Finite Group Databasebeta

← #14795080

Subgroups — #14795080

Order 2816.

912 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C211yesmaximal, characteristic, complemented
2C2×#10622448C211yesmaximal, characteristic, complemented
3#13076963C211yesmaximal, characteristic, complemented
4C4×#66948C211yesmaximal, characteristic
5#13070048C212yesmaximal, complemented
6#13069808C212yesmaximal
7#13069379C211yesmaximal, characteristic, complemented
8#13069358C212yesmaximal, complemented
9#13069311C212yesmaximal, complemented
10#13068617C211yesmaximal, characteristic, complemented
11C11×#1988C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999—21no—
14C2×#66948C2211yescharacteristic
15C2×C4×D44—21no—
16C2×C4×D44C2211yescharacteristic
17C2×C42×D11C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C4×C11×C4⋊C4C2211yescharacteristic
20#10622843—21no—
21C2×#66885C2212yes—
22C2×(C2×D11)⋊C8C2212yes—
23C2×#66879C2212yes—
24#10622700—24no—
25#10622601C2211yescharacteristic
26#10622600—21no—
27#10622600C2211yescharacteristic
28#10622600C2212yes—
29#10622598C2211yescharacteristic
30#10622586—21no—
31#10622586C2212yes—
32C2×#66873C2212yes—
33C2×#66872C2212yes—
34C2×#66871C2212yes—
35C4×(C2×D11)⋊C4—21no—
36#10622548C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622448—24no—
39#10622283—21no—
40#10622278—21no—
41C11×#340C2212yes—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×D44—21no—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×C4×D11D411yescharacteristic
50C22×C4×D11D411yescharacteristic
51C22×C4×D11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61#66999—44no—
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2311yescharacteristic
73C2×Dic11⋊C4—22no—
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11C2311yescharacteristic
77C22×C11⋊C8C2312yes—
78#66948—22no—
79#66948—22no—
80C4×D44—22no—
81C4×D44—22no—
82C4×D44—44no—
83C42×D11—22no—
84C42×D11—22no—
85C11×C4⋊C8—22no—
86C11×#95—21no—
87C11⋊#95—21no—
88C11⋊#95—21no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91#66885—24no—
92(C2×D11)⋊C8—24no—
93#66879—24no—
94#66873—24no—
95#66872—24no—
96#66871—24no—
97C4⋊(C11⋊C8)D414yescomplemented
98#24709—111nomaximal, Sylow
99C23×D11—21no—
100C23×D11C2×D411yescharacteristic
101C2×Q8×C11—42no—
102C2×Q8×C11—42no—
103C2×Q8×C11—42no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—22no—
111C22×Dic11—21no—
112C22×Dic11C2×D411yescharacteristic
113C22×Dic11C2×D411yescharacteristic
114C22×Dic11C2×D411yescharacteristic
115C2×D44—24no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—42no—
122C2×D44—42no—
123C2×D44#4112yes—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—21no—
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×C4×D11—41no—
136C2×C4×D11—42no—
137C2×C4×D11—42no—
138C2×C4×D11—42no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4#4112yes—
149C42×C11—42no—
150C42×C11C2×D412yes—
151C42×C11#4112yes—
152(C2×D11)⋊C4—24no—
153(C2×D11)⋊C4—42no—
154(C2×D11)⋊C4—44no—
155(C2×D11)⋊C4—42no—
156(C2×D11)⋊C4—42no—
157(C2×D11)⋊C4—42no—
158C4⋊Dic11—21no—
159C4⋊Dic11—22no—
160C4⋊Dic11—22no—
161C4⋊Dic11—21no—
162C4⋊Dic11—42no—
163C4⋊Dic11—42no—
164C4⋊Dic11—42no—
165Dic11⋊C4—44no—
166C4×Dic11—22no—
167C4×Dic11—22no—
168C4×Dic11—21no—
169C4×Dic11—21no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8C2×D414yes—
173C2×#474—111no—
174C2×#432—111no—
175#2857—111no—
176C4×#121—111no—
177#2076—112no—
178#2034—112no—
179#1988D1111yescharacteristic, complemented
180#1948—111no—
181#1944—112no—
182#1936—112no—
183#1802—111no—
184C23×C11C22×D411yescharacteristic
185C22×D11—21no—
186C22×D11—21no—
187C22×D11—21no—
