Finite Group Databasebeta

← C2×#13124856 #16730936

Subgroups — C2×#13124856 #16730936

Order 3328.

2202 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719184C211yesmaximal, characteristic, complemented
2C2×C4×#6127C211yesmaximal, characteristic, complemented
3#13124856C2116yesmaximal, direct product factor
4C2×#11718384C211yesmaximal, characteristic, complemented
5C2×#11718398C211yesmaximal, characteristic, complemented
6C2×#11718490C211yesmaximal, characteristic, complemented
7C2×#11718508C211yesmaximal, characteristic, complemented
8C2×#11718506C211yesmaximal, characteristic, complemented
9C2×#11718505C211yesmaximal, characteristic, complemented
10C2×#11718394C211yesmaximal, characteristic, complemented
11C2×#11718395C211yesmaximal, characteristic
12C2×C4×Dic52C211yesmaximal, characteristic, complemented
13C2×C4×#6095C211yesmaximal, characteristic, complemented
14C2×C4×#6095C211yesmaximal, characteristic, complemented
15C2×C4×D104C211yesmaximal, characteristic, complemented
16C2×C13×#431C211yesmaximal, characteristic, complemented
17C22×#6127C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C2×#88184C2211yescharacteristic
20C2×#88183—21no—
21C2×C4×C22⋊D13—21no—
22C2×C4×C22⋊D13—21no—
23C2×C4×C22⋊D13—21no—
24C2×#88180C2211yescharacteristic
25C2×#88178C2211yescharacteristic
26C22×Dic52C2211yescharacteristic
27C22×D104C2211yescharacteristic
28C22×#6095C2211yescharacteristic
29C22×#6095C2211yescharacteristic
30#11719184—24no—
31#11719184C2218yescomplemented
32C2×#88130—21no—
33C2×#88129C2211yescharacteristic
34C4×#6127—24no—
35C4×#6127C2218yescomplemented
36C2×C4×D52C2211yescharacteristic
37C2×C4×D52C2211yescharacteristic
38C2×C4×D52C2211yescharacteristic
39C2×#88126—21no—
40C2×#88126—21no—
41C2×C42×D13—21no—
42C2×#88124C2211yescharacteristic
43C2×C4×Dic26C2211yescharacteristic
44C2×C4×Dic26C2211yescharacteristic
45C2×C4×Dic26C2211yescharacteristic
46C13×#431C2218yescomplemented
47C2×C13×C4⋊C8C2211yescharacteristic
48C2×C13×C4⋊C8C2211yescharacteristic
49C2×C13×C22⋊C8C2211yescharacteristic
50C2×C13×C22⋊C8C2211yescharacteristic
51C2×C4×C8×C13C2211yescharacteristic
52C2×C4×C8×C13C2211yescharacteristic
53C2×#88061C2211yescharacteristic
54C2×#88061C2211yescharacteristic
55C2×#88061C2211yescharacteristic
56C2×#88061C2211yescharacteristic
57C2×#88058C2211yescharacteristic
58C2×#88058C2211yescharacteristic
59C2×#88057C2211yescharacteristic
60C2×#88057C2211yescharacteristic
61C2×#88056C2211yescharacteristic
62C2×#88056C2211yescharacteristic
63C2×#88056C2211yescharacteristic
64C2×#88056C2211yescharacteristic
65#11718508C2218yescomplemented
66#11718506C2218yescomplemented
67#11718505C2218yescomplemented
68#11718490C2218yescomplemented
69#11718398C2218yescomplemented
70#11718395C2218yes—
71#11718394C2218yescomplemented
72#11718384C2218yescomplemented
73C4×Dic52C2218yescomplemented
74C4×D104C2218yescomplemented
75C4×#6095C2218yescomplemented
