Finite Group Databasebeta

← #14656153

Subgroups — #14656153

Order 2816.

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

normal subgroups only

This group has 590 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, complemented
2#13078076C211yesmaximal, characteristic
3#13073785C211yesmaximal, characteristic, complemented
4#13067300C211yesmaximal, characteristic, complemented
5#13067008C211yesmaximal, characteristic, complemented
6#13066519C211yesmaximal, characteristic, complemented
7C11×#1502C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×#67002—21no—
10C2×C4×D44C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14#10622845—21no—
15#10622696—21no—
16#10622692—21no—
17#10622685—21no—
18#10622683—21no—
19#10622670—22no—
20#10622647—22no—
21#10622621—22no—
22#10622600—22no—
23#10622552—21no—
24#10622549—21no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27#10622286—22no—
28C11×#327—22no—
29#10622120—22no—
30#10622097—22no—
31C2×C11×#41—21no—
32C22×D44D411yescharacteristic
33C22×C4×D11—21no—
34C22×Dic22—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×#127D411yescharacteristic
37C11×#124—21no—
38C11×#121—21no—
39C11×#121—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C2×C11×C4⋊C4—21no—
43C2×C42×C11—21no—
44C2×C42×C11C2311yescharacteristic
45#67002—42no—
46#67002—42no—
47C2×#4325—22no—
48C2×#4323—22no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—24no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11D412yes—
53C2×C4⋊Dic11D411yescharacteristic
54C2×#4318—21no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44—21no—
58C4×D44—21no—
59#66922—21no—
60#66922—21no—
61#66922—21no—
62#66922—21no—
63C11×C4⋊C8—21no—
64C11×C22⋊C8—21no—
65C4×C8×C11—21no—
66C11×#95D412yes—
67#66899—22no—
68#66896—22no—
69#66896—24no—
70C11⋊#95—24no—
71C22⋊(C11⋊C8)—21no—
72#66872—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75C4⋊(C11⋊C8)D412yes—
76C4×C11⋊C8—21no—
77#10241—111nomaximal, Sylow
78C23×D11—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—41no—
88C22×C4×C11—22no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×Dic11—21no—
94C22×Dic11—22no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44SD1612yes—
101C2×C4×D11—44no—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×Dic22—41no—
105C2×Dic22—41no—
106C2×Dic22—82no—
107C2×C8×C11—41no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—42no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11—41no—
114C42×C11—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119#4325—44no—
120#4323—44no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—84no—
124C4⋊Dic11—22no—
125C4⋊Dic11—21no—
126C4⋊Dic11—22no—
127C4⋊Dic11—21no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130#4318—41no—
131#4318—41no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134#3227—111no—
135#3036—111no—
136#2563—111no—
137#1549—111no—
138#1502D1111yescharacteristic, complemented
139#1478—111no—
140#1303—111no—
141C23×C11—41no—
142C23×C11#12011yescharacteristic
143C22×D11—22no—
144C22×D11—42no—
145C22×D11—42no—
146C22×D11—41no—
147C22×D11—41no—
148Q8×C11—41no—
149Q8×C11—41no—
150D4×C11—41no—
151D4×C11—41no—
152D4×C11—42no—
153D4×C11—81no—
154D4×C11—81no—
155D4×C11—81no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12711yescharacteristic
170C2×C4×C11C2×SD1611yescharacteristic
171C2×C4×C11#13511yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11#13711yescharacteristic
174C2×Dic11—44no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—41no—
178D44—22no—
179D44—22no—
180D44—41no—
181D44—41no—
182C4×D11—82no—
183C4×D11—82no—
184Dic22—82no—
185Dic22—82no—
186C8×C11—81no—
187C11⋊C8—42no—
188C11⋊C8—42no—
189C2×AGL(1,ℤ/8)—221no—
190#532C2×D1111yescharacteristic
191C2×C4⋊Q8—111no—
192C2×C4×D4—111no—
193#498—221no—
194#486—221no—
195#481—222no—
196#476—222no—
197#463—222no—
198#461—221no—
199#459—221no—
200#431—111no—
201#431C2×D1111yescharacteristic
202#423—111no—
203#417—221no—
204#393—222no—
205#390—221no—
206#382—221no—
207#380—222no—
208C4×C4⋊C4C2×D1111yescharacteristic
209#332—222no—
210#327—22no—
211D4⋊C8—222no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11#39211yescharacteristic
218C22×C11#44811yescharacteristic
219C22×C11#44911yescharacteristic
