Finite Group Databasebeta

← #16022955

Subgroups — #16022955

Order 3328.

5502 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#6127C211yesmaximal, characteristic
2C2×#11719209C212yesmaximal, complemented
3#13117673C212yesmaximal, complemented
4#13117668C212yesmaximal, complemented
5#13117664C212yesmaximal, complemented
6#13117663C214yesmaximal, complemented
7#13117656C212yesmaximal, complemented
8C22⋊C4×C22⋊D13C214yesmaximal, complemented
9#13117429C212yesmaximal, complemented
10#13117425C214yesmaximal, complemented
11#13117219C211yesmaximal, characteristic, complemented
12#13117218C212yesmaximal, complemented
13D13×#380C212yesmaximal, complemented
14C2×C13×#380C211yesmaximal, characteristic, complemented
15C24×C4×C13C2211yescharacteristic
16C23×C22⋊D13C2212yes—
17C22×#6127—216no—
18C22×#6127C4116yescomplemented
19C22×#6127C2212yes—
20C22×#6127C2211yescharacteristic
21C22×#6127C2211yescharacteristic
22C22×#6127C2212yes—
23C22×#6127C2211yescharacteristic
24C22×#6127C2211yescharacteristic
25C23×D52C2211yescharacteristic
26C23×C4×D13C2212yes—
27C23×Dic26C2211yescharacteristic
28C22×C13×C4⋊C4C2212yescomplemented
29C22×C13×C22⋊C4C2212yes—
30C2×C4×C22⋊D13C2218yescomplemented
31C2×#88180C2212yescomplemented
32#11719209—216no—
33C2×#88147C2214yescomplemented
34C2×#88146C2214yescomplemented
35C2×C4⋊C4×D13C2214yescomplemented
36C2×#88141C2214yescomplemented
37C2×C22⋊C4×D13C2214yes—
38C13×#380C2212yes—
39C13×#380C2212yes—
40C13×#380C2212yescomplemented
41C13×#380C2212yescomplemented
42C2×C13×#95C2212yescomplemented
43#11718908C2212yes—
44#11718874C2218yescomplemented
45#11718873C2211yescharacteristic
46#11718873C2211yescharacteristic
47#11718873C2212yescomplemented
48#11718872C2212yescomplemented
49C4×C22⋊Dic13C2212yes—
50C4×C22⋊Dic13C2212yescomplemented
51#11718649C2214yescomplemented
52#11718648C2214yescomplemented
53#11718648C2214yescomplemented
54#11718635C2214yescomplemented
55#11718618C2218yescomplemented
56#11718617C2218yescomplemented
57#11718616C2214yes—
58#11718603C2214yes—
59C22⋊C4×Dic13C2214yes—
60#11718328C2214yescomplemented
61#11718327C2214yescomplemented
62#11718326C2218yescomplemented
63#11718325C2214yescomplemented
64D13×#95C2214yescomplemented
65#11718307C2218yescomplemented
66C25×C13C2311yescharacteristic
67C24×D13C2312yes—
68C23×C4×C13—28no—
69C23×C4×C13C2×C418yescomplemented
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2314yes—
76C23×C4×C13C2311yescharacteristic
77C22×C22⋊D13—216no—
78C22×C22⋊D13C2×C4116yescomplemented
79C22×C22⋊D13C2312yes—
80C22×C22⋊D13C2312yes—
81C22×C22⋊D13C2312yes—
82C22×C22⋊D13C2312yes—
