Finite Group Databasebeta

← C2×#13125945 #16734314

Subgroups — C2×#13125945 #16734314

Order 3328.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719239C211yesmaximal, characteristic, complemented
2#13125945C2116yesmaximal, direct product factor
3C2×#11718747C211yesmaximal, characteristic, complemented
4C2×#11718720C211yesmaximal, characteristic, complemented
5C2×#11718716C211yesmaximal, characteristic, complemented
6C2×#11718742C211yesmaximal, characteristic, complemented
7C2×#11718715C211yesmaximal, characteristic, complemented
8C2×#11718751C211yesmaximal, characteristic, complemented
9C2×#11718718C211yesmaximal, characteristic, complemented
10C2×#11718744C211yesmaximal, characteristic, complemented
11C2×#11718900C211yesmaximal, characteristic, complemented
12C2×#11718899C211yesmaximal, characteristic
13C2×#11718889C211yesmaximal, characteristic, complemented
14C2×#11718888C211yesmaximal, characteristic, complemented
15C2×#11718661C211yesmaximal, characteristic, complemented
16C2×C13×#536C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic
18C23×Q8×C13C2211yescharacteristic
19C13×#536—24no—
20C13×#536C2218yescomplemented
21C2×C13×C4⋊Q8C2211yescharacteristic
22C2×C13×C4⋊Q8C2211yescharacteristic
23C2×C13×#124C2211yescharacteristic
24C2×C13×#124C2211yescharacteristic
25C2×C13×#123—21no—
26C2×C13×#123—21no—
27C2×C13×C22⋊Q8—21no—
28C2×C13×C22⋊Q8—21no—
29C2×C13×#117C2211yescharacteristic
30C22×#6107C2211yescharacteristic
31C22×#6107C2211yescharacteristic
32C22×#6107C2211yescharacteristic
33C22×#6106C2211yescharacteristic
34C22×#6106C2211yescharacteristic
35C22×#6106C2211yescharacteristic
36C22×#6105C2211yescharacteristic
37C22×#6104C2211yescharacteristic
38C2×#88184C2211yescharacteristic
39C2×#88178C2211yescharacteristic
40#11719239—24no—
41#11719239C2218yescomplemented
42C2×#88152—21no—
43C2×#88150—21no—
44C2×#88139—21no—
45C2×#88137—21no—
46C2×#88129C2211yescharacteristic
47C2×C4×D52C2211yescharacteristic
48C2×#88123C2211yescharacteristic
49C2×C4×Dic26C2211yescharacteristic
50#11718900C2218yescomplemented
51#11718899C2218yes—
52#11718889C2218yescomplemented
53#11718888C2218yescomplemented
54C2×#88075C2211yescharacteristic
55C2×#88075C2211yescharacteristic
56C2×#88075C2211yescharacteristic
57C2×#88075C2211yescharacteristic
58C2×#88075C2211yescharacteristic
59C2×#88075C2211yescharacteristic
60C2×#88072C2211yescharacteristic
61C2×#88072C2211yescharacteristic
62C2×C22⋊#1055C2211yescharacteristic
63C2×C22⋊#1055C2211yescharacteristic
64#11718751C2218yescomplemented
65#11718747C2218yescomplemented
66#11718744C2218yescomplemented
67#11718742C2218yescomplemented
68#11718720C2218yescomplemented
69#11718718C2218yescomplemented
70#11718716C2218yescomplemented
71#11718715C2218yescomplemented
72#11718661C2218yescomplemented
73C2×C4⋊#1055C2211yescharacteristic
74C2×C4⋊#1055C2211yescharacteristic
75C2×#88043C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C2×C13×#41—22no—
