Finite Group Databasebeta

← #16022577

Subgroups — #16022577

Order 3328.

2322 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719327C211yesmaximal, characteristic
2#13117933C212yesmaximal, complemented
3#13117927C212yesmaximal, complemented
4#13117924C212yesmaximal, complemented
5#13117921C211yesmaximal, characteristic
6#13117919C211yesmaximal, characteristic
7#13117916C211yesmaximal, characteristic
8#13117891C212yesmaximal, complemented
9#13117842C212yesmaximal
10#13117836C212yesmaximal
11#13117315C212yesmaximal
12#13117311C212yesmaximal, complemented
13#13117309C212yesmaximal, complemented
14#13117309C212yesmaximal, complemented
15C4×#88141C212yesmaximal, complemented
16C4×#88131C212yesmaximal
17C4×#88131C211yesmaximal, characteristic
18C2×#11718310C211yesmaximal, characteristic
19C13×#2368C211yesmaximal, characteristic
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×Q8×Dic13C2211yescharacteristic
22C2×#88198C2211yescharacteristic
23C2×#88178C2211yescharacteristic
24C22×#6101C2212yes—
25C22×C4×Dic13C2212yes—
26C22×C4×Dic13C2211yescharacteristic
27#11719327C4116yescomplemented
28C2×#88143C2212yes—
29C2×#88142C2211yescharacteristic
30C2×#88141C2212yes—
31C2×#88141C2212yes—
32C2×#88141C2211yescharacteristic
33C2×#88132C2212yes—
34C2×#88131C2211yescharacteristic
35C2×#88131C2212yes—
36C2×#88131C2211yescharacteristic
37C2×C4×Dic26C2212yes—
38C13×#391C2212yes—
39C13×#387C2212yes—
40C13×#387C2212yes—
41C13×#385C2212yes—
42C4×C13×C4⋊C4C2212yes—
43C4×C13×C22⋊C4C2212yes—
44C4×C13×C22⋊C4C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46#11718891C2212yes—
47#11718871C2212yes—
48C4×C22⋊Dic13C2212yes—
49C4×C22⋊Dic13C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51#11718642C2212yes—
52#11718642C2212yes—
53C4⋊C4×Dic13C2212yes—
54C4⋊C4×Dic13C2212yes—
55C4⋊C4×Dic13C2212yes—
56#11718634C2212yes—
57#11718633C2212yes—
58#11718633C2212yes—
59#11718633C2212yes—
60#11718633C2212yes—
61#11718611C2212yes—
62#11718607C2212yes—
63C22⋊C4×Dic13C2211yescharacteristic
64C22⋊C4×Dic13C2212yes—
65C22⋊C4×Dic13C2211yescharacteristic
66C22⋊C4×Dic13C2212yes—
67#11718594C2212yes—
68#11718594C2212yes—
69C4×#6101C2212yes—
70C4×#6101C2212yes—
71C4×#6101C2212yes—
72C4×#6101C2212yes—
73C4×#6101C2212yes—
74C42×Dic13C2212yes—
75C42×Dic13C2212yes—
76C42×Dic13C2212yes—
77#11718589C2212yes—
78#11718315C2212yes—
79#11718315C2212yes—
80#11718314C2212yes—
81#11718314C2212yes—
82#11718313C2212yes—
83#11718313C2212yes—
84#11718310C2211yescharacteristic
85#11718310C2212yes—
86#11718310C2212yes—
87#11718310C2212yes—
88#11718310C2212yes—
89#11718310C2211yescharacteristic
90#11718310C2212yes—
91#11718310C2212yes—
92#11718310C2212yes—
93#11718310C2212yes—
94#11718310C2212yes—
95#11718310C2211yescharacteristic
96#11718310C2211yescharacteristic
97#11718309C2212yes—
98#11718309C2212yes—
99#11718309C2212yes—
100#11718308C2212yes—
101#11718308C2212yes—
102#11718308C2212yes—
