Finite Group Databasebeta

← #14655756

Subgroups — #14655756

Order 2816.

562 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C2×#10622697C211yesmaximal, characteristic, complemented
2#13078076C211yesmaximal, characteristic
3#13067301C211yesmaximal, characteristic, complemented
4#13067015C211yesmaximal, characteristic, complemented
5#13066936C211yesmaximal, characteristic, complemented
6#13066512C211yesmaximal, characteristic, complemented
7C11×#3206C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#67002—21no—
11C2×C4×D44C2211yescharacteristic
12C11×#492—21no—
13C11×#487—21no—
14C11×#461—22no—
15C11×#448—22no—
16C11×#431C2211yescharacteristic
17#10622845—21no—
18#10622697—22no—
19#10622697—22no—
20#10622696—21no—
21#10622685—21no—
22#10622670—22no—
23C2×#66873—21no—
24C2×#66872—21no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28#10622185—22no—
29D4⋊(C11⋊C8)—22no—
30#10622106—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×D44D411yescharacteristic
34C22×C4×D11—21no—
35C2×C11×SD16—24no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D412yes—
40C11×C4⋊Q8D411yescharacteristic
41C11×#127D411yescharacteristic
42C11×#124—21no—
43C11×#121—21no—
44C11×#121—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C42×C11C2311yescharacteristic
50#67002—42no—
51#67002—42no—
52C2×#4325—22no—
53C2×#4323—22no—
54C2×(C2×D11)⋊C4—21no—
55C2×C4⋊Dic11D411yescharacteristic
56C2×#4318—21no—
57C22×C11⋊C8—21no—
58C4×D44—21no—
59C4×D44—21no—
60C4×D44—21no—
61C4×D44—21no—
62C11×C4⋊C8—21no—
63C11×#103—24no—
64C11×C22⋊C8D412yes—
65C4×C8×C11—21no—
66#66899—22no—
67#66896—22no—
68C22⋊(C11⋊C8)—21no—
69#66873—24no—
70#66872—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
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×Q8×C11—22no—
85C2×Q8×C11—41no—
86C2×Q8×C11—82no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C22×Dic11—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44SD1612yescomplemented
103C2×C4×D11—41no—
104C2×C4×D11—41no—
105C2×C4×D11—82no—
106C11×SD16—84no—
107C2×C8×C11—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120#4325—44no—
121#4323—44no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126#4318—41no—
127#4318—41no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133#3206D1111yescharacteristic, complemented
134C2×#476—111no—
135#3036—111no—
136#1549—111no—
137#1480—111no—
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—44no—
148Q8×C11—41no—
149Q8×C11—41no—
150Q8×C11—82no—
151D4×C11—42no—
152D4×C11—41no—
153D4×C11—41no—
154D4×C11—42no—
155D4×C11—81no—
156D4×C11—81no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—82no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12711yescharacteristic
170C2×C4×C11C2×SD1611yescharacteristic
171C2×C4×C11#13511yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11#13711yescharacteristic
174C2×Dic11—41no—
175C2×Dic11—81no—
176D44—22no—
177D44—22no—
178D44—41no—
179D44—41no—
180C4×D11—82no—
181C4×D11—82no—
182C8×C11—42no—
183C11⋊C8—42no—
184C11⋊C8—42no—
185C11⋊C8—81no—
186C2×AGL(1,ℤ/8)—221no—
187#532C2×D1111yescharacteristic
188C2×C4⋊Q8C2×D1111yescharacteristic
189C2×C4×D4—111no—
190#492—21no—
191#487—21no—
192#476—222no—
193#476—222no—
194#463—222no—
195#461—22no—
196#461—221no—
197#459—221no—
198#448—22no—
199#431—111no—
200#431C2×D1111yescharacteristic
201C2×#106—221no—
202#423—111no—
203C2×C4⋊C8—111no—
204#417—221no—
205C2×#102—221no—
206#332—222no—
207D4⋊C8—222no—
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—82no—
227C4×C11#44811yescharacteristic
