Finite Group Databasebeta

← C2×#13127583 #16742662

Subgroups — C2×#13127583 #16742662

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×#11719284C211yesmaximal, characteristic, complemented
2#13127583C2116yesmaximal, direct product factor
3C2×#11718732C211yesmaximal, characteristic, complemented
4C2×#11718716C211yesmaximal, characteristic, complemented
5C2×#11718717C211yesmaximal, characteristic, complemented
6C2×#11718683C211yesmaximal, characteristic, complemented
7C2×#11718670C211yesmaximal, characteristic, complemented
8C2×#11718668C211yesmaximal, characteristic, complemented
9C2×#11718718C211yesmaximal, characteristic, complemented
10C2×#11718718C211yesmaximal, characteristic, complemented
11C2×#11718733C211yesmaximal, characteristic
12C2×#11718685C211yesmaximal, characteristic, complemented
13C2×#11718675C211yesmaximal, characteristic, complemented
14C2×#11718687C211yesmaximal, characteristic, complemented
15C2×C4×#6104C211yesmaximal, characteristic, complemented
16C2×C13×#559C211yesmaximal, characteristic, complemented
17C13×#559—24no—
18C13×#559C2218yescomplemented
19C2×C13×#127C2211yescharacteristic
20C2×C13×#124—21no—
21C2×C13×#124C2211yescharacteristic
22C2×C13×#124C2211yescharacteristic
23C2×C13×#123—21no—
24C2×C13×#123—21no—
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×D4×C13—21no—
28C2×C4×D4×C13C2211yescharacteristic
29C2×C4×D4×C13C2211yescharacteristic
30C2×#88200—21no—
31C22×#6106C2211yescharacteristic
32C22×#6104C2211yescharacteristic
33C22×#6104C2211yescharacteristic
34#11719284—24no—
35#11719284C2218yescomplemented
36C2×#88150—21no—
37C2×#88150—21no—
38C2×C4⋊C4×D13—21no—
39C2×C4×D52C2211yescharacteristic
40C2×C4×D52C2211yescharacteristic
41C2×C4×D52C2211yescharacteristic
42C2×#88124C2211yescharacteristic
43C2×#88124C2211yescharacteristic
44C2×#88123C2211yescharacteristic
45C2×#88075C2211yescharacteristic
46C2×#88075C2211yescharacteristic
47C2×#88075C2211yescharacteristic
48C2×#88072C2211yescharacteristic
49C2×#88072C2211yescharacteristic
50C2×#88072C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52C2×#88072C2211yescharacteristic
53C2×#88072C2211yescharacteristic
54#11718733C2218yes—
55#11718732C2218yescomplemented
56#11718718C2218yescomplemented
57#11718718C2218yescomplemented
58#11718717C2218yescomplemented
59#11718716C2218yescomplemented
60#11718687C2218yescomplemented
61#11718685C2218yescomplemented
62#11718683C2218yescomplemented
63#11718675C2218yescomplemented
64C4×#6104C2218yescomplemented
65#11718670C2218yescomplemented
66#11718668C2218yescomplemented
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×C13D411yescharacteristic
78C22×Q8×C13C2311yescharacteristic
79C22×D4×C13—21no—
80C22×D4×C13—21no—
81C22×D4×C13C2311yescharacteristic
82C22×D4×C13C2311yescharacteristic
83C23×C4×C13—21no—
84C23×C4×C13—21no—
85C22×D52C2311yescharacteristic
86C22×C4×D13—21no—
87C22×C4×D13—21no—
88C22×C4×D13—21no—
89C22×Dic26—21no—
90C13×#127—22no—
91C13×#127C2314yes—
92C13×#124—28no—
93C13×#124—22no—
94C13×#124—22no—
95C13×#124C2314yes—
96C13×#124C2314yes—
97C13×#123—28no—
98C13×#123—28no—
99C4×Q8×C13—22no—
100C4×Q8×C13D414yes—
101C4×Q8×C13C2314yes—
102C4×Q8×C13C2314yes—
103C4×D4×C13—28no—
104C4×D4×C13—22no—
105C4×D4×C13—22no—
106C4×D4×C13C2314yes—
107C4×D4×C13C2314yes—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4D411yescharacteristic
110C2×C13×C4⋊C4D411yescharacteristic
111C2×C13×C4⋊C4D411yescharacteristic
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⋊C4—21no—
118C2×C13×C22⋊C4—21no—
119C2×C42×C13—21no—
