Finite Group Databasebeta

← C2×#13117276 #16021255

Subgroups — C2×#13117276 #16021255

Order 3328.

4134 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×D4×Dic13C211yesmaximal, characteristic
2C22×#88131C211yesmaximal, characteristic, complemented
3C23×C4×Dic13C211yesmaximal, characteristic, complemented
4#13117276C2116yesmaximal, direct product factor
5C2×#11718606C211yesmaximal, characteristic, complemented
6C2×#11718605C211yesmaximal, characteristic, complemented
7C2×#11718314C211yesmaximal, characteristic, complemented
8C2×#11718315C211yesmaximal, characteristic, complemented
9C2×#11718881C211yesmaximal, characteristic
10C2×#11718871C211yesmaximal, characteristic, complemented
11C2×#11718607C211yesmaximal, characteristic, complemented
12C2×#11718310C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
15C2×#11718309C211yesmaximal, characteristic, complemented
16C2×C13×#386C211yesmaximal, characteristic
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
21C24×Dic13C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C2×D4×Dic13C4116yescomplemented
31C2×D4×Dic13C2218yes—
32C22×C4⋊Dic13C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×C4×Dic13—28no—
38C22×C4×Dic13C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2218yescomplemented
46C2×#88131—28no—
47C2×#88131C2218yescomplemented
48C13×#386C2218yes—
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51#11718881C2218yes—
52#11718871C2218yescomplemented
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61#11718607C2218yescomplemented
62#11718606C2218yescomplemented
63#11718605C2218yescomplemented
64C22⋊C4×Dic13C2218yescomplemented
65C22⋊C4×Dic13C2218yescomplemented
66#11718315C2218yescomplemented
67#11718314C2218yescomplemented
68#11718310C2218yescomplemented
69#11718309C2218yescomplemented
70C25×C13C2311yescharacteristic
71C25×C13C2311yescharacteristic
72C22×D4×C13—24no—
73C22×D4×C13—24no—
74C22×D4×C13C2×C418yes—
75C22×D4×C13C2314yes—
76C23×C4×C13—24no—
77C23×C4×C13—24no—
78C23×C4×C13—24no—
79C23×C4×C13C2314yes—
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×Dic13—24no—
86C23×Dic13—24no—
87C23×Dic13—24no—
88C23×Dic13—24no—
89C23×Dic13—24no—
90C23×Dic13—24no—
91C23×Dic13—24no—
92C23×Dic13C2×C418yes—
93C23×Dic13C2×C418yescomplemented
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2314yes—
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2314yes—
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2314yes—
102C23×Dic13C2311yescharacteristic
103C23×Dic13C2311yescharacteristic
104C23×Dic13C2311yescharacteristic
105C2×C13×C22⋊C4—24no—
106C2×C13×C22⋊C4—24no—
107C2×C13×C22⋊C4—24no—
108C2×C13×C22⋊C4C2314yes—
109C2×C13×C22⋊C4C2314yes—
110C2×C13×C22⋊C4C2314yes—
111C2×C22⋊Dic13—24no—
112C2×C22⋊Dic13—24no—
113C2×C22⋊Dic13—24no—
114C2×C22⋊Dic13C2×C418yes—
