Finite Group Databasebeta

← C2×#13123674 #16727023

Subgroups — C2×#13123674 #16727023

Order 3328.

2730 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88172C211yesmaximal, characteristic
2C2×#11719279C211yesmaximal, characteristic
3C2×#11719277C211yesmaximal, characteristic, complemented
4#13123674C2116yesmaximal, direct product factor
5C2×#11718845C211yesmaximal, characteristic, complemented
6C2×#11718691C211yesmaximal, characteristic, complemented
7C2×#11718550C211yesmaximal, characteristic, complemented
8C2×#11718687C211yesmaximal, characteristic, complemented
9C2×#11718451C211yesmaximal, characteristic, complemented
10C2×C4×#6095C211yesmaximal, characteristic, complemented
11C2×#11718449C211yesmaximal, characteristic, complemented
12C2×#11718542C211yesmaximal, characteristic, complemented
13C2×#11718465C211yesmaximal, characteristic
14C2×D13×#103C211yesmaximal, characteristic, complemented
15C2×#11718350C211yesmaximal, characteristic, complemented
16C2×C4×C13×Q16C211yesmaximal, characteristic, complemented
17C22×#6131C2211yescharacteristic
18C22×Q8×D13C2211yescharacteristic
19C22×C13×Q16C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×Q8×C13C2211yescharacteristic
22C2×Q8×Dic13C2211yescharacteristic
23C2×Q8×Dic13C2211yescharacteristic
24C22×#6107C2211yescharacteristic
25C22×#6106C2211yescharacteristic
26C2×#88172C4116yescomplemented
27C2×#88172C2218yes—
28C22×#6095C2211yescharacteristic
29C22×#6094C2211yescharacteristic
30C22×C8×D13C2211yescharacteristic
31#11719279—24no—
32#11719279C2218yes—
33#11719277—24no—
34#11719277C2218yescomplemented
35C2×#88147—21no—
36C2×#88147C2211yescharacteristic
37C2×#88146—21no—
38C2×#88146C2211yescharacteristic
39C2×C4⋊C4×D13—21no—
40C2×C4⋊C4×D13C2211yescharacteristic
41C2×#88141—21no—
42C2×#88141C2211yescharacteristic
43C2×C4×D52—21no—
44C2×C4×D52C2211yescharacteristic
45C2×#88126—21no—
46C2×#88126—21no—
47C2×#88126C2211yescharacteristic
48C2×C4×Dic26—21no—
49C2×C4×Dic26C2211yescharacteristic
50C4×C13×Q16C2218yescomplemented
51C2×C13×#107C2211yescharacteristic
52C2×C13×#103C2211yescharacteristic
53C2×C13×#103C2211yescharacteristic
54C2×C4×C8×C13C2211yescharacteristic
55C2×#88075C2211yescharacteristic
56C2×#88075C2211yescharacteristic
57#11718845C2218yescomplemented
58C2×#88061C2211yescharacteristic
59C2×#88057C2211yescharacteristic
60C2×#88056C2211yescharacteristic
61C2×#88055C2211yescharacteristic
62C2×C8×Dic13C2211yescharacteristic
63#11718691C2218yescomplemented
64#11718687C2218yescomplemented
65C2×#88050C2211yescharacteristic
66C2×#88049C2211yescharacteristic
67C2×#88048C2211yescharacteristic
68C2×#88047C2211yescharacteristic
69C2×#88043C2211yescharacteristic
70#11718550C2218yescomplemented
71#11718542C2218yescomplemented
72#11718465C2218yes—
73D13×#103C2218yescomplemented
74#11718451C2218yescomplemented
75#11718449C2218yescomplemented
76C4×#6095C2218yescomplemented
77#11718350C2218yescomplemented
78C22×Q8×C13C2311yescharacteristic
79C22×Q8×C13C2311yescharacteristic
80C2×#6131—22no—
81C2×#6131—24no—
