Finite Group Databasebeta

← C2×#13127327 #16741504

Subgroups — C2×#13127327 #16741504

Order 3328.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719340C211yesmaximal, characteristic, complemented
2C2×#11719323C211yesmaximal, characteristic
3#13127327C2116yesmaximal, direct product factor
4C2×#11718517C211yesmaximal, characteristic, complemented
5C2×#11718705C211yesmaximal, characteristic, complemented
6C2×#11718695C211yesmaximal, characteristic, complemented
7C2×#11718475C211yesmaximal, characteristic, complemented
8C2×#11718435C211yesmaximal, characteristic, complemented
9C2×#11718457C211yesmaximal, characteristic, complemented
10C2×#11718420C211yesmaximal, characteristic, complemented
11C2×#11718835C211yesmaximal, characteristic, complemented
12C2×#11718825C211yesmaximal, characteristic, complemented
13C2×#11718772C211yesmaximal, characteristic, complemented
14C2×#11718522C211yesmaximal, characteristic, complemented
15C22×#88058C211yesmaximal, characteristic, complemented
16C2×C13×#465C211yesmaximal, characteristic, complemented
17C22×C13×SD16C2211yescharacteristic
18C23×C8×C13C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×#121C2211yescharacteristic
21C2×#88200C2211yescharacteristic
22C2×Q8×Dic13C2211yescharacteristic
23C2×#88193—21no—
24C2×#88192C2211yescharacteristic
25C2×D4×Dic13—21no—
26C2×D4×Dic13C2211yescharacteristic
27C2×C4×C22⋊D13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×#6094C2211yescharacteristic
31#11719340—24no—
32#11719340C2218yescomplemented
33#11719323—24no—
34#11719323C2218yes—
35C2×#88151—21no—
36C2×#88146C2211yescharacteristic
37C2×C4⋊C4×D13C2211yescharacteristic
38C2×#88144C2211yescharacteristic
39C2×#88143—21no—
40C2×#88142C2211yescharacteristic
41C2×#88140—21no—
42C2×#88135—21no—
43C2×#88133—21no—
44C2×#88132—21no—
45C13×#465C2218yescomplemented
46C2×C13×#106C2211yescharacteristic
47C2×C13×#103C2211yescharacteristic
48C2×C13×#102C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×#88075C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52C2×#88072C2211yescharacteristic
53C2×C22⋊#1055C2211yescharacteristic
54#11718835C2218yescomplemented
55#11718825C2218yescomplemented
56#11718772C2218yescomplemented
57C2×#88060C2211yescharacteristic
58C2×#88058C2211yescharacteristic
59C2×#88058C2211yescharacteristic
60C2×#88058C2211yescharacteristic
61C2×#88058C2211yescharacteristic
62C2×#88058C2218yescomplemented
63C2×#88055C2211yescharacteristic
64C2×#88054C2211yescharacteristic
65#11718705C2218yescomplemented
66#11718695C2218yescomplemented
67C2×#88048C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69C2×#88047C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71#11718522C2218yescomplemented
72#11718517C2218yescomplemented
73#11718475C2218yescomplemented
