Finite Group Databasebeta

← C2×#13125559 #16732867

Subgroups — C2×#13125559 #16732867

Order 3328.

2018 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719184C211yesmaximal, characteristic, complemented
2#13125559C2116yesmaximal, direct product factor
3C2×#11718725C211yesmaximal, characteristic, complemented
4C2×#11718720C211yesmaximal, characteristic, complemented
5C2×#11718729C211yesmaximal, characteristic, complemented
6C2×#11718717C211yesmaximal, characteristic, complemented
7C2×#11718713C211yesmaximal, characteristic, complemented
8C2×#11718700C211yesmaximal, characteristic
9C2×#11718710C211yesmaximal, characteristic, complemented
10C2×#11718703C211yesmaximal, characteristic, complemented
11C2×#11718675C211yesmaximal, characteristic, complemented
12C2×#11718691C211yesmaximal, characteristic, complemented
13C2×#11718679C211yesmaximal, characteristic, complemented
14C2×#11718687C211yesmaximal, characteristic, complemented
15C2×C4×#6099C211yesmaximal, characteristic, complemented
16C2×C13×#529C211yesmaximal, characteristic, complemented
17C13×#529—24no—
18C13×#529C2218yescomplemented
19C2×C13×#126—21no—
20C2×C13×#125C2211yescharacteristic
21C2×C13×#124C2211yescharacteristic
22C2×C13×#123—21no—
23C2×C13×C22⋊Q8C2211yescharacteristic
24C2×C13×#121C2211yescharacteristic
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×D4×C13—21no—
27C2×C4×D4×C13C2211yescharacteristic
28C2×C13×#117—21no—
29C22×C42×C13C2211yescharacteristic
30C22×#6107C2211yescharacteristic
31C22×#6106C2211yescharacteristic
32C22×#6105C2211yescharacteristic
33C22×#6104C2211yescharacteristic
34C2×#88184C2211yescharacteristic
35C2×#88183—21no—
36C2×C4×C22⋊D13—21no—
37C2×#88178C2211yescharacteristic
38C22×#6099C2211yescharacteristic
39C22×#6099C2211yescharacteristic
40#11719184—24no—
41#11719184C2218yescomplemented
42C2×#88130—21no—
43C2×#88129C2211yescharacteristic
44C2×C4×D52C2211yescharacteristic
45C2×#88126—21no—
46C2×#88124C2211yescharacteristic
47C2×C4×Dic26C2211yescharacteristic
48C2×#88075C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×#88072C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52#11718729C2218yescomplemented
53#11718725C2218yescomplemented
54#11718720C2218yescomplemented
55#11718717C2218yescomplemented
56#11718713C2218yescomplemented
57#11718710C2218yescomplemented
58#11718703C2218yescomplemented
59#11718700C2218yes—
60#11718691C2218yescomplemented
61#11718687C2218yescomplemented
62#11718679C2218yescomplemented
63#11718675C2218yescomplemented
64C2×#88050C2211yescharacteristic
65C2×#88050C2211yescharacteristic
66C2×#88049C2211yescharacteristic
67C2×#88049C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71C2×#88047C2211yescharacteristic
72C4×#6099C2218yescomplemented
73C2×#88043C2211yescharacteristic
74C2×#88043C2211yescharacteristic
75C2×C4×#1055C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C22×Q8×C13C2311yescharacteristic
78C22×D4×C13—21no—
79C22×D4×C13C2311yescharacteristic
80C23×C4×C13—21no—
81C23×C4×C13D411yescharacteristic
82C23×C4×C13D411yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C22×C22⋊D13—21no—
85C22×D52C2311yescharacteristic
86C22×C4×D13—21no—
87C22×Dic26C2311yescharacteristic
88C13×#126—28no—
89C13×#125—22no—
90C13×#125C2314yes—
91C13×#124—22no—
92C13×#124C2314yes—
93C13×#123—28no—
