Finite Group Databasebeta

← C2×#13117853 #16022449

Subgroups — C2×#13117853 #16022449

Order 3328.

4782 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88193C211yesmaximal, characteristic
2C22×C4×C22⋊D13C211yesmaximal, characteristic, complemented
3C22×#88135C211yesmaximal, characteristic, complemented
4C23×#6101C211yesmaximal, characteristic, complemented
5#13117853C2116yesmaximal, direct product factor
6C2×#11718618C211yesmaximal, characteristic, complemented
7C2×#11718633C211yesmaximal, characteristic, complemented
8C2×#11718601C211yesmaximal, characteristic, complemented
9C2×#11718605C211yesmaximal, characteristic, complemented
10C2×#11718881C211yesmaximal, characteristic, complemented
11C2×#11718874C211yesmaximal, characteristic, complemented
12C2×#11718871C211yesmaximal, characteristic, complemented
13C2×#11718650C211yesmaximal, characteristic, complemented
14C2×C4×#6101C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic13C211yesmaximal, 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
24C23×C4×D13C2211yescharacteristic
25C2×C4×D4×C13—28no—
26C2×C4×D4×C13C2218yescomplemented
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C42×C13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C22⋊Dic13C2211yescharacteristic
35C2×#88193C4116yescomplemented
36C2×#88193C2218yes—
37C2×C4×C22⋊D13—28no—
38C2×C4×C22⋊D13C2218yescomplemented
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×#6103C2211yescharacteristic
42C22×#6103C2211yescharacteristic
43C22×#6101—28no—
44C22×#6101C2211yescharacteristic
45C22×#6101C2211yescharacteristic
46C22×#6101C2211yescharacteristic
47C22×#6101C2211yescharacteristic
48C22×#6101C2211yescharacteristic
49C22×#6101C2211yescharacteristic
50C22×#6101C2218yescomplemented
51C22×C4×Dic13C2211yescharacteristic
52C22×C4×Dic13C2211yescharacteristic
53C22×C4×Dic13C2211yescharacteristic
54C2×#88135—28no—
55C2×#88135C2218yescomplemented
56#11718881C2218yescomplemented
57#11718874C2218yescomplemented
58#11718871C2218yescomplemented
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62C2×#88071C2211yescharacteristic
63C2×#88071C2211yescharacteristic
64C2×#88071C2211yescharacteristic
65#11718650C2218yescomplemented
66#11718633C2218yescomplemented
67#11718618C2218yescomplemented
68#11718605C2218yescomplemented
69C22⋊C4×Dic13C2218yescomplemented
70#11718601C2218yescomplemented
71C4×#6101C2218yescomplemented
72C25×C13C2311yescharacteristic
73C25×C13C2311yescharacteristic
74C24×D13C2311yescharacteristic
75C22×D4×C13—24no—
76C22×D4×C13—24no—
77C22×D4×C13C2×C418yescomplemented
78C22×D4×C13C2314yes—
79C23×C4×C13—24no—
80C23×C4×C13—24no—
81C23×C4×C13—24no—
82C23×C4×C13—24no—
83C23×C4×C13—42no—
84C23×C4×C13—42no—
85C23×C4×C13C2311yescharacteristic
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⋊D13C2×C418yescomplemented
97C22×C22⋊D13C2×C418yescomplemented
98C22×C22⋊D13C2314yes—
99C22×C22⋊D13C2314yes—
100C23×Dic13—24no—
101C23×Dic13—24no—
102C23×Dic13—24no—
