Finite Group Databasebeta

← #16731337

Subgroups — #16731337

Order 3328.

2138 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128132C211yesmaximal, characteristic
2#13125007C214yesmaximal, complemented
3#13124966C212yesmaximal, complemented
4#13124958C212yesmaximal, complemented
5#13124916C214yesmaximal, complemented
6#13124875C212yesmaximal, complemented
7#13124867C212yesmaximal, complemented
8#13124759C212yesmaximal, complemented
9#13124641C212yesmaximal, complemented
10#13124308C212yesmaximal, complemented
11#13124070C212yesmaximal, complemented
12C4×#88196C214yesmaximal, complemented
13#13123469C211yesmaximal, characteristic, complemented
14C22×C4×Q8×C13C211yesmaximal, characteristic, complemented
15C23×Q8×C13C2211yescharacteristic
16C2×C4×Q8×C13—21no—
17C2×C4×Q8×C13—21no—
18C2×C4×Q8×C13—21no—
19C2×C4×Q8×C13—21no—
20C2×C4×Q8×C13—21no—
21C2×C4×Q8×C13—21no—
22C2×C4×Q8×C13C2212yes—
23C2×C4×Q8×C13C2212yes—
24C2×C4×Q8×C13C2212yes—
25C2×C4×Q8×C13C2212yes—
26C2×C4×Q8×C13C2212yes—
27C2×C4×Q8×C13C2212yes—
28C22×C13×C4⋊C4—21no—
29C22×C13×C4⋊C4C2211yescharacteristic
30C22×C42×C13—21no—
31C22×C42×C13C2211yescharacteristic
32C2×#88196C2214yes—
33#11719496—21no—
34#11719496—21no—
35#11719496C2212yes—
36#11719184—21no—
37#11719184—21no—
38#11719184—21no—
39#11719184—21no—
40#11719184C2212yes—
41#11719184C2212yes—
42#11719182C2211yescharacteristic
43#11719182C2211yescharacteristic
44#11719182C2211yescharacteristic
45C4×#6127—21no—
46C4×#6127—21no—
47C4×#6127C2212yes—
48#11719175C2211yescharacteristic
49#11719175C2211yescharacteristic
50#11719175C2211yescharacteristic
51#11718889C2214yes—
52#11718889C2214yes—
53#11718888C2214yes—
54#11718888C2214yes—
55#11718886C2214yes—
56#11718868C2212yes—
57#11718692C2214yescomplemented
58#11718691C2218yescomplemented
59C4×#6107C2218yescomplemented
60#11718689C2218yescomplemented
61#11718688C2214yescomplemented
62#11718687C2218yescomplemented
63C4×#6106C2218yescomplemented
64#11718683C2218yescomplemented
65#11718682C2214yescomplemented
66#11718681C2214yescomplemented
67#11718632C2214yes—
68#11718631C2214yes—
69#11718629C2214yes—
70#11718628C2214yes—
71#11718627C2214yes—
72#11718625C2214yes—
73#11718587C2212yes—
74#11718587C2212yes—
75#11718586C2212yes—
76#11718586C2212yes—
77#11718585C2212yes—
78C4×#6099C2212yes—
79C22×Q8×C13—28no—
80C22×Q8×C13—21no—
81C22×Q8×C13—21no—
82C22×Q8×C13—21no—
83C22×Q8×C13C2312yes—
84C22×Q8×C13C2312yes—
85C22×Q8×C13C2312yes—
86C23×C4×C13—21no—
87C23×C4×C13—21no—
88C23×C4×C13D411yescharacteristic
89C23×C4×C13D411yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C2×#6127—21no—
92C2×#6127—21no—
93C2×#6127C2312yes—
94C4×Q8×C13—22no—
95C4×Q8×C13—22no—
