Finite Group Databasebeta

← C2×#13118654 #16030669

Subgroups — C2×#13118654 #16030669

Order 3328.

3374 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88132C211yesmaximal, characteristic, complemented
2#13118654C2116yesmaximal, direct product factor
3C2×#11718647C211yesmaximal, characteristic, complemented
4C2×#11718645C211yesmaximal, characteristic, complemented
5C2×#11718609C211yesmaximal, characteristic, complemented
6C2×#11718608C211yesmaximal, characteristic, complemented
7C2×#11718590C211yesmaximal, characteristic, complemented
8C2×#11718594C211yesmaximal, characteristic, complemented
9C2×#11718881C211yesmaximal, characteristic
10C2×#11718881C211yesmaximal, characteristic
11C2×#11718611C211yesmaximal, characteristic, complemented
12C2×#11718871C211yesmaximal, characteristic, complemented
13C2×#11718871C211yesmaximal, characteristic, complemented
14C2×#11718873C211yesmaximal, characteristic, complemented
15C22×#88071C211yesmaximal, characteristic, complemented
16C22×C4×D4×C13C211yesmaximal, characteristic
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
21C24×Dic13C2211yescharacteristic
22C23×Dic26C2211yescharacteristic
23C2×C4×D4×C13—28no—
24C2×C4×D4×C13C2218yes—
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C42×C13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C22⋊Dic13C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×C4⋊Dic13C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C2×#88132—28no—
43C2×#88132C2218yescomplemented
44#11718881C2218yes—
45#11718881C2218yes—
46#11718873C2218yescomplemented
47#11718871C2218yescomplemented
48#11718871C2218yescomplemented
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2218yescomplemented
62#11718647C2218yescomplemented
63#11718645C2218yescomplemented
64#11718611C2218yescomplemented
65#11718609C2218yescomplemented
66#11718608C2218yescomplemented
67#11718594C2218yescomplemented
68#11718590C2218yescomplemented
69C25×C13C2311yescharacteristic
70C25×C13C2311yescharacteristic
71C22×D4×C13—24no—
72C22×D4×C13—24no—
73C22×D4×C13Q818yescomplemented
74C22×D4×C13C2314yes—
75C23×C4×C13—24no—
76C23×C4×C13—24no—
77C23×C4×C13—24no—
78C23×C4×C13—24no—
79C23×C4×C13—42no—
80C23×C4×C13—42no—
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2314yes—
83C23×C4×C13C2314yes—
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C23×Dic13—24no—
89C23×Dic13—24no—
90C23×Dic13—24no—
91C23×Dic13—42no—
92C23×Dic13—42no—
93C23×Dic13—42no—
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2314yes—
102C23×Dic13C2311yescharacteristic
103C23×Dic13C2314yes—
104C22×Dic26—24no—
105C22×Dic26—24no—
106C22×Dic26—42no—
107C22×Dic26C2314yes—
108C4×D4×C13—232no—
109C2×C13×C4⋊C4—24no—
110C2×C13×C4⋊C4C2314yes—
111C2×C13×C22⋊C4—24no—
112C2×C13×C22⋊C4D418yes—
113C2×C13×C22⋊C4C2314yes—
114C2×C13×C22⋊C4C2314yes—
115C2×C42×C13—24no—
116C2×C42×C13C2314yes—
117C2×C22⋊Dic13—24no—
118C2×C22⋊Dic13—24no—
119C2×C22⋊Dic13—24no—
120C2×C22⋊Dic13—42no—
121C2×C22⋊Dic13—42no—
122C2×C22⋊Dic13—42no—
123C2×C22⋊Dic13C2314yes—
124C2×C22⋊Dic13C2314yes—
125C2×C22⋊Dic13C2314yes—
126C2×C22⋊Dic13C2314yes—
127C2×C22⋊Dic13C2314yes—
128C2×C22⋊Dic13C2314yes—
129C2×C4⋊Dic13—24no—
130C2×C4⋊Dic13—42no—
