Finite Group Databasebeta

← C2×#13127381 #16741562

Subgroups — C2×#13127381 #16741562

Order 3328.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719270C211yesmaximal, characteristic
2#13127381C2116yesmaximal, direct product factor
3C2×#11718741C211yesmaximal, characteristic, complemented
4C2×#11718706C211yesmaximal, characteristic, complemented
5C2×#11718664C211yesmaximal, characteristic, complemented
6C2×#11718664C211yesmaximal, characteristic, complemented
7C2×#11718704C211yesmaximal, characteristic, complemented
8C2×#11718683C211yesmaximal, characteristic, complemented
9C2×#11718745C211yesmaximal, characteristic, complemented
10C2×#11718710C211yesmaximal, characteristic, complemented
11C2×#11718709C211yesmaximal, characteristic, complemented
12C2×#11718687C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic, complemented
14C2×#11718656C211yesmaximal, characteristic, complemented
15C2×#11718659C211yesmaximal, characteristic, complemented
16C2×C13×#556C211yesmaximal, characteristic, complemented
17C13×#556—24no—
18C13×#556C2218yescomplemented
19C2×C13×C4⋊Q8C2211yescharacteristic
20C2×C13×#126—21no—
21C2×C13×#126—21no—
22C2×C13×#124—21no—
23C2×C13×C22⋊Q8C2211yescharacteristic
24C2×C13×C22⋊Q8C2211yescharacteristic
25C2×C4×Q8×C13—21no—
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C2×C13×#117C2211yescharacteristic
29C2×C13×#117C2211yescharacteristic
30C22×#6106C2211yescharacteristic
31C2×#88193—21no—
32C2×#88184C2211yescharacteristic
33C2×#88184C2211yescharacteristic
34C2×#88180C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×#6099C2211yescharacteristic
37C23×#1055C2211yescharacteristic
38#11719270—24no—
39#11719270C2218yes—
40C2×#88152—21no—
41C2×#88137—21no—
42C2×#88135—21no—
43C2×C4×D52C2211yescharacteristic
44C2×#88124C2211yescharacteristic
45C2×#88075C2211yescharacteristic
46C2×#88075C2211yescharacteristic
47C2×#88075C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic
50#11718745C2218yescomplemented
51#11718741C2218yescomplemented
52#11718710C2218yescomplemented
53#11718709C2218yescomplemented
54#11718706C2218yescomplemented
55#11718704C2218yescomplemented
56#11718687C2218yescomplemented
57#11718683C2218yescomplemented
58#11718672C2218yescomplemented
59#11718664C2218yescomplemented
60#11718664C2218yescomplemented
61#11718659C2218yescomplemented
62#11718656C2218yescomplemented
63C2×#88049C2211yescharacteristic
64C2×#88049C2211yescharacteristic
65C2×#88049C2211yescharacteristic
66C2×#88048C2211yescharacteristic
67C2×#88048C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88048C2211yescharacteristic
71C2×#88047C2211yescharacteristic
72C2×#88047C2211yescharacteristic
73C2×#88047C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
77C22×Q8×C13—21no—
78C22×Q8×C13C2311yescharacteristic
79C22×D4×C13D411yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C22×C22⋊D13—21no—
83C22×C22⋊D13—21no—
84C23×Dic13—21no—
85C22×D52C2311yescharacteristic
86C22×C4×D13—21no—
87C13×C4⋊Q8—22no—
88C13×C4⋊Q8C2314yes—
89C13×#126—28no—
90C13×#126—28no—
91C13×#124—28no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8—22no—
94C13×C22⋊Q8C2314yes—
95C13×C22⋊Q8C2314yes—
96C4×Q8×C13—28no—
97C4×Q8×C13—22no—
