Finite Group Databasebeta

← #14642358

Subgroups — #14642358

Order 2816.

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

normal subgroups only

This group has 570 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#13068595C211yesmaximal, characteristic, complemented
3#13068308C211yesmaximal, characteristic, complemented
4#13066441C211yesmaximal, characteristic, complemented
5#13066441C211yesmaximal, characteristic, complemented
6#13066437C211yesmaximal, characteristic, complemented
7C11×#1270C211yesmaximal, characteristic, complemented
8C2×#66991C411yescharacteristic
9C2×#66989C411yescharacteristic
10C22×#4313—21no—
11C2×#66950C411yescharacteristic
12C2×C42×D11C2211yescharacteristic
13C11×#390C2211yescharacteristic
14C2×(C2×D11)⋊C8—21no—
15C2×Dic11⋊C8—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—
52C2×#4313—24no—
53C2×#4313—42no—
54C2×#4313—42no—
55#66950—42no—
56C42×D11—42no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61(C2×D11)⋊C8—42no—
62Dic11⋊C8—42no—
63#7710—111nomaximal, Sylow
64C24×C11—21no—
65C23×D11C22⋊C411yescharacteristic
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C22×C4×C11—21no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—42no—
75C2×C22⋊D11—42no—
76C2×C22⋊D11—42no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11C22⋊C411yescharacteristic
80C22×Dic11C22⋊C411yescharacteristic
81C22×Dic11C22⋊C411yescharacteristic
82C2×C4×D11—22no—
83C2×C4×D11—22no—
84C2×C4×D11—22no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—41no—
92C2×C4×D11—41no—
93C2×C4×D11—41no—
94C2×Dic22—21no—
95C2×Dic22—21no—
96C2×Dic22—41no—
97C2×Dic22—41no—
98C2×C8×C11—22no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C42×C11—41no—
110C22⋊Dic11—42no—
111C22⋊Dic11—42no—
112C22⋊Dic11—42no—
113(C2×D11)⋊C4—42no—
114C4⋊Dic11—41no—
115C4⋊Dic11—42no—
116C4×Dic11—22no—
117C4×Dic11—22no—
118C4×Dic11—41no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125#4313—48no—
126#2850—111no—
127#1797—111no—
128#1728—111no—
129#1272—111no—
130#1272—111no—
131#1270—111no—
132#1270D1111yescharacteristic, complemented
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11C2×C22⋊C411yescharacteristic
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11#10412yes—
148D4×C11—81no—
149D4×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#13111yescharacteristic
160C2×C4×C11#13111yescharacteristic
161C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C11#13711yescharacteristic
164C2×C4×C11#13711yescharacteristic
165C22⋊D11—84no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11#9912yes—
180C2×Dic11#10012yes—
181C4×D11—24no—
182C4×D11—24no—
183C4×D11—42no—
184C4×D11—42no—
185C4×D11—42no—
186C4×D11—42no—
187Dic22—81no—
188Dic22—81no—
189C8×C11—42no—
190C8×C11—81no—
191C11⋊C8—42no—
192C11⋊C8—81no—
193C22×M16—221no—
194C2×#124—111no—
195C2×C22⋊Q8—111no—
196C2×#121—111no—
197C22×C42—111no—
198C2×C4⋊C8—221no—
199C2×C22⋊C8—221no—
200#391—111no—
201#390C2×D1111yescharacteristic
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—81no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11#40811yescharacteristic
220C22×C11C2×#9911yescharacteristic
221C22×C11C2×#10011yescharacteristic
222C22×C11#41711yescharacteristic
223C22×C11#41711yescharacteristic
224C22×C11C2×#10411yescharacteristic
225C22×C11#42111yescharacteristic
226C2×D11—22no—
227C2×D11—22no—
228C2×D11—22no—
229C2×D11—41no—
230C2×D11—41no—
231C2×D11—41no—
232C2×D11—41no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—81no—
240Dic11—22no—
241Dic11—22no—
242Dic11—41no—
243Dic11—81no—
244Dic11—81no—
245C22×Q8—111no—
246C22×D4—221no—
247C22×D4C4×D1111yescharacteristic
248C23×C4—111no—