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8C2314yes—
96C13×#121—22no—
97C13×#121C2314yes—
98C4×Q8×C13—22no—
99C4×Q8×C13C2314yes—
100C4×D4×C13—28no—
101C4×D4×C13—22no—
102C4×D4×C13C2314yes—
103C13×#117—28no—
104C2×C13×C4⋊C4—21no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4C2311yescharacteristic
109C2×C13×C4⋊C4C2311yescharacteristic
110C2×C13×C22⋊C4—21no—
111C2×C13×C22⋊C4—21no—
112C2×C13×C22⋊C4—21no—
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C42×C13—21no—
116C2×C42×C13D411yescharacteristic
117C2×C42×C13D411yescharacteristic
118C2×C42×C13D414yes—
119C2×C42×C13C2311yescharacteristic
120C2×C42×C13C2311yescharacteristic
121C2×C42×C13C2314yes—
122C2×C22⋊Dic13—21no—
123C2×#6107—24no—
124C2×#6107C2314yes—
125C2×#6106—24no—
126C2×#6106C2314yes—
127C2×#6105—24no—
128C2×#6105C2314yes—
129C2×#6104—24no—
130C2×#6104C2314yes—
131#88184—22no—
132#88184C2314yes—
133#88183—28no—
134C4×C22⋊D13—28no—
135C2×#6103—21no—
136C2×#6103—21no—
137C2×#6103—21no—
138C2×#6103—21no—
139C2×C4⋊Dic13C2311yescharacteristic
140C2×C4⋊Dic13C2311yescharacteristic
141#88178—22no—
142#88178C2314yes—
143C2×#6101—21no—
144C2×#6101—21no—
145C2×#6101—21no—
146C2×#6101—21no—
147C2×C4×Dic13—21no—
148C2×#6099—24no—
149C2×#6099—24no—
150C2×#6099C2314yes—
151C2×#6099C2314yes—
152C22×#1055C2311yescharacteristic
153C22×#1055C2311yescharacteristic
154C22×#1055C2311yescharacteristic
155C22×#1055C2311yescharacteristic
156#88130—28no—
157#88129—22no—
158#88129C2314yes—
159C4×D52—22no—
160C4×D52C2314yes—
161#88126—28no—
162#88124—22no—
163#88124C2314yes—
164C4×Dic26—22no—
165C4×Dic26C2314yes—
166#88075C2314yes—
167#88075C2314yes—
168#88072C2314yes—
169#88072C2314yes—
170#88050C2314yes—
171#88050C2314yes—
172#88049C2314yes—
173#88049C2314yes—
174#88048C2314yes—
175#88048C2314yes—
176#88047C2314yes—
177#88047C2314yes—
178#88043C2314yes—
179#88043C2314yes—
180C4×#1055C2314yes—
181C4×#1055C2314yes—
182C2×#3183—131nomaximal, Sylow
183C24×C13—21no—
184C24×C13C2×D411yescharacteristic
185C23×D13—21no—
186C2×Q8×C13—21no—
187C2×Q8×C13—22no—
188C2×Q8×C13—22no—
189C2×Q8×C13C2412yes—
190C2×D4×C13—24no—
191C2×D4×C13—21no—
192C2×D4×C13—22no—
193C2×D4×C13—22no—
194C2×D4×C13—44no—
195C2×D4×C13C2412yes—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—24no—
202C22×C4×C13—42no—
203C22×C4×C13—42no—
204C22×C4×C13—44no—
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D411yescharacteristic
209C22×C4×C13C2×D411yescharacteristic
210C22×C4×C13C2×D412yes—
211C22×C4×C13C2×D414yes—
212C22×C4×C13C2×D414yes—
213C22×C4×C13C2412yes—
214C22×C4×C13C2411yescharacteristic
215C2×C22⋊D13—24no—
216C2×C22⋊D13—44no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C2×D52—22no—
221C2×D52—22no—
222C2×D52—21no—
223C2×D52C2412yes—
224C2×C4×D13—24no—
225C2×C4×D13—44no—
226C2×Dic26—22no—
227C2×Dic26—22no—
228C2×Dic26—21no—
229C2×Dic26C2412yes—
230C13×C4⋊C4—24no—
231C13×C4⋊C4—24no—
232C13×C4⋊C4—24no—
233C13×C4⋊C4—24no—
234C13×C4⋊C4—21no—
235C13×C4⋊C4—21no—
236C13×C4⋊C4C2412yes—
237C13×C4⋊C4C2412yes—
238C13×C22⋊C4—24no—
239C13×C22⋊C4—24no—
240C13×C22⋊C4—24no—
241C13×C22⋊C4—24no—
242C13×C22⋊C4—24no—
243C42×C13—24no—
244C42×C13C2×D412yes—
245C42×C13C2×D412yes—
246C42×C13C2×D414yes—
247C42×C13C2×D414yes—
248C42×C13C2412yes—
249C42×C13C2412yes—
250C22⋊Dic13—24no—
251#6107—28no—
252#6106—28no—
253#6105—28no—
254#6104—28no—
255#6103—24no—
256#6103—24no—
