Finite Group Databasebeta

← C2×#13118381 #16030637

Subgroups — C2×#13118381 #16030637

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×#88140C211yesmaximal, characteristic, complemented
2C22×#88189C211yesmaximal, characteristic, complemented
3C22×#88193C211yesmaximal, characteristic
4#13118381C2116yesmaximal, direct product factor
5C2×#11718644C211yesmaximal, characteristic, complemented
6C2×#11718614C211yesmaximal, characteristic, complemented
7C2×#11718655C211yesmaximal, characteristic, complemented
8C2×#11718622C211yesmaximal, characteristic, complemented
9C2×#11718589C211yesmaximal, characteristic, complemented
10C2×#11718601C211yesmaximal, characteristic, complemented
11C2×#11718874C211yesmaximal, characteristic, complemented
12C2×#11718874C211yesmaximal, characteristic, complemented
13C2×#11718611C211yesmaximal, characteristic, complemented
14C2×#11718873C211yesmaximal, characteristic, complemented
15C22×#88071C211yesmaximal, characteristic, complemented
16C22×C4×D4×C13C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C23×C22⋊D13C2211yescharacteristic
22C24×Dic13C2211yescharacteristic
23C24×Dic13C2211yescharacteristic
24C2×C4×D4×C13—28no—
25C2×C4×D4×C13C2218yescomplemented
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C42×C13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C2×#88193—28no—
35C2×#88193C2218yes—
36C2×#88189—28no—
37C2×#88189C2218yescomplemented
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×#6103C2211yescharacteristic
42C22×#6103C2211yescharacteristic
43C22×C4⋊Dic13C2211yescharacteristic
44C22×C4⋊Dic13C2211yescharacteristic
45C22×C4⋊Dic13C2211yescharacteristic
46C22×C4⋊Dic13C2211yescharacteristic
47C22×#6101C2211yescharacteristic
48C22×#6101C2211yescharacteristic
49C22×#6101C2211yescharacteristic
50C2×#88140—28no—
51C2×#88140C2218yescomplemented
52#11718874C2218yescomplemented
53#11718874C2218yescomplemented
54#11718873C2218yescomplemented
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62C2×#88071C2211yescharacteristic
63C2×#88071C2218yescomplemented
64#11718655C2218yescomplemented
65#11718644C2218yescomplemented
66#11718622C2218yescomplemented
67#11718614C2218yescomplemented
68#11718611C2218yescomplemented
69#11718601C2218yescomplemented
70#11718589C2218yescomplemented
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×C13—24no—
82C23×C4×C13—42no—
83C23×C4×C13—42no—
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2314yes—
86C23×C4×C13C2314yes—
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C22×C22⋊D13—24no—
92C22×C22⋊D13—24no—
93C22×C22⋊D13—24no—
94C22×C22⋊D13—24no—
95C22×C22⋊D13—24no—
96C22×C22⋊D13—42no—
97C22×C22⋊D13C2314yes—
98C22×C22⋊D13C2314yes—
99C23×Dic13—24no—
100C23×Dic13—24no—
101C23×Dic13—24no—
102C23×Dic13—24no—
103C23×Dic13—24no—
104C23×Dic13—42no—
105C23×Dic13C2314yes—
106C23×Dic13C2311yescharacteristic
107C23×Dic13C2311yescharacteristic
108C23×Dic13C2311yescharacteristic
109C23×Dic13C2311yescharacteristic
110C23×Dic13C2311yescharacteristic
111C23×Dic13C2311yescharacteristic
112C23×Dic13C2314yes—