131C2×C4⋊Dic13—42no—
132C2×C4⋊Dic13C2314yes—
133C2×C4⋊Dic13C2314yes—
134C2×C4⋊Dic13C2314yes—
135C2×#6101—24no—
136C2×#6101—24no—
137C2×#6101—24no—
138C2×#6101—42no—
139C2×#6101C2314yes—
140C2×#6101C2314yes—
141C2×#6101C2314yes—
142C2×#6101C2314yes—
143#88132—232no—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156C2×#2450—131nomaximal, Sylow
157C24×C13—22no—
158C24×C13—22no—
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×C13C2×D414yes—
168C24×C13C2×Q814yes—
169C24×C13C2×Q814yes—
170C24×C13#4114yes—
171C24×C13C2412yes—
172C24×C13C2412yes—
173C24×C13C2411yescharacteristic
174C2×D4×C13—232no—
175C2×D4×C13—28no—
176C2×D4×C13—28no—
177C2×D4×C13C2×Q8116yescomplemented
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—28no—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—28no—
191C22×C4×C13—28no—
192C22×C4×C13—28no—
193C22×C4×C13—44no—
194C22×C4×C13—44no—
195C22×C4×C13—416no—
196C22×C4×C13—416no—
197C22×C4×C13C2×D414yes—
198C22×C4×C13C2×D414yes—
199C22×C4×C13C2×Q814yes—
200C22×C4×C13#4114yes—
201C22×C4×C13C2412yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2412yes—
204C22×C4×C13C2412yes—
205C22×C4×C13C2412yes—
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13—28no—
209C22×Dic13—22no—
210C22×Dic13—22no—
211C22×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—22no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—28no—
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—28no—
232C22×Dic13—44no—
233C22×Dic13—44no—
234C22×Dic13—44no—
235C22×Dic13—416no—
236C22×Dic13—416no—
237C22×Dic13#4114yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C22×Dic13C2412yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C2×Dic26—28no—
247C2×Dic26—28no—
248C2×Dic26—44no—
249C2×Dic26—416no—
250C13×C4⋊C4—28no—
251C13×C22⋊C4—28no—
252C13×C22⋊C4C2×D4116yes—
253C42×C13—28no—
254C22⋊Dic13—28no—
255C22⋊Dic13—28no—
256C22⋊Dic13—28no—
257C22⋊Dic13—44no—
258C22⋊Dic13—44no—
259C22⋊Dic13—44no—
260C4⋊Dic13—28no—
261C4⋊Dic13—44no—
262C4⋊Dic13—44no—
263#6101—28no—
264#6101—28no—
265#6101—28no—
266#6101—44no—
267C22×C22⋊Q8—131no—
268C22×C4×D4D1311yescharacteristic
269#2450—1316no—
270C2×#400—131no—
271C2×#398—131no—
272C2×#396—131no—
273C2×#393—131no—
274C2×#391—131no—
275C2×#387—131no—
276C2×#386—131no—
277C2×#386—131no—
278C2×#385—131no—
279C2×#385—131no—
280C2×#385—131no—
281C2×#380—131no—
282C22×#95—131no—
283C23×C13—28no—
284C23×C13—28no—
285C23×C13—28no—
286C23×C13—28no—
287C23×C13—28no—
288C23×C13—28no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—28no—
294C23×C13—28no—
295C23×C13—28no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—44no—
303C23×C13—44no—
304C23×C13—44no—
305C23×C13—44no—
306C23×C13C22⋊Q8116yes—
307C23×C13C22×D414yes—
308C23×C13C22×D412yes—
309C23×C13C22×Q814yes—
310C23×C13C22×Q814yes—
311C23×C13C22×Q812yes—
312C23×C13C2×#4114yes—
313C23×C13C2×#4112yes—
314C23×C13C2×#4112yes—
315C23×C13C2×#4112yes—
316C23×C13H(5,𝔽2)12yes—
317C23×C13H(5,𝔽2)12yes—
318C23×C13C2511yescharacteristic
319D4×C13—232no—
320C2×C4×C13—28no—
321C2×C4×C13—28no—
322C2×C4×C13—28no—
323C2×C4×C13—28no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—416no—
336C2×C4×C13—416no—
337C2×C4×C13—44no—
