Finite Group Databasebeta

← C2×#13126949 #16739511

Subgroups — C2×#13126949 #16739511

Order 3328.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719248C211yesmaximal, characteristic, complemented
2C2×#11719257C211yesmaximal, characteristic
3#13126949C2116yesmaximal, direct product factor
4C2×#11718375C211yesmaximal, characteristic, complemented
5C2×#11718396C211yesmaximal, characteristic, complemented
6C2×#11718382C211yesmaximal, characteristic, complemented
7C2×#11718512C211yesmaximal, characteristic, complemented
8C2×#11718798C211yesmaximal, characteristic, complemented
9C2×#11718775C211yesmaximal, characteristic, complemented
10C2×#11718506C211yesmaximal, characteristic, complemented
11C2×#11718394C211yesmaximal, characteristic, complemented
12C2×#11718400C211yesmaximal, characteristic, complemented
13C2×#11718377C211yesmaximal, characteristic, complemented
14C2×#11718794C211yesmaximal, characteristic, complemented
15C22×#88056C211yesmaximal, characteristic, complemented
16C2×C13×#435C211yesmaximal, characteristic, complemented
17C22×#6127C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C22×C13×M16C2211yescharacteristic
20C23×C8×C13C2211yescharacteristic
21C2×C4×D4×C13C2211yescharacteristic
22C2×#88193—21no—
23C2×D4×Dic13—21no—
24C2×#88184C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C2×#88178C2211yescharacteristic
28C2×#88178C2211yescharacteristic
29C2×#88178C2211yescharacteristic
30C22×Dic52C2211yescharacteristic
31C22×Dic52C2211yescharacteristic
32C22×#6095C2211yescharacteristic
33#11719257—24no—
34#11719257C2218yes—
35#11719248—24no—
36#11719248C2218yescomplemented
37C2×#88150—21no—
38C2×#88144—21no—
39C2×#88139—21no—
40C2×#88135—21no—
41C2×#88132—21no—
42C2×#88132—21no—
43C2×#88129C2211yescharacteristic
44C2×#88123C2211yescharacteristic
45C2×C4×Dic26C2211yescharacteristic
46C2×C4×Dic26C2211yescharacteristic
47C13×#435C2218yescomplemented
48C2×C13×C4⋊C8C2211yescharacteristic
49C2×C13×C22⋊C8C2211yescharacteristic
50C2×C13×C22⋊C8C2211yescharacteristic
51C2×C13×#97C2211yescharacteristic
52#11718798C2218yescomplemented
53#11718794C2218yescomplemented
54#11718775C2218yescomplemented
55C2×#88061C2211yescharacteristic
56C2×#88061C2211yescharacteristic
57C2×#88061C2211yescharacteristic
58C2×#88057C2211yescharacteristic
59C2×#88057C2211yescharacteristic
60C2×#88057C2211yescharacteristic
61C2×#88056C2211yescharacteristic
62C2×#88056C2211yescharacteristic
63C2×#88056C2211yescharacteristic
64C2×#88056C2211yescharacteristic
65C2×#88056C2211yescharacteristic
66C2×#88056C2211yescharacteristic
67C2×#88056C2211yescharacteristic
68C2×#88056C2218yescomplemented
69#11718512C2218yescomplemented
70#11718506C2218yescomplemented
71#11718400C2218yescomplemented
72#11718396C2218yescomplemented
73#11718394C2218yescomplemented
74#11718382C2218yescomplemented
75#11718377C2218yescomplemented
76#11718375C2218yescomplemented
77C22×D4×C13D411yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C22×C22⋊D13—21no—
