Finite Group Databasebeta

← C2×#13119992 #16033292

Subgroups — C2×#13119992 #16033292

Order 3328.

4166 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88150C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D13C211yesmaximal, characteristic
3#13119992C2116yesmaximal, direct product factor
4C2×#11718336C211yesmaximal, characteristic, complemented
5C2×#11718613C211yesmaximal, characteristic, complemented
6C2×#11718334C211yesmaximal, characteristic, complemented
7C2×#11718608C211yesmaximal, characteristic, complemented
8C2×#11718606C211yesmaximal, characteristic, complemented
9C2×#11718601C211yesmaximal, characteristic, complemented
10C2×#11718651C211yesmaximal, characteristic, complemented
11C2×#11718325C211yesmaximal, characteristic, complemented
12C2×#11718325C211yesmaximal, characteristic, complemented
13C2×#11718616C211yesmaximal, characteristic
14C2×#11718616C211yesmaximal, characteristic
15C2×C4×#6103C211yesmaximal, characteristic, complemented
16C2×C13×#388C211yesmaximal, characteristic, complemented
17C25×D13C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C23×Dic26C2211yescharacteristic, complemented
21C22×C13×C4⋊C4C2211yescharacteristic, complemented
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C42×C13C2211yescharacteristic, complemented
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6101C2211yescharacteristic, complemented
40C22×#6101C2211yescharacteristic, complemented
41C22×C4×Dic13C2211yescharacteristic, complemented
42C2×#88150—28no—
43C2×#88150C2218yescomplemented
44C2×C22⋊C4×D13—28no—
45C2×C22⋊C4×D13C2218yes—
46C13×#388C2218yescomplemented
47C2×C13×#95C2211yescharacteristic, complemented
48C2×C13×#95C2211yescharacteristic, complemented
49C2×#88071C2211yescharacteristic, complemented
50C2×#88071C2211yescharacteristic, complemented
51C2×#88071C2211yescharacteristic, complemented
52C2×#88071C2211yescharacteristic, complemented
53C2×#88071C2211yescharacteristic, complemented
54C2×#88071C2211yescharacteristic, complemented
55C2×#88071C2211yescharacteristic, complemented
56C2×#88071C2211yescharacteristic, complemented
57#11718651C2218yescomplemented
58#11718616C2218yes—
59#11718616C2218yes—
60#11718613C2218yescomplemented
61#11718608C2218yescomplemented
62#11718606C2218yescomplemented
63#11718601C2218yescomplemented
64C4×#6103C2218yescomplemented
65#11718336C2218yescomplemented
66#11718334C2218yescomplemented
67#11718325C2218yescomplemented
68#11718325C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13—24no—
71C24×D13—24no—
72C24×D13—24no—
73C24×D13—24no—
74C24×D13—24no—
75C24×D13—42no—
76C24×D13—42no—
77C24×D13C2311yescharacteristic
78C24×D13C2314yes—
79C24×D13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C22×C4×D13—24no—
93C22×C4×D13—24no—
94C22×C4×D13—24no—
95C22×C4×D13—42no—
96C22×C4×D13—42no—
97C22×C4×D13D418yes—
98C22×C4×D13C2314yes—
99C22×C4×D13C2314yes—
100C22×Dic26—24no—
101C22×Dic26—42no—
102C22×Dic26—42no—
103C22×Dic26C2314yescomplemented
104C2×C13×C4⋊C4—24no—
105C2×C13×C4⋊C4C2314yescomplemented
106C2×C13×C22⋊C4—24no—
107C2×C13×C22⋊C4—24no—
108C2×C13×C22⋊C4—42no—
109C2×C13×C22⋊C4C2314yes—
110C2×C13×C22⋊C4C2314yes—
