Finite Group Databasebeta

← #14787717

Subgroups — #14787717

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C211yesmaximal, characteristic
2C2×#10622634C211yesmaximal, characteristic, complemented
3C2×C4×#4325C211yesmaximal, characteristic, complemented
4#13069798C212yesmaximal, complemented
5#13069617C212yesmaximal, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic, complemented
8#13068929C212yesmaximal, complemented
9#13068813C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic, complemented
11C11×#2538C211yesmaximal, characteristic, complemented
12C2×C11×C22⋊Q8C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C22×#4325C2211yescharacteristic
16C2×#66991—21no—
17C2×#66983C2212yes—
18C2×#66979C2212yes—
19#10623094—24no—
20#10623094—24no—
21C2×#66945—21no—
22C2×#66938—22no—
23C2×C4×D44C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C11×#396—22no—
26C11×#390—21no—
27C11×#389—21no—
28C11×#384C2211yescharacteristic
29C11×#380C2212yes—
30C2×#66899C2212yes—
31C2×#66899C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34C4×#4325—24no—
35#10622634—24no—
36C2×#66873C2211yescharacteristic
37C2×#66873C2212yes—
38C2×#66872C2211yescharacteristic
39C2×#66871C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11D411yescharacteristic
47C23×C4×C11C2312yes—
48C22×C22⋊D11—22no—
49C22×D44C2311yescharacteristic
50C22×C4×D11—21no—
51C22×Dic22—21no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—42no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4D412yes—
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11—22no—
71C2×#4325—22no—
72C2×#4325—22no—
73C2×#4325—22no—
74#66991—28no—
75#66983—24no—
76#66983—24no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—22no—
79#66979—24no—
80#66979—24no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2312yes—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4×Dic11—22no—
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2312yes—
87C22×C11⋊C8C2311yescharacteristic
88#66945—28no—
89#66938—216no—
90C4×D44—22no—
91C4×D44D414yes—
92#66922—22no—
93#66922D414yes—
94C11×#95—22no—
95#66899—24no—
96#66899—22no—
97C22⋊(C11⋊C8)—24no—
98C22⋊(C11⋊C8)—42no—
99#66873—22no—
100#66873—42no—
101#66872—22no—
102#66871—24no—
103C4⋊(C11⋊C8)—22no—
104C4×C11⋊C8—22no—
105#24121—111nomaximal, Sylow
106C24×C11C2×D412yes—
107C23×D11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11#4112yes—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—28no—
131C2×C22⋊D11—82no—
132C2×C22⋊D11—82no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44C2×D412yes—
141C2×C4×D11—24no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×Dic22—24no—
145C2×Dic22—81no—
146C2×Dic22—81no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—44no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—81no—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—44no—
158C11×C22⋊C4—82no—
159C42×C11—42no—
160C42×C11C2×D412yes—
161C42×C11C2×D412yes—
162C22⋊Dic11—28no—
163#4325—28no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—24no—
166C4⋊Dic11—24no—
167C4⋊Dic11—22no—
168C4⋊Dic11—21no—
169C4⋊Dic11C2×D414yes—
170C4⋊Dic11C2×D412yes—
171C4×Dic11—28no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8#4112yes—
181C2×#555—111no—
182C2×#477—111no—
183C2×C4×SD16—111no—
184#2538D1111yescharacteristic, complemented
185#2033—112no—
186#2000—112no—
187#1990—111no—
188#1954—111no—
189#1873—112no—
190#1854—112no—
191#1802—111no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11C22×D411yescharacteristic
200C22×D11—22no—
201C22×D11—41no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207Q8×C11—22no—
208Q8×C11—22no—
209Q8×C11—41no—
210Q8×C11—41no—
211D4×C11—44no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11#12012yes—
231C2×C4×C11#12012yes—
232C2×C4×C11#13512yes—
233C2×C4×C11#13712yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C22⋊D11—88no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247D44—22no—
248D44—22no—
249D44—41no—
250D44—41no—
251C4×D11—48no—
252Dic22—84no—
253C11⋊C8—22no—
254C11⋊C8—41no—
255C11⋊C8—42no—
256C22×SD16—111no—
257#555—224no—
258#555—224no—
259C2×C4⋊Q8—111no—
260C2×#124—222no—
261C2×C22⋊Q8C2×D1112yes—
262C2×#121—112no—
263C2×#121—221no—
264C2×C4×Q8C2×D1111yescharacteristic
265C2×C4×D4—111no—
266C2×C4×D4C2×D1111yescharacteristic
267C2×#117—112no—
268C2×#117—221no—
269#477—224no—
270C4×SD16—224no—
271C2×#107—112no—
272C2×#106—111no—
273C2×C4⋊C8—111no—
274C2×#103—112no—
275C2×#103—111no—
276C2×#102—111no—
277C2×#102—112no—
278C2×C22⋊C8—112no—
279C2×C22⋊C8—112no—
280C2×C4×C8—111no—
281#396—22no—
282#390—21no—
283#389—21no—
284#384C2×D1111yescharacteristic
285#380C2×D1112yes—
286#340—112no—
287#340—112no—
288#340—112no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11C2×#12011yescharacteristic
297C22×C11#54611yescharacteristic
298C22×C11#54711yescharacteristic
299C22×C11C2×#13511yescharacteristic
300C22×C11C2×#13711yescharacteristic
301C22×C11#57611yescharacteristic
302C22×C11#57711yescharacteristic
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—81no—
309C2×D11—81no—
310C4×C11—22no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—81no—
