Finite Group Databasebeta

← C2×#13118391 #16030644

Subgroups — C2×#13118391 #16030644

Order 3328.

3938 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×#88183C211yesmaximal, characteristic, complemented
2C22×#88193C211yesmaximal, characteristic
3C22×D4×Dic13C211yesmaximal, characteristic, complemented
4#13118391C2116yesmaximal, direct product factor
5C2×#11718645C211yesmaximal, characteristic, complemented
6C2×#11718613C211yesmaximal, characteristic, complemented
7C2×#11718655C211yesmaximal, characteristic, complemented
8C2×#11718620C211yesmaximal, characteristic, complemented
9C2×#11718633C211yesmaximal, characteristic, complemented
10C2×#11718651C211yesmaximal, characteristic, complemented
11C2×#11718619C211yesmaximal, characteristic, complemented
12C2×#11718619C211yesmaximal, characteristic, complemented
13C2×#11718607C211yesmaximal, characteristic, complemented
14C2×#11718603C211yesmaximal, characteristic, complemented
15C22×#88071C211yesmaximal, characteristic, complemented
16C22×C13×#123C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C24×Dic13C2211yescharacteristic
22C24×Dic13C2211yescharacteristic
23C24×Dic13C2211yescharacteristic
24C2×C13×#123—28no—
25C2×C13×#123C2218yescomplemented
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C2×#88193—28no—
35C2×#88193C2218yes—
36C2×D4×Dic13—28no—
37C2×D4×Dic13C2218yescomplemented
38C2×#88183—28no—
39C2×#88183C2218yescomplemented
40C22×#6103C2211yescharacteristic
41C22×#6103C2211yescharacteristic
42C22×#6103C2211yescharacteristic
43C22×#6103C2211yescharacteristic
44C22×#6103C2211yescharacteristic
45C22×C4⋊Dic13C2211yescharacteristic
46C22×#6101C2211yescharacteristic
47C22×#6101C2211yescharacteristic
48C22×#6101C2211yescharacteristic
49C22×#6101C2211yescharacteristic
50C22×#6101C2211yescharacteristic
51C22×C4×Dic13C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2218yescomplemented
61#11718655C2218yescomplemented
62#11718651C2218yescomplemented
63#11718645C2218yescomplemented
64#11718633C2218yescomplemented
65#11718620C2218yescomplemented
66#11718619C2218yescomplemented
67#11718619C2218yescomplemented
68#11718613C2218yescomplemented
69#11718607C2218yescomplemented
70#11718603C2218yescomplemented
71C25×C13C2311yescharacteristic
72C25×C13C2311yescharacteristic
73C24×D13C2311yescharacteristic
74C22×D4×C13—24no—
75C22×D4×C13—24no—
76C22×D4×C13D418yes—
77C22×D4×C13C2314yes—
78C23×C4×C13—24no—
79C23×C4×C13—24no—
80C23×C4×C13—24no—
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2314yes—
86C23×C4×C13C2311yescharacteristic
87C22×C22⋊D13—24no—
88C22×C22⋊D13—24no—
89C22×C22⋊D13—24no—
90C22×C22⋊D13—24no—
91C22×C22⋊D13—24no—
92C22×C22⋊D13—42no—
93C22×C22⋊D13C2314yes—
94C22×C22⋊D13C2314yes—
95C23×Dic13—24no—
96C23×Dic13—24no—
97C23×Dic13—24no—
98C23×Dic13—24no—
99C23×Dic13—24no—
100C23×Dic13—24no—
101C23×Dic13—42no—
102C23×Dic13—42no—
103C23×Dic13—42no—
