Finite Group Databasebeta

← #15832903

Subgroups — #15832903

Order 3328.

632 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124914C211yesmaximal, characteristic
2#13123814C211yesmaximal, characteristic
3C8×Q8×D13C211yesmaximal, characteristic, complemented
4#13113712C211yesmaximal, characteristic, complemented
5#13113709C211yesmaximal, characteristic, complemented
6#13113707C211yesmaximal, characteristic, complemented
7#13113642C211yesmaximal, characteristic, complemented
8#13113640C211yesmaximal, characteristic, complemented
9#13113639C211yesmaximal, characteristic, complemented
10SD16×#1055C211yesmaximal, characteristic, complemented
11#13113620C211yesmaximal, characteristic, complemented
12#13113281C211yesmaximal, characteristic, complemented
13#13113246C211yesmaximal, characteristic
14#13113115C211yesmaximal, characteristic, complemented
15C13×#1588C211yesmaximal, characteristic, complemented
16C4×Q8×D13C2211yescharacteristic
17#11719262C2211yescharacteristic
18C8×Q8×C13C2211yescharacteristic
19C4×C13×SD16C2211yescharacteristic
20C13×#436C2211yescharacteristic
21#11718831C411yescharacteristic
22#11718827C411yescharacteristic
23#11718788—21no—
24#11718783—21no—
25C4×#6107C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27C4×#6105C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29#11718523C411yescharacteristic
30#11718518C411yescharacteristic
31#11718496C2211yescharacteristic
32D13×C4⋊C8—21no—
33D13×C4⋊C8C2211yescharacteristic
34#11718491—21no—
35#11718491C2211yescharacteristic
36#11718491C2211yescharacteristic
37#11718469C411yescharacteristic
38#11718457C411yescharacteristic
39#11718435C411yescharacteristic
40#11718428C411yescharacteristic
41#11718386—21no—
42#11718381—21no—
43C4×Dic52C2211yescharacteristic
44C4×#6094C2211yescharacteristic
45#11718346C2211yescharacteristic
46C4×C8×D13—21no—
47C4×C8×D13C2211yescharacteristic
48#11718340C2211yescharacteristic
49C8×Dic26—21no—
50C8×Dic26C2211yescharacteristic
51C13×#335C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×Q8×D13C2×C411yescharacteristic
68C2×C13×SD16C2×C411yescharacteristic
69C2×C13×M16—21no—
70C4×Q8×C13C2311yescharacteristic
71C4×D4×C13C2311yescharacteristic
72Q8×Dic13C2×C411yescharacteristic
73C2×#6107C2×C411yescharacteristic
74#88192C2×C411yescharacteristic
75#88190C2×C411yescharacteristic
76C2×#6105C2×C411yescharacteristic
77C4×C22⋊D13—21no—
78#88180—21no—
79C22×#1055—21no—
80C2×Dic52C2×C411yescharacteristic
81C2×#6094—21no—
82C2×C8×D13—21no—
83C2×C8×D13D411yescharacteristic
84C2×C8×D13D411yescharacteristic
85#88151C2×C411yescharacteristic
86C4⋊C4×D13—21no—
87C4⋊C4×D13C2×C411yescharacteristic
88#88144C2×C411yescharacteristic
89#88141—21no—
90#88141C2×C411yescharacteristic
91#88137—21no—
92#88133—21no—
93C42×D13—21no—
94C42×D13C2311yescharacteristic
95C4×Dic26—21no—
96C4×Dic26C2311yescharacteristic
97C4×Dic26C2311yescharacteristic
98C13×#106C2×C411yescharacteristic
99C13×C4⋊C8—21no—
100C13×C4⋊C8C2311yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×#103C2×C411yescharacteristic
103C13×#102C2×C411yescharacteristic
104C13×C22⋊C8—21no—
105C4×C8×C13—21no—
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109#88075C2×C411yescharacteristic
110#88072C2×C411yescharacteristic
111C22⋊#1055—21no—
112#88060—21no—
113#88060C2×C411yescharacteristic
114#88060C2×C411yescharacteristic
115#88058C2×C411yescharacteristic
116#88056C2×C411yescharacteristic
117#88056C2×C411yescharacteristic
118#88055—21no—
119#88055—21no—
120#88055—21no—
121#88054—21no—
122#88054—21no—
123#88054—21no—
124#88054—21no—
125#88054—21no—
126#88054C2×C411yescharacteristic
127#88054C2×C411yescharacteristic
128C8×Dic13—21no—
129C8×Dic13—21no—
130C8×Dic13—21no—
131C8×Dic13D411yescharacteristic
132C8×Dic13D411yescharacteristic
133#88050C2×C411yescharacteristic
134#88050C2×C411yescharacteristic
135#88048C2×C411yescharacteristic
136#88047C2×C411yescharacteristic
137C4⋊#1055—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4×#1055—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17911—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13C22×C411yescharacteristic
147C22×C4×C13—21no—
