Finite Group Databasebeta

← C2×#13120445 #16034306

Subgroups — C2×#13120445 #16034306

Order 3328.

3330 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88137C211yesmaximal, characteristic, complemented
2C22×#88135C211yesmaximal, characteristic, complemented
3#13120445C2116yesmaximal, direct product factor
4C2×#11718654C211yesmaximal, characteristic, complemented
5C2×#11718622C211yesmaximal, characteristic, complemented
6C2×#11718622C211yesmaximal, characteristic, complemented
7C2×#11718884C211yesmaximal, characteristic
8C2×#11718589C211yesmaximal, characteristic, complemented
9C2×#11718606C211yesmaximal, characteristic, complemented
10C2×#11718606C211yesmaximal, characteristic, complemented
11C2×#11718612C211yesmaximal, characteristic, complemented
12C2×#11718642C211yesmaximal, characteristic, complemented
13C2×#11718881C211yesmaximal, characteristic, complemented
14C2×#11718611C211yesmaximal, characteristic, complemented
15C2×C4×#6103C211yesmaximal, characteristic, complemented
16C2×C13×#390C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C42×C13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic
39C22×C4⋊Dic13C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C2×#88137—28no—
45C2×#88137C2218yescomplemented
46C2×#88135—28no—
47C2×#88135C2218yescomplemented
48C13×#390C2218yescomplemented
49#11718884C2218yes—
50#11718881C2218yescomplemented
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59#11718654C2218yescomplemented
60#11718642C2218yescomplemented
61#11718622C2218yescomplemented
62#11718622C2218yescomplemented
63#11718612C2218yescomplemented
64#11718611C2218yescomplemented
65#11718606C2218yescomplemented
66#11718606C2218yescomplemented
67C4×#6103C2218yescomplemented
68#11718589C2218yescomplemented
69C25×C13C2311yescharacteristic
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C22×D4×C13—24no—
73C22×D4×C13—24no—
74C22×D4×C13—42no—
75C22×D4×C13C2314yes—
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⋊D13—42no—
86C22×C22⋊D13—42no—
87C22×C22⋊D13C2314yes—
88C22×C22⋊D13C2314yes—
89C23×Dic13—24no—
90C23×Dic13—42no—
91C23×Dic13—42no—
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2314yes—
100C22×C4×D13—42no—
101C22×C4×D13—42no—
102C22×C4×D13D418yescomplemented
103C22×C4×D13C2314yes—
104C2×C13×C4⋊C4—24no—
105C2×C13×C4⋊C4C2314yes—
106C2×C13×C22⋊C4—24no—
107C2×C13×C22⋊C4—24no—
108C2×C13×C22⋊C4—24no—
109C2×C13×C22⋊C4—24no—
110C2×C13×C22⋊C4C2314yes—
111C2×C13×C22⋊C4C2314yes—
112C2×C13×C22⋊C4C2314yes—
113C2×C13×C22⋊C4C2314yes—
114C2×C42×C13—42no—
115C2×C42×C13C2314yes—
116C2×C22⋊Dic13—24no—
117C2×C22⋊Dic13—24no—
118C2×C22⋊Dic13—24no—
119C2×C22⋊Dic13—42no—
120C2×C22⋊Dic13—42no—
121C2×C22⋊Dic13C2314yes—
122C2×C22⋊Dic13C2314yes—
123C2×C22⋊Dic13C2314yes—
124C2×C22⋊Dic13C2314yes—
125C2×C22⋊Dic13C2314yes—
126C2×#6103—24no—
127C2×#6103—24no—
128C2×#6103—24no—
129C2×#6103—24no—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×C4⋊Dic13—24no—
135C2×C4⋊Dic13—24no—
136C2×C4⋊Dic13—42no—
137C2×C4⋊Dic13C2314yes—
138C2×C4⋊Dic13C2314yes—
139C2×C4⋊Dic13C2314yes—
140C2×#6101—24no—
141C2×#6101—24no—
142C2×#6101C2314yes—
143C2×#6101C2314yes—
144C2×C4×Dic13—24no—
