Finite Group Databasebeta

← #14655824

Subgroups — #14655824

Order 2816.

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

normal subgroups only

This group has 518 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
2C2×#10622633C211yesmaximal, characteristic, complemented
3#13078088C211yesmaximal, characteristic
4#13067296C211yesmaximal, characteristic, complemented
5#13067016C211yesmaximal, characteristic
6#13066512C211yesmaximal, characteristic, complemented
7C11×#1461C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66995—21no—
10#10623008C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C2×#66899—21no—
15#10622644—21no—
16#10622641—22no—
17#10622640—21no—
18#10622633—22no—
19#10622633—22no—
20#10622579—21no—
21C2×#66872—21no—
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622455—22no—
25#10622348—22no—
26#10622307—21no—
27#10622293—21no—
28C11×#324—22no—
29#10622119—22no—
30#10622097—22no—
31C22×Q8×C11D411yescharacteristic
32C2×#4339—21no—
33C22×Dic22—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4326—22no—
43#66995—42no—
44#66995—42no—
45C2×#4325—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#66899—24no—
68#66885—24no—
69#66881—24no—
70#66874—22no—
71#66873—22no—
72#66872—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4⋊(C11⋊C8)D412yes—
77#10189—111nomaximal, Sylow
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11SD1612yes—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C2×C22⋊D11—41no—
90C22×Dic11—41no—
91#4339—41no—
92#4339—41no—
93#4339—41no—
94#4339—41no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×C4×D11—41no—
99C2×Dic22—21no—
100C2×Dic22—22no—
101C2×Dic22—41no—
102C2×Dic22—82no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C42×C11—41no—
110C42×C11—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115#4326—44no—
116#4325—44no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119C4⋊Dic11—22no—
120C4⋊Dic11—21no—
121C4⋊Dic11—22no—
122C4⋊Dic11—21no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125#4318—41no—
126#4318—41no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131#3227—111no—
132C2×#475—111no—
133#3037—111no—
134#1548—111no—
135#1480—111no—
136#1461D1111yescharacteristic, complemented
137#1301—111no—
138C23×C11#12111yescharacteristic
139C22×D11—41no—
140Q8×C11—22no—
141Q8×C11—22no—
142Q8×C11—41no—
143Q8×C11—41no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—81no—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12711yescharacteristic
157C2×C4×C11C2×SD1611yescharacteristic
158C2×C4×C11#13511yescharacteristic
159C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C11#13711yescharacteristic
161C22⋊D11—81no—
162C22⋊D11—81no—
163C2×Dic11—42no—
164C2×Dic11—41no—
165C2×Dic11—82no—
166D44—42no—
167D44—41no—
168D44—41no—
169D44—42no—
170C4×D11—81no—
171C4×D11—81no—
172Dic22—41no—
173Dic22—41no—
174Dic22—82no—
175Dic22—82no—
176C8×C11—42no—
177C8×C11—81no—
178C11⋊C8—42no—
179C11⋊C8—42no—
180C2×#137—221no—
181#532—111no—
182C2×C4⋊Q8—111no—
183C2×C4×Q8C2×D1111yescharacteristic
184#498—221no—
185#486—221no—
186#481—222no—
187#476—222no—
188#475—222no—
189#475—222no—
190#464—222no—
191#462—221no—
192#460—221no—
193#431C2×D1111yescharacteristic
194#431C2×D1111yescharacteristic
195C2×#106—221no—
196#423—111no—
197C2×C4⋊C8—111no—
198#417—221no—
199C2×#103—221no—
200#333—222no—
201D4⋊C8—222no—
202#324—22no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11#39211yescharacteristic
206C22×C11#46511yescharacteristic
207C22×C11#46811yescharacteristic
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—42no—
215C4×C11—81no—
216C4×C11#44811yescharacteristic
217C4×C11#44911yescharacteristic
218C4×C11#45011yescharacteristic
219C4×C11#45211yescharacteristic
220C4×C11#47112yes—
