Finite Group Databasebeta

← #15920535

Subgroups — #15920535

Order 3328.

702 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118527C211yesmaximal, characteristic
2#13117727C211yesmaximal, characteristic
3#13116405C211yesmaximal, characteristic, complemented
4#13116334C211yesmaximal, characteristic, complemented
5#13116329C211yesmaximal, characteristic, complemented
6#13116165C211yesmaximal, characteristic, complemented
7#13115787C211yesmaximal, characteristic, complemented
8#13115606C211yesmaximal, characteristic, complemented
9#13115429C211yesmaximal, characteristic, complemented
10#13115408C211yesmaximal, characteristic, complemented
11#13115037C211yesmaximal, characteristic
12#13114932C211yesmaximal, characteristic
13#13114865C211yesmaximal, characteristic
14#13114553C211yesmaximal, characteristic
15C13×#1850C211yesmaximal, characteristic
16C23×C8×C13C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C2×#88180C2211yescharacteristic
19C2×#88123C2211yescharacteristic
20C2×C13×C4⋊C8C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×C22⋊C8C2211yescharacteristic
23C4×C13×C22⋊C4C2211yescharacteristic
24#11718873C2211yescharacteristic
25#11718873C2211yescharacteristic
26C2×#88058C2211yescharacteristic
27C2×#88058C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88057C2211yescharacteristic
30#11718609—21no—
31#11718608—21no—
32#11718606—21no—
33#11718606—21no—
34#11718597C2211yescharacteristic
35C4×C4⋊Dic13C2211yescharacteristic
36C4×C4⋊Dic13C2211yescharacteristic
37#11718589C2211yescharacteristic
38#11718589C2211yescharacteristic
39#11718589C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718316—21no—
42#11718312—21no—
43#11718310—21no—
44#11718307—21no—
45C13×#336C2211yescharacteristic
46C13×#336C2211yescharacteristic
47#11718143C2211yescharacteristic
48#11718143C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C22×Dic26—21no—
61C22×C8×C13—22no—
62C22×C8×C13—22no—
63C22×C8×C13—41no—
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C2×C13×C22⋊C4D411yescharacteristic
69C2×C13×C22⋊C4D411yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76#88180—22no—
77#88180—22no—
78#88180—41no—
79#88180Q814yescomplemented
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97#88123—22no—
98#88123—41no—
99C13×C4⋊C8—22no—
100C13×C4⋊C8—41no—
101C13×C22⋊C8—22no—
102C13×#95D411yescharacteristic
103C13×#95D411yescharacteristic
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88058—22no—
115#88058—22no—
116#88058—41no—
117#88057—41no—
118#25989—131nomaximal, Sylow
119C24×C13C2×D411yescharacteristic
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×Q812yes—
130C22×C4×C13#4112yes—
131C22×C4×C13C2411yescharacteristic
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C2×Dic26—42no—
141C2×Dic26—42no—
142C2×Dic26—81no—
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—44no—
155C2×C8×C13#4112yes—
156C13×C22⋊C4—22no—
157C13×C22⋊C4—41no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13—21no—
162C22⋊Dic13—24no—
163C22⋊Dic13—42no—
164C22⋊Dic13—81no—
165C22⋊Dic13—81no—
166C4⋊Dic13—21no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—42no—
180C4⋊Dic13C2×Q812yes—
181C4⋊Dic13C2×Q812yes—
182C4⋊Dic13#4112yes—
183#6101—42no—
184#6101—42no—
185#6101—42no—
186#6101—81no—
187C4×Dic13—24no—
188C4×Dic13—42no—
189C4×Dic13—81no—
190C4×Dic13—81no—
191#2439—131no—
192#2347—131no—
193#2101—131no—
194#2088—131no—
195#2087—131no—
196#2057—131no—
197#1988—131no—
198#1949—131no—
199#1921—131no—
200#1918—131no—
201#1854—131no—
202#1850D1311yescharacteristic
