Finite Group Databasebeta

← C2×#13126710 #16739312

Subgroups — C2×#13126710 #16739312

Order 3328.

2158 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719216C211yesmaximal, characteristic
2C2×#11719337C211yesmaximal, characteristic
3#13126710C2116yesmaximal, direct product factor
4C2×#11718453C211yesmaximal, characteristic, complemented
5C2×#11718545C211yesmaximal, characteristic, complemented
6C2×#11718536C211yesmaximal, characteristic, complemented
7C2×#11718548C211yesmaximal, characteristic, complemented
8C2×#11718712C211yesmaximal, characteristic, complemented
9C2×#11718454C211yesmaximal, characteristic, complemented
10C2×#11718400C211yesmaximal, characteristic, complemented
11C2×#11718469C211yesmaximal, characteristic, complemented
12C2×#11718534C211yesmaximal, characteristic, complemented
13C2×#11718386C211yesmaximal, characteristic
14C22×#88050C211yesmaximal, characteristic, complemented
15C2×D13×#103C211yesmaximal, characteristic, complemented
16C2×C13×#484C211yesmaximal, characteristic, complemented
17C22×Q8×D13C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C2×#88198C2211yescharacteristic
22C22×#6107C2211yescharacteristic
23C2×C4×C22⋊D13—21no—
24C2×C4×C22⋊D13C2211yescharacteristic
25C2×#88178—21no—
26C2×#88178C2211yescharacteristic
27C23×#1055C2211yescharacteristic
28C22×Dic52C2211yescharacteristic
29C22×Dic52C2211yescharacteristic
30C22×C8×D13C2211yescharacteristic
31#11719337—24no—
32#11719337C2218yes—
33#11719216—24no—
34#11719216C2218yes—
35C2×#88151C2211yescharacteristic
36C2×#88151C2211yescharacteristic
37C2×#88150—21no—
38C2×#88150—21no—
39C2×C4⋊C4×D13C2211yescharacteristic
40C2×#88143—21no—
41C2×#88142—21no—
42C2×#88142C2211yescharacteristic
43C2×#88141C2211yescharacteristic
44C2×#88141C2211yescharacteristic
45C2×#88135—21no—
46C2×#88132—21no—
47C13×#484C2218yescomplemented
48C2×C13×#107C2211yescharacteristic
49C2×C13×#107C2211yescharacteristic
50C2×C13×#103C2211yescharacteristic
51C2×C13×#103C2211yescharacteristic
52C2×C13×C22⋊C8C2211yescharacteristic
53C2×#88075C2211yescharacteristic
54C2×#88060C2211yescharacteristic
55C2×#88056C2211yescharacteristic
56C2×#88056C2211yescharacteristic
57C2×#88054C2211yescharacteristic
58C2×C8×Dic13C2211yescharacteristic
59#11718712C2218yescomplemented
60C2×#88050C2211yescharacteristic
61C2×#88050C2211yescharacteristic
62C2×#88050C2211yescharacteristic
63C2×#88050C2211yescharacteristic
64C2×#88050C2211yescharacteristic
65C2×#88050C2218yescomplemented
66C2×#88047C2211yescharacteristic
67#11718548C2218yescomplemented
68#11718545C2218yescomplemented
69#11718536C2218yescomplemented
70#11718534C2218yescomplemented
71#11718469C2218yescomplemented
72D13×#103C2218yescomplemented
73#11718454C2218yescomplemented
74#11718453C2218yescomplemented
75#11718400C2218yescomplemented
76#11718386C2218yes—
77C22×Q8×C13C2311yescharacteristic
78C23×C4×C13—21no—