148C2×C22⋊D13—21no—
149Q8×D13—22no—
150Q8×D13—22no—
151C2×C4×D13—21no—
152C2×C4×D13—21no—
153C2×C4×D13C22×C411yescharacteristic
154C2×C4×D13C2×D411yescharacteristic
155C2×C4×D13#4111yescharacteristic
156C2×Dic26—21no—
157C2×Dic26C22×C411yescharacteristic
158C2×Dic26C22×C411yescharacteristic
159C13×SD16—22no—
160C13×M16—42no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C13×C4⋊C4—21no—
169C13×C4⋊C4C22×C411yescharacteristic
170C13×C4⋊C4C22×C411yescharacteristic
171C13×C22⋊C4—21no—
172C42×C13—21no—
173C42×C13C2411yescharacteristic
174C22⋊Dic13—21no—
175C22⋊Dic13—21no—
176C22⋊Dic13—21no—
177#6107—22no—
178#6105—22no—
179#6103—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13C22×C411yescharacteristic
184C4⋊Dic13C22×C411yescharacteristic
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13C22×C411yescharacteristic
195C4×Dic13C2×D411yescharacteristic
196C4×Dic13#4111yescharacteristic
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—42no—
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C2×D411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205Dic52—22no—
206#6094—24no—
207C8×D13—22no—
208C8×D13—41no—
209C8×D13—42no—
210#3108—131no—
211#2966—131no—
212C2×C8×Q8—131no—
213#1588—131no—
214#1588D1311yescharacteristic, complemented
215#1587—131no—
216#1587—131no—
217C8×Q16—131no—
218C8×Q16—131no—
219C8×SD16—131no—
220C8×SD16—131no—
221#1573—131no—
222#1491—131no—
223#1483—131no—
224C8×M16—131no—
225C23×C13—21no—
226C22×D13C4×D411yescharacteristic
227Q8×C13—21no—
228Q8×C13#13112yes—
229D4×C13—21no—
230D4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13C23×C411yescharacteristic
237C2×C4×C13C22×D411yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C22⋊D13—42no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13C4×D411yescharacteristic
245C2×Dic13C4×D411yescharacteristic
246C2×Dic13C4×D411yescharacteristic
247C4×D13—24no—
248C4×D13—22no—
249C4×D13—21no—
250C4×D13—21no—
251C4×D13—21no—
252C4×D13—21no—
253C4×D13—42no—
254Dic26—24no—
255Dic26—21no—
256Dic26—21no—
257Dic26—21no—
258Dic26#13112yes—
259C8×C13—22no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—21no—
263C8×C13—21no—
264C8×C13—41no—
265C8×C13—41no—
266#1055—22no—
267#1055—21no—
268#1055—21no—
269#1055—21no—
270#1055—41no—
271#1055—41no—
272#1055#13712yes—
273#529—131no—
274C2×C4×Q8—131no—
275#483—131no—
276#480—131no—
277#479—131no—
278#479—131no—
279#464—131no—
280#464—131no—
281#451—131no—
282#448—131no—
283#446—131no—
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8—261no—
289C8×Q8—261no—
290C8×Q8C2×D1311yescharacteristic
291C4×Q16—131no—
292C4×Q16—131no—
293C4×SD16—131no—
294C4×SD16C2×D1311yescharacteristic
295#436C2×D1311yescharacteristic
296#435—261no—
297C8×D4—131no—
298C8×D4—261no—
299#433—261no—
300#432—131no—
301#431—131no—
302C2×C4⋊C8—131no—
303C2×C4⋊C8—261no—
304#405—261no—
305C4×M16—131no—
306C2×C4×C8—131no—
307C2×C4×C8—261no—
308#335—131no—
309#335C2×D1311yescharacteristic
310#334—131no—
311#334—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8—131no—
317Q8⋊C8C2×D1311yescharacteristic
318D4⋊C8—131no—
319D4⋊C8C2×D1311yescharacteristic
320#322—131no—
321#322C2×D1311yescharacteristic
322C82—131no—
323C82—131no—
324C22×C13—41no—
325C22×C13—41no—
326C22×C13—41no—
327C22×C13C2×C4×D411yescharacteristic
328C2×D13—21no—
329C2×D13—21no—
330C2×D13#44312yes—
331C4×C13—22no—
332C4×C13—21no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13C2×#13111yescharacteristic
336C4×C13C2×#13111yescharacteristic
337C4×C13C2×#13711yescharacteristic
338C4×C13#57511yescharacteristic
339Dic13—21no—
340Dic13—22no—
341Dic13—21no—
342Dic13—21no—
343Dic13—41no—
344Dic13—41no—
345Dic13—41no—
346C22×Q8—131no—
347C2×Q16—131no—
348C2×Q16—131no—
349C2×SD16—131no—
350C2×SD16C4×D1311yescharacteristic
351C2×M16—21no—
352C2×M16—261no—
353C22×C8—131no—
354C22×C8—131no—
355C22×C8—261no—
356C22×C8—261no—
357#126—261no—
358#125—131no—
359#124—131no—
360#123—261no—
361C22⋊Q8—131no—
362#121—131no—
363C4×Q8—131no—
364C4×Q8—131no—
365C4×Q8—131no—
366C4×Q8—131no—
367C4×Q8—261no—
368C4×Q8—261no—
369C4×Q8C22×D1311yescharacteristic
370C4×D4—261no—