111C2×C13×C22⋊C4C2314yes—
112C2×C42×C13—42no—
113C2×C42×C13C2314yescomplemented
114C2×C22⋊Dic13—24no—
115C2×C22⋊Dic13—24no—
116C2×C22⋊Dic13—42no—
117C2×C22⋊Dic13C2314yes—
118C2×C22⋊Dic13C2314yes—
119C2×C22⋊Dic13C2314yes—
120C2×#6103—24no—
121C2×#6103—24no—
122C2×#6103—24no—
123C2×#6103—24no—
124C2×#6103—24no—
125C2×#6103—24no—
126C2×#6103—24no—
127C2×#6103—24no—
128C2×#6103—42no—
129C2×#6103—42no—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×#6103C2314yes—
136C2×#6103C2314yes—
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×#6101—24no—
141C2×#6101—24no—
142C2×#6101C2314yescomplemented
143C2×#6101C2314yescomplemented
144C2×C4×Dic13—42no—
145C2×C4×Dic13C2314yescomplemented
146#88150—232no—
147C22⋊C4×D13—232no—
148C13×#95C2314yescomplemented
149C13×#95C2314yescomplemented
150#88071C2314yescomplemented
151#88071C2314yescomplemented
152#88071C2314yescomplemented
153#88071C2314yescomplemented
154#88071C2314yescomplemented
155#88071C2314yescomplemented
156#88071C2314yescomplemented
157#88071C2314yescomplemented
158C2×#2561—131nomaximal, Sylow
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13#4114yes—
166C24×C13C2412yes—
167C24×C13C2411yescharacteristic
168C23×D13—22no—
169C23×D13—22no—
170C23×D13—22no—
171C23×D13—22no—
172C23×D13—232no—
173C23×D13—22no—
174C23×D13—28no—
175C23×D13—22no—
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13—28no—
181C23×D13—28no—
182C23×D13—28no—
183C23×D13—28no—
184C23×D13—44no—
185C23×D13—44no—
186C23×D13—416no—
187C23×D13—416no—
188C23×D13—416no—
189C23×D13—416no—
190C23×D13—416no—
191C23×D13—416no—
192C23×D13C2×D414yes—
193C23×D13#4114yes—
194C23×D13#4114yes—
195C23×D13#4114yes—
196C23×D13C2412yes—
197C23×D13C2412yes—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—22no—
201C22×C4×C13—22no—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—22no—
205C22×C4×C13—22no—
206C22×C4×C13—22no—
207C22×C4×C13—22no—
208C22×C4×C13—22no—
209C22×C4×C13—22no—
210C22×C4×C13—22no—
211C22×C4×C13—22no—
212C22×C4×C13—22no—
213C22×C4×C13—22no—
214C22×C4×C13—22no—
215C22×C4×C13C2×D414yes—
216C22×C4×C13C2412yes—
217C22×C4×C13C2412yes—
218C22×C4×C13C2412yes—
219C22×C4×C13C2412yes—
220C22×C4×C13C2412yes—
221C22×C4×C13C2412yes—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13—22no—
235C22×Dic13—22no—
236C22×Dic13—22no—
237C22×Dic13—22no—
238C22×Dic13—22no—
239C22×Dic13C2×D414yes—
240C22×Dic13C2412yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C2×C4×D13—28no—
247C2×C4×D13—28no—
248C2×C4×D13—28no—
249C2×C4×D13—416no—
250C2×C4×D13—44no—
251C2×C4×D13—44no—
252C2×C4×D13—416no—
253C2×C4×D13C2×D4116yes—
254C2×Dic26—28no—
255C2×Dic26—44no—
256C2×Dic26—44no—
257C2×Dic26—416no—
258C13×C4⋊C4—28no—
259C13×C22⋊C4—28no—
260C13×C22⋊C4—28no—
261C13×C22⋊C4—44no—
262C42×C13—44no—
263C22⋊Dic13—28no—
264C22⋊Dic13—28no—
265C22⋊Dic13—44no—
266#6103—28no—
267#6103—28no—
268#6103—28no—
269#6103—28no—
270#6103—28no—
271#6103—28no—
272#6103—28no—
273#6103—28no—
274#6103—44no—
275#6103—44no—
276#6101—28no—
277#6101—28no—
278C4×Dic13—44no—
279C22×C22⋊Q8—131no—
280C23×C22⋊C4—131no—
281#2561—1316no—
282C2×#397—131no—
283C2×#397—131no—
284C2×#393—131no—