78C2×C13×#41—42no—
79C2×C13×#41—42no—
80C2×C13×#41C2314yes—
81C22×Q8×C13—21no—
82C22×Q8×C13—22no—
83C22×Q8×C13—42no—
84C22×Q8×C13—42no—
85C22×Q8×C13C2311yescharacteristic
86C22×Q8×C13C2311yescharacteristic
87C22×Q8×C13C2311yescharacteristic
88C22×Q8×C13C2314yes—
89C22×D4×C13—21no—
90C22×D4×C13C2311yescharacteristic
91C23×C4×C13—21no—
92C23×C4×C13—21no—
93C23×C4×C13C2311yescharacteristic
94C22×C22⋊D13—21no—
95C22×D52C2311yescharacteristic
96C22×C4×D13—21no—
97C22×Dic26—21no—
98C22×Dic26C2311yescharacteristic
99C13×C4⋊Q8—22no—
100C13×C4⋊Q8—22no—
101C13×C4⋊Q8C2314yes—
102C13×C4⋊Q8C2314yes—
103C13×#124—22no—
104C13×#124—22no—
105C13×#124C2314yes—
106C13×#124C2314yes—
107C13×#123—28no—
108C13×#123—28no—
109C13×C22⋊Q8—28no—
110C13×C22⋊Q8—28no—
111C13×#117D414yes—
112C13×#117C2314yes—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4—21no—
115C2×C13×C4⋊C4—21no—
116C2×C13×C4⋊C4—21no—
117C2×C13×C4⋊C4D411yescharacteristic
118C2×C13×C4⋊C4D411yescharacteristic
119C2×C13×C22⋊C4—21no—
120C2×C13×C22⋊C4—21no—
121C2×C13×C22⋊C4—21no—
122C2×C13×C22⋊C4—21no—
123C2×C13×C22⋊C4D411yescharacteristic
124C2×C13×C22⋊C4D411yescharacteristic
125C2×C42×C13C2311yescharacteristic
126C2×C42×C13C2311yescharacteristic
127C2×C22⋊Dic13—21no—
128C2×#6107—42no—
129C2×#6107—42no—
130C2×#6107—42no—
131C2×#6107C2314yes—
132C2×#6107C2314yes—
133C2×#6107C2314yes—
134C2×#6106—42no—
135C2×#6106—42no—
136C2×#6106—42no—
137C2×#6106C2314yes—
138C2×#6106C2314yes—
139C2×#6106C2314yes—
140C2×#6105—42no—
141C2×#6105C2314yes—
142C2×#6104—42no—
143C2×#6104C2314yes—
144#88184—22no—
145#88184C2314yes—
146C2×#6103—21no—
147C2×#6103—21no—
148C2×#6103—21no—
149C2×#6103—21no—
150C2×C4⋊Dic13—21no—
151C2×C4⋊Dic13C2311yescharacteristic
152C2×C4⋊Dic13C2311yescharacteristic
153#88178—22no—
154#88178C2314yes—
155C2×#6101—21no—
156C2×#6101—21no—
157C2×C4×Dic13—21no—
158C22×#1055C2311yescharacteristic
159C22×#1055C2311yescharacteristic
160C22×#1055C2311yescharacteristic
161C22×#1055C2311yescharacteristic
162#88152—28no—
163#88150—28no—
164#88139—28no—
165#88137—28no—
166#88129—22no—
167#88129C2314yes—
168C4×D52—22no—
169C4×D52C2314yes—
170#88123—22no—
171#88123C2314yes—
172C4×Dic26—22no—
173C4×Dic26C2314yes—
174#88075C2314yes—
175#88075C2314yes—
176#88075C2314yes—
177#88075C2314yes—
178#88075C2314yes—
179#88075C2314yes—
180#88072C2314yes—
181#88072C2314yes—
182C22⋊#1055C2314yes—
183C22⋊#1055C2314yes—
184C4⋊#1055C2314yes—
185C4⋊#1055C2314yes—
186#88043C2314yes—
187C4×#1055C2314yes—
188C2×#3225—131nomaximal, Sylow
189C24×C13—21no—
190C24×C13C2×D411yescharacteristic
191C23×D13—21no—
192C13×#41—44no—
193C13×#41—44no—
194C13×#41—48no—
195C2×Q8×C13—24no—
196C2×Q8×C13—21no—
197C2×Q8×C13—21no—
198C2×Q8×C13—21no—
199C2×Q8×C13—22no—
200C2×Q8×C13—22no—
201C2×Q8×C13—22no—
202C2×Q8×C13—22no—
203C2×Q8×C13—22no—
204C2×Q8×C13—22no—
205C2×Q8×C13—44no—
206C2×Q8×C13—44no—
207C2×Q8×C13—44no—
208C2×Q8×C13—48no—
209C2×Q8×C13C2412yes—
210C2×Q8×C13C2412yes—