338C2×C4×C13C22×D414yes—
339C2×C4×C13C22×D414yes—
340C2×C4×C13C22×Q814yes—
341C2×C4×C13C2×#4114yes—
342C2×Dic13—28no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—22no—
360C2×Dic13—22no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—416no—
367C2×Dic13—416no—
368C2×Dic13—44no—
369C2×Dic13—44no—
370C2×Dic13—44no—
371C2×Dic13—44no—
372C2×Dic13—44no—
373C2×Dic13—44no—
374C2×Dic13—44no—
375C2×Dic13C2×#4114yes—
376Dic26—416no—
377C23×Q8—131no—
378C23×D4C2×D1311yescharacteristic
379C24×C4—131no—
380C24×C4—131no—
381C24×C4C2×D1311yescharacteristic
382C24×C4C2×D1311yescharacteristic
383C2×C22⋊Q8—138no—
384C2×C22⋊Q8—268no—
385C2×C4×D4—28no—
386C2×C4×D4C2×D1318yes—
387C22×C4⋊C4—131no—
388C22×C4⋊C4—131no—
389C22×C4⋊C4—131no—
390C22×C4⋊C4—131no—
391C22×C4⋊C4—131no—
392C22×C4⋊C4—131no—
393C22×C4⋊C4—131no—
394C22×C4⋊C4C2×D1311yescharacteristic
395C22×C22⋊C4—131no—
396C22×C22⋊C4—131no—
397C22×C22⋊C4—131no—
398C22×C22⋊C4—131no—
399C22×C22⋊C4—131no—
400C22×C22⋊C4—131no—
401C22×C22⋊C4C2×D1311yescharacteristic
402C22×C22⋊C4C2×D1311yescharacteristic
403C22×C42C2×D1311yescharacteristic
404#400—138no—
405#398—138no—
406#396—138no—
407#393—138no—
408#391—138no—
409#387—138no—
410#386—138no—
411#386—138no—
412#385—138no—
413#385—138no—
414#385—138no—
415#380—138no—
416C2×#95—131no—
417C2×#95—131no—
418C2×#95—131no—
419C2×#95—131no—
420C2×#95—131no—
421C2×#95—131no—
422C2×#95—131no—
423C2×#95—131no—
424C2×#95—131no—
425C2×#95—138no—
426C2×#95—131no—
427C2×#95—131no—
428C2×#95—131no—
429C22×C13—24no—
430C22×C13—24no—
431C22×C13—24no—
432C22×C13—24no—
433C22×C13—24no—
434C22×C13—24no—
435C22×C13—232no—
436C22×C13—24no—
437C22×C13—24no—
438C22×C13—24no—
439C22×C13—42no—
440C22×C13—42no—
441C22×C13—42no—
442C22×C13—42no—
443C22×C13—416no—
444C22×C13C2×C22⋊Q818yes—
445C22×C13C2×C22⋊Q814yes—
446C22×C13#52914yes—
447C22×C13#53814yes—
448C22×C13#54614yes—
449C22×C13#54614yes—
450C22×C13#55414yes—
451C22×C13#55414yes—
452C22×C13C23×D411yescharacteristic
453C22×C13C23×Q811yescharacteristic
454C22×C13C22×#4111yescharacteristic
455C22×C13C22×#4111yescharacteristic
456C22×C13C22×#4111yescharacteristic
457C22×C13C2×H(5,𝔽2)11yescharacteristic
458C22×C13C2×H(5,𝔽2)11yescharacteristic
459C4×C13—24no—
460C4×C13—24no—
461C4×C13—24no—
462C4×C13—24no—
463C4×C13—42no—
464Dic13—24no—
465Dic13—42no—
466Dic13—42no—
467Dic13—42no—
468Dic13—42no—
469Dic13—42no—
470Dic13—42no—
471Dic13—42no—
472C25C22×D1311yescharacteristic
473C25C22×D1311yescharacteristic
474C22×Q8—134no—
475C22×Q8—264no—
476C22×Q8—264no—
477C22×Q8—522no—
478C22×D4—24no—
479C22×D4—24no—
480C22×D4Dic2618yescomplemented
481C22×D4C22×D1314yes—
482C23×C4—24no—
483C23×C4—24no—
484C23×C4—24no—
485C23×C4—24no—
486C23×C4—42no—
487C23×C4—42no—
488C23×C4—131no—
489C23×C4—131no—
490C23×C4—131no—
491C23×C4—131no—
492C23×C4—131no—
493C23×C4—131no—
494C23×C4—131no—
495C23×C4—131no—
496C23×C4—134no—
497C23×C4—134no—
498C23×C4—264no—
499C23×C4—264no—
500C23×C4—264no—
501C23×C4—522no—
502C23×C4—522no—
503C23×C4—522no—
504C23×C4C22×D1311yescharacteristic
505C23×C4C22×D1314yes—
506C23×C4C22×D1314yes—
507C23×C4C22×D1311yescharacteristic
508C23×C4C22×D1311yescharacteristic
509C23×C4C22×D1311yescharacteristic
