Finite Group Databasebeta

← C2×#13127191 #16741340

Subgroups — C2×#13127191 #16741340

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×#11719216C211yesmaximal, characteristic, complemented
2C2×#11719316C211yesmaximal, characteristic
3#13127191C2116yesmaximal, direct product factor
4C2×#11718516C211yesmaximal, characteristic, complemented
5C2×#11718438C211yesmaximal, characteristic, complemented
6C2×#11718523C211yesmaximal, characteristic, complemented
7C2×#11718382C211yesmaximal, characteristic, complemented
8C2×#11718515C211yesmaximal, characteristic, complemented
9C2×#11718422C211yesmaximal, characteristic, complemented
10C2×#11718439C211yesmaximal, characteristic, complemented
11C2×#11718702C211yesmaximal, characteristic, complemented
12C2×#11718419C211yesmaximal, characteristic, complemented
13C2×#11718386C211yesmaximal, characteristic, complemented
14C22×#88048C211yesmaximal, characteristic, complemented
15C2×D13×#106C211yesmaximal, characteristic, complemented
16C2×C13×#481C211yesmaximal, characteristic, complemented
17C22×#6129—21no—
18C2×C13×#121C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C2×#88192C2211yescharacteristic
21C2×#88189—21no—
22C2×D4×Dic13C2211yescharacteristic
23C22×#6105C2211yescharacteristic
24C2×C4×C22⋊D13—21no—
25C2×C4×C22⋊D13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C2×#88178—21no—
28C2×#88178C2211yescharacteristic
29C23×#1055C2211yescharacteristic
30C22×C8×D13C2211yescharacteristic
31#11719316—24no—
32#11719316C2218yes—
33#11719216—24no—
34#11719216C2218yescomplemented
35C2×#88151C2211yescharacteristic
36C2×#88150—21no—
37C2×C4⋊C4×D13C2211yescharacteristic
38C2×C4⋊C4×D13C2211yescharacteristic
39C2×#88143—21no—
40C2×#88142C2211yescharacteristic
41C2×#88142C2211yescharacteristic
42C2×#88141C2211yescharacteristic
43C2×#88137—21no—
44C2×#88132—21no—
45C13×#481C2218yescomplemented
46C2×C13×#106C2211yescharacteristic
47C2×C13×#106C2211yescharacteristic
48C2×C13×#102C2211yescharacteristic
49C2×C13×#102C2211yescharacteristic
50C2×C13×C22⋊C8C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52C2×#88060C2211yescharacteristic
53C2×#88057C2211yescharacteristic
54C2×#88057C2211yescharacteristic
55C2×#88056C2211yescharacteristic
56C2×#88056C2211yescharacteristic
57C2×#88054C2211yescharacteristic
58C2×C8×Dic13C2211yescharacteristic
59#11718702C2218yescomplemented
60C2×#88050C2211yescharacteristic
61C2×#88048C2211yescharacteristic
62C2×#88048C2211yescharacteristic
63C2×#88048C2211yescharacteristic
64C2×#88048C2211yescharacteristic
65C2×#88048C2211yescharacteristic
66C2×#88048C2218yescomplemented
67#11718523C2218yescomplemented
68D13×#106C2218yescomplemented
69#11718516C2218yescomplemented
70#11718515C2218yescomplemented
71#11718439C2218yescomplemented
72#11718438C2218yescomplemented
73#11718422C2218yescomplemented
74#11718419C2218yescomplemented
75#11718386C2218yescomplemented
76#11718382C2218yescomplemented
77C22×D4×C13—21no—
78C22×D4×C13C2311yescharacteristic
79C23×C4×C13—21no—
80C23×C4×C13C2311yescharacteristic
81C22×C22⋊D13—21no—
82C22×C22⋊D13D411yescharacteristic
83C23×Dic13—21no—
84C23×Dic13—21no—
85C2×#6129—28no—
86C2×#6129—48no—
87C22×C4×D13—21no—
88C22×C4×D13—21no—
89C22×C4×D13C2311yescharacteristic
90C22×Dic26—21no—
91C22×Dic26—21no—
92C22×Dic26C2311yescharacteristic
93C22×C8×C13C2311yescharacteristic
94C22×C8×C13C2311yescharacteristic
95C13×#121—22no—
96C13×#121C2314yes—
97C2×C13×C4⋊C4—21no—
98C2×C13×C4⋊C4—22no—
99C2×C13×C4⋊C4C2311yescharacteristic
100C2×C13×C4⋊C4C2311yescharacteristic
