Finite Group Databasebeta

← C2×#13115328 #15864807

Subgroups — C2×#13115328 #15864807

Order 3328.

1678 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88196C211yesmaximal, characteristic
2C2×#11719517C211yesmaximal, characteristic, complemented
3C2×#11718800C211yesmaximal, characteristic
4C2×#11718667C211yesmaximal, characteristic
5#13115328C218yesmaximal, direct product factor
6C2×#11718151C211yesmaximal, characteristic, complemented
7C2×#11718123C211yesmaximal, characteristic, complemented
8C2×C13×#419C211yesmaximal, characteristic, complemented
9C23×Q8×C13C2211yescharacteristic
10C22×#6127C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C2×C13×#117C2211yescharacteristic
13#11719517—22no—
14#11719517—22no—
15#11719517—22no—
16#11719517C2214yescomplemented
17C2×Q8×Dic13—22no—
18C2×Q8×Dic13—22no—
19C22×#6107C412yescomplemented
20C2×#88196—22no—
21C2×#88196—22no—
22C2×#88196—22no—
23C2×#88196—22no—
24C2×#88196C414yescomplemented
25C2×#88196C2214yes—
26C22×#6106C412yescomplemented
27C2×#88180—22no—
28C2×#88180C2211yescharacteristic
29C2×#88180C2211yescharacteristic
30C22×#6099C2211yescharacteristic
31C13×#419—22no—
32C13×#419C2214yescomplemented
33C2×C13×#103—22no—
34#11718800—22no—
35#11718800C2214yes—
36C2×#88065—22no—
37#11718667—22no—
38#11718667C2214yes—
39C2×#88046—22no—
40#11718151C2214yescomplemented
41#11718123C2214yescomplemented
42C22×Q8×C13—21no—
43C22×Q8×C13—21no—
44C22×Q8×C13—21no—
45C22×Q8×C13—21no—
46C22×Q8×C13—21no—
47C22×Q8×C13—21no—
48C22×Q8×C13—21no—
49C22×Q8×C13C2×C412yes—
50C22×Q8×C13C2×C412yes—
51C22×Q8×C13D412yes—
52C22×Q8×C13D412yes—
53C22×Q8×C13D412yes—
54C22×Q8×C13D412yes—
55C22×Q8×C13C2312yes—
56C23×C4×C13—21no—
57C23×C4×C13C2311yescharacteristic
58C22×C22⋊D13—21no—
59C2×#6127—21no—
60C2×#6127—21no—
61C2×#6127—21no—
62C2×#6127—21no—
63C2×#6127—21no—
64C2×#6127—21no—
65C2×#6127—21no—
66C2×#6127—21no—
67C2×#6127—21no—
68C2×#6127—21no—
69C2×#6127C2×C412yes—
70C2×#6127C2312yes—
71C22×D52C2×C411yescharacteristic
72C22×C4×D13—21no—
73C22×Dic26C2×C411yescharacteristic
74C2×C13×M16—21no—
75C2×C13×M16—21no—
76C2×C13×M16—21no—
77C2×C13×M16—21no—
78C2×C13×M16—21no—
79C2×C13×M16C2312yes—
80C22×C8×C13—21no—
81C13×#117—21no—
82C13×#117—21no—
83C13×#117—21no—
84C13×#117C2312yes—
85C2×C13×C4⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C42×C13—21no—
88C2×C22⋊Dic13—21no—
89C2×C22⋊Dic13D412yes—
90Q8×Dic13—28no—
91Q8×Dic13—28no—
92Q8×Dic13—28no—
93Q8×Dic13—28no—
94C2×#6107—24no—
95C2×#6107—24no—
96C2×#6107C2×C418yescomplemented
97#88196—28no—
98#88196—28no—
99#88196—28no—
100#88196—28no—
101C2×#6106—24no—
102C2×#6106—24no—
103C2×#6106C2×C418yescomplemented
104#88180—28no—
105#88180—21no—
106#88180—21no—
107#88180—21no—
108#88180—21no—
109#88180—28no—
110#88180D412yes—
