Finite Group Databasebeta

← C2×#13118286 #16030873

Subgroups — C2×#13118286 #16030873

Order 3328.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88150C211yesmaximal, characteristic, complemented
2C22×#88132C211yesmaximal, characteristic, complemented
3C22×#88135C211yesmaximal, characteristic
4C23×#6101C211yesmaximal, characteristic, complemented
5#13118286C2116yesmaximal, direct product factor
6C2×#11718318C211yesmaximal, characteristic, complemented
7C2×#11718641C211yesmaximal, characteristic, complemented
8C2×#11718337C211yesmaximal, characteristic, complemented
9C2×#11718655C211yesmaximal, characteristic, complemented
10C2×#11718307C211yesmaximal, characteristic, complemented
11C2×#11718633C211yesmaximal, characteristic, complemented
12C2×#11718874C211yesmaximal, characteristic
13C2×#11718619C211yesmaximal, characteristic
14C2×#11718328C211yesmaximal, characteristic, complemented
15C2×#11718603C211yesmaximal, characteristic, complemented
16C2×C13×#380C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×Dic26C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C22×#6101—28no—
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×#6101C2218yescomplemented
45C22×C4×Dic13C2211yescharacteristic
46C2×#88150—28no—
47C2×#88150C2218yescomplemented
48C2×#88135—28no—
49C2×#88135C2218yes—
50C2×#88132—28no—
51C2×#88132C2218yescomplemented
52C13×#380C2218yescomplemented
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55#11718874C2218yes—
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62#11718655C2218yescomplemented
63#11718641C2218yescomplemented
64#11718633C2218yescomplemented
65#11718619C2218yes—
66#11718603C2218yescomplemented
67#11718337C2218yescomplemented
68#11718328C2218yescomplemented
69#11718318C2218yescomplemented
70#11718307C2218yescomplemented
71C25×C13C2311yescharacteristic
72C24×D13C2311yescharacteristic
73C23×C4×C13—24no—
74C23×C4×C13—24no—
75C23×C4×C13—42no—
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2314yes—
82C23×C4×C13C2311yescharacteristic
83C22×C22⋊D13—24no—
84C22×C22⋊D13—24no—
85C22×C22⋊D13Q818yescomplemented
86C22×C22⋊D13C2314yes—
87C23×Dic13—24no—
88C23×Dic13—24no—
89C23×Dic13—24no—
90C23×Dic13—24no—
91C23×Dic13—42no—
92C23×Dic13D418yes—
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2314yes—
97C23×Dic13C2314yes—
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2311yescharacteristic
102C22×C4×D13—24no—
103C22×C4×D13—24no—
104C22×C4×D13—24no—
105C22×C4×D13C2314yes—
106C22×Dic26—24no—
107C22×Dic26—24no—
108C22×Dic26—24no—
109C22×Dic26C2314yes—
110C2×C13×C4⋊C4—24no—
111C2×C13×C4⋊C4—42no—
112C2×C13×C4⋊C4C2314yes—
113C2×C13×C4⋊C4C2314yes—
114C2×C13×C22⋊C4—24no—
115C2×C13×C22⋊C4—24no—
116C2×C13×C22⋊C4C2314yes—
117C2×C13×C22⋊C4C2314yes—
118C2×C22⋊Dic13—24no—
119C2×C22⋊Dic13C2314yes—
120C2×#6103—24no—
121C2×#6103—24no—
122C2×#6103—24no—
123C2×#6103—42no—
124C2×#6103—42no—
125C2×#6103C2314yes—
126C2×#6103C2314yes—
127C2×#6103C2314yes—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×C4⋊Dic13—24no—
131C2×C4⋊Dic13C2314yes—
132C2×#6101—24no—
133C2×#6101—24no—
134C2×#6101—24no—
135C2×#6101—24no—
136C2×#6101—24no—
137C2×#6101—24no—
138C2×#6101—24no—
139C2×#6101—232no—
140C2×#6101—42no—
141C2×#6101D418yescomplemented
142C2×#6101C2314yes—
143C2×#6101C2314yes—
144C2×#6101C2314yes—
145C2×#6101C2314yes—
