic
425C2×D13—28no—
426C2×D13—22no—
427C2×D13—22no—
428C2×D13—42no—
429C2×D13—42no—
430C2×D13—42no—
431C2×D13—84no—
432C2×D13C22×SD1614yes—
433C4×C13—22no—
434C4×C13—42no—
435C4×C13—42no—
436C4×C13—42no—
437C4×C13—42no—
438C4×C13#54712yes—
439C4×C13C22×#4111yescharacteristic
440C4×C13C2×2−1+411yescharacteristic
441Dic13—22no—
442Dic13—22no—
443Dic13—42no—
444Dic13—42no—
445Dic13—42no—
446Dic13C22×SD1614yes—
447C2×#41—268no—
448C2×#41—528no—
449C22×Q8—261no—
450C22×Q8—261no—
451C22×Q8C22×D1311yescharacteristic
452C22×D4—131no—
453C22×D4—131no—
454C22×D4—261no—
455C22×D4—261no—
456C23×C4—21no—
457C23×C4—131no—
458C23×C4—261no—
459C23×C4—261no—
460C23×C4—261no—
461C23×C4—261no—
462C23×C4C22×D1311yescharacteristic
463C2×SD16—134no—
464C2×SD16—264no—
465C22×C8—131no—
466C22×C8—131no—
467C22×C8—134no—
468C22×C8—134no—
469C22×C8—264no—
470C22×C8—264no—
471C22×C8C22×D1311yescharacteristic
472C22×C8C22×D1311yescharacteristic
473C4⋊Q8—134no—
474C4⋊Q8—134no—
475C4⋊Q8—262no—
476C4⋊Q8—262no—
477#125—268no—
478#123—268no—
479#123—268no—
480C22⋊Q8—22no—
481C22⋊Q8—134no—
482C22⋊Q8—268no—
483C22⋊Q8—268no—
484C22⋊Q8—268no—
485C22⋊Q8—262no—
486C22⋊Q8C22×D1314yes—
487#121—134no—
488#121—134no—
489#121—262no—
490#121—262no—
491C4×Q8—134no—
492C4×Q8—262no—
493C4×D4—134no—
494C4×D4—134no—
495C4×D4—134no—
496C4×D4—262no—
497C4×D4—268no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—131no—
502C2×C4⋊C4—131no—
503C2×C4⋊C4—131no—
504C2×C4⋊C4—131no—
505C2×C4⋊C4—134no—
506C2×C4⋊C4—134no—
507C2×C4⋊C4—134no—
508C2×C4⋊C4—262no—
509C2×C4⋊C4—262no—
510C2×C4⋊C4—261no—
511C2×C4⋊C4—261no—
512C2×C4⋊C4—261no—
513C2×C4⋊C4—261no—
514C2×C4⋊C4—261no—
515C2×C4⋊C4—261no—
516C2×C4⋊C4—261no—
517C2×C4⋊C4—262no—
518C2×C4⋊C4C22×D1311yescharacteristic
519C2×C4⋊C4C22×D1311yescharacteristic
520C2×C4⋊C4C22×D1311yescharacteristic
521C2×C4⋊C4C22×D1314yes—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—131no—
524C2×C22⋊C4—131no—
525C2×C22⋊C4—261no—
526C2×C22⋊C4—261no—
527C2×C22⋊C4—261no—
528C2×C22⋊C4—261no—
529C2×C42—131no—
530C2×C42—261no—
531#106—134no—
532#106—134no—
533#106—134no—
534#106—134no—
535#106—134no—
536#106—134no—
537#106—134no—
538#106C22×D1314yes—
539#106C22×D1314yes—
540C4⋊C8—134no—
541#103—134no—
542#103C22×D1314yes—
543#103C22×D1314yes—
544#102—134no—
545#102—134no—
546#102—134no—
547C22⋊C8—134no—
548C22⋊C8C22×D1314yes—
549C4×C8—134no—
550C2×C13—24no—
551C2×C13#333514yescomplemented
552C2×C13C2×#54711yescharacteristic
553C2×C13C23×SD1611yescharacteristic
554C2×C13C2×#57711yescharacteristic
555D13—24no—
556D13—82no—
557C24—131no—
558C24—261no—
559C24D4×D1311yescharacteristic
560#41—5232no—
561C2×Q8—21no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—264no—
565C2×Q8—264no—
566C2×Q8—524no—
567C2×Q8—1042no—
568C2×Q8C23×D1312yes—
569C2×D4—138no—
570C2×D4—134no—
571C2×D4—132no—
572C2×D4—264no—
573C2×D4—264no—
574C2×D4—261no—
575C2×D4—262no—
576C2×D4—262no—
577C2×D4—524no—
578C2×D4—524no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—44no—
587C22×C4—131no—
588C22×C4—131no—
589C22×C4—131no—
590C22×C4—132no—
591C22×C4—132no—
592C22×C4—264no—
593C22×C4—264no—
594C22×C4—264no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—261no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—264no—
601C22×C4—524no—
602C22×C4—524no—
603C22×C4—1042no—
604C22×C4—1042no—
605C22×C4D4×D1312yes—
606C22×C4D4×D1311yescharacteristic
607C22×C4C23×D1312yes—
608C22×C4C23×D1311yescharacteristic
609SD16—268no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—134no—
613C2×C8—132no—
614C2×C8—132no—
615C2×C8—268no—
616C2×C8—268no—
617C2×C8—262no—
618C2×C8C23×D1312yes—
