Finite Group Databasebeta

← #14655817

Subgroups — #14655817

Order 2816.

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

normal subgroups only

This group has 550 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
1#13079746C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic, complemented
3#13078080C211yesmaximal, characteristic
4#13067296C211yesmaximal, characteristic, complemented
5#13067016C211yesmaximal, characteristic, complemented
6#13066512C211yesmaximal, characteristic, complemented
7C11×#1460C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66985—21no—
10#10623008C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C2×#66896—21no—
15#10622632—21no—
16#10622629—22no—
17#10622628—21no—
18#10622620—22no—
19#10622620—22no—
20#10622579—21no—
21C2×#66871—21no—
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622455—22no—
25#10622348—22no—
26#10622307—21no—
27#10622293—21no—
28C11×#323—22no—
29#10622119—22no—
30#10622097—22no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C2×#4339—21no—
34C22×Dic22—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4324—22no—
43#66985—42no—
44#66985—42no—
45C2×#4323—22no—
46#66983—21no—
47#66983—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×#4318—21no—
51C22×C11⋊C8—21no—
52#66928—21no—
53#66927D411yescharacteristic
54C4×D44—21no—
55C4×D44—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922D412yes—
60#66922D411yescharacteristic
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8D412yes—
65C4×C8×C11—21no—
66C4×C8×C11—21no—
67#66896—24no—
68#66885—24no—
69#66881—24no—
70#66874—22no—
71#66873—22no—
72#66871—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4⋊(C11⋊C8)D412yes—
77#10188—111nomaximal, Sylow
78C24×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11SD1612yes—
85C22×C4×C11—21no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—82no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C2×C22⋊D11—41no—
93C22×Dic11—41no—
94#4339—41no—
95#4339—41no—
96#4339—41no—
97#4339—41no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×C4×D11—41no—
102C2×Dic22—21no—
103C2×Dic22—22no—
104C2×Dic22—41no—
105C2×Dic22—82no—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116#4324—44no—
117#4323—44no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120C4⋊Dic11—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11—22no—
123C4⋊Dic11—21no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126#4318—41no—
127#4318—41no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132#3227—111no—
133C2×#474—111no—
134#3036—111no—
135#1548—111no—
136#1480—111no—
137#1460D1111yescharacteristic, complemented
138#1301—111no—
139C23×C11—22no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—81no—
143C23×C11—81no—
144C23×C11#12111yescharacteristic
145C22×D11—41no—
146D4×C11—22no—
147D4×C11—22no—
148D4×C11—41no—
149D4×C11—41no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—82no—
154C2×C4×C11—82no—
155C2×C4×C11—81no—
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12711yescharacteristic
162C2×C4×C11C2×SD1611yescharacteristic
163C2×C4×C11#13511yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11#13711yescharacteristic
166C22⋊D11—81no—
167C22⋊D11—81no—
168C2×Dic11—42no—
169C2×Dic11—41no—
170C2×Dic11—82no—
171D44—42no—
172D44—41no—
173D44—41no—
174D44—42no—
175C4×D11—81no—
176C4×D11—81no—
177Dic22—41no—
178Dic22—41no—
179Dic22—82no—
180Dic22—82no—
181C8×C11—42no—
182C8×C11—81no—
183C11⋊C8—42no—
184C11⋊C8—42no—
185C2×AGL(1,ℤ/8)—221no—
186#532—111no—
187C2×C4⋊Q8—111no—
188C2×C4×D4C2×D1111yescharacteristic
189#498—221no—
190#486—221no—
191#481—222no—
192#476—222no—
193#474—222no—
194#474—222no—
195#463—222no—
196#461—221no—
197#459—221no—
198#431C2×D1111yescharacteristic
199#431C2×D1111yescharacteristic
200C2×#107—221no—
201#423—111no—
202C2×C4⋊C8—111no—
203#417—221no—
204C2×#102—221no—
205#333—222no—
206D4⋊C8—222no—
207#323—22no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—42no—
211C22×C11—82no—
212C22×C11—82no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11#39211yescharacteristic
216C22×C11#46511yescharacteristic
217C22×C11#46811yescharacteristic
218C2×D11—81no—
