Finite Group Databasebeta

← #14660709

Subgroups — #14660709

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66870C212yesmaximal
2#13071191C211yesmaximal, characteristic
3C2×#10622164C211yesmaximal, characteristic, complemented
4C2×#10622165C212yesmaximal, complemented
5C11×#2315C211yesmaximal, characteristic, complemented
6C23×C22⋊D11C2211yescharacteristic
7C22×C11×C22⋊C4C2212yes—
8C22×C11×C22⋊C4C2211yescharacteristic
9C22×C22⋊Dic11C2211yescharacteristic
10C22×C22⋊Dic11C2212yes—
11C11×#385—24no—
12C11×#380—22no—
13#10622826—22no—
14#10622571—22no—
15#10622568C412yescomplemented
16C2×#66870—24no—
17C2×#66870—24no—
18C2×#66870—24no—
19#10622556C412yescomplemented
20#10622165—24no—
21#10622164—22no—
22C25×C11C2311yescharacteristic
23C24×D11C2×C411yescharacteristic
24C23×C4×C11—22no—
25C23×C4×C11D412yes—
26C22×C22⋊D11—22no—
27C22×C22⋊D11—22no—
28C22×C22⋊D11—21no—
29C22×C22⋊D11—21no—
30C22×C22⋊D11—22no—
31C22×C22⋊D11—21no—
32C22×C22⋊D11—21no—
33C22×C22⋊D11—22no—
34C22×C22⋊D11D412yes—
35C22×C22⋊D11Q812yes—
36C23×Dic11—21no—
37C23×Dic11—22no—
38C23×Dic11C2×C411yescharacteristic
39C2×C11×C4⋊C4—24no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4C2×C412yes—
48C2×C11×C22⋊C4D412yes—
49C2×C11×C22⋊C4D414yes—
50C2×C22⋊Dic11—22no—
51C2×C22⋊Dic11—22no—
52C2×C22⋊Dic11—22no—
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—21no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11C2×C412yes—
59C2×C22⋊Dic11D414yes—
60C2×(C2×D11)⋊C4—24no—
61C11×#95—24no—
62C11⋊#95—24no—
63#66870—216no—
64#11046—111nomaximal, Sylow
65C24×C11—82no—
66C24×C11C22×C411yescharacteristic
67C24×C11C2×D411yescharacteristic
68C24×C11C2×D411yescharacteristic
69C24×C11C2×D412yes—
70C24×C11C2×D411yescharacteristic
71C24×C11C2×D412yes—
72C24×C11C2×Q811yescharacteristic
73C24×C11#4112yes—
74C24×C11#4111yescharacteristic
75C24×C11#4111yescharacteristic
76C24×C11#4112yes—
77C23×D11—21no—
78C23×D11—21no—
79C23×D11—22no—
80C23×D11—22no—
81C23×D11—82no—
82C23×D11C4⋊C412yescomplemented
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—24no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—82no—
89C22×C4×C11—84no—
90C22×C4×C11C22⋊C414yes—
91C2×C22⋊D11—24no—
92C2×C22⋊D11—22no—
93C2×C22⋊D11—22no—
94C2×C22⋊D11—22no—
95C2×C22⋊D11—22no—
96C2×C22⋊D11—24no—
97C2×C22⋊D11—24no—
98C2×C22⋊D11—24no—
99C2×C22⋊D11—41no—
100C2×C22⋊D11—42no—
101C2×C22⋊D11—42no—
102C2×C22⋊D11—42no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—42no—
105C2×C22⋊D11—42no—
106C2×C22⋊D11—41no—
107C2×C22⋊D11—42no—
108C2×C22⋊D11—41no—
109C22×Dic11—21no—
110C22×Dic11—22no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—24no—
115C22×Dic11—42no—
116C22×Dic11—42no—
117C22×Dic11—42no—
118C22×Dic11—82no—
119C22×Dic11—84no—
120C22×Dic11C4⋊C412yescomplemented
121C11×C4⋊C4—84no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—24no—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—42no—
127C11×C22⋊C4—42no—
128C22⋊Dic11—24no—
129C22⋊Dic11—24no—
130C22⋊Dic11—24no—
131C22⋊Dic11—42no—
132C22⋊Dic11—42no—
133C22⋊Dic11—41no—
134C22⋊Dic11—41no—
135(C2×D11)⋊C4—84no—
136C22×#99—112no—
137#2315D1111yescharacteristic, complemented
138#2308—111no—
139C2×#342—112no—
140C2×#342—111no—
141C23×C11—42no—
142C23×C11—44no—
143C23×C11—42no—
144C23×C11—44no—
145C23×C11—42no—
146C23×C11—81no—
147C23×C11—82no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11—81no—
151C23×C11—82no—
152C23×C11C2×C22⋊C411yescharacteristic
153C23×C11C2×C4⋊C411yescharacteristic
154C23×C11#11711yescharacteristic
155C23×C11C4×D412yes—
156C23×C11C4×D412yes—
157C23×C11#12012yes—
158C23×C11#12011yescharacteristic
159C23×C11#12111yescharacteristic
160C23×C11#12112yes—
161C23×C11#12112yes—
162C23×C11#12111yescharacteristic
