Finite Group Databasebeta

← #14781153

Subgroups — #14781153

Order 2816.

1214 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623031C211yesmaximal, characteristic, complemented
2#13077135C212yesmaximal
3#13069777C214yesmaximal, complemented
4#13069772C214yesmaximal, complemented
5C2×#10622168C211yesmaximal, characteristic, complemented
6#13068326C212yesmaximal, complemented
7C11×#2311C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C2×#66979C2212yes—
12C2×#66977—22no—
13C22×#4318C2212yes—
14#10623031—22no—
15#10623031—24no—
16#10623031C2214yes—
17C2×#66943—22no—
18C2×#66941—22no—
19C11×#391C2212yes—
20C11×#390C2212yes—
21C11×#386—22no—
22C11×#380—22no—
23#10622846—24no—
24#10622845—22no—
25#10622845—22no—
26#10622838C2214yes—
27#10622828C2214yes—
28#10622168C2214yes—
29#10622161C2218yes—
30C2×C11×#41—22no—
31C2×C11×#41—22no—
32C2×C11×#41—22no—
33C2×C11×#41—24no—
34C2×C11×#41Q814yescomplemented
35C22×Q8×C11C2311yescharacteristic
36C22×D4×C11—21no—
37C22×D4×C11C2311yescharacteristic
38C23×C4×C11—21no—
39C23×C4×C11D412yes—
40C23×C4×C11C2311yescharacteristic
41C22×Dic22—22no—
42C11×#117—24no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D412yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—24no—
50C2×C42×C11C2312yes—
51C2×C22⋊Dic11—22no—
52#66979—22no—
53#66979—22no—
54#66979D414yes—
55#66979C2314yes—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11D412yes—
58C2×C4⋊Dic11D412yes—
59#66977—28no—
60#66977—28no—
61C2×Dic11⋊C4—24no—
62C2×C4×Dic11—22no—
63C2×#4318—22no—
64C2×#4318—24no—
65C2×#4318—24no—
66C2×#4318C2314yes—
67C22×C11⋊C8—22no—
68#66943—28no—
69#66943—28no—
70#66941—28no—
71#66941—28no—
72C11×#95—24no—
73#66899—24no—
74#66899—24no—
75#66896—24no—
76#66896—24no—
77#23462—111nomaximal, Sylow
78C24×C11—21no—
79C24×C11C2×D411yescharacteristic
80C11×#41—28no—
81C11×#41—28no—
82C11×#41—44no—
83C11×#41—44no—
84C2×Q8×C11—21no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11C2×Q812yescomplemented
88C2×D4×C11—24no—
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—21no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—42no—
95C2×D4×C11C2×Q812yescomplemented
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—24no—
100C22×C4×C11—22no—
101C22×C4×C11—42no—
102C22×C4×C11—42no—
103C22×C4×C11—82no—
104C22×C4×C11C2×D414yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×Q812yes—
109C22×C4×C11#4114yes—
110C22×C4×C11#4112yes—
111C22×C4×C11C2411yescharacteristic
112C22×Dic11—22no—
113C22×Dic11—22no—
114C2×Dic22—28no—
115C2×Dic22—84no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—42no—
119C11×C22⋊C4—42no—
120C11×C22⋊C4—84no—
121C42×C11—24no—
122C22⋊Dic11—24no—
123C22⋊Dic11—24no—
124C4⋊Dic11—28no—
125C4⋊Dic11—22no—
126C4⋊Dic11—22no—
127C4⋊Dic11C2×D414yes—
128C4⋊Dic11C2×D414yes—
129Dic11⋊C4—216no—
130C4×Dic11—24no—
131C4×Dic11—24no—
132#4318—24no—
133#4318—24no—
134#4318—44no—
135C2×C11⋊C8—24no—
136C2×C11⋊C8—44no—
137C2×#544—111no—
138#2896—112no—
139#2311D1111yescharacteristic
140#2028—114no—
141#2027—114no—
142C2×#343—111no—
143#1733—112no—