120C2×C42×C13C2311yescharacteristic
121C2×C42×C13C2311yescharacteristic
122C2×C42×C13C2311yescharacteristic
123#88200—28no—
124C2×#6106—24no—
125C2×#6106C2314yes—
126C2×#6104—24no—
127C2×#6104—24no—
128C2×#6104C2314yes—
129C2×#6104C2314yes—
130C2×#6103—21no—
131C2×#6103—21no—
132C2×#6103—21no—
133C2×C4⋊Dic13—21no—
134C2×C4⋊Dic13C2311yescharacteristic
135C2×C4⋊Dic13C2311yescharacteristic
136C2×C4⋊Dic13C2311yescharacteristic
137C2×#6101—21no—
138C2×#6101—21no—
139C2×#6101—21no—
140C2×#6101—21no—
141C22×#1055C2311yescharacteristic
142C22×#1055C2311yescharacteristic
143C22×#1055C2311yescharacteristic
144C22×#1055C2311yescharacteristic
145#88150—28no—
146#88150—28no—
147C4⋊C4×D13—28no—
148C4×D52—22no—
149C4×D52—22no—
150C4×D52—22no—
151C4×D52C2314yes—
152C4×D52C2314yes—
153C4×D52C2314yes—
154#88124—22no—
155#88124—22no—
156#88124C2314yes—
157#88124C2314yes—
158#88123—22no—
159#88123C2314yes—
160#88075C2314yes—
161#88075C2314yes—
162#88075C2314yes—
163#88072C2314yes—
164#88072C2314yes—
165#88072C2314yes—
166#88072C2314yes—
167#88072C2314yes—
168#88072C2314yes—
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—
181C24×C13—21no—
182C23×D13—21no—
183C2×Q8×C13—21no—
184C2×Q8×C13—22no—
185C2×Q8×C13—22no—
186C2×Q8×C13—42no—
187C2×Q8×C13C2×D414yes—
188C2×Q8×C13C2412yes—
189C2×D4×C13—21no—
190C2×D4×C13—21no—
191C2×D4×C13—24no—
192C2×D4×C13—24no—
193C2×D4×C13—22no—
194C2×D4×C13—22no—
195C2×D4×C13—22no—
196C2×D4×C13—22no—
197C2×D4×C13—44no—
198C2×D4×C13—82no—
199C2×D4×C13C2412yes—
200C2×D4×C13C2412yes—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—24no—
204C22×C4×C13—24no—
205C22×C4×C13—82no—
206C22×C4×C13—82no—
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D411yescharacteristic
209C22×C4×C13C2×D411yescharacteristic
210C22×C4×C13C2×D411yescharacteristic
211C22×C4×C13C2×D411yescharacteristic
212C22×C4×C13C2×D411yescharacteristic
213C22×C4×C13C2411yescharacteristic
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C2×D52—21no—
218C2×D52—22no—
219C2×D52#4114yes—
220C2×D52C2412yes—
221C2×C4×D13—24no—
222C2×C4×D13—24no—
223C2×C4×D13—24no—
224C2×C4×D13—44no—
225C2×C4×D13—82no—
226C2×C4×D13—82no—
227C2×Dic26—24no—
228C2×Dic26—82no—
229C13×C4⋊C4—24no—
230C13×C4⋊C4—21no—
231C13×C4⋊C4C2×D414yes—
232C13×C4⋊C4C2×D414yes—
233C13×C4⋊C4C2×D414yes—
234C13×C4⋊C4C2412yes—
235C13×C22⋊C4—24no—
236C13×C22⋊C4—24no—
237C13×C22⋊C4—24no—
238C13×C22⋊C4—24no—
239C13×C22⋊C4—24no—
240C13×C22⋊C4—24no—
241C42×C13—24no—
242C42×C13C2×D412yes—
243C42×C13C2×D412yes—
244C42×C13C2×D412yes—
245C42×C13C2412yes—
246C42×C13C2412yes—
247C42×C13C2412yes—
248#6106—28no—
249#6104—28no—
250#6104—28no—
251#6103—24no—
252#6103—24no—
253#6103—24no—
254C4⋊Dic13—21no—
255C4⋊Dic13—21no—
256C4⋊Dic13—24no—
257C4⋊Dic13—21no—
258C4⋊Dic13C2412yes—
259C4⋊Dic13C2412yes—
260C4⋊Dic13C2412yes—
261#6101—24no—
262#6101—24no—
263#6101—24no—
264#6101—24no—
265C2×#1055—22no—
266C2×#1055—22no—
267C2×#1055—22no—
268C2×#1055—22no—
269C2×#1055C2412yes—
270C2×#1055C2412yes—
271C2×#1055C2412yes—
272C2×#1055C2412yes—
273C2×#559D1311yescharacteristic, complemented
274C2×#554—131no—
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—22no—
290C23×C13—22no—
291C23×C13—42no—
292C23×C13—42no—
293C23×C13—42no—
294C23×C13—42no—
295C23×C13—42no—
296C23×C13—42no—
297C23×C13C22×D411yescharacteristic
298C22×D13—24no—
299C22×D13—22no—
300C22×D13—42no—
301C22×D13—42no—
302Q8×C13—22no—
303Q8×C13—22no—
304Q8×C13—44no—
305Q8×C13—42no—
306D4×C13—22no—
307D4×C13—22no—
308D4×C13—22no—
309D4×C13—22no—
310D4×C13—48no—
