Finite Group Databasebeta

← C2×#13127007 #16739541

Subgroups — C2×#13127007 #16739541

Order 3328.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719270C211yesmaximal, characteristic
2#13127007C2116yesmaximal, direct product factor
3C2×#11718743C211yesmaximal, characteristic, complemented
4C2×#11718705C211yesmaximal, characteristic, complemented
5C2×#11718706C211yesmaximal, characteristic, complemented
6C2×#11718683C211yesmaximal, characteristic, complemented
7C2×#11718710C211yesmaximal, characteristic, complemented
8C2×#11718709C211yesmaximal, characteristic, complemented
9C2×#11718744C211yesmaximal, characteristic, complemented
10C2×#11718888C211yesmaximal, characteristic, complemented
11C2×#11718888C211yesmaximal, characteristic, complemented
12C2×#11718687C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic, complemented
14C2×#11718886C211yesmaximal, characteristic, complemented
15C22×#88075C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C13C211yesmaximal, characteristic, complemented
17C23×Q8×C13C2211yescharacteristic
18C23×Q8×C13C2211yescharacteristic
19D4×Q8×C13—24no—
20D4×Q8×C13C2218yescomplemented
21C2×C13×C4⋊Q8—21no—
22C2×C13×C4⋊Q8C2211yescharacteristic
23C2×C13×C22⋊Q8—21no—
24C2×C13×C22⋊Q8—21no—
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C13×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×D4×C13—21no—
29C2×C4×D4×C13C2211yescharacteristic
30C22×#6106C2211yescharacteristic
31C22×#6106C2211yescharacteristic
32C22×#6106C2211yescharacteristic
33C2×#88193—21no—
34C2×#88184C2211yescharacteristic
35C2×#88184C2211yescharacteristic
36C2×#88180C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×#6099C2211yescharacteristic
39C23×#1055C2211yescharacteristic
40#11719270—24no—
41#11719270C2218yes—
42C2×#88152—21no—
43C2×#88137—21no—
44C2×#88135—21no—
45C2×C4×D52C2211yescharacteristic
46C2×#88124C2211yescharacteristic
47#11718888C2218yescomplemented
48#11718888C2218yescomplemented
49#11718886C2218yescomplemented
50C2×#88075C2211yescharacteristic
51C2×#88075C2211yescharacteristic
52C2×#88075C2211yescharacteristic
53C2×#88075C2211yescharacteristic
54C2×#88075C2211yescharacteristic
55C2×#88075C2211yescharacteristic
56C2×#88075C2211yescharacteristic
57C2×#88075C2211yescharacteristic
58C2×#88075C2211yescharacteristic
59C2×#88075C2218yescomplemented
60C2×C22⋊#1055C2211yescharacteristic
61C2×C22⋊#1055C2211yescharacteristic
62#11718744C2218yescomplemented
63#11718743C2218yescomplemented
64#11718710C2218yescomplemented
65#11718709C2218yescomplemented
66#11718706C2218yescomplemented
67#11718705C2218yescomplemented
68#11718687C2218yescomplemented
69#11718683C2218yescomplemented
70#11718672C2218yescomplemented
71C2×#88049C2211yescharacteristic
72C2×#88048C2211yescharacteristic
73C2×#88047C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
77C22×Q8×C13—21no—
78C22×Q8×C13—21no—
79C22×Q8×C13—22no—
80C22×Q8×C13—22no—
81C22×Q8×C13—24no—
82C22×Q8×C13—24no—
