Finite Group Databasebeta

← C2×#13126947 #16739509

Subgroups — C2×#13126947 #16739509

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
2#13126947C2116yesmaximal, direct product factor
3C2×#11718716C211yesmaximal, characteristic, complemented
4C2×#11718695C211yesmaximal, characteristic, complemented
5C2×#11718704C211yesmaximal, characteristic, complemented
6C2×#11718681C211yesmaximal, characteristic, complemented
7C2×#11718713C211yesmaximal, characteristic, complemented
8C2×#11718702C211yesmaximal, characteristic, complemented
9C2×#11718715C211yesmaximal, characteristic, complemented
10C2×#11718900C211yesmaximal, characteristic, complemented
11C2×#11718889C211yesmaximal, characteristic, complemented
12C2×#11718691C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic, complemented
14C2×#11718893C211yesmaximal, characteristic, complemented
15C22×#88075C211yesmaximal, characteristic, complemented
16C2×C13×#548C211yesmaximal, characteristic
17C22×C13×#41C2211yescharacteristic
18C23×Q8×C13C2211yescharacteristic
19C13×#548—24no—
20C13×#548C2218yes—
21C2×C13×#124—21no—
22C2×C13×#124C2211yescharacteristic
23C2×C13×C22⋊Q8—21no—
24C2×C13×C22⋊Q8C2211yescharacteristic
25C2×C13×#121—21no—
26C2×C13×#121C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×D4×C13—21no—
29C2×C4×D4×C13C2211yescharacteristic
30C22×#6107C2211yescharacteristic
31C22×#6107C2211yescharacteristic
32C2×D4×Dic13—21no—
33C22×#6105C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C2×#88178C2211yescharacteristic
37C2×#88178C2211yescharacteristic
38C22×#6099C2211yescharacteristic
39C23×#1055C2211yescharacteristic
40#11719248—24no—
41#11719248C2218yescomplemented
42C2×#88144—21no—
43C2×#88132—21no—
44C2×#88132—21no—
45C2×#88123C2211yescharacteristic
46C2×C4×Dic26C2211yescharacteristic
47#11718900C2218yescomplemented
48#11718893C2218yescomplemented
49#11718889C2218yescomplemented
50C2×#88075C2211yescharacteristic
51C2×#88075C2211yescharacteristic
52C2×#88075C2211yescharacteristic
53C2×#88075C2211yescharacteristic
54C2×#88075C2211yescharacteristic
55C2×#88075C2211yescharacteristic
56C2×#88075C2218yescomplemented
57C2×#88072C2211yescharacteristic
58C2×#88072C2211yescharacteristic
59C2×#88072C2211yescharacteristic
60C2×C22⋊#1055C2211yescharacteristic
61C2×C22⋊#1055C2211yescharacteristic
62#11718716C2218yescomplemented
63#11718715C2218yescomplemented
64#11718713C2218yescomplemented
65#11718704C2218yescomplemented
66#11718702C2218yescomplemented
67#11718695C2218yescomplemented
68#11718691C2218yescomplemented
69#11718681C2218yescomplemented
70#11718672C2218yescomplemented
71C2×#88050C2211yescharacteristic
72C2×#88048C2211yescharacteristic
73C2×#88048C2211yescharacteristic
74C2×#88048C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
