Finite Group Databasebeta

← C2×#13127589 #16742668

Subgroups — C2×#13127589 #16742668

Order 3328.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719290C211yesmaximal, characteristic, complemented
2#13127589C2116yesmaximal, direct product factor
3C2×#11718728C211yesmaximal, characteristic, complemented
4C2×#11718750C211yesmaximal, characteristic, complemented
5C2×#11718729C211yesmaximal, characteristic, complemented
6C2×#11718724C211yesmaximal, characteristic, complemented
7C2×#11718727C211yesmaximal, characteristic, complemented
8C2×#11718748C211yesmaximal, characteristic, complemented
9C2×#11718677C211yesmaximal, characteristic, complemented
10C2×#11718677C211yesmaximal, characteristic, complemented
11C2×#11718676C211yesmaximal, characteristic
12C2×#11718685C211yesmaximal, characteristic, complemented
13C2×#11718675C211yesmaximal, characteristic, complemented
14C2×#11718679C211yesmaximal, characteristic, complemented
15C2×C4×#6104C211yesmaximal, characteristic, complemented
16C2×C13×#554C211yesmaximal, characteristic, complemented
17C13×#554—24no—
18C13×#554C2218yescomplemented
19C2×C13×C4⋊Q8C2211yescharacteristic
20C2×C13×#125C2211yescharacteristic
21C2×C13×#125C2211yescharacteristic
22C2×C13×C22⋊Q8—21no—
23C2×C13×C22⋊Q8—21no—
24C2×C13×C22⋊Q8—21no—
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×D4×C13C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C2×C4×D4×C13C2211yescharacteristic
29C22×C13×C4⋊C4—21no—
30C2×#88201—21no—
31C22×#6105C2211yescharacteristic
32C22×#6104C2211yescharacteristic
33C22×#6104C2211yescharacteristic
34#11719290—24no—
35#11719290C2218yescomplemented
36C2×#88148—21no—
37C2×#88148—21no—
38C2×#88147—21no—
39C2×#88129C2211yescharacteristic
40C2×#88129C2211yescharacteristic
41C2×#88128C2211yescharacteristic
42C2×C4×D52C2211yescharacteristic
43C2×C4×D52C2211yescharacteristic
44C2×C4×Dic26C2211yescharacteristic
45C2×#88072C2211yescharacteristic
46#11718750C2218yescomplemented
47#11718748C2218yescomplemented
48#11718729C2218yescomplemented
49#11718728C2218yescomplemented
50#11718727C2218yescomplemented
51#11718724C2218yescomplemented
52#11718685C2218yescomplemented
53#11718679C2218yescomplemented
54#11718677C2218yescomplemented
55#11718677C2218yescomplemented
56#11718676C2218yes—
57#11718675C2218yescomplemented
58C4×#6104C2218yescomplemented
59C2×#88050C2211yescharacteristic
60C2×#88050C2211yescharacteristic
61C2×#88050C2211yescharacteristic
62C2×#88049C2211yescharacteristic
63C2×#88049C2211yescharacteristic
64C2×#88049C2211yescharacteristic
65C2×#88049C2211yescharacteristic
66C2×#88049C2211yescharacteristic
67C2×#88049C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69C2×#88047C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71C2×C4⋊#1055C2211yescharacteristic
72C2×C4⋊#1055C2211yescharacteristic