285C2×#393—131no—
286C2×#388—131no—
287C2×#388—131no—
288C2×#388—131no—
289C2×#388D1311yescharacteristic, complemented
290C2×#381—131no—
291C2×#381—131no—
292C2×#379—131no—
293C2×#379—131no—
294C2×C4×C22⋊C4—131no—
295C23×C13—28no—
296C23×C13—28no—
297C23×C13—28no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—44no—
305C23×C13—44no—
306C23×C13—44no—
307C23×C13—44no—
308C23×C13C22×D412yes—
309C23×C13C2×#4114yes—
310C23×C13C2×#4112yes—
311C23×C13C2×#4112yes—
312C23×C13C2×#4112yes—
313C23×C13C2×#4112yes—
314C23×C13H(5,𝔽2)12yes—
315C23×C13H(5,𝔽2)12yes—
316C23×C13C2511yescharacteristic
317C22×D13—28no—
318C22×D13—28no—
319C22×D13—28no—
320C22×D13—28no—
321C22×D13—28no—
322C22×D13—28no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—232no—
328C22×D13—28no—
329C22×D13—28no—
330C22×D13—28no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—22no—
336C22×D13—22no—
337C22×D13—416no—
338C22×D13—416no—
339C22×D13—416no—
340C22×D13—416no—
341C22×D13—4128no—
342C22×D13—416no—
343C22×D13—44no—
344C22×D13—44no—
345C22×D13—44no—
346C22×D13—44no—
347C22×D13—416no—
348C22×D13#124116yes—
349C22×D13C22×D414yes—
350C22×D13C2×#4114yes—
351C22×D13C2×#4114yes—
352C22×D13C2×#4114yes—
353C2×C4×C13—28no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
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—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—44no—
372C2×C4×C13—44no—
373C2×C4×C13—44no—
374C2×C4×C13—44no—
375C2×C4×C13—44no—
376C2×C4×C13C22×D414yes—
377C2×Dic13—28no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—44no—
396C2×Dic13—44no—
397C2×Dic13—44no—
398C2×Dic13—44no—
399C2×Dic13—44no—
400C2×Dic13C22×D414yes—
401C4×D13—416no—
402C4×D13—416no—
403Dic26—416no—
404C26—131no—
405C23×Q8—131no—
406C24×C4—131no—
407C24×C4—131no—
408C2×C22⋊Q8—138no—
409C2×C22⋊Q8—268no—
410C22×C4⋊C4—131no—
411C22×C4⋊C4—131no—
412C22×C4⋊C4C2×D1311yescharacteristic, complemented
413C22×C22⋊C4—131no—
414C22×C22⋊C4—131no—
415C22×C22⋊C4—131no—
416C22×C22⋊C4—131no—
417C22×C22⋊C4—131no—
418C22×C22⋊C4—131no—
419C22×C22⋊C4—131no—
420C22×C22⋊C4—131no—
421C22×C22⋊C4—131no—
422C22×C22⋊C4—131no—
423C22×C22⋊C4—131no—
424C22×C22⋊C4—131no—
425C22×C22⋊C4—131no—
426C22×C22⋊C4—138no—
427C22×C22⋊C4—268no—
428C22×C22⋊C4C2×D1311yescharacteristic
429C22×C22⋊C4C2×D1311yescharacteristic
430C22×C22⋊C4C2×D1311yescharacteristic
431C22×C42—131no—
432C22×C42C2×D1311yescharacteristic, complemented
433#397—138no—
434#397—138no—
435#393—138no—
436#393—138no—
437#388—138no—
438#388—138no—
439#388—138no—
440#388C2×D1318yescomplemented
441#381—138no—
442#381—138no—
443#379—138no—
444#379—138no—
445C4×C22⋊C4—138no—
446C2×#95—131no—
447C2×#95—131no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95—131no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95C2×D1311yescharacteristic, complemented
455C2×#95C2×D1311yescharacteristic, complemented
456C22×C13—24no—
457C22×C13—24no—
458C22×C13—24no—
459C22×C13—416no—
460C22×C13—42no—
461C22×C13—42no—
462C22×C13—42no—
463C22×C13—42no—
464C22×C13#52514yes—
465C22×C13C2×#12414yes—
466C22×C13#53414yes—
467C22×C13#55114yes—
468C22×C13#55114yes—
469C22×C13#55114yes—
470C22×C13#55114yes—