257#6103—24no—
258#6103—24no—
259C4⋊Dic13—21no—
260C4⋊Dic13—21no—
261C4⋊Dic13C2412yes—
262C4⋊Dic13C2412yes—
263#6101—24no—
264#6101—24no—
265#6101—24no—
266#6101—24no—
267C4×Dic13—24no—
268#6099—28no—
269#6099—28no—
270C2×#1055—22no—
271C2×#1055—22no—
272C2×#1055#4114yes—
273C2×#1055#4114yes—
274C2×#1055C2412yes—
275C2×#1055C2412yes—
276C2×#1055C2412yes—
277C2×#1055C2412yes—
278C2×#529—131no—
279C2×#529D1311yescharacteristic, complemented
280#3183—1316no—
281C2×#499—131no—
282C2×#495—131no—
283C2×#488—131no—
284C2×#488—131no—
285C2×#470—131no—
286C2×#469—131no—
287C2×#468—131no—
288C2×#468—131no—
289C2×#442—131no—
290C2×#441—131no—
291C2×#440—131no—
292C2×#440—131no—
293C2×C4×M16—131no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—42no—
299C23×C13—42no—
300C23×C13—42no—
301C23×C13C22×D412yes—
302C23×C13C22×D411yescharacteristic
303C22×D13—22no—
304C22×D13—42no—
305C22×D13—42no—
306C22×D13—42no—
307Q8×C13—22no—
308Q8×C13—22no—
309Q8×C13—42no—
310D4×C13—22no—
311D4×C13—22no—
312D4×C13—48no—
313D4×C13—42no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—24no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—44no—
326C2×C4×C13—44no—
327C2×C4×C13—48no—
328C2×C4×C13—42no—
329C2×C4×C13—42no—
330C2×C4×C13—42no—
331C2×C4×C13C22×D412yes—
332C2×C4×C13C22×D412yes—
333C2×C4×C13C22×D412yes—
334C2×C4×C13C22×D412yes—
335C2×C4×C13C22×D412yes—
336C2×C4×C13C22×D411yescharacteristic
337C2×C4×C13C2×#4112yes—
338C2×C4×C13C2×#4112yes—
339C2×C4×C13C2511yescharacteristic
340C22⋊D13—48no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—42no—
347D52—22no—
348D52—22no—
349D52—42no—
350C4×D13—48no—
351Dic26—22no—
352Dic26—22no—
353Dic26—42no—
354#1055—22no—
355#1055—22no—
356#1055C2×#4114yes—
357#1055C2×#4114yes—
358C22×Q16—131no—
359C22×SD16—131no—
360C22×SD16—131no—
361C22×D8—131no—
362C22×M16—131no—
363C22×M16—131no—
364#529—24no—
365#529—138no—
366#529—264no—
367#529C2×D1318yescomplemented
368C2×#126—21no—
369C2×#126—261no—
370C2×#125—131no—
371C2×#125C2×D1311yescharacteristic
372C2×#124—131no—
373C2×#124C2×D1311yescharacteristic
374C2×#123—21no—
375C2×#123—261no—
376C2×C22⋊Q8—131no—
377C2×C22⋊Q8C2×D1311yescharacteristic
378C2×#121—131no—
379C2×#121C2×D1311yescharacteristic
380C2×C4×Q8—131no—
381C2×C4×Q8C2×D1311yescharacteristic
382C2×C4×D4—21no—
383C2×C4×D4—131no—
384C2×C4×D4—261no—
385C2×C4×D4C2×D1311yescharacteristic
386C2×#117—21no—
387C2×#117—261no—
388C22×C42C2×D1311yescharacteristic
389#499—138no—
390#495—138no—
391#488—138no—
392#488—138no—
393#470—138no—
394#469—138no—
395#468—138no—
396#468—138no—
397#442—138no—
398#441—138no—
399#440—138no—
400#440—138no—
401C2×#107—131no—
402C2×#107—131no—
403C2×#106—131no—
404C2×#106—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#103—131no—
408C2×#103—131no—
409C2×#102—131no—
410C2×#102—131no—
411C2×#102—131no—
412C2×#102—131no—
413C4×M16—138no—
414C2×#97—131no—
415C2×#97—131no—
416C2×C4×C8—131no—
417C2×C4×C8—131no—
418C22×C13—22no—
419C22×C13—22no—
420C22×C13—22no—
421C22×C13—44no—
422C22×C13—42no—
423C22×C13—42no—
424C22×C13—42no—
425C22×C13—84no—
426C22×C13#53212yes—
427C22×C13#57512yes—
428C22×C13#57512yes—
429C22×C13C23×D411yescharacteristic
430C2×D13—42no—
431C2×D13—42no—
432C2×D13—42no—
433C2×D13—84no—
434C4×C13—22no—
435C4×C13—22no—
436C4×C13—22no—
437C4×C13—22no—
438C4×C13—22no—
439C4×C13—42no—
