Finite Group Databasebeta

← #28247545

Subgroups — #28247545

Order 13568.

4874 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811459C211yesmaximal, characteristic
2C2×#16811388C211yesmaximal, characteristic, complemented
3C2×#131×D53C211yesmaximal, characteristic, complemented
4#20283165C213yesmaximal, complemented
5#20283164C211yesmaximal, characteristic, complemented
6#20283163C213yesmaximal, complemented
7#20283163C213yesmaximal, complemented
8#20283162C211yesmaximal, characteristic, complemented
9#20283162C211yesmaximal, characteristic, complemented
10#20283161C213yesmaximal, complemented
11#20283158C213yesmaximal, complemented
12#20283157C213yesmaximal, complemented
13C2×#16810588C213yesmaximal, complemented
14#408×D53C213yesmaximal, complemented
15C53×#2880C211yesmaximal, characteristic, complemented
16#16811459—28no—
17#16811459—28no—
18C2×#13133265C411yescharacteristic
19C2×#13133265C411yescharacteristic
20C2×#13133264C413yes—
21C2×#13133264C411yescharacteristic
22C2×#13133263C411yescharacteristic
23C2×#13133263C413yes—
24C2×#13133262C413yes—
25C2×#13133262C413yes—
26C22×#11719945C2213yes—
27C22×#11719945C2213yes—
28C2×#41×D53C2213yes—
29C2×#41×D53C2211yescharacteristic
30C2×#41×D53C2213yes—
31C2×#41×D53C2211yescharacteristic
32#16811388—28no—
33C2×#13133225C2213yescomplemented
34C2×#13133225C2213yescomplemented
35C2×#13133224C2211yescharacteristic, complemented
36C2×#13133224C2211yescharacteristic, complemented
37C2×#13133223C2213yescomplemented
38C2×#13133223C2213yescomplemented
39#131×D53—28no—
40C22×#11719912C2213yescomplemented
41C2×M16×D53C2213yescomplemented
42C2×M16×D53C2213yescomplemented
43C22×C8×D53C2213yescomplemented
44#16810591C2213yescomplemented
45#16810591C2213yescomplemented
46#16810590C2213yescomplemented
47#16810590C2213yescomplemented
48#16810589C2213yescomplemented
49#16810589C2213yescomplemented
50#16810588C2213yescomplemented
51#16810588C2216yescomplemented
52#16810588C2211yescharacteristic, complemented
53#16810588C2213yescomplemented
54#16810588C2213yescomplemented
55#16810588C2213yescomplemented
56#16810588C2213yescomplemented
57#16810588C2213yescomplemented
58#16810588C2213yescomplemented
59#16810588C2216yescomplemented
60#16810588C2216yescomplemented
61#16810587C2213yescomplemented
62#16810586C2213yescomplemented
63#16810586C2213yescomplemented
64#16810585C2216yescomplemented
65#16810585C2216yescomplemented
66C2×C22⋊#88322C2213yescomplemented
67C2×#13133129C2213yescomplemented
68C2×#13133129C2213yescomplemented
69C22⋊C8×D53C2216yescomplemented
70C22⋊C8×D53C2216yescomplemented
71C22×#41×C53C2211yescharacteristic
72C2×#131×C53C2211yescharacteristic, complemented
73C2×#131×C53C2211yescharacteristic, complemented
74C53×#408C2213yescomplemented
75C53×#408C2213yescomplemented
76C53×#407C2213yescomplemented
