Finite Group Databasebeta

← C2×#13117847 #16022443

Subgroups — C2×#13117847 #16022443

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×D4×Dic13C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D13C211yesmaximal, characteristic, complemented
4C22×#88135C211yesmaximal, characteristic, complemented
5C23×#6101C211yesmaximal, characteristic, complemented
6#13117847C2116yesmaximal, direct product factor
7C2×#11718618C211yesmaximal, characteristic, complemented
8C2×#11718308C211yesmaximal, characteristic, complemented
9C2×#11718606C211yesmaximal, characteristic, complemented
10C2×#11718330C211yesmaximal, characteristic, complemented
11C2×#11718619C211yesmaximal, characteristic, complemented
12C2×#11718329C211yesmaximal, characteristic, complemented
13C2×#11718607C211yesmaximal, characteristic, complemented
14C2×#11718310C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C2×C13×#386C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C24×Dic13C2211yescharacteristic
22C24×Dic13C2211yescharacteristic
23C24×Dic13C2211yescharacteristic
24C23×C4×D13C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C2×#88193C4116yescomplemented
32C2×#88193C2218yes—
33C2×D4×Dic13—28no—
34C2×D4×Dic13C2218yescomplemented
35C2×C4×C22⋊D13—28no—
36C2×C4×C22⋊D13C2218yescomplemented
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×C4⋊Dic13C2211yescharacteristic
42C22×#6101—28no—
43C22×#6101C2211yescharacteristic
44C22×#6101C2211yescharacteristic
45C22×#6101C2211yescharacteristic
46C22×#6101C2211yescharacteristic
47C22×#6101C2211yescharacteristic
48C22×#6101C2211yescharacteristic
49C22×#6101C2218yescomplemented
50C22×C4×Dic13C2211yescharacteristic
51C22×C4×Dic13C2211yescharacteristic
52C22×C4×Dic13C2211yescharacteristic
53C22×C4×Dic13C2211yescharacteristic
54C2×#88135—28no—
55C2×#88135C2218yescomplemented
56C13×#386C2218yescomplemented
57C2×C13×#95C2211yescharacteristic
58C2×C13×#95C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62C2×#88071C2211yescharacteristic
63#11718619C2218yescomplemented
64#11718618C2218yescomplemented
65#11718607C2218yescomplemented
66#11718606C2218yescomplemented
67C22⋊C4×Dic13C2218yescomplemented
68#11718330C2218yescomplemented
69#11718329C2218yescomplemented
70#11718310C2218yescomplemented
71#11718308C2218yescomplemented
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—42no—
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2314yes—
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C22×C22⋊D13—24no—
89C22×C22⋊D13—24no—
90C22×C22⋊D13—24no—
91C22×C22⋊D13—24no—
92C22×C22⋊D13C2×C418yescomplemented
93C22×C22⋊D13C2×C418yescomplemented
94C22×C22⋊D13C2314yes—
95C22×C22⋊D13C2314yes—
96C23×Dic13—24no—
97C23×Dic13—24no—
98C23×Dic13—24no—
99C23×Dic13—24no—
100C23×Dic13—24no—
101C23×Dic13—24no—
102C23×Dic13—42no—
103C23×Dic13—42no—
104C23×Dic13C2×C418yescomplemented
105C23×Dic13C2311yescharacteristic
106C23×Dic13C2314yes—
107C23×Dic13C2314yes—