76C4×#6095C2218yescomplemented
77C23×C4×C13D411yescharacteristic
78C23×C4×C13D411yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C22×C22⋊D13—21no—
81C22×C22⋊D13—21no—
82C2×#6127—22no—
83C2×#6127—24no—
84C2×#6127—24no—
85C2×#6127C2314yes—
86C22×D52C2311yescharacteristic
87C22×D52C2311yescharacteristic
88C22×C4×D13—21no—
89C22×C4×D13—21no—
90C22×C4×D13—21no—
91C22×C4×D13—21no—
92C22×Dic26C2311yescharacteristic
93C22×Dic26C2311yescharacteristic
94C22×C8×C13C2311yescharacteristic
95C22×C8×C13C2311yescharacteristic
96C22×C8×C13C2311yescharacteristic
97C22×C8×C13C2311yescharacteristic
98C2×C42×C13D411yescharacteristic
99C2×C42×C13D411yescharacteristic
100C2×C42×C13D414yes—
101C2×C42×C13C2311yescharacteristic
102C2×C42×C13C2311yescharacteristic
103C2×C42×C13C2314yes—
104C2×C22⋊Dic13—21no—
105C2×C22⋊Dic13—21no—
106#88184—22no—
107#88184C2314yes—
108#88183—28no—
109C4×C22⋊D13—28no—
110C4×C22⋊D13—28no—
111C4×C22⋊D13—28no—
112C2×#6103—21no—
113C2×#6103—21no—
114C2×#6103—21no—
115C2×#6103—21no—
116C2×#6103—21no—
117C2×#6103—21no—
118#88180—22no—
119#88180C2314yes—
120C2×C4⋊Dic13C2311yescharacteristic
121C2×C4⋊Dic13C2311yescharacteristic
122C2×C4⋊Dic13C2311yescharacteristic
123C2×C4⋊Dic13C2311yescharacteristic
124#88178—22no—
125#88178C2314yes—
126C2×#6101—21no—
127C2×#6101—21no—
128C2×#6101—21no—
129C2×#6101—21no—
130C2×#6101—21no—
131C2×#6101—21no—
132C2×C4×Dic13—21no—
133C2×C4×Dic13—21no—
134C2×C4×Dic13—21no—
135C2×C4×Dic13—21no—
136C2×Dic52—24no—
137C2×Dic52C2314yes—
138C2×D104—24no—
139C2×D104C2314yes—
140C2×#6095—24no—
141C2×#6095—24no—
142C2×#6095C2314yes—
143C2×#6095C2314yes—
144#88130—28no—
145#88129—22no—
146#88129C2314yes—
147C4×D52—22no—
148C4×D52—22no—
149C4×D52—22no—
150C4×D52C2314yes—
151C4×D52C2314yes—
152C4×D52C2314yes—
153#88126—28no—
154#88126—28no—
155C42×D13—28no—
156#88124—22no—
157#88124C2314yes—
158C4×Dic26—22no—
159C4×Dic26—22no—
160C4×Dic26—22no—
161C4×Dic26C2314yes—
162C4×Dic26C2314yes—
163C4×Dic26C2314yes—
164C13×C4⋊C8C2314yes—
165C13×C4⋊C8C2314yes—
166C13×C22⋊C8C2314yes—
167C13×C22⋊C8C2314yes—
168C4×C8×C13C2314yes—
169C4×C8×C13C2314yes—
170#88061C2314yes—
171#88061C2314yes—
172#88061C2314yes—
173#88061C2314yes—
174#88058C2314yes—
175#88058C2314yes—
176#88057C2314yes—
177#88057C2314yes—
178#88056C2314yes—
179#88056C2314yes—
180#88056C2314yes—
181#88056C2314yes—
182C2×#3102—131nomaximal, Sylow
183C24×C13C2×D411yescharacteristic
184C23×D13—21no—
185C23×D13—21no—
186C22×C4×C13—24no—
187C22×C4×C13—22no—
188C22×C4×C13—22no—
189C22×C4×C13—42no—
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D411yescharacteristic
192C22×C4×C13C2×D411yescharacteristic
193C22×C4×C13C2×D411yescharacteristic
194C22×C4×C13C2×D412yes—
195C22×C4×C13C2×D414yes—
196C22×C4×C13C2×D414yes—
197C22×C4×C13C2×D411yescharacteristic
198C22×C4×C13C2412yes—
199C22×C4×C13C2411yescharacteristic
200C2×C22⋊D13—28no—
201C2×C22⋊D13—24no—
202C2×C22⋊D13—24no—