104C23×Dic13C2311yescharacteristic
105C23×Dic13C2311yescharacteristic
106C23×Dic13C2311yescharacteristic
107C23×Dic13C2314yes—
108C23×Dic13C2314yes—
109C23×Dic13C2314yes—
110C23×Dic13C2311yescharacteristic
111C23×Dic13C2311yescharacteristic
112C23×Dic13C2311yescharacteristic
113C23×Dic13C2311yescharacteristic
114C13×#123—232no—
115C2×C13×C4⋊C4—24no—
116C2×C13×C4⋊C4—24no—
117C2×C13×C4⋊C4C2314yes—
118C2×C13×C4⋊C4C2314yes—
119C2×C13×C22⋊C4—24no—
120C2×C13×C22⋊C4—24no—
121C2×C13×C22⋊C4—24no—
122C2×C13×C22⋊C4C2314yes—
123C2×C13×C22⋊C4C2314yes—
124C2×C13×C22⋊C4C2314yes—
125C2×C22⋊Dic13—24no—
126C2×C22⋊Dic13—24no—
127C2×C22⋊Dic13D418yescomplemented
128C2×C22⋊Dic13C2314yes—
129C2×C22⋊Dic13C2314yes—
130C2×C22⋊Dic13C2314yes—
131#88193—232no—
132D4×Dic13—232no—
133#88183—232no—
134C2×#6103—24no—
135C2×#6103—24no—
136C2×#6103—24no—
137C2×#6103—24no—
138C2×#6103—42no—
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141C2×#6103C2314yes—
142C2×#6103C2314yes—
143C2×#6103C2314yes—
144C2×C4⋊Dic13—24no—
145C2×C4⋊Dic13C2314yes—
146C2×#6101—24no—
147C2×#6101—24no—
148C2×#6101—24no—
149C2×#6101—24no—
150C2×#6101—42no—
151C2×#6101C2314yes—
152C2×#6101C2314yes—
153C2×#6101C2314yes—
154C2×#6101C2314yes—
155C2×#6101C2314yes—
156C2×C4×Dic13—24no—
157C2×C4×Dic13C2314yes—
158#88071C2314yes—
159#88071C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164#88071C2314yes—
165#88071C2314yes—
166C2×#2425—131nomaximal, Sylow
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13—22no—
172C24×C13—22no—
173C24×C13—22no—
174C24×C13—22no—
175C24×C13—22no—
176C24×C13—22no—
177C24×C13C2×D414yes—
178C24×C13C2×D414yes—
179C24×C13C2×D414yes—
180C24×C13#4114yes—
181C24×C13C2412yes—
182C24×C13C2412yes—
183C24×C13C2411yescharacteristic
184C23×D13—22no—
185C23×D13—22no—
186C23×D13—22no—
187C23×D13—22no—
188C23×D13—22no—
189C23×D13—22no—
190C23×D13—22no—
191C23×D13C2412yes—
192C2×D4×C13—232no—
193C2×D4×C13—28no—
194C2×D4×C13—28no—
195C2×D4×C13C2×D4116yes—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—28no—
201C22×C4×C13—22no—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—22no—
205C22×C4×C13—28no—
206C22×C4×C13—22no—
207C22×C4×C13—22no—
208C22×C4×C13—28no—
209C22×C4×C13—22no—
210C22×C4×C13—22no—
211C22×C4×C13—22no—
212C22×C4×C13—22no—
213C22×C4×C13—416no—
214C22×C4×C13C2×D414yes—
215C22×C4×C13C2412yes—
216C22×C4×C13C2412yes—
217C22×C4×C13C2412yes—
218C22×C4×C13C2412yes—
219C22×C4×C13C2412yes—
220C2×C22⋊D13—28no—
221C2×C22⋊D13—28no—
222C2×C22⋊D13—28no—
223C2×C22⋊D13—28no—
224C2×C22⋊D13—28no—
225C2×C22⋊D13—44no—
226C2×C22⋊D13—416no—
227C2×C22⋊D13—416no—
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×Dic13—22no—
240C22×Dic13—28no—
241C22×Dic13—28no—
242C22×Dic13—22no—
243C22×Dic13—22no—
244C22×Dic13—22no—
245C22×Dic13—22no—
246C22×Dic13—22no—
247C22×Dic13—28no—
248C22×Dic13—28no—
249C22×Dic13—28no—
250C22×Dic13—28no—