103#11718308C2212yes—
104#11718307C2212yes—
105#11718307C2212yes—
106#11718307C2212yes—
107#11718307C2212yes—
108C22×Q8×C13C2311yescharacteristic
109C23×C4×C13C2312yes—
110C23×C4×C13C2311yescharacteristic
111C23×Dic13C2312yes—
112C23×Dic13C2311yescharacteristic
113C23×Dic13C2311yescharacteristic
114C22×Dic26C2312yes—
115C22×Dic26C2311yescharacteristic
116C13×C22⋊Q8C2×C418yes—
117C2×C13×C4⋊C4C2312yes—
118C2×C13×C4⋊C4C2312yes—
119C2×C13×C4⋊C4C2312yes—
120C2×C13×C4⋊C4C2311yescharacteristic
121C2×C13×C22⋊C4C2311yescharacteristic
122C2×C13×C22⋊C4C2312yes—
123C2×C13×C22⋊C4C2311yescharacteristic
124C2×C42×C13C2312yes—
125C2×C42×C13C2312yes—
126C2×C42×C13C2312yes—
127C2×C22⋊Dic13C2311yescharacteristic
128C2×C22⋊Dic13C2312yes—
129C2×C22⋊Dic13C2311yescharacteristic
130Q8×Dic13C2×C418yescomplemented
131#88198C2×C418yescomplemented
132C2×C4⋊Dic13C2312yes—
133C2×C4⋊Dic13C2312yes—
134C2×C4⋊Dic13C2312yes—
135C2×C4⋊Dic13C2311yescharacteristic
136#88178C2×C418yes—
137C2×#6101—28no—
138C2×#6101C2312yes—
139C2×#6101C2312yes—
140C2×#6101C2312yes—
141C2×#6101C2312yes—
142C2×#6101C2312yes—
143C2×#6101C2312yes—
144C2×#6101C2312yes—
145C2×#6101C2312yes—
146C2×#6101C2312yes—
147C2×#6101C2312yes—
148C2×#6101C2312yes—
149C2×#6101C2312yes—
150C2×#6101C2312yes—
151C2×#6101C2312yes—
152C2×#6101C2312yes—
153C2×C4×Dic13—28no—
154C2×C4×Dic13C2×C418yes—
155C2×C4×Dic13C2312yes—
156C2×C4×Dic13C2312yes—
157C2×C4×Dic13C2312yes—
158C2×C4×Dic13C2312yes—
159C2×C4×Dic13C2312yes—
160C2×C4×Dic13C2312yes—
161C2×C4×Dic13C2312yes—
162C2×C4×Dic13C2312yes—
163C2×C4×Dic13C2312yes—
164C2×C4×Dic13C2312yes—
165C2×C4×Dic13C2312yes—
166C2×C4×Dic13C2312yes—
167C2×C4×Dic13C2312yes—
168C2×C4×Dic13C2312yes—
169C2×C4×Dic13C2312yes—
170C2×C4×Dic13C2312yes—
171C2×C4×Dic13C2311yescharacteristic
172C2×C4×Dic13C2311yescharacteristic
173C2×C4×Dic13C2311yescharacteristic
174C2×C4×Dic13C2311yescharacteristic
175C2×C4×Dic13C2312yes—
176#88143C2×C4116yescomplemented
177#88142C2×C418yescomplemented
178#88141—28no—
179#88141C2×C418yescomplemented
180#88141C2×C4116yescomplemented
181#88132C2×C4116yes—
182#88131—24no—
183#88131C2×C4116yes—
184#88131Q818yescomplemented
185C4×Dic26—28no—
186C13×#95C2312yes—
187C13×#95C2312yes—
188C13×#95C2312yes—
189C13×#95C2311yescharacteristic
190C13×#95C2312yes—
191C13×#95C2312yes—
192C13×#95C2311yescharacteristic
193C13×#95C2312yes—
194#88071C2312yes—
195#88071C2312yes—
196#88071C2312yes—
197#88071C2312yes—
198#88071C2312yes—
199#88071C2312yes—
200#88071C2312yes—
201#88071C2312yes—
202#88071C2312yes—
203#88071C2312yes—
204#88071C2312yes—
205#88071C2312yes—
206#88071C2312yes—
207#88071C2312yes—
208#88071C2312yes—
209#88071C2311yescharacteristic
210#88071C2311yescharacteristic
211#88071C2312yes—
212#34145—131nomaximal, Sylow
213C24×C13C2411yescharacteristic
214C2×Q8×C13—42no—
215C2×Q8×C13C22×C414yes—
216C22×C4×C13—24no—
217C22×C4×C13—24no—
218C22×C4×C13—42no—
219C22×C4×C13—42no—
