Finite Group Databasebeta

← #14651724

Subgroups — #14651724

Order 2816.

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

normal subgroups only

This group has 682 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#13077655C211yesmaximal, characteristic
2#13071975C211yesmaximal, characteristic
3#13068540C211yesmaximal, characteristic, complemented
4#13066952C211yesmaximal, characteristic
5#13066523C211yesmaximal, characteristic, complemented
6#13066521C211yesmaximal, characteristic, complemented
7C11×#1784C211yesmaximal, characteristic, complemented
8C23×Q8×C11C2211yescharacteristic
9C2×#66999—21no—
10C2×C4×C22⋊D11C2211yescharacteristic
11C2×C11×#101—22no—
12C11×#407C2211yescharacteristic
13C11×#407C2211yescharacteristic
14#10622844—21no—
15#10622843—21no—
16#10622842—21no—
17C2×#66900—22no—
18#10622826C412yes—
19#10622825C2211yescharacteristic
20#10622823C412yes—
21#10622820C2211yescharacteristic
22#10622820C2211yescharacteristic
23#10622741—22no—
24#10622342—22no—
25#10622339—21no—
26#10622331—21no—
27#10622107—21no—
28#10622106—21no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C22×Q8×C11—21no—
35C22×Q8×C11—44no—
36C23×C4×C11C2×C412yes—
37C23×C4×C11C2311yescharacteristic
38C22×C22⋊D11C2×C411yescharacteristic
39C22×C4×D11D411yescharacteristic
40C2×C11×M16—21no—
41C2×C11×M16D412yes—
42C2×C22⋊Dic11C2×C411yescharacteristic
43C2×C22⋊Dic11C2×C412yes—
44#66999—44no—
45C4×C22⋊D11—21no—
46C4×C22⋊D11—21no—
47C4×C22⋊D11—21no—
48C4×C22⋊D11—21no—
49C2×(C2×D11)⋊C4—22no—
50C2×(C2×D11)⋊C4D411yescharacteristic
51C2×C4⋊Dic11—21no—
52C2×Dic11⋊C4—22no—
53C2×Dic11⋊C4D411yescharacteristic
54C2×C4×Dic11D411yescharacteristic
55C2×#4318—21no—
56C2×#4318D412yes—
57C2×#4313—22no—
58C11×#101—44no—
59C11×C22⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63#66900—44no—
64C11⋊#95—21no—
65C11⋊#95—22no—
66C11⋊#95—22no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71(C2×D11)⋊C8—22no—
72Dic11⋊C8—22no—
73C8×Dic11—22no—
74#9506—111nomaximal, Sylow
75C24×C11C22×C411yescharacteristic
76C23×D11C22⋊C411yescharacteristic
77C2×Q8×C11—24no—
78C2×Q8×C11—24no—
79C2×Q8×C11—24no—
80C2×Q8×C11—42no—
81C2×Q8×C11—42no—
82C2×Q8×C11—42no—
83C2×Q8×C11—44no—
84C2×Q8×C11—44no—
85C2×Q8×C11—44no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—44no—
94C22×C4×C11—42no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C2×C22⋊D11—22no—
102C2×C22⋊D11—21no—
103C2×C22⋊D11—21no—
104C2×C22⋊D11—41no—
105C22×Dic11—22no—
106C22×Dic11C22⋊C411yescharacteristic
107C22×Dic11C22⋊C411yescharacteristic
108C22×Dic11C22⋊C411yescharacteristic
109C2×C4×D11—21no—
110C2×C4×D11—21no—
111C2×C4×D11—42no—
112C11×M16—42no—
113C11×M16—42no—
114C2×C8×C11—22no—
115C2×C8×C11—41no—
116C22⋊Dic11—21no—
117C22⋊Dic11—21no—
118C22⋊Dic11—42no—
119(C2×D11)⋊C4—21no—
120(C2×D11)⋊C4—21no—
121(C2×D11)⋊C4—44no—
122C4⋊Dic11—42no—
123Dic11⋊C4—21no—
124Dic11⋊C4—21no—
125Dic11⋊C4—44no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128#4318—42no—
129#4318—42no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—41no—
132#4313—82no—
133#2975—111no—
134#2409—111no—
135#1784—111no—
136#1784D1111yescharacteristic, complemented
137#1465—111no—
138#1305—111no—
139#1305—111no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11C2×C22⋊C411yescharacteristic
145C23×C11C4×D411yescharacteristic
146C23×C11C4×D411yescharacteristic
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—41no—
151C22×D11—41no—
152Q8×C11—44no—
153Q8×C11—44no—
154Q8×C11—44no—
155Q8×C11—44no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12311yescharacteristic
173C22⋊D11—42no—
174C22⋊D11—42no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11#10112yescomplemented
185C4×D11—42no—
186C4×D11—81no—
187C8×C11—42no—
188C8×C11—81no—
189C11⋊C8—42no—
190C11⋊C8—81no—
191C23×Q8C2×D1111yescharacteristic
192C2×C22⋊Q8—221no—
193C2×C4×D4—111no—
194#436—222no—
195#436—222no—
196#431—221no—
197C2×#101—22no—
198C2×#101—222no—
199#407—111no—
200#407—111no—
201#407—221no—
202#407C2×D1111yescharacteristic
203#407C2×D1111yescharacteristic
204#395—221no—
205#393—221no—
206#391—221no—
207#386—112no—
208#385—112no—
209#380—111no—
210#324—221no—
211#323—221no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11#38611yescharacteristic
