Finite Group Databasebeta

← #14642268

Subgroups — #14642268

Order 2816.

600 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 103 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#13076920C211yesmaximal, characteristic
2#13068377C211yesmaximal, characteristic, complemented
3D11×#336C211yesmaximal, characteristic, complemented
4#13066442C211yesmaximal, characteristic, complemented
5#13066436C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic, complemented
7C11×#1272C211yesmaximal, characteristic, complemented
8C2×#67000C411yescharacteristic
9C2×#66999C411yescharacteristic
10C22×C8×D11—21no—
11C2×#66948C411yescharacteristic
12C2×C42×D11C2211yescharacteristic
13C11×#391C2211yescharacteristic
14C2×(C2×D11)⋊C8—21no—
15C2×#66879—21no—
16#10622590C411yescharacteristic
17#10622552C2211yescharacteristic
18#10622282—21no—
19#10622282—21no—
20#10622278—21no—
21#10622278—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11C2×C411yescharacteristic
28C22×D44—21no—
29C22×D44C2×C411yescharacteristic
30C22×C4×D11C2×C411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37#67000—42no—
38#66999—42no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C22×C11⋊C8—21no—
51C22×C11⋊C8—21no—
52C2×C8×D11—24no—
53C2×C8×D11—42no—
54C2×C8×D11—42no—
55#66948—42no—
56C42×D11—42no—
57C11×#95—21no—
58C11×#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61(C2×D11)⋊C8—24no—
62#66879—42no—
63#7690—111nomaximal, Sylow
64C23×D11—21no—
65C23×D11C22⋊C411yescharacteristic
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11C22⋊C411yescharacteristic
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79C2×D44—21no—
80C2×D44—21no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—42no—
84C2×D44—42no—
85C2×D44—42no—
86C2×C4×D11—22no—
87C2×C4×D11—22no—
88C2×C4×D11—22no—
89C2×C4×D11—22no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11—41no—
97C2×C4×D11—41no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C11×C4⋊C4—41no—
105C42×C11—41no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114C4⋊Dic11—41no—
115Dic11⋊C4—42no—
116C4×Dic11—22no—
117C4×Dic11—22no—
118C4×Dic11—41no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125C8×D11—48no—
126#2850—111no—
127#1749—111no—
128C2×#336—111no—
129#1272—111no—
130#1272D1111yescharacteristic, complemented
131#1270—111no—
132#1270—111no—
133C23×C11C2×C22⋊C411yescharacteristic
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11#10012yes—
146C22×D11#10412yes—
147C22×D11#10412yes—
148Q8×C11—81no—
149Q8×C11—81no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11#13111yescharacteristic
163C2×C4×C11#13111yescharacteristic
164C2×C4×C11#13511yescharacteristic
165C2×C4×C11#13511yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C11#13711yescharacteristic
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11#9912yes—
180D44—81no—
181D44—81no—
182D44—84no—
183C4×D11—24no—
184C4×D11—24no—
185C4×D11—42no—
186C4×D11—42no—
187C4×D11—42no—
188C4×D11—42no—
189C8×C11—42no—
190C8×C11—42no—
191C11⋊C8—42no—
192C11⋊C8—42no—
193C23×C8—221no—
194C2×#124—111no—
195C2×C22⋊Q8—111no—
196C2×#121—111no—
197C22×C42—111no—
198C2×C22⋊C8—221no—
199C2×#97—221no—
200#391C2×D1111yescharacteristic
201#390—111no—
202#388—221no—
203#388—221no—
204#386—221no—
205#386—221no—
206#382—111no—
207#336—111no—
208#336—111no—
209#336—221no—
210#336C2×D1111yescharacteristic
211#336C2×D1111yescharacteristic
212C22×C11#40811yescharacteristic
213C22×C11C2×#9911yescharacteristic
214C22×C11C2×#10011yescharacteristic
215C22×C11#41611yescharacteristic
216C22×C11#41711yescharacteristic
217C22×C11C2×#10411yescharacteristic
218C22×C11C2×#10411yescharacteristic
219C2×D11—22no—
220C2×D11—22no—
221C2×D11—22no—
222C2×D11—22no—
223C2×D11—22no—
224C2×D11—22no—
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—81no—
231C2×D11—81no—
232C2×D11#32914yes—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—81no—
240C4×C11—81no—
241Dic11—22no—
242Dic11—41no—