73C2×C4⋊#1055C2211yescharacteristic
74C2×#88043C2211yescharacteristic
75C2×#88043C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C22×Q8×C13—21no—
78C22×Q8×C13D411yescharacteristic
79C22×D4×C13C2311yescharacteristic
80C23×C4×C13—21no—
81C23×C4×C13—21no—
82C23×C4×C13—21no—
83C22×D52—21no—
84C22×D52—21no—
85C22×D52C2311yescharacteristic
86C22×D52C2311yescharacteristic
87C22×C4×D13—21no—
88C22×C4×D13—21no—
89C22×Dic26C2311yescharacteristic
90C13×C4⋊Q8—22no—
91C13×C4⋊Q8C2314yes—
92C13×#125—22no—
93C13×#125—22no—
94C13×#125C2314yes—
95C13×#125C2314yes—
96C13×C22⋊Q8—28no—
97C13×C22⋊Q8—28no—
98C13×C22⋊Q8—28no—
99C4×Q8×C13D414yes—
100C4×Q8×C13C2314yes—
101C4×D4×C13—22no—
102C4×D4×C13—22no—
103C4×D4×C13—22no—
104C4×D4×C13C2314yes—
105C4×D4×C13C2314yes—
106C4×D4×C13C2314yes—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—21no—
112C2×C13×C4⋊C4—28no—
113C2×C13×C4⋊C4D411yescharacteristic
114C2×C13×C4⋊C4D411yescharacteristic
115C2×C13×C4⋊C4D411yescharacteristic
116C2×C13×C4⋊C4C2311yescharacteristic
117C2×C13×C4⋊C4C2311yescharacteristic
118C2×C13×C4⋊C4C2311yescharacteristic
119C2×C13×C22⋊C4—21no—
120C2×C13×C22⋊C4—21no—
121C2×C13×C22⋊C4—21no—
122C2×C42×C13C2311yescharacteristic
123C2×C42×C13C2311yescharacteristic
124C2×C42×C13C2311yescharacteristic
125#88201—28no—
126C2×#6105—24no—
127C2×#6105C2314yes—
128C2×#6104—24no—
129C2×#6104—24no—
130C2×#6104C2314yes—
131C2×#6104C2314yes—
132C2×#6103—21no—
133C2×#6103—21no—
134C2×#6103—21no—
135C2×#6103—21no—
136C2×#6103—21no—
137C2×#6103—21no—
138C2×C4⋊Dic13C2311yescharacteristic
139C2×#6101—21no—
140C2×C4×Dic13—21no—
141C22×#1055C2311yescharacteristic
142C22×#1055C2311yescharacteristic
143C22×#1055C2311yescharacteristic
144C22×#1055C2311yescharacteristic
145#88148—28no—
146#88148—28no—
147#88147—28no—
148#88129—22no—
149#88129—22no—
150#88129C2314yes—
151#88129C2314yes—
152#88128—22no—
153#88128C2314yes—
154C4×D52—22no—
155C4×D52—22no—
156C4×D52C2314yes—
157C4×D52C2314yes—
158C4×Dic26—22no—
159C4×Dic26C2314yes—
160#88072C2314yes—
161#88050C2314yes—
162#88050C2314yes—
163#88050C2314yes—
164#88049C2314yes—
165#88049C2314yes—
166#88049C2314yes—
167#88049C2314yes—
168#88049C2314yes—
169#88049C2314yes—
170#88048C2314yes—
171#88047C2314yes—
172#88047C2314yes—
173C4⋊#1055C2314yes—
174C4⋊#1055C2314yes—
175C4⋊#1055C2314yes—
176#88043C2314yes—
177#88043C2314yes—
178C4×#1055C2314yes—
179C2×#3370—131nomaximal, Sylow
180C24×C13—21no—
181C23×D13—21no—
182C23×D13—21no—
183C2×Q8×C13—24no—
184C2×Q8×C13—42no—
185C2×Q8×C13—82no—
186C2×Q8×C13C2×D414yes—
187C2×D4×C13—21no—
188C2×D4×C13—22no—
189C2×D4×C13#4114yes—
190C2×D4×C13C2412yes—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—24no—
195C22×C4×C13—24no—
196C22×C4×C13—24no—
197C22×C4×C13—44no—
198C22×C4×C13—82no—
199C22×C4×C13—82no—