220C22×C4×C13C22×C414yes—
221C22×C4×C13C2412yes—
222C22×C4×C13C2412yes—
223C22×C4×C13C2411yescharacteristic
224C22×C4×C13C2411yescharacteristic
225C22×C4×C13C2412yes—
226C22×C4×C13C2412yes—
227C22×C4×C13C2412yes—
228C22×C4×C13C2412yes—
229C22×Dic13—24no—
230C22×Dic13—24no—
231C22×Dic13—24no—
232C22×Dic13—42no—
233C22×Dic13C22×C414yes—
234C22×Dic13C22×C414yes—
235C22×Dic13C2×Q814yes—
236C22×Dic13#4114yes—
237C22×Dic13C2412yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C22×Dic13C2412yes—
241C22×Dic13C2411yescharacteristic
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C22×Dic13C2411yescharacteristic
245C22×Dic13C2411yescharacteristic
246C22×Dic13C2411yescharacteristic
247C2×Dic26—24no—
248C2×Dic26—24no—
249C2×Dic26—42no—
250C2×Dic26C22×C418yes—
251C2×Dic26C22×C414yes—
252C13×C4⋊C4—24no—
253C13×C4⋊C4—42no—
254C13×C4⋊C4C22×C414yes—
255C13×C4⋊C4C22×C418yes—
256C13×C22⋊C4—22no—
257C13×C22⋊C4C22×C418yes—
258C13×C22⋊C4C2×Q814yes—
259C42×C13—24no—
260C42×C13—42no—
261C42×C13—42no—
262C22⋊Dic13—22no—
263C22⋊Dic13C22×C418yes—
264C22⋊Dic13C2×Q814yes—
265C4⋊Dic13—24no—
266C4⋊Dic13—42no—
267C4⋊Dic13C22×C418yes—
268C4⋊Dic13C22×C414yes—
269#6101—24no—
270#6101—24no—
271#6101—24no—
272#6101—24no—
273#6101—24no—
274#6101—24no—
275#6101—42no—
276#6101—42no—
277#6101C22×C418yes—
278#6101C22×C418yes—
279#6101C22×C418yes—
280#6101C22×C418yes—
281#6101C22×C418yes—
282#6101C2×Q818yes—
283#6101#4118yes—
284C4×Dic13—24no—
285C4×Dic13—24no—
286C4×Dic13—24no—
287C4×Dic13—24no—
288C4×Dic13—24no—
289C4×Dic13—24no—
290C4×Dic13—24no—
291C4×Dic13—24no—
292C4×Dic13—24no—
293C4×Dic13—24no—
294C4×Dic13—42no—
295C4×Dic13—42no—
296C4×Dic13—42no—
297C4×Dic13—42no—
298C4×Dic13C22×C418yes—
299C4×Dic13C22×C418yes—
300C4×Dic13C22×C414yes—
301C4×Dic13C22×C414yes—
302C4×Dic13C22×C414yes—
303C4×Dic13C22×C414yes—
304C4×Dic13C2×Q818yes—
305C2×#533—131no—
306#2370—132no—
307#2370—132no—
308#2369—132no—
309#2368—131no—
310#2368—131no—
311#2368—131no—
312#2368D1311yescharacteristic
313#2365—132no—
314#2360—132no—
315#2360—132no—
316#2296—132no—
317#2295—132no—
318#2295—132no—
319#2295—132no—
320C42×Q8—132no—
321C4×#117—132no—
322C4×#117—131no—
323C2×C4×C4⋊C4—131no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13C23×C412yes—
327C23×C13C22×Q812yes—
328C23×C13C2×#4112yes—
329C23×C13C2511yescharacteristic
330Q8×C13—44no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
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—44no—
348C2×C4×C13—48no—
349C2×C4×C13C23×C412yes—
350C2×C4×C13C23×C412yes—
351C2×C4×C13C23×C414yes—
352C2×C4×C13C23×C414yes—
353C2×C4×C13C22×Q814yes—
354C2×C4×C13C2×#4114yes—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—22no—
360C2×Dic13—22no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—28no—
365C2×Dic13—22no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—48no—
372C2×Dic13C4×Q8116yescomplemented
373C2×Dic13C23×C412yes—
