Finite Group Databasebeta

← C2×#13125067 #16731200

Subgroups — C2×#13125067 #16731200

Order 3328.

2058 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×#11719239C211yesmaximal, characteristic
2C2×#11719221C211yesmaximal, characteristic, complemented
3#13125067C2116yesmaximal, direct product factor
4C2×#11718384C211yesmaximal, characteristic, complemented
5C2×#11718398C211yesmaximal, characteristic
6C2×#11718511C211yesmaximal, characteristic, complemented
7C2×#11718512C211yesmaximal, characteristic, complemented
8C2×#11718506C211yesmaximal, characteristic, complemented
9C2×#11718506C211yesmaximal, characteristic, complemented
10C2×#11718400C211yesmaximal, characteristic, complemented
11C2×#11718399C211yesmaximal, characteristic
12C2×#11718377C211yesmaximal, characteristic, complemented
13C2×#11718371C211yesmaximal, characteristic, complemented
14C2×C4×Dic52C211yesmaximal, characteristic, complemented
15C2×C4×#6095C211yesmaximal, characteristic, complemented
16C2×C13×#433C211yesmaximal, characteristic, complemented
17C23×Dic26C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×#88184C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C2×#88178C2211yescharacteristic
22C22×Dic52C2211yescharacteristic
23C22×Dic52C2211yescharacteristic
24C22×#6095C2211yescharacteristic
25C22×#6095C2211yescharacteristic
26#11719239—24no—
27#11719239C2218yes—
28#11719221—24no—
29#11719221C2218yescomplemented
30C2×#88152—21no—
31C2×#88150—21no—
32C2×#88141—21no—
33C2×#88141—21no—
34C2×#88139—21no—
35C2×#88137—21no—
36C2×#88131—21no—
37C2×#88131—21no—
38C2×#88129C2211yescharacteristic
39C2×C4×D52C2211yescharacteristic
40C2×#88123C2211yescharacteristic
41C2×C4×Dic26C2211yescharacteristic
42C2×C4×Dic26C2211yescharacteristic
43C2×C4×Dic26C2211yescharacteristic
44C2×C4×Dic26C2211yescharacteristic
45C2×C4×Dic26C2211yescharacteristic
46C13×#433C2218yescomplemented
47C2×C13×C4⋊C8C2211yescharacteristic
48C2×C13×C4⋊C8C2211yescharacteristic
49C2×C13×C22⋊C8C2211yescharacteristic
50C2×C13×C22⋊C8C2211yescharacteristic
51C2×C13×#97C2211yescharacteristic
52C2×C4×C8×C13C2211yescharacteristic
53C2×#88061C2211yescharacteristic
54C2×#88061C2211yescharacteristic
55C2×#88058C2211yescharacteristic
56C2×#88058C2211yescharacteristic
57C2×#88057C2211yescharacteristic
58C2×#88057C2211yescharacteristic
59C2×#88056C2211yescharacteristic
60C2×#88056C2211yescharacteristic
61C2×#88056C2211yescharacteristic
62C2×#88056C2211yescharacteristic
63C2×#88056C2211yescharacteristic
64C2×#88056C2211yescharacteristic
65#11718512C2218yescomplemented
66#11718511C2218yescomplemented
67#11718506C2218yescomplemented
68#11718506C2218yescomplemented
69#11718400C2218yescomplemented
70#11718399C2218yes—
71#11718398C2218yes—
72#11718384C2218yescomplemented
