Finite Group Databasebeta

← C2×#13117849 #16022445

Subgroups — C2×#13117849 #16022445

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×#88138C211yesmaximal, characteristic
2C22×C4×D52C211yesmaximal, characteristic, complemented
3C22×#88135C211yesmaximal, characteristic, complemented
4C22×#88135C211yesmaximal, characteristic, complemented
5C22×C4⋊C4×D13C211yesmaximal, characteristic, complemented
6#13117849C2116yesmaximal, direct product factor
7C2×#11718618C211yesmaximal, characteristic, complemented
8C2×#11718308C211yesmaximal, characteristic, complemented
9C2×#11718331C211yesmaximal, characteristic, complemented
10C2×#11718326C211yesmaximal, characteristic, complemented
11C2×#11718617C211yesmaximal, characteristic, complemented
12C2×#11718611C211yesmaximal, characteristic, complemented
13C2×#11718650C211yesmaximal, characteristic, complemented
14C2×C4×#6101C211yesmaximal, characteristic, complemented
15C2×#11718327C211yesmaximal, characteristic, complemented
16C2×C13×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C23×D52C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C23×C4×D13C2211yescharacteristic
24C23×C4×D13C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C42×C13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C2×C4⋊C4×D13—28no—
47C2×C4⋊C4×D13C2218yescomplemented
48C2×#88138C4116yescomplemented
49C2×#88138C2218yes—
50C2×#88135—28no—
51C2×#88135—28no—
52C2×#88135C2218yescomplemented
53C2×#88135C2218yescomplemented
54C2×C4×D52—28no—
55C2×C4×D52C2218yescomplemented
56C13×#388C2218yescomplemented
57C2×C13×#95C2211yescharacteristic
58C2×C13×#95C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62C2×#88071C2211yescharacteristic
63#11718650C2218yescomplemented
64#11718618C2218yescomplemented
65#11718617C2218yescomplemented
66#11718611C2218yescomplemented
67C4×#6101C2218yescomplemented
68#11718331C2218yescomplemented
69#11718327C2218yescomplemented
70#11718326C2218yescomplemented
71#11718308C2218yescomplemented
72C25×C13C2311yescharacteristic
73C24×D13C2311yescharacteristic
74C24×D13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C22×C22⋊D13—24no—
82C22×C22⋊D13—24no—
83C22×C22⋊D13—24no—
84C22×C22⋊D13—24no—
85C22×C22⋊D13C2×C418yescomplemented
86C22×C22⋊D13C2×C418yescomplemented
87C22×C22⋊D13C2314yes—
88C22×C22⋊D13C2314yes—
89C23×Dic13—24no—
90C23×Dic13—24no—
91C23×Dic13—42no—
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2314yes—
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C22×D52—24no—
100C22×D52—24no—
101C22×D52C2×C418yescomplemented
102C22×D52C2314yes—
103C22×C4×D13—24no—
104C22×C4×D13—24no—
105C22×C4×D13—24no—
106C22×C4×D13—24no—
107C22×C4×D13—24no—
108C22×C4×D13—24no—
109C22×C4×D13—24no—
110C22×C4×D13—24no—
111C22×C4×D13—42no—
112C22×C4×D13—42no—
113C22×C4×D13—42no—
114C22×C4×D13C2×C418yescomplemented
115C22×C4×D13C2314yes—
116C22×C4×D13C2314yes—
117C22×C4×D13C2314yes—
