Finite Group Databasebeta

← #15867567

Subgroups — #15867567

Order 3328.

1338 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719188C211yesmaximal, characteristic
2#13117448C211yesmaximal, characteristic
3#13117189C211yesmaximal, characteristic
4#13115819C218yesmaximal, complemented
5C2×#11718118C211yesmaximal, characteristic
6C2×#11718119C211yesmaximal, characteristic
7C2×#11718119C211yesmaximal, characteristic
8C2×C13×#342C211yesmaximal, characteristic
9C22×C13×C22⋊C4C2211yescharacteristic
10C22×C13×C22⋊C4C2211yescharacteristic
11C22×C13×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic13C2211yescharacteristic
13C22×C22⋊Dic13C2211yescharacteristic
14C22×C22⋊Dic13C2211yescharacteristic
15C22×C22⋊Dic13C2211yescharacteristic
16C2×#88178C414yescomplemented
17#11719188—22no—
18#11719188—22no—
19#11719188—22no—
20#11719188—22no—
21C2×#88132C414yescomplemented
22C2×#88132C2214yes—
23#11718871—22no—
24C4×C22⋊Dic13—22no—
25#11718607—22no—
26#11718603C2214yes—
27C22⋊C4×Dic13—22no—
28C22⋊C4×Dic13C2214yes—
29C13×#342C2214yes—
30#11718119C2214yes—
31#11718119C2214yes—
32#11718118C2214yes—
33C25×C13C2311yescharacteristic
34C23×C4×C13—21no—
35C23×C4×C13—21no—
36C23×C4×C13C2×C412yes—
37C23×Dic13—21no—
38C23×Dic13—21no—
39C23×Dic13C2×C412yes—
40C23×Dic13C2312yes—
41C22×Dic26C2×C414yescomplemented
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—22no—
48C2×C13×C22⋊C4—22no—
49C2×C13×C22⋊C4—22no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4C2×C412yes—
52C2×C13×C22⋊C4Q814yescomplemented
53C2×C13×C22⋊C4C2312yes—
54C2×C13×C22⋊C4C2312yes—
55C2×C13×C22⋊C4C2312yes—
56C2×C22⋊Dic13—21no—
57C2×C22⋊Dic13—21no—
58C2×C22⋊Dic13—21no—
59C2×C22⋊Dic13—21no—
60C2×C22⋊Dic13—21no—
61C2×C22⋊Dic13—22no—
62C2×C22⋊Dic13—22no—
63C2×C22⋊Dic13—22no—
64C2×C22⋊Dic13—21no—
65C2×C22⋊Dic13C2×C412yes—
66C2×C22⋊Dic13C2×C412yes—
67C2×C22⋊Dic13C2×C412yes—
68C2×C22⋊Dic13D412yes—
69C2×C22⋊Dic13D412yes—
70C2×C22⋊Dic13D412yes—
71C2×C22⋊Dic13D412yes—
72C2×C22⋊Dic13Q814yescomplemented
73C2×C22⋊Dic13C2312yes—
74C2×C22⋊Dic13C2312yes—
75C2×C22⋊Dic13C2312yes—
76C2×C4⋊Dic13C2×C414yescomplemented
77#88178—28no—
78#88178—28no—
79C2×#6101—24no—
80C2×#6101C2×C418yescomplemented
81C2×C4×Dic13—24no—
82#88132—28no—
83#88132—28no—
84#88132—28no—
85#88132—28no—
86#88071—24no—
87#88071—24no—
88#21333—131nomaximal, Sylow
89C24×C13—82no—
90C24×C13C22×C411yescharacteristic
91C24×C13C22×C411yescharacteristic
92C24×C13C2×D411yescharacteristic
93C24×C13C2×D411yescharacteristic
94C24×C13C2×D411yescharacteristic
95C24×C13C2×D411yescharacteristic
96C24×C13C2×Q812yes—
97C24×C13C2×Q812yes—
98C24×C13#4112yes—
99C24×C13#4112yes—
100C24×C13C2411yescharacteristic
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—24no—
105C22×C4×C13—22no—
106C22×C4×C13—42no—
107C22×C4×C13—82no—
108C22×C4×C13—82no—
109C22×C4×C13—82no—
110C22×C4×C13C22×C414yes—
111C22×Dic13—22no—