113C23×Dic13C2311yescharacteristic
114C4×D4×C13—232no—
115C2×C13×C4⋊C4—24no—
116C2×C13×C4⋊C4C2314yes—
117C2×C13×C22⋊C4—24no—
118C2×C13×C22⋊C4D418yescomplemented
119C2×C13×C22⋊C4C2314yes—
120C2×C13×C22⋊C4C2314yes—
121C2×C42×C13—24no—
122C2×C42×C13C2314yes—
123C2×C22⋊Dic13—24no—
124C2×C22⋊Dic13—24no—
125C2×C22⋊Dic13—24no—
126C2×C22⋊Dic13—24no—
127C2×C22⋊Dic13C2314yes—
128C2×C22⋊Dic13C2314yes—
129C2×C22⋊Dic13C2314yes—
130C2×C22⋊Dic13C2314yes—
131#88193—232no—
132#88189—232no—
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×C4⋊Dic13—24no—
144C2×C4⋊Dic13—24no—
145C2×C4⋊Dic13—24no—
146C2×C4⋊Dic13—42no—
147C2×C4⋊Dic13C2314yes—
148C2×C4⋊Dic13C2314yes—
149C2×C4⋊Dic13C2314yes—
150C2×C4⋊Dic13C2314yes—
151C2×#6101—24no—
152C2×#6101—24no—
153C2×#6101—24no—
154C2×#6101C2314yes—
155C2×#6101C2314yes—
156C2×#6101C2314yes—
157#88140—232no—
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—22no—
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—28no—
210C22×C4×C13—28no—
211C22×C4×C13—44no—
212C22×C4×C13—44no—
213C22×C4×C13—416no—
214C22×C4×C13—416no—
215C22×C4×C13C2×D414yes—
216C22×C4×C13C2×D414yes—
217C22×C4×C13C2×D414yes—
218C22×C4×C13#4114yes—
219C22×C4×C13C2412yes—
220C22×C4×C13C2412yes—
221C22×C4×C13C2412yes—
222C22×C4×C13C2412yes—
223C22×C4×C13C2412yes—
224C2×C22⋊D13—28no—
225C2×C22⋊D13—28no—
226C2×C22⋊D13—28no—
227C2×C22⋊D13—28no—
228C2×C22⋊D13—28no—
229C2×C22⋊D13—44no—
230C2×C22⋊D13—416no—
231C2×C22⋊D13—416no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13—28no—
235C22×Dic13—22no—
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—28no—
245C22×Dic13—28no—
246C22×Dic13—22no—
247C22×Dic13—22no—
248C22×Dic13—28no—
249C22×Dic13—22no—
250C22×Dic13—22no—
251C22×Dic13—22no—
252C22×Dic13—22no—
253C22×Dic13—22no—
254C22×Dic13—22no—
255C22×Dic13—22no—
256C22×Dic13—28no—
257C22×Dic13—44no—
258C22×Dic13—416no—
259C22×Dic13—416no—
260C22×Dic13#4114yes—
261C22×Dic13C2412yes—
262C22×Dic13C2412yes—
263C22×Dic13C2412yes—
264C22×Dic13C2412yes—
265C22×Dic13C2412yes—
266C22×Dic13C2412yes—
267C22×Dic13C2412yes—
268C13×C4⋊C4—28no—
269C13×C22⋊C4—28no—
270C13×C22⋊C4C2×D4116yescomplemented
271C42×C13—28no—
272C22⋊Dic13—28no—
273C22⋊Dic13—28no—
274C22⋊Dic13—28no—
275C22⋊Dic13—28no—
276#6103—28no—
277#6103—28no—
278#6103—28no—
279#6103—28no—
280#6103—44no—
281C4⋊Dic13—28no—
282C4⋊Dic13—28no—
283C4⋊Dic13—28no—
284C4⋊Dic13—44no—
285#6101—28no—
286#6101—28no—
287#6101—28no—
288C22×#123—131no—
289C22×#123—131no—
290C22×#121—131no—
291C22×C4×D4D1311yescharacteristic, complemented
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—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—416no—
371C2×C4×C13—416no—
372C2×C4×C13—44no—
373C2×C4×C13C22×D414yes—
374C2×C4×C13C22×D414yes—
375C2×C4×C13C22×D414yes—
376C2×C4×C13C2×#4114yes—
377C22⋊D13—416no—
378C22⋊D13—416no—
379C2×Dic13—28no—
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—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—416no—
401C2×Dic13—416no—
402C2×Dic13—44no—
403C2×Dic13—44no—
404C2×Dic13—44no—
405C2×Dic13—44no—
406C2×Dic13—44no—
407C2×Dic13—44no—