145C2×C4×Dic13—42no—
146C2×C4×Dic13C2314yes—
147C2×C4×Dic13C2314yes—
148#88137—232no—
149#88135—232no—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2602—131nomaximal, Sylow
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13—22no—
172C24×C13#4114yes—
173C24×C13C2412yes—
174C24×C13C2412yes—
175C24×C13C2411yescharacteristic
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13—22no—
181C23×D13—22no—
182C23×D13C2×D414yes—
183C23×D13C2412yes—
184C2×D4×C13—28no—
185C2×D4×C13—28no—
186C2×D4×C13—44no—
187C2×D4×C13—416no—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13C2×D414yes—
201C22×C4×C13#4114yes—
202C22×C4×C13#4114yes—
203C22×C4×C13C2412yes—
204C22×C4×C13C2412yes—
205C22×C4×C13C2412yes—
206C22×C4×C13C2412yes—
207C22×C4×C13C2412yes—
208C2×C22⋊D13—232no—
209C2×C22⋊D13—28no—
210C2×C22⋊D13—28no—
211C2×C22⋊D13—28no—
212C2×C22⋊D13—28no—
213C2×C22⋊D13—44no—
214C2×C22⋊D13—44no—
215C2×C22⋊D13—416no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13—22no—
235C22×Dic13—28no—
236C22×Dic13—44no—
237C22×Dic13—44no—
238C22×Dic13—416no—
239C22×Dic13C2×D414yes—
240C22×Dic13#4114yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C2×C4×D13—416no—
249C2×C4×D13—44no—
250C2×C4×D13—44no—
251C2×C4×D13C2×D4116yescomplemented
252C13×C4⋊C4—28no—
253C13×C22⋊C4—28no—
254C13×C22⋊C4—28no—
255C13×C22⋊C4—28no—
256C13×C22⋊C4—28no—
257C42×C13—44no—
258C22⋊Dic13—28no—
259C22⋊Dic13—28no—
260C22⋊Dic13—28no—
261C22⋊Dic13—44no—
262C22⋊Dic13—44no—
263#6103—28no—
264#6103—28no—
265#6103—28no—
266#6103—28no—
267C4⋊Dic13—28no—
268C4⋊Dic13—28no—
269C4⋊Dic13—44no—
270#6101—28no—
271#6101—28no—
272C4×Dic13—28no—
273C4×Dic13—44no—
274C22×#123—131no—
275C22×C4×D4—131no—
276#2602—1316no—
277C2×#397—131no—
278C2×#394—131no—
279C2×#394—131no—
280C2×#392—131no—
281C2×#390D1311yescharacteristic, complemented
282C2×#389—131no—
283C2×#388—131no—
284C2×#388—131no—
285C2×#388—131no—
286C2×#387—131no—
287C2×#386—131no—
288C2×#385—131no—
289C2×C4×C22⋊C4—131no—
290C23×C13—28no—
291C23×C13—28no—
292C23×C13—28no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—44no—
307C23×C13—44no—
308C23×C13—44no—
309C23×C13—44no—
310C23×C13—44no—
311C23×C13—44no—
312C23×C13—44no—
313C23×C13—44no—
314C23×C13—44no—
315C23×C13—44no—
316C23×C13—44no—
317C23×C13C22×D412yes—
318C23×C13C2×#4114yes—
319C23×C13C2×#4112yes—
320C23×C13C2×#4112yes—
321C23×C13C2×#4112yes—
322C23×C13C2×#4112yes—
323C23×C13H(5,𝔽2)12yes—
324C23×C13H(5,𝔽2)12yes—
325C23×C13C2511yescharacteristic
326C22×D13—28no—
327C22×D13—28no—
328C22×D13—28no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—44no—
336C22×D13—44no—
337C22×D13—44no—
338C22×D13—44no—
339C22×D13C22×D414yes—
340D4×C13—416no—
341C2×C4×C13—28no—
342C2×C4×C13—28no—
343C2×C4×C13—28no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—44no—
357C2×C4×C13—44no—
358C2×C4×C13C22×D414yes—
359C2×C4×C13C2×#4114yes—
360C2×C4×C13C2×#4114yes—
361C22⋊D13—232no—
362C22⋊D13—416no—
363C2×Dic13—28no—
364C2×Dic13—28no—
365C2×Dic13—22no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—416no—
385C2×Dic13—44no—
386C2×Dic13—44no—
387C2×Dic13—44no—
388C2×Dic13—44no—
389C2×Dic13—44no—
390C2×Dic13C22×D414yes—