219C2×D11—81no—
220C2×D11—81no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—81no—
225C4×C11#44811yescharacteristic
226C4×C11#44911yescharacteristic
227C4×C11#45011yescharacteristic
228C4×C11#45211yescharacteristic
229C4×C11#47212yes—
230Dic11—81no—
231Dic11—82no—
232C2×#41—221no—
233C22×Q8—221no—
234C22×D4D4411yescharacteristic
235C23×C4—21no—
236AGL(1,ℤ/8)—442no—
237AGL(1,ℤ/8)—442no—
238C2×SD16—222no—
239C2×D8—222no—
240C2×M16—221no—
241C22×C8—221no—
242C4⋊Q8—112no—
243C4⋊Q8—111no—
244C4⋊Q8—221no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247#127—111no—
248#124—221no—
249#121—221no—
250#121—221no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—221no—
256C4×D4—221no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4D4411yescharacteristic
260C2×C22⋊C4—21no—
261C2×C42C22×D1111yescharacteristic
262#107—224no—
263#106—224no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—112no—
267C4⋊C8—112no—
268C4⋊C8—221no—
269C4⋊C8—221no—
270#103—222no—
271#102—222no—
272#102—224no—
273#102—224no—
274C22⋊C8—21no—
275C22⋊C8C22⋊D1112yes—
276C4×C8—21no—
277C4×C8—21no—
278C2×C11—21no—
279C2×C11—21no—
280C2×C11—82no—
281C2×C11#200011yescharacteristic
282C2×C11#200911yescharacteristic
283C2×C11#201811yescharacteristic
284D11—161no—
285C24—21no—
286#41—441no—
287#41—441no—
288#41—441no—
289#41—441no—
290C2×Q8—221no—
291C2×Q8—222no—
292C2×Q8—441no—
293C2×Q8—882no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—441no—
303C2×D4#431412yes—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—82no—
308C22×C4—441no—
309C22×C4—441no—
310C22×C4C2×D4411yescharacteristic
311C22×C4#433911yescharacteristic
312C22×C4C2×C22⋊D1111yescharacteristic
313SD16—444no—
314D8—444no—
315M16—441no—
316M16—441no—
317C2×C8—22no—
318C2×C8—41no—
319C2×C8—222no—
320C2×C8—222no—
321C2×C8—441no—
322C2×C8—441no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—222no—
326C4⋊C4—221no—
327C4⋊C4—222no—
328C4⋊C4—221no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C42D4×D1111yescharacteristic
336C42D4×D1111yescharacteristic
337C42D4×D1111yescharacteristic
338C42D4×D1111yescharacteristic
339C11#1018811yescharacteristic, complemented, Sylow
340C23—22no—
341C23—41no—
342C23—41no—
343C23—81no—
344C23—81no—
345C23—441no—
346C23#6698311yescharacteristic
347Q8—441no—
348Q8—441no—
349Q8—882no—
350Q8—882no—
351D4—22no—
352D4—22no—
353D4—41no—
354D4—41no—
355D4—442no—
356D4—441no—
357D4—441no—
358D4—442no—
359D4—881no—
360D4—881no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—441no—
368C2×C4—442no—
369C2×C4—882no—
370C2×C4—881no—
371C2×C4—881no—
372C2×C4#6693511yescharacteristic
373C2×C4#6693511yescharacteristic
374C2×C4#6693711yescharacteristic
375C2×C4#6693711yescharacteristic
376C2×C4C2×#431411yescharacteristic
377C2×C4#6695711yescharacteristic
378C2×C4#6696111yescharacteristic
379C2×C4#6696211yescharacteristic
380C2×C4#6699011yescharacteristic
381C2×C4#6699311yescharacteristic
382C8—42no—
383C8—81no—
384C8—442no—
385C8—442no—
386C22—21no—
387C22—21no—
388C22—42no—
389C22—82no—
390C22—82no—
391C22—81no—
392C22—81no—
393C22—881no—
394C22—881no—
395C22—881no—
396C22#1062257311yescharacteristic
397C22#1062272711yescharacteristic
398C22#1062274711yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—81no—
403C4—881no—
404C4—882no—
405C4#1062234411yescharacteristic
406C4#1062234611yescharacteristic
407C4#1062234711yescharacteristic
408C4#1062235111yescharacteristic
409C4#1062236212yes—
410C2—21no—
411C2—21no—
412C2—82no—
413C2—1761no—
414C2#1306962111yescharacteristic
415C2#1306967511yescharacteristic
416C2#1306972411yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1460C2
socleC22×C11#392
prime radical#13078080C2
hypercenter#1460D11
hypocenterC11#10188
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
1. #13079746C2semidirect
2. C2×#10622620C2semidirect
4. #13067296C2semidirect
5. #13067016C2semidirect
6. #13066512C2semidirect
7. C11×#1460C2semidirect
137. #1460D11semidirect
339. C11#10188semidirect

Maximal subgroups

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

subgroupindex
#130797462
C2×#106226202
#130780802
#130672962
#130670162
#130665122
C11×#14602
#1018811