77C2×C22⋊C8×C53C2213yescomplemented
78#13133265—28no—
79#13133265—28no—
80#13133264—28no—
81#13133264—224no—
82#13133263—28no—
83#13133263—224no—
84#13133262—224no—
85#13133262—224no—
86C2×#11719949C2×C411yescharacteristic
87C2×#11719949C2×C413yes—
88C2×#11719949C2×C413yes—
89C2×#11719949C2×C411yescharacteristic
90C2×#11719945—212no—
91C2×#11719945—212no—
92C2×#11719945—212no—
93C2×#11719945—212no—
94C2×#11719945C2×C413yes—
95C2×#11719945C2×C413yes—
96C2×#11719945C2×C413yes—
97C2×#11719945C2×C413yes—
98C2×#11719945C2×C416yes—
99C2×#11719945C2×C413yes—
100C2×#11719945C2×C413yes—
101C2×#11719945C2313yes—
102C2×#11719945C2313yes—
103C2×#11719945C2311yescharacteristic
104C2×#11719945C2313yes—
105C2×#11719945C2313yes—
106C2×#11719945C2313yes—
107C2×#11719947C2×C413yes—
108C2×#11719947C2×C416yes—
109C2×#11719947C2×C416yes—
110C2×#11719947C2×C413yes—
111C2×#11719947C2×C413yes—
112C2×#11719947C2×C413yes—
113#41×D53—24no—
114#41×D53—24no—
115#41×D53—212no—
116#41×D53—212no—
117#41×D53—212no—
118#41×D53—212no—
119#41×D53D418yes—
120#41×D53D418yes—
121C22×Dic106C2×C413yes—
122C22×Dic106C2×C413yes—
123C2×Q8×D53C2×C411yescharacteristic
124C2×Q8×D53C2×C413yes—
125C2×Q8×D53C2×C413yes—
126C2×Q8×D53C2×C411yescharacteristic
127C22×D212C2×C413yes—
128C22×D212C2×C413yes—
129C22×C22⋊D53C2×C413yes—
130C22×C22⋊D53C2×C416yes—
131C22×C22⋊D53C2×C413yes—
132C2×D4×D53C2×C416yes—
133C2×D4×D53C2×C413yes—
134C2×D4×D53C2×C416yes—
135C2×D4×D53C2×C413yes—
136C2×D4×D53C2×C413yes—
137C2×D4×D53C2×C413yes—
138C22×C4×D53C2316yes—
139C22×C4×D53C2313yes—
140C22×C4×D53C2313yes—
141#13133225—212no—
142#13133225—212no—
143#13133224—24no—
144#13133224—24no—
145#13133223—212no—
146#13133223—212no—
147C2×#11719917C2313yes—
148C2×#11719917C2313yes—
149C2×#11719912—212no—
150C2×#11719912C2316yes—
151C2×#11719912C2313yes—
152C2×#11719912C2313yes—
153C2×#11719912C2313yes—
154C2×#11719912C2311yescharacteristic
155M16×D53—212no—
156M16×D53—212no—
157C22×#88322C2313yes—
158C22×#88322C2313yes—
159C2×C8×D53—212no—
160C2×C8×D53C2313yes—
161C2×C8×D53C2313yes—
162C2×C8×D53C2316yes—
163C2×C8×D53C2311yescharacteristic
164C2×C8×D53C2313yes—
165C22⋊#88322C2313yes—
166C22⋊#88322C2316yes—
167C22⋊#88322C2311yescharacteristic
168C22⋊#88322C2313yes—
169C22⋊#88322C2313yes—
170#13133129C2313yes—
171#13133129C2313yes—
172#13133129C2316yes—
173#13133129C2316yes—
174#13133129C2311yescharacteristic
175#13133129C2311yescharacteristic
176#13133129C2313yes—
177#13133129C2313yes—
178#13133129C2313yes—
179#13133129C2313yes—
180C2×#41×C53—24no—
181C2×#41×C53—24no—
182C2×#41×C53C2×C411yescharacteristic
183C2×#41×C53C2×C413yes—
184C2×#41×C53C2313yes—
185C2×#41×C53C2311yescharacteristic
186C22×Q8×C53C2×C411yescharacteristic
187C22×D4×C53C2×C413yes—
188C23×C4×C53C2313yes—
189#131×C53—24no—
190#131×C53—24no—