108C23×Dic13C2311yescharacteristic
109C23×Dic13C2311yescharacteristic
110C23×Dic13C2314yes—
111C23×Dic13C2311yescharacteristic
112C23×Dic13C2311yescharacteristic
113C23×Dic13C2311yescharacteristic
114C23×Dic13C2311yescharacteristic
115C22×C4×D13—24no—
116C22×C4×D13—24no—
117C22×C4×D13—42no—
118C22×C4×D13C2314yes—
119C2×C13×C22⋊C4—24no—
120C2×C13×C22⋊C4—24no—
121C2×C13×C22⋊C4—42no—
122C2×C13×C22⋊C4C2314yes—
123C2×C13×C22⋊C4C2314yes—
124C2×C13×C22⋊C4C2314yes—
125C2×C22⋊Dic13—24no—
126C2×C22⋊Dic13C2×C418yescomplemented
127C2×C22⋊Dic13D418yescomplemented
128C2×C22⋊Dic13C2314yes—
129C2×C22⋊Dic13C2314yes—
130C2×C22⋊Dic13C2314yes—
131#88193C2×C4164yescomplemented
132D4×Dic13—232no—
133C4×C22⋊D13—232no—
134C2×#6103—24no—
135C2×#6103—24no—
136C2×#6103—42no—
137C2×#6103C2×C418yescomplemented
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141C2×#6103C2314yes—
142C2×C4⋊Dic13—24no—
143C2×C4⋊Dic13C2314yes—
144C2×#6101—24no—
145C2×#6101—24no—
146C2×#6101—24no—
147C2×#6101—24no—
148C2×#6101—232no—
149C2×#6101C2×C418yescomplemented
150C2×#6101D418yescomplemented
151C2×#6101C2314yes—
152C2×#6101C2314yes—
153C2×#6101C2314yes—
154C2×#6101C2314yes—
155C2×#6101C2314yes—
156C2×#6101C2314yes—
157C2×C4×Dic13—24no—
158C2×C4×Dic13—24no—
159C2×C4×Dic13—24no—
160C2×C4×Dic13—24no—
161C2×C4×Dic13C2314yes—
162C2×C4×Dic13C2314yes—
163C2×C4×Dic13C2314yes—
164C2×C4×Dic13C2314yes—
165#88135—232no—
166C13×#95C2314yes—
167C13×#95C2314yes—
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—28no—
210C22×C4×C13—22no—
211C22×C4×C13—22no—
212C22×C4×C13—22no—
213C22×C4×C13—22no—
214C22×C4×C13—22no—
215C22×C4×C13—22no—
216C22×C4×C13—28no—
217C22×C4×C13—44no—
218C22×C4×C13—416no—
219C22×C4×C13C22×C414yes—
220C22×C4×C13C2×D414yes—
221C22×C4×C13C2412yes—
222C22×C4×C13C2412yes—
223C22×C4×C13C2412yes—
224C22×C4×C13C2412yes—
225C22×C4×C13C2412yes—
226C2×C22⋊D13—232no—
227C2×C22⋊D13—28no—
228C2×C22⋊D13—28no—
229C2×C22⋊D13—232no—
230C2×C22⋊D13—28no—
231C2×C22⋊D13—28no—
232C2×C22⋊D13C22×C4116yescomplemented
233C2×C22⋊D13C22×C4116yescomplemented
234C22×Dic13—22no—
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—232no—
245C22×Dic13—28no—
246C22×Dic13—28no—
247C22×Dic13—22no—
248C22×Dic13—22no—
249C22×Dic13—28no—
250C22×Dic13—22no—
251C22×Dic13—28no—
252C22×Dic13—28no—
253C22×Dic13—28no—
254C22×Dic13—44no—
255C22×Dic13—44no—
256C22×Dic13—416no—
257C22×Dic13—416no—
258C22×Dic13C22×C414yes—
259C22×Dic13C22×C414yes—
260C22×Dic13C22×C414yes—
261C22×Dic13C22×C4116yescomplemented
262C22×Dic13C2×D414yes—
263C22×Dic13C2×D414yes—
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×C22⋊C4—28no—
279C13×C22⋊C4—28no—
280C13×C22⋊C4—44no—
281C22⋊Dic13—28no—
282C22⋊Dic13C22×C4116yescomplemented
283C22⋊Dic13C2×D4116yescomplemented
284#6103—28no—
285#6103—28no—
286#6103—44no—
287#6103C22×C4116yescomplemented
288C4⋊Dic13—28no—
289#6101—28no—
290#6101—28no—
291#6101—28no—
292#6101—28no—
293#6101C22×C4116yescomplemented
