Finite Group Databasebeta

← #15770422

Subgroups — #15770422

Order 3328.

854 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718785C211yesmaximal, characteristic, complemented
2C2×#11718793C211yesmaximal, characteristic
3#13123280C211yesmaximal, characteristic
4C2×#11718790C211yesmaximal, characteristic
5C2×#11718150C211yesmaximal, characteristic, complemented
6C2×#11718150C211yesmaximal, characteristic, complemented
7C13×#1738C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C22×#6099C2211yescharacteristic
13C22×#6099C2211yescharacteristic
14C23×#1055C2211yescharacteristic
15C2×#88064C412yes—
16#11718793—22no—
17#11718793—22no—
18C2×#88063C412yes—
19#11718790—22no—
20#11718790—22no—
21#11718790—22no—
22#11718787—22no—
23#11718785—22no—
24#11718785—22no—
25C2×#88062—22no—
26#11718771—22no—
27C2×#88060—22no—
28C13×#341—22no—
29#11718150—22no—
30#11718150—22no—
31C23×C4×C13C2311yescharacteristic
32C22×C22⋊D13Q812yes—
33C2×#6127—21no—
34C2×#6127—21no—
35C2×#6127—21no—
36C2×#6127—21no—
37C2×#6127—21no—
38C2×#6127—21no—
39C2×#6127—21no—
40C2×#6127—21no—
41C2×#6127—21no—
42C2×#6127—21no—
43C2×#6127—21no—
44C2×#6127—21no—
45C22×D52C2×C411yescharacteristic
46C22×C4×D13D412yes—
47C22×Dic26C2×C411yescharacteristic
48C2×C13×M16—21no—
49C2×C13×M16—21no—
50C2×C13×M16—21no—
51C2×C13×M16—21no—
52C2×C13×M16—21no—
53C2×C13×M16—21no—
54C2×C13×M16—21no—
55C2×C13×M16—21no—
56C2×C13×M16—21no—
57C2×C13×M16—21no—
58C2×C13×M16—21no—
59C2×C13×M16—21no—
60C2×C13×M16—21no—
61C2×C13×M16—21no—
62C2×C13×M16—21no—
63C2×C13×M16C2×C412yes—
64C2×C13×M16D412yes—
65C2×C13×M16D412yes—
66C22×C8×C13—21no—
67C22×C8×C13—21no—
68C22×C8×C13—21no—
69C2×#6099—21no—
70C2×#6099—21no—
71C2×#6099—21no—
72C2×#6099—21no—
73C2×#6099—21no—
74C2×#6099—21no—
75C2×#6099—21no—
76C2×#6099—21no—
77C2×#6099C2×C412yes—
78C2×#6099D412yes—
79C2×#6099D412yes—
80C2×#6099D412yes—
81C22×#1055—21no—
82C22×#1055—21no—
83C22×#1055—21no—
84C22×#1055—21no—
85C22×#1055—21no—
86C22×#1055—21no—
87C22×#1055—21no—
88C22×#1055—21no—
89C22×#1055D412yes—
90#88064—24no—
91#88063—24no—
92#88062—28no—
93#88060—28no—
94#88060—28no—
95#11137—131nomaximal, Sylow
96C24×C13C2×Q811yescharacteristic
97C23×D13C4⋊C412yes—
98C22×C4×C13C22×C411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13#4111yescharacteristic
107C22×C4×C13#4111yescharacteristic
108C22×C4×C13#4111yescharacteristic
109C22×C4×C13#4111yescharacteristic
110C22×C4×C13#4111yescharacteristic
111C22×C4×C13#4111yescharacteristic
112C2×C22⋊D13—22no—
113C2×C22⋊D13—22no—
114C2×C22⋊D13—22no—
115C2×C22⋊D13—22no—
116C2×C22⋊D13—22no—
117C2×C22⋊D13—22no—
118C22×Dic13C4⋊C412yes—
119#6127—41no—
120#6127—41no—
121#6127—41no—
122#6127—41no—
123#6127—41no—
124#6127—41no—
125#6127—41no—
126#6127—41no—
127#6127—41no—
128#6127—41no—
129#6127—41no—
130#6127—41no—
131#6127—41no—
132#6127—41no—
133#6127—41no—
134#6127—41no—
135C2×D52—21no—
136C2×D52—21no—
137C2×D52—21no—
138C2×D52—21no—
139C2×D52—21no—
140C2×D52—21no—
141C2×C4×D13—22no—
142C2×C4×D13—22no—
143C2×C4×D13—22no—
144C2×C4×D13—22no—
145C2×C4×D13—22no—
146C2×C4×D13—22no—
147C2×Dic26—21no—
148C2×Dic26—21no—
149C2×Dic26—21no—
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C13×M16—22no—
154C13×M16—22no—
