Finite Group Databasebeta

← C2×#13128325 #16769880

Subgroups — C2×#13128325 #16769880

Order 3328.

12314 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#6131C211yesmaximal, characteristic, complemented
2C22×#41×D13C211yesmaximal, characteristic, complemented
3#13128325C2132yesmaximal, direct product factor
4C2×#11719539C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D13C211yesmaximal, characteristic, complemented
6C2×#11719281C211yesmaximal, characteristic, complemented
7C2×#11719336C213yesmaximal, complemented
8C2×#11719255C213yesmaximal, complemented
9C2×#11719381C213yesmaximal, complemented
10C2×#11719314C213yesmaximal, complemented
11C2×#11719373C213yesmaximal, complemented
12C2×#11719332C213yesmaximal, complemented
13C2×#11719311C213yesmaximal, complemented
14C2×C4×#6131C211yesmaximal, characteristic, complemented
15C2×C4×D4×D13C213yesmaximal, complemented
16C2×C13×#548C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic, complemented
18C23×Q8×C13C2211yescharacteristic, complemented
19C2×#41×D13—216no—
20C2×#41×D13C22116yescomplemented
21C22×#6131—216no—
22C22×#6131C2211yescharacteristic
23C22×#6131C2213yescomplemented
24C22×#6131C2211yescharacteristic, complemented
25C22×#6131C2213yescomplemented
26C22×#6131C22116yescomplemented
27C22×Q8×D13C2211yescharacteristic, complemented
28C22×#6129C2213yescomplemented
29C22×D4×D13C2213yes—
30C22×D4×D13C2213yescomplemented
31C22×#6127C2213yescomplemented
32C23×D52C2213yescomplemented
33C23×C4×D13C2213yescomplemented
34C23×C4×D13C2213yescomplemented
35C13×#548C22116yescomplemented
36C2×C13×#124C2213yescomplemented
37C2×C13×C22⋊Q8C2213yescomplemented
38C2×C13×#121C2213yescomplemented
39C2×C4×Q8×C13C2211yescharacteristic, complemented
40C2×C4×D4×C13C2213yescomplemented
41#11719539C22116yescomplemented
42Q8×C22⋊D13C22116yescomplemented
43C2×#88200C2213yescomplemented
44C2×Q8×Dic13C2211yescharacteristic, complemented
45C2×#88198C2213yescomplemented
46C2×#88194C2213yescomplemented
47C2×#88192C2213yescomplemented
48C2×#88191C2216yescomplemented
49C2×D4×Dic13C2213yescomplemented
50C2×#88184C2213yescomplemented
51C2×C4×C22⋊D13C2213yes—
52C2×C4×C22⋊D13C2213yescomplemented
53C2×#88178C2213yescomplemented
54#11719381C22148yescomplemented
55#11719373C22148yescomplemented
56#11719336C22148yescomplemented
57#11719332C22148yescomplemented
58#11719314C22148yescomplemented
59#11719311C22148yescomplemented
60#11719281C22116yescomplemented
61C4×#6131C22116yescomplemented
62#11719255C22148yescomplemented
63C4×D4×D13C22148yescomplemented
64C2×#88151C2213yescomplemented
65C2×#88149C2213yescomplemented
66C2×#88148C2216yescomplemented
67C2×#88147C2213yescomplemented
68C2×#88147C2213yescomplemented
69C2×#88146C2213yescomplemented
70C2×C4⋊C4×D13C2213yescomplemented
71C2×#88138C2216yescomplemented
72C2×#88138C2216yescomplemented
73C2×#88137C2216yescomplemented
74C2×#88136C2216yescomplemented
75C2×#88135C2211yescharacteristic
76C2×#88135C2213yescomplemented
77C2×#88135C2216yescomplemented
78C2×C22⋊C4×D13C2213yescomplemented