103C23×Dic13—24no—
104C23×Dic13—42no—
105C23×Dic13C2×C418yescomplemented
106C23×Dic13C2311yescharacteristic
107C23×Dic13C2311yescharacteristic
108C23×Dic13C2311yescharacteristic
109C23×Dic13C2314yes—
110C23×Dic13C2311yescharacteristic
111C23×Dic13C2311yescharacteristic
112C23×Dic13C2314yes—
113C23×Dic13C2311yescharacteristic
114C23×Dic13C2311yescharacteristic
115C22×C4×D13—24no—
116C22×C4×D13—24no—
117C22×C4×D13—42no—
118C22×C4×D13C2314yes—
119C4×D4×C13—232no—
120C2×C13×C4⋊C4—24no—
121C2×C13×C4⋊C4C2314yes—
122C2×C13×C22⋊C4—24no—
123C2×C13×C22⋊C4D418yescomplemented
124C2×C13×C22⋊C4C2314yes—
125C2×C13×C22⋊C4C2314yes—
126C2×C42×C13—24no—
127C2×C42×C13C2314yes—
128C2×C22⋊Dic13—24no—
129C2×C22⋊Dic13—24no—
130C2×C22⋊Dic13—42no—
131C2×C22⋊Dic13C2×C418yescomplemented
132C2×C22⋊Dic13C2314yes—
133C2×C22⋊Dic13C2314yes—
134C2×C22⋊Dic13C2314yes—
135C2×C22⋊Dic13C2314yes—
136#88193C2×C4164yescomplemented
137C4×C22⋊D13—232no—
138C2×#6103—24no—
139C2×#6103—24no—
140C2×#6103—42no—
141C2×#6103C2×C418yescomplemented
142C2×#6103C2314yes—
143C2×#6103C2314yes—
144C2×#6103C2314yes—
145C2×#6103C2314yes—
146C2×#6101—24no—
147C2×#6101—24no—
148C2×#6101—24no—
149C2×#6101—24no—
150C2×#6101—232no—
151C2×#6101C2×C418yescomplemented
152C2×#6101D418yescomplemented
153C2×#6101C2314yes—
154C2×#6101C2314yes—
155C2×#6101C2314yes—
156C2×#6101C2314yes—
157C2×#6101C2314yes—
158C2×#6101C2314yes—
159C2×C4×Dic13—24no—
160C2×C4×Dic13—24no—
161C2×C4×Dic13—24no—
162C2×C4×Dic13C2314yes—
163C2×C4×Dic13C2314yes—
164C2×C4×Dic13C2314yes—
165#88135—232no—
166#88071C2314yes—
167#88071C2314yes—
168#88071C2314yes—
169#88071C2314yes—
170#88071C2314yes—
171#88071C2314yes—
172C2×#2361—131nomaximal, Sylow
173C24×C13—22no—
174C24×C13—22no—
175C24×C13—22no—
176C24×C13—22no—
177C24×C13—22no—
178C24×C13—22no—
179C24×C13—22no—
180C24×C13—22no—
181C24×C13—22no—
182C24×C13—22no—
183C24×C13C22×C414yes—
184C24×C13C22×C414yes—
185C24×C13C2×D414yes—
186C24×C13#4114yes—
187C24×C13C2412yes—
188C24×C13C2412yes—
189C24×C13C2411yescharacteristic
190C23×D13—22no—
191C23×D13—22no—
192C23×D13—22no—
193C23×D13—22no—
194C23×D13—22no—
195C23×D13—22no—
196C23×D13C22×C414yes—
197C23×D13C2412yes—
198C2×D4×C13—232no—
199C2×D4×C13—28no—
200C2×D4×C13—28no—
201C2×D4×C13C22×C4116yescomplemented
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—28no—
213C22×C4×C13—22no—
214C22×C4×C13—28no—
215C22×C4×C13—28no—
216C22×C4×C13—28no—
217C22×C4×C13—44no—
218C22×C4×C13—44no—
219C22×C4×C13—416no—
220C22×C4×C13—416no—
221C22×C4×C13C22×C414yes—
222C22×C4×C13C2×D414yes—
223C22×C4×C13C2×D414yes—
224C22×C4×C13C2×D414yes—
225C22×C4×C13C2412yes—
226C22×C4×C13C2412yes—
227C22×C4×C13C2412yes—
228C22×C4×C13C2412yes—
229C22×C4×C13C2412yes—
230C2×C22⋊D13—232no—
231C2×C22⋊D13—28no—
232C2×C22⋊D13—28no—
233C2×C22⋊D13—232no—
234C2×C22⋊D13—28no—
235C2×C22⋊D13—28no—
236C2×C22⋊D13C22×C4116yescomplemented
237C2×C22⋊D13C22×C4116yescomplemented
238C22×Dic13—22no—
239C22×Dic13—22no—
240C22×Dic13—22no—
