Finite Group Databasebeta

← #15833133

Subgroups — #15833133

Order 3328.

590 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124873C211yesmaximal, characteristic
2#13123765C211yesmaximal, characteristic
3D13×#446C211yesmaximal, characteristic
4#13113733C211yesmaximal, characteristic, complemented
5#13113732C211yesmaximal, characteristic, complemented
6#13113730C211yesmaximal, characteristic, complemented
7#13113730C211yesmaximal, characteristic, complemented
8#13113688C211yesmaximal, characteristic, complemented
9#13113686C211yesmaximal, characteristic, complemented
10#13113684C211yesmaximal, characteristic, complemented
11#13113609C211yesmaximal, characteristic
12#13113263C211yesmaximal, characteristic
13#13113237C211yesmaximal, characteristic
14#13113121C211yesmaximal, characteristic
15C13×#1584C211yesmaximal, characteristic, complemented
16#11719283C2211yescharacteristic
17C4×Q8×D13C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C4×C13×Q16C2211yescharacteristic
21#11718847C411yescharacteristic
22#11718843C411yescharacteristic
23C4×#6107C2211yescharacteristic
24C4×#6107C2211yescharacteristic
25#11718685C2211yescharacteristic
26#11718685C2211yescharacteristic
27#11718545C411yescharacteristic
28#11718536C411yescharacteristic
29#11718500—21no—
30#11718498C2211yescharacteristic
31D13×C4⋊C8—21no—
32D13×C4⋊C8C2211yescharacteristic
33#11718492C2211yescharacteristic
34#11718492C2211yescharacteristic
35#11718489—21no—
36#11718489—21no—
37#11718470C411yescharacteristic
38#11718469C411yescharacteristic
39#11718455C411yescharacteristic
40#11718454C411yescharacteristic
41D13×#97—21no—
42#11718362—21no—
43C4×Dic52C2211yescharacteristic
44#11718350—21no—
45#11718346C2211yescharacteristic
46#11718346C2211yescharacteristic
47C4×C8×D13C2211yescharacteristic
48#11718340C2211yescharacteristic
49C8×Dic26—21no—
50C8×Dic26C2211yescharacteristic
51C13×#335C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718071C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718050C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718047C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×Q8×D13C2×C411yescharacteristic
68C2×C13×Q16C2×C411yescharacteristic
69C4×Q8×C13C2311yescharacteristic
70C4×Q8×C13C2311yescharacteristic
71#88200C2×C411yescharacteristic
72Q8×Dic13C2×C411yescharacteristic
73#88198C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75C2×#6107C2×C411yescharacteristic
76C2×Dic52C2×C411yescharacteristic
77C2×#6094—21no—
78C2×C8×D13—21no—
79C2×C8×D13D411yescharacteristic
80C2×C8×D13D411yescharacteristic
81#88151C2×C411yescharacteristic
82#88150—21no—
83C4⋊C4×D13—21no—
84C4⋊C4×D13C2×C411yescharacteristic
85#88143—21no—
86#88142C2×C411yescharacteristic
87#88141—21no—
88#88141C2×C411yescharacteristic
89#88126—21no—
90C42×D13—21no—
91C42×D13C2311yescharacteristic
92C4×Dic26—21no—
93C4×Dic26—21no—
94C4×Dic26C2311yescharacteristic
95C4×Dic26C2311yescharacteristic
96C13×#107C2×C411yescharacteristic
97C13×C4⋊C8—21no—
98C13×C4⋊C8—21no—
99C13×C4⋊C8C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×#103C2×C411yescharacteristic
102C13×#103C2×C411yescharacteristic
103C13×#97—21no—
104C4×C8×C13—21no—
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108#88075C2×C411yescharacteristic
109#88075C2×C411yescharacteristic
110#88060—21no—
111#88060C2×C411yescharacteristic
112#88060C2×C411yescharacteristic
113#88058C2×C411yescharacteristic
114#88056C2×C411yescharacteristic
115#88056C2×C411yescharacteristic
116#88055—21no—
117#88055—21no—
118#88055—21no—
119#88054—21no—
120#88054—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×Dic13D411yescharacteristic
130C8×Dic13D411yescharacteristic
131#88050C2×C411yescharacteristic
132#88050C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134#88047C2×C411yescharacteristic
135C4⋊#1055—21no—
136C4⋊#1055—21no—
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139#88043—21no—
140#88043—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17931—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×Q8×C13C22×C411yescharacteristic
147Q8×D13—41no—
148Q8×D13—41no—
149C2×C4×D13—21no—
