Finite Group Databasebeta

← C2×#13118571 #16030369

Subgroups — C2×#13118571 #16030369

Order 3328.

4002 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88148C211yesmaximal, characteristic, complemented
2C22×#88184C211yesmaximal, characteristic
3C22×C4×C22⋊D13C211yesmaximal, characteristic, complemented
4#13118571C2116yesmaximal, direct product factor
5C2×#11718653C211yesmaximal, characteristic, complemented
6C2×#11718645C211yesmaximal, characteristic, complemented
7C2×#11718654C211yesmaximal, characteristic, complemented
8C2×#11718652C211yesmaximal, characteristic, complemented
9C2×#11718651C211yesmaximal, characteristic, complemented
10C2×#11718642C211yesmaximal, characteristic, complemented
11C2×#11718874C211yesmaximal, characteristic, complemented
12C2×#11718874C211yesmaximal, characteristic, complemented
13C2×#11718874C211yesmaximal, characteristic, complemented
14C2×#11718871C211yesmaximal, characteristic, complemented
15C2×#11718650C211yesmaximal, characteristic, complemented
16C23×C13×C4⋊C4C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C23×C22⋊D13C2211yescharacteristic
22C23×D52C2211yescharacteristic
23C23×C4×D13C2211yescharacteristic
24C22×C13×C4⋊C4—28no—
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C22×C13×C4⋊C4C2218yescomplemented
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C2×#88184—28no—
33C2×#88184C2218yes—
34C2×C4×C22⋊D13—28no—
35C2×C4×C22⋊D13C2218yescomplemented
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×#6103C2211yescharacteristic
42C22×#6103C2211yescharacteristic
43C22×#6103C2211yescharacteristic
44C22×#6103C2211yescharacteristic
45C22×C4⋊Dic13C2211yescharacteristic
46C22×#6101C2211yescharacteristic
47C22×#6101C2211yescharacteristic
48C22×#6101C2211yescharacteristic
49C22×C4×Dic13C2211yescharacteristic
50C2×#88148—28no—
51C2×#88148C2218yescomplemented
52#11718874C2218yescomplemented
53#11718874C2218yescomplemented
54#11718874C2218yescomplemented
55#11718871C2218yescomplemented
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62C2×#88071C2211yescharacteristic
63C2×#88071C2211yescharacteristic
64#11718654C2218yescomplemented
65#11718653C2218yescomplemented
66#11718652C2218yescomplemented
67#11718651C2218yescomplemented
68#11718650C2218yescomplemented
69#11718645C2218yescomplemented
70#11718642C2218yescomplemented
71C25×C13C2311yescharacteristic
72C24×D13C2311yescharacteristic
73C24×D13C2311yescharacteristic
74C23×C4×C13—24no—
75C23×C4×C13—24no—
76C23×C4×C13—24no—
77C23×C4×C13—24no—
78C23×C4×C13—24no—
79C23×C4×C13—24no—
80C23×C4×C13—24no—
81C23×C4×C13—42no—
82C23×C4×C13—42no—
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2314yes—
86C23×C4×C13C2314yes—
87C23×C4×C13C2314yes—
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C23×C4×C13C2311yescharacteristic
92C22×C22⋊D13—24no—
93C22×C22⋊D13—24no—
94C22×C22⋊D13—24no—
95C22×C22⋊D13—24no—
96C22×C22⋊D13—24no—
97C22×C22⋊D13D418yes—
98C22×C22⋊D13C2314yes—
99C22×C22⋊D13C2314yes—
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2311yescharacteristic
102C23×Dic13C2311yescharacteristic
103C23×Dic13C2311yescharacteristic
104C23×Dic13C2311yescharacteristic
105C23×Dic13C2311yescharacteristic