146C2×#6101C2314yes—
147C2×#6101C2314yes—
148C2×#6101C2314yes—
149C2×#6101C2314yes—
150C2×#6101C2314yes—
151C2×C4×Dic13—24no—
152C2×C4×Dic13C2314yes—
153#88150—232no—
154#88135—232no—
155#88132—232no—
156C13×#95C2314yes—
157C13×#95C2314yes—
158#88071C2314yes—
159#88071C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164C2×#2417—131nomaximal, Sylow
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13C2×D414yes—
170C24×C13C2×Q814yes—
171C24×C13#4114yes—
172C24×C13C2412yes—
173C24×C13C2411yescharacteristic
174C23×D13—22no—
175C23×D13—22no—
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13C2×Q814yes—
181C23×D13C2412yes—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
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—28no—
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—28no—
201C22×C4×C13—44no—
202C22×C4×C13—416no—
203C22×C4×C13C2×D414yes—
204C22×C4×C13C2412yes—
205C22×C4×C13C2412yes—
206C22×C4×C13C2412yes—
207C22×C4×C13C2412yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C2×C22⋊D13—232no—
211C2×C22⋊D13—28no—
212C2×C22⋊D13—28no—
213C2×C22⋊D13C2×Q8116yescomplemented
214C22×Dic13—22no—
215C22×Dic13—22no—
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—28no—
229C22×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—28no—
234C22×Dic13—44no—
235C22×Dic13—416no—
236C22×Dic13C2×D4116yes—
237C22×Dic13C2×D414yes—
238C22×Dic13C2×D414yes—
239C22×Dic13C2×D414yes—
240C22×Dic13C2×D414yes—
241C22×Dic13C2×Q814yes—
242C22×Dic13#4114yes—
243C22×Dic13C2412yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C22×Dic13C2412yes—
249C22×Dic13C2412yes—
250C2×C4×D13—28no—
251C2×C4×D13—28no—
252C2×C4×D13—28no—
253C2×C4×D13—416no—
254C2×Dic26—28no—
255C2×Dic26—28no—
256C2×Dic26—28no—
257C2×Dic26—416no—
258C13×C4⋊C4—28no—
259C13×C4⋊C4—44no—
260C13×C22⋊C4—28no—
261C13×C22⋊C4—28no—
262C22⋊Dic13—28no—
263#6103—28no—
264#6103—28no—
265#6103—28no—
266#6103—44no—
267#6103—44no—
268C4⋊Dic13—28no—
269#6101—28no—
270#6101—28no—
271#6101—28no—
272#6101—28no—
273#6101—28no—
274#6101—28no—
275#6101—28no—
276#6101—44no—
277#6101C2×D4116yescomplemented
278C4×Dic13—28no—
279C22×C22⋊Q8—131no—
280C22×C22⋊Q8—131no—
281C22×C4×D4—131no—
282C23×C4⋊C4—131no—
283#2417—1316no—
284C2×#398—131no—
285C2×#398—131no—
286C2×#396—131no—
287C2×#396—131no—
288C2×#391—131no—
289C2×#389—131no—
290C2×#386—131no—
291C2×#386—131no—
292C2×#380—131no—
293C2×#380—131no—
294C2×#380D1311yescharacteristic, complemented
295C23×C13—28no—
296C23×C13—28no—
297C23×C13—28no—
298C23×C13—28no—
299C23×C13—28no—
300C23×C13—28no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13C22⋊Q8116yescomplemented
306C23×C13C22×D414yes—
307C23×C13C22×D412yes—
308C23×C13C22×D412yes—
309C23×C13C22×Q814yes—
310C23×C13C22×Q812yes—
311C23×C13C2×#4114yes—
312C23×C13C2×#4112yes—
313C23×C13C2×#4112yes—
314C23×C13H(5,𝔽2)12yes—
315C23×C132−1+412yes—
316C23×C13C2511yescharacteristic
317C22×D13—28no—
318C22×D13—28no—
319C22×D13—28no—
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—44no—
327C22×D13—44no—
328C22×D13—44no—
329C22×D13—44no—
330C22×D13C22×Q814yes—
331C2×C4×C13—28no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
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—416no—
350C2×C4×C13—44no—
351C2×C4×C13—44no—
352C2×C4×C13—44no—
353C2×C4×C13—44no—
354C2×C4×C13—44no—
355C2×C4×C13C22×D414yes—