191C2×M16×C53C2313yes—
192C2×M16×C53C2313yes—
193C22×C8×C53C2313yes—
194C22×C8×C53C2313yes—
195C22⋊C8×C53C2313yes—
196C22⋊C8×C53C2316yes—
197C22⋊C8×C53C2313yes—
198C22⋊C8×C53C2311yescharacteristic
199C22⋊C8×C53C2313yes—
200C24×C53C22×C413yes—
201C23×D53C22×C413yes—
202C23×D53C22×C416yes—
203C23×D53C22×C413yes—
204#41×C53—24no—
205#41×C53—212no—
206#41×C53—26no—
207#41×C53—26no—
208#41×C53C2×D414yes—
209#41×C53C2×D414yes—
210C2×Q8×C53—24no—
211C2×Q8×C53C22×C413yes—
212C2×Q8×C53C22×C411yescharacteristic
213C2×D4×C53—212no—
214C2×D4×C53C22×C416yes—
215C2×D4×C53C22×C413yes—
216C2×D4×C53C22×C413yes—
217C22×C4×C53—26no—
218C22×C4×C53—26no—
219C22×C4×C53C22×C413yes—
220C22×C4×C53C22×C413yes—
221C22×C4×C53C22×C413yes—
222C22×C4×C53C2411yescharacteristic
223C22×C4×C53C2413yes—
224C22×C4×C53C2413yes—
225C2×C22⋊D53—212no—
226C2×C22⋊D53—224no—
227C2×C22⋊D53—212no—
228C2×C22⋊D53C22×C416yes—
229C2×C22⋊D53C22×C413yes—
230C2×C22⋊D53C22×C413yes—
231C2×C22⋊D53C22×C413yes—
232C2×C22⋊D53C22×C413yes—
233C2×C22⋊D53C22×C413yes—
234C2×C22⋊D53C22×C411yescharacteristic
235C2×C22⋊D53C22×C411yescharacteristic
236C2×C22⋊D53C22×C413yes—
237C2×C22⋊D53C22×C416yes—
238C22×Dic53C22×C413yes—
239C22×Dic53C22×C416yes—
240C22×Dic53C22×C413yes—
241#11719949—24no—
242#11719949—212no—
243#11719949—212no—
244#11719949C22⋊C418yes—
245Q8×D53—24no—
246Q8×D53—212no—
247Q8×D53—212no—
248Q8×D53C22⋊C418yes—
249#11719947—212no—
250#11719947—224no—
251#11719947—224no—
252#11719947—212no—
253#11719947—212no—
254#11719947C22⋊C4124yes—
255D4×D53—224no—
256D4×D53—212no—
257D4×D53—224no—
258D4×D53—212no—
259D4×D53—212no—
260D4×D53C22⋊C4124yes—
261#11719945—26no—
262#11719945—26no—
263#11719945—224no—
264#11719945—212no—
265#11719945—212no—
266#11719945—212no—
267#11719945—212no—
268#11719945—212no—
269#11719945—26no—
270#11719945—26no—
271#11719945—26no—
272#11719945—26no—
273#11719945—26no—
274#11719945—26no—
275#11719945—22no—
276#11719945—22no—
277#11719945—212no—
278#11719945C2×D4112yes—
279#11719945C2×D4112yes—
280C2×D212—212no—
281C2×D212—212no—
282C2×D212C22×C413yes—
283C2×D212C22×C413yes—
284C2×D212C22×C413yes—
285C2×D212C22×C413yes—
286C2×D212C22×C411yescharacteristic
287C2×D212C22×C413yes—
288C2×C4×D53—26no—
289C2×C4×D53—26no—
290C2×C4×D53—212no—
291C2×C4×D53—212no—
292C2×C4×D53C22×C416yes—
293C2×C4×D53C22×C413yes—
294C2×C4×D53C22×C413yes—
295C2×C4×D53C22×C416yes—
296C2×C4×D53C22×C413yes—
297C2×C4×D53C22×C413yes—
298C2×C4×D53C2×D4112yes—
299C2×C4×D53C2×D4112yes—
300C2×C4×D53C2413yes—
301C2×C4×D53C2411yescharacteristic
302C2×C4×D53C2413yes—
303C2×C4×D53C2411yescharacteristic
304C2×Dic106—212no—
305C2×Dic106—212no—
306C2×Dic106C22×C413yes—
307C2×Dic106C22×C413yes—
308C2×Dic106C22×C413yes—
309C2×Dic106C22×C411yescharacteristic
310C2×Dic106C22×C413yes—
311C2×Dic106C22×C413yes—