96C4×Q8×C13—22no—
97C4×Q8×C13—22no—
98C4×Q8×C13—22no—
99C4×Q8×C13—22no—
100C4×Q8×C13—22no—
101C4×Q8×C13—22no—
102C4×Q8×C13—22no—
103C4×Q8×C13—22no—
104C4×Q8×C13—22no—
105C4×Q8×C13—22no—
106C4×Q8×C13C2314yes—
107C4×Q8×C13C2314yes—
108C4×Q8×C13C2314yes—
109C4×Q8×C13C2314yes—
110C2×C13×C4⋊C4—22no—
111C2×C13×C4⋊C4—22no—
112C2×C13×C4⋊C4—22no—
113C2×C13×C4⋊C4—22no—
114C2×C13×C4⋊C4—22no—
115C2×C13×C4⋊C4—22no—
116C2×C13×C4⋊C4—21no—
117C2×C13×C4⋊C4—21no—
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4C2312yes—
120C2×C13×C4⋊C4C2312yes—
121C2×C13×C4⋊C4C2312yes—
122C2×C42×C13—22no—
123C2×C42×C13—22no—
124C2×C42×C13—22no—
125C2×C42×C13—22no—
126C2×C42×C13—22no—
127C2×C42×C13—22no—
128C2×C42×C13D411yescharacteristic
129C2×C42×C13D411yescharacteristic
130C2×C42×C13D411yescharacteristic
131C2×C42×C13D411yescharacteristic
132C2×C42×C13D411yescharacteristic
133C2×C42×C13D411yescharacteristic
134C2×C42×C13C2311yescharacteristic
135C2×C42×C13C2311yescharacteristic
136C2×C42×C13C2311yescharacteristic
137C2×C42×C13C2311yescharacteristic
138C2×C42×C13C2311yescharacteristic
139C2×C42×C13C2311yescharacteristic
140#88207—22no—
141C2×#6107C2318yes—
142#88196—216no—
143C2×#6106C2318yes—
144#88184—21no—
145#88184—21no—
146#88184—21no—
147#88184—21no—
148#88184C2312yes—
149#88184C2312yes—
150#88183—22no—
151#88183—22no—
152#88183—22no—
153C4×C22⋊D13—22no—
154C4×C22⋊D13—22no—
155C4×C22⋊D13—22no—
156C4×C22⋊D13—22no—
157C4×C22⋊D13—22no—
158C4×C22⋊D13—22no—
159#88180—21no—
160#88180—21no—
161#88180C2312yes—
162#88178—21no—
163#88178—21no—
164#88178—21no—
165#88178—21no—
166#88178C2312yes—
167#88178C2312yes—
168C2×#6099C2314yes—
169#88130—22no—
170#88130—22no—
171#88129—21no—
172#88129—21no—
173#88129C2312yes—
174#88128C2311yescharacteristic
175C4×D52—21no—
176C4×D52—21no—
177C4×D52—21no—
178C4×D52—21no—
179C4×D52C2312yes—
180C4×D52C2312yes—
181#88126—22no—
182#88126—22no—
183#88126—22no—
184C42×D13—22no—
185#88124—21no—
186#88124—21no—
187#88124C2312yes—
188#88123C2311yescharacteristic
189#88123C2311yescharacteristic
190#88123C2311yescharacteristic
191C4×Dic26—21no—
192C4×Dic26—21no—
193C4×Dic26—21no—
194C4×Dic26—21no—
195C4×Dic26C2312yes—
196C4×Dic26C2312yes—
197#88075C2318yes—
198#88075C2318yes—
199C22⋊#1055C2314yes—
200C22⋊#1055C2314yes—
201#88050C2318yes—
202#88049C2318yes—
203#88048C2318yes—
204#88047C2318yes—
205C4⋊#1055C2314yes—
206C4⋊#1055C2314yes—
207#88043C2314yes—
208C4×#1055C2314yes—
209#60560—131nomaximal, Sylow
210C24×C13C2×D411yescharacteristic
211C2×Q8×C13—28no—
212C2×Q8×C13—28no—
213C2×Q8×C13—28no—
214C2×Q8×C13—28no—
215C2×Q8×C13—28no—
216C2×Q8×C13—22no—
217C2×Q8×C13—22no—
218C2×Q8×C13—22no—
219C2×Q8×C13—24no—