106C22×D52—24no—
107C22×D52—24no—
108C22×D52—42no—
109C22×D52C2314yes—
110C22×C4×D13—24no—
111C22×C4×D13—24no—
112C22×C4×D13—42no—
113C22×C4×D13C2314yes—
114C2×C13×C4⋊C4—24no—
115C2×C13×C4⋊C4—24no—
116C2×C13×C4⋊C4—24no—
117C2×C13×C4⋊C4—232no—
118C2×C13×C4⋊C4D418yescomplemented
119C2×C13×C4⋊C4C2314yes—
120C2×C13×C4⋊C4C2314yes—
121C2×C13×C4⋊C4C2314yes—
122C2×C13×C4⋊C4C2314yes—
123C2×C22⋊Dic13—24no—
124C2×C22⋊Dic13—24no—
125C2×C22⋊Dic13C2314yes—
126C2×C22⋊Dic13C2314yes—
127#88184—232no—
128C4×C22⋊D13—232no—
129C2×#6103—24no—
130C2×#6103—24no—
131C2×#6103—24no—
132C2×#6103—24no—
133C2×#6103—24no—
134C2×#6103—24no—
135C2×#6103—24no—
136C2×#6103—24no—
137C2×#6103—42no—
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141C2×#6103C2314yes—
142C2×#6103C2314yes—
143C2×#6103C2314yes—
144C2×#6103C2314yes—
145C2×#6103C2314yes—
146C2×#6103C2314yes—
147C2×C4⋊Dic13—24no—
148C2×C4⋊Dic13C2314yes—
149C2×#6101—24no—
150C2×#6101—24no—
151C2×#6101—42no—
152C2×#6101C2314yes—
153C2×#6101C2314yes—
154C2×#6101C2314yes—
155C2×C4×Dic13—24no—
156C2×C4×Dic13C2314yes—
157#88148—232no—
158#88071C2314yes—
159#88071C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164#88071C2314yes—
165#88071C2314yes—
166C2×#2443—131nomaximal, Sylow
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13C2×D414yes—
172C24×C13#4114yes—
173C24×C13#4114yes—
174C24×C13C2412yes—
175C24×C13C2411yescharacteristic
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13—22no—
181C23×D13—22no—
182C23×D13—22no—
183C23×D13—22no—
184C23×D13—22no—
185C23×D13—22no—
186C23×D13—22no—
187C23×D13—22no—
188C23×D13—22no—
189C23×D13C2×D414yes—
190C23×D13C2412yes—
191C23×D13C2412yes—
192C22×C4×C13—232no—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—28no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—22no—
201C22×C4×C13—22no—
202C22×C4×C13—28no—
203C22×C4×C13—28no—
204C22×C4×C13—22no—
205C22×C4×C13—22no—
206C22×C4×C13—28no—
207C22×C4×C13—28no—
208C22×C4×C13—22no—
209C22×C4×C13—22no—
210C22×C4×C13—22no—
211C22×C4×C13—22no—
212C22×C4×C13—28no—
213C22×C4×C13—28no—
214C22×C4×C13—44no—
215C22×C4×C13—44no—
216C22×C4×C13—416no—
217C22×C4×C13—416no—
218C22×C4×C13C2×D414yes—
219C22×C4×C13C2×D414yes—
220C22×C4×C13C2×D414yes—
221C22×C4×C13#4114yes—
222C22×C4×C13C2412yes—
223C22×C4×C13C2412yes—
224C22×C4×C13C2412yes—
225C22×C4×C13C2412yes—
226C22×C4×C13C2412yes—
227C22×C4×C13C2412yes—
228C2×C22⋊D13—232no—
229C2×C22⋊D13—28no—
230C2×C22⋊D13—28no—
231C2×C22⋊D13—28no—
232C2×C22⋊D13—28no—
233C2×C22⋊D13—28no—
234C2×C22⋊D13—416no—
235C2×C22⋊D13C2×D4116yes—
236C22×Dic13—22no—
237C22×Dic13—22no—
238C22×Dic13—22no—
239C22×Dic13—22no—
240C22×Dic13—22no—
241C22×Dic13—22no—
242C22×Dic13—22no—
243C22×Dic13—22no—
244C22×Dic13—22no—
245C22×Dic13—22no—
246C22×Dic13—22no—
247C22×Dic13—22no—
248C22×Dic13—22no—
249C22×Dic13—22no—
250C22×Dic13—22no—
251C22×Dic13—22no—
252C22×Dic13—22no—
253C22×Dic13C2×D414yes—
254C22×Dic13C2412yes—
255C22×Dic13C2412yes—
256C22×Dic13C2412yes—
257C22×Dic13C2412yes—
258C22×Dic13C2412yes—
259C22×Dic13C2412yes—
260C2×D52—28no—
261C2×D52—28no—
262C2×D52—44no—
263C2×D52—416no—
264C2×C4×D13—28no—
265C2×C4×D13—28no—
266C2×C4×D13—44no—
267C2×C4×D13—416no—
