Finite Group Databasebeta

← #14642174

Subgroups — #14642174

Order 2816.

538 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076916C211yesmaximal, characteristic
2#13068683C211yesmaximal, characteristic, complemented
3#13068373C211yesmaximal, characteristic, complemented
4#13066441C211yesmaximal, characteristic, complemented
5#13066441C211yesmaximal, characteristic, complemented
6#13066437C211yesmaximal, characteristic, complemented
7C11×#1270C211yesmaximal, characteristic, complemented
8C2×#66991C411yescharacteristic
9C2×#66989C411yescharacteristic
10C2×#66950C411yescharacteristic
11C2×C42×D11C2211yescharacteristic
12C11×#390C2211yescharacteristic
13C2×(C2×D11)⋊C8—21no—
14C2×(C2×D11)⋊C8—21no—
15C2×C8×Dic11—21no—
16#10622590C411yescharacteristic
17#10622569—21no—
18#10622569—21no—
19#10622564—21no—
20#10622564—21no—
21#10622542C2211yescharacteristic
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×D4×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C22×Dic22C2×C411yescharacteristic
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C42×C11C2311yescharacteristic
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42#66991—42no—
43#66989—42no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11C2×C411yescharacteristic
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C22×C11⋊C8—21no—
51C22×C11⋊C8—21no—
52#66950—42no—
53C42×D11—42no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58(C2×D11)⋊C8—24no—
59(C2×D11)⋊C8—42no—
60C8×Dic11—42no—
61#7670—111nomaximal, Sylow
62C24×C11—21no—
63C23×D11C22⋊C411yescharacteristic
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C22×C4×C11—21no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C2×C22⋊D11—42no—
73C2×C22⋊D11—42no—
74C2×C22⋊D11—42no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79C22×Dic11C22⋊C411yescharacteristic
80C2×C4×D11—22no—
81C2×C4×D11—22no—
82C2×C4×D11—22no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—41no—
90C2×C4×D11—41no—
91C2×C4×D11—41no—
92C2×Dic22—21no—
93C2×Dic22—21no—
94C2×Dic22—41no—
95C2×Dic22—41no—
96C2×C8×C11—22no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11—41no—
108C22⋊Dic11—42no—
109C22⋊Dic11—42no—
110C22⋊Dic11—42no—
111(C2×D11)⋊C4—42no—
112C4⋊Dic11—41no—
113C4⋊Dic11—42no—
114C4×Dic11—22no—
115C4×Dic11—22no—
116C4×Dic11—41no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123#2850—111no—
124#1817—111no—
125C4×C22⋊C8—111no—
126#1272—111no—
127#1272—111no—
128#1270—111no—
129#1270D1111yescharacteristic, complemented
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11C2×C22⋊C411yescharacteristic
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—21no—
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—21no—
144C22×D11#10412yes—
145D4×C11—81no—
146D4×C11—81no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11#13111yescharacteristic
157C2×C4×C11#13111yescharacteristic
158C2×C4×C11#13511yescharacteristic
159C2×C4×C11#13511yescharacteristic
160C2×C4×C11#13511yescharacteristic
161C2×C4×C11#13511yescharacteristic
162C22⋊D11—84no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11#9912yes—
177C2×Dic11#10012yes—
178C4×D11—42no—
179C4×D11—42no—
180C4×D11—42no—
181C4×D11—42no—
182C4×D11—42no—
183C4×D11—42no—
184Dic22—81no—
185Dic22—81no—
186C8×C11—42no—
187C8×C11—81no—
188C11⋊C8—42no—
189C11⋊C8—81no—
190C2×#124—111no—
191C2×C22⋊Q8—111no—
192C2×#121—111no—
193C22×C42—111no—
194C2×C22⋊C8—221no—
195C2×C22⋊C8—221no—
196C2×C4×C8—221no—
197#391—111no—
198#390C2×D1111yescharacteristic
199#388—221no—
200#388—221no—
201#386—221no—
202#386—221no—
203#382—111no—
204#336—111no—
205#336—111no—
206#336—221no—
207#336C2×D1111yescharacteristic
208#336C2×D1111yescharacteristic
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11#40811yescharacteristic
217C22×C11C2×#9911yescharacteristic
218C22×C11C2×#10011yescharacteristic
219C22×C11#41611yescharacteristic
220C22×C11#41611yescharacteristic
221C22×C11C2×#10411yescharacteristic
222C22×C11#42111yescharacteristic
223C2×D11—22no—
224C2×D11—22no—
225C2×D11—22no—