81C22×C22⋊D13—21no—
82C23×Dic13—21no—
83C23×Dic13—21no—
84C23×Dic13—21no—
85C2×#6127—22no—
86C2×#6127—24no—
87C2×#6127—42no—
88C2×#6127C2314yes—
89C22×D52C2311yescharacteristic
90C22×C4×D13—21no—
91C22×Dic26—24no—
92C22×Dic26—21no—
93C22×Dic26—22no—
94C22×Dic26—21no—
95C22×Dic26—42no—
96C22×Dic26C2311yescharacteristic
97C22×Dic26C2311yescharacteristic
98C22×Dic26C2314yes—
99C22×Dic26C2311yescharacteristic
100C2×C13×M16—42no—
101C2×C13×M16C2314yes—
102C22×C8×C13—42no—
103C22×C8×C13C2311yescharacteristic
104C22×C8×C13C2311yescharacteristic
105C22×C8×C13C2311yescharacteristic
106C22×C8×C13C2311yescharacteristic
107C22×C8×C13C2314yes—
108C4×D4×C13D414yes—
109C4×D4×C13C2314yes—
110C2×C13×C4⋊C4D411yescharacteristic
111C2×C13×C22⋊C4D411yescharacteristic
112C2×C13×C22⋊C4D411yescharacteristic
113C2×C42×C13C2311yescharacteristic
114C2×C22⋊Dic13—21no—
115C2×C22⋊Dic13—21no—
116C2×C22⋊Dic13—21no—
117#88193—28no—
118D4×Dic13—28no—
119#88184—22no—
120#88184C2314yes—
121C2×#6103—21no—
122C2×#6103—21no—
123C2×#6103—21no—
124C2×C4⋊Dic13—21no—
125C2×C4⋊Dic13—21no—
126C2×C4⋊Dic13—21no—
127C2×C4⋊Dic13—22no—
128C2×C4⋊Dic13—22no—
129C2×C4⋊Dic13C2311yescharacteristic
130C2×C4⋊Dic13C2311yescharacteristic
131C2×C4⋊Dic13C2311yescharacteristic
132C2×C4⋊Dic13C2311yescharacteristic
133C2×C4⋊Dic13C2314yes—
134C2×C4⋊Dic13C2314yes—
135#88178—22no—
136#88178—22no—
137#88178—22no—
138#88178C2314yes—
139#88178C2314yes—
140#88178C2314yes—
141C2×#6101—21no—
142C2×#6101—21no—
143C2×#6101—21no—
144C2×#6101—21no—
145C2×#6101—21no—
146C2×C4×Dic13—21no—
147C2×C4×Dic13—21no—
148C2×Dic52—24no—
149C2×Dic52—42no—
150C2×Dic52C2314yes—
151C2×Dic52C2314yes—
152C2×#6095—42no—
153C2×#6095C2314yes—
154#88150—28no—
155#88144—28no—
156#88139—28no—
157#88135—28no—
158#88132—28no—
159#88132—28no—
160#88129—22no—
161#88129C2314yes—
162#88123—22no—
163#88123C2314yes—
164C4×Dic26—22no—
165C4×Dic26—22no—
166C4×Dic26C2314yes—
167C4×Dic26C2314yes—
168C13×C4⋊C8C2314yes—
169C13×C22⋊C8C2314yes—
170C13×C22⋊C8C2314yes—
171C13×#97C2314yes—
172#88061C2314yes—
173#88061C2314yes—
174#88061C2314yes—
175#88057C2314yes—
176#88057C2314yes—
177#88057C2314yes—
178#88056C2314yes—
179#88056C2314yes—
180#88056C2314yes—
181#88056C2314yes—
182#88056C2314yes—
183#88056C2314yes—
184#88056C2314yes—
185C2×#3316—131nomaximal, Sylow
186C24×C13C2×D411yescharacteristic
187C24×C13C2×D411yescharacteristic
188C23×D13—21no—
189C2×D4×C13—24no—
190C2×D4×C13C2×D414yes—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13C2×D411yescharacteristic
196C22×C4×C13C2×D411yescharacteristic
197C22×C4×C13C2×D411yescharacteristic
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D412yes—
200C22×C4×C13C2×D412yes—
201C22×C4×C13C2412yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2411yescharacteristic
204C2×C22⋊D13—24no—
205C2×C22⋊D13—24no—
206C2×C22⋊D13—44no—
207C2×C22⋊D13—44no—
208C22×Dic13—21no—
209C22×Dic13—24no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—24no—