188C22×D11—21no—
189C22×D11—21no—
190C22×D11—21no—
191C22×D11—22no—
192C22×D11—41no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11#13712yes—
199Q8×C11—84no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—41no—
211C2×C4×C11#12112yes—
212C2×C4×C11#12112yes—
213C2×C4×C11AGL(1,ℤ/8)12yes—
214C2×C4×C11AGL(1,ℤ/8)12yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C112−1+411yescharacteristic
220C2×C4×C112−1+411yescharacteristic
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—21no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—41no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—42no—
236D44—22no—
237D44—22no—
238D44—48no—
239D44—41no—
240D44—41no—
241C4×D11—44no—
242C4×D11—41no—
243C4×D11—41no—
244C4×D11—41no—
245C4×D11—41no—
246C4×D11—44no—
247C4×D11—84no—
248C8×C11—42no—
249C11⋊C8—24no—
250C2×C4⋊Q8C2×D1111yescharacteristic
251C2×C22⋊Q8—221no—
252C2×#121—111no—
253C2×C4×D4—111no—
254C2×C4×D4—221no—
255C22×C42—111no—
256#474—224no—
257#432—224no—
258C2×#107—112no—
259C2×#106—112no—
260C2×C4⋊C8—111no—
261C2×C4⋊C8C2×D1111yescharacteristic
262C2×#102—112no—
263C2×#102—112no—
264C2×C22⋊C8—112no—
265C2×#97—112no—
266#391—221no—
267#390—111no—
268#389—112no—
269#389—111no—
270#389—221no—
271#388—221no—
272#386—221no—
273#384—111no—
274#380—111no—
275#380—112no—
276#380—221no—
277C4×C4⋊C4C2×D1111yescharacteristic
278C4×C22⋊C4—221no—
279#340—112no—
280#340—112no—
281#340C2×D1112yes—
282#340C2×D1112yes—
283C22×C11C2×#12111yescharacteristic
284C22×C11#52511yescharacteristic
285C22×C11#53611yescharacteristic
286C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C22×C11C2×#13711yescharacteristic
289C22×C11#57511yescharacteristic
290C2×D11—22no—
291C2×D11—22no—
292C2×D11—22no—
293C2×D11—41no—
294C2×D11—41no—
295C2×D11—41no—
296C2×D11—41no—
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11—81no—
304C4×C11—22no—
305C4×C11—42no—
306C4×C11—81no—
307C4×C11—82no—
308C4×C11#46914yes—
309C4×C11#54711yescharacteristic
310C4×C11#54811yescharacteristic
311C4×C11#55211yescharacteristic
312C4×C11#55611yescharacteristic
313Dic11—41no—
314Dic11—41no—
315Dic11—41no—
316Dic11—82no—
317Dic11—81no—
318C22×Q8—21no—
319C22×D4—111no—
320C22×D4—221no—
321C23×C4—111no—
322C23×C4—111no—
323C23×C4—111no—
324C23×C4—221no—
325C22×C8—112no—
326C22×C8C22×D1112yes—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C22⋊Q8—444no—
330#121—222no—
331#121—222no—
332C4×D4—222no—
333C4×D4—222no—
334C4×D4—444no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4—112no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4C22×D1112yes—
343C2×C4⋊C4C22×D1111yescharacteristic
344C2×C4⋊C4C22×D1111yescharacteristic
345C2×C22⋊C4—221no—
346C2×C22⋊C4—221no—
347C2×C22⋊C4—221no—
348C2×C22⋊C4—221no—
349C2×C22⋊C4—222no—
350C2×C22⋊C4—221no—
351C2×C42—21no—
352C2×C42—111no—
353C2×C42—111no—
354C2×C42—111no—
355C2×C42—222no—
356C2×C42—222no—
357C2×C42C22×D1111yescharacteristic
358#107—224no—
359#106—224no—
360C4⋊C8—22no—
361C4⋊C8—114no—
362#102—224no—
363#102—224no—
364C22⋊C8—224no—
365#97—224no—
366#95—21no—
367#95—221no—
368#95—221no—
369#95—222no—
370#95—222no—
371C2×C11#241511yescharacteristic
372C2×C11C2×#46911yescharacteristic
373C2×C11#305611yescharacteristic
374C2×C11#311011yescharacteristic
375C2×C11#311511yescharacteristic
376C2×C11#323511yescharacteristic
377C2×C11#323911yescharacteristic
378D11—42no—
379D11—82no—
380C24—111no—
381C24—221no—
382C2×Q8—42no—
383C2×Q8—42no—
384C2×Q8—42no—
385C2×D4—112no—
386C2×D4—224no—
387C2×D4—221no—
388C2×D4—221no—
389C2×D4—221no—
390C2×D4—221no—
391C2×D4—221no—
392C2×D4—442no—
393C2×D4—442no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—111no—