112C22×Dic13—22no—
113C22×Dic13—22no—
114C22×Dic13—24no—
115C22×Dic13—22no—
116C22×Dic13—42no—
117C22×Dic13—82no—
118C22×Dic13—82no—
119C22×Dic13—82no—
120C22×Dic13—82no—
121C22×Dic13C22×C414yes—
122C22×Dic13C22×C414yes—
123C22×Dic13C2×D414yes—
124C22×Dic13C2×D414yes—
125C2×Dic26—28no—
126C2×Dic26—84no—
127C13×C22⋊C4—22no—
128C13×C22⋊C4—22no—
129C13×C22⋊C4—24no—
130C13×C22⋊C4—22no—
131C13×C22⋊C4—22no—
132C13×C22⋊C4—22no—
133C13×C22⋊C4—22no—
134C13×C22⋊C4—22no—
135C13×C22⋊C4—42no—
136C13×C22⋊C4C2×Q814yes—
137C22⋊Dic13—22no—
138C22⋊Dic13—22no—
139C22⋊Dic13—24no—
140C22⋊Dic13—22no—
141C22⋊Dic13—22no—
142C22⋊Dic13—22no—
143C22⋊Dic13—22no—
144C22⋊Dic13—22no—
145C22⋊Dic13—42no—
146C22⋊Dic13C22⋊C414yes—
147C22⋊Dic13C22⋊C414yes—
148C22⋊Dic13C22⋊C414yes—
149C22⋊Dic13C22⋊C414yes—
150C22⋊Dic13C2×Q814yes—
151C4⋊Dic13—28no—
152#6101—216no—
153#6101—84no—
154C4×Dic13—84no—
155C2×#543—131no—
156#2315—131no—
157#2273—131no—
158#1996—138no—
159C2×#342—131no—
160C2×#342—131no—
161C2×#342—131no—
162C2×#342D1311yescharacteristic
163C23×C13—42no—
164C23×C13—42no—
165C23×C13—42no—
166C23×C13—42no—
167C23×C13—42no—
168C23×C13—42no—
169C23×C13—42no—
170C23×C13—82no—
171C23×C13—82no—
172C23×C13—82no—
173C23×C13—82no—
174C23×C13C2×C22⋊C411yescharacteristic
175C23×C13C2×C22⋊C411yescharacteristic
176C23×C13C2×C22⋊C411yescharacteristic
177C23×C13C2×C22⋊C411yescharacteristic
178C23×C13C4×Q812yes—
179C23×C13C4×Q812yes—
180C23×C13C4×Q812yes—
181C23×C13C4×Q812yes—
182C23×C13C22⋊Q812yes—
183C23×C13C22⋊Q812yes—
184C23×C13C22⋊Q812yes—
185C23×C13C22⋊Q812yes—
186C23×C13#12412yes—
187C23×C13#12412yes—
188C23×C13C4⋊Q812yes—
189C23×C13C4⋊Q812yes—
190C23×C13C23×C411yescharacteristic
191C23×C13C22×D411yescharacteristic
192C23×C13C22×D411yescharacteristic
193C23×C13C22×Q811yescharacteristic
194C23×C13C22×Q811yescharacteristic
195C23×C13C2×#4111yescharacteristic
196C23×C13C2×#4111yescharacteristic
197C2×C4×C13—24no—
198C2×C4×C13—24no—
199C2×C4×C13—44no—
200C2×C4×C13—44no—
201C2×C4×C13—44no—
202C2×C4×C13—42no—
203C2×C4×C13—82no—
204C2×C4×C13—82no—
205C2×C4×C13—84no—
206C2×C4×C13—84no—
207C2×Dic13—24no—
208C2×Dic13—24no—
209C2×Dic13—44no—
210C2×Dic13—44no—
211C2×Dic13—44no—
212C2×Dic13—44no—
213C2×Dic13—44no—
214C2×Dic13—44no—
215C2×Dic13—42no—
216C2×Dic13—82no—
217C2×Dic13—82no—
218C2×Dic13—84no—
219C2×Dic13—84no—
220C2×Dic13C2×C22⋊C418yes—
221Dic26—88no—
222#543—262no—
223#543—262no—
224#543—262no—
225#543—262no—
226C2×C22⋊Q8—134no—
227C2×C22⋊Q8—134no—
228C2×C22⋊Q8—134no—
229C22×C22⋊C4—131no—
230C22×C22⋊C4—131no—
231C22×C22⋊C4—131no—
232C22×C22⋊C4—131no—
233C22×C22⋊C4C2×D1311yescharacteristic
234C22×C22⋊C4C2×D1311yescharacteristic
235C22×C22⋊C4C2×D1311yescharacteristic
236#385—262no—
237#385—262no—
238#380—134no—
239C4×C22⋊C4—134no—
240C4×C22⋊C4—262no—
241C4×C22⋊C4—262no—
242#342—134no—
243#342—134no—
244#342—134no—
245#342C2×D1314yes—
246C22×C13—22no—
