Finite Group Databasebeta

← C2×#13127178 #16741326

Subgroups — C2×#13127178 #16741326

Order 3328.

2374 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719212C211yesmaximal, characteristic, complemented
2C2×#11719316C211yesmaximal, characteristic, complemented
3#13127178C2116yesmaximal, direct product factor
4C2×#11718535C211yesmaximal, characteristic, complemented
5C2×#11718543C211yesmaximal, characteristic, complemented
6C2×#11718397C211yesmaximal, characteristic, complemented
7C2×#11718435C211yesmaximal, characteristic, complemented
8C2×#11718551C211yesmaximal, characteristic, complemented
9C2×#11718420C211yesmaximal, characteristic, complemented
10C2×#11718436C211yesmaximal, characteristic, complemented
11C2×#11718699C211yesmaximal, characteristic, complemented
12C2×#11718417C211yesmaximal, characteristic, complemented
13C2×#11718386C211yesmaximal, characteristic, complemented
14C22×#88047C211yesmaximal, characteristic, complemented
15C2×D13×#107C211yesmaximal, characteristic, complemented
16C2×C13×#480C211yesmaximal, characteristic, complemented
17C22×#6129—21no—
18C22×#6127—21no—
19C2×C13×#121C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C2×#88192C2211yescharacteristic
22C2×#88189—21no—
23C2×D4×Dic13C2211yescharacteristic
24C22×#6104C2211yescharacteristic
25C2×#88184C2211yescharacteristic
26C2×#88183—21no—
27C2×C4×C22⋊D13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C23×#1055C2211yescharacteristic
30C22×C8×D13C2211yescharacteristic
31#11719316—24no—
32#11719316C2218yescomplemented
33C2×#88150—21no—
34#11719212—24no—
35#11719212C2218yescomplemented
36C2×#88149C2211yescharacteristic
37C2×#88148—21no—
38C2×#88147C2211yescharacteristic
39C2×C4⋊C4×D13C2211yescharacteristic
40C2×C4⋊C4×D13C2211yescharacteristic
41C2×#88142C2211yescharacteristic
42C2×#88142C2211yescharacteristic
43C2×#88137—21no—
44C2×#88132—21no—
45C13×#480C2218yescomplemented
46C2×C13×#107C2211yescharacteristic
47C2×C13×#107C2211yescharacteristic
48C2×C13×#102C2211yescharacteristic
49C2×C13×#102C2211yescharacteristic
50C2×C13×C22⋊C8C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52C2×#88061C2211yescharacteristic
53C2×#88061C2211yescharacteristic
54C2×#88060C2211yescharacteristic
55C2×#88058C2211yescharacteristic
56C2×#88058C2211yescharacteristic
57C2×#88054C2211yescharacteristic
58C2×C8×Dic13C2211yescharacteristic
59#11718699C2218yescomplemented
60C2×#88049C2211yescharacteristic
61C2×#88047C2211yescharacteristic
62C2×#88047C2211yescharacteristic
63C2×#88047C2211yescharacteristic
64C2×#88047C2211yescharacteristic
65C2×#88047C2211yescharacteristic
66C2×#88047C2218yescomplemented
67#11718551C2218yescomplemented
68#11718543C2218yescomplemented
69D13×#107C2218yescomplemented
70#11718535C2218yescomplemented
71#11718436C2218yescomplemented
72#11718435C2218yescomplemented
73#11718420C2218yescomplemented
74#11718417C2218yescomplemented
75#11718397C2218yescomplemented
76#11718386C2218yescomplemented
77C22×D4×C13—21no—