294#6101C2×D4116yescomplemented
295C4×Dic13—28no—
296C4×Dic13—28no—
297C4×Dic13—28no—
298C4×Dic13—28no—
299C22×#121—131no—
300C22×C4×D4—131no—
301C22×C4×D4—131no—
302C22×C4×D4—131no—
303C23×C4⋊C4—131no—
304#2361—1316no—
305C2×#390—131no—
306C2×#389—131no—
307C2×#388—131no—
308C2×#388—131no—
309C2×#386—131no—
310C2×#386D1311yescharacteristic, complemented
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—22no—
369C2×C4×C13—22no—
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—44no—
383C2×C4×C13—44no—
384C2×C4×C13—44no—
385C2×C4×C13C23×C414yes—
386C2×C4×C13C22×D414yes—
387C22⋊D13—232no—
388C22⋊D13—232no—
389C2×Dic13—28no—
390C2×Dic13—28no—
391C2×Dic13—28no—
392C2×Dic13—28no—
393C2×Dic13—28no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—232no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—416no—
409C2×Dic13—416no—
410C2×Dic13—44no—
411C2×Dic13C4×D4116yescomplemented
412C2×Dic13C23×C414yes—
413C2×Dic13C23×C414yes—
414C2×Dic13C23×C414yes—
415C2×Dic13C22×D414yes—
416C2×Dic13C22×D414yes—
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×C4—131no—
428C24×C4C2×D1311yescharacteristic
429C2×#121—1316no—
430C2×#121—138no—
431C2×C4×D4—138no—
432C2×C4×D4—138no—
433C2×C4×D4—138no—
434C2×C4×D4—268no—
435C2×C4×D4—268no—
436C2×C4×D4—268no—
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—131no—
445C22×C4⋊C4—268no—
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⋊C4C2×D1311yescharacteristic
454C22×C22⋊C4C2×D1311yescharacteristic
455C22×C22⋊C4C2×D1311yescharacteristic
456C22×C42—131no—
457C22×C42—131no—
458C22×C42—131no—
459C22×C42—131no—
460#390—138no—
461#389—138no—
462#388—138no—
463#388—138no—
464#386—138no—
465#386C2×D1318yescomplemented
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×#95C2×D1311yescharacteristic
475C2×#95C2×D1311yescharacteristic
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—42no—
517C4×C13—42no—
518C4×C13—42no—
519Dic13—24no—
520Dic13—24no—
521Dic13—24no—
522Dic13—24no—
523Dic13—24no—
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—42no—
544C23×C4—131no—
545C23×C4—138no—
546C23×C4—134no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4—131no—
550C23×C4—131no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—134no—
554C23×C4—134no—
555C23×C4—134no—
556C23×C4—264no—
557C23×C4—264no—
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×C4—522no—
567C23×C4C22×D1311yescharacteristic
568C23×C4C22×D1311yescharacteristic
569C23×C4C22×D1311yescharacteristic
570C23×C4C22×D1314yes—
571C23×C4C22×D1311yescharacteristic
572C23×C4C22×D1311yescharacteristic
573#121—1364no—
574C4×D4—2632no—
575C4×D4—2632no—
576C4×D4—2632no—
577C2×C4⋊C4—138no—
578C2×C4⋊C4—138no—
579C2×C4⋊C4—134no—
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⋊C4—264no—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—138no—
596C2×C22⋊C4—138no—
597C2×C22⋊C4—134no—
598C2×C22⋊C4—134no—
599C2×C22⋊C4—138no—
600C2×C22⋊C4—134no—