73#11718377C2218yescomplemented
74#11718371C2218yescomplemented
75C4×Dic52C2218yescomplemented
76C4×#6095C2218yescomplemented
77C23×C4×C13C2311yescharacteristic
78C22×C22⋊D13—21no—
79C23×Dic13—21no—
80C22×D52C2311yescharacteristic
81C22×C4×D13—21no—
82C22×Dic26—21no—
83C22×Dic26—22no—
84C22×Dic26—24no—
85C22×Dic26—24no—
86C22×Dic26—21no—
87C22×Dic26C2314yes—
88C22×Dic26C2311yescharacteristic
89C22×Dic26C2311yescharacteristic
90C22×Dic26C2311yescharacteristic
91C22×C8×C13C2311yescharacteristic
92C22×C8×C13C2311yescharacteristic
93C22×C8×C13C2311yescharacteristic
94C22×C8×C13C2311yescharacteristic
95C13×#117D414yes—
96C13×#117C2314yes—
97C2×C13×C4⋊C4D411yescharacteristic
98C2×C13×C4⋊C4D411yescharacteristic
99C2×C13×C22⋊C4D411yescharacteristic
100C2×C13×C22⋊C4D411yescharacteristic
101C2×C42×C13C2311yescharacteristic
102C2×C42×C13C2311yescharacteristic
103C2×C22⋊Dic13—21no—
104C2×C22⋊Dic13—21no—
105#88184—22no—
106#88184C2314yes—
107C2×#6103—21no—
108C2×#6103—21no—
109C2×#6103—21no—
110C2×#6103—21no—
111#88180—22no—
112#88180C2314yes—
113C2×C4⋊Dic13—21no—
114C2×C4⋊Dic13C2311yescharacteristic
115C2×C4⋊Dic13C2311yescharacteristic
116C2×C4⋊Dic13C2311yescharacteristic
117C2×C4⋊Dic13C2311yescharacteristic
118#88178—22no—
119#88178C2314yes—
120C2×#6101—21no—
121C2×#6101—21no—
122C2×#6101—21no—
123C2×#6101—21no—
124C2×#6101—21no—
125C2×#6101—21no—
126C2×C4×Dic13—21no—
127C2×C4×Dic13—21no—
128C2×C4×Dic13—21no—
129C2×C4×Dic13—21no—
130C2×C4×Dic13—21no—
131C2×C4×Dic13—21no—
132C2×Dic52—24no—
133C2×Dic52—24no—
134C2×Dic52C2314yes—
135C2×Dic52C2314yes—
136C2×#6095—24no—
137C2×#6095—24no—
138C2×#6095C2314yes—
139C2×#6095C2314yes—
140#88152—28no—
141#88150—28no—
142#88141—28no—
143#88141—28no—
144#88139—28no—
145#88137—28no—
146#88131—28no—
147#88131—28no—
148#88129—22no—
149#88129C2314yes—
150C4×D52—22no—
151C4×D52C2314yes—
152#88123—22no—
153#88123C2314yes—
154C4×Dic26—22no—
155C4×Dic26—22no—
156C4×Dic26—22no—
157C4×Dic26—22no—
158C4×Dic26—22no—
159C4×Dic26C2314yes—
160C4×Dic26C2314yes—
161C4×Dic26C2314yes—
162C4×Dic26C2314yes—
163C4×Dic26C2314yes—
164C13×C4⋊C8C2314yes—
165C13×C4⋊C8C2314yes—
166C13×C22⋊C8C2314yes—
167C13×C22⋊C8C2314yes—
168C13×#97C2314yes—
169C4×C8×C13C2314yes—
170#88061C2314yes—
171#88061C2314yes—
172#88058C2314yes—
173#88058C2314yes—
174#88057C2314yes—
175#88057C2314yes—
176#88056C2314yes—
177#88056C2314yes—
178#88056C2314yes—
179#88056C2314yes—
180#88056C2314yes—
181#88056C2314yes—
182C2×#3121—131nomaximal, Sylow
183C24×C13C2×D411yescharacteristic
184C23×D13—21no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D411yescharacteristic
192C22×C4×C13C2×D412yes—
193C22×C4×C13C2412yes—
194C22×C4×C13C2411yescharacteristic
195C2×C22⋊D13—24no—
196C2×C22⋊D13—82no—
197C22×Dic13—28no—