211C2×Q8×C13C2412yes—
212C2×D4×C13—24no—
213C2×D4×C13—21no—
214C2×D4×C13—22no—
215C2×D4×C13—22no—
216C2×D4×C13—44no—
217C2×D4×C13C2412yes—
218C22×C4×C13—22no—
219C22×C4×C13—22no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—24no—
224C22×C4×C13—24no—
225C22×C4×C13—44no—
226C22×C4×C13—44no—
227C22×C4×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D412yes—
231C22×C4×C13C2×D411yescharacteristic
232C22×C4×C13C2×D411yescharacteristic
233C22×C4×C13C2412yes—
234C22×C4×C13C2411yescharacteristic
235C2×C22⋊D13—24no—
236C2×C22⋊D13—82no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C2×D52—22no—
241C2×D52—22no—
242C2×D52—21no—
243C2×D52C2412yes—
244C2×C4×D13—24no—
245C2×C4×D13—82no—
246C2×Dic26—22no—
247C2×Dic26—22no—
248C2×Dic26—21no—
249C2×Dic26—24no—
250C2×Dic26—82no—
251C2×Dic26C2412yes—
252C13×C4⋊C4—24no—
253C13×C4⋊C4—24no—
254C13×C4⋊C4—24no—
255C13×C4⋊C4—24no—
256C13×C4⋊C4C2×D414yes—
257C13×C4⋊C4C2×D414yes—
258C13×C22⋊C4—24no—
259C13×C22⋊C4—24no—
260C13×C22⋊C4—24no—
261C13×C22⋊C4—24no—
262C13×C22⋊C4C2×D414yes—
263C13×C22⋊C4C2×D414yes—
264C42×C13C2×D412yes—
265C42×C13C2×D412yes—
266C42×C13C2412yes—
267C42×C13C2412yes—
268C22⋊Dic13—24no—
269#6107—44no—
270#6107—44no—
271#6107—44no—
272#6106—44no—
273#6106—44no—
274#6106—44no—
275#6105—44no—
276#6104—44no—
277#6103—24no—
278#6103—24no—
279#6103—24no—
280#6103—24no—
281C4⋊Dic13—21no—
282C4⋊Dic13—21no—
283C4⋊Dic13—24no—
284C4⋊Dic13C2412yes—
285C4⋊Dic13C2412yes—
286#6101—24no—
287#6101—24no—
288C4×Dic13—24no—
289C2×#1055—22no—
290C2×#1055—22no—
291C2×#1055—22no—
292C2×#1055—22no—
293C2×#1055C2412yes—
294C2×#1055C2412yes—
295C2×#1055C2412yes—
296C2×#1055C2412yes—
297C2×#542—131no—
298C2×#536D1311yescharacteristic, complemented
299#3225—1316no—
300C2×#497—131no—
301C2×#495—131no—
302C2×#489—131no—
303C2×#487—131no—
304C2×#464—131no—
305C2×#462—131no—
306C2×#463—131no—
307C2×#461—131no—
308C2×#452—131no—
309C2×#449—131no—
310C2×#451—131no—
311C2×#448—131no—
312C2×#433—131no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—42no—
318C23×C13—42no—
319C23×C13—42no—
320C23×C13C22×D412yes—
321C23×C13C22×D411yescharacteristic
322C22×D13—22no—
323C22×D13—42no—
324C22×D13—42no—
325C22×D13—42no—
326Q8×C13—22no—
327Q8×C13—22no—
328Q8×C13—22no—
329Q8×C13—22no—
330Q8×C13—22no—
331Q8×C13—22no—
332Q8×C13—48no—
333Q8×C13—42no—
334Q8×C13—42no—
335Q8×C13—42no—
336D4×C13—22no—
337D4×C13—22no—
338D4×C13—48no—
339D4×C13—42no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—24no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—48no—
352C2×C4×C13—48no—
353C2×C4×C13—42no—
354C2×C4×C13—42no—
355C2×C4×C13—42no—
356C2×C4×C13C22×D412yes—
357C2×C4×C13C22×D412yes—
358C2×C4×C13C22×D412yes—
359C2×C4×C13C22×D412yes—
360C2×C4×C13C22×D412yes—
361C2×C4×C13C22×D411yescharacteristic
362C2×C4×C13H(5,𝔽2)12yes—
363C2×C4×C13H(5,𝔽2)12yes—
364C2×C4×C13C2511yescharacteristic
365C22⋊D13—84no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—42no—