115C2×C22⋊Dic13C2×C418yescomplemented
116C2×C22⋊Dic13C2314yes—
117C2×C22⋊Dic13C2314yes—
118C2×C22⋊Dic13C2314yes—
119C2×C22⋊Dic13C2314yes—
120C2×C22⋊Dic13C2314yes—
121D4×Dic13C2×C4164yescomplemented
122C2×C4⋊Dic13C2×C418yescomplemented
123C2×C4⋊Dic13C2314yes—
124C2×#6101—24no—
125C2×#6101—24no—
126C2×#6101—24no—
127C2×#6101—24no—
128C2×#6101C2314yes—
129C2×#6101C2314yes—
130C2×#6101C2314yes—
131C2×#6101C2314yes—
132C2×C4×Dic13—24no—
133C2×C4×Dic13—24no—
134C2×C4×Dic13—24no—
135C2×C4×Dic13—24no—
136C2×C4×Dic13—24no—
137C2×C4×Dic13—232no—
138C2×C4×Dic13C2×C418yescomplemented
139C2×C4×Dic13D418yescomplemented
140C2×C4×Dic13C2314yes—
141C2×C4×Dic13C2314yes—
142C2×C4×Dic13C2314yes—
143C2×C4×Dic13C2314yes—
144C2×C4×Dic13C2314yes—
145C2×C4×Dic13C2314yes—
146C2×C4×Dic13C2314yes—
147#88131—232no—
148C13×#95C2314yes—
149C13×#95C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2290—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×C13C22×C414yes—
170C24×C13C22×C414yes—
171C24×C13#4114yes—
172C24×C13#4114yes—
173C24×C13C2412yes—
174C24×C13C2412yes—
175C24×C13C2411yescharacteristic
176C2×D4×C13—232no—
177C2×D4×C13—28no—
178C2×D4×C13—28no—
179C2×D4×C13C22×C4116yes—
180C22×C4×C13—232no—
181C22×C4×C13—22no—
182C22×C4×C13—28no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—28no—
189C22×C4×C13—28no—
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×C13C22×C414yes—
197C22×C4×C13C2×D414yes—
198C22×C4×C13#4114yes—
199C22×C4×C13C2412yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2412yes—
204C22×Dic13—232no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—28no—
211C22×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—22no—
216C22×Dic13—232no—
217C22×Dic13—232no—
218C22×Dic13—28no—
219C22×Dic13—28no—
220C22×Dic13—28no—
221C22×Dic13—28no—
222C22×Dic13—28no—
223C22×Dic13—28no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13—22no—
230C22×Dic13C22×C414yes—
231C22×Dic13C22×C414yes—
232C22×Dic13C22×C414yes—
233C22×Dic13C22×C4116yes—
234C22×Dic13C22×C414yes—
235C22×Dic13C22×C4116yescomplemented
236C22×Dic13C2×D414yes—
237C22×Dic13C2×D414yes—
238C22×Dic13#4114yes—
239C22×Dic13#4114yes—
240C22×Dic13C2412yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C13×C22⋊C4—28no—
249C13×C22⋊C4—28no—
250C13×C22⋊C4—28no—
251C22⋊Dic13—28no—
252C22⋊Dic13—28no—
253C22⋊Dic13—28no—
254C22⋊Dic13C22×C4116yes—
255C22⋊Dic13C22×C4116yescomplemented
256C4⋊Dic13C22×C4116yescomplemented
257#6101—28no—
258#6101—28no—
259#6101—28no—
260#6101—28no—
261C4×Dic13—28no—
262C4×Dic13—28no—
263C4×Dic13—28no—
264C4×Dic13—28no—
265C4×Dic13—28no—
266C4×Dic13C22×C4116yescomplemented
267C4×Dic13C2×D4116yescomplemented
268C22×C4×D4—131no—
269C22×#117—131no—
270C23×C42—131no—
271#2290—1316no—
272C2×#388—131no—
273C2×#388—131no—
274C2×#387—131no—
275C2×#387—131no—
276C2×#386—131no—
277C2×#386D1311yescharacteristic