82C2×#6131C2×C418yes—
83C2×#6131C2314yes—
84C2×Q8×D13—22no—
85C2×Q8×D13—24no—
86C2×Q8×D13C2×C418yescomplemented
87C2×Q8×D13C2314yes—
88C22×D52—21no—
89C22×D52C2311yescharacteristic
90C22×C4×D13—21no—
91C22×C4×D13—21no—
92C22×C4×D13—21no—
93C22×C4×D13—21no—
94C22×C4×D13—21no—
95C22×C4×D13C2311yescharacteristic
96C22×Dic26—21no—
97C22×Dic26C2311yescharacteristic
98C2×C13×Q16C2×C418yescomplemented
99C2×C13×Q16C2314yes—
100C22×C8×C13C2311yescharacteristic
101C22×C8×C13C2311yescharacteristic
102C4×Q8×C13—22no—
103C4×Q8×C13—22no—
104C4×Q8×C13C2314yes—
105C4×Q8×C13C2314yes—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4C2311yescharacteristic
109C2×C13×C4⋊C4C2311yescharacteristic
110C2×C42×C13—21no—
111C2×C42×C13—21no—
112C2×C42×C13C2311yescharacteristic
113Q8×Dic13—22no—
114Q8×Dic13—22no—
115Q8×Dic13C2314yes—
116Q8×Dic13C2314yes—
117C2×#6107C2×C418yescomplemented
118C2×#6107C2314yes—
119C2×#6106C2×C418yescomplemented
120C2×#6106C2314yes—
121C2×#6103—21no—
122C2×#6103—21no—
123C2×#6103—21no—
124C2×#6103D411yescharacteristic
125C2×#6103D411yescharacteristic
126C2×C4⋊Dic13—21no—
127C2×C4⋊Dic13—21no—
128C2×C4⋊Dic13C2311yescharacteristic
129C2×C4⋊Dic13C2311yescharacteristic
130C2×#6101—21no—
131C2×#6101—21no—
132C2×#6101—21no—
133C2×#6101D411yescharacteristic
134C2×#6101D411yescharacteristic
135C2×C4×Dic13—21no—
136C2×C4×Dic13—21no—
137C2×C4×Dic13—21no—
138C2×C4×Dic13—21no—
139C2×C4×Dic13—21no—
140C2×C4×Dic13C2311yescharacteristic
141C22×#1055C2311yescharacteristic
142C22×#1055C2311yescharacteristic
143#88172C2×C4164yescomplemented
144C2×#6095C2×C418yescomplemented
145C2×#6095C2314yes—
146C2×#6094C2×C418yescomplemented
147C2×#6094C2314yes—
148C2×C8×D13—24no—
149C2×C8×D13C2314yes—
150#88147—28no—
151#88147—22no—
152#88147C2314yes—
153#88146—22no—
154#88146—28no—
155#88146C2314yes—
156C4⋊C4×D13—22no—
157C4⋊C4×D13—28no—
158C4⋊C4×D13C2314yes—
159#88141—28no—
160#88141—22no—
161#88141C2314yes—
162C4×D52—22no—
163C4×D52—28no—
164C4×D52C2314yes—
165#88126—28no—
166#88126—28no—
167#88126D414yes—
168#88126C2314yes—
169C4×Dic26—22no—
170C4×Dic26—28no—
171C4×Dic26C2314yes—
172C13×#107C2314yes—
173C13×#103C2314yes—
174C13×#103C2314yes—
175C4×C8×C13C2314yes—
176#88075C2314yes—
177#88075C2314yes—
178#88061C2314yes—
179#88057C2314yes—
180#88056C2314yes—
181#88055C2314yes—
182C8×Dic13C2314yes—
183#88050C2314yes—
184#88049C2314yes—
185#88048C2314yes—
186#88047C2314yes—
187#88043C2314yes—
188C2×#2947—131nomaximal, Sylow
189C23×D13—21no—
190C23×D13C2×D411yescharacteristic
191C2×Q8×C13—21no—
192C2×Q8×C13—21no—
193C2×Q8×C13—22no—
194C2×Q8×C13—22no—
195C2×Q8×C13C22×C414yes—
196C2×Q8×C13C22×C414yes—
197C2×Q8×C13C2412yes—
198C2×Q8×C13C2412yes—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13C2×D411yescharacteristic
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2411yescharacteristic
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13C2×D411yescharacteristic
210C22×Dic13C2×D411yescharacteristic
211C22×Dic13C2×D411yescharacteristic
212#6131—216no—
213#6131—28no—
214#6131C22×C4116yes—