398C22×C4—111no—
399C22×C4—111no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—221no—
408C22×C4—221no—
409C22×C4—221no—
410C22×C4—221no—
411C22×C4—221no—
412C22×C4—222no—
413C22×C4—441no—
414C22×C4—442no—
415C22×C4—442no—
416C22×C4—442no—
417C22×C4D4×D1111yescharacteristic
418C22×C4D4×D1111yescharacteristic
419C22×C4C23×D1111yescharacteristic
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—114no—
424C2×C8—222no—
425C2×C8—222no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—42no—
432C4⋊C4—221no—
433C4⋊C4—221no—
434C4⋊C4—222no—
435C4⋊C4—222no—
436C4⋊C4—442no—
437C4⋊C4—442no—
438C4⋊C4—444no—
439C4⋊C4—442no—
440C4⋊C4#434312yes—
441C22⋊C4—224no—
442C22⋊C4—442no—
443C22⋊C4—442no—
444C22⋊C4—442no—
445C22⋊C4—444no—
446C22⋊C4—442no—
447C42—42no—
448C42—222no—
449C42—222no—
450C42—221no—
451C42—221no—
452C42#433912yes—
453C42D4×D1112yes—
454C11#2470911yescharacteristic, complemented, Sylow
455C23—112no—
456C23—221no—
457C23—221no—
458C23—221no—
459C23—221no—
460C23—221no—
461C23—221no—
462C23—222no—
463C23—441no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23—441no—
469C23C2×D4×D1111yescharacteristic
470Q8—84no—
471D4—222no—
472D4—222no—
473D4—448no—
474D4—441no—
475D4—441no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—221no—
488C2×C4—221no—
489C2×C4—221no—
490C2×C4—221no—
491C2×C4—221no—
492C2×C4—221no—
493C2×C4—221no—
494C2×C4—221no—
495C2×C4—221no—
496C2×C4—444no—
497C2×C4—441no—
498C2×C4—441no—
499C2×C4—441no—
500C2×C4—444no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—442no—
505C2×C4—441no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—884no—
509C2×C4#6693712yes—
510C2×C4#6693712yes—
511C2×C4#6696412yes—
512C2×C4#6696712yes—
513C2×C4C2×#433911yescharacteristic
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4C2×#434311yescharacteristic
516C2×C4#6704011yescharacteristic
517C2×C4#41×D1111yescharacteristic
518C2×C4#6704311yescharacteristic
519C8—42no—
520C8—224no—
521C22—222no—
522C22—222no—
523C22—222no—
524C22—441no—
525C22—441no—
526C22—441no—
527C22—441no—
528C22—442no—
529C22—442no—
530C22—442no—
531C22—881no—
532C22—881no—
533C22—881no—
534C22—881no—
535C22C2×#6693711yescharacteristic
536C22#1062315811yescharacteristic
537C22#1062315911yescharacteristic
538C22C2×#6696411yescharacteristic
539C22C2×#6696711yescharacteristic
540C22D11×#13711yescharacteristic
541C22#1062330811yescharacteristic
542C4—22no—
543C4—42no—
544C4—81no—
545C4—82no—
546C4—441no—
547C4—441no—
548C4—441no—
549C4—881no—
550C4—882no—
551C4#1062239514yes—
552C4#1062311211yescharacteristic
553C4#1062311511yescharacteristic
554C4#1062320811yescharacteristic
555C4#1062325711yescharacteristic
556C2—442no—
557C2—882no—
558C2#1307204811yescharacteristic
559C2C2×#1062239511yescharacteristic
560C2#1307824411yescharacteristic
561C2#1307871711yescharacteristic
562C2#1307877011yescharacteristic
563C2#1307981311yescharacteristic
564C2#1307985011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1988C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#1988D11
hypocenterC11#24709
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
1. C2×#10622700C2semidirect
2. C2×#10622448C2semidirect
3. #13076963C2semidirect
5. #13070048C2semidirect
7. #13069379C2semidirect
8. #13069358C2semidirect
9. #13069311C2semidirect
10. #13068617C2semidirect
11. C11×#1988C2semidirect
97. C4⋊(C11⋊C8)D4semidirect
179. #1988D11semidirect
454. C11#24709semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
C2×#106224482
#130769632
C4×#669482
#130700482
#130698082
#130693792
#130693582
#130693112
#130686172
C11×#19882
#2470911