Finite Group Databasebeta

← #14816849

Subgroups — #14816849

Order 2816.

900 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622455C211yesmaximal, characteristic
2C2×C4×#4314C211yesmaximal, characteristic
3#13072455C211yesmaximal, characteristic, complemented
4C4⋊C4×D44C211yesmaximal, characteristic
5#13070158C211yesmaximal, characteristic, complemented
6#13070094C211yesmaximal, characteristic, complemented
7#13069996C211yesmaximal, characteristic, complemented
8#13069950C211yesmaximal, characteristic, complemented
9#13069344C211yesmaximal, characteristic, complemented
10#13068949C211yesmaximal, characteristic
11#13068949C211yesmaximal, characteristic
12#13068887C211yesmaximal, characteristic, complemented
13#13068880C211yesmaximal, characteristic
14#13068880C211yesmaximal, characteristic
15C11×#1916C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×C4⋊C4×D11—21no—
18C2×C4×D44C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37#10622600—21no—
38#10622594—21no—
39#10622592—21no—
40#10622548C2211yescharacteristic
41#10622542C2211yescharacteristic
42#10622542C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622455—24no—
48C4×#4314—24no—
49#10622281—21no—
50#10622281—21no—
51#10622270—21no—
52#10622259—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×Dic22—21no—
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×#4314—22no—
95C2×#4314—22no—
96C2×#4314Q814yescomplemented
97C4⋊C4×D11—44no—
98C4×D44—22no—
99C4×D44—22no—
100C4×D44—22no—
101C4×D44—22no—
102C4×D44—41no—
103C4×D44—41no—
104#66922—22no—
105#66922—41no—
106C4×Dic22—22no—
107C4×Dic22—41no—
108C11×C4⋊C8—22no—
109C4×C8×C11—22no—
110C11×#95D411yescharacteristic
111C11×#95D411yescharacteristic
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66885—22no—
121#66885—22no—
122#66885D414yes—
123#66881—22no—
124#66881—22no—
125#66881—22no—
126#66881—22no—
127#66881—41no—
128#66880—22no—
129#66880—22no—
130#66880—41no—
131#26376—111nomaximal, Sylow
132C23×D11—21no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44C2×D412yes—
151C2×D44C2×Q812yes—
152C2×D44#4112yes—
153C2×C4×D11—24no—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—81no—
161C2×C4×D11—81no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—42no—
168C2×Dic22—42no—
169C2×Dic22—81no—
170C2×Dic22C2×Q812yes—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11C2×D412yes—
182C2×C8×C11C2×Q812yes—
183C11×C4⋊C4—41no—
184C11×C4⋊C4SD1614yescomplemented
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—42no—
205C4⋊Dic11—42no—
206C4⋊Dic11—81no—
207C4⋊Dic11C2×D412yes—
208C4⋊Dic11#4112yes—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211Dic11⋊C4—42no—
212Dic11⋊C4—81no—
213Dic11⋊C4—81no—
214C4×Dic11—42no—
215#4314—28no—
216C2×#476—111no—
217C2×C4×SD16—111no—
218#2451—111no—
219D4×C4⋊C4—111no—
220#2096—111no—
221#2084—111no—
222#2066—111no—
223#2058—111no—
224#1941—111no—
225#1916D1111yescharacteristic, complemented
226#1877—111no—
227#1877—111no—
228#1865—111no—
229#1864—111no—
230#1864—111no—
231C23×C11C22×D411yescharacteristic
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
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—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11C2×SD1612yes—
255C2×C4×C11C2×SD1612yes—
256C2×C4×C11C2×SD1612yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×Q811yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284D44—22no—
285D44—22no—
286D44—22no—
287D44C22⋊Q814yes—
288C4×D11—48no—
289C4×D11—84no—
290C4×D11—84no—
291Dic22—22no—
292Dic22—22no—
293Dic22—41no—
294Dic22—41no—
295Dic22—84no—
296C8×C11—22no—
297C8×C11—22no—
298C8×C11—41no—
299C8×C11—41no—
300C22×SD16—111no—
301C2×C4⋊Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×D4—111no—
304C2×C4×D4—111no—
305C2×C4×D4—111no—
306C22×C4⋊C4—221no—
307#476—224no—
308C4×SD16—224no—
309C2×#106—111no—
310C2×#106—111no—
311C2×#106—111no—
312C2×#106—111no—
313C2×#106—111no—
314C2×C4⋊C8C2×D1111yescharacteristic
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#102—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×C4×C8C2×D1111yescharacteristic
322#398—221no—
323#395—221no—
324#391—111no—
325#391—111no—
326#391—221no—
327#389—111no—
328#389—111no—
329#389—111no—
330#389—111no—
331#387—221no—
332#385—221no—
333#385—221no—
334#384—111no—
335#380—221no—
336C4×C4⋊C4C2×D1111yescharacteristic
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#336C2×D1111yescharacteristic
342#336C2×D1111yescharacteristic
343#336C2×D1111yescharacteristic
344#336C2×D1111yescharacteristic
345C22×C11#52511yescharacteristic
346C22×C11D4211yescharacteristic
347C22×C11D4×Q811yescharacteristic
348C22×C11C22×SD1611yescharacteristic
349C22×C11#57511yescharacteristic
350C22×C11#57711yescharacteristic
351C22×C11#57711yescharacteristic
352C2×D11—24no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—42no—
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—22no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11C2×C22⋊Q811yescharacteristic
366C4×C11#53911yescharacteristic