83C23×Dic13C2312yes—
84C2×#6127—28no—
85C2×#6127—216no—
86C2×#6127—2128no—
87C2×#6127—28no—
88C2×#6127—216no—
89C2×#6127—28no—
90C2×#6127C2×C418yes—
91C2×#6127C2×C418yescomplemented
92C2×#6127C2×C4116yescomplemented
93C2×#6127C2×C418yescomplemented
94C2×#6127C2×C4116yescomplemented
95C2×#6127C2×C418yescomplemented
96C2×#6127D4116yes—
97C22×D52—28no—
98C22×D52C2×C418yescomplemented
99C22×D52C2312yes—
100C22×D52C2311yescharacteristic
101C22×D52C2311yescharacteristic
102C22×C4×D13—216no—
103C22×C4×D13C2×C4116yescomplemented
104C22×C4×D13C2312yes—
105C22×C4×D13C2312yes—
106C22×C4×D13C2312yes—
107C22×C4×D13C2318yes—
108C22×C4×D13C2312yes—
109C22×Dic26—28no—
110C22×Dic26C2×C418yescomplemented
111C22×Dic26C2312yes—
112C22×Dic26C2311yescharacteristic
113C22×Dic26C2311yescharacteristic
114C2×C13×C4⋊C4—28no—
115C2×C13×C4⋊C4C2314yes—
116C2×C13×C4⋊C4C2314yes—
117C2×C13×C22⋊C4—44no—
118C2×C13×C22⋊C4C2314yes—
119C2×C13×C22⋊C4C2314yes—
120C2×C22⋊Dic13C2312yes—
121C2×C22⋊Dic13C2314yes—
122C2×C22⋊Dic13C2312yes—
123C2×C22⋊Dic13C2314yes—
124C4×C22⋊D13—232no—
125C2×#6103C2318yes—
126C2×#6103C2318yes—
127C2×#6103C2318yes—
128#88180—28no—
129C2×C4⋊Dic13C2312yes—
130C2×C4⋊Dic13C2312yes—
131C2×#6101C2318yes—
132C2×C4×Dic13C2318yes—
133C2×C4×Dic13C2314yes—
134#88147—216no—
135#88146—216no—
136C4⋊C4×D13—216no—
137#88141—216no—
138C22⋊C4×D13—48no—
139C13×#95C2314yes—
140C13×#95C2314yes—
141#88071C2314yes—
142#88071C2318yes—
143#88071C2318yes—
144#88071C2312yes—
145#88071C2312yes—
146#34175—131nomaximal, Sylow
147C24×C13—24no—
148C24×C13—22no—
149C24×C13—22no—
150C24×C13—42no—
151C24×C13C22×C414yes—
152C24×C13C2411yescharacteristic
153C24×C13C2411yescharacteristic
154C24×C13C2411yescharacteristic
155C23×D13—24no—
156C23×D13—24no—
157C23×D13—28no—
158C23×D13—44no—
159C23×D13C22×C418yes—
160C23×D13C2412yes—
161C23×D13C2412yes—
162C22×C4×C13—24no—
163C22×C4×C13—232no—
164C22×C4×C13—24no—
165C22×C4×C13—24no—
166C22×C4×C13—24no—
167C22×C4×C13—24no—
168C22×C4×C13—28no—
169C22×C4×C13—44no—
170C22×C4×C13—44no—
171C22×C4×C13C22×C414yes—
172C22×C4×C13C22×C414yes—
173C22×C4×C13C22×C414yes—
174C22×C4×C13C22×C414yes—
175C22×C4×C13C22×C414yes—
176C22×C4×C13C22×C414yes—
177C22×C4×C13C2×D418yes—
178C22×C4×C13C2418yes—
179C22×C4×C13C2411yescharacteristic
180C22×C4×C13C2411yescharacteristic
181C22×C4×C13C2411yescharacteristic
182C22×C4×C13C2411yescharacteristic
183C2×C22⋊D13—28no—
184C2×C22⋊D13—28no—
185C2×C22⋊D13—264no—
186C2×C22⋊D13—28no—
187C2×C22⋊D13C22×C418yes—
188C2×C22⋊D13C22×C418yes—
189C2×C22⋊D13C22×C418yes—
190C2×C22⋊D13C22×C418yes—
191C2×C22⋊D13C2×D4116yes—
