Finite Group Databasebeta

← #14660712

Subgroups — #14660712

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×#66898C212yesmaximal
2#13071230C211yesmaximal, characteristic, complemented
3C2×#10622164C211yesmaximal, characteristic, complemented
4C2×#10622165C212yesmaximal, complemented
5C11×#2308C211yesmaximal, characteristic
6C23×D4×C11C2211yescharacteristic
7C22×C11×C22⋊C4C2211yescharacteristic
8C22×C11×C22⋊C4C2211yescharacteristic
9C22×C22⋊Dic11C2212yes—
10C22×C22⋊Dic11C2212yes—
11C11×#386—22no—
12C11×#386—22no—
13C11×#381C412yescomplemented
14C11×#379C412yescomplemented
15C2×#66898—24no—
16C2×#66898—24no—
17C2×#66898—24no—
18#10622825—22no—
19#10622563—24no—
20#10622165—24no—
21#10622164—22no—
22C25×C11C2×C411yescharacteristic
23C25×C11C2311yescharacteristic
24C22×D4×C11—22no—
25C22×D4×C11—22no—
26C22×D4×C11—21no—
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11—22no—
31C22×D4×C11—22no—
32C22×D4×C11D412yes—
33C22×D4×C11Q812yes—
34C23×C4×C11—21no—
35C23×C4×C11C2×C411yescharacteristic
36C23×C4×C11D412yes—
37C23×Dic11—22no—
38C23×Dic11—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—24no—
45C2×C11×C22⋊C4C2×C412yes—
46C2×C11×C22⋊C4C2×C412yes—
47C2×C11×C22⋊C4D412yes—
48C2×C22⋊Dic11—22no—
49C2×C22⋊Dic11—22no—
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—22no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11D414yes—
59C2×C22⋊Dic11D414yes—
60C2×C4⋊Dic11—24no—
61C11×#95—24no—
62#66898—216no—
63C11⋊#95—24no—
64#11046—111nomaximal, Sylow
65C24×C11—21no—
66C24×C11—21no—
67C24×C11—22no—
68C24×C11—22no—
69C24×C11—82no—
70C24×C11—82no—
71C24×C11C4⋊C412yescomplemented
72C24×C11C22×C411yescharacteristic
73C24×C11C2×D411yescharacteristic
74C24×C11C2×D411yescharacteristic
75C24×C11C2×D412yes—
76C24×C11C2×D411yescharacteristic
77C24×C11C2×D412yes—
78C24×C11C2×Q811yescharacteristic
79C24×C11#4112yes—
80C24×C11#4111yescharacteristic
81C24×C11#4111yescharacteristic
82C24×C11#4112yes—
83C2×D4×C11—24no—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—24no—
89C2×D4×C11—24no—
90C2×D4×C11—24no—
91C2×D4×C11—41no—
92C2×D4×C11—42no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C2×D4×C11—41no—
96C2×D4×C11—42no—
97C2×D4×C11—42no—
98C2×D4×C11—41no—
99C2×D4×C11—42no—
100C2×D4×C11—41no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—42no—
109C22×C4×C11—82no—
110C22×C4×C11—82no—
111C22×C4×C11C22⋊C414yes—
112C22×C4×C11C4⋊C412yescomplemented
113C22×Dic11—24no—
114C22×Dic11—24no—
115C22×Dic11—42no—
116C22×Dic11—42no—
117C22×Dic11—42no—
118C22×Dic11—42no—
119C22×Dic11—84no—
120C22×Dic11—84no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—84no—
127C22⋊Dic11—24no—
128C22⋊Dic11—24no—
129C22⋊Dic11—24no—
130C22⋊Dic11—24no—
131C22⋊Dic11—42no—
132C22⋊Dic11—42no—
133C22⋊Dic11—42no—
134C22⋊Dic11—42no—
135C4⋊Dic11—84no—
136C22×#99—112no—
137#2315—111no—
138#2308D1111yescharacteristic
139C2×#342—112no—
140C2×#342—111no—
141C23×C11—22no—
142C23×C11—24no—
143C23×C11—44no—
144C23×C11—44no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—44no—
149C23×C11—41no—
150C23×C11—42no—
151C23×C11—41no—
152C23×C11—84no—
153C23×C11—81no—
154C23×C11—82no—
155C23×C11—81no—
156C23×C11—81no—
157C23×C11—81no—
158C23×C11—82no—
159C23×C11—82no—
160C23×C11—82no—
161C23×C11—84no—
162C23×C11C2×C22⋊C411yescharacteristic
163C23×C11C2×C4⋊C411yescharacteristic
