Finite Group Databasebeta

← #14648749

Subgroups — #14648749

Order 2816.

560 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 95 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#13077643C211yesmaximal, characteristic
2#13071873C211yesmaximal, characteristic
3#13068715C211yesmaximal, characteristic, complemented
4C4×#66870C211yesmaximal, characteristic
5#13066502C211yesmaximal, characteristic, complemented
6#13066501C211yesmaximal, characteristic, complemented
7C11×#1826C211yesmaximal, characteristic, complemented
8C2×C11×#117C2211yescharacteristic
9C2×C4×C22⋊D11C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C4×C11×C22⋊C4C2211yescharacteristic
12C4×C22⋊Dic11C2211yescharacteristic
13C4×C22⋊Dic11C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622740—22no—
16#10622606C411yescharacteristic, complemented
17#10622605C411yescharacteristic, complemented
18#10622595C411yescharacteristic, complemented
19#10622593C411yescharacteristic, complemented
20#10622572—21no—
21C2×#66870—21no—
22#10622565—21no—
23C4×(C2×D11)⋊C4—21no—
24C4×Dic11⋊C4—21no—
25#10622341—22no—
26D11×C22⋊C8—21no—
27#10622332—21no—
28C11×#339—22no—
29#10622170—22no—
30#10622165—21no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11D411yescharacteristic
33C22×C4×D11D411yescharacteristic
34C2×C11×M16D412yes—
35C11×#117—21no—
36C11×#117—21no—
37C11×#117—21no—
38C11×#117—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C42×C11—21no—
44C2×C42×C11—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11D411yescharacteristic
48C4×C22⋊D11—21no—
49C4×C22⋊D11—21no—
50C4×C22⋊D11—21no—
51C4×C22⋊D11—21no—
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4C2×C411yescharacteristic
55C2×Dic11⋊C4—21no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4C2×C411yescharacteristic
58C2×C4×Dic11—21no—
59C2×C4×Dic11—21no—
60C2×C4×Dic11D411yescharacteristic
61C2×#4318D412yes—
62C2×C8×D11—22no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95C2×C411yescharacteristic
72C11⋊#95C2×C411yescharacteristic
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75(C2×D11)⋊C8—22no—
76#66879—22no—
77Dic11⋊C8—22no—
78#66870—24no—
79#9011—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C23×D11C22⋊C411yescharacteristic
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—42no—
85C22×C4×C11—41no—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C2×C22⋊D11—21no—
93C2×C22⋊D11—21no—
94C2×C22⋊D11—22no—
95C2×C22⋊D11—41no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—41no—
99C22×Dic11C22⋊C411yescharacteristic
100C22×Dic11C22⋊C411yescharacteristic
101C22×Dic11C22⋊C411yescharacteristic
102C2×C4×D11—21no—
103C2×C4×D11—21no—
104C2×C4×D11—42no—
105C11×M16—42no—
106C2×C8×C11—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C22⋊C4—22no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11—42no—
116C42×C11—41no—
117C42×C11—41no—
118C22⋊Dic11—22no—
119C22⋊Dic11—21no—
120C22⋊Dic11—21no—
121C22⋊Dic11—41no—
122C22⋊Dic11—42no—
123(C2×D11)⋊C4—21no—
124(C2×D11)⋊C4—21no—
125(C2×D11)⋊C4—42no—
126(C2×D11)⋊C4—42no—
127Dic11⋊C4—21no—
128Dic11⋊C4—21no—
129Dic11⋊C4—42no—
130Dic11⋊C4—42no—
131C4×Dic11—21no—
132C4×Dic11—21no—
133C4×Dic11—42no—
134C4×Dic11—42no—
135#4318—42no—
136C2×C11⋊C8—22no—
137C8×D11—82no—
138#2973—111no—
139#2395—111no—
140#1826—111no—
141#1826D1111yescharacteristic, complemented
142C4×#99—111no—
143#1297—111no—
144#1297—111no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11C2×C22⋊C411yescharacteristic
150C23×C11#12111yescharacteristic
151C23×C11#12111yescharacteristic
152C22×D11—21no—
153C22×D11—21no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11#10412yes—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11C4×D411yescharacteristic
173C2×C4×C11C4×D411yescharacteristic
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12311yescharacteristic
176C22⋊D11—42no—
177C22⋊D11—42no—
178C2×Dic11—22no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—42no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—81no—
193C2×Dic11—81no—
194C4×D11—42no—
195C4×D11—81no—
196C8×C11—42no—
197C11⋊C8—42no—
198C2×C4×D4—111no—
199C2×#117C2×D1111yescharacteristic
200#435—222no—
201#435—222no—
202#432—221no—
203C2×#99—221no—
204#407—111no—
205#407C2×D1111yescharacteristic
206C2×C22⋊C8—221no—
207#400—111no—
208#399—111no—
209#398—111no—
210#397—111no—
211#397—221no—
212#394—221no—
213C4×C4⋊C4—221no—
214C4×C22⋊C4—111no—
215C4×C22⋊C4—111no—
216C4×C22⋊C4—221no—
217C4×C22⋊C4C2×D1111yescharacteristic
218#342—221no—
219#339—22no—
