Finite Group Databasebeta

← #14656140

Subgroups — #14656140

Order 2816.

610 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079737C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic
3#13067288C211yesmaximal, characteristic, complemented
4#13067110C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic, complemented
6#13066519C211yesmaximal, characteristic, complemented
7C11×#2547C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#124—21no—
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66985—21no—
12#10623008C2211yescharacteristic
13C11×#397—22no—
14C11×#391—21no—
15C11×#380—22no—
16C4×C11×C4⋊C4C2211yescharacteristic
17#10622701—21no—
18#10622700—22no—
19#10622691—21no—
20#10622632—21no—
21#10622629—22no—
22#10622628—21no—
23#10622580—22no—
24#10622579—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622185—22no—
29D4⋊(C11⋊C8)—22no—
30#10622089—22no—
31C22×Q8×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C2×#4339—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×#124—42no—
40C11×#124—42no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C4⋊C4D412yes—
49C2×C11×C22⋊C4—24no—
50C2×C11×C22⋊C4—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4324—22no—
54#66985—42no—
55#66985—42no—
56C2×#4323—22no—
57#66983—21no—
58#66983—21no—
59C2×#4318—21no—
60#66928—21no—
61#66927D411yescharacteristic
62C4×D44—21no—
63C4×D44—21no—
64#66922D411yescharacteristic
65C11×#95—24no—
66C11×#95D412yes—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#66874—22no—
70#66873—22no—
71#66873—24no—
72#66871—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4⋊(C11⋊C8)D412yes—
77C4×C11⋊C8—21no—
78C4×C11⋊C8—21no—
79#10239—111nomaximal, Sylow
80C24×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11D812yes—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—44no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—41no—
103#4339—41no—
104#4339—41no—
105#4339—41no—
106#4339—41no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×C4×D11—41no—
111C2×Dic22—21no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—48no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C42×C11—41no—
123C42×C11—41no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11#4111yescharacteristic
128#4324—44no—
129#4323—44no—
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4—41no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134#4318—41no—
135#4318—41no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—41no—
139#3226—111no—
140#3036—111no—
141#2547D1111yescharacteristic, complemented
142#1546—111no—
143#1502—111no—
144#1478—111no—
145#1303—111no—
146C23×C11—22no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11#12011yescharacteristic
152C22×D11—41no—
153Q8×C11—81no—
154Q8×C11—81no—
155Q8×C11—81no—
156Q8×C11—81no—
157D4×C11—22no—
158D4×C11—22no—
159D4×C11—41no—
160D4×C11—41no—
161C2×C4×C11—22no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—82no—
172C2×C4×C11—82no—
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12711yescharacteristic
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11#13511yescharacteristic
181C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
183C22⋊D11—81no—
184C22⋊D11—81no—
185C2×Dic11—41no—
186D44—41no—
187D44—41no—
188D44—42no—
189D44—81no—
190C4×D11—81no—
191C4×D11—81no—
192Dic22—41no—
193Dic22—41no—
194C11⋊C8—42no—
195C11⋊C8—42no—
196C11⋊C8—81no—
197C2×AGL(1,ℤ/8)—221no—
198#532—111no—
199C2×C4⋊Q8C2×D1111yescharacteristic
200C2×#124—21no—
201C2×C4×D4C2×D1111yescharacteristic
202#500—221no—
203#486—221no—
204#480—222no—
205#474—222no—
206#463—222no—
207#461—221no—
208#459—221no—
209#431—111no—
210#431—111no—
211#423—111no—
212#417—221no—
213#397—22no—
214#391—21no—
215#380—22no—
216C4×C4⋊C4C2×D1111yescharacteristic
217#332—222no—
218#327—222no—
219D4⋊C8—222no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—44no—
223C22×C11—42no—
224C22×C11—82no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11#39211yescharacteristic
228C22×C11#44711yescharacteristic
229C22×C11#44911yescharacteristic
230C2×D11—81no—
231C2×D11—81no—
232C2×D11—81no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—82no—
237C4×C11—82no—
238C4×C11—81no—