111#88180D412yes—
112#88180C2312yes—
113#88180C2312yes—
114C2×C4⋊Dic13—24no—
115C2×C4⋊Dic13—21no—
116C2×C4⋊Dic13—21no—
117C2×C4×Dic13—24no—
118C2×C4×Dic13—21no—
119C2×C4×Dic13D412yes—
120C2×#6099—21no—
121C2×#6099—21no—
122C2×#6099—21no—
123C2×#6099—21no—
124C2×#6099C2×C412yes—
125C2×#6099C2312yes—
126C22×#1055C2×C412yes—
127C13×#103—28no—
128#88065—28no—
129#88046—28no—
130C2×#1905—131nomaximal, Sylow
131C24×C13C2×D411yescharacteristic
132C23×D13—21no—
133C2×Q8×C13—22no—
134C2×Q8×C13—22no—
135C2×Q8×C13—22no—
136C2×Q8×C13—22no—
137C2×Q8×C13—22no—
138C2×Q8×C13—22no—
139C2×Q8×C13—22no—
140C2×Q8×C13—22no—
141C2×Q8×C13—22no—
142C2×Q8×C13—22no—
143C2×Q8×C13—22no—
144C2×Q8×C13—22no—
145C2×Q8×C13—22no—
146C2×Q8×C13—22no—
147C2×Q8×C13—22no—
148C2×Q8×C13—22no—
149C2×Q8×C13—22no—
150C2×Q8×C13—22no—
151C2×Q8×C13—22no—
152C2×Q8×C13—22no—
153C2×Q8×C13—22no—
154C2×Q8×C13C22⋊C414yes—
155C2×Q8×C13C22⋊C414yes—
156C2×Q8×C13C22⋊C414yes—
157C2×Q8×C13C22⋊C414yes—
158C2×Q8×C13C22×C414yes—
159C2×Q8×C13C2×D414yes—
160C2×Q8×C13C2×D414yes—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—41no—
169C22×C4×C13C22×C411yescharacteristic
170C22×C4×C13C22×C411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13#4111yescharacteristic
179C22×C4×C13#4111yescharacteristic
180C22×C4×C13#4111yescharacteristic
181C22×C4×C13#4111yescharacteristic
182C22×C4×C13C2411yescharacteristic
183C2×C22⋊D13—22no—
184C2×C22⋊D13—22no—
185C2×C22⋊D13—41no—
186C2×C22⋊D13—41no—
187C2×C22⋊D13—41no—
188C2×C22⋊D13—41no—
189C22×Dic13—21no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192#6127—22no—
193#6127—22no—
194#6127—22no—
195#6127—22no—
196#6127—22no—
197#6127—22no—
198#6127—22no—
199#6127—22no—
200#6127—41no—
201#6127—41no—
202#6127—41no—
203#6127—41no—
204#6127—41no—
205#6127—41no—
206#6127—41no—
207#6127—41no—
208C2×D52—21no—
209C2×D52—21no—
210C2×D52—21no—
211C2×D52—21no—
212C2×D52—21no—
213C2×D52C22×C412yes—
214C2×C4×D13—22no—
215C2×C4×D13—22no—
216C2×C4×D13—41no—
217C2×C4×D13—41no—
218C2×C4×D13—41no—
219C2×C4×D13—41no—
220C2×Dic26—21no—
221C2×Dic26—21no—
222C2×Dic26—21no—
223C2×Dic26—21no—
224C2×Dic26—21no—
225C2×Dic26C22×C412yes—
226C13×M16—22no—
227C13×M16—22no—
228C13×M16—41no—
229C13×M16—41no—
230C2×C8×C13—22no—
231C2×C8×C13—41no—
232C2×C8×C13—41no—
233C13×C4⋊C4—22no—
234C13×C4⋊C4—41no—
235C13×C22⋊C4—22no—
236C13×C22⋊C4—41no—
237C42×C13—22no—
238C42×C13—41no—
239C22⋊Dic13—22no—
240C22⋊Dic13—22no—
241C22⋊Dic13—22no—
242C22⋊Dic13C2×D414yes—
243#6107—216no—
244#6106—216no—
245C4⋊Dic13—216no—
246C4⋊Dic13—22no—
247C4⋊Dic13—22no—
248C4⋊Dic13—22no—
249C4⋊Dic13—22no—
250C4×Dic13—216no—
251C4×Dic13—22no—
252C4×Dic13—22no—
253C4×Dic13—22no—
254C4×Dic13C2×D414yes—
255#6099—22no—
256#6099—22no—
257#6099—22no—
258#6099—22no—
259C2×#1055—22no—