79C2×C22⋊C4×D13C2213yescomplemented
80C2×#88129C2213yescomplemented
81C2×C4×D52C2213yescomplemented
82C2×C4×D52C2213yescomplemented
83C2×C42×D13C2213yescomplemented
84C24×D13C2313yes—
85C24×D13C2313yes—
86C2×C13×#41—28no—
87C2×C13×#41C2318yescomplemented
88C22×Q8×C13—28no—
89C22×Q8×C13C2313yes—
90C22×Q8×C13C2311yescharacteristic
91C22×Q8×C13C2318yescomplemented
92C22×D4×C13C2313yes—
93C22×D4×C13C2313yes—
94C23×C4×C13C2313yes—
95C23×C4×C13C2313yes—
96C22×C22⋊D13C2313yes—
97C22×C22⋊D13C2316yes—
98C22×C22⋊D13C2316yes—
99C22×C22⋊D13C2311yescharacteristic
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2313yes—
102#41×D13—2128no—
103C2×#6131—28no—
104C2×#6131—2128no—
105C2×#6131—224no—
106C2×#6131—224no—
107C2×#6131D4116yescomplemented
108C2×#6131C2318yes—
109C2×#6131C2318yescomplemented
110C2×#6131C23124yescomplemented
111C2×#6131C23124yescomplemented
112C2×Q8×D13—28no—
113C2×Q8×D13C2318yescomplemented
114C2×#6129—224no—
115C2×#6129C23124yescomplemented
116C2×D4×D13—224no—
117C2×D4×D13—224no—
118C2×D4×D13C23124yes—
119C2×D4×D13C23124yescomplemented
120C2×#6127—224no—
121C2×#6127C23124yescomplemented
122C22×D52—224no—
123C22×D52C2313yes—
124C22×D52C2313yes—
125C22×D52C2316yes—
126C22×D52C2313yes—
127C22×D52C23124yescomplemented
128C22×C4×D13—224no—
129C22×C4×D13—224no—
130C22×C4×D13C2313yes—
131C22×C4×D13C2313yes—
132C22×C4×D13C2313yes—
133C22×C4×D13C2313yes—
134C22×C4×D13C2313yes—
135C22×C4×D13C2311yescharacteristic
136C22×C4×D13C2313yes—
137C22×C4×D13C2313yes—
138C22×C4×D13C2313yes—
139C22×C4×D13C23124yescomplemented
140C22×C4×D13C23124yescomplemented
141C22×Dic26C2313yes—
142C13×#124C23124yescomplemented
143C13×C22⋊Q8C23124yescomplemented
144C13×#121C23124yescomplemented
145C4×Q8×C13C2318yescomplemented
146C4×D4×C13C23124yescomplemented
147C2×C13×C4⋊C4C2313yes—
148C2×C13×C4⋊C4C2313yes—
149C2×C13×C22⋊C4C2311yescharacteristic
150C2×C13×C22⋊C4C2313yes—
151C2×C13×C22⋊C4C2316yes—
152C2×C42×C13C2313yes—
153C2×C22⋊Dic13C2313yes—
154C2×C22⋊Dic13C2313yes—
155#88200C23124yescomplemented
156Q8×Dic13C2318yescomplemented
157#88198C23124yescomplemented
158#88194C23124yescomplemented
159#88192C23124yescomplemented
160#88191C23148yescomplemented
161D4×Dic13C23124yescomplemented
162#88184C23124yescomplemented
163C4×C22⋊D13C23124yes—
164C4×C22⋊D13C23124yescomplemented
165C2×#6103C2311yescharacteristic
166C2×#6103C2313yes—
167C2×#6103C2316yes—
168C2×#6103C2316yes—
169C2×#6103C2313yes—
170C2×#6103C2313yes—
171C2×C4⋊Dic13C2313yes—
172C2×C4⋊Dic13C2313yes—
173#88178C23124yescomplemented
174C2×#6101C2311yescharacteristic
175C2×#6101C2316yes—
176C2×#6101C2313yes—
177C2×C4×Dic13C2311yescharacteristic
178C2×C4×Dic13C2313yes—
179C2×C4×Dic13C2313yes—
180#88151C23124yescomplemented
181#88149C23124yescomplemented
182#88148C23148yescomplemented
183#88147C23124yescomplemented
184#88147C23124yescomplemented
185#88146C23124yescomplemented
186C4⋊C4×D13C23124yescomplemented
187#88138C23148yescomplemented
188#88138C23148yescomplemented
189#88137C23148yescomplemented
190#88136C23148yescomplemented