220C2×Q8×C13#4118yescomplemented
221C2×Q8×C13C2414yes—
222C22×C4×C13—28no—
223C22×C4×C13—22no—
224C22×C4×C13—22no—
225C22×C4×C13—22no—
226C22×C4×C13—24no—
227C22×C4×C13—24no—
228C22×C4×C13—22no—
229C22×C4×C13—22no—
230C22×C4×C13—22no—
231C22×C4×C13—42no—
232C22×C4×C13—44no—
233C22×C4×C13C2×D411yescharacteristic
234C22×C4×C13C2×D411yescharacteristic
235C22×C4×C13C2×D411yescharacteristic
236C22×C4×C13C2×D411yescharacteristic
237C22×C4×C13C2×D411yescharacteristic
238C22×C4×C13C2×D411yescharacteristic
239C22×C4×C13C2×D411yescharacteristic
240C22×C4×C13C2×D411yescharacteristic
241C22×C4×C13C2×D411yescharacteristic
242C22×C4×C13C2×D411yescharacteristic
243C22×C4×C13C2×D411yescharacteristic
244C22×C4×C13C2×D411yescharacteristic
245C22×C4×C13C2×D411yescharacteristic
246C22×C4×C13C2×D411yescharacteristic
247C22×C4×C13C2×D411yescharacteristic
248C22×C4×C13C2411yescharacteristic
249C22×C4×C13C2411yescharacteristic
250C22×C4×C13C2411yescharacteristic
251C2×C22⋊D13—22no—
252C2×C22⋊D13—22no—
253C2×C22⋊D13—22no—
254#6127—28no—
255#6127—44no—
256#6127—44no—
257C2×D52—21no—
258C2×D52—21no—
259C2×D52C2412yes—
260C2×C4×D13—22no—
261C2×C4×D13—22no—
262C2×C4×D13—22no—
263C2×Dic26—21no—
264C2×Dic26—21no—
265C2×Dic26C2412yes—
266C13×C4⋊C4—24no—
267C13×C4⋊C4—24no—
268C13×C4⋊C4—24no—
269C13×C4⋊C4—24no—
270C13×C4⋊C4—22no—
271C13×C4⋊C4—22no—
272C13×C4⋊C4—22no—
273C13×C4⋊C4C2414yes—
274C42×C13—24no—
275C42×C13—24no—
276C42×C13—24no—
277C42×C13—24no—
278C42×C13C2×D411yescharacteristic
279C42×C13C2×D411yescharacteristic
280C42×C13C2×D411yescharacteristic
281C42×C13C2×D411yescharacteristic
282C42×C13C2×D411yescharacteristic
283C42×C13C2×D411yescharacteristic
284C42×C13C2×D411yescharacteristic
285C42×C13C2×D411yescharacteristic
286C42×C13C2×D411yescharacteristic
287C42×C13C2×D411yescharacteristic
288C42×C13C2×D411yescharacteristic
289C42×C13C2×D411yescharacteristic
290C42×C13C2411yescharacteristic
291C42×C13C2411yescharacteristic
292C42×C13C2411yescharacteristic
293C42×C13C2411yescharacteristic
294C22⋊Dic13—22no—
295C22⋊Dic13—22no—
296C22⋊Dic13—22no—
297#6107—216no—
298#6106—216no—
299#6103—22no—
300#6103—22no—
301#6103—22no—
302#6103—22no—
303#6103—22no—
304#6103—22no—
305C4⋊Dic13—21no—
306C4⋊Dic13—21no—
307C4⋊Dic13—21no—
308C4⋊Dic13—21no—
309C4⋊Dic13C2412yes—
310C4⋊Dic13C2412yes—
311#6101—22no—
312#6101—22no—
313#6101—22no—
314#6101—22no—
315#6101—22no—
316#6101—22no—
317C4×Dic13—22no—
318C4×Dic13—22no—
319C4×Dic13—22no—
320#6099—28no—
321C2×#1055C2418yes—
322#3444—131no—
323C22×C4×Q8D1311yescharacteristic, complemented
324#3117—134no—
325#3113—132no—
326#3112—132no—
327#3108—134no—
328#3104—132no—
329#3103—132no—
330#3092—132no—