601C2×C22⋊C4—134no—
602C2×C22⋊C4—134no—
603C2×C22⋊C4—134no—
604C2×C22⋊C4—134no—
605C2×C22⋊C4—264no—
606C2×C22⋊C4—264no—
607C2×C22⋊C4—264no—
608C2×C22⋊C4—522no—
609C2×C22⋊C4C22×D1314yes—
610C2×C22⋊C4C22×D1314yes—
611C2×C22⋊C4C22×D1314yes—
612C2×C42—134no—
613C2×C42—134no—
614C2×C42—134no—
615C2×C42—134no—
616C2×C42—264no—
617C2×C42—264no—
618C2×C42—264no—
619C2×C42—264no—
620#95—134no—
621#95—134no—
622#95—134no—
623#95—134no—
624#95C22×D1314yes—
625#95C22×D1314yes—
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—
657C24D4×D1314yes—
658C24#612914yes—
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—28no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—28no—
689C22×C4—44no—
690C22×C4—416no—
691C22×C4—134no—
692C22×C4—134no—
693C22×C4—134no—
694C22×C4—132no—
695C22×C4—134no—
696C22×C4—134no—
697C22×C4—1316no—
698C22×C4—134no—
699C22×C4—134no—
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—268no—
713C22×C4—268no—
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—268no—
727C22×C4—262no—
728C22×C4—268no—
729C22×C4—524no—
730C22×C4—5216no—
731C22×C4—524no—
732C22×C4—524no—
733C22×C4—5216no—
734C22×C4—5216no—
735C22×C4C2×C4×D1314yes—
736C22×C4D4×D1314yes—
737C22×C4C23×D1312yes—
738C22×C4C23×D1312yes—
739C22×C4C23×D1312yes—
740C22×C4C23×D1312yes—
741C22×C4C23×D1312yes—
742C4⋊C4—1316no—
743C4⋊C4—1316no—
744C4⋊C4—268no—
745C4⋊C4—268no—
746C4⋊C4—268no—
747C4⋊C4—268no—
748C4⋊C4—268no—
749C22⋊C4—28no—
750C22⋊C4—28no—
751C22⋊C4—44no—
752C22⋊C4—1316no—
753C22⋊C4—1316no—
754C22⋊C4—1316no—
755C22⋊C4—268no—
756C22⋊C4—268no—
757C22⋊C4—268no—
758C22⋊C4—524no—
759C42—268no—
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—
801C23#88135116yescomplemented
802C23C22×C4×D1314yes—
803C23C22×C4×D1314yes—
804C23C22×C4×D1312yes—
805C23C2×D4×D1314yes—
806C23C2×D4×D1312yes—
807C23C2×D4×D1312yes—
808C23C2×#612914yes—
809C23C2×#612912yes—
810C23#8825112yes—
811C23#41×D1312yes—
812C23#8825712yes—
813C23C24×D1311yescharacteristic
814D4—232no—
815D4—2632no—
816D4—2632no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—22no—
820C2×C4—22no—
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—44no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—1316no—
837C2×C4—134no—
838C2×C4—134no—
839C2×C4—134no—
840C2×C4—134no—
841C2×C4—134no—
842C2×C4—134no—
843C2×C4—134no—
844C2×C4—134no—
845C2×C4—2632no—
846C2×C4—268no—
847C2×C4—268no—
848C2×C4—268no—
849C2×C4—268no—
850C2×C4—268no—
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—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—5216no—
865C2×C4—5216no—
866C2×C4—5216no—
867C2×C4—524no—
868C2×C4C22×C4×D1314yes—
869C2×C4C2×D4×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—
893C22C2×#8813514yes—
894C22C2×#8813518yescomplemented
895C22C4×D4×D1314yes—
896C22#1171925114yes—
897C22#1171929514yes—
898C22#1171930314yes—
899C22#1171930614yes—
900C22#1171936014yes—
901C22C23×C4×D1311yescharacteristic