203C2×C22⋊D13—44no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210#6127—216no—
211#6127—28no—
212#6127—28no—
213C2×D52—21no—
214C2×D52—22no—
215C2×D52—22no—
216C2×D52—22no—
217C2×D52—21no—
218C2×D52#4114yes—
219C2×D52C2412yes—
220C2×D52C2412yes—
221C2×C4×D13—28no—
222C2×C4×D13—24no—
223C2×C4×D13—24no—
224C2×C4×D13—24no—
225C2×C4×D13—24no—
226C2×C4×D13—44no—
227C2×C4×D13—44no—
228C2×C4×D13—44no—
229C2×Dic26—21no—
230C2×Dic26—22no—
231C2×Dic26—22no—
232C2×Dic26—22no—
233C2×Dic26—21no—
234C2×Dic26#4114yes—
235C2×Dic26C2412yes—
236C2×Dic26C2412yes—
237C2×C8×C13—22no—
238C2×C8×C13—22no—
239C2×C8×C13—22no—
240C2×C8×C13—22no—
241C2×C8×C13C2412yes—
242C2×C8×C13C2412yes—
243C2×C8×C13C2412yes—
244C2×C8×C13C2412yes—
245C42×C13C2×D412yes—
246C42×C13C2×D412yes—
247C42×C13C2×D414yes—
248C42×C13C2×D414yes—
249C42×C13C2412yes—
250C42×C13C2412yes—
251C22⋊Dic13—24no—
252C22⋊Dic13—24no—
253#6103—24no—
254#6103—24no—
255#6103—24no—
256#6103—24no—
257#6103—24no—
258#6103—24no—
259C4⋊Dic13—21no—
260C4⋊Dic13—21no—
261C4⋊Dic13—21no—
262C4⋊Dic13—21no—
263C4⋊Dic13C2412yes—
264C4⋊Dic13C2412yes—
265C4⋊Dic13C2412yes—
266C4⋊Dic13C2412yes—
267#6101—24no—
268#6101—24no—
269#6101—24no—
270#6101—24no—
271#6101—24no—
272#6101—24no—
273C4×Dic13—24no—
274C4×Dic13—24no—
275C4×Dic13—24no—
276C4×Dic13—24no—
277Dic52—28no—
278D104—28no—
279#6095—28no—
280#6095—28no—
281C2×#529—131no—
282C2×C4×#41—131no—
283#3102—1316no—
284C2×#485—131no—
285C2×#482—131no—
286C2×#479—131no—
287C2×#478—131no—
288C2×#464—131no—
289C2×#463—131no—
290C2×#452—131no—
291C2×#449—131no—
292C2×C4×Q16—131no—
293C2×C4×SD16—131no—
294C2×C4×SD16—131no—
295C2×C4×D8—131no—
296C2×#431D1311yescharacteristic, complemented
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13C22×D412yes—
301C23×C13C22×D411yescharacteristic
302C22×D13—24no—
303C22×D13—22no—
304C22×D13—22no—
305C22×D13—42no—
306C22×D13—42no—
307C22×D13—42no—
308C22×D13—42no—
309C22×D13—42no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—24no—
315C2×C4×C13—28no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—44no—
319C2×C4×C13#13514yes—
320C2×C4×C13C22×D412yes—
321C2×C4×C13C22×D412yes—
322C2×C4×C13C22×D412yes—
323C2×C4×C13C22×D412yes—
324C2×C4×C13C22×D411yescharacteristic
325C2×C4×C13C22×D412yes—
326C2×C4×C13C2×#4112yes—
327C2×C4×C13C2×#4112yes—
328C2×C4×C13C2511yescharacteristic
329C22⋊D13—216no—
330C22⋊D13—48no—
331C2×Dic13—24no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343D52—24no—
344D52—22no—
345D52—22no—
346D52—22no—
347D52—42no—
348D52C2×#4114yes—
349C4×D13—216no—
350C4×D13—48no—
351C4×D13—48no—
352C4×D13—48no—
353Dic26—24no—
354Dic26—22no—
355Dic26—22no—
356Dic26—22no—
357Dic26—42no—
358Dic26C2×#4114yes—
359C8×C13—22no—
360C8×C13—22no—
361C8×C13—22no—
362C8×C13—22no—
363C22×#41—131no—
364C22×Q16—131no—
365C22×SD16—131no—
366C22×SD16—131no—
367C22×D8—131no—
368#529—138no—
369#529—264no—
370C2×#126—261no—
