Finite Group Databasebeta

← #14823678

Subgroups — #14823678

Order 2816.

806 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×#10622695C211yesmaximal, characteristic, complemented
2C2×#10622639C211yesmaximal, characteristic
3#13072488C211yesmaximal, characteristic
4#13070011C211yesmaximal, characteristic, complemented
5#13069954C211yesmaximal, characteristic, complemented
6#13069931C211yesmaximal, characteristic
7#13069699C211yesmaximal, characteristic
8#13069473C211yesmaximal, characteristic
9#13069312C211yesmaximal, characteristic
10#13069309C211yesmaximal, characteristic, complemented
11#13069295C211yesmaximal, characteristic, complemented
12#13068953C211yesmaximal, characteristic
13#13068884C211yesmaximal, characteristic, complemented
14#13068485C211yesmaximal, characteristic, complemented
15C11×#2446C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C11×#400—21no—
23C11×#398—21no—
24C11×#391C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#387—21no—
29C11×#387—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37#10622695—24no—
38#10622639—24no—
39#10622605—21no—
40#10622602—21no—
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622552C2211yescharacteristic
46#10622552C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622289—21no—
54#10622280—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—41no—
67C4×Q8×C11—22no—
68C4×Q8×C11—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×#4325—22no—
82C2×#4325—22no—
83C2×#4325—22no—
84C2×#4325—22no—
85C2×#4325—22no—
86C2×#4325—41no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C4×D44—22no—
104C4×D44—41no—
105#66923—22no—
106#66923—41no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116#66899—22no—
117#66899—22no—
118#66899—22no—
119#66899—22no—
120#66899—22no—
121#66899D414yes—
122C11⋊#95—21no—
123C11⋊#95—21no—
124#66873—22no—
125#66873—22no—
126#66872—41no—
127#66871—22no—
128C4⋊(C11⋊C8)—22no—
129#66867—22no—
130#66867—22no—
131C4×C11⋊C8—22no—
132#26845—111nomaximal, Sylow
133C23×D11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11C2×D412yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44#4112yes—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—81no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—42no—
186#4325—28no—
187#4325—44no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—81no—
191(C2×D11)⋊C4—81no—
192(C2×D11)⋊C4—81no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11C2×D412yes—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201Dic11⋊C4—81no—
202Dic11⋊C4—81no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C2×D412yes—
213C2×C11⋊C8#4112yes—
214C2×C11⋊C8#4112yes—
215C2×#491—111no—
216C2×#440—111no—
217#2454—111no—
218#2446D1111yescharacteristic, complemented
219#2068—111no—
220#2059—111no—
221#2055—111no—
222#2013—111no—
223#1968—111no—
224#1936—111no—
225#1935—111no—
226#1933—111no—
227#1877—111no—
228#1865—111no—
229#1770—111no—
230C23×C11C22×D411yescharacteristic
231C22×D11—22no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11—41no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
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—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11#13712yes—
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×C4×C112−1+411yescharacteristic
282C2×Dic11—22no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291D44—22no—
292D44—22no—
293D44—41no—
294D44—41no—
295C4×D11—84no—
296C11⋊C8—22no—
297C11⋊C8—22no—
298C11⋊C8—22no—
299C11⋊C8—41no—
300C22×SD16—111no—
301C22×SD16—111no—
302C2×C4⋊Q8C2×D1111yescharacteristic
303C2×#125—111no—
304C2×C4×Q8C2×D1111yescharacteristic
305C2×C4×D4—111no—
306#491—224no—
307#440—224no—
308C2×#107—111no—
309C2×#106—111no—
310C2×C4⋊C8—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#97—111no—
320C2×#97—111no—
321C2×C4×C8—111no—
322#400—21no—
323#399—221no—
324#398—21no—
325#396—221no—
326#391C2×D1111yescharacteristic
327#391C2×D1111yescharacteristic
328#391C2×D1111yescharacteristic
329#390—111no—
330#390—111no—
331#389—111no—
332#389—111no—
333#389C2×D1111yescharacteristic
334#387—21no—
335#387—21no—
336#385—221no—
337#380—221no—
338C4×C4⋊C4C2×D1111yescharacteristic
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#336—111no—
344#336—111no—
345C22×C11#53211yescharacteristic
346C22×C11D4211yescharacteristic
347C22×C11#54811yescharacteristic
348C22×C11C2×#13711yescharacteristic
349C22×C11#57511yescharacteristic
350C22×C11#57711yescharacteristic
351C22×C11#57711yescharacteristic
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—81no—
358C2×D11—81no—
359C4×C11—22no—
360C4×C11—41no—
361C4×C11—42no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—81no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11#52511yescharacteristic
