Finite Group Databasebeta

← #14781183

Subgroups — #14781183

Order 2816.

1506 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic, complemented
2#13071194C212yesmaximal
3#13069783C214yesmaximal, complemented
4#13069780C214yesmaximal, complemented
5C2×#10622164C211yesmaximal, characteristic, complemented
6C2×#10622165C212yesmaximal, complemented
7C11×#2308C211yesmaximal, characteristic
8C23×D4×C11C2211yescharacteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C22⋊Dic11C2212yes—
12C22×C22⋊Dic11C2212yes—
13C2×#66977—22no—
14#10623014—22no—
15#10623014—24no—
16#10623014C2214yes—
17C2×#66931—24no—
18C11×#386—22no—
19C11×#386—22no—
20C11×#381C2212yes—
21C11×#379C2212yes—
22#10622860C2214yes—
23#10622833—24no—
24#10622833—24no—
25#10622824C2214yes—
26#10622165C2218yes—
27#10622164C2214yes—
28C25×C11C2311yescharacteristic
29C25×C11C2311yescharacteristic
30C22×D4×C11—22no—
31C22×D4×C11—22no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—22no—
35C22×D4×C11—24no—
36C22×D4×C11Q814yescomplemented
37C23×C4×C11—21no—
38C23×C4×C11D412yes—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11—22no—
41C23×Dic11D414yes—
42C22×Dic22—22no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—24no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—24no—
48C2×C11×C22⋊C4D412yes—
49C2×C11×C22⋊C4C2312yes—
50C2×C11×C22⋊C4C2312yes—
51C2×C22⋊Dic11—22no—
52C2×C22⋊Dic11—22no—
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—24no—
56C2×C22⋊Dic11—24no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—28no—
59C2×C22⋊Dic11D414yes—
60C2×C22⋊Dic11C2314yes—
61C2×C22⋊Dic11C2314yes—
62C2×C4⋊Dic11—22no—
63#66977—28no—
64#66977—28no—
65C2×Dic11⋊C4—24no—
66#66931—216no—
67#66931—216no—
68C11×#95—24no—
69C11⋊#95—28no—
70#23468—111nomaximal, Sylow
71C24×C11—22no—
72C24×C11—21no—
73C24×C11—21no—
74C24×C11—22no—
75C24×C11—82no—
76C24×C11—82no—
77C24×C11C2×D412yes—
78C24×C11C2×D412yes—
79C24×C11C2×D411yescharacteristic
80C24×C11C2×D411yescharacteristic
81C24×C11C2×Q812yes—
82C24×C11C2×Q812yescomplemented
83C24×C11#4112yes—
84C24×C11#4114yes—
85C24×C11C2411yescharacteristic
86C2×D4×C11—28no—
87C2×D4×C11—28no—
88C2×D4×C11—24no—
89C2×D4×C11—24no—
90C2×D4×C11—41no—
91C2×D4×C11—42no—
92C2×D4×C11—41no—
93C2×D4×C11—44no—
94C2×D4×C11—44no—
95C2×D4×C11—42no—
96C2×D4×C11—42no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—42no—
105C22×C4×C11—82no—
106C22×C4×C11—82no—
107C22×C4×C11C2×D414yes—
108C22×C4×C11C2×Q812yescomplemented
109C22×Dic11—24no—
110C22×Dic11—24no—
111C22×Dic11—24no—
112C22×Dic11—44no—
113C22×Dic11—84no—
114C22×Dic11—84no—
115C22×Dic11C2×D418yes—
116C2×Dic22—28no—
117C2×Dic22—84no—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—42no—
122C11×C22⋊C4—84no—
123C22⋊Dic11—24no—
124C22⋊Dic11—24no—
125C22⋊Dic11—24no—
126C22⋊Dic11—24no—
127C22⋊Dic11—24no—
128C22⋊Dic11—24no—
129C22⋊Dic11—44no—
130C22⋊Dic11—88no—
131C4⋊Dic11—28no—
132Dic11⋊C4—216no—
133C2×#543—111no—
134#2308—112no—
135#2308D1111yescharacteristic
136#2030—114no—
137#2029—114no—
138C2×#342—112no—
139C2×#342—111no—
140C23×C11—24no—
141C23×C11—22no—
142C23×C11—44no—
143C23×C11—44no—
144C23×C11—42no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—48no—
148C23×C11—44no—
149C23×C11—41no—
150C23×C11—42no—
