Finite Group Databasebeta

← #14655760

Subgroups — #14655760

Order 2816.

562 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079538C211yesmaximal, characteristic, complemented
2C2×#10622455C211yesmaximal, characteristic, complemented
3#13078076C211yesmaximal, characteristic
4#13067300C211yesmaximal, characteristic, complemented
5#13066936C211yesmaximal, characteristic, complemented
6#13066513C211yesmaximal, characteristic, complemented
7C11×#1480C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×#67002—21no—
10C2×C4×D44C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14#10622845—21no—
15C2×#66885—21no—
16C2×#66881—21no—
17#10622706—21no—
18#10622696—21no—
19#10622689—21no—
20#10622685—21no—
21#10622670—22no—
22#10622653—22no—
23#10622632—22no—
24#10622538C2211yescharacteristic
25#10622537C2211yescharacteristic
26#10622455—22no—
27#10622455—22no—
28C11×D4⋊C8—22no—
29#10622120—22no—
30#10622106—22no—
31C2×C11×#41—21no—
32C22×D44D411yescharacteristic
33C22×C4×D11—21no—
34C22×Dic22—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8D411yescharacteristic
37C11×#127D411yescharacteristic
38C11×#124—21no—
39C11×#121—21no—
40C11×#121—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C2×C42×C11C2311yescharacteristic
44#67002—42no—
45#67002—42no—
46C2×#4325—22no—
47C2×#4324—24no—
48C2×#4323—22no—
49C2×(C2×D11)⋊C4—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11D411yescharacteristic
53C2×#4318—21no—
54C4×D44—21no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922D412yes—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×C22⋊C8—21no—
66C4×C8×C11—21no—
67#66899—22no—
68#66896—22no—
69C22⋊(C11⋊C8)D412yes—
70#66885—24no—
71#66881—24no—
72#66874—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4×C11⋊C8—21no—
77#10180—111nomaximal, Sylow
78C23×D11—21no—
79C11×#41—41no—
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C2×Q8×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×Dic11—21no—
93C22×Dic11—41no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44SD1612yescomplemented
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11—82no—
103C2×Dic22—22no—
104C2×Dic22—41no—
105C2×Dic22—82no—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118#4325—44no—
119#4324—84no—
120#4323—44no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123C4⋊Dic11—21no—
124C4⋊Dic11—22no—
125C4⋊Dic11—21no—
126C4⋊Dic11—22no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129#4318—41no—
130#4318—41no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133#3206—111no—
134C2×#476—111no—
135#3036—111no—
136#1549—111no—
137#1480D1111yescharacteristic, complemented
138#1460—111no—
139#1301—111no—
140C23×C11—41no—
141C23×C11#12111yescharacteristic
142C22×D11—22no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—81no—
146C22×D11—81no—
147Q8×C11—41no—
148Q8×C11—41no—
149D4×C11—42no—
150D4×C11—41no—
151D4×C11—41no—
152D4×C11—42no—
153D4×C11—81no—
154D4×C11—81no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12711yescharacteristic
166C2×C4×C11C2×SD1611yescharacteristic
167C2×C4×C11#13511yescharacteristic
168C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C11#13711yescharacteristic
170C2×Dic11—42no—
171C2×Dic11—41no—
172C2×Dic11—82no—
173C2×Dic11—81no—
174D44—22no—
175D44—22no—
176D44—41no—
177D44—41no—
178C4×D11—82no—
179C4×D11—82no—
180Dic22—44no—
181Dic22—82no—
182C8×C11—42no—
183C8×C11—81no—
184C11⋊C8—42no—
185C11⋊C8—42no—
186C2×AGL(1,ℤ/8)—221no—
187#532C2×D1111yescharacteristic
188C2×C4⋊Q8—111no—
189C2×C4×D4—111no—
190#492—221no—
191#487—221no—
192#476—222no—
193#476—222no—
194#463—222no—
195#461—222no—
196#461—221no—
197#459—221no—
198#448—222no—
199#431—111no—
200#431C2×D1111yescharacteristic
201C2×#106—221no—
202#423—111no—
203C2×C4⋊C8C2×D1111yescharacteristic
204#417—221no—
205C2×#102—221no—
206#332—222no—
207D4⋊C8—22no—
208#323—222no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11—81no—
214C22×C11#39211yescharacteristic
215C22×C11#46511yescharacteristic
216C22×C11#46811yescharacteristic
217C2×D11—42no—
218C2×D11—82no—
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—82no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—81no—
226C4×C11#44811yescharacteristic
