Finite Group Databasebeta

← #14826499

Subgroups — #14826499

Order 2816.

700 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073027C211yesmaximal, characteristic
2#13070034C211yesmaximal, characteristic, complemented
3#13070011C211yesmaximal, characteristic, complemented
4#13069816C211yesmaximal, characteristic
5#13069809C211yesmaximal, characteristic
6#13069384C211yesmaximal, characteristic, complemented
7#13069346C211yesmaximal, characteristic, complemented
8#13069224C211yesmaximal, characteristic
9#13069198C211yesmaximal, characteristic, complemented
10#13069187C211yesmaximal, characteristic, complemented
11#13068870C211yesmaximal, characteristic, complemented
12#13068804C211yesmaximal, characteristic
13#13068702C211yesmaximal, characteristic
14C4×#66899C211yesmaximal, characteristic, complemented
15C11×#2360C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#391C2211yescharacteristic
20C11×#389—21no—
21C11×#389C2211yescharacteristic
22C11×#387—21no—
23C11×#385—21no—
24C4×C11×C4⋊C4C2211yescharacteristic
25C4×C11×C22⋊C4—21no—
26C4×C11×C22⋊C4C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31#10622825C2211yescharacteristic
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622565—21no—
40#10622557—21no—
41#10622549C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622271—21no—
48#10622264—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11—41no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—41no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C11×#95—21no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95D411yescharacteristic
100C11×#95D411yescharacteristic
101#66899—22no—
102#66899—22no—
103#66899—22no—
104#66899—41no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C22⋊(C11⋊C8)—22no—
113C22⋊(C11⋊C8)—41no—
114#66872—22no—
115#66871—22no—
116#66871—22no—
117#66871—41no—
118C4⋊(C11⋊C8)—22no—
119C4×C11⋊C8—41no—
120#27035—111nomaximal, Sylow
121C24×C11C2×D411yescharacteristic
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11#4112yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—81no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—81no—
159C11×C4⋊C4#4112yes—
160C11×C4⋊C4#4112yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—42no—
169C42×C11—81no—
170C22⋊Dic11—42no—
171C22⋊Dic11—81no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180Dic11⋊C4—81no—
181Dic11⋊C4—81no—
182C4×Dic11—42no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
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#4112yes—
195#2495—111no—
196#2360D1111yescharacteristic
197#2074—111no—
198#2068—111no—
199#2036—111no—
200#2035—111no—
201#1949—111no—
202#1942—111no—
203#1923—111no—
204#1920—111no—
205#1918—111no—
206#1863—111no—
207#1852—111no—
208#1823—111no—
209C4×#103—111no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11#13512yes—
217C23×C11C22×D411yescharacteristic
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—41no—
221Q8×C11—41no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
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—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—84no—
253C2×C4×C11#13712yes—
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C112−1+411yescharacteristic
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—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C11⋊C8—22no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C2×C22⋊Q8C2×D1111yescharacteristic
277C2×C4×Q8C2×D1111yescharacteristic
278C22×C4⋊C4C2×D1111yescharacteristic
279C2×#107—111no—
280C2×#107—111no—
281C2×#107—111no—
282C2×#106—111no—
283C2×C4⋊C8—111no—
284C2×#103—111no—
285C2×#103—111no—
286C2×#103—111no—
287C2×#103—111no—
288C2×C22⋊C8—111no—
289C2×C22⋊C8—111no—
290C2×C4×C8—111no—
291#400—221no—
292#397—221no—
293#391C2×D1111yescharacteristic
294#389—21no—
295#389—111no—
296#389—111no—
297#389C2×D1111yescharacteristic
298#388—221no—
299#387—21no—
300#385—21no—
301#383—221no—
302#382—111no—
303#380—111no—
304#380—111no—
305C4×C4⋊C4—111no—
306C4×C4⋊C4C2×D1111yescharacteristic
307C4×C22⋊C4—21no—
308C4×C22⋊C4C2×D1111yescharacteristic
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#336—111no—
318#336—111no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11#52511yescharacteristic
327C22×C11#54611yescharacteristic
328C22×C11#54711yescharacteristic
329C22×C11C2×#13511yescharacteristic
330C22×C11C2×#13711yescharacteristic
331C22×C11#57611yescharacteristic
332C22×C11#57811yescharacteristic
333C4×C11—22no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—42no—
337C4×C11—41no—