191#88135C2318yes—
192#88135C23124yescomplemented
193#88135C23148yescomplemented
194C22⋊C4×D13C23124yescomplemented
195C22⋊C4×D13C23124yescomplemented
196#88129C23124yescomplemented
197C4×D52C23124yescomplemented
198C4×D52C23124yescomplemented
199C42×D13C23124yescomplemented
200C2×D4×#41—131nomaximal, Sylow
201C24×C13C2413yes—
202C24×C13C2411yescharacteristic
203C23×D13—212no—
204C23×D13—212no—
205C23×D13—212no—
206C23×D13—212no—
207C23×D13—46no—
208C23×D13—46no—
209C23×D13C2413yes—
210C23×D13C24112yes—
211C23×D13C24112yes—
212C23×D13C2413yes—
213C23×D13C2411yescharacteristic
214C13×#41—232no—
215C2×Q8×C13—232no—
216C2×Q8×C13—212no—
217C2×Q8×C13C2×D418yescomplemented
218C2×Q8×C13C24112yes—
219C2×Q8×C13C2414yes—
220C2×D4×C13—212no—
221C2×D4×C13—212no—
222C2×D4×C13C24112yes—
223C2×D4×C13C24112yes—
224C22×C4×C13—212no—
225C22×C4×C13—212no—
226C22×C4×C13C2413yes—
227C22×C4×C13C2411yescharacteristic
228C22×C4×C13C2413yes—
229C22×C4×C13C2411yescharacteristic
230C22×C4×C13C24112yes—
231C22×C4×C13C24112yes—
232C22×C4×C13C2413yes—
233C2×C22⋊D13—224no—
234C2×C22⋊D13—212no—
235C2×C22⋊D13—412no—
236C2×C22⋊D13#4118yescomplemented
237C2×C22⋊D13C24112yes—
238C2×C22⋊D13C24124yes—
239C2×C22⋊D13C24124yes—
240C2×C22⋊D13C2414yes—
241C22×Dic13—24no—
242C22×Dic13—212no—
243C22×Dic13C2414yes—
244C22×Dic13C24112yes—
245C22×Dic13C2413yes—
246C22×Dic13C2413yes—
247C22×Dic13C2411yescharacteristic
248C22×Dic13C2411yescharacteristic
249C22×Dic13C2411yescharacteristic
250#6131—232no—
251#6131—296no—
252#6131—296no—
253#6131C2×D4164yescomplemented
254Q8×D13—232no—
255#6129—296no—
256D4×D13—296no—
257D4×D13—296no—
258#6127—296no—
259C2×D52—224no—
260C2×D52—212no—
261C2×D52—212no—
262C2×D52—296no—
263C2×D52C2×D4124yescomplemented
264C2×D52C24112yes—
265C2×D52C24112yes—
266C2×D52C24124yes—
267C2×D52C24112yes—
268C2×C4×D13—212no—
269C2×C4×D13—212no—
270C2×C4×D13—212no—
271C2×C4×D13—212no—
272C2×C4×D13—24no—
273C2×C4×D13—212no—
274C2×C4×D13—212no—
275C2×C4×D13—296no—
276C2×C4×D13—296no—
277C2×C4×D13—46no—
278C2×C4×D13C2×D4124yescomplemented
279C2×C4×D13C24112yes—
280C2×C4×D13C24112yes—
281C2×C4×D13C24112yes—
282C2×C4×D13C24112yes—
283C2×C4×D13C24112yes—
284C2×C4×D13C2414yes—
285C2×C4×D13C24112yes—
286C2×C4×D13C24112yes—
287C2×C4×D13C24112yes—
288C2×Dic26—212no—
289C2×Dic26C24112yes—
290C13×C4⋊C4C24112yes—
291C13×C4⋊C4C24112yes—
292C13×C22⋊C4C2414yes—
293C13×C22⋊C4C24112yes—
294C13×C22⋊C4C24124yes—
295C42×C13C24112yes—
296C22⋊Dic13C24112yes—
297C22⋊Dic13C24112yes—
298#6103C2414yes—
299#6103C24112yes—
300#6103C24124yes—
301#6103C24124yes—
302#6103C24112yes—
303#6103C24112yes—
304C4⋊Dic13C24112yes—
305C4⋊Dic13C24112yes—
306#6101C2414yes—
307#6101C24124yes—
308#6101C24112yes—
309C4×Dic13C2414yes—
310C4×Dic13C24112yes—
311C4×Dic13C24112yes—
312C23×#41—131no—
313C23×#41—131no—
314D4×#41—1332no—
315C2×#550—131no—
316C2×D4×Q8—131no—
317C2×#548—131no—
318C2×#548D1311yescharacteristic, complemented
319C2×#547—133no—
320C2×#546—133no—
321C2×#546—133no—
322C2×D42—133no—
323C2×#532—133no—
324C2×#525—133no—