278C2×#385—131no—
279C2×#385—131no—
280C2×C4×C4⋊C4—131no—
281C2×C4×C22⋊C4—131no—
282C2×C4×C22⋊C4—131no—
283C2×#376—131no—
284C23×C13—28no—
285C23×C13—28no—
286C23×C13—28no—
287C23×C13—28no—
288C23×C13—28no—
289C23×C13—28no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—28no—
295C23×C13—28no—
296C23×C13—28no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—44no—
304C23×C13—44no—
305C23×C13—44no—
306C23×C13—44no—
307C23×C13#117116yescomplemented
308C23×C13C23×C414yes—
309C23×C13C23×C414yes—
310C23×C13C23×C412yes—
311C23×C13C22×D412yes—
312C23×C13C2×#4114yes—
313C23×C13C2×#4114yes—
314C23×C13C2×#4112yes—
315C23×C13C2×#4112yes—
316C23×C13C2×#4112yes—
317C23×C13C2×#4112yes—
318C23×C13C2×#4112yes—
319C23×C13C2511yescharacteristic
320D4×C13—232no—
321C2×C4×C13—232no—
322C2×C4×C13—28no—
323C2×C4×C13—28no—
324C2×C4×C13—28no—
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—22no—
336C2×C4×C13—22no—
337C2×C4×C13—44no—
338C2×C4×C13—44no—
339C2×C4×C13C23×C414yes—
340C2×C4×C13C22×D414yes—
341C2×C4×C13C2×#4114yes—
342C2×Dic13—232no—
343C2×Dic13—28no—
344C2×Dic13—28no—
345C2×Dic13—28no—
346C2×Dic13—28no—
347C2×Dic13—28no—
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—232no—
359C2×Dic13—232no—
360C2×Dic13—22no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—44no—
367C2×Dic13—44no—
368C2×Dic13C4×D4116yes—
369C2×Dic13C23×C414yes—
370C2×Dic13C23×C414yes—
371C2×Dic13C23×C414yes—
372C2×Dic13C23×C414yes—
373C2×Dic13C22×D414yes—
374C2×Dic13C22×D414yes—
375C2×Dic13C2×#4114yes—
376C2×Dic13C2×#4114yes—
377C23×D4C2×D1311yescharacteristic
378C24×C4—131no—
379C24×C4—131no—
380C24×C4—131no—
381C24×C4C2×D1311yescharacteristic
382C2×C4×D4—1316no—
383C2×C4×D4—138no—
384C2×#117—138no—
385C2×#117—268no—
386C22×C4⋊C4—131no—
387C22×C4⋊C4—131no—
388C22×C4⋊C4—131no—
389C22×C4⋊C4—131no—
390C22×C4⋊C4—131no—
391C22×C22⋊C4—131no—
392C22×C22⋊C4—131no—
393C22×C22⋊C4—131no—
394C22×C22⋊C4—131no—
395C22×C22⋊C4—131no—
396C22×C22⋊C4C2×D1311yescharacteristic
397C22×C22⋊C4C2×D1311yescharacteristic
398C22×C22⋊C4C2×D1311yescharacteristic
399C22×C42—131no—
400C22×C42—131no—
401C22×C42—131no—
402C22×C42—131no—
403C22×C42—131no—
404C22×C42—131no—
405C22×C42—131no—
406C22×C42—138no—
407C22×C42—268no—
408#388—138no—
409#388—138no—
410#387—138no—
411#387—138no—
412#386—138no—
413#386C2×D1318yes—
414#385—138no—
415#385—138no—
416C4×C4⋊C4—138no—
417C4×C22⋊C4—138no—
418C4×C22⋊C4—138no—
419#376—138no—
420C2×#95—131no—
421C2×#95—131no—
422C2×#95—131no—
423C2×#95—131no—
424C2×#95—131no—
425C2×#95—131no—
426C2×#95—131no—
427C2×#95—131no—
428C2×#95C2×D1311yescharacteristic
429C2×#95C2×D1311yescharacteristic
430C22×C13—24no—
431C22×C13—24no—
432C22×C13—24no—
433C22×C13—24no—
434C22×C13—24no—
435C22×C13—24no—
436C22×C13—232no—
437C22×C13—24no—
438C22×C13—24no—
439C22×C13—24no—
