Finite Group Databasebeta

← #15770558

Subgroups — #15770558

Order 3328.

804 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718666C211yesmaximal, characteristic
2C2×#11718800C211yesmaximal, characteristic
3C2×#11718793C211yesmaximal, characteristic
4#13114574C211yesmaximal, characteristic, complemented
5#13114545C211yesmaximal, characteristic, complemented
6C2×#11718152C211yesmaximal, characteristic, complemented
7C2×C13×#344C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C2×C13×#117C2211yescharacteristic
12C2×#88180C2211yescharacteristic
13C22×#6099C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15#11718800—22no—
16#11718800—22no—
17C2×#88065—22no—
18C2×#88064C412yescomplemented
19#11718793—22no—
20#11718793—22no—
21C2×#88063C412yescomplemented
22#11718666—22no—
23#11718666—22no—
24C2×#88045—22no—
25C13×#344—22no—
26#11718152—22no—
27#11718146—22no—
28#11718124—22no—
29C23×C4×C13C2311yescharacteristic
30C22×C22⋊D13—21no—
31C2×#6127—21no—
32C2×#6127—21no—
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×#6127D412yes—
42C2×#6127D412yes—
43C22×D52C2×C411yescharacteristic
44C22×C4×D13—21no—
45C22×Dic26C2×C411yescharacteristic
46C2×C13×M16—21no—
47C2×C13×M16—21no—
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×M16C2×C412yes—
57C2×C13×M16D412yes—
58C22×C8×C13—21no—
59C22×C8×C13—21no—
60C13×#117—21no—
61C13×#117—21no—
62C13×#117—21no—
63C13×#117D412yes—
64C2×C13×C4⋊C4—21no—
65C2×C13×C22⋊C4—21no—
66C2×C42×C13—21no—
67C2×C22⋊Dic13—21no—
68#88180—21no—
69#88180—21no—
70#88180—21no—
71#88180—21no—
72C2×C4⋊Dic13—21no—
73C2×C4×Dic13D412yes—
74C2×#6099—21no—
75C2×#6099—21no—
76C2×#6099—21no—
77C2×#6099—21no—
78C2×#6099—21no—
79C2×#6099—21no—
80C2×#6099—21no—
81C2×#6099—21no—
82C2×#6099—21no—
83C2×#6099—21no—
84C2×#6099C2×C412yes—
85C2×#6099D412yes—
86C22×#1055—21no—
87C22×#1055—21no—
88#88065—28no—
89#88064—24no—
90#88063—24no—
91#88045—28no—
92#11159—131nomaximal, Sylow
93C24×C13#4111yescharacteristic
94C23×D13—21no—
95C22×C4×C13—41no—
96C22×C4×C13C22×C411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13#4111yescharacteristic
104C22×C4×C13#4111yescharacteristic
105C22×C4×C13#4111yescharacteristic
106C22×C4×C13#4111yescharacteristic
107C22×C4×C13#4111yescharacteristic
108C22×C4×C13#4111yescharacteristic
109C22×C4×C13#4111yescharacteristic
110C2×C22⋊D13—22no—
111C2×C22⋊D13—22no—
112C2×C22⋊D13—41no—
113C2×C22⋊D13—41no—
114C2×C22⋊D13—41no—
115C2×C22⋊D13—41no—
116C22×Dic13—21no—
117C22×Dic13—22no—
118#6127—22no—
119#6127—22no—
120#6127—22no—
121#6127—22no—
122#6127—22no—
123#6127—22no—
124#6127—22no—
125#6127—22no—
126#6127—41no—
127#6127—41no—
128#6127—41no—
129#6127—41no—
130#6127—41no—
131#6127—41no—
132#6127—41no—
133#6127—41no—
134C2×D52—21no—
135C2×D52—21no—
136C2×D52—21no—
137C2×D52—21no—
138C2×D52—21no—
139C2×D52C22⋊C412yes—
140C2×C4×D13—22no—
141C2×C4×D13—22no—
142C2×C4×D13—41no—
143C2×C4×D13—41no—
144C2×C4×D13—41no—
145C2×C4×D13—41no—
146C2×Dic26—21no—
147C2×Dic26—21no—
148C2×Dic26—21no—
149C2×Dic26—21no—
150C2×Dic26—21no—
151C2×Dic26C22⋊C412yes—
152C13×M16—22no—
153C13×M16—22no—
154C13×M16—22no—
155C13×M16—22no—
156C13×M16—41no—
157C13×M16—41no—
158C13×M16—41no—
159C13×M16—41no—
160C2×C8×C13—22no—