220C2×D11—44no—
221C2×D11—42no—
222C2×D11—82no—
223C2×D11—81no—
224C2×D11—81no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—82no—
229C4×C11—81no—
230C4×C11#45011yescharacteristic
231C4×C11#45211yescharacteristic
232C4×C11#45412yes—
233C4×C11#46511yescharacteristic
234C4×C11#46811yescharacteristic
235Dic11—81no—
236Dic11—82no—
237C2×#41—21no—
238C22×Q8—221no—
239C22×D4—111no—
240C23×C4—221no—
241AGL(1,ℤ/8)—442no—
242AGL(1,ℤ/8)—442no—
243C2×SD16—222no—
244C2×D8—222no—
245C2×M16—221no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248C4⋊Q8—221no—
249C4⋊Q8—221no—
250C4⋊Q8D4411yescharacteristic
251#127D4411yescharacteristic
252#124—21no—
253#121—21no—
254#121—21no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—221no—
258C4×D4—221no—
259C4×D4—221no—
260C4×D4—221no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—224no—
267C2×C42—21no—
268C2×C42C22×D1111yescharacteristic
269#106—224no—
270C4⋊C8—21no—
271C4⋊C8—112no—
272C4⋊C8—112no—
273C4⋊C8—221no—
274#103—222no—
275#102—222no—
276#102—224no—
277C22⋊C8—21no—
278C22⋊C8—221no—
279C4×C8—21no—
280C4×C8—221no—
281#95—224no—
282#95C22⋊D1112yes—
283C2×C11—21no—
284C2×C11—21no—
285C2×C11—161no—
286C2×C11#200011yescharacteristic
287C2×C11#200311yescharacteristic
288C2×C11#200811yescharacteristic
289D11—82no—
290C24—221no—
291#41—41no—
292#41—41no—
293#41—41no—
294#41—41no—
295C2×Q8—21no—
296C2×Q8—441no—
297C2×Q8—441no—
298C2×Q8—882no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—41no—
303C2×D4—112no—
304C2×D4—221no—
305C2×D4—221no—
306C2×D4—221no—
307C2×D4—221no—
308C2×D4—221no—
309C22×C4—22no—
310C22×C4—41no—
311C22×C4—221no—
312C22×C4—222no—
313C22×C4—444no—
314C22×C4—441no—
315C22×C4—441no—
316C22×C4D4×D1111yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319SD16—444no—
320D8—444no—
321M16—441no—
322M16—441no—
323C2×C8—41no—
324C2×C8—222no—
325C2×C8—222no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—42no—
329C4⋊C4—221no—
330C4⋊C4—222no—
331C4⋊C4—221no—
332C4⋊C4—222no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C22⋊C4—884no—
340C42—41no—
341C42—41no—
342C42C2×D4411yescharacteristic
343C42#433911yescharacteristic
344C42D4×D1111yescharacteristic
345C42D4×D1111yescharacteristic
346C11#1024111yescharacteristic, complemented, Sylow
347C23—41no—
348C23—222no—
349C23—442no—
350C23—442no—
351C23—441no—
352C23—441no—
353C23#6699011yescharacteristic
354Q8—41no—
355Q8—41no—
356Q8—882no—
357Q8—882no—
358D4—41no—
359D4—41no—
360D4—42no—
361D4—81no—
362D4—81no—
363D4—81no—
364D4—222no—
365D4—222no—
366D4—441no—
367D4—441no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—444no—
377C2×C4—442no—
378C2×C4—441no—
379C2×C4—442no—
380C2×C4—882no—
381C2×C4—882no—
382C2×C4#6693511yescharacteristic
383C2×C4#6693511yescharacteristic
384C2×C4#6693711yescharacteristic
385C2×C4#6693711yescharacteristic
386C2×C4#6696411yescharacteristic
387C2×C4#6696511yescharacteristic
388C2×C4SD16×D1111yescharacteristic
389C2×C4#6696811yescharacteristic
390C2×C4#6698311yescharacteristic
391C2×C4#6699311yescharacteristic
392C8—81no—
393C8—442no—
394C8—442no—
395C22—21no—
396C22—21no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—444no—
401C22—442no—
402C22—882no—
403C22—881no—
404C22—881no—
405C22#1062257311yescharacteristic
406C22#1062277111yescharacteristic
407C22#1062278311yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—82no—
412C4—81no—
413C4—881no—
414C4—882no—
415C4#1062238911yescharacteristic
416C4#1062239111yescharacteristic
417C4#1062239311yescharacteristic
418C4#1062239611yescharacteristic
419C4#1062244012yes—
420C2—21no—
421C2—21no—
422C2—161no—
423C2—882no—
424C2#1306962011yescharacteristic
425C2#1306963711yescharacteristic
426C2#1306966811yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1502C2
socleC22×C11#392
prime radical#13078076C2
hypercenter#1502D11
hypocenterC11#10241
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
1. #13079741C2semidirect
3. #13073785C2semidirect
4. #13067300C2semidirect
5. #13067008C2semidirect
6. #13066519C2semidirect
7. C11×#1502C2semidirect
138. #1502D11semidirect
346. C11#10241semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130780762
#130737852
#130673002
#130670082
#130665192
C11×#15022
#1024111