151C23×C11—41no—
152C23×C11—82no—
153C23×C11—82no—
154C23×C11—82no—
155C23×C11—84no—
156C23×C11—82no—
157C23×C11—84no—
158C23×C11#12011yescharacteristic
159C23×C11#12012yes—
160C23×C11#12011yescharacteristic
161C23×C11C22⋊Q814yes—
162C23×C11C22⋊Q814yes—
163C23×C11C22⋊Q812yes—
164C23×C11C22⋊Q812yes—
165C23×C11#12414yes—
166C23×C11#12414yes—
167C23×C11#12412yes—
168C23×C11#12412yes—
169C23×C11C22×D412yes—
170C23×C11C22×D411yescharacteristic
171C23×C11C22×Q811yescharacteristic
172C23×C11C2×#4111yescharacteristic
173C23×C11C2×#4112yes—
174D4×C11—44no—
175D4×C11—48no—
176D4×C11—44no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—44no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—44no—
185C2×C4×C11—44no—
186C2×C4×C11—42no—
187C2×C4×C11—82no—
188C2×C4×C11—84no—
189C2×Dic11—28no—
190C2×Dic11—48no—
191C2×Dic11—48no—
192C2×Dic11—48no—
193C2×Dic11—44no—
194C2×Dic11—84no—
195C2×Dic11—88no—
196Dic22—88no—
197C23×D4C2×D1111yescharacteristic
198#543—114no—
199#543—224no—
200#543—222no—
201C2×C22⋊Q8—224no—
202C2×C22⋊Q8—222no—
203C22×C22⋊C4—112no—
204C22×C22⋊C4—112no—
205C22×C22⋊C4C2×D1111yescharacteristic
206C22×C22⋊C4C2×D1111yescharacteristic
207#386—22no—
208#386—22no—
209#386—224no—
210#386—224no—
211#381—114no—
212#381C2×D1112yes—
213#379—114no—
214#379C2×D1112yes—
215#342—114no—
216#342—118no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—24no—
221C22×C11—24no—
222C22×C11—42no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—42no—
226C22×C11—44no—
227C22×C11—44no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—44no—
231C22×C11—42no—
232C22×C11—44no—
233C22×C11—48no—
234C22×C11—44no—
235C22×C11—42no—
236C22×C11—84no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11#39312yes—
240C22×C11#39314yes—
241C22×C11#39312yes—
242C22×C11C2×#12011yescharacteristic
243C22×C11C2×C22⋊Q812yes—
244C22×C11C2×C22⋊Q811yescharacteristic
245C22×C11C2×#12412yes—
246C22×C11C2×#12411yescharacteristic
247C4×C11—42no—
248C4×C11—44no—
249C4×C11—82no—
250Dic11—48no—
251Dic11—84no—
252C25C22×D1111yescharacteristic
253C25C22×D1111yescharacteristic
254C22×Q8—222no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—24no—
259C22×D4—21no—
260C22×D4—21no—
261C22×D4Dic2214yescomplemented
262C23×C4—21no—
263C23×C4—114no—
264C23×C4—222no—
265C23×C4C22⋊D1112yes—
266C23×C4C22×D1111yescharacteristic
267C22⋊Q8—2216no—
268C22⋊Q8—2216no—
269C22⋊Q8—228no—
270C22⋊Q8—228no—
271C2×C4⋊C4—224no—
272C2×C4⋊C4—222no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—114no—
279C2×C22⋊C4—114no—
280C2×C22⋊C4—114no—
281C2×C22⋊C4—222no—
282C2×C22⋊C4—222no—
283C2×C22⋊C4—222no—
284C2×C22⋊C4—222no—
285C2×C22⋊C4—224no—
286C2×C22⋊C4—224no—
287C2×C22⋊C4—222no—
288C2×C22⋊C4—228no—
289C2×C22⋊C4C22⋊D1112yes—
290C2×C22⋊C4C22×D1112yes—
291C2×C22⋊C4C22×D1112yes—
292#95—24no—
293#95—228no—
294C2×C11—22no—
295C2×C11—21no—
296C2×C11—22no—
297C2×C11—21no—
298C2×C11—22no—
299C2×C11—22no—
300C2×C11—24no—
301C2×C11—82no—
302C2×C11C2×#39311yescharacteristic
303C2×C11#302612yes—
304C24—22no—
305C24—21no—
306C24—21no—
307C24—22no—
308C24—82no—
309C24—82no—
310C24C2×Dic2212yes—
311C24C2×Dic2212yescomplemented
312C24#433912yes—
313C24D4×D1112yes—
314C24D4×D1112yes—
315C24#434114yes—
316C24C2×C22⋊D1111yescharacteristic