77C2×C13×#41—22no—
78C2×C13×#41—24no—
79C2×C13×#41—42no—
80C2×C13×#41C2314yes—
81C22×Q8×C13—21no—
82C22×Q8×C13—22no—
83C22×Q8×C13—24no—
84C22×Q8×C13—42no—
85C22×Q8×C13C2311yescharacteristic
86C22×Q8×C13C2314yes—
87C22×Q8×C13C2311yescharacteristic
88C22×D4×C13—21no—
89C22×D4×C13—21no—
90C22×D4×C13D411yescharacteristic
91C22×D4×C13C2311yescharacteristic
92C23×C4×C13—21no—
93C23×C4×C13—21no—
94C23×C4×C13C2311yescharacteristic
95C23×C4×C13C2311yescharacteristic
96C23×Dic13—21no—
97C23×Dic13—21no—
98C22×Dic26—21no—
99C22×Dic26C2311yescharacteristic
100C13×#124—28no—
101C13×#124—22no—
102C13×#124C2314yes—
103C13×C22⋊Q8—22no—
104C13×C22⋊Q8—28no—
105C13×C22⋊Q8C2314yes—
106C13×#121—28no—
107C13×#121—22no—
108C13×#121C2314yes—
109C4×Q8×C13—22no—
110C4×Q8×C13C2314yes—
111C4×D4×C13—28no—
112C4×D4×C13D414yes—
113C4×D4×C13C2314yes—
114C2×C13×C4⋊C4—21no—
115C2×C13×C4⋊C4—21no—
116C2×C13×C4⋊C4D411yescharacteristic
117C2×C13×C4⋊C4C2311yescharacteristic
118C2×C13×C22⋊C4—21no—
119C2×C13×C22⋊C4—21no—
120C2×C13×C22⋊C4—21no—
121C2×C13×C22⋊C4—21no—
122C2×C13×C22⋊C4D411yescharacteristic
123C2×C13×C22⋊C4D411yescharacteristic
124C2×C42×C13—21no—
125C2×C42×C13C2311yescharacteristic
126C2×C22⋊Dic13—21no—
127C2×C22⋊Dic13—21no—
128C2×#6107—24no—
129C2×#6107—42no—
130C2×#6107C2314yes—
131C2×#6107C2314yes—
132D4×Dic13—28no—
133C2×#6105—42no—
134C2×#6105C2314yes—
135C2×C4⋊Dic13—21no—
136C2×C4⋊Dic13—21no—
137C2×C4⋊Dic13—21no—
138C2×C4⋊Dic13—22no—
139C2×C4⋊Dic13—22no—
140C2×C4⋊Dic13C2311yescharacteristic
141C2×C4⋊Dic13C2311yescharacteristic
142C2×C4⋊Dic13C2311yescharacteristic
143C2×C4⋊Dic13C2314yes—
144C2×C4⋊Dic13C2314yes—
145#88178—22no—
146#88178—22no—
147#88178C2314yes—
148#88178C2314yes—
149C2×#6101—21no—
150C2×#6101—21no—
151C2×#6101—21no—
152C2×C4×Dic13—21no—
153C2×#6099—42no—
154C2×#6099C2314yes—
155C22×#1055—42no—
156C22×#1055C2311yescharacteristic
157C22×#1055C2311yescharacteristic
158C22×#1055C2311yescharacteristic
159C22×#1055C2311yescharacteristic
160C22×#1055C2314yes—
161#88144—28no—
162#88132—28no—
163#88132—28no—
164#88123—22no—
165#88123C2314yes—
166C4×Dic26—22no—
167C4×Dic26C2314yes—
168#88075C2314yes—
169#88075C2314yes—
170#88075C2314yes—
171#88075C2314yes—
172#88075C2314yes—
173#88075C2314yes—
174#88072C2314yes—
175#88072C2314yes—
176#88072C2314yes—
177C22⋊#1055C2314yes—
178C22⋊#1055C2314yes—
179#88050C2314yes—
180#88048C2314yes—
181#88048C2314yes—
182#88048C2314yes—
183C4⋊#1055C2314yes—
184#88043C2314yes—
185C2×#3316—131nomaximal, Sylow
186C24×C13—21no—
187C24×C13C2×D411yescharacteristic
188C24×C13C2×D411yescharacteristic
189C13×#41—28no—
190C13×#41—44no—
191C13×#41—48no—
192C2×Q8×C13—21no—
193C2×Q8×C13—24no—
194C2×Q8×C13—21no—
195C2×Q8×C13—22no—
196C2×Q8×C13—28no—
197C2×Q8×C13—22no—
198C2×Q8×C13—22no—
199C2×Q8×C13—44no—