370C2×Dic13—42no—
371C2×Dic13—42no—
372D52—22no—
373D52—22no—
374D52—42no—
375C4×D13—84no—
376Dic26—22no—
377Dic26—22no—
378Dic26—42no—
379Dic26—84no—
380#1055—22no—
381#1055—22no—
382#1055—22no—
383#1055—22no—
384C22×#41C2×D1311yescharacteristic
385C23×Q8C2×D1311yescharacteristic
386C22×Q16—131no—
387C22×Q16—131no—
388C22×Q16—131no—
389C22×SD16—131no—
390C22×SD16—131no—
391C22×SD16—131no—
392C22×SD16—131no—
393C22×D8—131no—
394#542—138no—
395#542—264no—
396#536—24no—
397#536C2×D1318yescomplemented
398C2×C4⋊Q8—131no—
399C2×C4⋊Q8C2×D1311yescharacteristic
400C2×C4⋊Q8C2×D1311yescharacteristic
401C2×#126—261no—
402C2×#124—131no—
403C2×#124—261no—
404C2×#124C2×D1311yescharacteristic
405C2×#124C2×D1311yescharacteristic
406C2×#123—21no—
407C2×#123—21no—
408C2×#123—261no—
409C2×C22⋊Q8—21no—
410C2×C22⋊Q8—21no—
411C2×C22⋊Q8—131no—
412C2×C22⋊Q8—261no—
413C2×#121—131no—
414C2×C4×Q8—131no—
415C2×C4×D4—131no—
416C2×#117C2×D1311yescharacteristic
417#497—138no—
418#495—138no—
419#489—138no—
420#487—138no—
421#464—138no—
422#463—138no—
423#462—138no—
424#461—138no—
425#452—138no—
426#451—138no—
427#449—138no—
428#448—138no—
429#433—138no—
430C2×C4⋊C8—131no—
431C2×C4⋊C8—131no—
432C2×#103—131no—
433C2×#103—131no—
434C2×#103—131no—
435C2×#103—131no—
436C2×#103—131no—
437C2×#103—131no—
438C2×#102—131no—
439C2×#102—131no—
440C2×C22⋊C8—131no—
441C2×C22⋊C8—131no—
442C2×#97—131no—
443C2×C4×C8—131no—
444C22×C13—22no—
445C22×C13—22no—
446C22×C13—22no—
447C22×C13—44no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—42no—
451C22×C13—84no—
452C22×C13#53512yes—
453C22×C13#57712yes—
454C22×C13#57812yes—
455C22×C13C23×D411yescharacteristic
456C2×D13—42no—
457C2×D13—42no—
458C2×D13—42no—
459C2×D13—84no—
460C4×C13—22no—
461C4×C13—22no—
462C4×C13—22no—
463C4×C13—22no—
464C4×C13—22no—
465C4×C13—42no—
466C4×C13—42no—
467C4×C13—42no—
468C4×C13#53512yes—
469C4×C13C2×H(5,𝔽2)11yescharacteristic
470C4×C13C2×H(5,𝔽2)11yescharacteristic
471Dic13—42no—
472Dic13—42no—
473Dic13—42no—
474C2×#41—22no—
475C2×#41—42no—
476C2×#41—42no—
477C2×#41C22×D1314yes—
478C22×Q8—21no—
479C22×Q8—22no—
480C22×Q8—42no—
481C22×Q8—42no—
482C22×Q8—131no—
483C22×Q8—261no—
484C22×Q8C22×D1311yescharacteristic
485C22×Q8C22×D1311yescharacteristic
486C22×Q8C22×D1311yescharacteristic
487C22×Q8C22×D1314yes—
488C22×D4—21no—
489C22×D4—131no—
490C22×D4—261no—
491C22×D4C22×D1311yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—261no—
495C23×C4C22×D1311yescharacteristic
496C2×Q16—134no—
497C2×Q16—134no—
498C2×Q16—134no—
499C2×Q16—522no—
500C2×Q16—522no—
501C2×Q16—522no—
502C2×SD16—134no—
503C2×SD16—134no—
504C2×SD16—134no—
505C2×SD16—134no—
506C2×SD16—522no—
507C2×SD16—522no—
508C2×SD16—522no—
509C2×SD16—522no—
510C2×D8—134no—
511C2×D8—522no—
512C22×C8—131no—
513C22×C8—131no—
514C22×C8—131no—
515C22×C8—131no—
516C4⋊Q8—22no—
517C4⋊Q8—22no—
518C4⋊Q8—134no—
519C4⋊Q8—262no—
520C4⋊Q8C22×D1314yes—
521C4⋊Q8C22×D1314yes—
522#126—268no—
