Finite Group Databasebeta

← #15868781

Subgroups — #15868781

Order 3328.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719524C211yesmaximal, characteristic, complemented
2C2×#11718858C211yesmaximal, characteristic, complemented
3C2×#11718857C211yesmaximal, characteristic, complemented
4#13123540C211yesmaximal, characteristic, complemented
5#13115165C211yesmaximal, characteristic, complemented
6#13115165C211yesmaximal, characteristic, complemented
7#13115139C211yesmaximal, characteristic, complemented
8#13115113C211yesmaximal, characteristic, complemented
9#13115113C211yesmaximal, characteristic, complemented
10#13115043C211yesmaximal, characteristic, complemented
11#13114780C211yesmaximal, characteristic, complemented
12#13114683C211yesmaximal, characteristic, complemented
13#13114676C211yesmaximal, characteristic, complemented
14#13114622C211yesmaximal, characteristic, complemented
15C13×#3002C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C2×C13×#135C2211yescharacteristic
18C2×C13×#135C2211yescharacteristic
19C13×#525C2211yescharacteristic
20#11719524—24no—
21#11719524—24no—
22C2×#88202—21no—
23C2×#88202—21no—
24C2×#88202C2211yescharacteristic
25C2×#88202C2211yescharacteristic
26C2×#88202C2211yescharacteristic
27C2×#88202C2211yescharacteristic
28C2×#88202C2211yescharacteristic, complemented
29C22×#6099—21no—
30C22×#6099—21no—
31C22×#6099C2211yescharacteristic
32C22×#6099C2211yescharacteristic
33C13×#452C411yescharacteristic, complemented
34C13×#452C411yescharacteristic, complemented
35C13×#451C411yescharacteristic, complemented
36C13×#450C411yescharacteristic, complemented
37C13×#449C411yescharacteristic, complemented
38C13×#449C411yescharacteristic, complemented
39C13×#448C411yescharacteristic, complemented
40C13×#447C411yescharacteristic, complemented
41C13×#416C2211yescharacteristic
42C13×#416C2211yescharacteristic
43C2×C13×C22⋊C8C2211yescharacteristic
44C2×#88077C2211yescharacteristic
45C2×#88077C2211yescharacteristic
46C2×#88077C2211yescharacteristic
47C2×#88077C2211yescharacteristic
48C2×#88077C2211yescharacteristic, complemented
49C2×#88077C2211yescharacteristic, complemented
50#11718895C2211yescharacteristic, complemented
51C4×C22⋊Dic13C2211yescharacteristic
52#11718868C2211yescharacteristic
53#11718858—24no—
54#11718857—24no—
55C2×#88059C2211yescharacteristic, complemented
56C2×#88059C2211yescharacteristic, complemented
57C2×#88055C2211yescharacteristic, complemented
58C2×C8×Dic13C2211yescharacteristic, complemented
59#11718673—21no—
60#11718673—21no—
61#11718672—21no—
62#11718672—21no—
63#11718660C2211yescharacteristic, complemented
64#11718658C2211yescharacteristic, complemented
65#11718144C2211yescharacteristic, complemented
66#11718144C2211yescharacteristic, complemented
67#11718142C2211yescharacteristic, complemented
68#11718142C2211yescharacteristic, complemented
69#11718124C2211yescharacteristic, complemented
70#11718124C2211yescharacteristic, complemented
71C2×C13×#41—22no—
