Finite Group Databasebeta

← C2×#13127282 #16741456

Subgroups — C2×#13127282 #16741456

Order 3328.

2094 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×#11719347C211yesmaximal, characteristic, complemented
2C2×#11719316C211yesmaximal, characteristic
3#13127282C2116yesmaximal, direct product factor
4C2×#11718517C211yesmaximal, characteristic, complemented
5C2×#11718470C211yesmaximal, characteristic, complemented
6C2×#11718445C211yesmaximal, characteristic, complemented
7C2×#11718704C211yesmaximal, characteristic, complemented
8C2×#11718694C211yesmaximal, characteristic, complemented
9C2×#11718455C211yesmaximal, characteristic, complemented
10C2×#11718427C211yesmaximal, 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×#6129—21no—
18C22×C13×SD16C2211yescharacteristic
19C23×C8×C13C2211yescharacteristic
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×C13×#121C2211yescharacteristic
22C2×#88200C2211yescharacteristic
23C2×Q8×Dic13C2211yescharacteristic
24C2×#88192C2211yescharacteristic
25C2×#88189—21no—
26C2×D4×Dic13C2211yescharacteristic
27C2×C4×C22⋊D13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×#6094C2211yescharacteristic
31#11719347—24no—
32#11719347C2218yescomplemented
33#11719316—24no—
34#11719316C2218yes—
35C2×#88152—21no—
36C2×#88146C2211yescharacteristic
37C2×C4⋊C4×D13C2211yescharacteristic
38C2×#88144—21no—
39C2×#88144C2211yescharacteristic
40C2×#88142C2211yescharacteristic
41C2×#88140—21no—
42C2×#88137—21no—
43C2×#88132—21no—
44C2×#88131—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#11718704C2218yescomplemented
66#11718694C2218yescomplemented
67C2×#88048C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69C2×#88047C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71#11718522C2218yescomplemented
72#11718517C2218yescomplemented
73#11718470C2218yescomplemented
74#11718455C2218yescomplemented
75#11718445C2218yescomplemented
76#11718427C2218yescomplemented
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—
86C2×#6129—28no—
87C2×#6129—48no—
88C22×C4×D13—21no—
89C22×C4×D13C2311yescharacteristic
90C22×Dic26—21no—
91C2×C13×SD16—24no—
92C2×C13×SD16C2314yes—
93C22×C8×C13—24no—
94C22×C8×C13C2311yescharacteristic
95C22×C8×C13C2314yes—
96C22×C8×C13C2311yescharacteristic
97C13×C22⋊Q8—22no—
98C13×C22⋊Q8C2314yes—
99C13×#121—22no—
100C13×#121C2314yes—
101C2×C13×C4⋊C4—21no—
102C2×C13×C4⋊C4C2311yescharacteristic
103C2×C13×C4⋊C4C2311yescharacteristic
104C2×C13×C22⋊C4—21no—
105C2×C13×C22⋊C4—21no—
106C2×C22⋊Dic13—21no—
107C2×C22⋊Dic13—21no—
108C2×C22⋊Dic13D411yescharacteristic
109#88200—22no—
110#88200C2314yes—
111Q8×Dic13—22no—
112Q8×Dic13C2314yes—
113#88192—22no—
114#88192C2314yes—
115#88189—28no—
116D4×Dic13—22no—
117D4×Dic13C2314yes—
118C4×C22⋊D13D414yes—
119C4×C22⋊D13C2314yes—
120C2×#6103—21no—
121C2×#6103—21no—
122C2×#6103D411yescharacteristic
123C2×C4⋊Dic13—21no—
124C2×C4⋊Dic13—21no—
125C2×C4⋊Dic13—22no—
126C2×C4⋊Dic13—22no—
127C2×C4⋊Dic13—21no—
128C2×C4⋊Dic13—21no—
129C2×C4⋊Dic13C2311yescharacteristic
130C2×C4⋊Dic13C2311yescharacteristic
131C2×C4⋊Dic13C2314yes—
132C2×C4⋊Dic13C2311yescharacteristic
133C2×C4⋊Dic13C2311yescharacteristic