374C2×Dic13C23×C414yes—
375C2×Dic13C23×C414yes—
376C2×Dic13C23×C412yes—
377C2×Dic13C23×C412yes—
378C2×Dic13C23×C412yes—
379C2×Dic13C22×Q814yes—
380C2×Dic13C22×Q812yes—
381C2×Dic13C22×Q812yes—
382C2×Dic13C2×#4114yes—
383C2×Dic13C2×#4112yes—
384C2×Dic13C2×#4112yes—
385C2×Dic13C2×#4114yes—
386Dic26—216no—
387Dic26—44no—
388#533—1316no—
389C2×C4⋊Q8—131no—
390C2×C4⋊Q8—131no—
391C2×#125—132no—
392C2×C22⋊Q8—131no—
393C2×C22⋊Q8—132no—
394C2×C22⋊Q8C2×D1311yescharacteristic
395C2×C4×Q8—131no—
396C2×C4×Q8—132no—
397C2×C4×Q8—131no—
398C2×C4×Q8—132no—
399C2×C4×Q8—132no—
400C2×#117—132no—
401C2×#117—131no—
402C2×#117—131no—
403C22×C4⋊C4—132no—
404C22×C42—131no—
405C22×C42—132no—
406#391—132no—
407#391—132no—
408#391—132no—
409#391—132no—
410#391—132no—
411#391C2×D1312yes—
412#389—132no—
413#389—132no—
414#389—132no—
415#389—132no—
416#389—132no—
417#389—132no—
418#389—132no—
419#389—132no—
420#389—132no—
421#389—132no—
422#387—132no—
423#387—132no—
424#387—132no—
425#387—132no—
426#387—132no—
427#387—132no—
428#387—132no—
429#387—132no—
430#387—132no—
431#387—132no—
432#387C2×D1312yes—
433#387C2×D1312yes—
434#385—132no—
435#385—132no—
436#385—132no—
437#385C2×D1312yes—
438C4×C4⋊C4—132no—
439C4×C4⋊C4—132no—
440C4×C4⋊C4—132no—
441C4×C4⋊C4—132no—
442C4×C4⋊C4—132no—
443C4×C4⋊C4—132no—
444C4×C4⋊C4—132no—
445C4×C4⋊C4—132no—
446C4×C4⋊C4—132no—
447C4×C4⋊C4—132no—
448C4×C4⋊C4—132no—
449C4×C4⋊C4—132no—
450C4×C4⋊C4—132no—
451C4×C4⋊C4—132no—
452C4×C4⋊C4—131no—
453C4×C4⋊C4—131no—
454C4×C4⋊C4—131no—
455C4×C4⋊C4—131no—
456C4×C4⋊C4—132no—
457C4×C4⋊C4—132no—
458C4×C4⋊C4—132no—
459C4×C4⋊C4C2×D1312yes—
460C4×C22⋊C4—132no—
461C4×C22⋊C4—131no—
462C4×C22⋊C4—131no—
463C4×C22⋊C4—131no—
464C4×C22⋊C4—132no—
465C4×C22⋊C4—132no—
466C4×C22⋊C4C2×D1312yes—
467C4×C22⋊C4C2×D1311yescharacteristic
468#376—132no—
469#376—132no—
470#376—132no—
471C2×#95—131no—
472C2×#95C2×D1311yescharacteristic
473C43—132no—
474C43—132no—
475C43—132no—
476C22×C13—22no—
477C22×C13—22no—
478C22×C13—24no—
479C22×C13—24no—
480C22×C13C2×C4×Q814yes—
481C22×C13C24×C411yescharacteristic
482C22×C13C23×Q811yescharacteristic
483C22×C13C22×#4111yescharacteristic
484C22×C13C22×#4112yes—
485C22×C13#58512yes—
486C4×C13—24no—
487C4×C13—22no—
488C4×C13—22no—
489C4×C13—24no—
490C4×C13—24no—
491C4×C13—24no—
492C4×C13—42no—
493C4×C13—42no—
494Dic13—24no—
495Dic13—22no—
496Dic13—24no—
497Dic13—24no—
498Dic13—24no—
499Dic13—42no—
500Dic13—42no—
501Dic13C2×C4×Q814yes—
502Dic13C2×C4×Q814yes—
503Dic13C4×#4114yes—
504C22×Q8—132no—
505C22×Q8—131no—
506C22×Q8C22×D1311yescharacteristic
507C23×C4—131no—
508C23×C4—131no—
509C23×C4—132no—
510C23×C4C22×D1312yes—
511C23×C4C22×D1311yescharacteristic
512C4⋊Q8—138no—
513C4⋊Q8—138no—
514#125—1316no—
515C22⋊Q8—138no—
516C22⋊Q8—1316no—
517C22⋊Q8C4×D1318yes—
518C4×Q8—138no—
519C4×Q8—138no—
520C4×Q8—1316no—
521C4×Q8—268no—
522C4×Q8—268no—
523#117—1316no—
524#117—138no—
525#117—264no—
526C2×C4⋊C4—132no—