83C22×Q8×C13—42no—
84C22×Q8×C13—42no—
85C22×Q8×C13C2311yescharacteristic
86C22×Q8×C13C2311yescharacteristic
87C22×Q8×C13C2314yes—
88C22×Q8×C13C2314yes—
89C22×Q8×C13C2311yescharacteristic
90C22×D4×C13D411yescharacteristic
91C23×C4×C13—21no—
92C23×C4×C13—21no—
93C23×C4×C13C2311yescharacteristic
94C23×C4×C13C2311yescharacteristic
95C22×C22⋊D13—21no—
96C22×C22⋊D13—21no—
97C23×Dic13—21no—
98C22×D52C2311yescharacteristic
99C22×C4×D13—21no—
100C13×C4⋊Q8—28no—
101C13×C4⋊Q8—22no—
102C13×C4⋊Q8C2314yes—
103C13×C22⋊Q8—22no—
104C13×C22⋊Q8—22no—
105C13×C22⋊Q8—28no—
106C13×C22⋊Q8—28no—
107C13×C22⋊Q8C2314yes—
108C13×C22⋊Q8C2314yes—
109C4×Q8×C13—22no—
110C4×Q8×C13C2314yes—
111C4×D4×C13—28no—
112C4×D4×C13D414yes—
113C4×D4×C13C2314yes—
114C2×C13×C4⋊C4—21no—
115C2×C13×C4⋊C4—21no—
116C2×C13×C4⋊C4—21no—
117C2×C13×C4⋊C4—21no—
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4D411yescharacteristic
120C2×C13×C4⋊C4C2311yescharacteristic
121C2×C13×C22⋊C4—21no—
122C2×C13×C22⋊C4—21no—
123C2×C13×C22⋊C4D411yescharacteristic
124C2×C13×C22⋊C4D411yescharacteristic
125C2×C42×C13—21no—
126C2×C42×C13C2311yescharacteristic
127C2×C22⋊Dic13—21no—
128C2×#6106—24no—
129C2×#6106—42no—
130C2×#6106—42no—
131C2×#6106C2314yes—
132C2×#6106C2314yes—
133C2×#6106C2314yes—
134#88193—28no—
135#88184—22no—
136#88184—22no—
137#88184C2314yes—
138#88184C2314yes—
139C2×#6103—21no—
140C2×#6103—21no—
141C2×#6103—21no—
142#88180—22no—
143#88180C2314yes—
144C2×C4⋊Dic13—21no—
145C2×C4⋊Dic13—22no—
146C2×C4⋊Dic13C2311yescharacteristic
147C2×C4⋊Dic13C2311yescharacteristic
148C2×C4⋊Dic13C2311yescharacteristic
149C2×C4⋊Dic13C2314yes—
150C2×#6101—21no—
151C2×#6101—21no—
152C2×C4×Dic13—21no—
153C2×#6099—42no—
154C2×#6099C2314yes—
155C22×#1055—42no—
156C22×#1055C2311yescharacteristic
157C22×#1055C2311yescharacteristic
158C22×#1055C2311yescharacteristic
159C22×#1055C2311yescharacteristic
160C22×#1055C2314yes—
161#88152—28no—
162#88137—28no—
163#88135—28no—
164C4×D52—22no—
165C4×D52C2314yes—
166#88124—22no—
167#88124C2314yes—
168#88075C2314yes—
169#88075C2314yes—
170#88075C2314yes—
171#88075C2314yes—
172#88075C2314yes—
173#88075C2314yes—
174#88075C2314yes—
175#88075C2314yes—
176#88075C2314yes—
177C22⋊#1055C2314yes—
178C22⋊#1055C2314yes—
179#88049C2314yes—
180#88048C2314yes—
181#88047C2314yes—
182#88047C2314yes—
183C4⋊#1055C2314yes—
184#88043C2314yes—
185C2×#3320—131nomaximal, Sylow
186C24×C13C2×D411yescharacteristic
187C24×C13C2×D411yescharacteristic
188C23×D13—21no—
189C2×Q8×C13—21no—
190C2×Q8×C13—24no—
191C2×Q8×C13—24no—
192C2×Q8×C13—21no—
193C2×Q8×C13—21no—
194C2×Q8×C13—22no—
195C2×Q8×C13—28no—
196C2×Q8×C13—28no—
197C2×Q8×C13—22no—
198C2×Q8×C13—22no—
199C2×Q8×C13—22no—
200C2×Q8×C13—22no—
201C2×Q8×C13—44no—
202C2×Q8×C13—44no—
203C2×Q8×C13—44no—
204C2×Q8×C13—44no—
205C2×Q8×C13—48no—
206C2×Q8×C13—48no—
207C2×Q8×C13#4114yes—
208C2×Q8×C13C2412yes—
209C2×Q8×C13C2412yes—
210C2×Q8×C13C2412yes—
211C2×D4×C13—24no—
212C2×D4×C13C2×D414yes—