227C4×C11#44911yescharacteristic
228C4×C11#45011yescharacteristic
229C4×C11#45211yescharacteristic
230C4×C11#47112yes—
231Dic11—82no—
232Dic11—81no—
233C2×#41—21no—
234C22×Q8—221no—
235C22×D4—111no—
236C23×C4—221no—
237AGL(1,ℤ/8)—442no—
238AGL(1,ℤ/8)—442no—
239C2×SD16—222no—
240C2×SD16—224no—
241C2×D8—222no—
242C2×M16—221no—
243C22×C8—21no—
244C4⋊Q8—112no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248C4⋊Q8D4411yescharacteristic
249#127D4411yescharacteristic
250#124—21no—
251#121—21no—
252#121—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—221no—
256C4×D4—221no—
257C4×D4—221no—
258C4×D4—221no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C42C22×D1111yescharacteristic
264#106—224no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—112no—
268C4⋊C8—221no—
269C4⋊C8—221no—
270C4⋊C8C22⋊D1112yes—
271#103—224no—
272#103—222no—
273#102—224no—
274#102—222no—
275C22⋊C8—21no—
276C22⋊C8—112no—
277C4×C8—21no—
278C4×C8—221no—
279C2×C11—21no—
280C2×C11—21no—
281C2×C11—161no—
282C2×C11#200011yescharacteristic
283C2×C11#200811yescharacteristic
284C2×C11#201911yescharacteristic
285D11—82no—
286C24—221no—
287#41—41no—
288#41—41no—
289#41—41no—
290#41—41no—
291C2×Q8—21no—
292C2×Q8—222no—
293C2×Q8—441no—
294C2×Q8—882no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—41no—
299C2×D4—112no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—221no—
303C2×D4—221no—
304C2×D4—221no—
305C22×C4—41no—
306C22×C4—221no—
307C22×C4—441no—
308C22×C4—441no—
309C22×C4—441no—
310C22×C4—882no—
311C22×C4#433911yescharacteristic
312C22×C4D4×D1111yescharacteristic
313C22×C4D4×D1111yescharacteristic
314SD16—444no—
315SD16—884no—
316D8—444no—
317M16—441no—
318M16—441no—
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—222no—
324C2×C8—222no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—221no—
328C4⋊C4—222no—
329C4⋊C4—222no—
330C4⋊C4—221no—
331C4⋊C4—441no—
332C4⋊C4—441no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C42C2×D4411yescharacteristic
338C42D4×D1111yescharacteristic
339C42D4×D1111yescharacteristic
340C42C2×C22⋊D1111yescharacteristic
341C11#1018011yescharacteristic, complemented, Sylow
342C23—41no—
343C23—222no—
344C23—441no—
345C23—441no—
346C23—881no—
347C23—881no—
348C23#6693711yescharacteristic
349Q8—41no—
350Q8—41no—
351Q8—444no—
352Q8—882no—
353D4—42no—
354D4—42no—
355D4—41no—
356D4—41no—
357D4—81no—
358D4—81no—
359D4—222no—
360D4—222no—
361D4—441no—
362D4—441no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—441no—
369C2×C4—442no—
370C2×C4—882no—
371C2×C4—882no—
372C2×C4—882no—
373C2×C4—881no—
374C2×C4#6693511yescharacteristic
375C2×C4#6693511yescharacteristic
376C2×C4#6693711yescharacteristic
377C2×C4#6696411yescharacteristic
378C2×C4#6696511yescharacteristic
379C2×C4SD16×D1111yescharacteristic
380C2×C4#6696811yescharacteristic
381C2×C4#6698311yescharacteristic
382C2×C4#6699011yescharacteristic
383C2×C4#6699311yescharacteristic
384C8—42no—
385C8—81no—
386C8—442no—
387C8—442no—
388C22—21no—
389C22—21no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—442no—
394C22—882no—
395C22—882no—
396C22—881no—
397C22—881no—
398C22#1062239111yescharacteristic
399C22#1062239311yescharacteristic
400C22#1062257311yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—81no—
405C4—882no—
406C4—881no—
407C4#1062238911yescharacteristic
408C4#1062239611yescharacteristic
409C4#1062275412yes—
410C4#1062277111yescharacteristic
411C4#1062278311yescharacteristic
412C2—21no—
413C2—21no—
414C2—161no—
415C2—882no—
416C2#1306962011yescharacteristic
417C2#1306967011yescharacteristic
418C2#1306973111yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1480C2
socleC22×C11#392
prime radical#13078076C2
hypercenter#1480D11
hypocenterC11#10180
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
1. #13079538C2semidirect
2. C2×#10622455C2semidirect
4. #13067300C2semidirect
5. #13066936C2semidirect
6. #13066513C2semidirect
7. C11×#1480C2semidirect
99. C2×D44SD16semidirect
137. #1480D11semidirect
341. C11#10180semidirect

Maximal subgroups

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

subgroupindex
#130795382
C2×#106224552
#130780762
#130673002
#130669362
#130665132
C11×#14802
#1018011