391C2×Dic13C2×#4114yes—
392C4×D13—416no—
393C23×D4—131no—
394C23×D4—131no—
395C23×D4C2×D1311yescharacteristic
396C24×C4—131no—
397C24×C4—131no—
398C2×#123—138no—
399C2×#123—268no—
400C2×C4×D4—138no—
401C2×C4×D4—268no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4—131no—
405C22×C4⋊C4—131no—
406C22×C4⋊C4—131no—
407C22×C4⋊C4C2×D1311yescharacteristic
408C22×C22⋊C4—131no—
409C22×C22⋊C4—131no—
410C22×C22⋊C4—131no—
411C22×C22⋊C4—131no—
412C22×C22⋊C4—131no—
413C22×C22⋊C4—131no—
414C22×C22⋊C4—131no—
415C22×C22⋊C4—131no—
416C22×C22⋊C4—131no—
417C22×C22⋊C4C2×D1311yescharacteristic
418C22×C22⋊C4C2×D1311yescharacteristic
419C22×C22⋊C4C2×D1311yescharacteristic
420C22×C22⋊C4C2×D1311yescharacteristic
421C22×C42—131no—
422C22×C42—131no—
423C22×C42C2×D1311yescharacteristic
424#397—138no—
425#394—138no—
426#394—138no—
427#392—138no—
428#390C2×D1318yescomplemented
429#389—138no—
430#388—138no—
431#388—138no—
432#388—138no—
433#387—138no—
434#386—138no—
435#385—138no—
436C4×C22⋊C4—138no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C2×#95—131no—
445C22×C13—24no—
446C22×C13—24no—
447C22×C13—24no—
448C22×C13—416no—
449C22×C13—42no—
450C22×C13—42no—
451C22×C13—42no—
452C22×C13—42no—
453C22×C13—42no—
454C22×C13—42no—
455C22×C13—42no—
456C22×C13—42no—
457C22×C13—42no—
458C22×C13—42no—
459C22×C13—42no—
460C22×C13—88no—
461C22×C13#52514yes—
462C22×C13#53214yes—
463C22×C13#53414yes—
464C22×C13#55114yes—
465C22×C13#55314yes—
466C22×C13#55314yes—
467C22×C13#55914yes—
468C22×C13C23×D411yescharacteristic
469C22×C13C22×#4111yescharacteristic
470C22×C13C22×#4111yescharacteristic
471C22×C13C22×#4111yescharacteristic
472C22×C13C22×#4111yescharacteristic
473C22×C13C2×H(5,𝔽2)11yescharacteristic
474C22×C13C2×H(5,𝔽2)11yescharacteristic
475C2×D13—24no—
476C2×D13—24no—
477C2×D13—24no—
478C2×D13—416no—
479C2×D13—42no—
480C2×D13—42no—
481C2×D13—42no—
482C2×D13—42no—
483C4×C13—24no—
484C4×C13—24no—
485C4×C13—24no—
486C4×C13—42no—
487C4×C13—42no—
488Dic13—24no—
489Dic13—24no—
490Dic13—42no—
491Dic13—42no—
492Dic13—42no—
493Dic13—42no—
494Dic13—42no—
495C25—131no—
496C25C22×D1311yescharacteristic
497C25C22×D1311yescharacteristic
498C22×D4—24no—
499C22×D4—24no—
500C22×D4—42no—
501C22×D4—134no—
502C22×D4—134no—
503C22×D4—264no—
504C22×D4—264no—
505C22×D4—264no—
506C22×D4—264no—
507C22×D4—522no—
508C22×D4—522no—
509C22×D4C22×D1314yes—
510C23×C4—131no—
511C23×C4—131no—
512C23×C4—138no—
513C23×C4—134no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4—134no—
520C23×C4—264no—
521C23×C4—522no—
522C23×C4—522no—
523C23×C4—522no—
524C23×C4—522no—
525C23×C4C22×D1311yescharacteristic
526C23×C4C22×D1311yescharacteristic
527C23×C4C22×D1311yescharacteristic
528C23×C4C22×D1311yescharacteristic
529C23×C4C22×D1311yescharacteristic
530#123—2632no—
531C4×D4—2632no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—134no—
534C2×C4⋊C4—134no—
535C2×C4⋊C4—134no—
536C2×C4⋊C4—134no—
537C2×C4⋊C4—134no—
538C2×C4⋊C4—264no—
539C2×C4⋊C4—264no—
540C2×C4⋊C4—264no—
541C2×C4⋊C4—264no—
542C2×C4⋊C4—522no—
543C2×C4⋊C4C22×D1314yes—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—134no—
549C2×C22⋊C4—134no—
550C2×C22⋊C4—134no—
