Finite Group Databasebeta

← #14725496

Subgroups — #14725496

Order 2816.

618 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077704C211yesmaximal, characteristic
2#13077702C211yesmaximal, characteristic
3C4×Q16×D11C211yesmaximal, characteristic
4#13067523C211yesmaximal, characteristic, complemented
5#13067522C211yesmaximal, characteristic, complemented
6#13067468C211yesmaximal, characteristic, complemented
7#13067467C211yesmaximal, characteristic, complemented
8#13067465C211yesmaximal, characteristic, complemented
9#13067433C211yesmaximal, characteristic, complemented
10#13067432C211yesmaximal, characteristic, complemented
11#13067378C211yesmaximal, characteristic
12#13067061C211yesmaximal, characteristic
13#13067061C211yesmaximal, characteristic
14#13066904C211yesmaximal, characteristic
15C11×#1584C211yesmaximal, characteristic, complemented
16C2×Q16×D11C411yescharacteristic
17C4×Q8×D11C2211yescharacteristic
18C4×Q8×D11C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22Q16×Dic11C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4326C2211yescharacteristic
25#10622637C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27D11×#107C411yescharacteristic
28#10622486C411yescharacteristic
29#10622448—21no—
30#10622448C2211yescharacteristic
31#10622448C2211yescharacteristic
32#10622446—21no—
33#10622444—21no—
34#10622444C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622441—21no—
37D11×#103C411yescharacteristic
38D11×#103C411yescharacteristic
39#10622403C411yescharacteristic
40#10622403C411yescharacteristic
41#10622318—21no—
42#10622314—21no—
43C4×Dic44C2211yescharacteristic
44C4×#4313C2211yescharacteristic
45#10622298—21no—
46#10622298C2211yescharacteristic
47C4×C8×D11C2211yescharacteristic
48#10622292—21no—
49#10622292C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622096C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×Q8×D11C2×C411yescharacteristic
69C2×C11×Q16C2×C411yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71C4×Q8×C11C2311yescharacteristic
72Q8×Dic11C2×C411yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4326C2×C411yescharacteristic
76Q16×D11—24no—
77C2×Dic44C2×C411yescharacteristic
78C2×#4313—21no—
79C2×C8×D11C2×C411yescharacteristic
80C2×C8×D11C2×C411yescharacteristic
81C4⋊C4×D11—21no—
82C4⋊C4×D11—21no—
83C4⋊C4×D11C2×C411yescharacteristic
84C4⋊C4×D11C2×C411yescharacteristic
85#66940—21no—
86#66940—21no—
87#66940C2×C411yescharacteristic
88#66940C2×C411yescharacteristic
89C42×D11—21no—
90C42×D11—21no—
91C42×D11C2311yescharacteristic
92C4×Dic22—21no—
93C4×Dic22—21no—
94C4×Dic22C2311yescharacteristic
95C4×Dic22C2311yescharacteristic
96C11×#107C2×C411yescharacteristic
97C11×C4⋊C8—21no—
98C11×C4⋊C8—21no—
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×#103C2×C411yescharacteristic
102C11×#103C2×C411yescharacteristic
103C11×#97—21no—
104C4×C8×C11—21no—
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108#66899C2×C411yescharacteristic
109#66899C2×C411yescharacteristic
110(C2×D11)⋊C8—21no—
111(C2×D11)⋊C8—21no—
112(C2×D11)⋊C8D411yescharacteristic
113(C2×D11)⋊C8D411yescharacteristic
114#66882C2×C411yescharacteristic
115#66880C2×C411yescharacteristic
116#66880C2×C411yescharacteristic
117#66879—21no—
118#66879—21no—
119#66879—21no—
120#66879—21no—
121#66879—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8D411yescharacteristic
127Dic11⋊C8D411yescharacteristic
128C8×Dic11—21no—
129C8×Dic11—21no—
130C8×Dic11C2×C411yescharacteristic
131C8×Dic11C2×C411yescharacteristic
132#66874C2×C411yescharacteristic
133#66874C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135#66871C2×C411yescharacteristic