198C22×Dic13—24no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C2×D52—22no—
207C2×D52—22no—
208C2×D52—21no—
209C2×D52C2412yes—
210C2×C4×D13—24no—
211C2×C4×D13—82no—
212C2×Dic26—28no—
213C2×Dic26—216no—
214C2×Dic26—21no—
215C2×Dic26—21no—
216C2×Dic26—24no—
217C2×Dic26—22no—
218C2×Dic26—22no—
219C2×Dic26—28no—
220C2×Dic26—28no—
221C2×Dic26—22no—
222C2×Dic26—22no—
223C2×Dic26—21no—
224C2×Dic26—24no—
225C2×Dic26—82no—
226C2×Dic26#4114yes—
227C2×Dic26#4114yes—
228C2×Dic26C2412yes—
229C2×Dic26C2412yes—
230C2×Dic26C2412yes—
231C2×C8×C13—22no—
232C2×C8×C13—22no—
233C2×C8×C13—22no—
234C2×C8×C13—22no—
235C2×C8×C13C2412yes—
236C2×C8×C13C2412yes—
237C2×C8×C13C2412yes—
238C2×C8×C13C2412yes—
239C13×C4⋊C4C2×D414yes—
240C13×C4⋊C4C2×D414yes—
241C13×C22⋊C4C2×D414yes—
242C13×C22⋊C4C2×D414yes—
243C42×C13C2×D412yes—
244C42×C13C2×D412yes—
245C42×C13C2412yes—
246C42×C13C2412yes—
247C22⋊Dic13—24no—
248C22⋊Dic13—24no—
249#6103—24no—
250#6103—24no—
251#6103—24no—
252#6103—24no—
253C4⋊Dic13—21no—
254C4⋊Dic13—21no—
255C4⋊Dic13—21no—
256C4⋊Dic13—21no—
257C4⋊Dic13—24no—
258C4⋊Dic13C2412yes—
259C4⋊Dic13C2412yes—
260C4⋊Dic13C2412yes—
261C4⋊Dic13C2412yes—
262#6101—24no—
263#6101—24no—
264#6101—24no—
265#6101—24no—
266#6101—24no—
267#6101—24no—
268C4×Dic13—24no—
269C4×Dic13—24no—
270C4×Dic13—24no—
271C4×Dic13—24no—
272C4×Dic13—24no—
273C4×Dic13—24no—
274Dic52—28no—
275Dic52—28no—
276#6095—28no—
277#6095—28no—
278C2×#542—131no—
279C2×#519—131no—
280#3121—1316no—
281C2×#485—131no—
282C2×#482—131no—
283C2×#477—131no—
284C2×#475—131no—
285C2×#464—131no—
286C2×#464—131no—
287C2×#451—131no—
288C2×#448—131no—
289C2×#441—131no—
290C2×#440—131no—
291C2×C4×Q16—131no—
292C2×C4×SD16—131no—
293C2×#433D1311yescharacteristic, complemented
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13C22×D412yes—
298C23×C13C22×D411yescharacteristic
299C22×D13—22no—
300C22×D13—42no—
301C22×D13—42no—
302C22×D13—42no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—24no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13C22×D412yes—
312C2×C4×C13C22×D412yes—
313C2×C4×C13C22×D412yes—
314C2×C4×C13C22×D412yes—
315C2×C4×C13C22×D412yes—
316C2×C4×C13C22×D411yescharacteristic
317C2×C4×C13C2×#4112yes—
318C2×C4×C13C2×#4112yes—
319C2×C4×C13C2511yescharacteristic
320C22⋊D13—84no—
321C2×Dic13—216no—
322C2×Dic13—24no—
323C2×Dic13—24no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—42no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336D52—22no—
337D52—22no—
338D52—42no—
339C4×D13—84no—
340Dic26—216no—
341Dic26—24no—
342Dic26—24no—
343Dic26—22no—
344Dic26—22no—
345Dic26—22no—
346Dic26—22no—
347Dic26—42no—
348Dic26—84no—
349Dic26C2×#4114yes—
350Dic26C2×#4114yes—
351C8×C13—22no—
352C8×C13—22no—
353C8×C13—22no—
354C8×C13—22no—