98C4×Q8×C13C2314yes—
99C4×D4×C13D414yes—
100C4×D4×C13C2314yes—
101C13×#117—22no—
102C13×#117—22no—
103C13×#117C2314yes—
104C13×#117C2314yes—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4D411yescharacteristic
110C2×C13×C4⋊C4C2311yescharacteristic
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C4⋊C4C2311yescharacteristic
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—21no—
117C2×C13×C22⋊C4D411yescharacteristic
118C2×C13×C22⋊C4D411yescharacteristic
119C2×C42×C13—21no—
120C2×C42×C13—21no—
121C2×C42×C13—21no—
122C2×C42×C13C2311yescharacteristic
123C2×C22⋊Dic13—21no—
124C2×#6106—24no—
125C2×#6106C2314yes—
126#88193—28no—
127#88184—22no—
128#88184—22no—
129#88184C2314yes—
130#88184C2314yes—
131C2×#6103—21no—
132C2×#6103—21no—
133C2×#6103—21no—
134#88180—22no—
135#88180C2314yes—
136C2×C4⋊Dic13—21no—
137C2×C4⋊Dic13—22no—
138C2×C4⋊Dic13C2314yes—
139C2×C4⋊Dic13C2311yescharacteristic
140C2×C4⋊Dic13C2311yescharacteristic
141C2×C4⋊Dic13C2311yescharacteristic
142C2×#6101—21no—
143C2×#6101—21no—
144C2×C4×Dic13—21no—
145C2×#6099—24no—
146C2×#6099C2314yes—
147C22×#1055—24no—
148C22×#1055C2314yes—
149C22×#1055C2311yescharacteristic
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152C22×#1055C2311yescharacteristic
153#88152—28no—
154#88137—28no—
155#88135—28no—
156C4×D52—22no—
157C4×D52C2314yes—
158#88124—22no—
159#88124C2314yes—
160#88075C2314yes—
161#88075C2314yes—
162#88075C2314yes—
163C22⋊#1055C2314yes—
164C22⋊#1055C2314yes—
165#88049C2314yes—
166#88049C2314yes—
167#88049C2314yes—
168#88048C2314yes—
169#88048C2314yes—
170#88048C2314yes—
171#88048C2314yes—
172#88048C2314yes—
173#88047C2314yes—
174#88047C2314yes—
175#88047C2314yes—
176#88047C2314yes—
177C4⋊#1055C2314yes—
178#88043C2314yes—
179C2×#3350—131nomaximal, Sylow
180C24×C13C2×D411yescharacteristic
181C24×C13C2×D411yescharacteristic
182C23×D13—21no—
183C2×Q8×C13—21no—
184C2×Q8×C13—24no—
185C2×Q8×C13—22no—
186C2×Q8×C13—22no—
187C2×Q8×C13—44no—
188C2×Q8×C13C2412yes—
189C2×D4×C13—42no—
190C2×D4×C13C2×D414yes—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D411yescharacteristic
202C22×C4×C13C2×D411yescharacteristic
203C22×C4×C13C2×D412yes—
204C22×C4×C13C2×D412yes—
205C22×C4×C13C2412yes—
206C22×C4×C13C2412yes—
207C22×C4×C13C2411yescharacteristic
208C2×C22⋊D13—24no—
209C2×C22⋊D13—24no—
210C2×C22⋊D13—44no—
211C2×C22⋊D13—82no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—24no—
216C22×Dic13—82no—
217C2×D52—22no—
218C2×D52—22no—
219C2×D52—21no—
220C2×D52C2412yes—
221C2×C4×D13—24no—
222C2×C4×D13—82no—
223C13×C4⋊C4—24no—
224C13×C4⋊C4—24no—
225C13×C4⋊C4—24no—
226C13×C4⋊C4—24no—
227C13×C4⋊C4—21no—
228C13×C4⋊C4—21no—
229C13×C4⋊C4—21no—
230C13×C4⋊C4C2×D414yes—
231C13×C4⋊C4C2412yes—
232C13×C4⋊C4C2412yes—
233C13×C4⋊C4C2412yes—
234C13×C22⋊C4—24no—
235C13×C22⋊C4—24no—
236C13×C22⋊C4—24no—
237C13×C22⋊C4—24no—
238C13×C22⋊C4C2×D414yes—
239C13×C22⋊C4C2×D414yes—
240C42×C13—24no—
241C42×C13—24no—
242C42×C13—24no—
243C42×C13C2×D412yes—
244C42×C13C2412yes—
245C22⋊Dic13—24no—
246#6106—28no—
247#6103—24no—
248#6103—24no—
249#6103—24no—
250C4⋊Dic13—21no—
251C4⋊Dic13—21no—
252C4⋊Dic13—21no—
253C4⋊Dic13—24no—
254C4⋊Dic13C2412yes—
255C4⋊Dic13C2412yes—
256C4⋊Dic13C2412yes—
257#6101—24no—
