Finite Group Databasebeta

← #14656152

Subgroups — #14656152

Order 2816.

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

normal subgroups only

This group has 590 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#13078076C211yesmaximal, characteristic
2#13073790C211yesmaximal, characteristic, complemented
3#13067301C211yesmaximal, characteristic, complemented
4#13067111C211yesmaximal, characteristic, complemented
5#13067006C211yesmaximal, characteristic, complemented
6#13066518C211yesmaximal, characteristic, complemented
7C11×#3227C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#67002—21no—
11C2×C4×D44C2211yescharacteristic
12C11×#498—21no—
13C11×#486—21no—
14C11×#481—22no—
15C11×#476—22no—
16C11×#431C2211yescharacteristic
17#10622845—21no—
18#10622844—22no—
19#10622696—21no—
20#10622685—21no—
21#10622670—22no—
22#10622601—21no—
23#10622600—22no—
24#10622590—21no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622185—22no—
29#10622175—22no—
30#10622121—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×D44D411yescharacteristic
34C22×C4×D11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D411yescharacteristic
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#121—21no—
43C11×#121—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D412yes—
48C2×C42×C11C2311yescharacteristic
49#67002—42no—
50#67002—42no—
51C2×#4325—22no—
52C2×#4323—22no—
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—24no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11D411yescharacteristic
57C2×C4×Dic11—21no—
58C2×#4318—21no—
59C4×D44—21no—
60C4×D44—21no—
61C4×D44—21no—
62C4×D44—21no—
63C11×#106—24no—
64C11×C4⋊C8D412yes—
65C11×#102—24no—
66C11×C22⋊C8—21no—
67C4×C8×C11—21no—
68#66899—22no—
69#66896—22no—
70C11⋊#95—24no—
71C11⋊#95D412yes—
72C22⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
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×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—82no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—41no—
91C22×C4×C11—22no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×Dic11—21no—
97C22×Dic11—22no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44SD1612yes—
104C2×C4×D11—44no—
105C2×C4×D11—41no—
106C2×C4×D11—41no—
107C2×C8×C11—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120#4325—44no—
121#4323—44no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—84no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—42no—
128C4×Dic11—41no—
129C4×Dic11—41no—
130#4318—41no—
131#4318—41no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134#3227D1111yescharacteristic, complemented
135#3036—111no—
136#2563—111no—
137#1549—111no—
138#1502—111no—
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—
150Q8×C11—82no—
151Q8×C11—82no—
152D4×C11—41no—
153D4×C11—41no—
154D4×C11—42no—
155D4×C11—81no—
156D4×C11—81no—
157D4×C11—81no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—44no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12711yescharacteristic
171C2×C4×C11C2×SD1611yescharacteristic
172C2×C4×C11#13511yescharacteristic
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11#13711yescharacteristic
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—41no—
179C2×Dic11—42no—
180D44—22no—
181D44—22no—
182D44—41no—
183D44—41no—
184C4×D11—82no—
185C4×D11—82no—
186C8×C11—42no—
187C11⋊C8—42no—
188C11⋊C8—81no—
189C2×AGL(1,ℤ/8)—221no—
190#532C2×D1111yescharacteristic
191C2×C4⋊Q8C2×D1111yescharacteristic
192C2×C4×D4—111no—
193#498—21no—
194#486—21no—
195#481—22no—
196#476—22no—
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⋊C4—111no—
209#332—222no—
210#327—222no—
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—81no—
229C4×C11—82no—
230C4×C11#45011yescharacteristic
231C4×C11#45211yescharacteristic
232C4×C11#45412yes—
233C4×C11#46511yescharacteristic
234C4×C11#46811yescharacteristic
235Dic11—82no—
236Dic11—81no—
237C2×#41—21no—
238C22×Q8—21no—
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—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8C22⋊D1111yescharacteristic
251#127C22⋊D1111yescharacteristic
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—221no—
264C2×C4⋊C4C22⋊D1112yes—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—224no—
267C2×C42—221no—
268C2×C42C22×D1111yescharacteristic
269#106—24no—
270C4⋊C8—112no—
271C4⋊C8—221no—
272C4⋊C8—221no—
273C4⋊C8C22⋊D1112yes—
274#103—222no—
275#102—24no—
276#102—222no—
277C22⋊C8—21no—
278C22⋊C8—221no—
279C4×C8—21no—
280C4×C8—221no—
281#95—112no—
282#95—224no—
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—41no—
297C2×Q8—41no—
298C2×Q8—82no—
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—222no—
312C22×C4—221no—
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—22no—
324C2×C8—222no—
325C2×C8—441no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—22no—
329C4⋊C4—21no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—442no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C22⋊C4—884no—
340C42—441no—
341C42—441no—
342C42D4×D1111yescharacteristic
343C42#434111yescharacteristic
344C42C2×C22⋊D1111yescharacteristic
345C42C2×C22⋊D1111yescharacteristic
346C11#1024111yescharacteristic, complemented, Sylow
347C23—41no—
348C23—222no—
349C23—442no—
350C23—442no—
351C23—441no—
352C23—441no—
353C23#6699011yescharacteristic
354Q8—41no—
355Q8—41no—
356Q8—82no—
357Q8—82no—
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—44no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4—441no—
380C2×C4—882no—
381C2×C4—882no—
382C2×C4SD16×D1111yescharacteristic
383C2×C4#6696711yescharacteristic
384C2×C4#6696811yescharacteristic
385C2×C4#6696911yescharacteristic
386C2×C4#6699011yescharacteristic
387C2×C4#6699111yescharacteristic
388C2×C4#6699211yescharacteristic
389C2×C4#6699211yescharacteristic
390C2×C4#6699311yescharacteristic
391C2×C4#6700611yescharacteristic
392C8—42no—
393C8—442no—
394C8—881no—
395C22—21no—
396C22—21no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—444no—
401C22—442no—
402C22—882no—
403C22—881no—
404C22—881no—
405C22#1062278311yescharacteristic
406C22#1062278511yescharacteristic
407C22#1062283611yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—81no—
412C4—82no—
413C4—882no—
414C4—881no—
415C4#1062278211yescharacteristic
416C4#1062278411yescharacteristic
417C4#1062278611yescharacteristic
418C4#1062278711yescharacteristic
419C4#1062285812yes—
420C2—21no—
421C2—21no—
422C2—161no—
423C2—882no—
424C2#1306961611yescharacteristic
425C2#1306963611yescharacteristic
426C2#1306966711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3227C2
socleC22×C11#392
prime radical#13078076C2
hypercenter#3227D11
hypocenterC11#10241
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
2. #13073790C2semidirect
3. #13067301C2semidirect
4. #13067111C2semidirect
5. #13067006C2semidirect
6. #13066518C2semidirect
7. C11×#3227C2semidirect
134. #3227D11semidirect
346. C11#10241semidirect

Maximal subgroups

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

subgroupindex
#130780762
#130737902
#130673012
#130671112
#130670062
#130665182
C11×#32272
#1024111