Finite Group Databasebeta

← C2×#13119085 #16030530

Subgroups — C2×#13119085 #16030530

Order 3328.

4102 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88152C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D13C211yesmaximal, characteristic
3#13119085C2116yesmaximal, direct product factor
4C2×#11718336C211yesmaximal, characteristic, complemented
5C2×#11718654C211yesmaximal, characteristic, complemented
6C2×#11718614C211yesmaximal, characteristic, complemented
7C2×#11718606C211yesmaximal, characteristic, complemented
8C2×#11718651C211yesmaximal, characteristic, complemented
9C2×#11718605C211yesmaximal, characteristic, complemented
10C2×#11718650C211yesmaximal, characteristic, complemented
11C2×#11718650C211yesmaximal, characteristic, complemented
12C2×#11718648C211yesmaximal, characteristic, complemented
13C2×#11718616C211yesmaximal, characteristic
14C2×#11718616C211yesmaximal, characteristic
15C2×#11718327C211yesmaximal, characteristic, complemented
16C2×C13×#396C211yesmaximal, characteristic, complemented
17C25×D13C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic, complemented
21C22×C13×C4⋊C4C2211yescharacteristic, complemented
22C22×C13×C4⋊C4C2211yescharacteristic, complemented
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
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×C4⋊Dic13C2211yescharacteristic, complemented
40C22×#6101C2211yescharacteristic, complemented
41C22×#6101C2211yescharacteristic, complemented
42C22×C4×Dic13C2211yescharacteristic, complemented
43C22×C4×Dic13C2211yescharacteristic, complemented
44C2×#88152—28no—
45C2×#88152C2218yescomplemented
46C2×C22⋊C4×D13—28no—
47C2×C22⋊C4×D13C2218yes—
48C13×#396C2218yescomplemented
49C2×C13×#95C2211yescharacteristic, complemented
50C2×#88071C2211yescharacteristic, complemented
51C2×#88071C2211yescharacteristic, complemented
52C2×#88071C2211yescharacteristic, complemented
53C2×#88071C2211yescharacteristic, complemented
54C2×#88071C2211yescharacteristic, complemented
55C2×#88071C2211yescharacteristic, complemented
56C2×#88071C2211yescharacteristic, complemented
57#11718654C2218yescomplemented
58#11718651C2218yescomplemented
59#11718650C2218yescomplemented
60#11718650C2218yescomplemented
61#11718648C2218yescomplemented
62#11718616C2218yes—
63#11718616C2218yes—
64#11718614C2218yescomplemented
65#11718606C2218yescomplemented
66#11718605C2218yescomplemented
67#11718336C2218yescomplemented
68#11718327C2218yescomplemented
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—24no—
96C22×C4×D13—42no—
97C22×C4×D13—42no—
98C22×C4×D13C2314yes—
99C22×C4×D13C2314yes—
100C2×C13×C4⋊C4—24no—
101C2×C13×C4⋊C4—42no—
102C2×C13×C4⋊C4—42no—
103C2×C13×C4⋊C4C2314yescomplemented
104C2×C13×C4⋊C4C2314yescomplemented
105C2×C13×C4⋊C4C2314yescomplemented
106C2×C13×C22⋊C4—24no—
107C2×C13×C22⋊C4—42no—
108C2×C13×C22⋊C4—42no—
109C2×C13×C22⋊C4C2314yes—
110C2×C13×C22⋊C4C2314yes—
111C2×C13×C22⋊C4C2314yes—
112C2×C22⋊Dic13—24no—
113C2×C22⋊Dic13—24no—
114C2×C22⋊Dic13—24no—
115C2×C22⋊Dic13C2314yes—
116C2×C22⋊Dic13C2314yes—
117C2×C22⋊Dic13C2314yes—
118C2×#6103—24no—
119C2×#6103—24no—
120C2×#6103—24no—
121C2×#6103—24no—
122C2×#6103—24no—
123C2×#6103—24no—
124C2×#6103—24no—
125C2×#6103—42no—
126C2×#6103—42no—
