Finite Group Databasebeta

← #15935512

Subgroups — #15935512

Order 3328.

726 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117930C211yesmaximal, characteristic, complemented
2#13116210C211yesmaximal, characteristic
3#13116174C211yesmaximal, characteristic, complemented
4#13116166C211yesmaximal, characteristic, complemented
5#13115982C211yesmaximal, characteristic
6#13115789C211yesmaximal, characteristic, complemented
7#13115571C211yesmaximal, characteristic, complemented
8#13115460C211yesmaximal, characteristic
9#13115453C211yesmaximal, characteristic
10#13115418C211yesmaximal, characteristic, complemented
11#13115418C211yesmaximal, characteristic, complemented
12#13115402C211yesmaximal, characteristic, complemented
13#13115097C211yesmaximal, characteristic
14#13114661C211yesmaximal, characteristic
15C13×#2452C211yesmaximal, characteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8—21no—
18C2×C4×D4×C13C2211yescharacteristic
19C2×#88124C2211yescharacteristic
20C13×#396—21no—
21C13×#393—21no—
22C13×#390C2211yescharacteristic
23C13×#390C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C13×#385—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32#11718639—21no—
33#11718633—21no—
34C2×#88048C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40C4×C4⋊Dic13C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45#11718313—21no—
46#11718310—21no—
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13—21no—
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C13×C4⋊Q8—22no—
63C13×C4⋊Q8—41no—
64C13×C22⋊Q8—44no—
65C4×D4×C13—22no—
66C4×D4×C13—41no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4D411yescharacteristic
71C2×C13×C4⋊C4D411yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98#88124—22no—
99#88124—22no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95D411yescharacteristic
103C13×#95D411yescharacteristic
104#88072—22no—
105#88072—22no—
106#88072—41no—
107#88072Q814yescomplemented
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88048—22no—
114#88048—22no—
115#88048—41no—
116#88047—22no—
117C4⋊#1055—41no—
118#88043—41no—
119#27026—131nomaximal, Sylow
120C24×C13—21no—
121C2×Q8×C13—42no—
122C2×Q8×C13—42no—
123C2×Q8×C13—81no—
124C2×D4×C13—21no—
125C2×D4×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13C2×Q812yes—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—42no—
134C22×C4×C13—42no—
135C22×C4×C13—81no—
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2411yescharacteristic
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C13×C4⋊C4—22no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—41no—
154C13×C4⋊C4—42no—
155C13×C4⋊C4—42no—
156C13×C4⋊C4—42no—
157C13×C4⋊C4#4112yes—
158C13×C22⋊C4—42no—
159C13×C22⋊C4—42no—
160C13×C22⋊C4—42no—
161C13×C22⋊C4—42no—
162C13×C22⋊C4—81no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—21no—
168C42×C13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13C2×Q812yes—
175C4⋊Dic13#4112yes—
176C4⋊Dic13#4112yes—
177#6101—24no—
178#6101—24no—
179#6101—42no—
180#6101—81no—
181C4×Dic13—42no—
182C4×Dic13—81no—
183C4×Dic13—81no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055C2×Q812yes—
196#2452D1311yescharacteristic
197#2370—131no—
198#2065—131no—
199#2059—131no—
200#2058—131no—
201#2025—131no—
202#1988—131no—
203#1943—131no—
204#1926—131no—
205#1925—131no—
206#1920—131no—
207#1920—131no—
208#1917—131no—
209#1864—131no—
210#1762—131no—
211C23×C13—22no—
212C23×C13—41no—
213C23×C13—41no—
214C23×C13—41no—
215C23×C13—41no—
216C23×C13—41no—
217C23×C13—41no—
218C23×C13C22×D411yescharacteristic
219Q8×C13—84no—
220D4×C13—22no—
221D4×C13—22no—
222D4×C13—41no—
223D4×C13—41no—
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×C13—22no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—84no—
251C2×C4×C13AGL(1,ℤ/8)12yes—
252C2×C4×C13C22×Q811yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C2×C4×C13H(5,𝔽2)11yescharacteristic
257C2×C4×C132−1+411yescharacteristic
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270#1055—22no—
271#1055—41no—
272#1055—41no—
273#1055—41no—
274C2×C4⋊Q8C2×D1311yescharacteristic
275C2×#125—131no—
276C2×C22⋊Q8—21no—
277C2×C4×D4C2×D1311yescharacteristic
278C2×#107—131no—
279C2×#106—131no—
280C2×#106—131no—
281C2×#106—131no—
282C2×C4⋊C8—131no—
283C2×#102—131no—
284C2×#102—131no—
285C2×#102—131no—
286C2×#102—131no—
287C2×#97—131no—
288#396—21no—
289#393—21no—
290#390C2×D1311yescharacteristic
291#390C2×D1311yescharacteristic
292#389—131no—
293#389—131no—
294#389—261no—
295#389C2×D1311yescharacteristic
296#389C2×D1311yescharacteristic
297#387—261no—
298#387—261no—
299#385—21no—
300C4×C4⋊C4—131no—
301C4×C4⋊C4—131no—
302C4×C4⋊C4—131no—
303C4×C4⋊C4—261no—
304C4×C4⋊C4C2×D1311yescharacteristic
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#336—131no—
314#336—131no—
315#336—131no—
316#336—131no—
317C22×C13—42no—
318C22×C13—42no—
319C22×C13—42no—
320C22×C13—81no—
321C22×C13—81no—
322C22×C13—81no—
323C22×C13—81no—
324C22×C13#52511yescharacteristic
325C22×C13#54611yescharacteristic
326C22×C13D4×Q811yescharacteristic