260C2×#1055—22no—
261C2×#1055C22×C414yes—
262C22×#137—131no—
263C2×#519—131no—
264C2×#421—131no—
265C2×#419D1311yescharacteristic, complemented
266C2×#410—131no—
267#1905—138no—
268C2×#344—131no—
269C2×H(3,ℤ/4)—131no—
270C23×C13—42no—
271C23×C13C4×D411yescharacteristic
272C23×C13C4×D411yescharacteristic
273C23×C13#12011yescharacteristic
274C23×C13#12011yescharacteristic
275C23×C13#12111yescharacteristic
276C23×C13#12111yescharacteristic
277C23×C13C22×D411yescharacteristic
278C22×D13—22no—
279C22×D13—41no—
280C22×D13—41no—
281C22×D13—82no—
282Q8×C13—24no—
283Q8×C13—24no—
284Q8×C13—24no—
285Q8×C13—24no—
286Q8×C13—24no—
287Q8×C13—24no—
288Q8×C13—24no—
289Q8×C13C2×C22⋊C418yes—
290C2×C4×C13—24no—
291C2×C4×C13—24no—
292C2×C4×C13—24no—
293C2×C4×C13—24no—
294C2×C4×C13—24no—
295C2×C4×C13—24no—
296C2×C4×C13—24no—
297C2×C4×C13—42no—
298C2×C4×C13—82no—
299C2×C4×C13C2×C22⋊C411yescharacteristic
300C2×C4×C13C2×C22⋊C411yescharacteristic
301C2×C4×C13C2×C22⋊C411yescharacteristic
302C2×C4×C13C2×C22⋊C411yescharacteristic
303C2×C4×C13C4×D411yescharacteristic
304C2×C4×C13C4×D411yescharacteristic
305C2×C4×C13C4×D411yescharacteristic
306C2×C4×C13C4×D411yescharacteristic
307C2×C4×C13C4×D411yescharacteristic
308C2×C4×C13C4×D411yescharacteristic
309C2×C4×C13#12011yescharacteristic
310C2×C4×C13#12011yescharacteristic
311C2×C4×C13#12111yescharacteristic
312C2×C4×C13#12111yescharacteristic
313C2×C4×C13#12111yescharacteristic
314C2×C4×C13#12111yescharacteristic
315C2×C4×C13#12111yescharacteristic
316C2×C4×C13#12111yescharacteristic
317C2×C4×C13#12311yescharacteristic
318C2×C4×C13#12311yescharacteristic
319C2×C4×C13#12311yescharacteristic
320C2×C4×C13#12311yescharacteristic
321C2×C4×C13C23×C411yescharacteristic
322C2×C4×C13C22×D411yescharacteristic
323C2×C4×C13C22×D411yescharacteristic
324C2×C4×C13C22×D411yescharacteristic
325C2×C4×C13C2×#4111yescharacteristic
326C2×C4×C13C2×#4111yescharacteristic
327C22⋊D13—42no—
328C22⋊D13—42no—
329C22⋊D13—42no—
330C22⋊D13—42no—
331C2×Dic13—22no—
332C2×Dic13—24no—
333C2×Dic13—24no—
334C2×Dic13—44no—
335C2×Dic13—44no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338D52—22no—
339D52—22no—
340D52—41no—
341D52—41no—
342C4×D13—42no—
343C4×D13—42no—
344C4×D13—42no—
345C4×D13—42no—
346Dic26—22no—
347Dic26—22no—
348Dic26—41no—
349Dic26—41no—
350C8×C13—42no—
351#1055—24no—
352C22×#41—131no—
353C23×Q8C2×D1311yescharacteristic
354C2×#137—134no—
355C2×#137—134no—
356C2×#137—262no—
357C2×#137—262no—
358C2×#137—262no—
359C2×#137—262no—
360C22×Q16—132no—
361C22×SD16—132no—
362C22×M16—131no—
363C22×M16C2×D1311yescharacteristic
364#519—134no—
365#519—262no—
366#519—262no—
367#519—262no—
368C2×C4×Q8—262no—
369C2×C4×Q8—262no—
370C2×#117—131no—
371C2×#117—131no—
372C2×#117—262no—
373C2×#117C2×D1311yescharacteristic