314C4×C11—82no—
315C4×C11#45214yes—
316C4×C11#52511yescharacteristic
317C4×C11#53711yescharacteristic
318C4×C11#54811yescharacteristic
319C4×C11#55011yescharacteristic
320Dic11—42no—
321Dic11—44no—
322C22×Q8—221no—
323C22×Q8C22×D1111yescharacteristic
324C22×D4—111no—
325C22×D4—222no—
326C22×D4C22⋊D1111yescharacteristic
327C23×C4—221no—
328C23×C4C22×D1112yes—
329C2×SD16—222no—
330C2×SD16—222no—
331C2×SD16—222no—
332C22×C8—111no—
333C22×C8—111no—
334C22×C8—112no—
335C4⋊Q8—114no—
336C4⋊Q8—222no—
337#124—2216no—
338C22⋊Q8—24no—
339C22⋊Q8—42no—
340#121—224no—
341#121—224no—
342#121—228no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—114no—
348C4×D4—222no—
349#117—228no—
350#117—224no—
351#117—224no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4C22⋊D1111yescharacteristic
360C2×C4⋊C4C22×D1111yescharacteristic
361C2×C4⋊C4C22×D1112yes—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—222no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4C22⋊D1112yes—
368C2×C42—21no—
369C2×C42—222no—
370C2×C42C22×D1111yescharacteristic
371#107—224no—
372#106—222no—
373C4⋊C8—222no—
374#103—222no—
375#103—224no—
376#102—222no—
377#102—442no—
378C22⋊C8—224no—
379C22⋊C8—442no—
380C4×C8—222no—
381#95—22no—
382C2×C11—82no—
383C2×C11#240711yescharacteristic
384C2×C11C2×#45211yescharacteristic
385C2×C11#301211yescharacteristic
386C2×C11#330511yescharacteristic
387C2×C11#332911yescharacteristic
388C2×C11#334011yescharacteristic
389C2×C11#335711yescharacteristic
390D11—82no—
391C24—221no—
392C24C2×C22⋊D1112yes—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—224no—
399C2×Q8—881no—
400C2×Q8—881no—
401C2×Q8#434112yes—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—112no—
406C2×D4—228no—
407C2×D4—221no—
408C2×D4—221no—
409C2×D4—221no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—882no—
413C2×D4—882no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—221no—
424C22×C4—222no—
425C22×C4—224no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4C2×C22⋊D1112yes—
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C23×D1111yescharacteristic
432SD16—228no—
433C2×C8—112no—
434C2×C8—221no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—222no—
438C2×C8—221no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—221no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—44no—
448C4⋊C4—42no—
449C4⋊C4—42no—
450C4⋊C4—81no—
451C4⋊C4—112no—
452C4⋊C4—114no—
453C4⋊C4—224no—
454C4⋊C4—221no—
455C4⋊C4—222no—
456C22⋊C4—24no—
457C22⋊C4—44no—
458C22⋊C4—82no—
459C22⋊C4—228no—
460C22⋊C4—228no—
461C22⋊C4—224no—
462C42—42no—
463C42—228no—
464C42D4×D1112yes—
465C42D4×D1112yes—
466C11#2412111yescharacteristic, complemented, Sylow
467C23—22no—
468C23—22no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—222no—
475C23—441no—
476C23—441no—
477C23—441no—
478C23—441no—
479C23—441no—
480C23—441no—
481C23C22×C22⋊D1111yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—41no—
485Q8—41no—
486Q8—884no—
487D4—44no—
488D4—222no—
489D4—222no—
490D4—441no—
491D4—441no—
492D4—888no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—222no—
512C2×C4—224no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—448no—
518C2×C4#6699012yes—
519C2×C4#6699012yes—
520C2×C4#6699512yes—
521C2×C4#6700312yes—
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×#434111yescharacteristic
525C2×C4#6703711yescharacteristic
526C2×C4#41×D1111yescharacteristic
527C2×C4#6704311yescharacteristic
528C8—222no—
529C8—442no—
530C8—441no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—442no—
539C22—442no—
540C22—442no—
541C22—881no—
542C22—881no—
543C22—881no—
544C22—881no—
545C22C2×#6699011yescharacteristic
546C22#1062333711yescharacteristic
547C22C2×#6699511yescharacteristic
548C22C2×#6700311yescharacteristic
549C22#1062335511yescharacteristic
550C22#1062336611yescharacteristic
551C22#1062336811yescharacteristic
552C4—22no—
553C4—42no—
554C4—42no—
555C4—81no—
556C4—82no—
557C4—442no—
558C4—444no—
559C4#1062266014yes—
560C4#1062312911yescharacteristic
561C4#1062313011yescharacteristic
562C4#1062313711yescharacteristic
563C4#1062313911yescharacteristic
564C2—82no—
565C2—882no—
566C2#1307195711yescharacteristic
567C2C2×#1062266011yescharacteristic
568C2#1307791711yescharacteristic
569C2#1308056611yescharacteristic
570C2#1308091011yescharacteristic
571C2#1308102311yescharacteristic
572C2#1308124211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2538C2
socleC23×C11C22×D4
prime radicalC2×#10623094C2
hypercenter#2538D11
hypocenterC11#24121
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
2. C2×#10622634C2semidirect
3. C2×C4×#4325C2semidirect
4. #13069798C2semidirect
5. #13069617C2semidirect
6. #13069576C2semidirect
7. #13069411C2semidirect
8. #13068929C2semidirect
9. #13068813C2semidirect
10. #13068613C2semidirect
11. C11×#2538C2semidirect
184. #2538D11semidirect
466. C11#24121semidirect

Maximal subgroups

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

subgroupindex
C2×#106230942
C2×#106226342
C2×C4×#43252
#130697982
#130696172
#130695762
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