Finite Group Databasebeta

← C2×#13127300 #16741476

Subgroups — C2×#13127300 #16741476

Order 3328.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719260C211yesmaximal, characteristic, complemented
2#13127300C2116yesmaximal, direct product factor
3C2×#11718726C211yesmaximal, characteristic, complemented
4C2×#11718629C211yesmaximal, characteristic, complemented
5C2×#11718695C211yesmaximal, characteristic, complemented
6C2×#11718664C211yesmaximal, characteristic, complemented
7C2×#11718694C211yesmaximal, characteristic, complemented
8C2×#11718727C211yesmaximal, characteristic, complemented
9C2×#11718669C211yesmaximal, characteristic, complemented
10C2×#11718700C211yesmaximal, characteristic, complemented
11C2×#11718699C211yesmaximal, characteristic, complemented
12C2×#11718675C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic, complemented
14C2×#11718656C211yesmaximal, characteristic, complemented
15C22×#88048C211yesmaximal, characteristic, complemented
16C2×C13×#553C211yesmaximal, characteristic, complemented
17C22×#6129—21no—
18C13×#553—24no—
19C13×#553C2218yescomplemented
20C2×C13×#126—21no—
21C2×C13×#125C2211yescharacteristic
22C2×C13×#123—21no—
23C2×C13×#121—21no—
24C2×C13×#121C2211yescharacteristic
25C2×C13×#121C2211yescharacteristic
26C2×C4×D4×C13—21no—
27C2×C4×D4×C13C2211yescharacteristic
28C2×C4×D4×C13C2211yescharacteristic
29C2×C13×#117C2211yescharacteristic
30C22×C13×C4⋊C4C2211yescharacteristic
31C22×#6104C2211yescharacteristic
32C2×#88184C2211yescharacteristic
33C2×#88184C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×#6099C2211yescharacteristic
37C23×#1055C2211yescharacteristic
38#11719260—24no—
39#11719260C2218yescomplemented
40C2×#88151—21no—
41C2×#88140—21no—
42C2×#88140—21no—
43C2×C4×D52C2211yescharacteristic
44C2×#88123C2211yescharacteristic
45C2×#88072C2211yescharacteristic
46C2×#88072C2211yescharacteristic
47C2×#88072C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic
50#11718727C2218yescomplemented
51#11718726C2218yescomplemented
52#11718700C2218yescomplemented
53#11718699C2218yescomplemented
54#11718695C2218yescomplemented
55#11718694C2218yescomplemented
56#11718675C2218yescomplemented
57#11718672C2218yescomplemented
58#11718669C2218yescomplemented
59#11718664C2218yescomplemented
60#11718656C2218yescomplemented
61#11718629C2218yescomplemented
62C2×#88049C2211yescharacteristic
63C2×#88049C2211yescharacteristic
64C2×#88049C2211yescharacteristic
65C2×#88048C2211yescharacteristic
66C2×#88048C2211yescharacteristic
67C2×#88048C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88048C2211yescharacteristic
71C2×#88048C2218yescomplemented
72C2×#88047C2211yescharacteristic
73C2×#88047C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
77C22×D4×C13—21no—
78C22×D4×C13—21no—
