Finite Group Databasebeta

← C2×#13127046 #16739726

Subgroups — C2×#13127046 #16739726

Order 3328.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719255C211yesmaximal, characteristic
2#13127046C2116yesmaximal, direct product factor
3C2×#11718729C211yesmaximal, characteristic, complemented
4C2×#11718629C211yesmaximal, characteristic, complemented
5C2×#11718657C211yesmaximal, characteristic, complemented
6C2×#11718727C211yesmaximal, characteristic, complemented
7C2×#11718713C211yesmaximal, characteristic, complemented
8C2×#11718710C211yesmaximal, characteristic, complemented
9C2×#11718689C211yesmaximal, characteristic, complemented
10C2×#11718708C211yesmaximal, characteristic, complemented
11C2×#11718707C211yesmaximal, characteristic, complemented
12C2×C4×#6106C211yesmaximal, characteristic, complemented
13C2×#11718673C211yesmaximal, characteristic, complemented
14C2×#11718627C211yesmaximal, characteristic, complemented
15C2×#11718662C211yesmaximal, characteristic, complemented
16C2×C13×#552C211yesmaximal, characteristic, complemented
17C22×#6127C2211yescharacteristic
18C23×D52C2211yescharacteristic
19C13×#552—24no—
20C13×#552C2218yescomplemented
21C2×C13×#126—21no—
22C2×C13×#125—21no—
23C2×C13×#125C2211yescharacteristic, complemented
24C2×C13×#123—21no—
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C13×C22⋊Q8C2211yescharacteristic, complemented
27C2×C4×Q8×C13C2211yescharacteristic, complemented
28C2×C4×D4×C13C2211yescharacteristic
29C2×C13×#117—21no—
30C2×C13×#117C2211yescharacteristic
31C22×C13×C4⋊C4C2211yescharacteristic, complemented
32C22×#6107C2211yescharacteristic, complemented
33C22×#6106C2211yescharacteristic
34C22×#6106C2211yescharacteristic
35C2×#88191—21no—
36C2×#88184C2211yescharacteristic
37C2×#88178C2211yescharacteristic
38C22×#6099C2211yescharacteristic
39C22×#6099C2211yescharacteristic, complemented
40#11719255—24no—
41#11719255C2218yes—
42C2×#88148—21no—
43C2×#88138—21no—
44C2×C22⋊C4×D13—21no—
45C2×#88129C2211yescharacteristic
46C2×C4×D52C2211yescharacteristic
47C2×#88075C2211yescharacteristic, complemented
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic, complemented
50#11718729C2218yescomplemented
51#11718727C2218yescomplemented
52#11718713C2218yescomplemented
53#11718710C2218yescomplemented
54#11718708C2218yescomplemented
55#11718707C2218yescomplemented
56#11718689C2218yescomplemented
57C4×#6106C2218yescomplemented
58#11718673C2218yescomplemented
59#11718662C2218yescomplemented
60#11718657C2218yescomplemented
61C2×#88050C2211yescharacteristic, complemented
62C2×#88050C2211yescharacteristic, complemented
63C2×#88050C2211yescharacteristic, complemented
64#11718629C2218yescomplemented
65#11718627C2218yescomplemented
66C2×#88049C2211yescharacteristic