440C4×C13—42no—
441C4×C13—42no—
442C4×C13#53212yes—
443C4×C13C22×#4111yescharacteristic
444C4×C13C22×#4111yescharacteristic
445Dic13—42no—
446Dic13—42no—
447Dic13—42no—
448C22×Q8—131no—
449C22×Q8C22×D1311yescharacteristic
450C22×D4—21no—
451C22×D4—131no—
452C22×D4—261no—
453C22×D4C22×D1311yescharacteristic
454C23×C4—21no—
455C23×C4—261no—
456C23×C4C22⋊D1311yescharacteristic
457C23×C4C22⋊D1311yescharacteristic
458C23×C4C22×D1311yescharacteristic
459C2×Q16—134no—
460C2×Q16—264no—
461C2×SD16—134no—
462C2×SD16—134no—
463C2×SD16—264no—
464C2×SD16—264no—
465C2×D8—134no—
466C2×D8—264no—
467C2×M16—134no—
468C2×M16—134no—
469C2×M16—264no—
470C2×M16—264no—
471C22×C8—131no—
472C22×C8—131no—
473C22×C8—131no—
474C22×C8—131no—
475#126—28no—
476#126—268no—
477#125—22no—
478#125—134no—
479#125—262no—
480#125C22×D1314yes—
481#124—22no—
482#124—134no—
483#124—262no—
484#124C22×D1314yes—
485#123—28no—
486#123—268no—
487C22⋊Q8—22no—
488C22⋊Q8—134no—
489C22⋊Q8—262no—
490C22⋊Q8C22×D1314yes—
491#121—22no—
492#121—134no—
493#121—262no—
494#121C22×D1314yes—
495C4×Q8—22no—
496C4×Q8—134no—
497C4×Q8—262no—
498C4×Q8C22×D1314yes—
499C4×D4—28no—
500C4×D4—22no—
501C4×D4—134no—
502C4×D4—268no—
503C4×D4—262no—
504C4×D4C22×D1314yes—
505#117—28no—
506#117—268no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—131no—
512C2×C4⋊C4—131no—
513C2×C4⋊C4—261no—
514C2×C4⋊C4—261no—
515C2×C4⋊C4—261no—
516C2×C4⋊C4—261no—
517C2×C4⋊C4C22×D1311yescharacteristic
518C2×C4⋊C4C22×D1311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—261no—
525C2×C22⋊C4—261no—
526C2×C22⋊C4—261no—
527C2×C22⋊C4—261no—
528C2×C22⋊C4—261no—
529C2×C42—21no—
530C2×C42—261no—
531C2×C42C22⋊D1311yescharacteristic
532C2×C42C22⋊D1311yescharacteristic
533C2×C42C22⋊D1314yes—
534C2×C42C22×D1311yescharacteristic
535C2×C42C22×D1311yescharacteristic
536C2×C42C22×D1314yes—
537#107—134no—
538#107—134no—
539#106—134no—
540#106—134no—
541#103—134no—
542#103—134no—
543#103—134no—
544#103—134no—
545#102—134no—
546#102—134no—
547#102—134no—
548#102—134no—
549#97—134no—
550#97—134no—
551C4×C8—134no—
552C4×C8—134no—
553C2×C13—42no—
554C2×C13—82no—
555C2×C13#318314yescomplemented
556C2×C13C2×#53211yescharacteristic
557C2×C13C2×#57511yescharacteristic
558C2×C13C2×#57511yescharacteristic
559D13—82no—
560C24—21no—
561C24—261no—
562C24C2×C22⋊D1311yescharacteristic
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—132no—
567C2×Q8—261no—
568C2×Q8—262no—
569C2×Q8—262no—
570C2×Q8C23×D1312yes—
571C2×D4—24no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—44no—
576C2×D4—132no—
577C2×D4—264no—
578C2×D4—262no—
579C2×D4—262no—
580C2×D4—261no—
581C2×D4—524no—
582C2×D4C23×D1312yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—44no—
592C22×C4—261no—
593C22×C4—261no—
594C22×C4—261no—
595C22×C4—264no—
596C22×C4—524no—
597C22×C4C2×C22⋊D1312yes—
598C22×C4C2×C22⋊D1311yescharacteristic
599C22×C4C2×C22⋊D1311yescharacteristic
600C22×C4C2×C22⋊D1311yescharacteristic
601C22×C4C2×C22⋊D1311yescharacteristic
602C22×C4C2×C22⋊D1311yescharacteristic
603C22×C4C2×C22⋊D1314yes—
604C22×C4C2×C22⋊D1314yes—
605C22×C4C23×D1312yes—
606C22×C4C23×D1311yescharacteristic
607Q16—268no—
608SD16—268no—
609SD16—268no—
610D8—268no—
611M16—268no—
612M16—268no—
613C2×C8—134no—
614C2×C8—134no—
615C2×C8—132no—
616C2×C8—132no—
617C2×C8—132no—
618C2×C8—132no—
619C2×C8—262no—