134C2×C4⋊Dic13C2314yes—
135C2×#6101—21no—
136C2×#6101—21no—
137C2×#6101—21no—
138C2×#6101—21no—
139C2×#6101D411yescharacteristic
140C2×C4×Dic13—21no—
141C2×C4×Dic13—21no—
142C2×C4×Dic13C2311yescharacteristic
143C22×#1055C2311yescharacteristic
144C22×#1055C2311yescharacteristic
145C2×#6094—24no—
146C2×#6094C2314yes—
147#88152—28no—
148#88146—22no—
149#88146C2314yes—
150C4⋊C4×D13—22no—
151C4⋊C4×D13C2314yes—
152#88144—28no—
153#88144—22no—
154#88144C2314yes—
155#88142—22no—
156#88142C2314yes—
157#88140—28no—
158#88137—28no—
159#88132—28no—
160#88131—28no—
161C13×#106C2314yes—
162C13×#103C2314yes—
163C13×#102C2314yes—
164#88075C2314yes—
165#88075C2314yes—
166#88072C2314yes—
167#88072C2314yes—
168C22⋊#1055C2314yes—
169#88060C2314yes—
170#88058C2314yes—
171#88058C2314yes—
172#88058C2314yes—
173#88058C2314yes—
174#88055C2314yes—
175#88054C2314yes—
176#88048C2314yes—
177#88048C2314yes—
178#88047C2314yes—
179#88047C2314yes—
180C2×#3343—131nomaximal, Sylow
181C24×C13—21no—
182C24×C13C2×D411yescharacteristic
183C23×D13C2×D411yescharacteristic
184C2×Q8×C13—21no—
185C2×Q8×C13—22no—
186C2×Q8×C13—22no—
187C2×Q8×C13C2412yes—
188C2×D4×C13—24no—
189C2×D4×C13—21no—
190C2×D4×C13—22no—
191C2×D4×C13—22no—
192C2×D4×C13—44no—
193C2×D4×C13C2412yes—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2×D412yes—
201C22×C4×C13C2412yes—
202C22×C4×C13C2411yescharacteristic
203C2×C22⋊D13—24no—
204C2×C22⋊D13—24no—
205C2×C22⋊D13—44no—
206C2×C22⋊D13C2×D414yes—
207C22×Dic13—24no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—24no—
213C22×Dic13—24no—
214C22×Dic13—44no—
215C22×Dic13—44no—
216C22×Dic13—44no—
217C22×Dic13C2×D411yescharacteristic
218C22×Dic13C2×D411yescharacteristic
219C22×Dic13C2×D411yescharacteristic
220#6129—432no—
221C2×C4×D13—22no—
222C2×C4×D13—22no—
223C2×C4×D13—24no—
224C2×C4×D13—44no—
225C2×C4×D13C2×D412yes—
226C2×C4×D13C2412yes—
227C2×Dic26—24no—
228C2×Dic26—44no—
229C13×SD16—28no—
230C2×C8×C13—22no—
231C2×C8×C13—28no—
232C2×C8×C13#4114yescomplemented
233C2×C8×C13C2412yes—
234C2×C8×C13C2412yes—
235C13×C4⋊C4—21no—
236C13×C4⋊C4—21no—
237C13×C4⋊C4—24no—
238C13×C4⋊C4C2412yes—
239C13×C4⋊C4C2412yes—
240C13×C22⋊C4—24no—
241C13×C22⋊C4—24no—
242C22⋊Dic13—24no—
243C22⋊Dic13—24no—
244C22⋊Dic13C2×D414yes—
245#6103—24no—
246#6103—24no—
247#6103C2×D414yes—
248C4⋊Dic13—24no—
249C4⋊Dic13—21no—
250C4⋊Dic13—24no—
251C4⋊Dic13—21no—
252C4⋊Dic13—21no—
253C4⋊Dic13—21no—
254C4⋊Dic13—24no—
255C4⋊Dic13—24no—
256C4⋊Dic13C2412yes—
257C4⋊Dic13C2412yes—
258C4⋊Dic13C2412yes—
259C4⋊Dic13C2412yes—
260#6101—24no—
261#6101—24no—
262#6101—24no—
263#6101—24no—
264#6101C2×D414yes—
265C4×Dic13—24no—
266C4×Dic13—24no—
267C4×Dic13C2×D412yes—
268C4×Dic13C2412yes—
269C2×#1055—22no—
270C2×#1055—22no—
271C2×#1055C2412yes—
272C2×#1055C2412yes—
273#6094—28no—
274C2×#552—131no—
275C2×#547—131no—
276#3343—1316no—
277C2×#501—131no—
278C2×#484—131no—
279C2×#482—131no—
280C2×#483—131no—
281C2×#480—131no—
282C2×#477—131no—
283C2×#478—131no—
284C2×#468—131no—
285C2×#465D1311yescharacteristic, complemented
286C2×#440—131no—
287C2×#435—131no—
288C2×#428—131no—
289C22×#107—131no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—42no—
294C23×C13—42no—