79C23×C4×C13C2311yescharacteristic
80C22×C22⋊D13D411yescharacteristic
81C23×Dic13—21no—
82C2×Q8×D13—22no—
83C2×Q8×D13—24no—
84C2×Q8×D13—42no—
85C2×Q8×D13C2314yes—
86C22×C4×D13—21no—
87C22×C4×D13—21no—
88C22×C4×D13C2311yescharacteristic
89C22×Dic26—24no—
90C22×Dic26—21no—
91C22×Dic26—22no—
92C22×Dic26—21no—
93C22×Dic26—21no—
94C22×Dic26—42no—
95C22×Dic26C2311yescharacteristic
96C22×Dic26C2311yescharacteristic
97C22×Dic26C2314yes—
98C22×Dic26C2311yescharacteristic
99C22×C8×C13C2311yescharacteristic
100C22×C8×C13C2311yescharacteristic
101C13×C22⋊Q8—22no—
102C13×C22⋊Q8C2314yes—
103C2×C13×C4⋊C4—21no—
104C2×C13×C4⋊C4—21no—
105C2×C13×C4⋊C4—22no—
106C2×C13×C4⋊C4C2311yescharacteristic
107C2×C13×C4⋊C4C2311yescharacteristic
108C2×C13×C4⋊C4C2311yescharacteristic
109C2×C13×C4⋊C4C2314yes—
110C2×C13×C22⋊C4—21no—
111C2×C22⋊Dic13—21no—
112C2×C22⋊Dic13D411yescharacteristic
113#88198—22no—
114#88198C2314yes—
115C2×#6107—42no—
116C2×#6107C2314yes—
117C4×C22⋊D13—28no—
118C4×C22⋊D13D414yes—
119C4×C22⋊D13C2314yes—
120C2×#6103—21no—
121C2×#6103—21no—
122C2×#6103D411yescharacteristic
123C2×C4⋊Dic13—21no—
124C2×C4⋊Dic13—21no—
125C2×C4⋊Dic13C2311yescharacteristic
126#88178—22no—
127#88178—28no—
128#88178C2314yes—
129C2×#6101—21no—
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×Dic13—21no—
139C2×C4×Dic13C2311yescharacteristic
140C22×#1055—42no—
141C22×#1055C2311yescharacteristic
142C22×#1055C2311yescharacteristic
143C22×#1055C2314yes—
144C2×Dic52—24no—
145C2×Dic52—42no—
146C2×Dic52C2314yes—
147C2×Dic52C2314yes—
148C2×C8×D13—42no—
149C2×C8×D13C2314yes—
150#88151—22no—
151#88151—22no—
152#88151C2314yes—
153#88151C2314yes—
154#88150—28no—
155#88150—28no—
156C4⋊C4×D13—22no—
157C4⋊C4×D13C2314yes—
158#88143—28no—
159#88142—28no—
160#88142—22no—
161#88142C2314yes—
162#88141—22no—
163#88141—22no—
164#88141C2314yes—
165#88141C2314yes—
166#88135—28no—
167#88132—28no—
168C13×#107C2314yes—
169C13×#107C2314yes—
170C13×#103C2314yes—
171C13×#103C2314yes—
172C13×C22⋊C8C2314yes—
173#88075C2314yes—
174#88060C2314yes—
175#88056C2314yes—
176#88056C2314yes—
177#88054C2314yes—
178C8×Dic13C2314yes—
179#88050C2314yes—
180#88050C2314yes—
181#88050C2314yes—
182#88050C2314yes—
183#88050C2314yes—
184#88047C2314yes—
185C2×#3299—131nomaximal, Sylow
186C24×C13C2×D411yescharacteristic
187C23×D13C2×D411yescharacteristic
188C2×Q8×C13—21no—
189C2×Q8×C13—22no—
190C2×Q8×C13—22no—
191C2×Q8×C13C2412yes—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—24no—
199C22×C4×C13—82no—
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D412yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2411yescharacteristic
204C2×C22⋊D13Q1618yescomplemented
205C2×C22⋊D13C2×D414yes—
206C22×Dic13—21no—
207C22×Dic13—24no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—44no—
212C22×Dic13C2×D411yescharacteristic
213C22×Dic13C2×D411yescharacteristic
214C22×Dic13C2×D411yescharacteristic