74#11718457C2218yescomplemented
75#11718435C2218yescomplemented
76#11718420C2218yescomplemented
77C22×Q8×C13C2311yescharacteristic
78C22×D4×C13—21no—
79C22×D4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C22×C22⋊D13—21no—
82C22×C22⋊D13D411yescharacteristic
83C23×Dic13—21no—
84C23×Dic13—21no—
85C23×Dic13—21no—
86C22×C4×D13—21no—
87C22×C4×D13C2311yescharacteristic
88C22×Dic26—21no—
89C2×C13×SD16—24no—
90C2×C13×SD16C2314yes—
91C22×C8×C13—24no—
92C22×C8×C13C2311yescharacteristic
93C22×C8×C13C2314yes—
94C22×C8×C13C2311yescharacteristic
95C13×C22⋊Q8—22no—
96C13×C22⋊Q8C2314yes—
97C13×#121—22no—
98C13×#121C2314yes—
99C2×C13×C4⋊C4—21no—
100C2×C13×C4⋊C4C2311yescharacteristic
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C22⋊C4—21no—
103C2×C13×C22⋊C4—21no—
104C2×C22⋊Dic13—21no—
105C2×C22⋊Dic13—21no—
106C2×C22⋊Dic13D411yescharacteristic
107#88200—22no—
108#88200C2314yes—
109Q8×Dic13—22no—
110Q8×Dic13C2314yes—
111#88193—28no—
112#88192—22no—
113#88192C2314yes—
114D4×Dic13—28no—
115D4×Dic13—22no—
116D4×Dic13C2314yes—
117C4×C22⋊D13D414yes—
118C4×C22⋊D13C2314yes—
119C2×#6103—21no—
120C2×#6103—21no—
121C2×#6103D411yescharacteristic
122C2×C4⋊Dic13—21no—
123C2×C4⋊Dic13—21no—
124C2×C4⋊Dic13—22no—
125C2×C4⋊Dic13—22no—
126C2×C4⋊Dic13—21no—
127C2×C4⋊Dic13—21no—
128C2×C4⋊Dic13C2311yescharacteristic
129C2×C4⋊Dic13C2311yescharacteristic
130C2×C4⋊Dic13C2311yescharacteristic
131C2×C4⋊Dic13C2314yes—
132C2×C4⋊Dic13C2311yescharacteristic
133C2×C4⋊Dic13C2314yes—
134C2×#6101—21no—
135C2×#6101—21no—
136C2×#6101—21no—
137C2×#6101—21no—
138C2×#6101D411yescharacteristic
139C2×C4×Dic13—21no—
140C2×C4×Dic13—21no—
141C2×C4×Dic13C2311yescharacteristic
142C22×#1055C2311yescharacteristic
143C22×#1055C2311yescharacteristic
144C2×#6094—24no—
145C2×#6094C2314yes—
146#88151—28no—
147#88146—22no—
148#88146C2314yes—
149C4⋊C4×D13—22no—
150C4⋊C4×D13C2314yes—
151#88144—22no—
152#88144C2314yes—
153#88143—28no—
154#88142—22no—
155#88142C2314yes—
156#88140—28no—
157#88135—28no—
158#88133—28no—
159#88132—28no—
160C13×#106C2314yes—
161C13×#103C2314yes—
162C13×#102C2314yes—
163#88075C2314yes—
164#88075C2314yes—
165#88072C2314yes—
166#88072C2314yes—
167C22⋊#1055C2314yes—
168#88060C2314yes—
169#88058C2314yes—
170#88058C2314yes—
171#88058C2314yes—
172#88058C2314yes—
173#88055C2314yes—
174#88054C2314yes—
175#88048C2314yes—
176#88048C2314yes—
177#88047C2314yes—
178#88047C2314yes—
179C2×#3346—131nomaximal, Sylow
180C24×C13—21no—
181C24×C13C2×D411yescharacteristic
182C23×D13C2×D411yescharacteristic
183C2×Q8×C13—21no—
184C2×Q8×C13—22no—
185C2×Q8×C13—22no—
186C2×Q8×C13C2412yes—
187C2×D4×C13—24no—
188C2×D4×C13—21no—
189C2×D4×C13—22no—
190C2×D4×C13—22no—
191C2×D4×C13—44no—
192C2×D4×C13C2412yes—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D412yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2411yescharacteristic
