Finite Group Databasebeta

← #14655823

Subgroups — #14655823

Order 2816.

518 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079741C211yesmaximal, characteristic
2C2×#10622464C211yesmaximal, characteristic, complemented
3#13078084C211yesmaximal, characteristic
4#13067296C211yesmaximal, characteristic, complemented
5#13066939C211yesmaximal, characteristic, complemented
6#13066513C211yesmaximal, characteristic, complemented
7C11×#1480C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#67004—21no—
10C2×#66922C2211yescharacteristic
11C2×C4×Dic22C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14#10622845—21no—
15C2×#66881—21no—
16C2×#66880—21no—
17#10622703—21no—
18#10622692—21no—
19#10622688—21no—
20#10622683—21no—
21#10622667—22no—
22#10622647—22no—
23#10622621—22no—
24#10622538C2211yescharacteristic
25#10622537C2211yescharacteristic
26#10622464—22no—
27#10622464—22no—
28C11×D4⋊C8—22no—
29#10622119—22no—
30#10622107—22no—
31C2×C11×#41—21no—
32C22×Dic22—21no—
33C22×Dic22D411yescharacteristic
34C22×C8×C11—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×#127D411yescharacteristic
37C11×#124—21no—
38C11×#121—21no—
39C11×#121—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C2×C42×C11C2311yescharacteristic
43#67004—42no—
44#67004—42no—
45C2×#4326—22no—
46C2×#4324—22no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D411yescharacteristic
50C2×Dic11⋊C4—21no—
51C2×C4×Dic11—21no—
52C2×#4318—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922D412yes—
57C4×Dic22—21no—
58C4×Dic22—21no—
59C4×Dic22—21no—
60C4×Dic22—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×C22⋊C8—21no—
65C4×C8×C11—21no—
66#66899—22no—
67#66896—22no—
68#66896—24no—
69C22⋊(C11⋊C8)D412yes—
70#66881—24no—
71#66880—24no—
72#66872—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4×C11⋊C8—21no—
77#10189—111nomaximal, Sylow
78C11×#41—41no—
79C11×#41—41no—
80C11×#41—41no—
81C11×#41—41no—
82C2×Q8×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—41no—
94C2×Dic22—21no—
95C2×Dic22—21no—
96C2×Dic22—22no—
97C2×Dic22—21no—
98C2×Dic22—21no—
99C2×Dic22—21no—
100C2×Dic22—41no—
101C2×Dic22—82no—
102C2×Dic22SD1612yes—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115#4326—44no—
116#4324—44no—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125C4×Dic11—41no—
126C4×Dic11—41no—
127#4318—41no—
128#4318—41no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131#3227—111no—
132C2×#475—111no—
133#3037—111no—
134#1548—111no—
135#1480D1111yescharacteristic
136#1461—111no—
137#1301—111no—
138C23×C11—41no—
139C23×C11#12111yescharacteristic
140Q8×C11—41no—
141Q8×C11—41no—
142D4×C11—42no—
143D4×C11—41no—
144D4×C11—41no—
145D4×C11—42no—
146D4×C11—81no—
147D4×C11—81no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12711yescharacteristic
159C2×C4×C11C2×SD1611yescharacteristic
160C2×C4×C11#13511yescharacteristic
161C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C11#13711yescharacteristic
163C2×Dic11—22no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—42no—
168C2×Dic11—82no—
169C2×Dic11—81no—
170Dic22—22no—
171Dic22—22no—
172Dic22—41no—
173Dic22—41no—
174Dic22—82no—
175Dic22—82no—
176C8×C11—42no—
177C8×C11—81no—
178C11⋊C8—42no—
179C11⋊C8—42no—
180C2×#137—221no—
181#532C2×D1111yescharacteristic
182C2×C4⋊Q8—111no—
183C2×C4×Q8—111no—
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#431—111no—
194#431C2×D1111yescharacteristic
195C2×#106—221no—
196#423—111no—
197C2×C4⋊C8C2×D1111yescharacteristic
198#417—221no—
199C2×#103—221no—
200#333—222no—
201D4⋊C8—22no—
202#324—222no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11#39211yescharacteristic
209C22×C11#46511yescharacteristic
210C22×C11#46811yescharacteristic
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—81no—
215C4×C11#44811yescharacteristic
216C4×C11#44911yescharacteristic
217C4×C11#45011yescharacteristic
218C4×C11#45211yescharacteristic