215Q8×D13—216no—
216Q8×D13—28no—
217Q8×D13C22×C4116yescomplemented
218C2×D52—28no—
219C2×D52—24no—
220C2×D52—21no—
221C2×D52—22no—
222C2×D52C22×C414yes—
223C2×D52C2412yes—
224C2×C4×D13—28no—
225C2×C4×D13—24no—
226C2×C4×D13—28no—
227C2×C4×D13—24no—
228C2×C4×D13—24no—
229C2×C4×D13—24no—
230C2×C4×D13—24no—
231C2×C4×D13—82no—
232C2×C4×D13—82no—
233C2×C4×D13—82no—
234C2×C4×D13C22×C414yes—
235C2×C4×D13C2×D412yes—
236C2×C4×D13#4114yes—
237C2×C4×D13C2412yes—
238C2×Dic26—21no—
239C2×Dic26—22no—
240C2×Dic26—28no—
241C2×Dic26—24no—
242C2×Dic26C22×C414yes—
243C2×Dic26C2412yes—
244C13×Q16C22×C4116yescomplemented
245C2×C8×C13—22no—
246C2×C8×C13C22×C414yes—
247C2×C8×C13C2412yes—
248C2×C8×C13C2412yes—
249C13×C4⋊C4—24no—
250C13×C4⋊C4—21no—
251C13×C4⋊C4—24no—
252C13×C4⋊C4—21no—
253C13×C4⋊C4C2412yes—
254C13×C4⋊C4C2412yes—
255C42×C13—24no—
256C42×C13—24no—
257C42×C13C2×D412yes—
258C42×C13C2412yes—
259#6107C22×C4116yescomplemented
260#6106C22×C4116yescomplemented
261#6103—24no—
262#6103—24no—
263#6103—24no—
264#6103C2×D414yes—
265#6103C2×D414yes—
266C4⋊Dic13—21no—
267C4⋊Dic13—21no—
268C4⋊Dic13—24no—
269C4⋊Dic13—24no—
270C4⋊Dic13C2412yes—
271C4⋊Dic13C2412yes—
272#6101—24no—
273#6101—24no—
274#6101—24no—
275#6101C2×D414yes—
276#6101C2×D414yes—
277C4×Dic13—24no—
278C4×Dic13—24no—
279C4×Dic13—24no—
280C4×Dic13—24no—
281C4×Dic13—24no—
282C4×Dic13C2×D412yes—
283C4×Dic13C2412yes—
284C2×#1055—22no—
285C2×#1055C22×C414yes—
286C2×#1055C2412yes—
287C2×#1055C2412yes—
288#6095C22×C4116yescomplemented
289#6094C22×C4116yescomplemented
290C8×D13—28no—
291C22×#137—131no—
292C2×#520—131no—
293C2×#519—131no—
294#2947—1316no—
295C2×#441—131no—
296C2×#441—131no—
297C2×#440—131no—
298C2×#440—131no—
299C2×C4×Q16—131no—
300C2×C4×Q16D1311yescharacteristic, complemented
301C2×C4×SD16—131no—
302C2×C4×SD16—131no—
303C2×#428—131no—
304C2×#416—131no—
305C22×#103—131no—
306C2×#405—131no—
307C23×C13C22×D411yescharacteristic
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—24no—
311C22×D13—22no—
312C22×D13—42no—
313C22×D13—42no—
314C22×D13C4×D414yes—
315C22×D13C22×D412yes—
316Q8×C13—24no—
317Q8×C13—24no—
318Q8×C13—22no—
319Q8×C13—22no—
320Q8×C13C23×C414yes—
321Q8×C13C23×C414yes—
322C2×C4×C13—24no—
323C2×C4×C13—24no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—42no—
331C2×C4×C13—42no—
332C2×C4×C13C23×C412yes—
333C2×C4×C13C22×D412yes—
334C2×C4×C13C22×D412yes—
335C2×C4×C13C22×D411yescharacteristic
336C2×C4×C13C2×#4112yes—
337C2×C4×C13C2511yescharacteristic
338C2×Dic13—24no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13C4×D414yes—
347C2×Dic13C22×D412yes—
348C2×Dic13C22×D412yes—
349C2×Dic13C22×D412yes—
350D52—216no—
351D52—24no—
352D52—22no—
353D52C23×C414yes—
354C4×D13—216no—
355C4×D13—216no—
356C4×D13—84no—
357C4×D13—84no—
358C4×D13—84no—
359C4×D13C4×D418yes—
360C4×D13C23×C414yes—
361C4×D13C2×#4114yes—
362Dic26—24no—
363Dic26—22no—
364Dic26—216no—
365Dic26C23×C414yes—
366C8×C13—22no—
367C8×C13C23×C414yes—
368#1055—22no—
369#1055C23×C414yes—
370C22×#41—131no—
371C23×Q8—131no—