325C2×#525—133no—
326C2×C4×#41—131no—
327C22×C4×D4—133no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—26no—
331C23×C13—26no—
332C23×C13—26no—
333C23×C13C2×#4114yescomplemented
334C23×C13C2516yes—
335C23×C13C2512yes—
336C23×C13C2511yescharacteristic
337C22×D13—22no—
338C22×D13—26no—
339C22×D13—26no—
340C22×D13—22no—
341C22×D13—26no—
342C22×D13—26no—
343C22×D13—224no—
344C22×D13—26no—
345C22×D13—224no—
346C22×D13—224no—
347C22×D13—224no—
348C22×D13—412no—
349C22×D13—412no—
350C22×D13—448no—
351C22×D13—448no—
352C22×D13C22×D4112yes—
353C22×D13C2×#4114yescomplemented
354C22×D13C2516yes—
355C22×D13C2516yes—
356C22×D13C2512yes—
357Q8×C13—224no—
358Q8×C13C22×D4116yescomplemented
359D4×C13—224no—
360D4×C13—224no—
361C2×C4×C13—22no—
362C2×C4×C13—26no—
363C2×C4×C13—26no—
364C2×C4×C13—22no—
365C2×C4×C13—224no—
366C2×C4×C13—224no—
367C2×C4×C13C22×D4112yes—
368C2×C4×C13C2516yes—
369C2×C4×C13C2512yes—
370C2×C4×C13C2516yes—
371C2×C4×C13C2512yes—
372C2×C4×C13C2516yes—
373C22⋊D13—248no—
374C22⋊D13—224no—
375C22⋊D13—424no—
376C22⋊D13C2×#41116yescomplemented
377C2×Dic13—26no—
378C2×Dic13—22no—
379C2×Dic13—26no—
380C2×Dic13—28no—
381C2×Dic13—224no—
382C2×Dic13C22×D414yes—
383C2×Dic13C2×#4114yescomplemented
384C2×Dic13C2516yes—
385C2×Dic13C2516yes—
386C2×Dic13C2512yes—
387C2×Dic13C2512yes—
388C2×Dic13C2512yes—
389D52—248no—
390D52—224no—
391D52—224no—
392D52C22×D4148yescomplemented
393C4×D13—224no—
394C4×D13—224no—
395C4×D13—224no—
396C4×D13—224no—
397C4×D13—28no—
398C4×D13—224no—
399C4×D13—224no—
400C4×D13—412no—
401C4×D13C22×D4148yescomplemented
402Dic26—224no—
403C22×#41—1316no—
404C22×#41—131no—
405C22×#41—133no—
406C22×#41—133no—
407C22×#41—131no—
408C22×#41—1316no—
409C22×#41—133no—
410C22×#41—133no—
411C22×#41—2616no—
412C22×#41—2616no—
413C22×#41C2×D1311yescharacteristic, complemented
414C23×Q8—131no—
415C23×Q8C2×D1311yescharacteristic, complemented
416C23×D4—133no—
417C23×D4—133no—
418C23×D4—133no—
419C24×C4—133no—
420C24×C4—133no—
421#550—1316no—
422D4×Q8—1316no—
423#548—1316no—
424#548C2×D13116yescomplemented
425#547—1348no—
426#546—1348no—
427#546—1348no—
428D42—1348no—
429#532—1348no—
430C2×C4⋊Q8—133no—
431C2×#127—133no—
432C2×#124—133no—
433C2×#124C2×D1313yescomplemented
434#525—1348no—
435#525—1348no—
436C2×#123—136no—
437C2×#123—136no—
438C2×C22⋊Q8—133no—
439C2×C22⋊Q8—133no—
440C2×C22⋊Q8—133no—
441C2×C22⋊Q8C2×D1313yescomplemented
442C2×#121—133no—
443C2×#121—133no—
444C2×#121—133no—
445C2×#121—136no—
446C2×#121—136no—
447C2×#121C2×D1313yescomplemented
448C2×#120—136no—
449C2×#120—136no—
450C4×#41—1316no—
451C2×C4×Q8—131no—
452C2×C4×Q8C2×D1311yescharacteristic, complemented
453C2×C4×D4—133no—
454C2×C4×D4—133no—
455C2×C4×D4—133no—
456C2×C4×D4—1348no—
457C2×C4×D4—133no—
458C2×C4×D4—133no—
459C2×C4×D4—131no—
460C2×C4×D4—133no—
461C2×C4×D4—136no—
462C2×C4×D4—133no—
463C2×C4×D4—133no—
464C2×C4×D4C2×D1313yescomplemented
465C2×#117—133no—
466C22×C4⋊C4—133no—
467C22×C22⋊C4—133no—
468C22×C22⋊C4—133no—
469C22×C42—133no—
470C22×C13—22no—
471C22×C13—22no—
472C22×C13—28no—
