Finite Group Databasebeta

← #14813251

Subgroups — #14813251

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071527C211yesmaximal, characteristic
2#13070183C211yesmaximal, characteristic, complemented
3#13070183C211yesmaximal, characteristic, complemented
4#13070118C211yesmaximal, characteristic, complemented
5#13070107C211yesmaximal, characteristic, complemented
6#13069384C211yesmaximal, characteristic, complemented
7#13069340C211yesmaximal, characteristic, complemented
8#13068876C211yesmaximal, characteristic
9#13068862C211yesmaximal, characteristic
10#13068751C211yesmaximal, characteristic, complemented
11#13068623C211yesmaximal, characteristic
12#13068623C211yesmaximal, characteristic
13#13068613C211yesmaximal, characteristic
14#13068444C211yesmaximal, characteristic
15C11×#2571C211yesmaximal, characteristic, complemented
16C2×C4×D44C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C11×#400—21no—
20C11×#400—21no—
21C11×#389—21no—
22C11×#389C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#384C2211yescharacteristic
25C11×#382—21no—
26C11×#382C2211yescharacteristic
27C11×#382C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30#10622602—21no—
31#10622602—21no—
32C2×#66873C2211yescharacteristic
33C2×#66873C2211yescharacteristic
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38#10622549C2211yescharacteristic
39#10622541C2211yescharacteristic
40#10622541C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622280—21no—
46D11×#95—21no—
47#10622167C2211yescharacteristic
48#10622167C2211yescharacteristic
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C4×D44—22no—
90C4×D44—22no—
91C4×D44—22no—
92C4×D44—41no—
93C4×D44—41no—
94C4×D44Q814yes—
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—
108#66873—22no—
109#66873—22no—
110#66873—22no—
111#66873—22no—
112#66872—41no—
113#66871—41no—
114C4⋊(C11⋊C8)—22no—
115C4⋊(C11⋊C8)—41no—
116C4⋊(C11⋊C8)—41no—
117#66867—22no—
118#26125—111nomaximal, Sylow
119C23×D11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44C2×Q812yes—
138C2×D44#4112yes—
139C2×D44#4112yes—
140C2×C4×D11—24no—
141C2×C4×D11—42no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C4×D11—81no—
146C2×C4×D11—81no—
147C2×C4×D11—81no—
148C2×C4×D11—81no—
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—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—81no—
161C11×C4⋊C4—81no—
162C11×C4⋊C4—81no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—42no—
168C42×C11C2×Q812yes—
169C42×C11#4112yes—
170(C2×D11)⋊C4—24no—
171(C2×D11)⋊C4—42no—
172(C2×D11)⋊C4—42no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11C2×Q812yes—
179Dic11⋊C4—81no—
180Dic11⋊C4—81no—
181C2×C11⋊C8—21no—
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—21no—
193#2571D1111yescharacteristic, complemented
194#2349—111no—
195#2101—111no—
196#2101—111no—
197#2088—111no—
198#2086—111no—
199#1949—111no—
200#1940—111no—
201#1864—111no—
202#1862—111no—
203#1836—111no—
204#1804—111no—
205#1804—111no—
206#1802—111no—
207#1762—111no—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
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×C11C22⋊Q812yes—
245C2×C4×C11C22⋊Q812yes—
246C2×C4×C11C22×Q811yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×Dic11—22no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261D44—22no—
262D44—22no—
263D44—22no—
264D44#12514yes—
265C4×D11—84no—
266C4×D11—84no—
267C4×D11—84no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C2×C4×D4—111no—
273C2×C4×D4—111no—
274C2×C4×D4—111no—
275C2×#107—111no—
276C2×#106—111no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8—111no—
279C2×C4⋊C8—111no—
280C2×#102—111no—
281C2×#102—111no—
282C2×#102—111no—
283C2×#102—111no—
284C2×#97—111no—
285#400—21no—
286#400—21no—
287#389—21no—
288#389—111no—
289#389—111no—
290#389C2×D1111yescharacteristic
291#389C2×D1111yescharacteristic
292#385—221no—
293#385—221no—
294#384C2×D1111yescharacteristic
295#382—21no—
296#382—111no—
297#382C2×D1111yescharacteristic
298#382C2×D1111yescharacteristic
299#380—221no—
300C4×C4⋊C4C2×D1111yescharacteristic
301C4×C4⋊C4C2×D1111yescharacteristic
302C2×#95—221no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#336—111no—
314#336—111no—
315C22×C11C2×C22⋊Q811yescharacteristic
316C22×C11#54611yescharacteristic
317C22×C11#54811yescharacteristic
318C22×C11#57511yescharacteristic
319C22×C11#57511yescharacteristic
320C22×C11#57611yescharacteristic
321C22×C11#57711yescharacteristic