127C2×#6103D418yes—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×#6103C2314yes—
136C2×#6103C2314yes—
137C2×#6103C2314yes—
138C2×C4⋊Dic13—24no—
139C2×C4⋊Dic13C2314yescomplemented
140C2×#6101—24no—
141C2×#6101—42no—
142C2×#6101C2314yescomplemented
143C2×#6101C2314yescomplemented
144C2×C4×Dic13—24no—
145C2×C4×Dic13—42no—
146C2×C4×Dic13C2314yescomplemented
147C2×C4×Dic13C2314yescomplemented
148#88152—232no—
149C22⋊C4×D13—232no—
150C13×#95C2314yescomplemented
151#88071C2314yescomplemented
152#88071C2314yescomplemented
153#88071C2314yescomplemented
154#88071C2314yescomplemented
155#88071C2314yescomplemented
156#88071C2314yescomplemented
157#88071C2314yescomplemented
158C2×#2480—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—28no—
174C23×D13—22no—
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—28no—
250C2×C4×D13—44no—
251C2×C4×D13—44no—
252C2×C4×D13—416no—
253C2×C4×D13—416no—
254C13×C4⋊C4—28no—
255C13×C4⋊C4—44no—
256C13×C4⋊C4—44no—
257C13×C22⋊C4—28no—
258C13×C22⋊C4—44no—
259C13×C22⋊C4—44no—
260C22⋊Dic13—28no—
261C22⋊Dic13—28no—
262C22⋊Dic13—28no—
263#6103—28no—
264#6103—28no—
265#6103—28no—
266#6103—28no—
267#6103—28no—
268#6103—28no—
269#6103—28no—
270#6103—44no—
271#6103—44no—
272#6103C2×D4116yes—
273C4⋊Dic13—28no—
274#6101—28no—
275#6101—44no—
276C4×Dic13—28no—
277C4×Dic13—44no—
278C22×#126—131no—
279C23×C22⋊C4—131no—
280#2480—1316no—
281C2×#397—131no—
282C2×#397—131no—
283C2×#397—131no—
284C2×#396D1311yescharacteristic, complemented
285C2×#388—131no—
286C2×#388—131no—
287C2×#388—131no—
288C2×#385—131no—
289C2×#385—131no—
290C2×#380—131no—
291C2×#379—131no—
292C2×#379—131no—
293C2×C4×C22⋊C4—131no—
294C23×C13—28no—
295C23×C13—28no—
296C23×C13—28no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—44no—
304C23×C13—44no—
305C23×C13—44no—
306C23×C13—44no—
307C23×C13C22×D412yes—
308C23×C13C2×#4114yes—
309C23×C13C2×#4112yes—
310C23×C13C2×#4112yes—
311C23×C13C2×#4112yes—
312C23×C13C2×#4112yes—
313C23×C13H(5,𝔽2)12yes—
314C23×C13H(5,𝔽2)12yes—
315C23×C13C2511yescharacteristic
316C22×D13—28no—
317C22×D13—28no—
318C22×D13—28no—
319C22×D13—28no—
320C22×D13—28no—
321C22×D13—28no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—232no—
327C22×D13—28no—
328C22×D13—28no—
329C22×D13—28no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—22no—
336C22×D13—416no—
337C22×D13—416no—
338C22×D13—416no—
339C22×D13—416no—
340C22×D13—416no—
341C22×D13—4128no—
342C22×D13—44no—
343C22×D13—44no—
344C22×D13—44no—
345C22×D13—44no—
346C22×D13—416no—
347C22×D13#126116yescomplemented
348C22×D13C22×D414yes—
349C22×D13C2×#4114yes—
350C22×D13C2×#4114yes—
351C22×D13C2×#4114yes—
352C2×C4×C13—28no—
353C2×C4×C13—22no—
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—44no—
371C2×C4×C13—44no—
372C2×C4×C13—44no—
373C2×C4×C13—44no—
374C2×C4×C13—44no—
375C2×C4×C13C22×D414yes—
376C2×Dic13—28no—
377C2×Dic13—22no—
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—44no—
395C2×Dic13—44no—
396C2×Dic13—44no—
397C2×Dic13—44no—
398C2×Dic13—44no—
399C2×Dic13C22×D414yes—
400C4×D13—416no—
401C4×D13—416no—
402C26—131no—
403C24×C4—131no—
404C24×C4—131no—
405C2×#126—138no—
406C2×#126—268no—
407C22×C4⋊C4—131no—
408C22×C4⋊C4—131no—
409C22×C4⋊C4—131no—
410C22×C4⋊C4C2×D1311yescharacteristic, complemented
