Finite Group Databasebeta

← C2×#13118582 #16030652

Subgroups — C2×#13118582 #16030652

Order 3328.

3546 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic13C211yesmaximal, characteristic, complemented
2#13118582C2116yesmaximal, direct product factor
3C2×#11718647C211yesmaximal, characteristic, complemented
4C2×#11718613C211yesmaximal, characteristic, complemented
5C2×#11718614C211yesmaximal, characteristic, complemented
6C2×#11718883C211yesmaximal, characteristic, complemented
7C2×#11718605C211yesmaximal, characteristic, complemented
8C2×#11718639C211yesmaximal, characteristic, complemented
9C2×#11718881C211yesmaximal, characteristic, complemented
10C2×#11718881C211yesmaximal, characteristic, complemented
11C2×#11718881C211yesmaximal, characteristic, complemented
12C2×#11718881C211yesmaximal, characteristic, complemented
13C2×#11718871C211yesmaximal, characteristic, complemented
14C2×#11718604C211yesmaximal, characteristic, complemented
15C22×#88071C211yesmaximal, characteristic, complemented
16C22×C13×#121C211yesmaximal, characteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C23×D4×C13C2211yescharacteristic
20C24×C4×C13C2211yescharacteristic
21C24×Dic13C2211yescharacteristic
22C24×Dic13C2211yescharacteristic
23C24×Dic13C2211yescharacteristic
24C2×C13×#121—28no—
25C2×C13×#121C2218yes—
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C22⋊Dic13C2211yescharacteristic
35C22×C22⋊Dic13C2211yescharacteristic
36C22×C22⋊Dic13C2211yescharacteristic
37C22×C22⋊Dic13C2211yescharacteristic
38C2×D4×Dic13—28no—
39C2×D4×Dic13C2218yescomplemented
40C22×C4⋊Dic13C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44#11718883C2218yescomplemented
45#11718881C2218yescomplemented
46#11718881C2218yescomplemented
47#11718881C2218yescomplemented
48#11718881C2218yescomplemented
49#11718871C2218yescomplemented
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62C2×#88071C2218yescomplemented
63#11718647C2218yescomplemented
64#11718639C2218yescomplemented
65#11718614C2218yescomplemented
66#11718613C2218yescomplemented
67#11718605C2218yescomplemented
68#11718604C2218yescomplemented
69C25×C13C2311yescharacteristic
70C25×C13C2311yescharacteristic
71C25×C13C2311yescharacteristic
72C22×D4×C13—24no—
73C22×D4×C13—24no—
74C22×D4×C13—24no—
75C22×D4×C13—24no—
76C22×D4×C13—24no—
77C22×D4×C13—24no—
78C22×D4×C13—24no—
79C22×D4×C13—42no—
80C22×D4×C13D418yes—
81C22×D4×C13C2314yes—
82C22×D4×C13C2314yes—
83C22×D4×C13C2314yes—
84C23×C4×C13—24no—
85C23×C4×C13—24no—
86C23×C4×C13—42no—
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2314yes—
90C23×C4×C13C2311yescharacteristic
91C23×C4×C13C2311yescharacteristic
92C23×Dic13—24no—
93C23×Dic13—24no—
94C23×Dic13—24no—
95C23×Dic13—24no—
96C23×Dic13—24no—
97C23×Dic13—42no—
98C23×Dic13—42no—
99C23×Dic13—42no—
100C23×Dic13—42no—
101C23×Dic13C2311yescharacteristic
102C23×Dic13C2311yescharacteristic
103C23×Dic13C2311yescharacteristic
104C23×Dic13C2311yescharacteristic
105C23×Dic13C2311yescharacteristic
106C23×Dic13C2311yescharacteristic
107C23×Dic13C2311yescharacteristic
108C23×Dic13C2314yes—
109C23×Dic13C2314yes—
110C23×Dic13C2311yescharacteristic
111C23×Dic13C2314yes—
112C13×#121—232no—
113C2×C13×C4⋊C4—24no—
114C2×C13×C4⋊C4C2314yes—
115C2×C13×C22⋊C4—24no—
