Finite Group Databasebeta

← C2×#13119293 #16032506

Subgroups — C2×#13119293 #16032506

Order 3328.

3222 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×#88193C211yesmaximal, characteristic
2C22×#88131C211yesmaximal, characteristic, complemented
3#13119293C2116yesmaximal, direct product factor
4C2×#11718622C211yesmaximal, characteristic, complemented
5C2×#11718620C211yesmaximal, characteristic, complemented
6C2×#11718883C211yesmaximal, characteristic, complemented
7C2×#11718618C211yesmaximal, characteristic, complemented
8C2×#11718618C211yesmaximal, characteristic, complemented
9C2×#11718606C211yesmaximal, characteristic, complemented
10C2×#11718612C211yesmaximal, characteristic, complemented
11C2×#11718651C211yesmaximal, characteristic, complemented
12C2×#11718330C211yesmaximal, characteristic, complemented
13C2×#11718637C211yesmaximal, characteristic, complemented
14C2×#11718311C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C2×C13×#394C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C2×#88193—28no—
32C2×#88193C2218yes—
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C22×C4×Dic13C2211yescharacteristic
47C22×C4×Dic13C2211yescharacteristic
48C2×#88131—28no—
49C2×#88131C2218yescomplemented
50C13×#394C2218yescomplemented
51C2×C13×#95C2211yescharacteristic
52#11718883C2218yescomplemented
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58#11718651C2218yescomplemented
59#11718637C2218yescomplemented
60#11718622C2218yescomplemented
61#11718620C2218yescomplemented
62#11718618C2218yescomplemented
63#11718618C2218yescomplemented
64#11718612C2218yescomplemented
65#11718606C2218yescomplemented
66C22⋊C4×Dic13C2218yescomplemented
67#11718330C2218yescomplemented
68#11718311C2218yescomplemented
69C25×C13C2311yescharacteristic
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C22×D4×C13—24no—
73C22×D4×C13—42no—
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—24no—
91C23×Dic13D418yes—
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2314yes—
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C2×C13×C4⋊C4—42no—
101C2×C13×C4⋊C4C2314yes—
102C2×C13×C22⋊C4—24no—
103C2×C13×C22⋊C4—24no—
104C2×C13×C22⋊C4—24no—
105C2×C13×C22⋊C4—42no—
106C2×C13×C22⋊C4C2314yes—
107C2×C13×C22⋊C4C2314yes—
108C2×C13×C22⋊C4C2314yes—
109C2×C13×C22⋊C4C2314yes—
110C2×C22⋊Dic13—24no—
111C2×C22⋊Dic13—24no—
112C2×C22⋊Dic13—24no—
113C2×C22⋊Dic13—24no—
114C2×C22⋊Dic13—42no—
115C2×C22⋊Dic13C2314yes—
116C2×C22⋊Dic13C2314yes—
117C2×C22⋊Dic13C2314yes—
118C2×C22⋊Dic13C2314yes—
119C2×C22⋊Dic13C2314yes—
120#88193—232no—
121C2×#6103—24no—
122C2×#6103—24no—
123C2×#6103—24no—
124C2×#6103—42no—
125C2×#6103—42no—
126C2×#6103C2314yes—
127C2×#6103C2314yes—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×C4⋊Dic13—42no—
132C2×C4⋊Dic13C2314yes—
133C2×#6101—24no—
134C2×#6101—24no—
135C2×#6101—24no—
136C2×#6101—42no—
137C2×#6101—42no—
138C2×#6101C2314yes—
139C2×#6101C2314yes—
140C2×#6101C2314yes—
141C2×#6101C2314yes—
142C2×#6101C2314yes—
143C2×C4×Dic13—24no—
144C2×C4×Dic13—24no—
145C2×C4×Dic13—24no—
146C2×C4×Dic13—24no—
147C2×C4×Dic13C2314yes—
148C2×C4×Dic13C2314yes—
149C2×C4×Dic13C2314yes—
150C2×C4×Dic13C2314yes—
151#88131—232no—
152C13×#95C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2500—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×C13C2×D414yes—
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×D13—22no—
183C23×D13C2412yes—
184C2×D4×C13—28no—
185C2×D4×C13—44no—
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×C13—22no—
201C22×C4×C13—22no—
202C22×C4×C13#4114yes—
