Finite Group Databasebeta

← #14743151

Subgroups — #14743151

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080431C211yesmaximal, characteristic
2D4×#4325C211yesmaximal, characteristic, complemented
3#13080262C211yesmaximal, characteristic, complemented
4#13068286C211yesmaximal, characteristic, complemented
5#13068083C211yesmaximal, characteristic, complemented
6#13068060C211yesmaximal, characteristic, complemented
7#13068002C211yesmaximal, characteristic, complemented
8#13067979C211yesmaximal, characteristic, complemented
9#13067865C211yesmaximal, characteristic, complemented
10#13067850C211yesmaximal, characteristic, complemented
11#13067794C211yesmaximal, characteristic, complemented
12#13067719C211yesmaximal, characteristic, complemented
13#13067446C211yesmaximal, characteristic, complemented
14#13067426C211yesmaximal, characteristic, complemented
15Q8×C11×D8C211yesmaximal, characteristic, complemented
16D4×Q8×C11C2211yescharacteristic
17D4×Q8×C11C2211yescharacteristic, complemented
18C2×#66995—21no—
19C22×#4325—21no—
20#10623082C2211yescharacteristic
21D4×D44C2211yescharacteristic
22C11×#500—21no—
23C11×#500C2211yescharacteristic, complemented
24C11×#474—21no—
25C11×#474—21no—
26C11×#474C2211yescharacteristic
27C11×#474C2211yescharacteristic, complemented
28C8×Q8×C11C2211yescharacteristic, complemented
29C4×C11×D8—21no—
30C4×C11×D8C2211yescharacteristic
31#10622841—21no—
32#10622840—21no—
33#10622769—21no—
34#10622705C2211yescharacteristic, complemented
35#10622701C2211yescharacteristic
36#10622698C2211yescharacteristic
37#10622696C2211yescharacteristic
38#10622696C2211yescharacteristic
39#10622691C2211yescharacteristic, complemented
40#10622665—21no—
41#10622661—21no—
42#10622660—21no—
43#10622659—21no—
44#10622644C2211yescharacteristic, complemented
45#10622640C2211yescharacteristic
46C4×#4325C2211yescharacteristic
47#10622628C2211yescharacteristic
48#10622625C2211yescharacteristic, complemented
49D4×C11⋊C8C2211yescharacteristic
50#10622620C2211yescharacteristic
51#10622495—21no—
52#10622388—21no—
53D11×#102—21no—
54#10622307C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622185C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622124C2211yescharacteristic, complemented
62#10622123C2211yescharacteristic
63#10622121C2211yescharacteristic
64#10622117C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C22×Q8×C11—21no—
68C22×Q8×C11—21no—
69C2×D4×D11—21no—
70C2×#4339—21no—
71C22×D44—21no—
72C2×C11×D8D411yescharacteristic
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8—21no—
75C11×C4⋊Q8C2311yescharacteristic
76C11×C4⋊Q8C2311yescharacteristic
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—41no—
80C11×C22⋊Q8—41no—
81C4×Q8×C11C2311yescharacteristic
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11C2311yescharacteristic
85C4×D4×C11C2311yescharacteristic
86C2×#4326—21no—
87C2×#4326—21no—
88C2×#4326—21no—
89#66995—44no—
90C2×#4325—21no—
91C2×#4325—21no—
92C2×#4325—21no—
93C2×#4325—21no—
94C2×#4325—21no—
95C2×#4325—44no—
96C2×#4325D411yescharacteristic
97#66991—21no—
98C2×#4323—21no—
99#66983—21no—
100#66977—21no—
101C2×#4318—21no—
102C22×C11⋊C8—21no—
103C2×C8×D11—21no—
104#66948—21no—
105C4⋊C4×D11—21no—
106#66936—41no—
107#66935—41no—
108#66927C2311yescharacteristic
109C4×D44C2311yescharacteristic
110#66922C2311yescharacteristic
111C11×#107—21no—
112C11×#107—21no—
113C11×#107—21no—
114C11×#107—21no—
115C11×#107D411yescharacteristic
116C11×C4⋊C8—21no—
117C11×C4⋊C8C2311yescharacteristic
118C11×#102—21no—
119C11×#102—21no—
120C11×#102D411yescharacteristic
121C11×#102D411yescharacteristic
122C4×C8×C11—21no—
123C4×C8×C11C2311yescharacteristic
124#66899—21no—
125#66899—21no—
126#66899D411yescharacteristic
127#66896—21no—
128C22⋊(C11⋊C8)—21no—
129C22⋊(C11⋊C8)—21no—
130#66885—21no—
131#66885—21no—
132(C2×D11)⋊C8—21no—
133#66874—21no—
134#66873—21no—
135#66873—21no—
136#66873—41no—
137#66873D411yescharacteristic
138#66872D411yescharacteristic
139#66871—21no—
140#66871—41no—
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#19757—111nomaximal, Sylow
147C23×D11—41no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—41no—
151C2×Q8×C11—41no—
152C2×Q8×C11—42no—
153C2×Q8×C11—42no—
154C2×Q8×C11—81no—
155C2×Q8×C11—81no—
156C2×Q8×C11C2×D411yescharacteristic