239C4×C11#44711yescharacteristic
240C4×C11#44911yescharacteristic
241C4×C11#45412yes—
242C4×C11#46611yescharacteristic
243C4×C11#46911yescharacteristic
244Dic11—81no—
245C2×#41—221no—
246C22×Q8—21no—
247C22×D4C22⋊D1111yescharacteristic
248C23×C4—21no—
249AGL(1,ℤ/8)—442no—
250AGL(1,ℤ/8)—442no—
251C2×SD16—222no—
252C2×D8—222no—
253C2×M16—221no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—111no—
259#127—111no—
260#124—42no—
261#124—42no—
262#124—221no—
263#121—221no—
264#121—221no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—221no—
270C4×D4—221no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4C22⋊D1111yescharacteristic
274C2×C4⋊C4C22⋊D1112yes—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—21no—
277C2×C42—21no—
278C2×C42C22×D1111yescharacteristic
279#107—224no—
280C4⋊C8—112no—
281C4⋊C8—112no—
282C4⋊C8—221no—
283C4⋊C8—221no—
284#103—222no—
285#102—222no—
286#102—224no—
287C22⋊C8—221no—
288C22⋊C8—221no—
289C4×C8—221no—
290C4×C8—221no—
291#95—24no—
292#95C22⋊D1112yes—
293C2×C11—21no—
294C2×C11—21no—
295C2×C11—82no—
296C2×C11#199911yescharacteristic
297C2×C11#200311yescharacteristic
298C2×C11#200911yescharacteristic
299D11—161no—
300C24—21no—
301#41—441no—
302#41—441no—
303#41—441no—
304#41—441no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×Q8—221no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—221no—
318C2×D4—221no—
319C2×D4—221no—
320C2×D4—441no—
321C2×D4#432312yes—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—44no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—441no—
329C22×C4C2×C22⋊D1111yescharacteristic
330C22×C4C2×C22⋊D1111yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332SD16—444no—
333D8—444no—
334M16—441no—
335M16—441no—
336C2×C8—222no—
337C2×C8—222no—
338C2×C8—441no—
339C4⋊C4—21no—
340C4⋊C4—22no—
341C4⋊C4—21no—
342C4⋊C4—22no—
343C4⋊C4—42no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—221no—
347C4⋊C4—221no—
348C22⋊C4—48no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C42—41no—
354C42—41no—
355C42D4×D1111yescharacteristic
356C42D4×D1111yescharacteristic
357C42D4×D1111yescharacteristic
358C42#434111yescharacteristic
359C11#1023911yescharacteristic, complemented, Sylow
360C23—22no—
361C23—42no—
362C23—42no—
363C23—41no—
364C23—41no—
365C23—441no—
366C23#6700611yescharacteristic
367Q8—81no—
368Q8—81no—
369Q8—81no—
370Q8—81no—
371Q8—441no—
372Q8—441no—
373D4—22no—
374D4—22no—
375D4—41no—
376D4—41no—
377D4—441no—
378D4—441no—
379D4—442no—
380D4—881no—
381D4—881no—
382D4—881no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—441no—
396C2×C4—881no—
397C2×C4—881no—
398C2×C4C2×#432311yescharacteristic
399C2×C4#6698511yescharacteristic
400C2×C4#6699011yescharacteristic
401C2×C4#6699011yescharacteristic
402C2×C4#6699111yescharacteristic
403C2×C4#6699211yescharacteristic
404C2×C4#6699211yescharacteristic
405C2×C4#6699311yescharacteristic
406C2×C4#6700211yescharacteristic
407C2×C4#6700311yescharacteristic
408C8—442no—
409C8—442no—
410C8—881no—
411C22—21no—
412C22—21no—
413C22—44no—
414C22—42no—
415C22—82no—
416C22—81no—
417C22—81no—
418C22—881no—
419C22—881no—
420C22—881no—
421C22#1062283011yescharacteristic
422C22#1062283611yescharacteristic
423C22#1062285111yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—82no—
428C4—82no—
429C4—81no—
430C4—881no—
431C4#1062264911yescharacteristic
432C4#1062265011yescharacteristic
433C4#1062265111yescharacteristic
434C4#1062265211yescharacteristic
435C4#1062267512yes—
436C2—21no—
437C2—21no—
438C2—82no—
439C2—1761no—
440C2#1306961211yescharacteristic
441C2#1306963811yescharacteristic
442C2#1306967611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2547C2
socleC22×C11#392
prime radical#13078080C2
hypercenter#2547D11
hypocenterC11#10239
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2547

Complements

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

NH ≅ G/Ntype
1. #13079737C2semidirect
3. #13067288C2semidirect
4. #13067110C2semidirect
5. #13067007C2semidirect
6. #13066519C2semidirect
7. C11×#2547C2semidirect
141. #2547D11semidirect
359. C11#10239semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130780802
#130672882
#130671102
#130670072
#130665192
C11×#25472
#1023911