Finite Group Databasebeta

← #14764198

Subgroups — #14764198

Order 2816.

754 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
1C2×#10622452C211yesmaximal, characteristic
2#13071226C211yesmaximal, characteristic
3#13071221C211yesmaximal, characteristic
4#13069385C211yesmaximal, characteristic, complemented
5#13069382C211yesmaximal, characteristic, complemented
6#13069381C211yesmaximal, characteristic, complemented
7#13069375C211yesmaximal, characteristic, complemented
8#13069374C211yesmaximal, characteristic, complemented
9#13069373C211yesmaximal, characteristic, complemented
10#13069373C211yesmaximal, characteristic, complemented
11#13068648C211yesmaximal, characteristic
12#13068646C211yesmaximal, characteristic
13#13068644C211yesmaximal, characteristic
14#13068642C211yesmaximal, characteristic
15C11×#1949C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66925C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C11×#382C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66882C2211yescharacteristic
25C2×#66882C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28#10622600C2211yescharacteristic
29#10622600C2211yescharacteristic
30#10622600C2211yescharacteristic
31#10622600C2211yescharacteristic
32#10622590C2211yescharacteristic
33#10622589C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622553—21no—
41#10622548C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622546—21no—
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622452C418yescomplemented
46#10622283—21no—
47#10622283—21no—
48#10622282—21no—
49#10622268—21no—
50#10622268—21no—
51#10622265—21no—
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×C4×D11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4D411yescharacteristic
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4D411yescharacteristic
84C2×Dic11⋊C4D411yescharacteristic
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C2×#4313—41no—
92C2×#4313—41no—
93C2×#4313C2×C414yes—
94C2×C8×D11—41no—
95C2×C8×D11—41no—
96C2×C8×D11C2×C414yes—
97#66925C2×C414yes—
98#66925Q814yes—
99C11×#107—41no—
100C11×#106—41no—
101C11×C4⋊C8C2×C414yes—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114#66882—41no—
115#66882—41no—
116Dic11⋊C8C2×C414yes—
117Dic11⋊C8C2×C414yes—
118#66872—41no—
119#66871—41no—
120#66871—41no—
121#66871—41no—
122C4⋊(C11⋊C8)C2×C414yes—
123#21968—111nomaximal, Sylow
124C23×D11C2×D411yescharacteristic
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11C22×C412yes—
144C2×C4×D11C2×Q812yes—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11C22×C412yes—
150C2×C8×C11C22×C412yes—
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—21no—
158C11×C4⋊C4—21no—
159C42×C11—81no—
160C42×C11C22×C412yes—
161C42×C11C2×Q812yes—
162(C2×D11)⋊C4—81no—
163(C2×D11)⋊C4—81no—
164(C2×D11)⋊C4—81no—
165(C2×D11)⋊C4—81no—
166(C2×D11)⋊C4C4⋊C414yes—
167(C2×D11)⋊C4C4⋊C414yes—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—81no—
177C4⋊Dic11—81no—
178Dic11⋊C4—81no—
179Dic11⋊C4—81no—
180Dic11⋊C4C4⋊C414yes—
181Dic11⋊C4C4⋊C414yes—
182C4×Dic11—81no—
183C4×Dic11—81no—
184C4×Dic11—81no—
185C4×Dic11C22×C412yes—
186C4×Dic11C2×Q812yes—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8C22×C412yes—
192C2×C11⋊C8C22×C412yes—
193#4313—44no—
194C8×D11—44no—
195C2×#424—111no—
196#2314—111no—
197#2314—111no—
198#1949—111no—
199#1949—111no—
200#1949—111no—
201#1949D1111yescharacteristic, complemented
202#1947—111no—
203#1947—111no—
204#1947—111no—
205#1947—111no—
206#1809—111no—
207#1809—111no—
208#1808—111no—
209#1808—111no—
210C23×C11C22×D411yescharacteristic
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11C2×C4⋊C412yes—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11C2×C4⋊C412yes—
235C2×C4×C11C2×C4⋊C412yes—
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C22×Q811yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C2×C4×C112−1+411yescharacteristic
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11C2×C4⋊C412yes—
261C2×Dic11C2×C4⋊C412yes—
262C2×Dic11C2×C4⋊C412yes—
263C4×D11—22no—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—22no—
267C8×C11—22no—
268C8×C11—22no—
269C11⋊C8—22no—
270C11⋊C8—22no—
271C22×M16—111no—
272C23×C8—111no—
273C2×#117—111no—
274C2×#107—111no—
275C2×#107—111no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#107—111no—
279C2×#107C2×D1111yescharacteristic
280C2×#106—111no—
281C2×#106C2×D1111yescharacteristic
282#424—118no—
283C2×C4⋊C8—111no—
284C2×C4⋊C8—111no—
285C2×C4⋊C8—111no—
286C2×C4⋊C8C2×D1111yescharacteristic
287#388—221no—
288#388—221no—
289#388—221no—
290#388—221no—
291#387—221no—
292#387—221no—
293#387—221no—
294#387—221no—
295#384—111no—
296#384—111no—
297#382—111no—
298#382C2×D1111yescharacteristic
299#380—111no—
300#380—111no—
301#380—111no—
302#380—111no—
303C4×C4⋊C4—111no—
304C4×C4⋊C4—111no—
305C4×C4⋊C4—111no—
306C4×C4⋊C4C2×D1111yescharacteristic
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340C2×D1111yescharacteristic