268C13×C4⋊C4—28no—
269C13×C4⋊C4—28no—
270C13×C4⋊C4—28no—
271C13×C4⋊C4C2×D4116yescomplemented
272C22⋊Dic13—28no—
273C22⋊Dic13—28no—
274#6103—28no—
275#6103—28no—
276#6103—28no—
277#6103—28no—
278#6103—28no—
279#6103—28no—
280#6103—28no—
281#6103—28no—
282#6103—44no—
283C4⋊Dic13—28no—
284#6101—28no—
285#6101—28no—
286#6101—44no—
287C4×Dic13—28no—
288C22×#123—131no—
289C22×#121—131no—
290C22×C4×D4—131no—
291C23×C4⋊C4D1311yescharacteristic, complemented
292#2443—1316no—
293C2×#399—131no—
294C2×#398—131no—
295C2×#397—131no—
296C2×#394—131no—
297C2×#388—131no—
298C2×#387—131no—
299C2×#386—131no—
300C2×#386—131no—
301C2×#386—131no—
302C2×#385—131no—
303C2×#385—131no—
304C23×C13—28no—
305C23×C13—28no—
306C23×C13—28no—
307C23×C13—28no—
308C23×C13—28no—
309C23×C13—28no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13#123116yescomplemented
315C23×C13C22×D414yes—
316C23×C13C22×D412yes—
317C23×C13C22×D412yes—
318C23×C13C2×#4114yes—
319C23×C13C2×#4114yes—
320C23×C13C2×#4112yes—
321C23×C13C2×#4112yes—
322C23×C13C2×#4112yes—
323C23×C13H(5,𝔽2)12yes—
324C23×C132−1+412yes—
325C23×C13C2511yescharacteristic
326C22×D13—28no—
327C22×D13—28no—
328C22×D13—28no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—22no—
336C22×D13—22no—
337C22×D13—22no—
338C22×D13—22no—
339C22×D13—22no—
340C22×D13—22no—
341C22×D13—22no—
342C22×D13—44no—
343C22×D13—44no—
344C22×D13—44no—
345C22×D13—44no—
346C22×D13—44no—
347C22×D13—44no—
348C22×D13—44no—
349C22×D13—44no—
350C22×D13—44no—
351C22×D13—44no—
352C22×D13—44no—
353C22×D13C22×D414yes—
354C2×C4×C13—232no—
355C2×C4×C13—28no—
356C2×C4×C13—28no—
357C2×C4×C13—28no—
358C2×C4×C13—28no—
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—22no—
372C2×C4×C13—22no—
373C2×C4×C13—416no—
374C2×C4×C13—416no—
375C2×C4×C13—44no—
376C2×C4×C13—44no—
377C2×C4×C13C22×D414yes—
378C2×C4×C13C22×D414yes—
379C2×C4×C13C22×D414yes—
380C2×C4×C13C2×#4114yes—
381C22⋊D13—232no—
382C22⋊D13—416no—
383C2×Dic13—28no—
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—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—44no—
402C2×Dic13—44no—
403C2×Dic13—44no—
404C2×Dic13—44no—
405C2×Dic13—44no—
406C2×Dic13C22×D414yes—
407D52—416no—
408C4×D13—416no—
409C23×D4—131no—
410C23×D4—131no—
411C23×D4—131no—
412C24×C4—131no—
413C24×C4C2×D1311yescharacteristic
414C24×C4C2×D1311yescharacteristic
415C24×C4C2×D1311yescharacteristic
416C2×#123—138no—
417C2×#123—268no—
418C2×#121—138no—
419C2×#121—268no—
420C2×C4×D4—138no—
421C2×C4×D4—268no—
422C22×C4⋊C4—28no—
423C22×C4⋊C4—131no—
424C22×C4⋊C4—131no—
425C22×C4⋊C4—131no—
426C22×C4⋊C4—131no—
427C22×C4⋊C4C2×D1311yescharacteristic
428C22×C4⋊C4C2×D1311yescharacteristic
429C22×C4⋊C4C2×D1311yescharacteristic
430C22×C4⋊C4C2×D1311yescharacteristic
431C22×C4⋊C4C2×D1318yescomplemented
432C22×C22⋊C4—131no—
433C22×C22⋊C4—131no—
434C22×C22⋊C4—131no—
435C22×C22⋊C4—131no—
436C22×C22⋊C4—131no—
437C22×C22⋊C4—131no—
438C22×C22⋊C4—131no—
439C22×C22⋊C4—131no—
440C22×C22⋊C4—131no—
441C22×C22⋊C4—131no—
442C22×C22⋊C4—131no—
443C22×C42—131no—
444#399—138no—
445#398—138no—
446#397—138no—
447#394—138no—
448#388—138no—
449#387—138no—
450#386—138no—
451#386—138no—
452#386—138no—
453#385—138no—