228C4×C11#44911yescharacteristic
229C4×C11#45011yescharacteristic
230C4×C11#45211yescharacteristic
231C4×C11#47112yes—
232Dic11—81no—
233C2×#41—21no—
234C22×Q8—21no—
235C22×D4—111no—
236C23×C4—221no—
237AGL(1,ℤ/8)—442no—
238AGL(1,ℤ/8)—442no—
239C2×SD16—24no—
240C2×SD16—222no—
241C2×D8—222no—
242C2×M16—221no—
243C22×C8—221no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8C22⋊D1112yes—
248C4⋊Q8C22⋊D1111yescharacteristic
249#127C22⋊D1111yescharacteristic
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—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—111no—
262C2×C22⋊C4—221no—
263C2×C42C22×D1111yescharacteristic
264#106—224no—
265C4⋊C8—21no—
266C4⋊C8—112no—
267C4⋊C8—112no—
268C4⋊C8—221no—
269C4⋊C8—221no—
270C4⋊C8—221no—
271#103—24no—
272#103—222no—
273#102—224no—
274#102—222no—
275C22⋊C8—221no—
276C22⋊C8C22⋊D1112yes—
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—22no—
293C2×Q8—41no—
294C2×Q8—82no—
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—41no—
307C22×C4—221no—
308C22×C4—441no—
309C22×C4—441no—
310C22×C4—882no—
311C22×C4D4×D1111yescharacteristic
312C22×C4#434111yescharacteristic
313C22×C4C2×C22⋊D1111yescharacteristic
314SD16—84no—
315SD16—444no—
316D8—444no—
317M16—441no—
318M16—441no—
319C2×C8—22no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—441no—
323C2×C8—441no—
324C2×C8—441no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—21no—
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—41no—
343C23—222no—
344C23—441no—
345C23—441no—
346C23—881no—
347C23—881no—
348C23#6699111yescharacteristic
349Q8—44no—
350Q8—41no—
351Q8—41no—
352Q8—82no—
353D4—42no—
354D4—41no—
355D4—41no—
356D4—42no—
357D4—81no—
358D4—81no—
359D4—222no—
360D4—222no—
361D4—441no—
362D4—441no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—82no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—441no—
371C2×C4—882no—
372C2×C4—882no—
373C2×C4—881no—
374C2×C4SD16×D1111yescharacteristic
375C2×C4#6696711yescharacteristic
376C2×C4#6696811yescharacteristic
377C2×C4#6696911yescharacteristic
378C2×C4#6699011yescharacteristic
379C2×C4#6699011yescharacteristic
380C2×C4#6699211yescharacteristic
381C2×C4#6699211yescharacteristic
382C2×C4#6699311yescharacteristic
383C2×C4#6700611yescharacteristic
384C8—42no—
385C8—442no—
386C8—442no—
387C8—881no—
388C22—21no—
389C22—21no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—442no—
394C22—882no—
395C22—882no—
396C22—881no—
397C22—881no—
398C22#1062278411yescharacteristic
399C22#1062278711yescharacteristic
400C22#1062283611yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—81no—
405C4—82no—
406C4—881no—
407C4#1062278211yescharacteristic
408C4#1062278311yescharacteristic
409C4#1062278511yescharacteristic
410C4#1062278611yescharacteristic
411C4#1062281612yes—
412C2—21no—
413C2—21no—
414C2—161no—
415C2—882no—
416C2#1306961611yescharacteristic
417C2#1306966911yescharacteristic
418C2#1306972711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3206C2
socleC22×C11#392
prime radical#13078076C2
hypercenter#3206D11
hypocenterC11#10180
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3206

Complements

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

NH ≅ G/Ntype
1. C2×#10622697C2semidirect
3. #13067301C2semidirect
4. #13067015C2semidirect
5. #13066936C2semidirect
6. #13066512C2semidirect
7. C11×#3206C2semidirect
102. C2×D44SD16semidirect
133. #3206D11semidirect
341. C11#10180semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
#130780762
#130673012
#130670152
#130669362
#130665122
C11×#32062
#1018011