Finite Group Databasebeta

← #14812936

Subgroups — #14812936

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073647C211yesmaximal, characteristic, complemented
2#13070149C211yesmaximal, characteristic
3#13070144C211yesmaximal, characteristic
4#13070004C211yesmaximal, characteristic
5#13069990C211yesmaximal, characteristic
6#13069382C211yesmaximal, characteristic, complemented
7#13069379C211yesmaximal, characteristic, complemented
8#13069374C211yesmaximal, characteristic, complemented
9#13069340C211yesmaximal, characteristic, complemented
10#13069208C211yesmaximal, characteristic, complemented
11#13069194C211yesmaximal, characteristic, complemented
12#13068785C211yesmaximal, characteristic, complemented
13#13068616C211yesmaximal, characteristic
14#13068441C211yesmaximal, characteristic
15C11×#2357C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66943—21no—
18C11×#390C2211yescharacteristic
19C11×#390C2211yescharacteristic
20C11×#388—21no—
21C11×#388—21no—
22C11×#382C2211yescharacteristic
23C11×#381—21no—
24C4×C11×C4⋊C4C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C22⋊C4—21no—
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622598—21no—
33C2×#66872C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622548C2211yescharacteristic
40#10622548C2211yescharacteristic
41#10622548C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49#10622274—21no—
50#10622274—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C4×D4×C11—22no—
62C4×D4×C11Q814yes—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4D411yescharacteristic
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×C42×C11—21no—
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊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
95#66943—44no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95D411yescharacteristic
101C11×#95D411yescharacteristic
102#66896—22no—
103#66896—22no—
104#66896—41no—
105#66896—41no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109#66872—22no—
110#66872—41no—
111#66872—41no—
112#66871—22no—
113#66871—41no—
114#66871—41no—
115C4⋊(C11⋊C8)—22no—
116C4⋊(C11⋊C8)—22no—
117C4⋊(C11⋊C8)—22no—
118#66867—22no—
119#26102—111nomaximal, Sylow
120C24×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11C2×Q812yes—
127C22×C4×C11—21no—
128C22×C4×C11—24no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—81no—
132C22×C4×C11—81no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4C2×Q812yes—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—42no—
154C11×C22⋊C4—42no—
155C11×C22⋊C4—81no—
156C11×C22⋊C4—81no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—81no—
162C42×C11—81no—
163C42×C11C2×Q812yes—
164C42×C11#4112yes—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—42no—
174C4⋊Dic11—42no—
175C4⋊Dic11—42no—
176C4⋊Dic11—81no—
177C4⋊Dic11—81no—
178C4⋊Dic11—81no—
179Dic11⋊C4—42no—
180Dic11⋊C4—42no—
181C4×Dic11—42no—
182C2×C11⋊C8—21no—
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#4112yes—
193C2×C11⋊C8#4112yes—
194#2552—111no—
195#2357D1111yescharacteristic
196#2094—111no—
197#2093—111no—
198#2067—111no—
199#2065—111no—
200#1949—111no—
201#1948—111no—
202#1947—111no—
203#1940—111no—
204#1921—111no—
205#1919—111no—
206#1847—111no—
207#1802—111no—
208#1762—111no—
209C23×C11—22no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11C22×D411yescharacteristic
217D4×C11—22no—
218D4×C11—22no—
219D4×C11—41no—
220D4×C11—41no—
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—22no—
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—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—84no—
245C2×C4×C11C22⋊Q812yes—
246C2×C4×C11C22⋊Q812yes—
247C2×C4×C11AGL(1,ℤ/8)12yes—
248C2×C4×C11#13712yes—
249C2×C4×C11C22×Q811yescharacteristic
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—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
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—
267C11⋊C8—22no—
268C11⋊C8—22no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C2×#125—221no—
272C2×C4×D4C2×D1111yescharacteristic
273C2×#107—111no—
274C2×#107—111no—
275C2×#107—111no—
276C2×#106—111no—
277C2×#106—111no—
278C2×#106—111no—
279C2×C4⋊C8—111no—
280C2×C4⋊C8—111no—
281C2×C4⋊C8—111no—
282C2×#102—111no—
283C2×#102—111no—
284C2×#102—111no—
285C2×#102—111no—
286C2×#97—111no—
287#398—221no—
288#398—221no—
289#390C2×D1111yescharacteristic
290#390C2×D1111yescharacteristic
291#389—111no—
292#389—111no—
293#389—221no—
294#388—21no—
295#388—21no—
296#384—111no—
297#384—111no—
298#384—111no—
299#382C2×D1111yescharacteristic
300#381—21no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4C2×D1111yescharacteristic
303C4×C4⋊C4C2×D1111yescharacteristic
304C4×C4⋊C4C2×D1111yescharacteristic