144C23×C11—22no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11#12011yescharacteristic
152C23×C11#12011yescharacteristic
153C23×C11C22⋊Q812yes—
154C23×C11#12412yes—
155C23×C11C22×D411yescharacteristic
156Q8×C11—24no—
157Q8×C11—42no—
158D4×C11—24no—
159D4×C11—44no—
160D4×C11—44no—
161D4×C11—42no—
162C2×C4×C11—24no—
163C2×C4×C11—22no—
164C2×C4×C11—44no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—48no—
168C2×C4×C11—44no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—82no—
173C2×C4×C11#12012yes—
174C2×C4×C11C22⋊Q814yes—
175C2×C4×C11C22⋊Q814yes—
176C2×C4×C11C22⋊Q812yes—
177C2×C4×C11#12414yes—
178C2×C4×C11#12414yes—
179C2×C4×C11#12412yes—
180C2×C4×C11C22×D412yes—
181C2×C4×C11C22×Q811yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11C2×#4112yes—
184C2×Dic11—24no—
185C2×Dic11—24no—
186C2×Dic11—44no—
187C2×Dic11—44no—
188Dic22—88no—
189C11⋊C8—44no—
190C22×#41C2×D1111yescharacteristic
191C22×M16—112no—
192#544—114no—
193#544—224no—
194#544—222no—
195C2×C4⋊Q8—222no—
196C2×#125—222no—
197C2×C22⋊Q8—222no—
198C2×#117—112no—
199C2×#117C2×D1111yescharacteristic
200C22×C4⋊C4C2×D1111yescharacteristic
201#419—114no—
202#418—114no—
203#417—222no—
204#417—222no—
205#416—224no—
206#391C2×D1112yes—
207#390C2×D1112yes—
208#386—22no—
209#380—22no—
210#343—114no—
211#339—118no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—42no—
219C22×C11—42no—
220C22×C11—44no—
221C22×C11—42no—
222C22×C11—82no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11#39312yes—
226C22×C11#39312yes—
227C22×C11C2×#12011yescharacteristic
228C22×C11C2×C22⋊Q811yescharacteristic
229C22×C11C2×#12411yescharacteristic
230C4×C11—42no—
231C4×C11—44no—
232C4×C11—82no—
233C4×C11#39314yes—
234C4×C11C2×C22⋊Q812yes—
235C4×C11C2×#12412yes—
236Dic11—44no—
237Dic11—44no—
238C2×#41—22no—
239C2×#41—22no—
240C2×#41—22no—
241C2×#41—24no—
242C2×#41Dic2214yescomplemented
243C22×Q8—222no—
244C22×Q8C22×D1111yescharacteristic
245C22×D4—21no—
246C22×D4C22×D1111yescharacteristic
247C23×C4—21no—
248C23×C4C22⋊D1112yes—
249C23×C4C22×D1111yescharacteristic
250C2×M16—114no—
251C2×M16—222no—
252C2×M16—224no—
253C2×M16—224no—
254C22×C8—222no—
255C4⋊Q8—228no—
256C4⋊Q8—228no—
257#125—228no—
258#125—228no—
259C22⋊Q8—228no—
260C22⋊Q8—228no—
261#117—24no—
262#117—114no—
263#117—114no—
264#117—222no—
265#117—222no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—112no—
270C2×C4⋊C4—112no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4—224no—
273C2×C4⋊C4C22⋊D1112yes—
274C2×C4⋊C4C22×D1112yes—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—24no—
277C2×C22⋊C4—222no—
278C2×C42—222no—
279C2×C42C22×D1112yes—
280#103—224no—
281#103—224no—
282#102—224no—
283#102—224no—
284#95—24no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—22no—
288C2×C11—22no—
289C2×C11—82no—
290C2×C11C2×#39311yescharacteristic
291C2×C11#301911yescharacteristic
292C2×C11#302011yescharacteristic
293C24—21no—
294C24C2×C22⋊D1111yescharacteristic
295#41—28no—
296#41—28no—
297#41—44no—
298#41—44no—
299C2×Q8—21no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—228no—
303C2×Q8—884no—
304C2×Q8C2×Dic2212yescomplemented
