Finite Group Databasebeta

← #14816736

Subgroups — #14816736

Order 2816.

788 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622707C211yesmaximal, characteristic
2C2×C4×#4326C211yesmaximal, characteristic
3#13071536C211yesmaximal, characteristic
4#13070164C211yesmaximal, characteristic
5#13070097C211yesmaximal, characteristic
6#13069997C211yesmaximal, characteristic
7#13069941C211yesmaximal, characteristic
8#13069341C211yesmaximal, characteristic
9#13069175C211yesmaximal, characteristic
10#13068960C211yesmaximal, characteristic
11#13068960C211yesmaximal, characteristic
12#13068884C211yesmaximal, characteristic
13#13068883C211yesmaximal, characteristic
14#13068869C211yesmaximal, characteristic
15C11×#2451C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C11×#398—21no—
23C11×#395—21no—
24C11×#391—21no—
25C11×#391C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#387—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622707—24no—
35C4×#4326—24no—
36#10622585—21no—
37#10622585—21no—
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622549C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622263—21no—
52#10622262—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8—41no—
66C4×Q8×C11—22no—
67C4×Q8×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×#4326—22no—
82C2×#4326—22no—
83C2×#4326Q814yescomplemented
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C4×Dic22—22no—
100C4×Dic22—22no—
101C4×Dic22—22no—
102C4×Dic22—22no—
103C4×Dic22—41no—
104C4×Dic22—41no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
113#66899—22no—
114#66899—22no—
115#66899—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66874—22no—
121#66874—22no—
122#66874D414yes—
123#66872—22no—
124#66872—22no—
125#66872—22no—
126#66871—22no—
127#66871—41no—
128C4⋊(C11⋊C8)—22no—
129C4×C11⋊C8—22no—
130#26369—111nomaximal, Sylow
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—42no—
137C2×Q8×C11—42no—
138C2×Q8×C11—81no—
139C2×Q8×C11C2×Q812yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22C2×D412yes—
159C2×Dic22C2×Q812yes—
160C2×Dic22#4112yes—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—81no—
171C11×C4⋊C4—81no—
172C11×C4⋊C4C2×D412yes—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—42no—
180#4326—28no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11#4112yes—
187Dic11⋊C4—24no—
188Dic11⋊C4—42no—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192C4×Dic11—24no—
193C4×Dic11—42no—
194C4×Dic11—42no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C2×D412yes—
206C2×C11⋊C8C2×Q812yes—
207C2×#475—111no—
208C2×C4×Q16—111no—
209#2451D1111yescharacteristic
210#2351—111no—
211#2097—111no—
212#2085—111no—
213#2066—111no—
214#2057—111no—
215#1941—111no—
216#1916—111no—
217#1878—111no—
218#1878—111no—
219#1865—111no—
220#1865—111no—
221#1863—111no—
222C23×C11C22×D411yescharacteristic
223Q8×C11—22no—
224Q8×C11—22no—
225Q8×C11—41no—
226Q8×C11—41no—
227Q8×C11—84no—
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—22no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
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—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11#13512yes—
257C2×C4×C11#13712yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×Q811yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276Dic22—22no—
277Dic22—22no—
278Dic22—22no—
279Dic22C22⋊Q814yes—
280C11⋊C8—22no—
281C11⋊C8—22no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C22×Q16—111no—
285C2×C4⋊Q8C2×D1111yescharacteristic
286C2×C4×Q8—111no—
287C2×C4×Q8—111no—
288C2×C4×Q8—111no—
289C2×C4×Q8C2×D1111yescharacteristic
290#475—224no—
291C4×Q16—224no—
292C2×#107—111no—
293C2×#107—111no—
294C2×#106—111no—
295C2×#106—111no—
296C2×#106—111no—
297C2×C4⋊C8—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×#103—111no—
304C2×C4×C8—111no—
305#398—21no—
306#395—21no—
307#391—21no—
308#391C2×D1111yescharacteristic
309#391C2×D1111yescharacteristic
310#389—111no—
311#389—111no—
312#389—221no—
313#389—221no—
314#389C2×D1111yescharacteristic
315#389C2×D1111yescharacteristic
316#387—21no—
317#382—111no—
318#382—221no—
319C4×C4⋊C4—221no—
320C4×C4⋊C4C2×D1111yescharacteristic
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#336—111no—
326#336—111no—
327#336—111no—
328#336—111no—
329C22×C11#52511yescharacteristic