202C2×C22⋊D13—24no—
203C2×C22⋊D13—24no—
204C2×C22⋊D13—82no—
205C2×C22⋊D13C2×D414yes—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—24no—
211C22×Dic13—24no—
212C22×Dic13—24no—
213C22×Dic13—82no—
214C22×Dic13—82no—
215C22×Dic13—82no—
216C22×Dic13C2×D411yescharacteristic
217C22×Dic13C2×D411yescharacteristic
218C22×Dic13C2×D411yescharacteristic
219C2×C4×D13—22no—
220C2×C4×D13—22no—
221C2×C4×D13—24no—
222C2×C4×D13—82no—
223C2×C4×D13C2×D412yes—
224C2×C4×D13C2412yes—
225C2×Dic26—24no—
226C2×Dic26—82no—
227C13×SD16—28no—
228C2×C8×C13—22no—
229C2×C8×C13—28no—
230C2×C8×C13#4114yes—
231C2×C8×C13C2412yes—
232C2×C8×C13C2412yes—
233C13×C4⋊C4—21no—
234C13×C4⋊C4—24no—
235C13×C4⋊C4—21no—
236C13×C4⋊C4C2412yes—
237C13×C4⋊C4C2412yes—
238C13×C22⋊C4—24no—
239C13×C22⋊C4—24no—
240C22⋊Dic13—24no—
241C22⋊Dic13—24no—
242C22⋊Dic13C2×D414yes—
243#6103—24no—
244#6103—24no—
245#6103C2×D414yes—
246C4⋊Dic13—24no—
247C4⋊Dic13—21no—
248C4⋊Dic13—24no—
249C4⋊Dic13—21no—
250C4⋊Dic13—21no—
251C4⋊Dic13—21no—
252C4⋊Dic13—24no—
253C4⋊Dic13—24no—
254C4⋊Dic13C2412yes—
255C4⋊Dic13C2412yes—
256C4⋊Dic13C2412yes—
257C4⋊Dic13C2412yes—
258#6101—24no—
259#6101—24no—
260#6101—24no—
261#6101—24no—
262#6101C2×D414yes—
263C4×Dic13—24no—
264C4×Dic13—24no—
265C4×Dic13C2×D412yes—
266C4×Dic13C2412yes—
267C2×#1055—22no—
268C2×#1055—22no—
269C2×#1055C2412yes—
270C2×#1055C2412yes—
271#6094—28no—
272C2×#554—131no—
273C2×#553—131no—
274#3346—1316no—
275C2×#501—131no—
276C2×#484—131no—
277C2×#481—131no—
278C2×#485—131no—
279C2×#480—131no—
280C2×#479—131no—
281C2×#474—131no—
282C2×#468—131no—
283C2×#465D1311yescharacteristic, complemented
284C2×#440—131no—
285C2×#435—131no—
286C2×#428—131no—
287C22×#107—131no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—42no—
292C23×C13—42no—
293C23×C13—42no—
294C23×C13#13714yes—
295C23×C13C22×D412yes—
296C23×C13C22×D411yescharacteristic
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13C22×D412yes—
301Q8×C13—22no—
302Q8×C13—22no—
303Q8×C13—42no—
304D4×C13—22no—
305D4×C13—22no—
306D4×C13—48no—
307D4×C13—42no—
308C2×C4×C13—22no—
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—42no—
316C2×C4×C13—42no—
317C2×C4×C13—42no—
318C2×C4×C13C22×D412yes—
319C2×C4×C13C22×D411yescharacteristic
320C2×C4×C13C2×#4112yes—
321C2×C4×C132−1+412yes—
322C2×C4×C13C2511yescharacteristic
323C22⋊D13—28no—
324C22⋊D13—84no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13—84no—
337C2×Dic13—84no—
338C2×Dic13—84no—
339C2×Dic13C22×D412yes—
340C2×Dic13C22×D412yes—
341C2×Dic13C22×D412yes—
342C4×D13—24no—
343C4×D13—22no—
344C4×D13—22no—
345C4×D13—84no—
346Dic26—84no—
347C8×C13—22no—
348C8×C13C2×#4114yes—
349#1055—22no—
350#1055—22no—
351C22×SD16C2×D1311yescharacteristic
352C22×M16—131no—
353C23×C8C2×D1311yescharacteristic