510C23×C4C22×D1311yescharacteristic
511C22⋊Q8—2632no—
512C4×D4—232no—
513C2×C4⋊C4—24no—
514C2×C4⋊C4—134no—
515C2×C4⋊C4—134no—
516C2×C4⋊C4—134no—
517C2×C4⋊C4—134no—
518C2×C4⋊C4—134no—
519C2×C4⋊C4—134no—
520C2×C4⋊C4—134no—
521C2×C4⋊C4—264no—
522C2×C4⋊C4—264no—
523C2×C4⋊C4—264no—
524C2×C4⋊C4—264no—
525C2×C4⋊C4—522no—
526C2×C4⋊C4—522no—
527C2×C4⋊C4—522no—
528C2×C4⋊C4C22×D1314yes—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—134no—
531C2×C22⋊C4—134no—
532C2×C22⋊C4—134no—
533C2×C22⋊C4—134no—
534C2×C22⋊C4—134no—
535C2×C22⋊C4—134no—
536C2×C22⋊C4—264no—
537C2×C22⋊C4—264no—
538C2×C22⋊C4—264no—
539C2×C22⋊C4—522no—
540C2×C22⋊C4—522no—
541C2×C22⋊C4—522no—
542C2×C22⋊C4C22⋊D1318yes—
543C2×C22⋊C4C22×D1314yes—
544C2×C22⋊C4C22×D1314yes—
545C2×C42—24no—
546C2×C42C22×D1314yes—
547#95—134no—
548#95—134no—
549#95—134no—
550#95—134no—
551#95—134no—
552#95—134no—
553#95—134no—
554#95—134no—
555#95—134no—
556#95—134no—
557#95—134no—
558#95—134no—
559C2×C13—28no—
560C2×C13—44no—
561C2×C13#245018yescomplemented
562C2×C13C22×C22⋊Q811yescharacteristic
563C2×C13C2×#52911yescharacteristic
564C2×C13C2×#53811yescharacteristic
565C2×C13C2×#54611yescharacteristic
566C2×C13C2×#54611yescharacteristic
567C2×C13C2×#55411yescharacteristic
568C2×C13C2×#55411yescharacteristic
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24C2×Dic2614yes—
580C24C2×Dic2614yes—
581C24#612714yes—
582C24C2×C22⋊D1314yes—
583C24C23×D1312yes—
584C24C23×D1312yes—
585C24C23×D1311yescharacteristic
586C2×Q8—268no—
587C2×Q8—268no—
588C2×Q8—524no—
589C2×Q8—5216no—
590C2×D4—232no—
591C2×D4—28no—
592C2×D4—28no—
593C2×D4C2×Dic26116yescomplemented
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—416no—
612C22×C4—416no—
613C22×C4—134no—
614C22×C4—132no—
615C22×C4—132no—
616C22×C4—132no—
617C22×C4—132no—
618C22×C4—132no—
619C22×C4—132no—
620C22×C4—132no—
621C22×C4—132no—
622C22×C4—268no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—262no—
627C22×C4—268no—
628C22×C4—262no—
629C22×C4—262no—
630C22×C4—262no—
631C22×C4—262no—
632C22×C4—262no—
633C22×C4—262no—
634C22×C4—262no—
635C22×C4—262no—
636C22×C4—262no—
637C22×C4—262no—
638C22×C4—262no—
639C22×C4—262no—
640C22×C4—262no—
641C22×C4—262no—
642C22×C4—262no—
643C22×C4—262no—
644C22×C4—262no—
645C22×C4—262no—
646C22×C4—262no—
647C22×C4—268no—
648C22×C4—524no—
649C22×C4—524no—
650C22×C4—524no—
651C22×C4—5216no—
652C22×C4—5216no—
653C22×C4C2×Dic2614yes—
654C22×C4#612914yes—
655C22×C4C2×C22⋊D1314yes—
656C22×C4C2×C22⋊D1314yes—
657C22×C4C23×D1312yes—
658C22×C4C23×D1312yes—
659C22×C4C23×D1312yes—
660C22×C4C23×D1312yes—
661C22×C4C23×D1312yes—
662C4⋊C4—28no—
663C4⋊C4—268no—
664C4⋊C4—268no—
665C4⋊C4—268no—
666C4⋊C4—268no—
667C4⋊C4—524no—
668C4⋊C4—524no—
669C4⋊C4—524no—
670C22⋊C4—28no—
671C22⋊C4—268no—
672C22⋊C4—268no—
673C22⋊C4—268no—
674C22⋊C4—524no—
675C22⋊C4—524no—
676C22⋊C4—524no—
677C22⋊C4C2×C22⋊D13116yes—
678C42—28no—
679C13C2×#245011yescharacteristic, complemented, Sylow
680C23—28no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—28no—
691C23—28no—
692C23—28no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23#88178116yes—
704C23C22×Dic2614yes—
705C23C22×Dic2614yes—
706C23C22×Dic2612yes—