203C22×C4×C13C2412yes—
204C22×C4×C13C2412yes—
205C22×C4×C13C2412yes—
206C22×C4×C13C2412yes—
207C22×C4×C13C2412yes—
208C2×C22⋊D13—28no—
209C2×C22⋊D13—28no—
210C2×C22⋊D13—28no—
211C2×C22⋊D13—28no—
212C2×C22⋊D13—44no—
213C2×C22⋊D13—44no—
214C2×C22⋊D13—416no—
215C2×C22⋊D13—416no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—232no—
221C22×Dic13—28no—
222C22×Dic13—28no—
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×D4116yes—
236C22×Dic13C2×D414yes—
237C22×Dic13C2×D414yes—
238C22×Dic13#4114yes—
239C22×Dic13#4114yes—
240C22×Dic13#4114yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C13×C4⋊C4—44no—
249C13×C22⋊C4—28no—
250C13×C22⋊C4—28no—
251C13×C22⋊C4—28no—
252C13×C22⋊C4—44no—
253C22⋊Dic13—28no—
254C22⋊Dic13—28no—
255C22⋊Dic13—28no—
256C22⋊Dic13—28no—
257C22⋊Dic13—44no—
258#6103—28no—
259#6103—28no—
260#6103—28no—
261#6103—44no—
262#6103—44no—
263C4⋊Dic13—44no—
264#6101—28no—
265#6101—28no—
266#6101—28no—
267#6101—44no—
268#6101—44no—
269C4×Dic13—28no—
270C4×Dic13—28no—
271C4×Dic13—28no—
272C4×Dic13—28no—
273C22×#121—131no—
274C22×#117—131no—
275#2500—1316no—
276C2×#394—131no—
277C2×#394—131no—
278C2×#394—131no—
279C2×#394D1311yescharacteristic, complemented
280C2×#390—131no—
281C2×#390—131no—
282C2×#388—131no—
283C2×#388—131no—
284C2×#388—131no—
285C2×#388—131no—
286C2×#384—131no—
287C2×#382—131no—
288C2×C4×C22⋊C4—131no—
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—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—44no—
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×C13C22×D414yes—
317C23×C13C22×D412yes—
318C23×C13C2×#4112yes—
319C23×C13C2×#4112yes—
320C23×C13C2×#4112yes—
321C23×C13C2×#4112yes—
322C23×C13H(5,𝔽2)12yes—
323C23×C13H(5,𝔽2)12yes—
324C23×C13C2511yescharacteristic
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—44no—
333C22×D13—44no—
334C22×D13—44no—
335C22×D13—44no—
336C22×D13—44no—
337C22×D13—44no—
338C22×D13—44no—
339D4×C13—416no—
340C2×C4×C13—28no—
341C2×C4×C13—22no—
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—44no—
356C2×C4×C13—44no—
357C2×C4×C13—44no—
358C2×C4×C13—44no—
359C2×C4×C13C2×#4114yes—
360C22⋊D13—416no—
361C22⋊D13—416no—
362C2×Dic13—28no—
363C2×Dic13—28no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—232no—
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—44no—
382C2×Dic13—44no—
383C2×Dic13—44no—
384C2×Dic13—44no—
385C2×Dic13#123116yes—
386C2×Dic13C22×D414yes—
387C2×Dic13C22×D414yes—
388C2×Dic13C2×#4114yes—
389C2×Dic13C2×#4114yes—
390C2×Dic13C2×#4114yes—
391C23×D4—131no—
392C23×D4—131no—
393C23×D4C2×D1311yescharacteristic
394C24×C4—131no—
395C2×#121—138no—
396C2×#121—268no—
397C2×#117—138no—
398C2×#117—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⋊C4C2×D1311yescharacteristic
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⋊C4C2×D1311yescharacteristic
417C22×C22⋊C4C2×D1311yescharacteristic
418C22×C22⋊C4C2×D1311yescharacteristic
419C22×C22⋊C4C2×D1311yescharacteristic
420C22×C42—131no—
421C22×C42—131no—
422C22×C42—131no—
423C22×C42—131no—
424#394—138no—
425#394—138no—
426#394—138no—
427#394C2×D1318yescomplemented
428#390—138no—
429#390—138no—
430#388—138no—
431#388—138no—
432#388—138no—
433#388—138no—
434#384—138no—
435#382—138no—
436C4×C22⋊C4—138no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
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—42no—
452C22×C13—42no—
453C22×C13—42no—
454C22×C13—42no—
455C22×C13—42no—
456C22×C13—42no—
457C22×C13—42no—
458C22×C13—88no—
459C22×C13C2×#12314yes—
460C22×C13#53214yes—
461C22×C13#53514yes—
462C22×C13#55314yes—
463C22×C13#55314yes—