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140#66867—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18062—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148Q8×D11—22no—
149Q8×D11—22no—
150Q8×D11—41no—
151Q8×D11—41no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11C22×C411yescharacteristic
157C2×C4×D11C2×D411yescharacteristic
158C2×C4×D11#4111yescharacteristic
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22C22×C411yescharacteristic
162C2×Dic22C22×C411yescharacteristic
163C11×Q16—22no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C22×C411yescharacteristic
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C4⋊C4C22×C411yescharacteristic
175C42×C11—21no—
176C42×C11—21no—
177C42×C11C2411yescharacteristic
178#4326—22no—
179#4326M1614yescomplemented
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11C22×C411yescharacteristic
183C4⋊Dic11C22×C411yescharacteristic
184Dic11⋊C4—21no—
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11C22×C411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C4×Dic11#4111yescharacteristic
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206Dic44—22no—
207#4313—42no—
208C8×D11—22no—
209C8×D11—41no—
210#2984—111no—
211#2984—111no—
212C2×C4×Q16—111no—
213#1593—111no—
214#1593—111no—
215#1584—111no—
216#1584—111no—
217#1584—111no—
218#1584D1111yescharacteristic, complemented
219#1579—111no—
220#1579—111no—
221#1568—111no—
222#1491—111no—
223#1491—111no—
224#1451—111no—
225C22×D11C4×D411yescharacteristic
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11C2×M1612yes—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11C4×D411yescharacteristic
242C2×Dic11C4×D411yescharacteristic
243C2×Dic11C4×D411yescharacteristic
244C4×D11—22no—
245C4×D11—21no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—21no—
249C4×D11—42no—
250C4×D11—42no—
251C4×D11—42no—
252C4×D11—42no—
253Dic22—21no—
254Dic22—21no—
255Dic22—21no—
256Dic22—42no—
257Dic22—42no—
258Dic22C2×M1612yes—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—41no—
264C8×C11—41no—
265C8×C11—41no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8C2×M1612yes—
273C22×Q16—111no—
274C2×C4×Q8—111no—
275C2×C4×Q8—111no—
276#446—111no—
277#446—111no—
278#446—111no—
279#446—221no—
280#446—221no—
281#446—221no—
282#446—221no—
283#446C2×D1111yescharacteristic
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—111no—
287C8×Q8C2×D1111yescharacteristic
288C4×Q16—111no—
289C4×Q16—111no—
290C4×Q16—111no—
291C4×Q16—111no—
292C4×Q16—111no—
293C4×Q16—111no—
294C4×Q16—111no—
295C4×Q16C2×D1111yescharacteristic
296#432—111no—
297#432—111no—
298#432—221no—
299#432—221no—
300#431—111no—
301#431—221no—
302#431—221no—
303C2×#107—111no—
304C2×#103—111no—
305C2×#103—111no—
306C4×M16—111no—
307C2×C4×C8—111no—
308#335—111no—
309#335C2×D1111yescharacteristic
310#334—111no—
311#334—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8C2×D1111yescharacteristic
319Q8⋊C8C2×D1111yescharacteristic
320#322—111no—
321#322—111no—
322#322—111no—
323#322C2×D1111yescharacteristic
324C22×C11C2×C4×D411yescharacteristic
325C2×D11—21no—
326C2×D11—21no—
327C2×D11#44412yes—
328C4×C11—22no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11C22×M1611yescharacteristic
334C4×C11#56811yescharacteristic
335C4×C11#57811yescharacteristic
336C4×C11#57811yescharacteristic
337Dic11—22no—
338Dic11—21no—
339Dic11—21no—
340Dic11—21no—
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344C22×Q8—111no—
345C22×Q8—111no—
346C2×Q16—111no—
347C2×Q16—111no—
348C2×Q16—111no—
349C2×Q16—224no—
350C2×Q16C4×D1111yescharacteristic
351C2×M16—221no—
352C22×C8—111no—
353C22×C8—111no—
354C4×Q8—111no—
355C4×Q8—111no—
356C4×Q8—111no—
357C4×Q8—111no—
358C4×Q8—111no—
359C4×Q8—111no—
360C4×Q8—221no—
361C4×Q8—221no—
362C4×Q8—221no—