161C2×C8×C13—22no—
162C2×C8×C13—41no—
163C2×C8×C13—41no—
164C2×C8×C13—41no—
165C2×C8×C13—41no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—41no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—41no—
170C42×C13—22no—
171C42×C13—41no—
172C22⋊Dic13—41no—
173C22⋊Dic13—41no—
174C4⋊Dic13—41no—
175C4⋊Dic13—41no—
176C4×Dic13—22no—
177C4×Dic13—22no—
178#6099—22no—
179#6099—22no—
180#6099—22no—
181#6099—22no—
182#6099—41no—
183#6099—41no—
184#6099—41no—
185#6099—41no—
186C2×#1055—22no—
187C2×#1055—22no—
188C2×#1055—41no—
189C2×#1055—41no—
190C2×#1055—41no—
191C2×#1055—41no—
192C2×#421—131no—
193C2×#421—131no—
194C2×#413—131no—
195C2×#344D1311yescharacteristic, complemented
196#1742—131no—
197#1733—131no—
198C2×#338—131no—
199C23×C13—81no—
200C23×C13#11711yescharacteristic
201C23×C13#12111yescharacteristic
202C23×C13#12311yescharacteristic
203C23×C13#12311yescharacteristic
204C23×C13#12311yescharacteristic
205C23×C13#12411yescharacteristic
206C23×C13#12611yescharacteristic
207C22×D13—22no—
208C22×D13—41no—
209C22×D13—41no—
210C22×D13—82no—
211C2×C4×C13—42no—
212C2×C4×C13—82no—
213C2×C4×C13C2×C22⋊C411yescharacteristic
214C2×C4×C13#11711yescharacteristic
215C2×C4×C13C4×D411yescharacteristic
216C2×C4×C13C4×D411yescharacteristic
217C2×C4×C13C4×D411yescharacteristic
218C2×C4×C13C4×D411yescharacteristic
219C2×C4×C13#12011yescharacteristic
220C2×C4×C13#12011yescharacteristic
221C2×C4×C13#12111yescharacteristic
222C2×C4×C13#12111yescharacteristic
223C2×C4×C13#12111yescharacteristic
224C2×C4×C13#12111yescharacteristic
225C2×C4×C13#12111yescharacteristic
226C2×C4×C13#12111yescharacteristic
227C2×C4×C13#12111yescharacteristic
228C2×C4×C13#12311yescharacteristic
229C2×C4×C13#12311yescharacteristic
230C2×C4×C13#12311yescharacteristic
231C2×C4×C13#12311yescharacteristic
232C2×C4×C13#12311yescharacteristic
233C2×C4×C13#12311yescharacteristic
234C2×C4×C13#12311yescharacteristic
235C2×C4×C13#12411yescharacteristic
236C2×C4×C13#12411yescharacteristic
237C2×C4×C13#12411yescharacteristic
238C2×C4×C13#12611yescharacteristic
239C2×C4×C13#12611yescharacteristic
240C2×C4×C13#12611yescharacteristic
241C22⋊D13—42no—
242C22⋊D13—42no—
243C22⋊D13—42no—
244C22⋊D13—42no—
245C2×Dic13—22no—
246C2×Dic13—41no—
247C2×Dic13—41no—
248C2×Dic13—42no—
249C2×Dic13—82no—
250D52—22no—
251D52—22no—
252D52—41no—
253D52—41no—
254C4×D13—42no—
255C4×D13—42no—
256C4×D13—42no—
257C4×D13—42no—
258Dic26—22no—
259Dic26—22no—
260Dic26—41no—
261Dic26—41no—
262C8×C13—42no—
263C8×C13—42no—
264#1055—42no—
265#1055—42no—
266C22×#41—131no—
267C22×M16—131no—
268C22×M16—131no—
269C22×M16C2×D1311yescharacteristic
270C22×M16C2×D1311yescharacteristic
271C2×#117—131no—
272C2×#117C2×D1311yescharacteristic
273#421—262no—
274#421—262no—
275#421—262no—
276#421—262no—
277C2×#104—262no—
278C2×#104—262no—
279#413—262no—
280#413—262no—
281C2×#101—132no—
282C2×#100—132no—
283#344—22no—
284#343—262no—
285#339—262no—
286#338—262no—
287C22×C13—41no—
288C22×C13—41no—
289C22×C13—41no—
290C22×C13—41no—
291C22×C13—41no—
292C22×C13—41no—
293C22×C13—41no—
294C22×C13#38111yescharacteristic
295C22×C13#38811yescharacteristic
296C22×C13#38811yescharacteristic
297C22×C13#39411yescharacteristic
298C22×C13#39411yescharacteristic