356C22⋊D13—232no—
357C2×Dic13—28no—
358C2×Dic13—28no—
359C2×Dic13—28no—
360C2×Dic13—22no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—232no—
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—416no—
377C2×Dic13—44no—
378C2×Dic13—44no—
379C2×Dic13—44no—
380C2×Dic13#121116yes—
381C2×Dic13C22×D414yes—
382C2×Dic13C22×D414yes—
383C2×Dic13C22×D414yes—
384C2×Dic13C22×D414yes—
385C2×Dic13C22×Q814yes—
386C2×Dic13C2×#4114yes—
387C4×D13—416no—
388Dic26—416no—
389C23×Q8—131no—
390C23×D4—131no—
391C24×C4—131no—
392C24×C4—131no—
393C24×C4—131no—
394C24×C4C2×D1311yescharacteristic
395C2×C22⋊Q8—138no—
396C2×C22⋊Q8—138no—
397C2×C22⋊Q8—268no—
398C2×C22⋊Q8—268no—
399C2×C4×D4—138no—
400C2×C4×D4—268no—
401C22×C4⋊C4—131no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4—131no—
405C22×C4⋊C4—131no—
406C22×C4⋊C4—131no—
407C22×C4⋊C4—131no—
408C22×C4⋊C4—131no—
409C22×C4⋊C4—138no—
410C22×C4⋊C4—131no—
411C22×C4⋊C4—131no—
412C22×C4⋊C4—268no—
413C22×C4⋊C4C2×D1311yescharacteristic
414C22×C4⋊C4C2×D1311yescharacteristic
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#398—138no—
425#398—138no—
426#396—138no—
427#396—138no—
428#391—138no—
429#389—138no—
430#386—138no—
431#386—138no—
432#380—138no—
433#380—138no—
434#380C2×D1318yescomplemented
435C2×#95—131no—
436C2×#95—131no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95C2×D1311yescharacteristic
442C2×#95C2×D1311yescharacteristic
443C22×C13—24no—
444C22×C13—232no—
445C22×C13—24no—
446C22×C13—24no—
447C22×C13—24no—
448C22×C13—24no—
449C22×C13—24no—
450C22×C13C2×#12114yes—
451C22×C13C2×C22⋊Q814yes—
452C22×C13C2×C22⋊Q818yescomplemented
453C22×C13#53714yes—
454C22×C13#54614yes—
455C22×C13D4×Q814yes—
456C22×C13#55214yes—
457C22×C13#55414yes—
458C22×C13C23×D411yescharacteristic
459C22×C13C23×D411yescharacteristic
460C22×C13C23×Q811yescharacteristic
461C22×C13C22×#4111yescharacteristic
462C22×C13C22×#4111yescharacteristic
463C22×C13C2×H(5,𝔽2)11yescharacteristic
464C22×C13C2×2−1+411yescharacteristic
465C2×D13—24no—
466C2×D13—24no—
467C2×D13—24no—
468C2×D13—42no—
469C2×D13—416no—
470C2×D13—42no—
471C2×D13—42no—
472C2×D13—42no—
473C4×C13—24no—
474C4×C13—42no—
475C4×C13—42no—
476C4×C13—42no—
477C4×C13—42no—
478C4×C13—42no—
479Dic13—24no—
480Dic13—24no—
481Dic13—24no—
482Dic13—42no—
483Dic13—42no—
484Dic13—42no—
485Dic13C2×#12118yes—
486C25—131no—
487C25C22×D1311yescharacteristic
488C22×Q8—134no—
489C22×Q8—264no—
490C22×Q8—264no—
491C22×Q8—264no—
492C22×D4—138no—
493C22×D4—134no—
494C22×D4—264no—
495C22×D4—264no—
496C23×C4—24no—
497C23×C4—24no—
498C23×C4—42no—
499C23×C4—131no—
500C23×C4—138no—
501C23×C4—134no—
502C23×C4—131no—
503C23×C4—131no—
504C23×C4—131no—
505C23×C4—131no—
506C23×C4—131no—
507C23×C4—131no—
508C23×C4—134no—
509C23×C4—134no—
510C23×C4—264no—
511C23×C4—264no—
512C23×C4—264no—
513C23×C4—264no—
514C23×C4—264no—
515C23×C4—264no—
516C23×C4—264no—
517C23×C4—522no—
518C23×C4C22×D1311yescharacteristic
519C23×C4C22×D1311yescharacteristic
520C23×C4C22×D1311yescharacteristic
521C23×C4C22×D1311yescharacteristic
522C23×C4C22×D1311yescharacteristic
523C23×C4C22×D1314yes—
524C23×C4C22×D1311yescharacteristic
525C22⋊Q8—2632no—
526C22⋊Q8—2632no—
527C4×D4—2632no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—42no—
530C2×C4⋊C4—138no—
531C2×C4⋊C4—134no—
532C2×C4⋊C4—134no—
533C2×C4⋊C4—134no—