331#3078—132no—
332#3037—132no—
333#3004—132no—
334C4×#137—134no—
335#2920—131no—
336C23×C13—22no—
337C23×C13—22no—
338C23×C13—22no—
339C23×C13C22×D411yescharacteristic
340C23×C13C22×D411yescharacteristic
341C23×C13C22×D411yescharacteristic
342C22×D13—22no—
343Q8×C13—28no—
344Q8×C13—28no—
345Q8×C13—28no—
346Q8×C13—24no—
347Q8×C13C2×#4118yes—
348C2×C4×C13—28no—
349C2×C4×C13—28no—
350C2×C4×C13—28no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—24no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—24no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—44no—
370C2×C4×C13—44no—
371C2×C4×C13—44no—
372C2×C4×C13#13714yescomplemented
373C2×C4×C13C22×D411yescharacteristic
374C2×C4×C13C22×D411yescharacteristic
375C2×C4×C13C22×D411yescharacteristic
376C2×C4×C13C22×D411yescharacteristic
377C2×C4×C13C22×D411yescharacteristic
378C2×C4×C13C22×D411yescharacteristic
379C2×C4×C13C22×D411yescharacteristic
380C2×C4×C13C22×D411yescharacteristic
381C2×C4×C13C22×D411yescharacteristic
382C2×C4×C13C22×D411yescharacteristic
383C2×C4×C13C22×D411yescharacteristic
384C2×C4×C13C2×#4114yes—
385C2×C4×C13C2511yescharacteristic
386C22⋊D13—44no—
387C22⋊D13—44no—
388C22⋊D13—44no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392D52—24no—
393D52—42no—
394D52—42no—
395C4×D13—44no—
396C4×D13—44no—
397C4×D13—44no—
398Dic26—24no—
399Dic26—42no—
400Dic26—42no—
401#1055—28no—
402C23×Q8C2×D1311yescharacteristic
403C2×#137—134no—
404#533—131no—
405#533—131no—
406#533—131no—
407#532—131no—
408#532—131no—
409#532—131no—
410#529—132no—
411#529—132no—
412#529—261no—
413#529—261no—
414#529—261no—
415#529—261no—
416#525—132no—
417#525—261no—
418#525—261no—
419C4×#41—132no—
420C4×#41—261no—
421C4×#41—261no—
422C2×C4×Q8—21no—
423C2×C4×Q8—21no—
424C2×C4×Q8—21no—
425C2×C4×Q8—21no—
426C2×C4×Q8—21no—
427C2×C4×Q8—21no—
428C2×C4×Q8C2×D1312yes—
429C2×C4×Q8C2×D1312yes—
430C2×C4×Q8C2×D1312yes—
431C2×C4×Q8C2×D1312yes—
432C2×C4×Q8C2×D1312yes—
433C2×C4×Q8C2×D1312yes—
434C22×C4⋊C4—21no—
435C22×C4⋊C4C2×D1311yescharacteristic
436C22×C42—21no—
437C22×C42C2×D1311yescharacteristic
438#484—134no—
439#483—134no—
440#481—134no—
441#480—134no—
442#479—138no—
443#477—134no—
444#475—134no—
445#464—138no—
446#462—134no—
447#460—134no—
448#451—134no—
449#451—134no—
450#448—134no—
451#448—134no—
452#441—138no—
453#440—138no—
454C4×Q16—138no—
455C4×SD16—138no—
456#432—132no—
457#432—132no—
458#431—132no—
459#431—132no—
460#428—134no—
461#423—132no—
462#419—134no—
463#417—134no—
464#407—132no—
465C4×M16—132no—
466C22×C13—28no—
467C22×C13—21no—
468C22×C13—21no—
469C22×C13—21no—
470C22×C13—21no—
471C22×C13—21no—
472C22×C13—21no—
473C22×C13#52512yes—
474C22×C13C2×#13712yes—