200C2×Q8×C13—44no—
201C2×Q8×C13—48no—
202C2×Q8×C13#4114yes—
203C2×Q8×C13C2412yes—
204C2×Q8×C13C2412yes—
205C2×D4×C13—24no—
206C2×D4×C13—24no—
207C2×D4×C13—24no—
208C2×D4×C13—21no—
209C2×D4×C13—22no—
210C2×D4×C13—22no—
211C2×D4×C13—44no—
212C2×D4×C13—44no—
213C2×D4×C13C2×D414yes—
214C2×D4×C13C2412yes—
215C22×C4×C13—21no—
216C22×C4×C13—22no—
217C22×C4×C13—22no—
218C22×C4×C13—22no—
219C22×C4×C13—22no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—24no—
223C22×C4×C13—24no—
224C22×C4×C13—44no—
225C22×C4×C13—44no—
226C22×C4×C13C2×D411yescharacteristic
227C22×C4×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D412yes—
231C22×C4×C13C2×D412yes—
232C22×C4×C13C2412yes—
233C22×C4×C13C2412yes—
234C22×C4×C13C2411yescharacteristic
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—24no—
240C22×Dic13—24no—
241C22×Dic13—82no—
242C22×Dic13—82no—
243C2×Dic26—22no—
244C2×Dic26—22no—
245C2×Dic26—21no—
246C2×Dic26—24no—
247C2×Dic26—82no—
248C2×Dic26C2412yes—
249C13×C4⋊C4—24no—
250C13×C4⋊C4—24no—
251C13×C4⋊C4—21no—
252C13×C4⋊C4C2×D414yes—
253C13×C4⋊C4C2412yes—
254C13×C22⋊C4—24no—
255C13×C22⋊C4—24no—
256C13×C22⋊C4—24no—
257C13×C22⋊C4—24no—
258C13×C22⋊C4C2×D414yes—
259C13×C22⋊C4C2×D414yes—
260C42×C13—24no—
261C42×C13C2×D412yes—
262C42×C13C2412yes—
263C22⋊Dic13—24no—
264C22⋊Dic13—24no—
265#6107—28no—
266#6107—44no—
267#6105—44no—
268C4⋊Dic13—21no—
269C4⋊Dic13—21no—
270C4⋊Dic13—21no—
271C4⋊Dic13—24no—
272C4⋊Dic13—24no—
273C4⋊Dic13—24no—
274C4⋊Dic13C2412yes—
275C4⋊Dic13C2412yes—
276C4⋊Dic13C2412yes—
277#6101—24no—
278#6101—24no—
279#6101—24no—
280C4×Dic13—24no—
281#6099—44no—
282C2×#1055—22no—
283C2×#1055—22no—
284C2×#1055—22no—
285C2×#1055—22no—
286C2×#1055—44no—
287C2×#1055C2412yes—
288C2×#1055C2412yes—
289C2×#1055C2412yes—
290C2×#1055C2412yes—
291C2×#554—131no—
292C2×#548D1311yescharacteristic
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×#435—131no—
305C2×#417—131no—
306C22×#103—131no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—42no—
314C23×C13—42no—
315C23×C13—42no—
316C23×C13#13714yes—
317C23×C13C22×D412yes—
318C23×C13C22×D412yes—
319C23×C13C22×D411yescharacteristic
320Q8×C13—24no—
321Q8×C13—22no—
322Q8×C13—22no—
323Q8×C13—22no—
324Q8×C13—48no—
325Q8×C13—42no—
326Q8×C13C2×#4114yes—
327D4×C13—28no—
328D4×C13—22no—
329D4×C13—22no—
330D4×C13—48no—
331D4×C13—48no—
332D4×C13—42no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—24no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—24no—
340C2×C4×C13—24no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—48no—
348C2×C4×C13—48no—
349C2×C4×C13—42no—
350C2×C4×C13—42no—
351C2×C4×C13C22×D412yes—
352C2×C4×C13C22×D412yes—
353C2×C4×C13C22×D412yes—
354C2×C4×C13C22×D412yes—
355C2×C4×C13C22×D411yescharacteristic
356C2×C4×C13C2×#4112yes—
357C2×C4×C13H(5,𝔽2)12yes—