408C2×Dic13C2×#4114yes—
409C23×D4—131no—
410C23×D4—131no—
411C23×D4C2×D1311yescharacteristic
412C24×C4—131no—
413C24×C4—131no—
414C24×C4C2×D1311yescharacteristic
415C24×C4C2×D1311yescharacteristic
416C2×#123—138no—
417C2×#123—138no—
418C2×#123—268no—
419C2×#123—268no—
420C2×#121—138no—
421C2×#121—268no—
422C2×C4×D4—28no—
423C2×C4×D4C2×D1318yescomplemented
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⋊C4—131no—
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⋊C4—131no—
441C22×C22⋊C4C2×D1311yescharacteristic
442C22×C22⋊C4C2×D1311yescharacteristic
443C22×C42C2×D1311yescharacteristic
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—24no—
503C4×C13—24no—
504C4×C13—24no—
505C4×C13—42no—
506Dic13—24no—
507Dic13—42no—
508Dic13—42no—
509Dic13—42no—
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×D4D5218yes—
527C22×D4C22×D1314yes—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—24no—
532C23×C4—42no—
533C23×C4—42no—
534C23×C4—131no—
535C23×C4—134no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—131no—
540C23×C4—131no—
541C23×C4—131no—
542C23×C4—134no—
543C23×C4—264no—
544C23×C4—264no—
545C23×C4—264no—
546C23×C4—264no—
547C23×C4—264no—
548C23×C4—522no—
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#123—2632no—
558#121—2632no—
559C4×D4—232no—
560C2×C4⋊C4—24no—
561C2×C4⋊C4—134no—
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—264no—
574C2×C4⋊C4—522no—
575C2×C4⋊C4C22×D1314yes—
576C2×C22⋊C4—24no—
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—264no—
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—522no—
595C2×C22⋊C4C22⋊D1318yescomplemented
596C2×C22⋊C4C22×D1314yes—
597C2×C22⋊C4C22×D1314yes—
598C2×C42—24no—
599C2×C42C22×D1314yes—
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—
637C24C2×D5214yes—
638C24C2×D5214yes—
639C24#612714yes—
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×D52116yes—
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—28no—
668C22×C4—28no—
669C22×C4—28no—
670C22×C4—28no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—416no—
674C22×C4—416no—
675C22×C4—134no—
676C22×C4—132no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—268no—
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—268no—
693C22×C4—268no—
694C22×C4—268no—
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—5216no—
711C22×C4C2×D5214yes—
712C22×C4#612914yes—
713C22×C4C2×C22⋊D1314yes—
714C22×C4C2×C22⋊D1314yes—
715C22×C4C23×D1312yes—
716C22×C4C23×D1312yes—
717C22×C4C23×D1312yes—
718C22×C4C23×D1312yes—
719C22×C4C23×D1312yes—
720C4⋊C4—28no—
721C4⋊C4—268no—
722C4⋊C4—268no—
723C4⋊C4—268no—
724C4⋊C4—268no—
725C4⋊C4—268no—
726C4⋊C4—268no—
727C4⋊C4—524no—
728C22⋊C4—28no—
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—524no—
738C22⋊C4C2×C22⋊D13116yescomplemented
739C42—28no—
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#88184116yes—
779C23C22×D5214yes—
780C23C22×D5214yes—
781C23C22×D5212yes—
782C23C2×#612714yes—
783C23C2×#612712yes—
784C23C2×#612912yes—
785C23#8825112yes—
786C23#41×D1312yes—
787C23#8825712yes—