312M16×C53—26no—
313M16×C53—26no—
314C2×C8×C53—26no—
315C2×C8×C53—26no—
316C2×C8×C53C2411yescharacteristic
317C2×C8×C53C2411yescharacteristic
318C2×C8×C53C2413yes—
319C2×C8×C53C2413yes—
320#11719917—26no—
321#11719917—26no—
322C2×#88322—26no—
323C2×#88322—26no—
324C2×#88322C2411yescharacteristic
325C2×#88322C2413yes—
326C2×#88322C2413yes—
327C2×#88322C2411yescharacteristic
328#11719912—26no—
329#11719912—212no—
330#11719912—22no—
331#11719912—26no—
332#11719912—26no—
333C8×D53—22no—
334C8×D53—26no—
335C8×D53—26no—
336C8×D53—26no—
337C8×D53—212no—
338C23×C53—26no—
339C23×C53—43no—
340C23×C53—43no—
341C23×C53C23×C413yes—
342C23×C53C23×C411yescharacteristic
343C23×C53C23×C413yes—
344C22×D53—26no—
345C22×D53—212no—
346C22×D53—43no—
347C22×D53—43no—
348C22×D53—46no—
349C22×D53—46no—
350C22×D53—43no—
351C22×D53—43no—
352C22×D53C2×C22⋊C4112yes—
353C22×D53C23×C411yescharacteristic
354C22×D53C23×C413yes—
355C22×D53C23×C413yes—
356C22×D53C23×C411yescharacteristic
357Q8×C53—26no—
358Q8×C53C2×C22⋊C414yes—
359D4×C53—212no—
360D4×C53—26no—
361D4×C53C2×C22⋊C4112yes—
362C2×C4×C53—26no—
363C2×C4×C53—26no—
364C2×C4×C53—26no—
365C2×C4×C53—23no—
366C2×C4×C53—23no—
367C2×C4×C53—21no—
368C2×C4×C53—21no—
369C2×C4×C53C23×C411yescharacteristic
370C2×C4×C53C23×C413yes—
371C2×C4×C53C23×C413yes—
372C2×C4×C53C22×D416yes—
373C2×C4×C53C22×D416yes—
374C2×C4×C53C2511yescharacteristic
375C22⋊D53—212no—
376C22⋊D53—26no—
377C22⋊D53—22no—
378C22⋊D53—26no—
379C22⋊D53—26no—
380C22⋊D53—22no—
381C22⋊D53—26no—
382C22⋊D53—26no—
383C22⋊D53—26no—
384C22⋊D53C2×C22⋊C4124yes—
385C2×Dic53—26no—
386C2×Dic53—212no—
387C2×Dic53C2×C22⋊C4112yes—
388C2×Dic53C23×C413yes—
389C2×Dic53C23×C411yescharacteristic
390C2×Dic53C23×C411yescharacteristic
391C2×Dic53C23×C413yes—
392D212—26no—
393D212—22no—
394D212—26no—
395D212—26no—
396D212—26no—
397D212C2×C22⋊C4112yes—
398C4×D53—212no—
399C4×D53—26no—
400C4×D53—26no—
401C4×D53—21no—
402C4×D53—21no—
403C4×D53—23no—
404C4×D53—23no—
405C4×D53—212no—
406C4×D53C2×C22⋊C4112yes—
407C4×D53C2×C22⋊C4112yes—
408C4×D53C22×D416yes—
409C4×D53C22×D416yes—
410C4×D53C22×D412yes—
411C4×D53C22×D412yes—
412Dic106—26no—
413Dic106—22no—
414Dic106—26no—
415Dic106—26no—
416Dic106—26no—
417Dic106C2×C22⋊C4112yes—
418C8×C53—21no—
419C8×C53—23no—
420C8×C53—23no—
421C8×C53—21no—
422#88322—21no—
423#88322—23no—
424#88322—23no—
425#88322—21no—
426#60065—531nomaximal, Sylow
427C22×C53—23no—
428C22×C53—23no—
429C22×C53—23no—
430C22×C53—21no—
431C22×C53—23no—
432C22×C53—23no—
433C22×C53—21no—
434C22×C53—21no—
435C22×C53—86no—
436C22×C53C22×C22⋊C416yes—
437C22×C53C24×C411yescharacteristic
438C2×D53—21no—
439C2×D53—23no—
440C2×D53—21no—
441C2×D53—23no—
442C2×D53—21no—
443C2×D53—23no—
444C2×D53—23no—
445C2×D53—21no—
446C2×D53—23no—
447C2×D53—21no—
448C2×D53—412no—
449C2×D53—812no—
450C2×D53—86no—