251C22×Dic13—44no—
252C22×Dic13—44no—
253C22×Dic13—44no—
254C22×Dic13—416no—
255C22×Dic13—416no—
256C22×Dic13—416no—
257C22×Dic13C2×D414yes—
258C22×Dic13C2×D414yes—
259C22×Dic13#4114yes—
260C22×Dic13#4114yes—
261C22×Dic13C2412yes—
262C22×Dic13C2412yes—
263C22×Dic13C2412yes—
264C22×Dic13C2412yes—
265C22×Dic13C2412yes—
266C22×Dic13C2412yes—
267C22×Dic13C2412yes—
268C13×C4⋊C4—28no—
269C13×C4⋊C4—28no—
270C13×C22⋊C4—28no—
271C13×C22⋊C4—28no—
272C13×C22⋊C4—28no—
273C22⋊Dic13—28no—
274C22⋊Dic13—28no—
275C22⋊Dic13C2×D4116yescomplemented
276#6103—28no—
277#6103—28no—
278#6103—28no—
279#6103—28no—
280#6103—44no—
281C4⋊Dic13—28no—
282#6101—28no—
283#6101—28no—
284#6101—28no—
285#6101—28no—
286#6101—44no—
287C4×Dic13—28no—
288C22×#123—131no—
289C22×#123D1311yescharacteristic, complemented
290C22×#121—131no—
291C22×C4×D4—131no—
292#2425—1316no—
293C2×#398—131no—
294C2×#397—131no—
295C2×#396—131no—
296C2×#394—131no—
297C2×#389—131no—
298C2×#388—131no—
299C2×#386—131no—
300C2×#386—131no—
301C2×#385—131no—
302C2×#380—131no—
303C22×#95—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—28no—
315C23×C13—28no—
316C23×C13—28no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—44no—
324C23×C13—44no—
325C23×C13—44no—
326C23×C13—44no—
327C23×C13#121116yes—
328C23×C13C22×D414yes—
329C23×C13C22×D414yes—
330C23×C13C22×D414yes—
331C23×C13C22×D412yes—
332C23×C13C22×D412yes—
333C23×C13C2×#4114yes—
334C23×C13C2×#4112yes—
335C23×C13C2×#4112yes—
336C23×C13C2×#4112yes—
337C23×C13H(5,𝔽2)12yes—
338C23×C132−1+412yes—
339C23×C13C2511yescharacteristic
340C22×D13—22no—
341C22×D13—22no—
342C22×D13—22no—
343C22×D13—22no—
344C22×D13—22no—
345C22×D13—22no—
346C22×D13—22no—
347C22×D13—44no—
348C22×D13—44no—
349C22×D13—44no—
350C22×D13—44no—
351C22×D13—44no—
352C22×D13—44no—
353C22×D13—44no—
354D4×C13—232no—
355C2×C4×C13—28no—
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—416no—
371C2×C4×C13—44no—
372C2×C4×C13—44no—
373C2×C4×C13—44no—
374C2×C4×C13—44no—
375C2×C4×C13C22×D414yes—
376C22⋊D13—416no—
377C22⋊D13—416no—
378C2×Dic13—28no—
379C2×Dic13—28no—
380C2×Dic13—28no—
381C2×Dic13—28no—
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—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—416no—
400C2×Dic13—416no—
401C2×Dic13—416no—
402C2×Dic13—44no—
403C2×Dic13—44no—
404C2×Dic13—44no—
405C2×Dic13C22×D414yes—
406C2×Dic13C22×D414yes—
407C2×Dic13C2×#4114yes—
408C2×Dic13C2×#4114yes—
409C23×D4—131no—
410C23×D4—131no—
411C23×D4C2×D1311yescharacteristic
412C24×C4—131no—
413C24×C4—131no—
414C24×C4—131no—
415C24×C4C2×D1311yescharacteristic
416C2×#123—28no—
417C2×#123—138no—
418C2×#123—268no—
419C2×#123C2×D1318yescomplemented
420C2×#121—138no—
421C2×#121—268no—
422C2×C4×D4—138no—
423C2×C4×D4—268no—
424C22×C4⋊C4—131no—
425C22×C4⋊C4—131no—
426C22×C4⋊C4—131no—
427C22×C4⋊C4—131no—
428C22×C4⋊C4—131no—
429C22×C4⋊C4—131no—
430C22×C4⋊C4C2×D1311yescharacteristic
