Finite Group Databasebeta

← #14856899

Subgroups — #14856899

Order 2816.

724 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071093C211yesmaximal, characteristic, complemented
2#13070118C211yesmaximal, characteristic, complemented
3#13070008C211yesmaximal, characteristic, complemented
4#13070004C211yesmaximal, characteristic
5#13069933C211yesmaximal, characteristic
6#13069469C211yesmaximal, characteristic
7#13069346C211yesmaximal, characteristic, complemented
8#13069302C211yesmaximal, characteristic
9#13069291C211yesmaximal, characteristic, complemented
10#13069233C211yesmaximal, characteristic
11#13069198C211yesmaximal, characteristic, complemented
12#13068974C211yesmaximal, characteristic
13#13068869C211yesmaximal, characteristic, complemented
14C4×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
15C11×#2860C211yesmaximal, characteristic
16C2×C11×#126—21no—
17C22×#4324C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C11×#390C2211yescharacteristic
20C11×#390C2211yescharacteristic
21C11×#390C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#388—21no—
26C11×#388—21no—
27C11×#388—21no—
28C43×C11C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66874C2211yescharacteristic
33C2×#66874C2211yescharacteristic
34C2×#66874C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39#10622546—21no—
40#10622546—21no—
41#10622545—21no—
42C4×Dic11⋊C4—21no—
43#10622542C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×C4×C11⋊C8C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C22×Dic22C2311yescharacteristic
61C11×#126—44no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11D411yescharacteristic
75C2×C42×C11D411yescharacteristic
76C2×C42×C11D411yescharacteristic
77C2×C42×C11D411yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×#4324—22no—
82C2×#4324—22no—
83C2×#4324—41no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C4×Dic22—22no—
97C4×Dic22—22no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101#66896—22no—
102#66896—22no—
103#66896—41no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111#66874—22no—
112#66874—22no—
113#66874—41no—
114#66872—22no—
115#66871—22no—
116#66871—41no—
117C4⋊(C11⋊C8)—22no—
118C4⋊(C11⋊C8)—22no—
119C4×C11⋊C8—41no—
120C4×C11⋊C8—41no—
121#29435—111nomaximal, Sylow
122C24×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22#4112yes—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4—42no—
158C11×C22⋊C4—42no—
159C11×C22⋊C4—42no—
160C11×C22⋊C4—42no—
161C11×C22⋊C4—42no—
162C11×C22⋊C4—42no—
163C11×C22⋊C4—42no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174#4324—44no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11#4112yes—
181Dic11⋊C4—24no—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184C4×Dic11—24no—
185C4×Dic11—42no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8#4112yes—
197C2×C11⋊C8#4112yes—
198#2860D1111yescharacteristic
199#2295—111no—
200#2088—111no—
201#2068—111no—
202#2067—111no—
203#2055—111no—
204#1968—111no—
205#1942—111no—
206#1934—111no—
207#1933—111no—
208#1925—111no—
209#1920—111no—
210#1880—111no—
211#1863—111no—
212C4×C4⋊C8—111no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11C22×D411yescharacteristic
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—41no—
224D4×C11—41no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11#13512yes—
249C2×C4×C11#13512yes—
250C2×C4×C11AGL(1,ℤ/8)12yes—
251C2×C4×C11#13712yes—
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C112−1+411yescharacteristic
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270Dic22—22no—
271Dic22—22no—
272Dic22—41no—
273Dic22—41no—
274C11⋊C8—22no—
275C11⋊C8—22no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C22×SD16—111no—
279C2×#126—21no—
280C2×C4×Q8—111no—
281C2×#107—111no—
282C2×#107—111no—
283C2×#106—111no—
284C2×C4⋊C8—111no—
285C2×C4⋊C8—111no—
286C2×#103—111no—
287C2×#103—111no—
288C2×#103—111no—
289C2×#102—111no—
290C2×#102—111no—
291C2×#102—111no—
292C2×C4×C8—111no—
293C2×C4×C8—111no—
294#391—111no—
295#391—111no—
296#390C2×D1111yescharacteristic
297#390C2×D1111yescharacteristic
298#390C2×D1111yescharacteristic
299#389—111no—
300#389—111no—
301#389C2×D1111yescharacteristic
302#389C2×D1111yescharacteristic
303#389C2×D1111yescharacteristic
304#388—21no—
305#388—21no—
306#388—21no—
307#387—221no—
308#387—221no—
309C4×C4⋊C4—111no—
310C4×C4⋊C4—221no—
311#376—221no—
312C43C2×D1111yescharacteristic
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#336—111no—
320#336—111no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11#52511yescharacteristic