78C22×D4×C13C2311yescharacteristic
79C23×C4×C13—21no—
80C23×C4×C13C2311yescharacteristic
81C22×C22⋊D13—21no—
82C22×C22⋊D13—21no—
83C22×C22⋊D13D411yescharacteristic
84C23×Dic13—21no—
85C23×Dic13—21no—
86C2×#6129—28no—
87C2×#6129—48no—
88C2×#6127—28no—
89C2×#6127—48no—
90C22×D52—21no—
91C22×D52C2311yescharacteristic
92C22×C4×D13—21no—
93C22×C4×D13—21no—
94C22×C4×D13—21no—
95C22×C4×D13C2311yescharacteristic
96C22×Dic26—21no—
97C22×Dic26—21no—
98C22×C8×C13C2311yescharacteristic
99C22×C8×C13C2311yescharacteristic
100C13×#121—22no—
101C13×#121C2314yes—
102C2×C13×C4⋊C4—21no—
103C2×C13×C4⋊C4—22no—
104C2×C13×C4⋊C4C2311yescharacteristic
105C2×C13×C4⋊C4C2311yescharacteristic
106C2×C13×C4⋊C4C2311yescharacteristic
107C2×C13×C4⋊C4C2314yes—
108C2×C13×C22⋊C4—21no—
109C2×C22⋊Dic13—21no—
110C2×C22⋊Dic13—21no—
111C2×C22⋊Dic13D411yescharacteristic
112#88192—22no—
113#88192C2314yes—
114#88189—28no—
115D4×Dic13—22no—
116D4×Dic13C2314yes—
117C2×#6104—24no—
118C2×#6104C2314yes—
119#88184—22no—
120#88184C2314yes—
121#88183—28no—
122C4×C22⋊D13D414yes—
123C4×C22⋊D13C2314yes—
124C2×#6103—21no—
125C2×#6103—21no—
126C2×#6103—21no—
127C2×#6103D411yescharacteristic
128C2×C4⋊Dic13—21no—
129C2×C4⋊Dic13—22no—
130C2×C4⋊Dic13C2311yescharacteristic
131C2×C4⋊Dic13C2311yescharacteristic
132C2×C4⋊Dic13C2311yescharacteristic
133C2×C4⋊Dic13C2314yes—
134C2×#6101—21no—
135C2×#6101—21no—
136C2×#6101—21no—
137C2×#6101—21no—
138C2×#6101D411yescharacteristic
139C2×C4×Dic13C2311yescharacteristic
140C22×#1055—24no—
141C22×#1055C2314yes—
142C22×#1055C2311yescharacteristic
143C22×#1055C2311yescharacteristic
144C2×C8×D13—24no—
145C2×C8×D13C2314yes—
146#88150—28no—
147#88149—22no—
148#88149C2314yes—
149#88148—28no—
150#88147—22no—
151#88147C2314yes—
152C4⋊C4×D13—22no—
153C4⋊C4×D13—22no—
154C4⋊C4×D13C2314yes—
155C4⋊C4×D13C2314yes—
156#88142—22no—
157#88142—22no—
158#88142C2314yes—
159#88142C2314yes—
160#88137—28no—
161#88132—28no—
162C13×#107C2314yes—
163C13×#107C2314yes—
164C13×#102C2314yes—
165C13×#102C2314yes—
166C13×C22⋊C8C2314yes—
167#88072C2314yes—
168#88061C2314yes—
169#88061C2314yes—
170#88060C2314yes—
171#88058C2314yes—
172#88058C2314yes—
173#88054C2314yes—
174C8×Dic13C2314yes—
175#88049C2314yes—
176#88047C2314yes—
177#88047C2314yes—
178#88047C2314yes—
179#88047C2314yes—
180#88047C2314yes—
181C2×#3334—131nomaximal, Sylow
182C24×C13—21no—
183C24×C13C2×D411yescharacteristic
184C23×D13—21no—
185C23×D13C2×D411yescharacteristic
186C2×D4×C13—24no—
187C2×D4×C13—21no—
188C2×D4×C13—22no—
189C2×D4×C13—22no—
190C2×D4×C13—44no—
191C2×D4×C13C2412yes—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—24no—
198C22×C4×C13—44no—
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2×D412yes—
201C22×C4×C13C2412yes—
202C22×C4×C13C2411yescharacteristic
203C2×C22⋊D13—24no—
204C2×C22⋊D13—24no—
205C2×C22⋊D13—44no—
206C2×C22⋊D13—44no—
207C2×C22⋊D13D818yescomplemented
208C2×C22⋊D13C2×D414yes—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—24no—
