Finite Group Databasebeta

← C2×#13127189 #16741338

Subgroups — C2×#13127189 #16741338

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×#11719212C211yesmaximal, characteristic
3#13127189C2116yesmaximal, direct product factor
4C2×#11718516C211yesmaximal, characteristic, complemented
5C2×#11718524C211yesmaximal, characteristic, complemented
6C2×#11718629C211yesmaximal, characteristic, complemented
7C2×#11718523C211yesmaximal, characteristic, complemented
8C2×#11718632C211yesmaximal, characteristic, complemented
9C2×#11718515C211yesmaximal, characteristic, complemented
10C2×#11718531C211yesmaximal, characteristic, complemented
11C2×#11718525C211yesmaximal, characteristic, complemented
12C2×#11718775C211yesmaximal, characteristic, complemented
13C2×#11718513C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D13C211yesmaximal, characteristic, complemented
15C2×D13×#106C211yesmaximal, characteristic, complemented
16C22×C13×#106C211yesmaximal, characteristic, complemented
17C22×#6127—21no—
18C23×C8×C13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C2×#88184C2211yescharacteristic
22C2×#88183—21no—
23C2×C4×C22⋊D13—21no—
24C2×C4×C22⋊D13C2211yescharacteristic
25C2×#88178—21no—
26C2×#88178C2211yescharacteristic
27C22×#6095C2211yescharacteristic
28C22×C8×D13C2211yescharacteristic
29#11719216—24no—
30#11719216C2218yescomplemented
31C2×#88151C2211yescharacteristic
32C2×#88150—21no—
33C2×#88150—21no—
34#11719212—24no—
35#11719212C2218yes—
36C2×#88149C2211yescharacteristic
37C2×#88148—21no—
38C2×#88147C2211yescharacteristic
39C2×C4⋊C4×D13C2211yescharacteristic
40C2×C4⋊C4×D13C2211yescharacteristic
41C2×#88143—21no—
42C2×#88142C2211yescharacteristic
43C2×#88142C2211yescharacteristic
44C2×#88141C2211yescharacteristic
45C2×C13×#106C2211yescharacteristic
46C2×C13×#106C2211yescharacteristic
47C2×C13×#106C2211yescharacteristic
48C2×C13×#106C2211yescharacteristic
49C2×C13×#106C2218yescomplemented
50C2×C22⋊#1055C2211yescharacteristic
51#11718775C2218yescomplemented
52C2×#88061C2211yescharacteristic
53C8×C22⋊D13C2218yescomplemented
54C2×#88060C2211yescharacteristic
55C2×#88057C2211yescharacteristic
56C2×#88056C2211yescharacteristic
57C2×#88054C2211yescharacteristic
58C2×C8×Dic13C2211yescharacteristic
59#11718632C2218yescomplemented
60C2×#88050C2211yescharacteristic
61C2×#88050C2211yescharacteristic
62#11718629C2218yescomplemented
63C2×#88049C2211yescharacteristic
64C2×#88049C2211yescharacteristic
65C2×#88048C2211yescharacteristic
66C2×#88048C2211yescharacteristic
67C2×#88048C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69#11718531C2218yescomplemented
70#11718525C2218yescomplemented
71#11718524C2218yescomplemented
72#11718523C2218yescomplemented
73D13×#106C2218yescomplemented
74#11718516C2218yescomplemented
75#11718515C2218yescomplemented
76#11718513C2218yescomplemented
77C23×C4×C13—21no—
78C23×C4×C13—21no—
79C23×C4×C13C2311yescharacteristic
80C22×C22⋊D13—21no—
81C22×C22⋊D13D411yescharacteristic
82C2×#6127—28no—
83C2×#6127—48no—
84C22×D52—21no—
85C22×D52C2311yescharacteristic
86C22×C4×D13—21no—
87C22×C4×D13—21no—
88C22×C4×D13—21no—
89C22×C4×D13C2311yescharacteristic
90C22×Dic26—21no—
91C22×Dic26—21no—
92C22×Dic26C2311yescharacteristic
93C22×C8×C13—24no—
94C22×C8×C13C2311yescharacteristic
95C22×C8×C13C2314yes—
96C22×C8×C13C2311yescharacteristic
97C2×C13×C4⋊C4—21no—