72C2×C13×#41—22no—
73C2×C13×#41—22no—
74C2×C13×#41—22no—
75C2×C13×#41—21no—
76C2×C13×#41—21no—
77C2×C13×#41C2×C411yescharacteristic
78C2×C13×#41C2×C411yescharacteristic
79C2×C13×#41C2311yescharacteristic
80C2×C13×#41C2311yescharacteristic
81C2×C13×#41C2311yescharacteristic
82C22×Q8×C13C2×C411yescharacteristic
83C22×D4×C13—21no—
84C22×D4×C13C2×C411yescharacteristic
85C23×C4×C13—21no—
86C23×C4×C13C2311yescharacteristic
87C13×#135—22no—
88C13×#135—22no—
89C13×#135—22no—
90C13×#135—22no—
91C2×C13×Q16C2×C411yescharacteristic
92C2×C13×Q16C2×C411yescharacteristic
93C2×C13×SD16C2×C411yescharacteristic
94C2×C13×SD16C2×C411yescharacteristic
95C2×C13×SD16C2×C411yescharacteristic
96C2×C13×SD16C2×C411yescharacteristic
97C2×C13×D8C2×C411yescharacteristic
98C2×C13×D8C2×C411yescharacteristic
99C22×C8×C13C2311yescharacteristic
100C22×C8×C13C2311yescharacteristic
101C13×#123—21no—
102C13×C22⋊Q8C2×C411yescharacteristic
103C13×C22⋊Q8C2×C411yescharacteristic
104C13×#121C2×C411yescharacteristic
105C13×#121C2×C411yescharacteristic
106C13×#120—21no—
107C4×D4×C13—21no—
108C4×D4×C13—21no—
109C13×#117C2311yescharacteristic
110C2×C22⋊Dic13—21no—
111#88202—28no—
112#88202—28no—
113#88202—22no—
114#88202—22no—
115#88202—22no—
116#88202—22no—
117#88202—22no—
118#88202—22no—
119#88202—22no—
120#88202—22no—
121#88202D414yescomplemented
122#88202D414yescomplemented
123C2×C4×Dic13C2311yescharacteristic
124C2×C4×Dic13C2311yescharacteristic
125C2×#6099—28no—
126C2×#6099—28no—
127C2×#6099—21no—
128C2×#6099—22no—
129C2×#6099—22no—
130C2×#6099—21no—
131C2×#6099—21no—
132C2×#6099—21no—
133C2×#6099—21no—
134C2×#6099—22no—
135C2×#6099—22no—
136C2×#6099—21no—
137C2×#6099D411yescharacteristic
138C2×#6099D411yescharacteristic
139C2×#6099D411yescharacteristic
140C2×#6099D411yescharacteristic
141C2×#6099C2311yescharacteristic
142C2×#6099C2311yescharacteristic
143C2×#6099C2311yescharacteristic
144C2×#6099C2311yescharacteristic
145C22×#1055—21no—
146C22×#1055—21no—
147C22×#1055—21no—
148C22×#1055—21no—
149C22×#1055—21no—
150C22×#1055—21no—
151C22×#1055C2311yescharacteristic
152C22×#1055C2311yescharacteristic
153C13×#103C2×C411yescharacteristic
154C13×#103C2×C411yescharacteristic
155C13×#103C2×C411yescharacteristic
156C13×#103C2×C411yescharacteristic
157C13×#102C2×C411yescharacteristic
158C13×#102C2×C411yescharacteristic
159C13×#102C2×C411yescharacteristic
160C13×#102C2×C411yescharacteristic
161C13×C22⋊C8C2×C411yescharacteristic
162C13×C22⋊C8C2×C411yescharacteristic
163C13×C22⋊C8C2×C411yescharacteristic
164C13×C22⋊C8C2×C411yescharacteristic
165#88077—22no—
166#88077—22no—
167#88077—22no—
168#88077—22no—
169#88077—22no—
170#88077—22no—
171#88071—21no—
172C22⋊#1055—21no—
173C22⋊#1055—21no—
174C22⋊#1055—21no—
175C22⋊#1055—21no—
176#88059—22no—
177#88059—22no—
178#88055—22no—
179C8×Dic13—22no—
180C4⋊#1055—21no—
181C4⋊#1055—21no—
182#88043—21no—
183C4×#1055—21no—
184#21468—131nomaximal, Sylow
185C24×C13—21no—
186C24×C13#4111yescharacteristic
187C13×#41—24no—