473C22×C13—26no—
474C22×C13—26no—
475C22×C13—26no—
476C22×C13—412no—
477C22×C13C23×D412yes—
478C22×C13C22×#4112yes—
479C22×C13C22×#4114yescomplemented
480C22×C13#58512yes—
481C22×C13C2611yescharacteristic
482C2×D13—22no—
483C2×D13—26no—
484C2×D13—26no—
485C2×D13—22no—
486C2×D13—28no—
487C2×D13—224no—
488C2×D13—26no—
489C2×D13—26no—
490C2×D13—26no—
491C2×D13—448no—
492C2×D13—448no—
493C2×D13—412no—
494C2×D13C23×D4112yes—
495C2×D13C22×#4114yescomplemented
496C4×C13—22no—
497C4×C13—26no—
498C4×C13—26no—
499C4×C13—22no—
500C4×C13C23×D4112yes—
501Dic13—26no—
502Dic13—22no—
503Dic13—26no—
504Dic13C23×D414yes—
505Dic13C22×#4114yescomplemented
506C25—133no—
507C25—133no—
508C2×#41—28no—
509C2×#41—1316no—
510C2×#41—138no—
511C2×#41—1324no—
512C2×#41—1324no—
513C2×#41—138no—
514C2×#41—1324no—
515C2×#41—1324no—
516C2×#41—2624no—
517C2×#41—2624no—
518C2×#41—2624no—
519C2×#41—2624no—
520C2×#41—26128no—
521C2×#41—26128no—
522C2×#41—268no—
523C2×#41C22×D1318yescomplemented
524C22×Q8—28no—
525C22×Q8—138no—
526C22×Q8—133no—
527C22×Q8—268no—
528C22×Q8C22×D1313yes—
529C22×Q8C22×D1311yescharacteristic
530C22×Q8C22×D1318yescomplemented
531C22×D4—131no—
532C22×D4—133no—
533C22×D4—136no—
534C22×D4—136no—
535C22×D4—1324no—
536C22×D4—1324no—
537C22×D4—133no—
538C22×D4—133no—
539C22×D4—136no—
540C22×D4—133no—
541C22×D4—1324no—
542C22×D4—2624no—
543C22×D4—2624no—
544C22×D4—2624no—
545C22×D4C22×D1313yes—
546C22×D4C22×D1313yes—
547C23×C4—133no—
548C23×C4—131no—
549C23×C4—133no—
550C23×C4—133no—
551C23×C4—133no—
552C23×C4—133no—
553C23×C4—131no—
554C23×C4—133no—
555C23×C4—133no—
556C23×C4—133no—
557C23×C4—1324no—
558C23×C4—1324no—
559C23×C4—133no—
560C23×C4—2624no—
561C23×C4—2624no—
562C23×C4C22×D1313yes—
563C23×C4C22×D1313yes—
564C4⋊Q8—1324no—
565#127—1324no—
566#124—1324no—
567#124C22×D13124yescomplemented
568#123—1348no—
569#123—1348no—
570C22⋊Q8—1324no—
571C22⋊Q8—1324no—
572C22⋊Q8—1324no—
573C22⋊Q8C22×D13124yescomplemented
574#121—1324no—
575#121—1324no—
576#121—1324no—
577#121—1348no—
578#121—1348no—
579#121C22×D13124yescomplemented
580#120—1348no—
581#120—1348no—
582C4×Q8—138no—
583C4×Q8C22×D1318yescomplemented
584C4×D4—1324no—
585C4×D4—1324no—
586C4×D4—1324no—
587C4×D4—1324no—
588C4×D4—1324no—
589C4×D4—138no—
590C4×D4—1324no—
591C4×D4—1348no—
592C4×D4—1324no—
593C4×D4—1324no—
594C4×D4C22×D13124yescomplemented
595#117—1324no—
596C2×C4⋊C4—131no—
597C2×C4⋊C4—133no—
598C2×C4⋊C4—133no—
599C2×C4⋊C4—133no—
600C2×C4⋊C4—136no—
601C2×C4⋊C4—1324no—
602C2×C4⋊C4C22×D1313yes—
603C2×C4⋊C4C22×D1313yes—
604C2×C22⋊C4—133no—
605C2×C22⋊C4—133no—
606C2×C22⋊C4—131no—
607C2×C22⋊C4—133no—
608C2×C22⋊C4—133no—
609C2×C22⋊C4—133no—
610C2×C22⋊C4—136no—
611C2×C22⋊C4—136no—
612C2×C22⋊C4—1324no—
613C2×C22⋊C4—1324no—
614C2×C22⋊C4C22×D1311yescharacteristic
615C2×C22⋊C4C22×D1313yes—
616C2×C22⋊C4C22×D1316yes—
617C2×C42—133no—
618C2×C42—131no—
619C2×C42—133no—
620C2×C42—1324no—
621C2×C42C22×D1313yes—
622C2×C13—24no—
623C2×C13—46no—
624C2×C13D4×#4114yescomplemented
625C2×C13C24×D411yescharacteristic
626C2×C13C23×#4111yescharacteristic