371C2×#125—131no—
372C2×#124—131no—
373C2×#123—261no—
374C2×C22⋊Q8—131no—
375C2×#121—131no—
376C4×#41—138no—
377C4×#41—264no—
378C2×C4×Q8—131no—
379C2×C4×Q8—131no—
380C2×C4×Q8—131no—
381C2×C4×D4—131no—
382C2×C4×D4—131no—
383C2×C4×D4—131no—
384C2×C4×D4—261no—
385C2×C4×D4—261no—
386C2×C4×D4—261no—
387C2×#117—131no—
388C2×#117—261no—
389C2×#117—261no—
390C22×C42—261no—
391C22×C42C2×D1311yescharacteristic
392#485—138no—
393#482—138no—
394#479—138no—
395#478—138no—
396#464—138no—
397#463—138no—
398#452—138no—
399#449—138no—
400C4×Q16—138no—
401C4×SD16—138no—
402C4×SD16—138no—
403C4×D8—138no—
404#431C2×D1318yescomplemented
405C2×#107—131no—
406C2×#107—131no—
407C2×#106—131no—
408C2×#106—131no—
409C2×C4⋊C8C2×D1311yescharacteristic
410C2×C4⋊C8C2×D1311yescharacteristic
411C2×#103—131no—
412C2×#103—131no—
413C2×#103—131no—
414C2×#103—131no—
415C2×#102—131no—
416C2×#102—131no—
417C2×#102—131no—
418C2×#102—131no—
419C2×C22⋊C8C2×D1311yescharacteristic
420C2×C22⋊C8C2×D1311yescharacteristic
421C2×C4×C8C2×D1311yescharacteristic
422C2×C4×C8C2×D1311yescharacteristic
423C22×C13—22no—
424C22×C13—22no—
425C22×C13—22no—
426C22×C13—44no—
427C22×C13#52512yes—
428C22×C13C2×#13512yes—
429C22×C13#57512yes—
430C22×C13C23×D411yescharacteristic
431C2×D13—24no—
432C2×D13—48no—
433C2×D13—42no—
434C2×D13—42no—
435C2×D13—42no—
436C2×D13—42no—
437C2×D13—42no—
438C2×D13—84no—
439C4×C13—22no—
440C4×C13—22no—
441C4×C13—22no—
442C4×C13—22no—
443C4×C13#52512yes—
444C4×C13C2×#13514yes—
445C4×C13C22×#4111yescharacteristic
446C4×C13C22×#4111yescharacteristic
447Dic13—24no—
448Dic13—42no—
449Dic13—42no—
450Dic13—42no—
451Dic13—42no—
452Dic13—42no—
453C2×#41—134no—
454C2×#41—264no—
455C2×#41—264no—
456C2×#41—262no—
457C22×Q8—131no—
458C22×Q8—131no—
459C22×D4—131no—
460C22×D4—131no—
461C22×D4—261no—
462C22×D4—261no—
463C23×C4—261no—
464C23×C4—261no—
465C23×C4—261no—
466C23×C4—261no—
467C23×C4D5211yescharacteristic
468C23×C4D5211yescharacteristic
469C23×C4C22×D1311yescharacteristic
470C2×Q16—134no—
471C2×Q16—264no—
472C2×SD16—134no—
473C2×SD16—134no—
474C2×SD16—264no—
475C2×SD16—264no—
476C2×D8—134no—
477C2×D8—264no—
478C22×C8C22×D1311yescharacteristic
479C22×C8C22×D1311yescharacteristic
480C22×C8C22×D1311yescharacteristic
481C22×C8C22×D1311yescharacteristic
482#126—268no—
483#125—134no—
484#125—262no—
485#124—134no—
486#124—262no—
487#123—268no—
488C22⋊Q8—134no—
489C22⋊Q8—262no—
490#121—134no—
491#121—262no—
492C4×Q8—134no—
493C4×Q8—134no—
494C4×Q8—134no—
495C4×Q8—262no—
496C4×Q8—262no—
497C4×Q8—262no—
498C4×D4—134no—
499C4×D4—134no—
500C4×D4—134no—
501C4×D4—268no—
502C4×D4—268no—
503C4×D4—268no—
504C4×D4—262no—
505C4×D4—262no—
506C4×D4—262no—
507#117—134no—
508#117—262no—
509#117—268no—
510#117—268no—
511C2×C4⋊C4—131no—
512C2×C4⋊C4—131no—
513C2×C4⋊C4—131no—
514C2×C4⋊C4—131no—
515C2×C4⋊C4—261no—
516C2×C4⋊C4—261no—
517C2×C4⋊C4—261no—
518C2×C4⋊C4—261no—
519C2×C4⋊C4—261no—
520C2×C4⋊C4—261no—