471C22×C13C23×D411yescharacteristic
472C22×C13C22×#4111yescharacteristic
473C22×C13C22×#4111yescharacteristic
474C22×C13C22×#4111yescharacteristic
475C22×C13C22×#4111yescharacteristic
476C22×C13C2×H(5,𝔽2)11yescharacteristic
477C22×C13C2×H(5,𝔽2)11yescharacteristic
478C2×D13—232no—
479C2×D13—24no—
480C2×D13—24no—
481C2×D13—24no—
482C2×D13—24no—
483C2×D13—24no—
484C2×D13—24no—
485C2×D13—24no—
486C2×D13—24no—
487C2×D13—24no—
488C2×D13—464no—
489C2×D13—416no—
490C2×D13—42no—
491C2×D13—42no—
492C2×D13—42no—
493C2×D13—42no—
494C2×D13C2×#12418yes—
495C4×C13—24no—
496C4×C13—42no—
497C4×C13—42no—
498C4×C13—42no—
499C4×C13—42no—
500C4×C13—42no—
501Dic13—24no—
502Dic13—42no—
503Dic13—42no—
504Dic13—42no—
505Dic13—42no—
506Dic13—42no—
507C25—131no—
508C25—131no—
509C25—134no—
510C25—264no—
511C25—264no—
512C25—264no—
513C25—264no—
514C25—264no—
515C25—522no—
516C25—522no—
517C25C22×D1311yescharacteristic
518C22×Q8—134no—
519C22×Q8—264no—
520C22×Q8—522no—
521C22×Q8—522no—
522C23×C4—131no—
523C23×C4—138no—
524C23×C4—134no—
525C23×C4—131no—
526C23×C4—131no—
527C23×C4—131no—
528C23×C4—131no—
529C23×C4—131no—
530C23×C4—134no—
531C23×C4—264no—
532C23×C4—264no—
533C23×C4—264no—
534C23×C4—522no—
535C23×C4—522no—
536C23×C4C22×D1311yescharacteristic
537C23×C4C22×D1311yescharacteristic
538C23×C4C22×D1311yescharacteristic
539C23×C4C22×D1311yescharacteristic
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542C22⋊Q8—2632no—
543C2×C4⋊C4—24no—
544C2×C4⋊C4—134no—
545C2×C4⋊C4—134no—
546C2×C4⋊C4—264no—
547C2×C4⋊C4—264no—
548C2×C4⋊C4C22×D1314yescomplemented
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—134no—
553C2×C22⋊C4—134no—
554C2×C22⋊C4—134no—
555C2×C22⋊C4—134no—
556C2×C22⋊C4—134no—
557C2×C22⋊C4—134no—
558C2×C22⋊C4—134no—
559C2×C22⋊C4—134no—
560C2×C22⋊C4—134no—
561C2×C22⋊C4—134no—
562C2×C22⋊C4—134no—
563C2×C22⋊C4—134no—
564C2×C22⋊C4—134no—
565C2×C22⋊C4—2632no—
566C2×C22⋊C4—264no—
567C2×C22⋊C4—264no—
568C2×C22⋊C4—264no—
569C2×C22⋊C4—264no—
570C2×C22⋊C4—264no—
571C2×C22⋊C4—264no—
572C2×C22⋊C4—264no—
573C2×C22⋊C4—264no—
574C2×C22⋊C4—264no—
575C2×C22⋊C4—264no—
576C2×C22⋊C4—522no—
577C2×C22⋊C4—522no—
578C2×C22⋊C4—522no—
579C2×C22⋊C4C22×D1314yes—
580C2×C22⋊C4C22×D1314yes—
581C2×C22⋊C4C22×D1314yes—
582C2×C42—42no—
583C2×C42—134no—
584C2×C42—522no—
585C2×C42C22×D1314yescomplemented
586#95—134no—
587#95—134no—
588#95—134no—
589#95—134no—
590#95—134no—
591#95—134no—
592#95—134no—
593#95—134no—
594#95C22×D1314yescomplemented
595#95C22×D1314yescomplemented
596C2×C13—44no—
597C2×C13#256118yescomplemented
598C2×C13C2×#52511yescharacteristic
599C2×C13C22×#12411yescharacteristic
600C2×C13C2×#53411yescharacteristic
601C2×C13C2×#55111yescharacteristic
602C2×C13C2×#55111yescharacteristic
603C2×C13C2×#55111yescharacteristic
604C2×C13C2×#55111yescharacteristic
605D13—28no—
606D13—44no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—134no—
614C24—134no—
615C24—134no—
616C24—132no—
617C24—134no—
618C24—132no—
619C24—268no—
620C24—268no—
621C24—268no—
622C24—268no—
623C24—2632no—
624C24—262no—
625C24—262no—
626C24—262no—
627C24—262no—
628C24—268no—
629C24—262no—
630C24—262no—
631C24—262no—
632C24—262no—