374#421—134no—
375#421—262no—
376C2×#104—262no—
377#419—22no—
378#419C2×D1314yescomplemented
379C2×#103—22no—
380#410—134no—
381#410—262no—
382C2×#99—262no—
383#344—134no—
384H(3,ℤ/4)—134no—
385C22×C13—22no—
386C22×C13—22no—
387C22×C13—22no—
388C22×C13—41no—
389C22×C13—41no—
390C22×C13—41no—
391C22×C13—41no—
392C22×C13#38611yescharacteristic
393C22×C13#38611yescharacteristic
394C22×C13#38611yescharacteristic
395C22×C13#38611yescharacteristic
396C22×C13C2×C4×D411yescharacteristic
397C22×C13C2×#12011yescharacteristic
398C22×C13C2×#12111yescharacteristic
399C2×D13—42no—
400C2×D13—82no—
401C2×D13—82no—
402C2×D13—82no—
403C4×C13—28no—
404C4×C13—82no—
405C4×C13#38611yescharacteristic
406C4×C13#38611yescharacteristic
407C4×C13#38611yescharacteristic
408C4×C13#38611yescharacteristic
409C4×C13C22×C22⋊C411yescharacteristic
410C4×C13C2×C4×D411yescharacteristic
411C4×C13C2×#12111yescharacteristic
412C4×C13C2×#12311yescharacteristic
413Dic13—44no—
414Dic13—44no—
415Dic13—42no—
416C2×#41—132no—
417C2×#41—132no—
418C2×#41—261no—
419C2×#41—261no—
420C2×#41—261no—
421C2×#41—261no—
422C2×#41—261no—
423C2×#41—261no—
424C2×#41—261no—
425C2×#41—261no—
426C2×#41—261no—
427C2×#41—261no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—21no—
431C22×Q8—21no—
432C22×Q8—21no—
433C22×Q8—21no—
434C22×Q8—21no—
435C22×Q8—131no—
436C22×Q8C4×D1312yes—
437C22×Q8C4×D1312yes—
438C22×Q8D5212yes—
439C22×Q8D5212yes—
440C22×Q8C22⋊D1312yes—
441C22×Q8C22⋊D1312yes—
442C22×Q8C22×D1312yes—
443C22×D4—131no—
444C22×D4—261no—
445C23×C4—21no—
446C23×C4—261no—
447C23×C4C22×D1311yescharacteristic
448#137—268no—
449#137—268no—
450#137—268no—
451#137—268no—
452C2×Q16—138no—
453C2×Q16—264no—
454C2×Q16—264no—
455C2×SD16—138no—
456C2×SD16—264no—
457C2×SD16—264no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—132no—
464C2×M16—132no—
465C2×M16—261no—
466C2×M16—261no—
467C2×M16—261no—
468C2×M16—261no—
469C2×M16C22×D1312yes—
470C22×C8—21no—
471C22×C8—132no—
472C4×Q8—268no—
473C4×Q8—268no—
474C4×Q8—268no—
475C4×Q8—268no—
476#117—21no—
477#117—21no—
478#117—21no—
479#117—132no—
480#117—132no—
481#117—132no—
482#117—132no—
483#117—268no—
484#117—268no—
485#117—261no—
486#117—261no—
487#117—261no—
488#117—261no—
489#117C22×D1312yes—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—264no—
492C2×C4⋊C4—261no—
493C2×C4⋊C4—261no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—132no—
496C2×C22⋊C4—261no—
497C2×C42—21no—
498C2×C42—132no—
499C2×C42—264no—
500C2×C42—261no—
501#104—268no—
502#103—28no—
503#99—268no—
504C2×C13—21no—
505C2×C13—21no—
506C2×C13—21no—
507C2×C13—21no—
508C2×C13—21no—
509C2×C13—21no—
510C2×C13#190512yescomplemented
511C2×C13C2×#38611yescharacteristic
512D13—82no—
513C24—261no—
514C24D4×D1311yescharacteristic
515#41—262no—
