Finite Group Databasebeta

← C2×#13119896 #16032996

Subgroups — C2×#13119896 #16032996

Order 3328.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88130C211yesmaximal, characteristic, complemented
2C22×#88183C211yesmaximal, characteristic, complemented
3#13119896C2116yesmaximal, direct product factor
4C2×#11718318C211yesmaximal, characteristic, complemented
5C2×#11718609C211yesmaximal, characteristic, complemented
6C2×#11718333C211yesmaximal, characteristic, complemented
7C2×#11718621C211yesmaximal, characteristic
8C2×#11718600C211yesmaximal, characteristic, complemented
9C2×#11718618C211yesmaximal, characteristic, complemented
10C2×#11718618C211yesmaximal, characteristic, complemented
11C2×#11718601C211yesmaximal, characteristic, complemented
12C2×#11718330C211yesmaximal, characteristic, complemented
13C2×#11718330C211yesmaximal, characteristic, complemented
14C2×#11718874C211yesmaximal, characteristic, complemented
15C2×C4×#6101C211yesmaximal, characteristic, complemented
16C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×D52C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C22×C42×C13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C2×#88183—28no—
28C2×#88183C2218yescomplemented
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×C4⋊Dic13C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×#6101C2211yescharacteristic
45C22×#6101C2211yescharacteristic
46C22×C4×Dic13C2211yescharacteristic
47C22×C4×Dic13C2211yescharacteristic
48C2×#88130—28no—
49C2×#88130C2218yescomplemented
50C4×C13×C22⋊C4C2218yescomplemented
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53#11718874C2218yescomplemented
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58#11718621C2218yes—
59#11718618C2218yescomplemented
60#11718618C2218yescomplemented
61#11718609C2218yescomplemented
62#11718601C2218yescomplemented
63#11718600C2218yescomplemented
64C4×#6101C2218yescomplemented
65#11718333C2218yescomplemented
66#11718330C2218yescomplemented
67#11718330C2218yescomplemented
68#11718318C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C23×C4×C13—24no—
73C23×C4×C13—24no—
74C23×C4×C13—42no—
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2314yes—
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C22×C22⋊D13—24no—
83C22×C22⋊D13—24no—
84C22×C22⋊D13—24no—
85C22×C22⋊D13—24no—
86C22×C22⋊D13—42no—
87C22×C22⋊D13—42no—
88C22×C22⋊D13C2314yes—
89C22×C22⋊D13C2314yes—
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C22×D52—24no—
97C22×D52—42no—
98C22×D52—42no—
99C22×D52C2314yes—
100C2×C13×C22⋊C4—24no—
101C2×C13×C22⋊C4—24no—
102C2×C13×C22⋊C4C2314yes—
103C2×C13×C22⋊C4C2314yes—
104C2×C42×C13—24no—
105C2×C42×C13—42no—
106C2×C42×C13C2314yes—
107C2×C42×C13C2314yes—
108C2×C22⋊Dic13—24no—
109C2×C22⋊Dic13—42no—
110C2×C22⋊Dic13C2314yes—
111C2×C22⋊Dic13C2314yes—
112#88183—232no—
113C2×#6103—24no—
114C2×#6103—24no—
115C2×#6103—24no—
116C2×#6103—24no—
117C2×#6103—24no—
118C2×#6103—24no—
119C2×#6103—24no—
120C2×#6103—24no—
121C2×#6103—42no—
122C2×#6103—42no—
123C2×#6103C2314yes—
124C2×#6103C2314yes—
125C2×#6103C2314yes—
126C2×#6103C2314yes—
127C2×#6103C2314yes—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×C4⋊Dic13—42no—
134C2×C4⋊Dic13C2314yes—
135C2×#6101—24no—