79C22×D4×C13D411yescharacteristic
80C22×D4×C13C2311yescharacteristic
81C23×C4×C13—21no—
82C23×C4×C13—21no—
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C22×C22⋊D13—21no—
86C22×C22⋊D13—21no—
87C23×Dic13—21no—
88C23×Dic13—21no—
89C2×#6129—28no—
90C2×#6129—48no—
91C22×D52C2311yescharacteristic
92C22×C4×D13—21no—
93C22×Dic26—21no—
94C13×#126—28no—
95C13×#125—22no—
96C13×#125C2314yes—
97C13×#123—28no—
98C13×#121—28no—
99C13×#121—22no—
100C13×#121—22no—
101C13×#121C2314yes—
102C13×#121C2314yes—
103C4×D4×C13—28no—
104C4×D4×C13—22no—
105C4×D4×C13D414yes—
106C4×D4×C13C2314yes—
107C4×D4×C13C2314yes—
108C13×#117—22no—
109C13×#117C2314yes—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—22no—
112C2×C13×C4⋊C4—21no—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4D411yescharacteristic
115C2×C13×C4⋊C4C2311yescharacteristic
116C2×C13×C4⋊C4C2311yescharacteristic
117C2×C13×C4⋊C4C2314yes—
118C2×C13×C4⋊C4C2311yescharacteristic
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×C13—21no—
126C2×C42×C13C2311yescharacteristic
127C2×#6104—24no—
128C2×#6104C2314yes—
129#88184—22no—
130#88184—22no—
131#88184C2314yes—
132#88184C2314yes—
133C2×#6103—21no—
134C2×#6103—21no—
135C2×#6103—21no—
136C2×C4⋊Dic13—21no—
137C2×C4⋊Dic13—21no—
138C2×C4⋊Dic13—21no—
139C2×C4⋊Dic13—22no—
140C2×C4⋊Dic13—22no—
141C2×C4⋊Dic13C2314yes—
142C2×C4⋊Dic13C2311yescharacteristic
143C2×C4⋊Dic13C2311yescharacteristic
144C2×C4⋊Dic13C2311yescharacteristic
145C2×C4⋊Dic13C2314yes—
146C2×#6099—24no—
147C2×#6099C2314yes—
148C22×#1055—24no—
149C22×#1055C2314yes—
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152C22×#1055C2311yescharacteristic
153C22×#1055C2311yescharacteristic
154#88151—28no—
155#88140—28no—
156#88140—28no—
157C4×D52—22no—
158C4×D52C2314yes—
159#88123—22no—
160#88123C2314yes—
161#88072C2314yes—
162#88072C2314yes—
163#88072C2314yes—
164C22⋊#1055C2314yes—
165C22⋊#1055C2314yes—
166#88049C2314yes—
167#88049C2314yes—
168#88049C2314yes—
169#88048C2314yes—
170#88048C2314yes—
171#88048C2314yes—
172#88048C2314yes—
173#88048C2314yes—
174#88048C2314yes—
175#88047C2314yes—
176#88047C2314yes—
177#88047C2314yes—
178C4⋊#1055C2314yes—
179#88043C2314yes—
180C2×#3345—131nomaximal, Sylow
181C24×C13—21no—
182C24×C13C2×D411yescharacteristic
183C24×C13C2×D411yescharacteristic
184C23×D13—21no—
185C2×D4×C13—24no—
186C2×D4×C13—24no—
187C2×D4×C13—24no—
188C2×D4×C13—21no—
189C2×D4×C13—22no—
190C2×D4×C13—22no—
191C2×D4×C13—44no—
192C2×D4×C13—82no—
193C2×D4×C13C2×D414yes—
194C2×D4×C13C2412yes—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—24no—
203C22×C4×C13—24no—
204C22×C4×C13—82no—
205C22×C4×C13—82no—
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D411yescharacteristic
209C22×C4×C13C2×D412yes—
210C22×C4×C13C2×D412yes—
211C22×C4×C13C2×D411yescharacteristic