516#41—262no—
517#41—262no—
518#41—262no—
519#41—262no—
520#41—262no—
521#41—262no—
522#41—262no—
523#41—521no—
524#41—521no—
525#41—521no—
526#41—521no—
527#41—521no—
528#41—521no—
529#41—521no—
530#41—521no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—132no—
553C2×Q8—261no—
554C2×Q8—261no—
555C2×Q8—261no—
556C2×Q8—261no—
557C2×Q8—261no—
558C2×Q8#610314yes—
559C2×Q8#610314yes—
560C2×Q8#610314yes—
561C2×Q8#610314yes—
562C2×Q8C2×C4×D1314yes—
563C2×Q8C2×D5214yes—
564C2×Q8C2×C22⋊D1314yes—
565C2×D4—132no—
566C2×D4—262no—
567C2×D4—262no—
568C2×D4—261no—
569C2×D4—261no—
570C2×D4—261no—
571C2×D4—261no—
572C2×D4—261no—
573C2×D4—521no—
574C2×D4—521no—
575C2×D4—521no—
576C2×D4—521no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—41no—
585C22×C4—261no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—521no—
591C22×C4—521no—
592C22×C4—521no—
593C22×C4—521no—
594C22×C4C2×C4×D1311yescharacteristic
595C22×C4C2×C4×D1311yescharacteristic
596C22×C4C2×D5211yescharacteristic
597C22×C4C2×D5211yescharacteristic
598C22×C4D4×D1311yescharacteristic
599C22×C4D4×D1311yescharacteristic
600C22×C4D4×D1311yescharacteristic
601C22×C4#612911yescharacteristic
602C22×C4#612911yescharacteristic
603C22×C4#612911yescharacteristic
604C22×C4#612911yescharacteristic
605C22×C4C2×C22⋊D1311yescharacteristic
606C22×C4C2×C22⋊D1311yescharacteristic
607C22×C4C23×D1311yescharacteristic
608Q16—2616no—
609SD16—2616no—
610M16—22no—
611M16—22no—
612M16—41no—
613M16—41no—
614M16—262no—
615M16—262no—
616M16—262no—
617M16—262no—
618C2×C8—22no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—134no—
622C2×C8—262no—
623C2×C8—262no—
624C4⋊C4—22no—
625C4⋊C4—41no—
626C4⋊C4—2616no—
627C4⋊C4—262no—
628C4⋊C4—262no—
629C4⋊C4—262no—
630C4⋊C4—262no—
631C22⋊C4—22no—
632C22⋊C4—41no—
633C22⋊C4—134no—
634C22⋊C4—262no—
635C22⋊C4—262no—
636C22⋊C4—262no—
637C42—22no—
638C42—41no—
639C42—134no—
640C42—2616no—
641C42—262no—
642C42—262no—
643C42—262no—
644C13C2×#190511yescharacteristic, complemented, Sylow
645C23—42no—
646C23—262no—
647C23—521no—
648C23—521no—
649C23—1042no—
650C23#8813511yescharacteristic
651C23#8813511yescharacteristic
652C23#8813611yescharacteristic
653C23#8813611yescharacteristic
654C23#8819311yescharacteristic
655C23#8819311yescharacteristic
656C23C2×D4×D1311yescharacteristic
657Q8—24no—
658Q8—24no—
659Q8—24no—
660Q8—24no—
661Q8—24no—
662Q8—24no—
663Q8—24no—
664Q8—262no—
665Q8—262no—
666Q8—521no—
667Q8—521no—
668Q8C2×#610318yes—
669D4—262no—
670D4—262no—
671D4—522no—
672D4—522no—
673D4—522no—
674D4—522no—
675D4—521no—
676D4—521no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—42no—
685C2×C4—82no—
686C2×C4—262no—
687C2×C4—264no—
688C2×C4—264no—
689C2×C4—524no—
690C2×C4—524no—
691C2×C4—521no—
692C2×C4—521no—
693C2×C4—522no—
