Finite Group Databasebeta

← #14727764

Subgroups — #14727764

Order 2816.

912 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082021C211yesmaximal, characteristic
2#13079564C212yesmaximal, complemented
3#13067589C214yesmaximal, complemented
4#13067572C214yesmaximal
5#13067179C212yesmaximal, complemented
6#13066930C211yesmaximal, characteristic
7C11×#2628C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C2×#66979—21no—
11#10623050—22no—
12#10623050—22no—
13#10623048—24no—
14#10623031—21no—
15#10623031C2212yes—
16#10623014—21no—
17#10623014C2212yes—
18#10623001—21no—
19#10623001C2212yes—
20C11×#400—21no—
21C11×#399—21no—
22C11×#395C2212yes—
23C11×#393C2212yes—
24C11×#389—21no—
25C11×#382C2211yescharacteristic
26C11×#380—21no—
27#10622841C2218yes—
28#10622705—22no—
29#10622703—24no—
30#10622694—22no—
31#10622538C2212yes—
32#10622166C2212yes—
33#10622163C2212yes—
34#10622090C2218yes—
35C22×Q8×C11C2312yes—
36C23×C4×C11D411yescharacteristic
37C11×C4⋊Q8—22no—
38C11×C4⋊Q8—22no—
39C11×#117—22no—
40C11×#117—22no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C4⋊C4C2311yescharacteristic
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4D411yescharacteristic
49C2×C11×C22⋊C4C2311yescharacteristic
50C2×C42×C11D411yescharacteristic
51C2×C42×C11C2311yescharacteristic
52C2×C22⋊Dic11—22no—
53C2×#4326—28no—
54#66979—22no—
55#66979—22no—
56#66979—22no—
57#66979—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60#66977—22no—
61#66977—22no—
62#66977—22no—
63#66977C2314yes—
64C2×C4×Dic11—22no—
65#66943—24no—
66#66943—24no—
67#66941—24no—
68#66941—24no—
69#66931—24no—
70#66931—24no—
71#66931—24no—
72#66931—24no—
73#66923—22no—
74#66923—22no—
75#66922—21no—
76#66922—21no—
77#66922D412yes—
78#66922D412yes—
79C4×Dic22—22no—
80C4×Dic22—22no—
81C4×Dic22—22no—
82C4×Dic22D414yes—
83C11×#95—22no—
84C11×#95—21no—
85C11×#95—22no—
86C11×#95C2312yes—
87#66899—28no—
88C22⋊(C11⋊C8)C2314yes—
89C4⋊(C11⋊C8)—22no—
90C4×C11⋊C8—22no—
91#18303—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C2×Q8×C11—24no—
94C2×Q8×C11—82no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11Q1614yescomplemented
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—22no—
108C22×Dic11—22no—
109C2×Dic22—22no—
110C2×Dic22—22no—
111C2×Dic22—22no—
112C2×Dic22C2×D414yes—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—42no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—42no—
119C11×C4⋊C4—82no—
120C11×C22⋊C4—22no—
121C11×C22⋊C4—22no—
122C11×C22⋊C4—82no—
123C42×C11—21no—
124C42×C11—21no—
125C42×C11C2×D412yes—
126C42×C11C2×D412yes—
127C22⋊Dic11—24no—
128C22⋊Dic11—24no—
129#4326—88no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11—22no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11C2×D414yes—
138Dic11⋊C4—24no—
139Dic11⋊C4—24no—
140Dic11⋊C4—24no—
141Dic11⋊C4—24no—
142C4×Dic11—24no—
143C4×Dic11—24no—
144C2×C11⋊C8—24no—
145#3458—111no—
146#3209—112no—
147#2628D1111yescharacteristic
148#1605—114no—
149#1602—114no—
150#1518—112no—
151#1458—111no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11C2×Q1612yes—
157C23×C11C22×D411yescharacteristic
158Q8×C11—48no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11#12012yes—
176C2×C4×C11#12011yescharacteristic
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11C2×Q1612yes—
179C2×C4×C11C2×Q1612yes—
180C2×C4×C11#13712yes—
181C2×C4×C11C22×D412yes—
182C2×Dic11—24no—
183C2×Dic11—24no—
184C2×Dic11—82no—
185C2×Dic11—82no—
186Dic22—44no—
187Dic22—82no—
188Dic22—82no—
189Dic22—82no—
190C11⋊C8—44no—
191#544—112no—
192#544—222no—
193#544—222no—
194#544—221no—
195#543—112no—
196#543—221no—
197#533—112no—
198#533—224no—
199#533—221no—
200C2×C4⋊Q8C2×D1111yescharacteristic
201C2×#117—221no—
202C2×#117C2×D1111yescharacteristic
203#494—222no—
204#487—222no—
205#462—224no—
206#451—118no—
207#431—112no—
208#400—21no—
209#399—21no—
210#395C2×D1112yes—
211#393C2×D1112yes—
212#389—21no—
213#382C2×D1111yescharacteristic
214#380—21no—
215#328—118no—
216#324—112no—
217#323—112no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—22no—
221C22×C11—42no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—81no—