627C2×C13C2×#58511yescharacteristic
628D13—24no—
629D13—212no—
630D13—46no—
631C24—131no—
632C24—133no—
633C24—133no—
634C24—1312no—
635C24—1312no—
636C24—2612no—
637C24—2612no—
638C24—2612no—
639C24—2612no—
640C24—526no—
641C24—526no—
642C24C23×D1313yes—
643C24C23×D1311yescharacteristic
644#41—232no—
645#41—1364no—
646#41—2696no—
647#41—2696no—
648#41—2696no—
649#41—2696no—
650#41—2632no—
651C2×Q8—232no—
652C2×Q8—212no—
653C2×Q8—1312no—
654C2×Q8—2632no—
655C2×Q8—2612no—
656C2×Q8D4×D1318yescomplemented
657C2×Q8C23×D13112yes—
658C2×Q8C23×D1314yes—
659C2×D4—212no—
660C2×D4—212no—
661C2×D4—138no—
662C2×D4—134no—
663C2×D4—1312no—
664C2×D4—1324no—
665C2×D4—1324no—
666C2×D4—1324no—
667C2×D4—1312no—
668C2×D4—1312no—
669C2×D4—1324no—
670C2×D4—1312no—
671C2×D4—2696no—
672C2×D4—2624no—
673C2×D4—2612no—
674C2×D4—2612no—
675C2×D4—2696no—
676C2×D4—2696no—
677C2×D4—2624no—
678C2×D4—2612no—
679C2×D4—5212no—
680C2×D4C23×D13112yes—
681C2×D4C23×D13112yes—
682C22×C4—212no—
683C22×C4—212no—
684C22×C4—131no—
685C22×C4—131no—
686C22×C4—1324no—
687C22×C4—1312no—
688C22×C4—134no—
689C22×C4—1312no—
690C22×C4—133no—
691C22×C4—131no—
692C22×C4—133no—
693C22×C4—1312no—
694C22×C4—1312no—
695C22×C4—1312no—
696C22×C4—134no—
697C22×C4—1312no—
698C22×C4—1312no—
699C22×C4—1312no—
700C22×C4—1312no—
701C22×C4—264no—
702C22×C4—2612no—
703C22×C4—2696no—
704C22×C4—2696no—
705C22×C4—2612no—
706C22×C4—2612no—
707C22×C4—2612no—
708C22×C4—264no—
709C22×C4—2612no—
710C22×C4—2612no—
711C22×C4—2612no—
712C22×C4—526no—
713C22×C4C23×D13112yes—
714C22×C4C23×D13112yes—
715C22×C4C23×D1311yescharacteristic
716C22×C4C23×D1313yes—
717C22×C4C23×D1311yescharacteristic
718C22×C4C23×D1313yes—
719C22×C4C23×D1313yes—
720C4⋊C4—134no—
721C4⋊C4—1312no—
722C4⋊C4—1312no—
723C4⋊C4—1312no—
724C4⋊C4—1324no—
725C4⋊C4C23×D13112yes—
726C4⋊C4C23×D13112yes—
727C22⋊C4—1312no—
728C22⋊C4—1312no—
729C22⋊C4—134no—
730C22⋊C4—1312no—
731C22⋊C4—1312no—
732C22⋊C4—1312no—
733C22⋊C4—1324no—
734C22⋊C4—1324no—
735C22⋊C4C23×D1314yes—
736C22⋊C4C23×D13112yes—
737C22⋊C4C23×D13124yes—
738C42—134no—
739C42—1312no—
740C42—1312no—
741C42C23×D13112yes—
742C13C2×D4×#4111yescharacteristic, complemented, Sylow
743C23—22no—
744C23—22no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—1312no—
749C23—134no—
750C23—132no—
751C23—136no—
752C23—136no—
753C23—2624no—
754C23—2624no—
755C23—2624no—
756C23—262no—
757C23—266no—
758C23—266no—
759C23—262no—
760C23—266no—
761C23—266no—
762C23—2624no—
763C23—266no—
764C23—5212no—
765C23—5212no—
766C23—5248no—
767C23—5248no—
768C23#41×D1314yescomplemented
769C23C24×D1316yes—
770C23C24×D1312yes—
771C23C24×D1311yescharacteristic
772Q8—224no—
773Q8—2624no—
774Q8C2×D4×D13116yescomplemented
775D4—224no—
776D4—224no—
777D4—1316no—
778D4—1348no—
779D4—2624no—
780D4—2648no—
781D4—2624no—
782D4—2648no—
783D4—2624no—
784D4—5224no—
785C2×C4—22no—
786C2×C4—26no—
787C2×C4—26no—
788C2×C4—22no—
789C2×C4—224no—
790C2×C4—224no—
791C2×C4—134no—
792C2×C4—134no—
793C2×C4—132no—
794C2×C4—132no—
795C2×C4—1348no—
796C2×C4—136no—