223C22×C11C2×#10111yescharacteristic
224C22×C11#41311yescharacteristic
225C2×D11—42no—
226C2×D11—41no—
227C2×D11—41no—
228C2×D11—41no—
229C2×D11—81no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—44no—
234C4×C11B(4,𝔽2)12yes—
235Dic11—22no—
236Dic11—41no—
237Dic11—41no—
238Dic11—82no—
239C22×Q8—21no—
240C22×Q8—21no—
241C22×Q8—21no—
242C22×Q8—21no—
243C22×Q8—21no—
244C22×Q8—21no—
245C22×Q8—44no—
246C22×D4—111no—
247C23×C4—111no—
248C23×C4C4×D1112yes—
249C23×C4C22×D1111yescharacteristic
250C2×M16—21no—
251C2×M16—112no—
252C2×M16—222no—
253C2×M16—221no—
254C2×M16C22⋊D1112yes—
255C22⋊Q8—444no—
256C4×D4—221no—
257C4×D4—221no—
258C4×D4—221no—
259C4×D4—221no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—222no—
262C2×C4⋊C4—221no—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—111no—
265C2×C22⋊C4—112no—
266C2×C22⋊C4—222no—
267C2×C42—111no—
268C4⋊C8—222no—
269#101—44no—
270#101—444no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8—222no—
276C22⋊C8—221no—
277C22⋊C8—221no—
278C22⋊C8—221no—
279C22⋊C8—221no—
280C4×C8—222no—
281#95—222no—
282#95—222no—
283#95—221no—
284C2×C11—21no—
285C2×C11—21no—
286C2×C11—41no—
287C2×C11—41no—
288C2×C11#188911yescharacteristic
289C2×C11#190111yescharacteristic
290C2×C11#191511yescharacteristic
291D11—81no—
292C24—111no—
293C24C2×C4×D1111yescharacteristic
294C2×Q8—24no—
295C2×Q8—24no—
296C2×Q8—24no—
297C2×Q8—42no—
298C2×Q8—42no—
299C2×Q8—42no—
300C2×Q8—44no—
301C2×Q8—44no—
302C2×Q8—44no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×D4—222no—
308C2×D4—221no—
309C2×D4—221no—
310C2×D4—441no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—42no—
315C22×C4—44no—
316C22×C4—111no—
317C22×C4—111no—
318C22×C4—111no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—222no—
322C22×C4—442no—
323C22×C4#433911yescharacteristic
324C22×C4D4×D1111yescharacteristic
325C22×C4D4×D1111yescharacteristic
326C22×C4D4×D1111yescharacteristic
327C22×C4#434111yescharacteristic
328C22×C4C2×C22⋊D1111yescharacteristic
329M16—42no—
330M16—42no—
331M16—442no—
332M16—442no—
333M16—882no—
334C2×C8—22no—
335C2×C8—41no—
336C2×C8—222no—
337C2×C8—441no—
338C4⋊C4—221no—
339C4⋊C4—221no—
340C4⋊C4—444no—
341C4⋊C4—442no—
342C22⋊C4—221no—
343C22⋊C4—221no—
344C22⋊C4—221no—
345C22⋊C4—221no—
346C22⋊C4—444no—
347C22⋊C4—442no—
348C42—221no—
349C42—221no—
350C11#950611yescharacteristic, complemented, Sylow
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23—221no—
356C23—221no—
357C23—221no—
358C23—441no—
359C23—441no—
360C23C22⋊C4×D1111yescharacteristic
361C23(C22⋊D11)⋊C411yescharacteristic
362C23C4×C22⋊D1111yescharacteristic
363Q8—44no—
364Q8—44no—
365Q8—44no—
366Q8—44no—
367D4—442no—
368D4—442no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—112no—
383C2×C4—221no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—442no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—881no—
394C2×C4#6693611yescharacteristic
395C2×C4#6693711yescharacteristic
396C2×C4#6699011yescharacteristic
397C2×C4#6699111yescharacteristic
398C8—42no—
399C8—81no—
400C8—442no—
401C8—881no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—42no—
411C22—42no—
412C22—442no—
413C22—441no—
414C22—441no—
415C22—441no—
416C22—881no—
417C22D11×#10111yescharacteristic
418C22#1062236411yescharacteristic
419C22#1062256911yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—44no—
424C4—222no—
425C4—441no—
426C4—441no—
427C4—882no—
428C4#1062264512yes—
429C2—21no—
430C2—21no—
431C2—41no—
432C2—41no—
433C2—881no—
434C2#1306902111yescharacteristic
435C2#1306908111yescharacteristic
436C2#1306916511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1784C2
socleC22×C11#386
prime radicalC22×C22⋊D11C2×C4
cosocleC23×C4×C11C23
hypercenter#1784D11
hypocenterC11#9506
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1784

Complements

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

NH ≅ G/Ntype
3. #13068540C2semidirect
5. #13066523C2semidirect
6. #13066521C2semidirect
7. C11×#1784C2semidirect
136. #1784D11semidirect
184. C2×Dic11#101semidirect
350. C11#9506semidirect

Maximal subgroups

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

subgroupindex
#130776552
#130719752
#130685402
#130669522
#130665232
#130665212
C11×#17842
#950611