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D411yescharacteristic
202C22×C4×C13C2×D411yescharacteristic
203C22×C4×C13C2×D411yescharacteristic
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2411yescharacteristic
207C22×Dic13—21no—
208C22×Dic13—21no—
209C2×D52—22no—
210C2×D52—22no—
211C2×D52—22no—
212C2×D52—22no—
213C2×D52—21no—
214C2×D52—21no—
215C2×D52—24no—
216C2×D52—24no—
217C2×D52—44no—
218C2×D52—82no—
219C2×D52C2412yes—
220C2×D52C2412yes—
221C2×C4×D13—24no—
222C2×C4×D13—24no—
223C2×C4×D13—82no—
224C2×C4×D13—82no—
225C2×Dic26—22no—
226C2×Dic26—22no—
227C2×Dic26—21no—
228C2×Dic26C2412yes—
229C13×C4⋊C4—24no—
230C13×C4⋊C4—24no—
231C13×C4⋊C4—24no—
232C13×C4⋊C4—24no—
233C13×C4⋊C4—24no—
234C13×C4⋊C4—21no—
235C13×C4⋊C4—21no—
236C13×C4⋊C4—21no—
237C13×C4⋊C4C2×D414yes—
238C13×C4⋊C4C2×D414yes—
239C13×C4⋊C4C2×D414yes—
240C13×C4⋊C4C2412yes—
241C13×C4⋊C4C2412yes—
242C13×C4⋊C4C2412yes—
243C13×C22⋊C4—24no—
244C13×C22⋊C4—24no—
245C13×C22⋊C4—24no—
246C42×C13C2×D412yes—
247C42×C13C2×D412yes—
248C42×C13C2×D412yes—
249C42×C13C2412yes—
250C42×C13C2412yes—
251C42×C13C2412yes—
252#6105—28no—
253#6104—28no—
254#6104—28no—
255#6103—24no—
256#6103—24no—
257#6103—24no—
258#6103—24no—
259#6103—24no—
260#6103—24no—
261C4⋊Dic13—21no—
262C4⋊Dic13C2412yes—
263#6101—24no—
264C4×Dic13—24no—
265C2×#1055—22no—
266C2×#1055—22no—
267C2×#1055—22no—
268C2×#1055—22no—
269C2×#1055C2412yes—
270C2×#1055C2412yes—
271C2×#1055C2412yes—
272C2×#1055C2412yes—
273C2×#559—131no—
274C2×#554D1311yescharacteristic, complemented
275#3370—1316no—
276C2×#490—131no—
277C2×#489—131no—
278C2×#488—131no—
279C2×#479—131no—
280C2×#478—131no—
281C2×#474—131no—
282C2×#463—131no—
283C2×#463—131no—
284C2×#459—131no—
285C2×#446—131no—
286C2×#442—131no—
287C2×#440—131no—
288C2×C4×D8—131no—
289C23×C13—24no—
290C23×C13—22no—
291C23×C13—42no—
292C23×C13—42no—
293C23×C13C22×D411yescharacteristic
294C22×D13—22no—
295C22×D13—22no—
296C22×D13—42no—
297C22×D13—42no—
298C22×D13—42no—
299C22×D13—42no—
300C22×D13—42no—
301C22×D13—42no—
302Q8×C13—44no—
303Q8×C13—84no—
304D4×C13—24no—
305D4×C13—22no—
306D4×C13C2×#4114yes—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
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—48no—
317C2×C4×C13—42no—
318C2×C4×C13—42no—
319C2×C4×C13—42no—
320C2×C4×C13—84no—
321C2×C4×C13—84no—
322C2×C4×C13C22×D412yes—
323C2×C4×C13C22×D412yes—
324C2×C4×C13C22×D412yes—
325C2×C4×C13C22×D412yes—
326C2×C4×C13C22×D412yes—
327C2×C4×C13C22×D412yes—
328C2×C4×C13C22×D411yescharacteristic
329C2×C4×C13C2×#4112yes—
330C2×C4×C132−1+412yes—
331C2×C4×C13C2511yescharacteristic
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336D52—22no—
337D52—22no—
338D52—22no—
339D52—22no—
340D52—48no—
341D52—42no—
342D52—42no—
343D52—84no—
344C4×D13—84no—
345C4×D13—84no—
346Dic26—22no—
347Dic26—22no—
348Dic26—42no—
349#1055—22no—