797C2×C4—132no—
798C2×C4—136no—
799C2×C4—268no—
800C2×C4—2624no—
801C2×C4—2624no—
802C2×C4—2624no—
803C2×C4—2624no—
804C2×C4—268no—
805C2×C4—2624no—
806C2×C4—262no—
807C2×C4—266no—
808C2×C4—266no—
809C2×C4—2624no—
810C2×C4—2624no—
811C2×C4—5212no—
812C2×C4C2×D4×D13112yes—
813C2×C4C24×D1312yes—
814C2×C4C24×D1316yes—
815C2×C4C24×D1312yes—
816C2×C4C24×D1316yes—
817C2×C4C24×D1316yes—
818C22—28no—
819C22—22no—
820C22—22no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—1312no—
826C22—134no—
827C22—2624no—
828C22—268no—
829C22—262no—
830C22—266no—
831C22—266no—
832C22—262no—
833C22—266no—
834C22—266no—
835C22—266no—
836C22—5248no—
837C22—5248no—
838C22—5212no—
839C22C22×D4×D1312yes—
840C22C2×#41×D1312yes—
841C22C2×#41×D1314yescomplemented
842C22#1171965212yes—
843C22C25×D1311yescharacteristic
844C4—22no—
845C4—26no—
846C4—26no—
847C4—22no—
848C4—134no—
849C4—134no—
850C4—262no—
851C4—266no—
852C4—266no—
853C4C22×D4×D13112yes—
854C2—24no—
855C2—46no—
856C2—264no—
857C2—2612no—
858C2—526no—
859C2#1312832514yesdirect product factor
860C2C23×D4×D1311yescharacteristic
861C2C22×#41×D1311yescharacteristic
862C2C2×#1171965211yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#548C2
socleC23×C13C25
hypercenterC2×#548D13
hypocenterC13C2×D4×#41
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C23×#6131C2semidirect
2. C22×#41×D13C2semidirect
3. #13128325C2direct (N × H)
4. C2×#11719539C2semidirect
5. C2×Q8×C22⋊D13C2semidirect
6. C2×#11719281C2semidirect
7. C2×#11719336C2semidirect
8. C2×#11719255C2semidirect
9. C2×#11719381C2semidirect
10. C2×#11719314C2semidirect
11. C2×#11719373C2semidirect
12. C2×#11719332C2semidirect
13. C2×#11719311C2semidirect
14. C2×C4×#6131C2semidirect
15. C2×C4×D4×D13C2semidirect
16. C2×C13×#548C2semidirect
17. C22×C13×#41C22semidirect
18. C23×Q8×C13C22semidirect
20. C2×#41×D13C22semidirect
23. C22×#6131C22semidirect
24. C22×#6131C22semidirect
25. C22×#6131C22semidirect
26. C22×#6131C22semidirect
27. C22×Q8×D13C22semidirect
28. C22×#6129C22semidirect
30. C22×D4×D13C22semidirect
31. C22×#6127C22semidirect
32. C23×D52C22semidirect
33. C23×C4×D13C22semidirect
34. C23×C4×D13C22semidirect
35. C13×#548C22semidirect
36. C2×C13×#124C22semidirect
37. C2×C13×C22⋊Q8C22semidirect
38. C2×C13×#121C22semidirect
39. C2×C4×Q8×C13C22semidirect
40. C2×C4×D4×C13C22semidirect
41. #11719539C22semidirect
42. Q8×C22⋊D13C22semidirect
43. C2×#88200C22semidirect
44. C2×Q8×Dic13C22semidirect
45. C2×#88198C22semidirect
46. C2×#88194C22semidirect
47. C2×#88192C22semidirect
48. C2×#88191C22semidirect
49. C2×D4×Dic13C22semidirect
50. C2×#88184C22semidirect
52. C2×C4×C22⋊D13C22semidirect
53. C2×#88178C22semidirect
54. #11719381C22semidirect
55. #11719373C22semidirect
56. #11719336C22semidirect
57. #11719332C22semidirect
58. #11719314C22semidirect
59. #11719311C22semidirect
60. #11719281C22semidirect
61. C4×#6131C22semidirect
62. #11719255C22semidirect
63. C4×D4×D13C22semidirect
64. C2×#88151C22semidirect
65. C2×#88149C22semidirect
66. C2×#88148C22semidirect