358C2×C4×C13C2511yescharacteristic
359C2×Dic13—22no—
360C2×Dic13—22no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—42no—
364C2×Dic13—42no—
365C2×Dic13—42no—
366C2×Dic13—42no—
367C2×Dic13—84no—
368C2×Dic13—84no—
369Dic26—22no—
370Dic26—22no—
371Dic26—42no—
372Dic26—84no—
373#1055—22no—
374#1055—22no—
375#1055—22no—
376#1055—22no—
377C22×#41C2×D1311yescharacteristic
378C23×Q8C2×D1311yescharacteristic
379C22×Q16—131no—
380C22×Q16—131no—
381C22×SD16—131no—
382C22×M16—131no—
383C23×C8—131no—
384#554—138no—
385#554—264no—
386#548—24no—
387#548C2×D1318yes—
388C2×C4⋊Q8—131no—
389C2×#125—261no—
390C2×#124—21no—
391C2×#124C2×D1311yescharacteristic
392C2×C22⋊Q8—21no—
393C2×C22⋊Q8—131no—
394C2×C22⋊Q8—131no—
395C2×C22⋊Q8—261no—
396C2×C22⋊Q8—261no—
397C2×C22⋊Q8C2×D1311yescharacteristic
398C2×#121—21no—
399C2×#121C2×D1311yescharacteristic
400C2×C4×Q8—131no—
401C2×C4×Q8C2×D1311yescharacteristic
402C2×C4×D4—21no—
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#435—138no—
418C2×#106—131no—
419C2×#106—131no—
420C2×#106—131no—
421C2×C4⋊C8—131no—
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⋊C8—131no—
435C2×C22⋊C8—131no—
436C2×#97—131no—
437C22×C13—22no—
438C22×C13—28no—
439C22×C13—22no—
440C22×C13—22no—
441C22×C13—22no—
442C22×C13—22no—
443C22×C13—44no—
444C22×C13—42no—
445C22×C13—42no—
446C22×C13—42no—
447C22×C13—84no—
448C22×C13#54612yes—
449C22×C13C2×#13714yes—
450C22×C13C2×#13712yes—
451C22×C13#57712yes—
452C22×C13C23×D411yescharacteristic
453C4×C13—22no—
454C4×C13—22no—
455C4×C13—24no—
456C4×C13—22no—
457C4×C13—22no—
458C4×C13—42no—
459C4×C13—42no—
460C4×C13#54612yes—
461C4×C13C22×#4111yescharacteristic
462C4×C13C2×H(5,𝔽2)11yescharacteristic
463Dic13—42no—
464Dic13—42no—
465Dic13—42no—
466Dic13—42no—
467C2×#41—22no—
468C2×#41—24no—
469C2×#41—42no—
470C2×#41C22×D1314yes—
471C22×Q8—21no—
472C22×Q8—22no—
473C22×Q8—24no—
474C22×Q8—42no—
475C22×Q8—131no—
476C22×Q8—261no—
477C22×Q8C22×D1311yescharacteristic
478C22×Q8C22×D1314yes—
479C22×Q8C22×D1311yescharacteristic
480C22×D4—21no—
481C22×D4—21no—
482C22×D4C22⋊D1311yescharacteristic
483C22×D4C22×D1311yescharacteristic
484C23×C4—21no—
485C23×C4—21no—
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—134no—
497C2×M16—522no—
498C22×C8—131no—
499C22×C8—131no—
500C22×C8—131no—
501C22×C8—131no—
502C22×C8—134no—
503C22×C8—522no—
504C4⋊Q8—134no—
505C4⋊Q8—262no—
506#125—268no—
507#124—28no—
508#124—22no—
509#124C22×D1314yes—
510C22⋊Q8—22no—
511C22⋊Q8—28no—
512C22⋊Q8—134no—
513C22⋊Q8—134no—
514C22⋊Q8—262no—
515C22⋊Q8—262no—
516C22⋊Q8—268no—
517C22⋊Q8—268no—
518C22⋊Q8C22×D1314yes—
519#121—28no—
520#121—22no—
521#121C22×D1314yes—
522C4×Q8—22no—
523C4×Q8—134no—
524C4×Q8—262no—
525C4×Q8C22×D1314yes—
526C4×D4—28no—
527C4×D4—268no—
528C4×D4C22⋊D1314yes—