431C22×C4⋊C4C2×D1311yescharacteristic
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⋊C4C2×D1311yescharacteristic
441C22×C22⋊C4C2×D1311yescharacteristic
442C22×C22⋊C4C2×D1311yescharacteristic
443C22×C42—131no—
444#398—138no—
445#397—138no—
446#396—138no—
447#394—138no—
448#389—138no—
449#388—138no—
450#386—138no—
451#386—138no—
452#385—138no—
453#380—138no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—138no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95—131no—
463C22×C13—24no—
464C22×C13—232no—
465C22×C13—24no—
466C22×C13—24no—
467C22×C13—24no—
468C22×C13—24no—
469C22×C13—24no—
470C22×C13—24no—
471C22×C13—24no—
472C22×C13—24no—
473C22×C13—42no—
474C22×C13—416no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13C2×#12118yes—
479C22×C13C2×#12114yes—
480C22×C13#52914yes—
481C22×C13#53914yes—
482C22×C13#54614yes—
483C22×C13#54614yes—
484C22×C13#54714yes—
485C22×C13#54714yes—
486C22×C13C23×D411yescharacteristic
487C22×C13C23×D411yescharacteristic
488C22×C13C22×#4111yescharacteristic
489C22×C13C22×#4111yescharacteristic
490C22×C13C22×#4111yescharacteristic
491C22×C13C2×H(5,𝔽2)11yescharacteristic
492C22×C13C2×2−1+411yescharacteristic
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—42no—
503C4×C13—42no—
504C4×C13—42no—
505C4×C13—42no—
506Dic13—24no—
507Dic13—24no—
508Dic13—24no—
509Dic13—24no—
510Dic13—42no—
511Dic13—42no—
512Dic13—42no—
513C25—131no—
514C25C22×D1311yescharacteristic
515C25C22×D1311yescharacteristic
516C22×D4—24no—
517C22×D4—24no—
518C22×D4—134no—
519C22×D4—134no—
520C22×D4—264no—
521C22×D4—264no—
522C22×D4—264no—
523C22×D4—264no—
524C22×D4—264no—
525C22×D4—522no—
526C22×D4C22⋊D1318yes—
527C22×D4C22×D1314yes—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—134no—
539C23×C4—134no—
540C23×C4—134no—
541C23×C4—264no—
542C23×C4—264no—
543C23×C4—264no—
544C23×C4—264no—
545C23×C4—264no—
546C23×C4—264no—
547C23×C4—522no—
548C23×C4—522no—
549C23×C4—522no—
550C23×C4C22×D1314yes—
551C23×C4C22×D1311yescharacteristic
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1311yescharacteristic
554C23×C4C22×D1311yescharacteristic
555C23×C4C22×D1311yescharacteristic
556#123—232no—
557#123—2632no—
558#121—2632no—
559C4×D4—2632no—
560C2×C4⋊C4—24no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—134no—
563C2×C4⋊C4—134no—
564C2×C4⋊C4—134no—
565C2×C4⋊C4—134no—
566C2×C4⋊C4—134no—
567C2×C4⋊C4—134no—
568C2×C4⋊C4—264no—
569C2×C4⋊C4—264no—
570C2×C4⋊C4—264no—
571C2×C4⋊C4—264no—
572C2×C4⋊C4—264no—
573C2×C4⋊C4—522no—
574C2×C4⋊C4C22×D1314yes—
575C2×C4⋊C4C22×D1314yes—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—138no—
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—134no—
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—522no—
595C2×C22⋊C4C22×D1314yes—
596C2×C22⋊C4C22×D1314yes—
597C2×C22⋊C4C22×D1314yes—
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—44no—