225C22×C11C2×#12011yescharacteristic
226C22×C11C22×Q1611yescharacteristic
227C22×C11C2×#13711yescharacteristic
228C4×C11—22no—
229C4×C11—22no—
230C4×C11—22no—
231C4×C11—41no—
232C4×C11—41no—
233C4×C11—82no—
234C4×C11—82no—
235C4×C11#45112yes—
236C4×C11#45112yes—
237Dic11—44no—
238Dic11—44no—
239C22×Q8C22×D1112yes—
240C23×C4C22⋊D1111yescharacteristic
241C2×Q16—228no—
242C4⋊Q8—22no—
243C4⋊Q8—22no—
244C4⋊Q8—112no—
245C4⋊Q8—112no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248C4⋊Q8—224no—
249C4⋊Q8—224no—
250#125—222no—
251#125—224no—
252#125—224no—
253#125—222no—
254C22⋊Q8—114no—
255C22⋊Q8—224no—
256C22⋊Q8—224no—
257C22⋊Q8—224no—
258C22⋊Q8—224no—
259C22⋊Q8—222no—
260C22⋊Q8—222no—
261C22⋊Q8—222no—
262C4×Q8—114no—
263C4×Q8—222no—
264C4×Q8—222no—
265C4×Q8—222no—
266#117—22no—
267#117—22no—
268#117—222no—
269#117—222no—
270#117—222no—
271#117—222no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4—221no—
278C2×C4⋊C4C22⋊D1111yescharacteristic
279C2×C4⋊C4C22×D1111yescharacteristic
280C2×C22⋊C4—22no—
281C2×C22⋊C4—222no—
282C2×C22⋊C4C22⋊D1111yescharacteristic
283C2×C22⋊C4C22×D1111yescharacteristic
284C2×C42—222no—
285C2×C42C22⋊D1111yescharacteristic
286C2×C42C22×D1111yescharacteristic
287C4⋊C8—222no—
288#103—228no—
289C22⋊C8—114no—
290C4×C8—222no—
291#95—22no—
292#95—21no—
293#95—22no—
294#95C22×D1112yes—
295C2×C11—21no—
296C2×C11—21no—
297C2×C11—42no—
298C2×C11C2×#45111yescharacteristic
299C2×C11#302211yescharacteristic
300C2×C11#302711yescharacteristic
301C24C2×C22⋊D1111yescharacteristic
302C2×Q8—24no—
303C2×Q8—82no—
304C2×Q8—114no—
305C2×Q8—222no—
306C2×Q8—222no—
307C2×Q8—222no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—222no—
314C22×C4—222no—
315C22×C4#432614yescomplemented
316C22×C4C2×C22⋊D1111yescharacteristic
317C22×C4C2×C22⋊D1111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320C22×C4C2×C22⋊D1111yescharacteristic
321C22×C4C23×D1111yescharacteristic
322Q16—888no—
323C2×C8—224no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—42no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—42no—
330C4⋊C4—82no—
331C4⋊C4—114no—
332C4⋊C4—222no—
333C4⋊C4—222no—
334C4⋊C4—224no—
335C4⋊C4—224no—
336C4⋊C4—222no—
337C4⋊C4—222no—
338C4⋊C4—222no—
339C4⋊C4—222no—
340C4⋊C4—224no—
341C4⋊C4—222no—
342C4⋊C4—224no—
343C22⋊C4—22no—
344C22⋊C4—22no—
345C22⋊C4—82no—
346C22⋊C4—224no—
347C22⋊C4—224no—
348C42—21no—
349C42—21no—
350C42—224no—
351C42—224no—
352C42D4×D1112yes—
353C42D4×D1112yes—
354C11#1830311yescharacteristic, complemented, Sylow
355C23—21no—
356C23—21no—
357C23—41no—
358C23—41no—
359C23C2×#432612yes—
360C23C22×C22⋊D1111yescharacteristic
361Q8—48no—
362Q8—444no—
363Q8—882no—
364Q8—882no—
365Q8—882no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—224no—
383C2×C4—224no—
384C2×C4—882no—
385C2×C4—882no—
386C2×C4#6699012yes—
387C2×C4#6699011yescharacteristic
388C2×C4#6699011yescharacteristic
389C2×C4C2×#432612yes—
390C2×C4C2×#432612yes—
391C2×C4#6700412yes—
392C2×C4C2×D4×D1112yes—
393C8—444no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—42no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22C2×#6699011yescharacteristic
402C22C22×#432611yescharacteristic
403C22C2×#6700411yescharacteristic
404C4—22no—
405C4—22no—
406C4—22no—
407C4—41no—
408C4—41no—
409C4—82no—
410C4—82no—
411C4—444no—
412C4—444no—
413C4#1062266312yes—
414C4#1062266312yes—
415C2—21no—
416C2—21no—
417C2—42no—
418C2C2×#1062266311yescharacteristic
419C2#1307799411yescharacteristic
420C2#1307801711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2628C2
socleC22×C11C2×#120
prime radicalC24×C11C2×D4
hypercenter#2628D11
hypocenterC11#18303
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2628

Complements

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

NH ≅ G/Ntype
2. #13079564C2semidirect
3. #13067589C2semidirect
5. #13067179C2semidirect
100. C22×C4×C11Q16semidirect
315. C22×C4#4326semidirect
354. C11#18303semidirect

Maximal subgroups

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

subgroupindex
#130820212
#130795642
#130675892
#130675722
#130671792
#130669302
C11×#26282
#1830311