299C22×C13#39711yescharacteristic
300C22×C13#39711yescharacteristic
301C2×D13—42no—
302C2×D13—82no—
303C2×D13—82no—
304C2×D13—82no—
305C4×C13—82no—
306C4×C13#38611yescharacteristic
307C4×C13#38611yescharacteristic
308C4×C13#38811yescharacteristic
309C4×C13#38811yescharacteristic
310C4×C13#39411yescharacteristic
311C4×C13#39411yescharacteristic
312C4×C13#39711yescharacteristic
313C4×C13#39711yescharacteristic
314Dic13—42no—
315Dic13—82no—
316C2×#41—132no—
317C2×#41—132no—
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—
328C22×Q8—131no—
329C22×D4—131no—
330C22×D4—261no—
331C23×C4—261no—
332C23×C4C22×D1311yescharacteristic
333C2×M16—21no—
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—132no—
344C2×M16—132no—
345C2×M16—261no—
346C2×M16—261no—
347C2×M16—261no—
348C2×M16—261no—
349C2×M16—261no—
350C2×M16—261no—
351C2×M16—261no—
352C2×M16—261no—
353C2×M16—261no—
354C2×M16—261no—
355C2×M16C4×D1312yes—
356C2×M16D5212yes—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—261no—
360C22×C8—261no—
361#117—21no—
362#117—21no—
363#117—21no—
364#117—261no—
365#117—261no—
366#117—261no—
367#117—261no—
368#117C22⋊D1312yes—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—261no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—261no—
373C2×C42—21no—
374C2×C42—132no—
375#104—268no—
376#104—268no—
377#101—264no—
378#100—264no—
379C2×C13—21no—
380C2×C13—21no—
381C2×C13—21no—
382C2×C13—21no—
383C2×C13—21no—
384C2×C13—21no—
385C2×C13—21no—
386C2×C13#144011yescharacteristic
387D13—82no—
388C24—261no—
389C24#612711yescharacteristic
390#41—262no—
391#41—262no—
392#41—262no—
393#41—262no—
394#41—262no—
395#41—262no—
396#41—262no—
397#41—262no—
398#41—521no—
399#41—521no—
400#41—521no—
401#41—521no—
402#41—521no—
403#41—521no—
404#41—521no—
405#41—521no—
406C2×Q8—132no—
407C2×Q8—261no—
408C2×Q8—261no—
409C2×Q8—261no—
410C2×Q8—261no—
411C2×Q8—261no—
412C2×D4—132no—
413C2×D4—262no—
414C2×D4—262no—
415C2×D4—261no—
416C2×D4—261no—
417C2×D4—261no—
418C2×D4—261no—
419C2×D4—261no—
420C2×D4—521no—
421C2×D4—521no—
422C2×D4—521no—
423C2×D4—521no—
424C22×C4—41no—
425C22×C4—261no—
426C22×C4—262no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—521no—
430C22×C4—521no—
431C22×C4—521no—
432C22×C4—521no—
433C22×C4C2×C4×D1311yescharacteristic
434C22×C4C2×D5211yescharacteristic
435C22×C4#612711yescharacteristic
436C22×C4#612711yescharacteristic
437C22×C4#612711yescharacteristic
438C22×C4D4×D1311yescharacteristic
439C22×C4D4×D1311yescharacteristic
440C22×C4D4×D1311yescharacteristic
441C22×C4D4×D1311yescharacteristic
442C22×C4#612911yescharacteristic
443C22×C4#612911yescharacteristic
444C22×C4#613111yescharacteristic
445C22×C4#613111yescharacteristic
446C22×C4C2×C22⋊D1311yescharacteristic
447M16—22no—
448M16—22no—
449M16—22no—
450M16—22no—
451M16—41no—
452M16—41no—
453M16—41no—
454M16—41no—
455M16—262no—
456M16—262no—
457M16—262no—
458M16—262no—
459M16—521no—
460M16—521no—
461M16—521no—
462M16—521no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—41no—
469C2×C8—262no—
470C2×C8—262no—
471C2×C8—521no—
472C2×C8—521no—
473C2×C8—521no—
474C2×C8—521no—
475C4⋊C4—22no—
476C4⋊C4—41no—
477C4⋊C4—521no—
478C4⋊C4—521no—
479C22⋊C4—22no—
480C22⋊C4—41no—