330C22×C11D4211yescharacteristic
331C22×C11D4×Q811yescharacteristic
332C22×C11C2×#13511yescharacteristic
333C22×C11C2×#13711yescharacteristic
334C22×C11#57711yescharacteristic
335C22×C11#57811yescharacteristic
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—42no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—42no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11C2×C22⋊Q811yescharacteristic
347C4×C11#53911yescharacteristic
348C4×C11#54711yescharacteristic
349C4×C11#55411yescharacteristic
350Dic11—24no—
351Dic11—42no—
352Dic11—81no—
353Dic11—81no—
354C22×Q8—21no—
355C22×Q8—111no—
356C22×Q8C22×D1111yescharacteristic
357C2×Q16—114no—
358C2×Q16—222no—
359C2×Q16—222no—
360C22×C8—111no—
361C22×C8—111no—
362C22×C8—111no—
363C22×C8—111no—
364C4⋊Q8—22no—
365C4⋊Q8—41no—
366C4×Q8—22no—
367C4×Q8—41no—
368C4×Q8—222no—
369C4×Q8—222no—
370C4×Q8—222no—
371C4×Q8—222no—
372C4×Q8—441no—
373C4×Q8—441no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22⋊D1111yescharacteristic
387C2×C4⋊C4C22⋊D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C42—21no—
392C2×C42—221no—
393C2×C42—221no—
394C2×C42—221no—
395C2×C42C22×D1111yescharacteristic
396C2×C42C22×D1111yescharacteristic
397C2×C42C22×D1111yescharacteristic
398#107—222no—
399#107—441no—
400#106—222no—
401#106—222no—
402#106—222no—
403C4⋊C8—222no—
404#103—114no—
405#103—222no—
406#103—222no—
407#103—222no—
408#103—222no—
409#103—441no—
410C4×C8—222no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95C22⋊D1111yescharacteristic
422#95C22⋊D1111yescharacteristic
423C2×C11#244911yescharacteristic
424C2×C11#310711yescharacteristic
425C2×C11#312111yescharacteristic
426C2×C11#327011yescharacteristic
427C2×C11#328211yescharacteristic
428C2×C11#338311yescharacteristic
429C2×C11#338711yescharacteristic
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—42no—
436C2×Q8—42no—
437C2×Q8—81no—
438C2×Q8—112no—
439C2×Q8—112no—
440C2×Q8—112no—
441C2×Q8—221no—
442C2×Q8—221no—
443C2×Q8—221no—
444C2×Q8Q8×D1112yes—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C23×D1111yescharacteristic
460Q16—228no—
461C2×C8—112no—
462C2×C8—112no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4—112no—
485C4⋊C4—224no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—442no—
492C4⋊C4—442no—
493C4⋊C4—442no—
494C4⋊C4—442no—
495C4⋊C4D4×D1112yes—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—42no—
503C42—224no—
504C42—442no—
505C42—442no—
506C11#2636911yescharacteristic, complemented, Sylow
507C23C22×C22⋊D1111yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512Q8—84no—
513Q8—114no—
514Q8—222no—
515Q8—222no—
516Q8—222no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4#6699512yes—
558C2×C4#6700312yes—
559C2×C4C2×D4×D1111yescharacteristic
560C2×C4#6703711yescharacteristic
561C2×C4C2×Q8×D1111yescharacteristic
562C2×C4#6704011yescharacteristic
563C2×C4#41×D1111yescharacteristic
564C2×C4#41×D1111yescharacteristic
565C8—222no—
566C8—222no—
567C8—441no—
568C8—441no—
569C22D4×C22⋊D1111yescharacteristic
570C22C2×#6699511yescharacteristic
571C22Q8×C22⋊D1111yescharacteristic
572C22C2×#6700311yescharacteristic
573C22#1062335911yescharacteristic
574C22#1062336711yescharacteristic
575C22#1062336911yescharacteristic
576C4—22no—
577C4—22no—
578C4—42no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—224no—
587C4—442no—
588C4—881no—
589C4—881no—
590C4D11×C22⋊Q811yescharacteristic
591C4#1062316211yescharacteristic
592C4#1062316711yescharacteristic
593C4#1062316911yescharacteristic
594C2#1307242211yescharacteristic
595C2#1307868111yescharacteristic
596C2#1307883911yescharacteristic
597C2#1308018711yescharacteristic
598C2#1308031911yescharacteristic
599C2#1308150311yescharacteristic
600C2#1308154411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2451C2
socle, prime radicalC23×C11C22×D4
hypercenter#2451D11
hypocenterC11#26369
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2451

Complements

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

NH ≅ G/Ntype
83. C2×#4326Q8semidirect
506. C11#26369semidirect

Maximal subgroups

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

subgroupindex
C2×#106227072
C2×C4×#43262
#130715362
#130701642
#130700972
#130699972
#130699412
#130693412
#130691752
#130689602
#130688842
#130688832
#130688692
C11×#24512
#2636911