217C22×Dic13—24no—
218C22×Dic13—44no—
219C22×Dic13—82no—
220C22×Dic13—82no—
221#6127—28no—
222#6127—44no—
223#6127—48no—
224C2×D52—22no—
225C2×D52—22no—
226C2×D52—21no—
227C2×D52C2412yes—
228C2×C4×D13—24no—
229C2×C4×D13—44no—
230C2×Dic26—21no—
231C2×Dic26—22no—
232C2×Dic26—22no—
233C2×Dic26—22no—
234C2×Dic26—22no—
235C2×Dic26—22no—
236C2×Dic26—28no—
237C2×Dic26—21no—
238C2×Dic26—21no—
239C2×Dic26—24no—
240C2×Dic26—24no—
241C2×Dic26—44no—
242C2×Dic26—48no—
243C2×Dic26—44no—
244C2×Dic26—82no—
245C2×Dic26#4114yes—
246C2×Dic26C2412yes—
247C2×Dic26C2412yes—
248C2×Dic26C2412yes—
249C13×M16—44no—
250C2×C8×C13—22no—
251C2×C8×C13—22no—
252C2×C8×C13—22no—
253C2×C8×C13—22no—
254C2×C8×C13—44no—
255C2×C8×C13C2412yes—
256C2×C8×C13C2412yes—
257C2×C8×C13C2412yes—
258C2×C8×C13C2412yes—
259C13×C4⋊C4C2×D414yes—
260C13×C22⋊C4C2×D414yes—
261C13×C22⋊C4C2×D414yes—
262C42×C13C2×D412yes—
263C42×C13C2412yes—
264C22⋊Dic13—24no—
265C22⋊Dic13—24no—
266C22⋊Dic13—24no—
267#6103—24no—
268#6103—24no—
269#6103—24no—
270C4⋊Dic13—21no—
271C4⋊Dic13—21no—
272C4⋊Dic13—21no—
273C4⋊Dic13—21no—
274C4⋊Dic13—24no—
275C4⋊Dic13—24no—
276C4⋊Dic13—24no—
277C4⋊Dic13C2412yes—
278C4⋊Dic13C2412yes—
279C4⋊Dic13C2412yes—
280C4⋊Dic13C2412yes—
281#6101—24no—
282#6101—24no—
283#6101—24no—
284#6101—24no—
285#6101—24no—
286C4×Dic13—24no—
287C4×Dic13—24no—
288Dic52—28no—
289Dic52—44no—
290#6095—44no—
291C2×#554—131no—
292C2×#548—131no—
293#3316—1316no—
294C2×#489—131no—
295C2×#481—131no—
296C2×#483—131no—
297C2×#475—131no—
298C2×#470—131no—
299C2×#465—131no—
300C2×#464—131no—
301C2×#452—131no—
302C2×#451—131no—
303C2×#441—131no—
304C2×#435D1311yescharacteristic, complemented
305C2×#417—131no—
306C22×#103—131no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13#13714yes—
313C23×C13C22×D412yes—
314C23×C13C22×D412yes—
315C23×C13C22×D411yescharacteristic
316C22×D13—22no—
317C22×D13—42no—
318C22×D13—42no—
319C22×D13—42no—
320D4×C13—28no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—24no—
326C2×C4×C13—24no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13C22×D412yes—
332C2×C4×C13C22×D412yes—
333C2×C4×C13C22×D412yes—
334C2×C4×C13C22×D412yes—
335C2×C4×C13C22×D411yescharacteristic
336C2×C4×C13C2×#4112yes—
337C2×C4×C13H(5,𝔽2)12yes—
338C2×C4×C13C2511yescharacteristic
339C22⋊D13—48no—
340C22⋊D13—48no—
341C2×Dic13—24no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—48no—
350C2×Dic13—42no—
351C2×Dic13—42no—
352C2×Dic13—42no—
353C2×Dic13—42no—
354C2×Dic13—42no—
355C2×Dic13—42no—
356C2×Dic13—84no—
357C2×Dic13—84no—
358D52—22no—
359D52—22no—
360D52—42no—
361C4×D13—48no—
362Dic26—24no—
363Dic26—22no—
364Dic26—22no—
365Dic26—22no—
366Dic26—22no—
367Dic26—22no—
368Dic26—48no—
369Dic26—42no—
370Dic26—42no—
371Dic26—84no—
372Dic26C2×#4114yes—
373C8×C13—22no—
374C8×C13—22no—
375C8×C13—22no—
376C8×C13—22no—
377C22×#41—131no—
378C23×Q8—131no—
379C22×Q16—131no—
380C22×Q16—131no—
381C22×SD16—131no—
382C22×M16C2×D1311yescharacteristic