902C22C22×D4×D1311yescharacteristic
903C22C22×D4×D1311yescharacteristic
904C22C22×#612911yescharacteristic
905C22C2×#8825111yescharacteristic
906C22C2×#41×D1311yescharacteristic
907C22C2×#8825711yescharacteristic
908C4—24no—
909C4—24no—
910C4—42no—
911C4—42no—
912C4—42no—
913C4—138no—
914C4—264no—
915C4—264no—
916C4—264no—
917C4—264no—
918C4—264no—
919C4—522no—
920C2—28no—
921C2—44no—
922C2—524no—
923C2#1311784718yesdirect product factor
924C2C2×C4×D4×D1311yescharacteristic
925C2C22×#8813511yescharacteristic
926C2C2×#1171925111yescharacteristic
927C2C2×#1171929511yescharacteristic
928C2C2×#1171936011yescharacteristic
929C2C2×#1171930311yescharacteristic
930C2C2×#1171930611yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#386C2
socleC24×C13C24
prime radicalC22×#88193C2
cosocleC23×C13C25
hypercenterC2×#386D13
hypocenterC13C2×#2361
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×D4×Dic13C2semidirect
3. C22×C4×C22⋊D13C2semidirect
4. C22×#88135C2semidirect
5. C23×#6101C2semidirect
6. #13117847C2direct (N × H)
7. C2×#11718618C2semidirect
8. C2×#11718308C2semidirect
9. C2×#11718606C2semidirect
10. C2×#11718330C2semidirect
11. C2×#11718619C2semidirect
12. C2×#11718329C2semidirect
13. C2×#11718607C2semidirect
14. C2×#11718310C2semidirect
15. C2×C22⋊C4×Dic13C2semidirect
16. C2×C13×#386C2semidirect
31. C2×#88193C4semidirect
34. C2×D4×Dic13C22semidirect
36. C2×C4×C22⋊D13C22semidirect
49. C22×#6101C22semidirect
55. C2×#88135C22semidirect
56. C13×#386C22semidirect
63. #11718619C22semidirect
64. #11718618C22semidirect
65. #11718607C22semidirect
66. #11718606C22semidirect
67. C22⋊C4×Dic13C22semidirect
68. #11718330C22semidirect
69. #11718329C22semidirect
70. #11718310C22semidirect
71. #11718308C22semidirect
77. C22×D4×C13C2×C4semidirect
92. C22×C22⋊D13C2×C4semidirect
93. C22×C22⋊D13C2×C4semidirect
104. C23×Dic13C2×C4semidirect
126. C2×C22⋊Dic13C2×C4semidirect
127. C2×C22⋊Dic13D4semidirect
131. #88193C2×C4semidirect
137. C2×#6103C2×C4semidirect
149. C2×#6101C2×C4semidirect
150. C2×#6101D4semidirect
201. C2×D4×C13C22×C4semidirect
232. C2×C22⋊D13C22×C4semidirect
233. C2×C22⋊D13C22×C4semidirect
261. C22×Dic13C22×C4semidirect
282. C22⋊Dic13C22×C4semidirect
283. C22⋊Dic13C2×D4semidirect
287. #6103C22×C4semidirect
293. #6101C22×C4semidirect
294. #6101C2×D4semidirect
310. C2×#386D13semidirect
338. C23×C13C4×D4semidirect
411. C2×Dic13C4×D4semidirect
465. #386C2×D13semidirect
493. C22×C13C2×C4×D4semidirect
525. Dic13C2×C4×D4semidirect
539. C22×D4C4×D13semidirect
628. C2×C13#2361semidirect
673. C2×D4C2×C4×D13semidirect
763. C13C2×#2361semidirect
801. C23#88135semidirect
894. C22C2×#88135semidirect
923. C2#13117847direct (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×D4×Dic132
C22×C4×C22⋊D132
C22×#881352
C23×#61012
#131178472
C2×#117186182
C2×#117183082
C2×#117186062
C2×#117183302
C2×#117186192
C2×#117183292
C2×#117186072
C2×#117183102
C2×C22⋊C4×Dic132
C2×C13×#3862
C2×#236113