Finite Group Databasebeta

← C2×#13127375 #16741556

Subgroups — C2×#13127375 #16741556

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×#11719247C211yesmaximal, characteristic, complemented
2#13127375C2116yesmaximal, direct product factor
3C2×#11718726C211yesmaximal, characteristic, complemented
4C2×#11718657C211yesmaximal, characteristic, complemented
5C2×#11718696C211yesmaximal, characteristic, complemented
6C2×#11718696C211yesmaximal, characteristic, complemented
7C2×#11718632C211yesmaximal, characteristic, complemented
8C2×#11718724C211yesmaximal, characteristic, complemented
9C2×#11718669C211yesmaximal, characteristic, complemented
10C2×#11718703C211yesmaximal, characteristic, complemented
11C2×#11718702C211yesmaximal, characteristic, complemented
12C2×#11718679C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic, complemented
14C2×#11718625C211yesmaximal, characteristic, complemented
15C2×#11718659C211yesmaximal, characteristic, complemented
16C2×C13×#553C211yesmaximal, characteristic
17C13×#553—24no—
18C13×#553C2218yes—
19C2×C13×#126—21no—
20C2×C13×#125C2211yescharacteristic
21C2×C13×#123—21no—
22C2×C13×#121—21no—
23C2×C13×#121C2211yescharacteristic
24C2×C13×#121C2211yescharacteristic
25C2×C4×D4×C13—21no—
26C2×C4×D4×C13C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C2×C13×#117C2211yescharacteristic
29C22×C13×C4⋊C4C2211yescharacteristic
30C2×#88190—21no—
31C22×#6105C2211yescharacteristic
32C2×#88180C2211yescharacteristic
33C2×#88180C2211yescharacteristic
34C2×#88178C2211yescharacteristic
35C2×#88178C2211yescharacteristic
36C22×#6099C2211yescharacteristic
37C23×#1055C2211yescharacteristic
38#11719247—24no—
39#11719247C2218yescomplemented
40C2×#88141—21no—
41C2×#88133—21no—
42C2×#88133—21no—
43C2×#88123C2211yescharacteristic
44C2×C4×Dic26C2211yescharacteristic
45C2×#88072C2211yescharacteristic
46C2×#88072C2211yescharacteristic
47C2×#88072C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic
50#11718726C2218yescomplemented
51#11718724C2218yescomplemented
52#11718703C2218yescomplemented
53#11718702C2218yescomplemented
54#11718696C2218yescomplemented
55#11718696C2218yescomplemented
56#11718679C2218yescomplemented
57#11718672C2218yescomplemented
58#11718669C2218yescomplemented
59#11718659C2218yescomplemented
60#11718657C2218yescomplemented
61#11718632C2218yescomplemented
62C2×#88050C2211yescharacteristic
63C2×#88050C2211yescharacteristic
64C2×#88050C2211yescharacteristic
65#11718625C2218yescomplemented
66C2×#88048C2211yescharacteristic
67C2×#88048C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88048C2211yescharacteristic
71C2×#88047C2211yescharacteristic
72C2×#88047C2211yescharacteristic
73C2×#88047C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
77C22×D4×C13—21no—
78C22×D4×C13—21no—
79C22×D4×C13D411yescharacteristic
80C22×D4×C13C2311yescharacteristic
81C23×C4×C13—21no—
82C23×C4×C13—21no—
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C22×Dic26—21no—
86C22×Dic26C2311yescharacteristic
87C13×#126—28no—
88C13×#125—22no—
89C13×#125C2314yes—
90C13×#123—28no—
91C13×#121—28no—
92C13×#121—22no—
93C13×#121—22no—
94C13×#121C2314yes—
95C13×#121C2314yes—
96C4×D4×C13—28no—
97C4×D4×C13—22no—
98C4×D4×C13D414yes—
99C4×D4×C13C2314yes—
100C4×D4×C13C2314yes—
101C13×#117—22no—