67C2×#88049C2211yescharacteristic
68C2×#88049C2211yescharacteristic
69C2×#88049C2211yescharacteristic
70C2×#88049C2211yescharacteristic
71C2×#88049C2211yescharacteristic
72C2×#88048C2211yescharacteristic, complemented
73C2×#88048C2211yescharacteristic, complemented
74C2×#88047C2211yescharacteristic, complemented
75C2×C4⋊#1055C2211yescharacteristic, complemented
76C2×C4×#1055C2211yescharacteristic, complemented
77C24×D13—21no—
78C22×Q8×C13C2311yescharacteristic
79C22×D4×C13D411yescharacteristic
80C23×C4×C13—21no—
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C22×C22⋊D13—21no—
84C22×C22⋊D13—21no—
85C2×#6127—22no—
86C2×#6127—24no—
87C2×#6127—42no—
88C2×#6127C2314yes—
89C22×D52—24no—
90C22×D52—21no—
91C22×D52—22no—
92C22×D52—42no—
93C22×D52C2311yescharacteristic
94C22×D52C2314yes—
95C22×D52C2311yescharacteristic
96C22×C4×D13—21no—
97C22×C4×D13—21no—
98C22×Dic26C2311yescharacteristic
99C13×#126—28no—
100C13×#125—28no—
101C13×#125—22no—
102C13×#125C2314yescomplemented
103C13×#123—28no—
104C13×C22⋊Q8—22no—
105C13×C22⋊Q8—22no—
106C13×C22⋊Q8C2314yes—
107C13×C22⋊Q8C2314yescomplemented
108C4×Q8×C13—22no—
109C4×Q8×C13C2314yescomplemented
110C4×D4×C13D414yes—
111C4×D4×C13C2314yes—
112C13×#117—22no—
113C13×#117—28no—
114C13×#117C2314yes—
115C2×C13×C4⋊C4—21no—
116C2×C13×C4⋊C4—22no—
117C2×C13×C4⋊C4—21no—
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—21no—
121C2×C13×C4⋊C4—21no—
122C2×C13×C4⋊C4D411yescharacteristic
123C2×C13×C4⋊C4C2311yescharacteristic
124C2×C13×C4⋊C4C2311yescharacteristic
125C2×C13×C4⋊C4C2311yescharacteristic
126C2×C13×C4⋊C4C2314yescomplemented
127C2×C13×C22⋊C4—21no—
128C2×C13×C22⋊C4—21no—
129C2×C13×C22⋊C4—21no—
130C2×C13×C22⋊C4D411yescharacteristic
131C2×C13×C22⋊C4D411yescharacteristic
132C2×C42×C13—21no—
133C2×C42×C13—21no—
134C2×C42×C13C2311yescharacteristic
135C2×C22⋊Dic13—21no—
136C2×#6107—42no—
137C2×#6107C2314yescomplemented
138C2×#6106—24no—
139C2×#6106—42no—
140C2×#6106C2314yes—
141C2×#6106C2314yes—
142#88191—28no—
143#88184—22no—
144#88184C2314yes—
145C2×#6103—21no—
146C2×#6103—21no—
147C2×#6103—21no—
148C2×#6103—21no—
149C2×C4⋊Dic13C2311yescharacteristic
150#88178—22no—
151#88178C2314yes—
152C2×#6101—21no—
153C2×#6099—42no—
154C2×#6099—42no—
155C2×#6099C2314yes—
156C2×#6099C2314yescomplemented
157C22×#1055C2311yescharacteristic
158C22×#1055C2311yescharacteristic
159C22×#1055C2311yescharacteristic
160C22×#1055C2311yescharacteristic
161#88148—28no—
162#88138—28no—
163C22⋊C4×D13—28no—
164#88129—22no—
165#88129C2314yes—
166C4×D52—22no—
167C4×D52C2314yes—
168#88075C2314yescomplemented
169C22⋊#1055C2314yes—
170C22⋊#1055C2314yescomplemented
171#88050C2314yescomplemented
172#88050C2314yescomplemented
173#88050C2314yescomplemented
174#88049C2314yes—
175#88049C2314yes—
176#88049C2314yes—
177#88049C2314yes—