118C22×C4×D13C2314yes—
119C2×C13×C4⋊C4—24no—
120C2×C13×C4⋊C4C2314yes—
121C2×C13×C22⋊C4—24no—
122C2×C13×C22⋊C4—24no—
123C2×C13×C22⋊C4C2×C418yescomplemented
124C2×C13×C22⋊C4C2314yes—
125C2×C13×C22⋊C4C2314yes—
126C2×C13×C22⋊C4C2314yes—
127C2×C42×C13—24no—
128C2×C42×C13C2314yes—
129C2×C22⋊Dic13—42no—
130C2×C22⋊Dic13C2314yes—
131C2×#6103—24no—
132C2×#6103—24no—
133C2×#6103—24no—
134C2×#6103—42no—
135C2×#6103C2×C418yescomplemented
136C2×#6103D418yescomplemented
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141C2×#6103C2314yes—
142C2×#6103C2314yes—
143C2×C4⋊Dic13—24no—
144C2×C4⋊Dic13—24no—
145C2×C4⋊Dic13C2314yes—
146C2×C4⋊Dic13C2314yes—
147C2×#6101—24no—
148C2×#6101—24no—
149C2×#6101C2×C418yescomplemented
150C2×#6101D418yescomplemented
151C2×#6101C2314yes—
152C2×#6101C2314yes—
153C2×#6101C2314yes—
154C2×#6101C2314yes—
155C2×C4×Dic13—24no—
156C2×C4×Dic13—24no—
157C2×C4×Dic13—24no—
158C2×C4×Dic13C2314yes—
159C2×C4×Dic13C2314yes—
160C2×C4×Dic13C2314yes—
161C4⋊C4×D13—232no—
162#88138C2×C4164yescomplemented
163#88135—232no—
164#88135—232no—
165C4×D52—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×C13C22×C414yes—
180C24×C13C2412yes—
181C24×C13C2411yescharacteristic
182C23×D13—22no—
183C23×D13—22no—
184C23×D13—22no—
185C23×D13—22no—
186C23×D13—22no—
187C23×D13—22no—
188C23×D13—22no—
189C23×D13—22no—
190C23×D13—22no—
191C23×D13—22no—
192C23×D13C22×C414yes—
193C23×D13C22×C414yes—
194C23×D13C2×D414yes—
195C23×D13#4114yes—
196C23×D13C2412yes—
197C23×D13C2412yes—
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—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×C13C22×C414yes—
213C22×C4×C13C22×C414yes—
214C22×C4×C13C2×D414yes—
215C22×C4×C13C2×D414yes—
216C22×C4×C13C2412yes—
217C22×C4×C13C2412yes—
218C22×C4×C13C2412yes—
219C22×C4×C13C2412yes—
220C22×C4×C13C2412yes—
221C22×C4×C13C2412yes—
222C2×C22⋊D13—232no—
223C2×C22⋊D13—28no—
224C2×C22⋊D13—28no—
225C2×C22⋊D13—232no—
226C2×C22⋊D13—28no—
227C2×C22⋊D13—28no—
228C2×C22⋊D13C22×C4116yescomplemented
229C2×C22⋊D13C22×C4116yescomplemented
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—22no—
241C22×Dic13—22no—
242C22×Dic13—28no—
243C22×Dic13—28no—
244C22×Dic13—44no—
245C22×Dic13—416no—
246C22×Dic13C22×C414yes—
247C22×Dic13C22×C414yes—
248C22×Dic13C2×D414yes—
249C22×Dic13C2×D414yes—
250C22×Dic13C2×D414yes—
251C22×Dic13#4114yes—
252C22×Dic13C2412yes—
253C22×Dic13C2412yes—
254C22×Dic13C2412yes—
255C22×Dic13C2412yes—
256C22×Dic13C2412yes—
257C22×Dic13C2412yes—
258C2×D52—232no—
259C2×D52—28no—
260C2×D52—28no—
261C2×D52C22×C4116yescomplemented
262C2×C4×D13—232no—
263C2×C4×D13—28no—
264C2×C4×D13—28no—
265C2×C4×D13—28no—
266C2×C4×D13—28no—
267C2×C4×D13—28no—
268C2×C4×D13—28no—
269C2×C4×D13—28no—
270C2×C4×D13—28no—
271C2×C4×D13—44no—
272C2×C4×D13—44no—
273C2×C4×D13—44no—
274C2×C4×D13—416no—
275C2×C4×D13—416no—
276C2×C4×D13—416no—
277C2×C4×D13C22×C4116yescomplemented
278C13×C4⋊C4—28no—