188C13×#41—24no—
189C13×#41—24no—
190C13×#41—24no—
191C13×#41—22no—
192C13×#41—22no—
193C13×#41—22no—
194C13×#41—22no—
195C13×#41—21no—
196C13×#41—21no—
197C13×#41—21no—
198C13×#41—21no—
199C13×#41—21no—
200C13×#41—21no—
201C13×#41—21no—
202C13×#41—21no—
203C13×#41C2×D412yes—
204C13×#41C2×D412yes—
205C13×#41#4112yes—
206C13×#41#4112yes—
207C2×Q8×C13—22no—
208C2×Q8×C13—22no—
209C2×Q8×C13—21no—
210C2×Q8×C13C22×C411yescharacteristic
211C2×Q8×C13C22×C411yescharacteristic
212C2×Q8×C13C22×C411yescharacteristic
213C2×D4×C13—24no—
214C2×D4×C13—24no—
215C2×D4×C13—21no—
216C2×D4×C13—21no—
217C2×D4×C13—21no—
218C2×D4×C13—21no—
219C2×D4×C13—22no—
220C2×D4×C13—22no—
221C2×D4×C13—21no—
222C2×D4×C13—21no—
223C2×D4×C13—21no—
224C2×D4×C13—21no—
225C2×D4×C13C22×C411yescharacteristic
226C2×D4×C13C22×C411yescharacteristic
227C2×D4×C13C22×C411yescharacteristic
228C22×C4×C13—24no—
229C22×C4×C13—24no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13C22×C411yescharacteristic
241C22×C4×C13C22×C411yescharacteristic
242C22×C4×C13C2×D411yescharacteristic
243C22×C4×C13C2×D411yescharacteristic
244C22×C4×C13#4111yescharacteristic
245C22×C4×C13C2411yescharacteristic
246C22×Dic13—21no—
247C22×Dic13—21no—
248C13×Q16—22no—
249C13×Q16—22no—
250C13×SD16—22no—
251C13×SD16—22no—
252C13×SD16—22no—
253C13×SD16—22no—
254C13×D8—22no—
255C13×D8—22no—
256C2×C8×C13—21no—
257C2×C8×C13—21no—
258C2×C8×C13—21no—
259C2×C8×C13—21no—
260C2×C8×C13C22×C411yescharacteristic
261C2×C8×C13C22×C411yescharacteristic
262C2×C8×C13C22×C411yescharacteristic
263C2×C8×C13C22×C411yescharacteristic
264C13×C4⋊C4—21no—
265C13×C4⋊C4—21no—
266C13×C4⋊C4C22×C411yescharacteristic
267C13×C4⋊C4C22×C411yescharacteristic
268C13×C22⋊C4—21no—
269C13×C22⋊C4—21no—
270C13×C22⋊C4—21no—
271C13×C22⋊C4—21no—
272C13×C22⋊C4—21no—
273C42×C13—21no—
274C22⋊Dic13—42no—
275C4×Dic13—21no—
276C4×Dic13—21no—
277C4×Dic13—21no—
278C4×Dic13—21no—
279#6099—24no—
280#6099—24no—
281#6099—24no—
282#6099—21no—
283#6099—21no—
284#6099—22no—
285#6099—22no—
286#6099—24no—
287#6099—24no—
288#6099—22no—
289#6099—22no—
290#6099—21no—
291#6099—21no—
292#6099—21no—
293#6099—21no—
294#6099—42no—
295#6099C2×D412yes—
296#6099C2×D412yes—
297C2×#1055—24no—
298C2×#1055—24no—
299C2×#1055—24no—
300C2×#1055—21no—
301C2×#1055—21no—
302C2×#1055—21no—
303C2×#1055—21no—
304C2×#1055—24no—
305C2×#1055—24no—
306C2×#1055—21no—
307C2×#1055—21no—
308C2×#1055—42no—
309C2×#1055C2×D411yescharacteristic
310C2×#1055C2×D411yescharacteristic
311C2×#1055C2×D411yescharacteristic
312C2×#1055C2×D411yescharacteristic
313C2×#1055C2×D412yes—
314C2×#1055C2×D412yes—
315C2×#568—131no—
316#3002D1311yescharacteristic
317C2×#444—131no—
318C2×#443—131no—
319#2930—131no—
320#1876—131no—
321#1876—131no—
322#1871—131no—
323#1866—131no—
324#1866—131no—
325#1855—131no—
326#1789—131no—
327#1765—131no—
328#1764—131no—
329#1753—131no—
330C23×C13—24no—
331C23×C13—21no—
332C23×C13—21no—
333C23×C13—21no—
334C23×C13—21no—
335C23×C13—21no—
336C23×C13—41no—
337C23×C13—41no—
