Finite Group Databasebeta

← #14826501

Subgroups — #14826501

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#13071619C211yesmaximal, characteristic
2#13070035C211yesmaximal, characteristic, complemented
3#13070008C211yesmaximal, characteristic, complemented
4#13069819C211yesmaximal, characteristic
5#13069812C211yesmaximal, characteristic
6#13069382C211yesmaximal, characteristic, complemented
7#13069346C211yesmaximal, characteristic, complemented
8#13069224C211yesmaximal, characteristic
9#13069201C211yesmaximal, characteristic, complemented
10#13069184C211yesmaximal, characteristic, complemented
11#13068869C211yesmaximal, characteristic, complemented
12#13068803C211yesmaximal, characteristic
13#13068700C211yesmaximal, characteristic
14C4×#66874C211yesmaximal, characteristic, complemented
15C11×#2495C211yesmaximal, characteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C11×#400—21no—
20C11×#397—21no—
21C11×#389C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C11×#388—21no—
24C11×#383—21no—
25C11×#382C2211yescharacteristic
26C11×#380C2211yescharacteristic
27C11×#380C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66874C2211yescharacteristic
33C2×#66874C2211yescharacteristic
34C2×#66874C2211yescharacteristic
35C2×#66874C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622559—21no—
41C22⋊C4×Dic11—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622268—21no—
48#10622260—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×Dic11—21no—
61C22×Dic22C2311yescharacteristic
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—41no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82#66977—22no—
83#66977—22no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C4×Dic22—22no—
94C4×Dic22—41no—
95C11×#95—21no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95D411yescharacteristic
103C11×#95D411yescharacteristic
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C22⋊(C11⋊C8)—22no—
109C22⋊(C11⋊C8)—41no—
110#66874—22no—
111#66874—22no—
112#66874—22no—
113#66874—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
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×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×C11C2411yescharacteristic
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C22×Dic11—81no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22#4112yes—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—81no—
160C11×C4⋊C4—81no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—42no—
164C11×C22⋊C4—81no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—42no—
170C22⋊Dic11—24no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—42no—
176C4⋊Dic11#4112yes—
177C4⋊Dic11#4112yes—
178Dic11⋊C4—24no—
179Dic11⋊C4—42no—
180Dic11⋊C4—81no—
181C4×Dic11—42no—
182C4×Dic11—81no—
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#2495D1111yescharacteristic
196#2360—111no—
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
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
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—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
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#13712yes—
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—84no—
268Dic22—22no—
269Dic22—22no—
270Dic22—41no—
271Dic22—41no—
272C11⋊C8—22no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C2×C22⋊Q8—111no—
277C2×C4×Q8—111no—
278C22×C4⋊C4—111no—
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—21no—
292#397—21no—
293#391—111no—
294#389—111no—
295#389—221no—
296#389C2×D1111yescharacteristic
297#389C2×D1111yescharacteristic
298#388—21no—
299#387—221no—
300#385—221no—
301#383—21no—
302#382C2×D1111yescharacteristic
303#380C2×D1111yescharacteristic
304#380C2×D1111yescharacteristic
305C4×C4⋊C4—111no—
306C4×C4⋊C4C2×D1111yescharacteristic
307C4×C22⋊C4—221no—
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—41no—
337C4×C11—41no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11#52911yescharacteristic
343C4×C11#53911yescharacteristic
344C4×C11#55311yescharacteristic
345C4×C11#55611yescharacteristic
346Dic11—42no—
347Dic11—42no—
348Dic11—42no—
349Dic11—81no—
350C22×Q8—111no—
351C23×C4—221no—
352C23×C4C22×D1111yescharacteristic
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—111no—
357C22⋊Q8—222no—
358C22⋊Q8—222no—
359C4×Q8—222no—
360C4×Q8—441no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—441no—
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4C22⋊D1111yescharacteristic
380C2×C22⋊C4C22⋊D1111yescharacteristic
381C2×C42—21no—
382C2×C42—221no—
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—21no—
403#95—21no—
404#95—21no—
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—112no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8—221no—
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—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—442no—
441C22×C4—442no—
442C22×C4—881no—
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—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—112no—
472C4⋊C4—112no—
473C4⋊C4—224no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—442no—
479C4⋊C4—442no—
480C4⋊C4—881no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—42no—
484C22⋊C4—81no—
485C22⋊C4—224no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—442no—
492C42—881no—
493C11#2703511yescharacteristic, complemented, Sylow
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23#6700312yes—
501C23C22×C22⋊D1111yescharacteristic
502Q8—222no—
503Q8—222no—
504Q8—441no—
505Q8—441no—
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—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
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—222no—
537C2×C4—222no—
538C2×C4—222no—
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—884no—
549C2×C4#6700412yes—
550C2×C4#41×D1111yescharacteristic
551C2×C4#41×D1111yescharacteristic
552C2×C4#41×D1111yescharacteristic
553C2×C4#41×D1111yescharacteristic
554C2×C4#6704211yescharacteristic
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—
567C22C2×#6700311yescharacteristic
568C22C2×#6700411yescharacteristic
569C22#1062335511yescharacteristic
570C22#1062335911yescharacteristic
571C22#1062336011yescharacteristic
572C22#1062336611yescharacteristic
573C22#1062336911yescharacteristic
574C4—22no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—442no—
584C4—442no—
585C4—442no—
586C4—881no—
587C4#1062323311yescharacteristic
588C4#1062323711yescharacteristic
589C4#1062323811yescharacteristic
590C4#1062324011yescharacteristic
591C2—42no—
592C2#1307264811yescharacteristic
593C2#1307869211yescharacteristic
594C2#1307887211yescharacteristic
595C2#1308046011yescharacteristic
596C2#1308066111yescharacteristic
597C2#1308097811yescharacteristic
598C2#1308123611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2495C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2495D11
hypocenterC11#27035
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2495

Complements

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

NH ≅ G/Ntype
2. #13070035C2semidirect
3. #13070008C2semidirect
6. #13069382C2semidirect
7. #13069346C2semidirect
9. #13069201C2semidirect
10. #13069184C2semidirect
11. #13068869C2semidirect
14. C4×#66874C2semidirect
493. C11#27035semidirect

Maximal subgroups

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

subgroupindex
#130716192
#130700352
#130700082
#130698192
#130698122
#130693822
#130693462
#130692242
#130692012
#130691842
#130688692
#130688032
#130687002
C4×#668742
C11×#24952
#2703511