363C4×Q8—221no—
364C4×Q8C22×D1111yescharacteristic
365C4×Q8C22×D1111yescharacteristic
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C42—111no—
371C2×C42—221no—
372C2×C42—221no—
373#107—111no—
374#107—111no—
375#107—111no—
376#107C4×D1111yescharacteristic
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8C22×D1111yescharacteristic
390C4⋊C8C22×D1111yescharacteristic
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103C4×D1111yescharacteristic
398#103C4×D1111yescharacteristic
399C22⋊C8—111no—
400C22⋊C8—111no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—21no—
404#97—221no—
405#97—221no—
406#97—221no—
407#97—221no—
408#97—221no—
409#97—221no—
410C4×C8—21no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8C22×D1111yescharacteristic
420C4×C8C22×D1111yescharacteristic
421C4×C8C22×D1111yescharacteristic
422C2×C11D4×M1611yescharacteristic
423C2×C11#295011yescharacteristic
424C2×C11C2×#44411yescharacteristic
425D11—22no—
426C2×Q8—111no—
427C2×Q8—111no—
428C2×Q8—221no—
429C2×Q8—221no—
430C2×Q8—222no—
431C2×Q8—222no—
432C2×Q8—441no—
433C2×Q8—441no—
434C2×Q8C2×C4×D1111yescharacteristic
435C2×Q8C2×C4×D1111yescharacteristic
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443Q16—22no—
444Q16—114no—
445Q16—222no—
446Q16—222no—
447M16—442no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—222no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—441no—
460C2×C8C2×C4×D1111yescharacteristic
461C2×C8C2×C4×D1111yescharacteristic
462C2×C8D4×D1111yescharacteristic
463C2×C8D4×D1111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—111no—
467C4⋊C4—111no—
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⋊C4C2×C4×D1111yescharacteristic
477C4⋊C4C2×C4×D1111yescharacteristic
478C42—21no—
479C42—21no—
480C42—111no—
481C42—111no—
482C42—111no—
483C42—221no—
484C42—221no—
485C42—221no—
486C42—221no—
487C42—221no—
488C42—221no—
489C42C23×D1111yescharacteristic
490C11#1806211yescharacteristic, complemented, Sylow
491C23—111no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—112no—
496Q8—221no—
497Q8—221no—
498Q8—221no—
499Q8—442no—
500Q8—442no—
501Q8M16×D1112yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—111no—
507C2×C4—111no—
508C2×C4—111no—
509C2×C4—222no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4C22×C4×D1111yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4#41×D1111yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—112no—
533C8—221no—
534C8—221no—
535C8—221no—
536C8—441no—
537C8—441no—
538C8—441no—
539C22—112no—
540C22—221no—
541C22—221no—
542C22C4×D4×D1111yescharacteristic
543C4—21no—
544C4—22no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—221no—
549C4—221no—
550C4—222no—
551C4—221no—
552C4—441no—
553C4—441no—
554C4—441no—
555C4C2×M16×D1111yescharacteristic
556C4#1062328111yescharacteristic
557C4#1062329711yescharacteristic
558C4#1062330211yescharacteristic
559C2—222no—
560C2#1307734911yescharacteristic
561C2#1307747911yescharacteristic
562C2D11×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1584C2
socleC22×C11C2×C4×D4
prime radicalC22×D11C4×D4
cosocleC42×C11C24
hypercenter#1584D11
hypocenterC11#18062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #13067523C2semidirect
5. #13067522C2semidirect
6. #13067468C2semidirect
7. #13067467C2semidirect
8. #13067465C2semidirect
9. #13067433C2semidirect
10. #13067432C2semidirect
15. C11×#1584C2semidirect
179. #4326M16semidirect
218. #1584D11semidirect
490. C11#18062semidirect

Maximal subgroups

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

subgroupindex
#130777042
#130777022
C4×Q16×D112
#130675232
#130675222
#130674682
#130674672
#130674652
#130674332
#130674322
#130673782
#130670612
#130669042
C11×#15842
#1806211