521C2×C22⋊C4—261no—
522C2×C22⋊C4—261no—
523C2×C22⋊C4—261no—
524C2×C22⋊C4—261no—
525C2×C22⋊C4—261no—
526C2×C22⋊C4—261no—
527C2×C22⋊C4—261no—
528C2×C22⋊C4—261no—
529C2×C42—261no—
530C2×C42—261no—
531C2×C42—261no—
532C2×C42—261no—
533C2×C42—268no—
534C2×C42D5211yescharacteristic
535C2×C42D5214yes—
536C2×C42D5211yescharacteristic
537C2×C42C22×D1311yescharacteristic
538C2×C42C22×D1314yes—
539C2×C42C22×D1311yescharacteristic
540#107—134no—
541#107—134no—
542#106—134no—
543#106—134no—
544C4⋊C8C22×D1314yes—
545C4⋊C8C22×D1314yes—
546#103—134no—
547#103—134no—
548#103—134no—
549#103—134no—
550#102—134no—
551#102—134no—
552#102—134no—
553#102—134no—
554C22⋊C8C22×D1314yes—
555C22⋊C8C22×D1314yes—
556C4×C8C22×D1314yes—
557C4×C8C22×D1314yes—
558C2×C13—42no—
559C2×C13#310214yescomplemented
560C2×C13C2×#52511yescharacteristic
561C2×C13C22×#13511yescharacteristic
562C2×C13C2×#57511yescharacteristic
563D13—44no—
564D13—82no—
565C24—261no—
566C24—261no—
567C24C2×D5211yescharacteristic
568#41—268no—
569#41—268no—
570#41—2616no—
571C2×Q8—134no—
572C2×Q8—132no—
573C2×Q8—132no—
574C2×Q8—261no—
575C2×Q8—261no—
576C2×Q8—262no—
577C2×Q8—262no—
578C2×Q8—262no—
579C2×D4—134no—
580C2×D4—132no—
581C2×D4—132no—
582C2×D4—268no—
583C2×D4—264no—
584C2×D4—264no—
585C2×D4—261no—
586C2×D4—261no—
587C2×D4—262no—
588C2×D4—262no—
589C2×D4—262no—
590C2×D4—524no—
591C22×C4—24no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—42no—
595C22×C4—268no—
596C22×C4—261no—
597C22×C4—264no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—261no—
602C22×C4—261no—
603C22×C4—264no—
604C22×C4—264no—
605C22×C4—264no—
606C22×C4—524no—
607C22×C4—524no—
608C22×C4—524no—
609C22×C4C2×D5211yescharacteristic
610C22×C4C2×D5211yescharacteristic
611C22×C4C2×D5212yes—
612C22×C4C2×D5211yescharacteristic
613C22×C4C2×D5211yescharacteristic
614C22×C4C2×D5214yes—
615C22×C4C2×D5214yes—
616C22×C4C2×D5211yescharacteristic
617C22×C4C23×D1312yes—
618C22×C4C23×D1311yescharacteristic
619Q16—268no—
620SD16—268no—
621SD16—268no—
622D8—268no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8C23×D1312yes—
628C2×C8C23×D1312yes—
629C2×C8C23×D1312yes—
630C2×C8C23×D1312yes—
631C4⋊C4—132no—
632C4⋊C4—132no—
633C4⋊C4—132no—
634C4⋊C4—132no—
635C4⋊C4—261no—
636C4⋊C4—261no—
637C4⋊C4—261no—
638C4⋊C4—261no—
639C4⋊C4—264no—
640C4⋊C4—264no—
641C4⋊C4—264no—
642C4⋊C4—264no—
643C4⋊C4—264no—
644C4⋊C4—264no—
645C22⋊C4—264no—
646C22⋊C4—264no—
647C22⋊C4—264no—
648C22⋊C4—264no—
649C22⋊C4—264no—
650C22⋊C4—264no—
651C22⋊C4—264no—
652C22⋊C4—264no—
653C42—264no—
654C42—264no—
655C42—264no—
656C42—264no—
657C42C2×D5214yes—
658C42C2×D5214yes—
659C42C2×D5212yes—
660C42C2×D5212yes—
661C42C23×D1312yes—
662C42C23×D1312yes—
663C13C2×#310211yescharacteristic, complemented, Sylow
664C23—22no—
665C23—22no—
666C23—22no—
667C23—264no—
668C23—262no—
669C23—262no—
670C23—522no—
671C23—522no—
672C23—522no—
673C23—522no—
674C23—522no—