226C2×D11—41no—
227C2×D11—41no—
228C2×D11—41no—
229C2×D11—41no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—81no—
237Dic11—22no—
238Dic11—22no—
239Dic11—41no—
240Dic11—81no—
241Dic11—81no—
242C22×Q8—111no—
243C22×D4—221no—
244C22×D4C4×D1111yescharacteristic
245C23×C4—111no—
246C23×C4—111no—
247C23×C4—111no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—221no—
251C22×C8—221no—
252#124—442no—
253C22⋊Q8—442no—
254#121—442no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4C4×D1111yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—221no—
264C2×C42—111no—
265C2×C42—111no—
266C2×C42—111no—
267C2×C42—442no—
268C2×C42C22×D1111yescharacteristic
269C22⋊C8—224no—
270C22⋊C8—442no—
271C4×C8—442no—
272#95—221no—
273#95—221no—
274#95—221no—
275#95—221no—
276C2×C11—161no—
277C2×C11#147111yescharacteristic
278C2×C11#148211yescharacteristic
279C2×C11#149411yescharacteristic
280C2×C11#150111yescharacteristic
281C2×C11#151611yescharacteristic
282C2×C11#152711yescharacteristic
283C2×C11#154311yescharacteristic
284D11—42no—
285C24—21no—
286C24—111no—
287C2×Q8—221no—
288C2×Q8—221no—
289C2×Q8—441no—
290C2×Q8—441no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—442no—
296C2×D4—442no—
297C2×D4—442no—
298C22×C4—21no—
299C22×C4—111no—
300C22×C4—111no—
301C22×C4—111no—
302C22×C4—222no—
303C22×C4—222no—
304C22×C4—222no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—221no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—441no—
314C22×C4—441no—
315C22×C4—441no—
316C22×C4C2×C4×D1111yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4D4×D1111yescharacteristic
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—222no—
326C2×C8—441no—
327C2×C8—441no—
328C2×C8—441no—
329C2×C8—441no—
330C2×C8—441no—
331C4⋊C4—41no—
332C4⋊C4—441no—
333C4⋊C4—442no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—442no—
339C22⋊C4—442no—
340C22⋊C4—442no—
341C22⋊C4—442no—
342C42—41no—
343C42—222no—
344C42—222no—
345C42—441no—
346C11#767011yescharacteristic, complemented, Sylow
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—112no—
355C23—221no—
356C23—221no—
357C23—221no—
358C23—221no—
359C23—221no—
360C23—221no—
361C23C22⋊C4×D1111yescharacteristic
362Q8—881no—
363Q8—881no—
364D4—81no—
365D4—81no—
366D4—884no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—112no—
377C2×C4—112no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—221no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4#6695411yescharacteristic
398C2×C4#6696011yescharacteristic
399C2×C4#6696511yescharacteristic
400C2×C4#6696511yescharacteristic
401C2×C4#6696911yescharacteristic
402C2×C4#6696911yescharacteristic
403C8—42no—
404C8—81no—
405C8—442no—
406C8—881no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—222no—
415C22—222no—
416C22—222no—
417C22—441no—
418C22—441no—
419C22—441no—
420C22—441no—
421C22#1062234011yescharacteristic
422C22D11×#9911yescharacteristic
423C22D11×#10011yescharacteristic
424C22#1062238511yescharacteristic
425C22#1062238511yescharacteristic
426C22D11×#10411yescharacteristic
427C22#1062243411yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—81no—
435C4—222no—
436C4—222no—
437C4—441no—
438C4—881no—
439C4—881no—
440C2—161no—
441C2—442no—
442C2#1306697411yescharacteristic
443C2#1306702111yescharacteristic
444C2#1306707311yescharacteristic
445C2#1306710411yescharacteristic
446C2#1306716911yescharacteristic
447C2#1306721211yescharacteristic
448C2#1306727511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1270C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66991C4
cosocleC2×C42×C11C23
hypercenter#1270D11
hypocenterC11#7670
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #13068683C2semidirect
3. #13068373C2semidirect
4. #13066441C2semidirect
5. #13066441C2semidirect
6. #13066437C2semidirect
7. C11×#1270C2semidirect
129. #1270D11semidirect
346. C11#7670semidirect

Maximal subgroups

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

subgroupindex
#130769162
#130686832
#130683732
#130664412
#130664372
C11×#12702
#767011