258#6101—24no—
259C4×Dic13—24no—
260#6099—28no—
261C2×#1055—22no—
262C2×#1055—22no—
263C2×#1055—22no—
264C2×#1055—28no—
265C2×#1055#4114yes—
266C2×#1055C2412yes—
267C2×#1055C2412yes—
268C2×#1055C2412yes—
269C2×#1055C2412yes—
270C2×#556D1311yescharacteristic, complemented
271C2×#553—131no—
272#3350—1316no—
273C2×#501—131no—
274C2×#485—131no—
275C2×#482—131no—
276C2×#482—131no—
277C2×#483—131no—
278C2×#479—131no—
279C2×#476—131no—
280C2×#468—131no—
281C2×#465—131no—
282C2×#440—131no—
283C2×#435—131no—
284C2×#428—131no—
285C2×#427—131no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13C22×D412yes—
293C23×C13C22×D412yes—
294C23×C13C22×D411yescharacteristic
295C22×D13—22no—
296C22×D13—42no—
297C22×D13—42no—
298C22×D13—42no—
299Q8×C13—22no—
300Q8×C13—22no—
301Q8×C13—48no—
302Q8×C13—42no—
303D4×C13—44no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—24no—
309C2×C4×C13—24no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—42no—
319C2×C4×C13—42no—
320C2×C4×C13—42no—
321C2×C4×C13—42no—
322C2×C4×C13C22×D412yes—
323C2×C4×C13C22×D412yes—
324C2×C4×C13C22×D412yes—
325C2×C4×C13C22×D412yes—
326C2×C4×C13C22×D411yescharacteristic
327C2×C4×C13C2×#4112yes—
328C2×C4×C132−1+412yes—
329C2×C4×C13C2511yescharacteristic
330C22⋊D13—48no—
331C22⋊D13—84no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—42no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—84no—
339D52—22no—
340D52—22no—
341D52—42no—
342C4×D13—84no—
343#1055—22no—
344#1055—22no—
345#1055—22no—
346#1055C2×#4114yes—
347C22×SD16—131no—
348C22×M16—131no—
349C23×C8—131no—
350#556—24no—
351#556C2×D1318yescomplemented
352#553—138no—
353#553—264no—
354C2×C4⋊Q8C2×D1311yescharacteristic
355C2×#126—21no—
356C2×#126—21no—
357C2×#126—261no—
358C2×#125—131no—
359C2×#124—21no—
360C2×#123—261no—
361C2×C22⋊Q8C2×D1311yescharacteristic
362C2×C22⋊Q8C2×D1311yescharacteristic
363C2×#121—131no—
364C2×#121—131no—
365C2×#121—261no—
366C2×C4×Q8—21no—
367C2×C4×Q8C2×D1311yescharacteristic
368C2×C4×D4—131no—
369C2×C4×D4—261no—
370C2×C4×D4C2×D1311yescharacteristic
371C2×#117—131no—
372C2×#117C2×D1311yescharacteristic
373C2×#117C2×D1311yescharacteristic
374C22×C4⋊C4—131no—
375#501—138no—
376#485—138no—
377#483—138no—
378#482—138no—
379#482—138no—
380#479—138no—
381#476—138no—
382#468—138no—
383#465—138no—
384#440—138no—
385#435—138no—
386#428—138no—
387#427—138no—
388C2×#107—131no—
389C2×#107—131no—
390C2×#107—131no—
391C2×#107—131no—
392C2×#106—131no—
393C2×#106—131no—
394C2×#106—131no—
395C2×#106—131no—
396C2×#106—131no—
397C2×C4⋊C8—131no—
398C2×#103—131no—
399C2×#103—131no—
400C2×#103—131no—
401C2×#102—131no—
402C2×#102—131no—
403C2×#102—131no—
404C2×C22⋊C8—131no—
405C2×C22⋊C8—131no—
406C2×#97—131no—
407C22×C13—22no—
408C22×C13—22no—
409C22×C13—22no—
410C22×C13—22no—
411C22×C13—22no—
412C22×C13—22no—
413C22×C13—44no—
414C22×C13—44no—
415C22×C13#54712yes—
416C22×C13#57512yes—
417C22×C13#57712yes—
418C22×C13C23×D411yescharacteristic
419C2×D13—42no—
420C2×D13—42no—
421C2×D13—42no—
422C2×D13—84no—
423C4×C13—22no—
424C4×C13—22no—
425C4×C13—22no—
426C4×C13—22no—
427C4×C13—42no—
428C4×C13—42no—
429C4×C13—42no—
430C4×C13—42no—
431C4×C13#54712yes—
432C4×C13C22×#4111yescharacteristic