788C23C22×C22⋊D1314yes—
789C23C22×C22⋊D1312yes—
790C23C24×D1311yescharacteristic
791D4—232no—
792D4—5216no—
793D4—5216no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
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—416no—
811C2×C4—44no—
812C2×C4—134no—
813C2×C4—268no—
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—262no—
830C2×C4—262no—
831C2×C4—262no—
832C2×C4—262no—
833C2×C4—262no—
834C2×C4—5216no—
835C2×C4—5216no—
836C2×C4—524no—
837C2×C4—524no—
838C2×C4—524no—
839C2×C4—524no—
840C2×C4—524no—
841C2×C4—524no—
842C2×C4C22×D5214yes—
843C2×C4C2×#612914yes—
844C2×C4C22×C22⋊D1314yes—
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#1171924314yes—
870C22#1171925914yes—
871C22#1171926014yes—
872C22#1171926914yes—
873C22C2×#8818418yes—
874C22C2×#8818414yes—
875C22#1171951114yes—
876C22#1171952914yes—
877C22C23×D5211yescharacteristic
878C22C22×#612711yescharacteristic
879C22C22×#612911yescharacteristic
880C22C2×#8825111yescharacteristic
881C22C2×#41×D1311yescharacteristic
882C22C2×#8825711yescharacteristic
883C22C23×C22⋊D1311yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—42no—
889C4—264no—
890C4—522no—
891C4—522no—
892C4—522no—
893C4—522no—
894C4—522no—
895C4—522no—
896C2—28no—
897C2—44no—
898C2—1042no—
899C2#1311838118yesdirect product factor
900C2C22×#8818411yescharacteristic
901C2C2×#1171924311yescharacteristic
902C2C2×#1171926911yescharacteristic
903C2C2×#1171951111yescharacteristic
904C2C2×#1171925911yescharacteristic
905C2C2×#1171952911yescharacteristic
906C2C2×#1171926011yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C4×D4×C13C2
socleC24×C13C24
prime radicalC22×#88193C2
hypercenterC22×C4×D4D13
hypocenterC13C2×#2425
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#88140C2semidirect
2. C22×#88189C2semidirect
4. #13118381C2direct (N × H)
5. C2×#11718644C2semidirect
6. C2×#11718614C2semidirect
7. C2×#11718655C2semidirect
8. C2×#11718622C2semidirect
9. C2×#11718589C2semidirect
10. C2×#11718601C2semidirect
11. C2×#11718874C2semidirect
12. C2×#11718874C2semidirect
13. C2×#11718611C2semidirect
14. C2×#11718873C2semidirect
15. C22×#88071C2semidirect
16. C22×C4×D4×C13C2semidirect
25. C2×C4×D4×C13C22semidirect
37. C2×#88189C22semidirect
51. C2×#88140C22semidirect
52. #11718874C22semidirect
53. #11718874C22semidirect
54. #11718873C22semidirect
63. C2×#88071C22semidirect
64. #11718655C22semidirect
65. #11718644C22semidirect
66. #11718622C22semidirect
67. #11718614C22semidirect
68. #11718611C22semidirect
69. #11718601C22semidirect
70. #11718589C22semidirect
118. C2×C13×C22⋊C4D4semidirect
270. C13×C22⋊C4C2×D4semidirect
291. C22×C4×D4D13semidirect
423. C2×C4×D4C2×D13semidirect
595. C2×C22⋊C4C22⋊D13semidirect
610. C2×C13#2425semidirect
738. C22⋊C4C2×C22⋊D13semidirect
740. C13C2×#2425semidirect
899. C2#13118381direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881402
C22×#881892
C22×#881932
#131183812
C2×#117186442
C2×#117186142
C2×#117186552
C2×#117186222
C2×#117185892
C2×#117186012
C2×#117188742
C2×#117186112
C2×#117188732
C22×#880712
C22×C4×D4×C132
C2×#242513