213C22×C4×C13—21no—
214C22×C4×C13—22no—
215C22×C4×C13—22no—
216C22×C4×C13—22no—
217C22×C4×C13—22no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—24no—
222C22×C4×C13—24no—
223C22×C4×C13—44no—
224C22×C4×C13—44no—
225C22×C4×C13C2×D411yescharacteristic
226C22×C4×C13C2×D411yescharacteristic
227C22×C4×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D412yes—
230C22×C4×C13C2×D412yes—
231C22×C4×C13C2412yes—
232C22×C4×C13C2412yes—
233C22×C4×C13C2411yescharacteristic
234C2×C22⋊D13—24no—
235C2×C22⋊D13—24no—
236C2×C22⋊D13—44no—
237C2×C22⋊D13—82no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—24no—
242C22×Dic13—82no—
243C2×D52—22no—
244C2×D52—22no—
245C2×D52—21no—
246C2×D52C2412yes—
247C2×C4×D13—24no—
248C2×C4×D13—82no—
249C13×C4⋊C4—24no—
250C13×C4⋊C4—24no—
251C13×C4⋊C4—24no—
252C13×C4⋊C4—24no—
253C13×C4⋊C4—24no—
254C13×C4⋊C4—21no—
255C13×C4⋊C4C2×D414yes—
256C13×C4⋊C4C2412yes—
257C13×C22⋊C4—24no—
258C13×C22⋊C4—24no—
259C13×C22⋊C4C2×D414yes—
260C13×C22⋊C4C2×D414yes—
261C42×C13—24no—
262C42×C13C2×D412yes—
263C42×C13C2412yes—
264C22⋊Dic13—24no—
265#6106—28no—
266#6106—44no—
267#6106—44no—
268#6103—24no—
269#6103—24no—
270#6103—24no—
271C4⋊Dic13—21no—
272C4⋊Dic13—21no—
273C4⋊Dic13—21no—
274C4⋊Dic13—24no—
275C4⋊Dic13C2412yes—
276C4⋊Dic13C2412yes—
277C4⋊Dic13C2412yes—
278#6101—24no—
279#6101—24no—
280C4×Dic13—24no—
281#6099—44no—
282C2×#1055—22no—
283C2×#1055—22no—
284C2×#1055—22no—
285C2×#1055—22no—
286C2×#1055—44no—
287C2×#1055C2412yes—
288C2×#1055C2412yes—
289C2×#1055C2412yes—
290C2×#1055C2412yes—
291C2×#553—131no—
292C2×D4×Q8D1311yescharacteristic, complemented
293#3320—1316no—
294C2×#491—131no—
295C2×#484—131no—
296C2×#485—131no—
297C2×#479—131no—
298C2×#468—131no—
299C2×#465—131no—
300C2×#461—131no—
301C2×#448—131no—
302C2×#448—131no—
303C2×#440—131no—
304C2×#435—131no—
305C2×#419—131no—
306C22×#103—131no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13#13714yes—
313C23×C13C22×D412yes—
314C23×C13C22×D412yes—
315C23×C13C22×D411yescharacteristic
316C22×D13—22no—
317C22×D13—42no—
318C22×D13—42no—
319C22×D13—42no—
320Q8×C13—24no—
321Q8×C13—22no—
322Q8×C13—22no—
323Q8×C13—22no—
324Q8×C13—22no—
325Q8×C13—22no—
326Q8×C13—48no—
327Q8×C13—48no—
328Q8×C13—42no—
329Q8×C13—42no—
330Q8×C13C2×#4114yes—
331D4×C13—28no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—24no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—24no—
339C2×C4×C13—24no—
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—48no—
348C2×C4×C13—48no—
349C2×C4×C13—42no—
350C2×C4×C13—42no—
351C2×C4×C13—42no—
352C2×C4×C13C22×D412yes—
353C2×C4×C13C22×D412yes—
354C2×C4×C13C22×D412yes—
355C2×C4×C13C22×D412yes—
356C2×C4×C13C22×D411yescharacteristic
357C2×C4×C13C2×#4112yes—
358C2×C4×C13H(5,𝔽2)12yes—
359C2×C4×C13C2511yescharacteristic
360C22⋊D13—48no—
361C22⋊D13—84no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—42no—
366C2×Dic13—42no—
367C2×Dic13—42no—
368C2×Dic13—84no—
369D52—22no—
370D52—22no—