694C2×C4—522no—
695C2×C4—522no—
696C2×C4—522no—
697C2×C4#8813511yescharacteristic
698C2×C4#8813511yescharacteristic
699C2×C4#8813511yescharacteristic
700C2×C4#8813511yescharacteristic
701C2×C4#8813511yescharacteristic
702C2×C4#8813511yescharacteristic
703C2×C4#8813611yescharacteristic
704C2×C4#8813611yescharacteristic
705C2×C4#8814011yescharacteristic
706C2×C4#8814011yescharacteristic
707C2×C4#8814011yescharacteristic
708C2×C4#8814011yescharacteristic
709C2×C4C2×#610311yescharacteristic
710C2×C4C2×#610311yescharacteristic
711C2×C4C2×#610311yescharacteristic
712C2×C4C2×#610311yescharacteristic
713C2×C4#8819311yescharacteristic
714C2×C4#8819311yescharacteristic
715C2×C4#8819311yescharacteristic
716C2×C4#8819311yescharacteristic
717C2×C4#8819311yescharacteristic
718C2×C4#8819311yescharacteristic
719C2×C4C22×C4×D1311yescharacteristic
720C2×C4C22×D5211yescharacteristic
721C2×C4C2×D4×D1311yescharacteristic
722C2×C4C2×#612911yescharacteristic
723C2×C4C2×#612911yescharacteristic
724C2×C4C22×C22⋊D1311yescharacteristic
725C8—42no—
726C8—264no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—522no—
735C22—1042no—
736C22—1042no—
737C22—1042no—
738C22#1171861911yescharacteristic
739C22#1171861911yescharacteristic
740C22#1171861911yescharacteristic
741C22#1171861911yescharacteristic
742C22C2×#8813511yescharacteristic
743C22C2×#8813611yescharacteristic
744C22C2×#8819311yescharacteristic
745C4—28no—
746C4—82no—
747C4—524no—
748C4—524no—
749C4—522no—
750C4#1171861911yescharacteristic
751C4#1171861911yescharacteristic
752C4#1171861911yescharacteristic
753C4#1171861911yescharacteristic
754C4C2×#8813511yescharacteristic
755C4C2×#8814011yescharacteristic
756C4C22×#610311yescharacteristic
757C4C2×#8819311yescharacteristic
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—1042no—
765C2#1311532812yesdirect product factor
766C2C2×#1171861911yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#419C2
socleC22×C13#386
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenterC2×#419D13
hypocenterC13C2×#1905
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
2. C2×#11719517C2semidirect
5. #13115328C2direct (N × H)
6. C2×#11718151C2semidirect
7. C2×#11718123C2semidirect
8. C2×C13×#419C2semidirect
16. #11719517C22semidirect
19. C22×#6107C4semidirect
24. C2×#88196C4semidirect
26. C22×#6106C4semidirect
32. C13×#419C22semidirect
40. #11718151C22semidirect
41. #11718123C22semidirect
96. C2×#6107C2×C4semidirect
103. C2×#6106C2×C4semidirect
265. C2×#419D13semidirect
378. #419C2×D13semidirect
510. C2×C13#1905semidirect
644. C13C2×#1905semidirect
765. C2#13115328direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881962
C2×#117195172
C2×#117188002
C2×#117186672
#131153282
C2×#117181512
C2×#117181232
C2×C13×#4192
C2×#190513