464C22×C13#55514yes—
465C22×C13#55514yes—
466C22×C13C23×D411yescharacteristic
467C22×C13C22×#4111yescharacteristic
468C22×C13C22×#4111yescharacteristic
469C22×C13C22×#4111yescharacteristic
470C22×C13C22×#4111yescharacteristic
471C22×C13C2×H(5,𝔽2)11yescharacteristic
472C22×C13C2×H(5,𝔽2)11yescharacteristic
473C2×D13—42no—
474C2×D13—42no—
475C2×D13—42no—
476C2×D13—42no—
477C2×D13—42no—
478C2×D13—42no—
479C2×D13—42no—
480C2×D13—88no—
481C4×C13—24no—
482C4×C13—42no—
483C4×C13—42no—
484C4×C13—42no—
485C4×C13—42no—
486Dic13—24no—
487Dic13—24no—
488Dic13—42no—
489Dic13—42no—
490Dic13—42no—
491Dic13—42no—
492Dic13C2×#12318yes—
493C25—131no—
494C25C22×D1311yescharacteristic
495C25C22×D1311yescharacteristic
496C22×D4—24no—
497C22×D4—42no—
498C22×D4—42no—
499C22×D4—134no—
500C22×D4—134no—
501C22×D4—264no—
502C22×D4—264no—
503C22×D4—264no—
504C22×D4—264no—
505C22×D4—522no—
506C22×D4—522no—
507C22×D4C22×D1314yes—
508C23×C4—131no—
509C23×C4—138no—
510C23×C4—134no—
511C23×C4—131no—
512C23×C4—131no—
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—264no—
518C23×C4—264no—
519C23×C4C22×D1311yescharacteristic
520C23×C4C22×D1311yescharacteristic
521C23×C4C22×D1311yescharacteristic
522C23×C4C22×D1311yescharacteristic
523C23×C4C22×D1311yescharacteristic
524#121—2632no—
525#117—2632no—
526C2×C4⋊C4—42no—
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—264no—
534C2×C4⋊C4—264no—
535C2×C4⋊C4—264no—
536C2×C4⋊C4—522no—
537C2×C4⋊C4—522no—
538C2×C4⋊C4—522no—
539C2×C4⋊C4C22×D1314yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—42no—
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—522no—
562C2×C22⋊C4—522no—
563C2×C22⋊C4—522no—
564C2×C22⋊C4C22×D1314yes—
565C2×C22⋊C4C22×D1314yes—
566C2×C22⋊C4C22×D1314yes—
567C2×C22⋊C4C22×D1314yes—
568C2×C42—134no—
569C2×C42—134no—
570C2×C42—134no—
571C2×C42—134no—
572C2×C42—264no—
573C2×C42—264no—
574C2×C42—264no—
575C2×C42—264no—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—134no—
580#95—134no—
581#95C22×D1314yes—
582C2×C13—44no—
583C2×C13—82no—
584C2×C13#250018yescomplemented
585C2×C13C22×#12311yescharacteristic
586C2×C13C2×#53211yescharacteristic
587C2×C13C2×#53511yescharacteristic
588C2×C13C2×#55311yescharacteristic
589C2×C13C2×#55311yescharacteristic
590C2×C13C2×#55511yescharacteristic
591C2×C13C2×#55511yescharacteristic
592D13—82no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—132no—
607C24—262no—
608C24—262no—
609C24—262no—
610C24—262no—
611C24—262no—
612C24—262no—
613C24—262no—
614C24D4×D1314yes—
615C24C23×D1312yes—
616C24C23×D1312yes—
617C24C23×D1311yescharacteristic
618C2×D4—28no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—416no—
622C2×D4—268no—
623C2×D4—268no—
624C2×D4—268no—
625C2×D4—268no—
626C2×D4—5216no—
627C2×D4—524no—
628C2×D4—524no—
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—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—134no—
645C22×C4—134no—
646C22×C4—134no—
647C22×C4—132no—
648C22×C4—134no—
649C22×C4—1316no—
650C22×C4—134no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—132no—
656C22×C4—132no—
657C22×C4—2632no—
658C22×C4—268no—
659C22×C4—268no—
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—262no—
675C22×C4—262no—
676C22×C4#612914yes—
677C22×C4C23×D1312yes—
678C22×C4C23×D1312yes—
679C22×C4C23×D1312yes—
680C22×C4C23×D1312yes—
681C22×C4C23×D1312yes—
682C4⋊C4—44no—
683C4⋊C4—268no—
684C4⋊C4—268no—
685C4⋊C4—268no—
686C4⋊C4—524no—
687C4⋊C4—524no—
688C4⋊C4—524no—
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—28no—
692C22⋊C4—44no—
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—268no—