192C22×Dic13—28no—
193C22×Dic13C22×C418yes—
194C22×Dic13C2414yes—
195C22×Dic13C2414yes—
196C22×Dic13C2412yes—
197C22×Dic13C2412yes—
198#6127—232no—
199#6127—264no—
200#6127—232no—
201#6127—264no—
202#6127—232no—
203#6127C22⋊C4164yescomplemented
204C2×D52—28no—
205C2×D52—24no—
206C2×D52—232no—
207C2×D52C22×C418yes—
208C2×D52C22×C414yes—
209C2×D52C22×C414yes—
210C2×D52C2×D418yes—
211C2×C4×D13—28no—
212C2×C4×D13—28no—
213C2×C4×D13—28no—
214C2×C4×D13—264no—
215C2×C4×D13—216no—
216C2×C4×D13—48no—
217C2×C4×D13—48no—
218C2×C4×D13C22×C418yes—
219C2×C4×D13C22×C418yes—
220C2×C4×D13C22×C418yes—
221C2×C4×D13C22×C418yes—
222C2×C4×D13C2×D4116yes—
223C2×Dic26—24no—
224C2×Dic26—28no—
225C2×Dic26—232no—
226C2×Dic26C22×C414yes—
227C2×Dic26C22×C418yes—
228C2×Dic26C22×C414yes—
229C2×Dic26C2×D418yes—
230C13×C4⋊C4—28no—
231C13×C4⋊C4—28no—
232C13×C22⋊C4—28no—
233C13×C22⋊C4—44no—
234C22⋊Dic13—28no—
235C22⋊Dic13—24no—
236C22⋊Dic13—24no—
237C22⋊Dic13—44no—
238#6103—216no—
239#6103—48no—
240#6103—48no—
241C4⋊Dic13—24no—
242C4⋊Dic13—24no—
243#6101—216no—
244C4×Dic13—28no—
245C4×Dic13—216no—
246C23×#41—131no—
247C2×#520—132no—
248#2341—132no—
249Q8×C22⋊C4—132no—
250#2339—132no—
251#2339—134no—
252D4×C22⋊C4—132no—
253D4×C22⋊C4—134no—
254#2311—134no—
255#2311—132no—
256#2280—132no—
257#2280—131no—
258C2×#380—132no—
259C2×#380D1311yescharacteristic, complemented
260C23×C13—22no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—22no—
264C23×C13—22no—
265C23×C13—28no—
266C23×C13—28no—
267C23×C13—22no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—22no—
271C23×C13—44no—
272C23×C13—48no—
273C23×C13—48no—
274C23×C13C23×C412yes—
275C23×C13C23×C412yes—
276C23×C13C23×C412yes—
277C23×C13C22×D414yes—
278C23×C13H(5,𝔽2)12yes—
279C23×C132−1+412yes—
280C23×C13C2511yescharacteristic
281C22×D13—22no—
282C22×D13—22no—
283C22×D13—24no—
284C22×D13—216no—
285C22×D13—24no—
286C22×D13—22no—
287C22×D13—22no—
288C22×D13—24no—
289C22×D13—216no—
290C22×D13—48no—
291C22×D13—416no—
292C22×D13—416no—
293C22×D13C23×C414yes—
294C22×D13C23×C414yes—
295C22×D13C22×D418yes—
296C2×C4×C13—28no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—28no—
300C2×C4×C13—28no—
301C2×C4×C13—28no—
302C2×C4×C13—28no—
303C2×C4×C13—28no—
304C2×C4×C13—28no—
305C2×C4×C13—28no—
306C2×C4×C13—88no—
307C2×C4×C13C2×C22⋊C4116yescomplemented
308C2×C4×C13C23×C412yes—
309C2×C4×C13C23×C412yes—
310C2×C4×C13C23×C412yes—
311C2×C4×C13C23×C412yes—
312C2×C4×C13C22×D414yes—
313C2×C4×C13C22×D414yes—
314C22⋊D13—216no—
315C22⋊D13—216no—
316C22⋊D13—216no—
317C22⋊D13C2×C22⋊C4132yescomplemented
318C2×Dic13—24no—
319C2×Dic13—216no—