534C2×C4⋊C4—134no—
535C2×C4⋊C4—134no—
536C2×C4⋊C4—134no—
537C2×C4⋊C4—134no—
538C2×C4⋊C4—134no—
539C2×C4⋊C4—134no—
540C2×C4⋊C4—134no—
541C2×C4⋊C4—2632no—
542C2×C4⋊C4—264no—
543C2×C4⋊C4—264no—
544C2×C4⋊C4—264no—
545C2×C4⋊C4—264no—
546C2×C4⋊C4—264no—
547C2×C4⋊C4—264no—
548C2×C4⋊C4—264no—
549C2×C4⋊C4—264no—
550C2×C4⋊C4—522no—
551C2×C4⋊C4C22×D1314yes—
552C2×C4⋊C4C22×D1314yes—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
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—264no—
562C2×C22⋊C4—264no—
563C2×C22⋊C4—264no—
564C2×C22⋊C4—264no—
565C2×C22⋊C4—522no—
566C2×C22⋊C4—522no—
567C2×C22⋊C4C22×D1314yes—
568C2×C22⋊C4C22×D1314yes—
569C2×C42—134no—
570C2×C42—264no—
571#95—134no—
572#95—134no—
573#95—134no—
574#95—134no—
575#95—134no—
576#95—134no—
577#95C22×D1314yes—
578#95C22×D1314yes—
579C2×C13—28no—
580C2×C13#241718yescomplemented
581C2×C13C22×#12111yescharacteristic
582C2×C13C22×C22⋊Q811yescharacteristic
583C2×C13C2×#53711yescharacteristic
584C2×C13C2×#54611yescharacteristic
585C2×C13C2×D4×Q811yescharacteristic
586C2×C13C2×#55211yescharacteristic
587C2×C13C2×#55411yescharacteristic
588D13—44no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—134no—
594C24—132no—
595C24—262no—
596C24—262no—
597C24—262no—
598C24—262no—
599C24—262no—
600C24—262no—
601C24#612714yes—
602C24D4×D1314yes—
603C24Q8×D1314yes—
604C24C23×D1312yes—
605C24C23×D1311yescharacteristic
606C2×Q8—268no—
607C2×Q8—268no—
608C2×Q8—268no—
609C2×Q8—5216no—
610C2×D4—1316no—
611C2×D4—2632no—
612C2×D4—268no—
613C2×D4—268no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—28no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—28no—
633C22×C4—44no—
634C22×C4—416no—
635C22×C4—134no—
636C22×C4—134no—
637C22×C4—134no—
638C22×C4—132no—
639C22×C4—134no—
640C22×C4—134no—
641C22×C4—1316no—
642C22×C4—134no—
643C22×C4—132no—
644C22×C4—132no—
645C22×C4—132no—
646C22×C4—132no—
647C22×C4—132no—
648C22×C4—132no—
649C22×C4—268no—
650C22×C4—268no—
651C22×C4—268no—
652C22×C4—268no—
653C22×C4—2632no—
654C22×C4—268no—
655C22×C4—268no—
656C22×C4—262no—
657C22×C4—262no—
658C22×C4—262no—
659C22×C4—262no—
660C22×C4—262no—
661C22×C4—262no—
662C22×C4—268no—
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—5216no—
673C22×C4—524no—
674C22×C4—5216no—
675C22×C4D4×D1314yes—
676C22×C4C23×D1312yes—
677C22×C4C23×D1312yes—
678C22×C4C23×D1312yes—
679C22×C4C23×D1312yes—
680C22×C4C23×D1312yes—
681C22×C4C23×D1312yes—
682C4⋊C4—28no—
683C4⋊C4—44no—
684C4⋊C4—1316no—
685C4⋊C4—268no—
686C4⋊C4—268no—
687C4⋊C4—268no—
688C4⋊C4—268no—
689C4⋊C4—268no—
690C4⋊C4—268no—
691C4⋊C4—268no—
692C4⋊C4—268no—
693C4⋊C4—524no—
694C22⋊C4—28no—
695C22⋊C4—28no—
696C22⋊C4—268no—
697C22⋊C4—268no—
698C22⋊C4—268no—
699C22⋊C4—268no—
700C22⋊C4—524no—
701C22⋊C4—524no—
702C42—268no—
703C13C2×#241711yescharacteristic, complemented, Sylow
704C23—28no—
705C23—28no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—28no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—134no—
715C23—268no—
716C23—268no—
717C23—268no—
718C23—262no—
719C23—262no—
720C23—262no—
721C23—262no—
722C23—262no—
723C23—262no—
724C23—524no—
725C23—524no—
726C23—524no—
727C23—524no—
728C23#88150116yescomplemented
729C23C2×#612714yes—
730C23C2×#612712yes—
731C23C2×D4×D1314yes—
732C23C2×D4×D1312yes—
733C23C2×D4×D1312yes—
734C23#8825112yes—
735C23C2×Q8×D1314yes—
736C23C2×Q8×D1312yes—