383C23×C8C2×D1311yescharacteristic
384#554—138no—
385#554—264no—
386#548—138no—
387#548—264no—
388C2×C4⋊Q8—131no—
389C2×#125—261no—
390C2×#124—131no—
391C2×#124—261no—
392C2×C22⋊Q8—131no—
393C2×C22⋊Q8—131no—
394C2×C22⋊Q8—131no—
395C2×C22⋊Q8—261no—
396C2×C22⋊Q8—261no—
397C2×C22⋊Q8—261no—
398C2×#121—131no—
399C2×#121—261no—
400C2×C4×Q8—131no—
401C2×C4×Q8—131no—
402C2×C4×D4—261no—
403C2×C4×D4—261no—
404C2×C4×D4C2×D1311yescharacteristic
405C22×C4⋊C4—131no—
406C22×C4⋊C4—131no—
407#489—138no—
408#483—138no—
409#481—138no—
410#475—138no—
411#470—138no—
412#465—138no—
413#464—138no—
414#452—138no—
415#451—138no—
416#441—138no—
417#435C2×D1318yescomplemented
418C2×#106—131no—
419C2×#106—131no—
420C2×#106—131no—
421C2×C4⋊C8C2×D1311yescharacteristic
422#417—138no—
423C2×#103—131no—
424C2×#103—131no—
425C2×#103—131no—
426C2×#103—131no—
427C2×#103—131no—
428C2×#103—131no—
429C2×#103—138no—
430C2×#103—131no—
431C2×#102—131no—
432C2×#102—131no—
433C2×#102—131no—
434C2×C22⋊C8C2×D1311yescharacteristic
435C2×C22⋊C8C2×D1311yescharacteristic
436C2×#97C2×D1311yescharacteristic
437C22×C13—22no—
438C22×C13—28no—
439C22×C13—22no—
440C22×C13—22no—
441C22×C13—22no—
442C22×C13—22no—
443C22×C13—44no—
444C22×C13#54612yes—
445C22×C13C2×#13714yes—
446C22×C13C2×#13712yes—
447C22×C13#57712yes—
448C22×C13C23×D411yescharacteristic
449C2×D13—42no—
450C2×D13—42no—
451C2×D13—42no—
452C2×D13—84no—
453C4×C13—22no—
454C4×C13—22no—
455C4×C13—22no—
456C4×C13—22no—
457C4×C13#54612yes—
458C4×C13C22×#4111yescharacteristic
459C4×C13C2×H(5,𝔽2)11yescharacteristic
460Dic13—24no—
461Dic13—42no—
462Dic13—42no—
463Dic13—42no—
464Dic13—42no—
465Dic13—42no—
466Dic13—42no—
467C2×#41—134no—
468C2×#41—264no—
469C2×#41—262no—
470C2×#41—522no—
471C22×Q8—131no—
472C22×Q8—131no—
473C22×Q8—131no—
474C22×Q8—134no—
475C22×Q8—264no—
476C22×Q8—261no—
477C22×Q8—262no—
478C22×Q8—261no—
479C22×Q8—522no—
480C22×D4—131no—
481C22×D4—261no—
482C22×D4—261no—
483C22×D4D5211yescharacteristic
484C23×C4—261no—
485C23×C4—261no—
486C23×C4—261no—
487C23×C4—261no—
488C23×C4C22×D1311yescharacteristic
489C23×C4C22×D1311yescharacteristic
490C2×Q16—134no—
491C2×Q16—134no—
492C2×Q16—264no—
493C2×Q16—522no—
494C2×SD16—134no—
495C2×SD16—522no—
496C2×M16—42no—
497C2×M16C22×D1314yes—
498C22×C8—42no—
499C22×C8C22×D1311yescharacteristic
500C22×C8C22×D1311yescharacteristic
501C22×C8C22×D1311yescharacteristic
502C22×C8C22×D1311yescharacteristic
503C22×C8C22×D1314yes—
504C4⋊Q8—134no—
505C4⋊Q8—262no—
506#125—268no—
507#124—134no—
508#124—268no—
509#124—262no—
510C22⋊Q8—134no—
511C22⋊Q8—134no—
512C22⋊Q8—134no—
513C22⋊Q8—262no—
514C22⋊Q8—262no—
515C22⋊Q8—262no—
516C22⋊Q8—268no—
517C22⋊Q8—268no—
518C22⋊Q8—268no—
519#121—134no—
520#121—268no—
521#121—262no—
522C4×Q8—134no—
523C4×Q8—134no—
524C4×Q8—262no—
525C4×Q8—262no—
526C4×D4—268no—
527C4×D4—268no—
528C4×D4D5214yes—
529C4×D4C22×D1314yes—
530C2×C4⋊C4—131no—
531C2×C4⋊C4—131no—
532C2×C4⋊C4—131no—
533C2×C4⋊C4—134no—