451C2×D53C22×C22⋊C416yes—
452C2×D53C22×C22⋊C412yes—
453C4×C53—21no—
454C4×C53—23no—
455C4×C53C22×C22⋊C416yes—
456C4×C53C23×D411yescharacteristic
457C4×C53C23×D411yescharacteristic
458Dic53—23no—
459Dic53—21no—
460Dic53C22×C22⋊C412yes—
461Dic53C22×C22⋊C416yes—
462C2×#585—531no—
463C2×#568—531no—
464C22×#131—531no—
465#2880—533no—
466#2880—533no—
467#2880—533no—
468#2880—533no—
469#2880—531no—
470#2880—531no—
471#2880—531no—
472#2880D5311yescharacteristic, complemented
473#2879—533no—
474#2879—533no—
475C2×#408—533no—
476C2×#408—533no—
477C2×C53—26no—
478C2×C53—43no—
479C2×C53—41no—
480C2×C53C23×C22⋊C411yescharacteristic
481C2×C53#357311yescharacteristic
482C2×C53#357311yescharacteristic
483D53—22no—
484D53—26no—
485D53—43no—
486D53—41no—
487#585—1068no—
488#585—1068no—
489C2×2−1+4—531no—
490C2×2−1+4—533no—
491C2×2−1+4—531no—
492C2×2−1+4—531no—
493C2×H(5,𝔽2)—533no—
494C2×H(5,𝔽2)—531no—
495C2×H(5,𝔽2)—533no—
496C2×H(5,𝔽2)—533no—
497C22×#41—531no—
498C22×#41—533no—
499C22×#41—533no—
500C22×#41—531no—
501C22×#41—533no—
502C22×#41—533no—
503C22×#41C2×D5311yescharacteristic
504#568—1068no—
505C2×#131—531no—
506C2×#131—531no—
507C2×#131—533no—
508C2×#131—533no—
509C2×#131—533no—
510C2×#131—533no—
511C2×#131—1068no—
512C2×#131C2×D5311yescharacteristic, complemented
513C2×#131C2×D5311yescharacteristic, complemented
514C22×M16—533no—
515C22×M16—533no—
516C22×M16—533no—
517C23×C8—533no—
518#408—533no—
519#408—533no—
520#408—533no—
521#408—533no—
522#408—533no—
523#408—533no—
524#408—533no—
525#408—531no—
526#408—536no—
527#408—533no—
528#408—533no—
529#408—533no—
530#408—533no—
531#408—533no—
532#408—533no—
533#408—536no—
534#408—536no—
535#408C2×D5313yescomplemented
536#408C2×D5313yescomplemented
537#407—533no—
538#407—533no—
539#407—533no—
540#407—536no—
541#407—536no—
542#407C2×D5313yescomplemented
543C2×C22⋊C8—533no—
544C2×C22⋊C8—533no—
545C2×C22⋊C8—533no—
546C2×C22⋊C8—536no—
547C2×C22⋊C8—536no—
548C2×C22⋊C8C2×D5313yescomplemented
549C53#6006511yescharacteristic, complemented, Sylow
5502−1+4—1068no—
5512−1+4—1068no—
5522−1+4—1068no—
5532−1+4—10624no—
554H(5,𝔽2)—10624no—
555H(5,𝔽2)—10624no—
556H(5,𝔽2)—10624no—
557H(5,𝔽2)—1068no—
558C2×#41—24no—
559C2×#41—24no—
560C2×#41—538no—
561C2×#41—538no—
562C2×#41—531no—
563C2×#41—533no—
564C2×#41—533no—
565C2×#41—531no—
566C2×#41—533no—
567C2×#41—536no—
568C2×#41—533no—
569C2×#41—536no—
570C2×#41—533no—
571C2×#41—533no—
572C2×#41—533no—
573C2×#41—533no—
574C2×#41—533no—
575C2×#41—533no—
576C2×#41—536no—
577C2×#41—533no—
578C2×#41—533no—
579C2×#41—533no—
580C2×#41—533no—
581C2×#41—533no—
582C2×#41—531no—
583C2×#41—533no—
584C2×#41—533no—
585C2×#41—10612no—
586C2×#41—10612no—
587C2×#41—10612no—
588C2×#41—10612no—
589C2×#41—10612no—
590C2×#41—10612no—
591C2×#41—10612no—
592C2×#41—10612no—
593C2×#41—1064no—