212C22×C4×C13C2412yes—
213C22×C4×C13C2412yes—
214C22×C4×C13C2411yescharacteristic
215C2×C22⋊D13—24no—
216C2×C22⋊D13—24no—
217C2×C22⋊D13—44no—
218C2×C22⋊D13—44no—
219C22×Dic13—24no—
220C22×Dic13—24no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—44no—
225C22×Dic13—44no—
226#6129—432no—
227C2×D52—22no—
228C2×D52—22no—
229C2×D52—21no—
230C2×D52C2412yes—
231C2×C4×D13—24no—
232C2×C4×D13—44no—
233C2×Dic26—24no—
234C2×Dic26—44no—
235C13×C4⋊C4—21no—
236C13×C4⋊C4—21no—
237C13×C4⋊C4—24no—
238C13×C4⋊C4—24no—
239C13×C4⋊C4—24no—
240C13×C4⋊C4—21no—
241C13×C4⋊C4C2×D414yes—
242C13×C4⋊C4C2412yes—
243C13×C4⋊C4C2412yes—
244C13×C4⋊C4C2412yes—
245C13×C22⋊C4—24no—
246C13×C22⋊C4—24no—
247C13×C22⋊C4—24no—
248C13×C22⋊C4—24no—
249C13×C22⋊C4C2×D414yes—
250C13×C22⋊C4C2×D414yes—
251C42×C13—24no—
252C42×C13C2×D412yes—
253C42×C13C2412yes—
254#6104—28no—
255#6103—24no—
256#6103—24no—
257#6103—24no—
258C4⋊Dic13—21no—
259C4⋊Dic13—21no—
260C4⋊Dic13—24no—
261C4⋊Dic13—21no—
262C4⋊Dic13—24no—
263C4⋊Dic13—24no—
264C4⋊Dic13C2412yes—
265C4⋊Dic13C2412yes—
266C4⋊Dic13C2412yes—
267#6099—28no—
268C2×#1055—22no—
269C2×#1055—22no—
270C2×#1055—22no—
271C2×#1055—28no—
272C2×#1055#4114yescomplemented
273C2×#1055C2412yes—
274C2×#1055C2412yes—
275C2×#1055C2412yes—
276C2×#1055C2412yes—
277C2×#553D1311yescharacteristic, complemented
278C2×#547—131no—
279#3345—1316no—
280C2×#501—131no—
281C2×#481—131no—
282C2×#481—131no—
283C2×#482—131no—
284C2×#480—131no—
285C2×#478—131no—
286C2×#476—131no—
287C2×#469—131no—
288C2×#466—131no—
289C2×#442—131no—
290C2×#435—131no—
291C2×#428—131no—
292C22×#106—131no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—42no—
300C23×C13—42no—
301C23×C13—42no—
302C23×C13AGL(1,ℤ/8)14yes—
303C23×C13C22×D412yes—
304C23×C13C22×D412yes—
305C23×C13C22×D411yescharacteristic
306C22×D13—22no—
307C22×D13—42no—
308C22×D13—42no—
309C22×D13—42no—
310D4×C13—28no—
311D4×C13—22no—
312D4×C13—22no—
313D4×C13—48no—
314D4×C13—42no—
315D4×C13—84no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—24no—
321C2×C4×C13—24no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—42no—
330C2×C4×C13—42no—
331C2×C4×C13—42no—
332C2×C4×C13—84no—
333C2×C4×C13—84no—
334C2×C4×C13C22×D412yes—
335C2×C4×C13C22×D412yes—
336C2×C4×C13C22×D412yes—
337C2×C4×C13C22×D412yes—
338C2×C4×C13C22×D411yescharacteristic
339C2×C4×C13C2×#4112yes—
340C2×C4×C132−1+412yes—
341C2×C4×C13C2511yescharacteristic
342C22⋊D13—48no—
343C22⋊D13—48no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—48no—
348C2×Dic13—42no—
349C2×Dic13—42no—
350C2×Dic13—42no—
351C2×Dic13—48no—
352D52—22no—
353D52—22no—
354D52—42no—
355C4×D13—48no—
356Dic26—48no—
357#1055—22no—
358#1055—22no—
359#1055—22no—
360#1055C2×#4114yescomplemented
361C22×#41—261no—
362C22×D8—131no—
363C22×M16—131no—
364C23×C8—131no—