350#1055—22no—
351#1055—22no—
352#1055—22no—
353C22×SD16—131no—
354C22×D8—131no—
355C22×D8—131no—
356#559—138no—
357#559—264no—
358#554—24no—
359#554C2×D1318yescomplemented
360C2×C4⋊Q8C2×D1311yescharacteristic
361C2×#127—131no—
362C2×#125C2×D1311yescharacteristic
363C2×#125C2×D1311yescharacteristic
364C2×#124—131no—
365C2×#124—131no—
366C2×#124—261no—
367C2×#123—261no—
368C2×#123—261no—
369C2×C22⋊Q8—21no—
370C2×C22⋊Q8—21no—
371C2×C22⋊Q8—21no—
372C2×C4×Q8—131no—
373C2×C4×Q8C2×D1311yescharacteristic
374C2×C4×D4—131no—
375C2×C4×D4—131no—
376C2×C4×D4—261no—
377C2×C4×D4C2×D1311yescharacteristic
378C2×C4×D4C2×D1311yescharacteristic
379C2×C4×D4C2×D1311yescharacteristic
380C22×C4⋊C4—21no—
381#490—138no—
382#489—138no—
383#488—138no—
384#479—138no—
385#478—138no—
386#474—138no—
387#463—138no—
388#463—138no—
389#459—138no—
390#446—138no—
391#442—138no—
392#440—138no—
393C4×D8—138no—
394C2×#107—131no—
395C2×#107—131no—
396C2×#106—131no—
397C2×C4⋊C8—131no—
398C2×C4⋊C8—131no—
399C2×C4⋊C8—131no—
400C2×#103—131no—
401C2×#103—131no—
402C2×#103—131no—
403C2×#102—131no—
404C2×#102—131no—
405C2×#102—131no—
406C2×#102—131no—
407C2×#102—131no—
408C2×#102—131no—
409C2×#102—131no—
410C2×#97—131no—
411C2×#97—131no—
412C2×C4×C8—131no—
413C22×C13—24no—
414C22×C13—48no—
415C22×C13—42no—
416C22×C13—42no—
417C22×C13#54812yes—
418C22×C13#57512yes—
419C22×C13#57612yes—
420C22×C13C23×D411yescharacteristic
421C2×D13—42no—
422C2×D13—42no—
423C2×D13—42no—
424C2×D13—42no—
425C2×D13—42no—
426C2×D13—42no—
427C2×D13—84no—
428C2×D13—84no—
429C4×C13—22no—
430C4×C13—22no—
431C4×C13—22no—
432C4×C13—22no—
433C4×C13—22no—
434C4×C13—22no—
435C4×C13—42no—
436C4×C13—42no—
437C4×C13—42no—
438C4×C13#54812yes—
439C4×C13C22×#4111yescharacteristic
440C4×C13C2×2−1+411yescharacteristic
441Dic13—42no—
442Dic13—42no—
443C22×Q8—21no—
444C22×Q8—131no—
445C22×Q8C22⋊D1311yescharacteristic
446C22×D4—131no—
447C22×D4—131no—
448C22×D4—261no—
449C22×D4—261no—
450C22×D4C22×D1311yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4—21no—
454C23×C4—261no—
455C23×C4—261no—
456C2×SD16—134no—
457C2×SD16—264no—
458C2×D8—134no—
459C2×D8—134no—
460C2×D8—264no—
461C2×D8—264no—
462C22×C8—131no—
463C22×C8—131no—
464C22×C8—131no—
465C22×C8—131no—
466C4⋊Q8—22no—
467C4⋊Q8C22×D1314yes—
468#127—134no—
469#127—262no—
470#125—22no—
471#125—22no—
472#125C22×D1314yes—
473#125C22×D1314yes—
474#124—134no—
475#124—134no—
476#124—268no—
477#124—262no—
478#124—262no—
479#123—268no—
480#123—268no—
481C22⋊Q8—28no—
482C22⋊Q8—28no—
483C22⋊Q8—28no—
484C4×Q8—134no—
485C4×Q8—262no—
486C4×Q8C22⋊D1314yes—
487C4×Q8C22×D1314yes—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—134no—
492C4×D4—134no—
493C4×D4—268no—
494C4×D4—262no—
495C4×D4—262no—
496C4×D4C22×D1314yes—
497C4×D4C22×D1314yes—
498C4×D4C22×D1314yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—28no—
