Finite Group Databasebeta

← #14811374

Subgroups — #14811374

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072318C211yesmaximal, characteristic
2#13071483C211yesmaximal, characteristic
3#13070175C211yesmaximal, characteristic, complemented
4#13070104C211yesmaximal, characteristic, complemented
5#13070104C211yesmaximal, characteristic, complemented
6#13069945C211yesmaximal, characteristic, complemented
7#13069567C211yesmaximal, characteristic, complemented
8#13069375C211yesmaximal, characteristic, complemented
9#13069188C211yesmaximal, characteristic, complemented
10#13069188C211yesmaximal, characteristic, complemented
11#13068806C211yesmaximal, characteristic
12#13068703C211yesmaximal, characteristic
13#13068645C211yesmaximal, characteristic
14C2×#10622189C211yesmaximal, characteristic
15C11×#1850C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66931—21no—
20C2×#66930—21no—
21C2×#66922C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26#10622825C2211yescharacteristic
27#10622825C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32#10622563—21no—
33#10622556—21no—
34#10622548C2211yescharacteristic
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37#10622541C2211yescharacteristic
38#10622541C2211yescharacteristic
39#10622541C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622274—21no—
42#10622269—21no—
43#10622266—21no—
44#10622266—21no—
45C11×#336C2211yescharacteristic
46C11×#336C2211yescharacteristic
47#10622189C2211yescharacteristic
48#10622189C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×Dic11—21no—
61C23×Dic11—21no—
62C22×Dic22—21no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11—41no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—41no—
84C2×C4⋊Dic11Q814yescomplemented
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99#66931—44no—
100#66930—44no—
101#66922—22no—
102#66922—41no—
103C11×C4⋊C8—22no—
104C11×C4⋊C8—41no—
105C11×C22⋊C8—22no—
106C11×#95D411yescharacteristic
107C11×#95D411yescharacteristic
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116#66882—22no—
117#66882—22no—
118#66882—41no—
119#66882—41no—
120#25988—111nomaximal, Sylow
121C24×C11C2×D411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×Q812yes—
132C22×C4×C11#4112yes—
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—24no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—42no—
144C22×Dic11—42no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C22×Dic11—81no—
148C2×Dic22—42no—
149C2×Dic22—42no—
150C2×Dic22—81no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—44no—
163C2×C8×C11#4112yes—
164C11×C22⋊C4—22no—
165C11×C22⋊C4D814yes—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C22⋊Dic11—42no—
171C22⋊Dic11—42no—
172C4⋊Dic11—24no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—42no—
187C4⋊Dic11—42no—
188C4⋊Dic11—42no—
189C4⋊Dic11—81no—
190C4⋊Dic11C2×Q812yes—
191C4⋊Dic11C2×Q812yes—
192C4⋊Dic11#4112yes—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197C4×Dic11—42no—
198C4×Dic11—42no—
199#2440—111no—
200#2344—111no—
201#2099—111no—
202#2086—111no—
203#2086—111no—
204#2057—111no—
205#1988—111no—
206#1947—111no—
207#1918—111no—
208#1918—111no—
209#1852—111no—
210#1850D1111yescharacteristic
211#1823—111no—
212#1808—111no—
213C2×#340—111no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11C22⋊Q812yes—
219C23×C11C2×D812yes—
220C23×C11#13712yes—
221C23×C11C22×D411yescharacteristic
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—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
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×C11C22⋊Q812yes—
239C2×C4×C11C2×D812yes—
240C2×C4×C11C2×D812yes—
241C2×C4×C11C22×Q811yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×C4×C112−1+411yescharacteristic
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—48no—
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—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—84no—
273Dic22—84no—
274C8×C11—22no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—41no—
278C23×C8C2×D1111yescharacteristic
279C2×C4⋊Q8—111no—
280C2×C22⋊Q8—221no—
281C2×#117—221no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4—111no—
284C2×#107—111no—
285C2×#107—111no—
286C2×#107—111no—
287C2×#107—111no—
288C2×C4⋊C8C2×D1111yescharacteristic
289C2×C4⋊C8C2×D1111yescharacteristic
290C2×C22⋊C8C2×D1111yescharacteristic
291#398—221no—
292#395—221no—
293#389—111no—
294#389—111no—
295#389—111no—
296#389—111no—
297#387—221no—
298#387—221no—
299#385—221no—
300#384—111no—
301#381—221no—
302#380—111no—
303#380—111no—
304C4×C4⋊C4—111no—
305C4×C4⋊C4—111no—
306C4×C22⋊C4C2×D1111yescharacteristic
307#340—111no—
308#340—111no—
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#340—111no—
318#340—111no—
319#336C2×D1111yescharacteristic
320#336C2×D1111yescharacteristic
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11#47414yes—