102C13×#117C2314yes—
103C2×C13×C4⋊C4—21no—
104C2×C13×C4⋊C4—22no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4D411yescharacteristic
108C2×C13×C4⋊C4C2311yescharacteristic
109C2×C13×C4⋊C4C2311yescharacteristic
110C2×C13×C4⋊C4C2314yes—
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C22⋊C4—21no—
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4D411yescharacteristic
117C2×C13×C22⋊C4D411yescharacteristic
118C2×C42×C13—21no—
119C2×C42×C13C2311yescharacteristic
120C2×C22⋊Dic13—21no—
121C2×C22⋊Dic13—21no—
122C2×C22⋊Dic13—21no—
123C2×C22⋊Dic13—21no—
124#88190—28no—
125C2×#6105—24no—
126C2×#6105C2314yes—
127#88180—22no—
128#88180—22no—
129#88180C2314yes—
130#88180C2314yes—
131C2×C4⋊Dic13—21no—
132C2×C4⋊Dic13C2311yescharacteristic
133C2×C4⋊Dic13C2311yescharacteristic
134C2×C4⋊Dic13C2311yescharacteristic
135#88178—22no—
136#88178—22no—
137#88178C2314yes—
138#88178C2314yes—
139C2×#6101—21no—
140C2×#6101—21no—
141C2×#6101—21no—
142C2×C4×Dic13—21no—
143C2×C4×Dic13—21no—
144C2×C4×Dic13—21no—
145C2×#6099—24no—
146C2×#6099C2314yes—
147C22×#1055—24no—
148C22×#1055C2314yes—
149C22×#1055C2311yescharacteristic
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152C22×#1055C2311yescharacteristic
153#88141—28no—
154#88133—28no—
155#88133—28no—
156#88123—22no—
157#88123C2314yes—
158C4×Dic26—22no—
159C4×Dic26C2314yes—
160#88072C2314yes—
161#88072C2314yes—
162#88072C2314yes—
163C22⋊#1055C2314yes—
164C22⋊#1055C2314yes—
165#88050C2314yes—
166#88050C2314yes—
167#88050C2314yes—
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×C13—21no—
181C24×C13C2×D411yescharacteristic
182C24×C13C2×D411yescharacteristic
183C2×D4×C13—24no—
184C2×D4×C13—24no—
185C2×D4×C13—21no—
186C2×D4×C13—22no—
187C2×D4×C13—22no—
188C2×D4×C13—42no—
189C2×D4×C13—44no—
190C2×D4×C13—82no—
191C2×D4×C13C2×D414yes—
192C2×D4×C13C2412yes—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—24no—
201C22×C4×C13—24no—
202C22×C4×C13—82no—
203C22×C4×C13—82no—
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D412yes—
209C22×C4×C13C2×D412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
212C22×C4×C13C2411yescharacteristic
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C2×Dic26—22no—
218C2×Dic26—22no—
219C2×Dic26—21no—
220C2×Dic26—24no—
221C2×Dic26—44no—
222C2×Dic26C2412yes—
223C13×C4⋊C4—21no—
224C13×C4⋊C4—21no—
225C13×C4⋊C4—24no—
226C13×C4⋊C4—24no—
227C13×C4⋊C4—24no—
228C13×C4⋊C4—21no—
229C13×C4⋊C4C2×D414yes—
230C13×C4⋊C4C2412yes—
231C13×C4⋊C4C2412yes—
232C13×C4⋊C4C2412yes—
233C13×C22⋊C4—24no—
234C13×C22⋊C4—24no—
235C13×C22⋊C4—24no—
236C13×C22⋊C4—24no—
237C13×C22⋊C4C2×D414yes—
238C13×C22⋊C4C2×D414yes—
239C42×C13—24no—
240C42×C13C2×D412yes—
241C42×C13C2412yes—
242C22⋊Dic13—24no—
243C22⋊Dic13—24no—
244C22⋊Dic13—24no—
245C22⋊Dic13—24no—
246#6105—28no—
247C4⋊Dic13—21no—
248C4⋊Dic13—21no—
249C4⋊Dic13—21no—
250C4⋊Dic13—24no—
251C4⋊Dic13C2412yes—
252C4⋊Dic13C2412yes—
253C4⋊Dic13C2412yes—
254#6101—24no—
255#6101—24no—
256#6101—24no—
257C4×Dic13—24no—
258C4×Dic13—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×#556—131no—
271C2×#553D1311yescharacteristic
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×C13—22no—
293C23×C13—42no—
294C23×C13—42no—
295C23×C13—42no—
296C23×C13C22×D412yes—
297C23×C13C22×D412yes—