155C13×M16—22no—
156C13×M16—22no—
157C13×M16—22no—
158C13×M16—22no—
159C13×M16—41no—
160C13×M16—41no—
161C13×M16—41no—
162C13×M16—41no—
163C13×M16—41no—
164C13×M16—41no—
165C2×C8×C13—22no—
166C2×C8×C13—22no—
167C2×C8×C13—22no—
168C2×C8×C13—41no—
169C2×C8×C13—41no—
170C2×C8×C13—41no—
171C2×C8×C13—41no—
172C2×C8×C13—41no—
173C2×C8×C13—41no—
174#6099—22no—
175#6099—22no—
176#6099—22no—
177#6099—22no—
178#6099—22no—
179#6099—41no—
180#6099—41no—
181#6099C22⋊C414yes—
182C2×#1055—22no—
183C2×#1055—22no—
184C2×#1055—22no—
185C2×#1055—22no—
186C2×#1055—22no—
187C2×#1055—22no—
188C2×#1055—22no—
189C2×#1055—41no—
190C2×#1055—41no—
191C2×#1055—41no—
192C2×#1055—41no—
193C2×#1055—41no—
194C2×#1055—41no—
195C2×#430—131no—
196C2×#413—131no—
197#2879—131no—
198C2×#408—131no—
199#1738D1311yescharacteristic, complemented
200C2×#341—131no—
201C2×#341—131no—
202C23×C13—42no—
203C23×C13C2×C4⋊C411yescharacteristic
204C23×C13C22⋊Q811yescharacteristic
205C23×C13C22⋊Q811yescharacteristic
206C23×C13C22⋊Q811yescharacteristic
207C23×C13C22⋊Q811yescharacteristic
208C23×C13C22⋊Q811yescharacteristic
209C23×C13C22⋊Q811yescharacteristic
210C22×D13—22no—
211C22×D13—22no—
212C22×D13—22no—
213C22×D13—44no—
214C2×C4×C13C2×C22⋊C411yescharacteristic
215C2×C4×C13#11711yescharacteristic
216C2×C4×C13C4×D411yescharacteristic
217C2×C4×C13C4×D411yescharacteristic
218C2×C4×C13C4×D411yescharacteristic
219C2×C4×C13C4×D411yescharacteristic
220C2×C4×C13#12011yescharacteristic
221C2×C4×C13#12011yescharacteristic
222C2×C4×C13#12011yescharacteristic
223C2×C4×C13#12111yescharacteristic
224C2×C4×C13#12111yescharacteristic
225C2×C4×C13#12111yescharacteristic
226C2×C4×C13#12111yescharacteristic
227C2×C4×C13#12111yescharacteristic
228C2×C4×C13#12111yescharacteristic
229C2×C4×C13#12111yescharacteristic
230C2×C4×C13#12111yescharacteristic
231C2×C4×C13#12311yescharacteristic
232C2×C4×C13#12311yescharacteristic
233C2×C4×C13#12311yescharacteristic
234C2×C4×C13#12311yescharacteristic
235C2×C4×C13#12311yescharacteristic
236C2×C4×C13#12411yescharacteristic
237C2×C4×C13#12411yescharacteristic
238C2×C4×C13#12411yescharacteristic
239C2×C4×C13#12611yescharacteristic
240C2×C4×C13#12611yescharacteristic
241C2×C4×C13#12711yescharacteristic
242C22⋊D13—42no—
243C22⋊D13—42no—
244C22⋊D13—42no—
245C22⋊D13—42no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249D52—41no—
250D52—41no—
251D52—41no—
252D52—41no—
253C4×D13—42no—
254C4×D13—42no—
255C4×D13—42no—
256C4×D13—42no—
257Dic26—41no—
258Dic26—41no—
259Dic26—41no—
260Dic26—41no—
261C8×C13—42no—
262C8×C13—42no—
263C8×C13—42no—
264#1055—24no—
265#1055—42no—
266#1055—42no—
267C22×#41—131no—
268C22×M16—131no—
269C22×M16—131no—
270C22×M16C2×D1311yescharacteristic
271C22×M16C2×D1311yescharacteristic
272C22×M16C2×D1311yescharacteristic
273C23×C8—131no—
274#430—262no—
275#430—262no—
276C2×#108—262no—
277#413—262no—
278#413—262no—
279C2×#101—132no—
280C2×#100—132no—
281#408—262no—
282#408—262no—
283#408—262no—
284#408—262no—
285#407—262no—
286C2×C22⋊C8—262no—
287#341—22no—
288#341—262no—
289#341—262no—
290C22×C13—22no—
291C22×C13—22no—
292C22×C13—22no—
293C22×C13—41no—
294C22×C13—41no—
295C22×C13—41no—
296C22×C13—41no—
297C22×C13#38011yescharacteristic