241C22×Dic13—22no—
242C22×Dic13—22no—
243C22×Dic13—22no—
244C22×Dic13—232no—
245C22×Dic13—28no—
246C22×Dic13—28no—
247C22×Dic13—28no—
248C22×Dic13—22no—
249C22×Dic13—22no—
250C22×Dic13—22no—
251C22×Dic13—22no—
252C22×Dic13—22no—
253C22×Dic13—22no—
254C22×Dic13—22no—
255C22×Dic13—22no—
256C22×Dic13—22no—
257C22×Dic13—28no—
258C22×Dic13—44no—
259C22×Dic13—416no—
260C22×Dic13C22×C414yes—
261C22×Dic13C22×C414yes—
262C22×Dic13C22×C414yes—
263C22×Dic13C22×C4116yescomplemented
264C22×Dic13C2×D414yes—
265C22×Dic13C2×D414yes—
266C22×Dic13#4114yes—
267C22×Dic13C2412yes—
268C22×Dic13C2412yes—
269C22×Dic13C2412yes—
270C22×Dic13C2412yes—
271C22×Dic13C2412yes—
272C22×Dic13C2412yes—
273C22×Dic13C2412yes—
274C2×C4×D13—28no—
275C2×C4×D13—28no—
276C2×C4×D13—44no—
277C2×C4×D13—416no—
278C13×C4⋊C4—28no—
279C13×C22⋊C4—28no—
280C13×C22⋊C4C2×D4116yescomplemented
281C42×C13—28no—
282C22⋊Dic13—28no—
283C22⋊Dic13—28no—
284C22⋊Dic13—44no—
285C22⋊Dic13C22×C4116yescomplemented
286#6103—28no—
287#6103—28no—
288#6103—44no—
289#6103C22×C4116yescomplemented
290#6101—28no—
291#6101—28no—
292#6101—28no—
293#6101—28no—
294#6101C22×C4116yescomplemented
295#6101C2×D4116yescomplemented
296C4×Dic13—28no—
297C4×Dic13—28no—
298C4×Dic13—28no—
299C22×#121—131no—
300C22×C4×D4—131no—
301C22×C4×D4—131no—
302C22×C4×D4D1311yescharacteristic, complemented
303C23×C4⋊C4—131no—
304#2361—1316no—
305C2×#390—131no—
306C2×#389—131no—
307C2×#388—131no—
308C2×#388—131no—
309C2×#386—131no—
310C2×#386—131no—
311C2×#385—131no—
312C2×#385—131no—
313C2×C4×C4⋊C4—131no—
314C2×C4×C22⋊C4—131no—
315C23×C13—28no—
316C23×C13—28no—
317C23×C13—28no—
318C23×C13—28no—
319C23×C13—28no—
320C23×C13—28no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—28no—
326C23×C13—28no—
327C23×C13—28no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
334C23×C13—44no—
335C23×C13—44no—
336C23×C13—44no—
337C23×C13—44no—
338C23×C13C4×D4116yescomplemented
339C23×C13C23×C414yes—
340C23×C13C23×C414yes—
341C23×C13C23×C412yes—
342C23×C13C22×D414yes—
343C23×C13C22×D412yes—
344C23×C13C22×D412yes—
345C23×C13C2×#4114yes—
346C23×C13C2×#4112yes—
347C23×C13C2×#4112yes—
348C23×C13H(5,𝔽2)12yes—
349C23×C132−1+412yes—
350C23×C13C2511yescharacteristic
351C22×D13—28no—
352C22×D13—28no—
353C22×D13—28no—
354C22×D13—22no—
355C22×D13—22no—
356C22×D13—22no—
357C22×D13—22no—
358C22×D13—22no—
359C22×D13—22no—
360C22×D13—44no—
361C22×D13—44no—
362C22×D13—44no—
363C22×D13—44no—
364C22×D13C23×C414yes—
365D4×C13—232no—
366C2×C4×C13—28no—
367C2×C4×C13—28no—
368C2×C4×C13—28no—
369C2×C4×C13—28no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—416no—
382C2×C4×C13—416no—
383C2×C4×C13—44no—
384C2×C4×C13C23×C414yes—
385C2×C4×C13C22×D414yes—
386C2×C4×C13C22×D414yes—
387C2×C4×C13C22×D414yes—
388C22⋊D13—232no—
389C22⋊D13—232no—
390C2×Dic13—28no—
391C2×Dic13—28no—
392C2×Dic13—28no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—232no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—416no—
410C2×Dic13—44no—