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C4⋊C4C2314yes—
103C2×C13×C22⋊C4—21no—
104C2×C22⋊Dic13—21no—
105C2×C22⋊Dic13—21no—
106C2×C22⋊Dic13—21no—
107C2×C22⋊Dic13D411yescharacteristic
108#88192—22no—
109#88192C2314yes—
110#88189—28no—
111D4×Dic13—22no—
112D4×Dic13C2314yes—
113C2×#6105—24no—
114C2×#6105C2314yes—
115C4×C22⋊D13—28no—
116C4×C22⋊D13D414yes—
117C4×C22⋊D13C2314yes—
118C2×#6103—21no—
119C2×#6103D411yescharacteristic
120C2×C4⋊Dic13—21no—
121C2×C4⋊Dic13—22no—
122C2×C4⋊Dic13—21no—
123C2×C4⋊Dic13C2311yescharacteristic
124C2×C4⋊Dic13C2311yescharacteristic
125C2×C4⋊Dic13C2311yescharacteristic
126C2×C4⋊Dic13C2314yes—
127#88178—22no—
128#88178—28no—
129#88178C2314yes—
130C2×#6101—21no—
131C2×#6101—21no—
132C2×#6101—21no—
133C2×#6101—21no—
134C2×#6101—21no—
135C2×#6101—21no—
136C2×#6101D411yescharacteristic
137C2×C4×Dic13—21no—
138C2×C4×Dic13C2311yescharacteristic
139C22×#1055—24no—
140C22×#1055C2314yes—
141C22×#1055C2311yescharacteristic
142C22×#1055C2311yescharacteristic
143C2×C8×D13—24no—
144C2×C8×D13C2314yes—
145#88151—22no—
146#88151C2314yes—
147#88150—28no—
148C4⋊C4×D13—22no—
149C4⋊C4×D13—22no—
150C4⋊C4×D13C2314yes—
151C4⋊C4×D13C2314yes—
152#88143—28no—
153#88142—22no—
154#88142—22no—
155#88142C2314yes—
156#88142C2314yes—
157#88141—22no—
158#88141C2314yes—
159#88137—28no—
160#88132—28no—
161C13×#106C2314yes—
162C13×#106C2314yes—
163C13×#102C2314yes—
164C13×#102C2314yes—
165C13×C22⋊C8C2314yes—
166#88072C2314yes—
167#88060C2314yes—
168#88057C2314yes—
169#88057C2314yes—
170#88056C2314yes—
171#88056C2314yes—
172#88054C2314yes—
173C8×Dic13C2314yes—
174#88050C2314yes—
175#88048C2314yes—
176#88048C2314yes—
177#88048C2314yes—
178#88048C2314yes—
179#88048C2314yes—
180C2×#3335—131nomaximal, Sylow
181C24×C13—21no—
182C24×C13C2×D411yescharacteristic
183C23×D13C2×D411yescharacteristic
184C2×D4×C13—24no—
185C2×D4×C13—21no—
186C2×D4×C13—22no—
187C2×D4×C13—22no—
188C2×D4×C13—44no—
189C2×D4×C13C2412yes—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—24no—
196C22×C4×C13—82no—
197C22×C4×C13C2×D411yescharacteristic
198C22×C4×C13C2×D412yes—
199C22×C4×C13C2412yes—
200C22×C4×C13C2411yescharacteristic
201C2×C22⋊D13—24no—
202C2×C22⋊D13—44no—
203C2×C22⋊D13SD1618yescomplemented
204C2×C22⋊D13C2×D414yes—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—24no—
210C22×Dic13—24no—
211C22×Dic13—44no—
212C22×Dic13—44no—
213C22×Dic13C2×D411yescharacteristic
214C22×Dic13C2×D411yescharacteristic
215C22×Dic13C2×D411yescharacteristic
216#6129—432no—
217C2×C4×D13—22no—
218C2×C4×D13—22no—
219C2×C4×D13—24no—
220C2×C4×D13—24no—
221C2×C4×D13—44no—
222C2×C4×D13—82no—
223C2×C4×D13C2×D412yes—
224C2×C4×D13C2412yes—
225C2×Dic26—22no—
226C2×Dic26—22no—
227C2×Dic26—21no—
228C2×Dic26—24no—
229C2×Dic26—24no—
230C2×Dic26—44no—
231C2×Dic26—82no—
232C2×Dic26C2412yes—
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—21no—
240C13×C4⋊C4—24no—
241C13×C4⋊C4C2412yes—
242C13×C4⋊C4C2412yes—
243C13×C4⋊C4C2412yes—
244C13×C22⋊C4—24no—
245C22⋊Dic13—24no—
246C22⋊Dic13—24no—
247C22⋊Dic13—24no—
248C22⋊Dic13C2×D414yes—
249#6105—28no—
250#6103—24no—
251#6103C2×D414yes—
252C4⋊Dic13—24no—
253C4⋊Dic13—21no—
254C4⋊Dic13—21no—
255C4⋊Dic13—21no—
256C4⋊Dic13—24no—
257C4⋊Dic13C2412yes—
258C4⋊Dic13C2412yes—
259C4⋊Dic13C2412yes—
260#6101—24no—
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×#481D1311yescharacteristic, complemented
282C2×#483—131no—
283C2×#483—131no—
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×C13—22no—
295C23×C13—42no—
296C23×C13—42no—
297C23×C13—42no—
298C23×C13C2×SD1614yes—
299C23×C13C22×D412yes—