98C2×C13×C4⋊C4—21no—
99C2×C13×C4⋊C4—22no—
100C2×C13×C4⋊C4—22no—
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C4⋊C4C2311yescharacteristic
103C2×C13×C4⋊C4C2311yescharacteristic
104C2×C13×C4⋊C4C2311yescharacteristic
105C2×C13×C4⋊C4C2314yes—
106C2×C13×C4⋊C4C2314yes—
107C2×C22⋊Dic13—21no—
108C2×C22⋊Dic13D411yescharacteristic
109#88184—22no—
110#88184C2314yes—
111#88183—28no—
112C4×C22⋊D13—28no—
113C4×C22⋊D13D414yes—
114C4×C22⋊D13C2314yes—
115C2×#6103—21no—
116C2×#6103—21no—
117C2×#6103—21no—
118C2×#6103—21no—
119C2×#6103D411yescharacteristic
120C2×C4⋊Dic13—21no—
121C2×C4⋊Dic13C2311yescharacteristic
122C2×C4⋊Dic13C2311yescharacteristic
123#88178—22no—
124#88178—28no—
125#88178C2314yes—
126C2×#6101—21no—
127C2×#6101—21no—
128C2×#6101—21no—
129C2×#6101—21no—
130C2×#6101—21no—
131C2×#6101—21no—
132C2×#6101D411yescharacteristic
133C2×C4×Dic13—21no—
134C2×C4×Dic13C2311yescharacteristic
135C22×#1055C2311yescharacteristic
136C22×#1055C2311yescharacteristic
137C2×#6095—24no—
138C2×#6095C2314yes—
139C2×C8×D13—24no—
140C2×C8×D13C2314yes—
141#88151—22no—
142#88151C2314yes—
143#88150—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#88141—22no—
160#88141C2314yes—
161C13×#106C2314yes—
162C13×#106C2314yes—
163C13×#106C2314yes—
164C13×#106C2314yes—
165C22⋊#1055C2314yes—
166#88061C2314yes—
167#88060C2314yes—
168#88057C2314yes—
169#88056C2314yes—
170#88054C2314yes—
171C8×Dic13C2314yes—
172#88050C2314yes—
173#88050C2314yes—
174#88049C2314yes—
175#88049C2314yes—
176#88048C2314yes—
177#88048C2314yes—
178#88048C2314yes—
179#88048C2314yes—
180C2×#3335—131nomaximal, Sylow
181C24×C13C2×D411yescharacteristic
182C23×D13—21no—
183C23×D13C2×D411yescharacteristic
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—24no—
191C22×C4×C13—24no—
192C22×C4×C13—44no—
193C22×C4×C13—82no—
194C22×C4×C13C2×D411yescharacteristic
195C22×C4×C13C2×D412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2411yescharacteristic
198C2×C22⋊D13—24no—
199C2×C22⋊D13—44no—
200C2×C22⋊D13SD1618yescomplemented
201C2×C22⋊D13C2×D414yes—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13C2×D411yescharacteristic
206C22×Dic13C2×D411yescharacteristic
207C22×Dic13C2×D411yescharacteristic
208#6127—432no—
209C2×D52—22no—
210C2×D52—22no—
211C2×D52—24no—
212C2×D52—21no—
213C2×D52—44no—
214C2×D52C2412yes—
215C2×C4×D13—22no—
216C2×C4×D13—22no—
217C2×C4×D13—24no—
218C2×C4×D13—24no—
219C2×C4×D13—24no—
220C2×C4×D13—44no—
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—28no—
235C2×C8×C13#4114yescomplemented
236C2×C8×C13C2412yes—
237C2×C8×C13C2412yes—
238C13×C4⋊C4—21no—
239C13×C4⋊C4—21no—
240C13×C4⋊C4—21no—
241C13×C4⋊C4—24no—
242C13×C4⋊C4—21no—
243C13×C4⋊C4—24no—
244C13×C4⋊C4C2412yes—
245C13×C4⋊C4C2412yes—
246C13×C4⋊C4C2412yes—
247C13×C4⋊C4C2412yes—
248C22⋊Dic13—24no—
249C22⋊Dic13C2×D414yes—
250#6103—24no—
251#6103—24no—
252#6103—24no—
253#6103—24no—
254#6103C2×D414yes—
255C4⋊Dic13—21no—
256C4⋊Dic13—21no—
257C4⋊Dic13—24no—
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—22no—
272C2×#1055C2412yes—
273C2×#1055C2412yes—
274#6095—28no—
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×#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×#106D1311yescharacteristic, complemented
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—
305C2×C4×C13—22no—
306C2×C4×C13—24no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13—48no—