411C2×Dic13—44no—
412C2×Dic13—44no—
413C2×Dic13C4×D4116yescomplemented
414C2×Dic13C23×C414yes—
415C2×Dic13C23×C414yes—
416C2×Dic13C23×C414yes—
417C2×Dic13C22×D414yes—
418C2×Dic13C22×D414yes—
419C2×Dic13C2×#4114yes—
420C4×D13—416no—
421C23×D4—131no—
422C23×D4—131no—
423C23×D4C2×D1311yescharacteristic
424C24×C4—131no—
425C24×C4—131no—
426C24×C4—131no—
427C24×C4C2×D1311yescharacteristic
428C24×C4C2×D1311yescharacteristic
429C2×#121—1316no—
430C2×#121—138no—
431C2×C4×D4—28no—
432C2×C4×D4—138no—
433C2×C4×D4—138no—
434C2×C4×D4—268no—
435C2×C4×D4—268no—
436C2×C4×D4C2×D1318yescomplemented
437C22×C4⋊C4—131no—
438C22×C4⋊C4—131no—
439C22×C4⋊C4—138no—
440C22×C4⋊C4—131no—
441C22×C4⋊C4—131no—
442C22×C4⋊C4—131no—
443C22×C4⋊C4—131no—
444C22×C4⋊C4—268no—
445C22×C4⋊C4C2×D1311yescharacteristic
446C22×C22⋊C4—131no—
447C22×C22⋊C4—131no—
448C22×C22⋊C4—131no—
449C22×C22⋊C4—131no—
450C22×C22⋊C4—131no—
451C22×C22⋊C4—131no—
452C22×C22⋊C4—131no—
453C22×C22⋊C4—131no—
454C22×C22⋊C4C2×D1311yescharacteristic
455C22×C22⋊C4C2×D1311yescharacteristic
456C22×C42—131no—
457C22×C42—131no—
458C22×C42—131no—
459C22×C42C2×D1311yescharacteristic
460#390—138no—
461#389—138no—
462#388—138no—
463#388—138no—
464#386—138no—
465#386—138no—
466#385—138no—
467#385—138no—
468C4×C4⋊C4—138no—
469C4×C22⋊C4—138no—
470C2×#95—131no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C22×C13—232no—
477C22×C13—24no—
478C22×C13—24no—
479C22×C13—24no—
480C22×C13—24no—
481C22×C13—24no—
482C22×C13—24no—
483C22×C13—24no—
484C22×C13—24no—
485C22×C13—24no—
486C22×C13—416no—
487C22×C13—42no—
488C22×C13—42no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13C2×C4×D414yes—
492C22×C13C2×C4×D414yes—
493C22×C13C2×C4×D418yescomplemented
494C22×C13#52014yes—
495C22×C13D4214yes—
496C22×C13#54714yes—
497C22×C13#54814yes—
498C22×C13#55314yes—
499C22×C13C24×C411yescharacteristic
500C22×C13C23×D411yescharacteristic
501C22×C13C23×D411yescharacteristic
502C22×C13C22×#4111yescharacteristic
503C22×C13C22×#4111yescharacteristic
504C22×C13C2×H(5,𝔽2)11yescharacteristic
505C22×C13C2×2−1+411yescharacteristic
506C2×D13—24no—
507C2×D13—24no—
508C2×D13—24no—
509C2×D13—416no—
510C2×D13—42no—
511C2×D13—42no—
512C2×D13—42no—
513C2×D13—42no—
514C4×C13—24no—
515C4×C13—24no—
516C4×C13—24no—
517C4×C13—24no—
518C4×C13—42no—
519Dic13—24no—
520Dic13—24no—
521Dic13—24no—
522Dic13—42no—
523Dic13—42no—
524Dic13—42no—
525Dic13C2×C4×D418yescomplemented
526C25—131no—
527C25C22×D1311yescharacteristic
528C25C22×D1311yescharacteristic
529C22×D4—24no—
530C22×D4—24no—
531C22×D4—138no—
532C22×D4—138no—
533C22×D4—134no—
534C22×D4—134no—
535C22×D4—264no—
536C22×D4—264no—
537C22×D4—264no—
538C22×D4—264no—
539C22×D4C4×D1318yescomplemented
540C22×D4C22×D1314yes—
541C23×C4—24no—
542C23×C4—24no—
543C23×C4—24no—
544C23×C4—24no—
545C23×C4—42no—
546C23×C4—42no—
547C23×C4—131no—
548C23×C4—138no—
549C23×C4—134no—
550C23×C4—131no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—131no—
556C23×C4—134no—