243Dic11—41no—
244Dic11—81no—
245C22×Q8C4×D1111yescharacteristic
246C22×D4—111no—
247C22×D4—221no—
248C23×C4—111no—
249C23×C4—111no—
250C23×C4—111no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—224no—
254C22×C8—221no—
255C22×C8—221no—
256C22×C8—442no—
257C22×C8—442no—
258#124—442no—
259C22⋊Q8—442no—
260#121—442no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4C4×D1111yescharacteristic
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—221no—
270C2×C42—111no—
271C2×C42—111no—
272C2×C42—111no—
273C2×C42—442no—
274C2×C42C22×D1111yescharacteristic
275C22⋊C8—224no—
276#97—442no—
277#95—21no—
278#95—21no—
279#95—221no—
280#95—221no—
281C2×C11#147111yescharacteristic
282C2×C11#148311yescharacteristic
283C2×C11#149411yescharacteristic
284C2×C11#150111yescharacteristic
285C2×C11#150411yescharacteristic
286C2×C11C2×#32911yescharacteristic
287C2×C11#155111yescharacteristic
288D11—24no—
289D11—161no—
290C24—111no—
291C24—221no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—442no—
301C2×D4—442no—
302C2×D4—442no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—111no—
308C22×C4—222no—
309C22×C4—222no—
310C22×C4—222no—
311C22×C4—222no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—441no—
320C22×C4—441no—
321C22×C4C2×C4×D1111yescharacteristic
322C22×C4D4×D1111yescharacteristic
323C22×C4D4×D1111yescharacteristic
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—222no—
331C2×C8—222no—
332C2×C8—448no—
333C2×C8—441no—
334C2×C8—441no—
335C2×C8—441no—
336C2×C8—441no—
337C4⋊C4—41no—
338C4⋊C4—441no—
339C4⋊C4—442no—
340C22⋊C4—442no—
341C22⋊C4—442no—
342C22⋊C4—442no—
343C22⋊C4—442no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—441no—
348C42—41no—
349C42—222no—
350C42—222no—
351C42—441no—
352C11#769011yescharacteristic, complemented, Sylow
353C23—112no—
354C23—112no—
355C23—112no—
356C23—221no—
357C23—221no—
358C23—221no—
359C23—221no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23—441no—
364C23—441no—
365C23—441no—
366C23—441no—
367C23C22⋊C4×D1111yescharacteristic
368Q8—81no—
369Q8—81no—
370D4—881no—
371D4—881no—
372D4—884no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—112no—
386C2×C4—224no—
387C2×C4—224no—
388C2×C4—221no—
389C2×C4—221no—
390C2×C4—221no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—221no—
395C2×C4—221no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4#6695411yescharacteristic
404C2×C4#6696011yescharacteristic
405C2×C4#6696711yescharacteristic
406C2×C4#6696911yescharacteristic
407C2×C4#6697111yescharacteristic
408C2×C4#6697211yescharacteristic
409C8—42no—
410C8—42no—
411C8—442no—
412C8—442no—
413C22—114no—
414C22—222no—
415C22—222no—
416C22—222no—
417C22—222no—
418C22—222no—
419C22—222no—
420C22—881no—
421C22—881no—
422C22—881no—
423C22—881no—
424C22—881no—
425C22—881no—
426C22—881no—
427C22#1062234011yescharacteristic
428C22D11×#9911yescharacteristic
429C22D11×#10011yescharacteristic
430C22#1062241611yescharacteristic
431C22#1062241711yescharacteristic
432C22D11×#10411yescharacteristic
433C22D11×#10411yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—81no—
441C4—81no—
442C4—222no—
443C4—441no—
444C4—441no—
445C4—881no—
446C2—224no—
447C2—1761no—
448C2#1306697411yescharacteristic
449C2#1306702811yescharacteristic
450C2#1306707511yescharacteristic
451C2#1306710611yescharacteristic
452C2#1306711911yescharacteristic
453C2D11×#32911yescharacteristic
454C2#1306731011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66948C4
cosocleC2×C42×C11C23
hypercenter#1272D11
hypocenterC11#7690
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #13068377C2semidirect
3. D11×#336C2semidirect
4. #13066442C2semidirect
5. #13066436C2semidirect
6. #13066436C2semidirect
7. C11×#1272C2semidirect
130. #1272D11semidirect
352. C11#7690semidirect

Maximal subgroups

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

subgroupindex
#130769202
#130683772
D11×#3362
#130664422
#130664362
C11×#12722
#769011