317C24C2×C22⋊D1111yescharacteristic
318C24C23×D1111yescharacteristic
319C2×Q8—228no—
320C2×Q8—884no—
321C2×D4—28no—
322C2×D4—28no—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—44no—
326C2×D4—44no—
327C2×D4—42no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—41no—
331C2×D4—41no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—42no—
340C22×C4—82no—
341C22×C4—82no—
342C22×C4—118no—
343C22×C4—224no—
344C22×C4—224no—
345C22×C4—224no—
346C22×C4—444no—
347C22×C4—884no—
348C22×C4—884no—
349C22×C4C2×Dic2212yescomplemented
350C22×C4C2×C22⋊D1114yes—
351C4⋊C4—2216no—
352C4⋊C4—228no—
353C22⋊C4—24no—
354C22⋊C4—24no—
355C22⋊C4—24no—
356C22⋊C4—42no—
357C22⋊C4—84no—
358C22⋊C4—224no—
359C22⋊C4—224no—
360C22⋊C4—224no—
361C22⋊C4—224no—
362C22⋊C4—224no—
363C22⋊C4—224no—
364C22⋊C4—444no—
365C22⋊C4—888no—
366C11#2346811yescharacteristic, complemented, Sylow
367C23—24no—
368C23—22no—
369C23—42no—
370C23—42no—
371C23—44no—
372C23—44no—
373C23—42no—
374C23—44no—
375C23—48no—
376C23—42no—
377C23—41no—
378C23—41no—
379C23—82no—
380C23—82no—
381C23—82no—
382C23—84no—
383C23—82no—
384C23—84no—
385C23#6693114yes—
386C23#6693114yes—
387C23#6693814yes—
388C23#6693814yes—
389C23#6697712yes—
390C23#6697712yes—
391C23#6698912yes—
392C23#6698912yes—
393C23#6699012yes—
394C23#6699011yescharacteristic
395C23#6699011yescharacteristic
396C23C22×Dic2211yescharacteristic
397C23C2×#433911yescharacteristic
398C23C2×D4×D1112yes—
399C23C2×#434112yes—
400C23C22×C22⋊D1111yescharacteristic
401Q8—888no—
402D4—44no—
403D4—48no—
404D4—44no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—82no—
416C2×C4—84no—
417C2×C4—228no—
418C2×C4—448no—
419C2×C4—448no—
420C2×C4—448no—
421C2×C4—444no—
422C2×C4—884no—
423C2×C4—888no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—24no—
428C22—24no—
429C22—42no—
430C22—44no—
431C22—41no—
432C22—41no—
433C22—42no—
434C22—44no—
435C22—44no—
436C22—44no—
437C22—42no—
438C22—42no—
439C22—42no—
440C22—48no—
441C22—44no—
442C22—42no—
443C22—82no—
444C22—84no—
445C22—82no—
446C22#1062256012yes—
447C22#1062256014yes—
448C22#1062256012yes—
449C22C2×#6693112yes—
450C22C2×#6693812yes—
451C22C2×#6697711yescharacteristic
452C22C2×#6698911yescharacteristic
453C22C2×#6699011yescharacteristic
454C4—42no—
455C4—44no—
456C4—82no—
457C4—448no—
458C4—884no—
459C2—21no—
460C2—22no—
461C2—22no—
462C2—21no—
463C2—22no—
464C2—22no—
465C2—24no—
466C2—82no—
467C2C2×#1062256011yescharacteristic
468C2#1307801212yes—
subgroupG/H
centerC22C2×#66990
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#2308C2
socleC22×C11C2×#120
prime radicalC23×D4×C11C22
hypercenter#2308D11
hypocenterC11#23468
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #2308

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
3. #13069783C2semidirect
4. #13069780C2semidirect
5. C2×#10622164C2semidirect
6. C2×#10622165C2semidirect
36. C22×D4×C11Q8semidirect
82. C24×C11C2×Q8semidirect
108. C22×C4×C11C2×Q8semidirect
261. C22×D4Dic22semidirect
311. C24C2×Dic22semidirect
349. C22×C4C2×Dic22semidirect
366. C11#23468semidirect

Maximal subgroups

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

subgroupindex
C2×#106230142
#130711942
#130697832
#130697802
C2×#106221642
C2×#106221652
C11×#23082
#2346811