295C23×C13—42no—
296C23×C13AGL(1,ℤ/8)14yes—
297C23×C13C22×D412yes—
298C23×C13C22×D411yescharacteristic
299C22×D13—22no—
300C22×D13—22no—
301C22×D13—22no—
302C22×D13C22×D412yes—
303Q8×C13—22no—
304Q8×C13—22no—
305Q8×C13—42no—
306D4×C13—22no—
307D4×C13—22no—
308D4×C13—48no—
309D4×C13—42no—
310C2×C4×C13—22no—
311C2×C4×C13—24no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—42no—
318C2×C4×C13—42no—
319C2×C4×C13—42no—
320C2×C4×C13C22×D412yes—
321C2×C4×C13C22×D411yescharacteristic
322C2×C4×C13C2×#4112yes—
323C2×C4×C132−1+412yes—
324C2×C4×C13C2511yescharacteristic
325C22⋊D13—28no—
326C22⋊D13—48no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—48no—
335C2×Dic13—42no—
336C2×Dic13—42no—
337C2×Dic13—48no—
338C2×Dic13—48no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13C22×D412yes—
342C2×Dic13C22×D412yes—
343C2×Dic13C22×D412yes—
344C4×D13—24no—
345C4×D13—22no—
346C4×D13—22no—
347C4×D13—48no—
348Dic26—48no—
349C8×C13—22no—
350C8×C13C2×#4114yescomplemented
351#1055—22no—
352#1055—22no—
353C22×#41—261no—
354C22×SD16C2×D1311yescharacteristic
355C22×M16—131no—
356C23×C8C2×D1311yescharacteristic
357#552—138no—
358#552—264no—
359#547—138no—
360#547—264no—
361C2×C4⋊Q8—131no—
362C2×#126—261no—
363C2×#125—131no—
364C2×#125—261no—
365C2×#123—261no—
366C2×#123—261no—
367C2×#123—261no—
368C2×C22⋊Q8—131no—
369C2×C22⋊Q8—261no—
370C2×C22⋊Q8C2×D1311yescharacteristic
371C2×#121—131no—
372C2×#121C2×D1311yescharacteristic
373C2×C4×Q8—131no—
374C2×C4×D4—131no—
375C2×C4×D4—131no—
376C2×#117—131no—
377C2×#117—261no—
378C22×C4⋊C4—131no—
379C22×C4⋊C4—131no—
380C22×C4⋊C4—131no—
381#501—138no—
382#484—138no—
383#483—138no—
384#482—138no—
385#480—138no—
386#478—138no—
387#477—138no—
388#468—138no—
389#465C2×D1318yescomplemented
390#440—138no—
391#435—138no—
392#428—138no—
393C2×#107—131no—
394C2×#107—131no—
395C2×#107—138no—
396C2×#107—131no—
397C2×#107—131no—
398C2×#107—131no—
399C2×#107—131no—
400C2×#106—131no—
401C2×#106—131no—
402C2×#106C2×D1311yescharacteristic
403C2×C4⋊C8—131no—
404C2×#103—131no—
405C2×#103—131no—
406C2×#103C2×D1311yescharacteristic
407C2×#102—131no—
408C2×#102—131no—
409C2×#102C2×D1311yescharacteristic
410C2×C22⋊C8—131no—
411C2×C22⋊C8—131no—
412C2×#97—131no—
413C22×C13—28no—
414C22×C13—22no—
415C22×C13—22no—
416C22×C13—42no—
417C22×C13—42no—
418C22×C13—42no—
419C22×C13—84no—
420C22×C13#54712yes—
421C22×C13C2×AGL(1,ℤ/8)14yes—
422C22×C13C2×AGL(1,ℤ/8)12yes—
423C22×C13#57812yes—
424C22×C13C23×D411yescharacteristic
425C2×D13—22no—
426C2×D13—22no—
427C2×D13—22no—
428C2×D13—44no—
429C4×C13—22no—
430C4×C13—42no—
431C4×C13—42no—
432C4×C13—42no—
433C4×C13#54712yes—
434C4×C13C22×#4111yescharacteristic
435C4×C13C2×2−1+411yescharacteristic
436Dic13—22no—
437Dic13—22no—
438Dic13—22no—
439Dic13—42no—
440Dic13—42no—
441Dic13—42no—
442Dic13—42no—
443C2×#41—268no—
444C2×#41—528no—
445C22×Q8—261no—
446C22×Q8C22×D1311yescharacteristic
447C22×D4—21no—
448C22×D4—131no—
449C22×D4—261no—
450C22×D4C22×D1311yescharacteristic
451C23×C4—131no—
452C23×C4—261no—
453C23×C4—261no—
454C23×C4—261no—
455C23×C4—261no—
456C23×C4C22×D1311yescharacteristic
457C2×SD16—24no—
458C2×SD16C22×D1314yes—
