Finite Group Databasebeta

← #14666158

Subgroups — #14666158

Order 2816.

498 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 59 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#13075123C211yesmaximal, characteristic, complemented
2#13067602C211yesmaximal, characteristic, complemented
3#13067534C211yesmaximal, characteristic
4#13066615C211yesmaximal, characteristic, complemented
5#13066612C211yesmaximal, characteristic, complemented
6#13066564C211yesmaximal, characteristic, complemented
7C11×#2044C211yesmaximal, characteristic, complemented
8C11×#534C2211yescharacteristic
9C2×#66936—21no—
10C2×C11×#99—21no—
11C11×#386—21no—
12C11×#385C2211yescharacteristic
13#10622826—21no—
14#10622649—21no—
15#10622646—21no—
16#10622607—21no—
17#10622600—21no—
18#10622573C2211yescharacteristic
19#10622566C2211yescharacteristic
20#10622278—21no—
21#10622272—21no—
22C11×#342C2211yescharacteristic
23#10622175—21no—
24#10622175—21no—
25#10622163C2211yescharacteristic
26#10622163C2211yescharacteristic
27C22×D4×C11—21no—
28C23×C4×C11D411yescharacteristic
29C22×C22⋊D11—21no—
30C22×D44D411yescharacteristic
31C22×C4×D11—21no—
32C11×#123—41no—
33C11×#121—21no—
34C11×#121—21no—
35C11×#120—41no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—41no—
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C11×C22⋊C4C2311yescharacteristic
41C2×C22⋊Dic11—21no—
42C2×#4323—41no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11D411yescharacteristic
49C2×Dic11⋊C4—21no—
50#66936—42no—
51#66936—42no—
52C11×#99—42no—
53C11×#95—21no—
54C11×#95—41no—
55#66896—41no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95D411yescharacteristic
60C11⋊#95D411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62C22⋊(C11⋊C8)—21no—
63#66873—41no—
64#66871—41no—
65#12149—111nomaximal, Sylow
66C24×C11—21no—
67C24×C11C2×D411yescharacteristic
68C23×D11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—81no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C2×C22⋊D11—42no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—81no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C2×D44—41no—
93C2×D44—42no—
94C2×C4×D11—42no—
95C2×C4×D11—42no—
96C2×C4×D11—81no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—81no—
100C11×C22⋊C4—21no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—82no—
107C11×C22⋊C4D812yescomplemented
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110#4323—82no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—81no—
113(C2×D11)⋊C4—81no—
114(C2×D11)⋊C4—81no—
115C4⋊Dic11—41no—
116C4⋊Dic11—42no—
117Dic11⋊C4—42no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120#2693—111no—
121#2044D1111yescharacteristic, complemented
122#1607—111no—
123#1595—111no—
124#1344—111no—
125#1343—111no—
126#1326—111no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—81no—
135C23×C11—81no—
136C23×C11#12011yescharacteristic
137C23×C11C2×D811yescharacteristic
138C23×C11AGL(1,ℤ/8)11yescharacteristic
139C22×D11—22no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146D4×C11—81no—
147D4×C11—81no—
148D4×C11—81no—
149D4×C11—81no—
150D4×C11—81no—
151D4×C11—81no—
152C2×C4×C11—22no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C22⋊D11—82no—
171C22⋊D11—82no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181D44—42no—
182D44—81no—
183C4×D11—84no—
184C11⋊C8—81no—
185C11⋊C8—81no—
186#534C2×D1111yescharacteristic
187C2×#123—221no—
188#480—221no—
189#447—221no—
190C2×#99—21no—
191#400—221no—
192#397—111no—
193#396—221no—
194#392—111no—
195#386—21no—
196#386—221no—
197#386—221no—
198#385C2×D1111yescharacteristic
199#380—221no—
200#342C2×D1111yescharacteristic
201#327—221no—
202#327—221no—
203#323—111no—
204#323—111no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—81no—
214C22×C11—82no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—161no—
219C22×C11#44711yescharacteristic