220#339—222no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11#38611yescharacteristic
232C22×C11C2×#10411yescharacteristic
233C22×C11#42111yescharacteristic
234C2×D11—22no—
235C2×D11—41no—
236C2×D11—41no—
237C2×D11—42no—
238C2×D11—81no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—82no—
243C4×C11—81no—
244C4×C11—81no—
245C4×C11#45812yes—
246Dic11—42no—
247Dic11—41no—
248Dic11—41no—
249Dic11—41no—
250Dic11—81no—
251Dic11—82no—
252C22×D4—111no—
253C23×C4—111no—
254C23×C4C22×D1111yescharacteristic
255C2×M16—112no—
256C2×M16C22⋊D1112yes—
257C22×C8—222no—
258C4×D4—221no—
259C4×D4—221no—
260C4×D4—221no—
261C4×D4—221no—
262#117—21no—
263#117—21no—
264#117—21no—
265#117—21no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4C4×D1111yescharacteristic
270C2×C4⋊C4C4×D1111yescharacteristic
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—111no—
274C2×C22⋊C4—111no—
275C2×C22⋊C4—221no—
276C2×C22⋊C4—221no—
277C2×C22⋊C4—221no—
278C2×C22⋊C4—221no—
279C2×C42—21no—
280C2×C42—21no—
281C2×C42—111no—
282C2×C42—221no—
283C2×C42—221no—
284C4⋊C8—222no—
285#99—224no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—222no—
289C22⋊C8—221no—
290C22⋊C8—221no—
291#97—222no—
292#95—21no—
293#95—111no—
294#95—111no—
295#95—221no—
296#95—221no—
297#95—221no—
298#95—221no—
299#95—221no—
300C2×C11—21no—
301C2×C11—21no—
302C2×C11—41no—
303C2×C11—41no—
304C2×C11#187111yescharacteristic
305C2×C11#188411yescharacteristic
306C2×C11#189011yescharacteristic
307D11—42no—
308C24—111no—
309C24D4×D1111yescharacteristic
310C2×D4—222no—
311C2×D4—221no—
312C2×D4—221no—
313C2×D4—441no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—42no—
317C22×C4—41no—
318C22×C4—111no—
319C22×C4—111no—
320C22×C4—111no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—442no—
326C22×C4—441no—
327C22×C4C2×C4×D1111yescharacteristic
328C22×C4#433911yescharacteristic
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4#434111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333M16—42no—
334M16—442no—
335C2×C8—22no—
336C2×C8—222no—
337C2×C8—882no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—221no—
343C4⋊C4—221no—
344C4⋊C4—442no—
345C4⋊C4—442no—
346C22⋊C4—22no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—221no—
351C22⋊C4—221no—
352C22⋊C4—221no—
353C22⋊C4—221no—
354C22⋊C4—222no—
355C22⋊C4—442no—
356C22⋊C4—442no—
357C22⋊C4—442no—
358C22⋊C4—441no—
359C42—42no—
360C42—41no—
361C42—41no—
362C42—221no—
363C42—221no—
364C42—442no—
365C42—442no—
366C11#901111yescharacteristic, complemented, Sylow
367C23—21no—
368C23—21no—
369C23—41no—
370C23—41no—
371C23—112no—
372C23—221no—
373C23—221no—
374C23—441no—
375C23—441no—
376C23C22⋊C4×D1111yescharacteristic
377C23#6693711yescharacteristic
378C23#6699111yescharacteristic
379D4—442no—
380D4—442no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—222no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—221no—
401C2×C4—221no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—442no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—442no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—881no—
412C2×C4—881no—
413C2×C4—881no—
414C2×C4(C22⋊D11)⋊C411yescharacteristic
415C2×C4#6693611yescharacteristic
416C2×C4C4×C22⋊D1111yescharacteristic
417C2×C4#6699011yescharacteristic
418C8—42no—
419C8—442no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—81no—
429C22—81no—
430C22—222no—
431C22—442no—
432C22—441no—
433C22—441no—
434C22—881no—
435C22D11×#10411yescharacteristic
436C22#1062243411yescharacteristic
437C22#1062256911yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—81no—
443C4—81no—
444C4—442no—
445C4—441no—
446C4—441no—
447C4—441no—
448C4—881no—
449C4—882no—
450C4#1062266612yes—
451C2—21no—
452C2—21no—
453C2—41no—
454C2—41no—
455C2—442no—
456C2#1306891511yescharacteristic
457C2#1306899611yescharacteristic
458C2#1306902611yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1826C2
socleC22×C11#386
prime radicalC22×C22⋊D11D4
cosocleC23×C4×C11C23
hypercenter#1826D11
hypocenterC11#9011
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
3. #13068715C2semidirect
5. #13066502C2semidirect
6. #13066501C2semidirect
7. C11×#1826C2semidirect
16. #10622606C4semidirect
17. #10622605C4semidirect
18. #10622595C4semidirect
19. #10622593C4semidirect
141. #1826D11semidirect
366. C11#9011semidirect

Maximal subgroups

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

subgroupindex
#130776432
#130718732
#130687152
C4×#668702
#130665022
#130665012
C11×#18262
#901111