475C22×C13#57512yes—
476C22×C13C23×D411yescharacteristic
477C2×D13—42no—
478C2×D13—42no—
479C2×D13—42no—
480C4×C13—28no—
481C4×C13—21no—
482C4×C13—21no—
483C4×C13—21no—
484C4×C13—21no—
485C4×C13—21no—
486C4×C13—21no—
487C4×C13—21no—
488C4×C13—21no—
489C4×C13—44no—
490C4×C13#52512yes—
491C4×C13C2×#13712yes—
492C4×C13C2×#13712yes—
493C4×C13C22×#4112yes—
494Dic13—42no—
495Dic13—42no—
496Dic13—42no—
497C2×#41—132no—
498C2×#41—261no—
499C2×#41—261no—
500C22×Q8—28no—
501C22×Q8—21no—
502C22×Q8—21no—
503C22×Q8—21no—
504C22×Q8C22×D1312yes—
505C22×Q8C22×D1312yes—
506C22×Q8C22×D1312yes—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C22⋊D1311yescharacteristic
510C23×C4C22⋊D1311yescharacteristic
511C23×C4C22×D1311yescharacteristic
512#137—2616no—
513C2×Q16—138no—
514C2×SD16—138no—
515C2×M16—134no—
516C4⋊Q8—131no—
517C4⋊Q8—131no—
518C4⋊Q8—131no—
519#127—131no—
520#126—262no—
521#126—262no—
522#125—132no—
523#125—261no—
524#125—261no—
525#124—132no—
526#124—261no—
527#124—261no—
528#123—262no—
529#123—262no—
530#123—262no—
531C22⋊Q8—132no—
532C22⋊Q8—132no—
533C22⋊Q8—261no—
534C22⋊Q8—261no—
535C22⋊Q8—261no—
536C22⋊Q8—261no—
537#121—132no—
538#121—132no—
539#121—261no—
540#121—261no—
541#121—261no—
542#121—261no—
543#120—262no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×Q8—132no—
557C4×Q8—132no—
558C4×Q8—261no—
559C4×Q8—261no—
560C4×Q8—261no—
561C4×Q8—261no—
562C4×Q8C22×D1314yes—
563C4×Q8C22×D1314yes—
564C4×Q8C22×D1314yes—
565C4×Q8C22×D1314yes—
566C4×D4—132no—
567C4×D4—132no—
568C4×D4—262no—
569C4×D4—262no—
570C4×D4—262no—
571C4×D4—262no—
572C4×D4—262no—
573C4×D4—262no—
574C4×D4—261no—
575C4×D4—261no—
576C4×D4—261no—
577C4×D4—261no—
578#117—132no—
579#117—261no—
580#117—261no—
581#117—262no—
582#117—262no—
583#117—262no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4C22×D1312yes—
594C2×C4⋊C4C22×D1312yes—
595C2×C4⋊C4C22×D1312yes—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—262no—
603C2×C42C22⋊D1311yescharacteristic
604C2×C42C22⋊D1311yescharacteristic
605C2×C42C22⋊D1311yescharacteristic
606C2×C42C22⋊D1311yescharacteristic
607C2×C42C22⋊D1311yescharacteristic
608C2×C42C22⋊D1311yescharacteristic
609C2×C42C22×D1311yescharacteristic
610C2×C42C22×D1311yescharacteristic
611C2×C42C22×D1311yescharacteristic
612C2×C42C22×D1311yescharacteristic
613C2×C42C22×D1311yescharacteristic
614C2×C42C22×D1311yescharacteristic
615#107—138no—
616#106—138no—
617C4⋊C8—134no—
618C4⋊C8—134no—
619#103—138no—
620#103—138no—
621#103—138no—
622#102—138no—
623C22⋊C8—134no—
624C22⋊C8—134no—
625#97—134no—
626C4×C8—134no—
627C2×C13—22no—
628C2×C13—22no—
629C2×C13—22no—
630C2×C13C2×#52511yescharacteristic
631C2×C13C22×#13711yescharacteristic
