Finite Group Databasebeta

← #15875183

Subgroups — #15875183

Order 3328.

740 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718507C211yesmaximal, characteristic
2#13117584C211yesmaximal, characteristic, complemented
3#13117480C211yesmaximal, characteristic
4#13115783C211yesmaximal, characteristic, complemented
5#13115606C211yesmaximal, characteristic, complemented
6#13115574C211yesmaximal, characteristic, complemented
7#13115569C211yesmaximal, characteristic, complemented
8#13115533C211yesmaximal, characteristic
9#13115519C211yesmaximal, characteristic
10#13115464C211yesmaximal, characteristic
11#13115457C211yesmaximal, characteristic
12#13115429C211yesmaximal, characteristic, complemented
13#13115408C211yesmaximal, characteristic, complemented
14#13114847C211yesmaximal, characteristic
15C13×#1768C211yesmaximal, characteristic, complemented
16C2×C4×D52C2211yescharacteristic
17C2×#88123C2211yescharacteristic
18C2×C13×C4⋊C8C2211yescharacteristic
19C2×C13×C4⋊C8C2211yescharacteristic
20C2×C13×#97C2211yescharacteristic
21C2×C4×C8×C13C2211yescharacteristic
22C13×#376C2211yescharacteristic
23C2×#88061C2211yescharacteristic
24C2×#88061C2211yescharacteristic
25C2×#88061C2211yescharacteristic
26C2×#88061C2211yescharacteristic
27C2×#88058C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88058C2211yescharacteristic
30C2×#88057C2211yescharacteristic
31#11718600C2211yescharacteristic
32#11718600C2211yescharacteristic
33#11718597C2211yescharacteristic
34C4×C4⋊Dic13C2211yescharacteristic
35C4×C4⋊Dic13C2211yescharacteristic
36C4×C4⋊Dic13C2211yescharacteristic
37#11718589C2211yescharacteristic
38#11718589C2211yescharacteristic
39#11718589C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718507C418yescomplemented
42#11718330—21no—
43#11718330—21no—
44#11718328—21no—
45#11718325—21no—
46#11718315—21no—
47#11718315—21no—
48#11718307—21no—
49#11718307—21no—
50C13×#336C2211yescharacteristic
51C13×#336C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C22×Dic26—21no—
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C2×C42×C13C2311yescharacteristic
68C2×C42×C13C2311yescharacteristic
69C2×C42×C13C2311yescharacteristic
70C2×#6103—21no—
71C2×#6103—21no—
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103—21no—
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13C2311yescharacteristic
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×#6101—21no—
84C2×#6101—21no—
85C2×#6101—21no—
86C2×#6101—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C4×D52—22no—
91C4×D52C2×C414yes—
92#88123—22no—
93#88123C2×C414yes—
94C13×C4⋊C8—22no—
95C13×C4⋊C8C2×C414yes—
96C13×#97—41no—
97C4×C8×C13—41no—
98C13×#95D411yescharacteristic
99C13×#95D411yescharacteristic
100C13×#95D411yescharacteristic
101C13×#95D411yescharacteristic
102#88071—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88061—41no—
112#88061—41no—
113#88061C2×C414yes—
114#88061C2×C414yes—
115#88058—41no—
116#88058C2×C414yes—
117#88058C2×C414yes—
118#88057—41no—
119#22127—131nomaximal, Sylow
120C23×D13—21no—
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×D411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2411yescharacteristic
128C22×Dic13—21no—
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C2×D52—21no—
136C2×D52—21no—
137C2×D52—21no—
138C2×D52—21no—
139C2×D52—21no—
140C2×D52C22×C412yes—
141C2×C4×D13—24no—
142C2×C4×D13—81no—
143C2×C4×D13—81no—
144C2×Dic26—24no—
145C2×Dic26—81no—
146C2×Dic26—81no—
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—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13C22×C412yes—
158C2×C8×C13C22×C412yes—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13C22×C412yes—
164C42×C13#4112yes—
165#6103—24no—
166#6103—81no—
167#6103—81no—
168#6103—81no—
169#6103—81no—
170C4⋊Dic13—24no—