298C23×C13C22×D411yescharacteristic
299D4×C13—22no—
300D4×C13—22no—
301D4×C13—44no—
302D4×C13—48no—
303D4×C13—42no—
304D4×C13—84no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—24no—
310C2×C4×C13—24no—
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—84no—
322C2×C4×C13—84no—
323C2×C4×C13C22×D412yes—
324C2×C4×C13C22×D412yes—
325C2×C4×C13C22×D412yes—
326C2×C4×C13C22×D412yes—
327C2×C4×C13C22×D411yescharacteristic
328C2×C4×C13C2×#4112yes—
329C2×C4×C132−1+412yes—
330C2×C4×C13C2511yescharacteristic
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—42no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339Dic26—22no—
340Dic26—22no—
341Dic26—48no—
342Dic26—42no—
343#1055—22no—
344#1055—22no—
345#1055—22no—
346#1055C2×#4114yes—
347C22×SD16—131no—
348C22×M16—131no—
349C23×C8—131no—
350#556—138no—
351#556—264no—
352#553—24no—
353#553C2×D1318yes—
354C2×C4⋊Q8—131no—
355C2×#126—21no—
356C2×#126—261no—
357C2×#126—261no—
358C2×#125C2×D1311yescharacteristic
359C2×#124—261no—
360C2×#123—21no—
361C2×C22⋊Q8—131no—
362C2×C22⋊Q8—131no—
363C2×#121—21no—
364C2×#121C2×D1311yescharacteristic
365C2×#121C2×D1311yescharacteristic
366C2×C4×Q8—131no—
367C2×C4×Q8—261no—
368C2×C4×D4—21no—
369C2×C4×D4C2×D1311yescharacteristic
370C2×C4×D4C2×D1311yescharacteristic
371C2×#117—131no—
372C2×#117—131no—
373C2×#117C2×D1311yescharacteristic
374C22×C4⋊C4C2×D1311yescharacteristic
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—42no—
416C22×C13—42no—
417C22×C13—42no—
418C22×C13—84no—
419C22×C13#54712yes—
420C22×C13#57512yes—
421C22×C13#57712yes—
422C22×C13C23×D411yescharacteristic
423C4×C13—22no—
424C4×C13—22no—
425C4×C13—22no—
426C4×C13—22no—
427C4×C13—42no—
428C4×C13—42no—
429C4×C13—42no—
430C4×C13#54712yes—
431C4×C13C22×#4111yescharacteristic
432C4×C13C2×2−1+411yescharacteristic
433Dic13—42no—
434Dic13—42no—
435Dic13—42no—
436Dic13—42no—
437C22×Q8—131no—
438C22×Q8—261no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C22⋊D1311yescharacteristic
442C22×D4C22×D1311yescharacteristic
443C23×C4—21no—
444C23×C4—21no—
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—134no—
458C4⋊Q8—262no—
459#126—28no—
460#126—268no—
461#126—268no—
462#125—22no—
463#125C22×D1314yes—
464#124—268no—
465#123—28no—
466C22⋊Q8—134no—
467C22⋊Q8—134no—
468C22⋊Q8—262no—
469C22⋊Q8—262no—
470#121—28no—
471#121—22no—
472#121—22no—
473#121C22×D1314yes—
474#121C22×D1314yes—
475C4×Q8—134no—
476C4×Q8—268no—
477C4×Q8—262no—
478C4×D4—28no—
479C4×D4—22no—
480C4×D4C22⋊D1314yes—
481C4×D4C22×D1314yes—
482C4×D4C22×D1314yes—
483#117—22no—
484#117—134no—
485#117—134no—
486#117—262no—
487#117—262no—
488#117C22×D1314yes—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—131no—
494C2×C4⋊C4—131no—
495C2×C4⋊C4—131no—
496C2×C4⋊C4—261no—
497C2×C4⋊C4—261no—
498C2×C4⋊C4—261no—
499C2×C4⋊C4—261no—
500C2×C4⋊C4C22⋊D1311yescharacteristic
501C2×C4⋊C4C22×D1311yescharacteristic
502C2×C4⋊C4C22×D1311yescharacteristic
503C2×C4⋊C4C22×D1314yes—
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—261no—
517C2×C42—261no—
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—82no—
542C2×C13#335014yescomplemented
543C2×C13C2×#54711yescharacteristic
544C2×C13C2×#57511yescharacteristic
545C2×C13C2×#57711yescharacteristic
546C24—21no—
547C24C2×C22⋊D1311yescharacteristic