354#554—138no—
355#554—264no—
356#553—138no—
357#553—264no—
358C2×C4⋊Q8—131no—
359C2×#126—261no—
360C2×#125—131no—
361C2×#125—261no—
362C2×#123—261no—
363C2×C22⋊Q8—131no—
364C2×C22⋊Q8—261no—
365C2×C22⋊Q8—261no—
366C2×C22⋊Q8C2×D1311yescharacteristic
367C2×#121—131no—
368C2×#121—261no—
369C2×#121C2×D1311yescharacteristic
370C2×C4×Q8—131no—
371C2×C4×D4—131no—
372C2×C4×D4—131no—
373C2×C4×D4—261no—
374C2×C4×D4—261no—
375C2×#117—131no—
376C22×C4⋊C4—131no—
377C22×C4⋊C4—131no—
378C22×C4⋊C4—131no—
379#501—138no—
380#485—138no—
381#484—138no—
382#481—138no—
383#480—138no—
384#479—138no—
385#474—138no—
386#468—138no—
387#465C2×D1318yescomplemented
388#440—138no—
389#435—138no—
390#428—138no—
391C2×#107—131no—
392C2×#107—131no—
393C2×#107—138no—
394C2×#107—131no—
395C2×#107—131no—
396C2×#107—131no—
397C2×#107—131no—
398C2×#106—131no—
399C2×#106—131no—
400C2×#106C2×D1311yescharacteristic
401C2×C4⋊C8—131no—
402C2×#103—131no—
403C2×#103—131no—
404C2×#103C2×D1311yescharacteristic
405C2×#102—131no—
406C2×#102—131no—
407C2×#102C2×D1311yescharacteristic
408C2×C22⋊C8—131no—
409C2×C22⋊C8—131no—
410C2×#97—131no—
411C22×C13—28no—
412C22×C13—22no—
413C22×C13—22no—
414C22×C13—42no—
415C22×C13—42no—
416C22×C13—42no—
417C22×C13—84no—
418C22×C13#54712yes—
419C22×C13C2×#13714yes—
420C22×C13C2×#13712yes—
421C22×C13#57612yes—
422C22×C13C23×D411yescharacteristic
423C2×D13—22no—
424C2×D13—22no—
425C2×D13—22no—
426C2×D13—44no—
427C4×C13—22no—
428C4×C13—42no—
429C4×C13—42no—
430C4×C13—42no—
431C4×C13#54712yes—
432C4×C13C22×#4111yescharacteristic
433C4×C13C2×2−1+411yescharacteristic
434Dic13—22no—
435Dic13—22no—
436Dic13—22no—
437Dic13—42no—
438Dic13—42no—
439Dic13—42no—
440Dic13—42no—
441C22×Q8—261no—
442C22×Q8C22×D1311yescharacteristic
443C22×D4—21no—
444C22×D4—131no—
445C22×D4—261no—
446C22×D4C22×D1311yescharacteristic
447C23×C4—131no—
448C23×C4—261no—
449C23×C4—261no—
450C23×C4—261no—
451C23×C4—261no—
452C23×C4C22×D1311yescharacteristic
453C2×SD16—24no—
454C2×SD16C22×D1314yes—
455C2×M16—134no—
456C2×M16—264no—
457C22×C8—24no—
458C22×C8—131no—
459C22×C8—131no—
460C22×C8C22×D1311yescharacteristic
461C22×C8C22×D1314yes—
462C22×C8C22×D1311yescharacteristic
463C4⋊Q8—134no—
464C4⋊Q8—262no—
465#126—268no—
466#125—134no—
467#125—262no—
468#125—268no—
469#123—268no—
470C22⋊Q8—22no—
471C22⋊Q8—134no—
472C22⋊Q8—268no—
473C22⋊Q8—268no—
474C22⋊Q8—262no—
475C22⋊Q8C22×D1314yes—
476#121—22no—
477#121—134no—
478#121—262no—
479#121—268no—
480#121C22×D1314yes—
481C4×Q8—134no—
482C4×Q8—262no—
483C4×D4—134no—
484C4×D4—134no—
485C4×D4—134no—
486C4×D4—262no—
487C4×D4—268no—
488C4×D4—268no—
489#117—134no—
490#117—262no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—131no—
493C2×C4⋊C4—131no—
494C2×C4⋊C4—131no—
495C2×C4⋊C4—131no—
496C2×C4⋊C4—131no—