707C23C2×#612714yes—
708C23C2×#612712yes—
709C23C2×#612912yes—
710C23#8825112yes—
711C23#41×D1312yes—
712C23#8825612yes—
713C23C22×C22⋊D1314yes—
714C23C22×C22⋊D1312yes—
715C23C24×D1311yescharacteristic
716Q8—5216no—
717D4—232no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—416no—
734C2×C4—416no—
735C2×C4—44no—
736C2×C4—134no—
737C2×C4—268no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—262no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—262no—
748C2×C4—262no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—262no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—262no—
761C2×C4—5216no—
762C2×C4—5216no—
763C2×C4—524no—
764C2×C4—524no—
765C2×C4—524no—
766C2×C4—524no—
767C2×C4—524no—
768C2×C4—524no—
769C2×C4—524no—
770C2×C4C22×Dic2614yes—
771C2×C4C2×#612914yes—
772C2×C4C22×C22⋊D1314yes—
773C2×C4C22×C22⋊D1314yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—232no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—416no—
788C22—42no—
789C22#1171924314yes—
790C22#1171924414yes—
791C22#1171924814yes—
792C22#1171926514yes—
793C22C2×#8817818yes—
794C22C2×#8817814yes—
795C22#1171951114yes—
796C22#1171953414yes—
797C22C23×Dic2611yescharacteristic
798C22C22×#612711yescharacteristic
799C22C22×#612911yescharacteristic
800C22C2×#8825111yescharacteristic
801C22C2×#41×D1311yescharacteristic
802C22C2×#8825611yescharacteristic
803C22C23×C22⋊D1311yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—264no—
810C4—522no—
811C4—522no—
812C4—522no—
813C4—522no—
814C4—522no—
815C4—522no—
816C4—522no—
817C2—28no—
818C2—44no—
819C2#1311865418yesdirect product factor
820C2C22×#8817811yescharacteristic
821C2C2×#1171924311yescharacteristic
822C2C2×#1171926511yescharacteristic
823C2C2×#1171953411yescharacteristic
824C2C2×#1171951111yescharacteristic
825C2C2×#1171924811yescharacteristic
826C2C2×#1171924411yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C4×D4×C13C2
socleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC22×C4×D4D13
hypocenterC13C2×#2450
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#88132C2semidirect
2. #13118654C2direct (N × H)
3. C2×#11718647C2semidirect
4. C2×#11718645C2semidirect
5. C2×#11718609C2semidirect
6. C2×#11718608C2semidirect
7. C2×#11718590C2semidirect
8. C2×#11718594C2semidirect
11. C2×#11718611C2semidirect
12. C2×#11718871C2semidirect
13. C2×#11718871C2semidirect
14. C2×#11718873C2semidirect
15. C22×#88071C2semidirect
43. C2×#88132C22semidirect
46. #11718873C22semidirect
47. #11718871C22semidirect
48. #11718871C22semidirect
61. C2×#88071C22semidirect
62. #11718647C22semidirect
63. #11718645C22semidirect
64. #11718611C22semidirect
65. #11718609C22semidirect
66. #11718608C22semidirect
67. #11718594C22semidirect
68. #11718590C22semidirect
73. C22×D4×C13Q8semidirect
177. C2×D4×C13C2×Q8semidirect
480. C22×D4Dic26semidirect
561. C2×C13#2450semidirect
593. C2×D4C2×Dic26semidirect
679. C13C2×#2450semidirect
819. C2#13118654direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881322
#131186542
C2×#117186472
C2×#117186452
C2×#117186092
C2×#117186082
C2×#117185902
C2×#117185942
C2×#117188812
C2×#117186112
C2×#117188712
C2×#117188732
C22×#880712
C22×C4×D4×C132
C2×#245013