548C24C2×C22⋊D1311yescharacteristic
549C2×Q8—132no—
550C2×Q8—261no—
551C2×Q8—264no—
552C2×Q8—262no—
553C2×Q8—262no—
554C2×Q8—524no—
555C2×D4—24no—
556C2×D4—24no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—42no—
561C2×D4—44no—
562C2×D4—82no—
563C2×D4C2×C22⋊D1314yes—
564C2×D4C23×D1312yes—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—82no—
575C22×C4—82no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
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—21no—
601C4⋊C4—21no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—132no—
607C4⋊C4—132no—
608C4⋊C4—132no—
609C4⋊C4—261no—
610C4⋊C4—261no—
611C4⋊C4—261no—
612C4⋊C4—264no—
613C4⋊C4—264no—
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—264no—
632C42—264no—
633C42—264no—
634C42C2×C22⋊D1312yes—
635C42C23×D1312yes—
636C13C2×#335011yescharacteristic, complemented, Sylow
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23C22×C22⋊D1312yes—
648C23C22×C22⋊D1312yes—
649C23C22×C22⋊D1311yescharacteristic
650Q8—262no—
651Q8—262no—
652Q8—528no—
653Q8—522no—
654D4—22no—
655D4—22no—
656D4—44no—
657D4—48no—
658D4—42no—
659D4—84no—
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—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—84no—
677C2×C4—84no—
678C2×C4—262no—
679C2×C4—262no—
680C2×C4—262no—
681C2×C4—262no—
682C2×C4—522no—
683C2×C4—522no—
684C2×C4—522no—
685C2×C4—522no—
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—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22#1171952712yes—
711C22#1171952912yes—
712C22#1171954112yes—
713C22C23×C22⋊D1311yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—522no—
722C4—522no—
723C4—522no—
724C4—522no—
725C4#1171952912yes—
726C4C2×#41×D1311yescharacteristic
727C4C2×#8825711yescharacteristic
728C2—42no—
729C2—42no—
730C2—82no—
731C2#1312737514yesdirect product factor
732C2C2×#1171952911yescharacteristic
733C2C2×#1171952711yescharacteristic
734C2C2×#1171954111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
Fitting, prime radicalC2×C13×#553C2
socleC23×C13C22×D4
hypercenterC2×#553D13
hypocenterC13C2×#3350
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#11719247C2semidirect
2. #13127375C2direct (N × H)
3. C2×#11718726C2semidirect
4. C2×#11718657C2semidirect
5. C2×#11718696C2semidirect
6. C2×#11718696C2semidirect
7. C2×#11718632C2semidirect
8. C2×#11718724C2semidirect
9. C2×#11718669C2semidirect
10. C2×#11718703C2semidirect
11. C2×#11718702C2semidirect
12. C2×#11718679C2semidirect
13. C2×#11718672C2semidirect
14. C2×#11718625C2semidirect
15. C2×#11718659C2semidirect
39. #11719247C22semidirect
50. #11718726C22semidirect
51. #11718724C22semidirect
52. #11718703C22semidirect
53. #11718702C22semidirect
54. #11718696C22semidirect
55. #11718696C22semidirect
56. #11718679C22semidirect
57. #11718672C22semidirect
58. #11718669C22semidirect
59. #11718659C22semidirect
60. #11718657C22semidirect
61. #11718632C22semidirect
65. #11718625C22semidirect
542. C2×C13#3350semidirect
636. C13C2×#3350semidirect
731. C2#13127375direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192472
#131273752
C2×#117187262
C2×#117186572
C2×#117186962
C2×#117186322
C2×#117187242
C2×#117186692
C2×#117187032
C2×#117187022
C2×#117186792
C2×#117186722
C2×#117186252
C2×#117186592
C2×C13×#5532
C2×#335013