314#340C2×D1111yescharacteristic
315C22×C11C22×C4⋊C411yescharacteristic
316C22×C11#53711yescharacteristic
317C22×C11#53711yescharacteristic
318C22×C11#57611yescharacteristic
319C22×C11#57611yescharacteristic
320C22×C11#57811yescharacteristic
321C22×C11#57811yescharacteristic
322C2×D11—22no—
323C2×D11—22no—
324C2×D11—22no—
325C2×D11—41no—
326C2×D11—41no—
327C2×D11—41no—
328C2×D11—41no—
329C4×C11—22no—
330C4×C11—22no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11#51811yescharacteristic
336C4×C11#51911yescharacteristic
337C4×C11#54411yescharacteristic
338C4×C11#54411yescharacteristic
339Dic11—22no—
340Dic11—22no—
341Dic11—22no—
342Dic11—81no—
343Dic11—81no—
344Dic11—81no—
345Dic11—81no—
346C23×C4—111no—
347C2×M16—114no—
348C2×M16—441no—
349C2×M16—441no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—114no—
353C22×C8—441no—
354C22×C8—441no—
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357#117—114no—
358#117—114no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
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×C22⋊C4—111no—
374C2×C22⋊C4—111no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C42—21no—
380C2×C42—111no—
381C2×C42—221no—
382C2×C42—221no—
383C2×C42—221no—
384C2×C42C22×D1111yescharacteristic
385#107—41no—
386#107—441no—
387#107—441no—
388#107—441no—
389#107—441no—
390#107—441no—
391#106—41no—
392#106—441no—
393C4⋊C8—114no—
394C4⋊C8—114no—
395C4⋊C8—114no—
396C4⋊C8C4×D1114yes—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409C2×C11#231611yescharacteristic
410C2×C11#291311yescharacteristic
411C2×C11#291311yescharacteristic
412C2×C11#325911yescharacteristic
413C2×C11#326111yescharacteristic
414C2×C11#326211yescharacteristic
415C2×C11#326211yescharacteristic
416D11—42no—
417C24—111no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—112no—
426C22×C4—112no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4D4×D1111yescharacteristic
436C22×C4D4×D1111yescharacteristic
437C22×C4C23×D1111yescharacteristic
438M16—444no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—112no—
444C2×C8—112no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—444no—
450C2×C8C2×C4×D1112yes—
451C2×C8C2×C4×D1112yes—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—114no—
461C4⋊C4—114no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—881no—
471C4⋊C4—881no—
472C4⋊C4—881no—
473C4⋊C4—881no—
474C22⋊C4—114no—
475C22⋊C4—114no—
476C22⋊C4—881no—
477C22⋊C4—881no—
478C22⋊C4—881no—
479C22⋊C4—881no—
480C42—81no—
481C42—112no—
482C42—112no—
483C42—881no—
484C42—881no—
485C42—881no—
486C42C2×C4×D1112yes—
487C42Q8×D1112yes—
488C11#2196811yescharacteristic, complemented, Sylow
489C23—112no—
490C23—221no—
491C23—221no—
492C23—221no—
493C23—221no—
494C23—221no—
495C23—221no—
496C23C2×D4×D1111yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—112no—
514C2×C4—112no—
515C2×C4—112no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
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—441no—
537C2×C4—441no—
538C2×C4C4⋊C4×D1112yes—
539C2×C4C4⋊C4×D1112yes—
540C2×C4C22×C4×D1111yescharacteristic
541C2×C4#6703711yescharacteristic
542C2×C4C2×Q8×D1111yescharacteristic
543C2×C4#6704011yescharacteristic
544C2×C4#6704211yescharacteristic
545C2×C4#6704311yescharacteristic
546C8—22no—
547C8—22no—
548C8—222no—
549C8—222no—
550C22—222no—
551C22—222no—
552C22—222no—
553C22—441no—
554C22—441no—
555C22—441no—
556C22—441no—
557C22C2×C4⋊C4×D1111yescharacteristic
558C22#1062313911yescharacteristic
559C22#1062316011yescharacteristic
560C22#1062330011yescharacteristic
561C22#1062330211yescharacteristic
562C22#1062330511yescharacteristic
563C22#1062331011yescharacteristic
564C4—22no—
565C4—22no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—222no—
571C4—222no—
572C4—222no—
573C4—881no—
574C4—881no—
575C4—881no—
576C4—881no—
577C4#1062307611yescharacteristic
578C4#1062310311yescharacteristic
579C4#1062322011yescharacteristic
580C4#1062326011yescharacteristic
581C2—442no—
582C2#1307123111yescharacteristic
583C2#1307721311yescharacteristic
584C2#1307721511yescharacteristic
585C2#1308005411yescharacteristic
586C2#1308006911yescharacteristic
587C2#1308007411yescharacteristic
588C2#1308007511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1949C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1949D11
hypocenterC11#21968
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #13069385C2semidirect
5. #13069382C2semidirect
6. #13069381C2semidirect
7. #13069375C2semidirect
8. #13069374C2semidirect
9. #13069373C2semidirect
10. #13069373C2semidirect
15. C11×#1949C2semidirect
45. #10622452C4semidirect
201. #1949D11semidirect
488. C11#21968semidirect

Maximal subgroups

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

subgroupindex
C2×#106224522
#130712262
#130712212
#130693852
#130693822
#130693812
#130693752
#130693742
#130693732
#130686482
#130686462
#130686442
#130686422
C11×#19492
#2196811