370C4×C11#54211yescharacteristic
371C4×C11#54711yescharacteristic
372C4×C11#55111yescharacteristic
373Dic11—42no—
374Dic11—81no—
375Dic11—81no—
376C22×Q8C22×D1111yescharacteristic
377C22×Q8C22×D1111yescharacteristic
378C22×D4—111no—
379C23×C4—221no—
380C2×SD16—222no—
381C2×SD16—222no—
382C2×SD16—222no—
383C2×SD16—222no—
384C2×SD16—222no—
385C2×SD16—441no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8—111no—
389C22×C8—111no—
390C4⋊Q8—22no—
391C4⋊Q8—41no—
392#125—222no—
393#125—441no—
394C4×Q8—22no—
395C4×Q8—41no—
396C4×D4—222no—
397C4×D4—441no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
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⋊C4C22⋊D1111yescharacteristic
410C2×C4⋊C4C22⋊D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—21no—
419C2×C42C22×D1111yescharacteristic
420C2×C42C22×D1111yescharacteristic
421C2×C42C22×D1111yescharacteristic
422#107—222no—
423#106—441no—
424C4⋊C8—222no—
425#103—114no—
426#103—222no—
427#103—222no—
428#103—222no—
429#103—222no—
430#103—222no—
431#102—222no—
432#102—222no—
433#97—222no—
434#97—222no—
435C4×C8—222no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—221no—
444#95—221no—
445#95C22⋊D1111yescharacteristic
446#95C22⋊D1111yescharacteristic
447C2×C11#246111yescharacteristic
448C2×C11#317411yescharacteristic
449C2×C11#318111yescharacteristic
450C2×C11#327511yescharacteristic
451C2×C11#327811yescharacteristic
452C2×C11#337211yescharacteristic
453C2×C11#337611yescharacteristic
454D11—82no—
455C24—221no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8D4×D1112yes—
468C2×D4—112no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—442no—
482C22×C4—442no—
483C22×C4—881no—
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C23×D1111yescharacteristic
491SD16—228no—
492SD16—444no—
493C2×C8—112no—
494C2×C8—112no—
495C2×C8—112no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—42no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—42no—
515C4⋊C4—112no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—442no—
522C4⋊C4—442no—
523C4⋊C4—881no—
524C4⋊C4—881no—
525C22⋊C4—442no—
526C22⋊C4—442no—
527C22⋊C4—881no—
528C22⋊C4—881no—
529C22⋊C4—881no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—42no—
537C11#2684511yescharacteristic, complemented, Sylow
538C23—222no—
539C23—441no—
540C23—441no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23C22×C22⋊D1111yescharacteristic
546Q8—22no—
547Q8—22no—
548Q8—41no—
549Q8—41no—
550Q8—41no—
551Q8—41no—
552Q8—41no—
553Q8—41no—
554D4—222no—
555D4—222no—
556D4—441no—
557D4—441no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—222no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—884no—
597C2×C4#6699512yes—
598C2×C4C2×D4×D1111yescharacteristic
599C2×C4#6703711yescharacteristic
600C2×C4#41×D1111yescharacteristic
601C2×C4#41×D1111yescharacteristic
602C2×C4#41×D1111yescharacteristic
603C2×C4#6704311yescharacteristic
604C8—222no—
605C8—222no—
606C8—222no—
607C8—441no—
608C22—442no—
609C22—442no—
610C22—442no—
611C22—881no—
612C22—881no—
613C22—881no—
614C22—881no—
615C22D4×C22⋊D1111yescharacteristic
616C22C2×#6699511yescharacteristic
617C22#1062335311yescharacteristic
618C22#1062336211yescharacteristic
619C22#1062336311yescharacteristic
620C22#1062336811yescharacteristic
621C22#1062336811yescharacteristic
622C4—22no—
623C4—41no—
624C4—41no—
625C4—42no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—81no—
630C4—81no—
631C4—81no—
632C4—442no—
633C4—881no—
634C4—881no—
635C4#1062318611yescharacteristic
636C4#1062318711yescharacteristic
637C4#1062319011yescharacteristic
638C4#1062319311yescharacteristic
639C2—882no—
640C2#1307258211yescharacteristic
641C2#1307924511yescharacteristic
642C2#1307931911yescharacteristic
643C2#1308024811yescharacteristic
644C2#1308027811yescharacteristic
645C2#1308139311yescharacteristic
646C2#1308143711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2446C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2446D11
hypocenterC11#26845
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2446

Complements

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

NH ≅ G/Ntype
1. C2×#10622695C2semidirect
4. #13070011C2semidirect
5. #13069954C2semidirect
10. #13069309C2semidirect
11. #13069295C2semidirect
13. #13068884C2semidirect
14. #13068485C2semidirect
15. C11×#2446C2semidirect
218. #2446D11semidirect
537. C11#26845semidirect

Maximal subgroups

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

subgroupindex
C2×#106226952
C2×#106226392
#130724882
#130700112
#130699542
#130699312
#130696992
#130694732
#130693122
#130693092
#130692952
#130689532
#130688842
#130684852
C11×#24462
#2684511