551C2×C22⋊C4—134no—
552C2×C22⋊C4—134no—
553C2×C22⋊C4—134no—
554C2×C22⋊C4—134no—
555C2×C22⋊C4—134no—
556C2×C22⋊C4—134no—
557C2×C22⋊C4—264no—
558C2×C22⋊C4—264no—
559C2×C22⋊C4—264no—
560C2×C22⋊C4—264no—
561C2×C22⋊C4—264no—
562C2×C22⋊C4—264no—
563C2×C22⋊C4—264no—
564C2×C22⋊C4—522no—
565C2×C22⋊C4—522no—
566C2×C22⋊C4C22×D1314yes—
567C2×C22⋊C4C22×D1314yes—
568C2×C22⋊C4C22×D1314yes—
569C2×C22⋊C4C22×D1314yes—
570C2×C42—42no—
571C2×C42—134no—
572C2×C42—134no—
573C2×C42—264no—
574C2×C42—522no—
575C2×C42C22×D1314yes—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—134no—
580#95—134no—
581#95—134no—
582#95—134no—
583#95—134no—
584C2×C13—44no—
585C2×C13—82no—
586C2×C13#260218yescomplemented
587C2×C13C2×#52511yescharacteristic
588C2×C13C2×#53211yescharacteristic
589C2×C13C2×#53411yescharacteristic
590C2×C13C2×#55111yescharacteristic
591C2×C13C2×#55311yescharacteristic
592C2×C13C2×#55311yescharacteristic
593C2×C13C2×#55911yescharacteristic
594D13—44no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—134no—
609C24—132no—
610C24—262no—
611C24—262no—
612C24—262no—
613C24—262no—
614C24—262no—
615C24—262no—
616C24#612714yes—
617C24C23×D1312yes—
618C24C23×D1312yes—
619C24C23×D1311yescharacteristic
620C2×D4—28no—
621C2×D4—28no—
622C2×D4—44no—
623C2×D4—416no—
624C2×D4—268no—
625C2×D4—268no—
626C2×D4—2632no—
627C2×D4—268no—
628C2×D4—268no—
629C2×D4—524no—
630C2×D4—524no—
631C2×D4—5216no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—134no—
645C22×C4—134no—
646C22×C4—132no—
647C22×C4—132no—
648C22×C4—1316no—
649C22×C4—132no—
650C22×C4—132no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—268no—
655C22×C4—262no—
656C22×C4—262no—
657C22×C4—262no—
658C22×C4—262no—
659C22×C4—262no—
660C22×C4—262no—
661C22×C4—262no—
662C22×C4—262no—
663C22×C4—262no—
664C22×C4—262no—
665C22×C4—262no—
666C22×C4—262no—
667C22×C4—262no—
668C22×C4—262no—
669C22×C4—262no—
670C22×C4—262no—
671C22×C4—262no—
672C22×C4—262no—
673C22×C4—262no—
674C22×C4—5216no—
675C22×C4—524no—
676C22×C4—524no—
677C22×C4—524no—
678C22×C4—524no—
679C22×C4—5216no—
680C22×C4D4×D1314yes—
681C22×C4#612914yes—
682C22×C4#612914yes—
683C22×C4C23×D1312yes—
684C22×C4C23×D1312yes—
685C22×C4C23×D1312yes—
686C22×C4C23×D1312yes—
687C22×C4C23×D1312yes—
688C4⋊C4—28no—
689C4⋊C4—268no—
690C4⋊C4—268no—
691C4⋊C4—268no—
692C4⋊C4—268no—
693C4⋊C4—524no—
694C22⋊C4—28no—
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—28no—
698C22⋊C4—268no—
699C22⋊C4—268no—
700C22⋊C4—268no—
701C22⋊C4—268no—
702C22⋊C4—268no—
703C22⋊C4—268no—
704C22⋊C4—268no—
705C22⋊C4—524no—
706C22⋊C4—524no—
707C42—44no—
708C42—268no—
709C42—524no—
710C13C2×#260211yescharacteristic, complemented, Sylow
711C23—28no—
712C23—28no—
713C23—28no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—134no—
739C23—268no—
740C23—268no—
741C23—262no—
742C23—262no—
743C23—262no—
744C23—262no—
745C23—262no—
746C23—262no—
747C23—268no—
748C23—524no—
749C23—524no—
750C23—524no—
751C23—524no—
752C23C2×#612714yes—
753C23C2×#612712yes—
754C23C2×D4×D1312yes—
755C23C2×#612912yes—
756C23C2×#612912yes—
757C23#8825112yes—
758C23#41×D1312yes—
759C23#8825612yes—
760C23C24×D1311yescharacteristic
761D4—416no—