620C2×C8—262no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—132no—
628C4⋊C4—132no—
629C4⋊C4—261no—
630C4⋊C4—261no—
631C4⋊C4—264no—
632C4⋊C4—264no—
633C4⋊C4—264no—
634C4⋊C4—264no—
635C4⋊C4C23×D1312yes—
636C4⋊C4C23×D1312yes—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—264no—
643C22⋊C4—264no—
644C22⋊C4—264no—
645C22⋊C4—264no—
646C22⋊C4—264no—
647C42—24no—
648C42—264no—
649C42C2×C22⋊D1314yes—
650C42C2×C22⋊D1314yes—
651C42C2×C22⋊D1312yes—
652C42C2×C22⋊D1312yes—
653C42C23×D1312yes—
654C42C23×D1312yes—
655C13C2×#318311yescharacteristic, complemented, Sylow
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—262no—
664C23—522no—
665C23—522no—
666C23—522no—
667C23C22×C22⋊D1312yes—
668C23C22×C22⋊D1311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—262no—
673Q8—262no—
674Q8—522no—
675D4—22no—
676D4—22no—
677D4—48no—
678D4—42no—
679D4—262no—
680D4—262no—
681D4—528no—
682D4—522no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—262no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—528no—
704C2×C4—522no—
705C2×C4—522no—
706C2×C4—522no—
707C2×C4#41×D1312yes—
708C2×C4#41×D1312yes—
709C2×C4C22×C22⋊D1312yes—
710C2×C4C22×C22⋊D1312yes—
711C2×C4C22×C22⋊D1312yes—
712C2×C4C22×C22⋊D1312yes—
713C2×C4C22×C22⋊D1312yes—
714C2×C4C22×C22⋊D1311yescharacteristic
715C2×C4C24×D1311yescharacteristic
716C8—134no—
717C8—134no—
718C8—262no—
719C8—262no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—522no—
729C22—522no—
730C22—522no—
731C22—1044no—
732C22#1171952712yes—
733C22#1171952712yes—
734C22#1171953712yes—
735C22C23×C22⋊D1311yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—522no—
745C4—522no—
746C4—522no—
747C4#1171953712yes—
748C4C2×#41×D1311yescharacteristic
749C4C2×#41×D1311yescharacteristic
750C2—42no—
751C2—82no—
752C2—1042no—
753C2#1312555914yesdirect product factor
754C2C2×#1171953711yescharacteristic
755C2C2×#1171952711yescharacteristic
756C2C2×#1171952711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#529C2
socleC23×C13C22×D4
prime radicalC2×#11718700C2
hypercenterC2×#529D13
hypocenterC13C2×#3183
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#11719184C2semidirect
2. #13125559C2direct (N × H)
3. C2×#11718725C2semidirect
4. C2×#11718720C2semidirect
5. C2×#11718729C2semidirect
6. C2×#11718717C2semidirect
7. C2×#11718713C2semidirect
9. C2×#11718710C2semidirect
10. C2×#11718703C2semidirect
11. C2×#11718675C2semidirect
12. C2×#11718691C2semidirect
13. C2×#11718679C2semidirect
14. C2×#11718687C2semidirect
15. C2×C4×#6099C2semidirect
16. C2×C13×#529C2semidirect
18. C13×#529C22semidirect
41. #11719184C22semidirect
52. #11718729C22semidirect
53. #11718725C22semidirect
54. #11718720C22semidirect
55. #11718717C22semidirect
56. #11718713C22semidirect
57. #11718710C22semidirect
58. #11718703C22semidirect
60. #11718691C22semidirect
61. #11718687C22semidirect
62. #11718679C22semidirect
63. #11718675C22semidirect
72. C4×#6099C22semidirect
279. C2×#529D13semidirect
367. #529C2×D13semidirect
555. C2×C13#3183semidirect
655. C13C2×#3183semidirect
753. C2#13125559direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191842
#131255592
C2×#117187252
C2×#117187202
C2×#117187292
C2×#117187172
C2×#117187132
C2×#117187002
C2×#117187102
C2×#117187032
C2×#117186752
C2×#117186912
C2×#117186792
C2×#117186872
C2×C4×#60992
C2×C13×#5292
C2×#318313