523#124—22no—
524#124—22no—
525#124—134no—
526#124—268no—
527#124—262no—
528#124C22×D1314yes—
529#124C22×D1314yes—
530#123—28no—
531#123—28no—
532#123—268no—
533C22⋊Q8—28no—
534C22⋊Q8—28no—
535C22⋊Q8—134no—
536C22⋊Q8—262no—
537C22⋊Q8—268no—
538#121—134no—
539#121—262no—
540C4×Q8—134no—
541C4×Q8—262no—
542C4×D4—134no—
543C4×D4—262no—
544#117C22⋊D1314yes—
545#117C22×D1314yes—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—131no—
551C2×C4⋊C4—131no—
552C2×C4⋊C4—261no—
553C2×C4⋊C4—261no—
554C2×C4⋊C4—261no—
555C2×C4⋊C4C22⋊D1311yescharacteristic
556C2×C4⋊C4C22⋊D1311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—261no—
562C2×C22⋊C4—261no—
563C2×C22⋊C4—261no—
564C2×C22⋊C4—261no—
565C2×C22⋊C4—261no—
566C2×C22⋊C4C22⋊D1311yescharacteristic
567C2×C22⋊C4C22⋊D1311yescharacteristic
568C2×C42—261no—
569C2×C42C22×D1311yescharacteristic
570C2×C42C22×D1311yescharacteristic
571C4⋊C8—134no—
572C4⋊C8—134no—
573#103—134no—
574#103—134no—
575#103—134no—
576#103—134no—
577#103—134no—
578#103—134no—
579#102—134no—
580#102—134no—
581C22⋊C8—134no—
582C22⋊C8—134no—
583#97—134no—
584C4×C8—134no—
585C2×C13—42no—
586C2×C13—82no—
587C2×C13#322514yescomplemented
588C2×C13C2×#53511yescharacteristic
589C2×C13C2×#57711yescharacteristic
590C2×C13C2×#57811yescharacteristic
591D13—82no—
592C24—21no—
593C24—261no—
594C24C2×C22⋊D1311yescharacteristic
595#41—44no—
596#41—44no—
597#41—48no—
598C2×Q8—24no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—44no—
609C2×Q8—44no—
610C2×Q8—44no—
611C2×Q8—48no—
612C2×Q8—132no—
613C2×Q8—261no—
614C2×Q8—264no—
615C2×Q8—262no—
616C2×Q8—262no—
617C2×Q8—1042no—
618C2×Q8C23×D1312yes—
619C2×Q8C23×D1312yes—
620C2×Q8C23×D1312yes—
621C2×D4—24no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—21no—
625C2×D4—44no—
626C2×D4—132no—
627C2×D4—264no—
628C2×D4—262no—
629C2×D4—262no—
630C2×D4—261no—
631C2×D4—1042no—
632C2×D4C23×D1312yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—24no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—261no—
643C22×C4—261no—
644C22×C4—261no—
645C22×C4—264no—
646C22×C4—1042no—
647C22×C4C2×C22⋊D1312yes—
648C22×C4C2×C22⋊D1311yescharacteristic
649C22×C4C2×C22⋊D1311yescharacteristic
650C22×C4C2×C22⋊D1311yescharacteristic
651C22×C4C2×C22⋊D1311yescharacteristic
652C22×C4C2×C22⋊D1311yescharacteristic
653C22×C4C23×D1312yes—
654C22×C4C23×D1311yescharacteristic
655Q16—524no—
656Q16—524no—
657Q16—524no—
658SD16—524no—
659SD16—524no—
660SD16—524no—
661SD16—524no—
662D8—524no—
663C2×C8—132no—
664C2×C8—132no—
665C2×C8—132no—
666C2×C8—132no—
667C2×C8—262no—
668C2×C8—262no—
669C2×C8—262no—
670C2×C8—262no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—132no—
676C4⋊C4—132no—
677C4⋊C4—261no—
678C4⋊C4—261no—
679C4⋊C4—264no—
680C4⋊C4—264no—
681C4⋊C4—264no—
682C4⋊C4C2×C22⋊D1314yes—
683C4⋊C4C2×C22⋊D1314yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—264no—
689C22⋊C4—264no—
690C22⋊C4—264no—
691C22⋊C4—264no—
692C22⋊C4—264no—
693C22⋊C4C2×C22⋊D1314yes—