320C2×Dic13—24no—
321C2×Dic13—24no—
322C2×Dic13—24no—
323C2×Dic13—24no—
324C2×Dic13—24no—
325C2×Dic13—24no—
326C2×Dic13C23×C414yes—
327C2×Dic13C23×C414yes—
328C2×Dic13C22×D418yes—
329D52—216no—
330D52—28no—
331D52C2×C22⋊C4116yescomplemented
332C4×D13—216no—
333C4×D13—216no—
334C4×D13—216no—
335C4×D13—816no—
336C4×D13C2×C22⋊C4132yescomplemented
337Dic26—28no—
338Dic26—216no—
339Dic26C2×C22⋊C4116yescomplemented
340C22×#41—1316no—
341C22×#41—131no—
342C22×#41—132no—
343C22×#41—131no—
344C22×#41—131no—
345C22×#41—132no—
346C22×#41—131no—
347C22×#41—2616no—
348C23×Q8—131no—
349C23×D4—132no—
350C23×D4—131no—
351C24×C4—132no—
352C24×C4C2×D1311yescharacteristic
353#520—2616no—
354C2×C4×Q8—134no—
355C2×C4×D4—138no—
356C2×C4×D4—134no—
357C2×#117—132no—
358C2×#117—134no—
359C22×C4⋊C4—134no—
360C22×C4⋊C4C2×D1312yescomplemented
361C22×C22⋊C4—134no—
362C22×C22⋊C4C2×D1312yes—
363#391—134no—
364#391—138no—
365#390—134no—
366#390—138no—
367#386—138no—
368#386—138no—
369#386—138no—
370#381—132no—
371#381—134no—
372#380—132no—
373#380—131no—
374#380—131no—
375#380—134no—
376#380—134no—
377#380—134no—
378#380—134no—
379#380C2×D1312yes—
380#380C2×D1312yes—
381#380C2×D1312yescomplemented
382#380C2×D1312yescomplemented
383#379—132no—
384#379—134no—
385C4×C22⋊C4—132no—
386C4×C22⋊C4—132no—
387C4×C22⋊C4—134no—
388C4×C22⋊C4—134no—
389C2×#95—134no—
390C2×#95C2×D1312yescomplemented
391C22×C13—22no—
392C22×C13—22no—
393C22×C13—22no—
394C22×C13—22no—
395C22×C13—24no—
396C22×C13—24no—
397C22×C13—24no—
398C22×C13—24no—
399C22×C13—22no—
400C22×C13—22no—
401C22×C13—22no—
402C22×C13—416no—
403C22×C13—42no—
404C22×C13—42no—
405C22×C13C22×C22⋊C414yes—
406C22×C13#52014yescomplemented
407C22×C13C24×C411yescharacteristic
408C22×C13C23×D412yes—
409C22×C13C2×H(5,𝔽2)11yescharacteristic
410C22×C13C2×2−1+411yescharacteristic
411C22×C13#58512yes—
412C2×D13—24no—
413C2×D13—24no—
414C2×D13—28no—
415C2×D13—28no—
416C2×D13—24no—
417C2×D13—24no—
418C2×D13—24no—
419C2×D13—432no—
420C2×D13—44no—
421C2×D13—44no—
422C2×D13C22×C22⋊C418yes—
423C4×C13—22no—
424C4×C13—22no—
425C4×C13—48no—
426C4×C13C22×C22⋊C414yes—
427C4×C13C22×C22⋊C414yes—
428Dic13—24no—
429Dic13—44no—
430Dic13—44no—
431Dic13C22×C22⋊C418yes—
432C25—132no—
433C25C22×D1311yescharacteristic
434C2×#41—138no—
435C2×#41—1316no—
436C2×#41—1316no—
437C2×#41—138no—
438C2×#41—138no—
439C2×#41—138no—
440C2×#41—1316no—
441C2×#41—2616no—
442C2×#41—2616no—
443C2×#41—268no—
444C2×#41—268no—
445C2×#41—26128no—
446C2×#41—268no—
447C22×Q8—138no—
448C22×Q8—131no—
449C22×Q8—132no—
450C22×Q8—131no—
451C22×Q8—268no—
452C22×D4—132no—
453C22×D4—1316no—