440C22×C13—42no—
441C22×C13—42no—
442C22×C13—42no—
443C22×C13—42no—
444C22×C13—416no—
445C22×C13C2×#11714yes—
446C22×C13C2×#11718yescomplemented
447C22×C13C2×C4×D414yes—
448C22×C13C4×#4114yes—
449C22×C13#52514yes—
450C22×C13#52514yes—
451C22×C13#52914yes—
452C22×C13#52914yes—
453C22×C13C24×C411yescharacteristic
454C22×C13C23×D411yescharacteristic
455C22×C13C22×#4111yescharacteristic
456C22×C13C22×#4111yescharacteristic
457C22×C13C22×#4111yescharacteristic
458C22×C13C22×#4111yescharacteristic
459C22×C13C22×#4111yescharacteristic
460C4×C13—24no—
461C4×C13—24no—
462C4×C13—24no—
463C4×C13—42no—
464C4×C13—42no—
465Dic13—24no—
466Dic13—24no—
467Dic13—24no—
468Dic13—24no—
469Dic13—24no—
470Dic13—42no—
471Dic13—42no—
472Dic13C2×C4×D418yes—
473C25C22×D1311yescharacteristic
474C25C22×D1311yescharacteristic
475C22×D4—24no—
476C22×D4—24no—
477C22×D4C4×D1318yes—
478C22×D4C22×D1314yes—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—131no—
483C23×C4—138no—
484C23×C4—138no—
485C23×C4—134no—
486C23×C4—134no—
487C23×C4—131no—
488C23×C4—131no—
489C23×C4—131no—
490C23×C4—131no—
491C23×C4—131no—
492C23×C4—134no—
493C23×C4—131no—
494C23×C4—131no—
495C23×C4—264no—
496C23×C4—264no—
497C23×C4—264no—
498C23×C4—264no—
499C23×C4—264no—
500C23×C4—264no—
501C23×C4—264no—
502C23×C4C22×D1314yes—
503C23×C4C22×D1311yescharacteristic
504C23×C4C22×D1311yescharacteristic
505C23×C4C22×D1311yescharacteristic
506C23×C4C22×D1311yescharacteristic
507C23×C4C22×D1311yescharacteristic
508C4×D4—1364no—
509#117—2632no—
510C2×C4⋊C4—138no—
511C2×C4⋊C4—134no—
512C2×C4⋊C4—134no—
513C2×C4⋊C4—134no—
514C2×C4⋊C4—134no—
515C2×C4⋊C4—134no—
516C2×C4⋊C4—264no—
517C2×C4⋊C4—264no—
518C2×C4⋊C4—264no—
519C2×C4⋊C4—264no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—138no—
524C2×C22⋊C4—138no—
525C2×C22⋊C4—134no—
526C2×C22⋊C4—134no—
527C2×C22⋊C4—134no—
528C2×C22⋊C4—134no—
529C2×C22⋊C4—134no—
530C2×C22⋊C4—264no—
531C2×C22⋊C4—264no—
532C2×C22⋊C4—264no—
533C2×C22⋊C4C22×D1314yes—
534C2×C22⋊C4C22×D1314yes—
535C2×C22⋊C4C22×D1314yes—
536C2×C42—138no—
537C2×C42—138no—
538C2×C42—134no—
539C2×C42—134no—
540C2×C42—134no—
541C2×C42—134no—
542C2×C42—134no—
543C2×C42—134no—
544C2×C42—134no—
545C2×C42—2632no—
546C2×C42—264no—
547C2×C42—264no—
548C2×C42—264no—
549C2×C42—264no—
550C2×C42—264no—
551#95—134no—
552#95—134no—
553#95—134no—
554#95—134no—
555#95—134no—
556#95—134no—
557#95—134no—
558#95—134no—
559#95C22×D1314yes—
560#95C22×D1314yes—
561C2×C13—28no—
562C2×C13—44no—
563C2×C13#229018yescomplemented
564C2×C13C22×#11711yescharacteristic
565C2×C13C22×C4×D411yescharacteristic
566C2×C13C2×C4×#4111yescharacteristic
567C2×C13C2×#52511yescharacteristic
568C2×C13C2×#52511yescharacteristic
569C2×C13C2×#52911yescharacteristic
570C2×C13C2×#52911yescharacteristic
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24C2×C4×D1314yes—