298C22×C13#38511yescharacteristic
299C22×C13#38511yescharacteristic
300C22×C13#39311yescharacteristic
301C22×C13#39611yescharacteristic
302C22×C13#39611yescharacteristic
303C22×C13#39911yescharacteristic
304C2×D13—44no—
305C2×D13—44no—
306C2×D13—42no—
307C2×D13—82no—
308C4×C13#38611yescharacteristic
309C4×C13#38811yescharacteristic
310C4×C13#38811yescharacteristic
311C4×C13#39011yescharacteristic
312C4×C13#39211yescharacteristic
313C4×C13#39411yescharacteristic
314C4×C13#39411yescharacteristic
315C4×C13#39711yescharacteristic
316Dic13—42no—
317C2×#41—261no—
318C2×#41—261no—
319C2×#41—261no—
320C2×#41—261no—
321C2×#41—261no—
322C2×#41—261no—
323C2×#41—261no—
324C2×#41—261no—
325C2×#41—261no—
326C2×#41—261no—
327C2×#41—261no—
328C2×#41—261no—
329C22×Q8—131no—
330C22×D4—132no—
331C22×D4—131no—
332C23×C4—132no—
333C23×C4C22×D1311yescharacteristic
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—132no—
350C2×M16—132no—
351C2×M16—132no—
352C2×M16—132no—
353C2×M16—261no—
354C2×M16—261no—
355C2×M16—261no—
356C2×M16—261no—
357C2×M16—261no—
358C2×M16—261no—
359C2×M16—261no—
360C2×M16—261no—
361C2×M16C4×D1312yes—
362C2×M16D5212yes—
363C2×M16C22⋊D1312yes—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—132no—
368C22×C8—261no—
369C22×C8—261no—
370C22×C8—261no—
371C22×C8—261no—
372C22×C8—261no—
373C22×C8—261no—
374C22×C8—261no—
375C22×C8—261no—
376#108—268no—
377#101—264no—
378#100—264no—
379C22⋊C8—268no—
380C22⋊C8—268no—
381C2×C13—21no—
382C2×C13—21no—
383C2×C13—21no—
384C2×C13—21no—
385C2×C13—21no—
386C2×C13—21no—
387C2×C13#143911yescharacteristic
388C2×C13#185812yes—
389D13—82no—
390C24—132no—
391C24Q8×D1311yescharacteristic
392#41—521no—
393#41—521no—
394#41—521no—
395#41—521no—
396#41—521no—
397#41—521no—
398#41—521no—
399#41—521no—
400#41—521no—
401#41—521no—
402#41—521no—
403#41—521no—
404#41—521no—
405#41—521no—
406#41—521no—
407#41—521no—
408C2×Q8—261no—
409C2×Q8—261no—
410C2×Q8—261no—
411C2×Q8—261no—
412C2×Q8—261no—
413C2×Q8—261no—
414C2×D4—262no—
415C2×D4—262no—
416C2×D4—262no—
417C2×D4—262no—
418C2×D4—262no—
419C2×D4—262no—
420C2×D4—261no—
421C2×D4—261no—
422C2×D4—261no—
423C2×D4—261no—
424C2×D4—261no—
425C2×D4—261no—
426C22×C4—132no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—262no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4C2×C4×D1311yescharacteristic
434C22×C4C2×D5211yescharacteristic
435C22×C4#612711yescharacteristic
436C22×C4#612711yescharacteristic
437C22×C4#612711yescharacteristic
438C22×C4#612711yescharacteristic
439C22×C4D4×D1311yescharacteristic
440C22×C4D4×D1311yescharacteristic
441C22×C4D4×D1311yescharacteristic
442C22×C4D4×D1311yescharacteristic
443C22×C4D4×D1311yescharacteristic
444C22×C4#612911yescharacteristic
445C22×C4#613111yescharacteristic
446C22×C4C2×C22⋊D1311yescharacteristic
447M16—22no—
448M16—22no—
449M16—22no—
450M16—22no—
451M16—22no—
452M16—22no—
453M16—41no—
454M16—41no—
455M16—41no—
456M16—41no—
457M16—41no—
458M16—41no—
459M16—134no—
460M16—262no—
461M16—262no—
462M16—262no—
463M16—262no—
464M16—262no—
465M16—521no—
466M16—521no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—262no—
477C2×C8—262no—
478C2×C8—262no—
479C2×C8—262no—
480C2×C8—262no—
481C2×C8—262no—
482C2×C8—262no—