279C13×C22⋊C4—28no—
280C13×C22⋊C4—28no—
281C13×C22⋊C4C22×C4116yescomplemented
282C42×C13—28no—
283C22⋊Dic13—44no—
284#6103—28no—
285#6103—28no—
286#6103—28no—
287#6103—44no—
288#6103C22×C4116yescomplemented
289#6103C2×D4116yescomplemented
290C4⋊Dic13—28no—
291C4⋊Dic13—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×D4—131no—
303C23×C4⋊C4—131no—
304#2361—1316no—
305C2×#390—131no—
306C2×#389—131no—
307C2×#388—131no—
308C2×#388D1311yescharacteristic, complemented
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—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—44no—
325C23×C13—44no—
326C23×C13—44no—
327C23×C13—44no—
328C23×C13C23×C414yes—
329C23×C13C23×C412yes—
330C23×C13C22×D412yes—
331C23×C13C22×D412yes—
332C23×C13C2×#4112yes—
333C23×C13C2×#4112yes—
334C23×C13H(5,𝔽2)12yes—
335C23×C132−1+412yes—
336C23×C13C2511yescharacteristic
337C22×D13—28no—
338C22×D13—28no—
339C22×D13—28no—
340C22×D13—28no—
341C22×D13—28no—
342C22×D13—28no—
343C22×D13—22no—
344C22×D13—22no—
345C22×D13—22no—
346C22×D13—22no—
347C22×D13—28no—
348C22×D13—28no—
349C22×D13—28no—
350C22×D13—22no—
351C22×D13—22no—
352C22×D13—22no—
353C22×D13—22no—
354C22×D13—22no—
355C22×D13—22no—
356C22×D13—44no—
357C22×D13—44no—
358C22×D13—44no—
359C22×D13—44no—
360C22×D13C4×D4116yescomplemented
361C22×D13C23×C414yes—
362C22×D13C23×C414yes—
363C22×D13C22×D414yes—
364C22×D13C2×#4114yes—
365C2×C4×C13—28no—
366C2×C4×C13—28no—
367C2×C4×C13—28no—
368C2×C4×C13—28no—
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—22no—
382C2×C4×C13—22no—
383C2×C4×C13—44no—
384C2×C4×C13—44no—
385C2×C4×C13C23×C414yes—
386C2×C4×C13C23×C414yes—
387C2×C4×C13C22×D414yes—
388C2×C4×C13C22×D414yes—
389C22⋊D13—232no—
390C22⋊D13—232no—
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—22no—
405C2×Dic13—22no—
406C2×Dic13—416no—
407C2×Dic13—44no—
408C2×Dic13—44no—
409C2×Dic13C4×D4116yescomplemented
410C2×Dic13C23×C414yes—
411C2×Dic13C23×C414yes—
412C2×Dic13C22×D414yes—
413C2×Dic13C22×D414yes—
414C2×Dic13C22×D414yes—
415C2×Dic13C2×#4114yes—
416D52—232no—
417C4×D13—232no—
418C4×D13—416no—
419C4×D13—416no—
420C4×D13—416no—
421C23×D4—131no—
422C23×D4—131no—
423C23×D4—131no—
424C24×C4—131no—
425C24×C4—131no—
426C24×C4—131no—
427C24×C4—131no—
428C24×C4—131no—
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—131no—
440C22×C4⋊C4—131no—
441C22×C4⋊C4—131no—
442C22×C4⋊C4—131no—
443C22×C4⋊C4—138no—
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⋊C4C2×D1311yescharacteristic
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#388C2×D1318yescomplemented
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×#95C2×D1311yescharacteristic
475C2×#95C2×D1311yescharacteristic
476C22×C13—24no—
477C22×C13—24no—
478C22×C13—24no—
479C22×C13—416no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—42no—
483C22×C13—42no—
484C22×C13C2×C4×D414yes—
485C22×C13C2×C4×D414yes—
486C22×C13#52014yes—
487C22×C13D4214yes—