610C2×C13#242518yescomplemented
611C2×C13C22×#12111yescharacteristic
612C2×C13C2×#52911yescharacteristic
613C2×C13C2×#53911yescharacteristic
614C2×C13C2×#54611yescharacteristic
615C2×C13C2×#54611yescharacteristic
616C2×C13C2×#54711yescharacteristic
617C2×C13C2×#54711yescharacteristic
618D13—82no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—132no—
630C24—262no—
631C24—262no—
632C24—262no—
633C24—262no—
634C24—262no—
635C24—262no—
636C24—262no—
637C24D4×D1314yes—
638C24#612914yes—
639C24C2×C22⋊D1314yes—
640C24C2×C22⋊D1314yes—
641C24C23×D1312yes—
642C24C23×D1312yes—
643C24C23×D1311yescharacteristic
644C2×D4—232no—
645C2×D4—28no—
646C2×D4—28no—
647C2×D4—268no—
648C2×D4—268no—
649C2×D4—268no—
650C2×D4—268no—
651C2×D4—268no—
652C2×D4—524no—
653C2×D4—5216no—
654C2×D4—5216no—
655C2×D4C2×C22⋊D13116yes—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—28no—
661C22×C4—28no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—28no—
673C22×C4—416no—
674C22×C4—134no—
675C22×C4—134no—
676C22×C4—134no—
677C22×C4—134no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—132no—
685C22×C4—268no—
686C22×C4—268no—
687C22×C4—268no—
688C22×C4—268no—
689C22×C4—262no—
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—268no—
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—524no—
710C22×C4—524no—
711C22×C4—5216no—
712C22×C4—5216no—
713C22×C4—5216no—
714C22×C4C2×C22⋊D1314yes—
715C22×C4C23×D1312yes—
716C22×C4C23×D1312yes—
717C22×C4C23×D1312yes—
718C22×C4C23×D1312yes—
719C22×C4C23×D1312yes—
720C4⋊C4—28no—
721C4⋊C4—28no—
722C4⋊C4—268no—
723C4⋊C4—268no—
724C4⋊C4—268no—
725C4⋊C4—268no—
726C4⋊C4—268no—
727C4⋊C4—524no—
728C22⋊C4—28no—
729C22⋊C4—28no—
730C22⋊C4—28no—
731C22⋊C4—1316no—
732C22⋊C4—268no—
733C22⋊C4—268no—
734C22⋊C4—268no—
735C22⋊C4—268no—
736C22⋊C4—268no—
737C22⋊C4—268no—
738C22⋊C4—524no—
739C42—268no—
740C13C2×#242511yescharacteristic, complemented, Sylow
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—28no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—28no—
752C23—28no—
753C23—28no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—262no—
765C23—262no—
766C23—262no—
767C23—262no—
768C23—262no—
769C23—262no—
770C23—262no—
771C23—524no—
772C23—524no—
773C23—524no—
774C23—524no—
775C23—524no—
776C23—524no—
777C23—524no—
778C23#88193116yes—
779C23C2×D4×D1314yes—
780C23C2×D4×D1312yes—
781C23C2×#612914yes—
782C23C2×#612912yes—
783C23#41×D1312yes—
784C23#41×D1312yes—
785C23#8825612yes—
786C23#8825712yes—
787C23C22×C22⋊D1314yes—
788C23C22×C22⋊D1314yes—
789C23C22×C22⋊D1312yes—
790C23C24×D1311yescharacteristic
791D4—232no—
792D4—5216no—
793D4—5216no—
794C2×C4—28no—
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—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—416no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—134no—
815C2×C4—134no—
816C2×C4—134no—
817C2×C4—134no—
818C2×C4—268no—