454C22×D4—132no—
455C22×D4—132no—
456C22×D4—132no—
457C22×D4—138no—
458C22×D4—131no—
459C22×D4—132no—
460C22×D4—131no—
461C22×D4—268no—
462C22×D4—2616no—
463C23×C4—28no—
464C23×C4—132no—
465C23×C4—132no—
466C23×C4—1316no—
467C23×C4—132no—
468C23×C4—132no—
469C23×C4—132no—
470C23×C4—138no—
471C23×C4—2616no—
472C23×C4C4×D1318yescomplemented
473C23×C4C22×D1311yescharacteristic
474C23×C4C22×D1311yescharacteristic
475C23×C4C22×D1311yescharacteristic
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1311yescharacteristic
478C23×C4C22×D1314yes—
479C23×C4C22×D1311yescharacteristic
480C4×Q8—2616no—
481C4×D4—2616no—
482C4×D4—2632no—
483#117—2616no—
484#117—268no—
485C2×C4⋊C4—28no—
486C2×C4⋊C4—132no—
487C2×C4⋊C4—138no—
488C2×C4⋊C4—132no—
489C2×C4⋊C4—2616no—
490C2×C4⋊C4C22×D1314yes—
491C2×C4⋊C4C22×D1314yes—
492C2×C22⋊C4—44no—
493C2×C22⋊C4—132no—
494C2×C22⋊C4—134no—
495C2×C22⋊C4—132no—
496C2×C22⋊C4—138no—
497C2×C22⋊C4—134no—
498C2×C22⋊C4—138no—
499C2×C22⋊C4—138no—
500C2×C22⋊C4—528no—
501C2×C22⋊C4C22×D1314yes—
502C2×C22⋊C4C22×D1314yes—
503C2×C42—138no—
504C2×C42—134no—
505#95—132no—
506#95—138no—
507#95—132no—
508#95—138no—
509#95—134no—
510#95C22×D1314yes—
511#95C22×D1314yes—
512C2×C13—24no—
513C2×C13—24no—
514C2×C13—42no—
515C2×C13C23×C22⋊C411yescharacteristic
516C2×C13C2×#52011yescharacteristic
517C2×C13#342811yescharacteristic
518C2×C13#348812yes—
519C2×C13#348912yes—
520D13—28no—
521D13—44no—
522C24—24no—
523C24—22no—
524C24—22no—
525C24—42no—
526C24—132no—
527C24—132no—
528C24—138no—
529C24—268no—
530C24—264no—
531C24—264no—
532C24—524no—
533C24C2×C4×D1314yes—
534C24C23×D1311yescharacteristic
535C24C23×D1311yescharacteristic
536C24C23×D1311yescharacteristic
537#41—1364no—
538#41—2664no—
539#41—2664no—
540#41—2632no—
541#41—2632no—
542#41—2632no—
543C2×Q8—134no—
544C2×Q8—138no—
545C2×Q8—134no—
546C2×Q8—138no—
547C2×Q8—268no—
548C2×Q8—2632no—
549C2×Q8—264no—
550C2×D4—138no—
551C2×D4—1316no—
552C2×D4—138no—
553C2×D4—138no—
554C2×D4—138no—
555C2×D4—134no—
556C2×D4—138no—
557C2×D4—134no—
558C2×D4—138no—
559C2×D4—2632no—
560C2×D4—268no—
561C2×D4—268no—
562C2×D4—2664no—
563C2×D4—268no—
564C2×D4—268no—
565C2×D4—264no—
566C22×C4—24no—
567C22×C4—232no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—28no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—132no—
576C22×C4—138no—
577C22×C4—1316no—
578C22×C4—138no—
579C22×C4—132no—
580C22×C4—138no—
581C22×C4—138no—
582C22×C4—138no—
583C22×C4—134no—
584C22×C4—134no—
585C22×C4—268no—
586C22×C4—2664no—
587C22×C4—268no—
588C22×C4—2616no—
589C22×C4—268no—
590C22×C4—268no—
591C22×C4—528no—
592C22×C4—528no—