675C23C22×D5212yes—
676C23C22×D5211yescharacteristic
677Q8—134no—
678Q8—264no—
679Q8—262no—
680Q8—262no—
681Q8—262no—
682Q8—522no—
683D4—134no—
684D4—2616no—
685D4—264no—
686D4—262no—
687D4—262no—
688D4—262no—
689D4—528no—
690D4—522no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—28no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—2616no—
701C2×C4—264no—
702C2×C4—262no—
703C2×C4—262no—
704C2×C4—262no—
705C2×C4—262no—
706C2×C4—262no—
707C2×C4—262no—
708C2×C4—528no—
709C2×C4—522no—
710C2×C4—522no—
711C2×C4—522no—
712C2×C4—522no—
713C2×C4—522no—
714C2×C4—528no—
715C2×C4—528no—
716C2×C4#8815814yes—
717C2×C4C22×D5212yes—
718C2×C4C22×D5212yes—
719C2×C4C22×D5212yes—
720C2×C4C22×D5212yes—
721C2×C4C22×D5212yes—
722C2×C4C22×D5211yescharacteristic
723C2×C4#41×D1312yes—
724C2×C4#41×D1312yes—
725C2×C4C24×D1311yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—264no—
735C22—522no—
736C22—522no—
737C22—528no—
738C22—522no—
739C22—522no—
740C22—522no—
741C22—1044no—
742C22#1171922912yes—
743C22C2×#8815812yes—
744C22#1171945312yes—
745C22C23×D5211yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—264no—
751C4—522no—
752C4—522no—
753C4—522no—
754C4—522no—
755C4—522no—
756C4#1171922912yes—
757C4C2×#8815814yes—
758C4C2×#41×D1311yescharacteristic
759C4C2×#41×D1311yescharacteristic
760C2—42no—
761C2—524no—
762C2—1042no—
763C2#1312485614yesdirect product factor
764C2C2×#1171922911yescharacteristic
765C2C22×#8815811yescharacteristic
766C2C2×#1171945311yescharacteristic
subgroupG/H
centerC22×C4C2×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#431C2
socleC23×C13C22×D4
prime radicalC2×#11718395C2
hypercenterC2×#431D13
hypocenterC13C2×#3102
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
1. C2×#11719184C2semidirect
2. C2×C4×#6127C2semidirect
3. #13124856C2direct (N × H)
4. C2×#11718384C2semidirect
5. C2×#11718398C2semidirect
6. C2×#11718490C2semidirect
7. C2×#11718508C2semidirect
8. C2×#11718506C2semidirect
9. C2×#11718505C2semidirect
10. C2×#11718394C2semidirect
12. C2×C4×Dic52C2semidirect
13. C2×C4×#6095C2semidirect
14. C2×C4×#6095C2semidirect
15. C2×C4×D104C2semidirect
16. C2×C13×#431C2semidirect
31. #11719184C22semidirect
35. C4×#6127C22semidirect
46. C13×#431C22semidirect
65. #11718508C22semidirect
66. #11718506C22semidirect
67. #11718505C22semidirect
68. #11718490C22semidirect
69. #11718398C22semidirect
71. #11718394C22semidirect
72. #11718384C22semidirect
73. C4×Dic52C22semidirect
74. C4×D104C22semidirect
75. C4×#6095C22semidirect
76. C4×#6095C22semidirect
296. C2×#431D13semidirect
404. #431C2×D13semidirect
559. C2×C13#3102semidirect
663. C13C2×#3102semidirect
763. C2#13124856direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191842
C2×C4×#61272
#131248562
C2×#117183842
C2×#117183982
C2×#117184902
C2×#117185082
C2×#117185062
C2×#117185052
C2×#117183942
C2×#117183952
C2×C4×Dic522
C2×C4×#60952
C2×C4×D1042
C2×C13×#4312
C2×#310213