527C2×C4⋊C4—132no—
528C2×C4⋊C4—132no—
529C2×C4⋊C4—132no—
530C2×C4⋊C4—132no—
531C2×C4⋊C4—132no—
532C2×C4⋊C4—132no—
533C2×C4⋊C4—132no—
534C2×C4⋊C4—131no—
535C2×C4⋊C4—132no—
536C2×C4⋊C4—132no—
537C2×C4⋊C4—132no—
538C2×C4⋊C4—132no—
539C2×C4⋊C4—132no—
540C2×C4⋊C4—132no—
541C2×C4⋊C4—132no—
542C2×C4⋊C4—132no—
543C2×C4⋊C4—132no—
544C2×C4⋊C4—132no—
545C2×C4⋊C4—268no—
546C2×C4⋊C4C22×D1312yes—
547C2×C4⋊C4C22×D1312yes—
548C2×C4⋊C4C22×D1312yes—
549C2×C4⋊C4C22×D1311yescharacteristic
550C2×C22⋊C4—132no—
551C2×C22⋊C4—131no—
552C2×C22⋊C4—131no—
553C2×C22⋊C4C22×D1311yescharacteristic
554C2×C22⋊C4C22×D1312yes—
555C2×C22⋊C4C22×D1311yescharacteristic
556C2×C42—138no—
557C2×C42—132no—
558C2×C42—132no—
559C2×C42—132no—
560C2×C42—131no—
561C2×C42—131no—
562C2×C42—131no—
563C2×C42—131no—
564C2×C42—132no—
565C2×C42—132no—
566C2×C42—132no—
567C2×C42—132no—
568C2×C42—132no—
569C2×C42—132no—
570C2×C42—132no—
571C2×C42—132no—
572C2×C42—132no—
573C2×C42—132no—
574C2×C42—132no—
575C2×C42—132no—
576C2×C42—132no—
577C2×C42—132no—
578C2×C42—268no—
579C2×C42C22×D1312yes—
580C2×C42C22×D1312yes—
581C2×C42C22×D1312yes—
582#95—131no—
583#95—131no—
584#95—132no—
585#95—132no—
586#95—132no—
587#95—132no—
588#95—132no—
589#95—132no—
590#95—132no—
591#95—132no—
592#95—132no—
593#95—132no—
594#95—132no—
595#95—132no—
596#95—132no—
597#95—132no—
598#95—132no—
599#95—132no—
600#95C22×D1311yescharacteristic
601#95C22×D1311yescharacteristic
602#95C22×D1312yes—
603#95C22×D1312yes—
604#95C22×D1312yes—
605#95C22×D1312yes—
606#95C22×D1312yes—
607#95C22×D1312yes—
608C2×C13—24no—
609C2×C13C22×C4×Q811yescharacteristic
610C2×C13C2×C4×#4111yescharacteristic
611C2×C13#342811yescharacteristic
612C2×C13#347512yes—
613C2×C13Q8×#4112yes—
614C24C23×D1311yescharacteristic
615C2×Q8—42no—
616C2×Q8—138no—
617C2×Q8—134no—
618C2×Q8—264no—
619C2×Q8—264no—
620C2×Q8—522no—
621C2×Q8C2×C4×D1314yes—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—134no—
627C22×C4—134no—
628C22×C4—134no—
629C22×C4—131no—
630C22×C4—131no—
631C22×C4—131no—
632C22×C4—134no—
633C22×C4—132no—
634C22×C4—132no—
635C22×C4—132no—
636C22×C4—132no—
637C22×C4—131no—
638C22×C4—132no—
639C22×C4—132no—
640C22×C4—264no—
641C22×C4—264no—
642C22×C4—264no—
643C22×C4—522no—
644C22×C4C2×C4×D1314yes—
645C22×C4C23×D1312yes—
646C22×C4C23×D1312yes—
647C22×C4C23×D1311yescharacteristic
648C22×C4C23×D1311yescharacteristic
649C22×C4C23×D1312yes—
650C22×C4C23×D1312yes—
651C22×C4C23×D1312yes—
652C22×C4C23×D1312yes—
653C4⋊C4—24no—
654C4⋊C4—42no—
655C4⋊C4—138no—
656C4⋊C4—138no—
657C4⋊C4—138no—
658C4⋊C4—138no—
659C4⋊C4—138no—
660C4⋊C4—138no—
661C4⋊C4—134no—
662C4⋊C4—138no—
663C4⋊C4—138no—
664C4⋊C4—264no—
665C4⋊C4—264no—
666C4⋊C4—264no—
667C4⋊C4—264no—
668C4⋊C4—264no—
669C4⋊C4—264no—
670C4⋊C4—264no—
671C4⋊C4—522no—
672C4⋊C4—522no—
673C4⋊C4—522no—
674C4⋊C4C2×C4×D1318yes—
675C4⋊C4C2×C4×D1314yes—
676C22⋊C4—22no—
677C22⋊C4—138no—
678C22⋊C4—134no—
679C22⋊C4—262no—