67. C2×#88147C22semidirect
68. C2×#88147C22semidirect
69. C2×#88146C22semidirect
70. C2×C4⋊C4×D13C22semidirect
71. C2×#88138C22semidirect
72. C2×#88138C22semidirect
73. C2×#88137C22semidirect
74. C2×#88136C22semidirect
76. C2×#88135C22semidirect
77. C2×#88135C22semidirect
78. C2×C22⋊C4×D13C22semidirect
79. C2×C22⋊C4×D13C22semidirect
80. C2×#88129C22semidirect
81. C2×C4×D52C22semidirect
82. C2×C4×D52C22semidirect
83. C2×C42×D13C22semidirect
87. C2×C13×#41C23semidirect
91. C22×Q8×C13C23semidirect
107. C2×#6131D4semidirect
109. C2×#6131C23semidirect
110. C2×#6131C23semidirect
111. C2×#6131C23semidirect
113. C2×Q8×D13C23semidirect
115. C2×#6129C23semidirect
119. C2×D4×D13C23semidirect
121. C2×#6127C23semidirect
127. C22×D52C23semidirect
139. C22×C4×D13C23semidirect
140. C22×C4×D13C23semidirect
142. C13×#124C23semidirect
143. C13×C22⋊Q8C23semidirect
144. C13×#121C23semidirect
145. C4×Q8×C13C23semidirect
146. C4×D4×C13C23semidirect
155. #88200C23semidirect
156. Q8×Dic13C23semidirect
157. #88198C23semidirect
158. #88194C23semidirect
159. #88192C23semidirect
160. #88191C23semidirect
161. D4×Dic13C23semidirect
162. #88184C23semidirect
164. C4×C22⋊D13C23semidirect
173. #88178C23semidirect
180. #88151C23semidirect
181. #88149C23semidirect
182. #88148C23semidirect
183. #88147C23semidirect
184. #88147C23semidirect
185. #88146C23semidirect
186. C4⋊C4×D13C23semidirect
187. #88138C23semidirect
188. #88138C23semidirect
189. #88137C23semidirect
190. #88136C23semidirect
192. #88135C23semidirect
193. #88135C23semidirect
194. C22⋊C4×D13C23semidirect
195. C22⋊C4×D13C23semidirect
196. #88129C23semidirect
197. C4×D52C23semidirect
198. C4×D52C23semidirect
199. C42×D13C23semidirect
217. C2×Q8×C13C2×D4semidirect
236. C2×C22⋊D13#41semidirect
253. #6131C2×D4semidirect
263. C2×D52C2×D4semidirect
278. C2×C4×D13C2×D4semidirect
318. C2×#548D13semidirect
333. C23×C13C2×#41semidirect
353. C22×D13C2×#41semidirect
358. Q8×C13C22×D4semidirect
376. C22⋊D13C2×#41semidirect
383. C2×Dic13C2×#41semidirect
392. D52C22×D4semidirect
401. C4×D13C22×D4semidirect
413. C22×#41C2×D13semidirect
415. C23×Q8C2×D13semidirect
424. #548C2×D13semidirect
433. C2×#124C2×D13semidirect
441. C2×C22⋊Q8C2×D13semidirect
447. C2×#121C2×D13semidirect
452. C2×C4×Q8C2×D13semidirect
464. C2×C4×D4C2×D13semidirect
479. C22×C13C22×#41semidirect
495. C2×D13C22×#41semidirect
505. Dic13C22×#41semidirect
523. C2×#41C22×D13semidirect
530. C22×Q8C22×D13semidirect
567. #124C22×D13semidirect
573. C22⋊Q8C22×D13semidirect
579. #121C22×D13semidirect
583. C4×Q8C22×D13semidirect
594. C4×D4C22×D13semidirect
624. C2×C13D4×#41semidirect
656. C2×Q8D4×D13semidirect
742. C13C2×D4×#41semidirect
768. C23#41×D13semidirect
774. Q8C2×D4×D13semidirect
841. C22C2×#41×D13semidirect
859. C2#13128325direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#61312
C22×#41×D132
#131283252
C2×#117195392
C2×Q8×C22⋊D132
C2×#117192812
C2×#117193362
C2×#117192552
C2×#117193812
C2×#117193142
C2×#117193732
C2×#117193322
C2×#117193112
C2×C4×#61312
C2×C4×D4×D132
C2×C13×#5482
C2×D4×#4113