372C2×#137—1316no—
373C2×#137—138no—
374C22×Q16—131no—
375C22×Q16C2×D1311yescharacteristic
376C22×SD16—131no—
377C22×SD16—131no—
378C22×M16—131no—
379C23×C8—131no—
380#520—138no—
381#520—264no—
382#519—138no—
383#519—264no—
384C2×C4×Q8—131no—
385C2×C4×Q8—131no—
386C2×C4×Q8—131no—
387C2×C4×Q8—131no—
388C2×C4×Q8—261no—
389C2×C4×Q8—261no—
390C2×C4×Q8C2×D1311yescharacteristic
391C2×C4×Q8C2×D1311yescharacteristic
392C2×C4×D4—131no—
393C2×C4×D4—131no—
394C2×C4×D4—261no—
395C2×C4×D4—261no—
396C2×#117—131no—
397C2×#117—131no—
398C2×#117—261no—
399C2×#117—261no—
400C2×#117—261no—
401C22×C4⋊C4—131no—
402C22×C4⋊C4—261no—
403#441—138no—
404#441—138no—
405#440—138no—
406#440—138no—
407C4×Q16—138no—
408C4×Q16C2×D1318yescomplemented
409C4×SD16—138no—
410C4×SD16—138no—
411#428—138no—
412C2×#107—131no—
413C2×#107C2×D1311yescharacteristic
414C2×#106—131no—
415C2×#106—131no—
416#416—138no—
417C2×#103—131no—
418C2×#103—131no—
419C2×#103—131no—
420C2×#103—131no—
421C2×#103—138no—
422C2×#103C2×D1311yescharacteristic
423C2×#103C2×D1311yescharacteristic
424C2×#102—131no—
425C2×#102—131no—
426#405—138no—
427C2×#97—131no—
428C2×#97—131no—
429C2×C4×C8—131no—
430C2×C4×C8C2×D1311yescharacteristic
431C22×C13C2×C4×D412yes—
432C22×C13#57712yes—
433C22×C13#57812yes—
434C22×C13C23×D411yescharacteristic
435C2×D13—28no—
436C2×D13—22no—
437C2×D13—22no—
438C2×D13—24no—
439C2×D13—48no—
440C2×D13—42no—
441C2×D13—42no—
442C2×D13C2×C4×D414yes—
443C4×C13—24no—
444C4×C13—24no—
445C4×C13—22no—
446C4×C13—22no—
447C4×C13—42no—
448C4×C13—42no—
449C4×C13C2×C4×D412yes—
450C4×C13C24×C411yescharacteristic
451C4×C13C22×#4111yescharacteristic
452Dic13—24no—
453Dic13—22no—
454Dic13—22no—
455Dic13—42no—
456Dic13—42no—
457Dic13C2×C4×D414yes—
458C2×#41—138no—
459C2×#41—134no—
460C2×#41—262no—
461C2×#41—264no—
462C22×Q8—138no—
463C22×Q8—134no—
464C22×Q8—131no—
465C22×Q8—261no—
466C22×Q8—262no—
467C22×Q8—264no—
468C22×Q8C22×D1311yescharacteristic
469C22×Q8C22×D1311yescharacteristic
470C22×D4—131no—
471C22×D4—261no—
472C23×C4—131no—
473C23×C4—261no—
474C23×C4—261no—
475C23×C4—261no—
476C23×C4—261no—
477C23×C4—261no—
478#137—1364no—
479C2×Q16—138no—
480C2×Q16—134no—
481C2×Q16C4×D1318yescomplemented
482C2×Q16C22×D1314yes—
483C2×SD16—138no—
484C2×SD16—134no—
485C2×SD16—138no—
486C2×SD16—134no—
487C2×M16—138no—
488C2×M16—134no—
489C22×C8—131no—
490C22×C8—131no—
491C22×C8—134no—
492C22×C8—264no—
493C22×C8C22×D1311yescharacteristic
494C22×C8C22×D1311yescharacteristic
495C4×Q8—22no—
496C4×Q8—22no—
497C4×Q8—134no—
498C4×Q8—134no—
499C4×Q8—134no—
500C4×Q8—134no—
501C4×Q8—268no—
502C4×Q8—262no—
503C4×Q8—262no—
504C4×Q8—262no—
505C4×Q8—268no—
506C4×Q8—262no—
507C4×Q8C22×D1314yes—
508C4×Q8C22×D1314yes—
509C4×D4—134no—
510C4×D4—134no—
511C4×D4—268no—
512C4×D4—262no—
513C4×D4—268no—
514C4×D4—262no—
515#117—134no—
516#117—134no—
517#117—134no—
518#117—268no—
519#117—268no—
520#117—268no—
521#117—262no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—131no—
525C2×C4⋊C4—131no—
526C2×C4⋊C4—131no—
527C2×C4⋊C4—131no—
528C2×C4⋊C4—134no—