247C22×C13—22no—
248C22×C13—22no—
249C22×C13—22no—
250C22×C13—22no—
251C22×C13—22no—
252C22×C13—22no—
253C22×C13—42no—
254C22×C13—42no—
255C22×C13—42no—
256C22×C13—42no—
257C22×C13—42no—
258C22×C13—42no—
259C22×C13—42no—
260C22×C13—42no—
261C22×C13—42no—
262C22×C13—42no—
263C22×C13—42no—
264C22×C13—42no—
265C22×C13—41no—
266C22×C13—41no—
267C22×C13—41no—
268C22×C13—41no—
269C22×C13#39112yes—
270C22×C13#39112yes—
271C22×C13#39112yes—
272C22×C13#39112yes—
273C22×C13C22×C22⋊C411yescharacteristic
274C22×C13C2×C4×Q811yescharacteristic
275C22×C13C2×C4×Q811yescharacteristic
276C22×C13C2×C22⋊Q811yescharacteristic
277C22×C13C2×C22⋊Q811yescharacteristic
278C22×C13C2×#12411yescharacteristic
279C22×C13C2×C4⋊Q811yescharacteristic
280C4×C13—44no—
281C4×C13—44no—
282C4×C13—82no—
283Dic13—28no—
284Dic13—44no—
285Dic13—44no—
286Dic13—82no—
287C25C22×D1311yescharacteristic
288C22×Q8—134no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—132no—
292C23×C4—132no—
293C23×C4—261no—
294C23×C4—261no—
295C23×C4C4×D1312yes—
296C22⋊Q8—268no—
297C22⋊Q8—268no—
298C22⋊Q8—268no—
299C22⋊Q8—268no—
300C22⋊Q8—268no—
301C22⋊Q8—268no—
302C2×C4⋊C4—138no—
303C2×C4⋊C4—134no—
304C2×C4⋊C4—264no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—132no—
315C2×C22⋊C4—132no—
316C2×C22⋊C4—132no—
317C2×C22⋊C4—132no—
318C2×C22⋊C4—132no—
319C2×C22⋊C4—132no—
320C2×C22⋊C4—134no—
321C2×C22⋊C4—132no—
322C2×C22⋊C4—132no—
323C2×C22⋊C4—132no—
324C2×C22⋊C4—132no—
325C2×C22⋊C4—262no—
326C2×C22⋊C4—261no—
327C2×C22⋊C4—261no—
328C2×C22⋊C4—261no—
329C2×C22⋊C4—261no—
330C2×C22⋊C4—261no—
331C2×C22⋊C4—262no—
332C2×C22⋊C4—262no—
333C2×C22⋊C4—261no—
334C2×C22⋊C4Dic2614yescomplemented
335C2×C22⋊C4C4×D1312yes—
336C2×C22⋊C4C22×D1312yes—
337C2×C22⋊C4C22×D1312yes—
338C2×C22⋊C4C22×D1312yes—
339C2×C42—264no—
340#95—264no—
341#95—264no—
342C2×C13—21no—
343C2×C13—21no—
344C2×C13—21no—
345C2×C13—21no—
346C2×C13—21no—
347C2×C13—21no—
348C2×C13—22no—
349C2×C13—22no—
350C2×C13—22no—
351C2×C13—22no—
352C2×C13C2×#39111yescharacteristic
353C2×C13#288312yes—
354C24—82no—
355C24C2×Dic2612yes—
356C24C2×C4×D1311yescharacteristic
357C24C2×C4×D1311yescharacteristic
358C24#612712yes—
359C24D4×D1311yescharacteristic
360C24D4×D1311yescharacteristic
361C24D4×D1311yescharacteristic
362C24D4×D1311yescharacteristic
363C24#612912yes—
364C24Q8×D1312yes—
365C24C23×D1311yescharacteristic
366C2×Q8—268no—
367C2×Q8—1044no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—42no—
374C22×C4—82no—
375C22×C4—82no—
376C22×C4—82no—
377C22×C4—134no—
378C22×C4—134no—
379C22×C4—134no—
380C22×C4—134no—
381C22×C4—262no—
382C22×C4—262no—
383C22×C4—262no—
384C22×C4—264no—
385C22×C4—262no—
386C22×C4—522no—
387C22×C4—1042no—
388C22×C4—1042no—
389C22×C4—1042no—
390C22×C4—1042no—
391C22×C4C2×C4×D1314yes—
392C4⋊C4—2616no—
393C4⋊C4—268no—
394C4⋊C4—1044no—
395C22⋊C4—24no—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—22no—