178#88049C2314yes—
179#88049C2314yes—
180#88048C2314yescomplemented
181#88048C2314yescomplemented
182#88047C2314yescomplemented
183C4⋊#1055C2314yescomplemented
184C4×#1055C2314yescomplemented
185C2×#3323—131nomaximal, Sylow
186C24×C13C2×D411yescharacteristic
187C24×C13C2×D411yescharacteristic
188C23×D13—21no—
189C23×D13—21no—
190C23×D13—24no—
191C23×D13—44no—
192C23×D13—44no—
193C23×D13—82no—
194C2×Q8×C13—21no—
195C2×Q8×C13—22no—
196C2×Q8×C13—22no—
197C2×Q8×C13C2412yes—
198C2×D4×C13—42no—
199C2×D4×C13C2×D414yes—
200C22×C4×C13—22no—
201C22×C4×C13—22no—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—24no—
209C22×C4×C13—44no—
210C22×C4×C13C2×D411yescharacteristic
211C22×C4×C13C2×D412yes—
212C22×C4×C13C2×D411yescharacteristic
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13C2×D411yescharacteristic
215C22×C4×C13C2×D412yes—
216C22×C4×C13C2412yes—
217C22×C4×C13C2412yes—
218C22×C4×C13C2411yescharacteristic
219C2×C22⋊D13—24no—
220C2×C22⋊D13—24no—
221C2×C22⋊D13—44no—
222C2×C22⋊D13—82no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225#6127—28no—
226#6127—44no—
227#6127—48no—
228C2×D52—21no—
229C2×D52—22no—
230C2×D52—22no—
231C2×D52—22no—
232C2×D52—28no—
233C2×D52—21no—
234C2×D52—24no—
235C2×D52—44no—
236C2×D52—48no—
237C2×D52—44no—
238C2×D52#4114yes—
239C2×D52C2412yes—
240C2×D52C2412yes—
241C2×C4×D13—24no—
242C2×C4×D13—24no—
243C2×C4×D13—44no—
244C2×C4×D13—82no—
245C2×Dic26—22no—
246C2×Dic26—22no—
247C2×Dic26—21no—
248C2×Dic26C2412yes—
249C13×C4⋊C4—21no—
250C13×C4⋊C4—21no—
251C13×C4⋊C4—24no—
252C13×C4⋊C4—24no—
253C13×C4⋊C4—24no—
254C13×C4⋊C4—24no—
255C13×C4⋊C4—24no—
256C13×C4⋊C4—24no—
257C13×C4⋊C4—21no—
258C13×C4⋊C4C2×D414yes—
259C13×C4⋊C4C2412yes—
260C13×C4⋊C4C2412yes—
261C13×C4⋊C4C2412yes—
262C13×C22⋊C4—24no—
263C13×C22⋊C4—24no—
264C13×C22⋊C4—24no—
265C13×C22⋊C4C2×D414yes—
266C13×C22⋊C4C2×D414yes—
267C42×C13—24no—
268C42×C13—24no—
269C42×C13C2×D412yes—
270C42×C13C2412yes—
271C22⋊Dic13—24no—
272#6107—44no—
273#6106—28no—
274#6106—44no—
275#6103—24no—
276#6103—24no—
277#6103—24no—
278#6103—24no—
279C4⋊Dic13—21no—
280C4⋊Dic13C2412yes—
281#6101—24no—
282#6099—44no—
283#6099—44no—
284C2×#1055—22no—
285C2×#1055—22no—
286C2×#1055—22no—
287C2×#1055—22no—
288C2×#1055C2412yes—
289C2×#1055C2412yes—
290C2×#1055C2412yes—
291C2×#1055C2412yes—
292C2×#552D1311yescharacteristic, complemented
293C2×#546—131no—
294#3323—1316no—
295C2×#488—131no—
296C2×#481—131no—
297C2×#485—131no—
298C2×#478—131no—
299C2×#470—131no—
300C2×#468—131no—
301C2×#464—131no—
302C2×#452—131no—
303C2×#450—131no—
304C2×C4×SD16—131no—
305C2×#436—131no—
306C2×#417—131no—
307C2×#418—131no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13C22×D412yes—
315C23×C13C22×D412yes—
316C23×C13C22×D411yescharacteristic