163C23×C11#12112yes—
164C23×C11C22⋊Q812yes—
165C23×C11C22⋊Q811yescharacteristic
166C23×C11C22⋊Q811yescharacteristic
167C23×C11C22⋊Q812yes—
168C23×C11#12312yes—
169C23×C11#12312yes—
170C23×C11#12311yescharacteristic
171C23×C11#12412yes—
172C23×C11#12411yescharacteristic
173C23×C11#12612yes—
174C23×C11#12711yescharacteristic
175C22×D11—22no—
176C22×D11—24no—
177C22×D11—44no—
178C22×D11—41no—
179C22×D11—42no—
180C22×D11—41no—
181C22×D11—82no—
182C22×D11—82no—
183C22×D11—84no—
184C22×D11—84no—
185C2×C4×C11—24no—
186C2×C4×C11—44no—
187C2×C4×C11—44no—
188C2×C4×C11—48no—
189C2×C4×C11—44no—
190C2×C4×C11—82no—
191C2×C4×C11—84no—
192C2×C4×C11—84no—
193C22⋊D11—42no—
194C22⋊D11—42no—
195C22⋊D11—44no—
196C22⋊D11—44no—
197C22⋊D11—42no—
198C22⋊D11—42no—
199C2×Dic11—22no—
200C2×Dic11—24no—
201C2×Dic11—41no—
202C2×Dic11—42no—
203C2×Dic11—41no—
204C2×Dic11—44no—
205C2×Dic11—42no—
206C2×Dic11—44no—
207C2×Dic11—84no—
208C2×Dic11—84no—
209C2×Dic11—84no—
210C2×Dic11—84no—
211C23×D4—111no—
212C22×C22⋊C4—111no—
213C22×C22⋊C4—112no—
214C22×C22⋊C4C2×D1112yes—
215C22×C22⋊C4C2×D1111yescharacteristic
216C2×#99—224no—
217C2×#99—224no—
218C2×#99—224no—
219#386—222no—
220#386—222no—
221#385—24no—
222#381—112no—
223#380—22no—
224#379—112no—
225#342—224no—
226#342—222no—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—24no—
231C22×C11—24no—
232C22×C11—42no—
233C22×C11—42no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—42no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—41no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—41no—
250C22×C11#38011yescharacteristic
251C22×C11#38512yes—
252C22×C11#38611yescharacteristic
253C22×C11#38812yes—
254C22×C11#39011yescharacteristic
255C22×C11#39211yescharacteristic
256C22×C11#39311yescharacteristic
257C22×C11#39412yes—
258C22×C11#39612yes—
259C22×C11#39711yescharacteristic
260C22×C11#39911yescharacteristic
261C2×D11—44no—
262C2×D11—42no—
263C2×D11—82no—
264C2×D11—84no—
265C2×D11—82no—
266C2×D11—84no—
267C4×C11—44no—
268C4×C11—84no—
269Dic11—42no—
270Dic11—82no—
271Dic11—84no—
272C25—111no—
273C25C22×D1111yescharacteristic
274C22×D4—112no—
275C22×D4—112no—
276C22×D4—221no—
277C22×D4—222no—
278C22×D4—222no—
279C22×D4—221no—
280C22×D4—221no—
281C22×D4—222no—
282C22×D4—221no—
283C22×D4—222no—
284C23×C4—22no—
285C23×C4—111no—
286C23×C4—221no—
287C23×C4—222no—
288C23×C4C22⋊D1112yes—
289C2×C4⋊C4—24no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—112no—
298C2×C22⋊C4—114no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—222no—
301C2×C22⋊C4—222no—
302C2×C22⋊C4—222no—
303C2×C22⋊C4—222no—
304C2×C22⋊C4—222no—
305C2×C22⋊C4—222no—
306C2×C22⋊C4—221no—
307C2×C22⋊C4—224no—
308C2×C22⋊C4C4×D1112yes—
309C2×C22⋊C4D4412yes—
310C2×C22⋊C4C22⋊D1114yes—
311#99—2216no—
312#95—24no—
313#95—224no—
314C2×C11—21no—
315C2×C11—22no—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11—22no—
319C2×C11—22no—
320C2×C11—21no—
321C2×C11—22no—
322C2×C11—21no—
323C2×C11—21no—
324C2×C11#143911yescharacteristic
325C2×C11#191312yes—
326D11—82no—
327C24—82no—
328C24—112no—
329C24—221no—
330C24—221no—
331C24—222no—
332C24—222no—
333C24—882no—
334C24C2×C4×D1111yescharacteristic
335C24C2×D4411yescharacteristic
336C24#433912yes—
337C24D4×D1111yescharacteristic
338C24D4×D1112yes—
339C24#434111yescharacteristic
340C24Q8×D1111yescharacteristic
341C24#434311yescharacteristic
342C24#434312yes—
343C24C2×C22⋊D1111yescharacteristic
344C24C2×C22⋊D1112yes—
345C2×D4—224no—
346C2×D4—222no—
347C2×D4—224no—
348C2×D4—222no—
349C2×D4—224no—
350C2×D4—222no—
351C2×D4—222no—
352C2×D4—224no—
353C2×D4—442no—
354C2×D4—442no—
355C2×D4—442no—
356C2×D4—441no—
357C2×D4—442no—
358C2×D4—442no—
359C2×D4—441no—
360C2×D4—441no—
361C2×D4—442no—