411C22×C4⋊C4C2×D1311yescharacteristic, complemented
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×C42—131no—
433#397—138no—
434#397—138no—
435#397—138no—
436#396C2×D1318yescomplemented
437#388—138no—
438#388—138no—
439#388—138no—
440#385—138no—
441#385—138no—
442#380—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×#95C2×D1311yescharacteristic, complemented
454C22×C13—24no—
455C22×C13—24no—
456C22×C13—24no—
457C22×C13—42no—
458C22×C13—42no—
459C22×C13—42no—
460C22×C13—42no—
461C22×C13—416no—
462C22×C13#52514yes—
463C22×C13C2×#12614yes—
464C22×C13#53814yes—
465C22×C13#54614yes—
466C22×C13#54614yes—
467C22×C13#55114yes—
468C22×C13#55114yes—
469C22×C13C23×D411yescharacteristic
470C22×C13C22×#4111yescharacteristic
471C22×C13C22×#4111yescharacteristic
472C22×C13C22×#4111yescharacteristic
473C22×C13C22×#4111yescharacteristic
474C22×C13C2×H(5,𝔽2)11yescharacteristic
475C22×C13C2×H(5,𝔽2)11yescharacteristic
476C2×D13—24no—
477C2×D13—24no—
478C2×D13—24no—
479C2×D13—24no—
480C2×D13—24no—
481C2×D13—24no—
482C2×D13—232no—
483C2×D13—24no—
484C2×D13—24no—
485C2×D13—24no—
486C2×D13—464no—
487C2×D13—42no—
488C2×D13—42no—
489C2×D13—42no—
490C2×D13—42no—
491C2×D13—416no—
492C2×D13C2×#12618yescomplemented
493C4×C13—24no—
494C4×C13—42no—
495C4×C13—42no—
496C4×C13—42no—
497C4×C13—42no—
498C4×C13—42no—
499Dic13—24no—
500Dic13—42no—
501Dic13—42no—
502Dic13—42no—
503Dic13—42no—
504Dic13—42no—
505C25—131no—
506C25—131no—
507C25—134no—
508C25—264no—
509C25—264no—
510C25—264no—
511C25—264no—
512C25—264no—
513C25—522no—
514C25—522no—
515C25C22×D1311yescharacteristic
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4—131no—
520C23×C4—131no—
521C23×C4—131no—
522C23×C4—134no—
523C23×C4—134no—
524C23×C4—264no—
525C23×C4—264no—
526C23×C4—264no—
527C23×C4—264no—
528C23×C4—522no—
529C23×C4—522no—
530C23×C4C22×D1311yescharacteristic
531C23×C4C22×D1311yescharacteristic
532C23×C4C22×D1311yescharacteristic
533C23×C4C22×D1311yescharacteristic
534C23×C4C22×D1311yescharacteristic
535C23×C4C22×D1311yescharacteristic
536#126—2632no—
537C2×C4⋊C4—24no—
538C2×C4⋊C4—42no—
539C2×C4⋊C4—42no—
540C2×C4⋊C4—134no—
541C2×C4⋊C4—134no—
542C2×C4⋊C4—134no—
543C2×C4⋊C4—264no—
544C2×C4⋊C4—264no—
545C2×C4⋊C4—522no—
546C2×C4⋊C4C22×D1314yescomplemented
547C2×C4⋊C4C22×D1314yescomplemented
548C2×C4⋊C4C22×D1314yescomplemented
549C2×C22⋊C4—24no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—138no—
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—134no—
566C2×C22⋊C4—2632no—
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—264no—
577C2×C22⋊C4—522no—
578C2×C22⋊C4—522no—
579C2×C22⋊C4C22×D1314yes—
580C2×C22⋊C4C22×D1314yes—
581C2×C22⋊C4C22×D1314yes—
582C2×C42—134no—
583C2×C42—134no—
584C2×C42—264no—
585C2×C42—522no—
586#95—134no—
587#95—134no—
588#95—134no—
589#95—134no—
590#95—134no—
591#95—134no—
592#95—134no—
593#95C22×D1314yescomplemented
594C2×C13—44no—
595C2×C13#248018yescomplemented
596C2×C13C2×#52511yescharacteristic
597C2×C13C22×#12611yescharacteristic
598C2×C13C2×#53811yescharacteristic
599C2×C13C2×#54611yescharacteristic
600C2×C13C2×#54611yescharacteristic
601C2×C13C2×#55111yescharacteristic
602C2×C13C2×#55111yescharacteristic
603D13—28no—
604D13—44no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—134no—