157C2×D4×C11C2×D411yescharacteristic
158C2×D4×C11C2×D411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—41no—
162C22×C4×C11—41no—
163C2×C22⋊D11—41no—
164C2×C22⋊D11—41no—
165D4×D11—42no—
166D4×D11—81no—
167#4339—42no—
168#4339—81no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—41no—
173C2×D44—42no—
174C2×D44—81no—
175C2×D44C2×D411yescharacteristic
176C2×C4×D11—21no—
177C2×C4×D11—41no—
178C2×Dic22—21no—
179C11×D8—22no—
180C2×C8×C11—21no—
181C2×C8×C11C2×D411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—41no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4C2×D411yescharacteristic
191C11×C4⋊C4C2×D411yescharacteristic
192C11×C4⋊C4C2×D411yescharacteristic
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—41no—
196C11×C22⋊C4—41no—
197C42×C11—21no—
198C42×C11C2411yescharacteristic
199C22⋊Dic11—41no—
200#4326—42no—
201#4326—42no—
202#4326—81no—
203#4325—42no—
204#4325—42no—
205#4325—42no—
206#4325—42no—
207#4325—81no—
208#4325D814yescomplemented
209#4323—81no—
210(C2×D11)⋊C4—21no—
211(C2×D11)⋊C4—41no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11C2×D411yescharacteristic
215Dic11⋊C4—41no—
216#4318—42no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—42no—
222C2×C11⋊C8C2×D411yescharacteristic
223C2×C11⋊C8C2×D411yescharacteristic
224C8×D11—81no—
225Q8×D8D1111yescharacteristic, complemented
226#3294—111no—
227D4×SD16—111no—
228#3276—111no—
229#1722—111no—
230#1685—111no—
231#1682—111no—
232#1673—111no—
233#1669—111no—
234#1649—111no—
235#1647—111no—
236#1639—111no—
237#1627—111no—
238#1581—111no—
239SD16⋊C8—111no—
240C23×C11—21no—
241C23×C11—21no—
242C22×D11—21no—
243C22×D11—41no—
244C22×D11—82no—
245C22×D11—82no—
246C22×D11—161no—
247Q8×C11—21no—
248Q8×C11—41no—
249Q8×C11—41no—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11—82no—
253Q8×C11—82no—
254Q8×C11C2×D812yes—
255D4×C11—21no—
256D4×C11—21no—
257D4×C11—21no—
258D4×C11#13712yescomplemented
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—82no—
270C2×C4×C11—82no—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C22⋊D11—82no—
275C22⋊D11—82no—
276C2×Dic11—21no—
277C2×Dic11—41no—
278D44—21no—
279D44—41no—
280D44—41no—
281D44—41no—
282D44—41no—
283D44—81no—
284D44—82no—
285D44C2×D812yes—
286C4×D11—41no—
287C4×D11—41no—
288C4×D11—82no—
289Dic22—41no—
290Dic22—41no—
291C8×C11—21no—
292C8×C11—21no—
293C8×C11—41no—
294C11⋊C8—21no—
295C11⋊C8—41no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8C2×D812yes—
300C2×#137—221no—
301C22×SD16—221no—
302D4×Q8C2×D1111yescharacteristic
303D4×Q8C2×D1111yescharacteristic, complemented
304#547—111no—
305D42—111no—
306#500—21no—
307#500—111no—
308#500C2×D1111yescharacteristic, complemented
309#494—111no—
310#492—111no—
311#486—111no—
312#486—111no—
313#480—221no—
314#474—21no—
315#474—21no—
316#474—111no—
317#474C2×D1111yescharacteristic
318#474C2×D1111yescharacteristic, complemented
319#470—221no—
320#466—221no—
321#465—221no—
322#462—111no—
323#461—111no—
324#461—111no—
325#460—111no—
326#459—111no—
327#452—221no—
328#451—221no—
329#450—221no—
330#448—221no—
331#447—221no—
332C8×Q8C2×D1111yescharacteristic, complemented
333C4×SD16—111no—
334C4×D8—21no—
335C4×D8C2×D1111yescharacteristic
336#436—111no—
337C8×D4—111no—
338C8×D4—111no—
339C2×#102—221no—
340#335—111no—
341#335—111no—
342#332—111no—
343#332—111no—
344#332—111no—
345#331—111no—
346Q8⋊C8—111no—
347D4⋊C8—111no—
348D4⋊C8—111no—
349D4⋊C8—111no—
350#322—111no—
351C22×C11—22no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11D4211yescharacteristic
358C2×D11—22no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—81no—
362C2×D11—81no—
363C2×D11—81no—
364C2×D11—164no—
365C4×C11—22no—
366C4×C11—21no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—81no—
371C4×C11—81no—
372C4×C11C22×D811yescharacteristic
373C4×C11C2×#13711yescharacteristic
374C4×C11#57611yescharacteristic
375C4×C11#57711yescharacteristic
376Dic11—41no—
377Dic11—81no—
378C2×#41—221no—
379C22×Q8—21no—
380C22×Q8—21no—
381C22×D4—221no—
382C22×D4—221no—
383#137—444no—
384C2×Q16—221no—
385C2×Q16—221no—
386C2×Q16—221no—
387C2×SD16—111no—
388C2×SD16—221no—
389C2×SD16—221no—
390C2×SD16—221no—
391C2×SD16—221no—
392C2×SD16—221no—
393C2×SD16—444no—
394C2×D8—221no—
395C2×D8C22⋊D1111yescharacteristic