594C2×#41—1064no—
595C2×#41C4×D5311yescharacteristic
596C2×#41C4×D5313yes—
597C2×#41C22×D5313yes—
598C2×#41C22×D5311yescharacteristic
599C22×Q8—531no—
600C22×Q8—533no—
601C22×Q8—533no—
602C22×Q8—531no—
603C22×Q8—533no—
604C22×Q8—533no—
605C22×Q8C4×D5311yescharacteristic
606C22×D4—533no—
607C22×D4—533no—
608C22×D4—536no—
609C22×D4—533no—
610C22×D4—533no—
611C22×D4—536no—
612C22×D4—533no—
613C22×D4—536no—
614C22×D4—533no—
615C22×D4—533no—
616C22×D4—533no—
617C22×D4C4×D5313yes—
618C23×C4—533no—
619C23×C4—536no—
620C23×C4—533no—
621C23×C4C22×D5313yes—
622#131—24no—
623#131—24no—
624#131—10612no—
625#131—10612no—
626#131—10612no—
627#131—10612no—
628#131—1064no—
629#131—1064no—
630C2×M16—533no—
631C2×M16—533no—
632C2×M16—533no—
633C2×M16—531no—
634C2×M16—536no—
635C2×M16—533no—
636C2×M16—533no—
637C2×M16—10612no—
638C2×M16—10612no—
639C2×M16—10612no—
640C2×M16C22×D5313yes—
641C2×M16C22×D5313yes—
642C22×C8—533no—
643C22×C8—533no—
644C22×C8—531no—
645C22×C8—533no—
646C22×C8—533no—
647C22×C8—533no—
648C22×C8—536no—
649C22×C8—10612no—
650C22×C8C22×D5313yes—
651C22×C8C22×D5313yes—
652C22⋊C8—533no—
653C22⋊C8—531no—
654C22⋊C8—536no—
655C22⋊C8—533no—
656C22⋊C8—533no—
657C22⋊C8—533no—
658C22⋊C8—531no—
659C22⋊C8—533no—
660C22⋊C8—531no—
661C22⋊C8—536no—
662C22⋊C8—536no—
663C22⋊C8—533no—
664C22⋊C8—533no—
665C22⋊C8—533no—
666C22⋊C8—533no—
667C22⋊C8C22×D5313yes—
668C22⋊C8C22×D5316yes—
669C22⋊C8C22×D5311yescharacteristic
670C22⋊C8C22×D5313yes—
671C22⋊C8C22×D5313yes—
672C24—533no—
673C24—536no—
674C24—533no—
675C24C2×C4×D5313yes—
676#41—24no—
677#41—212no—
678#41—26no—
679#41—26no—
680#41—538no—
681#41—5324no—
682#41—5312no—
683#41—5312no—
684#41—1062no—
685#41—1066no—
686#41—1066no—
687#41—1062no—
688#41—1066no—
689#41—1066no—
690#41—1066no—
691#41—1066no—
692#41—10612no—
693#41—10612no—
694#41—10612no—
695#41—10612no—
696#41—10624no—
697#41—10612no—
698#41—10612no—
699#41—10624no—
700#41—10612no—
701#41—10612no—
702#41—10624no—
703#41—10612no—
704#41—10612no—
705#41—1064no—
706#41—10612no—
707#41—1066no—
708#41—1066no—
709#41D4×D5314yes—
710#41D4×D5314yes—
711C2×Q8—24no—
712C2×Q8—538no—
713C2×Q8—533no—
714C2×Q8—533no—
715C2×Q8—533no—
716C2×Q8—531no—
717C2×Q8—533no—
718C2×Q8—533no—
719C2×Q8—10612no—
720C2×Q8—10612no—
721C2×Q8—10612no—
722C2×Q8—10612no—
723C2×Q8—1064no—
724C2×Q8C2×C4×D5313yes—
725C2×Q8C2×C4×D5311yescharacteristic
726C2×D4—212no—
727C2×D4—536no—
728C2×D4—5324no—
729C2×D4—533no—
730C2×D4—533no—
731C2×D4—531no—
732C2×D4—533no—
733C2×D4—533no—
734C2×D4—533no—
735C2×D4—531no—
736C2×D4—533no—
737C2×D4—536no—
738C2×D4—533no—
739C2×D4—533no—
740C2×D4—533no—
741C2×D4—531no—
742C2×D4—533no—
743C2×D4—533no—
744C2×D4—10612no—
745C2×D4—10612no—
746C2×D4—10612no—
747C2×D4—10612no—
748C2×D4—10624no—
749C2×D4—10612no—
750C2×D4—10624no—
751C2×D4—10624no—