322C2×D11—24no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—42no—
328C2×D11—42no—
329C4×C11—22no—
330C4×C11—22no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11C2×#12511yescharacteristic
340C4×C11#54411yescharacteristic
341C4×C11#55211yescharacteristic
342C4×C11#55311yescharacteristic
343Dic11—42no—
344Dic11—81no—
345Dic11—81no—
346C22×D4—111no—
347C23×C4—221no—
348C23×C4—221no—
349C23×C4—221no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—111no—
354C4×D4—114no—
355C4×D4—222no—
356C4×D4—222no—
357C4×D4—222no—
358C4×D4—441no—
359C4×D4—441no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4C22⋊D1111yescharacteristic
370C2×C4⋊C4C22⋊D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C42—21no—
379C2×C42C22×D1111yescharacteristic
380C2×C42C22×D1111yescharacteristic
381C2×C42C22×D1111yescharacteristic
382#107—441no—
383#106—441no—
384C4⋊C8—222no—
385C4⋊C8—441no—
386C4⋊C8—441no—
387#102—222no—
388#102—222no—
389#102—222no—
390#102—222no—
391#97—222no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95C22⋊D1111yescharacteristic
404#95C22⋊D1111yescharacteristic
405C2×C11#244211yescharacteristic
406C2×C11#308011yescharacteristic
407C2×C11#308111yescharacteristic
408C2×C11#331111yescharacteristic
409C2×C11#331911yescharacteristic
410C2×C11#337011yescharacteristic
411C2×C11#337611yescharacteristic
412D11—44no—
413C24—221no—
414C2×D4—112no—
415C2×D4—112no—
416C2×D4—112no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—221no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—221no—
425C22×C4—224no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—442no—
429C22×C4—442no—
430C22×C4—442no—
431C22×C4—442no—
432C22×C4—881no—
433C22×C4—881no—
434C22×C4—881no—
435C22×C4—881no—
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—42no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4—112no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—881no—
476C4⋊C4—881no—
477C22⋊C4—224no—
478C22⋊C4—442no—
479C22⋊C4—442no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—42no—
485C42Q8×D1112yes—
486C42#434312yes—
487C11#2612511yescharacteristic, complemented, Sylow
488C23—222no—
489C23—222no—
490C23—222no—
491C23—441no—
492C23—441no—
493C23—441no—
494C23—441no—
495C23C22×C22⋊D1111yescharacteristic
496D4—114no—
497D4—222no—
498D4—222no—
499D4—222no—
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—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
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—222no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—884no—
538C2×C4—884no—
539C2×C4—884no—
540C2×C4#6699912yes—
541C2×C4#6699912yes—
542C2×C4C2×Q8×D1111yescharacteristic
543C2×C4C2×#434311yescharacteristic
544C2×C4#41×D1111yescharacteristic
545C2×C4#41×D1111yescharacteristic
546C2×C4#6704211yescharacteristic
547C2×C4#6704311yescharacteristic
548C8—441no—
549C8—441no—
550C8—441no—
551C8—441no—
552C22—224no—
553C22—442no—
554C22—442no—
555C22—442no—
556C22—442no—
557C22—442no—
558C22—442no—
559C22C2×#6699911yescharacteristic
560C22#1062335311yescharacteristic
561C22#1062335311yescharacteristic
562C22#1062336011yescharacteristic
563C22#1062336211yescharacteristic
564C22#1062336611yescharacteristic
565C22#1062336811yescharacteristic
566C4—22no—
567C4—22no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—442no—
577C4—881no—
578C4—881no—
579C4D11×#12511yescharacteristic
580C4#1062322011yescharacteristic
581C4#1062322511yescharacteristic
582C4#1062322611yescharacteristic
583C2—444no—
584C2#1307233611yescharacteristic
585C2#1307843411yescharacteristic
586C2#1307844111yescharacteristic
587C2#1308064611yescharacteristic
588C2#1308076611yescharacteristic
589C2#1308136311yescharacteristic
590C2#1308143711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2571C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2571D11
hypocenterC11#26125
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2571

Complements

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

NH ≅ G/Ntype
2. #13070183C2semidirect
3. #13070183C2semidirect
4. #13070118C2semidirect
5. #13070107C2semidirect
6. #13069384C2semidirect
7. #13069340C2semidirect
10. #13068751C2semidirect
15. C11×#2571C2semidirect
193. #2571D11semidirect
487. C11#26125semidirect

Maximal subgroups

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

subgroupindex
#130715272
#130701832
#130701182
#130701072
#130693842
#130693402
#130688762
#130688622
#130687512
#130686232
#130686132
#130684442
C11×#25712
#2612511