203#1825—131no—
204#1808—131no—
205#1735—131no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13—21no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13C22⋊Q812yes—
213C23×C13C22×D411yescharacteristic
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13C22⋊Q812yes—
232C2×C4×C13#13512yes—
233C2×C4×C13C22×Q811yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C13H(5,𝔽2)11yescharacteristic
238C2×C4×C132−1+411yescharacteristic
239C2×Dic13—22no—
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—41no—
243C2×Dic13—41no—
244C2×Dic13—41no—
245C2×Dic13—41no—
246C2×Dic13—41no—
247C2×Dic13—41no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263Dic26—84no—
264C8×C13—22no—
265C8×C13—41no—
266C8×C13—41no—
267C8×C13—41no—
268C23×C8C2×D1311yescharacteristic
269C2×C4⋊Q8—131no—
270C2×#117—131no—
271C2×#117—131no—
272C2×#107—131no—
273C2×#107—131no—
274C2×#107—131no—
275C2×#106—131no—
276C2×C4⋊C8C2×D1311yescharacteristic
277C2×C4⋊C8C2×D1311yescharacteristic
278C2×C22⋊C8C2×D1311yescharacteristic
279#396—261no—
280#393—261no—
281#391—261no—
282#389—131no—
283#389—131no—
284#389—131no—
285#389—131no—
286#388—261no—
287#388—261no—
288#387—261no—
289#383—261no—
290#382—131no—
291#380—131no—
292#380—131no—
293C4×C4⋊C4—131no—
294C4×C4⋊C4—131no—
295C4×C4⋊C4—261no—
296C4×C22⋊C4C2×D1311yescharacteristic
297#340—131no—
298#340—131no—
299#340—131no—
300#340—131no—
301#340—131no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#336C2×D1311yescharacteristic
310#336C2×D1311yescharacteristic
311C22×C13—22no—
312C22×C13—22no—
313C22×C13—22no—
314C22×C13—41no—
315C22×C13—41no—
316C22×C13—41no—
317C22×C13—41no—
318C22×C13C2×C22⋊Q811yescharacteristic
319C22×C13#54611yescharacteristic
320C22×C13#54711yescharacteristic
321C22×C13C2×#13511yescharacteristic
322C22×C13#57511yescharacteristic
323C22×C13#57611yescharacteristic
324C22×C13#57811yescharacteristic
325C4×C13—22no—
326C4×C13—22no—
327C4×C13—41no—
328C4×C13—41no—
329C4×C13—41no—
330C4×C13#53311yescharacteristic
331C4×C13#54411yescharacteristic
332C4×C13#55111yescharacteristic
333C4×C13#55211yescharacteristic
334Dic13—42no—
335Dic13—42no—
336Dic13—42no—
337Dic13—81no—
338Dic13—81no—
339Dic13—81no—
340Dic13—81no—
341Dic13—81no—
342C22×Q8—261no—
343C23×C4C22×D1311yescharacteristic
344C22×C8—22no—
345C22×C8—22no—
346C22×C8—41no—
347C22×C8C22×D1311yescharacteristic
348C22×C8C22×D1311yescharacteristic
349C22×C8C22×D1311yescharacteristic
350C22×C8C22×D1311yescharacteristic
351C4⋊Q8—262no—
352C4⋊Q8—521no—
353#117—134no—
354#117—262no—
355#117—262no—
356#117—521no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—131no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—261no—
370C2×C22⋊C4—261no—
371C2×C22⋊C4—261no—
372C2×C22⋊C4—261no—
373C2×C22⋊C4—261no—
374C2×C22⋊C4D5211yescharacteristic
375C2×C22⋊C4D5211yescharacteristic
376C2×C42—261no—
377C2×C42—261no—
378C2×C42—261no—
379C2×C42—261no—
380C2×C42C22×D1311yescharacteristic
381C2×C42C22×D1311yescharacteristic
382#107—262no—
383#107—262no—
384#107—521no—
385#106—521no—
386C4⋊C8—22no—
387C4⋊C8—41no—
388C22⋊C8—22no—
389#95—261no—
390#95—261no—
391#95—261no—
392#95—261no—
393#95—261no—
394#95—261no—
395#95—261no—
396#95—261no—
397#95—261no—
398#95—261no—
399#95D5211yescharacteristic
400#95D5211yescharacteristic
401C2×C13—42no—
402C2×C13#243811yescharacteristic
403C2×C13#307611yescharacteristic
404C2×C13#308311yescharacteristic
405C2×C13#329711yescharacteristic
406C2×C13#331311yescharacteristic
407C2×C13#334211yescharacteristic
408C2×C13#334711yescharacteristic