365#553—24no—
366#553C2×D1318yescomplemented
367#547—138no—
368#547—264no—
369C2×C4⋊Q8—131no—
370C2×#126—21no—
371C2×#125C2×D1311yescharacteristic
372C2×#123—21no—
373C2×#123—261no—
374C2×#123—261no—
375C2×C22⋊Q8—261no—
376C2×#121—21no—
377C2×#121—131no—
378C2×#121—131no—
379C2×#121C2×D1311yescharacteristic
380C2×#121C2×D1311yescharacteristic
381C2×C4×D4—21no—
382C2×C4×D4—131no—
383C2×C4×D4C2×D1311yescharacteristic
384C2×C4×D4C2×D1311yescharacteristic
385C2×#117C2×D1311yescharacteristic
386C22×C4⋊C4—131no—
387C22×C4⋊C4—131no—
388C22×C4⋊C4C2×D1311yescharacteristic
389#501—138no—
390#482—138no—
391#481—138no—
392#481—138no—
393#480—138no—
394#478—138no—
395#476—138no—
396#469—138no—
397#466—138no—
398#442—138no—
399#435—138no—
400#428—138no—
401C2×#107—131no—
402C2×#107—131no—
403C2×#107—131no—
404C2×#106—131no—
405C2×#106—131no—
406C2×#106—131no—
407C2×#106—131no—
408C2×#106—138no—
409C2×#106—131no—
410C2×#106—131no—
411C2×C4⋊C8—131no—
412C2×#102—131no—
413C2×#102—131no—
414C2×#102—131no—
415C2×#102—131no—
416C2×#102—131no—
417C2×#102—131no—
418C2×C22⋊C8—131no—
419C2×C22⋊C8—131no—
420C2×#97—131no—
421C22×C13—28no—
422C22×C13—22no—
423C22×C13—22no—
424C22×C13—22no—
425C22×C13—22no—
426C22×C13—22no—
427C22×C13—44no—
428C22×C13—42no—
429C22×C13—42no—
430C22×C13—42no—
431C22×C13—84no—
432C22×C13#54712yes—
433C22×C13C2×AGL(1,ℤ/8)14yes—
434C22×C13C2×AGL(1,ℤ/8)12yes—
435C22×C13#57712yes—
436C22×C13C23×D411yescharacteristic
437C2×D13—42no—
438C2×D13—42no—
439C2×D13—42no—
440C2×D13—84no—
441C4×C13—22no—
442C4×C13—22no—
443C4×C13—22no—
444C4×C13—22no—
445C4×C13—42no—
446C4×C13—42no—
447C4×C13—42no—
448C4×C13#54712yes—
449C4×C13C22×#4111yescharacteristic
450C4×C13C2×2−1+411yescharacteristic
451Dic13—42no—
452Dic13—42no—
453Dic13—42no—
454C2×#41—268no—
455C2×#41—528no—
456C22×Q8—261no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—131no—
460C22×D4—261no—
461C22×D4—261no—
462C22×D4C22⋊D1311yescharacteristic
463C22×D4C22×D1311yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—261no—
467C23×C4—261no—
468C23×C4—261no—
469C23×C4C22×D1311yescharacteristic
470C23×C4C22×D1311yescharacteristic
471C2×D8—134no—
472C2×D8—264no—
473C2×M16—134no—
474C2×M16—264no—
475C22×C8—131no—
476C22×C8—131no—
477C22×C8—134no—
478C22×C8—131no—
479C22×C8—131no—
480C22×C8—264no—
481C4⋊Q8—134no—
482C4⋊Q8—262no—
483#126—28no—
484#125—22no—
485#125C22×D1314yes—
486#123—28no—
487#123—268no—
488#123—268no—
489C22⋊Q8—268no—
490#121—28no—
491#121—22no—
492#121—22no—
493#121—134no—
494#121—134no—
495#121—262no—
496#121—262no—
497#121C22×D1314yes—
498#121C22×D1314yes—
499C4×D4—28no—
500C4×D4—22no—
501C4×D4—134no—
502C4×D4—262no—
503C4×D4C22⋊D1314yes—
504C4×D4C22×D1314yes—
505C4×D4C22×D1314yes—
506#117—22no—
507#117C22×D1314yes—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—131no—