317C22×D13—24no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—48no—
321C22×D13—42no—
322C22×D13—42no—
323C22×D13—48no—
324C22×D13—42no—
325C22×D13—42no—
326C22×D13—42no—
327C22×D13—84no—
328C22×D13—816no—
329Q8×C13—22no—
330Q8×C13—22no—
331Q8×C13—42no—
332D4×C13—44no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—24no—
338C2×C4×C13—24no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—48no—
348C2×C4×C13—42no—
349C2×C4×C13—42no—
350C2×C4×C13—42no—
351C2×C4×C13—42no—
352C2×C4×C13C22×D412yes—
353C2×C4×C13C22×D412yes—
354C2×C4×C13C22×D412yes—
355C2×C4×C13C22×D412yes—
356C2×C4×C13C22×D411yescharacteristic
357C2×C4×C13C2×#4112yes—
358C2×C4×C13H(5,𝔽2)12yes—
359C2×C4×C13C2511yescharacteristic
360C22⋊D13—48no—
361C22⋊D13—84no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—42no—
365C2×Dic13—42no—
366D52—24no—
367D52—22no—
368D52—22no—
369D52—22no—
370D52—48no—
371D52—42no—
372D52C2×#4114yes—
373C4×D13—48no—
374C4×D13—84no—
375Dic26—22no—
376Dic26—22no—
377Dic26—42no—
378#1055—22no—
379#1055—22no—
380#1055—22no—
381#1055—22no—
382C22×#41—131no—
383C23×D4—131no—
384C22×Q16—131no—
385C22×SD16—131no—
386C22×SD16—131no—
387C22×M16—131no—
388C22×M16—131no—
389#552—24no—
390#552C2×D1318yescomplemented
391#546—138no—
392#546—264no—
393C2×#126—21no—
394C2×#125—21no—
395C2×#125C2×D1311yescharacteristic, complemented
396C2×#124—131no—
397C2×#123—21no—
398C2×#123—261no—
399C2×C22⋊Q8—131no—
400C2×C22⋊Q8C2×D1311yescharacteristic
401C2×C22⋊Q8C2×D1311yescharacteristic, complemented
402C2×#121—131no—
403C2×#121—261no—
404C2×#120—261no—
405C2×C4×Q8C2×D1311yescharacteristic, complemented
406C2×C4×D4—131no—
407C2×C4×D4C2×D1311yescharacteristic
408C2×#117—21no—
409C2×#117C2×D1311yescharacteristic
410C22×C4⋊C4C2×D1311yescharacteristic, complemented
411C22×C22⋊C4—261no—
412#488—138no—
413#485—138no—
414#481—138no—
415#478—138no—
416#470—138no—
417#468—138no—
418#464—138no—
419#452—138no—
420#450—138no—
421C4×SD16—138no—
422#436—138no—
423C2×#107—131no—
424C2×#106—131no—
425C2×#106—131no—
426C2×C4⋊C8—131no—
427#418—138no—
428#417—138no—
429C2×#103—131no—
430C2×#103—131no—
431C2×#103—131no—
432C2×#103—131no—
433C2×#102—131no—
434C2×#102—131no—
435C2×#102—131no—
436C2×#102—131no—
437C2×#102—131no—
438C2×#102—131no—
439C2×C22⋊C8—131no—
440C2×C22⋊C8—131no—
441C2×C4×C8—131no—
442C22×C13—22no—
443C22×C13—22no—
444C22×C13—22no—
445C22×C13—22no—
446C22×C13—22no—
447C22×C13—22no—
448C22×C13—44no—
449C22×C13—44no—
450C22×C13#54612yes—
451C22×C13#57512yes—
452C22×C13#57712yes—
453C22×C13C23×D411yescharacteristic
454C2×D13—24no—
455C2×D13—48no—
456C2×D13—42no—
457C2×D13—42no—
458C2×D13—42no—
459C2×D13—42no—
460C2×D13—42no—
461C2×D13—816no—
462C2×D13—84no—
463C4×C13—22no—
464C4×C13—22no—
465C4×C13—22no—
466C4×C13—22no—
467C4×C13—42no—
468C4×C13—42no—