305C4×C22⋊C4—21no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#336—111no—
313#336—111no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11C2×C22⋊Q811yescharacteristic
322C22×C11#54711yescharacteristic
323C22×C11#55011yescharacteristic
324C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C11C2×#13711yescharacteristic
326C22×C11#57611yescharacteristic
327C22×C11#57711yescharacteristic
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—22no—
331C4×C11—22no—
332C4×C11—42no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11#53311yescharacteristic
338C4×C11#54411yescharacteristic
339C4×C11#55211yescharacteristic
340C4×C11#55311yescharacteristic
341Dic11—81no—
342Dic11—81no—
343Dic11—81no—
344Dic11—81no—
345C22×D4C22×D1111yescharacteristic
346C23×C4—21no—
347C22×C8—111no—
348C22×C8—111no—
349C22×C8—111no—
350C22×C8—111no—
351#125—444no—
352C4×D4—22no—
353C4×D4Dic2214yes—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4C22⋊D1111yescharacteristic
367C2×C4⋊C4C22⋊D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—221no—
379C2×C42C22×D1111yescharacteristic
380C2×C42C22×D1111yescharacteristic
381C2×C42C22×D1111yescharacteristic
382#107—222no—
383#107—441no—
384#107—441no—
385#106—222no—
386#106—441no—
387#106—441no—
388C4⋊C8—222no—
389C4⋊C8—222no—
390C4⋊C8—222no—
391#102—222no—
392#102—222no—
393#102—441no—
394#102—441no—
395#97—222no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95C22⋊D1111yescharacteristic
404#95C22⋊D1111yescharacteristic
405C2×C11—82no—
406C2×C11#244111yescharacteristic
407C2×C11#307911yescharacteristic
408C2×C11#308111yescharacteristic
409C2×C11#334511yescharacteristic
410C2×C11#334611yescharacteristic
411C2×C11#339911yescharacteristic
412C2×C11#340011yescharacteristic
413C24—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4C2×Dic2212yes—
420C22×C4—21no—
421C22×C4—24no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—81no—
425C22×C4—81no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C23×D1111yescharacteristic
437C2×C8—112no—
438C2×C8—112no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—442no—
465C4⋊C4—442no—
466C4⋊C4—442no—
467C4⋊C4—442no—
468C4⋊C4—442no—
469C4⋊C4—881no—
470C4⋊C4—881no—
471C4⋊C4—881no—
472C4⋊C4C2×Dic2212yes—
473C22⋊C4—24no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—81no—
477C22⋊C4—81no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—81no—
483C42—81no—
484C42—442no—
485C42C2×Dic2212yes—
486C42#433912yes—
487C11#2610211yescharacteristic, complemented, Sylow
488C23—22no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23C22×C22⋊D1111yescharacteristic
496D4—22no—
497D4—22no—
498D4—41no—
499D4—41no—
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—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—84no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4#6697712yes—
537C2×C4#6697712yes—
538C2×C4#6700212yes—
539C2×C4#6700412yes—
540C2×C4C22×Dic2211yescharacteristic
541C2×C4C2×#433911yescharacteristic
542C2×C4#41×D1111yescharacteristic
543C2×C4#41×D1111yescharacteristic
544C2×C4#6704211yescharacteristic
545C2×C4#6704311yescharacteristic
546C8—222no—
547C8—222no—
548C8—441no—
549C8—441no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×#6697711yescharacteristic
558C22C2×#6700211yescharacteristic
559C22C2×#6700411yescharacteristic
560C22#1062335511yescharacteristic
561C22#1062336511yescharacteristic
562C22#1062336611yescharacteristic
563C22#1062336711yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—22no—
568C4—41no—
569C4—42no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—881no—
574C4—881no—
575C4—881no—
576C4—881no—
577C4#1062304811yescharacteristic
578C4#1062305011yescharacteristic
579C4#1062306011yescharacteristic
580C4#1062306111yescharacteristic
581C2—82no—
582C2#1307232311yescharacteristic
583C2#1307843111yescharacteristic
584C2#1307844711yescharacteristic
585C2#1308108011yescharacteristic
586C2#1308110111yescharacteristic
587C2#1308165411yescharacteristic
588C2#1308166911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2357C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2357D11
hypocenterC11#26102
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
1. #13073647C2semidirect
6. #13069382C2semidirect
7. #13069379C2semidirect
8. #13069374C2semidirect
9. #13069340C2semidirect
10. #13069208C2semidirect
11. #13069194C2semidirect
12. #13068785C2semidirect
487. C11#26102semidirect

Maximal subgroups

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

subgroupindex
#130736472
#130701492
#130701442
#130700042
#130699902
#130693822
#130693792
#130693742
#130693402
#130692082
#130691942
#130687852
#130686162
#130684412
C11×#23572
#2610211