513C2×C4⋊C4—131no—
514C2×C4⋊C4—131no—
515C2×C4⋊C4—134no—
516C2×C4⋊C4—134no—
517C2×C4⋊C4—261no—
518C2×C4⋊C4—261no—
519C2×C4⋊C4—262no—
520C2×C4⋊C4—262no—
521C2×C4⋊C4—261no—
522C2×C4⋊C4C22⋊D1311yescharacteristic
523C2×C4⋊C4C22×D1311yescharacteristic
524C2×C4⋊C4C22×D1311yescharacteristic
525C2×C4⋊C4C22×D1314yes—
526C2×C4⋊C4C22×D1311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—261no—
532C2×C22⋊C4—261no—
533C2×C22⋊C4—261no—
534C2×C22⋊C4C22⋊D1311yescharacteristic
535C2×C22⋊C4C22⋊D1311yescharacteristic
536C2×C42—21no—
537C2×C42C22×D1311yescharacteristic
538#107—134no—
539#107—134no—
540#107—134no—
541#106—134no—
542#106—134no—
543#106—134no—
544#106—134no—
545#106—134no—
546#106—134no—
547C4⋊C8—134no—
548#102—134no—
549#102—134no—
550#102—134no—
551#102—134no—
552#102—134no—
553#102—134no—
554C22⋊C8—134no—
555C22⋊C8—134no—
556#97—134no—
557C2×C13—24no—
558C2×C13—42no—
559C2×C13—82no—
560C2×C13#334514yescomplemented
561C2×C13C2×#54711yescharacteristic
562C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
563C2×C13C2×#57711yescharacteristic
564D13—82no—
565C24—21no—
566C24—261no—
567C24C2×C22⋊D1311yescharacteristic
568C24C2×C22⋊D1311yescharacteristic
569#41—5232no—
570C2×Q8—264no—
571C2×Q8—524no—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—44no—
579C2×D4—82no—
580C2×D4—132no—
581C2×D4—264no—
582C2×D4—264no—
583C2×D4—262no—
584C2×D4—262no—
585C2×D4—261no—
586C2×D4—524no—
587C2×D4—524no—
588C2×D4C2×C22⋊D1314yes—
589C2×D4C23×D1312yes—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4—264no—
602C22×C4—264no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—264no—
607C22×C4—524no—
608C22×C4—524no—
609C22×C4—524no—
610C22×C4C2×C22⋊D1312yes—
611C22×C4C2×C22⋊D1312yes—
612C22×C4C2×C22⋊D1311yescharacteristic
613C22×C4C2×C22⋊D1311yescharacteristic
614C22×C4C2×C22⋊D1311yescharacteristic
615C22×C4C2×C22⋊D1311yescharacteristic
616C22×C4C23×D1312yes—
617C22×C4C23×D1312yes—
618C22×C4C23×D1311yescharacteristic
619D8—268no—
620M16—268no—
621C2×C8—134no—
622C2×C8—132no—
623C2×C8—132no—
624C2×C8—132no—
625C2×C8—132no—
626C2×C8—268no—
627C2×C8—262no—
628C2×C8—262no—
629C2×C8—262no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—132no—
637C4⋊C4—132no—
638C4⋊C4—132no—
639C4⋊C4—261no—
640C4⋊C4—261no—
641C4⋊C4—261no—
642C4⋊C4—264no—
643C4⋊C4—264no—
644C4⋊C4—264no—
645C4⋊C4C2×C22⋊D1314yes—
646C4⋊C4C23×D1312yes—
647C4⋊C4C23×D1312yes—
648C4⋊C4C23×D1312yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—264no—
654C22⋊C4—264no—
655C22⋊C4—264no—
656C22⋊C4C2×C22⋊D1314yes—
657C22⋊C4C2×C22⋊D1314yes—
658C42—24no—
659C42C2×C22⋊D1312yes—
660C42C23×D1312yes—
661C13C2×#334511yescharacteristic, complemented, Sylow
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—262no—
672C23—522no—
