Finite Group Databasebeta

← #14856989

Subgroups — #14856989

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071260C211yesmaximal, characteristic
2#13070118C211yesmaximal, characteristic, complemented
3#13070011C211yesmaximal, characteristic, complemented
4#13070001C211yesmaximal, characteristic
5#13069931C211yesmaximal, characteristic
6#13069473C211yesmaximal, characteristic
7#13069346C211yesmaximal, characteristic, complemented
8#13069312C211yesmaximal, characteristic
9#13069309C211yesmaximal, characteristic, complemented
10#13069254C211yesmaximal, characteristic, complemented
11#13069198C211yesmaximal, characteristic, complemented
12#13068953C211yesmaximal, characteristic
13#13068862C211yesmaximal, characteristic
14#13068473C211yesmaximal, characteristic, complemented
15C11×#2645C211yesmaximal, characteristic, complemented
16C22×#4325C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C11×#401—21no—
19C11×#400—21no—
20C11×#400—21no—
21C11×#400—21no—
22C11×#391C2211yescharacteristic
23C11×#391C2211yescharacteristic
24C11×#391C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#376C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66873C2211yescharacteristic
33C2×#66873C2211yescharacteristic
34C2×#66873C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38#10622552C2211yescharacteristic
39#10622552C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622282—21no—
48#10622282—21no—
49#10622280—21no—
50#10622277—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
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×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×#4325—22no—
72C2×#4325—22no—
73C2×#4325—41no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×C4×Dic11—21no—
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C4×D44—22no—
90C4×D44—22no—
91C11×#95—21no—
92C11×#95—21no—
93C11×#95—21no—
94C11×#95—21no—
95C11×#95—21no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95D411yescharacteristic
101C11×#95D411yescharacteristic
102C11×#95D411yescharacteristic
103C11×#95D411yescharacteristic
104#66899—22no—
105#66899—22no—
106#66899—41no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110#66873—22no—
111#66873—22no—
112#66873—41no—
113#66872—22no—
114#66871—22no—
115#66871—41no—
116C4⋊(C11⋊C8)—22no—
117C4⋊(C11⋊C8)—22no—
118#66867—41no—
119C4×C11⋊C8—41no—
120#29441—111nomaximal, Sylow
121C23×D11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×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×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44#4112yes—
148C2×C4×D11—24no—
149C2×C4×D11—81no—
150C2×C4×D11—81no—
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—81no—
158C11×C4⋊C4—81no—
159C11×C4⋊C4—81no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166#4325—44no—
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4—81no—
169(C2×D11)⋊C4—81no—
170(C2×D11)⋊C4—81no—
171(C2×D11)⋊C4—81no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11#4112yes—
178Dic11⋊C4—81no—
179Dic11⋊C4—81no—
180C4×Dic11—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#4112yes—
192C2×C11⋊C8#4112yes—
193#2645D1111yescharacteristic, complemented
194#2319—111no—
195#2088—111no—
196#2068—111no—
197#2067—111no—
198#2055—111no—
199#1968—111no—
200#1942—111no—
201#1936—111no—
202#1935—111no—
203#1928—111no—
204#1920—111no—
205#1877—111no—
206#1862—111no—
207#1768—111no—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216Q8×C11—41no—
217Q8×C11—41no—
218Q8×C11—41no—
219Q8×C11—41no—
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—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
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—41no—
249C2×C4×C11—41no—
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×Dic11—22no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265D44—22no—
266D44—22no—
267D44—41no—
268D44—41no—
269C4×D11—84no—
270C11⋊C8—22no—
271C11⋊C8—22no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C22×SD16—111no—
275C2×C4×D4—111no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#106—111no—
279C2×C4⋊C8—111no—
280C2×C4⋊C8—111no—
281C2×#103—111no—
282C2×#103—111no—
283C2×#103—111no—
284C2×#102—111no—
285C2×#102—111no—
286C2×#102—111no—
287C2×#97—111no—
288C2×C4×C8—111no—
289#401—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#391C2×D1111yescharacteristic
294#391C2×D1111yescharacteristic
295#391C2×D1111yescharacteristic
296#390—111no—
297#390—111no—
298#389—111no—
299#389—111no—
300#389C2×D1111yescharacteristic
301#389C2×D1111yescharacteristic
302#389C2×D1111yescharacteristic
303#388—221no—
304#388—221no—
305#381—221no—
306#380—221no—
307C4×C4⋊C4—111no—
308#376C2×D1111yescharacteristic
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#336—111no—