762D4—2632no—
763D4—5216no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—134no—
782C2×C4—134no—
783C2×C4—268no—
784C2×C4—268no—
785C2×C4—262no—
786C2×C4—262no—
787C2×C4—262no—
788C2×C4—262no—
789C2×C4—262no—
790C2×C4—262no—
791C2×C4—262no—
792C2×C4—262no—
793C2×C4—262no—
794C2×C4—262no—
795C2×C4—262no—
796C2×C4—262no—
797C2×C4—262no—
798C2×C4—262no—
799C2×C4—262no—
800C2×C4—262no—
801C2×C4—262no—
802C2×C4—262no—
803C2×C4—262no—
804C2×C4—5216no—
805C2×C4—5216no—
806C2×C4—524no—
807C2×C4—524no—
808C2×C4—524no—
809C2×C4—524no—
810C2×C4—524no—
811C2×C4C2×D4×D1314yes—
812C2×C4C2×#612914yes—
813C2×C4C2×#612914yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—416no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—88no—
830C22—264no—
831C22—264no—
832C22—264no—
833C22—522no—
834C22—522no—
835C22—522no—
836C22—5216no—
837C22—522no—
838C22#1171920014yes—
839C22#1171925214yes—
840C22#1171927014yes—
841C22#1171930614yes—
842C22#1171931014yes—
843C22#1171938614yes—
844C22#1171942114yes—
845C22C22×#612711yescharacteristic
846C22C22×D4×D1311yescharacteristic
847C22C22×#612911yescharacteristic
848C22C22×#612911yescharacteristic
849C22C2×#8825111yescharacteristic
850C22C2×#41×D1311yescharacteristic
851C22C2×#8825611yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—42no—
857C4—264no—
858C4—264no—
859C4—522no—
860C4—522no—
861C4—522no—
862C4—522no—
863C4—522no—
864C2—44no—
865C2—82no—
866C2—524no—
867C2#1312044518yesdirect product factor
868C2C2×#1171925211yescharacteristic
869C2C2×#1171942111yescharacteristic
870C2C2×#1171931011yescharacteristic
871C2C2×#1171920011yescharacteristic
872C2C2×#1171930611yescharacteristic
873C2C2×#1171927011yescharacteristic
874C2C2×#1171938611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#390C2
socleC24×C13C24
prime radicalC2×#11718884C2
hypercenterC2×#390D13
hypocenterC13C2×#2602
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#88137C2semidirect
2. C22×#88135C2semidirect
3. #13120445C2direct (N × H)
4. C2×#11718654C2semidirect
5. C2×#11718622C2semidirect
6. C2×#11718622C2semidirect
8. C2×#11718589C2semidirect
9. C2×#11718606C2semidirect
10. C2×#11718606C2semidirect
11. C2×#11718612C2semidirect
12. C2×#11718642C2semidirect
13. C2×#11718881C2semidirect
14. C2×#11718611C2semidirect
15. C2×C4×#6103C2semidirect
16. C2×C13×#390C2semidirect
45. C2×#88137C22semidirect
47. C2×#88135C22semidirect
48. C13×#390C22semidirect
50. #11718881C22semidirect
59. #11718654C22semidirect
60. #11718642C22semidirect
61. #11718622C22semidirect
62. #11718622C22semidirect
63. #11718612C22semidirect
64. #11718611C22semidirect
65. #11718606C22semidirect
66. #11718606C22semidirect
67. C4×#6103C22semidirect
68. #11718589C22semidirect
102. C22×C4×D13D4semidirect
251. C2×C4×D13C2×D4semidirect
281. C2×#390D13semidirect
428. #390C2×D13semidirect
586. C2×C13#2602semidirect
710. C13C2×#2602semidirect
867. C2#13120445direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881372
C22×#881352
#131204452
C2×#117186542
C2×#117186222
C2×#117188842
C2×#117185892
C2×#117186062
C2×#117186122
C2×#117186422
C2×#117188812
C2×#117186112
C2×C4×#61032
C2×C13×#3902
C2×#260213