673C23—522no—
674C23—522no—
675C23#8820314yes—
676C23C22×C22⋊D1312yes—
677C23C22×C22⋊D1312yes—
678C23C22×C22⋊D1311yescharacteristic
679Q8—528no—
680D4—28no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—42no—
685D4—84no—
686D4—262no—
687D4—262no—
688D4—528no—
689D4—528no—
690D4—522no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—528no—
713C2×C4—528no—
714C2×C4—522no—
715C2×C4—522no—
716C2×C4—522no—
717C2×C4—528no—
718C2×C4#41×D1312yes—
719C2×C4#8825712yes—
720C2×C4C22×C22⋊D1312yes—
721C2×C4C22×C22⋊D1312yes—
722C2×C4C22×C22⋊D1312yes—
723C2×C4C22×C22⋊D1312yes—
724C2×C4C22×C22⋊D1311yescharacteristic
725C2×C4C24×D1311yescharacteristic
726C8—134no—
727C8—262no—
728C8—262no—
729C8—262no—
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—84no—
741C22—522no—
742C22—522no—
743C22—522no—
744C22—1044no—
745C22C2×#8820314yes—
746C22C2×#8820312yes—
747C22#1171952912yes—
748C22#1171954112yes—
749C22C23×C22⋊D1311yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—522no—
758C4—522no—
759C4—522no—
760C4#1171952912yes—
761C4C2×#41×D1311yescharacteristic
762C4C2×#8825711yescharacteristic
763C2—24no—
764C2—42no—
765C2—82no—
766C2—1042no—
767C2#1312730014yesdirect product factor
768C2C2×#1171952911yescharacteristic
769C2C22×#8820311yescharacteristic
770C2C2×#1171954111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#553C2
socleC23×C13C22×D4
hypercenterC2×#553D13
hypocenterC13C2×#3345
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#11719260C2semidirect
2. #13127300C2direct (N × H)
3. C2×#11718726C2semidirect
4. C2×#11718629C2semidirect
5. C2×#11718695C2semidirect
6. C2×#11718664C2semidirect
7. C2×#11718694C2semidirect
8. C2×#11718727C2semidirect
9. C2×#11718669C2semidirect
10. C2×#11718700C2semidirect
11. C2×#11718699C2semidirect
12. C2×#11718675C2semidirect
13. C2×#11718672C2semidirect
14. C2×#11718656C2semidirect
15. C22×#88048C2semidirect
16. C2×C13×#553C2semidirect
19. C13×#553C22semidirect
39. #11719260C22semidirect
50. #11718727C22semidirect
51. #11718726C22semidirect
52. #11718700C22semidirect
53. #11718699C22semidirect
54. #11718695C22semidirect
55. #11718694C22semidirect
56. #11718675C22semidirect
57. #11718672C22semidirect
58. #11718669C22semidirect
59. #11718664C22semidirect
60. #11718656C22semidirect
61. #11718629C22semidirect
71. C2×#88048C22semidirect
272. C2×#1055#41semidirect
277. C2×#553D13semidirect
360. #1055C2×#41semidirect
366. #553C2×D13semidirect
560. C2×C13#3345semidirect
661. C13C2×#3345semidirect
767. C2#13127300direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192602
#131273002
C2×#117187262
C2×#117186292
C2×#117186952
C2×#117186642
C2×#117186942
C2×#117187272
C2×#117186692
C2×#117187002
C2×#117186992
C2×#117186752
C2×#117186722
C2×#117186562
C22×#880482
C2×C13×#5532
C2×#334513