215Q8×D13—28no—
216Q8×D13—44no—
217Q8×D13—48no—
218C2×C4×D13—22no—
219C2×C4×D13—22no—
220C2×C4×D13—24no—
221C2×C4×D13—24no—
222C2×C4×D13—44no—
223C2×C4×D13—82no—
224C2×C4×D13C2×D412yes—
225C2×C4×D13C2412yes—
226C2×Dic26—21no—
227C2×Dic26—22no—
228C2×Dic26—22no—
229C2×Dic26—22no—
230C2×Dic26—22no—
231C2×Dic26—22no—
232C2×Dic26—28no—
233C2×Dic26—21no—
234C2×Dic26—24no—
235C2×Dic26—21no—
236C2×Dic26—24no—
237C2×Dic26—24no—
238C2×Dic26—44no—
239C2×Dic26—48no—
240C2×Dic26—44no—
241C2×Dic26—44no—
242C2×Dic26—82no—
243C2×Dic26#4114yes—
244C2×Dic26C2412yes—
245C2×Dic26C2412yes—
246C2×Dic26C2412yes—
247C2×C8×C13—22no—
248C2×C8×C13—22no—
249C2×C8×C13C2412yes—
250C2×C8×C13C2412yes—
251C13×C4⋊C4—21no—
252C13×C4⋊C4—21no—
253C13×C4⋊C4—24no—
254C13×C4⋊C4—21no—
255C13×C4⋊C4—24no—
256C13×C4⋊C4C2412yes—
257C13×C4⋊C4C2412yes—
258C13×C4⋊C4C2412yes—
259C13×C22⋊C4—24no—
260C22⋊Dic13—24no—
261C22⋊Dic13C2×D414yes—
262#6107—44no—
263#6103—24no—
264#6103—24no—
265#6103C2×D414yes—
266C4⋊Dic13—21no—
267C4⋊Dic13—24no—
268C4⋊Dic13—24no—
269C4⋊Dic13C2412yes—
270#6101—24no—
271#6101—24no—
272#6101—24no—
273#6101—24no—
274#6101—24no—
275#6101—24no—
276#6101—24no—
277#6101C2×D414yes—
278C4×Dic13—24no—
279C4×Dic13—24no—
280C4×Dic13C2×D412yes—
281C4×Dic13C2412yes—
282C2×#1055—22no—
283C2×#1055—22no—
284C2×#1055—44no—
285C2×#1055C2412yes—
286C2×#1055C2412yes—
287Dic52—28no—
288Dic52—44no—
289C8×D13—44no—
290C2×#554—131no—
291C2×D4×Q8—131no—
292#3299—1316no—
293C2×#487—131no—
294C2×#484—131no—
295C2×#484D1311yescharacteristic, complemented
296C2×#477—131no—
297C2×#467—131no—
298C2×#467—131no—
299C2×#462—131no—
300C2×#451—131no—
301C2×#451—131no—
302C2×C4×Q16—131no—
303C2×C8×D4—131no—
304C22×#103—131no—
305C22×#103—131no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13C2×Q1614yes—
309C23×C13C22×D412yes—
310C23×C13C22×D411yescharacteristic
311C22×D13—22no—
312C22×D13—22no—
313C22×D13C2×Q1614yes—
314C22×D13C22×D412yes—
315Q8×C13—22no—
316Q8×C13—22no—
317Q8×C13—42no—
318C2×C4×C13—22no—
319C2×C4×C13—24no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—42no—
327C2×C4×C13—42no—
328C2×C4×C13—42no—
329C2×C4×C13—42no—
330C2×C4×C13—84no—
331C2×C4×C13C22×D412yes—
332C2×C4×C13C22×D411yescharacteristic
333C2×C4×C13C2×#4112yes—
334C2×C4×C13H(5,𝔽2)12yes—
335C2×C4×C13C2511yescharacteristic
336C22⋊D13C2×Q16116yescomplemented
337C2×Dic13—24no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—48no—
345C2×Dic13—42no—
346C2×Dic13—42no—
347C2×Dic13—42no—
348C2×Dic13C2×Q1614yes—
349C2×Dic13C22×D412yes—
350C2×Dic13C22×D412yes—
351C2×Dic13C22×D412yes—
352C4×D13—24no—
353C4×D13—22no—
354C4×D13—22no—
355C4×D13—48no—
356C4×D13—84no—
357Dic26—24no—
358Dic26—22no—
359Dic26—22no—
360Dic26—22no—
361Dic26—22no—
362Dic26—22no—
363Dic26—48no—
364Dic26—48no—
365Dic26—42no—
366Dic26—42no—
367Dic26—84no—
368Dic26C2×#4114yes—
369C8×C13—22no—
370C8×C13—22no—
371#1055—22no—
372#1055—22no—