329C22×C11#53211yescharacteristic
330C22×C11#53711yescharacteristic
331C22×C11C2×#13511yescharacteristic
332C22×C11C2×#13511yescharacteristic
333C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C11C2×#13711yescharacteristic
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—22no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11#55111yescharacteristic
345C4×C11#55211yescharacteristic
346C4×C11#55311yescharacteristic
347C4×C11#55611yescharacteristic
348Dic11—42no—
349Dic11—42no—
350Dic11—81no—
351Dic11—81no—
352C22×Q8—111no—
353C22×D4C22×D1111yescharacteristic
354C2×SD16—222no—
355C2×SD16—222no—
356C2×SD16—441no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—111no—
360C22×C8—111no—
361#126—44no—
362C4×Q8—222no—
363C4×Q8—222no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C42—221no—
383C2×C42—221no—
384C2×C42C22⋊D1111yescharacteristic
385C2×C42C22⋊D1111yescharacteristic
386C2×C42C22⋊D1111yescharacteristic
387C2×C42C22⋊D1111yescharacteristic
388C2×C42C22×D1111yescharacteristic
389C2×C42C22×D1111yescharacteristic
390C2×C42C22×D1111yescharacteristic
391#107—222no—
392#107—441no—
393#106—222no—
394C4⋊C8—222no—
395C4⋊C8—222no—
396#103—222no—
397#103—222no—
398#103—441no—
399#102—222no—
400#102—222no—
401#102—441no—
402C4×C8—441no—
403C4×C8—441no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414C2×C11—161no—
415C2×C11#260111yescharacteristic
416C2×C11#310611yescharacteristic
417C2×C11#310811yescharacteristic
418C2×C11#316811yescharacteristic
419C2×C11#318211yescharacteristic
420C2×C11#324711yescharacteristic
421C2×C11#324811yescharacteristic
422C24—21no—
423C2×Q8—112no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×Q8—221no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C2×C22⋊D1111yescharacteristic
444C22×C4C2×C22⋊D1111yescharacteristic
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449SD16—444no—
450C2×C8—112no—
451C2×C8—112no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—112no—
472C4⋊C4—224no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—442no—
479C4⋊C4—442no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C42—22no—
487C42—22no—
488C42—22no—
489C42—22no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—224no—
497C42—442no—
498C11#2943511yescharacteristic, complemented, Sylow
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23C22×C22⋊D1111yescharacteristic
507Q8—222no—
508Q8—222no—
509Q8—441no—
510Q8—441no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
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—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4#6698512yes—
551C2×C4#6700312yes—
552C2×C4#6700312yes—
553C2×C4#6700412yes—
554C2×C4#41×D1111yescharacteristic
555C2×C4#41×D1111yescharacteristic
556C2×C4#41×D1111yescharacteristic
557C2×C4#41×D1111yescharacteristic
558C2×C4#6704211yescharacteristic
559C2×C4#6704311yescharacteristic
560C8—222no—
561C8—222no—
562C8—441no—
563C8—441no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22C2×#6698511yescharacteristic
572C22C2×#6700311yescharacteristic
573C22C2×#6700311yescharacteristic
574C22C2×#6700411yescharacteristic
575C22#1062335911yescharacteristic
576C22#1062336311yescharacteristic
577C22#1062336411yescharacteristic
578C4—22no—
579C4—22no—
580C4—22no—
581C4—22no—
582C4—41no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—442no—
588C4—442no—
589C4—881no—
590C4—881no—
591C4#1062323311yescharacteristic
592C4#1062323611yescharacteristic
593C4#1062323911yescharacteristic
594C4#1062324011yescharacteristic
595C2—161no—
596C2#1307421511yescharacteristic
597C2#1307867011yescharacteristic
598C2#1307869211yescharacteristic
599C2#1307918011yescharacteristic
600C2#1307933011yescharacteristic
601C2#1307993611yescharacteristic
602C2#1307995311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2860C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2860D11
hypocenterC11#29435
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #2860

Complements

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

NH ≅ G/Ntype
1. #13071093C2semidirect
2. #13070118C2semidirect
3. #13070008C2semidirect
7. #13069346C2semidirect
9. #13069291C2semidirect
11. #13069198C2semidirect
13. #13068869C2semidirect
14. C4×C4⋊(C11⋊C8)C2semidirect
498. C11#29435semidirect

Maximal subgroups

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

subgroupindex
#130710932
#130701182
#130700082
#130700042
#130699332
#130694692
#130693462
#130693022
#130692912
#130692332
#130691982
#130689742
#130688692
C4×C4⋊(C11⋊C8)2
C11×#28602
#2943511