150C2×C4×D13—21no—
151C2×C4×D13C22×C411yescharacteristic
152C2×C4×D13C2×D411yescharacteristic
153C2×C4×D13#4111yescharacteristic
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26C22×C411yescharacteristic
157C2×Dic26C22×C411yescharacteristic
158C13×Q16—41no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13C22×C411yescharacteristic
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C2×D411yescharacteristic
165C2×C8×C13C2×D411yescharacteristic
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4C22×C411yescharacteristic
169C13×C4⋊C4C22×C411yescharacteristic
170C42×C13—21no—
171C42×C13—21no—
172C42×C13C2411yescharacteristic
173#6107—41no—
174#6107—41no—
175#6103—21no—
176#6103—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13C22×C411yescharacteristic
180C4⋊Dic13C22×C411yescharacteristic
181#6101—21no—
182#6101—21no—
183#6101—21no—
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189C4×Dic13—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13C22×C411yescharacteristic
194C4×Dic13C2×D411yescharacteristic
195C4×Dic13#4111yescharacteristic
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055C22×C411yescharacteristic
200C2×#1055C22×C411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203Dic52—41no—
204#6094—42no—
205C8×D13—22no—
206C8×D13—42no—
207C8×D13Q1614yescomplemented
208#3104—131no—
209#2960—131no—
210C2×#446—131no—
211#1591—131no—
212#1591—131no—
213#1591—131no—
214#1591—131no—
215#1584—131no—
216#1584—131no—
217#1584—131no—
218#1584D1311yescharacteristic, complemented
219#1571—131no—
220#1487—131no—
221#1481—131no—
222#1450—131no—
223C22×D13C4×D411yescharacteristic
224Q8×C13—21no—
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13C23×C411yescharacteristic
233C2×C4×C13C22×D411yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C2×Dic13—21no—
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13C4×D411yescharacteristic
240C2×Dic13C4×D411yescharacteristic
241C2×Dic13C4×D411yescharacteristic
242C4×D13—21no—
243C4×D13—21no—
244C4×D13—41no—
245C4×D13—42no—
246C4×D13—42no—
247C4×D13C2×Q1612yes—
248C4×D13#13512yes—
249Dic26—21no—
250Dic26—21no—
251Dic26—21no—
252Dic26—21no—
253Dic26—42no—
254Dic26—42no—
255C8×C13—21no—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—41no—
259C8×C13—41no—
260C8×C13—41no—
261C8×C13C2×Q1612yes—
262#1055—21no—
263#1055—21no—
264#1055—21no—
265#1055—41no—
266#1055—41no—
267#1055—41no—
268#1055C2×Q1612yes—
269#533—131no—
270C2×C4×Q8—131no—
271#484—131no—
272#484—131no—
273#477—131no—
274#477—131no—
275#462—131no—
276#462—131no—
277#451—131no—
278#451—131no—
279#446—131no—
280#446—131no—
281#446—131no—
282#446—131no—
283#446—131no—
284#446—261no—
285#446—261no—
286#446—261no—
287#446C2×D1311yescharacteristic
288C8×Q8—131no—
289C8×Q8—261no—
290C8×Q8C2×D1311yescharacteristic
291C4×Q16—131no—
292C4×Q16—131no—
293C4×Q16—131no—
294C4×Q16C2×D1311yescharacteristic
295#431—131no—
296#431—131no—
297#424—261no—
298#423—131no—
299C2×C4⋊C8—131no—
300C2×C4⋊C8—261no—
301#405—261no—
302C2×#97—261no—
303C2×C4×C8—131no—
304#335—131no—
305#335—131no—
306#335—131no—
307#335C2×D1311yescharacteristic
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8C2×D1311yescharacteristic
315Q8⋊C8C2×D1311yescharacteristic
316#322—131no—
317#322C2×D1311yescharacteristic
318C82—131no—
319C82—131no—
320C22×C13C2×C4×D411yescharacteristic
321C2×D13—21no—
322C2×D13—21no—
323C2×D13C4×Q1612yes—
324C4×C13—21no—
325C4×C13—41no—
326C4×C13—41no—
327C4×C13—41no—
328C4×C13—41no—
329C4×C13#56811yescharacteristic
330C4×C13#56811yescharacteristic
331C4×C13C22×Q1611yescharacteristic
332C4×C13C2×#13511yescharacteristic
333Dic13—21no—
334Dic13—21no—
335Dic13—41no—
336Dic13—41no—
337Dic13—41no—
338Dic13—41no—
339Dic13C4×Q1612yes—
340C22×Q8—131no—
341C2×Q16—131no—
342C2×Q16—131no—
343C2×Q16—131no—
344C2×Q16C4×D1311yescharacteristic
345C2×M16—261no—
346C22×C8—131no—
347C22×C8—131no—
348C22×C8—261no—
349C4⋊Q8—131no—
350C4⋊Q8—131no—
351#125—261no—
352C22⋊Q8—131no—
353C22⋊Q8—131no—
354C22⋊Q8—261no—
355C4×Q8—131no—
356C4×Q8—131no—
357C4×Q8—131no—
358C4×Q8—131no—
359C4×Q8—261no—
360C4×Q8—261no—