355C23×Q8—131no—
356C22×Q16—131no—
357C22×Q16—131no—
358C22×SD16—131no—
359C22×SD16—131no—
360#542—138no—
361#542—264no—
362C2×C4⋊Q8—131no—
363C2×#126—261no—
364C2×#124—131no—
365C2×#124—261no—
366C2×#123—261no—
367C2×C22⋊Q8—131no—
368C2×C22⋊Q8—261no—
369C2×#121—131no—
370#519—138no—
371#519—264no—
372C2×C4×Q8—131no—
373C2×C4×Q8—131no—
374C2×C4×Q8—131no—
375C2×C4×Q8—131no—
376C2×C4×Q8—131no—
377C2×C4×Q8—261no—
378C2×C4×Q8—261no—
379C2×C4×D4—131no—
380C2×#117—131no—
381C2×#117—261no—
382C2×#117—261no—
383C2×#117C2×D1311yescharacteristic
384#485—138no—
385#482—138no—
386#477—138no—
387#475—138no—
388#464—138no—
389#464—138no—
390#451—138no—
391#448—138no—
392#441—138no—
393#440—138no—
394C4×Q16—138no—
395C4×SD16—138no—
396#433C2×D1318yescomplemented
397C2×#107—131no—
398C2×#107—131no—
399C2×#106—131no—
400C2×#106—131no—
401C2×C4⋊C8C2×D1311yescharacteristic
402C2×C4⋊C8C2×D1311yescharacteristic
403C2×#103—131no—
404C2×#103—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#103—131no—
408C2×#103—131no—
409C2×#102—131no—
410C2×#102—131no—
411C2×C22⋊C8C2×D1311yescharacteristic
412C2×C22⋊C8C2×D1311yescharacteristic
413C2×#97C2×D1311yescharacteristic
414C2×C4×C8C2×D1311yescharacteristic
415C22×C13—22no—
416C22×C13—22no—
417C22×C13—22no—
418C22×C13—44no—
419C22×C13#52512yes—
420C22×C13#57712yes—
421C22×C13#57812yes—
422C22×C13C23×D411yescharacteristic
423C2×D13—42no—
424C2×D13—42no—
425C2×D13—42no—
426C2×D13—84no—
427C4×C13—22no—
428C4×C13—22no—
429C4×C13—22no—
430C4×C13—22no—
431C4×C13—22no—
432C4×C13#52512yes—
433C4×C13C22×#4111yescharacteristic
434C4×C13C22×#4111yescharacteristic
435Dic13—24no—
436Dic13—24no—
437Dic13—42no—
438Dic13—42no—
439Dic13—42no—
440Dic13—42no—
441Dic13—42no—
442C22×Q8—131no—
443C22×Q8—131no—
444C22×Q8—131no—
445C22×Q8—134no—
446C22×Q8—264no—
447C22×Q8—264no—
448C22×Q8—261no—
449C22×Q8—262no—
450C22×Q8—261no—
451C22×D4—131no—
452C22×D4—261no—
453C23×C4—261no—
454C23×C4—261no—
455C23×C4C22×D1311yescharacteristic
456C2×Q16—134no—
457C2×Q16—134no—
458C2×Q16—264no—
459C2×Q16—264no—
460C2×SD16—134no—
461C2×SD16—134no—
462C2×SD16—264no—
463C2×SD16—264no—
464C22×C8C22×D1311yescharacteristic
465C22×C8C22×D1311yescharacteristic
466C22×C8C22×D1311yescharacteristic
467C22×C8C22×D1311yescharacteristic
468C4⋊Q8—134no—
469C4⋊Q8—262no—
470#126—268no—
471#124—134no—
472#124—268no—
473#124—262no—
474#123—268no—
475C22⋊Q8—134no—
476C22⋊Q8—262no—
477C22⋊Q8—268no—
478#121—134no—
479#121—262no—
480C4×Q8—134no—
481C4×Q8—134no—
482C4×Q8—134no—
483C4×Q8—134no—
484C4×Q8—134no—
485C4×Q8—268no—
486C4×Q8—268no—
487C4×Q8—262no—
488C4×Q8—262no—
489C4×Q8—262no—
490C4×Q8—262no—
491C4×Q8—262no—
492C4×D4—134no—
493C4×D4—262no—
494#117—134no—
495#117—262no—
496#117—268no—
497#117—268no—
498#117D5214yes—