327C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
328C22×C13#57511yescharacteristic
329C22×C13#57711yescharacteristic
330C22×C13#57711yescharacteristic
331C4×C13—22no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—42no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13—81no—
339C4×C13—81no—
340C4×C13#53311yescharacteristic
341C4×C13#54211yescharacteristic
342C4×C13#55411yescharacteristic
343C4×C13#55611yescharacteristic
344Dic13—42no—
345Dic13—42no—
346Dic13—42no—
347Dic13—81no—
348C22×Q8—21no—
349C22×D4C22×D1311yescharacteristic
350C23×C4—21no—
351C22×C8—131no—
352C22×C8—131no—
353C22×C8—131no—
354C22×C8—131no—
355C4⋊Q8—22no—
356C4⋊Q8—41no—
357#125—262no—
358#125—262no—
359C22⋊Q8—44no—
360C4×D4—22no—
361C4×D4—41no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4C22⋊D1311yescharacteristic
374C2×C4⋊C4C22⋊D1311yescharacteristic
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C4⋊C4C22×D1311yescharacteristic
377C2×C4⋊C4C22×D1311yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C42—261no—
384C2×C42—261no—
385C2×C42—261no—
386C2×C42C22×D1311yescharacteristic
387C2×C42C22×D1311yescharacteristic
388C2×C42C22×D1311yescharacteristic
389#107—262no—
390#106—262no—
391#106—262no—
392#106—521no—
393C4⋊C8—521no—
394#102—134no—
395#102—262no—
396#102—262no—
397#102—521no—
398#97—521no—
399#95—21no—
400#95—21no—
401#95—261no—
402#95—261no—
403#95—261no—
404#95—261no—
405#95—261no—
406#95C22⋊D1311yescharacteristic
407#95C22⋊D1311yescharacteristic
408C2×C13—82no—
409C2×C13#246511yescharacteristic
410C2×C13#311511yescharacteristic
411C2×C13#312511yescharacteristic
412C2×C13#331011yescharacteristic
413C2×C13#332611yescharacteristic
414C2×C13#338411yescharacteristic
415C2×C13#338811yescharacteristic
416C24—21no—
417C2×Q8—42no—
418C2×Q8—42no—
419C2×Q8—81no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4Q8×D1312yes—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—81no—
432C22×C4—261no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4C2×C22⋊D1311yescharacteristic
437C22×C4C2×C22⋊D1311yescharacteristic
438C22×C4C2×C22⋊D1311yescharacteristic
439C22×C4C2×C22⋊D1311yescharacteristic
440C22×C4C2×C22⋊D1311yescharacteristic
441C22×C4C2×C22⋊D1311yescharacteristic
442C22×C4C23×D1311yescharacteristic
443C2×C8—132no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—261no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—41no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—132no—
466C4⋊C4—132no—
467C4⋊C4—132no—
468C4⋊C4—264no—
469C4⋊C4—264no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—522no—
476C4⋊C4—1041no—
477C4⋊C4#612912yes—
478C22⋊C4—42no—
479C22⋊C4—42no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—81no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—522no—
490C42—1041no—
491C42—1041no—
492C13#2702611yescharacteristic, complemented, Sylow
493C23—22no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23C22×C22⋊D1311yescharacteristic
501Q8—84no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—84no—
533C2×C4—262no—
534C2×C4—262no—
535C2×C4—262no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4#8818612yes—
546C2×C4C2×#612911yescharacteristic
547C2×C4#8825111yescharacteristic
548C2×C4C2×Q8×D1311yescharacteristic
549C2×C4#8825411yescharacteristic
550C2×C4#41×D1311yescharacteristic
551C2×C4#41×D1311yescharacteristic
552C8—262no—
553C8—521no—
554C8—521no—
555C8—521no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22C2×#8818611yescharacteristic
564C22#1171951111yescharacteristic
565C22Q8×C22⋊D1311yescharacteristic
566C22#1171952711yescharacteristic
567C22#1171953311yescharacteristic
568C22#1171954111yescharacteristic
569C22#1171954211yescharacteristic
570C4—22no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—42no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—522no—
580C4—522no—
581C4—522no—
582C4—1041no—
583C4#1171932711yescharacteristic
584C4#1171934111yescharacteristic
585C4#1171934511yescharacteristic
586C4#1171934611yescharacteristic
587C2—82no—
588C2#1311885311yescharacteristic
589C2#1312498111yescharacteristic
590C2#1312510711yescharacteristic
591C2#1312685711yescharacteristic
592C2#1312708911yescharacteristic
593C2#1312773111yescharacteristic
594C2#1312778111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2452C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenter#2452D13
hypocenterC13#27026
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2452

Complements

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

NH ≅ G/Ntype
1. #13117930C2semidirect
3. #13116174C2semidirect
4. #13116166C2semidirect
6. #13115789C2semidirect
7. #13115571C2semidirect
10. #13115418C2semidirect
11. #13115418C2semidirect
12. #13115402C2semidirect
107. #88072Q8semidirect
492. C13#27026semidirect

Maximal subgroups

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

subgroupindex
#131179302
#131162102
#131161742
#131161662
#131159822
#131157892
#131155712
#131154602
#131154532
#131154182
#131154022
#131150972
#131146612
C13×#24522
#2702613