632C2×C13C2×#57511yescharacteristic
633D13—82no—
634C24C2×C22⋊D1311yescharacteristic
635#41—268no—
636#41—524no—
637#41—524no—
638C2×Q8—28no—
639C2×Q8—28no—
640C2×Q8—28no—
641C2×Q8—28no—
642C2×Q8—28no—
643C2×Q8—24no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—132no—
648C2×Q8—261no—
649C2×Q8—261no—
650C2×Q8#612718yescomplemented
651C2×Q8C23×D1314yes—
652C2×D4—132no—
653C2×D4—262no—
654C2×D4—262no—
655C2×D4—262no—
656C2×D4—261no—
657C2×D4—261no—
658C22×C4—28no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—42no—
668C22×C4—44no—
669C22×C4—262no—
670C22×C4—262no—
671C22×C4—262no—
672C22×C4C2×C22⋊D1311yescharacteristic
673C22×C4C2×C22⋊D1311yescharacteristic
674C22×C4C2×C22⋊D1311yescharacteristic
675C22×C4C2×C22⋊D1311yescharacteristic
676C22×C4C2×C22⋊D1311yescharacteristic
677C22×C4C2×C22⋊D1311yescharacteristic
678C22×C4C2×C22⋊D1311yescharacteristic
679C22×C4C2×C22⋊D1311yescharacteristic
680C22×C4C2×C22⋊D1311yescharacteristic
681C22×C4C2×C22⋊D1311yescharacteristic
682C22×C4C2×C22⋊D1311yescharacteristic
683C22×C4C2×C22⋊D1311yescharacteristic
684C22×C4C2×C22⋊D1311yescharacteristic
685C22×C4C2×C22⋊D1311yescharacteristic
686C22×C4C2×C22⋊D1311yescharacteristic
687C22×C4C23×D1311yescharacteristic
688C22×C4C23×D1311yescharacteristic
689C22×C4C23×D1311yescharacteristic
690Q16—2616no—
691SD16—2616no—
692M16—268no—
693C2×C8—138no—
694C4⋊C4—24no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—132no—
702C4⋊C4—132no—
703C4⋊C4—262no—
704C4⋊C4—262no—
705C4⋊C4—261no—
706C4⋊C4—261no—
707C4⋊C4—261no—
708C4⋊C4—261no—
709C4⋊C4—262no—
710C4⋊C4—262no—
711C4⋊C4—262no—
712C4⋊C4—262no—
713C4⋊C4C23×D1314yes—
714C22⋊C4—262no—
715C22⋊C4—262no—
716C22⋊C4—262no—
717C22⋊C4—262no—
718C22⋊C4—262no—
719C22⋊C4—262no—
720C22⋊C4—262no—
721C22⋊C4—262no—
722C22⋊C4—262no—
723C42—24no—
724C42—24no—
725C42—24no—
726C42—24no—
727C42—262no—
728C42—262no—
729C42—262no—
730C42C2×C22⋊D1311yescharacteristic
731C42C2×C22⋊D1311yescharacteristic
732C42C2×C22⋊D1311yescharacteristic
733C42C2×C22⋊D1311yescharacteristic
734C42C2×C22⋊D1311yescharacteristic
735C42C2×C22⋊D1311yescharacteristic
736C42C2×C22⋊D1311yescharacteristic
737C42C2×C22⋊D1311yescharacteristic
738C42C2×C22⋊D1311yescharacteristic
739C42C2×C22⋊D1311yescharacteristic
740C42C2×C22⋊D1311yescharacteristic
741C42C2×C22⋊D1311yescharacteristic
742C42C23×D1311yescharacteristic
743C42C23×D1311yescharacteristic
744C42C23×D1311yescharacteristic
745C42C23×D1311yescharacteristic
746C13#6056011yescharacteristic, complemented, Sylow
747C23—22no—
748C23—22no—
749C23—22no—
750C23—262no—
751C23C22×C22⋊D1311yescharacteristic
752C23C22×C22⋊D1311yescharacteristic
753C23C22×C22⋊D1311yescharacteristic