469C4×C13—42no—
470C4×C13—42no—
471C4×C13#54612yes—
472C4×C13C22×#4111yescharacteristic
473C4×C13C2×H(5,𝔽2)11yescharacteristic
474Dic13—42no—
475Dic13—42no—
476C25—261no—
477C2×#41—134no—
478C2×#41—264no—
479C2×#41—262no—
480C2×#41—522no—
481C22×Q8—131no—
482C22×Q8C22×D1311yescharacteristic
483C22×D4—131no—
484C22×D4—131no—
485C22×D4—134no—
486C22×D4—264no—
487C22×D4—261no—
488C22×D4—261no—
489C22×D4—261no—
490C22×D4—262no—
491C22×D4—522no—
492C22×D4C22⋊D1311yescharacteristic
493C23×C4—21no—
494C23×C4—261no—
495C23×C4—261no—
496C23×C4C22×D1311yescharacteristic
497C23×C4C22×D1311yescharacteristic
498C2×Q16—134no—
499C2×Q16—522no—
500C2×SD16—134no—
501C2×SD16—134no—
502C2×SD16—264no—
503C2×SD16—522no—
504C2×M16—134no—
505C2×M16—134no—
506C2×M16—522no—
507C2×M16—522no—
508C22×C8—131no—
509C22×C8—131no—
510C22×C8—131no—
511C22×C8—131no—
512#126—28no—
513#125—28no—
514#125—22no—
515#125C22×D1314yescomplemented
516#124—134no—
517#124—262no—
518#123—28no—
519#123—268no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522C22⋊Q8—134no—
523C22⋊Q8—262no—
524C22⋊Q8C22×D1314yes—
525C22⋊Q8C22×D1314yescomplemented
526#121—134no—
527#121—262no—
528#121—268no—
529#120—268no—
530C4×Q8—22no—
531C4×Q8C22×D1314yescomplemented
532C4×D4—134no—
533C4×D4—262no—
534C4×D4C22⋊D1314yes—
535C4×D4C22×D1314yes—
536#117—22no—
537#117—28no—
538#117C22×D1314yes—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—131no—
547C2×C4⋊C4—261no—
548C2×C4⋊C4C22⋊D1311yescharacteristic
549C2×C4⋊C4C22×D1311yescharacteristic
550C2×C4⋊C4C22×D1311yescharacteristic
551C2×C4⋊C4C22×D1311yescharacteristic
552C2×C4⋊C4C22×D1314yescomplemented
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—261no—
557C2×C22⋊C4—261no—
558C2×C22⋊C4—261no—
559C2×C22⋊C4—261no—
560C2×C22⋊C4—261no—
561C2×C22⋊C4—268no—
562C2×C22⋊C4C22⋊D1311yescharacteristic
563C2×C22⋊C4C22⋊D1311yescharacteristic
564C2×C42—21no—
565C2×C42—21no—
566C2×C42C22×D1311yescharacteristic
567#107—134no—
568#106—134no—
569#106—134no—
570C4⋊C8—134no—
571#103—134no—
572#103—134no—
573#103—134no—
574#103—134no—
575#102—134no—
576#102—134no—
577#102—134no—
578#102—134no—
579#102—134no—
580#102—134no—
581C22⋊C8—134no—
582C22⋊C8—134no—
583C4×C8—134no—
584C2×C13—42no—
585C2×C13—42no—
586C2×C13#332314yescomplemented
587C2×C13C2×#54611yescharacteristic
588C2×C13C2×#57511yescharacteristic
589C2×C13C2×#57711yescharacteristic
590D13—44no—
591D13—82no—
592C24—261no—
593C24—261no—
594C24—264no—
595C24—524no—
596C24—524no—
597C24—1042no—
598C24C2×C22⋊D1311yescharacteristic
599C24C2×C22⋊D1311yescharacteristic
600#41—268no—
601#41—524no—
602#41—528no—
603C2×Q8—21no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—132no—
607C2×Q8—261no—
608C2×Q8—262no—
609C2×Q8—262no—
610C2×Q8C23×D1312yes—
611C2×D4—42no—
612C2×D4—134no—