396C2×M16—221no—
397C22×C8—221no—
398C22×C8—221no—
399C4⋊Q8—21no—
400C4⋊Q8—21no—
401C4⋊Q8—111no—
402C4⋊Q8C22×D1111yescharacteristic
403C4⋊Q8C22×D1111yescharacteristic
404#127—111no—
405#123—441no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—41no—
409C22⋊Q8—41no—
410C22⋊Q8—221no—
411#121—221no—
412#121—221no—
413#121—221no—
414#120—441no—
415C4×Q8C22×D1111yescharacteristic
416C4×D4—21no—
417C4×D4—21no—
418C4×D4—111no—
419C4×D4C22×D1111yescharacteristic
420C4×D4C22×D1111yescharacteristic
421C2×C4⋊C4—221no—
422#107—21no—
423#107—21no—
424#107—21no—
425#107—21no—
426#107—221no—
427#107—441no—
428#107C22⋊D1111yescharacteristic
429#106—111no—
430C4⋊C8—21no—
431C4⋊C8—111no—
432C4⋊C8—111no—
433C4⋊C8—111no—
434C4⋊C8C22×D1111yescharacteristic
435#103—111no—
436#103—221no—
437#103—221no—
438#103—221no—
439#102—21no—
440#102—21no—
441#102—111no—
442#102—221no—
443#102—221no—
444#102—221no—
445#102—221no—
446#102—221no—
447#102—441no—
448#102C22⋊D1111yescharacteristic
449#102C22⋊D1111yescharacteristic
450C22⋊C8—221no—
451C22⋊C8—221no—
452C22⋊C8—221no—
453C4×C8—21no—
454C4×C8—111no—
455C4×C8—111no—
456C4×C8C22×D1111yescharacteristic
457C2×C11—42no—
458C2×C11—81no—
459C2×C11#326611yescharacteristic
460C2×C11D4×D811yescharacteristic
461C2×C11#328911yescharacteristic
462D11—42no—
463D11—161no—
464C24—441no—
465#41—442no—
466#41—881no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—41no—
470C2×Q8—41no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—81no—
474C2×Q8—81no—
475C2×Q8—221no—
476C2×Q8D4×D1111yescharacteristic
477C2×D4—111no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—441no—
482C2×D4—442no—
483C2×D4—441no—
484C2×D4—442no—
485C2×D4—441no—
486C2×D4—881no—
487C2×D4—881no—
488C2×D4C2×C22⋊D1111yescharacteristic
489C2×D4C2×C22⋊D1111yescharacteristic
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—221no—
495C22×C4—441no—
496Q16—442no—
497Q16—442no—
498Q16—881no—
499SD16—114no—
500SD16—442no—
501SD16—442no—
502SD16—442no—
503SD16—442no—
504SD16—881no—
505D8—22no—
506D8—881no—
507M16—442no—
508C2×C8—21no—
509C2×C8—111no—
510C2×C8—111no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—442no—
516C2×C8—881no—
517C2×C8C2×C22⋊D1111yescharacteristic
518C2×C8C2×C22⋊D1111yescharacteristic
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—111no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—441no—
530C4⋊C4D4×D1111yescharacteristic
531C4⋊C4C2×C22⋊D1111yescharacteristic
532C4⋊C4C2×C22⋊D1111yescharacteristic
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—221no—
538C22⋊C4—441no—
539C22⋊C4—441no—
540C42—21no—
541C42C23×D1111yescharacteristic
542C11#1975711yescharacteristic, complemented, Sylow
543C23—21no—
544C23—21no—
545C23—221no—
546C23—441no—
547C23—882no—
548C23—882no—
549C23—1761no—
550Q8—21no—
551Q8—41no—
552Q8—41no—
553Q8—41no—
554Q8—41no—
555Q8—82no—
556Q8—82no—
557Q8—441no—
558Q8—441no—
559Q8D8×D1112yes—
560D4—21no—
561D4—21no—
562D4—21no—
563D4—112no—
564D4—221no—
565D4—441no—
566D4—441no—
567D4—441no—
568D4—441no—
569D4—881no—
570D4—882no—
571D4—882no—
572D4—882no—
573D4#6699512yescomplemented
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—82no—
585C2×C4—82no—
586C2×C4—221no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—882no—
591C2×C4C2×D4×D1111yescharacteristic
592C2×C4#6703711yescharacteristic
593C2×C4C22×C22⋊D1111yescharacteristic
594C8—21no—
595C8—21no—
596C8—41no—
597C8—112no—
598C8—221no—
599C8—441no—
600C8—441no—
601C8—441no—
602C8—441no—
603C22—22no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—222no—
610C22—441no—
611C22—441no—
612C22—881no—
613C22—881no—
614C22—881no—
615C22—1764no—
616C22D4×C22⋊D1111yescharacteristic
617C4—21no—
618C4—22no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—81no—
623C4—81no—
624C4—441no—
625C4—881no—
626C4C2×D8×D1111yescharacteristic
627C4#1062328811yescharacteristic
628C4C2×#6699511yescharacteristic
629C4#1062336811yescharacteristic
630C2—42no—
631C2—81no—
632C2—442no—
633C2—1761no—
634C2#1308012711yescharacteristic
635C2D8×C22⋊D1111yescharacteristic
636C2#1308038711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingQ8×C11×D8C2
socleC22×C11D42
prime radical#13080431C2
hypercenterQ8×D8D11
hypocenterC11#19757
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ Q8×D8