316#336—111no—
317C22×C11#52511yescharacteristic
318C22×C11#53211yescharacteristic
319C22×C11#53711yescharacteristic
320C22×C11#57611yescharacteristic
321C22×C11#57711yescharacteristic
322C22×C11#57711yescharacteristic
323C22×C11#57811yescharacteristic
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11#55111yescharacteristic
342C4×C11#55211yescharacteristic
343C4×C11#55311yescharacteristic
344C4×C11#55611yescharacteristic
345Dic11—42no—
346Dic11—81no—
347Dic11—81no—
348C22×Q8C22×D1111yescharacteristic
349C22×D4—111no—
350C23×C4—221no—
351C2×SD16—222no—
352C2×SD16—222no—
353C2×SD16—441no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—111no—
357C22×C8—111no—
358C4×D4—222no—
359C4×D4—222no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C42—221no—
377C2×C42C22×D1111yescharacteristic
378C2×C42C22×D1111yescharacteristic
379C2×C42C22×D1111yescharacteristic
380#107—222no—
381#107—441no—
382#106—222no—
383C4⋊C8—222no—
384C4⋊C8—222no—
385#103—222no—
386#103—222no—
387#103—441no—
388#102—222no—
389#102—222no—
390#102—441no—
391#97—441no—
392C4×C8—441no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95C22⋊D1111yescharacteristic
406#95C22⋊D1111yescharacteristic
407#95C22⋊D1111yescharacteristic
408#95C22⋊D1111yescharacteristic
409C2×C11#260111yescharacteristic
410C2×C11#311811yescharacteristic
411C2×C11#312011yescharacteristic
412C2×C11#317411yescharacteristic
413C2×C11#317511yescharacteristic
414C2×C11#325711yescharacteristic
415C2×C11#325811yescharacteristic
416D11—82no—
417C24—221no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×D4—112no—
425C2×D4—221no—
426C2×D4—221no—
427C2×D4—221no—
428C2×D4—221no—
429C2×D4—221no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—224no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—881no—
439C22×C4—881no—
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C2×C22⋊D1111yescharacteristic
444C22×C4C2×C22⋊D1111yescharacteristic
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C23×D1111yescharacteristic
447SD16—444no—
448C2×C8—112no—
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—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
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—881no—
479C22⋊C4—881no—
480C22⋊C4—881no—
481C22⋊C4—881no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—881no—
489C11#2944111yescharacteristic, complemented, Sylow
490C23—222no—
491C23—441no—
492C23—441no—
493C23—441no—
494C23—441no—
495C23—441no—
496C23—441no—
497C23C22×C22⋊D1111yescharacteristic
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502D4—222no—
503D4—222no—
504D4—441no—
505D4—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—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
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—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—884no—
546C2×C4#41×D1111yescharacteristic
547C2×C4#41×D1111yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#41×D1111yescharacteristic
550C2×C4#6704211yescharacteristic
551C2×C4#6704311yescharacteristic
552C8—222no—
553C8—222no—
554C8—441no—
555C8—441no—
556C22—442no—
557C22—442no—
558C22—442no—
559C22—881no—
560C22—881no—
561C22—881no—
562C22—881no—
563C22#1062335911yescharacteristic
564C22#1062336311yescharacteristic
565C22#1062336411yescharacteristic
566C22#1062336611yescharacteristic
567C22#1062336811yescharacteristic
568C22#1062336811yescharacteristic
569C22#1062336911yescharacteristic
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—442no—
581C4—881no—
582C4—881no—
583C4#1062323311yescharacteristic
584C4#1062323611yescharacteristic
585C4#1062323911yescharacteristic
586C4#1062324011yescharacteristic
587C2—882no—
588C2#1307421511yescharacteristic
589C2#1307879411yescharacteristic
590C2#1307882411yescharacteristic
591C2#1307924511yescharacteristic
592C2#1307924911yescharacteristic
593C2#1308002711yescharacteristic
594C2#1308003611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2645C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2645D11
hypocenterC11#29441
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2645

Complements

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

NH ≅ G/Ntype
2. #13070118C2semidirect
3. #13070011C2semidirect
7. #13069346C2semidirect
9. #13069309C2semidirect
10. #13069254C2semidirect
11. #13069198C2semidirect
14. #13068473C2semidirect
15. C11×#2645C2semidirect
193. #2645D11semidirect
489. C11#29441semidirect

Maximal subgroups

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

subgroupindex
#130712602
#130701182
#130700112
#130700012
#130699312
#130694732
#130693462
#130693122
#130693092
#130692542
#130691982
#130689532
#130688622
#130684732
C11×#26452
#2944111