752C2×D4—10612no—
753C2×D4—10612no—
754C2×D4C2×C4×D5316yes—
755C2×D4C2×C4×D5313yes—
756C2×D4C2×C4×D5313yes—
757C22×C4—26no—
758C22×C4—26no—
759C22×C4—533no—
760C22×C4—533no—
761C22×C4—533no—
762C22×C4—5312no—
763C22×C4—5312no—
764C22×C4—531no—
765C22×C4—533no—
766C22×C4—536no—
767C22×C4—533no—
768C22×C4—536no—
769C22×C4—536no—
770C22×C4—533no—
771C22×C4—533no—
772C22×C4—533no—
773C22×C4—531no—
774C22×C4—10612no—
775C22×C4—10612no—
776C22×C4—1066no—
777C22×C4—1066no—
778C22×C4C2×C4×D5313yes—
779C22×C4C2×C4×D5313yes—
780C22×C4C2×C4×D5313yes—
781C22×C4C23×D5313yes—
782C22×C4C23×D5311yescharacteristic
783C22×C4C23×D5313yes—
784M16—26no—
785M16—26no—
786M16—1062no—
787M16—1066no—
788M16—1066no—
789M16—1066no—
790M16—10612no—
791M16—1066no—
792M16—1066no—
793C2×C8—26no—
794C2×C8—26no—
795C2×C8—531no—
796C2×C8—531no—
797C2×C8—533no—
798C2×C8—533no—
799C2×C8—1062no—
800C2×C8—1066no—
801C2×C8—1066no—
802C2×C8—1066no—
803C2×C8—10612no—
804C2×C8—1066no—
805C2×C8—1066no—
806C2×C8C23×D5311yescharacteristic
807C2×C8C23×D5313yes—
808C2×C8C23×D5313yes—
809C2×C8C23×D5311yescharacteristic
810C23—26no—
811C23—43no—
812C23—43no—
813C23—531no—
814C23—533no—
815C23—5312no—
816C23—533no—
817C23—531no—
818C23—10612no—
819C23—1066no—
820C23—2123no—
821C23—2123no—
822C23—2126no—
823C23—2126no—
824C23—2123no—
825C23—2123no—
826C23C22×C4×D5313yes—
827C23C22×C4×D5311yescharacteristic
828C23C22×C4×D5313yes—
829Q8—26no—
830Q8—5312no—
831Q8—1062no—
832Q8—1066no—
833Q8—1066no—
834Q8—1066no—
835Q8—1066no—
836Q8C22⋊C4×D5314yes—
837D4—212no—
838D4—26no—
839D4—5324no—
840D4—5312no—
841D4—1062no—
842D4—1066no—
843D4—1066no—
844D4—1066no—
845D4—1062no—
846D4—1066no—
847D4—1066no—
848D4—1066no—
849D4—1062no—
850D4—1066no—
851D4—1066no—
852D4—1066no—
853D4—10612no—
854D4—1066no—
855D4C22⋊C4×D53112yes—
856C2×C4—26no—
857C2×C4—26no—
858C2×C4—26no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—23no—
862C2×C4—23no—
863C2×C4—5312no—
864C2×C4—531no—
865C2×C4—533no—
866C2×C4—5312no—
867C2×C4—5312no—
868C2×C4—532no—
869C2×C4—536no—
870C2×C4—536no—
871C2×C4—532no—
872C2×C4—533no—
873C2×C4—531no—
874C2×C4—10612no—
875C2×C4—10612no—
876C2×C4—10612no—
877C2×C4—1066no—
878C2×C4—1066no—
879C2×C4—1066no—
880C2×C4—1063no—
881C2×C4—1063no—
882C2×C4—1061no—
883C2×C4—1061no—
884C2×C4C22×C4×D5313yes—
885C2×C4C22×C4×D5311yescharacteristic
886C2×C4C22×C4×D5313yes—
887C2×C4C2×D4×D5316yes—
888C2×C4C2×D4×D5316yes—
889C2×C4C24×D5311yescharacteristic
890C8—21no—
891C8—21no—
892C8—23no—
893C8—23no—
894C8—1061no—
895C8—1063no—
896C8—1063no—
897C8—1061no—
898C22—23no—
899C22—23no—
900C22—21no—
901C22—23no—
902C22—21no—
903C22—23no—
904C22—21no—
905C22—23no—
906C22—86no—
907C22—532no—
908C22—536no—
909C22—1063no—
910C22—1061no—
911C22—1063no—
912C22—1061no—
913C22—1063no—
914C22—1061no—
915C22—1061no—