403C22⋊C4—42no—
404C22⋊C4—134no—
405C22⋊C4—134no—
406C22⋊C4—134no—
407C22⋊C4—134no—
408C22⋊C4—134no—
409C22⋊C4—262no—
410C22⋊C4—262no—
411C22⋊C4—264no—
412C22⋊C4—262no—
413C22⋊C4—262no—
414C22⋊C4—262no—
415C22⋊C4—262no—
416C22⋊C4—262no—
417C22⋊C4—522no—
418C22⋊C4C2×Dic2614yes—
419C42—1044no—
420C13#2133311yescharacteristic, complemented, Sylow
421C23—42no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23—82no—
429C23—82no—
430C23—82no—
431C23—82no—
432C23C4×Dic2612yes—
433C23C4×Dic2612yes—
434C23#8813212yes—
435C23#8813212yes—
436C23C22⋊C4×D1311yescharacteristic
437C23C22⋊C4×D1311yescharacteristic
438C23C22⋊C4×D1311yescharacteristic
439C23C22⋊C4×D1311yescharacteristic
440C23#8813912yes—
441C23#8813912yes—
442C23#8814112yes—
443C23#8814112yes—
444C23#8814212yes—
445C23#8814212yes—
446C23#8815012yes—
447C23#8815012yes—
448C23C22×Dic2611yescharacteristic
449C23C22×C4×D1311yescharacteristic
450C23C2×#612711yescharacteristic
451C23C2×D4×D1311yescharacteristic
452C23C2×D4×D1311yescharacteristic
453C23C2×#612911yescharacteristic
454C23C2×Q8×D1311yescharacteristic
455Q8—1048no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—44no—
459C2×C4—44no—
460C2×C4—44no—
461C2×C4—42no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—84no—
465C2×C4—84no—
466C2×C4—138no—
467C2×C4—264no—
468C2×C4—264no—
469C2×C4—524no—
470C2×C4—524no—
471C2×C4—524no—
472C2×C4—524no—
473C2×C4—524no—
474C2×C4—524no—
475C2×C4—522no—
476C2×C4—1042no—
477C2×C4—1042no—
478C2×C4—1044no—
479C2×C4—1044no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22#1171830712yes—
504C22#1171830712yes—
505C22#1171830712yes—
506C22#1171830712yes—
507C22C2×C4×Dic2611yescharacteristic
508C22C2×#8813211yescharacteristic
509C22C2×C22⋊C4×D1311yescharacteristic
510C22C2×#8813911yescharacteristic
511C22C2×#8814111yescharacteristic
512C22C2×#8814211yescharacteristic
513C22C2×#8815011yescharacteristic
514C4—44no—
515C4—44no—
516C4—82no—
517C4—268no—
518C4—524no—
519C4—524no—
520C4—1042no—
521C2—21no—
522C2—21no—
523C2—21no—
524C2—21no—
525C2—21no—
526C2—21no—
527C2—22no—
528C2—22no—
529C2—22no—
530C2—22no—
531C2C2×#1171830711yescharacteristic
532C2#1312329412yes—
subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC2×C13×#342C2
socleC22×C13C22×C22⋊C4
prime radicalC25×C13C23
cosocleC24×C13C24
hypercenterC2×#342D13
hypocenterC13#21333
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. #13115819C2semidirect
16. C2×#88178C4semidirect
21. C2×#88132C4semidirect
41. C22×Dic26C2×C4semidirect
52. C2×C13×C22⋊C4Q8semidirect
72. C2×C22⋊Dic13Q8semidirect
76. C2×C4⋊Dic13C2×C4semidirect
80. C2×#6101C2×C4semidirect
334. C2×C22⋊C4Dic26semidirect
420. C13#21333semidirect

Maximal subgroups

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

subgroupindex
C2×#117191882
#131174482
#131171892
#131158192
C2×#117181182
C2×#117181192
C2×C13×#3422
#2133313