819C2×C4—268no—
820C2×C4—268no—
821C2×C4—268no—
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—262no—
837C2×C4—262no—
838C2×C4—262no—
839C2×C4—5216no—
840C2×C4—5216no—
841C2×C4—5216no—
842C2×C4—524no—
843C2×C4—524no—
844C2×C4—524no—
845C2×C4C22×C22⋊D1314yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—232no—
852C22—24no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—416no—
860C22—42no—
861C22—522no—
862C22—522no—
863C22—522no—
864C22—522no—
865C22—522no—
866C22—522no—
867C22—522no—
868C22—1048no—
869C22#1171935414yes—
870C22#1171935914yes—
871C22#1171936014yes—
872C22#1171937014yes—
873C22C2×#8819318yes—
874C22C2×#8819314yes—
875C22#1171952914yes—
876C22#1171953414yes—
877C22C22×D4×D1311yescharacteristic
878C22C22×#612911yescharacteristic
879C22C2×#41×D1311yescharacteristic
880C22C2×#41×D1311yescharacteristic
881C22C2×#8825611yescharacteristic
882C22C2×#8825711yescharacteristic
883C22C23×C22⋊D1311yescharacteristic
884C4—24no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—264no—
890C4—264no—
891C4—264no—
892C4—264no—
893C4—522no—
894C4—522no—
895C4—522no—
896C2—28no—
897C2—44no—
898C2—1042no—
899C2#1311839118yesdirect product factor
900C2C22×#8819311yescharacteristic
901C2C2×#1171935411yescharacteristic
902C2C2×#1171937011yescharacteristic
903C2C2×#1171953411yescharacteristic
904C2C2×#1171935911yescharacteristic
905C2C2×#1171936011yescharacteristic
906C2C2×#1171952911yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×#123C2
socleC24×C13C24
prime radicalC22×#88193C2
hypercenterC22×#123D13
hypocenterC13C2×#2425
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×#88183C2semidirect
3. C22×D4×Dic13C2semidirect
4. #13118391C2direct (N × H)
5. C2×#11718645C2semidirect
6. C2×#11718613C2semidirect
7. C2×#11718655C2semidirect
8. C2×#11718620C2semidirect
9. C2×#11718633C2semidirect
10. C2×#11718651C2semidirect
11. C2×#11718619C2semidirect
12. C2×#11718619C2semidirect
13. C2×#11718607C2semidirect
14. C2×#11718603C2semidirect
15. C22×#88071C2semidirect
16. C22×C13×#123C2semidirect
25. C2×C13×#123C22semidirect
37. C2×D4×Dic13C22semidirect
39. C2×#88183C22semidirect
60. C2×#88071C22semidirect
61. #11718655C22semidirect
62. #11718651C22semidirect
63. #11718645C22semidirect
64. #11718633C22semidirect
65. #11718620C22semidirect
66. #11718619C22semidirect
67. #11718619C22semidirect
68. #11718613C22semidirect
69. #11718607C22semidirect
70. #11718603C22semidirect
127. C2×C22⋊Dic13D4semidirect
275. C22⋊Dic13C2×D4semidirect
289. C22×#123D13semidirect
419. C2×#123C2×D13semidirect
610. C2×C13#2425semidirect
740. C13C2×#2425semidirect
899. C2#13118391direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881832
C22×#881932
C22×D4×Dic132
#131183912
C2×#117186452
C2×#117186132
C2×#117186552
C2×#117186202
C2×#117186332
C2×#117186512
C2×#117186192
C2×#117186072
C2×#117186032
C22×#880712
C22×C13×#1232
C2×#242513