338C23×C13—81no—
339C23×C13—81no—
340C23×C13C4×D411yescharacteristic
341C23×C13C4×D411yescharacteristic
342C23×C13C2×#4111yescharacteristic
343Q8×C13—24no—
344Q8×C13—21no—
345Q8×C13—21no—
346Q8×C13—21no—
347Q8×C13—21no—
348Q8×C13C4×D412yes—
349Q8×C13C4×D412yes—
350D4×C13—24no—
351D4×C13—24no—
352D4×C13—24no—
353D4×C13—22no—
354D4×C13—22no—
355D4×C13—22no—
356D4×C13—22no—
357D4×C13—21no—
358D4×C13—21no—
359D4×C13—21no—
360D4×C13—21no—
361D4×C13—41no—
362D4×C13—41no—
363D4×C13—81no—
364D4×C13—81no—
365D4×C13C4×D412yes—
366D4×C13C4×D412yes—
367C2×C4×C13—24no—
368C2×C4×C13—24no—
369C2×C4×C13—24no—
370C2×C4×C13—21no—
371C2×C4×C13—21no—
372C2×C4×C13—21no—
373C2×C4×C13—21no—
374C2×C4×C13—21no—
375C2×C4×C13—21no—
376C2×C4×C13—21no—
377C2×C4×C13—21no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—21no—
381C2×C4×C13—21no—
382C2×C4×C13—21no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—21no—
386C2×C4×C13—21no—
387C2×C4×C13—21no—
388C2×C4×C13—21no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13C4×D411yescharacteristic
392C2×C4×C13C4×D411yescharacteristic
393C2×C4×C13C23×C411yescharacteristic
394C2×C4×C13C22×D411yescharacteristic
395C2×C4×C13C22×D411yescharacteristic
396C2×C4×C13C22×D411yescharacteristic
397C2×C4×C13C2×#4111yescharacteristic
398C2×C4×C13C2×#4111yescharacteristic
399C2×Dic13—22no—
400C2×Dic13—41no—
401C2×Dic13—41no—
402C2×Dic13—41no—
403C2×Dic13—41no—
404C2×Dic13—41no—
405C8×C13—21no—
406C8×C13—21no—
407C8×C13—21no—
408C8×C13—21no—
409#1055—22no—
410#1055—22no—
411#1055—21no—
412#1055—21no—
413#1055—41no—
414#1055—41no—
415#1055#12012yes—
416#1055#12012yes—
417C22×#41C2×D1311yescharacteristic
418C2×#135C2×D1311yescharacteristic
419C2×#135C2×D1311yescharacteristic
420#568—264no—
421#568—264no—
422C2×#131—131no—
423C2×#131—131no—
424C2×#131—131no—
425C2×#131—131no—
426C2×#131—131no—
427C2×#131—261no—
428C2×#131—261no—
429C22×M16—131no—
430C22×M16—131no—
431C22×M16—261no—
432C22×M16—261no—
433#525C2×D1311yescharacteristic
434#452Dic1311yescharacteristic, complemented
435#452Dic1311yescharacteristic, complemented
436#451Dic1311yescharacteristic, complemented
437#450Dic1311yescharacteristic, complemented
438#449Dic1311yescharacteristic, complemented
439#449Dic1311yescharacteristic, complemented
440#448Dic1311yescharacteristic, complemented
441#447Dic1311yescharacteristic, complemented
442#444—264no—
443#443—264no—
444#436—261no—
445#436—261no—
446#435—261no—
447#435—261no—
448C2×#108—131no—
449C2×#108—131no—
450#424—131no—
451C2×#104—131no—
452C2×#104—131no—
453C2×#104—131no—
454C2×#104—131no—
455C2×#104—131no—
456C2×#104—131no—
457#416C2×D1311yescharacteristic
458#416C2×D1311yescharacteristic
459#408—131no—
460#407—131no—
461C2×C22⋊C8C2×D1311yescharacteristic
462#405—131no—
463C2×#97—131no—
464C2×C4×C8—131no—
465C4×C22⋊C4—131no—
466#341—131no—
467#341—131no—
468#339—131no—
469#339—131no—
470#336—131no—
471#336—131no—
472C22×C13—21no—
473C22×C13—21no—
474C22×C13—21no—
475C22×C13—21no—
476C22×C13—21no—