116C2×C13×C22⋊C4—24no—
117C2×C13×C22⋊C4C2314yes—
118C2×C13×C22⋊C4C2314yes—
119C2×C22⋊Dic13—24no—
120C2×C22⋊Dic13—24no—
121C2×C22⋊Dic13—24no—
122C2×C22⋊Dic13—24no—
123C2×C22⋊Dic13—42no—
124C2×C22⋊Dic13—42no—
125C2×C22⋊Dic13—42no—
126C2×C22⋊Dic13—42no—
127C2×C22⋊Dic13—42no—
128C2×C22⋊Dic13C2314yes—
129C2×C22⋊Dic13C2314yes—
130C2×C22⋊Dic13C2314yes—
131C2×C22⋊Dic13C2314yes—
132C2×C22⋊Dic13C2314yes—
133C2×C22⋊Dic13C2314yes—
134C2×C22⋊Dic13C2314yes—
135C2×C22⋊Dic13C2314yes—
136C2×C22⋊Dic13C2314yes—
137D4×Dic13—232no—
138C2×C4⋊Dic13—24no—
139C2×C4⋊Dic13C2314yes—
140C2×#6101—24no—
141C2×#6101—42no—
142C2×#6101C2314yes—
143C2×#6101C2314yes—
144C2×C4×Dic13—24no—
145C2×C4×Dic13C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2444—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—22no—
173C24×C13—22no—
174C24×C13—22no—
175C24×C13—22no—
176C24×C13C2×D414yes—
177C24×C13C2×D414yes—
178C24×C13#4114yes—
179C24×C13#4114yes—
180C24×C13C2412yes—
181C24×C13C2412yes—
182C24×C13C2412yes—
183C24×C13C2411yescharacteristic
184C2×D4×C13—232no—
185C2×D4×C13—28no—
186C2×D4×C13—28no—
187C2×D4×C13—28no—
188C2×D4×C13—28no—
189C2×D4×C13—28no—
190C2×D4×C13—28no—
191C2×D4×C13—28no—
192C2×D4×C13—44no—
193C2×D4×C13—416no—
194C2×D4×C13—416no—
195C2×D4×C13C2×D4116yes—
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—28no—
203C22×C4×C13—22no—
204C22×C4×C13—22no—
205C22×C4×C13—22no—
206C22×C4×C13—22no—
207C22×C4×C13—28no—
208C22×C4×C13—44no—
209C22×C4×C13—416no—
210C22×C4×C13C2×D414yes—
211C22×C4×C13#4114yes—
212C22×C4×C13C2412yes—
213C22×C4×C13C2412yes—
214C22×C4×C13C2412yes—
215C22×C4×C13C2412yes—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—28no—
222C22×Dic13—28no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—28no—
229C22×Dic13—22no—
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—44no—
246C22×Dic13—44no—
247C22×Dic13—44no—
248C22×Dic13—416no—
249C22×Dic13—416no—
250C22×Dic13—416no—
251C22×Dic13#4114yes—
252C22×Dic13C2412yes—
253C22×Dic13C2412yes—
254C22×Dic13C2412yes—
255C22×Dic13C2412yes—
256C22×Dic13C2412yes—
257C22×Dic13C2412yes—
258C22×Dic13C2412yes—
259C22×Dic13C2412yes—
260C13×C4⋊C4—28no—
261C13×C22⋊C4—28no—
262C13×C22⋊C4—28no—
263C22⋊Dic13—28no—
264C22⋊Dic13—28no—
265C22⋊Dic13—28no—
266C22⋊Dic13—28no—
267C22⋊Dic13—44no—
268C22⋊Dic13—44no—
269C22⋊Dic13—44no—
270C22⋊Dic13—44no—
271C22⋊Dic13—44no—
272C4⋊Dic13—28no—
273#6101—28no—
274#6101—44no—
275C4×Dic13—28no—
276C22×#121D1311yescharacteristic
277C22×C4×D4—131no—
278#2444—1316no—
279C2×#400—131no—
280C2×#397—131no—
281C2×#397—131no—
282C2×#394—131no—
283C2×#388—131no—
284C2×#387—131no—
285C2×#386—131no—
286C2×#386—131no—
287C2×#386—131no—
288C2×#386—131no—
289C2×#385—131no—
290C2×#381—131no—
291C22×#95—131no—
292C23×C13—28no—
293C23×C13—28no—
294C23×C13—28no—
295C23×C13—28no—
296C23×C13—28no—
297C23×C13—28no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—28no—
303C23×C13—28no—
304C23×C13—28no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—44no—
319C23×C13—44no—
320C23×C13—44no—
321C23×C13—44no—
322C23×C13—44no—
323C23×C13—44no—
324C23×C13—44no—
325C23×C13—44no—
326C23×C13—44no—
327C23×C13—44no—
328C23×C13—44no—
329C23×C13#123116yes—
330C23×C13C22×D414yes—
331C23×C13C22×D414yes—
332C23×C13C22×D412yes—