633C24—262no—
634C24—262no—
635C24—524no—
636C24—524no—
637C24—5216no—
638C24—5216no—
639C24—5216no—
640C24—5216no—
641C24—5216no—
642C24—5216no—
643C24#612714yes—
644C24C23×D1312yes—
645C24C23×D1311yescharacteristic
646C2×Q8—268no—
647C2×Q8—524no—
648C2×Q8—524no—
649C2×Q8—5216no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—134no—
668C22×C4—132no—
669C22×C4—1316no—
670C22×C4—132no—
671C22×C4—132no—
672C22×C4—132no—
673C22×C4—132no—
674C22×C4—132no—
675C22×C4—268no—
676C22×C4—268no—
677C22×C4—268no—
678C22×C4—262no—
679C22×C4—262no—
680C22×C4—262no—
681C22×C4—262no—
682C22×C4—262no—
683C22×C4—262no—
684C22×C4—262no—
685C22×C4—262no—
686C22×C4—262no—
687C22×C4—262no—
688C22×C4—262no—
689C22×C4—262no—
690C22×C4—262no—
691C22×C4—262no—
692C22×C4—262no—
693C22×C4—262no—
694C22×C4—262no—
695C22×C4—5216no—
696C22×C4—524no—
697C22×C4—524no—
698C22×C4—5216no—
699C22×C4D4×D1314yes—
700C22×C4C23×D1312yes—
701C22×C4C23×D1312yes—
702C22×C4C23×D1312yes—
703C22×C4C23×D1312yes—
704C22×C4C23×D1312yes—
705C22×C4C23×D1312yes—
706C4⋊C4—28no—
707C4⋊C4—268no—
708C4⋊C4—268no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—44no—
712C22⋊C4—268no—
713C22⋊C4—268no—
714C22⋊C4—268no—
715C22⋊C4—268no—
716C22⋊C4—268no—
717C22⋊C4—268no—
718C22⋊C4—268no—
719C22⋊C4—268no—
720C22⋊C4—268no—
721C22⋊C4—268no—
722C22⋊C4—524no—
723C22⋊C4—524no—
724C22⋊C4—524no—
725C42—44no—
726C42—524no—
727C13C2×#256111yescharacteristic, complemented, Sylow
728C23—28no—
729C23—28no—
730C23—28no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—1316no—
742C23—134no—
743C23—134no—
744C23—134no—
745C23—134no—
746C23—2632no—
747C23—268no—
748C23—268no—
749C23—268no—
750C23—268no—
751C23—268no—
752C23—262no—
753C23—262no—
754C23—262no—
755C23—262no—
756C23—268no—
757C23—268no—
758C23—268no—
759C23—262no—
760C23—262no—
761C23—262no—
762C23—262no—
763C23—262no—
764C23—262no—
765C23—268no—
766C23—5216no—
767C23—5216no—
768C23—5216no—
769C23—5216no—
770C23—5216no—
771C23—5216no—
772C23—52128no—
773C23—524no—
774C23—524no—
775C23—524no—
776C23—524no—
777C23C2×#612714yes—
778C23C2×#612712yes—
779C23C2×D4×D1312yes—
780C23#8825112yes—
781C23#41×D1312yes—
782C23#41×D1312yes—
783C23#41×D1312yes—
784C23#8825612yes—
785C23C24×D1311yescharacteristic
786Q8—5216no—
787C2×C4—28no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—134no—
811C2×C4—268no—
812C2×C4—262no—
813C2×C4—262no—
814C2×C4—262no—
815C2×C4—262no—
816C2×C4—262no—
817C2×C4—262no—
818C2×C4—262no—
819C2×C4—262no—
820C2×C4—262no—
821C2×C4—262no—
822C2×C4—262no—
823C2×C4—262no—
824C2×C4—262no—
825C2×C4—262no—
826C2×C4—262no—
827C2×C4—262no—
828C2×C4—262no—
829C2×C4—5216no—
830C2×C4—5216no—
831C2×C4—524no—
832C2×C4—524no—
833C2×C4—524no—
834C2×C4—524no—
835C2×C4—524no—
836C2×C4C2×D4×D1314yes—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—416no—
845C22—138no—
846C22—264no—
847C22—264no—
848C22—264no—
849C22—264no—
850C22—264no—
851C22—264no—
852C22—2632no—
853C22—264no—
854C22—264no—
855C22—264no—
856C22—5264no—
857C22—522no—
858C22—522no—
859C22—522no—
860C22—522no—
861C22—5216no—
862C22#1171923214yes—
863C22#1171925214yes—
864C22#1171926114yes—
865C22#1171931014yes—