477C22×C13—21no—
478C22×C13—21no—
479C22×C13—21no—
480C22×C13—22no—
481C22×C13—22no—
482C22×C13—41no—
483C22×C13—41no—
484C22×C13—41no—
485C22×C13—41no—
486C22×C13—41no—
487C22×C13—41no—
488C22×C13—41no—
489C22×C13—81no—
490C22×C13—81no—
491C22×C13—84no—
492C22×C13C2×C4×D411yescharacteristic
493C22×C13#52511yescharacteristic
494C22×C13#52511yescharacteristic
495C4×C13—21no—
496C4×C13—22no—
497C4×C13—22no—
498C4×C13—21no—
499C4×C13—41no—
500C4×C13—41no—
501C4×C13—41no—
502C4×C13C2×C4×D411yescharacteristic
503C4×C13C2×C4×D411yescharacteristic
504C4×C13C2×#12011yescharacteristic
505C4×C13#52511yescharacteristic
506Dic13—42no—
507Dic13—81no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—21no—
513C2×#41—21no—
514C2×#41C2×Dic1311yescharacteristic
515C2×#41C2×Dic1311yescharacteristic
516C2×#41C22×D1311yescharacteristic
517C2×#41C22×D1311yescharacteristic
518C2×#41C22×D1311yescharacteristic
519C22×Q8C2×Dic1311yescharacteristic
520C22×D4—21no—
521C22×D4C2×Dic1311yescharacteristic
522C23×C4—21no—
523C23×C4C22×D1311yescharacteristic
524#135—22no—
525#135—22no—
526#135—22no—
527#135—22no—
528C2×Q16C2×Dic1311yescharacteristic
529C2×Q16C2×Dic1311yescharacteristic
530C2×SD16C2×Dic1311yescharacteristic
531C2×SD16C2×Dic1311yescharacteristic
532C2×SD16C2×Dic1311yescharacteristic
533C2×SD16C2×Dic1311yescharacteristic
534C2×D8C2×Dic1311yescharacteristic
535C2×D8C2×Dic1311yescharacteristic
536#131—134no—
537#131—134no—
538#131—262no—
539#131—262no—
540#131—262no—
541#131—262no—
542#131—262no—
543#131—262no—
544#131—268no—
545#131—268no—
546#131—262no—
547#131—262no—
548C2×M16—131no—
549C2×M16—131no—
550C2×M16—131no—
551C2×M16—131no—
552C2×M16—131no—
553C2×M16—131no—
554C2×M16—131no—
555C2×M16—131no—
556C2×M16—262no—
557C2×M16—262no—
558C2×M16—261no—
559C2×M16—261no—
560C2×M16—261no—
561C2×M16—261no—
562C2×M16—261no—
563C2×M16—262no—
564C2×M16—262no—
565C2×M16—268no—
566C2×M16—268no—
567C2×M16—261no—
568C22×C8—131no—
569C22×C8—131no—
570C22×C8—261no—
571C22×C8—261no—
572C22×C8—261no—
573C22×C8—261no—
574C22×C8—261no—
575C22×C8—261no—
576C22×C8C22×D1311yescharacteristic
577C22×C8C22×D1311yescharacteristic
578#123—21no—
579C22⋊Q8C2×Dic1311yescharacteristic
580C22⋊Q8C2×Dic1311yescharacteristic
581#121C2×Dic1311yescharacteristic
582#121C2×Dic1311yescharacteristic
583#120—21no—
584C4×D4—21no—
585C4×D4—21no—
586#117C22×D1311yescharacteristic
587C2×C22⋊C4—261no—
588C2×C42—131no—
589C2×C42—131no—
590#108—262no—
591#108—262no—
592C4⋊C8—261no—
593C4⋊C8—261no—
594#104—262no—
595#104—262no—
596#104—262no—
597#104—262no—
598#104—262no—
599#104—262no—
600#103C2×Dic1311yescharacteristic
601#103C2×Dic1311yescharacteristic
602#103C2×Dic1311yescharacteristic
603#103C2×Dic1311yescharacteristic
604#102C2×Dic1311yescharacteristic
605#102C2×Dic1311yescharacteristic
606#102C2×Dic1311yescharacteristic
607#102C2×Dic1311yescharacteristic
608C22⋊C8—261no—
609C22⋊C8—261no—
610C22⋊C8—261no—
611C22⋊C8—261no—
612C22⋊C8C2×Dic1311yescharacteristic