454#385—138no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95—131no—
463C22×C13—24no—
464C22×C13—24no—
465C22×C13—24no—
466C22×C13—24no—
467C22×C13—24no—
468C22×C13—232no—
469C22×C13—24no—
470C22×C13C2×#12314yes—
471C22×C13C2×#12318yescomplemented
472C22×C13#52514yes—
473C22×C13#53914yes—
474C22×C13D4214yes—
475C22×C13#54714yes—
476C22×C13#54814yes—
477C22×C13#55314yes—
478C22×C13C23×D411yescharacteristic
479C22×C13C23×D411yescharacteristic
480C22×C13C22×#4111yescharacteristic
481C22×C13C22×#4111yescharacteristic
482C22×C13C22×#4111yescharacteristic
483C22×C13C2×H(5,𝔽2)11yescharacteristic
484C22×C13C2×2−1+411yescharacteristic
485C2×D13—24no—
486C2×D13—24no—
487C2×D13—24no—
488C2×D13—42no—
489C2×D13—42no—
490C2×D13—42no—
491C2×D13—416no—
492C2×D13—42no—
493C2×D13—42no—
494C2×D13—42no—
495C2×D13—42no—
496C2×D13—42no—
497C2×D13—42no—
498C2×D13—42no—
499C2×D13—42no—
500C2×D13—88no—
501C4×C13—24no—
502C4×C13—24no—
503C4×C13—24no—
504C4×C13—24no—
505C4×C13—42no—
506C4×C13—42no—
507Dic13—24no—
508Dic13—42no—
509Dic13—42no—
510Dic13—42no—
511Dic13—42no—
512Dic13—42no—
513C25—131no—
514C25—131no—
515C25C22×D1311yescharacteristic
516C22×D4—138no—
517C22×D4—134no—
518C22×D4—134no—
519C22×D4—134no—
520C22×D4—264no—
521C22×D4—264no—
522C22×D4—264no—
523C22×D4—264no—
524C22×D4—264no—
525C22×D4—264no—
526C22×D4—264no—
527C22×D4—522no—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—24no—
532C23×C4—24no—
533C23×C4—24no—
534C23×C4—24no—
535C23×C4—42no—
536C23×C4—42no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—131no—
540C23×C4—131no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—134no—
544C23×C4—264no—
545C23×C4—264no—
546C23×C4—522no—
547C23×C4C22×D1314yes—
548C23×C4C22×D1311yescharacteristic
549C23×C4C22×D1311yescharacteristic
550C23×C4C22×D1314yes—
551C23×C4C22×D1314yes—
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1311yescharacteristic
554C23×C4C22×D1311yescharacteristic
555C23×C4C22×D1311yescharacteristic
556#123—2632no—
557#121—2632no—
558C4×D4—2632no—
559C2×C4⋊C4—24no—
560C2×C4⋊C4—24no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—232no—
563C2×C4⋊C4—134no—
564C2×C4⋊C4—134no—
565C2×C4⋊C4—134no—
566C2×C4⋊C4—134no—
567C2×C4⋊C4—264no—
568C2×C4⋊C4—264no—
569C2×C4⋊C4—264no—
570C2×C4⋊C4—522no—
571C2×C4⋊C4C22⋊D1318yescomplemented
572C2×C4⋊C4C22×D1314yes—
573C2×C4⋊C4C22×D1314yes—
574C2×C4⋊C4C22×D1314yes—
575C2×C4⋊C4C22×D1314yes—
576C2×C22⋊C4—134no—
577C2×C22⋊C4—134no—
578C2×C22⋊C4—134no—
579C2×C22⋊C4—134no—
580C2×C22⋊C4—134no—
581C2×C22⋊C4—134no—
582C2×C22⋊C4—134no—
583C2×C22⋊C4—134no—
584C2×C22⋊C4—134no—
585C2×C22⋊C4—134no—
586C2×C22⋊C4—134no—
587C2×C22⋊C4—264no—
588C2×C22⋊C4—264no—
589C2×C22⋊C4—264no—
590C2×C22⋊C4—264no—
591C2×C22⋊C4—264no—
592C2×C22⋊C4—264no—
593C2×C22⋊C4—264no—
594C2×C22⋊C4—264no—
595C2×C22⋊C4—264no—
596C2×C22⋊C4—264no—
597C2×C22⋊C4—522no—
598C2×C42—134no—
599C2×C42—264no—
600#95—134no—
601#95—134no—
602#95—134no—
603#95—134no—
604#95—134no—
605#95—134no—
606#95—134no—
607#95—134no—
608C2×C13—28no—
609C2×C13#244318yescomplemented
610C2×C13C22×#12311yescharacteristic
611C2×C13C2×#52511yescharacteristic
612C2×C13C2×#53911yescharacteristic
613C2×C13C2×D4211yescharacteristic