219C4×C11#47112yes—
220Dic11—42no—
221Dic11—81no—
222Dic11—82no—
223C2×#41—21no—
224C22×Q8—111no—
225C22×Q8—221no—
226#137—442no—
227#137—442no—
228C2×Q16—222no—
229C2×SD16—222no—
230C2×M16—221no—
231C22×C8—21no—
232C4⋊Q8—112no—
233C4⋊Q8—221no—
234C4⋊Q8—221no—
235C4⋊Q8—221no—
236C4⋊Q8D4411yescharacteristic
237#127D4411yescharacteristic
238#124—21no—
239#121—21no—
240#121—21no—
241C4×Q8—221no—
242C4×Q8—221no—
243C4×Q8—221no—
244C4×Q8—221no—
245C4×D4—21no—
246C4×D4—21no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4—221no—
251C2×C42—221no—
252C2×C42C22×D1111yescharacteristic
253#106—224no—
254#106—224no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—112no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260C4⋊C8C22⋊D1112yes—
261#103—224no—
262#103—222no—
263#102—222no—
264#102—224no—
265C22⋊C8—21no—
266C22⋊C8—112no—
267C4×C8—21no—
268C4×C8—221no—
269C2×C11—21no—
270C2×C11—21no—
271C2×C11—161no—
272C2×C11#200011yescharacteristic
273C2×C11#200911yescharacteristic
274C2×C11#201911yescharacteristic
275#41—41no—
276#41—41no—
277#41—41no—
278#41—41no—
279C2×Q8—21no—
280C2×Q8—112no—
281C2×Q8—221no—
282C2×Q8—221no—
283C2×Q8—222no—
284C2×Q8—221no—
285C2×Q8—221no—
286C2×Q8—221no—
287C2×Q8—441no—
288C2×Q8—882no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—41no—
293C22×C4—41no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—441no—
297C22×C4#433911yescharacteristic
298C22×C4D4×D1111yescharacteristic
299C22×C4D4×D1111yescharacteristic
300Q16—444no—
301SD16—444no—
302M16—441no—
303M16—441no—
304C2×C8—22no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—222no—
309C2×C8—222no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—221no—
313C4⋊C4—222no—
314C4⋊C4—222no—
315C4⋊C4—221no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C4⋊C4—441no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C42—441no—
323C42—441no—
324C42C2×D4411yescharacteristic
325C42D4×D1111yescharacteristic
326C42D4×D1111yescharacteristic
327C42C2×C22⋊D1111yescharacteristic
328C11#1018911yescharacteristic, complemented, Sylow
329C23—41no—
330C23#6693711yescharacteristic
331Q8—41no—
332Q8—41no—
333Q8—222no—
334Q8—222no—
335Q8—441no—
336Q8—441no—
337Q8—882no—
338Q8—882no—
339D4—42no—
340D4—42no—
341D4—41no—
342D4—41no—
343D4—81no—
344D4—81no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—222no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—442no—
355C2×C4—882no—
356C2×C4—881no—
357C2×C4#6693511yescharacteristic
358C2×C4#6693511yescharacteristic
359C2×C4#6693711yescharacteristic
360C2×C4#6696411yescharacteristic
361C2×C4#6696511yescharacteristic
362C2×C4SD16×D1111yescharacteristic
363C2×C4#6696811yescharacteristic
364C2×C4#6698311yescharacteristic
365C2×C4#6699011yescharacteristic
366C2×C4#6699311yescharacteristic
367C8—42no—
368C8—81no—
369C8—442no—
370C8—442no—
371C22—21no—
372C22—21no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22#1062239111yescharacteristic
377C22#1062239311yescharacteristic
378C22#1062257311yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—81no—
383C4—442no—
384C4—881no—
385C4—882no—
386C4#1062238911yescharacteristic
387C4#1062239611yescharacteristic
388C4#1062275412yes—
389C4#1062277111yescharacteristic
390C4#1062278311yescharacteristic
391C2—21no—
392C2—21no—
393C2—161no—
394C2#1306962011yescharacteristic
395C2#1306967711yescharacteristic
396C2#1306973111yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1480C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1480D11
hypocenterC11#10189
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. C2×#10622464C2semidirect
4. #13067296C2semidirect
5. #13066939C2semidirect
6. #13066513C2semidirect
328. C11#10189semidirect

Maximal subgroups

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

subgroupindex
#130797412
C2×#106224642
#130780842
#130672962
#130669392
#130665132
C11×#14802
#1018911