371D52—42no—
372C4×D13—84no—
373#1055—22no—
374#1055—22no—
375#1055—22no—
376#1055—22no—
377C23×Q8C2×D1311yescharacteristic
378C23×Q8C2×D1311yescharacteristic
379C22×SD16—131no—
380C22×SD16—131no—
381C22×SD16—131no—
382C22×M16—131no—
383C23×C8—131no—
384#553—138no—
385#553—264no—
386D4×Q8—24no—
387D4×Q8C2×D1318yescomplemented
388C2×C4⋊Q8—21no—
389C2×C4⋊Q8C2×D1311yescharacteristic
390C2×#126—261no—
391C2×#125—131no—
392C2×#123—261no—
393C2×C22⋊Q8—21no—
394C2×C22⋊Q8—21no—
395C2×C22⋊Q8C2×D1311yescharacteristic
396C2×C22⋊Q8C2×D1311yescharacteristic
397C2×#121—131no—
398C2×#121—131no—
399C2×#121—261no—
400C2×C4×Q8C2×D1311yescharacteristic
401C2×C4×D4—21no—
402C2×C4×D4—131no—
403C2×C4×D4—261no—
404C2×C4×D4C2×D1311yescharacteristic
405C2×#117—131no—
406C22×C4⋊C4—131no—
407#491—138no—
408#485—138no—
409#484—138no—
410#479—138no—
411#468—138no—
412#465—138no—
413#461—138no—
414#448—138no—
415#448—138no—
416#440—138no—
417#435—138no—
418C2×#107—131no—
419C2×#107—131no—
420C2×#106—131no—
421C2×C4⋊C8—131no—
422#419—138no—
423C2×#103—131no—
424C2×#103—131no—
425C2×#103—131no—
426C2×#103—131no—
427C2×#103—131no—
428C2×#103—131no—
429C2×#103—131no—
430C2×#103—131no—
431C2×#103—131no—
432C2×#103—138no—
433C2×#102—131no—
434C2×C22⋊C8—131no—
435C2×C22⋊C8—131no—
436C2×#97—131no—
437C22×C13—22no—
438C22×C13—28no—
439C22×C13—22no—
440C22×C13—22no—
441C22×C13—22no—
442C22×C13—22no—
443C22×C13—44no—
444C22×C13#54612yes—
445C22×C13C2×#13714yes—
446C22×C13C2×#13712yes—
447C22×C13#57712yes—
448C22×C13C23×D411yescharacteristic
449C2×D13—42no—
450C2×D13—42no—
451C2×D13—42no—
452C2×D13—84no—
453C4×C13—22no—
454C4×C13—22no—
455C4×C13—24no—
456C4×C13—22no—
457C4×C13—22no—
458C4×C13—42no—
459C4×C13—42no—
460C4×C13—42no—
461C4×C13#54612yes—
462C4×C13C22×#4111yescharacteristic
463C4×C13C2×H(5,𝔽2)11yescharacteristic
464Dic13—42no—
465Dic13—42no—
466Dic13—42no—
467C22×Q8—21no—
468C22×Q8—21no—
469C22×Q8—22no—
470C22×Q8—22no—
471C22×Q8—24no—
472C22×Q8—24no—
473C22×Q8—42no—
474C22×Q8—42no—
475C22×Q8C22×D1311yescharacteristic
476C22×Q8C22×D1311yescharacteristic
477C22×Q8C22×D1314yes—
478C22×Q8C22×D1314yes—
479C22×Q8C22×D1311yescharacteristic
480C22×D4—131no—
481C22×D4—261no—
482C22×D4—261no—
483C22×D4C22⋊D1311yescharacteristic
484C23×C4—21no—
485C23×C4—21no—
486C23×C4—261no—
487C23×C4—261no—
488C23×C4C22×D1311yescharacteristic
489C23×C4C22×D1311yescharacteristic
490C2×SD16—134no—
491C2×SD16—134no—
492C2×SD16—134no—
493C2×SD16—264no—
494C2×SD16—522no—
495C2×SD16—522no—
496C2×M16—134no—
497C2×M16—522no—
498C22×C8—131no—
499C22×C8—131no—
500C22×C8—131no—
501C22×C8—131no—
502C22×C8—134no—
503C22×C8—522no—
504C4⋊Q8—28no—
505C4⋊Q8—22no—
506C4⋊Q8C22×D1314yes—
507#126—268no—
508#125—134no—
509#125—262no—
510#123—268no—
511C22⋊Q8—22no—
512C22⋊Q8—22no—
513C22⋊Q8—28no—
514C22⋊Q8—28no—
515C22⋊Q8C22×D1314yes—
516C22⋊Q8C22×D1314yes—
517#121—134no—
518#121—134no—
519#121—268no—
520#121—262no—
521#121—262no—
522C4×Q8—22no—