409C24C2×D5211yescharacteristic
410C2×Q8—522no—
411C2×Q8—522no—
412C2×Q8—1041no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—261no—
418C22×C4—261no—
419C22×C4—261no—
420C22×C4—261no—
421C22×C4—261no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4C2×D5211yescharacteristic
426C22×C4C2×D5211yescharacteristic
427C22×C4C2×D5211yescharacteristic
428C22×C4C2×D5211yescharacteristic
429C22×C4C2×D5211yescharacteristic
430C22×C4#612912yes—
431C22×C4Q8×D1312yes—
432C22×C4C23×D1311yescharacteristic
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—44no—
445C2×C8#612912yes—
446C4⋊C4—132no—
447C4⋊C4—132no—
448C4⋊C4—132no—
449C4⋊C4—261no—
450C4⋊C4—261no—
451C4⋊C4—261no—
452C4⋊C4—261no—
453C4⋊C4—261no—
454C4⋊C4—261no—
455C4⋊C4—261no—
456C4⋊C4—261no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—522no—
463C4⋊C4—522no—
464C4⋊C4—522no—
465C4⋊C4—522no—
466C4⋊C4—1041no—
467C22⋊C4—22no—
468C22⋊C4—41no—
469C22⋊C4—264no—
470C22⋊C4—522no—
471C22⋊C4—1041no—
472C22⋊C4—1041no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—264no—
478C42—522no—
479C42—1041no—
480C42—1041no—
481C13#2598911yescharacteristic, complemented, Sylow
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23#8815112yes—
489C23C22×D5211yescharacteristic
490Q8—1044no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—262no—
509C2×C4—262no—
510C2×C4—262no—
511C2×C4—521no—
512C2×C4—521no—
513C2×C4—521no—
514C2×C4—521no—
515C2×C4—521no—
516C2×C4—521no—
517C2×C4—521no—
518C2×C4—521no—
519C2×C4—521no—
520C2×C4—521no—
521C2×C4—521no—
522C2×C4—521no—
523C2×C4—521no—
524C2×C4—521no—
525C2×C4—521no—
526C2×C4—521no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4#8815112yes—
533C2×C4#8815812yes—
534C2×C4C2×#612911yescharacteristic
535C2×C4C2×#612911yescharacteristic
536C2×C4#8825111yescharacteristic
537C2×C4C2×Q8×D1311yescharacteristic
538C2×C4#41×D1311yescharacteristic
539C2×C4#8825711yescharacteristic
540C8—22no—
541C8—41no—
542C8—41no—
543C8—41no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22C2×#8815111yescharacteristic
552C22#1171925911yescharacteristic
553C22#1171926011yescharacteristic
554C22C2×#8815811yescharacteristic
555C22#1171945311yescharacteristic
556C22#1171945711yescharacteristic
557C22#1171945811yescharacteristic
558C4—22no—
559C4—22no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—522no—
564C4—522no—
565C4—522no—
566C4—1041no—
567C4—1041no—
568C4—1041no—
569C4—1041no—
570C4—1041no—
571C4#1171929211yescharacteristic
572C4#1171932711yescharacteristic
573C4#1171932811yescharacteristic
574C4#1171935511yescharacteristic
575C2—42no—
576C2#1311851011yescharacteristic
577C2#1312462611yescharacteristic
578C2#1312468911yescharacteristic
579C2#1312668811yescharacteristic
580C2#1312690411yescharacteristic
581C2#1312726711yescharacteristic
582C2#1312733811yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1850C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1850D13
hypocenterC13#25989
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
3. #13116405C2semidirect
4. #13116334C2semidirect
5. #13116329C2semidirect
6. #13116165C2semidirect
7. #13115787C2semidirect
8. #13115606C2semidirect
9. #13115429C2semidirect
10. #13115408C2semidirect
79. #88180Q8semidirect
481. C13#25989semidirect

Maximal subgroups

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

subgroupindex
#131185272
#131177272
#131164052
#131163342
#131163292
#131161652
#131157872
#131156062
#131154292
#131154082
#131150372
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