Complements

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

NH ≅ G/Ntype
2. D4×#4325C2semidirect
3. #13080262C2semidirect
4. #13068286C2semidirect
5. #13068083C2semidirect
6. #13068060C2semidirect
7. #13068002C2semidirect
8. #13067979C2semidirect
9. #13067865C2semidirect
10. #13067850C2semidirect
11. #13067794C2semidirect
12. #13067719C2semidirect
13. #13067446C2semidirect
14. #13067426C2semidirect
15. Q8×C11×D8C2semidirect
17. D4×Q8×C11C22semidirect
23. C11×#500C22semidirect
27. C11×#474C22semidirect
28. C8×Q8×C11C22semidirect
34. #10622705C22semidirect
39. #10622691C22semidirect
44. #10622644C22semidirect
48. #10622625C22semidirect
56. #10622185C22semidirect
57. #10622185C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622124C22semidirect
64. #10622117C22semidirect
65. #10622096C22semidirect
66. #10622092C22semidirect
208. #4325D8semidirect
225. Q8×D8D11semidirect
258. D4×C11#137semidirect
303. D4×Q8C2×D11semidirect
308. #500C2×D11semidirect
318. #474C2×D11semidirect
332. C8×Q8C2×D11semidirect
542. C11#19757semidirect
573. D4#66995semidirect

Maximal subgroups

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

subgroupindex
#130804312
D4×#43252
#130802622
#130682862
#130680832
#130680602
#130680022
#130679792
#130678652
#130678502
#130677942
#130677192
#130674462
#130674262
Q8×C11×D82
#1975711