433C4×C13C2×2−1+411yescharacteristic
434Dic13—42no—
435Dic13—42no—
436Dic13—42no—
437C22×Q8—21no—
438C22×Q8C22×D1311yescharacteristic
439C22×D4—131no—
440C22×D4—261no—
441C22×D4—261no—
442C22×D4C22⋊D1311yescharacteristic
443C23×C4—261no—
444C23×C4—261no—
445C23×C4C22×D1311yescharacteristic
446C23×C4C22×D1311yescharacteristic
447C2×SD16—134no—
448C2×SD16—264no—
449C2×M16—134no—
450C2×M16—264no—
451C22×C8—131no—
452C22×C8—131no—
453C22×C8—134no—
454C22×C8—131no—
455C22×C8—131no—
456C22×C8—264no—
457C4⋊Q8—22no—
458C4⋊Q8C22×D1314yes—
459#126—28no—
460#126—28no—
461#126—268no—
462#125—134no—
463#125—262no—
464#124—28no—
465#123—268no—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8C22×D1314yes—
469C22⋊Q8C22×D1314yes—
470#121—134no—
471#121—134no—
472#121—268no—
473#121—262no—
474#121—262no—
475C4×Q8—28no—
476C4×Q8—22no—
477C4×Q8C22×D1314yes—
478C4×D4—134no—
479C4×D4—268no—
480C4×D4—262no—
481C4×D4C22⋊D1314yes—
482C4×D4C22×D1314yes—
483#117—22no—
484#117—22no—
485#117—134no—
486#117—262no—
487#117C22×D1314yes—
488#117C22×D1314yes—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—131no—
494C2×C4⋊C4—131no—
495C2×C4⋊C4—134no—
496C2×C4⋊C4—131no—
497C2×C4⋊C4—261no—
498C2×C4⋊C4—262no—
499C2×C4⋊C4—261no—
500C2×C4⋊C4—261no—
501C2×C4⋊C4C22⋊D1311yescharacteristic
502C2×C4⋊C4C22×D1311yescharacteristic
503C2×C4⋊C4C22×D1311yescharacteristic
504C2×C4⋊C4C22×D1311yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—261no—
510C2×C22⋊C4—261no—
511C2×C22⋊C4—261no—
512C2×C22⋊C4—261no—
513C2×C22⋊C4C22⋊D1311yescharacteristic
514C2×C22⋊C4C22⋊D1311yescharacteristic
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—261no—
519C2×C42C22×D1311yescharacteristic
520#107—134no—
521#107—134no—
522#107—134no—
523#107—134no—
524#106—134no—
525#106—134no—
526#106—134no—
527#106—134no—
528#106—134no—
529C4⋊C8—134no—
530#103—134no—
531#103—134no—
532#103—134no—
533#102—134no—
534#102—134no—
535#102—134no—
536C22⋊C8—134no—
537C22⋊C8—134no—
538#97—134no—
539C2×C13—42no—
540C2×C13—42no—
541C2×C13#335014yescomplemented
542C2×C13C2×#54711yescharacteristic
543C2×C13C2×#57511yescharacteristic
544C2×C13C2×#57711yescharacteristic
545D13—82no—
546C24—261no—
547C24C2×C22⋊D1311yescharacteristic
548C24C2×C22⋊D1311yescharacteristic
549C2×Q8—21no—
550C2×Q8—24no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—44no—
554C2×Q8C23×D1312yes—
555C2×D4—42no—
556C2×D4—132no—
557C2×D4—264no—
558C2×D4—264no—
559C2×D4—262no—
560C2×D4—262no—
561C2×D4—261no—
562C2×D4—524no—
563C2×D4—1042no—
564C2×D4C2×C22⋊D1314yes—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—264no—
577C22×C4—264no—
578C22×C4—1042no—
579C22×C4—1042no—
580C22×C4C2×C22⋊D1312yes—
581C22×C4C2×C22⋊D1312yes—
582C22×C4C2×C22⋊D1311yescharacteristic
583C22×C4C2×C22⋊D1311yescharacteristic
584C22×C4C2×C22⋊D1311yescharacteristic
585C22×C4C2×C22⋊D1311yescharacteristic
586C22×C4C23×D1312yes—
587C22×C4C23×D1312yes—
588C22×C4C23×D1311yescharacteristic
589SD16—268no—
590M16—268no—
591C2×C8—134no—
592C2×C8—132no—
593C2×C8—132no—
594C2×C8—132no—
595C2×C8—132no—
596C2×C8—268no—
597C2×C8—262no—
598C2×C8—262no—
599C2×C8—262no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—132no—
608C4⋊C4—132no—
609C4⋊C4—132no—
610C4⋊C4—261no—