612C24—134no—
613C24—134no—
614C24—132no—
615C24—134no—
616C24—132no—
617C24—268no—
618C24—268no—
619C24—268no—
620C24—268no—
621C24—2632no—
622C24—262no—
623C24—262no—
624C24—262no—
625C24—262no—
626C24—262no—
627C24—262no—
628C24—268no—
629C24—262no—
630C24—262no—
631C24—262no—
632C24—262no—
633C24—524no—
634C24—524no—
635C24—5216no—
636C24—5216no—
637C24—5216no—
638C24—5216no—
639C24—5216no—
640C24—5216no—
641C24#613114yes—
642C24C23×D1312yes—
643C24C23×D1311yescharacteristic
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
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—134no—
662C22×C4—132no—
663C22×C4—132no—
664C22×C4—132no—
665C22×C4—132no—
666C22×C4—132no—
667C22×C4—132no—
668C22×C4—268no—
669C22×C4—268no—
670C22×C4—268no—
671C22×C4—262no—
672C22×C4—262no—
673C22×C4—262no—
674C22×C4—262no—
675C22×C4—262no—
676C22×C4—262no—
677C22×C4—262no—
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—268no—
689C22×C4—524no—
690C22×C4—524no—
691C22×C4—5216no—
692C22×C4—5216no—
693C22×C4D4×D1314yes—
694C22×C4C23×D1312yes—
695C22×C4C23×D1312yes—
696C22×C4C23×D1312yes—
697C22×C4C23×D1312yes—
698C22×C4C23×D1312yes—
699C22×C4C23×D1312yes—
700C4⋊C4—28no—
701C4⋊C4—44no—
702C4⋊C4—44no—
703C4⋊C4—268no—
704C4⋊C4—268no—
705C4⋊C4—524no—
706C22⋊C4—28no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C22⋊C4—1316no—
710C22⋊C4—268no—
711C22⋊C4—268no—
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—524no—
721C22⋊C4—524no—
722C42—268no—
723C42—524no—
724C13C2×#248011yescharacteristic, complemented, Sylow
725C23—28no—
726C23—28no—
727C23—28no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—134no—
739C23—134no—
740C23—134no—
741C23—1316no—
742C23—134no—
743C23—2632no—
744C23—268no—
745C23—268no—
746C23—268no—
747C23—268no—
748C23—268no—
749C23—268no—
750C23—262no—
751C23—262no—
752C23—262no—
753C23—262no—
754C23—268no—
755C23—268no—
756C23—268no—
757C23—262no—
758C23—262no—
759C23—262no—
760C23—262no—
761C23—262no—
762C23—262no—
763C23—5216no—
764C23—5216no—
765C23—5216no—
766C23—5216no—
767C23—5216no—
768C23—52128no—
769C23—5216no—
770C23—524no—
771C23—524no—
772C23—524no—
773C23—524no—
774C23C2×D4×D1312yes—
775C23#8825112yes—
776C23#8825112yes—
777C23C2×#613114yes—
778C23C2×#613112yes—
779C23#41×D1312yes—
780C23#41×D1312yes—
781C23#41×D1312yes—
782C23C24×D1311yescharacteristic
783C2×C4—28no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
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—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—134no—
807C2×C4—268no—
808C2×C4—262no—
809C2×C4—262no—
810C2×C4—262no—
811C2×C4—262no—
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—5216no—
826C2×C4—5216no—
827C2×C4—524no—
828C2×C4—524no—
829C2×C4—524no—
830C2×C4—524no—
831C2×C4—524no—
832C2×C4C2×D4×D1314yes—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—42no—
837C22—42no—
838C22—416no—
839C22—42no—
840C22—42no—
841C22—138no—
842C22—264no—
843C22—264no—
844C22—2632no—
845C22—264no—
846C22—264no—
847C22—264no—
848C22—264no—
849C22—264no—
850C22—264no—
851C22—264no—
852C22—5264no—
853C22—5216no—
854C22—522no—
855C22—522no—
856C22—522no—
857C22—522no—
858C22#1171931514yes—
859C22#1171931714yes—
860C22#1171931814yes—
861C22#1171933214yes—