488C22×C13#54714yes—
489C22×C13#54814yes—
490C22×C13#55314yes—
491C22×C13C24×C411yescharacteristic
492C22×C13C23×D411yescharacteristic
493C22×C13C23×D411yescharacteristic
494C22×C13C22×#4111yescharacteristic
495C22×C13C22×#4111yescharacteristic
496C22×C13C2×H(5,𝔽2)11yescharacteristic
497C22×C13C2×2−1+411yescharacteristic
498C2×D13—232no—
499C2×D13—24no—
500C2×D13—24no—
501C2×D13—24no—
502C2×D13—24no—
503C2×D13—24no—
504C2×D13—24no—
505C2×D13—24no—
506C2×D13—24no—
507C2×D13—24no—
508C2×D13—416no—
509C2×D13—42no—
510C2×D13—42no—
511C2×D13—42no—
512C2×D13—42no—
513C2×D13C2×C4×D418yescomplemented
514C4×C13—24no—
515C4×C13—24no—
516C4×C13—24no—
517C4×C13—24no—
518C4×C13—42no—
519C4×C13—42no—
520Dic13—24no—
521Dic13—24no—
522Dic13—24no—
523Dic13—42no—
524Dic13—42no—
525Dic13C2×C4×D418yescomplemented
526C25—131no—
527C25—131no—
528C25C22×D1311yescharacteristic
529C22×D4—138no—
530C22×D4—138no—
531C22×D4—134no—
532C22×D4—134no—
533C22×D4—138no—
534C22×D4—134no—
535C22×D4—264no—
536C22×D4—264no—
537C22×D4—264no—
538C22×D4—264no—
539C22×D4—264no—
540C22×D4—264no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4—138no—
546C23×C4—134no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4—134no—
550C23×C4—134no—
551C23×C4—134no—
552C23×C4—134no—
553C23×C4—264no—
554C23×C4—264no—
555C23×C4—264no—
556C23×C4—264no—
557C23×C4—264no—
558C23×C4—264no—
559C23×C4—264no—
560C23×C4—264no—
561C23×C4—264no—
562C23×C4—264no—
563C23×C4—522no—
564C23×C4—522no—
565C23×C4—522no—
566C23×C4—522no—
567C23×C4C22×D1311yescharacteristic
568C23×C4C22×D1311yescharacteristic
569C23×C4C22×D1311yescharacteristic
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1311yescharacteristic
572C23×C4C22×D1311yescharacteristic
573#121—1364no—
574C4×D4—2632no—
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—24no—
594C2×C22⋊C4—138no—
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—522no—
607C2×C22⋊C4—522no—
608C2×C22⋊C4C4×D1318yescomplemented
609C2×C22⋊C4C22×D1314yes—
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#95C22×D1314yes—
625#95C22×D1314yes—
626C2×C13—44no—
627C2×C13#236118yescomplemented
628C2×C13C22×C4×D411yescharacteristic
629C2×C13C22×C4×D411yescharacteristic
630C2×C13C2×#52011yescharacteristic
631C2×C13C2×D4211yescharacteristic
632C2×C13C2×#54711yescharacteristic
633C2×C13C2×#54811yescharacteristic
634C2×C13C2×#55311yescharacteristic
635D13—28no—
636D13—44no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—134no—
644C24—134no—
645C24—134no—
646C24—132no—
647C24—134no—
648C24—132no—
649C24—262no—
650C24—262no—
651C24—262no—
652C24—262no—
653C24—262no—
654C24—262no—
655C24—262no—
656C24—262no—
657C24—262no—
658C24—262no—
659C24C2×C4×D1314yes—
660C24C23×D1312yes—
661C24C23×D1311yescharacteristic
662C2×D4—1316no—
663C2×D4—1316no—
664C2×D4—1316no—
665C2×D4—268no—
666C2×D4—2632no—
667C2×D4—268no—
668C2×D4—268no—
669C2×D4—2632no—
670C2×D4—268no—