136C2×#6101—24no—
137C2×#6101—24no—
138C2×#6101—24no—
139C2×#6101—42no—
140C2×#6101D418yescomplemented
141C2×#6101C2314yes—
142C2×#6101C2314yes—
143C2×#6101C2314yes—
144C2×#6101C2314yes—
145C2×#6101C2314yes—
146C2×#6101C2314yes—
147C2×C4×Dic13—24no—
148C2×C4×Dic13—42no—
149C2×C4×Dic13C2314yes—
150C2×C4×Dic13C2314yes—
151#88130—232no—
152C13×#95C2314yes—
153C13×#95C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2554—131nomaximal, Sylow
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13#4114yes—
166C24×C13C2412yes—
167C24×C13C2411yescharacteristic
168C23×D13—22no—
169C23×D13—22no—
170C23×D13—22no—
171C23×D13—22no—
172C23×D13—22no—
173C23×D13—22no—
174C23×D13—22no—
175C23×D13—22no—
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13—22no—
181C23×D13—22no—
182C23×D13C2412yes—
183C23×D13C2412yes—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
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—28no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—28no—
201C22×C4×C13—44no—
202C22×C4×C13—416no—
203C22×C4×C13C2×D414yes—
204C22×C4×C13#4114yes—
205C22×C4×C13#4114yes—
206C22×C4×C13C2412yes—
207C22×C4×C13C2412yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
212C2×C22⋊D13—28no—
213C2×C22⋊D13—28no—
214C2×C22⋊D13—28no—
215C2×C22⋊D13—28no—
216C2×C22⋊D13—44no—
217C2×C22⋊D13—44no—
218C2×C22⋊D13—416no—
219C2×C22⋊D13—416no—
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×Dic13C2×D414yes—
236C22×Dic13C2×D414yes—
237C22×Dic13#4114yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C22×Dic13C2412yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C2×D52—28no—
245C2×D52—44no—
246C2×D52—44no—
247C2×D52—416no—
248C13×C22⋊C4—28no—
249C13×C22⋊C4—28no—
250C42×C13—28no—
251C42×C13—44no—
252C22⋊Dic13—28no—
253C22⋊Dic13—44no—
254#6103—28no—
255#6103—28no—
256#6103—28no—
257#6103—28no—
258#6103—28no—
259#6103—28no—
260#6103—28no—
261#6103—28no—
262#6103—44no—
263#6103—44no—
264C4⋊Dic13—44no—
265#6101—28no—
266#6101—28no—
267#6101—28no—
268#6101—28no—
269#6101—44no—
270#6101C2×D4116yescomplemented
271C4×Dic13—28no—
272C4×Dic13—44no—
273C22×#126—131no—
274C22×#123—131no—
275#2554—1316no—
276C2×#398—131no—
277C2×#396—131no—
278C2×#394—131no—
279C2×#392—131no—
280C2×#390—131no—
281C2×#390—131no—
282C2×#390—131no—
283C2×#388—131no—
284C2×#388—131no—
285C2×#388—131no—
286C2×#386—131no—
287C2×C4×C4⋊C4—131no—
288C2×C4×C22⋊C4D1311yescharacteristic, complemented
289C23×C13—28no—
290C23×C13—28no—
291C23×C13—28no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—44no—
299C23×C13—44no—
300C23×C13—44no—
301C23×C13—44no—
302C23×C13C22×D412yes—
303C23×C13C2×#4114yes—
304C23×C13C2×#4112yes—
305C23×C13C2×#4112yes—
306C23×C13C2×#4112yes—
307C23×C13C2×#4112yes—
308C23×C13H(5,𝔽2)12yes—
309C23×C13H(5,𝔽2)12yes—
310C23×C13C2511yescharacteristic
311C22×D13—22no—
312C22×D13—22no—
313C22×D13—22no—
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—44no—
326C22×D13—44no—
327C22×D13—44no—
328C22×D13—44no—
329C22×D13—44no—
330C22×D13—44no—
331C22×D13—44no—
332C22×D13—44no—
333C22×D13—44no—
334C22×D13—44no—
335C22×D13—44no—
336C22×D13—44no—
337C22×D13—44no—
338C22×D13—44no—
339C2×C4×C13—28no—
340C2×C4×C13—28no—
341C2×C4×C13—28no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