333C23×C13C2×#4114yes—
334C23×C13C2×#4114yes—
335C23×C13C2×#4112yes—
336C23×C13C2×#4112yes—
337C23×C13C2×#4112yes—
338C23×C13C2×#4112yes—
339C23×C13H(5,𝔽2)12yes—
340C23×C13H(5,𝔽2)12yes—
341C23×C13C2511yescharacteristic
342D4×C13—232no—
343D4×C13—416no—
344D4×C13—416no—
345C2×C4×C13—28no—
346C2×C4×C13—28no—
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×C13C22×D414yes—
361C2×C4×C13C2×#4114yes—
362C2×Dic13—28no—
363C2×Dic13—22no—
364C2×Dic13—22no—
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—22no—
385C2×Dic13—22no—
386C2×Dic13—416no—
387C2×Dic13—416no—
388C2×Dic13—416no—
389C2×Dic13—44no—
390C2×Dic13—44no—
391C2×Dic13—44no—
392C2×Dic13—44no—
393C2×Dic13—44no—
394C2×Dic13—44no—
395C2×Dic13—44no—
396C2×Dic13C2×#4114yes—
397C23×D4C2×D1311yescharacteristic
398C23×D4C2×D1311yescharacteristic
399C23×D4C2×D1311yescharacteristic
400C24×C4—131no—
401C24×C4—131no—
402C24×C4—131no—
403C24×C4C2×D1311yescharacteristic
404C2×#121—28no—
405C2×#121C2×D1318yes—
406C2×C4×D4—138no—
407C2×C4×D4—268no—
408C22×C4⋊C4—131no—
409C22×C4⋊C4—131no—
410C22×C4⋊C4—131no—
411C22×C4⋊C4C2×D1311yescharacteristic
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⋊C4—131no—
419C22×C22⋊C4—131no—
420C22×C22⋊C4—131no—
421C22×C22⋊C4C2×D1311yescharacteristic
422C22×C22⋊C4C2×D1311yescharacteristic
423C22×C42—131no—
424#400—138no—
425#397—138no—
426#397—138no—
427#394—138no—
428#388—138no—
429#387—138no—
430#386—138no—
431#386—138no—
432#386—138no—
433#386—138no—
434#385—138no—
435#381—138no—
436C2×#95—131no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C2×#95—131no—
445C2×#95—138no—
446C2×#95—131no—
447C2×#95—131no—
448C2×#95—131no—
449C22×C13—24no—
450C22×C13—24no—
451C22×C13—24no—
452C22×C13—24no—
453C22×C13—232no—
454C22×C13—24no—
455C22×C13—24no—
456C22×C13—24no—
457C22×C13—24no—
458C22×C13—24no—
459C22×C13—42no—
460C22×C13—42no—
461C22×C13—416no—
462C22×C13—42no—
463C22×C13—42no—
464C22×C13—42no—
465C22×C13—42no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—88no—
472C22×C13C2×#12318yes—
473C22×C13C2×#12314yes—
474C22×C13#52914yes—
475C22×C13#53814yes—
476C22×C13#54614yes—
477C22×C13#54614yes—
478C22×C13#55314yes—
479C22×C13#55314yes—
480C22×C13C23×D411yescharacteristic
481C22×C13C22×#4111yescharacteristic
482C22×C13C22×#4111yescharacteristic
483C22×C13C22×#4111yescharacteristic
484C22×C13C22×#4111yescharacteristic
485C22×C13C2×H(5,𝔽2)11yescharacteristic
486C22×C13C2×H(5,𝔽2)11yescharacteristic
487C4×C13—24no—
488C4×C13—24no—
489C4×C13—42no—
490C4×C13—42no—
491Dic13—24no—
492Dic13—42no—
493Dic13—42no—
494Dic13—42no—
495Dic13—42no—
496Dic13—42no—
497Dic13—42no—
498Dic13—42no—
499C25C22×D1311yescharacteristic
500C25C22×D1311yescharacteristic
501C25C22×D1311yescharacteristic
502C22×D4—24no—
503C22×D4—24no—
504C22×D4—24no—
505C22×D4—24no—
506C22×D4—24no—
507C22×D4—24no—
508C22×D4—24no—
509C22×D4—42no—
510C22×D4C22⋊D1318yes—
511C22×D4C22×D1314yes—
512C22×D4C22×D1314yes—
513C22×D4C22×D1314yes—
514C23×C4—24no—
515C23×C4—24no—
516C23×C4—42no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4—131no—
520C23×C4—131no—
521C23×C4—131no—
522C23×C4—131no—
523C23×C4—131no—
524C23×C4—131no—
525C23×C4—134no—
526C23×C4—134no—
527C23×C4—134no—
528C23×C4—264no—
529C23×C4—264no—
530C23×C4—264no—