311D4×C13—42no—
312D4×C13—42no—
313D4×C13—84no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—42no—
323C2×C4×C13—42no—
324C2×C4×C13—84no—
325C2×C4×C13—84no—
326C2×C4×C13C22×D412yes—
327C2×C4×C13C22×D412yes—
328C2×C4×C13C22×D412yes—
329C2×C4×C13C22×D412yes—
330C2×C4×C13C22×D412yes—
331C2×C4×C13C22×D412yes—
332C2×C4×C13C22×D411yescharacteristic
333C2×C4×C13C2×#4112yes—
334C2×C4×C132−1+412yes—
335C2×C4×C13C2511yescharacteristic
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342D52—24no—
343D52—22no—
344D52C2×#4114yes—
345C4×D13—48no—
346C4×D13—84no—
347C4×D13—84no—
348Dic26—84no—
349#1055—22no—
350#1055—22no—
351#1055—22no—
352#1055—22no—
353C22×SD16—131no—
354C22×D8—131no—
355C22×D8—131no—
356#559—24no—
357#559C2×D1318yescomplemented
358#554—138no—
359#554—264no—
360C2×C4⋊Q8—131no—
361C2×#127C2×D1311yescharacteristic
362C2×#125—131no—
363C2×#125—131no—
364C2×#124—21no—
365C2×#124C2×D1311yescharacteristic
366C2×#124C2×D1311yescharacteristic
367C2×#123—21no—
368C2×#123—21no—
369C2×C22⋊Q8—261no—
370C2×C22⋊Q8—261no—
371C2×C22⋊Q8—261no—
372C2×C4×Q8C2×D1311yescharacteristic
373C2×C4×Q8C2×D1311yescharacteristic
374C2×C4×D4—21no—
375C2×C4×D4—131no—
376C2×C4×D4—131no—
377C2×C4×D4—131no—
378C2×C4×D4C2×D1311yescharacteristic
379C2×C4×D4C2×D1311yescharacteristic
380C22×C4⋊C4—261no—
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—42no—
414C22×C13—42no—
415C22×C13—42no—
416C22×C13—42no—
417C22×C13—42no—
418C22×C13—42no—
419C22×C13—84no—
420C22×C13—84no—
421C22×C13#54812yes—
422C22×C13#57512yes—
423C22×C13#57612yes—
424C22×C13C23×D411yescharacteristic
425C2×D13—24no—
426C2×D13—48no—
427C2×D13—42no—
428C2×D13—42no—
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#54812yes—
438C4×C13C22×#4111yescharacteristic
439C4×C13C2×2−1+411yescharacteristic
440Dic13—42no—
441Dic13—42no—
442Dic13—42no—
443C22×Q8—261no—
444C22×Q8C22⋊D1311yescharacteristic
445C22×Q8C22×D1311yescharacteristic
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—131no—
449C22×D4C22×D1311yescharacteristic
450C22×D4C22×D1311yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4—261no—
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—134no—
467C4⋊Q8—262no—
468#127—22no—
469#127C22×D1314yes—
470#125—134no—
471#125—134no—
472#125—262no—
473#125—262no—
474#124—28no—
475#124—22no—
476#124—22no—
477#124C22×D1314yes—
478#124C22×D1314yes—
479#123—28no—
480#123—28no—
481C22⋊Q8—268no—
482C22⋊Q8—268no—
483C22⋊Q8—268no—
484C4×Q8—22no—
485C4×Q8C22⋊D1314yes—
486C4×Q8C22×D1314yes—
487C4×Q8C22×D1314yes—
488C4×D4—28no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—134no—
492C4×D4—134no—
493C4×D4—134no—
494C4×D4—262no—
495C4×D4—262no—
496C4×D4—262no—
497C4×D4C22×D1314yes—
498C4×D4C22×D1314yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—131no—
501C2×C4⋊C4—131no—
502C2×C4⋊C4—131no—
503C2×C4⋊C4—261no—
504C2×C4⋊C4—261no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4—268no—
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—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—261no—
520C2×C22⋊C4—261no—
521C2×C22⋊C4—261no—
522C2×C42—21no—
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—82no—
546C2×C13—82no—
547C2×C13#337014yescomplemented
548C2×C13C2×#54811yescharacteristic
549C2×C13C2×#57511yescharacteristic
550C2×C13C2×#57611yescharacteristic
551D13—44no—
552C24—21no—
553C24—21no—
554C24—261no—
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—42no—
559C2×Q8—264no—
560C2×Q8—1042no—
561C2×Q8C2×C22⋊D1314yes—
562C2×Q8C23×D1312yes—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—44no—