582C24C2×C4×D1314yes—
583C24#612914yes—
584C24#612914yes—
585C24C23×D1312yes—
586C24C23×D1312yes—
587C24C23×D1311yescharacteristic
588C2×D4—232no—
589C2×D4—28no—
590C2×D4—28no—
591C2×D4C2×C4×D13116yes—
592C22×C4—232no—
593C22×C4—22no—
594C22×C4—28no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—28no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—134no—
609C22×C4—134no—
610C22×C4—134no—
611C22×C4—132no—
612C22×C4—134no—
613C22×C4—134no—
614C22×C4—134no—
615C22×C4—1316no—
616C22×C4—1316no—
617C22×C4—134no—
618C22×C4—134no—
619C22×C4—132no—
620C22×C4—132no—
621C22×C4—132no—
622C22×C4—132no—
623C22×C4—132no—
624C22×C4—132no—
625C22×C4—132no—
626C22×C4—268no—
627C22×C4—268no—
628C22×C4—268no—
629C22×C4—2632no—
630C22×C4—2632no—
631C22×C4—268no—
632C22×C4—268no—
633C22×C4—268no—
634C22×C4—2632no—
635C22×C4—262no—
636C22×C4—262no—
637C22×C4—262no—
638C22×C4—262no—
639C22×C4—268no—
640C22×C4—262no—
641C22×C4—262no—
642C22×C4—262no—
643C22×C4—262no—
644C22×C4—262no—
645C22×C4—262no—
646C22×C4—262no—
647C22×C4—262no—
648C22×C4—262no—
649C22×C4—262no—
650C22×C4—262no—
651C22×C4—262no—
652C22×C4C2×C4×D1314yes—
653C22×C4D4×D1314yes—
654C22×C4#612914yes—
655C22×C4C23×D1312yes—
656C22×C4C23×D1312yes—
657C22×C4C23×D1312yes—
658C22×C4C23×D1312yes—
659C22×C4C23×D1312yes—
660C4⋊C4—1316no—
661C4⋊C4—268no—
662C4⋊C4—268no—
663C4⋊C4—268no—
664C4⋊C4—268no—
665C22⋊C4—28no—
666C22⋊C4—28no—
667C22⋊C4—28no—
668C22⋊C4—1316no—
669C22⋊C4—1316no—
670C22⋊C4—268no—
671C22⋊C4—268no—
672C22⋊C4—268no—
673C42—1316no—
674C42—1316no—
675C42—268no—
676C42—268no—
677C42—268no—
678C42—268no—
679C42—268no—
680C13C2×#229011yescharacteristic, complemented, Sylow
681C23—28no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—28no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—28no—
692C23—28no—
693C23—28no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23#88131116yescomplemented
705C23C22×C4×D1314yes—
706C23C22×C4×D1314yes—
707C23C22×C4×D1312yes—
708C23C2×D4×D1312yes—
709C23C2×#612914yes—
710C23C2×#612914yes—
711C23C2×#612912yes—
712C23C2×#612912yes—
713C23C2×#612912yes—
714C23#41×D1312yes—
715C23#41×D1312yes—
716C23C24×D1311yescharacteristic
717D4—232no—
718C2×C4—232no—
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—22no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—1316no—
737C2×C4—134no—
738C2×C4—134no—
739C2×C4—134no—
740C2×C4—134no—
741C2×C4—134no—
742C2×C4—134no—
743C2×C4—134no—
744C2×C4—134no—
745C2×C4—2632no—
746C2×C4—2632no—
747C2×C4—2632no—
748C2×C4—268no—
749C2×C4—268no—
750C2×C4—268no—
751C2×C4—268no—
752C2×C4—268no—
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—262no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—262no—
765C2×C4—262no—
766C2×C4—262no—
767C2×C4—262no—
768C2×C4—262no—
769C2×C4—524no—
770C2×C4—524no—
771C2×C4C22×C4×D1314yes—