505C2×C4⋊C4—131no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4C22⋊D1311yescharacteristic
508C2×C4⋊C4C22⋊D1311yescharacteristic
509C2×C4⋊C4C22⋊D1311yescharacteristic
510C2×C4⋊C4C22×D1311yescharacteristic
511C2×C4⋊C4C22×D1311yescharacteristic
512C2×C4⋊C4C22×D1311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—261no—
517C2×C22⋊C4—261no—
518C2×C22⋊C4—261no—
519C2×C22⋊C4—261no—
520C2×C22⋊C4—261no—
521C2×C22⋊C4—261no—
522C2×C42—261no—
523C2×C42C22×D1311yescharacteristic
524C2×C42C22×D1311yescharacteristic
525C2×C42C22×D1311yescharacteristic
526#107—134no—
527#107—134no—
528#106—134no—
529C4⋊C8—134no—
530C4⋊C8—134no—
531C4⋊C8—134no—
532#103—134no—
533#103—134no—
534#103—134no—
535#102—134no—
536#102—134no—
537#102—134no—
538#102—134no—
539#102—134no—
540#102—134no—
541#102—134no—
542#97—134no—
543#97—134no—
544C4×C8—134no—
545C2×C13—44no—
546C2×C13#337014yescomplemented
547C2×C13C2×#54811yescharacteristic
548C2×C13C2×#57511yescharacteristic
549C2×C13C2×#57611yescharacteristic
550D13—82no—
551D13—82no—
552C24—21no—
553C24—261no—
554C24—261no—
555C2×Q8—24no—
556C2×Q8—42no—
557C2×Q8—82no—
558C2×Q8—132no—
559C2×Q8—261no—
560C2×Q8—262no—
561C2×Q8—262no—
562C2×Q8C2×C22⋊D1314yes—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—132no—
566C2×D4—132no—
567C2×D4—262no—
568C2×D4—262no—
569C2×D4—262no—
570C2×D4—262no—
571C2×D4—264no—
572C2×D4—261no—
573C2×D4—261no—
574C2×D4—264no—
575C2×D4—524no—
576C2×D4—1042no—
577C2×D4#613114yes—
578C2×D4C23×D1312yes—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—44no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—264no—
591C22×C4—264no—
592C22×C4—1042no—
593C22×C4—1042no—
594C22×C4C2×C22⋊D1311yescharacteristic
595C22×C4C2×C22⋊D1311yescharacteristic
596C22×C4C2×C22⋊D1311yescharacteristic
597C22×C4C2×C22⋊D1311yescharacteristic
598C22×C4C2×C22⋊D1311yescharacteristic
599C22×C4C2×C22⋊D1311yescharacteristic
600C22×C4C23×D1311yescharacteristic
601SD16—268no—
602D8—268no—
603D8—268no—
604C2×C8—132no—
605C2×C8—132no—
606C2×C8—132no—
607C2×C8—132no—
608C2×C8—262no—
609C2×C8—262no—
610C2×C8—262no—
611C2×C8—262no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—132no—
621C4⋊C4—261no—
622C4⋊C4—264no—
623C4⋊C4C2×C22⋊D1314yes—
624C4⋊C4C2×C22⋊D1314yes—
625C4⋊C4C2×C22⋊D1314yes—
626C4⋊C4C23×D1312yes—
627C4⋊C4C23×D1312yes—
628C4⋊C4C23×D1312yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—264no—
633C22⋊C4—264no—
634C22⋊C4—264no—
635C22⋊C4—264no—
636C22⋊C4—264no—
637C22⋊C4—264no—
638C42—264no—
639C42C2×C22⋊D1312yes—
640C42C2×C22⋊D1312yes—
641C42C2×C22⋊D1312yes—
642C42C23×D1312yes—
643C42C23×D1312yes—
644C42C23×D1312yes—
645C13C2×#337011yescharacteristic, complemented, Sylow
646C23—24no—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—262no—
651C23—262no—
652C23—522no—