611C4⋊C4—261no—
612C4⋊C4—264no—
613C4⋊C4—261no—
614C4⋊C4—264no—
615C4⋊C4—264no—
616C4⋊C4C2×C22⋊D1314yes—
617C4⋊C4C23×D1312yes—
618C4⋊C4C23×D1312yes—
619C4⋊C4C23×D1312yes—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—264no—
625C22⋊C4—264no—
626C22⋊C4—264no—
627C22⋊C4—264no—
628C22⋊C4C2×C22⋊D1314yes—
629C22⋊C4C2×C22⋊D1314yes—
630C42—24no—
631C42—24no—
632C42—24no—
633C42—264no—
634C42C2×C22⋊D1312yes—
635C42C23×D1312yes—
636C13C2×#335011yescharacteristic, complemented, Sylow
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—262no—
644C23—522no—
645C23—522no—
646C23—522no—
647C23C22×C22⋊D1312yes—
648C23C22×C22⋊D1312yes—
649C23C22×C22⋊D1311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—48no—
653Q8—42no—
654D4—44no—
655D4—262no—
656D4—262no—
657D4—528no—
658D4—522no—
659D4—1044no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—262no—
679C2×C4—262no—
680C2×C4—262no—
681C2×C4—522no—
682C2×C4—522no—
683C2×C4—522no—
684C2×C4—1044no—
685C2×C4—1044no—
686C2×C4#41×D1312yes—
687C2×C4#8825712yes—
688C2×C4C22×C22⋊D1312yes—
689C2×C4C22×C22⋊D1312yes—
690C2×C4C22×C22⋊D1312yes—
691C2×C4C22×C22⋊D1312yes—
692C2×C4C22×C22⋊D1311yescharacteristic
693C2×C4C24×D1311yescharacteristic
694C8—134no—
695C8—262no—
696C8—262no—
697C8—262no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—522no—
707C22—522no—
708C22—522no—
709C22—1044no—
710C22#1171952712yes—
711C22#1171952912yes—
712C22#1171954212yes—
713C22C23×C22⋊D1311yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—522no—
723C4—522no—
724C4—522no—
725C4#1171952912yes—
726C4C2×#41×D1311yescharacteristic
727C4C2×#8825711yescharacteristic
728C2—42no—
729C2—42no—
730C2—1042no—
731C2#1312738114yesdirect product factor
732C2C2×#1171952911yescharacteristic
733C2C2×#1171952711yescharacteristic
734C2C2×#1171954211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#556C2
socleC23×C13C22×D4
prime radicalC2×#11719270C2
hypercenterC2×#556D13
hypocenterC13C2×#3350
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. #13127381C2direct (N × H)
3. C2×#11718741C2semidirect
4. C2×#11718706C2semidirect
5. C2×#11718664C2semidirect
6. C2×#11718664C2semidirect
7. C2×#11718704C2semidirect
8. C2×#11718683C2semidirect
9. C2×#11718745C2semidirect
10. C2×#11718710C2semidirect
11. C2×#11718709C2semidirect
12. C2×#11718687C2semidirect
13. C2×#11718672C2semidirect
14. C2×#11718656C2semidirect
15. C2×#11718659C2semidirect
16. C2×C13×#556C2semidirect
18. C13×#556C22semidirect
50. #11718745C22semidirect
51. #11718741C22semidirect
52. #11718710C22semidirect
53. #11718709C22semidirect
54. #11718706C22semidirect
55. #11718704C22semidirect
56. #11718687C22semidirect
57. #11718683C22semidirect
58. #11718672C22semidirect
59. #11718664C22semidirect
60. #11718664C22semidirect
61. #11718659C22semidirect
62. #11718656C22semidirect
270. C2×#556D13semidirect
351. #556C2×D13semidirect
541. C2×C13#3350semidirect
636. C13C2×#3350semidirect
731. C2#13127381direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192702
#131273812
C2×#117187412
C2×#117187062
C2×#117186642
C2×#117187042
C2×#117186832
C2×#117187452
C2×#117187102
C2×#117187092
C2×#117186872
C2×#117186722
C2×#117186562
C2×#117186592
C2×C13×#5562
C2×#335013