373C23×Q8—131no—
374C23×Q8—131no—
375C22×Q16—131no—
376C22×Q16—131no—
377C22×Q16—131no—
378C23×C8—131no—
379C23×C8—131no—
380#554—138no—
381#554—264no—
382D4×Q8—138no—
383D4×Q8—264no—
384C2×C4⋊Q8—131no—
385C2×C4⋊Q8—131no—
386C2×C4⋊Q8—261no—
387C2×#125—261no—
388C2×C22⋊Q8—131no—
389C2×C22⋊Q8—131no—
390C2×C22⋊Q8—131no—
391C2×C22⋊Q8—261no—
392C2×C22⋊Q8—261no—
393C2×C22⋊Q8—261no—
394C2×C22⋊Q8—261no—
395C2×C22⋊Q8C2×D1311yescharacteristic
396C2×C4×Q8—131no—
397C2×C4×Q8—131no—
398C2×C4×D4—131no—
399C2×C4×D4—261no—
400C2×C4×D4—261no—
401C22×C4⋊C4—131no—
402C22×C4⋊C4C2×D1311yescharacteristic
403#487—138no—
404#484—138no—
405#484C2×D1318yescomplemented
406#477—138no—
407#467—138no—
408#467—138no—
409#462—138no—
410#451—138no—
411#451—138no—
412C4×Q16—138no—
413C8×D4—138no—
414C2×#107—131no—
415C2×#107C2×D1311yescharacteristic
416C2×#107C2×D1311yescharacteristic
417C2×C4⋊C8—131no—
418C2×#103—131no—
419C2×#103—131no—
420C2×#103—131no—
421C2×#103—131no—
422C2×#103—131no—
423C2×#103—131no—
424C2×#103—131no—
425C2×#103—138no—
426C2×#103—131no—
427C2×#103—138no—
428C2×#103C2×D1311yescharacteristic
429C2×#103C2×D1311yescharacteristic
430C2×C22⋊C8—131no—
431C2×C22⋊C8C2×D1311yescharacteristic
432C2×C4×C8—131no—
433C22×C13—22no—
434C22×C13—28no—
435C22×C13—22no—
436C22×C13#54612yes—
437C22×C13C22×Q1614yes—
438C22×C13C22×Q1612yes—
439C22×C13#57712yes—
440C22×C13C23×D411yescharacteristic
441C2×D13—22no—
442C2×D13—28no—
443C2×D13—22no—
444C2×D13C22×Q1614yes—
445C4×C13—22no—
446C4×C13—42no—
447C4×C13—42no—
448C4×C13—42no—
449C4×C13—42no—
450C4×C13#54612yes—
451C4×C13C22×#4111yescharacteristic
452C4×C13C2×H(5,𝔽2)11yescharacteristic
453Dic13—24no—
454Dic13—22no—
455Dic13—22no—
456Dic13—42no—
457Dic13—42no—
458Dic13—42no—
459Dic13C22×Q1614yes—
460C22×Q8—134no—
461C22×Q8—131no—
462C22×Q8—131no—
463C22×Q8—131no—
464C22×Q8—134no—
465C22×Q8—261no—
466C22×Q8—261no—
467C22×Q8—264no—
468C22×Q8—262no—
469C22×Q8—261no—
470C22×Q8—262no—
471C22×Q8—264no—
472C22×Q8—522no—
473C22×Q8—522no—
474C22×Q8C22×D1311yescharacteristic
475C22×D4—131no—
476C23×C4—21no—
477C23×C4—131no—
478C23×C4—261no—
479C23×C4—261no—
480C23×C4—261no—
481C23×C4C22×D1311yescharacteristic
482C2×Q16—134no—
483C2×Q16—134no—
484C2×Q16—134no—
485C2×Q16—264no—
486C2×Q16—522no—
487C2×Q16—522no—
488C22×C8—131no—
489C22×C8—131no—
490C22×C8—134no—
491C22×C8—134no—
492C22×C8—522no—
493C22×C8—522no—
494C22×C8C22×D1311yescharacteristic
495C22×C8C22×D1311yescharacteristic
496C4⋊Q8—134no—
497C4⋊Q8—134no—
498C4⋊Q8—262no—
499C4⋊Q8—262no—
500C4⋊Q8—268no—
501#125—268no—
502C22⋊Q8—22no—
503C22⋊Q8—134no—
504C22⋊Q8—134no—
505C22⋊Q8—134no—
506C22⋊Q8—268no—
507C22⋊Q8—268no—
508C22⋊Q8—268no—
509C22⋊Q8—268no—
510C22⋊Q8—262no—
511C22⋊Q8—262no—
512C22⋊Q8—262no—
513C22⋊Q8C22×D1314yes—
514C4×Q8—134no—
515C4×Q8—134no—
516C4×Q8—262no—
517C4×Q8—262no—
518C4×D4—134no—
519C4×D4—134no—
520C4×D4—268no—