653C23—522no—
654C23—522no—
655C23—522no—
656C23—522no—
657C23—522no—
658C23C22×C22⋊D1311yescharacteristic
659Q8—44no—
660Q8—84no—
661Q8—262no—
662Q8—262no—
663Q8—522no—
664D4—24no—
665D4—22no—
666D4—262no—
667D4—262no—
668D4—262no—
669D4—262no—
670D4—528no—
671D4—522no—
672D4—522no—
673D4—1044no—
674D4C2×#613114yes—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—84no—
689C2×C4—84no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—522no—
693C2×C4—522no—
694C2×C4—1044no—
695C2×C4—1044no—
696C2×C4C2×#613112yes—
697C2×C4#8825412yes—
698C2×C4C22×C22⋊D1312yes—
699C2×C4C22×C22⋊D1312yes—
700C2×C4C22×C22⋊D1312yes—
701C2×C4C22×C22⋊D1312yes—
702C2×C4C22×C22⋊D1312yes—
703C2×C4C22×C22⋊D1312yes—
704C2×C4C22×C22⋊D1311yescharacteristic
705C2×C4C24×D1311yescharacteristic
706C8—262no—
707C8—262no—
708C8—262no—
709C8—262no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—522no—
715C22—522no—
716C22—522no—
717C22—522no—
718C22—522no—
719C22—522no—
720C22—1044no—
721C22—1044no—
722C22#1171952212yes—
723C22#1171952712yes—
724C22#1171954012yes—
725C22C23×C22⋊D1311yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—522no—
736C4—522no—
737C4#1171952212yes—
738C4C22×#613111yescharacteristic
739C4C2×#8825411yescharacteristic
740C2—44no—
741C2—1042no—
742C2—1042no—
743C2#1312758914yesdirect product factor
744C2C2×#1171952211yescharacteristic
745C2C2×#1171952711yescharacteristic
746C2C2×#1171954011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#554C2
socleC23×C13C22×D4
prime radicalC2×#11718676C2
hypercenterC2×#554D13
hypocenterC13C2×#3370
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#11719290C2semidirect
2. #13127589C2direct (N × H)
3. C2×#11718728C2semidirect
4. C2×#11718750C2semidirect
5. C2×#11718729C2semidirect
6. C2×#11718724C2semidirect
7. C2×#11718727C2semidirect
8. C2×#11718748C2semidirect
9. C2×#11718677C2semidirect
10. C2×#11718677C2semidirect
12. C2×#11718685C2semidirect
13. C2×#11718675C2semidirect
14. C2×#11718679C2semidirect
15. C2×C4×#6104C2semidirect
16. C2×C13×#554C2semidirect
18. C13×#554C22semidirect
35. #11719290C22semidirect
46. #11718750C22semidirect
47. #11718748C22semidirect
48. #11718729C22semidirect
49. #11718728C22semidirect
50. #11718727C22semidirect
51. #11718724C22semidirect
52. #11718685C22semidirect
53. #11718679C22semidirect
54. #11718677C22semidirect
55. #11718677C22semidirect
57. #11718675C22semidirect
58. C4×#6104C22semidirect
274. C2×#554D13semidirect
359. #554C2×D13semidirect
546. C2×C13#3370semidirect
645. C13C2×#3370semidirect
743. C2#13127589direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192902
#131275892
C2×#117187282
C2×#117187502
C2×#117187292
C2×#117187242
C2×#117187272
C2×#117187482
C2×#117186772
C2×#117186762
C2×#117186852
C2×#117186752
C2×#117186792
C2×C4×#61042
C2×C13×#5542
C2×#337013