529C4×D4C22×D1314yes—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—131no—
533C2×C4⋊C4—131no—
534C2×C4⋊C4—131no—
535C2×C4⋊C4—134no—
536C2×C4⋊C4—134no—
537C2×C4⋊C4—261no—
538C2×C4⋊C4—261no—
539C2×C4⋊C4—262no—
540C2×C4⋊C4—262no—
541C2×C4⋊C4—261no—
542C2×C4⋊C4—261no—
543C2×C4⋊C4—261no—
544C2×C4⋊C4—261no—
545C2×C4⋊C4C22⋊D1311yescharacteristic
546C2×C4⋊C4C22×D1311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—261no—
552C2×C22⋊C4—261no—
553C2×C22⋊C4C22⋊D1311yescharacteristic
554C2×C22⋊C4C22⋊D1311yescharacteristic
555C2×C42—21no—
556C2×C42—261no—
557C2×C42C22×D1311yescharacteristic
558#106—134no—
559#106—134no—
560#106—134no—
561C4⋊C8—134no—
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⋊C8—134no—
573C22⋊C8—134no—
574#97—134no—
575C2×C13—24no—
576C2×C13—42no—
577C2×C13—82no—
578C2×C13#331614yescomplemented
579C2×C13C2×#54611yescharacteristic
580C2×C13C22×#13711yescharacteristic
581C2×C13C2×#57711yescharacteristic
582C24—21no—
583C24C2×C22⋊D1311yescharacteristic
584C24C2×C22⋊D1311yescharacteristic
585#41—28no—
586#41—44no—
587#41—48no—
588C2×Q8—22no—
589C2×Q8—21no—
590C2×Q8—24no—
591C2×Q8—21no—
592C2×Q8—28no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—44no—
596C2×Q8—44no—
597C2×Q8—48no—
598C2×Q8—132no—
599C2×Q8—261no—
600C2×Q8—264no—
601C2×Q8—262no—
602C2×Q8—262no—
603C2×Q8—1042no—
604C2×Q8#612914yes—
605C2×Q8C23×D1312yes—
606C2×Q8C23×D1312yes—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4C2×C22⋊D1314yes—
616C2×D4C23×D1312yes—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—24no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—24no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—261no—
629C22×C4—261no—
630C22×C4—261no—
631C22×C4—261no—
632C22×C4—264no—
633C22×C4—264no—
634C22×C4—1042no—
635C22×C4—1042no—
636C22×C4C2×C22⋊D1312yes—
637C22×C4C2×C22⋊D1312yes—
638C22×C4C2×C22⋊D1311yescharacteristic
639C22×C4C2×C22⋊D1311yescharacteristic
640C22×C4C2×C22⋊D1311yescharacteristic
641C22×C4C2×C22⋊D1311yescharacteristic
642C22×C4C23×D1312yes—
643C22×C4C23×D1312yes—
644C22×C4C23×D1311yescharacteristic
645Q16—268no—
646Q16—524no—
647SD16—524no—
648M16—524no—
649C2×C8—132no—
650C2×C8—132no—
651C2×C8—132no—
652C2×C8—132no—
653C2×C8—262no—
654C2×C8—262no—
655C2×C8—262no—
656C2×C8—262no—
657C2×C8—524no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—132no—
662C4⋊C4—132no—
663C4⋊C4—132no—
664C4⋊C4—261no—
665C4⋊C4—264no—
666C4⋊C4—264no—
667C4⋊C4—261no—
668C4⋊C4—261no—
669C4⋊C4—264no—
670C4⋊C4—264no—
671C4⋊C4—264no—
672C4⋊C4—264no—
673C4⋊C4C2×C22⋊D1314yes—
674C4⋊C4C23×D1312yes—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—264no—
680C22⋊C4—264no—
681C22⋊C4C2×C22⋊D1314yes—
682C22⋊C4C2×C22⋊D1314yes—
683C42—24no—
684C42—264no—
685C42C2×C22⋊D1312yes—
686C42C23×D1312yes—