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—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13C22×C412yes—
183C4⋊Dic13C22×C412yes—
184C4⋊Dic13C22×C412yes—
185#6101—81no—
186#6101—81no—
187#6101—81no—
188#6101—81no—
189C4×Dic13—81no—
190C4×Dic13—81no—
191C4×Dic13—81no—
192C2×#474—131no—
193#2331—131no—
194#2319—131no—
195#1987—131no—
196#1949—131no—
197#1943—131no—
198#1942—131no—
199#1936—131no—
200#1934—131no—
201#1926—131no—
202#1925—131no—
203#1921—131no—
204#1918—131no—
205#1804—131no—
206#1768D1311yescharacteristic, complemented
207C23×C13C22×D411yescharacteristic
208C22×D13—22no—
209C22×D13—41no—
210C22×D13—41no—
211C22×D13—41no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—41no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
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×C13C4×D412yes—
232C2×C4×C13C4×D412yes—
233C2×C4×C13C23×C411yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C2×C4×C13H(5,𝔽2)11yescharacteristic
236C2×C4×C132−1+411yescharacteristic
237C2×C4×C132−1+411yescharacteristic
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—
260D52—22no—
261D52—22no—
262D52—41no—
263D52—41no—
264C4×D13—84no—
265Dic26—84no—
266C8×C13—22no—
267C8×C13—22no—
268C8×C13—41no—
269C8×C13—41no—
270C2×C4⋊Q8—131no—
271C2×C4×D4—131no—
272#474—138no—
273C2×#107—131no—
274C2×#107—131no—
275C2×#107—131no—
276C2×#106—131no—
277C2×C4⋊C8C2×D1311yescharacteristic
278C2×C4⋊C8C2×D1311yescharacteristic
279C2×#102—131no—
280C2×#102—131no—
281C2×#102—131no—
282C2×#102—131no—
283C2×#97C2×D1311yescharacteristic
284C2×C4×C8C2×D1311yescharacteristic
285#391—261no—
286#391—261no—
287#390—131no—
288#390—131no—
289#389—131no—
290#389—131no—
291#389—131no—
292#389—131no—
293#388—261no—
294#388—261no—
295#387—261no—
296#387—261no—
297#382—131no—
298#381—261no—
299#380—261no—
300C4×C4⋊C4—131no—
301C4×C4⋊C4—131no—
302C4×C4⋊C4—131no—
303#376C2×D1311yescharacteristic
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#336C2×D1311yescharacteristic
313#336C2×D1311yescharacteristic
314C22×C13C2×C4×D411yescharacteristic
315C22×C13#53611yescharacteristic
316C22×C13#53711yescharacteristic
317C22×C13#57611yescharacteristic
318C22×C13#57611yescharacteristic
319C22×C13#57711yescharacteristic
320C22×C13#57811yescharacteristic
321C2×D13—42no—
322C2×D13—42no—
323C2×D13—42no—
324C2×D13—81no—
325C2×D13—81no—
326C2×D13—81no—
327C2×D13—81no—
328C4×C13—22no—
329C4×C13—22no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13#51911yescharacteristic
335C4×C13#52011yescharacteristic
336C4×C13#54111yescharacteristic
337C4×C13#54211yescharacteristic
338Dic13—42no—
339Dic13—42no—
340Dic13—42no—
341Dic13—81no—
342Dic13—81no—
343Dic13—81no—
344Dic13—81no—
345C22×Q8—261no—
346C22×D4—131no—
347C23×C4—261no—
348C22×C8C22×D1311yescharacteristic
349C22×C8C22×D1311yescharacteristic
350C22×C8C22×D1311yescharacteristic
351C22×C8C22×D1311yescharacteristic
352C4⋊Q8—134no—
353C4⋊Q8—262no—
354C4×D4—134no—
355C4×D4—262no—
356C2×C4⋊C4—131no—
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—261no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C22⋊C4—261no—
369C2×C22⋊C4—261no—
370C2×C22⋊C4—261no—
371C2×C22⋊C4—261no—
372C2×C22⋊C4—261no—
373C2×C42—261no—
374C2×C42—261no—
375C2×C42—261no—
376C2×C42C22×D1311yescharacteristic
377C2×C42C22×D1311yescharacteristic
378C2×C42C22×D1311yescharacteristic
379#107—134no—
380#107—134no—
381#107—521no—
382#106—521no—
383C4⋊C8—22no—
384C4⋊C8C4×D1314yes—
385#102—134no—
386#102—134no—
387#102—521no—
388#102—521no—
389#97—41no—
390C4×C8—41no—
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#95—261no—
400#95D5211yescharacteristic
401#95D5211yescharacteristic
402#95D5211yescharacteristic
403#95D5211yescharacteristic
404C2×C13#232311yescharacteristic
405C2×C13#294711yescharacteristic
406C2×C13#294811yescharacteristic
407C2×C13#324111yescharacteristic