459C2×M16—134no—
460C2×M16—264no—
461C22×C8—24no—
462C22×C8—131no—
463C22×C8—131no—
464C22×C8C22×D1311yescharacteristic
465C22×C8C22×D1314yes—
466C22×C8C22×D1311yescharacteristic
467C4⋊Q8—134no—
468C4⋊Q8—262no—
469#126—268no—
470#125—134no—
471#125—262no—
472#125—268no—
473#123—268no—
474#123—268no—
475#123—268no—
476C22⋊Q8—22no—
477C22⋊Q8—134no—
478C22⋊Q8—268no—
479C22⋊Q8—262no—
480C22⋊Q8C22×D1314yes—
481#121—22no—
482#121—134no—
483#121—262no—
484#121C22×D1314yes—
485C4×Q8—134no—
486C4×Q8—262no—
487C4×D4—134no—
488C4×D4—134no—
489C4×D4—134no—
490C4×D4—262no—
491#117—134no—
492#117—268no—
493#117—262no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—131no—
496C2×C4⋊C4—131no—
497C2×C4⋊C4—131no—
498C2×C4⋊C4—131no—
499C2×C4⋊C4—131no—
500C2×C4⋊C4—134no—
501C2×C4⋊C4—134no—
502C2×C4⋊C4—134no—
503C2×C4⋊C4—262no—
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⋊C4—261no—
512C2×C4⋊C4—262no—
513C2×C4⋊C4—262no—
514C2×C4⋊C4C22×D1311yescharacteristic
515C2×C4⋊C4C22×D1311yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—131no—
519C2×C22⋊C4—131no—
520C2×C22⋊C4—261no—
521C2×C22⋊C4—261no—
522C2×C22⋊C4—261no—
523C2×C22⋊C4—261no—
524C2×C42—131no—
525C2×C42—261no—
526C2×C42—261no—
527#107—134no—
528#107—134no—
529#107—134no—
530#107—134no—
531#107—134no—
532#107—134no—
533#106—134no—
534#106—134no—
535#106C22×D1314yes—
536C4⋊C8—134no—
537#103—134no—
538#103—134no—
539#103C22×D1314yes—
540#102—134no—
541#102—134no—
542#102C22×D1314yes—
543C22⋊C8—134no—
544C22⋊C8—134no—
545#97—134no—
546C2×C13—24no—
547C2×C13—82no—
548C2×C13#334314yescomplemented
549C2×C13C2×#54711yescharacteristic
550C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
551C2×C13C2×#57811yescharacteristic
552D13—42no—
553C24—21no—
554C24—131no—
555C24D4×D1311yescharacteristic
556#41—5232no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—264no—
561C2×Q8—524no—
562C2×Q8C23×D1312yes—
563C2×D4—24no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—44no—
568C2×D4—134no—
569C2×D4—264no—
570C2×D4—264no—
571C2×D4—524no—
572C2×D4C23×D1312yes—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—131no—
579C22×C4—131no—
580C22×C4—131no—
581C22×C4—132no—
582C22×C4—132no—
583C22×C4—264no—
584C22×C4—264no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—264no—
588C22×C4—264no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—524no—
594C22×C4—524no—
595C22×C4—524no—
596C22×C4—524no—
597C22×C4D4×D1312yes—
598C22×C4D4×D1311yescharacteristic
599C22×C4C23×D1312yes—
600C22×C4C23×D1311yescharacteristic
601SD16—28no—
602M16—268no—
603C2×C8—22no—
604C2×C8—28no—
605C2×C8—132no—
606C2×C8—132no—
607C2×C8—262no—
608C2×C8—262no—
609C2×C8#612914yescomplemented
610C2×C8C23×D1312yes—
611C2×C8C23×D1312yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—134no—
616C4⋊C4—132no—
617C4⋊C4—132no—
618C4⋊C4—132no—
619C4⋊C4—132no—
620C4⋊C4—264no—
621C4⋊C4—264no—
622C4⋊C4—264no—
623C4⋊C4—264no—
624C4⋊C4—264no—
625C4⋊C4—264no—
626C4⋊C4—261no—
627C4⋊C4—261no—
628C4⋊C4—261no—
629C4⋊C4—264no—
630C4⋊C4—261no—
631C4⋊C4—264no—
632C4⋊C4C23×D1312yes—
633C4⋊C4C23×D1312yes—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—134no—
637C22⋊C4—134no—