499#117C22×D1314yes—
500C2×C4⋊C4—131no—
501C2×C4⋊C4—131no—
502C2×C4⋊C4—131no—
503C2×C4⋊C4—131no—
504C2×C4⋊C4—261no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4—261no—
509C2×C4⋊C4—261no—
510C2×C4⋊C4—261no—
511C2×C4⋊C4D5211yescharacteristic
512C2×C4⋊C4D5211yescharacteristic
513C2×C22⋊C4—261no—
514C2×C22⋊C4—261no—
515C2×C22⋊C4—261no—
516C2×C22⋊C4—261no—
517C2×C22⋊C4—261no—
518C2×C22⋊C4—261no—
519C2×C22⋊C4D5211yescharacteristic
520C2×C22⋊C4D5211yescharacteristic
521C2×C42—261no—
522C2×C42—261no—
523C2×C42—261no—
524C2×C42—261no—
525C2×C42—261no—
526C2×C42—261no—
527C2×C42C22×D1311yescharacteristic
528C2×C42C22×D1311yescharacteristic
529#107—134no—
530#107—134no—
531#106—134no—
532#106—134no—
533C4⋊C8C22×D1314yes—
534C4⋊C8C22×D1314yes—
535#103—134no—
536#103—134no—
537#103—134no—
538#103—134no—
539#103—134no—
540#103—134no—
541#102—134no—
542#102—134no—
543C22⋊C8C22×D1314yes—
544C22⋊C8C22×D1314yes—
545#97C22×D1314yes—
546C4×C8C22×D1314yes—
547C2×C13—42no—
548C2×C13#312114yescomplemented
549C2×C13C2×#52511yescharacteristic
550C2×C13C2×#57711yescharacteristic
551C2×C13C2×#57811yescharacteristic
552D13—82no—
553C24—261no—
554C24C2×D5211yescharacteristic
555C2×Q8—134no—
556C2×Q8—134no—
557C2×Q8—132no—
558C2×Q8—132no—
559C2×Q8—132no—
560C2×Q8—268no—
561C2×Q8—268no—
562C2×Q8—268no—
563C2×Q8—2616no—
564C2×Q8—264no—
565C2×Q8—261no—
566C2×Q8—261no—
567C2×Q8—261no—
568C2×Q8—264no—
569C2×Q8—262no—
570C2×Q8—262no—
571C2×Q8—262no—
572C2×Q8—262no—
573C2×Q8—1042no—
574C2×D4—132no—
575C2×D4—264no—
576C2×D4—261no—
577C2×D4—262no—
578C2×D4—262no—
579C2×D4—1042no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—268no—
583C22×C4—264no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—264no—
592C22×C4—1042no—
593C22×C4C2×D5212yes—
594C22×C4C2×D5211yescharacteristic
595C22×C4C2×D5211yescharacteristic
596C22×C4C2×D5211yescharacteristic
597C22×C4C2×D5211yescharacteristic
598C22×C4C2×D5211yescharacteristic
599C22×C4C23×D1312yes—
600C22×C4C23×D1311yescharacteristic
601Q16—268no—
602Q16—268no—
603SD16—268no—
604SD16—268no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8C23×D1312yes—
610C2×C8C23×D1312yes—
611C2×C8C23×D1312yes—
612C2×C8C23×D1312yes—
613C4⋊C4—132no—
614C4⋊C4—132no—
615C4⋊C4—132no—
616C4⋊C4—132no—
617C4⋊C4—261no—
618C4⋊C4—261no—
619C4⋊C4—261no—
620C4⋊C4—261no—
621C4⋊C4—264no—
622C4⋊C4—264no—
623C4⋊C4—264no—
624C4⋊C4—264no—
625C4⋊C4—264no—
626C4⋊C4—264no—
627C4⋊C4—264no—
628C4⋊C4C2×D5214yes—
629C4⋊C4C2×D5214yes—
630C22⋊C4—264no—
631C22⋊C4—264no—
632C22⋊C4—264no—
633C22⋊C4—264no—
634C22⋊C4—264no—
635C22⋊C4—264no—
636C22⋊C4C2×D5214yes—
637C22⋊C4C2×D5214yes—
638C42—264no—
639C42—264no—
640C42—264no—
641C42—264no—
642C42—264no—
643C42—264no—
644C42C2×D5212yes—
645C42C2×D5212yes—
646C42C23×D1312yes—