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—22no—
357C2×C4×C13—416no—
358C2×C4×C13—44no—
359C2×C4×C13—44no—
360C2×C4×C13—44no—
361C2×C4×C13C22×D414yes—
362C2×C4×C13C2×#4114yes—
363C2×C4×C13C2×#4114yes—
364C22⋊D13—416no—
365C22⋊D13—416no—
366C2×Dic13—28no—
367C2×Dic13—28no—
368C2×Dic13—28no—
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—44no—
385C2×Dic13—44no—
386C2×Dic13—44no—
387C2×Dic13C22×D414yes—
388C2×Dic13C22×D414yes—
389C2×Dic13C2×#4114yes—
390D52—416no—
391C23×D4—131no—
392C23×D4—131no—
393C23×D4—131no—
394C24×C4C2×D1311yescharacteristic
395C2×#126—138no—
396C2×#126—268no—
397C2×#123—138no—
398C2×#123—268no—
399C22×C4⋊C4—131no—
400C22×C4⋊C4—131no—
401C22×C4⋊C4—131no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4—131no—
405C22×C4⋊C4—131no—
406C22×C22⋊C4—131no—
407C22×C22⋊C4—131no—
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⋊C4—131no—
418C22×C22⋊C4C2×D1311yescharacteristic
419C22×C22⋊C4C2×D1311yescharacteristic
420C22×C42—131no—
421C22×C42—131no—
422C22×C42C2×D1311yescharacteristic
423C22×C42C2×D1311yescharacteristic
424#398—138no—
425#396—138no—
426#394—138no—
427#392—138no—
428#390—138no—
429#390—138no—
430#390—138no—
431#388—138no—
432#388—138no—
433#388—138no—
434#386—138no—
435C4×C4⋊C4—138no—
436C4×C22⋊C4C2×D1318yescomplemented
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95C2×D1311yescharacteristic
442C2×#95C2×D1311yescharacteristic
443C22×C13—24no—
444C22×C13—24no—
445C22×C13—24no—
446C22×C13—42no—
447C22×C13—42no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—416no—
451C22×C13#52914yes—
452C22×C13#53214yes—
453C22×C13#53814yes—
454C22×C13#54614yes—
455C22×C13#55014yes—
456C22×C13#55114yes—
457C22×C13#55314yes—
458C22×C13C23×D411yescharacteristic
459C22×C13C22×#4111yescharacteristic
460C22×C13C22×#4111yescharacteristic
461C22×C13C22×#4111yescharacteristic
462C22×C13C22×#4111yescharacteristic
463C22×C13C2×H(5,𝔽2)11yescharacteristic
464C22×C13C2×H(5,𝔽2)11yescharacteristic
465C2×D13—42no—
466C2×D13—42no—
467C2×D13—42no—
468C2×D13—42no—
469C2×D13—42no—
470C2×D13—42no—
471C2×D13—42no—
472C2×D13—42no—
473C2×D13—42no—
474C2×D13—42no—
475C2×D13—42no—
476C2×D13—42no—
477C2×D13—42no—
478C2×D13—42no—
479C2×D13—88no—
480C2×D13—88no—
481C4×C13—24no—
482C4×C13—24no—
483C4×C13—24no—
484C4×C13—42no—
485C4×C13—42no—
486C4×C13—42no—
487Dic13—24no—
488Dic13—24no—
489Dic13—24no—
490Dic13—42no—
491Dic13—42no—
492Dic13—42no—
493C25—131no—
494C25—131no—
495C25C22×D1311yescharacteristic
496C22×D4—134no—
497C22×D4—134no—
498C22×D4—134no—
499C22×D4—264no—
500C22×D4—264no—
501C22×D4—264no—
502C22×D4—264no—
503C22×D4—264no—
504C22×D4—522no—
505C22×D4—522no—
506C22×D4—522no—
507C22×D4—522no—
508C23×C4—24no—
509C23×C4—24no—
510C23×C4—42no—
511C23×C4—131no—
512C23×C4—131no—
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4C22×D1311yescharacteristic
518C23×C4C22×D1311yescharacteristic
519C23×C4C22×D1311yescharacteristic
520C23×C4C22×D1314yes—
521C23×C4C22×D1311yescharacteristic
522C23×C4C22×D1311yescharacteristic
523C23×C4C22×D1311yescharacteristic
524#126—2632no—
525#123—2632no—
526C2×C4⋊C4—138no—
527C2×C4⋊C4—134no—
528C2×C4⋊C4—134no—
529C2×C4⋊C4—134no—
530C2×C4⋊C4—134no—
531C2×C4⋊C4—134no—
532C2×C4⋊C4—134no—