694C22⋊C4C2×C22⋊D1314yes—
695C42—264no—
696C42C2×C22⋊D1312yes—
697C42C2×C22⋊D1312yes—
698C42C23×D1312yes—
699C42C23×D1312yes—
700C13C2×#322511yescharacteristic, complemented, Sylow
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—262no—
709C23—522no—
710C23—522no—
711C23—522no—
712C23C22×C22⋊D1312yes—
713C23C22×C22⋊D1311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—48no—
721Q8—42no—
722Q8—42no—
723Q8—42no—
724Q8—262no—
725Q8—262no—
726Q8—522no—
727Q8—1044no—
728D4—22no—
729D4—22no—
730D4—48no—
731D4—42no—
732D4—262no—
733D4—262no—
734D4—522no—
735D4—1044no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—522no—
756C2×C4—522no—
757C2×C4—522no—
758C2×C4—1044no—
759C2×C4#8825112yes—
760C2×C4#8825112yes—
761C2×C4C22×C22⋊D1312yes—
762C2×C4C22×C22⋊D1312yes—
763C2×C4C22×C22⋊D1312yes—
764C2×C4C22×C22⋊D1312yes—
765C2×C4C22×C22⋊D1312yes—
766C2×C4C22×C22⋊D1311yescharacteristic
767C2×C4C24×D1311yescharacteristic
768C8—262no—
769C8—262no—
770C8—262no—
771C8—262no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—522no—
781C22—522no—
782C22—522no—
783C22—1044no—
784C22#1171951012yes—
785C22#1171954212yes—
786C22#1171954312yes—
787C22C23×C22⋊D1311yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—522no—
797C4—522no—
798C4—522no—
799C4#1171951012yes—
800C4C2×#8825111yescharacteristic
801C4C2×#8825111yescharacteristic
802C2—42no—
803C2—82no—
804C2—1042no—
805C2#1312594514yesdirect product factor
806C2C2×#1171951011yescharacteristic
807C2C2×#1171954211yescharacteristic
808C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#536C2
socleC23×C13C22×D4
prime radicalC2×#11718899C2
hypercenterC2×#536D13
hypocenterC13C2×#3225
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#11719239C2semidirect
2. #13125945C2direct (N × H)
3. C2×#11718747C2semidirect
4. C2×#11718720C2semidirect
5. C2×#11718716C2semidirect
6. C2×#11718742C2semidirect
7. C2×#11718715C2semidirect
8. C2×#11718751C2semidirect
9. C2×#11718718C2semidirect
10. C2×#11718744C2semidirect
11. C2×#11718900C2semidirect
13. C2×#11718889C2semidirect
14. C2×#11718888C2semidirect
15. C2×#11718661C2semidirect
16. C2×C13×#536C2semidirect
20. C13×#536C22semidirect
41. #11719239C22semidirect
50. #11718900C22semidirect
52. #11718889C22semidirect
53. #11718888C22semidirect
64. #11718751C22semidirect
65. #11718747C22semidirect
66. #11718744C22semidirect
67. #11718742C22semidirect
68. #11718720C22semidirect
69. #11718718C22semidirect
70. #11718716C22semidirect
71. #11718715C22semidirect
72. #11718661C22semidirect
298. C2×#536D13semidirect
397. #536C2×D13semidirect
587. C2×C13#3225semidirect
700. C13C2×#3225semidirect
805. C2#13125945direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192392
#131259452
C2×#117187472
C2×#117187202
C2×#117187162
C2×#117187422
C2×#117187152
C2×#117187512
C2×#117187182
C2×#117187442
C2×#117189002
C2×#117188992
C2×#117188892
C2×#117188882
C2×#117186612
C2×C13×#5362
C2×#322513