521C4×D4—268no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—131no—
526C2×C4⋊C4—131no—
527C2×C4⋊C4—134no—
528C2×C4⋊C4—262no—
529C2×C4⋊C4—261no—
530C2×C4⋊C4—261no—
531C2×C4⋊C4—261no—
532C2×C4⋊C4—261no—
533C2×C4⋊C4—261no—
534C2×C4⋊C4—261no—
535C2×C4⋊C4—261no—
536C2×C4⋊C4—261no—
537C2×C4⋊C4—261no—
538C2×C4⋊C4C22×D1311yescharacteristic
539C2×C4⋊C4C22×D1311yescharacteristic
540C2×C4⋊C4C22×D1314yes—
541C2×C4⋊C4C22×D1311yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—131no—
544C2×C22⋊C4—131no—
545C2×C22⋊C4—261no—
546C2×C22⋊C4—261no—
547C2×C22⋊C4—261no—
548C2×C42—131no—
549C2×C42—261no—
550C2×C42—261no—
551#107—134no—
552#107C22×D1314yes—
553#107C22×D1314yes—
554C4⋊C8—134no—
555#103—134no—
556#103—134no—
557#103—134no—
558#103—134no—
559#103—134no—
560#103—134no—
561#103—134no—
562#103—134no—
563#103C22×D1314yes—
564#103C22×D1314yes—
565C22⋊C8—134no—
566C22⋊C8C22×D1314yes—
567C4×C8—134no—
568C2×C13—24no—
569C2×C13#329914yescomplemented
570C2×C13C2×#54611yescharacteristic
571C2×C13C23×Q1611yescharacteristic
572C2×C13C2×#57711yescharacteristic
573D13—24no—
574C24—131no—
575C24D4×D1311yescharacteristic
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—134no—
580C2×Q8—132no—
581C2×Q8—132no—
582C2×Q8—132no—
583C2×Q8—264no—
584C2×Q8—264no—
585C2×Q8—268no—
586C2×Q8—261no—
587C2×Q8—261no—
588C2×Q8—264no—
589C2×Q8—261no—
590C2×Q8—262no—
591C2×Q8—268no—
592C2×Q8—262no—
593C2×Q8—262no—
594C2×Q8—262no—
595C2×Q8—262no—
596C2×Q8—524no—
597C2×Q8—524no—
598C2×Q8—528no—
599C2×Q8—524no—
600C2×Q8—524no—
601C2×Q8—528no—
602C2×Q8—1042no—
603C2×Q8C23×D1312yes—
604C2×D4—138no—
605C2×D4—134no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—24no—
613C22×C4—82no—
614C22×C4—131no—
615C22×C4—131no—
616C22×C4—131no—
617C22×C4—132no—
618C22×C4—132no—
619C22×C4—264no—
620C22×C4—264no—
621C22×C4—261no—
622C22×C4—262no—
623C22×C4—262no—
624C22×C4—264no—
625C22×C4—261no—
626C22×C4—261no—
627C22×C4—261no—
628C22×C4—524no—
629C22×C4—524no—
630C22×C4—1042no—
631C22×C4D4×D1312yes—
632C22×C4D4×D1311yescharacteristic
633C22×C4C23×D1312yes—
634C22×C4C23×D1311yescharacteristic
635Q16—268no—
636Q16—524no—
637Q16—524no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—132no—
641C2×C8—132no—
642C2×C8—262no—
643C2×C8—262no—
644C2×C8—524no—
645C2×C8—524no—
646C2×C8C23×D1312yes—
647C2×C8C23×D1312yes—
648C4⋊C4—21no—
649C4⋊C4—24no—
650C4⋊C4—21no—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—134no—
654C4⋊C4—132no—
655C4⋊C4—264no—
656C4⋊C4—264no—
657C4⋊C4—264no—
658C4⋊C4—264no—
659C4⋊C4—264no—
660C4⋊C4—264no—
661C4⋊C4—264no—
662C4⋊C4—264no—
663C4⋊C4—261no—
664C4⋊C4—264no—
665C4⋊C4C23×D1312yes—
666C4⋊C4C23×D1312yes—
667C4⋊C4C23×D1312yes—
668C22⋊C4—24no—
669C22⋊C4—134no—
670C22⋊C4—134no—
671C22⋊C4—264no—
672C22⋊C4—264no—
673C22⋊C4—264no—
674C42—132no—
675C42—132no—
676C42—264no—
677C42—264no—
678C13C2×#329911yescharacteristic, complemented, Sylow