534C2×C4⋊C4—134no—
535C2×C4⋊C4—131no—
536C2×C4⋊C4—261no—
537C2×C4⋊C4—261no—
538C2×C4⋊C4—262no—
539C2×C4⋊C4—262no—
540C2×C4⋊C4—261no—
541C2×C4⋊C4—261no—
542C2×C4⋊C4—261no—
543C2×C4⋊C4—261no—
544C2×C4⋊C4—261no—
545C2×C4⋊C4—261no—
546C2×C4⋊C4D5211yescharacteristic
547C2×C22⋊C4—261no—
548C2×C22⋊C4—261no—
549C2×C22⋊C4—261no—
550C2×C22⋊C4—261no—
551C2×C22⋊C4—261no—
552C2×C22⋊C4—261no—
553C2×C22⋊C4D5211yescharacteristic
554C2×C22⋊C4D5211yescharacteristic
555C2×C42—261no—
556C2×C42—261no—
557C2×C42C22×D1311yescharacteristic
558#106—134no—
559#106—134no—
560#106—134no—
561C4⋊C8C22×D1314yes—
562#103—134no—
563#103—134no—
564#103—134no—
565#103—134no—
566#103—134no—
567#103—134no—
568#103—134no—
569#102—134no—
570#102—134no—
571#102—134no—
572C22⋊C8C22×D1314yes—
573C22⋊C8C22×D1314yes—
574#97C22×D1314yes—
575C2×C13—24no—
576C2×C13—42no—
577C2×C13#331614yescomplemented
578C2×C13C2×#54611yescharacteristic
579C2×C13C22×#13711yescharacteristic
580C2×C13C2×#57711yescharacteristic
581D13—82no—
582C24—261no—
583C24C2×D5211yescharacteristic
584C24C2×D5211yescharacteristic
585#41—268no—
586#41—524no—
587#41—528no—
588C2×Q8—134no—
589C2×Q8—132no—
590C2×Q8—132no—
591C2×Q8—132no—
592C2×Q8—268no—
593C2×Q8—261no—
594C2×Q8—261no—
595C2×Q8—264no—
596C2×Q8—261no—
597C2×Q8—264no—
598C2×Q8—262no—
599C2×Q8—262no—
600C2×Q8—262no—
601C2×Q8—262no—
602C2×Q8—262no—
603C2×Q8—524no—
604C2×Q8—524no—
605C2×Q8—528no—
606C2×Q8—1042no—
607C2×D4—24no—
608C2×D4—132no—
609C2×D4—264no—
610C2×D4—264no—
611C2×D4—261no—
612C2×D4—262no—
613C2×D4—262no—
614C2×D4—524no—
615C2×D4—524no—
616C2×D4C2×D5214yes—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—261no—
622C22×C4—264no—
623C22×C4—261no—
624C22×C4—261no—
625C22×C4—261no—
626C22×C4—261no—
627C22×C4—261no—
628C22×C4—261no—
629C22×C4—264no—
630C22×C4—264no—
631C22×C4—264no—
632C22×C4—524no—
633C22×C4—524no—
634C22×C4—1042no—
635C22×C4—1042no—
636C22×C4C2×D5212yes—
637C22×C4C2×D5212yes—
638C22×C4C2×D5211yescharacteristic
639C22×C4C2×D5211yescharacteristic
640C22×C4C2×D5211yescharacteristic
641C22×C4C2×D5211yescharacteristic
642C22×C4C23×D1312yes—
643C22×C4C23×D1312yes—
644C22×C4C23×D1311yescharacteristic
645Q16—268no—
646Q16—524no—
647SD16—524no—
648M16—44no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—44no—
654C2×C8C23×D1312yes—
655C2×C8C23×D1312yes—
656C2×C8C23×D1312yes—
657C2×C8C23×D1312yes—
658C4⋊C4—132no—
659C4⋊C4—132no—
660C4⋊C4—132no—
661C4⋊C4—132no—
662C4⋊C4—261no—
663C4⋊C4—264no—
664C4⋊C4—264no—
665C4⋊C4—261no—
666C4⋊C4—261no—
667C4⋊C4—261no—
668C4⋊C4—264no—
669C4⋊C4—264no—
670C4⋊C4—264no—
671C4⋊C4—264no—
672C4⋊C4—264no—
673C4⋊C4—264no—
674C4⋊C4C2×D5214yes—
675C22⋊C4—264no—
676C22⋊C4—264no—
677C22⋊C4—264no—
678C22⋊C4—264no—
679C22⋊C4—264no—
680C22⋊C4—264no—
681C22⋊C4C2×D5214yes—
682C22⋊C4C2×D5214yes—
683C42—264no—
684C42—264no—
685C42C2×D5212yes—
686C42C23×D1312yes—
687C13C2×#331611yescharacteristic, complemented, Sylow
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—262no—