367C4×C11#54711yescharacteristic
368C4×C11#55411yescharacteristic
369Dic11—42no—
370Dic11—42no—
371Dic11—42no—
372Dic11—81no—
373Dic11—81no—
374Dic11—81no—
375Dic11—81no—
376C22×Q8—111no—
377C22×Q8—221no—
378C22×D4—111no—
379C23×C4—221no—
380C23×C4—221no—
381C23×C4—221no—
382C2×SD16—114no—
383C2×SD16—222no—
384C2×SD16—222no—
385C22×C8C22×D1111yescharacteristic
386C22×C8C22×D1111yescharacteristic
387C22×C8C22×D1111yescharacteristic
388C22×C8C22×D1111yescharacteristic
389C4⋊Q8—222no—
390C4⋊Q8—441no—
391C4×Q8—222no—
392C4×Q8—441no—
393C4×D4—222no—
394C4×D4—222no—
395C4×D4—222no—
396C4×D4—222no—
397C4×D4—441no—
398C4×D4—441no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—444no—
414C2×C4⋊C4D4411yescharacteristic
415C2×C4⋊C4D4411yescharacteristic
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C42—221no—
420C2×C42C22×D1111yescharacteristic
421C2×C42C22×D1111yescharacteristic
422C2×C42C22×D1111yescharacteristic
423#106—222no—
424#106—222no—
425#106—222no—
426#106—222no—
427#106—441no—
428C4⋊C8—22no—
429#103—222no—
430#103—222no—
431#103—441no—
432#102—114no—
433#102—222no—
434#102—222no—
435C4×C8—22no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95D4411yescharacteristic
445#95D4411yescharacteristic
446C2×C11#244911yescharacteristic
447C2×C11#310111yescharacteristic
448C2×C11#312511yescharacteristic
449C2×C11#326711yescharacteristic
450C2×C11D4×SD1611yescharacteristic
451C2×C11Q8×SD1611yescharacteristic
452C2×C11#338811yescharacteristic
453D11—44no—
454C24—221no—
455C2×Q8—112no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—442no—
462C2×Q8—442no—
463C2×Q8—881no—
464C2×D4—112no—
465C2×D4—112no—
466C2×D4—112no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C22×C4—224no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—442no—
479C22×C4—442no—
480C22×C4—442no—
481C22×C4—442no—
482C22×C4—442no—
483C22×C4—442no—
484C22×C4—881no—
485C22×C4—881no—
486C22×C4C2×D4411yescharacteristic
487C22×C4C2×D4411yescharacteristic
488C22×C4C2×D4411yescharacteristic
489C22×C4C2×D4411yescharacteristic
490C22×C4C2×D4411yescharacteristic
491C22×C4C2×D4411yescharacteristic
492C22×C4C23×D1111yescharacteristic
493SD16—228no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8D4×D1112yes—
505C2×C8Q8×D1112yes—
506C4⋊C4—41no—
507C4⋊C4—112no—
508C4⋊C4—112no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—442no—
520C4⋊C4—442no—
521C4⋊C4—442no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—881no—
525C4⋊C4—881no—
526C4⋊C4—881no—
527C4⋊C4#431414yescomplemented
528C22⋊C4—224no—
529C22⋊C4—442no—
530C22⋊C4—442no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—442no—
538C11#2637611yescharacteristic, complemented, Sylow
539C23—222no—
540C23—222no—
541C23—222no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23C22×D4411yescharacteristic
547Q8—222no—
548Q8—222no—
549Q8—441no—
550Q8—441no—
551Q8—884no—
552D4—114no—
553D4—222no—
554D4—222no—
555D4—222no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—448no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—884no—
594C2×C4—884no—
595C2×C4C2×#431412yes—
596C2×C4C2×#431412yes—
597C2×C4C2×#431412yes—
598C2×C4C2×D4×D1111yescharacteristic
599C2×C4C2×Q8×D1111yescharacteristic
600C2×C4#41×D1111yescharacteristic
601C2×C4#41×D1111yescharacteristic
602C2×C4#6704211yescharacteristic
603C2×C4#6704311yescharacteristic
604C8—22no—
605C8—22no—
606C8—41no—
607C8—41no—
608C22—224no—
609C22—442no—
610C22—442no—
611C22—442no—
612C22—442no—
613C22—442no—
614C22—442no—
615C22#1062305511yescharacteristic
616C22D4×D4411yescharacteristic
617C22Q8×D4411yescharacteristic
618C22C22×#431411yescharacteristic
619C22#1062327911yescharacteristic
620C22#1062328211yescharacteristic
621C22#1062328211yescharacteristic
622C4—22no—
623C4—22no—
624C4—22no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—442no—
629C4—442no—
630C4—442no—
631C4—881no—
632C4—881no—
633C4—881no—
634C4—881no—
635C4D11×C22⋊Q811yescharacteristic
636C4#1062318611yescharacteristic
637C4#1062322111yescharacteristic
638C4#1062323811yescharacteristic
639C2—444no—
640C2#1307243011yescharacteristic
641C2#1307862511yescharacteristic
642C2#1307889511yescharacteristic
643C2#1308014611yescharacteristic
644C2D4×#431411yescharacteristic
645C2Q8×#431411yescharacteristic
646C2#1308156311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1916D11
hypocenterC11#26376
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
3. #13072455C2semidirect
5. #13070158C2semidirect
6. #13070094C2semidirect
7. #13069996C2semidirect
8. #13069950C2semidirect
9. #13069344C2semidirect
12. #13068887C2semidirect
15. C11×#1916C2semidirect
96. C2×#4314Q8semidirect
184. C11×C4⋊C4SD16semidirect
225. #1916D11semidirect
527. C4⋊C4#4314semidirect
538. C11#26376semidirect

Maximal subgroups

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

subgroupindex
C2×#106224552
C2×C4×#43142
#130724552
C4⋊C4×D442
#130701582
#130700942
#130699962
#130699502
#130693442
#130689492
#130688872
#130688802
C11×#19162
#2637611