Finite Group Databasebeta

← #14655757

Subgroups — #14655757

Order 2816.

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

normal subgroups only

This group has 562 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#13079541C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic
3#13067301C211yesmaximal, characteristic, complemented
4#13067014C211yesmaximal, characteristic, complemented
5#13066937C211yesmaximal, characteristic, complemented
6#13066513C211yesmaximal, characteristic, complemented
7C2×C11×#476C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66985—21no—
11#10623008C2211yescharacteristic
12C11×#476—22no—
13C11×#476—22no—
14C2×C11×#106—21no—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#102—21no—
17#10622840—22no—
18#10622698—21no—
19#10622696—22no—
20#10622694—21no—
21#10622632—21no—
22#10622629—22no—
23#10622628—21no—
24#10622579—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622185—22no—
29#10622163—22no—
30#10622121—22no—
31C22×Q8×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C2×#4339—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D412yes—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4325—24no—
50C2×#4324—22no—
51#66985—42no—
52#66985—42no—
53C2×#4323—22no—
54#66983—21no—
55#66983—21no—
56C2×#4318—21no—
57#66928—21no—
58#66927D411yescharacteristic
59C4×D44—21no—
60C4×D44—21no—
61#66922D411yescharacteristic
62C11×#106—24no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×#102—24no—
66#66899—24no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)D412yes—
69#66874—22no—
70#66873—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10180—111nomaximal, Sylow
78C24×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—41no—
81C2×Q8×C11—82no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11SD1612yescomplemented
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—82no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C2×C22⋊D11—41no—
97#4339—41no—
98#4339—41no—
99#4339—41no—
100#4339—41no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—21no—
104C2×C4×D11—41no—
105C2×Dic22—21no—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121#4325—84no—
122#4324—44no—
123#4323—44no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128#4318—41no—
129#4318—41no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—41no—
133#3206—111no—
134C2×#476D1111yescharacteristic, complemented
135#3036—111no—
136#1549—111no—
137#1480—111no—
138#1460—111no—
139#1301—111no—
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—81no—
144C23×C11—81no—
145C23×C11#12111yescharacteristic
146C22×D11—41no—
147Q8×C11—44no—
148Q8×C11—82no—
149D4×C11—22no—
150D4×C11—22no—
151D4×C11—41no—
152D4×C11—41no—
153C2×C4×C11—22no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—82no—
158C2×C4×C11—82no—
159C2×C4×C11—82no—
160C2×C4×C11—81no—
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12711yescharacteristic
167C2×C4×C11C2×SD1611yescharacteristic
168C2×C4×C11#13511yescharacteristic
169C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C11#13711yescharacteristic
171C22⋊D11—81no—
172C22⋊D11—81no—
173C2×Dic11—41no—
174D44—42no—
175D44—41no—
176D44—41no—
177D44—42no—
178C4×D11—81no—
179C4×D11—81no—
180Dic22—41no—
181Dic22—41no—
182C8×C11—42no—
183C11⋊C8—42no—
184C11⋊C8—42no—
185C11⋊C8—81no—
186C2×AGL(1,ℤ/8)—221no—
187#532—111no—
188C2×C4⋊Q8C2×D1111yescharacteristic
189C2×C4×D4C2×D1111yescharacteristic
190#492—221no—
191#487—221no—
192#476—22no—
193#476—22no—
194#463—222no—
195#461—221no—
196#461—222no—
197#459—221no—
198#448—222no—
199#431—111no—
200#431—111no—
201C2×#106—21no—
202#423—111no—
203C2×C4⋊C8C2×D1111yescharacteristic
204#417—221no—
205C2×#102—21no—
206#332—222no—
207D4⋊C8—222no—
208#323—222no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—42no—
212C22×C11—82no—
213C22×C11—82no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11#39211yescharacteristic
217C22×C11#46511yescharacteristic
218C22×C11#46811yescharacteristic
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—81no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—82no—