497C2×C4⋊C4—134no—
498C2×C4⋊C4—134no—
499C2×C4⋊C4—134no—
500C2×C4⋊C4—262no—
501C2×C4⋊C4—261no—
502C2×C4⋊C4—261no—
503C2×C4⋊C4—261no—
504C2×C4⋊C4—261no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4—261no—
509C2×C4⋊C4—262no—
510C2×C4⋊C4—262no—
511C2×C4⋊C4C22×D1311yescharacteristic
512C2×C4⋊C4C22×D1311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—131no—
516C2×C22⋊C4—131no—
517C2×C22⋊C4—261no—
518C2×C22⋊C4—261no—
519C2×C22⋊C4—261no—
520C2×C22⋊C4—261no—
521C2×C42—131no—
522C2×C42—261no—
523C2×C42—261no—
524#107—134no—
525#107—134no—
526#107—134no—
527#107—134no—
528#107—134no—
529#107—134no—
530#106—134no—
531#106—134no—
532#106C22×D1314yes—
533C4⋊C8—134no—
534#103—134no—
535#103—134no—
536#103C22×D1314yes—
537#102—134no—
538#102—134no—
539#102C22×D1314yes—
540C22⋊C8—134no—
541C22⋊C8—134no—
542#97—134no—
543C2×C13—24no—
544C2×C13—82no—
545C2×C13#334614yescomplemented
546C2×C13C2×#54711yescharacteristic
547C2×C13C22×#13711yescharacteristic
548C2×C13C2×#57611yescharacteristic
549D13—42no—
550C24—21no—
551C24—131no—
552C24D4×D1311yescharacteristic
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—264no—
557C2×Q8—1042no—
558C2×Q8C23×D1312yes—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—44no—
564C2×D4—134no—
565C2×D4—264no—
566C2×D4—264no—
567C2×D4—1042no—
568C2×D4C23×D1312yes—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—131no—
575C22×C4—131no—
576C22×C4—131no—
577C22×C4—132no—
578C22×C4—132no—
579C22×C4—264no—
580C22×C4—264no—
581C22×C4—262no—
582C22×C4—262no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—264no—
588C22×C4—264no—
589C22×C4—1042no—
590C22×C4—1042no—
591C22×C4—1042no—
592C22×C4—1042no—
593C22×C4D4×D1312yes—
594C22×C4D4×D1311yescharacteristic
595C22×C4C23×D1312yes—
596C22×C4C23×D1311yescharacteristic
597SD16—28no—
598M16—268no—
599C2×C8—22no—
600C2×C8—28no—
601C2×C8—132no—
602C2×C8—132no—
603C2×C8—262no—
604C2×C8—262no—
605C2×C8#612914yes—
606C2×C8C23×D1312yes—
607C2×C8C23×D1312yes—
608C4⋊C4—24no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—134no—
612C4⋊C4—132no—
613C4⋊C4—132no—
614C4⋊C4—132no—
615C4⋊C4—132no—
616C4⋊C4—264no—
617C4⋊C4—264no—
618C4⋊C4—264no—
619C4⋊C4—264no—
620C4⋊C4—264no—
621C4⋊C4—264no—
622C4⋊C4—261no—
623C4⋊C4—261no—
624C4⋊C4—261no—
625C4⋊C4—264no—
626C4⋊C4—261no—
627C4⋊C4—264no—
628C4⋊C4C23×D1312yes—
629C4⋊C4C23×D1312yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—134no—
633C22⋊C4—134no—
634C22⋊C4—264no—
635C22⋊C4—264no—
636C22⋊C4—264no—
637C22⋊C4—264no—
638C42—132no—
639C42—132no—
640C42—264no—
641C42—264no—
642C13C2×#334611yescharacteristic, complemented, Sylow
643C23—22no—
644C23—22no—
645C23—22no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—132no—
650C23—262no—
651C23—262no—
652C23—262no—
653C23#8816914yes—
654C23C2×D4×D1312yes—