164C23×C11#11711yescharacteristic
165C23×C11C4×D412yes—
166C23×C11C4×D412yes—
167C23×C11#12012yes—
168C23×C11#12011yescharacteristic
169C23×C11#12112yes—
170C23×C11#12111yescharacteristic
171C23×C11#12111yescharacteristic
172C23×C11#12112yes—
173C23×C11#12112yes—
174C23×C11C22⋊Q812yes—
175C23×C11C22⋊Q812yes—
176C23×C11C22⋊Q811yescharacteristic
177C23×C11C22⋊Q811yescharacteristic
178C23×C11#12312yes—
179C23×C11#12312yes—
180C23×C11#12311yescharacteristic
181C23×C11#12412yes—
182C23×C11#12411yescharacteristic
183C23×C11#12612yes—
184C23×C11#12711yescharacteristic
185D4×C11—42no—
186D4×C11—42no—
187D4×C11—44no—
188D4×C11—44no—
189D4×C11—42no—
190D4×C11—42no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—44no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—44no—
199C2×C4×C11—44no—
200C2×C4×C11—42no—
201C2×C4×C11—82no—
202C2×C4×C11—84no—
203C2×Dic11—48no—
204C2×Dic11—44no—
205C2×Dic11—44no—
206C2×Dic11—84no—
207C2×Dic11—84no—
208C2×Dic11—84no—
209C2×Dic11—84no—
210C2×Dic11—84no—
211C23×D4C2×D1111yescharacteristic
212C22×C22⋊C4—112no—
213C22×C22⋊C4—112no—
214C22×C22⋊C4C2×D1111yescharacteristic
215C22×C22⋊C4C2×D1111yescharacteristic
216C2×#99—224no—
217C2×#99—224no—
218C2×#99—224no—
219#386—22no—
220#386—22no—
221#385—224no—
222#381Dic1112yescomplemented
223#380—222no—
224#379Dic1112yescomplemented
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—41no—
234C22×C11—41no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—41no—
248C22×C11—42no—
249C22×C11—41no—
250C22×C11—44no—
251C22×C11—42no—
252C22×C11—84no—
253C22×C11—82no—
254C22×C11—84no—
255C22×C11—82no—
256C22×C11#38011yescharacteristic
257C22×C11#38512yes—
258C22×C11#38611yescharacteristic
259C22×C11#38812yes—
260C22×C11#39011yescharacteristic
261C22×C11#39211yescharacteristic
262C22×C11#39311yescharacteristic
263C22×C11#39412yes—
264C22×C11#39612yes—
265C22×C11#39711yescharacteristic
266C22×C11#39911yescharacteristic
267C4×C11—44no—
268C4×C11—42no—
269C4×C11—82no—
270Dic11—84no—
271Dic11—84no—
272C25C2×Dic1111yescharacteristic
273C25C22×D1111yescharacteristic
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4Dic2212yes—
283C22×D4D4412yes—
284C23×C4—21no—
285C23×C4—222no—
286C23×C4—222no—
287C23×C4C2×Dic1111yescharacteristic
288C23×C4C22⋊D1112yes—
289C2×C4⋊C4—224no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—114no—
297C2×C22⋊C4—114no—
298C2×C22⋊C4—222no—
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—222no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4C2×Dic1112yes—
309C2×C22⋊C4C2×Dic1112yes—
310C2×C22⋊C4C22⋊D1112yes—
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—82no—
325C2×C11#143911yescharacteristic
326C2×C11#191312yes—
327C24—21no—
328C24—21no—
329C24—22no—
330C24—22no—
331C24—82no—
332C24—82no—
333C24C4⋊Dic1112yescomplemented
334C24C2×Dic2211yescharacteristic
335C24C2×D4411yescharacteristic
336C24#433911yescharacteristic
337C24#433911yescharacteristic
338C24D4×D1112yes—
339C24D4×D1112yes—
340C24#434112yes—
341C24#434112yes—
342C24C22×Dic1111yescharacteristic
343C24C2×C22⋊D1111yescharacteristic
344C24C2×C22⋊D1111yescharacteristic
345C2×D4—24no—
346C2×D4—24no—
347C2×D4—24no—
348C2×D4—24no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—42no—
354C2×D4—42no—
355C2×D4—42no—
356C2×D4—42no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—41no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—42no—