213C22×Dic13—24no—
214C22×Dic13—44no—
215C22×Dic13—44no—
216C22×Dic13C2×D411yescharacteristic
217C22×Dic13C2×D411yescharacteristic
218C22×Dic13C2×D411yescharacteristic
219#6129—432no—
220#6127—432no—
221C2×D52—22no—
222C2×D52—22no—
223C2×D52—24no—
224C2×D52—21no—
225C2×D52—44no—
226C2×D52C2412yes—
227C2×C4×D13—22no—
228C2×C4×D13—22no—
229C2×C4×D13—24no—
230C2×C4×D13—24no—
231C2×C4×D13—24no—
232C2×C4×D13—44no—
233C2×C4×D13—44no—
234C2×C4×D13—44no—
235C2×C4×D13C2×D412yes—
236C2×C4×D13C2412yes—
237C2×Dic26—24no—
238C2×Dic26—24no—
239C2×Dic26—44no—
240C2×Dic26—44no—
241C2×C8×C13—22no—
242C2×C8×C13—22no—
243C2×C8×C13C2412yes—
244C2×C8×C13C2412yes—
245C13×C4⋊C4—21no—
246C13×C4⋊C4—21no—
247C13×C4⋊C4—21no—
248C13×C4⋊C4—24no—
249C13×C4⋊C4C2412yes—
250C13×C4⋊C4C2412yes—
251C13×C4⋊C4C2412yes—
252C13×C22⋊C4—24no—
253C22⋊Dic13—24no—
254C22⋊Dic13—24no—
255C22⋊Dic13C2×D414yes—
256#6104—28no—
257#6103—24no—
258#6103—24no—
259#6103—24no—
260#6103C2×D414yes—
261C4⋊Dic13—24no—
262C4⋊Dic13—21no—
263C4⋊Dic13—21no—
264C4⋊Dic13—21no—
265C4⋊Dic13C2412yes—
266C4⋊Dic13C2412yes—
267C4⋊Dic13C2412yes—
268#6101—24no—
269#6101—24no—
270#6101—24no—
271#6101—24no—
272#6101C2×D414yes—
273C4×Dic13C2×D412yes—
274C4×Dic13C2412yes—
275C2×#1055—22no—
276C2×#1055—28no—
277C2×#1055#4114yescomplemented
278C2×#1055C2412yes—
279C2×#1055C2412yes—
280C8×D13—28no—
281C2×#547—131no—
282C2×#547—131no—
283#3334—1316no—
284C2×#500—131no—
285C2×#480—131no—
286C2×#480—131no—
287C2×#480—131no—
288C2×#480D1311yescharacteristic, complemented
289C2×#474—131no—
290C2×#474—131no—
291C2×#466—131no—
292C2×#466—131no—
293C2×C4×D8—131no—
294C2×C8×D4—131no—
295C22×#107—131no—
296C22×#107—131no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—42no—
301C23×C13—42no—
302C23×C13—42no—
303C23×C13C2×D814yes—
304C23×C13C22×D412yes—
305C23×C13C22×D411yescharacteristic
306C22×D13—22no—
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—42no—
310C22×D13—42no—
311C22×D13—42no—
312C22×D13C2×D814yes—
313C22×D13C22×D412yes—
314D4×C13—22no—
315D4×C13—22no—
316D4×C13—48no—
317D4×C13—42no—
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—42no—
326C2×C4×C13—42no—
327C2×C4×C13—42no—
328C2×C4×C13—48no—
329C2×C4×C13C22×D412yes—
330C2×C4×C13C22×D411yescharacteristic
331C2×C4×C13C2×#4112yes—
332C2×C4×C132−1+412yes—
333C2×C4×C13C2511yescharacteristic
334C22⋊D13—48no—
335C22⋊D13—48no—
336C22⋊D13C2×D8116yescomplemented
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—48no—
346C2×Dic13—48no—
347C2×Dic13C2×D814yes—
348C2×Dic13C22×D412yes—
349C2×Dic13C22×D412yes—
350C2×Dic13C22×D412yes—
351D52—22no—
352D52—22no—
353D52—48no—
354D52—42no—
355C4×D13—24no—
356C4×D13—22no—
357C4×D13—22no—
358C4×D13—48no—
359C4×D13—48no—
360C4×D13—48no—
361Dic26—48no—
362Dic26—48no—
363C8×C13—22no—
364C8×C13—22no—
365#1055—22no—
366#1055C2×#4114yescomplemented
367C22×#41—261no—
368C22×#41—261no—
369C22×D8—131no—
370C23×C8—131no—
371C23×C8—131no—
372#547—138no—
373#547—138no—
374#547—264no—