361C4×Q8—261no—
362C4×Q8C22×D1311yescharacteristic
363C4×Q8C22×D1311yescharacteristic
364#117—261no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—261no—
367C2×C42—131no—
368C2×C42—261no—
369#107—131no—
370#107—131no—
371#107—131no—
372#107C4×D1311yescharacteristic
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8—131no—
376C4⋊C8—131no—
377C4⋊C8—131no—
378C4⋊C8—131no—
379C4⋊C8—261no—
380C4⋊C8—261no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8C22×D1311yescharacteristic
389C4⋊C8C22×D1311yescharacteristic
390#103—131no—
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103C4×D1311yescharacteristic
397#103C4×D1311yescharacteristic
398C22⋊C8—131no—
399C22⋊C8—131no—
400C22⋊C8—261no—
401#97—21no—
402#97—261no—
403#97—261no—
404#97—261no—
405#97—261no—
406#97—261no—
407C4×C8—21no—
408C4×C8—131no—
409C4×C8—131no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—261no—
414C4×C8C22×D1311yescharacteristic
415C4×C8C22×D1311yescharacteristic
416C4×C8C22×D1311yescharacteristic
417C2×C13#293011yescharacteristic
418C2×C13C2×C4×Q1611yescharacteristic
419C2×C13#295511yescharacteristic
420D13—22no—
421C2×Q8—131no—
422C2×Q8—131no—
423C2×Q8—261no—
424C2×Q8—261no—
425C2×Q8—521no—
426C2×Q8—521no—
427C2×Q8C2×C4×D1311yescharacteristic
428C2×Q8C2×C4×D1311yescharacteristic
429C22×C4—131no—
430C22×C4—131no—
431C22×C4—131no—
432C22×C4—261no—
433C22×C4—261no—
434Q16—41no—
435Q16—521no—
436Q16—521no—
437Q16—521no—
438M16—522no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—131no—
443C2×C8—134no—
444C2×C8—131no—
445C2×C8—131no—
446C2×C8—131no—
447C2×C8—262no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—522no—
452C2×C8C2×C4×D1311yescharacteristic
453C2×C8C2×C4×D1311yescharacteristic
454C2×C8D4×D1311yescharacteristic
455C2×C8D4×D1311yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—131no—
459C4⋊C4—131no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4C2×C4×D1311yescharacteristic
471C4⋊C4C2×C4×D1311yescharacteristic
472C22⋊C4—261no—
473C22⋊C4—261no—
474C42—21no—
475C42—21no—
476C42—131no—
477C42—131no—
478C42—131no—
479C42—261no—
480C42—261no—
481C42—261no—
482C42—261no—
483C42C23×D1311yescharacteristic
484C13#1793111yescharacteristic, complemented, Sylow
485C23—131no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—261no—
491Q8—261no—
492Q8—261no—
493Q8—261no—
494Q8—522no—
495Q8—522no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—131no—
501C2×C4—132no—
502C2×C4—132no—
503C2×C4—131no—
504C2×C4—131no—
505C2×C4—261no—
506C2×C4—261no—
507C2×C4—261no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—521no—
512C2×C4—522no—
513C2×C4—522no—
514C2×C4C22×C4×D1311yescharacteristic
515C2×C4C2×D4×D1311yescharacteristic
516C2×C4#41×D1311yescharacteristic
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—132no—
524C8—261no—
525C8—261no—
526C8—261no—
527C8—521no—
528C8—521no—
529C8—521no—
530C8Q16×D1312yes—
531C22—132no—
532C22—261no—
533C22—261no—
534C22C4×D4×D1311yescharacteristic
535C4—21no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—132no—
541C4—261no—
542C4—261no—
543C4—521no—
544C4—521no—
545C4—521no—
546C4—521no—
547C4#1171945011yescharacteristic
548C4#1171945511yescharacteristic
549C4C2×Q16×D1311yescharacteristic
550C4D13×#13511yescharacteristic
551C2—262no—
552C2#1312353411yescharacteristic
553C2C4×Q16×D1311yescharacteristic
554C2#1312373611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1584C2
socleC22×C13C2×C4×D4
prime radicalC22×D13C4×D4
cosocleC42×C13C24
hypercenter#1584D13
hypocenterC13#17931
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #13113733C2semidirect
5. #13113732C2semidirect
6. #13113730C2semidirect
7. #13113730C2semidirect
8. #13113688C2semidirect
9. #13113686C2semidirect
10. #13113684C2semidirect
15. C13×#1584C2semidirect
207. C8×D13Q16semidirect
218. #1584D13semidirect
484. C13#17931semidirect

Maximal subgroups

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

subgroupindex
#131248732
#131237652
D13×#4462
#131137332
#131137322
#131137302
#131136882
#131136862
#131136842
#131136092
#131132632
#131132372
#131131212
C13×#15842
#1793113