572C2×D4—82no—
573C2×D4—134no—
574C2×D4—132no—
575C2×D4—262no—
576C2×D4—261no—
577C2×D4C23×D1312yes—
578C2×D4C23×D1312yes—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—264no—
589C22×C4—264no—
590C22×C4—264no—
591C22×C4—524no—
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—21no—
614C4⋊C4—132no—
615C4⋊C4—132no—
616C4⋊C4—132no—
617C4⋊C4—261no—
618C4⋊C4—261no—
619C4⋊C4—261no—
620C4⋊C4—264no—
621C4⋊C4—264no—
622C4⋊C4—264no—
623C4⋊C4—264no—
624C4⋊C4—264no—
625C4⋊C4C2×C22⋊D1314yes—
626C4⋊C4C2×C22⋊D1314yes—
627C4⋊C4C2×C22⋊D1314yes—
628C4⋊C4C23×D1312yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—264no—
636C22⋊C4—264no—
637C22⋊C4—264no—
638C42—24no—
639C42C2×C22⋊D1312yes—
640C42C2×C22⋊D1312yes—
641C42C2×C22⋊D1312yes—
642C42C23×D1312yes—
643C42C23×D1312yes—
644C42C23×D1312yes—
645C13C2×#337011yescharacteristic, complemented, Sylow
646C23—22no—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—264no—
655C23—262no—
656C23—522no—
657C23—522no—
658C23C22×C22⋊D1311yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—44no—
662Q8—42no—
663Q8—1044no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—42no—
670D4—42no—
671D4—84no—
672D4—134no—
673D4—264no—
674D4—262no—
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—42no—
684C2×C4—42no—
685C2×C4—84no—
686C2×C4—84no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—528no—
691C2×C4—522no—
692C2×C4—522no—
693C2×C4—522no—
694C2×C4—1044no—
695C2×C4—1044no—
696C2×C4#41×D1312yes—
697C2×C4#8825712yes—
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—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22—84no—
718C22—264no—
719C22—522no—
720C22—522no—
721C22—528no—
722C22#1171952712yes—
723C22#1171953612yes—
724C22#1171954012yes—
725C22C23×C22⋊D1311yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—522no—
735C4—522no—
736C4—522no—
737C4#1171953612yes—
738C4C2×#41×D1311yescharacteristic
739C4C2×#8825711yescharacteristic
740C2—82no—
741C2—82no—
742C2—524no—
743C2#1312758314yesdirect product factor
744C2C2×#1171953611yescharacteristic
745C2C2×#1171952711yescharacteristic
746C2C2×#1171954011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#559C2
socleC23×C13C22×D4
prime radicalC2×#11718733C2
hypercenterC2×#559D13
hypocenterC13C2×#3370
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#11719284C2semidirect
2. #13127583C2direct (N × H)
3. C2×#11718732C2semidirect
4. C2×#11718716C2semidirect
5. C2×#11718717C2semidirect
6. C2×#11718683C2semidirect
7. C2×#11718670C2semidirect
8. C2×#11718668C2semidirect
9. C2×#11718718C2semidirect
10. C2×#11718718C2semidirect
12. C2×#11718685C2semidirect
13. C2×#11718675C2semidirect
14. C2×#11718687C2semidirect
15. C2×C4×#6104C2semidirect
16. C2×C13×#559C2semidirect
18. C13×#559C22semidirect
35. #11719284C22semidirect
55. #11718732C22semidirect
56. #11718718C22semidirect
57. #11718718C22semidirect
58. #11718717C22semidirect
59. #11718716C22semidirect
60. #11718687C22semidirect
61. #11718685C22semidirect
62. #11718683C22semidirect
63. #11718675C22semidirect
64. C4×#6104C22semidirect
65. #11718670C22semidirect
66. #11718668C22semidirect
273. C2×#559D13semidirect
357. #559C2×D13semidirect
547. C2×C13#3370semidirect
645. C13C2×#3370semidirect
743. C2#13127583direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192842
#131275832
C2×#117187322
C2×#117187162
C2×#117187172
C2×#117186832
C2×#117186702
C2×#117186682
C2×#117187182
C2×#117187332
C2×#117186852
C2×#117186752
C2×#117186872
C2×C4×#61042
C2×C13×#5592
C2×#337013