687C13C2×#331611yescharacteristic, complemented, Sylow
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23#8820514yes—
698C23C22×C22⋊D1312yes—
699C23C22×C22⋊D1312yes—
700C23C22×C22⋊D1311yescharacteristic
701Q8—24no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—48no—
706Q8—42no—
707Q8—262no—
708Q8—262no—
709Q8—522no—
710Q8—1044no—
711Q8C2×#612914yes—
712D4—28no—
713D4—22no—
714D4—22no—
715D4—48no—
716D4—48no—
717D4—42no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—522no—
741C2×C4—522no—
742C2×C4—522no—
743C2×C4—522no—
744C2×C4—1044no—
745C2×C4—1044no—
746C2×C4C2×#612912yes—
747C2×C4#8825112yes—
748C2×C4C22×C22⋊D1312yes—
749C2×C4C22×C22⋊D1312yes—
750C2×C4C22×C22⋊D1312yes—
751C2×C4C22×C22⋊D1312yes—
752C2×C4C22×C22⋊D1311yescharacteristic
753C2×C4C24×D1311yescharacteristic
754C8—262no—
755C8—262no—
756C8—262no—
757C8—262no—
758C22—28no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22#1171951112yes—
770C22C2×#8820514yes—
771C22C2×#8820512yes—
772C22#1171954212yes—
773C22C23×C22⋊D1311yescharacteristic
774C4—22no—
775C4—22no—
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—522no—
782C4—522no—
783C4—522no—
784C4—522no—
785C4#1171951112yes—
786C4C22×#612911yescharacteristic
787C4C2×#8825111yescharacteristic
788C2—24no—
789C2—42no—
790C2—82no—
791C2#1312694714yesdirect product factor
792C2C2×#1171951111yescharacteristic
793C2C22×#8820511yescharacteristic
794C2C2×#1171954211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
Fitting, prime radicalC2×C13×#548C2
socleC23×C13C22×D4
hypercenterC2×#548D13
hypocenterC13C2×#3316
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#11719248C2semidirect
2. #13126947C2direct (N × H)
3. C2×#11718716C2semidirect
4. C2×#11718695C2semidirect
5. C2×#11718704C2semidirect
6. C2×#11718681C2semidirect
7. C2×#11718713C2semidirect
8. C2×#11718702C2semidirect
9. C2×#11718715C2semidirect
10. C2×#11718900C2semidirect
11. C2×#11718889C2semidirect
12. C2×#11718691C2semidirect
13. C2×#11718672C2semidirect
14. C2×#11718893C2semidirect
15. C22×#88075C2semidirect
41. #11719248C22semidirect
47. #11718900C22semidirect
48. #11718893C22semidirect
49. #11718889C22semidirect
56. C2×#88075C22semidirect
62. #11718716C22semidirect
63. #11718715C22semidirect
64. #11718713C22semidirect
65. #11718704C22semidirect
66. #11718702C22semidirect
67. #11718695C22semidirect
68. #11718691C22semidirect
69. #11718681C22semidirect
70. #11718672C22semidirect
578. C2×C13#3316semidirect
687. C13C2×#3316semidirect
791. C2#13126947direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192482
#131269472
C2×#117187162
C2×#117186952
C2×#117187042
C2×#117186812
C2×#117187132
C2×#117187022
C2×#117187152
C2×#117189002
C2×#117188892
C2×#117186912
C2×#117186722
C2×#117188932
C22×#880752
C2×C13×#5482
C2×#331613