704C42—268no—
705C42—268no—
706C42—268no—
707C13C2×#250011yescharacteristic, complemented, Sylow
708C23—28no—
709C23—28no—
710C23—28no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—262no—
736C23—262no—
737C23—262no—
738C23—262no—
739C23—262no—
740C23—262no—
741C23—262no—
742C23—524no—
743C23—524no—
744C23—524no—
745C23—524no—
746C23—524no—
747C23—524no—
748C23—524no—
749C23C2×D4×D1314yes—
750C23C2×D4×D1312yes—
751C23C2×#612912yes—
752C23#8825112yes—
753C23#8825112yes—
754C23#41×D1312yes—
755C23#41×D1312yes—
756C23#41×D1312yes—
757C23C24×D1311yescharacteristic
758D4—416no—
759D4—5216no—
760D4—5216no—
761C2×C4—28no—
762C2×C4—22no—
763C2×C4—22no—
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—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—1316no—
781C2×C4—134no—
782C2×C4—134no—
783C2×C4—134no—
784C2×C4—134no—
785C2×C4—134no—
786C2×C4—2632no—
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—262no—
805C2×C4—524no—
806C2×C4—524no—
807C2×C4—524no—
808C2×C4—524no—
809C2×C4C2×#612914yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—416no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—88no—
826C22—522no—
827C22—522no—
828C22—522no—
829C22—522no—
830C22—522no—
831C22—522no—
832C22—522no—
833C22—1048no—
834C22#1171929714yes—
835C22#1171930114yes—
836C22#1171930614yes—
837C22#1171932114yes—
838C22D13×#12314yes—
839C22#1171936614yes—
840C22#1171937514yes—
841C22C22×D4×D1311yescharacteristic
842C22C22×#612911yescharacteristic
843C22C2×#8825111yescharacteristic
844C22C2×#8825111yescharacteristic
845C22C2×#41×D1311yescharacteristic
846C22C2×#41×D1311yescharacteristic
847C22C2×#41×D1311yescharacteristic
848C4—24no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—138no—
854C4—264no—
855C4—264no—
856C4—522no—
857C4—522no—
858C4—522no—
859C4—522no—
860C2—44no—
861C2—82no—
862C2—1042no—
863C2#1311929318yesdirect product factor
864C2C2×D13×#12311yescharacteristic
865C2C2×#1171930111yescharacteristic
866C2C2×#1171929711yescharacteristic
867C2C2×#1171930611yescharacteristic
868C2C2×#1171936611yescharacteristic
869C2C2×#1171937511yescharacteristic
870C2C2×#1171932111yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#394C2
socleC24×C13C24
prime radicalC22×#88193C2
hypercenterC2×#394D13
hypocenterC13C2×#2500
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#88131C2semidirect
3. #13119293C2direct (N × H)
4. C2×#11718622C2semidirect
5. C2×#11718620C2semidirect
6. C2×#11718883C2semidirect
7. C2×#11718618C2semidirect
8. C2×#11718618C2semidirect
9. C2×#11718606C2semidirect
10. C2×#11718612C2semidirect
11. C2×#11718651C2semidirect
12. C2×#11718330C2semidirect
13. C2×#11718637C2semidirect
14. C2×#11718311C2semidirect
15. C2×C22⋊C4×Dic13C2semidirect
16. C2×C13×#394C2semidirect
49. C2×#88131C22semidirect
50. C13×#394C22semidirect
52. #11718883C22semidirect
58. #11718651C22semidirect
59. #11718637C22semidirect
60. #11718622C22semidirect
61. #11718620C22semidirect
62. #11718618C22semidirect
63. #11718618C22semidirect
64. #11718612C22semidirect
65. #11718606C22semidirect
66. C22⋊C4×Dic13C22semidirect
67. #11718330C22semidirect
68. #11718311C22semidirect
279. C2×#394D13semidirect
427. #394C2×D13semidirect
584. C2×C13#2500semidirect
707. C13C2×#2500semidirect
863. C2#13119293direct (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×#881312
#131192932
C2×#117186222
C2×#117186202
C2×#117188832
C2×#117186182
C2×#117186062
C2×#117186122
C2×#117186512
C2×#117183302
C2×#117186372
C2×#117183112
C2×C22⋊C4×Dic132
C2×C13×#3942
C2×#250013