638C22⋊C4—264no—
639C22⋊C4—264no—
640C22⋊C4—264no—
641C22⋊C4—264no—
642C42—132no—
643C42—132no—
644C42—264no—
645C42—264no—
646C13C2×#334311yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—132no—
654C23—262no—
655C23—262no—
656C23—262no—
657C23#8816814yes—
658C23C2×D4×D1312yes—
659C23C2×D4×D1311yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—528no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—42no—
668D4—268no—
669D4—528no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—132no—
681C2×C4—132no—
682C2×C4—132no—
683C2×C4—262no—
684C2×C4—262no—
685C2×C4—262no—
686C2×C4—264no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—528no—
694C2×C4—528no—
695C2×C4—528no—
696C2×C4—522no—
697C2×C4—522no—
698C2×C4—522no—
699C2×C4—522no—
700C2×C4—528no—
701C2×C4C2×D4×D1312yes—
702C2×C4C2×D4×D1311yescharacteristic
703C2×C4C2×#612912yes—
704C2×C4#8825712yes—
705C2×C4C24×D1311yescharacteristic
706C8—22no—
707C8—262no—
708C8—262no—
709C8C2×#612914yescomplemented
710C22—22no—
711C22—28no—
712C22—22no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22—262no—
718C22—262no—
719C22—262no—
720C22—524no—
721C22#1171931612yes—
722C22C2×#8816814yes—
723C22C2×#8816812yes—
724C22#1171947612yes—
725C22C22×D4×D1311yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—262no—
731C4—262no—
732C4—262no—
733C4—522no—
734C4—522no—
735C4—522no—
736C4—522no—
737C4#1171931612yes—
738C4C22×#612911yescharacteristic
739C4C2×#8825711yescharacteristic
740C2—24no—
741C2—82no—
742C2—522no—
743C2#1312728214yesdirect product factor
744C2C2×#1171931611yescharacteristic
745C2C22×#8816811yescharacteristic
746C2C2×#1171947611yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#465C2
socleC23×C13C22×D4
prime radicalC2×#11719316C2
hypercenterC2×#465D13
hypocenterC13C2×#3343
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×#11719347C2semidirect
3. #13127282C2direct (N × H)
4. C2×#11718517C2semidirect
5. C2×#11718470C2semidirect
6. C2×#11718445C2semidirect
7. C2×#11718704C2semidirect
8. C2×#11718694C2semidirect
9. C2×#11718455C2semidirect
10. C2×#11718427C2semidirect
11. C2×#11718835C2semidirect
12. C2×#11718825C2semidirect
13. C2×#11718772C2semidirect
14. C2×#11718522C2semidirect
15. C22×#88058C2semidirect
16. C2×C13×#465C2semidirect
32. #11719347C22semidirect
45. C13×#465C22semidirect
54. #11718835C22semidirect
55. #11718825C22semidirect
56. #11718772C22semidirect
62. C2×#88058C22semidirect
65. #11718704C22semidirect
66. #11718694C22semidirect
71. #11718522C22semidirect
72. #11718517C22semidirect
73. #11718470C22semidirect
74. #11718455C22semidirect
75. #11718445C22semidirect
76. #11718427C22semidirect
232. C2×C8×C13#41semidirect
285. C2×#465D13semidirect
350. C8×C13C2×#41semidirect
389. #465C2×D13semidirect
548. C2×C13#3343semidirect
609. C2×C8#6129semidirect
646. C13C2×#3343semidirect
709. C8C2×#6129semidirect
743. C2#13127282direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193472
C2×#117193162
#131272822
C2×#117185172
C2×#117184702
C2×#117184452
C2×#117187042
C2×#117186942
C2×#117184552
C2×#117184272
C2×#117188352
C2×#117188252
C2×#117187722
C2×#117185222
C22×#880582
C2×C13×#4652
C2×#334313