220C22×C11#45411yescharacteristic
221C22×C11B(4,𝔽2)11yescharacteristic
222C2×D11—42no—
223C2×D11—42no—
224C2×D11—42no—
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C4×C11—42no—
230C4×C11—41no—
231C4×C11—41no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11—161no—
235Dic11—81no—
236Dic11—81no—
237Dic11—81no—
238C22×D4—21no—
239C22×D4—111no—
240C22×D4—221no—
241C23×C4—221no—
242C23×C4C22⋊D1111yescharacteristic
243C2×D8—441no—
244#123—41no—
245#123—442no—
246#123—442no—
247#121—21no—
248#121—21no—
249#120—41no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4—221no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—41no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4C22⋊D1111yescharacteristic
262C2×C22⋊C4C22×D1111yescharacteristic
263#107—441no—
264#102—441no—
265#102—441no—
266#99—42no—
267C22⋊C8—221no—
268C22⋊C8—221no—
269#95—21no—
270#95—41no—
271#95—111no—
272#95—111no—
273#95—221no—
274#95—221no—
275#95—221no—
276C2×C11—21no—
277C2×C11—21no—
278C2×C11—41no—
279C2×C11—41no—
280C2×C11—161no—
281C2×C11#159811yescharacteristic
282C2×C11#219711yescharacteristic
283C2×C11#220011yescharacteristic
284D11—82no—
285C24—21no—
286C24—221no—
287C24C2×C22⋊D1111yescharacteristic
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—441no—
297C2×D4—442no—
298C2×D4—442no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—881no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—81no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—221no—
311C22×C4—442no—
312C22×C4—442no—
313C22×C4—881no—
314C22×C4D4×D1111yescharacteristic
315C22×C4D4×D1111yescharacteristic
316D8—882no—
317C2×C8—441no—
318C2×C8—441no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—81no—
322C4⋊C4—441no—
323C4⋊C4—442no—
324C4⋊C4—442no—
325C22⋊C4—21no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—82no—
332C22⋊C4—442no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C22⋊C4—881no—
336C22⋊C4—881no—
337C22⋊C4—881no—
338C22⋊C4#432312yescomplemented
339C11#1214911yescharacteristic, complemented, Sylow
340C23—21no—
341C23—21no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—81no—
348C23—81no—
349C23—222no—
350C23—441no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23—441no—
355C23—441no—
356C23C2×#432311yescharacteristic
357C23#6699011yescharacteristic
358C23#6700211yescharacteristic
359D4—81no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4—81no—
364D4—81no—
365D4—442no—
366D4—881no—
367D4—882no—
368D4—882no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—884no—
397C8—881no—
398C8—881no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—81no—
408C22—82no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—161no—
413C22—442no—
414C22—442no—
415C22—442no—
416C22—881no—
417C22—881no—
418C22—881no—
419C22—881no—
420C22#1062264511yescharacteristic
421C22#1062264911yescharacteristic
422C22#1062267511yescharacteristic
423C4—42no—
424C4—41no—
425C4—41no—
426C4—81no—
427C4—81no—
428C4—161no—
429C4—881no—
430C4—881no—
431C4—881no—
432C2—21no—
433C2—21no—
434C2—41no—
435C2—41no—
436C2—161no—
437C2—882no—
438C2#1306755011yescharacteristic
439C2#1307060311yescharacteristic
440C2#1307062111yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2044C2
socleC22×C11B(4,𝔽2)
prime radical#13067534C2
hypercenter#2044D11
hypocenterC11#12149
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2044

Complements

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

NH ≅ G/Ntype
1. #13075123C2semidirect
2. #13067602C2semidirect
4. #13066615C2semidirect
5. #13066612C2semidirect
6. #13066564C2semidirect
7. C11×#2044C2semidirect
107. C11×C22⋊C4D8semidirect
121. #2044D11semidirect
338. C22⋊C4#4323semidirect
339. C11#12149semidirect

Maximal subgroups

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

subgroupindex
#130751232
#130676022
#130675342
#130666152
#130666122
#130665642
C11×#20442
#1214911