533C2×C4⋊C4—134no—
534C2×C4⋊C4—264no—
535C2×C4⋊C4—264no—
536C2×C4⋊C4—264no—
537C2×C4⋊C4—264no—
538C2×C4⋊C4—522no—
539C2×C4⋊C4—522no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—134no—
543C2×C22⋊C4—134no—
544C2×C22⋊C4—134no—
545C2×C22⋊C4—134no—
546C2×C22⋊C4—134no—
547C2×C22⋊C4—134no—
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—264no—
555C2×C22⋊C4—264no—
556C2×C22⋊C4—264no—
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—522no—
564C2×C22⋊C4—522no—
565C2×C22⋊C4—522no—
566C2×C22⋊C4C22×D1314yes—
567C2×C22⋊C4C22×D1314yes—
568C2×C42—24no—
569C2×C42—42no—
570C2×C42—134no—
571C2×C42—134no—
572C2×C42—264no—
573C2×C42—522no—
574C2×C42C22×D1314yes—
575C2×C42C22×D1314yes—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—134no—
580#95C22×D1314yes—
581#95C22×D1314yes—
582C2×C13—44no—
583C2×C13#255418yescomplemented
584C2×C13C2×#52911yescharacteristic
585C2×C13C2×#53211yescharacteristic
586C2×C13C2×#53811yescharacteristic
587C2×C13C2×#54611yescharacteristic
588C2×C13C2×#55011yescharacteristic
589C2×C13C2×#55111yescharacteristic
590C2×C13C2×#55311yescharacteristic
591D13—82no—
592D13—82no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—132no—
600C24—132no—
601C24—262no—
602C24—262no—
603C24—262no—
604C24—262no—
605C24—262no—
606C24—262no—
607C24—262no—
608C24—262no—
609C24—262no—
610C24—262no—
611C24—262no—
612C24—262no—
613C24—262no—
614C24—262no—
615C24#612714yes—
616C24C23×D1312yes—
617C24C23×D1311yescharacteristic
618C2×D4—268no—
619C2×D4—268no—
620C2×D4—268no—
621C2×D4—268no—
622C2×D4—268no—
623C2×D4—524no—
624C2×D4—524no—
625C2×D4—5216no—
626C2×D4—524no—
627C2×D4—524no—
628C2×D4—5216no—
629C2×D4—5216no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—28no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—28no—
647C22×C4—44no—
648C22×C4—416no—
649C22×C4—134no—
650C22×C4—134no—
651C22×C4—134no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—132no—
656C22×C4—132no—
657C22×C4—132no—
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#612714yes—
674C22×C4#612714yes—
675C22×C4D4×D1314yes—
676C22×C4C23×D1312yes—
677C22×C4C23×D1312yes—
678C22×C4C23×D1312yes—
679C22×C4C23×D1312yes—
680C22×C4C23×D1312yes—
681C22×C4C23×D1312yes—
682C4⋊C4—1316no—
683C4⋊C4—268no—
684C4⋊C4—268no—
685C4⋊C4—268no—
686C4⋊C4—268no—
687C4⋊C4—524no—
688C4⋊C4—524no—
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—268no—
692C22⋊C4—268no—
693C22⋊C4—268no—
694C22⋊C4—268no—
695C22⋊C4—268no—
696C22⋊C4—268no—
697C22⋊C4—268no—
698C22⋊C4—268no—
699C22⋊C4—268no—
700C22⋊C4—524no—
701C22⋊C4—524no—
702C22⋊C4—524no—
703C42—28no—
704C42—44no—
705C42—268no—
706C42—524no—
707C13C2×#255411yescharacteristic, complemented, Sylow
708C23—28no—
709C23—28no—
710C23—28no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—262no—
722C23—262no—
723C23—262no—
724C23—262no—
725C23—262no—
726C23—262no—
727C23—262no—
728C23—262no—
729C23—262no—
730C23—262no—
731C23—262no—
732C23—262no—
733C23—262no—
734C23—262no—
735C23—524no—
736C23—524no—
737C23—524no—
738C23—524no—
739C23—524no—
740C23—524no—
741C23—524no—
742C23—524no—
743C23—524no—
744C23—524no—
745C23—524no—
746C23—524no—
747C23—524no—
748C23—524no—
749C23C2×#612714yes—
750C23C2×#612712yes—
751C23C2×#612712yes—