679C23—22no—
680C23—22no—
681C23—134no—
682C23—132no—
683C23—262no—
684C23—262no—
685C23Q16×D1314yes—
686C23C2×D4×D1312yes—
687C23C2×D4×D1311yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—134no—
692Q8—264no—
693Q8—262no—
694Q8—262no—
695Q8—262no—
696Q8—262no—
697Q8—262no—
698Q8—528no—
699Q8—528no—
700Q8—522no—
701Q8—522no—
702Q8—1044no—
703D4—1316no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—84no—
717C2×C4—134no—
718C2×C4—132no—
719C2×C4—132no—
720C2×C4—132no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—264no—
724C2×C4—262no—
725C2×C4—264no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—528no—
732C2×C4—528no—
733C2×C4—522no—
734C2×C4—522no—
735C2×C4—522no—
736C2×C4—1044no—
737C2×C4C2×D4×D1312yes—
738C2×C4C2×D4×D1311yescharacteristic
739C2×C4#41×D1312yes—
740C2×C4#8825612yes—
741C2×C4C24×D1311yescharacteristic
742C8—22no—
743C8—22no—
744C8—262no—
745C8—262no—
746C22—28no—
747C22—22no—
748C22—22no—
749C22—134no—
750C22—268no—
751C22—262no—
752C22—262no—
753C22#1171935912yes—
754C22C2×Q16×D1314yes—
755C22C2×Q16×D1312yes—
756C22#1171948012yes—
757C22C22×D4×D1311yescharacteristic
758C4—22no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—134no—
764C4—262no—
765C4—264no—
766C4—262no—
767C4—522no—
768C4—522no—
769C4—522no—
770C4#1171935912yes—
771C4C2×#41×D1311yescharacteristic
772C4C2×#8825611yescharacteristic
773C2—24no—
774C2—264no—
775C2#1312671014yesdirect product factor
776C2C2×#1171935911yescharacteristic
777C2C22×Q16×D1311yescharacteristic
778C2C2×#1171948011yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#484C2
socleC23×C13C22×D4
prime radicalC22×C22⋊D13D4
hypercenterC2×#484D13
hypocenterC13C2×#3299
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #13126710C2direct (N × H)
4. C2×#11718453C2semidirect
5. C2×#11718545C2semidirect
6. C2×#11718536C2semidirect
7. C2×#11718548C2semidirect
8. C2×#11718712C2semidirect
9. C2×#11718454C2semidirect
10. C2×#11718400C2semidirect
11. C2×#11718469C2semidirect
12. C2×#11718534C2semidirect
14. C22×#88050C2semidirect
15. C2×D13×#103C2semidirect
16. C2×C13×#484C2semidirect
47. C13×#484C22semidirect
59. #11718712C22semidirect
65. C2×#88050C22semidirect
67. #11718548C22semidirect
68. #11718545C22semidirect
69. #11718536C22semidirect
70. #11718534C22semidirect
71. #11718469C22semidirect
72. D13×#103C22semidirect
73. #11718454C22semidirect
74. #11718453C22semidirect
75. #11718400C22semidirect
204. C2×C22⋊D13Q16semidirect
295. C2×#484D13semidirect
336. C22⋊D13C2×Q16semidirect
405. #484C2×D13semidirect
569. C2×C13#3299semidirect
678. C13C2×#3299semidirect
775. C2#13126710direct (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×#117193372
#131267102
C2×#117184532
C2×#117185452
C2×#117185362
C2×#117185482
C2×#117187122
C2×#117184542
C2×#117184002
C2×#117184692
C2×#117185342
C2×#117183862
C22×#880502
C2×D13×#1032
C2×C13×#4842
C2×#329913