531C23×C4—264no—
532C23×C4—264no—
533C23×C4—522no—
534C23×C4—522no—
535C23×C4—522no—
536C23×C4—522no—
537C23×C4C22×D1311yescharacteristic
538C23×C4C22×D1311yescharacteristic
539C23×C4C22×D1314yes—
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542#121—232no—
543C4×D4—2632no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—134no—
546C2×C4⋊C4—134no—
547C2×C4⋊C4—134no—
548C2×C4⋊C4—264no—
549C2×C4⋊C4—264no—
550C2×C4⋊C4—522no—
551C2×C4⋊C4C22×D1314yes—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—134no—
555C2×C22⋊C4—134no—
556C2×C22⋊C4—134no—
557C2×C22⋊C4—134no—
558C2×C22⋊C4—134no—
559C2×C22⋊C4—134no—
560C2×C22⋊C4—134no—
561C2×C22⋊C4—134no—
562C2×C22⋊C4—134no—
563C2×C22⋊C4—264no—
564C2×C22⋊C4—264no—
565C2×C22⋊C4—264no—
566C2×C22⋊C4—264no—
567C2×C22⋊C4—522no—
568C2×C22⋊C4—522no—
569C2×C22⋊C4—522no—
570C2×C22⋊C4—522no—
571C2×C22⋊C4—522no—
572C2×C22⋊C4C22×D1314yes—
573C2×C22⋊C4C22×D1314yes—
574C2×C42—134no—
575C2×C42—264no—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—134no—
580#95—134no—
581#95—134no—
582#95—134no—
583#95—134no—
584#95—134no—
585#95—134no—
586#95—134no—
587#95—134no—
588C2×C13—28no—
589C2×C13—44no—
590C2×C13—82no—
591C2×C13#244418yescomplemented
592C2×C13C22×#12311yescharacteristic
593C2×C13C2×#52911yescharacteristic
594C2×C13C2×#53811yescharacteristic
595C2×C13C2×#54611yescharacteristic
596C2×C13C2×#54611yescharacteristic
597C2×C13C2×#55311yescharacteristic
598C2×C13C2×#55311yescharacteristic
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24#612914yes—
617C24#612914yes—
618C24C2×C22⋊D1314yes—
619C24C2×C22⋊D1314yes—
620C24C23×D1312yes—
621C24C23×D1312yes—
622C24C23×D1312yes—
623C24C23×D1311yescharacteristic
624C2×D4—232no—
625C2×D4—28no—
626C2×D4—28no—
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—28no—
631C2×D4—28no—
632C2×D4—44no—
633C2×D4—416no—
634C2×D4—416no—
635C2×D4C2×C22⋊D13116yes—
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—22no—
645C22×C4—22no—
646C22×C4—28no—
647C22×C4—28no—
648C22×C4—44no—
649C22×C4—416no—
650C22×C4—134no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—132no—
656C22×C4—132no—
657C22×C4—132no—
658C22×C4—132no—
659C22×C4—268no—
660C22×C4—268no—
661C22×C4—262no—
662C22×C4—262no—
663C22×C4—262no—
664C22×C4—262no—
665C22×C4—262no—
666C22×C4—262no—
667C22×C4—268no—
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—262no—
677C22×C4—262no—
678C22×C4—262no—
679C22×C4—262no—
680C22×C4—262no—
681C22×C4—262no—
682C22×C4—262no—
683C22×C4—262no—
684C22×C4—262no—
685C22×C4—268no—
686C22×C4—268no—
687C22×C4—524no—
688C22×C4—524no—
689C22×C4—524no—
690C22×C4—524no—
691C22×C4—5216no—
692C22×C4—5216no—
693C22×C4—5216no—
694C22×C4#612914yes—
695C22×C4C2×C22⋊D1314yes—
696C22×C4C23×D1312yes—
697C22×C4C23×D1312yes—
698C22×C4C23×D1312yes—
699C22×C4C23×D1312yes—
700C4⋊C4—28no—
701C4⋊C4—268no—
702C4⋊C4—268no—
703C4⋊C4—524no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—268no—
707C22⋊C4—268no—
708C22⋊C4—268no—
709C22⋊C4—268no—
710C22⋊C4—524no—
711C22⋊C4—524no—
712C22⋊C4—524no—
713C22⋊C4—524no—
714C22⋊C4—524no—
715C42—268no—
716C13C2×#244411yescharacteristic, complemented, Sylow
717C23—28no—
718C23—28no—
719C23—28no—
720C23—28no—
721C23—28no—
722C23—28no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23#88189116yes—