613C22⋊C8C2×Dic1311yescharacteristic
614C22⋊C8C2×Dic1311yescharacteristic
615C22⋊C8C2×Dic1311yescharacteristic
616#97—261no—
617#97—262no—
618C4×C8—261no—
619C4×C8—262no—
620#95—261no—
621C2×C13—21no—
622C2×C13—21no—
623C2×C13—41no—
624C2×C13—41no—
625C2×C13—42no—
626C2×C13—42no—
627C2×C13—81no—
628C2×C13C4×#12011yescharacteristic
629C2×C13#295611yescharacteristic
630C2×C13#295711yescharacteristic
631C24—21no—
632C24#612911yescharacteristic
633#41—24no—
634#41—24no—
635#41—24no—
636#41—24no—
637#41—22no—
638#41—22no—
639#41—22no—
640#41—22no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—21no—
647#41—21no—
648#41—21no—
649#41D4×D1312yes—
650#41D4×D1312yes—
651#41#612912yes—
652#41#612912yes—
653C2×Q8—22no—
654C2×Q8—22no—
655C2×Q8—21no—
656C2×Q8C22×Dic1311yescharacteristic
657C2×Q8C22×Dic1311yescharacteristic
658C2×Q8C22×Dic1311yescharacteristic
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4C22×Dic1311yescharacteristic
672C2×D4C22×Dic1311yescharacteristic
673C2×D4C22×Dic1311yescharacteristic
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—261no—
687C22×C4—261no—
688C22×C4D4×D1311yescharacteristic
689C22×C4D4×D1311yescharacteristic
690C22×C4#612911yescharacteristic
691C22×C4C22×Dic1311yescharacteristic
692C22×C4C22×Dic1311yescharacteristic
693C22×C4C23×D1311yescharacteristic
694Q16—22no—
695Q16—22no—
696SD16—22no—
697SD16—22no—
698SD16—22no—
699SD16—22no—
700D8—22no—
701D8—22no—
702M16—132no—
703M16—132no—
704M16—262no—
705M16—262no—
706M16—262no—
707M16—262no—
708M16—264no—
709M16—264no—
710M16—264no—
711M16—264no—
712M16—264no—
713M16—261no—
714M16—261no—
715M16—261no—
716M16—261no—
717M16—261no—
718M16—261no—
719M16—522no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—132no—
725C2×C8—132no—
726C2×C8—131no—
727C2×C8—131no—
728C2×C8—131no—
729C2×C8—131no—
730C2×C8—264no—
731C2×C8—264no—
732C2×C8—264no—
733C2×C8—264no—
734C2×C8—264no—
735C2×C8—261no—
736C2×C8—261no—
737C2×C8—261no—
738C2×C8—261no—
739C2×C8—261no—
740C2×C8—261no—
741C2×C8—522no—
742C2×C8C22×Dic1311yescharacteristic
743C2×C8C22×Dic1311yescharacteristic
744C2×C8C22×Dic1311yescharacteristic
745C2×C8C22×Dic1311yescharacteristic
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4C22×Dic1311yescharacteristic
749C4⋊C4C22×Dic1311yescharacteristic
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—522no—
756C42—21no—
757C42—261no—
758C42—261no—
759C42—261no—
760C42—261no—
761C13#2146811yescharacteristic, complemented, Sylow
762C23—24no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—41no—
769C23—41no—
770C23—81no—
771C23—81no—
772C23D4×Dic1311yescharacteristic
773C23D4×Dic1311yescharacteristic
774C23C2×#612911yescharacteristic
775Q8—24no—
776Q8—21no—
777Q8—21no—
778Q8—21no—
779Q8—21no—
780Q8D4×Dic1312yes—
781Q8D4×Dic1312yes—
782D4—24no—
783D4—24no—
784D4—24no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—21no—
793D4—41no—
794D4—41no—
795D4—81no—
796D4—81no—
797D4D4×Dic1312yes—