614C2×C13C2×#54711yescharacteristic
615C2×C13C2×#54811yescharacteristic
616C2×C13C2×#55311yescharacteristic
617D13—44no—
618D13—82no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—134no—
624C24—132no—
625C24—132no—
626C24—262no—
627C24—262no—
628C24—262no—
629C24—262no—
630C24—262no—
631C24—262no—
632C24—262no—
633C24—262no—
634C24—262no—
635C24—262no—
636C24—262no—
637C24—262no—
638C24—262no—
639C24#612714yes—
640C24D4×D1314yes—
641C24#613114yes—
642C24C23×D1312yes—
643C24C23×D1311yescharacteristic
644C2×D4—1316no—
645C2×D4—268no—
646C2×D4—2632no—
647C2×D4—268no—
648C2×D4—268no—
649C2×D4—268no—
650C2×D4—268no—
651C2×D4—268no—
652C2×D4—268no—
653C2×D4—524no—
654C2×D4—5216no—
655C2×D4—5216no—
656C22×C4—232no—
657C22×C4—28no—
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—28no—
667C22×C4—28no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—28no—
671C22×C4—28no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—28no—
677C22×C4—28no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—416no—
681C22×C4—416no—
682C22×C4—134no—
683C22×C4—132no—
684C22×C4—132no—
685C22×C4—132no—
686C22×C4—132no—
687C22×C4—132no—
688C22×C4—132no—
689C22×C4—268no—
690C22×C4—262no—
691C22×C4—262no—
692C22×C4—262no—
693C22×C4—262no—
694C22×C4—262no—
695C22×C4—262no—
696C22×C4—262no—
697C22×C4—262no—
698C22×C4—262no—
699C22×C4—262no—
700C22×C4—262no—
701C22×C4—262no—
702C22×C4—262no—
703C22×C4—262no—
704C22×C4—262no—
705C22×C4—262no—
706C22×C4—262no—
707C22×C4—268no—
708C22×C4—524no—
709C22×C4—5216no—
710C22×C4#612714yes—
711C22×C4C2×C22⋊D1314yes—
712C22×C4C2×C22⋊D1314yes—
713C22×C4C2×C22⋊D1314yes—
714C22×C4C23×D1312yes—
715C22×C4C23×D1312yes—
716C22×C4C23×D1312yes—
717C22×C4C23×D1312yes—
718C22×C4C23×D1312yes—
719C22×C4C23×D1312yes—
720C4⋊C4—28no—
721C4⋊C4—28no—
722C4⋊C4—28no—
723C4⋊C4—268no—
724C4⋊C4—268no—
725C4⋊C4—268no—
726C4⋊C4—524no—
727C4⋊C4C2×C22⋊D13116yescomplemented
728C22⋊C4—268no—
729C22⋊C4—268no—
730C22⋊C4—268no—
731C22⋊C4—268no—
732C22⋊C4—268no—
733C22⋊C4—268no—
734C22⋊C4—268no—
735C22⋊C4—268no—
736C22⋊C4—268no—
737C22⋊C4—268no—
738C22⋊C4—524no—
739C42—268no—
740C13C2×#244311yescharacteristic, complemented, Sylow
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—28no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—134no—
752C23—268no—
753C23—268no—
754C23—268no—
755C23—262no—
756C23—262no—
757C23—262no—
758C23—262no—
759C23—262no—
760C23—262no—
761C23—262no—
762C23—262no—
763C23—262no—
764C23—262no—
765C23—262no—
766C23—262no—
767C23—262no—
768C23—524no—
769C23—524no—
770C23—524no—
771C23—524no—
772C23—524no—
773C23—524no—
774C23—524no—
775C23—524no—
776C23—524no—
777C23—524no—
778C23—524no—
779C23#88148116yescomplemented
780C23C2×#612714yes—
781C23C2×#612712yes—
782C23C2×#612712yes—
783C23C2×D4×D1314yes—
784C23C2×D4×D1312yes—
785C23#8825112yes—
786C23C2×#613114yes—
787C23C2×#613112yes—
788C23#8825412yes—
789C23C22×C22⋊D1312yes—
790C23C24×D1311yescharacteristic
791D4—2632no—
792D4—5216no—
793D4—5216no—
794C2×C4—232no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—416no—
814C2×C4—416no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—134no—
818C2×C4—268no—