557C23×C4—134no—
558C23×C4—264no—
559C23×C4—264no—
560C23×C4—264no—
561C23×C4—264no—
562C23×C4—264no—
563C23×C4—264no—
564C23×C4—522no—
565C23×C4—522no—
566C23×C4C22×D1311yescharacteristic
567C23×C4C22×D1314yes—
568C23×C4C22×D1314yes—
569C23×C4C22×D1311yescharacteristic
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1311yescharacteristic
572C23×C4C22×D1311yescharacteristic
573#121—1364no—
574C4×D4—232no—
575C4×D4—2632no—
576C4×D4—2632no—
577C2×C4⋊C4—24no—
578C2×C4⋊C4—138no—
579C2×C4⋊C4—138no—
580C2×C4⋊C4—134no—
581C2×C4⋊C4—134no—
582C2×C4⋊C4—134no—
583C2×C4⋊C4—134no—
584C2×C4⋊C4—134no—
585C2×C4⋊C4—134no—
586C2×C4⋊C4—2632no—
587C2×C4⋊C4—264no—
588C2×C4⋊C4—264no—
589C2×C4⋊C4—264no—
590C2×C4⋊C4—264no—
591C2×C4⋊C4C22×D1314yes—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—138no—
594C2×C22⋊C4—134no—
595C2×C22⋊C4—138no—
596C2×C22⋊C4—134no—
597C2×C22⋊C4—134no—
598C2×C22⋊C4—134no—
599C2×C22⋊C4—134no—
600C2×C22⋊C4—134no—
601C2×C22⋊C4—134no—
602C2×C22⋊C4—134no—
603C2×C22⋊C4—264no—
604C2×C22⋊C4—264no—
605C2×C22⋊C4—264no—
606C2×C22⋊C4—264no—
607C2×C22⋊C4—522no—
608C2×C22⋊C4—522no—
609C2×C22⋊C4C22⋊D1318yescomplemented
610C2×C22⋊C4C22×D1314yes—
611C2×C22⋊C4C22×D1314yes—
612C2×C42—24no—
613C2×C42—134no—
614C2×C42—134no—
615C2×C42—134no—
616C2×C42—264no—
617C2×C42—264no—
618C2×C42—264no—
619C2×C42C22×D1314yes—
620#95—134no—
621#95—134no—
622#95—134no—
623#95—134no—
624#95—134no—
625#95—134no—
626C2×C13—28no—
627C2×C13—44no—
628C2×C13#236118yescomplemented
629C2×C13C22×C4×D411yescharacteristic
630C2×C13C22×C4×D411yescharacteristic
631C2×C13C2×#52011yescharacteristic
632C2×C13C2×D4211yescharacteristic
633C2×C13C2×#54711yescharacteristic
634C2×C13C2×#54811yescharacteristic
635C2×C13C2×#55311yescharacteristic
636D13—44no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—134no—
648C24—132no—
649C24—262no—
650C24—262no—
651C24—262no—
652C24—262no—
653C24—262no—
654C24—262no—
655C24C2×C4×D1314yes—
656C24C2×C4×D1314yes—
657C24#612714yes—
658C24C2×C22⋊D1314yes—
659C24C23×D1312yes—
660C24C23×D1312yes—
661C24C23×D1311yescharacteristic
662C2×D4—232no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—1316no—
666C2×D4—1316no—
667C2×D4—268no—
668C2×D4—2632no—
669C2×D4—268no—
670C2×D4—2632no—
671C2×D4—268no—
672C2×D4—268no—
673C2×D4C2×C4×D13116yescomplemented
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—28no—
686C22×C4—28no—
687C22×C4—28no—
688C22×C4—28no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—416no—
692C22×C4—416no—
693C22×C4—134no—
694C22×C4—134no—
695C22×C4—134no—
696C22×C4—132no—
697C22×C4—134no—
698C22×C4—134no—
699C22×C4—1316no—
700C22×C4—134no—
701C22×C4—132no—
702C22×C4—132no—
703C22×C4—132no—
704C22×C4—132no—
705C22×C4—132no—
706C22×C4—132no—
707C22×C4—268no—
708C22×C4—268no—
709C22×C4—2632no—
710C22×C4—268no—
711C22×C4—268no—
712C22×C4—262no—
713C22×C4—262no—
714C22×C4—262no—
715C22×C4—262no—
716C22×C4—262no—
717C22×C4—262no—
718C22×C4—262no—
719C22×C4—262no—
720C22×C4—262no—