613C2×D4—132no—
614C2×D4—132no—
615C2×D4—268no—
616C2×D4—264no—
617C2×D4—264no—
618C2×D4—262no—
619C2×D4—262no—
620C2×D4—262no—
621C2×D4—261no—
622C2×D4—264no—
623C2×D4—261no—
624C2×D4—524no—
625C2×D4—528no—
626C2×D4—524no—
627C2×D4—524no—
628C2×D4—1042no—
629C2×D4C2×C22⋊D1314yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—44no—
640C22×C4—261no—
641C22×C4—261no—
642C22×C4—264no—
643C22×C4—264no—
644C22×C4—524no—
645C22×C4—1042no—
646C22×C4C2×C22⋊D1312yes—
647C22×C4C2×C22⋊D1312yes—
648C22×C4C2×C22⋊D1311yescharacteristic
649C22×C4C2×C22⋊D1311yescharacteristic
650C22×C4C2×C22⋊D1311yescharacteristic
651C22×C4C2×C22⋊D1311yescharacteristic
652C22×C4C23×D1312yes—
653C22×C4C23×D1312yes—
654C22×C4C23×D1311yescharacteristic
655Q16—524no—
656SD16—268no—
657SD16—524no—
658M16—524no—
659M16—524no—
660C2×C8—132no—
661C2×C8—132no—
662C2×C8—132no—
663C2×C8—132no—
664C2×C8—262no—
665C2×C8—262no—
666C2×C8—262no—
667C2×C8—262no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—21no—
677C4⋊C4—132no—
678C4⋊C4—261no—
679C4⋊C4—264no—
680C4⋊C4C2×C22⋊D1314yes—
681C4⋊C4C23×D1312yes—
682C4⋊C4C23×D1312yes—
683C4⋊C4C23×D1312yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—264no—
688C22⋊C4—264no—
689C22⋊C4—264no—
690C22⋊C4—264no—
691C22⋊C4—264no—
692C22⋊C4C2×C22⋊D1314yes—
693C22⋊C4C2×C22⋊D1314yes—
694C42—24no—
695C42—24no—
696C42C2×C22⋊D1312yes—
697C42C23×D1312yes—
698C13C2×#332311yescharacteristic, complemented, Sylow
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—264no—
706C23—262no—
707C23—262no—
708C23—528no—
709C23—528no—
710C23—522no—
711C23—522no—
712C23—522no—
713C23—522no—
714C23—522no—
715C23—1044no—
716C23—10416no—
717C23C22×C22⋊D1312yes—
718C23C22×C22⋊D1312yes—
719C23C22×C22⋊D1311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—262no—
724Q8—262no—
725Q8—522no—
726D4—44no—
727D4—134no—
728D4—264no—
729D4—262no—
730D4—262no—
731D4—262no—
732D4—528no—
733D4—528no—
734D4—522no—
735D4—1044no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—262no—
756C2×C4—262no—
757C2×C4—528no—
758C2×C4—522no—
759C2×C4—522no—
760C2×C4—1044no—
761C2×C4#41×D1312yes—
762C2×C4#8825612yes—
763C2×C4C22×C22⋊D1312yes—
764C2×C4C22×C22⋊D1312yes—
765C2×C4C22×C22⋊D1312yes—
766C2×C4C22×C22⋊D1312yes—
767C2×C4C22×C22⋊D1311yescharacteristic
768C2×C4C24×D1311yescharacteristic
769C8—262no—
770C8—262no—
771C8—262no—
772C8—262no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—44no—
780C22—44no—
781C22—264no—
782C22—522no—
783C22—522no—
784C22—528no—
785C22—522no—
786C22—522no—
787C22—522no—
788C22—10416no—
789C22—1044no—
790C22#1171952712yes—
791C22#1171953412yes—
792C22#1171954212yes—
793C22C23×C22⋊D1311yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—522no—
803C4—522no—
804C4#1171953412yes—
805C4C2×#41×D1311yescharacteristic