483C2×C8—521no—
484C2×C8—521no—
485C2×C8—521no—
486C2×C8—521no—
487C2×C8—521no—
488C2×C8—521no—
489C13#1113711yescharacteristic, complemented, Sylow
490C23—42no—
491C23—262no—
492C23—262no—
493C23—262no—
494C23—524no—
495C23C4⋊C4×D1311yescharacteristic
496C23#8815011yescharacteristic
497C23#8815011yescharacteristic
498C23#8815011yescharacteristic
499C23#8815011yescharacteristic
500C23#8815111yescharacteristic
501C23#8820011yescharacteristic
502Q8—521no—
503Q8—521no—
504Q8—521no—
505Q8—521no—
506D4—522no—
507D4—522no—
508D4—522no—
509D4—522no—
510D4—521no—
511D4—521no—
512D4—521no—
513D4—521no—
514C2×C4—262no—
515C2×C4—262no—
516C2×C4—262no—
517C2×C4—522no—
518C2×C4—522no—
519C2×C4—522no—
520C2×C4—522no—
521C2×C4#8812611yescharacteristic
522C2×C4C4×D5211yescharacteristic
523C2×C4#8812911yescharacteristic
524C2×C4#8813011yescharacteristic
525C2×C4C22⋊C4×D1311yescharacteristic
526C2×C4#8813511yescharacteristic
527C2×C4#8813611yescharacteristic
528C2×C4#8813611yescharacteristic
529C2×C4#8813711yescharacteristic
530C2×C4#8813811yescharacteristic
531C2×C4#8813811yescharacteristic
532C2×C4#8813811yescharacteristic
533C2×C4#8813811yescharacteristic
534C2×C4#8813811yescharacteristic
535C2×C4#8813911yescharacteristic
536C2×C4#8813911yescharacteristic
537C2×C4#8814711yescharacteristic
538C2×C4#8814811yescharacteristic
539C2×C4#8814811yescharacteristic
540C2×C4#8814811yescharacteristic
541C2×C4#8814911yescharacteristic
542C2×C4#8815211yescharacteristic
543C2×C4C4×C22⋊D1311yescharacteristic
544C2×C4#8818311yescharacteristic
545C2×C4#8818411yescharacteristic
546C2×C4#8819111yescharacteristic
547C2×C4#8819311yescharacteristic
548C2×C4#8819411yescharacteristic
549C8—42no—
550C8—42no—
551C8—42no—
552C8—264no—
553C8—522no—
554C8—522no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—524no—
563C22—524no—
564C22—522no—
565C22—1042no—
566C22#1171832811yescharacteristic
567C22#1171832911yescharacteristic
568C22#1171833411yescharacteristic
569C22#1171833711yescharacteristic
570C22#1171865011yescharacteristic
571C22#1171865311yescharacteristic
572C22#1171865511yescharacteristic
573C4—522no—
574C4#1171832611yescharacteristic
575C4#1171833011yescharacteristic
576C4#1171833311yescharacteristic
577C4#1171833611yescharacteristic
578C4#1171860111yescharacteristic
579C4#1171861811yescharacteristic
580C4#1171862011yescharacteristic
581C4#1171862111yescharacteristic
582C2—21no—
583C2—21no—
584C2—21no—
585C2—21no—
586C2—21no—
587C2—21no—
588C2—1042no—
589C2#1311308011yescharacteristic
590C2#1311505412yes—
subgroupG/H
centerC2×C4#88191
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1738C2
socleC22×C13#385
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenter#1738D13
hypocenterC13#11137
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1738

Complements

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

NH ≅ G/Ntype
1. C2×#11718785C2semidirect
5. C2×#11718150C2semidirect
6. C2×#11718150C2semidirect
7. C13×#1738C2semidirect
199. #1738D13semidirect
489. C13#11137semidirect

Maximal subgroups

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

subgroupindex
C2×#117187852
C2×#117187932
#131232802
C2×#117187902
C2×#117181502
C13×#17382
#1113713