798D4D4×Dic1312yes—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—262no—
824C2×C4—521no—
825C2×C4—521no—
826C2×C4—521no—
827C2×C4—521no—
828C2×C4—521no—
829C2×C4D4×Dic1311yescharacteristic
830C2×C4D4×Dic1311yescharacteristic
831C2×C4C2×D4×D1311yescharacteristic
832C2×C4C2×D4×D1311yescharacteristic
833C2×C4C2×D4×D1311yescharacteristic
834C2×C4C2×#612911yescharacteristic
835C2×C4C2×#612911yescharacteristic
836C2×C4C23×Dic1311yescharacteristic
837C8—21no—
838C8—21no—
839C8—21no—
840C8—21no—
841C8—132no—
842C8—132no—
843C8—261no—
844C8—261no—
845C8—262no—
846C8—262no—
847C8—521no—
848C8—521no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—22no—
854C22—22no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—81no—
867C22—81no—
868C22—84no—
869C22#1171929111yescharacteristic
870C22#1171929111yescharacteristic
871C22C2×D4×Dic1311yescharacteristic
872C4—21no—
873C4—22no—
874C4—22no—
875C4—21no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—522no—
880C4—1041no—
881C4#1171929111yescharacteristic
882C4D13×#12011yescharacteristic
883C4C2×D4×Dic1311yescharacteristic
884C4C2×D4×Dic1311yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—42no—
890C2—42no—
891C2—81no—
892C2#120×Dic1311yescharacteristic
893C2#1312374611yescharacteristic
894C2#1312375311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC13×#3002C2
socleC22×C13C2×C4×D4
cosocleC22×C4×C13C24
hypercenter#3002D13
hypocenterC13#21468
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. C2×#11719524C2semidirect
2. C2×#11718858C2semidirect
3. C2×#11718857C2semidirect
4. #13123540C2semidirect
5. #13115165C2semidirect
6. #13115165C2semidirect
7. #13115139C2semidirect
8. #13115113C2semidirect
9. #13115113C2semidirect
10. #13115043C2semidirect
11. #13114780C2semidirect
12. #13114683C2semidirect
13. #13114676C2semidirect
14. #13114622C2semidirect
28. C2×#88202C22semidirect
33. C13×#452C4semidirect
34. C13×#452C4semidirect
35. C13×#451C4semidirect
36. C13×#450C4semidirect
37. C13×#449C4semidirect
38. C13×#449C4semidirect
39. C13×#448C4semidirect
40. C13×#447C4semidirect
48. C2×#88077C22semidirect
49. C2×#88077C22semidirect
50. #11718895C22semidirect
55. C2×#88059C22semidirect
56. C2×#88059C22semidirect
57. C2×#88055C22semidirect
58. C2×C8×Dic13C22semidirect
63. #11718660C22semidirect
64. #11718658C22semidirect
65. #11718144C22semidirect
66. #11718144C22semidirect
67. #11718142C22semidirect
68. #11718142C22semidirect
69. #11718124C22semidirect
70. #11718124C22semidirect
121. #88202D4semidirect
122. #88202D4semidirect
434. #452Dic13semidirect
435. #452Dic13semidirect
436. #451Dic13semidirect
437. #450Dic13semidirect
438. #449Dic13semidirect
439. #449Dic13semidirect
440. #448Dic13semidirect
441. #447Dic13semidirect
761. C13#21468semidirect

Maximal subgroups

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

subgroupindex
C2×#117195242
C2×#117188582
C2×#117188572
#131235402
#131151652
#131151392
#131151132
#131150432
#131147802
#131146832
#131146762
#131146222
C13×#30022
#2146813