375#547—264no—
376C2×C4⋊Q8—131no—
377C2×C4⋊Q8—131no—
378C2×#123—261no—
379C2×#123—261no—
380C2×#123—261no—
381C2×#123—261no—
382C2×C22⋊Q8—261no—
383C2×C22⋊Q8—261no—
384C2×#121—131no—
385C2×#121—131no—
386C2×#121—131no—
387C2×#121C2×D1311yescharacteristic
388C2×C4×D4—131no—
389C2×C4×D4—131no—
390C2×C4×D4—131no—
391C22×C4⋊C4—131no—
392C22×C4⋊C4—131no—
393C22×C4⋊C4—131no—
394C22×C4⋊C4C2×D1311yescharacteristic
395#500—138no—
396#480—138no—
397#480—138no—
398#480—138no—
399#480C2×D1318yescomplemented
400#474—138no—
401#474—138no—
402#466—138no—
403#466—138no—
404C4×D8—138no—
405C8×D4—138no—
406C2×#107—131no—
407C2×#107—131no—
408C2×#107—138no—
409C2×#107—131no—
410C2×#107—131no—
411C2×#107—131no—
412C2×#107—131no—
413C2×#107—131no—
414C2×#107—138no—
415C2×#107C2×D1311yescharacteristic
416C2×#107C2×D1311yescharacteristic
417C2×C4⋊C8—131no—
418C2×#102—131no—
419C2×#102—131no—
420C2×#102—131no—
421C2×#102—131no—
422C2×#102C2×D1311yescharacteristic
423C2×#102C2×D1311yescharacteristic
424C2×C22⋊C8—131no—
425C2×C22⋊C8C2×D1311yescharacteristic
426C2×C4×C8—131no—
427C22×C13—28no—
428C22×C13—22no—
429C22×C13—22no—
430C22×C13—42no—
431C22×C13—42no—
432C22×C13—42no—
433C22×C13—84no—
434C22×C13#54712yes—
435C22×C13C22×D814yes—
436C22×C13C22×D812yes—
437C22×C13#57812yes—
438C22×C13C23×D411yescharacteristic
439C2×D13—28no—
440C2×D13—22no—
441C2×D13—22no—
442C2×D13—42no—
443C2×D13—42no—
444C2×D13—42no—
445C2×D13—84no—
446C2×D13C22×D814yes—
447C4×C13—22no—
448C4×C13—42no—
449C4×C13—42no—
450C4×C13—42no—
451C4×C13#54712yes—
452C4×C13C22×#4111yescharacteristic
453C4×C13C2×2−1+411yescharacteristic
454Dic13—22no—
455Dic13—22no—
456Dic13—42no—
457Dic13—42no—
458Dic13—42no—
459Dic13C22×D814yes—
460C2×#41—268no—
461C2×#41—268no—
462C2×#41—528no—
463C2×#41—528no—
464C22×Q8—261no—
465C22×Q8—261no—
466C22×D4—21no—
467C22×D4—131no—
468C22×D4—131no—
469C22×D4—261no—
470C22×D4—261no—
471C22×D4—261no—
472C22×D4C22×D1311yescharacteristic
473C23×C4—21no—
474C23×C4—131no—
475C23×C4—261no—
476C23×C4—261no—
477C23×C4—261no—
478C23×C4—261no—
479C23×C4—261no—
480C23×C4C22×D1311yescharacteristic
481C2×D8—134no—
482C2×D8—264no—
483C22×C8—131no—
484C22×C8—131no—
485C22×C8—134no—
486C22×C8—134no—
487C22×C8—264no—
488C22×C8—264no—
489C22×C8C22×D1311yescharacteristic
490C22×C8C22×D1311yescharacteristic
491C4⋊Q8—134no—
492C4⋊Q8—134no—
493C4⋊Q8—262no—
494C4⋊Q8—262no—
495#123—268no—
496#123—268no—
497#123—268no—
498#123—268no—
499C22⋊Q8—268no—
500C22⋊Q8—268no—
501#121—22no—
502#121—134no—
503#121—134no—
504#121—134no—
505#121—262no—
506#121—262no—
507#121—262no—
508#121C22×D1314yes—
509C4×D4—134no—
510C4×D4—134no—
511C4×D4—134no—
512C4×D4—134no—
513C4×D4—262no—
514C4×D4—262no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—131no—
518C2×C4⋊C4—131no—
519C2×C4⋊C4—131no—
520C2×C4⋊C4—131no—
521C2×C4⋊C4—134no—
522C2×C4⋊C4—134no—
523C2×C4⋊C4—134no—
524C2×C4⋊C4—262no—
525C2×C4⋊C4—262no—
526C2×C4⋊C4—261no—
527C2×C4⋊C4—261no—
528C2×C4⋊C4—261no—
529C2×C4⋊C4—261no—