866C22#1171936414yes—
867C22D13×#12414yes—
868C22#1171941014yes—
869C22C22×#612711yescharacteristic
870C22C22×D4×D1311yescharacteristic
871C22C2×#8825111yescharacteristic
872C22C2×#41×D1311yescharacteristic
873C22C2×#41×D1311yescharacteristic
874C22C2×#41×D1311yescharacteristic
875C22C2×#8825611yescharacteristic
876C4—24no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—264no—
883C4—522no—
884C4—522no—
885C4—522no—
886C4—522no—
887C4—522no—
888C2—44no—
889C2—268no—
890C2—524no—
891C2#1311999218yesdirect product factor
892C2C2×#1171925211yescharacteristic
893C2C2×D13×#12411yescharacteristic
894C2C2×#1171931011yescharacteristic
895C2C2×#1171923211yescharacteristic
896C2C2×#1171941011yescharacteristic
897C2C2×#1171936411yescharacteristic
898C2C2×#1171926111yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#388C2
socleC24×C13C24
prime radicalC25×D13C22
hypercenterC2×#388D13
hypocenterC13C2×#2561
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#88150C2semidirect
3. #13119992C2direct (N × H)
4. C2×#11718336C2semidirect
5. C2×#11718613C2semidirect
6. C2×#11718334C2semidirect
7. C2×#11718608C2semidirect
8. C2×#11718606C2semidirect
9. C2×#11718601C2semidirect
10. C2×#11718651C2semidirect
11. C2×#11718325C2semidirect
12. C2×#11718325C2semidirect
15. C2×C4×#6103C2semidirect
16. C2×C13×#388C2semidirect
20. C23×Dic26C22semidirect
21. C22×C13×C4⋊C4C22semidirect
25. C22×C42×C13C22semidirect
39. C22×#6101C22semidirect
40. C22×#6101C22semidirect
41. C22×C4×Dic13C22semidirect
43. C2×#88150C22semidirect
46. C13×#388C22semidirect
47. C2×C13×#95C22semidirect
48. C2×C13×#95C22semidirect
49. C2×#88071C22semidirect
50. C2×#88071C22semidirect
51. C2×#88071C22semidirect
52. C2×#88071C22semidirect
53. C2×#88071C22semidirect
54. C2×#88071C22semidirect
55. C2×#88071C22semidirect
56. C2×#88071C22semidirect
57. #11718651C22semidirect
60. #11718613C22semidirect
61. #11718608C22semidirect
62. #11718606C22semidirect
63. #11718601C22semidirect
64. C4×#6103C22semidirect
65. #11718336C22semidirect
66. #11718334C22semidirect
67. #11718325C22semidirect
68. #11718325C22semidirect
103. C22×Dic26C23semidirect
105. C2×C13×C4⋊C4C23semidirect
113. C2×C42×C13C23semidirect
142. C2×#6101C23semidirect
143. C2×#6101C23semidirect
145. C2×C4×Dic13C23semidirect
148. C13×#95C23semidirect
149. C13×#95C23semidirect
150. #88071C23semidirect
151. #88071C23semidirect
152. #88071C23semidirect
153. #88071C23semidirect
154. #88071C23semidirect
155. #88071C23semidirect
156. #88071C23semidirect
157. #88071C23semidirect
289. C2×#388D13semidirect
412. C22×C4⋊C4C2×D13semidirect
432. C22×C42C2×D13semidirect
440. #388C2×D13semidirect
454. C2×#95C2×D13semidirect
455. C2×#95C2×D13semidirect
548. C2×C4⋊C4C22×D13semidirect
585. C2×C42C22×D13semidirect
594. #95C22×D13semidirect
595. #95C22×D13semidirect
597. C2×C13#2561semidirect
727. C13C2×#2561semidirect
891. C2#13119992direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881502
C22×C22⋊C4×D132
#131199922
C2×#117183362
C2×#117186132
C2×#117183342
C2×#117186082
C2×#117186062
C2×#117186012
C2×#117186512
C2×#117183252
C2×#117186162
C2×C4×#61032
C2×C13×#3882
C2×#256113