316C2×C4×C13—42no—
317C2×C4×C13—42no—
318C2×C4×C13—84no—
319C2×C4×C13C22×D412yes—
320C2×C4×C13C22×D411yescharacteristic
321C2×C4×C13C2×#4112yes—
322C2×C4×C132−1+412yes—
323C2×C4×C13C2511yescharacteristic
324C22⋊D13—48no—
325C22⋊D13C2×SD16116yescomplemented
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—42no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13C2×SD1614yes—
335C2×Dic13C22×D412yes—
336C2×Dic13C22×D412yes—
337C2×Dic13C22×D412yes—
338D52—22no—
339D52—22no—
340D52—48no—
341D52—42no—
342C4×D13—24no—
343C4×D13—22no—
344C4×D13—22no—
345C4×D13—48no—
346C4×D13—48no—
347C4×D13—84no—
348Dic26—22no—
349Dic26—22no—
350Dic26—42no—
351Dic26—48no—
352Dic26—84no—
353C8×C13—22no—
354C8×C13C2×#4114yescomplemented
355#1055—22no—
356#1055—22no—
357C22×#41—261no—
358C22×SD16—131no—
359C23×C8—131no—
360C23×C8C2×D1311yescharacteristic
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×#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⋊C4C2×D1311yescharacteristic
384C22×C4⋊C4C2×D1311yescharacteristic
385#498—138no—
386#483—138no—
387#483—138no—
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—131no—
400C2×#106—131no—
401C2×#106—138no—
402C2×#106C2×D1311yescharacteristic
403C2×#106C2×D1311yescharacteristic
404C2×#106C2×D1311yescharacteristic
405C2×#106C2×D1311yescharacteristic
406C2×#106C2×D1318yescomplemented
407C2×C4⋊C8—131no—
408C2×#103—131no—
409C2×#103—131no—
410C2×#103—131no—
411C2×#102—131no—
412C2×#102—131no—
413C2×#102—131no—
414C2×C22⋊C8—131no—
415C2×C22⋊C8—131no—
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—131no—
450C22×Q8—261no—
451C22×Q8—261no—
452C22×D4—131no—
453C22×D4—131no—
454C22×D4—261no—
455C22×D4—261no—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—131no—
459C23×C4—261no—
460C23×C4—261no—
461C23×C4—261no—
462C23×C4C22×D1311yescharacteristic
463C2×SD16—134no—
464C2×SD16—264no—
465C22×C8—24no—
466C22×C8—131no—
467C22×C8—131no—
468C22×C8—134no—
469C22×C8—264no—
470C22×C8C22×D1311yescharacteristic
471C22×C8C22×D1314yes—
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—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—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—131no—
503C2×C4⋊C4—131no—
504C2×C4⋊C4—131no—
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⋊C4C22×D1311yescharacteristic
517C2×C4⋊C4C22×D1311yescharacteristic
518C2×C4⋊C4C22×D1311yescharacteristic
519C2×C4⋊C4C22×D1311yescharacteristic
520C2×C4⋊C4C22×D1314yes—
521C2×C4⋊C4C22×D1314yes—
522C2×C22⋊C4—131no—
523C2×C22⋊C4—131no—
524C2×C22⋊C4—261no—
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#106C22×D1314yes—
537#106C22×D1314yes—
538#106C22×D1314yes—
539#106C22×D1314yes—
540C4⋊C8—134no—
541#103—134no—
542#103—134no—
543#103—134no—
544#102—134no—
545#102—134no—
546#102—134no—
547C22⋊C8—134no—
548C22⋊C8—134no—
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—132no—
562C2×Q8—264no—
563C2×Q8—264no—
564C2×Q8—261no—
565C2×Q8—262no—
566C2×Q8—262no—
567C2×Q8—524no—
568C2×Q8—1042no—
569C2×D4—138no—
570C2×D4—134no—
571C2×D4—132no—
572C2×D4—264no—
573C2×D4—264no—
574C2×D4—262no—
575C2×D4—261no—
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—24no—
587C22×C4—44no—
588C22×C4—82no—
589C22×C4—131no—
590C22×C4—131no—
591C22×C4—131no—
592C22×C4—132no—
593C22×C4—132no—
594C22×C4—264no—
595C22×C4—264no—