300C23×C13C22×D411yescharacteristic
301C22×D13—22no—
302C22×D13—22no—
303C22×D13C2×SD1614yes—
304C22×D13C22×D412yes—
305D4×C13—22no—
306D4×C13—22no—
307D4×C13—48no—
308D4×C13—42no—
309C2×C4×C13—22no—
310C2×C4×C13—24no—
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—84no—
320C2×C4×C13C22×D412yes—
321C2×C4×C13C22×D411yescharacteristic
322C2×C4×C13C2×#4112yes—
323C2×C4×C132−1+412yes—
324C2×C4×C13C2511yescharacteristic
325C22⋊D13—48no—
326C22⋊D13C2×SD16116yescomplemented
327C2×Dic13—22no—
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—48no—
337C2×Dic13—42no—
338C2×Dic13—48no—
339C2×Dic13C2×SD1614yes—
340C2×Dic13C22×D412yes—
341C2×Dic13C22×D412yes—
342C2×Dic13C22×D412yes—
343C4×D13—24no—
344C4×D13—22no—
345C4×D13—22no—
346C4×D13—48no—
347C4×D13—84no—
348Dic26—22no—
349Dic26—22no—
350Dic26—42no—
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—131no—
372C2×C22⋊Q8—261no—
373C2×C22⋊Q8—261no—
374C2×C22⋊Q8—261no—
375C2×#121—131no—
376C2×#121C2×D1311yescharacteristic
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#483—138no—
388#481—138no—
389#481C2×D1318yescomplemented
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×#103—131no—
410C2×#103—131no—
411C2×#102—131no—
412C2×#102C2×D1311yescharacteristic
413C2×#102C2×D1311yescharacteristic
414C2×C22⋊C8—131no—
415C2×C22⋊C8C2×D1311yescharacteristic
416C2×C4×C8—131no—
417C22×C13—28no—
418C22×C13—22no—
419C22×C13—22no—
420C22×C13—42no—
421C22×C13—42no—
422C22×C13—42no—
423C22×C13—84no—
424C22×C13#54712yes—
425C22×C13C22×SD1614yes—
426C22×C13C22×SD1612yes—
427C22×C13#57712yes—
428C22×C13C23×D411yescharacteristic
429C2×D13—28no—
430C2×D13—22no—
431C2×D13—22no—
432C2×D13C22×SD1614yes—
433C4×C13—22no—
434C4×C13—42no—
435C4×C13—42no—
436C4×C13—42no—
437C4×C13#54712yes—
438C4×C13C22×#4111yescharacteristic
439C4×C13C2×2−1+411yescharacteristic
440Dic13—22no—
441Dic13—22no—
442Dic13—42no—
443Dic13—42no—
444Dic13—42no—
445Dic13—42no—
446Dic13C22×SD1614yes—
447C2×#41—268no—
448C2×#41—528no—
449C22×Q8—131no—
450C22×Q8—261no—
451C22×Q8—261no—
452C22×D4—21no—
453C22×D4—131no—
454C22×D4—261no—
455C22×D4C22×D1311yescharacteristic
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—134no—
481C22⋊Q8—134no—
482C22⋊Q8—268no—
483C22⋊Q8—268no—
484C22⋊Q8—268no—
485C22⋊Q8—262no—
486C22⋊Q8—262no—
487#121—22no—
488#121—134no—
489#121—262no—
490#121C22×D1314yes—
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—131no—
501C2×C4⋊C4—131no—
502C2×C4⋊C4—131no—
503C2×C4⋊C4—131no—
504C2×C4⋊C4—134no—
505C2×C4⋊C4—134no—
506C2×C4⋊C4—134no—
507C2×C4⋊C4—262no—
508C2×C4⋊C4—262no—
509C2×C4⋊C4—261no—
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—262no—
517C2×C4⋊C4—261no—
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#103—134no—
543#103—134no—
544#102—134no—
545#102C22×D1314yes—
546#102C22×D1314yes—
547C22⋊C8—134no—
548C22⋊C8C22×D1314yes—
549C4×C8—134no—
550C2×C13—24no—
551C2×C13—82no—
552C2×C13#333514yescomplemented
553C2×C13C2×#54711yescharacteristic
554C2×C13C23×SD1611yescharacteristic
555C2×C13C2×#57711yescharacteristic
556D13—24no—
557C24—21no—
558C24—131no—
559C24D4×D1311yescharacteristic
560#41—5232no—
561C2×Q8—132no—
562C2×Q8—264no—
563C2×Q8—264no—
564C2×Q8—261no—
565C2×Q8—262no—
566C2×Q8—262no—
567C2×Q8—524no—
568C2×Q8—1042no—
569C2×D4—24no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—44no—
574C2×D4—138no—
575C2×D4—134no—
576C2×D4—264no—
577C2×D4—524no—
578C2×D4C23×D1312yes—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—82no—
586C22×C4—131no—
587C22×C4—131no—
588C22×C4—131no—