671C2×D4—268no—
672C2×D4—2632no—
673C2×D4—268no—
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—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—134no—
689C22×C4—134no—
690C22×C4—134no—
691C22×C4—132no—
692C22×C4—134no—
693C22×C4—134no—
694C22×C4—134no—
695C22×C4—132no—
696C22×C4—132no—
697C22×C4—132no—
698C22×C4—1316no—
699C22×C4—132no—
700C22×C4—132no—
701C22×C4—268no—
702C22×C4—2632no—
703C22×C4—268no—
704C22×C4—268no—
705C22×C4—268no—
706C22×C4—268no—
707C22×C4—268no—
708C22×C4—268no—
709C22×C4—268no—
710C22×C4—262no—
711C22×C4—262no—
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—268no—
723C22×C4—268no—
724C22×C4—524no—
725C22×C4—524no—
726C22×C4—524no—
727C22×C4—5216no—
728C22×C4—5216no—
729C22×C4—5216no—
730C22×C4—524no—
731C22×C4—5216no—
732C22×C4C2×C4×D1314yes—
733C22×C4C2×C4×D1314yes—
734C22×C4D4×D1314yes—
735C22×C4D4×D1314yes—
736C22×C4C23×D1312yes—
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—28no—
751C22⋊C4—1316no—
752C22⋊C4—1316no—
753C22⋊C4—268no—
754C22⋊C4—268no—
755C22⋊C4—268no—
756C22⋊C4—524no—
757C22⋊C4—524no—
758C22⋊C4C2×C4×D13116yescomplemented
759C42—28no—
760C42—268no—
761C42—268no—
762C42—268no—
763C13C2×#236111yescharacteristic, complemented, Sylow
764C23—28no—
765C23—28no—
766C23—28no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—1316no—
778C23—134no—
779C23—134no—
780C23—134no—
781C23—134no—
782C23—268no—
783C23—268no—
784C23—268no—
785C23—268no—
786C23—268no—
787C23—262no—
788C23—262no—
789C23—262no—
790C23—262no—
791C23—268no—
792C23—268no—
793C23—268no—
794C23—268no—
795C23—262no—
796C23—262no—
797C23—262no—
798C23—262no—
799C23—262no—
800C23—262no—
801C23—524no—
802C23—524no—
803C23—524no—
804C23—524no—
805C23C22×C4×D1314yes—
806C23C22×C4×D1312yes—
807C23C2×D4×D1312yes—
808C23C2×D4×D1312yes—
809C23#41×D1312yes—
810C23#41×D1312yes—
811C23#8825612yes—
812C23#8825712yes—
813C23C24×D1311yescharacteristic
814D4—2632no—
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—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—1316no—
838C2×C4—134no—
839C2×C4—134no—
840C2×C4—134no—
841C2×C4—134no—
842C2×C4—134no—
843C2×C4—134no—
844C2×C4—2632no—
845C2×C4—268no—
846C2×C4—268no—
847C2×C4—268no—
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—5216no—
861C2×C4—5216no—
862C2×C4—5216no—
863C2×C4—5216no—
864C2×C4—524no—
865C2×C4—524no—
866C2×C4C22×C4×D1314yes—
867C2×C4C22×C4×D1314yes—
868C2×C4C2×D4×D1314yes—
869C2×C4C2×D4×D1314yes—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—416no—
877C22—42no—
878C22—138no—
879C22—264no—
880C22—264no—
881C22—264no—
882C22—264no—
883C22—264no—
884C22—2632no—
885C22—264no—
886C22—264no—
887C22—264no—
888C22—264no—
889C22—522no—
890C22—522no—
891C22—522no—
892C22—5216no—
893C22—522no—
894C22#1171922814yes—
895C22C4×D4×D1314yes—
896C22C4×D4×D1314yes—
897C22#1171931414yes—
898C22#1171936014yes—
899C22#1171938214yes—
900C22#1171941414yes—