593C22×C4C2×C4×D1314yes—
594C22×C4C2×C4×D1314yes—
595C22×C4C2×C4×D1314yes—
596C22×C4C2×C4×D1314yes—
597C22×C4C2×C4×D1314yes—
598C22×C4C2×C4×D1314yes—
599C22×C4D4×D1318yes—
600C22×C4C23×D1318yes—
601C22×C4C23×D1311yescharacteristic
602C22×C4C23×D1311yescharacteristic
603C22×C4C23×D1311yescharacteristic
604C22×C4C23×D1311yescharacteristic
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—2616no—
608C4⋊C4—264no—
609C4⋊C4—264no—
610C22⋊C4—28no—
611C22⋊C4—44no—
612C22⋊C4—2616no—
613C22⋊C4—268no—
614C22⋊C4—264no—
615C22⋊C4—264no—
616C22⋊C4—528no—
617C22⋊C4—528no—
618C22⋊C4—524no—
619C42—2616no—
620C42—268no—
621C13#3417511yescharacteristic, complemented, Sylow
622C23—22no—
623C23—21no—
624C23—21no—
625C23—22no—
626C23—22no—
627C23—28no—
628C23—28no—
629C23—22no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—44no—
634C23—48no—
635C23—48no—
636C23—134no—
637C23—138no—
638C23—134no—
639C23—2616no—
640C23—262no—
641C23—262no—
642C23—264no—
643C23—2616no—
644C23—264no—
645C23—262no—
646C23—262no—
647C23—264no—
648C23—528no—
649C23—5216no—
650C23—5216no—
651C23C22×C4×D1312yes—
652C23C22×C4×D1312yes—
653C23C22×C4×D1312yes—
654C23C2×D4×D1314yes—
655C23#8825112yes—
656C23#8825412yes—
657C23C24×D1311yescharacteristic
658Q8—1316no—
659Q8—2616no—
660Q8—268no—
661D4—1332no—
662D4—1316no—
663D4—2616no—
664D4—2616no—
665D4—2616no—
666D4—2616no—
667D4—268no—
668C2×C4—28no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—28no—
672C2×C4—28no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—28no—
677C2×C4—28no—
678C2×C4—88no—
679C2×C4—134no—
680C2×C4—138no—
681C2×C4—1332no—
682C2×C4—134no—
683C2×C4—2616no—
684C2×C4—2616no—
685C2×C4—2616no—
686C2×C4—264no—
687C2×C4—2616no—
688C2×C4—264no—
689C2×C4—264no—
690C2×C4—264no—
691C2×C4—264no—
692C2×C4—264no—
693C2×C4—264no—
694C2×C4—10416no—
695C2×C4C22⋊C4×D13116yescomplemented
696C2×C4C22×C4×D1312yes—
697C2×C4C22×C4×D1312yes—
698C2×C4C22×C4×D1312yes—
699C2×C4C22×C4×D1312yes—
700C2×C4C2×D4×D1314yes—
701C2×C4C2×D4×D1314yes—
702C22—24no—
703C22—24no—
704C22—22no—
705C22—24no—
706C22—24no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—416no—
714C22—42no—
715C22—42no—
716C22—138no—
717C22—268no—
718C22—268no—
719C22—264no—
720C22—264no—
721C22—264no—
722C22—264no—
723C22—264no—
724C22—5232no—
725C22—524no—
726C22—524no—
727C22C2×C22⋊C4×D1314yes—
728C22#1171920914yescomplemented
729C22C23×C4×D1311yescharacteristic
730C22C22×D4×D1312yes—
731C22C2×#8825111yescharacteristic
732C22C2×#8825411yescharacteristic
733C22#1171964812yes—
734C4—22no—
735C4—22no—
736C4—48no—
737C4—138no—
738C4—264no—