530C2×C4⋊C4—261no—
531C2×C4⋊C4—262no—
532C2×C4⋊C4C22×D1311yescharacteristic
533C2×C4⋊C4C22×D1311yescharacteristic
534C2×C4⋊C4C22×D1311yescharacteristic
535C2×C4⋊C4C22×D1314yes—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—131no—
538C2×C22⋊C4—131no—
539C2×C22⋊C4—261no—
540C2×C22⋊C4—261no—
541C2×C22⋊C4—261no—
542C2×C22⋊C4—261no—
543C2×C22⋊C4—261no—
544C2×C42—131no—
545#107—134no—
546#107—134no—
547#107—134no—
548#107—134no—
549#107—134no—
550#107—134no—
551#107—134no—
552#107C22×D1314yes—
553#107C22×D1314yes—
554C4⋊C8—134no—
555#102—134no—
556#102—134no—
557#102—134no—
558#102—134no—
559#102C22×D1314yes—
560#102C22×D1314yes—
561C22⋊C8—134no—
562C22⋊C8C22×D1314yes—
563C4×C8—134no—
564C2×C13—24no—
565C2×C13—82no—
566C2×C13#333414yescomplemented
567C2×C13C2×#54711yescharacteristic
568C2×C13C23×D811yescharacteristic
569C2×C13C2×#57811yescharacteristic
570D13—24no—
571D13—82no—
572C24—21no—
573C24—131no—
574C24—261no—
575C24D4×D1311yescharacteristic
576#41—5232no—
577#41—5232no—
578C2×Q8—264no—
579C2×Q8—264no—
580C2×Q8—524no—
581C2×Q8—524no—
582C2×D4—24no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—44no—
587C2×D4—138no—
588C2×D4—134no—
589C2×D4—132no—
590C2×D4—264no—
591C2×D4—264no—
592C2×D4—264no—
593C2×D4—261no—
594C2×D4—262no—
595C2×D4—262no—
596C2×D4—524no—
597C2×D4—524no—
598C2×D4—524no—
599C2×D4C23×D1312yes—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—24no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—44no—
607C22×C4—131no—
608C22×C4—131no—
609C22×C4—131no—
610C22×C4—132no—
611C22×C4—132no—
612C22×C4—264no—
613C22×C4—264no—
614C22×C4—264no—
615C22×C4—264no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—264no—
619C22×C4—261no—
620C22×C4—261no—
621C22×C4—261no—
622C22×C4—524no—
623C22×C4—524no—
624C22×C4—524no—
625C22×C4—524no—
626C22×C4—524no—
627C22×C4D4×D1312yes—
628C22×C4D4×D1311yescharacteristic
629C22×C4C23×D1312yes—
630C22×C4C23×D1311yescharacteristic
631D8—268no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—134no—
635C2×C8—132no—
636C2×C8—132no—
637C2×C8—268no—
638C2×C8—268no—
639C2×C8—262no—
640C2×C8C23×D1312yes—
641C2×C8C23×D1312yes—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—134no—
647C4⋊C4—132no—
648C4⋊C4—132no—
649C4⋊C4—132no—
650C4⋊C4—264no—
651C4⋊C4—264no—
652C4⋊C4—264no—
653C4⋊C4—264no—
654C4⋊C4—261no—
655C4⋊C4—261no—
656C4⋊C4—261no—
657C4⋊C4—264no—
658C4⋊C4C23×D1312yes—
659C4⋊C4C23×D1312yes—
660C4⋊C4C23×D1312yes—
661C22⋊C4—24no—
662C22⋊C4—134no—
663C22⋊C4—134no—
664C22⋊C4—264no—
665C22⋊C4—264no—
666C22⋊C4—264no—
667C22⋊C4—264no—
668C22⋊C4—264no—
669C42—132no—
670C42—132no—
671C13C2×#333411yescharacteristic, complemented, Sylow
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—134no—
679C23—132no—
680C23—262no—
681C23—262no—
682C23—262no—
683C23—522no—
684C23—522no—
685C23—522no—
686C23D8×D1314yes—
687C23C2×D4×D1312yes—
688C23C2×D4×D1311yescharacteristic
689Q8—528no—
690Q8—528no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—42no—