529C2×C4⋊C4—268no—
530C2×C4⋊C4—262no—
531C2×C4⋊C4—261no—
532C2×C4⋊C4—261no—
533C2×C4⋊C4—261no—
534C2×C4⋊C4—261no—
535C2×C4⋊C4—261no—
536C2×C4⋊C4C22×D1311yescharacteristic
537C2×C4⋊C4C22×D1311yescharacteristic
538C2×C22⋊C4—131no—
539C2×C22⋊C4—131no—
540C2×C22⋊C4—261no—
541C2×C22⋊C4—261no—
542C2×C22⋊C4—261no—
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—131no—
546C2×C42—261no—
547C2×C42—261no—
548C2×C42—261no—
549C2×C42—261no—
550C2×C42—261no—
551C2×C42C22×D1311yescharacteristic
552#107—134no—
553#107C22×D1314yes—
554#106—134no—
555#106—134no—
556#103—134no—
557#103—134no—
558#103—134no—
559#103—134no—
560#103C22×D1314yes—
561#103C22×D1314yes—
562#102—134no—
563#102—134no—
564#97—134no—
565#97—134no—
566C4×C8—134no—
567C4×C8C22×D1314yes—
568C2×C13#294714yescomplemented
569C2×C13C22×C4×D411yescharacteristic
570C2×C13C2×#57711yescharacteristic
571C2×C13C2×#57811yescharacteristic
572D13—24no—
573D13—44no—
574C24—131no—
575C24—261no—
576#41—1316no—
577#41—2616no—
578#41—268no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—1316no—
584C2×Q8—134no—
585C2×Q8—132no—
586C2×Q8—264no—
587C2×Q8—268no—
588C2×Q8—2616no—
589C2×Q8—268no—
590C2×Q8—261no—
591C2×Q8—262no—
592C2×Q8C2×C4×D1314yes—
593C2×Q8C2×C4×D1314yes—
594C2×Q8C23×D1312yes—
595C2×Q8C23×D1312yes—
596C2×D4—134no—
597C2×D4—132no—
598C2×D4—264no—
599C2×D4—268no—
600C2×D4—261no—
601C2×D4—262no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—131no—
607C22×C4—134no—
608C22×C4—132no—
609C22×C4—134no—
610C22×C4—132no—
611C22×C4—131no—
612C22×C4—131no—
613C22×C4—264no—
614C22×C4—268no—
615C22×C4—264no—
616C22×C4—264no—
617C22×C4—268no—
618C22×C4—264no—
619C22×C4—261no—
620C22×C4—261no—
621C22×C4—261no—
622C22×C4—264no—
623C22×C4—1042no—
624C22×C4—1042no—
625C22×C4—1042no—
626C22×C4D4×D1311yescharacteristic
627C22×C4D4×D1311yescharacteristic
628C22×C4C23×D1311yescharacteristic
629Q16—1316no—
630Q16C2×C4×D13116yescomplemented
631SD16—1316no—
632SD16—1316no—
633M16—1316no—
634C2×C8—22no—
635C2×C8—134no—
636C2×C8—132no—
637C2×C8—132no—
638C2×C8—268no—
639C2×C8—262no—
640C2×C8C2×C4×D1314yes—
641C2×C8C23×D1312yes—
642C2×C8C23×D1312yes—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—134no—
648C4⋊C4—134no—
649C4⋊C4—132no—
650C4⋊C4—132no—
651C4⋊C4—264no—
652C4⋊C4—264no—
653C4⋊C4—264no—
654C4⋊C4—264no—
655C4⋊C4—261no—
656C4⋊C4—261no—
657C4⋊C4—264no—
658C4⋊C4C23×D1312yes—
659C4⋊C4C23×D1312yes—
660C22⋊C4—134no—
661C22⋊C4—134no—
662C22⋊C4—264no—
663C22⋊C4—264no—
664C22⋊C4—264no—
665C42—24no—
666C42—24no—
667C42—132no—
668C42—132no—
669C42—264no—
670C42—264no—
671C42—264no—
672C42—264no—
673C42—264no—
674C42D4×D1312yes—
675C42C23×D1312yes—
676C13C2×#294711yescharacteristic, complemented, Sylow
677C23—134no—
678C23—132no—
679C23—262no—
680C23—262no—
681C23—264no—
682C23—262no—
683C23—522no—
684C23—522no—
685C23C2×D4×D1311yescharacteristic
686Q8—24no—
687Q8—24no—
688Q8—22no—
689Q8—22no—
690Q8—134no—
691Q8—2616no—
692Q8—264no—
693Q8—262no—
694Q8C22×C4×D1314yes—
695Q8C22×C4×D1314yes—
696D4—134no—
697D4—2616no—
698D4—264no—