862C22#1171934214yes—
863C22#1171934214yes—
864C22D13×#12614yes—
865C22C22×D4×D1311yescharacteristic
866C22C2×#8825111yescharacteristic
867C22C2×#8825111yescharacteristic
868C22C22×#613111yescharacteristic
869C22C2×#41×D1311yescharacteristic
870C22C2×#41×D1311yescharacteristic
871C22C2×#41×D1311yescharacteristic
872C4—24no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—264no—
879C4—522no—
880C4—522no—
881C4—522no—
882C4—522no—
883C4—522no—
884C2—44no—
885C2—268no—
886C2—524no—
887C2#1311908518yesdirect product factor
888C2C2×#1171933211yescharacteristic
889C2C2×D13×#12611yescharacteristic
890C2C2×#1171931811yescharacteristic
891C2C2×#1171931511yescharacteristic
892C2C2×#1171931711yescharacteristic
893C2C2×#1171934211yescharacteristic
894C2C2×#1171934211yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#396C2
socleC24×C13C24
prime radicalC25×D13C22
hypercenterC2×#396D13
hypocenterC13C2×#2480
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#88152C2semidirect
3. #13119085C2direct (N × H)
4. C2×#11718336C2semidirect
5. C2×#11718654C2semidirect
6. C2×#11718614C2semidirect
7. C2×#11718606C2semidirect
8. C2×#11718651C2semidirect
9. C2×#11718605C2semidirect
10. C2×#11718650C2semidirect
11. C2×#11718650C2semidirect
12. C2×#11718648C2semidirect
15. C2×#11718327C2semidirect
16. C2×C13×#396C2semidirect
20. C22×C13×C4⋊C4C22semidirect
21. C22×C13×C4⋊C4C22semidirect
22. C22×C13×C4⋊C4C22semidirect
39. C22×C4⋊Dic13C22semidirect
40. C22×#6101C22semidirect
41. C22×#6101C22semidirect
42. C22×C4×Dic13C22semidirect
43. C22×C4×Dic13C22semidirect
45. C2×#88152C22semidirect
48. C13×#396C22semidirect
49. C2×C13×#95C22semidirect
50. C2×#88071C22semidirect
51. C2×#88071C22semidirect
52. C2×#88071C22semidirect
53. C2×#88071C22semidirect
54. C2×#88071C22semidirect
55. C2×#88071C22semidirect
56. C2×#88071C22semidirect
57. #11718654C22semidirect
58. #11718651C22semidirect
59. #11718650C22semidirect
60. #11718650C22semidirect
61. #11718648C22semidirect
64. #11718614C22semidirect
65. #11718606C22semidirect
66. #11718605C22semidirect
67. #11718336C22semidirect
68. #11718327C22semidirect
103. C2×C13×C4⋊C4C23semidirect
104. C2×C13×C4⋊C4C23semidirect
105. C2×C13×C4⋊C4C23semidirect
139. C2×C4⋊Dic13C23semidirect
142. C2×#6101C23semidirect
143. C2×#6101C23semidirect
146. C2×C4×Dic13C23semidirect
147. C2×C4×Dic13C23semidirect
150. C13×#95C23semidirect
151. #88071C23semidirect
152. #88071C23semidirect
153. #88071C23semidirect
154. #88071C23semidirect
155. #88071C23semidirect
156. #88071C23semidirect
157. #88071C23semidirect
284. C2×#396D13semidirect
347. C22×D13#126semidirect
410. C22×C4⋊C4C2×D13semidirect
411. C22×C4⋊C4C2×D13semidirect
412. C22×C4⋊C4C2×D13semidirect
436. #396C2×D13semidirect
453. C2×#95C2×D13semidirect
492. C2×D13C2×#126semidirect
546. C2×C4⋊C4C22×D13semidirect
547. C2×C4⋊C4C22×D13semidirect
548. C2×C4⋊C4C22×D13semidirect
593. #95C22×D13semidirect
595. C2×C13#2480semidirect
724. C13C2×#2480semidirect
887. C2#13119085direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881522
C22×C22⋊C4×D132
#131190852
C2×#117183362
C2×#117186542
C2×#117186142
C2×#117186062
C2×#117186512
C2×#117186052
C2×#117186502
C2×#117186482
C2×#117186162
C2×#117183272
C2×C13×#3962
C2×#248013