916C22—1063no—
917C22—1061no—
918C22—1063no—
919C22—4246no—
920C22—42412no—
921C22—21212no—
922C22C2×C22⋊C4×D5316yes—
923C22C23×C4×D5311yescharacteristic
924C4—21no—
925C4—23no—
926C4—532no—
927C4—536no—
928C4—1063no—
929C4—1061no—
930C4C2×C22⋊C4×D5316yes—
931C4C22×D4×D5311yescharacteristic
932C4C22×D4×D5311yescharacteristic
933C2—26no—
934C2—41no—
935C2—43no—
936C2—1066no—
937C2—1062no—
938C2—2121no—
939C2—2123no—
940C2C22×C22⋊C4×D5311yescharacteristic
941C2#2028942611yescharacteristic
942C2#2028942811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D53
commutator, socleC22×C53C24×C4
FittingC53×#2880C2
prime radicalC2×#16811459C2
cosocleC2×C4×C53C25
hypercenter#2880D53
hypocenterC53#60065
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#16811388C2semidirect
3. C2×#131×D53C2semidirect
4. #20283165C2semidirect
5. #20283164C2semidirect
6. #20283163C2semidirect
7. #20283163C2semidirect
8. #20283162C2semidirect
9. #20283162C2semidirect
10. #20283161C2semidirect
11. #20283158C2semidirect
12. #20283157C2semidirect
13. C2×#16810588C2semidirect
14. #408×D53C2semidirect
15. C53×#2880C2semidirect
33. C2×#13133225C22semidirect
34. C2×#13133225C22semidirect
35. C2×#13133224C22semidirect
36. C2×#13133224C22semidirect
37. C2×#13133223C22semidirect
38. C2×#13133223C22semidirect
40. C22×#11719912C22semidirect
41. C2×M16×D53C22semidirect
42. C2×M16×D53C22semidirect
43. C22×C8×D53C22semidirect
44. #16810591C22semidirect
45. #16810591C22semidirect
46. #16810590C22semidirect
47. #16810590C22semidirect
48. #16810589C22semidirect
49. #16810589C22semidirect
50. #16810588C22semidirect
51. #16810588C22semidirect
52. #16810588C22semidirect
53. #16810588C22semidirect
54. #16810588C22semidirect
55. #16810588C22semidirect
56. #16810588C22semidirect
57. #16810588C22semidirect
58. #16810588C22semidirect
59. #16810588C22semidirect
60. #16810588C22semidirect
61. #16810587C22semidirect
62. #16810586C22semidirect
63. #16810586C22semidirect
64. #16810585C22semidirect
65. #16810585C22semidirect
66. C2×C22⋊#88322C22semidirect
67. C2×#13133129C22semidirect
68. C2×#13133129C22semidirect
69. C22⋊C8×D53C22semidirect
70. C22⋊C8×D53C22semidirect
72. C2×#131×C53C22semidirect
73. C2×#131×C53C22semidirect
74. C53×#408C22semidirect
75. C53×#408C22semidirect
76. C53×#407C22semidirect
77. C2×C22⋊C8×C53C22semidirect
472. #2880D53semidirect
512. C2×#131C2×D53semidirect
513. C2×#131C2×D53semidirect
535. #408C2×D53semidirect
536. #408C2×D53semidirect
542. #407C2×D53semidirect
548. C2×C22⋊C8C2×D53semidirect
549. C53#60065semidirect

Maximal subgroups

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

subgroupindex
C2×#168114592
C2×#168113882
C2×#131×D532
#202831652
#202831642
#202831632
#202831622
#202831612
#202831582
#202831572
C2×#168105882
#408×D532
C53×#28802
#6006553