408C2×C13#324311yescharacteristic
409C2×C13#325711yescharacteristic
410C2×C13#326211yescharacteristic
411D13—82no—
412C24—261no—
413C2×Q8—264no—
414C2×Q8—1041no—
415C2×Q8—1041no—
416C2×D4—132no—
417C2×D4—261no—
418C2×D4—261no—
419C2×D4—261no—
420C2×D4—261no—
421C2×D4—261no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—264no—
426C22×C4—261no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—1041no—
431C22×C4—1041no—
432C22×C4C2×D5211yescharacteristic
433C22×C4C2×D5211yescharacteristic
434C22×C4C2×D5211yescharacteristic
435C22×C4C2×D5211yescharacteristic
436C22×C4C2×D5211yescharacteristic
437C22×C4C2×D5211yescharacteristic
438C22×C4C23×D1311yescharacteristic
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8C2×C4×D1312yes—
450C2×C8C2×C4×D1312yes—
451C4⋊C4—132no—
452C4⋊C4—132no—
453C4⋊C4—132no—
454C4⋊C4—264no—
455C4⋊C4—261no—
456C4⋊C4—261no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—1041no—
467C4⋊C4—1041no—
468C4⋊C4—1041no—
469C4⋊C4—1041no—
470C22⋊C4—264no—
471C22⋊C4—1041no—
472C22⋊C4—1041no—
473C22⋊C4—1041no—
474C22⋊C4—1041no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—1041no—
480C42—1041no—
481C42—1041no—
482C42C2×C4×D1312yes—
483C42#612712yes—
484C13#2212711yescharacteristic, complemented, Sylow
485C23—262no—
486C23—521no—
487C23—521no—
488C23—521no—
489C23—521no—
490C23—521no—
491C23—521no—
492C23C22×D5211yescharacteristic
493Q8—1044no—
494D4—262no—
495D4—262no—
496D4—521no—
497D4—521no—
498C2×C4—21no—
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—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—262no—
515C2×C4—262no—
516C2×C4—262no—
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—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—1044no—
536C2×C4C4×D5212yes—
537C2×C4C4×D5212yes—
538C2×C4C22×C4×D1311yescharacteristic
539C2×C4C2×#612711yescharacteristic
540C2×C4#8825111yescharacteristic
541C2×C4#8825411yescharacteristic
542C2×C4#8825711yescharacteristic
543C2×C4#8825711yescharacteristic
544C8—22no—
545C8—22no—
546C8—41no—
547C8—41no—
548C22—522no—
549C22—522no—
550C22—522no—
551C22—1041no—
552C22—1041no—
553C22—1041no—
554C22—1041no—
555C22C2×C4×D5211yescharacteristic
556C22#1171921511yescharacteristic
557C22#1171923111yescharacteristic
558C22#1171945611yescharacteristic
559C22#1171945711yescharacteristic
560C22#1171945711yescharacteristic
561C22#1171945811yescharacteristic
562C4—22no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—522no—
569C4—522no—
570C4—522no—
571C4—1041no—
572C4—1041no—
573C4—1041no—
574C4—1041no—
575C4#1171925111yescharacteristic
576C4#1171926611yescharacteristic
577C4#1171927711yescharacteristic
578C4#1171928811yescharacteristic
579C2—1042no—
580C2#1311751911yescharacteristic
581C2#1312368111yescharacteristic
582C2#1312368911yescharacteristic
583C2#1312609111yescharacteristic
584C2#1312612111yescharacteristic
585C2#1312624911yescharacteristic
586C2#1312629711yescharacteristic
subgroupG/H
centerC23C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1768C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1768D13
hypocenterC13#22127
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376 ◁ #1768

Complements

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

NH ≅ G/Ntype
2. #13117584C2semidirect
4. #13115783C2semidirect
5. #13115606C2semidirect
6. #13115574C2semidirect
7. #13115569C2semidirect
12. #13115429C2semidirect
13. #13115408C2semidirect
15. C13×#1768C2semidirect
41. #11718507C4semidirect
206. #1768D13semidirect
484. C13#22127semidirect

Maximal subgroups

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

subgroupindex
C2×#117185072
#131175842
#131174802
#131157832
#131156062
#131155742
#131155692
#131155332
#131155192
#131154642
#131154572
#131154292
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