305C2×D4—24no—
306C2×D4—21no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—42no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4C2×Dic2212yescomplemented
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—24no—
317C22×C4—22no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—82no—
321C22×C4—222no—
322C22×C4—222no—
323C22×C4C2×Dic2212yes—
324C22×C4#433912yes—
325C22×C4D4×D1112yes—
326C22×C4D4×D1112yes—
327C22×C4#434114yes—
328C22×C4C2×C22⋊D1114yes—
329C22×C4C2×C22⋊D1111yescharacteristic
330C22×C4C23×D1111yescharacteristic
331M16—224no—
332M16—224no—
333M16—444no—
334C2×C8—224no—
335C2×C8—444no—
336C4⋊C4—24no—
337C4⋊C4—24no—
338C4⋊C4—42no—
339C4⋊C4—114no—
340C4⋊C4—114no—
341C4⋊C4—228no—
342C4⋊C4—2216no—
343C4⋊C4—222no—
344C4⋊C4—222no—
345C22⋊C4—42no—
346C22⋊C4—84no—
347C22⋊C4—224no—
348C22⋊C4—224no—
349C42—24no—
350C42—224no—
351C42—224no—
352C11#2346211yescharacteristic, complemented, Sylow
353C23—22no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23#6697712yes—
361C23#6698912yes—
362C23#6699011yescharacteristic
363C23#6699011yescharacteristic
364C23C22×C22⋊D1111yescharacteristic
365Q8—24no—
366Q8—42no—
367Q8—888no—
368D4—24no—
369D4—44no—
370D4—44no—
371D4—42no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—44no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—48no—
378C2×C4—44no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—224no—
384C2×C4—224no—
385C2×C4—444no—
386C2×C4—444no—
387C2×C4#6693114yes—
388C2×C4#6693114yes—
389C2×C4#6693814yes—
390C2×C4#6693814yes—
391C2×C4#6697712yes—
392C2×C4#6698912yes—
393C2×C4#6699012yes—
394C2×C4C22×Dic2211yescharacteristic
395C2×C4C2×#433911yescharacteristic
396C2×C4C2×D4×D1112yes—
397C2×C4C2×#434112yes—
398C8—444no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—42no—
406C22—42no—
407C22—44no—
408C22—42no—
409C22—82no—
410C22—81no—
411C22—81no—
412C22#1062256012yes—
413C22#1062256012yes—
414C22C2×#6697711yescharacteristic
415C22C2×#6698911yescharacteristic
416C22C2×#6699011yescharacteristic
417C4—42no—
418C4—44no—
419C4—82no—
420C4—444no—
421C4—444no—
422C4#1062256014yes—
423C4C2×#6693112yes—
424C4C2×#6693812yes—
425C2—21no—
426C2—21no—
427C2—22no—
428C2—22no—
429C2—82no—
430C2C2×#1062256011yescharacteristic
431C2#1307797211yescharacteristic
432C2#1307797911yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2311C2
socleC22×C11C2×#120
prime radicalC22×C11×#41C22
hypercenter#2311D11
hypocenterC11#23462
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2311

Complements

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

NH ≅ G/Ntype
1. C2×#10623031C2semidirect
3. #13069777C2semidirect
4. #13069772C2semidirect
5. C2×#10622168C2semidirect
6. #13068326C2semidirect
34. C2×C11×#41Q8semidirect
87. C2×Q8×C11C2×Q8semidirect
95. C2×D4×C11C2×Q8semidirect
242. C2×#41Dic22semidirect
304. C2×Q8C2×Dic22semidirect
312. C2×D4C2×Dic22semidirect
352. C11#23462semidirect

Maximal subgroups

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

subgroupindex
C2×#106230312
#130771352
#130697772
#130697722
C2×#106221682
#130683262
C11×#23112
#2346211