655C23C2×D4×D1311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—1044no—
660D4—22no—
661D4—22no—
662D4—48no—
663D4—42no—
664D4—268no—
665D4—1044no—
666C2×C4—22no—
667C2×C4—24no—
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—132no—
677C2×C4—132no—
678C2×C4—132no—
679C2×C4—262no—
680C2×C4—262no—
681C2×C4—262no—
682C2×C4—264no—
683C2×C4—262no—
684C2×C4—262no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—522no—
690C2×C4—522no—
691C2×C4—522no—
692C2×C4—522no—
693C2×C4—1044no—
694C2×C4—1044no—
695C2×C4—1044no—
696C2×C4—1044no—
697C2×C4C2×D4×D1312yes—
698C2×C4C2×D4×D1311yescharacteristic
699C2×C4C2×#612912yes—
700C2×C4#8825712yes—
701C2×C4C24×D1311yescharacteristic
702C8—22no—
703C8—262no—
704C8—262no—
705C8C2×#612914yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—84no—
713C22—262no—
714C22—262no—
715C22—262no—
716C22—524no—
717C22#1171931612yes—
718C22C2×#8816914yes—
719C22C2×#8816912yes—
720C22#1171947412yes—
721C22C22×D4×D1311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—262no—
727C4—262no—
728C4—262no—
729C4—522no—
730C4—522no—
731C4—522no—
732C4—522no—
733C4#1171931612yes—
734C4C22×#612911yescharacteristic
735C4C2×#8825711yescharacteristic
736C2—24no—
737C2—82no—
738C2—522no—
739C2#1312732714yesdirect product factor
740C2C2×#1171931611yescharacteristic
741C2C22×#8816911yescharacteristic
742C2C2×#1171947411yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#465C2
socleC23×C13C22×D4
prime radicalC2×#11719323C2
hypercenterC2×#465D13
hypocenterC13C2×#3346
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#11719340C2semidirect
3. #13127327C2direct (N × H)
4. C2×#11718517C2semidirect
5. C2×#11718705C2semidirect
6. C2×#11718695C2semidirect
7. C2×#11718475C2semidirect
8. C2×#11718435C2semidirect
9. C2×#11718457C2semidirect
10. C2×#11718420C2semidirect
11. C2×#11718835C2semidirect
12. C2×#11718825C2semidirect
13. C2×#11718772C2semidirect
14. C2×#11718522C2semidirect
15. C22×#88058C2semidirect
16. C2×C13×#465C2semidirect
32. #11719340C22semidirect
45. C13×#465C22semidirect
54. #11718835C22semidirect
55. #11718825C22semidirect
56. #11718772C22semidirect
62. C2×#88058C22semidirect
65. #11718705C22semidirect
66. #11718695C22semidirect
71. #11718522C22semidirect
72. #11718517C22semidirect
73. #11718475C22semidirect
74. #11718457C22semidirect
75. #11718435C22semidirect
76. #11718420C22semidirect
283. C2×#465D13semidirect
387. #465C2×D13semidirect
545. C2×C13#3346semidirect
642. C13C2×#3346semidirect
739. C2#13127327direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193402
C2×#117193232
#131273272
C2×#117185172
C2×#117187052
C2×#117186952
C2×#117184752
C2×#117184352
C2×#117184572
C2×#117184202
C2×#117188352
C2×#117188252
C2×#117187722
C2×#117185222
C22×#880582
C2×C13×#4652
C2×#334613