Finite Group Databasebeta

← #14787730

Subgroups — #14787730

Order 2816.

1134 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic
2C2×#10622463C211yesmaximal, characteristic, complemented
3C2×C4×Dic44C211yesmaximal, characteristic, complemented
4#13073538C211yesmaximal, characteristic
5#13069820C212yesmaximal, complemented
6#13069626C212yesmaximal, complemented
7#13069577C211yesmaximal, characteristic, complemented
8#13068921C212yesmaximal, complemented
9#13068806C212yesmaximal, complemented
10#13068622C211yesmaximal, characteristic, complemented
11C11×#1954C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×D4×Dic11—21no—
14C22×C4⋊Dic11C2212yes—
15C2×#66977C2212yes—
16C2×#66977C2212yes—
17C22×Dic44C2211yescharacteristic
18#10623074—24no—
19#10623074—24no—
20C2×#66943—21no—
21C2×#66931—22no—
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2212yes—
27C2×C11×C22⋊C8C2212yes—
28C2×C4×C8×C11C2211yescharacteristic
29#10622834—21no—
30#10622825C2212yes—
31C2×#66882C2211yescharacteristic
32C2×#66882C2212yes—
33C2×#66880C2212yes—
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2212yes—
37#10622586—21no—
38#10622561—22no—
39#10622548C2211yescharacteristic
40#10622463—24no—
41C4×Dic44—24no—
42#10622189C2212yes—
43#10622189C2212yes—
44#10622189C2212yes—
45C22×D4×C11D411yescharacteristic
46C23×C4×C11C2312yes—
47C23×Dic11—22no—
48C22×Dic22—21no—
49C22×Dic22C2311yescharacteristic
50C22×Dic22C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C22×C8×C11C2311yescharacteristic
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C22⋊C4D412yes—
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62D4×Dic11—28no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—24no—
66C2×C4⋊Dic11—24no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2312yes—
73#66977—24no—
74#66977—24no—
75#66977—24no—
76#66977—42no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—22no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11—21no—
83C2×Dic44—22no—
84C2×Dic44—22no—
85C2×Dic44—22no—
86#66943—28no—
87#66931—216no—
88#66922—22no—
89#66922D414yes—
90C4×Dic22—22no—
91C4×Dic22—22no—
92C4×Dic22—22no—
93C4×Dic22D414yes—
94C11×C4⋊C8—22no—
95C11×C22⋊C8—24no—
96C11×C22⋊C8—42no—
97C4×C8×C11—22no—
98C11⋊#95—22no—
99#66882—22no—
100#66882—24no—
101#66880—22no—
102#66880—22no—
103#66880—24no—
104#66880—42no—
105#24122—111nomaximal, Sylow
106C24×C11C2×D412yes—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11Q1614yescomplemented
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—28no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—22no—
125C22×Dic11—21no—
126C22×Dic11—22no—
127C22×Dic11—82no—
128C22×Dic11—82no—
129C2×Dic22—24no—
130C2×Dic22—21no—
131C2×Dic22—21no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22—21no—
135C2×Dic22—21no—
136C2×Dic22—21no—
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—21no—
140C2×Dic22—81no—
141C2×Dic22—81no—
142C2×Dic22C2×D412yes—
143C2×Dic22#4112yes—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11#4112yes—
153C11×C4⋊C4—22no—
154C11×C22⋊C4—24no—
155C42×C11C2×D412yes—
156C42×C11C2×D412yes—
157C22⋊Dic11—28no—
158C22⋊Dic11—44no—
159C22⋊Dic11—82no—
160C4⋊Dic11—28no—
161C4⋊Dic11—24no—
162C4⋊Dic11—21no—
163C4⋊Dic11—22no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11—42no—
169C4⋊Dic11—81no—
170C4⋊Dic11C2×D412yes—
171C4⋊Dic11C2×D414yes—
172Dic11⋊C4—28no—
173Dic11⋊C4—24no—
174Dic11⋊C4—44no—
175Dic11⋊C4—42no—
176C4×Dic11—24no—
177C4×Dic11—42no—
178Dic44—28no—
179C2×#554—111no—
180C2×#477—111no—
181C2×C4×Q16—111no—