481C22⋊C4—521no—
482C22⋊C4—521no—
483C42—22no—
484C42—41no—
485C42—262no—
486C42—262no—
487C13#1115911yescharacteristic, complemented, Sylow
488C23—81no—
489C23—262no—
490C23—521no—
491C23—521no—
492C23—1042no—
493C23#8812611yescharacteristic
494C23#8812911yescharacteristic
495C23#8813711yescharacteristic
496C23#8813811yescharacteristic
497C23#8814811yescharacteristic
498C23#8815211yescharacteristic
499C23#8818311yescharacteristic
500Q8—262no—
501Q8—262no—
502Q8—521no—
503Q8—521no—
504D4—262no—
505D4—262no—
506D4—522no—
507D4—522no—
508D4—522no—
509D4—522no—
510D4—521no—
511D4—521no—
512C2×C4—42no—
513C2×C4—82no—
514C2×C4—262no—
515C2×C4—521no—
516C2×C4—521no—
517C2×C4—522no—
518C2×C4—522no—
519C2×C4—522no—
520C2×C4—522no—
521C2×C4—522no—
522C2×C4—1042no—
523C2×C4C4×D5211yescharacteristic
524C2×C4#8813011yescharacteristic
525C2×C4C22⋊C4×D1311yescharacteristic
526C2×C4#8813511yescharacteristic
527C2×C4#8813611yescharacteristic
528C2×C4#8813711yescharacteristic
529C2×C4#8813711yescharacteristic
530C2×C4#8813811yescharacteristic
531C2×C4#8813811yescharacteristic
532C2×C4#8813911yescharacteristic
533C2×C4#8813911yescharacteristic
534C2×C4#8814011yescharacteristic
535C2×C4#8814611yescharacteristic
536C2×C4#8814711yescharacteristic
537C2×C4#8814811yescharacteristic
538C2×C4#8814811yescharacteristic
539C2×C4#8814811yescharacteristic
540C2×C4#8814811yescharacteristic
541C2×C4#8814911yescharacteristic
542C2×C4#8814911yescharacteristic
543C2×C4#8815211yescharacteristic
544C2×C4#8815211yescharacteristic
545C2×C4C4×C22⋊D1311yescharacteristic
546C2×C4#8818411yescharacteristic
547C2×C4#8819111yescharacteristic
548C2×C4#8819211yescharacteristic
549C2×C4#8819311yescharacteristic
550C2×C4#8820111yescharacteristic
551C8—42no—
552C8—42no—
553C8—522no—
554C8—522no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—522no—
563C22—1042no—
564C22—1042no—
565C22—1042no—
566C22#1171832511yescharacteristic
567C22#1171833011yescharacteristic
568C22#1171833311yescharacteristic
569C22#1171833511yescharacteristic
570C22#1171860111yescharacteristic
571C22#1171862011yescharacteristic
572C22#1171865411yescharacteristic
573C4—82no—
574C4—522no—
575C4—1042no—
576C4#1171832611yescharacteristic
577C4#1171833111yescharacteristic
578C4#1171833611yescharacteristic
579C4#1171833611yescharacteristic
580C4#1171861711yescharacteristic
581C4#1171862211yescharacteristic
582C4#1171865111yescharacteristic
583C4#1171865211yescharacteristic
584C2—21no—
585C2—21no—
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—1042no—
592C2#1311308411yescharacteristic
subgroupG/H
centerC4#11718336
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#344C2
socleC2×C13#1440
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenterC2×#344D13
hypocenterC13#11159
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. #13114574C2semidirect
5. #13114545C2semidirect
6. C2×#11718152C2semidirect
7. C2×C13×#344C2semidirect
18. C2×#88064C4semidirect
21. C2×#88063C4semidirect
195. C2×#344D13semidirect
487. C13#11159semidirect

Maximal subgroups

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

subgroupindex
C2×#117186662
C2×#117188002
C2×#117187932
#131145742
#131145452
C2×#117181522
C2×C13×#3442
#1115913