737C23#41×D1312yes—
738C23#8825712yes—
739C23C24×D1311yescharacteristic
740Q8—5216no—
741D4—2632no—
742C2×C4—28no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—416no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—1316no—
767C2×C4—134no—
768C2×C4—134no—
769C2×C4—134no—
770C2×C4—134no—
771C2×C4—134no—
772C2×C4—134no—
773C2×C4—2632no—
774C2×C4—268no—
775C2×C4—268no—
776C2×C4—268no—
777C2×C4—262no—
778C2×C4—262no—
779C2×C4—262no—
780C2×C4—262no—
781C2×C4—262no—
782C2×C4—262no—
783C2×C4—262no—
784C2×C4—262no—
785C2×C4—262no—
786C2×C4—262no—
787C2×C4—262no—
788C2×C4—262no—
789C2×C4—262no—
790C2×C4—262no—
791C2×C4—262no—
792C2×C4—5216no—
793C2×C4—5216no—
794C2×C4—524no—
795C2×C4—524no—
796C2×C4—524no—
797C2×C4C2×D4×D1314yes—
798C22—232no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—264no—
806C22—264no—
807C22—264no—
808C22—5216no—
809C22—522no—
810C22—522no—
811C22—522no—
812C22—522no—
813C22#1171919514yes—
814C22C2×#8815014yes—
815C22C2×#8815018yescomplemented
816C22#1171923614yes—
817C22#1171930214yes—
818C22D13×#12114yes—
819C22#1171933714yes—
820C22#1171934114yes—
821C22C22×#612711yescharacteristic
822C22C22×D4×D1311yescharacteristic
823C22C22×D4×D1311yescharacteristic
824C22C2×#8825111yescharacteristic
825C22C22×Q8×D1311yescharacteristic
826C22C2×#41×D1311yescharacteristic
827C22C2×#8825711yescharacteristic
828C4—24no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—138no—
835C4—264no—
836C4—264no—
837C4—264no—
838C4—522no—
839C4—522no—
840C4—522no—
841C2—28no—
842C2—524no—
843C2#1311828618yesdirect product factor
844C2C2×D13×#12111yescharacteristic
845C2C22×#8815011yescharacteristic
846C2C2×#1171930211yescharacteristic
847C2C2×#1171919511yescharacteristic
848C2C2×#1171933711yescharacteristic
849C2C2×#1171923611yescharacteristic
850C2C2×#1171934111yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#380C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#380D13
hypocenterC13C2×#2417
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#88150C2semidirect
2. C22×#88132C2semidirect
4. C23×#6101C2semidirect
5. #13118286C2direct (N × H)
6. C2×#11718318C2semidirect
7. C2×#11718641C2semidirect
8. C2×#11718337C2semidirect
9. C2×#11718655C2semidirect
10. C2×#11718307C2semidirect
11. C2×#11718633C2semidirect
14. C2×#11718328C2semidirect
15. C2×#11718603C2semidirect
16. C2×C13×#380C2semidirect
44. C22×#6101C22semidirect
47. C2×#88150C22semidirect
51. C2×#88132C22semidirect
52. C13×#380C22semidirect
62. #11718655C22semidirect
63. #11718641C22semidirect
64. #11718633C22semidirect
66. #11718603C22semidirect
67. #11718337C22semidirect
68. #11718328C22semidirect
69. #11718318C22semidirect
70. #11718307C22semidirect
85. C22×C22⋊D13Q8semidirect
141. C2×#6101D4semidirect
213. C2×C22⋊D13C2×Q8semidirect
277. #6101C2×D4semidirect
294. C2×#380D13semidirect
305. C23×C13C22⋊Q8semidirect
434. #380C2×D13semidirect
452. C22×C13C2×C22⋊Q8semidirect
580. C2×C13#2417semidirect
703. C13C2×#2417semidirect
728. C23#88150semidirect
815. C22C2×#88150semidirect
843. C2#13118286direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881502
C22×#881322
C22×#881352
C23×#61012
#131182862
C2×#117183182
C2×#117186412
C2×#117183372
C2×#117186552
C2×#117183072
C2×#117186332
C2×#117188742
C2×#117186192
C2×#117183282
C2×#117186032
C2×C13×#3802
C2×#241713