589C22×C4—132no—
590C22×C4—132no—
591C22×C4—264no—
592C22×C4—264no—
593C22×C4—264no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—264no—
597C22×C4—261no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—524no—
602C22×C4—524no—
603C22×C4—524no—
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—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—134no—
625C4⋊C4—132no—
626C4⋊C4—132no—
627C4⋊C4—132no—
628C4⋊C4—264no—
629C4⋊C4—264no—
630C4⋊C4—264no—
631C4⋊C4—264no—
632C4⋊C4—264no—
633C4⋊C4—264no—
634C4⋊C4—261no—
635C4⋊C4—261no—
636C4⋊C4—264no—
637C4⋊C4—261no—
638C4⋊C4—264no—
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—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—134no—
660C23—132no—
661C23—262no—
662C23—262no—
663C23SD16×D1314yes—
664C23C2×D4×D1312yes—
665C23C2×D4×D1311yescharacteristic
666Q8—262no—
667Q8—262no—
668Q8—528no—
669Q8—522no—
670Q8—1044no—
671D4—22no—
672D4—22no—
673D4—48no—
674D4—42no—
675D4—1316no—
676D4—528no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—134no—
689C2×C4—132no—
690C2×C4—132no—
691C2×C4—132no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—264no—
695C2×C4—262no—
696C2×C4—262no—
697C2×C4—262no—
698C2×C4—262no—
699C2×C4—262no—
700C2×C4—262no—
701C2×C4—528no—
702C2×C4—528no—
703C2×C4—522no—
704C2×C4—522no—
705C2×C4—528no—
706C2×C4—522no—
707C2×C4—522no—
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—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—134no—
726C22—268no—
727C22—262no—
728C22—262no—
729C22#1171936012yes—
730C22C2×SD16×D1314yes—
731C22C2×SD16×D1312yes—
732C22#1171948012yes—
733C22C22×D4×D1311yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—134no—
739C4—262no—
740C4—262no—
741C4—522no—
742C4—522no—
743C4—522no—
744C4—522no—
745C4#1171936012yes—
746C4C2×#41×D1311yescharacteristic
747C4C2×#8825711yescharacteristic
748C2—24no—
749C2—82no—
750C2—264no—
751C2#1312719114yesdirect product factor
752C2C2×#1171936011yescharacteristic
753C2C22×SD16×D1311yescharacteristic
754C2C2×#1171948011yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#481C2
socleC23×C13C22×D4
prime radicalC2×#11719316C2
hypercenterC2×#481D13
hypocenterC13C2×#3335
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#11719216C2semidirect
3. #13127191C2direct (N × H)
4. C2×#11718516C2semidirect
5. C2×#11718438C2semidirect
6. C2×#11718523C2semidirect
7. C2×#11718382C2semidirect
8. C2×#11718515C2semidirect
9. C2×#11718422C2semidirect
10. C2×#11718439C2semidirect
11. C2×#11718702C2semidirect
12. C2×#11718419C2semidirect
13. C2×#11718386C2semidirect
14. C22×#88048C2semidirect
15. C2×D13×#106C2semidirect
16. C2×C13×#481C2semidirect
34. #11719216C22semidirect
45. C13×#481C22semidirect
59. #11718702C22semidirect
66. C2×#88048C22semidirect
67. #11718523C22semidirect
68. D13×#106C22semidirect
69. #11718516C22semidirect
70. #11718515C22semidirect
71. #11718439C22semidirect
72. #11718438C22semidirect
73. #11718422C22semidirect
74. #11718419C22semidirect
75. #11718386C22semidirect
76. #11718382C22semidirect
203. C2×C22⋊D13SD16semidirect
272. C2×#1055#41semidirect
281. C2×#481D13semidirect
326. C22⋊D13C2×SD16semidirect
356. #1055C2×#41semidirect
389. #481C2×D13semidirect
552. C2×C13#3335semidirect
652. C13C2×#3335semidirect
751. C2#13127191direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192162
C2×#117193162
#131271912
C2×#117185162
C2×#117184382
C2×#117185232
C2×#117183822
C2×#117185152
C2×#117184222
C2×#117184392
C2×#117187022
C2×#117184192
C2×#117183862
C22×#880482
C2×D13×#1062
C2×C13×#4812
C2×#333513