695D4—1316no—
696D4—262no—
697D4—262no—
698D4—528no—
699D4—528no—
700D4—528no—
701D4—522no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—48no—
712C2×C4—42no—
713C2×C4—134no—
714C2×C4—132no—
715C2×C4—132no—
716C2×C4—132no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—264no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—528no—
726C2×C4—528no—
727C2×C4—528no—
728C2×C4—528no—
729C2×C4—522no—
730C2×C4—522no—
731C2×C4—522no—
732C2×C4—528no—
733C2×C4C2×D4×D1312yes—
734C2×C4C2×D4×D1311yescharacteristic
735C2×C4#41×D1312yes—
736C2×C4#8825712yes—
737C2×C4C24×D1311yescharacteristic
738C8—22no—
739C8—22no—
740C8—134no—
741C8—262no—
742C22—28no—
743C22—22no—
744C22—22no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—84no—
749C22—134no—
750C22—268no—
751C22—262no—
752C22—262no—
753C22—522no—
754C22—522no—
755C22—522no—
756C22—1044no—
757C22#1171936012yes—
758C22C2×D8×D1314yes—
759C22C2×D8×D1312yes—
760C22#1171948412yes—
761C22C22×D4×D1311yescharacteristic
762C4—22no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—134no—
767C4—262no—
768C4—262no—
769C4—522no—
770C4—522no—
771C4—522no—
772C4#1171936012yes—
773C4C2×#41×D1311yescharacteristic
774C4C2×#8825711yescharacteristic
775C2—24no—
776C2—82no—
777C2—264no—
778C2—1042no—
779C2#1312717814yesdirect product factor
780C2C2×#1171936011yescharacteristic
781C2C22×D8×D1311yescharacteristic
782C2C2×#1171948411yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#480C2
socleC23×C13C22×D4
hypercenterC2×#480D13
hypocenterC13C2×#3334
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#11719212C2semidirect
2. C2×#11719316C2semidirect
3. #13127178C2direct (N × H)
4. C2×#11718535C2semidirect
5. C2×#11718543C2semidirect
6. C2×#11718397C2semidirect
7. C2×#11718435C2semidirect
8. C2×#11718551C2semidirect
9. C2×#11718420C2semidirect
10. C2×#11718436C2semidirect
11. C2×#11718699C2semidirect
12. C2×#11718417C2semidirect
13. C2×#11718386C2semidirect
14. C22×#88047C2semidirect
15. C2×D13×#107C2semidirect
16. C2×C13×#480C2semidirect
32. #11719316C22semidirect
35. #11719212C22semidirect
45. C13×#480C22semidirect
59. #11718699C22semidirect
66. C2×#88047C22semidirect
67. #11718551C22semidirect
68. #11718543C22semidirect
69. D13×#107C22semidirect
70. #11718535C22semidirect
71. #11718436C22semidirect
72. #11718435C22semidirect
73. #11718420C22semidirect
74. #11718417C22semidirect
75. #11718397C22semidirect
76. #11718386C22semidirect
207. C2×C22⋊D13D8semidirect
277. C2×#1055#41semidirect
288. C2×#480D13semidirect
336. C22⋊D13C2×D8semidirect
366. #1055C2×#41semidirect
399. #480C2×D13semidirect
566. C2×C13#3334semidirect
671. C13C2×#3334semidirect
779. C2#13127178direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192122
C2×#117193162
#131271782
C2×#117185352
C2×#117185432
C2×#117183972
C2×#117184352
C2×#117185512
C2×#117184202
C2×#117184362
C2×#117186992
C2×#117184172
C2×#117183862
C22×#880472
C2×D13×#1072
C2×C13×#4802
C2×#333413