523C4×Q8C22×D1314yes—
524C4×D4—28no—
525C4×D4—134no—
526C4×D4—268no—
527C4×D4—262no—
528C4×D4C22⋊D1314yes—
529C4×D4C22×D1314yes—
530#117—134no—
531#117—262no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—131no—
538C2×C4⋊C4—131no—
539C2×C4⋊C4—134no—
540C2×C4⋊C4—131no—
541C2×C4⋊C4—261no—
542C2×C4⋊C4—262no—
543C2×C4⋊C4—261no—
544C2×C4⋊C4—261no—
545C2×C4⋊C4C22⋊D1311yescharacteristic
546C2×C4⋊C4C22×D1311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—261no—
550C2×C22⋊C4—261no—
551C2×C22⋊C4—261no—
552C2×C22⋊C4—261no—
553C2×C22⋊C4C22⋊D1311yescharacteristic
554C2×C22⋊C4C22⋊D1311yescharacteristic
555C2×C42—21no—
556C2×C42—261no—
557C2×C42C22×D1311yescharacteristic
558#107—134no—
559#107—134no—
560#106—134no—
561C4⋊C8—134no—
562#103—134no—
563#103—134no—
564#103—134no—
565#103—134no—
566#103—134no—
567#103—134no—
568#103—134no—
569#103—134no—
570#103—134no—
571#102—134no—
572C22⋊C8—134no—
573C22⋊C8—134no—
574#97—134no—
575C2×C13—24no—
576C2×C13—42no—
577C2×C13#332014yescomplemented
578C2×C13C2×#54611yescharacteristic
579C2×C13C22×#13711yescharacteristic
580C2×C13C2×#57711yescharacteristic
581D13—82no—
582C24—261no—
583C24C2×C22⋊D1311yescharacteristic
584C24C2×C22⋊D1311yescharacteristic
585C2×Q8—22no—
586C2×Q8—21no—
587C2×Q8—24no—
588C2×Q8—24no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—28no—
592C2×Q8—28no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—44no—
598C2×Q8—44no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8—48no—
602C2×Q8—48no—
603C2×Q8#612914yes—
604C2×Q8C23×D1312yes—
605C2×Q8C23×D1312yes—
606C2×Q8C23×D1312yes—
607C2×D4—24no—
608C2×D4—132no—
609C2×D4—264no—
610C2×D4—264no—
611C2×D4—262no—
612C2×D4—262no—
613C2×D4—261no—
614C2×D4—524no—
615C2×D4—1042no—
616C2×D4C2×C22⋊D1314yes—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—261no—
630C22×C4—261no—
631C22×C4—261no—
632C22×C4—264no—
633C22×C4—264no—
634C22×C4—1042no—
635C22×C4—1042no—
636C22×C4C2×C22⋊D1312yes—
637C22×C4C2×C22⋊D1312yes—
638C22×C4C2×C22⋊D1311yescharacteristic
639C22×C4C2×C22⋊D1311yescharacteristic
640C22×C4C2×C22⋊D1311yescharacteristic
641C22×C4C2×C22⋊D1311yescharacteristic
642C22×C4C23×D1312yes—
643C22×C4C23×D1312yes—
644C22×C4C23×D1311yescharacteristic
645SD16—268no—
646SD16—524no—
647SD16—524no—
648M16—524no—
649C2×C8—132no—
650C2×C8—132no—
651C2×C8—132no—
652C2×C8—132no—
653C2×C8—262no—
654C2×C8—262no—
655C2×C8—262no—
656C2×C8—262no—
657C2×C8—524no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—132no—
665C4⋊C4—132no—
666C4⋊C4—132no—
667C4⋊C4—261no—
668C4⋊C4—261no—
669C4⋊C4—264no—
670C4⋊C4—261no—
671C4⋊C4—264no—
672C4⋊C4—264no—
673C4⋊C4C2×C22⋊D1314yes—
674C4⋊C4C23×D1312yes—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—264no—
678C22⋊C4—264no—
679C22⋊C4—264no—
680C22⋊C4—264no—
681C22⋊C4C2×C22⋊D1314yes—
682C22⋊C4C2×C22⋊D1314yes—
683C42—24no—
684C42—264no—
685C42C2×C22⋊D1312yes—
686C42C23×D1312yes—
687C13C2×#332011yescharacteristic, complemented, Sylow