226C4×C11—81no—
227C4×C11#44811yescharacteristic
228C4×C11#44911yescharacteristic
229C4×C11#45011yescharacteristic
230C4×C11#45211yescharacteristic
231C4×C11#47112yes—
232Dic11—81no—
233C2×#41—221no—
234C22×Q8—21no—
235C22×D4C22⋊D1111yescharacteristic
236C23×C4—21no—
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—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—111no—
248C4⋊Q8C22⋊D1112yes—
249#127—111no—
250#124—221no—
251#121—221no—
252#121—221no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—221no—
258C4×D4—221no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4C22⋊D1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C42C22×D1111yescharacteristic
264#106—24no—
265C4⋊C8—21no—
266C4⋊C8—112no—
267C4⋊C8—221no—
268C4⋊C8—221no—
269C4⋊C8—221no—
270C4⋊C8C22⋊D1112yes—
271#103—222no—
272#103—224no—
273#102—24no—
274#102—222no—
275C22⋊C8—112no—
276C22⋊C8—221no—
277C4×C8—221no—
278C4×C8—221no—
279C2×C11—21no—
280C2×C11—21no—
281C2×C11—82no—
282C2×C11#200011yescharacteristic
283C2×C11#200811yescharacteristic
284C2×C11#201911yescharacteristic
285D11—161no—
286C24—21no—
287#41—441no—
288#41—441no—
289#41—441no—
290#41—441no—
291C2×Q8—22no—
292C2×Q8—41no—
293C2×Q8—82no—
294C2×Q8—221no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—221no—
303C2×D4—441no—
304C2×D4#432512yescomplemented
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—82no—
310C22×C4—441no—
311C22×C4D4×D1111yescharacteristic
312C22×C4#434111yescharacteristic
313C22×C4C2×C22⋊D1111yescharacteristic
314SD16—444no—
315SD16—884no—
316D8—444no—
317M16—441no—
318M16—441no—
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—222no—
323C2×C8—222no—
324C2×C8—441no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—21no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—221no—
332C4⋊C4—221no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C42D4×D1111yescharacteristic
338C42D4×D1111yescharacteristic
339C42C2×C22⋊D1111yescharacteristic
340C42C2×C22⋊D1111yescharacteristic
341C11#1018011yescharacteristic, complemented, Sylow
342C23—22no—
343C23—41no—
344C23—41no—
345C23—81no—
346C23—81no—
347C23—441no—
348C23#6699211yescharacteristic
349Q8—44no—
350Q8—82no—
351Q8—441no—
352Q8—441no—
353D4—22no—
354D4—22no—
355D4—41no—
356D4—41no—
357D4—442no—
358D4—442no—
359D4—441no—
360D4—441no—
361D4—881no—
362D4—881no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—81no—
371C2×C4—441no—
372C2×C4—881no—
373C2×C4—881no—
374C2×C4#6699011yescharacteristic
375C2×C4#6699011yescharacteristic
376C2×C4#6699111yescharacteristic
377C2×C4#6699211yescharacteristic
378C2×C4#6699311yescharacteristic
379C2×C4C2×#432511yescharacteristic
380C2×C4#6699511yescharacteristic
381C2×C4#6700211yescharacteristic
382C2×C4#6700311yescharacteristic
383C2×C4#6700611yescharacteristic
384C8—42no—
385C8—442no—
386C8—442no—
387C8—881no—
388C22—21no—
389C22—21no—
390C22—42no—
391C22—82no—
392C22—82no—
393C22—81no—
394C22—81no—
395C22—881no—
396C22—881no—
397C22—881no—
398C22#1062266111yescharacteristic
399C22#1062266211yescharacteristic
400C22#1062283611yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—82no—
405C4—81no—
406C4—881no—
407C4#1062265911yescharacteristic
408C4#1062266011yescharacteristic
409C4#1062279012yes—
410C4#1062284011yescharacteristic
411C4#1062285111yescharacteristic
412C2—21no—
413C2—21no—
414C2—82no—
415C2—1761no—
416C2#1306961711yescharacteristic
417C2#1306966711yescharacteristic
418C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#476C2
socleC22×C11#392
prime radical#13078080C2
hypercenterC2×#476D11
hypocenterC11#10180
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. #13079541C2semidirect
3. #13067301C2semidirect
4. #13067014C2semidirect
5. #13066937C2semidirect
6. #13066513C2semidirect
7. C2×C11×#476C2semidirect
87. C2×D4×C11SD16semidirect
134. C2×#476D11semidirect
304. C2×D4#4325semidirect
341. C11#10180semidirect

Maximal subgroups

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

subgroupindex
#130795412
#130780802
#130673012
#130670142
#130669372
#130665132
C2×C11×#4762
#1018011