328C22×C11C2×C22⋊Q811yescharacteristic
329C22×C11#54611yescharacteristic
330C22×C11#54711yescharacteristic
331C22×C11C22×D811yescharacteristic
332C22×C11C2×#13711yescharacteristic
333C22×C11#57711yescharacteristic
334C22×C11#57811yescharacteristic
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11#53311yescharacteristic
341C4×C11#54411yescharacteristic
342C4×C11#55111yescharacteristic
343C4×C11#55211yescharacteristic
344Dic11—42no—
345Dic11—42no—
346Dic11—42no—
347Dic11—81no—
348Dic11—81no—
349Dic11—81no—
350Dic11—81no—
351Dic11—81no—
352C22×Q8—221no—
353C23×C4—221no—
354C23×C4—221no—
355C23×C4C22×D1111yescharacteristic
356C22×C8—22no—
357C22×C8—22no—
358C22×C8—41no—
359C22×C8C22×D1111yescharacteristic
360C22×C8C22×D1111yescharacteristic
361C22×C8C22×D1111yescharacteristic
362C22×C8C22×D1111yescharacteristic
363C4⋊Q8—222no—
364C4⋊Q8—441no—
365C22⋊Q8—444no—
366#117—444no—
367C2×C4⋊C4—114no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—441no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4D4411yescharacteristic
391C2×C22⋊C4D4411yescharacteristic
392C2×C42—221no—
393C2×C42—221no—
394C2×C42C22×D1111yescharacteristic
395C2×C42C22×D1111yescharacteristic
396#107—222no—
397#107—222no—
398#107—441no—
399#107—441no—
400C4⋊C8—22no—
401C4⋊C8—41no—
402C22⋊C8—22no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95D4411yescharacteristic
412#95D4411yescharacteristic
413C2×C11—24no—
414C2×C11#243811yescharacteristic
415C2×C11C2×#47411yescharacteristic
416C2×C11#308211yescharacteristic
417C2×C11#329411yescharacteristic
418C2×C11#331211yescharacteristic
419C2×C11#333411yescharacteristic
420C2×C11#334411yescharacteristic
421C24C2×D4411yescharacteristic
422C2×Q8—442no—
423C2×Q8—442no—
424C2×Q8—881no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—224no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—442no—
439C22×C4—442no—
440C22×C4—442no—
441C22×C4—442no—
442C22×C4—881no—
443C22×C4C2×D4411yescharacteristic
444C22×C4C2×D4411yescharacteristic
445C22×C4C2×D4411yescharacteristic
446C22×C4C2×D4411yescharacteristic
447C22×C4C2×D4411yescharacteristic
448C22×C4#434112yes—
449C22×C4Q8×D1112yes—
450C22×C4C23×D1111yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—44no—
463C2×C8#434112yes—
464C4⋊C4—112no—
465C4⋊C4—112no—
466C4⋊C4—112no—
467C4⋊C4—224no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—442no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4—442no—
487C4⋊C4—442no—
488C4⋊C4—881no—
489C22⋊C4—22no—
490C22⋊C4—442no—
491C22⋊C4—442no—
492C22⋊C4D8814yes—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—442no—
498C42—442no—
499C11#2598811yescharacteristic, complemented, Sylow
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23#6695012yes—
505C23C2×D8812yes—
506C23#6696212yes—
507C23C22×D4411yescharacteristic
508Q8—884no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—448no—
535C2×C4—441no—
536C2×C4—441no—
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—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—884no—
551C2×C4#6695012yes—
552C2×C4C2×D8812yes—
553C2×C4C2×D8812yes—
554C2×C4C2×#434111yescharacteristic
555C2×C4C2×#434111yescharacteristic
556C2×C4#6703711yescharacteristic
557C2×C4C2×Q8×D1111yescharacteristic
558C2×C4#41×D1111yescharacteristic
559C2×C4#6704311yescharacteristic
560C8—22no—
561C8—41no—
562C8—41no—
563C8—41no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22#1062245914yes—
571C22C2×#6695011yescharacteristic
572C22#1062308511yescharacteristic
573C22#1062308611yescharacteristic
574C22C22×D8811yescharacteristic
575C22C2×#6696211yescharacteristic
576C22#1062328211yescharacteristic
577C22#1062328411yescharacteristic
578C4—22no—
579C4—22no—
580C4—22no—
581C4—41no—
582C4—41no—
583C4—442no—
584C4—442no—
585C4—442no—
586C4—881no—
587C4—881no—
588C4—881no—
589C4—881no—
590C4—881no—
591C4#1062311811yescharacteristic
592C4#1062315311yescharacteristic
593C4#1062315411yescharacteristic
594C4#1062318111yescharacteristic
595C2—24no—
596C2#1307229011yescharacteristic
597C2C2×#1062245911yescharacteristic
598C2#1307845911yescharacteristic
599C2#1308043011yescharacteristic
600C2#1308066911yescharacteristic
601C2#1308096411yescharacteristic
602C2#1308107311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1850C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1850D11
hypocenterC11#25988
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
3. #13070175C2semidirect
4. #13070104C2semidirect
5. #13070104C2semidirect
6. #13069945C2semidirect
7. #13069567C2semidirect
8. #13069375C2semidirect
9. #13069188C2semidirect
10. #13069188C2semidirect
84. C2×C4⋊Dic11Q8semidirect
499. C11#25988semidirect

Maximal subgroups

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

subgroupindex
#130723182
#130714832
#130701752
#130701042
#130699452
#130695672
#130693752
#130691882
#130688062
#130687032
#130686452
C2×#106221892
C11×#18502
#2598811