754Q8—28no—
755Q8—28no—
756Q8—28no—
757Q8—24no—
758Q8—264no—
759Q8—522no—
760Q8—522no—
761Q8C2×#612718yes—
762D4—264no—
763D4—522no—
764D4—524no—
765D4—524no—
766D4—524no—
767D4—522no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—262no—
793C2×C4—262no—
794C2×C4—262no—
795C2×C4—524no—
796C2×C4—524no—
797C2×C4—524no—
798C2×C4#8819614yescomplemented
799C2×C4C2×#612714yes—
800C2×C4C22×C22⋊D1311yescharacteristic
801C2×C4C22×C22⋊D1311yescharacteristic
802C2×C4C22×C22⋊D1311yescharacteristic
803C2×C4C22×C22⋊D1311yescharacteristic
804C2×C4C22×C22⋊D1311yescharacteristic
805C2×C4C22×C22⋊D1311yescharacteristic
806C2×C4C22×C22⋊D1311yescharacteristic
807C2×C4C22×C22⋊D1311yescharacteristic
808C2×C4C22×C22⋊D1311yescharacteristic
809C2×C4C22×C22⋊D1311yescharacteristic
810C2×C4C22×C22⋊D1311yescharacteristic
811C2×C4C24×D1311yescharacteristic
812C8—268no—
813C22—28no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—522no—
821C22—522no—
822C22—522no—
823C22#1171949612yes—
824C22C2×#8819612yes—
825C22#1171952712yes—
826C22C23×C22⋊D1311yescharacteristic
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—28no—
834C4—21no—
835C4—21no—
836C4—44no—
837C4—522no—
838C4—522no—
839C4—522no—
840C4#1171949612yes—
841C4C2×#8819612yes—
842C4C2×#8819612yes—
843C4C22×#612712yes—
844C2—22no—
845C2—22no—
846C2—22no—
847C2—1042no—
848C2C2×#1171949611yescharacteristic
849C2C22×#8819611yescharacteristic
850C2C2×#1171952711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C4×Q8×C13C2
socleC22×C13C23×D4
prime radical#13128132C2
hypercenterC22×C4×Q8D13
hypocenterC13#60560
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #13125007C2semidirect
3. #13124966C2semidirect
4. #13124958C2semidirect
5. #13124916C2semidirect
6. #13124875C2semidirect
7. #13124867C2semidirect
8. #13124759C2semidirect
9. #13124641C2semidirect
10. #13124308C2semidirect
11. #13124070C2semidirect
12. C4×#88196C2semidirect
13. #13123469C2semidirect
14. C22×C4×Q8×C13C2semidirect
57. #11718692C22semidirect
58. #11718691C22semidirect
59. C4×#6107C22semidirect
60. #11718689C22semidirect
61. #11718688C22semidirect
62. #11718687C22semidirect
63. C4×#6106C22semidirect
64. #11718683C22semidirect
65. #11718682C22semidirect
66. #11718681C22semidirect
220. C2×Q8×C13#41semidirect
323. C22×C4×Q8D13semidirect
372. C2×C4×C13#137semidirect
650. C2×Q8#6127semidirect
746. C13#60560semidirect
798. C2×C4#88196semidirect

Maximal subgroups

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

subgroupindex
#131281322
#131250072
#131249662
#131249582
#131249162
#131248752
#131248672
#131247592
#131246412
#131243082
#131240702
C4×#881962
#131234692
C22×C4×Q8×C132
#6056013