752C23C2×#612712yes—
753C23C2×D4×D1312yes—
754C23#8825112yes—
755C23#41×D1312yes—
756C23#8825612yes—
757C23C24×D1311yescharacteristic
758D4—5216no—
759D4—5216no—
760D4—5216no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
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—416no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—134no—
784C2×C4—134no—
785C2×C4—134no—
786C2×C4—268no—
787C2×C4—268no—
788C2×C4—268no—
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—524no—
805C2×C4—524no—
806C2×C4—524no—
807C2×C4C2×#612714yes—
808C2×C4C2×#612714yes—
809C2×C4C2×D4×D1314yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—42no—
814C22—416no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—522no—
819C22—522no—
820C22—522no—
821C22—522no—
822C22—522no—
823C22—522no—
824C22—522no—
825C22—522no—
826C22—522no—
827C22—522no—
828C22—522no—
829C22—522no—
830C22—522no—
831C22—522no—
832C22—1048no—
833C22—1048no—
834C22#1171918414yes—
835C22#1171919514yes—
836C22#1171923214yes—
837C22#1171924514yes—
838C22#1171925314yes—
839C22#1171925814yes—
840C22#1171926514yes—
841C22C22×#612711yescharacteristic
842C22C22×#612711yescharacteristic
843C22C22×#612711yescharacteristic
844C22C22×D4×D1311yescharacteristic
845C22C2×#8825111yescharacteristic
846C22C2×#41×D1311yescharacteristic
847C22C2×#8825611yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—264no—
855C4—264no—
856C4—264no—
857C4—522no—
858C4—522no—
859C4—522no—
860C2—44no—
861C2—1042no—
862C2—1042no—
863C2#1311989618yesdirect product factor
864C2C2×#1171918411yescharacteristic
865C2C2×#1171925311yescharacteristic
866C2C2×#1171926511yescharacteristic
867C2C2×#1171919511yescharacteristic
868C2C2×#1171925811yescharacteristic
869C2C2×#1171923211yescharacteristic
870C2C2×#1171924511yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C4×C13×C22⋊C4C2
socleC24×C13C24
prime radicalC2×#11718621C2
hypercenterC2×C4×C22⋊C4D13
hypocenterC13C2×#2554
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#88130C2semidirect
2. C22×#88183C2semidirect
3. #13119896C2direct (N × H)
4. C2×#11718318C2semidirect
5. C2×#11718609C2semidirect
6. C2×#11718333C2semidirect
8. C2×#11718600C2semidirect
9. C2×#11718618C2semidirect
10. C2×#11718618C2semidirect
11. C2×#11718601C2semidirect
12. C2×#11718330C2semidirect
13. C2×#11718330C2semidirect
14. C2×#11718874C2semidirect
15. C2×C4×#6101C2semidirect
16. C2×C4×C13×C22⋊C4C2semidirect
28. C2×#88183C22semidirect
49. C2×#88130C22semidirect
50. C4×C13×C22⋊C4C22semidirect
53. #11718874C22semidirect
59. #11718618C22semidirect
60. #11718618C22semidirect
61. #11718609C22semidirect
62. #11718601C22semidirect
63. #11718600C22semidirect
64. C4×#6101C22semidirect
65. #11718333C22semidirect
66. #11718330C22semidirect
67. #11718330C22semidirect
68. #11718318C22semidirect
140. C2×#6101D4semidirect
270. #6101C2×D4semidirect
288. C2×C4×C22⋊C4D13semidirect
436. C4×C22⋊C4C2×D13semidirect
583. C2×C13#2554semidirect
707. C13C2×#2554semidirect
863. C2#13119896direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881302
C22×#881832
#131198962
C2×#117183182
C2×#117186092
C2×#117183332
C2×#117186212
C2×#117186002
C2×#117186182
C2×#117186012
C2×#117183302
C2×#117188742
C2×C4×#61012
C2×C4×C13×C22⋊C42
C2×#255413