721C22×C4—262no—
722C22×C4—262no—
723C22×C4—262no—
724C22×C4—262no—
725C22×C4—262no—
726C22×C4—262no—
727C22×C4—268no—
728C22×C4—268no—
729C22×C4—524no—
730C22×C4—5216no—
731C22×C4—524no—
732C22×C4—5216no—
733C22×C4C2×C4×D1314yes—
734C22×C4D4×D1314yes—
735C22×C4C2×C22⋊D1314yes—
736C22×C4C2×C22⋊D1314yes—
737C22×C4C23×D1312yes—
738C22×C4C23×D1312yes—
739C22×C4C23×D1312yes—
740C22×C4C23×D1312yes—
741C22×C4C23×D1312yes—
742C4⋊C4—28no—
743C4⋊C4—1316no—
744C4⋊C4—1316no—
745C4⋊C4—268no—
746C4⋊C4—268no—
747C4⋊C4—268no—
748C4⋊C4—268no—
749C22⋊C4—28no—
750C22⋊C4—1316no—
751C22⋊C4—1316no—
752C22⋊C4—268no—
753C22⋊C4—268no—
754C22⋊C4—268no—
755C22⋊C4—268no—
756C22⋊C4—524no—
757C22⋊C4—524no—
758C22⋊C4C2×C22⋊D13116yescomplemented
759C42—28no—
760C42—268no—
761C42—268no—
762C42—268no—
763C13C2×#236111yescharacteristic, complemented, Sylow
764C23—28no—
765C23—28no—
766C23—28no—
767C23—28no—
768C23—28no—
769C23—28no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—28no—
775C23—28no—
776C23—28no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—134no—
788C23—268no—
789C23—268no—
790C23—268no—
791C23—262no—
792C23—262no—
793C23—262no—
794C23—262no—
795C23—262no—
796C23—262no—
797C23—524no—
798C23—524no—
799C23—524no—
800C23—524no—
801C23C4×C22⋊D13116yescomplemented
802C23C22×C4×D1314yes—
803C23C22×C4×D1314yes—
804C23C22×C4×D1312yes—
805C23C2×#612714yes—
806C23C2×#612712yes—
807C23C2×D4×D1312yes—
808C23#8825112yes—
809C23#41×D1312yes—
810C23#8825712yes—
811C23C22×C22⋊D1314yes—
812C23C22×C22⋊D1312yes—
813C23C24×D1311yescharacteristic
814D4—232no—
815D4—2632no—
816D4—2632no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—28no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—416no—
833C2×C4—416no—
834C2×C4—44no—
835C2×C4—1316no—
836C2×C4—134no—
837C2×C4—134no—
838C2×C4—134no—
839C2×C4—134no—
840C2×C4—134no—
841C2×C4—134no—
842C2×C4—2632no—
843C2×C4—268no—
844C2×C4—268no—
845C2×C4—268no—
846C2×C4—262no—
847C2×C4—262no—
848C2×C4—262no—
849C2×C4—262no—
850C2×C4—262no—
851C2×C4—262no—
852C2×C4—262no—
853C2×C4—262no—
854C2×C4—262no—
855C2×C4—262no—
856C2×C4—262no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—5216no—
862C2×C4—5216no—
863C2×C4—524no—
864C2×C4—524no—
865C2×C4—524no—
866C2×C4C22×C4×D1314yes—
867C2×C4C2×D4×D1314yes—
868C2×C4C22×C22⋊D1314yes—
869C2×C4C22×C22⋊D1314yes—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—24no—
875C22—232no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—24no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—416no—
884C22—42no—
885C22—264no—
886C22—264no—
887C22—264no—
888C22—522no—
889C22—522no—
890C22—522no—
891C22—5216no—
892C22—522no—
893C22#1171924514yes—
894C22C4×D4×D1314yes—
895C22#1171925114yes—
896C22#1171925714yes—
897C22C2×C4×C22⋊D1314yes—
898C22C2×C4×C22⋊D1318yescomplemented
899C22D4×C22⋊D1314yes—
900C22#1171952914yes—
901C22C23×C4×D1311yescharacteristic
902C22C22×#612711yescharacteristic
903C22C22×D4×D1311yescharacteristic