755C23C2×#612914yes—
756C23C2×#612914yes—
757C23C2×#612912yes—
758C23C2×#612912yes—
759C23C2×#612912yes—
760C23#8825112yes—
761C23#41×D1312yes—
762C23#8825612yes—
763C23C22×C22⋊D1314yes—
764C23C22×C22⋊D1314yes—
765C23C22×C22⋊D1312yes—
766C23C24×D1311yescharacteristic
767D4—232no—
768D4—416no—
769D4—416no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—416no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—134no—
786C2×C4—268no—
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—262no—
805C2×C4—262no—
806C2×C4—262no—
807C2×C4—262no—
808C2×C4—262no—
809C2×C4—262no—
810C2×C4—5216no—
811C2×C4—5216no—
812C2×C4—5216no—
813C2×C4—524no—
814C2×C4—524no—
815C2×C4—524no—
816C2×C4—524no—
817C2×C4—524no—
818C2×C4—524no—
819C2×C4—524no—
820C2×C4C2×#612914yes—
821C2×C4C22×C22⋊D1314yes—
822C22—24no—
823C22—24no—
824C22—232no—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—24no—
829C22—24no—
830C22—24no—
831C22—24no—
832C22—416no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—88no—
845C22#1171930514yes—
846C22#1171930614yes—
847C22#1171932214yes—
848C22#1171932314yes—
849C22C2×#8818918yes—
850C22C2×#8818914yes—
851C22#1171951114yes—
852C22#1171953414yes—
853C22C22×#612911yescharacteristic
854C22C22×#612911yescharacteristic
855C22C22×#612911yescharacteristic
856C22C2×#8825111yescharacteristic
857C22C2×#41×D1311yescharacteristic
858C22C2×#8825611yescharacteristic
859C22C23×C22⋊D1311yescharacteristic
860C4—24no—
861C4—24no—
862C4—42no—
863C4—42no—
864C4—264no—
865C4—522no—
866C4—522no—
867C4—522no—
868C4—522no—
869C4—522no—
870C4—522no—
871C4—522no—
872C2—28no—
873C2—44no—
874C2—82no—
875C2#1311858218yesdirect product factor
876C2C22×#8818911yescharacteristic
877C2C2×#1171930511yescharacteristic
878C2C2×#1171932211yescharacteristic
879C2C2×#1171953411yescharacteristic
880C2C2×#1171951111yescharacteristic
881C2C2×#1171930611yescharacteristic
882C2C2×#1171932311yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
Fitting, prime radicalC22×C13×#121C2
socleC24×C13C24
hypercenterC22×#121D13
hypocenterC13C2×#2444
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic13C2semidirect
2. #13118582C2direct (N × H)
3. C2×#11718647C2semidirect
4. C2×#11718613C2semidirect
5. C2×#11718614C2semidirect
6. C2×#11718883C2semidirect
7. C2×#11718605C2semidirect
8. C2×#11718639C2semidirect
9. C2×#11718881C2semidirect
10. C2×#11718881C2semidirect
11. C2×#11718881C2semidirect
12. C2×#11718881C2semidirect
13. C2×#11718871C2semidirect
14. C2×#11718604C2semidirect
15. C22×#88071C2semidirect
39. C2×D4×Dic13C22semidirect
44. #11718883C22semidirect
45. #11718881C22semidirect
46. #11718881C22semidirect
47. #11718881C22semidirect
48. #11718881C22semidirect
49. #11718871C22semidirect
62. C2×#88071C22semidirect
63. #11718647C22semidirect
64. #11718639C22semidirect
65. #11718614C22semidirect
66. #11718613C22semidirect
67. #11718605C22semidirect
68. #11718604C22semidirect
591. C2×C13#2444semidirect
716. C13C2×#2444semidirect
875. C2#13118582direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×Dic132
#131185822
C2×#117186472
C2×#117186132
C2×#117186142
C2×#117188832
C2×#117186052
C2×#117186392
C2×#117188812
C2×#117188712
C2×#117186042
C22×#880712
C22×C13×#1212
C2×#244413