182#2538—111no—
183#2036—112no—
184#2001—112no—
185#1990—111no—
186#1954D1111yescharacteristic
187#1872—112no—
188#1852—112no—
189#1803—111no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11C2×Q1614yes—
197C23×C11C22×D411yescharacteristic
198D4×C11—28no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11#12012yes—
209C2×C4×C11#12012yes—
210C2×C4×C11C2×Q1612yes—
211C2×C4×C11#13712yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11H(5,𝔽2)11yescharacteristic
217C2×C4×C112−1+411yescharacteristic
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—24no—
221C2×Dic11—22no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—42no—
227C2×Dic11—41no—
228C2×Dic11—42no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—88no—
237Dic22—22no—
238Dic22—22no—
239Dic22—22no—
240Dic22—22no—
241Dic22—41no—
242Dic22—41no—
243Dic22—41no—
244Dic22—41no—
245Dic22—84no—
246C8×C11—22no—
247C8×C11—41no—
248C8×C11—42no—
249C22×Q16—111no—
250#554—224no—
251#554—224no—
252C2×C4⋊Q8—111no—
253C2×#125—221no—
254C2×C22⋊Q8—112no—
255C2×C22⋊Q8—112no—
256C2×C22⋊Q8—222no—
257C2×C4×Q8—111no—
258C2×C4×Q8—111no—
259C2×C4×D4—221no—
260C2×C4×D4C2×D1111yescharacteristic
261C22×C4⋊C4—112no—
262#477—224no—
263C4×Q16—224no—
264C2×#107—112no—
265C2×#107—111no—
266C2×C4⋊C8C2×D1111yescharacteristic
267C2×#103—112no—
268C2×#103—111no—
269C2×#103—111no—
270C2×#103—112no—
271C2×C22⋊C8C2×D1112yes—
272C2×C22⋊C8C2×D1112yes—
273C2×C4×C8C2×D1111yescharacteristic
274#396—222no—
275#390—221no—
276#389—221no—
277#384—111no—
278#380—112no—
279#340—112no—
280#340—112no—
281#340—112no—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11C2×#12011yescharacteristic
290C22×C11#54611yescharacteristic
291C22×C11#54711yescharacteristic
292C22×C11C22×Q1611yescharacteristic
293C22×C11C2×#13711yescharacteristic
294C22×C11#57611yescharacteristic
295C22×C11#57711yescharacteristic
296C4×C11—22no—
297C4×C11—42no—
298C4×C11#45114yes—
299C4×C11#52511yescharacteristic
300C4×C11#53711yescharacteristic
301C4×C11#54811yescharacteristic
302C4×C11#55011yescharacteristic
303Dic11—42no—
304Dic11—42no—
305Dic11—44no—
306Dic11—42no—
307Dic11—82no—
308Dic11—81no—
309C22×Q8—111no—
310C22×Q8—111no—
311C22×Q8—221no—
312C22×D4D4411yescharacteristic
313C23×C4—222no—
314C23×C4C22×D1112yes—
315C2×Q16—222no—
316C2×Q16—222no—
317C2×Q16—222no—
318C22×C8C22×D1111yescharacteristic
319C22×C8C22×D1112yes—
320C22×C8C22×D1111yescharacteristic
321C4⋊Q8—114no—
322C4⋊Q8—222no—
323#125—228no—
324C22⋊Q8—2216no—
325C22⋊Q8—224no—
326C22⋊Q8—224no—
327C22⋊Q8—224no—
328C22⋊Q8—442no—
329C4×Q8—114no—
330C4×Q8—222no—
331C4×Q8—222no—
332C4×Q8—222no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—228no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4—112no—
338C2×C4⋊C4—111no—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—224no—
341C2×C4⋊C4—224no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4D4411yescharacteristic
351C2×C22⋊C4—222no—
352C2×C22⋊C4—222no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4D4412yes—
355C2×C42—221no—
356C2×C42—221no—
357C2×C42C22×D1111yescharacteristic
358#107—222no—
359#107—224no—
360C4⋊C8—22no—
361#103—222no—
362#103—224no—
363#103—222no—
364#103—442no—
365C22⋊C8—24no—
366C22⋊C8—42no—
367C4×C8—22no—
368#95—222no—
369C2×C11—44no—
370C2×C11#240711yescharacteristic
371C2×C11C2×#45111yescharacteristic
372C2×C11#301211yescharacteristic
373C2×C11#329911yescharacteristic
374C2×C11#333311yescharacteristic
375C2×C11#333811yescharacteristic
376C2×C11#335611yescharacteristic
377C24C2×D4412yes—
378C2×Q8—112no—