806C4C2×#8825611yescharacteristic
807C2—42no—
808C2—42no—
809C2—524no—
810C2—1042no—
811C2#1312704614yesdirect product factor
812C2C2×#1171953411yescharacteristic
813C2C2×#1171952711yescharacteristic
814C2C2×#1171954211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#552C2
socleC23×C13C22×D4
prime radicalC2×#11719255C2
hypercenterC2×#552D13
hypocenterC13C2×#3323
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #13127046C2direct (N × H)
3. C2×#11718729C2semidirect
4. C2×#11718629C2semidirect
5. C2×#11718657C2semidirect
6. C2×#11718727C2semidirect
7. C2×#11718713C2semidirect
8. C2×#11718710C2semidirect
9. C2×#11718689C2semidirect
10. C2×#11718708C2semidirect
11. C2×#11718707C2semidirect
12. C2×C4×#6106C2semidirect
13. C2×#11718673C2semidirect
14. C2×#11718627C2semidirect
15. C2×#11718662C2semidirect
16. C2×C13×#552C2semidirect
20. C13×#552C22semidirect
23. C2×C13×#125C22semidirect
26. C2×C13×C22⋊Q8C22semidirect
27. C2×C4×Q8×C13C22semidirect
31. C22×C13×C4⋊C4C22semidirect
32. C22×#6107C22semidirect
39. C22×#6099C22semidirect
47. C2×#88075C22semidirect
49. C2×C22⋊#1055C22semidirect
50. #11718729C22semidirect
51. #11718727C22semidirect
52. #11718713C22semidirect
53. #11718710C22semidirect
54. #11718708C22semidirect
55. #11718707C22semidirect
56. #11718689C22semidirect
57. C4×#6106C22semidirect
58. #11718673C22semidirect
59. #11718662C22semidirect
60. #11718657C22semidirect
61. C2×#88050C22semidirect
62. C2×#88050C22semidirect
63. C2×#88050C22semidirect
64. #11718629C22semidirect
65. #11718627C22semidirect
72. C2×#88048C22semidirect
73. C2×#88048C22semidirect
74. C2×#88047C22semidirect
75. C2×C4⋊#1055C22semidirect
76. C2×C4×#1055C22semidirect
102. C13×#125C23semidirect
107. C13×C22⋊Q8C23semidirect
109. C4×Q8×C13C23semidirect
126. C2×C13×C4⋊C4C23semidirect
137. C2×#6107C23semidirect
156. C2×#6099C23semidirect
168. #88075C23semidirect
170. C22⋊#1055C23semidirect
171. #88050C23semidirect
172. #88050C23semidirect
173. #88050C23semidirect
180. #88048C23semidirect
181. #88048C23semidirect
182. #88047C23semidirect
183. C4⋊#1055C23semidirect
184. C4×#1055C23semidirect
292. C2×#552D13semidirect
390. #552C2×D13semidirect
395. C2×#125C2×D13semidirect
401. C2×C22⋊Q8C2×D13semidirect
405. C2×C4×Q8C2×D13semidirect
410. C22×C4⋊C4C2×D13semidirect
515. #125C22×D13semidirect
525. C22⋊Q8C22×D13semidirect
531. C4×Q8C22×D13semidirect
552. C2×C4⋊C4C22×D13semidirect
586. C2×C13#3323semidirect
698. C13C2×#3323semidirect
811. C2#13127046direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192552
#131270462
C2×#117187292
C2×#117186292
C2×#117186572
C2×#117187272
C2×#117187132
C2×#117187102
C2×#117186892
C2×#117187082
C2×#117187072
C2×C4×#61062
C2×#117186732
C2×#117186272
C2×#117186622
C2×C13×#5522
C2×#332313