371C22×C4—82no—
372C22×C4—82no—
373C22×C4—224no—
374C22×C4—224no—
375C22×C4—442no—
376C22×C4—442no—
377C22×C4—442no—
378C22×C4—442no—
379C22×C4—884no—
380C22×C4—884no—
381C22×C4C4⋊Dic1112yescomplemented
382C22×C4C22⋊Dic1114yes—
383C4⋊C4—884no—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—84no—
390C22⋊C4—224no—
391C22⋊C4—224no—
392C22⋊C4—224no—
393C22⋊C4—224no—
394C22⋊C4—442no—
395C22⋊C4—442no—
396C22⋊C4—442no—
397C22⋊C4—442no—
398C11#1104611yescharacteristic, complemented, Sylow
399C23—22no—
400C23—24no—
401C23—42no—
402C23—42no—
403C23—44no—
404C23—44no—
405C23—42no—
406C23—44no—
407C23—42no—
408C23—41no—
409C23—41no—
410C23—84no—
411C23—81no—
412C23—81no—
413C23—81no—
414C23—81no—
415C23—82no—
416C23—82no—
417C23—82no—
418C23—82no—
419C23—84no—
420C23#6693112yes—
421C23#6693112yes—
422C23#6693212yes—
423C23#6693512yes—
424C23#6693612yes—
425C23#6693712yes—
426C23#6693812yes—
427C23#6693912yes—
428C23#6697711yescharacteristic
429C23#6697711yescharacteristic
430C23C2×C4⋊Dic1111yescharacteristic
431C23#6697911yescharacteristic
432C23#6698311yescharacteristic
433C23#6698311yescharacteristic
434C23D4×Dic1112yes—
435C23D4×Dic1112yes—
436C23#6698811yescharacteristic
437C23#6698911yescharacteristic
438C23#6699011yescharacteristic
439C23#6699112yes—
440C23#6699212yes—
441C23#6699311yescharacteristic
442C23C2×C22⋊Dic1111yescharacteristic
443D4—42no—
444D4—44no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—44no—
449C2×C4—24no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—44no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—44no—
457C2×C4—44no—
458C2×C4—42no—
459C2×C4—82no—
460C2×C4—84no—
461C2×C4—448no—
462C2×C4—444no—
463C2×C4—444no—
464C2×C4—884no—
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—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—44no—
493C22—42no—
494C22—84no—
495C22—82no—
496C22—84no—
497C22—82no—
498C22#1062256011yescharacteristic
499C22#1062256112yes—
500C22#1062256211yescharacteristic
501C22#1062256312yes—
502C22#1062256412yes—
503C22#1062256611yescharacteristic
504C22#1062257311yescharacteristic
505C22#1062257412yes—
506C22#1062282511yescharacteristic
507C22#1062283311yescharacteristic
508C22#1062283411yescharacteristic
509C4—44no—
510C4—42no—
511C4—82no—
512C4—884no—
513C4—884no—
514C2—21no—
515C2—21no—
516C2—22no—
517C2—21no—
518C2—22no—
519C2—22no—
520C2—21no—
521C2—22no—
522C2—21no—
523C2—21no—
524C2—82no—
525C2#1306686111yescharacteristic
526C2#1306915912yes—
subgroupG/H
centerC22#10622833
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC11×#2308C2
socleC22×C11#386
prime radicalC23×D4×C11C22
cosocleC25×C11C23
hypercenter#2308D11
hypocenterC11#11046
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #2308

Complements

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

NH ≅ G/Ntype
2. #13071230C2semidirect
3. C2×#10622164C2semidirect
4. C2×#10622165C2semidirect
13. C11×#381C4semidirect
14. C11×#379C4semidirect
71. C24×C11C4⋊C4semidirect
112. C22×C4×C11C4⋊C4semidirect
222. #381Dic11semidirect
224. #379Dic11semidirect
333. C24C4⋊Dic11semidirect
381. C22×C4C4⋊Dic11semidirect
398. C11#11046semidirect

Maximal subgroups

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

subgroupindex
C22×#668982
#130712302
C2×#106221642
C2×#106221652
C11×#23082
#1104611