699D4—262no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—134no—
711C2×C4—132no—
712C2×C4—138no—
713C2×C4—134no—
714C2×C4—134no—
715C2×C4—132no—
716C2×C4—132no—
717C2×C4—2616no—
718C2×C4—2616no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—264no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—522no—
726C2×C4—522no—
727C2×C4—1044no—
728C2×C4—1044no—
729C2×C4—1044no—
730C2×C4C22×C4×D1312yes—
731C2×C4C2×D4×D1312yes—
732C2×C4C2×D4×D1312yes—
733C2×C4C2×D4×D1311yescharacteristic
734C2×C4#41×D1312yes—
735C2×C4C24×D1311yescharacteristic
736C8—22no—
737C8—134no—
738C8—262no—
739C8C22×C4×D1314yes—
740C22—134no—
741C22—268no—
742C22—262no—
743C22—262no—
744C22—264no—
745C22—528no—
746C22—522no—
747C22—522no—
748C22C4×D4×D1312yes—
749C22#1171947112yes—
750C22#1171947512yes—
751C22C22×D4×D1311yescharacteristic
752C4—24no—
753C4—24no—
754C4—22no—
755C4—22no—
756C4—42no—
757C4—42no—
758C4—134no—
759C4—264no—
760C4—262no—
761C4—262no—
762C4—522no—
763C4—522no—
764C4C4×D4×D1312yes—
765C4C23×C4×D1311yescharacteristic
766C4C2×#41×D1311yescharacteristic
767C2—264no—
768C2—524no—
769C2#1312367414yesdirect product factor
770C2C2×C4×D4×D1311yescharacteristic
771C2C2×#1171947511yescharacteristic
772C2C2×#1171947111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C4×C13×Q16C2
socleC23×C13C22×D4
prime radicalC22×#6131C22
cosocleC2×C4×C13C25
hypercenterC2×C4×Q16D13
hypocenterC13C2×#2947
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. C2×#11719277C2semidirect
4. #13123674C2direct (N × H)
5. C2×#11718845C2semidirect
6. C2×#11718691C2semidirect
7. C2×#11718550C2semidirect
8. C2×#11718687C2semidirect
9. C2×#11718451C2semidirect
10. C2×C4×#6095C2semidirect
11. C2×#11718449C2semidirect
12. C2×#11718542C2semidirect
14. C2×D13×#103C2semidirect
15. C2×#11718350C2semidirect
16. C2×C4×C13×Q16C2semidirect
26. C2×#88172C4semidirect
34. #11719277C22semidirect
50. C4×C13×Q16C22semidirect
57. #11718845C22semidirect
63. #11718691C22semidirect
64. #11718687C22semidirect
70. #11718550C22semidirect
71. #11718542C22semidirect
73. D13×#103C22semidirect
74. #11718451C22semidirect
75. #11718449C22semidirect
76. C4×#6095C22semidirect
77. #11718350C22semidirect
86. C2×Q8×D13C2×C4semidirect
98. C2×C13×Q16C2×C4semidirect
117. C2×#6107C2×C4semidirect
119. C2×#6106C2×C4semidirect
143. #88172C2×C4semidirect
144. C2×#6095C2×C4semidirect
146. C2×#6094C2×C4semidirect
217. Q8×D13C22×C4semidirect
244. C13×Q16C22×C4semidirect
259. #6107C22×C4semidirect
260. #6106C22×C4semidirect
288. #6095C22×C4semidirect
289. #6094C22×C4semidirect
300. C2×C4×Q16D13semidirect
408. C4×Q16C2×D13semidirect
481. C2×Q16C4×D13semidirect
568. C2×C13#2947semidirect
630. Q16C2×C4×D13semidirect
676. C13C2×#2947semidirect
769. C2#13123674direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881722
C2×#117192792
C2×#117192772
#131236742
C2×#117188452
C2×#117186912
C2×#117185502
C2×#117186872
C2×#117184512
C2×C4×#60952
C2×#117184492
C2×#117185422
C2×#117184652
C2×D13×#1032
C2×#117183502
C2×C4×C13×Q162
C2×#294713