772C2×C4C2×D4×D1314yes—
773C2×C4C2×#612914yes—
774C22—24no—
775C22—24no—
776C22—232no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—416no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22C2×#8813114yes—
790C22C2×#8813118yescomplemented
791C22C4×#612914yes—
792C22C4×D4×D1314yes—
793C22#1171929114yes—
794C22#1171930514yes—
795C22#1171931114yes—
796C22#1171935414yes—
797C22C23×C4×D1311yescharacteristic
798C22C22×D4×D1311yescharacteristic
799C22C22×#612911yescharacteristic
800C22C22×#612911yescharacteristic
801C22C22×#612911yescharacteristic
802C22C2×#41×D1311yescharacteristic
803C22C2×#41×D1311yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—138no—
810C4—264no—
811C4—264no—
812C4—264no—
813C4—264no—
814C4—264no—
815C4—522no—
816C4—522no—
817C2—28no—
818C2—44no—
819C2#1311727618yesdirect product factor
820C2C22×#8813111yescharacteristic
821C2C2×C4×D4×D1311yescharacteristic
822C2C2×C4×#612911yescharacteristic
823C2C2×#1171929111yescharacteristic
824C2C2×#1171931111yescharacteristic
825C2C2×#1171935411yescharacteristic
826C2C2×#1171930511yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#386C2
socleC24×C13C24
prime radicalC23×D4×C13C22
cosocleC23×C13C25
hypercenterC2×#386D13
hypocenterC13C2×#2290
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×#88131C2semidirect
3. C23×C4×Dic13C2semidirect
4. #13117276C2direct (N × H)
5. C2×#11718606C2semidirect
6. C2×#11718605C2semidirect
7. C2×#11718314C2semidirect
8. C2×#11718315C2semidirect
10. C2×#11718871C2semidirect
11. C2×#11718607C2semidirect
12. C2×#11718310C2semidirect
13. C2×C22⋊C4×Dic13C2semidirect
14. C2×C22⋊C4×Dic13C2semidirect
15. C2×#11718309C2semidirect
30. C2×D4×Dic13C4semidirect
45. C22×C4×Dic13C22semidirect
47. C2×#88131C22semidirect
52. #11718871C22semidirect
61. #11718607C22semidirect
62. #11718606C22semidirect
63. #11718605C22semidirect
64. C22⋊C4×Dic13C22semidirect
65. C22⋊C4×Dic13C22semidirect
66. #11718315C22semidirect
67. #11718314C22semidirect
68. #11718310C22semidirect
69. #11718309C22semidirect
93. C23×Dic13C2×C4semidirect
115. C2×C22⋊Dic13C2×C4semidirect
121. D4×Dic13C2×C4semidirect
122. C2×C4⋊Dic13C2×C4semidirect
138. C2×C4×Dic13C2×C4semidirect
139. C2×C4×Dic13D4semidirect
235. C22×Dic13C22×C4semidirect
255. C22⋊Dic13C22×C4semidirect
256. C4⋊Dic13C22×C4semidirect
266. C4×Dic13C22×C4semidirect
267. C4×Dic13C2×D4semidirect
307. C23×C13#117semidirect
446. C22×C13C2×#117semidirect
563. C2×C13#2290semidirect
680. C13C2×#2290semidirect
704. C23#88131semidirect
790. C22C2×#88131semidirect
819. C2#13117276direct (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
C22×#881312
C23×C4×Dic132
#131172762
C2×#117186062
C2×#117186052
C2×#117183142
C2×#117183152
C2×#117188812
C2×#117188712
C2×#117186072
C2×#117183102
C2×C22⋊C4×Dic132
C2×#117183092
C2×C13×#3862
C2×#229013