249C23×C4—111no—
250C23×C4—111no—
251C2×M16—224no—
252C2×M16—442no—
253C2×M16—442no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—221no—
257C22×C8—221no—
258#124—442no—
259C22⋊Q8—442no—
260#121—442no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4C4×D1111yescharacteristic
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
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
275C4⋊C8—442no—
276C22⋊C8—442no—
277#95—221no—
278#95—221no—
279#95—221no—
280#95—221no—
281C2×C11—161no—
282C2×C11#147111yescharacteristic
283C2×C11#148311yescharacteristic
284C2×C11#149511yescharacteristic
285C2×C11#150411yescharacteristic
286C2×C11#151311yescharacteristic
287C2×C11#152711yescharacteristic
288C2×C11#156011yescharacteristic
289D11—42no—
290C24—21no—
291C24—111no—
292C2×Q8—221no—
293C2×Q8—221no—
294C2×Q8—441no—
295C2×Q8—441no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—442no—
301C2×D4—442no—
302C2×D4—442no—
303C22×C4—21no—
304C22×C4—111no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—222no—
308C22×C4—222no—
309C22×C4—222no—
310C22×C4—221no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—441no—
319C22×C4—441no—
320C22×C4—441no—
321C22×C4C2×C4×D1111yescharacteristic
322C22×C4D4×D1111yescharacteristic
323C22×C4D4×D1111yescharacteristic
324M16—448no—
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—222no—
332C2×C8—441no—
333C2×C8—441no—
334C2×C8—441no—
335C2×C8—441no—
336C2×C8—441no—
337C4⋊C4—41no—
338C4⋊C4—441no—
339C4⋊C4—442no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—442no—
345C22⋊C4—442no—
346C22⋊C4—442no—
347C22⋊C4—442no—
348C42—41no—
349C42—222no—
350C42—222no—
351C42—441no—
352C11#771011yescharacteristic, complemented, Sylow
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—112no—
361C23—221no—
362C23—221no—
363C23—221no—
364C23—221no—
365C23—221no—
366C23—221no—
367C23C22⋊C4×D1111yescharacteristic
368Q8—881no—
369Q8—881no—
370D4—81no—
371D4—81no—
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—112no—
383C2×C4—112no—
384C2×C4—224no—
385C2×C4—224no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—221no—
390C2×C4—221no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4#6695411yescharacteristic
404C2×C4#6696011yescharacteristic
405C2×C4#6696411yescharacteristic
406C2×C4#6696411yescharacteristic
407C2×C4#6696811yescharacteristic
408C2×C4#6696811yescharacteristic
409C8—42no—
410C8—81no—
411C8—442no—
412C8—881no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—222no—
421C22—222no—
422C22—222no—
423C22—441no—
424C22—441no—
425C22—441no—
426C22—441no—
427C22#1062234011yescharacteristic
428C22D11×#9911yescharacteristic
429C22D11×#10011yescharacteristic
430C22#1062238411yescharacteristic
431C22#1062238411yescharacteristic
432C22D11×#10411yescharacteristic
433C22#1062243411yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—81no—
441C4—222no—
442C4—222no—
443C4—441no—
444C4—881no—
445C4—881no—
446C2—161no—
447C2—442no—
448C2#1306697411yescharacteristic
449C2#1306702611yescharacteristic
450C2#1306707811yescharacteristic
451C2#1306711711yescharacteristic
452C2#1306715611yescharacteristic
453C2#1306721211yescharacteristic
454C2#1306734811yescharacteristic
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#7710
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. #13068595C2semidirect
3. #13068308C2semidirect
4. #13066441C2semidirect
5. #13066441C2semidirect
6. #13066437C2semidirect
7. C11×#1270C2semidirect
132. #1270D11semidirect
352. C11#7710semidirect

Maximal subgroups

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

subgroupindex
#130769162
#130685952
#130683082
#130664412
#130664372
C11×#12702
#771011