338C4×C11—42no—
339C4×C11—41no—
340C4×C11—42no—
341C4×C11—81no—
342C4×C11#52911yescharacteristic
343C4×C11#53911yescharacteristic
344C4×C11#55311yescharacteristic
345C4×C11#55611yescharacteristic
346Dic11—81no—
347Dic11—81no—
348Dic11—81no—
349Dic11—81no—
350C22×Q8C22×D1111yescharacteristic
351C23×C4—21no—
352C23×C4C22×D1111yescharacteristic
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—111no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C4×Q8—22no—
360C4×Q8—41no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—41no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
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—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4C22⋊D1111yescharacteristic
380C2×C22⋊C4C22⋊D1111yescharacteristic
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—221no—
384C2×C42C22×D1111yescharacteristic
385C2×C42C22×D1111yescharacteristic
386#107—222no—
387#107—222no—
388#107—441no—
389#106—222no—
390C4⋊C8—222no—
391#103—222no—
392#103—222no—
393#103—222no—
394#103—441no—
395C22⋊C8—222no—
396C22⋊C8—441no—
397C4×C8—441no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95C22⋊D1111yescharacteristic
410#95C22⋊D1111yescharacteristic
411C2×C11—42no—
412C2×C11#246611yescharacteristic
413C2×C11#310811yescharacteristic
414C2×C11#312411yescharacteristic
415C2×C11#329711yescharacteristic
416C2×C11#331211yescharacteristic
417C2×C11#333611yescharacteristic
418C2×C11#335711yescharacteristic
419C24C2×C22⋊D1111yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8#433912yes—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—81no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4C2×C22⋊D1111yescharacteristic
444C22×C4C2×C22⋊D1111yescharacteristic
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449C2×C8—112no—
450C2×C8—221no—
451C2×C8—221no—
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—
461C4⋊C4—24no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—81no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—881no—
478C4⋊C4—881no—
479C4⋊C4#433912yes—
480C4⋊C4#434112yes—
481C22⋊C4—24no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—442no—
485C22⋊C4—881no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—81no—
492C42—442no—
493C11#2703511yescharacteristic, complemented, Sylow
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23#6700312yes—
501C23C22×C22⋊D1111yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—41no—
505Q8—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—21no—
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—41no—
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—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—84no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
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#6699512yes—
550C2×C4C2×#433911yescharacteristic
551C2×C4C2×#433911yescharacteristic
552C2×C4C2×#434111yescharacteristic
553C2×C4#6703711yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C2×C4#6704311yescharacteristic
556C8—222no—
557C8—441no—
558C8—441no—
559C8—441no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22#1062332211yescharacteristic
568C22#1062333711yescharacteristic
569C22C2×#6699511yescharacteristic
570C22C2×#6700311yescharacteristic
571C22#1062335511yescharacteristic
572C22#1062336611yescharacteristic
573C22#1062336911yescharacteristic
574C4—22no—
575C4—41no—
576C4—42no—
577C4—42no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—881no—
584C4—881no—
585C4—881no—
586C4—881no—
587C4#1062306911yescharacteristic
588C4#1062307311yescharacteristic
589C4#1062308911yescharacteristic
590C4#1062309511yescharacteristic
591C2—42no—
592C2#1307264611yescharacteristic
593C2#1307869611yescharacteristic
594C2#1307887811yescharacteristic
595C2#1308046611yescharacteristic
596C2#1308066711yescharacteristic
597C2#1308097811yescharacteristic
598C2#1308124211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2360C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2360D11
hypocenterC11#27035
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. #13070034C2semidirect
3. #13070011C2semidirect
6. #13069384C2semidirect
7. #13069346C2semidirect
9. #13069198C2semidirect
10. #13069187C2semidirect
11. #13068870C2semidirect
14. C4×#66899C2semidirect
493. C11#27035semidirect

Maximal subgroups

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

subgroupindex
#130730272
#130700342
#130700112
#130698162
#130698092
#130693842
#130693462
#130692242
#130691982
#130691872
#130688702
#130688042
#130687022
C4×#668992
C11×#23602
#2703511