680C22⋊C4C2×C4×D1318yes—
681C22⋊C4Q8×D1314yes—
682C42—24no—
683C42—42no—
684C42—42no—
685C42—134no—
686C42—134no—
687C42—134no—
688C42—134no—
689C42—138no—
690C42—138no—
691C42—138no—
692C42—264no—
693C42—264no—
694C42—264no—
695C42—264no—
696C42—264no—
697C42—264no—
698C42—264no—
699C42—264no—
700C42—264no—
701C42—264no—
702C42—522no—
703C42—522no—
704C42—522no—
705C42—522no—
706C13#3414511yescharacteristic, complemented, Sylow
707C23—22no—
708C23—22no—
709C23C22×C4×D1312yes—
710C23C2×Q8×D1312yes—
711C23#41×D1312yes—
712C23C24×D1311yescharacteristic
713Q8—44no—
714Q8—2616no—
715Q8—524no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—44no—
733C2×C4—48no—
734C2×C4—1316no—
735C2×C4—132no—
736C2×C4—132no—
737C2×C4—132no—
738C2×C4—132no—
739C2×C4—132no—
740C2×C4—132no—
741C2×C4—132no—
742C2×C4—134no—
743C2×C4—132no—
744C2×C4—134no—
745C2×C4—134no—
746C2×C4—134no—
747C2×C4—134no—
748C2×C4—268no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—262no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—262no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—528no—
765C2×C4C22×C4×D1312yes—
766C2×C4C22×C4×D1312yes—
767C2×C4C22×C4×D1314yes—
768C2×C4C22×C4×D1314yes—
769C2×C4C2×Q8×D1314yes—
770C2×C4#41×D1314yes—
771C22—22no—
772C22—22no—
773C22—24no—
774C22—24no—
775C22C4×Q8×D1314yes—
776C22C23×C4×D1311yescharacteristic
777C22C22×Q8×D1311yescharacteristic
778C22C2×#41×D1311yescharacteristic
779C22C2×#41×D1312yes—
780C22#1171965012yes—
781C4—24no—
782C4—22no—
783C4—22no—
784C4—24no—
785C4—24no—
786C4—24no—
787C4—42no—
788C4—42no—
789C4—134no—
790C4—134no—
791C4—134no—
792C4—262no—
793C4—264no—
794C4—264no—
795C4—264no—
796C4—264no—
797C4—522no—
798C4—522no—
799C2—24no—
800C2C2×C4×Q8×D1311yescharacteristic
801C2C4×#41×D1311yescharacteristic
802C2#1312803411yescharacteristic
803C2#1312839112yes—
804C2#1312841512yes—
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2368C2
socle, cosocleC23×C13C25
prime radicalC24×C13C24
hypercenter#2368D13
hypocenterC13#34145
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2368

Complements

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

NH ≅ G/Ntype
2. #13117933C2semidirect
3. #13117927C2semidirect
4. #13117924C2semidirect
8. #13117891C2semidirect
12. #13117311C2semidirect
13. #13117309C2semidirect
14. #13117309C2semidirect
15. C4×#88141C2semidirect
27. #11719327C4semidirect
130. Q8×Dic13C2×C4semidirect
131. #88198C2×C4semidirect
176. #88143C2×C4semidirect
177. #88142C2×C4semidirect
179. #88141C2×C4semidirect
180. #88141C2×C4semidirect
184. #88131Q8semidirect
372. C2×Dic13C4×Q8semidirect
706. C13#34145semidirect

Maximal subgroups

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

subgroupindex
C2×#117193272
#131179332
#131179272
#131179242
#131179212
#131179192
#131179162
#131178912
#131178422
#131178362
#131173152
#131173112
#131173092
C4×#881412
C4×#881312
C2×#117183102
C13×#23682
#3414513