901C22C23×C4×D1311yescharacteristic
902C22C22×D4×D1311yescharacteristic
903C22C22×D4×D1311yescharacteristic
904C22C2×#41×D1311yescharacteristic
905C22C2×#41×D1311yescharacteristic
906C22C2×#8825611yescharacteristic
907C22C2×#8825711yescharacteristic
908C4—24no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—42no—
913C4—42no—
914C4—138no—
915C4—264no—
916C4—264no—
917C4—264no—
918C4—522no—
919C4—522no—
920C2—44no—
921C2—268no—
922C2—524no—
923C2#1311784918yesdirect product factor
924C2C2×C4×D4×D1311yescharacteristic
925C2C2×C4×D4×D1311yescharacteristic
926C2C2×#1171922811yescharacteristic
927C2C2×#1171931411yescharacteristic
928C2C2×#1171936011yescharacteristic
929C2C2×#1171938211yescharacteristic
930C2C2×#1171941411yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#388C2
socleC24×C13C24
prime radicalC22×#88138C2
cosocleC23×C13C25
hypercenterC2×#388D13
hypocenterC13C2×#2361
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×D52C2semidirect
3. C22×#88135C2semidirect
4. C22×#88135C2semidirect
5. C22×C4⋊C4×D13C2semidirect
6. #13117849C2direct (N × H)
7. C2×#11718618C2semidirect
8. C2×#11718308C2semidirect
9. C2×#11718331C2semidirect
10. C2×#11718326C2semidirect
11. C2×#11718617C2semidirect
12. C2×#11718611C2semidirect
13. C2×#11718650C2semidirect
14. C2×C4×#6101C2semidirect
15. C2×#11718327C2semidirect
16. C2×C13×#388C2semidirect
47. C2×C4⋊C4×D13C22semidirect
48. C2×#88138C4semidirect
52. C2×#88135C22semidirect
53. C2×#88135C22semidirect
55. C2×C4×D52C22semidirect
56. C13×#388C22semidirect
63. #11718650C22semidirect
64. #11718618C22semidirect
65. #11718617C22semidirect
66. #11718611C22semidirect
67. C4×#6101C22semidirect
68. #11718331C22semidirect
69. #11718327C22semidirect
70. #11718326C22semidirect
71. #11718308C22semidirect
85. C22×C22⋊D13C2×C4semidirect
86. C22×C22⋊D13C2×C4semidirect
101. C22×D52C2×C4semidirect
114. C22×C4×D13C2×C4semidirect
123. C2×C13×C22⋊C4C2×C4semidirect
135. C2×#6103C2×C4semidirect
136. C2×#6103D4semidirect
149. C2×#6101C2×C4semidirect
150. C2×#6101D4semidirect
162. #88138C2×C4semidirect
228. C2×C22⋊D13C22×C4semidirect
229. C2×C22⋊D13C22×C4semidirect
261. C2×D52C22×C4semidirect
277. C2×C4×D13C22×C4semidirect
281. C13×C22⋊C4C22×C4semidirect
288. #6103C22×C4semidirect
289. #6103C2×D4semidirect
294. #6101C22×C4semidirect
295. #6101C2×D4semidirect
308. C2×#388D13semidirect
360. C22×D13C4×D4semidirect
409. C2×Dic13C4×D4semidirect
463. #388C2×D13semidirect
513. C2×D13C2×C4×D4semidirect
525. Dic13C2×C4×D4semidirect
608. C2×C22⋊C4C4×D13semidirect
627. C2×C13#2361semidirect
758. C22⋊C4C2×C4×D13semidirect
763. C13C2×#2361semidirect
923. C2#13117849direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881382
C22×C4×D522
C22×#881352
C22×C4⋊C4×D132
#131178492
C2×#117186182
C2×#117183082
C2×#117183312
C2×#117183262
C2×#117186172
C2×#117186112
C2×#117186502
C2×C4×#61012
C2×#117183272
C2×C13×#3882
C2×#236113