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—262no—
694C23—522no—
695C23—522no—
696C23—522no—
697C23#8819614yes—
698C23C22×C22⋊D1312yes—
699C23C22×C22⋊D1312yes—
700C23C22×C22⋊D1311yescharacteristic
701Q8—24no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—48no—
708Q8—48no—
709Q8—42no—
710Q8—42no—
711Q8C2×#612914yes—
712D4—28no—
713D4—262no—
714D4—262no—
715D4—528no—
716D4—522no—
717D4—1044no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—48no—
734C2×C4—48no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—522no—
742C2×C4—522no—
743C2×C4—522no—
744C2×C4—1044no—
745C2×C4—1044no—
746C2×C4C2×#612912yes—
747C2×C4#8825112yes—
748C2×C4C22×C22⋊D1312yes—
749C2×C4C22×C22⋊D1312yes—
750C2×C4C22×C22⋊D1312yes—
751C2×C4C22×C22⋊D1312yes—
752C2×C4C22×C22⋊D1311yescharacteristic
753C2×C4C24×D1311yescharacteristic
754C8—262no—
755C8—262no—
756C8—262no—
757C8—262no—
758C22—22no—
759C22—28no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—522no—
766C22—522no—
767C22—522no—
768C22—1044no—
769C22#1171951112yes—
770C22C2×#8819614yes—
771C22C2×#8819612yes—
772C22#1171954212yes—
773C22C23×C22⋊D1311yescharacteristic
774C4—22no—
775C4—22no—
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—522no—
783C4—522no—
784C4—522no—
785C4#1171951112yes—
786C4C22×#612911yescharacteristic
787C4C2×#8825111yescharacteristic
788C2—24no—
789C2—42no—
790C2—1042no—
791C2#1312700714yesdirect product factor
792C2C2×#1171951111yescharacteristic
793C2C22×#8819611yescharacteristic
794C2C2×#1171954211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×D4×Q8×C13C2
socleC23×C13C22×D4
prime radicalC2×#11719270C2
hypercenterC2×D4×Q8D13
hypocenterC13C2×#3320
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. #13127007C2direct (N × H)
3. C2×#11718743C2semidirect
4. C2×#11718705C2semidirect
5. C2×#11718706C2semidirect
6. C2×#11718683C2semidirect
7. C2×#11718710C2semidirect
8. C2×#11718709C2semidirect
9. C2×#11718744C2semidirect
10. C2×#11718888C2semidirect
11. C2×#11718888C2semidirect
12. C2×#11718687C2semidirect
13. C2×#11718672C2semidirect
14. C2×#11718886C2semidirect
15. C22×#88075C2semidirect
16. C2×D4×Q8×C13C2semidirect
20. D4×Q8×C13C22semidirect
47. #11718888C22semidirect
48. #11718888C22semidirect
49. #11718886C22semidirect
59. C2×#88075C22semidirect
62. #11718744C22semidirect
63. #11718743C22semidirect
64. #11718710C22semidirect
65. #11718709C22semidirect
66. #11718706C22semidirect
67. #11718705C22semidirect
68. #11718687C22semidirect
69. #11718683C22semidirect
70. #11718672C22semidirect
292. C2×D4×Q8D13semidirect
387. D4×Q8C2×D13semidirect
577. C2×C13#3320semidirect
687. C13C2×#3320semidirect
791. C2#13127007direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192702
#131270072
C2×#117187432
C2×#117187052
C2×#117187062
C2×#117186832
C2×#117187102
C2×#117187092
C2×#117187442
C2×#117188882
C2×#117186872
C2×#117186722
C2×#117188862
C22×#880752
C2×D4×Q8×C132
C2×#332013