221Dic11—81no—
222Dic11—82no—
223C2×#41—221no—
224C22×Q8—221no—
225C22×Q8D4411yescharacteristic
226#137—442no—
227#137—442no—
228C2×Q16—222no—
229C2×SD16—222no—
230C2×M16—221no—
231C22×C8—221no—
232C4⋊Q8—112no—
233C4⋊Q8—111no—
234C4⋊Q8—221no—
235C4⋊Q8—221no—
236C4⋊Q8—221no—
237#127—111no—
238#124—221no—
239#121—221no—
240#121—221no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×D4—221no—
246C4×D4—221no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4D4411yescharacteristic
251C2×C42—21no—
252C2×C42C22×D1111yescharacteristic
253#106—224no—
254#106—224no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—112no—
258C4⋊C8—112no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261#103—222no—
262#103—224no—
263#102—222no—
264#102—224no—
265C22⋊C8—21no—
266C22⋊C8C22⋊D1112yes—
267C4×C8—21no—
268C4×C8—21no—
269C2×C11—21no—
270C2×C11—21no—
271C2×C11#200011yescharacteristic
272C2×C11#200911yescharacteristic
273C2×C11#201911yescharacteristic
274D11—161no—
275#41—441no—
276#41—441no—
277#41—441no—
278#41—441no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—221no—
285C2×Q8—222no—
286C2×Q8—441no—
287C2×Q8—882no—
288C2×Q8#431412yes—
289C2×D4—221no—
290C2×D4—221no—
291C2×D4—221no—
292C2×D4—441no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—441no—
296C22×C4—441no—
297C22×C4C2×D4411yescharacteristic
298C22×C4#433911yescharacteristic
299C22×C4C2×C22⋊D1111yescharacteristic
300Q16—444no—
301SD16—444no—
302M16—441no—
303M16—441no—
304C2×C8—22no—
305C2×C8—41no—
306C2×C8—222no—
307C2×C8—222no—
308C2×C8—441no—
309C2×C8—441no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—222no—
315C4⋊C4—221no—
316C4⋊C4—222no—
317C4⋊C4—221no—
318C4⋊C4—441no—
319C4⋊C4—441no—
320C22⋊C4—441no—
321C22⋊C4—441no—
322C42—41no—
323C42—41no—
324C42D4×D1111yescharacteristic
325C42D4×D1111yescharacteristic
326C42D4×D1111yescharacteristic
327C42D4×D1111yescharacteristic
328C11#1018911yescharacteristic, complemented, Sylow
329C23—441no—
330C23#6698311yescharacteristic
331Q8—22no—
332Q8—22no—
333Q8—41no—
334Q8—41no—
335Q8—441no—
336Q8—441no—
337Q8—882no—
338Q8—882no—
339D4—442no—
340D4—441no—
341D4—441no—
342D4—442no—
343D4—881no—
344D4—881no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—81no—
352C2×C4—441no—
353C2×C4—442no—
354C2×C4—882no—
355C2×C4—881no—
356C2×C4—881no—
357C2×C4#6693511yescharacteristic
358C2×C4#6693511yescharacteristic
359C2×C4#6693711yescharacteristic
360C2×C4#6693711yescharacteristic
361C2×C4C2×#431411yescharacteristic
362C2×C4#6695711yescharacteristic
363C2×C4#6696111yescharacteristic
364C2×C4#6696211yescharacteristic
365C2×C4#6699011yescharacteristic
366C2×C4#6699311yescharacteristic
367C8—42no—
368C8—81no—
369C8—442no—
370C8—442no—
371C22—21no—
372C22—21no—
373C22—881no—
374C22—881no—
375C22—881no—
376C22#1062257311yescharacteristic
377C22#1062272711yescharacteristic
378C22#1062274711yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—81no—
384C4—881no—
385C4—882no—
386C4#1062234411yescharacteristic
387C4#1062234611yescharacteristic
388C4#1062234711yescharacteristic
389C4#1062235111yescharacteristic
390C4#1062236712yes—
391C2—21no—
392C2—21no—
393C2—1761no—
394C2#1306962111yescharacteristic
395C2#1306967511yescharacteristic
396C2#1306972911yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1461C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1461D11
hypocenterC11#10189
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. C2×#10622633C2semidirect
4. #13067296C2semidirect
6. #13066512C2semidirect
7. C11×#1461C2semidirect
136. #1461D11semidirect
328. C11#10189semidirect

Maximal subgroups

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

subgroupindex
#130797462
C2×#106226332
#130780882
#130672962
#130670162
#130665122
C11×#14612
#1018911