Finite Group Databasebeta

← #14655759

Subgroups — #14655759

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#13079538C211yesmaximal, characteristic, complemented
2C2×#10622621C211yesmaximal, characteristic, complemented
3#13067302C211yesmaximal, characteristic, complemented
4#13067015C211yesmaximal, characteristic, complemented
5#13066937C211yesmaximal, characteristic, complemented
6#13066511C211yesmaximal, characteristic, complemented
7C11×#3036C211yesmaximal, characteristic
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#463—22no—
13C11×#461—21no—
14C11×#459—21no—
15C11×#423C2211yescharacteristic
16C11×#417—21no—
17C2×#66896—21no—
18#10622706—21no—
19#10622689—21no—
20#10622653—22no—
21#10622632—22no—
22#10622621—22no—
23#10622621—22no—
24C2×#66872—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28D4⋊(C11⋊C8)—22no—
29#10622163—22no—
30#10622124—22no—
31C2×C11×#41—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C22×Dic22—21no—
35C11×AGL(1,ℤ/8)—42no—
36C11×AGL(1,ℤ/8)—42no—
37C2×C11×SD16—22no—
38C2×C11×D8—22no—
39C2×C11×M16—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×#127D411yescharacteristic
42C11×#124—21no—
43C11×#121—21no—
44C11×#121—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×#4324—24no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C22×C11⋊C8—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922D412yes—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×#103—22no—
65C11×#102—22no—
66#66896—24no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)D412yes—
69#66874—24no—
70#66872—24no—
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—
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—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—41no—
93C2×D4×C11SD1612yescomplemented
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—82no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×Dic11—41no—
103C2×Dic22—22no—
104C2×Dic22—41no—
105C2×Dic22—82no—
106C11×SD16—44no—
107C11×D8—44no—
108C11×M16—41no—
109C11×M16—41no—
110C2×C8×C11—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123#4324—84no—
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133#3206—111no—
134C2×#476—111no—
135#3036D1111yescharacteristic
136#1549—111no—
137#1480—111no—
138#1460—111no—
139#1301—111no—
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—81no—
145C23×C11—81no—
146C23×C11#12111yescharacteristic
147Q8×C11—41no—
148Q8×C11—41no—
149D4×C11—22no—
150D4×C11—22no—
151D4×C11—42no—
152D4×C11—41no—
153D4×C11—41no—
154D4×C11—41no—
155D4×C11—41no—
156D4×C11—42no—
157D4×C11—81no—
158D4×C11—81no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—82no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C2×C4×C11—82no—
167C2×C4×C11—81no—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12711yescharacteristic
174C2×C4×C11C2×SD1611yescharacteristic
175C2×C4×C11#13511yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C11#13711yescharacteristic
178C2×Dic11—42no—
179C2×Dic11—82no—
180Dic22—44no—
181Dic22—82no—
182C8×C11—42no—
183C11⋊C8—42no—
184C11⋊C8—42no—
185C11⋊C8—81no—
186C2×AGL(1,ℤ/8)—21no—
187#532C2×D1111yescharacteristic
188C2×C4⋊Q8—111no—
189C2×C4×D4C2×D1111yescharacteristic
190#492—221no—
191#487—221no—
192#476—222no—
193#476—222no—
194#463—22no—
195#461—21no—
196#461—222no—
197#459—21no—
198#448—222no—
199#431—111no—
200#431—111no—
201C2×#106—221no—
202#423C2×D1111yescharacteristic
203C2×C4⋊C8—111no—
204#417—21no—
205C2×#102—221no—
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—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11#39211yescharacteristic
220C22×C11#46511yescharacteristic
221C22×C11#46811yescharacteristic
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—81no—
226C4×C11—81no—
227C4×C11#44811yescharacteristic
228C4×C11#44911yescharacteristic
229C4×C11#45011yescharacteristic
230C4×C11#45211yescharacteristic
231C4×C11#47112yes—
232Dic11—82no—
233C2×#41—21no—
234C22×Q8—221no—
235C22×D4C22⋊D1111yescharacteristic
236C23×C4—21no—
237AGL(1,ℤ/8)—42no—
238AGL(1,ℤ/8)—42no—
239C2×SD16—22no—
240C2×SD16—224no—
241C2×D8—22no—
242C2×M16—21no—
243C22×C8—221no—
244C4⋊Q8—112no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248C4⋊Q8C22⋊D1111yescharacteristic
249#127C22⋊D1111yescharacteristic
250#124—21no—
251#121—21no—
252#121—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4C22⋊D1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C42C22×D1111yescharacteristic
264#106—224no—
265C4⋊C8—21no—
266C4⋊C8—112no—
267C4⋊C8—221no—
268C4⋊C8—221no—
269C4⋊C8—221no—
270C4⋊C8C22⋊D1112yes—
271#103—22no—
272#103—224no—
273#102—22no—
274#102—224no—
275C22⋊C8—112no—
276C22⋊C8—221no—
277C4×C8—221no—
278C4×C8—221no—
279C2×C11—21no—
280C2×C11—21no—
281C2×C11—82no—
282C2×C11—161no—
283C2×C11#200011yescharacteristic
284C2×C11#200811yescharacteristic
285C2×C11#201911yescharacteristic
286C24—21no—
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—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4#432412yescomplemented
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—44no—
315SD16—884no—
316D8—44no—
317M16—41no—
318M16—41no—
319C2×C8—22no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—441no—
323C2×C8—441no—
324C2×C8—441no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—222no—
330C4⋊C4—222no—
331C4⋊C4—441no—
332C4⋊C4—441no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C42D4×D1111yescharacteristic
338C42D4×D1111yescharacteristic
339C42C2×C22⋊D1111yescharacteristic
340C42C2×C22⋊D1111yescharacteristic
341C11#1018011yescharacteristic, complemented, Sylow
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—81no—
347C23—81no—
348C23#6699211yescharacteristic
349Q8—41no—
350Q8—41no—
351Q8—444no—
352Q8—882no—
353D4—22no—
354D4—22no—
355D4—42no—
356D4—42no—
357D4—41no—
358D4—41no—
359D4—41no—
360D4—41no—
361D4—81no—
362D4—81no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—442no—
373C2×C4—882no—
374C2×C4#6698511yescharacteristic
375C2×C4C2×#432411yescharacteristic
376C2×C4#6699011yescharacteristic
377C2×C4#6699011yescharacteristic
378C2×C4#6699111yescharacteristic
379C2×C4#6699211yescharacteristic
380C2×C4#6699311yescharacteristic
381C2×C4#6700311yescharacteristic
382C2×C4#6700411yescharacteristic
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—81no—
396C22—81no—
397C22—81no—
398C22#1062265411yescharacteristic
399C22#1062265511yescharacteristic
400C22#1062283611yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—81no—
405C4—81no—
406C4—882no—
407C4#1062265011yescharacteristic
408C4#1062265311yescharacteristic
409C4#1062281312yes—
410C4#1062283111yescharacteristic
411C4#1062285211yescharacteristic
412C2—21no—
413C2—21no—
414C2—82no—
415C2—161no—
416C2#1306961911yescharacteristic
417C2#1306966611yescharacteristic
418C2#1306973011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3036C2
socleC22×C11#392
hypercenter#3036D11
hypocenterC11#10180
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13079538C2semidirect
2. C2×#10622621C2semidirect
3. #13067302C2semidirect
4. #13067015C2semidirect
5. #13066937C2semidirect
6. #13066511C2semidirect
93. C2×D4×C11SD16semidirect
304. C2×D4#4324semidirect
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×#106226212
#130673022
#130670152
#130669372
#130665112
C11×#30362
#1018011