619C2×C8C23×D1312yes—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—134no—
626C4⋊C4—132no—
627C4⋊C4—132no—
628C4⋊C4—132no—
629C4⋊C4—264no—
630C4⋊C4—264no—
631C4⋊C4—264no—
632C4⋊C4—264no—
633C4⋊C4—264no—
634C4⋊C4—264no—
635C4⋊C4—261no—
636C4⋊C4—261no—
637C4⋊C4—264no—
638C4⋊C4—261no—
639C4⋊C4C23×D1312yes—
640C4⋊C4C23×D1312yes—
641C4⋊C4C23×D1312yes—
642C22⋊C4—24no—
643C22⋊C4—134no—
644C22⋊C4—134no—
645C22⋊C4—264no—
646C22⋊C4—264no—
647C22⋊C4—264no—
648C22⋊C4—264no—
649C42—132no—
650C42—132no—
651C42—264no—
652C13C2×#333511yescharacteristic, complemented, Sylow
653C23—22no—
654C23—22no—
655C23—134no—
656C23—132no—
657C23—262no—
658C23—262no—
659C23—262no—
660C23—522no—
661C23—522no—
662C23—522no—
663C23SD16×D1314yes—
664C23C2×D4×D1312yes—
665C23C2×D4×D1311yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—528no—
670Q8—1044no—
671D4—1316no—
672D4—262no—
673D4—262no—
674D4—528no—
675D4—528no—
676D4—522no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—134no—
691C2×C4—132no—
692C2×C4—132no—
693C2×C4—132no—
694C2×C4—262no—
695C2×C4—262no—
696C2×C4—264no—
697C2×C4—262no—
698C2×C4—262no—
699C2×C4—262no—
700C2×C4—262no—
701C2×C4—262no—
702C2×C4—528no—
703C2×C4—528no—
704C2×C4—522no—
705C2×C4—522no—
706C2×C4—522no—
707C2×C4—1044no—
708C2×C4—1044no—
709C2×C4C2×D4×D1312yes—
710C2×C4C2×D4×D1311yescharacteristic
711C2×C4#41×D1312yes—
712C2×C4#8825712yes—
713C2×C4C24×D1311yescharacteristic
714C8—22no—
715C8—22no—
716C8—134no—
717C8—262no—
718C22—28no—
719C22—22no—
720C22—22no—
721C22—134no—
722C22—268no—
723C22—262no—
724C22—262no—
725C22—522no—
726C22—522no—
727C22—522no—
728C22—1044no—
729C22#1171936012yes—
730C22C2×SD16×D1314yes—
731C22C2×SD16×D1312yes—
732C22#1171948312yes—
733C22C22×D4×D1311yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—134no—
740C4—262no—
741C4—262no—
742C4—522no—
743C4—522no—
744C4—522no—
745C4#1171936012yes—
746C4C2×#41×D1311yescharacteristic
747C4C2×#8825711yescharacteristic
748C2—24no—
749C2—264no—
750C2—1042no—
751C2#1312718614yesdirect product factor
752C2C2×#1171936011yescharacteristic
753C2C22×SD16×D1311yescharacteristic
754C2C2×#1171948311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#483C2
socleC23×C13C22×D4
prime radicalC2×#11719212C2
hypercenterC2×#483D13
hypocenterC13C2×#3335
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#11719340C2semidirect
3. #13127186C2direct (N × H)
4. C2×#11718516C2semidirect
5. C2×#11718524C2semidirect
6. C2×#11718396C2semidirect
7. C2×#11718466C2semidirect
8. C2×#11718452C2semidirect
9. C2×#11718531C2semidirect
10. C2×#11718468C2semidirect
11. C2×#11718709C2semidirect
12. C2×#11718449C2semidirect
13. C2×#11718386C2semidirect
14. C22×#88048C2semidirect
15. C2×D13×#106C2semidirect
16. C2×C13×#483C2semidirect
30. #11719340C22semidirect
45. C13×#483C22semidirect
59. #11718709C22semidirect
66. C2×#88048C22semidirect
67. #11718531C22semidirect
68. #11718524C22semidirect
69. D13×#106C22semidirect
70. #11718516C22semidirect
71. #11718468C22semidirect
72. #11718466C22semidirect
73. #11718452C22semidirect
74. #11718449C22semidirect
75. #11718396C22semidirect
76. #11718386C22semidirect
202. C2×C22⋊D13SD16semidirect
272. C2×#1055#41semidirect
283. C2×#483D13semidirect
327. C22⋊D13C2×SD16semidirect
356. #1055C2×#41semidirect
387. #483C2×D13semidirect
551. C2×C13#3335semidirect
652. C13C2×#3335semidirect
751. C2#13127186direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193402
C2×#117192122
#131271862
C2×#117185162
C2×#117185242
C2×#117183962
C2×#117184662
C2×#117184522
C2×#117185312
C2×#117184682
C2×#117187092
C2×#117184492
C2×#117183862
C22×#880482
C2×D13×#1062
C2×C13×#4832
C2×#333513