379C2×Q8—112no—
380C2×Q8—224no—
381C2×Q8—221no—
382C2×Q8—221no—
383C2×Q8—221no—
384C2×Q8—221no—
385C2×Q8—221no—
386C2×Q8—221no—
387C2×Q8—221no—
388C2×Q8—221no—
389C2×Q8—221no—
390C2×Q8—221no—
391C2×Q8—881no—
392C2×Q8—881no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4Dic4414yescomplemented
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4—221no—
405C22×C4—222no—
406C22×C4—228no—
407C22×C4—221no—
408C22×C4—222no—
409C22×C4—882no—
410C22×C4—882no—
411C22×C4C2×D4412yes—
412C22×C4C2×D4411yescharacteristic
413C22×C4C2×D4411yescharacteristic
414C22×C4C23×D1111yescharacteristic
415Q16—228no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—21no—
422C2×C8—22no—
423C2×C8—21no—
424C2×C8#434112yes—
425C4⋊C4—22no—
426C4⋊C4—112no—
427C4⋊C4—114no—
428C4⋊C4—228no—
429C4⋊C4—228no—
430C4⋊C4—224no—
431C4⋊C4—224no—
432C4⋊C4—221no—
433C4⋊C4—222no—
434C4⋊C4—221no—
435C4⋊C4—221no—
436C4⋊C4—222no—
437C4⋊C4—222no—
438C4⋊C4—444no—
439C4⋊C4—442no—
440C4⋊C4—442no—
441C4⋊C4—881no—
442C22⋊C4—24no—
443C22⋊C4—228no—
444C22⋊C4—444no—
445C22⋊C4—882no—
446C42—224no—
447C42—442no—
448C42D4×D1112yes—
449C42D4×D1112yes—
450C11#2412211yescharacteristic, complemented, Sylow
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23C2×Dic4414yes—
458C23C22×D4411yescharacteristic
459Q8—222no—
460Q8—222no—
461Q8—222no—
462Q8—222no—
463Q8—441no—
464Q8—441no—
465Q8—441no—
466Q8—441no—
467Q8—884no—
468D4—28no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—224no—
481C2×C4—222no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—442no—
485C2×C4—441no—
486C2×C4—442no—
487C2×C4—441no—
488C2×C4—441no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4—442no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—888no—
497C2×C4#6693512yes—
498C2×C4#6693512yes—
499C2×C4C2×Dic4412yes—
500C2×C4#6696212yes—
501C2×C4C2×D4×D1111yescharacteristic
502C2×C4C2×D4×D1111yescharacteristic
503C2×C4C2×#434111yescharacteristic
504C2×C4#6703711yescharacteristic
505C2×C4#41×D1111yescharacteristic
506C2×C4#6704311yescharacteristic
507C8—22no—
508C8—42no—
509C8—41no—
510C22—24no—
511C22—24no—
512C22—24no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22C2×#6693511yescharacteristic
518C22#1062308511yescharacteristic
519C22#1062308611yescharacteristic
520C22C22×Dic4411yescharacteristic
521C22C2×#6696211yescharacteristic
522C22#1062328211yescharacteristic
523C22#1062328311yescharacteristic
524C4—22no—
525C4—42no—
526C4—442no—
527C4—442no—
528C4—442no—
529C4—444no—
530C4—882no—
531C4—881no—
532C4#1062235214yes—
533C4#1062313711yescharacteristic
534C4#1062313911yescharacteristic
535C4#1062320811yescharacteristic
536C4#1062324911yescharacteristic
537C2—44no—
538C2#1307195911yescharacteristic
539C2C2×#1062235211yescharacteristic
540C2#1307792311yescharacteristic
541C2#1308049311yescharacteristic
542C2#1308095511yescharacteristic
543C2#1308100911yescharacteristic
544C2#1308123211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1954C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#1954D11
hypocenterC11#24122
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. C2×#10622463C2semidirect
3. C2×C4×Dic44C2semidirect
5. #13069820C2semidirect
6. #13069626C2semidirect
7. #13069577C2semidirect
8. #13068921C2semidirect
9. #13068806C2semidirect
10. #13068622C2semidirect
109. C2×D4×C11Q16semidirect
395. C2×D4Dic44semidirect
450. C11#24122semidirect

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106224632
C2×C4×Dic442
#130735382
#130698202
#130696262
#130695772
#130689212
#130688062
#130686222
C11×#19542
#2412211