739C4—524no—
740C4—524no—
741C4C2×C22⋊C4×D1314yes—
742C4C2×C22⋊C4×D1314yes—
743C2—24no—
744C2—24no—
745C2—42no—
746C2—268no—
747C2—524no—
748C2C22×C22⋊C4×D1311yescharacteristic
749C2C2×#1171920911yescharacteristic
750C2#1312803711yescharacteristic
751C2#1312850112yes—
752C2#1312851212yes—
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC2×C13×#380C2
socle, cosocleC23×C13C25
prime radicalC23×#6127C2
hypercenterC2×#380D13
hypocenterC13#34175
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#11719209C2semidirect
3. #13117673C2semidirect
4. #13117668C2semidirect
5. #13117664C2semidirect
6. #13117663C2semidirect
7. #13117656C2semidirect
8. C22⋊C4×C22⋊D13C2semidirect
9. #13117429C2semidirect
10. #13117425C2semidirect
11. #13117219C2semidirect
12. #13117218C2semidirect
13. D13×#380C2semidirect
14. C2×C13×#380C2semidirect
18. C22×#6127C4semidirect
28. C22×C13×C4⋊C4C22semidirect
30. C2×C4×C22⋊D13C22semidirect
31. C2×#88180C22semidirect
33. C2×#88147C22semidirect
34. C2×#88146C22semidirect
35. C2×C4⋊C4×D13C22semidirect
36. C2×#88141C22semidirect
40. C13×#380C22semidirect
41. C13×#380C22semidirect
42. C2×C13×#95C22semidirect
44. #11718874C22semidirect
47. #11718873C22semidirect
48. #11718872C22semidirect
50. C4×C22⋊Dic13C22semidirect
51. #11718649C22semidirect
52. #11718648C22semidirect
53. #11718648C22semidirect
54. #11718635C22semidirect
55. #11718618C22semidirect
56. #11718617C22semidirect
60. #11718328C22semidirect
61. #11718327C22semidirect
62. #11718326C22semidirect
63. #11718325C22semidirect
64. D13×#95C22semidirect
65. #11718307C22semidirect
69. C23×C4×C13C2×C4semidirect
78. C22×C22⋊D13C2×C4semidirect
91. C2×#6127C2×C4semidirect
92. C2×#6127C2×C4semidirect
93. C2×#6127C2×C4semidirect
94. C2×#6127C2×C4semidirect
95. C2×#6127C2×C4semidirect
98. C22×D52C2×C4semidirect
103. C22×C4×D13C2×C4semidirect
110. C22×Dic26C2×C4semidirect
203. #6127C22⋊C4semidirect
259. C2×#380D13semidirect
307. C2×C4×C13C2×C22⋊C4semidirect
317. C22⋊D13C2×C22⋊C4semidirect
331. D52C2×C22⋊C4semidirect
336. C4×D13C2×C22⋊C4semidirect
339. Dic26C2×C22⋊C4semidirect
360. C22×C4⋊C4C2×D13semidirect
381. #380C2×D13semidirect
382. #380C2×D13semidirect
390. C2×#95C2×D13semidirect
406. C22×C13#520semidirect
472. C23×C4C4×D13semidirect
621. C13#34175semidirect
695. C2×C4C22⋊C4×D13semidirect
728. C22#11719209semidirect

Maximal subgroups

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

subgroupindex
C23×#61272
C2×#117192092
#131176732
#131176682
#131176642
#131176632
#131176562
C22⋊C4×C22⋊D132
#131174292
#131174252
#131172192
#131172182
D13×#3802
C2×C13×#3802
#3417513