362C2×D4—441no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—24no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—82no—
369C22×C4—84no—
370C22×C4—112no—
371C22×C4—221no—
372C22×C4—222no—
373C22×C4—221no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—224no—
377C22×C4—442no—
378C22×C4—442no—
379C22×C4—442no—
380C22×C4—882no—
381C22×C4—884no—
382C22×C4(C2×D11)⋊C414yes—
383C4⋊C4—84no—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—24no—
388C22⋊C4—42no—
389C22⋊C4—42no—
390C22⋊C4—224no—
391C22⋊C4—224no—
392C22⋊C4—224no—
393C22⋊C4—442no—
394C22⋊C4—441no—
395C22⋊C4—441no—
396C22⋊C4—442no—
397C22⋊C4—884no—
398C11#1104611yescharacteristic, complemented, Sylow
399C23—42no—
400C23—44no—
401C23—42no—
402C23—44no—
403C23—42no—
404C23—81no—
405C23—82no—
406C23—81no—
407C23—81no—
408C23—81no—
409C23—82no—
410C23—222no—
411C23—224no—
412C23—444no—
413C23—441no—
414C23—441no—
415C23—442no—
416C23—884no—
417C23—882no—
418C23—882no—
419C23—884no—
420C23C4⋊C4×D1111yescharacteristic
421C23#6694511yescharacteristic
422C23#6694612yes—
423C23#6694712yes—
424C23#6694712yes—
425C23#6694811yescharacteristic
426C23#6694812yes—
427C23#6694912yes—
428C23#6695011yescharacteristic
429C23#6695112yes—
430C23C2×(C2×D11)⋊C411yescharacteristic
431C23C4×C22⋊D1112yes—
432C23#6698211yescharacteristic
433C23#6698312yes—
434C23#6699012yes—
435C23#6699111yescharacteristic
436C23#6699212yes—
437C23#6699311yescharacteristic
438C23#6699911yescharacteristic
439C23#6699912yes—
440C23#6700011yescharacteristic
441C23#6700012yes—
442C23#6700611yescharacteristic
443D4—442no—
444D4—442no—
445D4—444no—
446D4—442no—
447D4—442no—
448D4—444no—
449C2×C4—24no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—48no—
453C2×C4—44no—
454C2×C4—82no—
455C2×C4—84no—
456C2×C4—84no—
457C2×C4—222no—
458C2×C4—224no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—442no—
462C2×C4—444no—
463C2×C4—442no—
464C2×C4—444no—
465C2×C4—884no—
466C2×C4—884no—
467C2×C4—884no—
468C2×C4—884no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—24no—
473C22—24no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—41no—
480C22—41no—
481C22—42no—
482C22—41no—
483C22—42no—
484C22—41no—
485C22—42no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—42no—
490C22—41no—
491C22—42no—
492C22—444no—
493C22—442no—
494C22—884no—
495C22—882no—
496C22—884no—
497C22—882no—
498C22#1062260011yescharacteristic
499C22#1062260111yescharacteristic
500C22#1062260212yes—
501C22#1062260312yes—
502C22#1062260412yes—
503C22#1062260511yescharacteristic
504C22#1062260611yescharacteristic
505C22#1062260712yes—
506C22#1062282611yescharacteristic
507C22#1062283611yescharacteristic
508C22#1062284411yescharacteristic
509C4—44no—
510C4—84no—
511C4—442no—
512C4—882no—
513C4—884no—
514C2—21no—
515C2—21no—
516C2—22no—
517C2—21no—
518C2—22no—
519C2—22no—
520C2—21no—
521C2—21no—
522C2—21no—
523C2—22no—
524C2—882no—
525C2#1306685811yescharacteristic
526C2#1306915812yes—
subgroupG/H
centerC22#10622826
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC11×#2315C2
socleC22×C11#386
prime radicalC23×C22⋊D11C22
cosocleC25×C11C23
hypercenter#2315D11
hypocenterC11#11046
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #2315

Complements

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

NH ≅ G/Ntype
3. C2×#10622164C2semidirect
4. C2×#10622165C2semidirect
5. C11×#2315C2semidirect
15. #10622568C4semidirect
19. #10622556C4semidirect
82. C23×D11C4⋊C4semidirect
120. C22×Dic11C4⋊C4semidirect
137. #2315D11semidirect
398. C11#11046semidirect

Maximal subgroups

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

subgroupindex
C22×#668702
#130711912
C2×#106221642
C2×#106221652
C11×#23152
#1104611