596C22×C4—264no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—261no—
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—28no—
612C2×C8—132no—
613C2×C8—132no—
614C2×C8—262no—
615C2×C8—262no—
616C2×C8—268no—
617C2×C8#612714yescomplemented
618C2×C8C23×D1312yes—
619C2×C8C23×D1312yes—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—134no—
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⋊C4C23×D1312yes—
639C4⋊C4C23×D1312yes—
640C4⋊C4C23×D1312yes—
641C4⋊C4C23×D1312yes—
642C22⋊C4—134no—
643C22⋊C4—134no—
644C22⋊C4—264no—
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—262no—
667Q8—262no—
668Q8—528no—
669Q8—522no—
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—84no—
691C2×C4—134no—
692C2×C4—132no—
693C2×C4—132no—
694C2×C4—132no—
695C2×C4—262no—
696C2×C4—262no—
697C2×C4—264no—
698C2×C4—262no—
699C2×C4—262no—
700C2×C4—262no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—528no—
704C2×C4—528no—
705C2×C4—522no—
706C2×C4—522no—
707C2×C4—522no—
708C2×C4—1044no—
709C2×C4C2×#612712yes—
710C2×C4C2×D4×D1312yes—
711C2×C4C2×D4×D1311yescharacteristic
712C2×C4#8825412yes—
713C2×C4C24×D1311yescharacteristic
714C8—22no—
715C8—262no—
716C8—262no—
717C8C2×#612714yescomplemented
718C22—28no—
719C22—22no—
720C22—22no—
721C22—134no—
722C22—268no—
723C22—262no—
724C22—262no—
725C22—522no—
726C22—522no—
727C22—522no—
728C22—1044no—
729C22#1171921212yes—
730C22C2×SD16×D1314yes—
731C22C2×SD16×D1312yes—
732C22#1171946712yes—
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#1171921212yes—
746C4C22×#612711yescharacteristic
747C4C2×#8825411yescharacteristic
748C2—24no—
749C2—264no—
750C2—1042no—
751C2#1312718914yesdirect product factor
752C2C2×#1171921211yescharacteristic
753C2C22×SD16×D1311yescharacteristic
754C2C2×#1171946711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×#106C2
socleC23×C13C22×D4
prime radicalC2×#11719212C2
hypercenterC22×#106D13
hypocenterC13C2×#3335
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
1. C2×#11719216C2semidirect
3. #13127189C2direct (N × H)
4. C2×#11718516C2semidirect
5. C2×#11718524C2semidirect
6. C2×#11718629C2semidirect
7. C2×#11718523C2semidirect
8. C2×#11718632C2semidirect
9. C2×#11718515C2semidirect
10. C2×#11718531C2semidirect
11. C2×#11718525C2semidirect
12. C2×#11718775C2semidirect
13. C2×#11718513C2semidirect
14. C2×C8×C22⋊D13C2semidirect
15. C2×D13×#106C2semidirect
16. C22×C13×#106C2semidirect
30. #11719216C22semidirect
49. C2×C13×#106C22semidirect
51. #11718775C22semidirect
53. C8×C22⋊D13C22semidirect
59. #11718632C22semidirect
62. #11718629C22semidirect
69. #11718531C22semidirect
70. #11718525C22semidirect
71. #11718524C22semidirect
72. #11718523C22semidirect
73. D13×#106C22semidirect
74. #11718516C22semidirect
75. #11718515C22semidirect
76. #11718513C22semidirect
200. C2×C22⋊D13SD16semidirect
235. C2×C8×C13#41semidirect
291. C22×#106D13semidirect
325. C22⋊D13C2×SD16semidirect
354. C8×C13C2×#41semidirect
406. C2×#106C2×D13semidirect
551. C2×C13#3335semidirect
617. C2×C8#6127semidirect
652. C13C2×#3335semidirect
717. C8C2×#6127semidirect
751. C2#13127189direct (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×#117192122
#131271892
C2×#117185162
C2×#117185242
C2×#117186292
C2×#117185232
C2×#117186322
C2×#117185152
C2×#117185312
C2×#117185252
C2×#117187752
C2×#117185132
C2×C8×C22⋊D132
C2×D13×#1062
C22×C13×#1062
C2×#333513