904C22C2×#8825111yescharacteristic
905C22C2×#41×D1311yescharacteristic
906C22C2×#8825711yescharacteristic
907C22C23×C22⋊D1311yescharacteristic
908C4—24no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—42no—
913C4—138no—
914C4—264no—
915C4—264no—
916C4—264no—
917C4—522no—
918C4—522no—
919C4—522no—
920C2—28no—
921C2—44no—
922C2—524no—
923C2#1311785318yesdirect product factor
924C2C2×C4×D4×D1311yescharacteristic
925C2C22×C4×C22⋊D1311yescharacteristic
926C2C2×#1171925111yescharacteristic
927C2C2×D4×C22⋊D1311yescharacteristic
928C2C2×#1171952911yescharacteristic
929C2C2×#1171925711yescharacteristic
930C2C2×#1171924511yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC22×C4×D4×C13C2
socleC24×C13C24
prime radicalC22×#88193C2
cosocleC23×C13C25
hypercenterC22×C4×D4D13
hypocenterC13C2×#2361
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D13C2semidirect
3. C22×#88135C2semidirect
4. C23×#6101C2semidirect
5. #13117853C2direct (N × H)
6. C2×#11718618C2semidirect
7. C2×#11718633C2semidirect
8. C2×#11718601C2semidirect
9. C2×#11718605C2semidirect
10. C2×#11718881C2semidirect
11. C2×#11718874C2semidirect
12. C2×#11718871C2semidirect
13. C2×#11718650C2semidirect
14. C2×C4×#6101C2semidirect
15. C2×C22⋊C4×Dic13C2semidirect
16. C22×C4×D4×C13C2semidirect
26. C2×C4×D4×C13C22semidirect
35. C2×#88193C4semidirect
38. C2×C4×C22⋊D13C22semidirect
50. C22×#6101C22semidirect
55. C2×#88135C22semidirect
56. #11718881C22semidirect
57. #11718874C22semidirect
58. #11718871C22semidirect
65. #11718650C22semidirect
66. #11718633C22semidirect
67. #11718618C22semidirect
68. #11718605C22semidirect
69. C22⋊C4×Dic13C22semidirect
70. #11718601C22semidirect
71. C4×#6101C22semidirect
77. C22×D4×C13C2×C4semidirect
96. C22×C22⋊D13C2×C4semidirect
97. C22×C22⋊D13C2×C4semidirect
105. C23×Dic13C2×C4semidirect
123. C2×C13×C22⋊C4D4semidirect
131. C2×C22⋊Dic13C2×C4semidirect
136. #88193C2×C4semidirect
141. C2×#6103C2×C4semidirect
151. C2×#6101C2×C4semidirect
152. C2×#6101D4semidirect
201. C2×D4×C13C22×C4semidirect
236. C2×C22⋊D13C22×C4semidirect
237. C2×C22⋊D13C22×C4semidirect
263. C22×Dic13C22×C4semidirect
280. C13×C22⋊C4C2×D4semidirect
285. C22⋊Dic13C22×C4semidirect
289. #6103C22×C4semidirect
294. #6101C22×C4semidirect
295. #6101C2×D4semidirect
302. C22×C4×D4D13semidirect
338. C23×C13C4×D4semidirect
413. C2×Dic13C4×D4semidirect
436. C2×C4×D4C2×D13semidirect
493. C22×C13C2×C4×D4semidirect
525. Dic13C2×C4×D4semidirect
539. C22×D4C4×D13semidirect
609. C2×C22⋊C4C22⋊D13semidirect
628. C2×C13#2361semidirect
673. C2×D4C2×C4×D13semidirect
758. C22⋊C4C2×C22⋊D13semidirect
763. C13C2×#2361semidirect
801. C23C4×C22⋊D13semidirect
898. C22C2×C4×C22⋊D13semidirect
923. C2#13117853direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881932
C22×C4×C22⋊D132
C22×#881352
C23×#61012
#131178532
C2×#117186182
C2×#117186332
C2×#117186012
C2×#117186052
C2×#117188812
C2×#117188742
C2×#117188712
C2×#117186502
C2×C4×#61012
C2×C22⋊C4×Dic132
C22×C4×D4×C132
C2×#236113