371C4×D4C22×D1311yescharacteristic
372#117—261no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—261no—
375C2×C42—131no—
376C2×C42—261no—
377#107—131no—
378#107—131no—
379#106—131no—
380#106C4×D1311yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—131no—
383C4⋊C8—131no—
384C4⋊C8—131no—
385C4⋊C8—131no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8—261no—
392C4⋊C8C22×D1311yescharacteristic
393C4⋊C8C22×D1311yescharacteristic
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#103—131no—
399#103C4×D1311yescharacteristic
400#102—131no—
401#102C4×D1311yescharacteristic
402C22⋊C8—21no—
403C22⋊C8—131no—
404C22⋊C8—131no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407#97—261no—
408#97—261no—
409#97—261no—
410C4×C8—21no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8—261no—
420C4×C8C22×D1311yescharacteristic
421C4×C8C22×D1311yescharacteristic
422C4×C8C22×D1311yescharacteristic
423C2×C13—81no—
424C2×C13#292911yescharacteristic
425C2×C13C4×#13711yescharacteristic
426C2×C13C2×#44311yescharacteristic
427D13—22no—
428C2×Q8—131no—
429C2×Q8—131no—
430C2×Q8—261no—
431C2×Q8—262no—
432C2×Q8—262no—
433C2×Q8C2×C4×D1311yescharacteristic
434C2×D4—261no—
435C2×D4C2×C4×D1311yescharacteristic
436C22×C4—21no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4—261no—
441C22×C4—261no—
442Q16—262no—
443Q16—262no—
444SD16—22no—
445SD16—262no—
446M16—42no—
447M16—264no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—262no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—521no—
460C2×C8—522no—
461C2×C8—522no—
462C2×C8C2×C4×D1311yescharacteristic
463C2×C8C2×C4×D1311yescharacteristic
464C2×C8D4×D1311yescharacteristic
465C2×C8D4×D1311yescharacteristic
466C4⋊C4—21no—
467C4⋊C4—131no—
468C4⋊C4—131no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4C2×C4×D1311yescharacteristic
478C4⋊C4C2×C4×D1311yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C22⋊C4—261no—
483C22⋊C4—261no—
484C42—21no—
485C42—131no—
486C42—131no—
487C42—131no—
488C42—261no—
489C42—261no—
490C42—261no—
491C42—261no—
492C42C23×D1311yescharacteristic
493C13#1791111yescharacteristic, complemented, Sylow
494C23—21no—
495C23—131no—
496Q8—21no—
497Q8—132no—
498Q8—264no—
499Q8—261no—
500Q8—261no—
501Q8—261no—
502Q8#8816112yes—
503D4—21no—
504D4—21no—
505D4—522no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—131no—
512C2×C4—131no—
513C2×C4—131no—
514C2×C4—262no—
515C2×C4—264no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—522no—
525C2×C4C22×C4×D1311yescharacteristic
526C2×C4C2×D4×D1311yescharacteristic
527C2×C4#41×D1311yescharacteristic
528C8—22no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—132no—
536C8—262no—
537C8—261no—
538C8—261no—
539C8—261no—
540C8—521no—
541C8—521no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—132no—
546C22—261no—
547C22—261no—
548C22C4×D4×D1311yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—261no—
554C4—261no—
555C4—261no—
556C4—262no—
557C4—521no—
558C4—521no—
559C4—521no—
560C4C2×#8816111yescharacteristic
561C4D13×#13111yescharacteristic
562C4#1171947811yescharacteristic
563C4D13×#13711yescharacteristic
564C2—81no—
565C2—262no—
566C2#1312352711yescharacteristic
567C2#1312365811yescharacteristic
568C2D13×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1588C2
socleC22×C13C2×C4×D4
prime radical#88192C2×C4
cosocleC42×C13C24
hypercenter#1588D13
hypocenterC13#17911
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1588

Complements

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

NH ≅ G/Ntype
3. C8×Q8×D13C2semidirect
4. #13113712C2semidirect
5. #13113709C2semidirect
6. #13113707C2semidirect
7. #13113642C2semidirect
8. #13113640C2semidirect
9. #13113639C2semidirect
10. SD16×#1055C2semidirect
11. #13113620C2semidirect
12. #13113281C2semidirect
14. #13113115C2semidirect
15. C13×#1588C2semidirect
214. #1588D13semidirect
493. C13#17911semidirect

Maximal subgroups

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

subgroupindex
#131249142
#131238142
C8×Q8×D132
#131137122
#131137092
#131137072
#131136422
#131136402
#131136392
SD16×#10552
#131136202
#131132812
#131132462
#131131152
C13×#15882
#1791113