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—262no—
830C2×C4—262no—
831C2×C4—262no—
832C2×C4—262no—
833C2×C4—262no—
834C2×C4—262no—
835C2×C4—262no—
836C2×C4—5216no—
837C2×C4—524no—
838C2×C4—524no—
839C2×C4—524no—
840C2×C4—524no—
841C2×C4—524no—
842C2×C4C2×#612714yes—
843C2×C4C22×C22⋊D1314yes—
844C2×C4C22×C22⋊D1314yes—
845C2×C4C22×C22⋊D1314yes—
846C22—24no—
847C22—24no—
848C22—232no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—264no—
854C22—264no—
855C22—264no—
856C22—5216no—
857C22—522no—
858C22—522no—
859C22—522no—
860C22—522no—
861C22—522no—
862C22—522no—
863C22—522no—
864C22—522no—
865C22—522no—
866C22—522no—
867C22—522no—
868C22—1048no—
869C22C2×#8814814yes—
870C22C2×#8814818yescomplemented
871C22#1171921214yes—
872C22#1171921914yes—
873C22#1171922014yes—
874C22#1171949614yes—
875C22D4×C22⋊D1314yes—
876C22#1171952214yes—
877C22C22×#612711yescharacteristic
878C22C22×#612711yescharacteristic
879C22C22×D4×D1311yescharacteristic
880C22C2×#8825111yescharacteristic
881C22C22×#613111yescharacteristic
882C22C2×#8825411yescharacteristic
883C22C23×C22⋊D1311yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—42no—
889C4—42no—
890C4—264no—
891C4—522no—
892C4—522no—
893C4—522no—
894C4—522no—
895C4—522no—
896C2—28no—
897C2—524no—
898C2—1042no—
899C2#1311857118yesdirect product factor
900C2C22×#8814811yescharacteristic
901C2C2×#1171949611yescharacteristic
902C2C2×#1171922011yescharacteristic
903C2C2×D4×C22⋊D1311yescharacteristic
904C2C2×#1171921211yescharacteristic
905C2C2×#1171952211yescharacteristic
906C2C2×#1171921911yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC23×C13×C4⋊C4C2
socleC24×C13C24
prime radicalC22×#88184C2
hypercenterC23×C4⋊C4D13
hypocenterC13C2×#2443
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#88148C2semidirect
3. C22×C4×C22⋊D13C2semidirect
4. #13118571C2direct (N × H)
5. C2×#11718653C2semidirect
6. C2×#11718645C2semidirect
7. C2×#11718654C2semidirect
8. C2×#11718652C2semidirect
9. C2×#11718651C2semidirect
10. C2×#11718642C2semidirect
11. C2×#11718874C2semidirect
12. C2×#11718874C2semidirect
13. C2×#11718874C2semidirect
14. C2×#11718871C2semidirect
15. C2×#11718650C2semidirect
16. C23×C13×C4⋊C4C2semidirect
29. C22×C13×C4⋊C4C22semidirect
35. C2×C4×C22⋊D13C22semidirect
51. C2×#88148C22semidirect
52. #11718874C22semidirect
53. #11718874C22semidirect
54. #11718874C22semidirect
55. #11718871C22semidirect
64. #11718654C22semidirect
65. #11718653C22semidirect
66. #11718652C22semidirect
67. #11718651C22semidirect
68. #11718650C22semidirect
69. #11718645C22semidirect
70. #11718642C22semidirect
118. C2×C13×C4⋊C4D4semidirect
271. C13×C4⋊C4C2×D4semidirect
291. C23×C4⋊C4D13semidirect
314. C23×C13#123semidirect
431. C22×C4⋊C4C2×D13semidirect
471. C22×C13C2×#123semidirect
571. C2×C4⋊C4C22⋊D13semidirect
609. C2×C13#2443semidirect
727. C4⋊C4C2×C22⋊D13semidirect
740. C13C2×#2443semidirect
779. C23#88148semidirect
870. C22C2×#88148semidirect
899. C2#13118571direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881482
C22×#881842
C22×C4×C22⋊D132
#131185712
C2×#117186532
C2×#117186452
C2×#117186542
C2×#117186522
C2×#117186512
C2×#117186422
C2×#117188742
C2×#117188712
C2×#117186502
C23×C13×C4⋊C42
C2×#244313