647C42C23×D1312yes—
648C13C2×#312111yescharacteristic, complemented, Sylow
649C23—22no—
650C23—22no—
651C23—22no—
652C23—262no—
653C23—522no—
654C23—522no—
655C23—522no—
656C23C22×D5212yes—
657C23C22×D5211yescharacteristic
658Q8—134no—
659Q8—134no—
660Q8—2616no—
661Q8—264no—
662Q8—264no—
663Q8—262no—
664Q8—262no—
665Q8—262no—
666Q8—262no—
667Q8—522no—
668Q8—1044no—
669D4—262no—
670D4—262no—
671D4—522no—
672D4—1044no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—2616no—
682C2×C4—264no—
683C2×C4—264no—
684C2×C4—262no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—522no—
692C2×C4—522no—
693C2×C4—522no—
694C2×C4—522no—
695C2×C4—522no—
696C2×C4—1044no—
697C2×C4C22×D5212yes—
698C2×C4C22×D5212yes—
699C2×C4C22×D5212yes—
700C2×C4C22×D5212yes—
701C2×C4C22×D5212yes—
702C2×C4C22×D5211yescharacteristic
703C2×C4#41×D1312yes—
704C2×C4#41×D1312yes—
705C2×C4C24×D1311yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—522no—
715C22—522no—
716C22—522no—
717C22—1044no—
718C22#1171922912yes—
719C22#1171945612yes—
720C22#1171945812yes—
721C22C23×D5211yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—264no—
728C4—264no—
729C4—522no—
730C4—522no—
731C4—522no—
732C4—522no—
733C4—522no—
734C4#1171922912yes—
735C4C2×#41×D1311yescharacteristic
736C4C2×#41×D1311yescharacteristic
737C2—42no—
738C2—1042no—
739C2#1312506714yesdirect product factor
740C2C2×#1171922911yescharacteristic
741C2C2×#1171945611yescharacteristic
742C2C2×#1171945811yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#433C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenterC2×#433D13
hypocenterC13C2×#3121
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. C2×#11719221C2semidirect
3. #13125067C2direct (N × H)
4. C2×#11718384C2semidirect
6. C2×#11718511C2semidirect
7. C2×#11718512C2semidirect
8. C2×#11718506C2semidirect
9. C2×#11718506C2semidirect
10. C2×#11718400C2semidirect
12. C2×#11718377C2semidirect
13. C2×#11718371C2semidirect
14. C2×C4×Dic52C2semidirect
15. C2×C4×#6095C2semidirect
16. C2×C13×#433C2semidirect
29. #11719221C22semidirect
46. C13×#433C22semidirect
65. #11718512C22semidirect
66. #11718511C22semidirect
67. #11718506C22semidirect
68. #11718506C22semidirect
69. #11718400C22semidirect
72. #11718384C22semidirect
73. #11718377C22semidirect
74. #11718371C22semidirect
75. C4×Dic52C22semidirect
76. C4×#6095C22semidirect
293. C2×#433D13semidirect
396. #433C2×D13semidirect
548. C2×C13#3121semidirect
648. C13C2×#3121semidirect
739. C2#13125067direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192392
C2×#117192212
#131250672
C2×#117183842
C2×#117183982
C2×#117185112
C2×#117185122
C2×#117185062
C2×#117184002
C2×#117183992
C2×#117183772
C2×#117183712
C2×C4×Dic522
C2×C4×#60952
C2×C13×#4332
C2×#312113