694C23—522no—
695C23—522no—
696C23—522no—
697C23#8816314yes—
698C23C22×D5212yes—
699C23C22×D5212yes—
700C23C22×D5211yescharacteristic
701Q8—134no—
702Q8—264no—
703Q8—262no—
704Q8—262no—
705Q8—262no—
706Q8—262no—
707Q8—262no—
708Q8—528no—
709Q8—522no—
710Q8—522no—
711Q8—1044no—
712D4—28no—
713D4—262no—
714D4—262no—
715D4—528no—
716D4—528no—
717D4—522no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—264no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—262no—
735C2×C4—262no—
736C2×C4—528no—
737C2×C4—528no—
738C2×C4—522no—
739C2×C4—522no—
740C2×C4—522no—
741C2×C4—522no—
742C2×C4—522no—
743C2×C4—522no—
744C2×C4—1044no—
745C2×C4—1044no—
746C2×C4C22×D5212yes—
747C2×C4C22×D5212yes—
748C2×C4C22×D5212yes—
749C2×C4C22×D5212yes—
750C2×C4C22×D5211yescharacteristic
751C2×C4#8825112yes—
752C2×C4#41×D1312yes—
753C2×C4C24×D1311yescharacteristic
754C8—22no—
755C8—22no—
756C8—22no—
757C8—22no—
758C22—28no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—522no—
766C22—522no—
767C22—522no—
768C22—1044no—
769C22#1171925912yes—
770C22C2×#8816314yes—
771C22C2×#8816312yes—
772C22#1171945612yes—
773C22C23×D5211yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—264no—
779C4—522no—
780C4—522no—
781C4—522no—
782C4—522no—
783C4—522no—
784C4—522no—
785C4#1171925912yes—
786C4C2×#8825111yescharacteristic
787C4C2×#41×D1311yescharacteristic
788C2—24no—
789C2—42no—
790C2—1042no—
791C2#1312694914yesdirect product factor
792C2C2×#1171925911yescharacteristic
793C2C22×#8816311yescharacteristic
794C2C2×#1171945611yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#435C2
socleC23×C13C22×D4
prime radicalC2×#11719257C2
hypercenterC2×#435D13
hypocenterC13C2×#3316
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#11719248C2semidirect
3. #13126949C2direct (N × H)
4. C2×#11718375C2semidirect
5. C2×#11718396C2semidirect
6. C2×#11718382C2semidirect
7. C2×#11718512C2semidirect
8. C2×#11718798C2semidirect
9. C2×#11718775C2semidirect
10. C2×#11718506C2semidirect
11. C2×#11718394C2semidirect
12. C2×#11718400C2semidirect
13. C2×#11718377C2semidirect
14. C2×#11718794C2semidirect
15. C22×#88056C2semidirect
16. C2×C13×#435C2semidirect
36. #11719248C22semidirect
47. C13×#435C22semidirect
52. #11718798C22semidirect
53. #11718794C22semidirect
54. #11718775C22semidirect
68. C2×#88056C22semidirect
69. #11718512C22semidirect
70. #11718506C22semidirect
71. #11718400C22semidirect
72. #11718396C22semidirect
73. #11718394C22semidirect
74. #11718382C22semidirect
75. #11718377C22semidirect
76. #11718375C22semidirect
304. C2×#435D13semidirect
417. #435C2×D13semidirect
577. C2×C13#3316semidirect
687. C13C2×#3316semidirect
791. C2#13126949direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192482
C2×#117192572
#131269492
C2×#117183752
C2×#117183962
C2×#117183822
C2×#117185122
C2×#117187982
C2×#117187752
C2×#117185062
C2×#117183942
C2×#117184002
C2×#117183772
C2×#117187942
C22×#880562
C2×C13×#4352
C2×#331613